摘要:

Determination of Relative Intramolecular Configuration by Nuclear Quadrupole Double Resonance BY NORBERT AND ALARICH WEIDEN WEISS Institut fur Physikalische Chemie Physikalische Chemie 111 Technische Hochschule Petersenstr. 20 D-6100 Darmstadt W. Germany Received 31st July 1978 The influence of a nuclear quadrupole spin system B on the spin echo of a nuclear quadrupole system A is governed by a l/r6 law. This relation was used to determine relative intramolecular arrangements within molecules and complex ions in solids. By heteronuclear double resonance 81Br++27Al in KA12Br7 the bridging bromine has been determined and also the Br frequencies have been assigned to certain Br-A1 bonds. Homonuclear double resonance 35Cl+-+35CIwas applied to molecular compounds of C13CC02H and the close-lying frequencies of two molecules in the asymmetric unit were split-up into the appropriate groups.Finally from isotopic 81Br t-)79Br double resonance in 3,5-dichlorophenoxy aluminiumdibromide and 4-chlorophenoxy aluminiumdi- bromide a structure is proposed for these molecules. The aluminium atoms in these dimeric compounds are connected by bridging oxygen atoms whereas the bromine atoms are in terminal positions. The use of nuclear double resonance (n.d.r.) methods applied to solids is focused on the problem of increasing the signal-to-noise ratio. By these techniques many nuclei may be studied which are inaccessible to the single resonance methods because of their low resonance frequencies and/or low abundance in the solid considered.Apart from the effort to cover as many different nuclei as possible n.d.r. offers a means of assigning the different resonance frequencies found to atoms in certain positions within a chemical unit (molecule complex ion etc.) in the solid. The prob- lem of assignment geometrical positions f-) resonance frequency is usually done by involved single crystal studies. In cases of unknown crystal structure they do not lead to a unique solution of the problem. Although an n.d.r. experiment is not a unique solution of the difficulties it is valuable in both applications mentioned above. In the following the technique proposed by Emshwiller Hahn and Kaplan' (EHK) (nuclear quadrupole-nuclear quadrupole double resonance) is applied to three different groups of chemical problems by taking advantage of the l/r6-dependence of echo amplitude damping (Y = distance of the two nuclei of interest within the solid).The first problem is the relative assignment of 81Br and 27Al quadrupole resonance frequencies within the complex ion [AI,Br,]- of the ionic solid KA12Br,. Both the 1/r6-dependence and the improvement of the signal-to-noise ratio are illustrated by application of the EHK technique to "Br +-w 27AI.2 Secondly the use of " homonuclear " double resonance ++35Cl,tested on a few molecular compounds of trichloroacetic acid (TCA) with organic molecules is described and the consequences of these experiments for relative intramolecular assignment discussed. Here n.d.r. allows the assignment of n.q.r. signals with very little frequency separation to different groups e.g.-CCI,. Finally we study how to investigate the molecular structure by using the technique as " isotopic " n.d.r. 'lBr ++ 79Br e.g. on the samples of (3,5-dichlorophenoxy aluminiumdibromide)2,(3,5-CI,C,H,0AlBr2)2 and of (4-chlorophenoxyaluminium dibr0mide)~,(4-ClC~H~OAIBr~)~. NUCLEAR QUADRUPOLE DOUBLE RESONANCE EXPERIMENTAL In applying the EHK method a pulse-pulse double resonance spectrometer was used the block diagram of which is shown in fig. I together with the applied pulse programs. In the detection channel the A-channel the power stage is a I kW wide band amplifier (1-200 MHz). The final stage in the second channel the B-channel is a 700 W amplifier with a band width of 1-30 MHz which was replaced by an amplifier covering the range of 37-42 MHz for the 35Cl f-) 35Cl n.d.r.experiments. In the isotopic n.d.r. ''Br f-) 79Br only the A-channel was used serving as the detection channel as well as the search channel. In this case the complete pulse program was fed to the sample through one probe coil whereby the 180" pulse for the B-system was following 'A'' -CHANNEL J. -BROAD RE-90" GATE ~BAND-~PROBE-)r AMPL ft t -\----+-I /+l 90" 180" FIG.1.-Block diagram and pulse programs of the nuclear quadrupole-nuclear quadrupole double resonance spectrometer. Dashed line shows B-pulse in single channel operation. immediately after the 180" pulse for the A-system (see fig. 1). The pulse lengths were individ- ually adjusted according to the different requirements of the experiments.For the "Br 27Al experiment on KAI 2Br7 the 90" A-pulse was 6-10 ps and the 180" B-pulse was about 200 ps in order to prevent line broadening due to the Fourier components. z = 300 ps was chosen for the 9Oo-.r-180" sequence. In the homonuclear 35C1-35Cl experiment the 90" pulse width was 20-40 ps (A-channel) whereas the B- pulse was extended to -250 ps; T was around I ms. In the n.d.r. experiments on (33-C12CsH30AlBr2)2 and (4-CIC6H,OAIBr,) a small permanent magnet was placed near the probe to create a weak magnetic field at the site of the nuclei. The Zeeman splitting leads to a decoupling of the nuclear spins and thereby to a lowering of the mutual spin flipping rate. Thereby the effective transversal relaxation time T2is raised and can be extended up to 400~s.Again the width of the A-pulse was lops(90"). A B-pulse of -250 ps was adequate. The samples were synthesized according to the prescriptions given in the literature. KAI2Br, prepared from the melt of 1 KBr + 2AIBr3 was zone refined and handled in closed ampoules because of its high sensitivity to moist air. The molecular compounds (C13- CC02H),X can also be prepared from a melt of the individual compound^.^ Some of the N. WEIDEN AND A. WEISS 95 TCA compounds are difficult to crystallize since they form glasses. For example the com- pound TCA-vanillin melts incongruently and has to be crystallized very slowly (12 h at 18 "0. TCANa.3H20 crystallizes from an aqueous solution of TCA neutralized with Na2C03.(3,5-ClzC6H30A1Brz)z are prepared at elevated tempera- and (4-CIC6H40AlBrz)2 tures by reaction of the respective phenoles and AlBr dissolved in CS2.4 THEORETICAL The nuclear quadrupole-nuclear quadrupole double resonance experiments reported here are based on the theory developed by Emshwiller Hahn and Kaplan.' By a conventional spin echo experiment an easily observable spin system A is moni- tored. At a time z a second spin system B is irradiated by a 180" pulse whereby the local magnetic field due to the B-spins at the sites of the A-spins hAB -pB/riB changes its sign hAB -+ -hAB. The sign reversal disturbs the phase memory of the A-spins and changes the A-echo amplitude. Assuming TIA= co the damping AE term of the A-echo due to the excitation of the B-spins by the 180" pulse is AE == 2 (CO~B)Z2E~c(2 Z).Z)TAA(~ (1) E, is the term in the A-echo due to the presence of the spin system C besides A and B. TAA describes the free induction decay signal of the A-system caused by the interactions A ++ A. Part of the second moment of the A-signal is due to the B-system and is given by (co~~) Y, yB are the gyromagnetic ratios of the A- and B-nuclei respectively; IBis the spin of the B-nuclei gjk a geometrical factor and rjk the distance between the nuclei Aj and Bk. For fixed experimental condition z = constant the terms EAc(2Z)and TAA(~~) may be considered constant and It is this l/r6-dependence which is used in our EHK experiments to determine relative assignments of n.q.r.signals with respect to the geometry of the molecules considered. RESULTS AND DISCUSSION HETERONUCLEAR DOUBLE RESONANCE The crystal structure of KA12Br7 is known.5 The geometry of the ion [AI,Br,]- is shown in fig. 2. In accordance with the crystal structure seven n.q.r. signals of 81Br in the frequency range 83.5 6 v/MHz 6 91 are detected at 77 K. No simple relation between the n.q.r. frequencies and the structure of the ion [AI,Br,]- is ap- parent. In the following Roman numeralsgive thenumbering of the atoms according to the crystal structure (fig. 2) Arabic numbers are used in listing n.q.r. frequencies coup- ling constants etc. The relation between Arabic and Roman numerals is found through the n.d.r. experiments. Using the EHK n.d.r.81Br f-+ 27AI the weak n.q.r. signals of 27A1,were found; their frequencies are given in table 1. The grouping of the 4 signals into two sets bf1*f7 (A41)) Vf ;*f&441hI and [v* 1 f-+ * d (A42)) I.'* 1f--+ * &442JI can be achieved by the following arguments NUCLEAR QUADRUPOLE DOUBLE RESONANCE from 0 < q < 1 the condition 2 3vf +-+ ;/v* + 4 31 follows. The ratios of the signal intensities 1,; ++*;/Irtt t--+*; should be -1 :2. V(AI(~Jand q(A4,J should be of comparable magnitude. Br * B ry FIG.2.-Geometry of the ion [AlzBr7]-in KAl2Br7 The assignment of the different signals is shown in table 1 together with e'qQ/h and q calculated from the tables of Livingston and Zeldes.6 The structure of the ion [AI,Br,]-is such that from the l/r6-dependence the relative positions of Br .. . vlI with respect to the atoms All and All and also with respect to the internal grouping of the Br-atoms is possible. For example Br, Brlr and Br,, (see fig. 2) should show a much stronger n.d.r. effect with All than with All,. AE of the bridging atom BrIv should be strongly influenced by Al and AI,, etc. The influence of the neighbouring ions can be estimated from the crystal structure data. The shortest interionic.distance AI-Br is >4 A. Compared with the largest bond distance Al-Br = 2.43 A the ratio (AEinter)/(A€intra) = (2.43/4)6 z 0.05. Therefore the influence of intermolecular interactions on the EHK experiment is negligible for KAI,Br,. In two series of experi- ments the relative assignment (Br(l .. . ,)) ++ A1(1,2)was determined. (a) With con- stant parameters of the A-channel the influence of the four A1 resonances on the seven "Br resonances was studied. Each of the two nuclei influences four 81Br reso- nances strongly three 81Br resonances only weakly. The influence of both2,A1 nuclei on one 81Br signal is of equal strength so this signal belongs to the bridging Br(Iv). TABLE 1 .-27AI N.Q.R. FREQUENCIES COUPLING CONSTANTS AND ASYMMETRY PARAMETERS IN KAI,Br, T = 77 K ''A](,) 1.304 2.562 8.652 0.117 1.628 3.068 10.324 0.220 A complete assignment of the next neighbours was found as given in fig. 3. This experiment also gives a unique determination of the four frequencies to the two crystallographically inequivalent A1 atoms within the ion [A12Br7]-.(b)With constant parameters of the B-channel for all "Br frequencies the four 27Al transitions were studied. The results of this experiment are in accordance with experiments (a).' The double resonance studies on KA12Br are in agreement with the single crystal n.q.r. study of Yamada on this substance. N. WEIDEN AND A. WEISS v (*IB~)/ MHZ Bq,) 83.583 f3ti2] 85.152 8.562 Bq,) 85.596 Br14) 86.142 Brl,) 66.319 10324 B561 86.928 Brol 90.906 FIG. 3-Assignment of the seven *'Br n.q.r. frequencies and the two 27Al coupling constants in KA12Br7 to terminal and bridging bromine atoms and to Al(, and AI(*,,respectively. T = 77 K. HOMONUCLEAR DOUBLE RESONANCE In molecular compounds (TCA),X and salts of TCA the mean 35Cl n.q.r.fre- When n quency of the adducts is -1-2 MHz higher than that of the ~alts.~~~*~ = 2 rn = 1 or when two or more TCA molecules are present within the asymmetric unit more than three 35Cl signals are found. 35Clc)-35Cl n.d.r. offers a chance to assign the signals to the individual CC13 groups of the TCA molecules. Two crystal struc- ture determinations are found in the literature for TCA X one is TCA itself," the other TCA pyridine-N-oxide.11y12 In each case three 35Cl signals are ob-ser~ed.~~~'~ These substances are useful to study the intermolecular and the intra- molecular influence on AE separately by an isotopic n.d.r. 35Cl ft37Cl. Numbering the C1-atoms in C13CC02H by Cl,,, CI,, and Cl(3, respectively AE in an n.d.r.experiment 35Cl(1) .c)37Cl(2) and 35Cl(1 f-) 37C1(3 contains both intermolecular and intramolecular terms. The n.d.r. 35CI(,,ft37Cl,l, 35Cl(2) ++ 37Cl(2 and 35Cl(3 ftj7C1(, etc. shows only intermolecular effects. In fig. 4 three of the n.d.r. signals of TCA found are shown. As expected from the crystal structure the . r . . s2 s3 5. QJb+w 31.717 > i 0.0 74 I I . 31.654 . 31.501 . /-i NUCLEAR QUADRUPOLE DOUBLE RESONANCE intermolecular terms are small compared with the intramolecular ones. Similar results have been gained for TCA pyridine-N-oxide. Investigating TCA X with more than one TCA within the asymmetric unit the assignment of the 35C1-n.q.r. signals to a distinct CCl is not restricted to the isotopic n.d.r.Much shorter sampling times can be achieved by 35Cl++ n.d.r. because (a) the mutual abundance of 35Cl is a factor of three larger than that of 37Cl (b) y(35Cl) z 1.2 Y(,~CI)which influences AE by a factor of (1.2)'. In total the S/N ratio improves by a factor of 4.3 compared with a 35Clf-t37Cl experiment and thereby the time for an experiment decreases by a factor of 18 to 19. FIG.5-Homonuclear n.d.r. 3'Cl ft35Cl in TCANa-3H2O. A-channel frequency is 39.383 MHz. S1 Sz S4 intermolecular n.d.r; S3. S5 intramolecular n.d.r. T= 77 K. The numbers in the figure are the respective frequencies in MHz. Four molecular compounds with TCA and the sodium salt TCANa 3H,O were studied by 35Cl ++35Cl n.d.r. In TCA * vanillin two signals overlap at 77 K (39.799 MHz).At T = 168 K this unresolved doublet splits into two lines 39.386 and 39.432 MHz. The other lines at 168 K are (in MHz) 38.919; 39.608; 39.780; 39.849 (all +0.005). In fig. 5 the n.d.r. of the upper signal (39.383 MHz) with the five other signals of TCANa 3H20 is shown. (AEintra)/(AEinter) was in all experiments 2 3-4 so that n.d.r. ,'Cl ft35Cl was done for each possible coordina- tion within one compound (15 measurements of a six line spectrum). In table 2 the results of the assignment are given. As can be seen the splitting of the n.q.r. (in which no systematic differences in the frequencies can be observed) within one compound is mainly due to the crystal field effect but not to a pronounced chemical inequivalence of the two CC1,-groups.TABLEASSIGNMENT OF 35c1FREQUENCIES TO TWO CI3C-GROUPS IN FIVE TCA COM-POUNDS. T=77 K. TCA* TCA. 2 TCA. TCA. TCANa*3H20 compound p-chlorphenol dibenzylether 1,4-dioxan vanillin -40.620I 40.370 39.855-1 1-39.715 ~' 1-40.320 -40.23 2 -40.122 39.383 39.329 V(3TI) ~ 40.1021 39.702-1 /MHz 1-40.0151 -39.709 I 39.533-j L39.462 ' 39.380-'-39.348 39.325-' 139.353 38.544 37.980 N. WEIDEN AND A. WEISS ISOTOPIC DOUBLE RESONANCE The halogen n.q.r. on (3,5-C12C6H30A1Br2)2 shows two "Br signals and two 35Cl signals at 77 K. For (4-C1C6H4OA1Br2) one 35Cl and two slBr signals are found. The halogen n.q.r. frequencies are listed in table 3. The crystal structures of these compounds are unknown. On the basis of the n.q.r. results four structure models for the molecules are possible which are shown in fig.6. The dimeric character of R R R (41 / R R FIG.&Four molecular structure models for (3,5-C12C6H30A1Br2)2 and (4-CIC6H40AIBr2)2which are in agreement with pure n.q.r. data. (4-ClC,H40AlBr2)2 was proved by determination of the molecular weight4 and is supported by the crystal structure of a similar compound dibromotrimethylsiloxy- aluminium.l5 The n.q.r. frequencies of 27Al were determined by 81Br -27Al n.d.r. at 77 K. Each substance shows only two 27Al resonances the data are listed in table 3. Since TABLE3.-N.Q.R. DATA OF (3,5-DICHLOROPHENOXY ALUMINIUMDIBROMIDE)2 AND (4-CHLORO-PHENOXY ALUMINIUMDIBROMIDE)~ AT 77 K compound (3,5-C12C6H30A1Br2)2 (4-ClCsH40AIBr2)2 [~(~lBr~~,)/(~~Br~ 86.150/103.128 86.650/ 103.732 ,,)]/MHz [v('lBr( 2,)/( 79Br( ,,)]/MHz 89.466/ 107.097 87.846/105.162 v(~~CI)/MHZ 35.382 36.428 36.35 I [v(I!Z+ c)~tt)(~'Al)]/MHz 1.620 1.806 [v(f-$ ++ +~)(27Al)]/MHz 3.152 3.211 e2qQh-'(27Al)/MHz 10.552 10.910 q(27~1) 0.148 0.317 one 27Al nuclear quadrupole coupling constant was found the two A1 atoms within the molecules are equivalent and the structures (1) and (4) of fig.6 can be neglected. From 81Br -27Al n.d.r. structures (2) and (3) are indistinguishable. However isotopic double resonance 81Br ft 79Br offers a way to solve the problem. In this experiment the models (2) and (3) are inequivalent. Assuming structure (2) to be NUCLEAR QUADRUPOLE DOUBLE RESONANCE the correct one the n.d.r."Brtl f-) 79Br(, should show a strong effect since the intramolecular distance BI-(~)-B~(~) is the shortest Br-Br distance within the molecule. The echo amplitude should be much less influenced by the EHK experiment on *lBr(, c)79Br(1) and 81Br(2) 79Br(2) respectively. f-) If structure (3) of fig. 6 were present the damping of the echo by the n.d.r. 81Br(l)c)79Br(2) and S1Br(2 +t79Br(2 would be pronounced because of the rela- tively short intramolecular distances Br(l)-Br.(2) and Brc2)-Brc2). The experiment 81Br(l,c)79Br(1) should show only a small effect. The n.d.r. experiments 81Br f-) 79Br show that structure (2) fig. 6 is the correct one for both compounds (3,5-C1,C,H3OA1Br,) and (4-C1C6H4OAlBr2),. CONCLUSION In the three different n.d.r.experiments applied here the use of the EHK method in increasing sensitivity and gaining information about the molecular geometry and the assignment of frequencies is shown. The main limitation in structural studies is that the intermolecular distances have to be considerably larger than the intramolecular ones. The ratio of those distances should be at least 1.3. For this reason the deter- mination of a relative bond length scale in molecules and complex ions may often be impossible because of the small differences in the interatomic distances. The resolu- tion of the homonuclear double resonance is high at least better than 20 kHz as shown in fig. 5 for the sodium salt of trichloroacetic acid TCANa 3H,O. Isotopic double resonance is useful for 81Br ct79Br 35Cl f-) 37Cl and should be successfully applicable in other cases e.g.123Sbf-) '?3b. We are grateful to the Deutsche Forschungsgemeinschaft for financial support of this work. M. Emshwiller E. L. Hahn and D. Kaplan Phys. Rev. 1960 118,414. N. Weiden and A]. Weiss J. Magnetic Resonance 1978 30 403. D. Biedenkapp and Al. Weiss Ber. Bunsenges. phys. Chem. 1966 70 788. T. Deeg and Al. Weiss Ber. Bunsenges. phys. Chem. 1976 80 2. E. Rytter B. E. D. Rytter and H. A. Oye Acta Crysf. 1973 B29 1541. R. Livingston and H. Zeldes Tables of Eigenvalues for Pure Quadrupole Spectra Spin 512 (Oak Ridge National Laboratory Report 1955 ORNL-1912). K. Yamada J. Sci. Hiroshima Univ. Ser. A 1977 41 77. * Yu. K. Maksyutin E. N. Gur'yanova and G.K. Semin Uspekhi Khim. 1970,39 727. Al. Weiss Adv. Nuclear Quadrupole Resonance 1974 1 1. lo P.-G. Jonsson and W. C. Hamilton J. Chem. Phys. 1972,56,4433. l1 L. GoliE and F. Lazarini Vestnik Slovensk. kem. Drustva 1974 21 17. l2 L. GoliE D. Had5 and F. Lazarini J. Chem. SOC. D 1971 860. l3 H. C. Allen Jr. J. Phys. Chem. 1953 57 501. l4 H. Chihara and N. Nakamura J. Phys. SOC. Japan 1974,37 156. l5 M. Bonamico and G. Dessy J. Chem. SOC.A 1967 1786.

ISSN:0301-5696    

DOI:10.1039/FS9781300093

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Torsional Spectroscopy by Nuclear Spin Polarization Losses in the Rotating Frame BY MILANM. PINTAR Physics Department University of Waterloo Waterloo Ontario N2L 3G1 Canada Received 30th January 1979 In some solids with moderately hindered torsional oscillators such as NH4 and CH3 groups it is possible to excite nuclear Zeeman-torsional transitions (double resonance). This type of resonance makes possible observations of resonant magnetization loss torsional specific heat torsion-phonon relaxation time and torsional energy spectrum. A brief description of these experiments is presented. In 1977 the Zeeman-torsional double resonance spectroscopy was introduced.' It was shown that when the nuclear Zeeman energy in the rotating frame is brought into resonance with the energy of the torsional oscillator on which the nuclear spins reside a semi-equilibrium between the two systems is established in a time of the order of the nuclear spin-spin relaxation time.The nuclear Zeeman energy states can be quickly polarized in the rotating frame. Since some of this order can be transferred in a few ps to the torsional oscillators (while the two systems are essentially isolated from the lattice) several experiments were made possible. In the magnetization loss experiment the proton Zeeman polarization was estab- lished in the rotating frame by the spin-locking sequence. In the rotating frame therefore Zeeman populations were characterized by a spin temperature which was some three orders of magnitude smaller than the lattice temperature.Since initially the torsional oscillators were in equilibrium with the lattice the polarizations of the two energy systems were drastically different. This difference vanished in a time of the order of 100 ,us if the matching between the two sets of levels was good. The equilibration time increased to several ms if matching was off by z 10 G. Thus if the two systems were allowed to evolve towards the semi-equilibrium for a fixed time of 100ps at different strengths of the r.f. field H, the degree of mixing varied. At those H where matching between the two energies was good as much as 40% of the proton magnetization was lost. If matching was off by z 10 G almost no magnetiza- tion was lost. A proton magnetization loss during a 100ps long spin-locking pulse of variable strength H in polycrystalline NHJ at 67 K is shown in fig.1 upper curve. The magnetization loss is more than z20 per cent at H between 5 and 20 G. Such a proton magnetization loss spectrum provides information on the energy range in which the nuclear Zeeman and the torsional oscillator energy spectra match. With a similar experiment' the specific heat of the torsional spectrum was deter- mined. If enough time is allowed for mixing Zeeman and torsional reservoirs a semi-equilibrium between the two is established over a wide range of r.f. fields. In such a case the magnetization loss dependence on H takes on a shape known from the dipolar local field e~periment.~ The torsional specific heat is derived from the r.f. field at which the proton magnetization decays to half its initial value; in complete analogy with the case of mixing the Zeeman and dipolar energies.Clearly the TORSIONAL SPECTROSCOPY torsional specific heat does not give the torsional spectrum. However it does provide for an independent evaluation of a proposed spectrum. The torsional specific heat was determined from the proton M dependence on Hl in polycrystalline NHJ at 67 K under the condition of a torsional-Zeeman semi-equilibrium. The spin- 16 12 I /a 8 4 0 10 20 30 40 Hi/G FIG.1.-Proton magnetization of polycrystalline NHJ as a function of HIat 50 K. The magnetiza- tion was spin-locked in an r.f. field for 100ps (upper graph) and for 4 ms (middle graph). The lowest graph shows the SPOTS magnetization observed after the pulse sequence n/2 FP1(400 ps) delay of 1 ms FP2(100 ps).locking field was 1 ms long (fig. 1 middle graph). M reached its half value at Hl = 11 & 2 G. At this field the torsional specific heat equals the Zeeman specific heat. In semi-equilibrium cz ~ (1) M = Mo CZ + CT’ where Cz = aHi and CT = aH$. The effective torsional field HT equals 11 & 2 G. C can be derived more accurately from the dispersion of the proton relaxation time in the rotating frame. In Zeeman-torsional semi-equilibrium the familiar spin thermometric equation holds (Cz + CT)Tib = CzTyi + CTTi;. (2) TlPis the common Zeeman-torsional relaxation time and TI and TITare the Zeeman and torsional relaxation times respectively.To a good approximation TTi = cz/H with a a constant. Eqn (2) is valid if the spin-locking pulse is at least 1 ms long. Eqn (2) was computer-fitted to the experimental data fig. 2. The value HT = 14 & 1 M. M. PINTAR G was obtained for NH,I at 72 K. The torsional relaxation time was determined in an independent experiment as described below. The same information can be derived also by a modified spin-locking pulse se- quence n/2,FP1 (400 ps) T( 1 ms) FP (1OOps). With the spin-locking pulse pair the Zeeman system is polarized and some of its order transferred to the torsional system. The delay T of 1 ms was much shorter than the torsion-phonon relaxation time of 20 10 I I I I 0 FIG.2.-Dependence of the proton Ti;of the polycrystalline NHJ on H ;'.The computer fitted curve corresponds to an effective torsional field HT = 14 & 1 G. T = 72 K. 60 ms. With FP (100 ps) a Zeeman system with no polarization is introduced while the torsional system has all the order it received while interacting with the Zeeman reservoir during FP (400ps). During FP1 the torsional inverse temperature becomes PTL =Pzl H H' + H; During FP2 the Zeeman and torsional systems reach a semi- equilibrium with the final inverse temperature pz2-pzl Hi + H;' H; As a result a Zeeman magnetization appears Its maximum value is Mo/4at H = HT. This magnetization is plotted at the bottom of fig. 1. The maximum is at H z 12 G in agreement with HT of 11 + 1 G derived from the specific heat experiment.The order transfer experiment was tested with resonantly coupled Zeeman and dipolar energies. The measurements were done at room temperature on NH,CI at 17 MHz fig. 3. The pulse sequence was n/2 FP (200 ps) t,FP (200 ps). The magnetization after the pulse FP depends on H as in eqn (1) with HT replaced by the dipolar local field in the rotating frame HL. This equation was fitted to the experi- mental points (fig. 3 upper curve). The derived value of the local field Hkwas 1.O 0.2 TORSIONAL SPECTROSCOPY G. The magnetization Mi following the pulse FP depends on H as in eqn (3). The computer fit of eqn (3) to the experiment gives the local field HL = 1.1 & 0.2 G. Both fields are in good agreement with the calculated HL of 1.08 -+ 0.05 G. The dependence of Mi on the delay z between FP and FP was found to be exponential with the characteristic time equal to 24 & 3 ms.With the Jeener-Brockaert pulse sequence the proton dipolar relaxation time TI of 27 & 2 ms was obtained. This agreement confirmed that the order was transferred from the Zeeman to the dipolar system since it relaxed to the lattice with T,,. 1.0 0.8 8 0.6 \ 22 0.4 0.2 0 2 4 8 HI/G FIG.3.-Proton magnetization of polycrystalline NH,CI in arbitrary units against the r.f. field at 273 K. The top line is the computer fit to M = M,N:/(H -H:); the experimental values of MXIMO are represented by circles. The bottom line is the computer fit to Mi = MoN;fH:/(H:+ H;f)’. The resonance frequency was 17 MHz.An interesting result of this double resonance technique was the development of a method for measuring the torsional oscillator relaxation time TIT. This torsion- phonon relaxation time is measured with the following pulse sequence 42,FP (I ms) z FP (100 ps). The first part is as above the spin-locking pulse sequence with the field H set close to the resonance. The torsional spectrum is polarized during the pulse FP (1 ms). As the Zeeman spectrum is removed by removing FP (1 ms) the torsional oscillator is allowed to relax undisturbed towards equilibrium with the lattice bath during the time z. Any torsional polarization left after the time zis then shared with the Zeeman spectrum which is reestablished by the second field pulse FP (100 ps). Since the FP pulse is applied without a preceeding 42 pulse there is no initial Zeeman polarization in FP,.During the pulse FP (100 ps) the torsional order is shared with the Zeeman system resulting in a small Zeeman signal M which depends exponentially on z. With this method Ty; was measured in polycrystalline NH41 as a function of temperature between 4 and 60 K fig. 4. The most interesting feature of the Ti; temperature dependence is the linear region 4-40 K. This dependence M. M. PINTAR implies a one-phonon process between two torsional levels separated by no more than z 12 K. However it is known from neutron spectroscopy that the 1st excited state is ~430 It is possible to speculate that a 24 fold degener- K above the ground ~tate.~ ate ground state of the NH4 oscillator is split into two sets of lines separated by less than z 12 K.Each rnultiplet has energy splittings no larger than z 100 kHz. At temperatures above 40 K multi-phonon processes contribute to Ti;causing an ex- ponential rise in Ti;with temperature. At z75 K this rate becomes so fast that the tunnelling spectrum disappears because of the torsional lifetime broadening. At essentially the same temperature the dipolar line narrows. Thus at this temper- ature TITis the correlation time for the NH4 group reorientation. -1 I 0 10 20 30 40 50 r/ K FIG.4.-Relaxation rate of the NH torsional oscillator in polycrystalline NH41 plotted against temperature. During the search for a better resolution of the magnetization loss spectrum it was soon realized that the non-equilibrium regime had to be explored.In this time regime the magnetization undergoes damped oscillations which were believed initially to have a frequency ~co, as in the case of Zeeman and dipolar mixing. When the field pulse was set to a few ,us duration and varied in 1 ,us steps beats appeared in the time evolution of the magnetization indicating at least two freq~encies.~ The 71/2 FP1(t) pulse sequence was applied with the FP,(t) duration varied from 1 to 200 ,us in 1 ,us steps. The magnetization M,(t) was recorded for each t. As the field pulse was made progressively longer the magnetization evolved towards the semi-equilibrium in the rotating frame. The analysis showed that in this evolution the frequencies 204 1204 & wTiI and mTi are present.By a Fourier transformation of M,(t) a spectrum was arrived at fig. 5 and 6. A brief summary of the perturbation calculation is as follows. The Hamiltonian of Zeeman (Z) torsional (R) and dipolar (D) energies in the rotating frame at exact resonance reads if = ifz + ZR-3Xg' + (3/8)"2(Xg'+ XL-"). (4) TORSIONAL SPECTROSCOPY 1.8 1.6 CI 0 1.4 32>- s v 1.2 1.01 0.8 I I I l l l r l l l 1 1 1 1 20 40 60 80 100 120 140 t/ 16%i 10 20 30 40 50 v/4kHz FIG.5.4~) Proton magnetization time evolution of polycrystalline CH3CD21in the rotating frame at 12.5 G measured at 17 MHz. M was recorded 9 psafter the end of the spin-locking pulse. The duration of the r.f. pulse was varied from 1 to 148 ps in 1 ps steps.(b) Fourier transform of the time evolution in (a) (the SPOTS spectrum). Note that only frequencies 20 + oTand 2wl -wTappear. Frequency is in units of 4 kHz. M. M. PINTAR 1 .o n 0.6 \ 0.4 0.2 0 10 20 30 40 50 v/4 kHz FIG.6.-SPOTS spectrum of the polycrystalline NHJ at 30 K. Proton magnetization was observed at 17 MHz with window position at 24 ,us. Time increments were in 1 ps steps the r.f. pulse was varied from 1 to 200 ,us. Observations were made at 2H1 of 26.9 and 29.5 G. The two spectra are shown as full and dotted lines respectively. Those terms in XDwhich are time dependent with frequencies mo = yHoor 2m0,have been dropped and the z-axis has been chosen along the direction of the r.f.field HI. In this case the non-diagonal spin operators in the dipolar interaction connect only states whose spin quantum numbers M differ by AM = 0 *2. Since the operators Xzand XRcommute we choose as a basis their common eigenfunctions (<M) (%R + xZ)l<M) = EcMIM) = (5 -fimM)lcM)-(5) We now examine the time evolution of the spin-torsional system due to the part D of the dipolar Hamiltonian in the rotating frame which does not commute with ZZ or ZR. Starting at time t = 0 the non-equilibrium density matrix in the high temper- ature approximation reads P(0) = Q-’(l -EoZz -PO~R). (6) Here Q = Tr(1 -&VR}and uo and Poare the initial inverse temperatures. The zero of energy may be chosen such that the trace of XRalso vanishes. 1 is the unit operator.In the interaction picture defined by U(t)= exp [i(Xz + %&/ti] the density matrix obeys the following equation of motion ap -= -i/h[D(t) p”(t)] (7) at in which D(t) = U(t)DUt(t). The solution of this equation is p”(t)= p”(0)-i/k ds[D(t) p”(O)] -1/h2[ dr [dr’{D(r) [D(r‘),p”(O)]}. 0 The expectation value of the Zeeman energy is then given by (XZ(t))= Tr{sz,5(t)). TORSIONAL SPECTROSCOPY The selection rule imposed by the operator D(t) allows frequencies 12w 5 wTl and 20,. The SPOTS spectrum of CH3CG21,fig. 5(b) consists of ]2w1 + uTland 120 -mTl lines of approximately equal intensity. The 2w line is not observed. This is not surprising considering that the ratio of Zeeman to dipolar specific heat is only a few percent.In solid NH41 the SPOTS spectrum of NH4 exhibits a very /-A2 / (11-N’ /- 3f2 (9)-/’ / //- E2 (4)-:I (9)-_ / .- El 3FI f F - -f E F f -FF F FIG.7.-Ground state splitting of the NH- torsional oscillator in various crystal fields (a)octahedral (6)octahedral with a small tetrahedral perturbation (c)tetrahedral (d)trigonal and (e)no symmetry. intense 20>,line in addition to several other lines fig. 6. In a trigonal crystal field6*’ four tunnelling frequencies are allowed fig. 7. The NH41spectrum shows more than seven lines. A possible origin of these lines is the existence of two nonequivalent oscillators in the NH41lattice. Pulse sequences with finer time increments are needed to resolve and assign the spectrum. Experimental and theoretical work of this nature is now being carried out in Waterloo.R. S. Hallsworth D. W. Nicoll J. Peternelj and M. M. Pintar Bull. Amer. Phys. SOC.,1977 22 550. ’R. S. Hallsworth D. W. Nicoll J. Peternelj and M. M. Pintar Phys. Rev. Letters 1977 39 1493 R. S. Hallsworth Ph.D. Thesis (University of Waterloo 1977 unpublished). M. Goldman Spin Temperature and Nuclear Magnetic Resonance in Solids (Oxford University Press London 1970) chap. 2. G. Venkataraman J. Phys. Chent. Solids 1966 27 1103. D. W. Nicoll and M. M. Pintar Phys. Reu. Letters 1978 41 1496 D. W. Nicoll Ph.D. Thesis (University of Waterloo 1978 unpublished). T. Nagamiya Progr. Theor. Phys. 1951 6 702. A. Huller and J. Raich Torsional Ground State Splitting for Tetrahedral Molecules to be pub- lished.

ISSN:0301-5696    

DOI:10.1039/FS9781300101

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Deuterium Nuclear Magnetic Resonance Spin Echo Spectroscopy in Molecular Crystals BODEN,LESLIE SEANM. HANLON BY NEVILLE D. CLARK AND MICHAEL .1-MORTIMER Department of Physical Chemistry University of Leeds Leeds LS2 9JT Received 15th September 1978 The effects of quadrupole dipole chemical shielding and spin-lattice interactions on the properties of the deuterium spin echo response to a 90"-~-90'~~0 pulse sequence in powdered molecular crystals are investigated. Procedures are delineated for the selective measurement of these interactions. It is argued that these experiments should contribute to the realisation of the potential of deuterium n.m.r. spectroscopy for studying orientational disorder and motion in molecular solids. 1. INTRODUCTION Proton n.m.r.spectroscopy has been widely used in the investigation of the structure and dynamical properties of molecular solids. The shape of the spectrum is governed by dipolar interactions and it has been necessary to employ the method of moments to extract information. The electric quadrupole interaction experienced by a deuterium spin in a C-D bond is much greater than its dipolar coupling to neighbouring spins whether deuterium or hydrogen and consequently dominates the properties of the spectrum and spin-lattice intera~tion.'-~ The shape of the spectrum may be directly related to the orientational distribution in partially ordered solids such as drawn polymers4 or liquid crystal~~9~-' and also to the mechanism of molecular reorienta- ti~n.~'~ Deuterium double quantum spectra are devoid of quadrupole splittings and may be used for chemical shift measurements in disordered solids." Substituting deuterium for hydrogen at selected molecular sites combined with proton spin decoupling provides the possibility of probing the microscopic structure and dynamics in complex materials.In powders or amorphous materials such as liquid crystals glasses and polymers the distribution of quadrupole interactions makes the spectrum broad (up to 270 kHz for organic solids where the quadrupole coupling constant e2qQ/hz 180 kHz) of low intensity and difficult to measure without distortion by C.W. techniques. The f.i.d. signal following an intense radio-frequency pulse is correspondingly very short and partially obscured by the spectrometer " dead-time '' td.$ It will not in general be possible to correct for the lost signal with confidence even when high-field spectro- meters are used with td z 10 ps.The reason is most easily understood by consider- ing the shapes of the f.i.d. signals shown in fig. 1. The Pake spectrumI3 [fig. l(a)] obtains for an axially symmetric electric field gradient with an isotropic orientational 7 Present address The Open University Milton Keynes MK7 6AA. $ For the spectrometer used in this study a Bruker SXP operating at 9.8 MHz fd M 50 ps but the magneto-acoustic ringing"*'* may persist for several hundred ps. It is possible though difficult to suppress the latter by special probe construction. The preferred solution is to use a cryomagnet and operate at a frequency in excess of 30 MHz where the effect is absent and td z 10 ,us.2H N.M.R. SPIN-ECHO SPECTROSCOPY L-U I I -250 0 +250 0 50 ibo igo i I I J t I I I -250 0 +250 0 50 100 150 kHz PS FIG.1 .-Comparison of deuterium frequency and time domain spectra for (a) an isotropic orienta- tional distribution of an axially symmetric field gradient tensor (Pake spectrum) with e'qQ/h = 180 kHz (6) an orientational distribution giving a rectangular frequency spectrum of width 135 kHz corresponding to the splitting between the singularities in the above Pake spectrum. Note the simi- larity in the short time behaviour of the time domain spectra for both distributions. distribution the first node is at t z 1.4/6vmax(i.e. 5.2 ps for a spectral width dv,, of 270 kHz) and the second a factor 2.61 later.The f.i.d. signal for the simple rectangu- lar distribution [fig. l(b)] has the form (sin x)/x the first node is at t -0.73/6vm, (Le. 5.4 ps for the example considered) and the second-to-first node ratio is 2.0. Both signals converge on the form cos x at long time and the period is determined by the frequencies of the " singularities " in the spectra. Clearly the short time part of the f.i.d. signal must be obtained without distortion if the fourier transformed spectrum is to be used in studies of molecular motion or orientational distributions On the other hand an accurate value for the separation of the principal singularities is always obtained as it is reflected by the signal at long time.A possible route to the deuterium frequency spectrum of a solid is to calculate the fourier transform of the spin echo produced at time 7 following a resonant 90"- ~-90~~~0 pulse sequence with T2> z > td. This procedure is valid for isolated spins-1 subject to quadrupole interactions as predicted by So10mon.'~ In molecular crystals however the deuterium spins are also subjected to other spin interactions which include dipolar chemical shift and spin-lattice interactions. We must there- fore consider the effects of these interactions on the echo responses. Only perdeuteri- ated materials will be examined here and for these ZQ X,,. Nevertheless the dipolar interaction has a marked effect on the general properties of the spin echo responses to 90"-~-& pulse sequence^.'^^'^ They distort the fourier spectrum of the 90"-~-90"~,,~ echo but the effect will be shown to be negligible.Other sources of distortion both instrumental and those inherent in the technique are also discussed. Measurement of the 9O0-~-9oo9,~ echo maximum as a function of 7 yields a direct measurement of the dipolar interaction^.'^*'^ The echo response is also dependent N. BODEN L. D. CLARK S. M. HANLON AND M. MORTIMER 111 on the chemical shielding interaction and enables the centre of gravity of the fre- quency spectrum to be simply yet accurately measured. The various applications of spin echo spectroscopy are illustrated by studies of the spectrum spin-lattice relaxation and chemical shielding in polycrystalline [2H,]benzene.2. EFFECTS OF DIPOLAR INTERACTIONS ON DEUTERIUM SPIN ECHOES Consider first the nature of the spin echo response for a system of isolated deu- terium spins. The hamiltonian for a deuterium spin coupled to a local electric field gradient in a static magnetic field Bo is for wo B wQ c&? XZ -wOIz + 3wQ{312-I(I + I)} (1) where wo= yBo and wQ = 3eQV2,/4h where V, is the secular component of the electric field gradient tensor. The frequency spectrum will be a doublet with splitting 20.1 centred on wo. For a system of deuterons with a distribution of quadrupole interactions P(wQ),the spectrum will be broadened and reflect both wQand the nature of P(wQ). In the case of a pow- dered molecular crystal there is a continuous distribution in the values of wQ giving a broad resonance up to 270 kHz in width.The f.i.d. signal following a short intense pulse (0.1~ 9 wQ; LC) = wo) will therefore decay very rapidly and be obscured at short time as already discussed by the spectrometer dead-time. Application of a second pulse at t = r with proper- ties such that it changes the sign of the quadrupole interaction initiates a refocusing of the dephased magnetization which leads to a well-defined echo at t = 22. To obtain the properties of this echo we follow Solomon’s procedure14 and calculate the transient response of the spins in the rotating frame to a 9Oo-z-&t’ sequence (0.1 = coo) from (Ix(t)) = tr{exp (-iZit’)R-’(P 4)exp (-iZiz)Ix x exp (ixi z)R(P 4)exp (izif‘)Ix}/tr{I:} (4) where here Zi= %$ t’ = t -z and R(P 4) is a rotation operator.Evaluation of the trace” in eqn (4) yields for an XY sequence (4= 90°) the echo response ExU(p,t’ r) = sin’P(1 -M2(t’-~)~/2! -+ M4(t’-~)~/4!. . .} (5) and for an XX sequence (4= OO) The XY echo has the same shape as the f.i.d. signal G(t) = 1 -M,t2/2! + M4t4/4!-. . *7 (7) showing that for a 90°-z-90090~sequence spin refocusing is complete with the excep- tion of the decay due to T processes at t’ = 5. The form of the transient signals is described elsewhere. l7 'H N.M.R. SPIN-ECHO SPECTROSCOPY For deuterium spins in powdered molecular crystals we have found l59I6 Exu(p,z) = a(z) sin' p + b(z)sin' p cos' p Exx(/3,z) = -c(z) sin' p cos p where the coefficients a(z) b(z)and c(z) represent the dependence of the echo ampli- tudes on z.The sin2p component dominates Ex@ 7) at short z but decays much faster than the sin2p cos2p component so that the echo maximum shifts to p < 90" with increasing z. The dependence of the echo amplitudes on z and the occurrence of the XX echo and the sin'p cos'p component of the XY echo are determined by the dipolar interactions between the deuterons. This is seen by calculating the echo response for a model hamiltonian of two dipolar coupled spins-1 xi= 2:+ x; x = UQ11:z + mQ21222 (9) 2:= (yvqr3)(1 -3 cos20e){1,,1, -*(I,+I'-+ 1,-1~+)1 where Y is the internuclear separation and 0 is the angle this vector makes with the field. Since in practice Z; 9 A?:,2':was truncated so as to commute with 2:; this facilitates the calculation of (I,(t)) in eqn (4).* The results for the p dependences of the echo responses are as given in eqn (8).An interesting result is that the ampli- tudes of the XXecho and the sin2P cos2p component of the XXecho are zero at z = 0 but increase to a maximum before decreasing with z. This behaviour is due to their origin through interference between terms of opposite sign they are better regarded as " subsidiary " echoes in contrast to the " principal " sin2p one. The model also predicts for the 7 dependence of the 9o0-z-9Oc9,~ maximum echo amplitude EXy(9Oc, z) x 1 -$ MzVz2/2!+ --(10) where MzV is the van Vleck second moment. The ratio of Mp to MF (=-d'Exy (90" ~S)/d7~~+~) measured for both benzene and acetone (table 1) is 19.7 1.0 and is TABLECOMPARISON OF M,H AND M FOR BENZENE AND ACETONE material T,K M Tz M;/ lop8TZ M,HfM2 benzene 200 1.55 0.05 0.079 & 0.002 19.65 i0.81 acetone 150 7.25 3 0.36 0.367 + 0.003 19.75 1.00 Errors quoted represent standard deviations.The values for MF were obtained from proton f.i.d. measurements. close to the value of 17.92 calculated for MF/$Mp. The small discrepancy might originate from systematic errors in the measurements differences in the vibrational averaging of the two interactions or limitations of the model for a real solid. Never-theless despite its simplicity the predictions of the model are in remarkable agreement with experiment. It is important to consider how the dipolar interactions affect the shape of the echo.For a 90"-z-9Oo9,~sequence E,y(90" 7 t') = 1 -M2(t' -~)~/2! -+ Md(t' -~)~/4!. . . -M,Et'z/2!+ higher order error terms. (1 1) * Kleinen-Hammans and Levine have recently shown that the echo responses calculated without truncating 3;are identical provided X%> 3 A?;,a condition always fulfilled for deuterium spins in organic solids. (J. W. Kleinen-Hammans and Y. K. Levine personal communication.) N. BODEN L. D. CLARK s. M. HANLON AND M. MORTIMER 113 The " error " terms will shift the position of the echo maximum to t < 27 and dis- tort the shape of the echo profile. Conversely if the echo maximum occurs at t = 22 distortion of the echo profile will be negligible. The position of the echo maximum may be estimated to second order in time from eqn (1 1) t x (I + M2 -M2 For powdered [2H6] benzene in its " rigid" lattice M2/Mfz 3.6 x lo4.In this and other perdeuterated solids the dipolar interactions though markedly influencing the general properties of the echo responses significantly distort neither the position nor the shape of the echo for experimentally accessible values of z (up to z s). Fourier transformation of the 90°-~-900900 echo profile is thus at least in principle a valid route to deuterium frequency spectra in such materials. 3. DISTORTION OF SPIN ECHO SPECTRA It was shown in the preceding section that it is possible at least in principle to obtain distortion free deuterium frequency spectra by calculating the fourier trans- form of the echo profile starting at t = 22.We now briefly consider the practical problems involved in the measurement of undistorted spin echo signals and also delineate phenomenological effects which can lead to departures from equilibrium spectra. Practical complications arise from the incompatible demands of the sample coil circuitry. The problem is more severe than for say proton solid state pulse spectro- scopy. A high Q circuit is required first because of the inherently poor signal-to- noise ratio of the deuterium resonance and secondly to achieve a high r.f. power level. The latter is required to obtain a uniform irradiation intensity over the entire width dv,, of the spectrum this requires 1/nt > dv,,, i.e. 1 ps for " rigid " lattice powder spectra. It is possible to operate with P < 90° but transients of the form17 GXdP t>= cos2P (13) will occur.The echo signals can however be corrected for the presence of these transients if their intensities have not decayed to zero by t = 25. In contrast a low Q (large bandwidth dw) circuit is required to avoid distortion of the echo signal. Essentially a circuit time constant TR< T,/lO where T is the shortest signal time constant is required. For a " rigid " x 7"' lattice Pake spectrum s making TR< lO-'s and Q (eco/dco x wTR)< cc) or Q < 6 for a resonance frequency of 10 MHz as employed in our experiments. The effect of the coil Q on the echo response is illustrated in fig. 2 by the echo signal observed for [2H40]n-nonadecane at 165 K.At this temperature the spectrum of the -CD groups is motionally nar- rowed (dv,, z 75 kHz) due to reorientation about their C3 axes whilst that for the -CD2 -groups is still " rigid " (dvmaxx 250 kHz). The echo signal in fig. 2(a) was recorded using Q x 80 the echo maximum for the -CD spins occurs at t = 22 (400 ps) but that for the -CD2- spins is displaced to 406 ps. Reducing the Q to 20 [fig. 2(b)] shifts the -CD -echo maximum close to 2s but this value of Q is still too large to avoid signal distortion. The value of Q chosen in practice" must be a com-promise determined by both the system and objectives of the investigation. Band-width distortion of the echo provided it is not excessive can be software-corrected.18 * In our experiments the value of Q is varied by inserting a resistor between coil and ground.Note that the value of Q will be sample dependent. 2H N.M.R. SPIN-ECHO SPECTROSCOPY lbl 27 27 1100AS] FIG.2.-Effect of sample circuit Q factor on the spin echo signals observed for a resonant 90"-r-90°w pulse sequence in polycrystalline [2H40]n-nonadecane at 165 K (a) Q x 80 and (b) Q x 20. The signals are the average of 25 scans and were recorded with T = 200 ps and a pulse repetition rate of 3 x 10-3s-1. The desirability of working at high r.f. frequencies is however obvious. Moreover with the frequencies now accessible using cryomagnets magneto-acoustic ringing is quenched. Phenomenological distortion of the echo spectrum may arise whenever the molecule contains distinguishable groups of deuterium spins.The spins will be subjected to different dipolar interactions and consequently the echo responses will exhibit correspondingly different 7 dependences this will give rise to a distortion in the relative intensities of their respective spectra. This phenomenon is illustrated by the 2Hspectrum of C2Hd0]n-nonadecane at 165 K [fig. 3(a)]. The signal-to-noise ratio is not particularly good due to the limited number of scans (25) averaged because of the long TI (x100 s) of the -CD -spins. Nevertheless the spectrum is seen to be a superposition of two Pake powder functions corresponding to the -CD2 -and -CD3 groups but the relative intensity of the latter (25%) is greater than predicted from the stoichiometry (15%). Of course by studying the 7 dependences of the relative intensities in the echo spectra the dipolar interactions characterizing the two groups may be resolved.Spectral distortion will also occur whenever the spin system of one group of spins is partially saturated with respect to the others. This is possible in perdeuterated solids since spin diffusion is slow and groups undergoing different motions exhibit their own characteristic relaxation behaviour. This effect is illustrated rather dramati- cally by the spectrum of [2H40]n-nonadecane shown in fig. 3(b). It was recorded under identical conditions to those in fig. 3(a)except that the pulse repetition rate was increased from 3 x to 10s-l. The spin system of -CD2 -(TI w 100s) is completely saturated whilst that of the -CD3 groups (T FZ 3 ms) remains in equili- brium with the lattice.This means that only the spectrum for the -CD3 groups is measured. This is a novel technique for resolving the spectra of different groups in complex molecules. Alternatively a 180"-t-(90"-z-90",,~) sequence could be em- ployed and the spin system examined as a function of the relaxation interval t but TI may be angular dependent and the resulting powder spectrum would be distorted. N. BODEN L. D. CLARK s. M. HANLON AND M. MORTIMEK 115 1 1 r I 1 I -180 0 +180 kHz 'L I j -180 0 +180 kHz FIG.3.-(a) Deuterium frequency spectrum for polycrystalline [ZH,oJn-nonadecane at 165 K as ob- tained by calculating the fourier transform of the 90"-t-90"90~ spin echo in fig.2(b)starting at t = 27 z = 200 ps t = 3.25 ps.Values of 168.0 iI .3 kHz and 49.9 I .3 kHz are obtained for the ap- parent quadrupole coupling constants of the -CD2-and -CD3groups respectively. The band- width of the sample coil circuit was % 500 kHz. (b)Spectrum obtained under identical conditions to that above but with the pulse repetition rate increased from 3 x 1O-j s-' to 10 s-' and the number of scans increased to 5000. [2H,,]n-Nonadecane has an orthorhombic structure up to 295 K at which tempera- ture it undergoes a transition to a phase with hexagonal structure before melting at 305 K. The spectrum obtained in this phase is shown in fig. 4. It is far more com- plex than a superposition of two Pake spectra (low temperature spectrum) as pre- dicted for reorientation about a molecular symmetry axis.Echo formation is unaffected by molecular motion in both the rigid lattice and motionally averaged regimes of ZQ.But when I IZalI z l/z spin echo formation is disrupted. The nature of the spin echo response in the motional narrowing regime will be a function of XQ,z T~ and the mechanism of the motion. 2H N.M.R. SPIN-ECHO SPECTROSCOPY I I -100 0 +loo kHz FIG.4.-Deuterium spin echo spectrum obtained for polycrystalline [2H40]n-nonadecane in its hexa- gonal phase at 297 K. The spectrum is the average of 1000 scans and was measured with z = 400 ,us a pulse repetition rate of 2.0 s-' and tp = 3.25 ,us. The bandwidth of the sample coil circuit was -500 kHz. 4. SPIN ECHO STUDY OF MOLECULAR ROTATION IN [*H,]B EN Z E NE Deuterium spin echo spectroscopy is a particularly attractive technique for the characterization and measurement of the rates of anisotropic molecular rotation in organic solids.To illustrate this point we present here the results of a combined 2H lineshape and spin-lattice relaxation investigation of molecular reorientation in solid [2H,]benzene. It has been well established by proton n.m.r. that in benzene the mole- cules undergo thermally activated reorientation about their six-fold symmetry a~is,'~'~~ but the detailed mechanism of the process has been a controversial subject. The analysis of the proton spin relaxation measurements is complicated by the difficulties encountered in the calculation of the correlation functions for the intermolecular dipolar interactions.The relaxation of a deuterium spin is governed by its quad- rupole interaction. Provided the orientation of the principal axes of the field gradient tensor (Vll V22,V3J in the molecular frame is known the spin-lattice relaxation rate can be directly related to the mechanism and correlation time z for the motion.24 The 2H spin-lattice relaxation times TI measured in polycrystalline [2H6]benzene at 9.82 mHz are summarized in fig. 5. The measurements were obtained by monitor- ing the maximum echo amplitude following a 90°( 180°)-t-(900-~-90090~) sequence with the relaxation interval t z. The spin-lattice relaxation rate due to modulation of the deuterium spin quadrupole interaction through random molecular jumps in a symmetric potential is 24 where J(o) = TJ(1 + co2z,2) N.BODEN L. D. CLARK s. M. HANLON AND M. MORTIMER 117 and F(O CD q) = sin2 O(1 + +q cos2CD) x (4 -3 sin20(1 + +q cos2CD)) + $q2 where VII -v22 v33 * O is the angle between the 3-axis and the direction of the rotation axis and CD is the angle by which the 2-axis is rotated out of the plane defined by the 3-axis and the rotation axis. 1.0 -0.1 VI \ k-0.01 0.00) 1 8 Fig 5 Deuterium spin-lattice relaxation times TI measured at 9.82 MHz in polycrystalline [’HJbenzene plotted as a function of reciprocal temperature. The solid line drawn through the experimental measurements was calculated from the 7c in fig. 8 using eqn (20) with values of 177.0 kHz and 0.041 for respectively the parameters e2qQ/hand v.Barnes and have obtained from the powder spectrum at 77 K the values e2qQ/h= 180.7 1.5 kHz and = 0.041 i 0.007. To fix the values of O and CD we need to relate the principal axes of the field gradient tensor to the molecular frame. Theoretically the 3-axis must coincide with the direction of the C-D bond.26 There-fore the 2-axis will be either along assignment (i) or perpendicular to assignment (ii) the rotation axis. We can distinguish between these two possibilities by investi- gating the effect of molecular rotation on the spectrum as has been used for the assignment of chemical shielding tensors.” The averaged field gradient tensor will be axially symmetric with respect to the rotation axis VJR) = v22(R) = ‘(1 .-cos2a sin2B)Vll + f(1 -sin2a sin2p) v, + sin2p~~~ V33(R)= sin’ p cos2a~,,+ sin2,G sin’ Mv, + cost PV, (16) 2H N.M.R.SPIN-ECHO SPECTROSCOPY where the Euler angles (a,p) relate the orientation of the rotation axis to the principal axes of the tensor. For assignment (i) (a = 90" and p = 90") VllW = V (R) = 1 22 Z(VI1 + V33) and vp = v22 = -*(I + vW33-Transforming the averaged tensor to the laboratory frame we obtain where 0 is the angle between the rotation axis and the direction of the magnetic field Boand eq = V33. A powder sample will therefore exhibit a Pake spectrum with the singularities separated by Avs = + ex(1 + q). h For assignment (ii) (a = 0" and p = 90") We may therefore distinguish between the two assignments by measuring the split- ting Avs in the rotationally averaged spectrum.Fig. 6 shows the 90°-~-9009,~ echo for powdered ['HJbenzene at 200 K and fig. 7 the corresponding frequency spectrum. The latter has the general shape of a Pake spectrum as predicted but close examination of the singularities shows the presence of fine structure which is reflected by the low frequency modulation seen on the spin FIG.6.-Deuterium free induction decay and spin echo signal obtained with a resonant 90 "-~-90"~~ sequence in polycrystalline ['HJbenzene at 200 K. The " spectrum " is the average of 1000 scans; it was recorded with a dwell time of 1.0 ps a pulse repetition rate of 10 s-' a pulse width of 3.25 ps and a bandwidth of 500 kHz. In the insert the signal amplitude is x3.N. BODEN L. D. CLARK s. M. HANLON AND M. MORTIMER 119 echo signal. This structure is due to dipolar interactions and its presence limits the accuracy to which the powder splitting dv can be measured; it has the value 69.10 & 1.0 kHz. Substitution of this value together with that for q into eqn (18) and (19) yields values for e2qQ/h of 177.0 + 2.4 kHz and 192.2 x 2.4 kHz respectively. I -100 0 + 100 kHz FIG.7.-Experimental (-) and calculated (--) deuterium spectra of polycrystalline ['H6]benzene at 200 K. The experimental spectrum was obtained by calculating the fourier transform of the echo signal in fig. 6 starting at t = 2t. The calculated spectrum was obtained using e'qQ/h = 177.0 kHz and ~7 = 0.041.In the insert the frequency scale is x 8. Clearly assignment (i) must be the appropriate one. The value obtained for the quadrupole coupling constant was independent of temperature in the interval 150-250 K. For assignment (i) 0 = 90" and CD = 0" so that @ rl) = (1 -v/3l2 and eqn (14) becomes Substituting values for e2qQ/hand 'Iwe calculate a value for TI at the minimum of 0.64 0.02 ms. This is very close to the experimental one of 0.66 & 0.04 ms at 152.5 +-1.5 K. The contribution from dipolar interactions is 0.124 s-' as calculated from (1/Ty)= 675/TF and is negligible. The values calculated for z from the TI measurements using eqn (20) are sum- marized in fig. 8 as a plot of In zagainst 1/Tand are seen to exhibit a well defined Arrhenius temperature dependence over the temperature interval 133-280 K.It would therefore seem that molecular reorientation in benzene is well described by a simple exponential correlation function. Moreover the data for zc are unequivocal. They compare with those obtained by Haeberlen and Maier" (7 = 9.2 x s and EA = 17.57 kJ mol-' 162-178 K) and Noack et ~21.~~ (4.98 x s and EA = 2H N.M.R. SPIN-ECHO SPECTROSCOPY 18.79 kJ mol-' 100-173 K) from respectively proton Tl and TIPmeasurements assuming uncorrelated molecular rotations.21 This model predicts that the minimum value for TIoccurs when wozc= 0.86 as compared with the value 0.62 obtained from eqn (20). At 9.82 MHz the frequency of the deuterium Tl measurements the proton Tl minimum occurs at 148.5 K2'qZ2at which our data give 0.94 for woz, a result consistent with uncorrelated rotation.Wendt and Noack22 have reported FIG.8.-Reorientational correlation times T~ in polycrystalline [*H6]bemene plotted as a function of reciprocal temperature. The z values were calculated from the TImeasurements in fig. 5 using values of 177.0 kHz for e*qQ/hand 0.041 for 11 in eqn (20). The solid line drawn through the data points corresponds to 5 = (3.14& 0.02) x exp ((19.01 f0.10 kJ rnol-')/RT}. that the proton Tl measurements suggest an increase in the activation energy for molecular rotation on approaching the melting point. They have attributed this behaviour together with the shape in the region of the minimum of the In Tl against l/T plot to correlated molecular rotation.There is however no evidence in our data for 5 for such a change in activation energy. The complexities in the proton relaxation measurements alluded to by Noack et al. must consequently originate in the behaviour of the intermolecular dipolar interactions. 5. MEASUREMENT OF DEUTERIUM CHEMICAL SHIFTS It has so far been assumed that the chemical shift interaction is zero and experi- ments have been conducted with the resonance offset A =wo -w = 0. Consider now how lifting the latter restriction but retaining the former affects the echo response to a 90"-z-90",~ pulse sequence. A principal echo will be observed whenever Az=(n++)n n=0,1,2 ,...... (21) since the motion of the magnetization relative to the rotating coordinate system pro- duces an effective phase shift between the two pulses.It can be shown that E,,(t A) = Ex,(?,0) sin (at +At') sin AT (22) N. BODEN L. D. CLARK S. M. HANLON AND M. MORTIMER 121 which predicts for the echo maximum at z =22 as observed by diode detection Exx(22,A) = Ex,(2z 0) sin AT. (23) Exx(22,A) should therefore vary periodically with either T at fixed A or A at fixed T and will exhibit nodes at A.~=nn n=0,1,2 ,...... (24) Alternatively eqn (24) may be written which shows that measurement of the dependence of the nth node on v and z can lead to a value for vo with an accuracy determined by the inhomogeneity in the magnetic field. The above experiment offers a possible route to deuterium chemical shift measure- ments in materials where the spectrum is broadened by a distribution of quadrupole interactions.The echo response will reflect the chemical shift distribution according to Exx(22,A) =2 Ej(22,0) sin (cot +Ajz) sin Ajz (26) i where the sum is taken over all chemically shifted spinsj. The simplest situation per- tains for a powdered sample of chemically equivalent deuterium spins. Diode detec- tion and the use of eqn (25) yields the centre of gravity Q of the spectrum. This corresponds to the isotropic chemical shift oifor axially symmetric chemical shift spectra,28 as studied here. Fig. 9 shows the results of such an experiment for poly- 10 'rr v iil FIG.9.-Plot of {v -vo(l))/vo(l) against l/rvo(l) for polycrystalline ['HJbenzene at 212 K where v corresponds to the frequency of the first node (n = I) in the response to a 90"-r-9OoO~ sequence.The solid line represents the least square fits of the experimental results to eqn (25) slope = *0.499 *0.001 intercept = 5.2 *0.5 p.p.m. 2H N.M.R. SPIN-ECHO SPECTROSCOPY crystalline [%,]benzene. The intercept l/z = 0 gives a value for w+to an accuracy of &5 Hz determined by the inhomogeneity of our magnet. There is a liquid-to-solid chemical shift of -5.2 5 0.5 p.p.m. (the deuterium spin is less shielded in the solid) indicating a large intermolecular " ring-current " contribution. Table 2 summarizes TABLE 2.-LIQUID-TO-SOLID DEUTERIUM CHEMICAL SHIFTS compound temperature/K m)/P.P.m.t 212 -5.21 217 -1.1 153 +0.6 183 +2.9 t b(a1) O'(S) -a&) = -(vO(s)vo(l)vo(l)).$ Uncertainty in the value of &(a,) is 10.5 p.p.m. and is determined by the inhomogeneity of the magnetic field. corresponding measurements for other materials. In the equimolar mixture C6&/ C6F6the shift is much smaller implying a different crystal structure. For [2H6]-acetone the shift is zero within experimental uncertainty whilst for [2H,]acetonitrile there is a large up-field shift which must be associated with the anisotropy of the -C=N group. The spin echo experiment would seem to offer a simple method for the accurate measurement of deuterium chemical shifts in solids. The possibility of resolving chemical shifts for different deuterium spins and determining chemical shift tensors for powders is being investigated.6. CONCLUSION We have shown that deuterium frequency spectra for orientationally disordered molecular solids may be obtained by calculating the fourier transform of the 90"-z-90"9,0spin echo profile starting at t = 22 the time of the echo maximum. There is no significant distortion from dipolar interactions. This has previously been as- sumed in the application of this technique to liquid Care must be taken to ensure there is no excessive distortion of the echo signal through use of a limited sample circuit bandwidth. For the linewidths encountered in "rigid " organic solids a high frequency (>30 MHz) spectrometer is really essential ; the magneto- acoustic ringing of the probe which plagues low frequency pulse experiments is also eliminated.The possibility of examining the spectrum under non-equilibrium conditions is of particular interest. In materials containing complex molecules this can lead to resolution of the spectra and the selective measurement of the dipolar interactions for different groups of spins in the molecule. The spin echo experiment also provides a simple method for the accurate measure- ment of deuterium chemical shifts in disordered solids where the spectra are broadened by a distribution of quadrupole interactions. The quadrupole interaction and the much smaller dipolar one are refocused at the echo maximum enabling the chemical shift to be resolved. The above experiments should contribute to the realisation of the potential of deuterium n.m.r. spectroscopy for studying orientational and dynamic disorder in molecular solids.N. BODEN L. D. CLARK s. M. HANLON AND M. MORTIMER 123 The techniques as described herein are only applicable to the rigid lattice and motionally averaged regimes of the spectrum. The effects of spin motion on the echo response in the motional narrowing regime are being investigated. We thank the S.R.C. for financial support and for research studentships to L. D. C.and S. M. H. We also thank Dr. M. Gibb for assisting with the ['H,]benzene deuterium spin relaxation measurements. M. H. Cohen and F. Reif Solid State Phys. 1957 5 321. 'R. G. Barnes in Advances in N.Q.R.,ed. J. A. S. Smith (Heyden London 1974) vol. 1 chap. 26. J. Seelig Quart. Rev. Biophys. 1977 10 353. R. Hentschel J.Schlitter H. Sillescu and H. W. Spiess J. Chem. Phys. 1978 68 56. J. C. Rowell W. D. Phillips L. R. Melby and M. Panar J. Chem. Phys. 1965,43 3442. G. R. Luckhurst in Liquid Crystals and Plastic Crystals ed. G. W. Gray and P. A. Winsor (J. Wiley and Sons London 1974) vol. 2 chap. 7. P. J. Bos J. Pirs P. Ukleja J. W. Doane and M. E. Neubert Mol. Cryst. Liq. Cryst. 1977 40 59. M. Mehring in N.M.R. Basic Principles and Progress ed. P. Diehl E. Fluck and R. Kosfeld (Springer-Verlag New York 1976) vol. 11. H. W. Spiess in N.M.R. Basic Principles and Progress ed. P. Diehl E. Fluck and R. Kosfeld (Springer-Verlag New York 1978) in press. lo A. Pines D. J. Ruben S. Vega and M. Mehring Phys. Rev. Letters 1976,36 110. l1 W. G. Clark Rev.Sci. Instr. 1964 35 316. l2 P. A. Speight K. R. Jeffrey and J. A. Courtney J. Phys. E 1974,7 801. l3 G. E. Pake J. Chem. Phys. 1948 16 327. l4 I. Solomon Phys. Rev. 1958 110 61. l5 N. Boden S. M. Hanlon Y. K. Levine and M. Mortimer Chem. Phys. Letters 1978,57 151. l6 N. Boden S. M. Hanlon Y. K. Levine and M. Mortimer Mol. Phys. 1978,36 519. l7 N. Boden and Y.K. Levine J. Magnetic Resonance 1978 30 327. D. E. Barnaal and I. J. Lowe Rev. Sci. Instr. 1966 37 428. l9 E. R. Andrew and R. G. Eades Proc. Roy. SOC. A 1953,218,537. 2o J. E. Anderson J. Chem. Phys. 1965 43 3575. 21 U. Haeberlen and G. Maier 2.Naturforsch. 1967 22a 1236. 22 J. Wendt and F. Noack Z. Naturforsch. 1974,29a 1660. 23 F. Noack M. Weithase and J. von Schutz Z. Naturforsch. 1975,30a 1707.24 P. S. Allen J. Phys. C 1973 6 3174. 25 R. G. Barnes and J. W. Bloom J. Chem. Phys. 1972,57 3082. 26 R. Bersohn Mol. Phys. 1974 27 605. 27 M. Mehring R. G. Griffin and J. S. Waugh J. Chem. Phys. 1971,55 746. 28 U. Haeberlen in Advances in Magnetic Resonance ed. J. S. Waugh (Academic Press London 1976) supplement 1 chap. 3. 29 J. H. Davis K. R. Jeffrey M. Bloom M. I. Valic and T. P. Higgs Chenr. Phys. Letters 1976 42 390.

ISSN:0301-5696    

DOI:10.1039/FS9781300109

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Nuclear Quadrupole Resonance and Nuclear Magnetic Resonance Studies of K,PtCl Type Mixed Crystals BY COSTASDIMITROPOULOS J. VAN DER KLINK AND JACQUES Experimental Physics Laboratory Ecole Polytechnique Fedkale de Lausanne 33 Av. de Cour CH- 1007 Lausanne Switzerland AND J. PELZLAND M. REGELSBERGER Experimental Physics Institute VI Ruhr University Bochum W. Germany AND K. ROSSLER Inorganic Chemistry Institute K.F.A.-Julich W. Germany Received 19th January 1979 Phase transitions from cubic to lower symmetry phases in antifluorite (K,PtCI,) structures have been ascribed to lattice mode-softening. We study the effect of impurities on lattice vibrations and transition temperatures in such structures. For mixed rhenates we find a lowering of the frequency of the lattice vibrations with increasing impurity content and a corresponding increase in transition temperature.For mixed stannates the n.q.r. signal disappears at high temperature perhaps due to reorientational motion of the stannate anion. Many compounds of the K2PtC16 (R2MX6) type exhibit the cubic antifluorite structure at room temperature. Upon lowering the temperature some of them (but not e.g. K2PtCl itself) undergo one or several structural phase transitions to lower symmetry forms.' We will be concerned only with the high-temperature purely dis- placive transitions that destroy the cubic symmetry. These transitions can be described in terms of a reorientation of the MXg-octahedra combined with a distor-tion of the cubic R+-array. Theoretical descriptions2 of the lattice dynamics at the transition involve a de- crease in frequency (" softening ") of the optical phonon which describes the rotational oscillation of the rigid octahedra within the cation environment.The distortion of the lattice below the transition is then a consequence of the freezing-out of the eigen- vector of the same soft-mode phonon. In the low-temperature phases these phonons may be observed by Raman and infrared spectroscopy it has been shown by O'Leary and Wheeler2 that in the cubic phase the n.q.r. frequency of the halogens in the anion octahedra reflects the soft-mode behaviour. There exist other factors affecting the n.q.r. frequency however and we will attempt in the following a systematic decomposition of the experimental results into the various contributions.In suitably chosen systems such a decomposition may be facilitated by the study of mixed crystals. If one of the components is present in only low concentration it may be considered a random point defect in the matrix of c. DIMITROPOULOS et al. the other c~mponent.~ If the point defect distorts the lattice by its size the effect may be described by an elastic variation assuming an electric field gradient that varies linearly with the stress. If the point defect fits neatly in the host lattice its different mass may shift the frequency of the lattice vibrations and thus change the temperature dependence of the n.q.r. frequency. The results we have obtained4 on K2(ReC1,),-,(ReBr,) can be satisfactorily described by a combination of these effects.In those mixed crystals the phase transi- tion seems to be of the same type as in the pure hexa~hlororhenate,~ i.e. driven by softening of the zone-centre rotary-lattice mode frequency. The data on [K,-,(NH,),] SnCI indicate a phase transition in the pure potassium compound driven by softening of a rotary mode6 that has not been unambiguously assigned due to a lack of crystallographic data in the low-temperature phase. Our first data on the mixed crystal however indicate that a blocking of SnCli- octahedra nearest to the ammonium ions seems to influence the occurrence of the transition. Both in the pure and mixed crystals we observe that the n.q.r. signals disappear at ~350K; a tentative hypothesis connects this phenomenon to a possible anomaly in the NHZ proton relaxation in the pure ammonium compound.’ MECHANISMS THAT CONTRIBUTE TO THE N.Q.R.FREQUENCY The field gradients that determine the n.q.r. frequency arise partly from the (mainly) covalent bonds within the MXi-octahedron and partly from the ionic lattice of all other ions. Calculations show the former to be the more important.’ Far above the transition the resonance frequency usually decreases when the temperature is raised. Bayer’ has attributed this decrease to increasing amplitudes of torsional motions internal to the molecules effectively averaging the field gradient. Later author^^^'^ have refined this description and have pointed out that Bayer’s effect really was (av/W), whereas the usual experimental results give (2v/o’T),.The thermodynamical relation between these quantities has been derived by Kushida Benedek and Bloembergen’ as where C( is the thermal expansion coefficient and IC the compressibility of the crystal. In most cases (av/ 2P)Tis small and positive and the last term may be safely neglected. In some instances however of which K,ReCl is an example (av/JP),is large and negative.” This has been explained by Haas and MarramI2 using the Townes and Dailey theory13 to include the effect of the destruction of x-bonding with increasing temperature. In K,PtCI type crystals approaching the transition temperature from the high-temperature side one usually finds a drop in the observed frequency below the value extrapolated from high temperatures.This behaviour has been identified by O’Leary and Wheeler2 as representative of the occurrence of mode-softening. If the impurity atom has a mass different from the original one the resulting change in vibrational frequencies will change the slope (av/aT) of Bayer’s theory but the value extrapolated to zero temperature should remain unaltered. Addi-tionally in mixed-crystal systems the strain field resulting from the inclusion of point defects gives rise to a temperature-independent shift of the n.q.r. frequency that is also proportional to the increase in the lattice parameter Aa.3*4 N.Q.R. + N.M.R. OF KzPtCI6 TYPE MIXED CRYSTALS 35C1 N .Q .R . I N K2(ReC16),- ,.(ReBr,) The 35Cl n.q.r. frequencies measured in the cubic phase of these mixed crystals4 are shown again in fig.1. To separate the different contributions the data have been analysed as follows. f f + ** -i+ 13.8901 + ,.1 * it 5? + 0 st Of I N + it 57 t I + it 0 I 13.8801 n +F. \ t-+ 0 x c n 3 + sc '9 I sc 0 13.870 * In m 13.860 1 tL9 I Ill1 111 I1 I1 I I1 I1 I1 1 111 I11 I Ill I I/ /I ,I It II 1 1 150 200 250 200 temperature l/K FIG.1.-Ti n.q.r. frequency in the cubic phase of K,(ReC16),-,(ReBr6)x mixed crystals as a func-x tion of temperature for different impurity fractions x * x = 0.000; 0,= 0.023; +t x = 0.076; + x = 0.279. The region above room temperature has been extrapolated down to zero temperature.Differences in the extrapolated values for different x have been attributed to the temperature-independent effect of the strain field. Three samples with x = 0.019 x = 0.023 and x = 0.076 yielded an average value of 90x kHz for this shift. The calculated value4 is 120x kHz and in view of the uncertainty in the values of the parameters entering this calculation we consider the agreement satisfactory. The fourth sample with x = 0.279 gave approximately 45x kHz for this shift. We suppose that at this concentration the linear elasticity theory is no longer valid. Next a correction was applied' to obtain (dv/W) according to eqn (1). Finally c. DIMITROPOULOSet al. in fig (2) we show the normalized n.q.r. frequency,f obtained from ~(x,T)in fig.1 as where (3) 1-20 1-0 = 2.16 - 1 a". Aa (4) The meaning of the symbols is the same as bef~re,~ and vo = 13.868 MHz is the extrapolated frequency at zero temperature and zero impurity c~ncentration.~ For x = 0.279 we halved the value of [ in view of the extrapolation discussed above. --_ ---_ 0.998 -**-***@@ -_-_ -__-..---_ 0.gg6t /a/ ;:;;; --_ 0.996 *@ a-* lel -_;-*-a-.-. 150 200 250 300 temperature 7/K FIG.2.-Normalized 35CIn.q.r. frequency f in mixed rhenates. The data from fig. 1 have been corrected for specific volume effects and impurity strain field effects according to eqn (2). The value Jr = 1 in (a)corresponds to 13.868 MHz. The slope of the dashed line changes with x showing that the average lattice vibration frequencies diminish with increasing substitution.The levelling-off of f towards the transition temperature indicates mode-softening. (a) x = 0 (6)x = 0.0190 (c) x = 0.0234 (d) x = 0.0760 (e) x = 0.2790. N.Q.R. + N.M.R. OF K,PtCI TYPE MIXED CRYSTALS The dashed lines in fig. 2 represent the fit to the highest-temperature points and indi- cate the Bayer behaviour. The systematic change in the slope (from 165 Hz K-' for x = 0 to 177 Hz K-l for x = 0.076) reflects the lowering in the frequency of the lattice vibrations due to the difference in mass between the impurity and the original ion. A similar decrease in frequency has been observed for the internal vibrations of (ReC1,)'-in the cubic phase.4 At a given temperature far above the transition we expect therefore that the fre- quency of the rotary lattice mode responsible for the transition will also be lower in the mixed crystal than in the pure compound.It seems probable then that the rotary lattice mode frequency as the temperature decreases will approach zero at a higher temperature when the impurity fraction x is increased so that the transition will occur at a higher temperature. This corresponds to what is actually observed the transition temperature increases z 7 K when changing x from 0.0 to 0.076 and the experimental frequencies near the transition show the deviation characteristic2 for a soft-mode process. 35Cl N .Q. R . IN [(NH4)xK1-x]2 SnCI Experiments on these systems are still in progress so some of our conclusions will be incomplete and tentative.Fig. 3 shows the observed n.q.r. frequencies in mixed 15.30C 15.250 2 T x 15.200 0-2 Y-Li z G 15.150 In m b 15.100 260 280 300 320 340 temperature TIK FIG.3.-35Cl n.q.r. frequency in [(NH4)0.01K0.99]2 SnCI as a function of temperature. Above 260 K the crystal structure is cubic but additional lines are found around 15.14 MHz. These are supposed to arise from NH4+-nearest neighbours. All signals disappear around 350 K. c. DIMITROPOULOS et al. crystals of lowest impurity concentration above and just below the high-temperature transition. The behaviour is similar to that of the pure omp pound'^*'^ except that additional lines occur in the cubic phase of the mixed crystal.We attribute these to those chlorine atoms that are nearest-neighbours to the (NH,)+. In contrast to the case of the rhenates the lattice distortion upon substitution is extremely small in the stannates l6 so that the signals of nearest-neighbours are not necessarily wiped out but only shifted towards higher frequency. Our observation that the intensity of these additional lines relative to the normal low-frequency line increases with increasing (NH,)+ concentration lends further support to this assumption. The well-resolved doublet observed immediztely above the transition might correspond to two possible orientations of the NH4+. In the pure ammonium compound one orientation" is energetically favoured; but perhaps the slightly different geometry in the mixed crystal diminishes this energy difference to a sufficient extent.At higher temperatures the splitting disappears and a single broad line is observed. This then might indicate rapid changes from one orientation to the other. We expect the corrections that had to be applied to the observed frequencies in the rhenates in order to bring out the Bayer-type of behaviour to be less important in the stannates since here at least the observed (av/aT),is of normal sign. No measure-ments of (av/aP) are available however to corroborate this supposition. The shift due to the strain field can probably be neglected since Aa/a is an order of magnitude smaller16 than in the rhenates. Any data reduction is made virtually impossible however by the fact that the n.q.r.signals both in the pure potassium compound and in the mixed crystal disappear at z 350 K. The highest temperature attained in previous investigation^'^ of 35Cln.q.r. in KzSnC16was 320 K and this signal loss has not been observed. As is clear from the reduced plots in fig. 2 a temperature range of a few times T is necessary for a reliable extrapolation to byo. Thus although the temperature-dependence of the low-frequency line in the cubic phase is consistent with soft-mode behaviour as observed from Raman spectra6 and 35Cl n.q.r. relaxation timesI5 in KzSnC16 no cIear presentation as in the case of the rhenates (cf. fig. 2) is possible. The effect of substitution on the transition temperature shown in fig. 4 however seems too important to be explained by a change in phonon frequencies alone.The points show transition temperatures as measured by n.q.r.; the line has been derived from d.s.c. (differential scanning calorimetry) measurements.16 The latter results have been interpreted as an indication that the regions near the (NH,)+ ion do not undergo a structural transformation consistent with our interpretation of the additional doublet in the mixed crystals. An empirical rule has been established by BrownI8 relating the occurrence of a structural phase transition to the relative sizes of cations and anions. If this ratio is unfavourable the anion reorientation that accompanies the transition cannot take place and the compound remains undistorted. Since the pure (NH4)2 SnCI does not show a tran~ition,'~ we suppose that the ammonium ion in the K&C& matrix blocks the rotation of the SnC162- octahedra.Since the structural transformation involves a small rotation of the octahedra the mean transition temperature is depressed by the restoring torque exerted by the ammoniuni ions. PROTON N.M.R. IN [(NH,) K1J2 SnCI The proton spin-lattice relaxation times T1in (NH4)2 SnBr,' and (NH4)Z PtBr6l9 have been shown to exhibit discontinuities at the temperature where the phase transi- tion occurs. The results of our investigation of Tl in a mixed crystal are shown in N.Q.R. + N.M.R. OF KZPtCI TYPE MIXED CRYSTALS FIG.4.-Phase transition temperature from cubic to lower symmetry T in mixed stannates [(NH,) K1-J2 SnC16 as a function of impurity fraction x.The points have been determined by n.q.r.; the line represents results obtained by differential scanning calorimetry. The fairly large slope of -516 K suggests geometric hindering of the anion reorientation by the ammonium ion as the main cause for the change of T with x. 102 --8---5- -3-m / / 1 -/ h" 2-/ / ,/. *. .-E 10' -A . --.s 8 -a 4' 0- -/. L L a 5 ;d4 -C 0 w 2 3-Q 2-I I I I I 5 4 3 2 FIG.5.-Ammonium proton spin-lattice relaxation time in [(NH4)0.01 SnCI as a function of temperature at a Larmor frequency of 92 MHz. The phase transition occurs around lo3 T-' = 3.9 K-'. The onset around T = 300 K of a new relaxation mechanism tentatively ascribed to anion reorientation may mask the change in slope expected at the phase transition.The slope of the dashed line corresponds to an activation energy of 590 K as determined by quasielastic neutron scattering in the pure ammonium compound. c. DIMITROPOULOS et al. fig. 5. The phase transition occurs around lo3 T-' = 3.9 K-'. The slope of the dashed line indicates the activation energy E = 590 K for rotational motion of the (NH,) + ion in (NH4)2SnC16 derived from quasielastic neutron ~cattering.'~A significant deviation from this slope implying a maximum in T, occurs at tempera- tures higher than the transition temperature. We tentatively correlate this to the Tl and Tlpbehaviour in (NH4)2SnCl found by Strange and Teren~i.~ They observe a maximum in Tlpand suggest that it might be due to (SnCl,)2- reorientation analogous to an effect they find in (NH,),SiF,.In the same temperature region a change of 15.070 1 temperature TlK FIG.6.-The frequency of the 35CI n.q.r. low-frequency line in the cubic phase for the pure potassium stannate (filled circles) and for [(NH4)0.035 SnC& (open circles). The change of slope with x at high temperatures (and final disappearance of the signal) are considered anomalous and may be related to the proton relaxation results of fig. 5. (av/aT') for the 35Cln.q.r. frequency has been 0b~erved.l~ Their Tl data suggest a maximum at higher temperature as well although they do not comment on this. Such an onset of (SnC16)2- reorientation might be also the cause of the rapid decrease in the 35Cln.q.r.frequency for [(NH,) K1-,l2 SnCI and the final disappearance of the n.q.r. signal around 350 K shown in fig. 6. This question will need further experi- mental and theoretical work to be settled however. R. L. Armstrong and H. M. van Driel Ado. Nuclear Quadrupole Resonance 1975 2 179. G. P. O'Leary and R. G. Wheeler Phys. Rev. B 1970,1,4409. J. Pelzl H. Vargas D. Dautreppe and H. Schulz J. Phys. Chem. Solids 1975,36 791. C. Dimitropoulos J. Pelzl H. Lerchner M. Regelsberger K. Rossler and A. Weiss J. Mag-netic Resonance 1978 30 415. N.Q.R. + N.M.R. OF K,PtCI TYPE MIXED CRYSTALS H. M. van Driel R. L. Armstrong and M. M. McEnnan Phys. Rev. B 1975,12,488. J. Pelzl P. Engels and R. Florian Phys. Stat.Sol. b 1977 82 145. J. H. Strange and M. Terenzi J. Phys. Chem. Solids 1972 33 923. H. Bayer 2.Phys. 1951 130 227. T. Kushida G. B. Benedek and N. Bloembergen Phys. Rev. 1956 104 1364. 'O.H. S. Gutowsky and G. A. Williams Phys. Rev. 1957 105 464. l1 R. L. Armstrong G. L. Baker and H. M. van Driel Phys. Rev. B 1971 3 3072. l2 T. E. Haas and E. P. Marram J. Chem. Phys. 1965 43 3985. l3 C. H. Townes and B. P. Dailey J. Chem. Phys. 1949 17 782. Ip A. Sasane D. Nakamura and M. Kubo J. Magnetic Resonance 1970 3 76. l5 K. R. Jeffrey J. Magnetic Resonance 1972 7 184. l6 M. Regelsberger and J. Pelzl Solid State Comm. 1979 28 in press. l7 M. Prager W. Press B. Alefield and A. Huller J. Chem. Phys. 1977 67 5126. l8I. D. Brown Canad. J. Chem. 1964 42 2758. l9 R. L. Armstrong H. M. van Driel and A. R. Sharp Canad. J. Phys. 1974 52 369.

ISSN:0301-5696    

DOI:10.1039/FS9781300124

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Some Nuclear Resonance Properties of Nearly Free Methyl Rotors in the Solid State BY PETERS. ALLEN Department of Physics University of Nottingham Nottingham NG7 2RD Received 31st July 1978 This paper is primarily concerned to show how nuclear resonance can be used to investigate the rotational energy states and transition rates of weakly hindered symmetric rotors in the solid state while at the same time developing an explanation for the nuclear resonance data from the methyl protons in CHJLiCOO * 2D20. The discourse introduces the ideas involved in the context of a simple threefold free rotor before extending them first to a weakly hindered rotor and then to a pair of coaxial rotors. The kernel is that by exploiting the angular variation of temperature and frequency dependent studies experimental data of sufficient precision are available to enable meaningful molecular information to be obtained.Though space restricts this presentation to a limited explanation of the spectrum quantitative derivations from transient signals and relaxation data will be presented for discussion. 1. OUTLINE OF THE FREE METHYL ROTOR A free two dimensional rigid rotor whose orientation relative to some arbitrary datum can be described in terms of a single angular coordinate x,has energy states which are readily derived from a simple wave equation. In fact the energy eigen- functionsU (x)are given by U&) = (2n)-+exp (imx) (1.1) and the eigenvalues Emby h2 m2 Em = -21 where rn = 0 &I &2 . . . is the rotational quantum number h is Planck’s constant divided by 271 and I is the moment of inertia about the rotor axis.Substituting into eqn (1.2) the moment of inertia of a methyl group and converting to temperature units gives Em 2 7.5m2K. In this free rotor limit the energy eigenvalues are not affected by the detailed symmetry of the rotor but only by its moment of inertia. However if we are to proceed into a more detailed discussion involving hindering potential barriers nuclear spin func- tions nuclear dipole-dipole interactions and transition rates it is expedient to classify these free rotor states under a symmetry group to which the rotor corresponds. Now the group of permutations to which the feasible transformations of a methyl triangle do correspond is isomorphous with the rotational symmetry group C3and it follows that the free rotor representation can be reduced under that rotation group.To be precise the angle x only enters the rotational energy eigenfunctions by way of the factor exp(imX). Thus the specific transformation C [-e(1 23) for a triangle labelled clockwise looking along the positive rotation axis] has the effect of multiplying the METHYL ROTORS IN THE SOLID STATE energy eigenfunctions by exp(-iim2~/3). We can see therefore that the three pos- sible effects on the eigenfunctions of the transformation C3 will be to transform an eigenfunction into itself into E times itself or into E* times itself where E = exp(i2~/3). These three possibilities are identical to the behaviour of the three irreducible repre- sentations (respectively A E and E as shown in the character table of table 1) of the free hindered free hindered 0 0.5 1.0 1.5 0 0.5 1.0 1.5 V3/ kJ mol-' Vs/ kJ mol-' FIG.1.-Classification of the free methyl rotor energy states under the symmetry groups C3and C,.Also shown is how these states are perturbed in both cases by the growth of a hindering potential barrier. V3 is the amplitude of a three-fold sinusoidal barrier whereas VSrepresents the amplitude of a six-fold sinusoid. symmetry group C3,under the specific transformation C,. Thus each of free rotor functions transforms as one or other of the irreducible representations of the C symmetry group. The classification of the lower free rotor states under the group C is indicated in fig.1 together with their classification under the Cbsymmetry group to which reference will be made later. Turning to the nuclear spins the most simple methyl group spin representation R,,is the set of eight functions Iaaa) [cap> l&> Ipacc) IpPa) Ipap) I&?> and IPpD) where ct represents a proton spin parallel to the applied field B and p an anti- parallel proton spin. Under the symmetry group C3,R,has the characters given in table 1 which may be decomposed to show that R,= 4A + 2E + 2E,. TABLEI .-CHARACTERS UNDER SYMMETRY GROUP C, OF THE IRREDUCIBLE REPRESENTA-TIONS A EaAND Eb AND OF THE SPIN REPRESENTATION R, OF THREE SPINS 1 1*. c3 E c3 c5 A 1 1 1 Ea 1 &* & E = exp (i2ni3) Eb 1 E &* R 8 2 2 P.S. ALLEN In other words an alternative but symmetrically more acceptable spin representation would consist of four linear combinations of the original functions which transform as the A irreducible representation and two pairs each of which has either € or Eb symmetry respectively. The form of these linear combinations may be obtained by applying the theorem stated by Tinkham’ and the resulting methyl spin functions VR,mIare given in table 2. TABLE 2.-METHYL GROUP NUCLEAR SPIN FUNCTIONS FOR POSITIVE ml (WHERE mi IS THE METHYL SPIN COMPONENTS PARALLEL TO &). THE NEGATIVE 1711 COMPONENTS ARE OBTAINED BY REPLACING c1 BY etc. The coupling of these spin functions to the previously described rotor functions is by no means arbitrary; it is the result of this coupling which forms the basis for the interesting nuclear resonance behaviour of methyl groups and which in turn enables nuclear resonance to probe their rotational states.Because each symmetry element of the group C3is equivalent to an even number of interchanges of a pair of identical particles Pauli’s exclusion principle demands that the overall wavefunction must be totally symmetric to the operation of any symmetry element. The overall wave-function must therefore transform according to the A symmetry species. As a result the acceptable rotor-spin product wavefunctions are restricted by the C3multiplication table to the three types A x A € x & and Eb x €,. Before sketching the nuclear spin energy states of a free methyl rotor it is neces- sary to take account of the nuclear dipole-dipole interaction which operates on both the methyl spin and rotor functions.Each of the six standard parts (A to F) of the dipolar hamiltonian XD,can be rewritten in terms of the orientation x and of the angle ly between B and the methyl C axis. Moreoever the terms can be subse- quently collected together in a symmetry adapted fashion (see for example Haupt)2 to formcomponents for each of the six parts which are either A x A € x Eb or Eb x E space x spin operator products. The dipolar energy shifts depending on the first two parts of XD(A and B) are straightforward in the limit when the dipolar energy is very much less than the separation of the A and € rotor states. They are zero for the E states and d for the A states where y’h’ -.r3 (3 cos2 ly -&t,l .A>. (1.3) In eqn (1.3)’ 1’ is the proton gyromagnetic ratio Y is the intramethyl proton separation and the Kronecker delta is zero unless the subscripts are identical in which case it is unity. As a result the nuclear spin states of the lower rotational levels of a free methyl rotor are as illustrated in fig. 2. 2. WEAKLY HINDERED METHYL ROTORS In real systems in their solid states either the crystalline or the intramolecular environment of the methyl group invariably introduces a hindering potential which in turn modifies the energy states of the methyl rotor. The nature of these modifica- tions depends both upon the symmetry of the hindering potential and upon its magni- METHYL ROTORS IN THE SOLID STATE m m I FIG.2.-Effects on the methyl nuclear energy states of the application of the rotational the Zeeman and the dipolar haniiltonians (XR, Z and XD)shown schematically.E is Zeeman energy split- ting and dis the dipolar shift of eqn ( 1.3). Also illustrated is the r.f. absorption spectrum to which these energy states would give rise. The contribution of each r.f. transition is indicated by the side of the corresponding component. tude. For example changes in symmetry modify the number and classification of states which comprise a complete basis set. This is illustrated in fig. 1 where the free rotor states are classified under the symmetry group C6,which is isomorphous with the permutation group of a triangle in a six-fold potential as well as under C3.Increases in the magnitude on the other hand modify the energy eigenvalues bringing together all those states which comprise a complete set while at the same time separat- ing one set from another. This is also illustrated in fig. 1 where the effect of increas- ing a six-fold potential is shown to be different from that of increasing a three-fold barrier. This difference which effectively changes the number of lower energy states has a significant effect on the nuclear resonance properties. To digress for a moment we can see from fig. 1 that if the magnitude of the barrier is increased indefinitely then (in the case of C3 symmetry for example) the first pair of degenerate E states converges on the ground A state and their small separation is then referred to as a tunnelling splitting.Together they will form the torsional ground state of a highly hindered methyl group. Returning to the weakly hindered methyl groups we are now in a position to appreciate how their nuclear resonance properties in addition to being governed by the ordinary nuclear transition processes are compounded by restrictions due to the symmetry species of the various nuclear energy states. For example the phonon reservoir by itself is unable to maintain thermal equilibrium between all the weakly hindered rotor levels because alone it cannot promote symmetry conversion transi- tions. As a result the situation following a sudden temperature change is expected to be the rapid re-establishment of internal equilibrium within each symmetry species but a departure of the absolute populations from their overall thermal equilibrium values because of the inequality of the partition functions of the symmetry species sub-systems.On the basis of this expectation if Z,(L) and Z,(L) represent the partition functions of the A and E sub-systems respectively at a lattice temperatureL and p(L) = Z,(L)/Z,(L) then the post-jump deviation Ansl,from thermal equilibrium population n,, for the state i of symmetry s is given by = n.4 -P(LJl/[l + P(U1) (2.1) and At? = AnE,, }?El {[p(L.2) -P(L1)1/dL2)[1 + dLI)11* (2.2 P. S. ALLEN 137 Thus the A and the E deviations will be opposite in sign of a relative magnitude which depends on the ratio of their partition functions and will increase as the magnitude of the temperature jump increases.In consequence such observables as the spectrum which depends on the populations through the intensities of its components and the spin-lattice relaxation rates which are dominated by the symmetry conversion transi- tions and are therefore driven by the A to E population difference both vary with time during the approach to overall thermal equilibrium. Moreover when such equili- brium is established they continue to depend on these population differences and therefore provide a means by way of the Boltzmann factor to evaluate the rotor energies. The approach to equilibrium of the Zeeman spin-lattice relaxation of methyl protons in lithium acetate is illustrated in fig.3 from which it is clear that I1 II d .. a a 4 a I1 II .a II time Ih FIG.3.-Experimental data on the efficiency of the spin-lattice relaxation process for the methyl protons in lithium acetate following a sudden temperature change from 77 to 4.2 K when ty = 0. TIrepresents a “ global ” spin-lattice relaxation time which turns a blind eye to minor deviations from a perfect exponential recovery of the magnetization. Vertical dotted lines represent alternately either a lowering or raising of the temperature between 77 and 4.2K. The zero of time is defined as the time when the cryostat equilibrated at 4.2 K following the first temperature change. the relaxation efficiency increases markedly immediately following the temperature jump before slowly falling back to its equilibrium value at 4.2 K as the A to E popu-lation imbalance is destroyed.An interesting transient phenomenon which occurs for weakly hindered symmetric groups and which owes its very existence to this population imbalance between symmetry species is the dipolar polarization generated by a sudden temperature jump. This phenomenon was first observed by Haupt3 in 7-picolene and is illustrated for lithium acetate in fig. 4. This dipolar signal whose intensity can be lo4 times greater than its equilibrium value appears (following a short r.f. pulse) in quadrature with the Zeeman signal. It reflects an asymmetry about the central Larmor frequency uL,in the frequency distribution of the rotating frame magnetization.For a collec- tion of isolated but aligned methyl groups whose spectrum would be simply the stick pattern generated from fig. 2 this quadrature signal could only arise from an asym- metry of the intensities of the r.f. transitions within the A symmetry species since only they produce satellites away from uL. The E states in such a system can only generate magnetization precessing at uLitself. The growth and decay of the intensity of the quadrature signal could then reflect a transient departure of the A species from a unique spin temperature in accompaniment with the equilibration of relative popula- tions of the symmetry species. The identification of which relaxational transitions are dominant in the generation and decay of the dipolar polarization and in the transient and equilibrium spin-lattice relaxation process is important to the understanding of symmetric molecular groups.METHYL ROTORS IN THE SOLID STATE In the past isotropic sums over all possible transitions have been used to compare with experimental data from polycrystalline samples. The different angular depend- ence of these transitions has not been exploited. However issues such as inter- versus intramethyl transitions the relative roles of E type perturbations (caus- ing A to E transitions) and A type perturbations (causing symmetry retention transitions) and competition between A,,, = 1 and A,,, = 2 transitions are all amen- able to angular investigation. For example under the C3 symmetry classifications .-Y c 3 x a .--I I 1-1 I 1 1 1 I 1 I 0 200 LOO 600 800 time Is FIG.4.-Time evolution of the intensity of the dipolar polarization signal from the methyl protons in lithium acetate following a temperature change from 4.2 to 10 K when ty = 0.The zero of time is defined by the equilibration of the cryostat at 10 K 20 s after initiation of the temperature jump. when t,v = 0 all AmI = 1 intramethyl transition rates go to zero but an intramethyl perturbation of E symmetry causing A,,, = 2 transitions remains. The reason for the neglect of angular studies has been the complete absence of single crystal samples. Lithium acetate has removed this restriction and provided the first example of a weakly hindered methyl rotor in single crystal form. In the following section we shall out- line the exploitation of angular effects in lithium acetate and because of limitations of space we shall concentrate on the resonance spectrum.3. METHYL ROTORS IN LITHIUM ACETATE In the solid state of the deuterated analogue of lithium acetate dihydrate (CH,COOLi 2D,O) the methyl groups are essentially arranged in coaxial pairs with a methyl plane separation of 0.25 nm.4 The next nearest magnetic nuclei ('Li) are at a distance of 0.41 nm from the methyl centres and for the purposes of this discussion we shall neglect their presence in comparison with the mutual effects of all the methyl protons. The proton-proton dipolar interaction can be sub-divided into the intra- methyl and the intermethyl parts; the fact that the inter part is significant when com- pared to its intra counterpart makes it expedient to treat the whole of the proton- proton interaction in terms of a single symmetry group.If the two methyl triangles are labelled clockwise looking along their respective positive C3 axes with group I comprising protons 1 2 and 3 and group I1 containing protons 4 5 and 6 then their feasible transformations can be represented by the nine permutation elements formed from (123) (132) (456) (465) and their products. These nine elements form a group which is isomorphous with the direct-product P. S. ALLEN 139 group 'C x "C,. Since all of these nine elements are conjugate there will be nine one-dimensional irreducible representations which we shall label rl to T9,where rl is the totally symmetric representation and the remaining identities are given in table 3.If the rotor functions are simply taken to be the products of the two individual free TABLE 3.-IDENTIFICATION OF THE IRREDUCIBLE REPRESENTATIONS OF THE DIRECT PRODUCT GROUP 'c,X "c3WITH THE ROTATIONAL AND SPIN STATES OF A PAIR OF FREE COAXIAL METHYL ROTORS. ~~~ energy/K rotor states spin states rotor functions the energy states for the methyl pair together with their symmetry classifications will also be as illustrated in table 3. The spin representation R,,for the six spins Z = + is of order 64 but can be reduced under the direct-product group according to R,= i6r1+ ~(r, + r3+ r4+ r,)+ 4(r + r7+ rS+ r9). The sixteen-fold degeneracy of the rlspin state is made up from a septet a quintet a triplet and a singlet.The eight-fold r2to Tsspin states each comprise a quintet and a triplet whereas a triplet and a singlet constitute the four-fold r6to T9 spin states. The coupling of these spin functions to the free rotor states are as shown in table 3. The nuclear resonance properties of this six spin symmetry conscious system are undoubtedly time consuming to describe and so we shall focus attention only on the spectrum and the truncated part of XD. The intramethyl components of XD(one from each group) each have a rlsymmetry spin operator whose angular dependence is (3 cos2 ry -1). In addition r2to T5spin operator terms exist for the intra interac- tion which depend on sin2 ry. The intermethyl interaction on the other hand con- tains spin operator terms of all symmetry species.Those which transform as rl follow (3 cos2 ry -l) the same angular dependence holds for T6and T9terms where- as terms of all other symmetry species are proportional to sin ry. The multiplication table of the direct product group will establish which terms in XDmight have finite matrix elements between the various spin states. However it is clear that all diagonal elements if they are finite will vary as (3 cos2 ry -1). The predominance of these elements is apparent from the magic-angle spectrum of fig. 5(a) (ie. ry = 54"44') which has a second moment of (1.8 & 0.2)G' at 4.2 K no discernible structure and which broadens only very slightly with increasing temperature as it picks up small amounts of intermethyl dipolar shifted intensity as the E x E rotor states increase in population.Changing to a parallel orientation of the C3axes relative to B will re- METHYL ROTORS IN THE SOLID STATE move all the finite off-diagonal elements depending on sin ty and at the same time maximise the dipolar shifts of the diagonal elements. Unfortunately the angular dependence of both the inter and intra diagonal interactions is the same and it is necessary to evaluate the matrix elements to see their effects. The intra dipolar interaction by itself produces a spectrum identical to that generated by a collection of isolated groups whose energy states are illustrated in fig. 2. It is the inter interaction which gives the ty = 0 spectrum its characteristic 0 20 400 20 40 60 0 20 40 60 kHz k Hz kHz Fig.5.-Equilibrium spectra (normalized to the same peak height) of the methyl protons in lithium acetate. The conditions relating to each spectrum are (a) tp = 54" 44' and T = 4.2 K (b) ty = 0 and T = 4.2 K and (c) v/ = 0 and T = 77 K. shape [see fig. 5(b) and (c)]. For the ground state alone the inter interaction lifts all but one of the sixteen-fold spin degeneracies produces twelve symmetrically shifted pairs of transitions and most importantly leaves no ground state transition at the Zeeman energy. The central intensity shown in the experimental data of fig. 5(b) arises from unshifted components from the higher E x E rotor states and from overlap due to extra-methyl broadening.Fig. 5(c) shows how the ty = 0 spectrum changes in going to 77 K. The relative increase in peak heights is due to the increased contribu- tions from the next higher rlrotational states which require temperature increases of this magnitude to populate them appreciably. If as is likely the barrier to rotation is not zero then the states of table 3 will converge with increasing barrier height in a manner analogous to that portrayed in fig. 1. If moreoever the hindering barrier is six-fold the problem must be re- analysed in terms of a larger direct-product group. Thus a detailed analysis of the spectral components of each rotational state enables the temperature dependence of the angular variations in the spectrum to be employed to obtain an estimate of the rotor energies and through them the symmetry and magnitude of the hindering potential.In addition to explaining the equilibrium spectrum this analysis is also needed to account for the shape of the transient dipolar signal depending as it does on the non-equilibrium-population-differencedriving force for transitions between spin states. The growth and decay of the intensity of that signal meanwhile will require the analysis of the matrix elements of the non-secular parts of X,,. The foregoing is intended to provide a meaningful framework within which more extensive examples relating the behaviour of the spectrum the dipolar polarization signal and the relaxation data to the evaluation of methyl rotor states and transition rates can be presented for discussion at the meeting.P. S. ALLEN 141 I am grateful to both Peter Branson and Michael McCall for their painstaking collection of the experimental data presented here and to the S.R.C. for equipment grants which furnished much of the apparatus. M. Tinkham Group Theory and Quantum Mechanics (McGraw Hill New York 1964) pp. 39-43. J. Haupt Z. Naturforsch. 1971 26A 1578. J. Haupt Phys. Letters 1972 38A 389. J. L. Galigne M. Mouret and J. Falgueirettes Acta Cryst. 1970 B26 368.

ISSN:0301-5696    

DOI:10.1039/FS9781300133

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Proton Magnetic Relaxation Study of Molecular Motion in Anilinium Chloride Bromide Iodide and Sulphate BY CHRISTOPHER AND BASILA. DUNELL 1. RATCLIFFE~ Chemistry Department University of British Columbia Vancouver British Columbia V6T 1 W5,Canada Received 8th August 1978 Spin-lattice relaxation times of anilinium chloride bromide iodide and sulphate have been measured at 31 MHz by pulsed n.m.r. spectrometry over appropriate temperature ranges between 80 and 550 K. Each halide salt has a minimum in T of 38 ms which has been ascribed to reorientation of the -NHJ+ group about its C3axis. Activation energies for this motion are 37.1 11.2 and 8.5 kJ mol-' for the chloride bromide and iodide respectively. The iodide has a second minimum of 178 ms at much higher temperature (513 K) and this has been ascribed to reorientation of the phenyl ring among more than two (probably four) potential wells about the C-N axis.Although this minimum is not reached by the bromide before decomposition and melting occur a similar mechanism is likely and one may estimate an activation energy for this motion as 96 kJ mol-' compared with 75 kJ mol-' for the iodide. Irregular features of the variation of TI between about 200 and 300 K in the bromide and iodide can be interpreted in terms of a higher order phase change. The sulphate shows three minima in T,. The two at lower temperature are nearly equal at about 81 ms and have been attributed to relaxation by C3 reorientation of -NH$ groups in two different crystallographic sites with activation energies of 11.2 and 27.4 kJ mol-l.The third minimum at higher temperature has been assigned to a pseudo-C. reorientation of the phenyl group with an activa- tion energy of 59 kJ mol-'. The activation energy of the -NH; reorientation has been found to be proportional to the tem- perature of the corresponding minimum in T, the constant of proportionality being related to 7 for the motion. The activation energies of the -NH; motion are compared with results for other com- pounds and their variation in magnitude discussed in terms of hydrogen bonding strength and the symmetry of the environment of the group. In the salts of aniline one would expect the internal barrier to the rotation of the C3symmetric -NH$ group against the C symmetric phenyl group to be principally 6-fold and by analogy with toluene small.The barrier in gaseous toluene has been determined' to be 0.059 kJ mol-' or almost freely rotating.2 In solid 4-methyl pyridine the hindering potential for the methyl group has been found to be 1 kJ mol-I from inelastic neutron scattering measurements3 and in solid 4-methyl-2,6-ditertiary-butyl phenol the 4-methyl group has an activation energy for rotation of 1.008 kJ mol-' as determined by n.m.r.4 Since the solid phase measurements give a combin- ation of internal and external hindrances the internal barrier must be even smaller than the above. In the anilinium salts then one has the possibility of effectively isolating and measuring the external hindrance (predominantly hydrogen bonding) to the rotation of the -NH,f group.Here we present a proton magnetic resonance study of the spin-lattice relaxation times of the solid chloride bromide iodide and sulphate salts of aniline over a wide temperature range from which results the rotational motions have been identified and their activation energies obtained. Known differences between the symmetry of the halide ions about -NH in the chloride5 as compared with the bromide6 will be important in interpreting the signifi- cance of the activation energies obtained. t Present address Physics Department King's College Strand London. C. 1. RATCLJFFE AND B. A. DUNELL EXPERIMENTAL Reagent grade chloride (B.D.H.) and sulphate (Baker) were available commercially. The bromide and iodide were prepared from aniline (Mallinckrodt A.R.) and the appro- priate acid.The samples were recrystallised from ethanol and checked by melting points and their infrared spectra (Perkin-Elmer 225 grating spectrophotometer). Samples for the n.m.r. experiment were sealed in glass tubes under argon after degassing. Proton spin-lattice relaxation times were measured at 31 MHz using a n-t-n/2 pulse sequence on a Bruker B-KR 322s spectrometer as described previ~usly.',~ Values of T1of 5 s and longer were measured using a saturation sequence of several closely spaced n/2 pulses followed a time t later by a ni2 measuring pulse. The relaxation was exponential within experimental error except for the regions in the bromide and iodide results where the phase change was occurring and also to a smaller degree where Tl was longer than z 10 s.The phenomenon was more acute in the iodide than the bromide. A measure of " TI" in these cases was obtained from the initial parts of the decay. RESULTS AND ANALYSIS ASSIGNMENT OF MOTIONS TO MINIMA Fig. 1 and 2 show log Tl plotted against T-'. The assignment of a molecular motion to each of the several minima is based mainly on a comparison of the experi- mental minimum in Tl with theoretical values of minima in Tl calculated for various 100 50 10 5 0.1 0,o 5 1 I 1 I I I I I I I I I 1 3 5 7 9 11 1000KIT FIG.1.-Spin-lattice relaxation time (TI)as a function of reciprocal temperature for anilinium chloride 0, bromide 0 and iodide V at 31 mHz. The solid lines represent calculated values based on parameters given in table 2.The dashed lines are extrapolations to emphasise the deviations caused by the phase changes in the bromide and iodide. kinds of molecular motion from BPP theory' extended and applied by other~.'O-'~ We shall consider mainly reorientation of the -NH 3 group about its C axis [C,(NH,) motion] reorientation of the phenyl group in both 180"and 90"jumps about the C2axis of the ring and isotropic tumbling of the whole ion. For calcuIation of internuclear distances the following molecular geometry has been assumed r(N-H) = 1.045A,' r(C-C) = 1.393 A,5-6*14 r(C-N) = 1.47 A,6*14 r(C-H) = 1.08 all ring angles MOLECULAR MOTION IN ANILINIUM SALTS 120° all bond angles at N tetrahedral.This gives the H - H distance in -NH$ as rN = 1.706 A; the inter-proton distances in the ring as ~2.3= 2.473 A r2.4 = 4.283 A and r2.5 = 4.946 A where the subscripts are ring positions; and the distances from the ring protons to the centre of the " condensed "12 protons of the -NH$ group when < 1 for its rotation are r2*= 2.913 A r3*= 4.938 A and r4*= 5.685 A. wO~ 4.0-' ' ' ' """"'~ 3.0-2.0 --v) 'r t-.- 2 3 4 5 6 7 8 9 1011 12 1000K/T FIG.2.-Spin-lattice relaxation time (TI)as a function of reciprocal temperature for anilinium sulphate at 31 MHz. The solid line represents calculated values based on the parameters given in table 3. Note that the scale changes at lo3 K/T = 5 for clarity. For C3(NH3) motion we shall consider only the H - -H and N * .H dipolar interactions within -NH $. The intra-NH, inter-proton contribution to the relaxa- tion rate due to C3motion is where zCNis the correlation time for this C motion and f'(Wo5) = OoT/(l -/-OgZ') + 4woT/(l + 4W;T'). The contribution to relaxation made by interaction between the protons and 14N is given by a term16 h2yhykI~(I~ + 1)[(1/12)J'"(wO -wN) + (3/2)J'"(Wo) + (3/4)J'"(w0 + wN>l where J(4'(w)is a spectral density function. For C motion with the approximation that coo & c'jN 2 wo,one obtains A cos2 d/5 + sin4 A/~O)[COOT,N/(~ (T1l)H.N 2 20y~y~tz'~,'r~6~(2sin~ + w$rfN)] (2) where A = 70.5" is the angle between the N-H bond and the C axis. The combined relaxation rate + (Ti')H,N] has a maximum of 89.25 s-' at CO~T,~ 0.66'7.= Thus the predicted minimum in T1 for an isolated NHS group is 11.20 ms. In the anilinium ion where ring protons would relax by spin diffusion" to the NH; (Tl)min should be (8 x 11.20)/3 = 29.87 ms. Although the difference between this value and the observed value of z 38 ms in the halides is considerable such dis- crepancies have been observed before in the reorientation of methyl groups.'*-'' Johnson2' has indicated that the partial averaging of the dipolar hamiltonian by torsional vibrations of the methyl group decreases the effectiveness of the C relaxa-tion process by a factor which is close to 0.87 over a fairly wide range of temperature and of energy barriers. This effect would account for a large part of the difference between theory and observation.The predicted value of depends strongly on C. I. RATCLIFFE AND B. A. DUNELL the geometry of the -NH group; e.g. if the HNH angle were 113.5",the predicted minimum would be 34.4 ms and Johnson's explanation would raise this value to the experimental value. Our minimum in TI agrees when allowance is made for the total number of protons being relaxed and for the Larmor frequency with observed minima in other systems involving reorientation of -NHf groups. For the group -NH relaxing only itself at 31 MHz (TJminranges from 14.2 to 15.4 ms in these anilinium salts as compared with 12-14 ms in NzHg+salts,2113.2 ms in N2Hf salts22 and 13.0 to 16.6 ms in a number of amino In the sulphate TI at the two lower temperature minima is very nearly double that at the minimum in each of the halides; the interpretation is suggested that two crystallographically inequivalent anilinium ions are present in the sulphate.At each minimum the three protons of one -NHf group relax via spin diffusion the 5 ring protons in their own ion and all 8 protons of a crystallographically inequivalent ion i.e. 16 protons instead of 8 relax through the motion of 3 and the minimum is doubled. Since the infrared spectra of all four compounds had been obtained at room tempera- ture to check for impurities confirmation of the existence of inequivalent anilinium ions in the sulphate was sought there. Although some of the low frequency bands in the sulphate spectrum were split or rather more structured than those of the halides no firm conclusions could be drawn.In an attempt to assign the high temperature minimum of the iodide (z178 ms at 513 K) and of the sulphate (z160 ms at 463 K) we have calculated the theoretical minima in TI for various motions of the phenyl group superimposed on very fast C,(NH3) motion. The protons of the -NH$ group are considered to be " con-densed '' at the centre of their C3motion'' and the vectors between this point and the ring protons reorient with correlation times zcp,which are those of the ring motions. For reorientation of the ring in 180"jumps about its principal axis C2(coincident with C3 of the -NH$ group) one has 9 y4h2 69 Trl= -f(co,,zCp) 2 2 sin2Aij cos' AijrG6 + 80 coo i=2 j=2 i#i 96 1 where Aijis the angle between rijand C2,protons 2 to 6 are on the ring and 7 to 9 are in the " condensed " -NH$ group and the relaxation rates of the 8 individual pro- tons are averaged by spin diffusion and the existence of a spin temperature in the solid.Reorientations by 180"jumps about an axis C which lies in the plane of the ring and is perpendicular to C2or about an axis Cbwhich is perpendicular to the plane of the ring could also be considered and the TI minima for such motions calculated by eqn (3) with the appropriate changes in Aij. Motions of this type seem unlikely both because they are about axes which are not two fold symmetry axes and because they involve the motion of all the atoms of the ion and probably large energy barriers. As one may see from the values of the theoretical TI minima collected in table 1 none of these motions gives reasonable agreement with the observed high temperature minimum for anilinium iodide or sulphate.No evidence suggests the existence of inequivalent anilinium ions in the iodide and the high temperature minimum in the sulphate has essentially the same depth as that of the iodide. Although we have postulated in- equivalent anilinium ions in two crystallographic sites for the sulphate the large difference in energy barriers to reorientation of -NHS groups in the two sites oc- casioned by the inequivalence does not necessarily imply a large difference in the MOLECULAR MOTION IN ANILINIUM SALTS TABLE 1 .-EXPERIMENTAL VALUES OF MINIMA IN ANILINIUM SALTS AND THEORETICAL VALUES OF Ti MINIMA FOR VARIOUS MOTIONS OF THE ANILINIUM ION ~~ motion TI minimum/ms NHf group phenyl group theoretical experimental chloride C (all ions) none 29.9 38 bromide (07cN -1) (07cP > 1) iodide C3 (half the ions) 59.8 80 82 sulphate (other half 07,N >1 none or 07cN <1) fast C3 (os,N < 1) C2(I 80" jumps) 252.5 fast C C (1 80" jumps) 252.5 fast C3 Cb(180" jumps) a) fast C3(07cN <1) isotropic (C()Scl -1) 52.6 and isotropic 0TC1 1 *-160* suphate fast C3 C2(90" jumps) 169.8 178 iodide fast C C (90" jumps) 148.1 fast C3 Cb (90Ojumps) 149.3 * Observed minimum of 150 ms corrected for overlap of adjacent minimum.barriers to the reorientation of the phenyl groups. We believe therefore that the phenyl groups in the two types of anilinium ion in the sulphate may behave quite similarly.The possibility of an isotropic tumbling of the anilinium ions with superimposed fast C3(NH3)motion should be considered. For this motion the rate of relaxation is given by where the final term is a good approximation to the 14N H interactions in the -NH group10*'6 and A is defined in eqn (2). As shown in table 1 the theoretical Ti minimum for such motion is one third of the experimental high temperature mini- mum in the iodide or the sulphate. Consideration of yet other motions is then ap- propriate. Look and LOW^^^ have considered the spin-lattice relaxation of a molecule with twofold symmetry reorientating among two pairs of unequal potential wells having angular separations of 90".For a pair of nuclei whose internuclear vector is at 90" to the rotation axis in a crystalline powder sample they found the relaxation rate to be where a is the ratio of equilibrium populations in the adjacent unequal wells. For wells of equal depth both a and the factor in square brackets are unity and if the wells differ in depth by 0.7 kT a = 2 and the relaxation rate is decreased by z 10%. C. I. RATCLIFFE AND B. A. DUNELL If we assume that the anilinium ion can reorient among four positions of equal energy (a = 1) about its principal (C,)axis we can modify eqn (5)to allow for the fact that not all the interproton vectors are orthogonal to the rotation axis and that there is also C,(NH,) motion and write rij' .(6) 1 From this expression a theoretical T minimum of 169.8 ms is found in reasonable agreement with the experimental high temperature minimum in the iodide and the sulphate. As indicated above a small difference in the depths of adjacent minima will not greatly increase the disagreement in the case of the sulphate and might improve the agreement in the iodide. Reorientations among four minima about axes C and C were also considered and although either of these motions would allow a greater difference in energy between the two pairs of wells and give good agreement with experiment the motions are thought to be inherently less plausible than motion about the C axis. Thus we favour the assignment of the high temperature minimum in anilinium iodide and sulphate to reorientation of the phenyl group about its C2axis among four potential minima of nearly equal depth together with fast(wczcN << 1) C3(NH,) motion.DETERMINATION OF RELAXATION PARAMETERS For the halide salts the experimental relaxation rates for the minimum due to the -NH& relaxation mechanism were fitted by a non-linear least squares computer program to Ti1= -Af(uozcN) + BwotcpJ(l + w;CL) (7) with zCN= zZNexp (E/RT)where the ratio A/B was fixed as the ratio of the coeffi- cients of the functions of wz in eqn (1) and (2). The value of that ratio is a function of the angle A but the values of the relaxation parameters were not significantly affected by changes in A within the range A = 70.5 5 10" E by 0.1 % or less z& by 3.4 or less and by 0.14 % or less.Care was taken in the cases of the bromide and iodide to exclude results bordering on the region of their respective phase changes. A minimum of 178 ms in Tl was assumed for the high temperature processes of both the iodide and bromide. From this assumption and the values of TIon the low temperature side of the minimum values of the activation energy and zEp have been obtained. For the sulphate salt the lowest temperature minimum was fitted below 167 K where the effects of overlap with the higher temperature minima are very small by the computer program to eqn (7). Using the parameters determined for this minimum to fix the contribution from the corresponding mechanism we could then fit the re- maining points to an expression for the relaxation rate which was the sum of an equa- tion of type (7) for the middle T' minimurn and one simple B.P.P.relaxation function for the high temperature minimum. All the parameters are shown in tables 2 and 3 and the fits are illustrated by the solid lines in fig. 1 and 2. The indicated uncertainties are one standard deviation in the least squares fits. MOLECULAR MOTION IN ANILINIUM SALTS TABLE 2.-RELAXATION PARAMETERS FOR ANILINIUM HALIDES chloride bromide iodide C3(NH,) motion E/kJ mol-' 37.1 60.6 11.2 & 0.1 8.5 0.1 :Nh (7.0 k 1.5) x (4.4 0.4) x 10-14 (5.3 i0.4) x 10-14 (Tdmin ex~*/ms 37.6 5 1.1 37.3 i0.8 39.4 i0.6 (Tl)min theor./ms 29.9 29.9 29.9 Tm/K 418 i5 119 f2 92 i2 pseudo-C4 (phenyl) motion E/kJ mol-I 96 63 75 3 cp/s 2 x 10-17 9 x 10-17 (Tdrnin ex~t./ms (178)" 178 ( theor./ms 170 170 TmK (613)t 513 * Assumed.1-Calculated extrapolation. TABLE 3.-RELAXATION PARAMETERS FOR ANILINIUM SULPHATE C,( NH3)moti on anilinium I C,(NH3)motionanilinium I1 pseudo-C4( phenyl) motion ~~~ E/kJ mol-'GIs 11.2 i0.1 (3.8 i0.4) x 27.4 5 0.3 (4.6 i0.6) x 59.1 & 2.9 - TcDp/S(T1)rnin ex~./ms theor./ms Tm/K -82 f2 59.8 119 -80 f2 59.8 296 (6.9 & 5.5) x 159 i-4 170 463 10-l6 DISCUSSION PHASE CHANGES IN BROMIDE AND IODIDE Above 27.5 "Cthe bromide is orthorhombic and the -NH group must be orien- Below 27.5 "Cthe structure is monoclinic tationally disordered or freely r~tating.~.~~ with an angle j3 that increases as the temperature drops to an asymptotic value of 91" 22' which appears to be reached at about 200 K.25 The heat capacity curve has a typical A type of singularity with the most rapid change occurring at 22 "C and with a slow return on cooling to normal behaviour at about 200 K.26 The reported infra- red spectra of the iodide and bromide2' suggest that their phase changes are similar.In both the bromide and iodide the deviation in TI from the linear slopes of the high temperature side of their low temperature minimum is probably attributable to this phase change. If we assume that the activation energy for the reorientation of the -NH group decreases with increasing temperature following the change in the axial angle /3 toward go" we can account qualitatively for an anomalously rapid decrease in zCNand increase in TI.An approximate temperature range for the phase change in the iodide would be 180-250 K judging from a comparison of the bromide and iodide TIresults. C. I. RATCLIFFE AND B. A. DUNELL DEPENDENCE OE ACTIVATION ENERGY ON TEMPERATURE OF MINIMUM At the temperature of a minimum in TI we have (co0~Jm= 047 exp (E/RTm) where subscript m indicates the value at the minimum and whence For a given type of motion and geometry of the reorienting group (coosc) is fixed. The fact then that a plot of E against T for the three halides and the two lower temperature minima of the sulphate is a very good straight line indicates that L is the same for these cases. The slope of the line in fig.3 gives 7G= 4.63 x s for 804 0 1 1-1 soop -0 IUU 3vv 3uu temperature at minimum /K FIG.3.-Activation energy plotted against the temperature of the T minimum. a -NH re-orientation; 0,phenyl. (cooz,) = 0.667. This value agrees in general with the values of 7,0N obtained from the fits of the individual minima. The fact that the (Tm,E) points of the two lower temperature minima of the sulphate fall on the straight line but the point for the high temperature minimum does not is taken as support for the assignment of the two lower temperature minima to C,(NH,) motion. No comparable relation exists for the motion of the phenyl group in the sulphate and iodide and (with extrapolation and assumptions) the bromide. EXTERNAL BARRIERS If the inference made in the introduction is correct that the internal barrier to the reorientation of -NHZ is extremely small the activation energies for -NH re-orientation should represent external hindrances almost exclusively and one should be able to interpret the range of activation energies in terms of the nature of the external barriers.The magnitude of a barrier is determined principally by the mag- nitudes of the attractive and repulsive interactions between the atoms and by the relative symmetries of the rotor and its environment. For one atom (i) of a rotor such as -NHZ with C3symmetry interacting with a field of n identical neighbour MOLECULAR MOTION IN ANILINIUM SALTS atoms distributed with C symmetry about the rotor axis the rotational potential may be expressed as a sum of sinusoidal potentials Vi(a) = 2(Vm,/2)(1 -cos rnn a) rn = 1,2,3 .. . m where a is the rotation angle and Vm becomes smaller as rnn becomes larger. Adding the contributions of the other two atoms of the C3 rotor gives V(a)= 2(3 VI,,/2)(1 -cos mn a) mn = 3 6 9 . . . l?1 and for other values of mn V(X)is invariant to a. Hence if n = 3 V(a) = (3V3/2)(l -cos 3a) + terms in V6 V9. . . and if n = 4 V(a)= (3VI2/2)(1 -cos 12~) + terms in V24 V36. . . V3should be much larger than VI2. Table 4 compares the activation energies for -NH$ reorientation in a number of different halides and sulphates and shows that the values for the anilinium bromide and iodide and for one of the anilinium ions in the sulphate are rather low.We suggest that this reflects mainly a lack of correspondence between the symmetries of the rotor and its environment. The known structures of N2H6C12,28 (CH2NH3)2C1229 and C6H,NH3C1’show the common feature that the chloride ion has a C3,or near C, arrangement about -NH$ at distances which imply hydrogen bonding. There TABLE 4.-cOMPARISON OF ACTIVATION ENERGIES FOR -NH GROUP REORIENTATION IN SEVERAL COMPOUNDS OBTAINED BY N.M.R. SPIN-LATTICE RELAXATION STUDIES (kJ mol-I) cation c1- Br- I- so:- ref. (CH3)3CNH3+ + H3N-N H,f 37.5 45.2* 33.2 32.7* 27.3 - -24.3$ 8 21i CH,-NH,tICH,-NH,f 41.4 12.3* 9.2* 30.7* 34t 11.2 this CGHS-NH,+ 37.1 11.2 8.5 27.4 work ~- * Average of two slightly different slopes on each side of the TI minimum t Approximate pre- liminary values small amendments to these numbers may occur in the final analysi~.~~~~~ $ For the -NH$ group in the orthorhombic phase which has a near 3-fold environment.are spectroscopic arguments which suggest a similar stiuation in the t-butylammonium halides’ and N2H,Br2 is apparently isostructural 30 with N2H6C12. For these cases where the symmetries of the rotor and its environment match the activation energies are high with decreasing values as one goes from chloride to bromide to iodide. Such a decrease must represent to some extent at least decreasing strength in hydrogen bonding. In the warm temperature phase of anilinium bromide the -NHS group has a 2-fold environment which is in fact also a slightly distorted 4-fold environment of Br-ions at distances which imply hydrogen bonding6 In that phase with n = 4 one would expect a low barrier to the -NHZ rotor with VI2 the coefficient of the first component of the potential to depend on the angle a being small compared with V3.The small distortion may make some contribution to the barrier. Just above the phase transition in the bromide and iodide it is clear that the TIresults are in a region C. I. RATCLIFFE AND B. A. DUNELL where there is overlap of the high temperature mechanism and a lower temperature mechanism of the orthorhombic phase. If the contribution of the high temperature mechanism is extrapolated and subtracted the residual values of TI just above the phase transition are found to level off. This could be interpreted as consistent with a very low barrier for -NH motion in the orthorhombic phase.In the low tempera- ture phase on which the TI measurements were made the environment cannot have C3 symmetry because the relatively small activation energy indicates too small a barrier Some further distortion of the approximate C4 symmetry of the bromide ions is probable however as p changes from 90" to 91" 22' and this could certainly produce a barrier of height between the large V characteristic of a 3-fold rotor in a 3-fold environment and the small V, characteristic of a 3-fold rotor in an exactly 4-fold environment. We assume that similar considerations apply to the iodide. Ethylene diammoniuni sulphate has identical -NH f groups3' and the nearest neighbour environment of each is essentially a 3-fold hydrogen bonding system of oxygen atoms although next-nearest neighbours perturb this.The activation energy for C3(NH3) motion is correspondingly high. The two ends of the hydrazinium ion in orthorhombic N,H,S04 are different 32 and the difference is clearly manifested in the TI results for this phase,,' which sets a precedent for crystallographically different -NH$ groups in a sulphate salt. We suggest that in anilinium sulphate one anilinium ion (corresponding to the minimum with E = 27.4 kJ mol-') may be in a near 3-fold environment of hydrogen bonding oxygen atoms and the other in a much less sym- metric environment of sulphate oxygens. lncoherent inelastic neutron scattering (i.n.s.) meas~rernents~~ gave 442 cm- and 294 cm-' as the transition energy from the ground to the first excited level of the -NH torsional mode in anilinium chloride and bromide respectively at -77 K.These frequencies correspond to cosine barrier heights (V,) of 47.6 and 21.7 kJ rno1-I if a regular 3-fold potential is assumed and the moment of inertia of -NH,' is derived from the bond parameters used in this paper. If it is assumed that V3is the sum of the activation and zero point energies the estimate of activation energy from i.n.s. is 45 and 20 kJ mol-l for the chloride and bromide respectively. Quantitative agreement is better for the chloride than for the bromide where the disagreement is almost a factor of 2. We suggest that this again reflects the asymmetry of the environment in the bromide and the absence of a regular or symmetrical 3-fold cosine potential which was assumed in the calculation of barrier height from the transition frequency for the ground to first excited level.The two techniques give then complementary informa- tion about the nature of rotational barriers. We are indebted to the National Research Council of Canada for a Grant-in-Aid of this research. H. D. Rudolph H. Dreizler A. Jaeschke and P. Wendline Z. Naturfursch. 1967,22A 940. A. B. Dempster D. B. Powell and N. Sheppard Spectruchitn. Acta 1975 31A 245. B. Alefeld A. Kollmar and B. A. Dasannacharya J. Cheni. Phys. 1975 63,4415. S. Clough and J. W. Hennel J. Phys. C 1975,8 31 15. C. J. Brown Acta Crysf. 1949 2 228. I. Nitta T. Watanabe and I.Taguchi Bull. Chettr. SOC.Jnpati 1961 34 1405. 'T. T. Ang and B. A. Dunell J.C.S. Faraduy 11 1972,68 1331. C. I. Ratcliffe and B. A. Dunell J.C.S. Fnruday 11 1977,73,493. N. Bloembergen E. M. Purcell and R. V. Pound Phys. Rev. 1948 73 679. lo D. E. Woessner J. Chetu. Phys. 1962 36 1. l1 M. B. Dunn and C. A. McDowell Mu/. Phys. 1972,24 969. l2 S. Albert H. S. Gutowsky and J. A. Ripmeester J. Chetii. Phys. 1972 56 3672. l3 E. 0. Stejskal and H. S. Gutowsky J. Cheni. Phys. 1958 28 388. MOLECULAR MOTION IN ANILINIUM SALTS j4 K. P. Larsen Acta Cheni. Scatid. 1974 28A 194. R. W. G. Wyckoff Crystal Structures (Wiley New York 2nd edn 1969) vol. 6( l),p. 1. l6 A. Abragam The Principles of Nuclear Magnetism (Clarendon Press Oxford 1961) p. 295. J.E. Anderson and W. P. Slichter J. Phys. Chetn. 1965 69 3099. S. Albert H. S. Gutowsky and J. A. Ripmeester J. Chem. Phys. 1972 56 1332. T. T. Ang and B. A. Dunell Catlad. J. Chem. 1974 52 1840. ’O C. S. Johnson Jr. J. Magtietic Resotiatice 1976 24 63. C. I. Ratcliffe to be published. ’’C. I. Ratcliffe B. A. Dunell and T. C. Waddington J.C.S. Faradcty I/ 1978 74 1417. 23 E. R. Andrew W. S. Hinshaw M. G. Hutchins and R. 0. I. Sjoblom Mol. Phys. 1977 34 1695. 24 D. C. Look and I. J. Lowe J. Chenr. Phys. 1965 69 3099. ’’I. Taguchi Bdl. Cheni. SOC.Japan 1961 34 392. 26 H. Suga Bi~ll.Cheni. SOC.Japati 1961 34 426. ” A. Cabana and C. Sandorfy Catiad. J. Cheni. 1962 40 622. ’*J. Donohue and W. N. Lipscomb J. Chem. Phys. 1947 15 115. 29 T. Ashida and S.Hirokawa Bdl. Chew. SOC.Japan 1963 36 704. 30 C. J. Ludman C. I. Ratcliffe and T. C. Waddington J.C.S. Faraday ZZ 1976,72 1741. 31 K. Sakurai J. Phj*s. SOC. Jupati 1961 16 1205. 32 P.-G. Johnson and W. C. Hamilton Acta Cryst. 1970 B26,536. 33 C. I. Ratcliffe Ph.D. Thesis (Durham 1975). 34 C. 1. Ratcliffe to be published.

ISSN:0301-5696    

DOI:10.1039/FS9781300142

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

Self-diffusion Studies in Solids Using Nuclear Magnetic Resonance Techniques BY ROY E. GORDON AND JOHNH. STRANGE Physics Laboratory The University Canterbury Kent CT2 7NR Received 31st July 1978 N.m.r. measurements of spin-lattice relaxation time T,,and spin-spin relaxation time T, give valuable information on diffusive motion in a wide variety of solids when self-diffusion provides the dominant relaxation mechanism. These measurements however have a limited useful range. As the mean time 7 between jumps increases the effects of paramagnetic impurities can dominate TIand T2reaches a constant rigid lattice value. These limitations can be overcome by measuring the spin- lattice relaxation time in the presence of an r.f. field TIP, or the spin-latticerelaxation time in the dipolar field TID.Recent theoretical developments often allow z to be evaluated with reasonable accuracy and if the jump distance is known then the self-diffusion coefficient D,can be calculated. Paramagneticim-purity effects can also cause anomalous results in the solid in the fast diffusion range. The technique and its limitations will be illustrated by recent work on 19F-diffusion studies in fluorite lattices. Mea-surements of these relaxation times provide information at the microscopic level on the atomic motion and thus can indicate the dominant diffusion mechanism. Diffusion coefficients can be measured by macroscopic methods and in particular by using the pulsed field gradient n.m.r. spin echo technique in which pulsed magnetic field gradients are applied to the sample during a T2measurement sequence.Since it is a direct measurement of D this technique also serves to complement the information from relaxation studies and can provide a useful check on existing theoretical interpretation. Comparisons with the results of other experimental methods such as radio-tracer or ionic conduc- tivity for ionic solids are similarly informative. F-diffusion in barium fluoride and lead fluoride together with new results for strontium fluoride are discussed. N.m.r. measurements are seen to be particularly useful in the regions of fast ion diffusion above the high temperature phase transitions. The phenomenon of self-diffusion in solids has attracted considerable interest in recent years. Theoretical models for defect assisted mass transport in various classes of solid have been proposed and experiments performed in attempts to verify them.One area where this type of study has recently assumed much greater importance is the study of ionic motion in solids. Fast ion conductors in particular have attracted considerable attention primarily because of the increased technological importance of solid-state electrochemistry. Solid-state electrodes in batteries hydrogen storage and electrochromic display devices for example require solids exhibiting fast ion conduction. The diffusion mechanisms and point defect structures of such solids are not well understood. Electrical conductivity measurements often combined with radio-tracer diffusion studies have been widely used to investigate ionic transport in solids.Powerful alternative methods which are capable of providing information at a microscopic as well as macroscopic level are to be found in the techniques of nuclear magnetic resonance. These techniques have been applied to a wide variety of materials both solid and liquid and are particularly valuable when radio-tracer methods fail due to the lack of a suitable isotope. In this paper we shall describe the n.m.r. relaxation methods by which the (micro- scopic) mean residence time of atoms in their lattice position can be determined and the n.m.r. spin-echo techniques (macroscopic) by which diffusion coefficients are ob- I54 SELF-DIFFUSION IN SOLIDS USING N.M.R. tained directly. To illustrate the application of these techniques to solids we will pre- sent previously unreported measurements on fluorine ion diffusion in strontium fluoride and compare themwith recent work on other fluorites BaF and PbF2.Although they have no direct technological importance themselves these solids undergo an order- disorder phase transition before they melt and exhibit fast ion diffusion. The simple fluorite structure allows n.m.r. theory to be rigorously tested and also permits theoreti- cal model calculations of defect formation and migration parameters relevant to fast ion diffusion in disordered systems to be made. Experimental investigations of ionic motion at both microscopic and macroscopic levels are important for the under- standing of fast ion conductors.In 1839 the " conducting power " of PbF was first investigated by Michael Faraday.' Although behaving as an insulator at room tem- perature when introduced into a simple electrical circuit Faraday noted that "being heated it acquired conducting powers before it was visibly red hot in daylight ". The problem of understanding ionic conduction and self-diffusion in solids is not new. Much has been learnt and we shall show how n.m.r. has recently contributed to this interesting field of study. INDIRECT DIFFUSION MEASUR EMEN T-S PI N RELAXAT1ON Although other relaxation mechanisms may occur the modulation of nuclear magnetic dipole-dipole interactions by the relative translational motion of atoms is the relaxation mechanism most commonly encountered in diffusion studies.The general perturbation theory of this spin relaxation mechanism is well established. For inter- actions between like spins the spin-lattice relaxation time T, is given by T; = + cc[J")(coo) + J'2'(2m0)] (1) where J(q)(co) are the spectral densities of the dipolar interaction fluctuations at fre- quency o,coo is the Larmor frequency and a = y4h21(1+ 1). y is the gyromagnetic ratio of the nuclei with spin quantum number I. A similar expression applies to the spin-spin relaxation time T2when T2& T2r.,.,the rigid lattice value of T2 TT1 = &Cc[J'O'(O)+ lOJ"'(W0) + J'"'(2W,)]. (2) The spin-lattice relaxation in the presence of a resonant rotating magnetic field HI in addition to the steady field Ho has a characteristic time TlPgiven3 by Tlpl = 3 or[J'0'(2io,) + lOJ"'(co,) + J'2'(2coo)] (3) where co = yH,.Eqn (3) is valid when Ho 9 H 9 Hdand Hdis the local dipolar field of the nuclei. When H 5 Hd the perturbation approach fails and provided that the mean time between atomic jumps z is >T2r.,.,a strong collision theory4 can be used. In the limit of H = 0 the spin-lattice relaxation time (in the local di- polar field) TID,is given by where (a -p) is a calculable5 dipolar order parameter. A theoretical treatment which unites the perturbation and strong collision approaches has recently been developed by Wolf and Jung6 The main theoretical problem with the interpretation of relaxation time data is the precise calculation of J(q)(w)or (a -p) in terms of the mean residence time of an atom on a lattice site.R. E. GORDON AND J. H. STRANGE A variety of model^**^-'^ has been used for this purpose. In particular Eisenstadt and Redfield proposed an " encounter model " to take account of the special n.m.r. correlation effects arising with defect-assisted self-diffusion. This model has recently been significantly refined and extended by Wolf 5,11 and extensively tested experiment- ally for anion diffusion on a fluorite latti~e.'~,'~ Using calculations of J(q)(u)for a specific lattice and diffusion process zvalues obtained can be related to the diffusion coefficient D,using the Einstein-Smoluchowsky relation modified to include effects of correlated motion where (r2) is the mean square atomic jump distance and f is the relevant geometrical correlation fa~t0r.l~ The correlation effects mentioned above are sensitive to the mechanism of diffusion and their determination can allow identification of the dominant diffusion mechanism.The general form ofJ(4)(u) is such that it has a maximum when uz 21 1 resulting in characteristic minima for Tl and Tlpwhen measured as functions of temperature. When co,z < 1 theory predicts Tlp= T2and when cooz < 1 Tl = T1 = T2. Relaxation time measurements of 19Fin a pure single crystal of SrF are shown in fig. 1 and exhibit clearly defined minima in Tl and Tlp. On either side of the minima the relaxation times exhibit an Arrhenius behaviour. T2decreases with temperature until the temperature independent rigid lattice value is reached. Below about 750 K another relaxation mechanism influences T, believed to be due to a low level (-1 p.p.m.) of residual paramagnetic impurity.Such impurities which are difficult to 10 10' loo 10-.-E c c -2 .c 10 c -8 2! -3 10 I 1 I I I I 1 I I 1 1.0 1.4 1.8 2.2 1000 KIT FIG. l.-19F relaxation times at 10 MHz for nominally pure SrF, TI 0;T2 0;TI at HI = 30 G A. TI data for SrF + LaF3 (225 p.p.m.),*. The solid lines illustrate the 19F relaxation behaviour found l8 in nominally pure PbF2. SELF-DIFFUSION IN SOLIDS USING N.M.R. remove often limit the useful range of relaxation time measurements in ionic solids. TIPis valuable in following the diffusion process to lower diffusion rates. From eqn (3)it can be seen that the spectral density at CO~(CL)~< coo) makes TlPsensitive to much slower motion than Tl.DIRECT DIFFUSION MEASURE M E NT-S P I N ECHOES When self-diffusion is sufficiently fast a direct n.m.r. method of determining D is available. Aspin echo produced by a 90"-180" pulse sequence applied to a sample in a magnetic field gradient will be attenuated if the nuclei move in the field gradient during the experiment. Attenuation is the result of a loss in the phase coherence of the precessing nuclei. The nuclear spin state of the diffusing atom serves as a label and under favourable experimental conditions permits a convenient and direct measure- ment of D. Larger field gradients permit the measurement of slower diffusion but ulti-mately result in signals being difficult or impossible to observe.These technical problems have been elegantly overcome and greater precision obtained by applying large field gradients '' as pulses during the time when signals were not being observed. The relevant theory of this experiment is to be found in the literature.'' The tech- nique has hitherto been primarily restricted in its application to liquids. Recently an apparatus suitable for operation with solids at high temperatures has been described16 and has been used to measure F-diffusion in fluorites over a wide temperature range.17p1s The slow diffusion limit for this technique is primarily set by the T2of the spin system under study and the maximum pulsed magnetic field gradients that can be obtained. Asmotion slows T2decreases until it is no longer possible to achieve dis- cernible spin echo attenuation during the time available (T,).Modifications 19-,1 to the original pulse sequence have circumvented this limitation to some extent and dif- in suitable sytems. fusion coefficients as low as 3 x m2s-' have been mea~ured'~ COMPARISON 0F TECH N 1Q U ES-EX PER I MEN T S 0N F L UO R I T E S 17922 Recent F-diffusion studies in the fluorite crystals BaF, PbF2 and SrF illustrate well the application of n.m.r. techniques and allow comparison with transport data obtained by the completely independent techniques of ionic conductivity and radio-tracer diffusion. Due to the short half-life of the most convenient fluorine radioisotope "F tracer experiments are very difficult are limited to very fast diffusion rates and have been attempted only for BaF,.Tracer diffusion is also subject to spatial correlation effects. Electrical conductivity measures the movement of charged defects (e.g.,vacancies or interstitials) whose motion is usually uncorrelated. The movement of defects results in a (correlated) motion of ions. The measured conductivity CJ at a temperature Tcan be related to the diffusion coefficient [eqn (5)] using the Nernst-Einstein equation. For anion diffusion on a fluorite lattice pro- ceeding by a monovacancy mechanism this relationship is D =f(k/Ne2)aT (6) where N is the ion density e the effective charge of the defect and k is Boltzmann's constant. The spatial correlation factorI4 f is 0.653 in this case [eqn (5) and (6)].Conductivity measurements have been made22,23 on the same samples used in the n.m.r. investigations and can therefore be used for comparison. The range of applicability of the various techniques is illustrated in fig. 2. In principle the n.m.r. methods can be used throughout the ranges shown by full and broken lines. In the fluorites a practical lower limit is determined by paramagnetic R. E. GORDON AND J. H. STRANGE impurities and is marked by the full lines. Upper limits are determined by the chemi- cal reactivity of samples and the problems of sample containment. Relaxation time measurements of T, T, TIPand TI for 19F have been ma,de from 300 to 1200K in pure and doped single crystals of Ba ,,Fand provide some of the most comprehensive diffusion studies by relaxation.In the pure crystal intrinsic diffusion I f--tracer ----> I I 1 I 1 I 1 I 1 1 I I 1 1 Idle 1o-IL 10-l0 D t m2s' FIG.2.-Ranges of applicability of the various techniques for studying F-diffusion in fluorite crystals. The upper scale is z the mean residence time for ions on a lattice site. The lower scale is D the diffusion coefficient. The scales are related by eqn (5). due to the random motion of thermally generated point defects was followed from 475 to 1200 K. Measurements on this material also serve to illustrate the strong dependence of relaxation rates on crystal orientation.'2*24 The interpretation of relaxation time data obtained from crystals of unknown orientation or from poly- crystalline samples should be treated with caution especially for TIPwhen IO~T< 1 < cL)oz.Relaxation measurements for SrF, shown in fig. 1 exhibit the same general features that were found for BaF,. Also shown on fig. 1 are previously r2ported" relaxation time data for PbF from 300 K to its melting point 1095 K. Both materials have metal ions with weak nuclear magnetic moments but their influence on 19F relaxation appears negligible. The PbF2 data below the temperature of the TI minimum are again qualitatively similar to that for BaF and SrF,. Activation energies naturally differ and the T minimum occurs at a much lower temperature showing correspond- ingly faster F-diffusion in PbF,. The PbF2 data obtained above the TI minimum differ markedly from the expected classical behaviour found in BaF and SrF,.This anomalous behaviour when first observed25 was attributed to the presence of highly correlated modes of ionic motion associated with the phase transition at 705 K. Extensive linewidth26 and subsequent n.m.r. diffusion and relaxation measurements have demonstrated that the anomaly is probably due to paramagnetic impurities. The intrinsic point defects in the fluorites are believed to be predominantly anion- Frenkel pairs.27 The activation enthalpy for anion migration may be expressed as (&/2 + 11,~). h is the formation enthalpy of the Frenkel pair and IT, the migration enthalpy of the defect of type ,j (vacancy or interstitial) providing the dominant diffusion n~echanism. The two most probable mechanisms for the F- diffusion are the vacancy IT,^) and non-collinear interstitialcy (11,~) mechani~ms.~~ SELF-DIFFUSION IN SOLIDS USING N.M.R.The intrinsic ionic diffusion can be modified by the incorporation of aliovalent impurities into the lattice. Doping difluorides with trivalent or monovalent cations can create F-interstitials and vacancies respectively. Defects so produced can deter- mine the dominant diffusion mechanism and their concentration will determine the temperature range over which extrinsic behaviour extends. The activation energy in this region will be given by hmjand doping experiments can therefore be combined with the results for the intrinsic range to obtain values for h and hmjseparately. A typical effect of doping on TI relaxation can be seen in the results for SrF containing 225 p.p.m.LaF shown in fig. 1. The temperature dependence of T is reduced corre- sponding in this case to an activation enthalpy hmi. Similar effects are observed' in T2,TI and T, and reliable values for defect parameters can be obtained. Table 1 lists the values obtained for the fluorites studied by n.m.r. and also the values obtained from theoretical calculations.'* TABLE 1.-F-DIFFUSION PARAMETERS IN FLUORITES defect enthalpies /eV for F-diffusion fluorite melting order-disorder lattice point transition parameter n.m.r. studies* theoretical valuesz8 TmIK temperature TcjK rlA /I r /hV huii 1117 h,ur Ilmi SrF BaFZLL PbF,'" 1723 1560 1095 1450 1235 705 2.8998 3.101 2.969 2.58 kO.18 1.80&0.11 0.88 * 0.10 0.59 50.02 0.6250.05 0.29 * 0.02 0.80& 0.04 0.77*0.01 - 2.38 0.43 1.98 0.46 0.80 0.72 - * The defect enthalpies quoted for SrF should be considered as preliminary since studies using different levelsof alioval- ent dopant are still in progress.The intrinsic point defect concentration lid can also be estimated from doping studies. The extrinsic and intrinsic regions meet at the temperature where nd is equal to the (known) concentration of dissolved aliovalent dopant. By studying crystals with various concentrations of dopant the temperature dependence of nd can be obtained. Such information at temperatures Tc of the order-disorder phase transition is particularly interesting as there is currently considerable debate on the extent of anion disorder at this tran~ition.'~.~' Self-diffusion coefficients D,derived from relaxation data using Wolf's method of analysis and eqn (5) are presented in fig.3. A monovacancy mechanism was assumed for all pure samples as this is thought to be the dominant mechanism for most of the temperature range studied. Values for D obtained from the conductivity measurements using eqn (6) with J' = 0.653 appropriate to a monovacancy mechan- ism are shown together with those measured by n.m.r. directly. Agreement between the results of the different methods is very satisfactory particularly in BaF where measurements span eleven orders of magnitude and strongly suggest a diffusion mechanism controlled by point defects even above Tc. The region of the phase transition in each material deserves special attention.The n.m.r. pulsed field gradient measurements in BaF and PbFz show a marked decrease in the activation enthalpy in the fast diffusion region above Tcand in both materials the phase transition apparently occurs when D e2 x m2s-'. Further studies of SrF and CaF are in progress to establish whether this is a general feature of fluorites. For PbF in particular the agreement between conductivity and n.ni.r. diffusion measurements above Tc is such that extensive disorder and a high occupancy of anion interstitial sites as suggested previo~sly,~~ seems unlikely. An anion exchange mechanism of diffusion '* also appears to be inoperative. The picture of anion diffusion in fluorites above Tc that is currently emerging is R.E. GORDON AND J. H. STRANGE TIK 1000 714 500 417 1000K/ T FIG. 3.-Temperature dependence of F-diffusion coefficients in fluorite crystals. SrF2 0 ~ n.m.r. relaxation; 2 n.m.r. pulsed field gradient; ionic conductivity. BaF 0 n.m.r. relaxation; A n.m.r. pulsed field gradient; --ionic conductivity. PbF 0n.m.r. relaxation; A n.m.r. pulsed field gradient; -. -. -ionic conductivity. very rapid hopping on regular lattice sites with defect concentrations <10%. The anion radial distribution function g(r) has recently been obtained by molecular dynamics calculation~~~*~~ above Tc for CaF,. The spectral density functions for TI relaxation by translational diffusion in a liquid may be expressed33 in terms of g(r) using where N is the spin density and Tr is a differential operator.It will be interesting to apply this " liquid " model to the fluorites we have studied when g(r) data become available. One might expect a markedly different result to be obtained for TI than is found using the lattice diffusion model that we have found to be so satisfactory. The n.m.r. pulsed field gradient experiments measure displacements arising from many atomic jumps whereas conductivity measures any corresponding motion of charged defects. In contrast the n.m.r. relaxation methods probe the " local motion " on an atomic scale and diffusion coefficients can only be calculated by adopting a suitable model for the motion and employing a rather complex theoretical treatment. 160 SELF-DIFFUSION IN SOLIDS USING N.M.R.The agreement obtained between these three different approaches for the fluorites adds considerable confidence to the understanding of the atomic diffusion and defect structure of these solids. The authors gratefully acknowledge the financial assistance of the S.R.C ' M. Faraday E.vp-periiiietitn1Researches iti Electricity (R. and J. E. Taylor London 1839) vol. 1 para. 1340 426. 'A. Abragani The Priiiciples of Nriclenr Mngtietism (Clarendon Oxford 1962) chap. VIII. D. C. Look and I. J. Lowe J. Cheni. Phys. 1966 44 2995. C. P. Slichter and D. C. Ailion Phys. Rev. A 1964 135 1099. D. Wolf Phys. Rev. B 1974 10 2724. D. Wolf and P. Jung Phys. Rev. B 1975 12 3596. H. C. Torrey Phjls. Rev. 1953 92 962. * M.Eisenstadt and A. G. Redfield Phys. Rev. 1963 132 635. C. A. Sholl J. Phys. C 1974 7,3378. lo C. A. Sholl J. Phys. C 1975 8 1737. D. Wolf PIiys. Rev. B 1974 10 2710. l2 D. Wolf D. R. Figueroa and J. H. Strange Phys. Rev. B 1977 15 2545. l3 D. R. Figueroa J. H. Strange and D. Wolf Phys. Rev. B in press. l4 K. Compaan and Y. Haven Trans. Fnradny Soc. 1958 54 1498. l5 E. 0.Stejskal and J. E. Tanner J. Phys. Cheni. 1965 42 288. l6 R. E. Gordon J. H. Strange and J. B. W. Webber J. Phys. E 1978 in press. R. E. Gordon and J. H. Strange Proc. XIXrh Coiigress Anipere (Heidelberg 1976) p. 495. R. E. Gordon and J. H. Strange J. Pliys. C 1978 11 3213. l9 J. E. Tanner J. Cheni. Phys. 1972 56 3850. *O K. J. Packer C. Rees and D. J. Tomlinson Mol.Phj-s. 1970 18 421. 'I I. Zupanic J. Pirs M. Luzar R. Blinc and J. W. Doane Solid State Coiizti~.,1974 15 227. 22 D. R. Figueroa A. V. Chadwick and J. H. Strange J. Phys. C 1978 11 55. 23 V. M. Carr. A. V. Chadwick and R. Saghafian J. Phys. C 1978 11 L637. 24 D. R. Figueroa and J. H. Strange J. Phys. C 1976 9 L203. 25 J. B. Boyce J. C. Mikkelsen and M. O'Keeffe Solid State Coimz. 1977 21 955. 26 R. D. Hogg S. P. Vernon and V. Jaccarino Phys. Rev. Letters 1977 39 481. ''A. B. Lidiard Crystnls M.ith the Fliiorite Strrtctiire ed. W. Hayes (Clarendon Oxford 1974). 28 C. R. A. Catlow M. J. Norgett and T. A. Ross J. Phys. C 1977 10 1627. 29 C. R. A. Catlow R. T. Harley and W. Hayes J. Phys. C 1977 10 L559. 30 A. S. Dworkin and M. A. Bredig J. Phys. Chetii. 1968 72 1277. 'I A. Rahman J. Clieni. Phys. 1976 65 4845. 32 M. Dixon and M. J. Gillan J. Phys. C. 1978 11 L165. 33 L.-P. Hwang and J. H. Freed J. Chetii. Phys. 1975 63 4017.

ISSN:0301-5696    

DOI:10.1039/FS9781300153

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

GENERAL DISCUSSION At one point during the Discussion Prof. E. L. Hahn (Berkeley)raised the general question of the potential value to chemists of multipulse line-narrowing techniques and cross-polarization double resonance techniques. It is convenient to separate the replies to Prof. Hahn’s query from the main body of the Discussion so they are printed first. Dr. P. Mansfield (Nottingham) said The question as to whether multiple pulse techniques will ever gain the popularity and acceptance of chemists as a tool for “ high resolution ” studies of spin systems seems to me to depend on several factors. The first is that the heyday of multipulse development was undoubtedly the period from 1968-1973. In this five year period sophisticated schemes were developed for homonuclear line narrowing which culminated in some very efficient fully compensated cycles which for reasons about which we can only speculate have not yet been prop- erly exploited by physical chemists interested in pure application.But in any case it seems that new ideas especially complicated ones usually take about 5 years to emerge and be adopted so one must be patient. During the last 5 years one or two groups have sprung up and are using multiple pulse sequences both in Europe and America. But often they are using the simplest and therefore the least efficient cycles. 1 can only assume that the apparent com- plexities of the 16 pulse cycles (and longer) frighten off the prospective user. However I would like to urge interested researchers into trying some of the more sophisticated pulse sequences.With the possibility which now exists of fully com- pensating cycles for various pulse imperfections the sequences are relatively easy to set up and once set up remain stable for days. The second point is that originators of the multipulse schemes have without exception all been apparatus designers and builders as well. Whilst commercial firms offered the necessary number of r.f. channels and pulse programmers to enable some of the first multiple pulse sequences to be performed at an early stage in their development it would seem that few if any people were able to obtain results with the commercial equipment. In this respect it must be pointed out that we had found r.f. stability and phase coherence rather important instrumental factors.However as far as I know modern commercial machines are now capable of performing multiple pulse experiments in solids. Indeed one can now buy a computer controlled pro- grammer with sufficient flexibility to perform some of the more sophisticated cycles referred to earlier. 1 can only assume that the lack of success with those early commercial machines dulled the appetite of the more adventurous chemists and physicists who by and large have now moved on to other things. The third point concerns the value of experimental results obtained by multiple pulse experiments. The popularity of I3C double resonance experiments and the wealth of information coming from them should kill the old myth still put about by some chemists that interest lies only in the isotropic chemical shielding tensor.The full shift tensor contains valuable information on the bonding and structure of mole- cules and would 1 feel sure be the normal expectation if it were not considered too GENERAL DISCUSSION difficult to measure. My feeling is that as with 13Cexperiments there is a wealth of information to be obtained from combined multipulse and sample spinning experi- ments and this approach has only just begun to be tried and investigated by a few groups. I do not see multipulse experiments as in some way competing with low abundance double resonance experiments. It is simply a matter of which nucleus is of interest. Undoubtedly 'H and I9F (in solids) must always be studied by multipulse methods.However although 100 isotopically abundant 31Pis a good candidate for double resonance experiments. But I am bound to say that in our own 31P-1H double resonance work (unpublished) results were somewhat disappointing invariably because of the very short rotating frame spin-lattice relaxation times of the protons. In some of the materials we studied the 31P-31Pdipolar interaction also seemed to be important so that some combined form of multipulse and double resonance experiment was indicated. Dr. A. N. Garroway (Washington) said Cross-polarization techniques are many times combined with magic angle spinning so that both dipolar and chemical shift anisotropy broadenings are suppressed. Multiple pulse methods are generally applied in single crystals or when the spectrum is sufficiently simple that anisotropy effects are not a severe complication.Most chemists with backgrounds in proton or 13C liquid state spectroscopy are reluctant to embrace single crystal studies especially of complex molecules. Cross-polarization and magic angle spinning on the other hand give spectra not too different than in the liquid state. I think that the popularity of cross-polarization techniques at least in the newest commercial spectrometers reflects more the ease of its marriage to magic angle spinning rather than the inherent difficulties of each technique. Dr. R. K. Harris (Norwich)said One very good measure of the immediate poten- tial of techniques such as these is the involvement of commercial companies since they respond to what they see as the market demand from chemists interested in applications.Several companies are already offering equipment for the cross-polarisation magic angle spinning experiment and others are developing such equip- ment. There is much less commercial activity on multiple-pulse experiments. In my view this implies that at least in the medium term the cross-polarisation technique is going to be more utilised than multiple pulse experiments. Dr. K. J. Packer (Norwich) said It is a fact that the single-resonance multiple pulse-cycle techniques for suppression of homonuclear dipolar interactions are complementary to the dipolar-decoupling cross-polarisation magic angle spinning techniques in that they are not applicable to the same systems.The former generally are applicable to abundant spin-species such as 'H and I9F whereas the second group of techniques require the dilute spinlabudant spin combination. It is generally believed by chemists however that the multiple pulse techniques are rather more demanding on apparatus and experimenter than the double resonance methods and as such have not yet proved particularly popular as a tool for the chemist. On the other hand there is every evidence that the double-resonance methods are in the process of being adopted and developed in a large number of chemistry laboratories and commercial manufacturers of n.m.r. spectrometers are already offering equipment for this type of work. Time will tell whether this is the correct choice for large scale applications work but it is my opinion that it is.GENERAL DISCUSSION Dr. P. Mansfield (Nottingharn)said I would like to comment on Dr. Erofeev's paper as follows Most of the early work on multipulse experiments was performed at or close to resonance and the theories developed were based on the projection of magnetization loss at the second solid echo. This procedure gives an exponential decay of successive echo peakes with an effective decay time constant T,,CCZ-~.This rather simple approach seemed to be confirmed by the experimental behaviour of the 19Fresonance dependence appeared to be confirmed over in single crystals of CaF,. Indeed the T-~ three and a half decades of T2evariation in these experiments. Further unpublished work on 31P in powdered Zn3P2 performed by Dr.K. Richards in 1969 and now shown in fig. 1 also strongly suggests that T2eis proportional to 10001 1 l 101d3 1OC o 10' T2e's 1 o 10 10 FIG.1 .-Plot of z against T, for 31P in powdered Zn3Pz. Slope of solid line is -5. T-~ over about three decades. The 90" r.f. pulse lengths used in these experiments were approximately 2.0 ,us. The solid line in fig. 1 is drawn with a slope of -5. The plateau in T, above 2.0 s is caused by rundown of the power supply with consequent degradation of the r.f. pulses from 90" to a smaller angle. In spite of this fact however the magnitude of T2eis observed to vary exponentially from about 50 ms to a value in excess of 1.0 s before equipment limitations are manifest.The shortest value of the pulse spacing z which still gives a good fit on the solid line is about 50 ps. The relatively longer T2of the phosphorus resonance allows a larger pulse spacing than could be used for 19Fin CaF, but still produces a greater effective line narrowing. In this sense the experiment corresponds much more to the ideal case where delta function 90" r.f. pulses are used. A difference between CaF and Zn3P2 which might play a significant role in pro- ducing the 2-5 dependence is that 31P exhibits some chemical shift anisotropy. This means that unlike 19Fin CaF, there is a built-in offset effect. On the other hand as I recall for relatively small offsets there were no significant changes in T2e. More recent work on line narrowing sequences like the MREV 8 cycle for example which is specifically designed to work off resonance shows a comfortable consistency with the zV5results on resonance in that theoretically the line width W slightly off resonance varies as Wccz4/Aw where Am is the offset angular frequency.This be- haviour seems to be confirmed experimentally. Dr. Erofeev's paper raises several questions (1) How are the different quanta1 absorption processes referred to in fig. 4 of his paper measu_red experimentally? In particular how is the process charac- terized by the operator &(t) isolated? (2) For z less than 6.0 ps there is a decrease in T2eindicated. Is this a pulse degradation effect similar to the one described above? (3) It is difficult to tell from the data corresponding to the &(t) process how good a fit GENERAL DISCUSSION it is to a slope of -4.In view of the roll-off for z< 6.0 ps and the fact that T2eis observed over less than two decades could it be that the observed slope is itself a manifestation of pulse droop? Prof. T. C. Waddington (Durham) (communicated) Could Dr. Haeberlen comment on the sensitivity of his final values for the difference tensor o& -to his chosen values of X(Pb2+) and X(Ca2+)? The reason I ask is that the value chosen in the paper for x(Ca2+) -27 x is nearly twice the value of x(K+) selected by Trew and Husain,l and also supported by my own analysis’ of the theoretical calculations and magnetic susceptibility data x(K+) = -14.5 x The tighter nuclear binding of the electrons in the isoelectronic Ca2+ ion would lead one to expect a lower value for x(Ca2+) than for x(K+).It is very difficult to establish an accurate value for x(Ca2+) but two separate calculations using the range of values ofX(Mg’+) given by Trew Husain and Siddiqi3 and then (a) assuming X(Mg2+)/X(Ca2+) = X(Na +)/x(K’) or (6) taking the difference between the measured values of X(Ca0) and X(MgO) give a value for x(Ca’+) of between -6 x and -8 x Dr. U. Haeberlen (Heidelberg) (communicated) As a matter of fact the value chosen for x(Ca2+) was not -27 x as given in the paper but -22 x cgs. units. I am grateful to Prof. Waddington for drawing my attention to this error. In order to bring internal consistency into his numbers I must assume that the number quoted for X(Mg2+) (-6 -8) x lop6 c.g.s.units is actually meant to be the value for Ca2+. If we insert a number in this range in the formula for ointer, eqn (1) of my paper it is not possible to obtain for the two proton sites in Ca-formate proton shielding tensors which have the same characteristics i.e. which have their most intermediate and least shielded directions along the same molecular directions. The value we have chosen for X(Ca2+) was obtained by comparing experimental suscepti- bilities of Pb- and Ca salts and by assuming X(Pb2+) = -47 x c.g.s. units. We are well aware that this procedure may introduce some uncertainties indeed the need of molecular and ionic susceptibilities which are not themselves experimentally definable quantities is one of the critical points in our analysis of intermolecular shielding contribution.Dr. P. Mansfield (Nottingham)said In spite of the remarkably fine data presented on amongst other compounds calcium formate where ‘H line widths of 34 Hz are quoted Haeberlen refers to the general difficulty of performing such line narrowing experiments except in well chosen single crystals. All the work reported has been achieved using the phase compensated MREV 8 multipulse sequence. In this cycle it is necessary to perform the experiments off resonance in order to achieve additional offset line narrowing or second averaging. It is well known however that too much offset either introduced experimentally or caused by intrinsic chemical shifts results in a broadening of the line.(A shift of 5 p.p.m. at 240 MHz is after all nearly 1.0 kHz!) For comparison with other line narrowing sequences the unscaled line width for ideal 90” r.f. pulses should be multiplied by 3/42 resulting in a true line width of about 72 Hz for the protons in Ca(HCOO),. There are a few multipulse cycles which although somewhat more complicated V. C. G.Trew and S. F. A. Husain Trans. Furaduy SOC.,1961 57,223. T. C. Waddington Trans. Furaduy SOC.,1966 62 1482. V. C. G.Trew S. F. A. Husain and A. J. Siddiqi Trans. Furaday SOC.,1965,61 1086. GENERAL DISCUSSION than the MREV 8 cycle are slightly better at line narrowing especially near to reso- nance. The PP 16 pulse sequence (see my paper) is one such cycle which has a scaling factor of -v’6 for ideal pulses.Nevertheless for a single crystal of CaF the 19F resonance with Bo along the [I 111 direction yields a true scaled line width of 70 Hz. with z = 6.4 ps. It would be interesting to see how well the PP 16 cycle performs for ‘H on Dr. Haeberlen’s spectrometer. Dr. U. Haeberlen (Heidelberg) said We have not tried the PP 16 cycle on our spectrometer. I am hesitant of using cycles with ever smaller scaling factors. There are good reasons to believe that the minimum linewidths which we have seen both from Ca-formate and CaF were not limited by any property of the multiple pulse sequence used but rather by such seemingly trivial things such as applied field homo- geneity. Remember we cannot shim using the actual crystal samples the values of TI are simply too long.When “ true ” linewidths are down to M 100 Hz or so the shape of the samples and details of their mountings have a strong influence on the ultimate resolution. This may not be so at 9 MHz but it is certainly true for spectro- meter frequencies of 90 and a fortiori 270 MHz. In spite of using spherical crystal samples and a “ shim sample ” of doped water matching in its geometry closely the crystal samples we have not mastered fully the applied field homogeneity problem. I would like to stress that although we are never satisfied with the resolution achieved we feel that meaningful applications of the multiple pulse techniques see e.g. your paper and interpretation of actual data obtained at some limited resolution are what is called for now and not so much the hunt for new records in terms of linewidths.Dr. Joan Mason (Open University) (communicated) Measurements such as those reported by Dr. Haeberlen given that they require great expertise and resourcefulness offer a unique opportunity to test and improve the theory of “ distant ’’ contributions to nuclear magnetic shielding. Because of well-known difficulties of shielding theory many or most theoretical treatments are restricted to the local term (arising from electrons on the resonant atom only). The “ distant ” contribution therefore includes even those from next (bonded) neighbours although the local term cannot of course be observed separately from these. Recourse to neighbour anisotropy approximations for the distant terms raises intractable problems of the extension of the neighbouring dipoles (since point dipoles give poor results) and their positioning (whether on atoms or bonds) as well as the distance at which the approximation is expected to be valid (discussed by Dr.Haeberlen). Flygare has remarked that group anisotropies derived from n.m.r. shift measurements are usually too small and sometimes not even of the right sign (adding “ The fact that magnetic susceptibility anisotropies derived from chemical shifts agree so poorly with direct measurements would seem to indicate that some other contribution to the chemical shift has not been properly evaluated .”)‘ Dr. Haeberlen’s experiments with metal formates have important advantages for a study in which the shielding contributions from the resonant atom and the near neighbours are held effectively constant so that the variation in the distant contribu- tion from different cations can be measured.Advantageous are the high sensitivity of the proton the small local shielding and the relatively large metal ion contribution. Furthermore with isostructural M” formates the variation in the shielding tensor should correlate with the increase in magnetic susceptibility of the cation down the ’ T. G. Schmalz C. L. Norris and W. H. Flygare J. Anier. Cheni. SOC.,1973 95 7961 ; W. H. Flygare Cheni. Rev. 1974 74 653; cf. also W. Haberditzl Angew. Chem. (Itit. Edn) 1966 5 288. GENERAL DISCUSSION group of the periodic table and the tendency (with the usual periodic irregularities) to decrease across the row.' If the technical difficulties can be surmounted the variation in the shielding contri- bution with distance from the metal ion and also with its electron configuration might be observed by comparison (for example) of the proton shielding in the metal hydride formate and a suitable acetylacetonate with appropriate metal ions.H H I I H C -?ho I 11 M 'M' 00 'M' In the acetylacetonates the (isotropic) shielding of the 3-proton tends to increase down the group of the metal and decrease across the row.' As an improvement on the dipole approximation simplified versions of the Ramsey theory have been used to calculate the shielding tensor for 19Fin crystalline MgF? and for the proton in d6 and ds metal hydrides4 and have been given also for d" and dlosZ ions such as Hg" and Pb".5*6 lnformation on the shielding tensor of a proton attached to a transition metal is eagerly awaited by inorganic chemists.Dr. A. M. Achlama (Rehocot) said Dr. Y. Zur and 1 have measured the e.f.g. tensors at the carboxylic and olefinic deuterons in potassium hydrogen maleate. As has been pointed out by Prof. J. A. S. Smith the orientation of the e.f.g. tensor of the carboxylic deuterons was the same as that of the chemical shift tensor of these protons.' In the case of the olefinic fragment however the least shielded component was in the direction of the C-H bond,8 but this also was the direction of the largest component of the (nearly axially symmetric) e.f.g.tensor. This component was in the molecular plane building an angle of 117.3 & 0.3" with the C=C bond whereas the crystallo- graphic value for the C-H bond direction was 1 15.8 1.5".9 Intermolecular interactions have been invoked for the interpretation of spectra of potassium hydrogen maleate where only olefinic protons have been substituted by deuterons. Pake doublets have been observed in the spectra of these deuterons originating in the dipolar interaction with the carboxylic proton of a neighbouring molecule. Dr. J. W. Emsley (Southampton) (partly communicated) The paper by Morris et al. is ambiguous about the presence of internal motion in the perfluoroalkyl chain. It is claimed that X-ray data and the S values show the impossibility of an all-trans configuration for the chain.But if rotational isomerism occurs the CF groups will have S values which vary along the chain a conclusion rejected on the basis that the P. W. Selwood Mugnetochemistry (Interscience New York 1956); G. Malli and S. Fraga. Theor. Chitn. Acta 1966 5 284. J. Mason unpublished observations. R. W. Vaughan D. D. Elleman W. K. Rhim and L. M. Stacey J. Chetti. Phys. 1972,57 5383. A. D. Buckingham and P. J. Stephens J. Chem. SOC. 1964,2747 and 4583. L. E. Orgel Mol. Phys. 1958 1 322. W. G. Schneider and A. D. Buckingham Disc. Firrcrclcry SOC.,1962 34 137. A. M. Achlama U. Kohlschiitter and U. Haeberlen Chetti. Phys. 1975 7 287. * A. M. Achlama H. Post and U. Haeberlen Cheni. Phys. 1978 31 203. S. F. Darlow Acta Cryst.1961 14 1257. GENERAL DISCUSSION 19Fspectra can be reproduced by a model which uses a constant S, value for each part of the alkyl chain excepting the end CF,. This contradiction may be a conse-quence of the assumptions made in analysing the data which for convenience I will discuss in separate parts. (1) The experiments measure @! the partially-averaged component of oialong the director (or perpendicular in the case of the hexagonal phase but a:. = -30;). This quantity 6; is related to components of O' in a molecule-fixed frame xyz with z along a CF bond by = OiSO+ S:zafzi-;(& -O;y)(s;xs:,) 0,; -+ s$dy + SSxdz + Sy2O;z. The superscript i refers to the seven CF groups. In their work Morris et al. assume xyz to be principal axes for O,in which case the terms involving off-diagonal elements of S are zero.But symmetry does not restrict the principal axes to lie in these directions and hence all the terms may be significant in magnitude. (2) If xyz is assumed to be a principal set of axes then 6; is a/ = o:so+ S:Zaiz+ ;(& -Ofy)(S;x -Even if values of atZ (oLX -a:,) are assumed from experiments on solids and ofsofrom isotropic solutions then there are still two unknowns on the RHS of the equation. It is doubtful that the lineshape for the CF resonances cannot be repro- duced by a model which assumes constant values of the matrix elements of ai as i varies but varying values of Siz and (Six -Sfy). (3) If the chain is rigid then it is possible to relate the individual 5,:to one molecule- fixed set of axes as suggested by Morris et al.However it is not possible to choose these axes on symmetry grounds to be principak axes for S because even in the all- trans shape there is at most only a molecular mirror plane. Rotation of the whole molecule does not affect this conclusion for a liquid crystal phase and thus the analogy with rotation of molecules in solids is misleading. (4) For hydrocarbon chains in lyotropic mesogens it is usually assumed that internal motion does take place and also that it is possible to describe the partial averaging of second-rank quantities in terms of one ordering matrix which is diagonal and axially symmetric when one axis is chosen to lie along " the long axis of the molecule ". However the assumption of a single S matrix depends upon the relative rates of internal motion \lint and motion of the whole molecule relative to the director IJ~,,~.If IJ,"~ Y~~~ the averaging can be done with one S matrix but which is not necessarily axially symmetric. If bvint 4vmOIthe averaging process cannot be done with one S matrix but must invoke a matrix S" for all n configurations adopted by the chain and each S" has a differently orientated set of principal axes. (5) 1 conclude with the observation that liquid crystal solutions are complex! The presence of internal motion in a mesogen introduces several additional unknown quantities and it is not possible to reach precise conclusions on conformational mobility unless there is a wealth of experimental data.I doubt that the present experiment can yield enough information to decide between rigid and flexible chains. Dr. P. Morris (Nottinghanz) (communicated) For perfluoro-octanoate groups in liquid crystal phases the 19Fchemical shift tensor is unquestionably axially symmetric with a,!oriented parallel to the long molecular axis. [See our ref. (2) fig. 4.1 Our experiment measures the shift components a; a (a; # -i-a,f) which depend on the motional averaging in a complex manner. However this dependence manifests itself in terms of a simple scaling S' of the shift anisotropy Ao' = a,f -aiL. Whilst GENERAL DISCUSSION it is just conceivable that the same scaling factors S’ could arise from averaging pro- cesses which vary down the chain the strong implication is that within experimental error the motion is independent of position.To estimate “ absolute ” order parameters the known shift tensor for low tem- perature PTFE (whose principal axis system does not correspond to the usual molecu- lar frame) is averaged by rapid rotation about the long molecular axis. The result is an axially symmetric tensor with anisotropy Ao % 104 p.p.m. Any reduction from this value is attributed to motion about the normal to the surfactant water interface which can be described by a single order parameter S owing to the axial symmetry imposed by the rapid rotation. That it is not unreasonable to average over the rota- tion first is indicated by the good agreement obtained between the shift anisotropy of a rotating PTFE molecule calculated from the static shift tensor and that observed experimentally at room temperature.Finally we make the comment that higher frequency measurements would allow separation of the inequivalent 19F resonances allowing accurate measurements of the shift anisotropy as a function of chain position. This would be a rather more sensi- tive test of the degree to which Sremains constant. Dr. G. J. T. Tiddy (Port Sunlight) (conzrnunicated) In answer to Dr. Emsley’s comments 1 would like to make the following observations. Concerning his second point; it is of course possible to use more parameters (Sizetc. dependent on i) to fit the spectrum. But we thought it generally undesirable to introduce more parameters than necessary to explain the results.Concerning his third point; the chain is not “rigid”. Concerning point (4); for hydrocarbons the liquid-like nature of the chains is deduced from the magnitude of transition heats for the l.c./gel phase transition (almost the same as for melting hydrocarbons) the rapid self-diffusion of surfactant (E -loF8 cm’ s-I) the n.m.r. proton second moment (too small for rigid solids) the ’H order parameters (also too small for rigid solids) and the absence of sharp high angle X-ray lines. However order parameters are similar for the part of the chain adjacent to the head group and only decrease for the last 3 or 4 carbons. For fluorocarbons we can say (i) Transition heats for solid + H,O -+ 1.c have similar magnitude. or solid -+ liquid (ii) The 19Fsecond moment is smaller than for PTFE.(iii) The self-diffusion coefficient = 3 x lo-’ cmz s-’ for Li PFO. (iv) No high-angle X-ray spacing (as might indicate ordered rigid chains). (v) The order parameters are too small for no molecular motion. Thus we conclude that we have disordered chains with motion. Now let us consider the arrangement of chains. We have data from X-rays that the fluorocarbon layer thickness is about 17 A in our samples and we expect ~22.5 A for a bilayer with all-trans chains at right angles. This is clearly inconsistent. The three models (fig. 2)could account for the reduced bilayer thickness. Case (a) the order parameters exclude this model with ordered packing because the tilt angle required is too large.If chains have no regular packing then they will undergo exchange between different directions and conformations and will look like (c). Case (6) if we consider the cross-sectional area of each segment of chain the order parameter will relate (in part) to the fraction of “ all-trans ” molecules present. GENERAL DISCUSSION Chain segments near the head group have a large surface area and so a small order parameter. Segments near the tail have half the surface area and so are nearly “ all-trans ”. From X-ray data we estimate the surface area/mol to be 45-50 A2. Half of this is close to the area required for close-packed “ all-trans ” groups. Thus for interpenetration or interdigitation we expect very high order parameters for the ter- minal CF and CF groups (>0.6) and low order parameters for groups near the head group.(A rough calculation from X-rays shows that half the chain in “ all-trans ” is interdigited.) If the first part of the chain is extended one may ask what occupies the residual space. (a1 (b) (C) FIG.2.-Models explaining reduced bilayer thickness (a) tilted chains (b) interpenetration and (c) disorder. The solubility of fluorocarbons is less than hydrocarbons. If we suppose that H20is there then the dimensions calculated from X-ray studies would be incorrect because they involve the assumption of separate alkyl and water regions and there would be much less need to postulate any interdigitation. Again we get higher S values with the hexagonal rather than the lamellar phase in agreement with the X-ray dimensions.If the lamellar phase is interdigited the question which naturally arises is why the hexagonal phase occurs. It is unlikely to have the same interdigitation yet the order parameters are higher. This would sug- gest that our model for LiPFO is the most plausible one. Dr. P.Mansfield(Nottingharn) (communicated) In reply to Dr. Emsley’s comments I would like to take each point in turn. First let me say that we do not claim that all alkyl groups along the LiPFO chain have the same order parameter S only that we cannot distinguish experimentally between them. Indeed had we the facility to work at frequencies higher than 9.0 MHz it would be possible to separate each alkyl group known on the basis of their high resolution isotropic shifts to be chemically slightly different.The changes in S along the chain due to rotational isomerism could if present then be studied directly. It is of course appreciated that the principal axes system for the chemical shift tensor in I9Fmay not quite coincide with the z axis lying along the C-F bond but it seems a plausible and good approximation. As stated above a single value of S does allow quite good fits to the observed experimental data. Small changes in Sof the order of -&0.02 give marked deviation from the best fit of our data. Such small changes in S although applied to all alkyl groups along the chain would seem to suggest that a significant spread in S values along the chain would result in a worse fit than we obtain.In the rigid chain the individual C-F bond directions are tilted (as in PTFE for example) and presumably form part of a helix. However we assume implicitly that the C-F bonds are all normal to the chain axis. [See ref. (20) in our paper to our earlier work on PTFE.] In this case it is possible to define one transformation from 170 GENERAL DISCUSSION the PAX system to the MOL system. The rotational transformations about the molecular axis then follow. It is not intended to suggest that the motion and conformation of the alkyl chain is in reality simple. However the model of LiPFO which we have analysed does seem to give remarkably good agreement with the experimental results. Some of the agreement could well be fortuitous in the sense that higher resolution data may well indicate interesting deviations from our model.But with our present experimental limitations this must remain in the realm of speculation. Dr. N. Boden (Leeds)said The partially averaged values obtained for the principal components of the 19Fchemical shift tensor are seen to be essentially the same for all CF2 groups in the perfluoro-octanoate chain in the lamellar phase. This is an interesting result which could be interpreted as implying that either (i) the amphiphile reorients as a " rigid " molecule or (ii) all CF2 segments are similarly affected by internal rotation. The latter behaviour would be in marked contrast to that observed for hydrocarbon amphiphiles. Nevertheless on the basis of the consistency between the chain length calculated from and that obtained from X-ray data Morris et a/.conclude that this is the correct explanation for their measurements. I would like to ask whether this agreement is a coincidence? The reasons why 1 think it might be are as follows. (a) Using the molecular dimensions given in the paper the numerical coefficient in the above formula comes out as 1.54. (b)The table below compares values of bilayer thicknesses simi- larly obtained for the lamellar phase in a 45% w/w mixture of caesium perfluoro- octanoate and water.' temp/"C 23 25 30 35 40 45 50 &/A (neutron diffraction) 17.5 16.9 16.0 15.5 15.2 15.1 15.0 do/A(order parameter) 17.3 17.2 17.1 16.9 16.8 16.5 16.0 Note how the two sets of values cross at low temperatures but diverge at higher temperatures particularly in the mid-temperature range.Dr. G. J. T. Tiddy (Port Sunlight) (coniniunicafed):If the amphiphiles are rigid and in the " all-trans " conformation then our order parameters would not be con- sistent with the bilayer dimensions. Alternative bilayer models are set out in answers to Dr. Emsley's question. Since the equation for (L) is derived for CH2 groups'it is perhaps surprising that it fits our results and the agreement with our results is possibly a coincidence but of course the chains are not stiff rods. Dr. Boden's data are for a CsPFO sample in the " nematic-lamellar phase " which has a viscosity that is sufficiently low for the sample to align in a magnetic field. Such low viscosities are unlikely with stiff chain molecules.For example the " gel " phases prepared from hydrocarbon surfactants which are known to have rigid chains have high viscosities. The calculations of aggregate dimensions using X-ray or neutron diffraction involve an assumption about the density of the fluorocarbon layer (assumed to be independ- ent of water thickness i.e. independent of surfactant surface area). In my opinion this may not be valid and so the dimensions quoted by Dr. Boden may not be correct. N. Boden M. C. Holnies K. J. McMullen and P. J. Jackson unpublished results. GENERAL DISCUSSION 1think that a correct model for the chains is one with chains having rapid motion about a long axis (7; z 10-lossay) and (possibly) " slow " interconversion between different conformations z > 10 z:.This must mean that the " free " space in the fluorocarbon layer is more than in a liquid hydrocarbon i.e. that the chains do not pack together all that well. 1 note that P. J. Flory in his book Statistical Mechanics of Chain Molecules (J. Wiley N.Y. 1969) says on p. 157 '' . . . a chain molecule must be endowed with a minimum tortuosity as a requisite for packing to high density in the random-coiled form . . ." Dr. J. W. Emsley (Southampton)said The case of the multiple quantum spectrum of the protons in the liquid crystal 5-CB raises additional points to those mentioned for benzene. First the interacting spins are eight protons and eleven deuterons. At least one 2H-1H dipolar coupling is large (z60 Hz depending on the reduced tem- perature) and might be expected to affect the spectra.However does the use of a spin-echo to improve line widths complicate the interpretation of a spectrum from strongly coupled protons which are interacting with strongly coupled deuteriums? Secondly the eight protons give rise to a spectrum which depends on fifteen inde- pendent parameters twelve dipolar couplings and three shifts. Is it practicable to deduce all these quantities with high precision from the q = 7 and 6 spectra? Third computer resolution is a major problem for complex single-quantum proton spectra of liquid crystals. in the TPPI echo spectra it seems to be necessary to record all orders of q simultaneously which would seem to impose even greater demands on computer storage than when only the q = 1 spectrum is obtained.How much computer storage is required to define the TPPI echo spectrum of 5-CB? Mr. D. P. Weitekamp (Berkeley) said The use of a single echo pulse will lead to complications in the spectrum of the proton spins to the extent that the proton deuterium interactions do not commute with the interactions between like spins. This will necessitate deuterium decoupling which could be achieved by double quantum decoupling,' irradiation of the quadrupole satellites of the offending deu- terons,2 or perhaps more simply by a train of proton TC pulses during the evolution period tl. The latter means of decoupling has the additional recommendation that it will simultaneously remove chemical shifts. This not only reduces the number of inde-pendent parameters but removes those parameters most difficult to estimate and of least interest for a structural determination.Further reduction in the number of parameters is possible to the extent that one is willing to incorporate chemical intuition and literature values of certain bond distances into a model which relates the various dipolar couplings. Ultimate precision will of course depend on the sensitivity of resolved transitions to variations in the parameter set. A confirmation of a para- meter set derived by the relatively simple analysis of the higher order spectra would be the successful calculation with this set of lower orders. The computer storage requirements needed do indeed grow large. The time incre- ment in the f dimension needs to be sufficient for a Nyquist frequency of NAw and Aw needs to be as great as the width of a single order.For N = 8 Aw = 40 kHz and a spectral resolution of 10 Hz per point storage of 64 kwords is needed. Dr. D. T. Edmonds (Oxford)said The interpretation of a multiple quantum spec- trum is tractable only if the N spin flips occur within a single system and not partially A. Pines S. Vega and M. Mehring Phys. Rev.3,1978 18 112. * J. W. Emsley G. R. Luckhurst G. W. Gray and A. Mosley Mol. Phys. 1978,35 1499. GENERAL DISCUSSION within the system and partially within near-neighbour systems. Taking a single molecule as the system this means that intramolecular spin-spin interactions must be much stronger than any intermolecular spin-spin interaction.(i) In general how do you envisage that the molecule under study be isolated from its environment and how can the efficacy of such isolation be tested experimentally? (ii) Will the necessity for such isolation prove a serious limitation of the applica- bility of the technique? Mr. D. P. Weitekamp (Berkeley)said In the liquid crystal systems with which we are currently concerned molecular diffusion reduces the intermolecular couplings and allows a treatment in terms of intramolecular terms alone. Of course the dipole Hamiltonian does not formally distinguish between intermolecular and intramolecular terms and in general one would need to dilute a molecule in an isotopically distinct background to be certain that only intramolecular terms were effective.One may prevent certain lines from developing by keeping z much shorter than the inverse of some small dipolar couplings. This will reduce the magnitude of those transitions which depended on this coupling for their intensity and thus give some measure of control over intermolecular transitions if intermolecular couplings are the smallest ones. This control will allow work at practical isotopic or chemical dilutions in systems where diffusion does not provide sufficient isolation. One experimental test of isolation is spectral simulation including the simplest test of checking that the only significant contribution to the N order spectrum of a presumed N spin 1 system is a single line at Nhw. Another test would be further dilution to the point of diminishing change in the spectrum.Prof. E. L. Hahn (Berkeleq,) said 1 would like to hear a discussion of the signifi- cance of RF pulse amplitude for the various pulses of the TPPI echo experiment. Mr. D. P. Weitekamp (Berkeley)said The amplitude requirement for the prepara- tion pulses is not at all stringent. The derivation of eqn (1 1) of our paper holds equally well for a preparation sequence of arbitrary amplitude frequency and phase so long as the high field approximation holds. It merely states the manner in which any coherences which may be produced are altered when this arbitrary sequence is repeated with all radiation phase shifted by q. If one hopes substantially to excite all or most of the multiple quantum coherences then the preparation sequence should supply irradiation over a substantial part of the spectral width and should extend in time for a period of at least the inverse of some dipolar couplings.Many such schemes can be imagined. The echo pulse should be much shorter than the inverse couplings if we are to neglect the internal Hamiltonian during the pulse. This requires that the nutation frequency cul be greater than the dipolar couplings. This is technically less difficult to achieve than it is in a multiple pulse line narrowing experiment in which the probe Q must be suppressed. Of course the echo is unnecessary if magnet homogeneity is sufficient. The requirements of a detection pulse or sequence are similar to those of the preparation sequences and a variety of schemes deserve consideration.Dr. P. Mansfield (Nottingham) said The multiple quantum transitions are ob-served in an effective rotating frame so that the truncated dipolar interaction is re- sponsible for the observed multi-line spectra. If this is the case then presumably all quantum transitions have the same spectral density coupling to the lattice. However GENERAL DISCUSSION it would be valuable if laboratory frame multiple quantum transitions could be ob- served in small molecules with such clarity. Such experiments if possible might yield useful spectral density information over a wider frequency range. (1) Have you any comment on this aspect of multiple quantum transitions? (2) Even in the rotating frame inequivalent nuclei in small molecules may relax differently.Can such differential spin lattice relaxation effects be observed in the TPPI echo spectra? Mr. D. P. Weitekamp (Berkeley)said Within the range of validity of the Bloch- Wangsness-Redfield type of relaxation theory spectral densities at frequencies higher than twice the Larmor frequency do not appear. This is because the effects of random time dependent terms in the Hamiltonian are accounted for only up to the first non- vanishing order in the perturbation theory. This involves correlation functions of first and second rank tensor operators. For the relevant case of dipolar relaxation and a dipolar spectrum this approach is certainly valid when Q~T ',,* 1 where (riD indicates a typical eigenfrequency of the average dipolar Hamiltonian and T a correla- tion time for the motion.The high field approximation which leads to the use of the truncated dipolar Hamiltonian enforces the conditions that the eigenoperators of HDare also eigenoperators of Iz with eigenvalue q and that the relaxation matrix does not connect eigenoperators with different q. One might relax these conditions by following the relaxation in low field but then one has reduced the range of the spectral densities involved by reducing the Larmor frequency. The possibility of observing a truly multiple phonon relaxation mechanism is an intriguing one. Such a pheno- menon must be sought in a situation where the lower order terms are not sufficient and a treatment including multiple time correlation functions is warranted.Thus in neither high nor low field is the frequency range of spectral densities substantially different for the single and multiple quantum experiments. The familiar relaxation matrices suffice and it is the initial conditions and the observables which increase in variety. This makes it possible to measure many more linear combinations of spectral densities and thus to sort out individual spectral densities. These consti- tute the information available from the different relaxation times of the spin system. The TPPI echo experiment is a convenient way to separate the orders and eliminate inhomogeneous broadening. It will be valuable for measurement of both line widths and spin lattice relaxation rates with a variety of initial conditions.Work in progress in our laboratory has demonstrated its usefulness in studies of relaxation by para- magnetic impurities and by con formational exchange. Dr. K. J. Packer (East Anglia) said 1 would like to support Mr. Weitekamp's answer to this question by mentioning some work we have recently carried out.' We have calculated the response to a 90,-~-U,-T-0 -+ t pulse sequence of a spin-1 subject to the Hamiltonian H = Hz f 11 + HQ(~) where H is the Zeeman interaction 11 a secular quadrupole interaction. h pro-duces a doublet splitting in the spectrum 2QQ whilst H,(t) determines the relaxation properties via its spectral densities j,(c~). The 90,-~-0, pulse pair distributes the entropy associated with the equilibrium magnetisation Mo amongst the diagonal (zero quantum) single and double quantum elements of the spin density matrix in a manner determined by the product R,T and the value of 0.For example if R,T = nn/2 (n odd) and 0 = 45" then three quarters of the order is placed into the zero S. B. Ahmad and K. J. Packer Mol. Phyh. 1979,37 47. GENERAL DISCUSSION quantum states and the remaining quarter in the double quantum states. The third pulse produces a signal S,,(t),which can be analysed to give the relaxation properties of the various density matrix elements in the interval T. All density matrix elements relax by combinations of the spectral densities jQ(0),jQ(~,,) and jQ(204). For ex- ample the double quantum elements relax according to a rate given by 6jQ(o,) -+ 12jQ(2u0).Thus it is the mechanism of relaxation (quadrupolar in this example) which determines which frequencies are involved in the spectral densities not the quantum multiplicity of the states relaxing. What this means as Mr. Weitekamp has already pointed out is that by studying the relaxation of the various multiple quantum states one may determine the values of the individual spectral densities. Mr. D. P. Weitekamp (Berkeley) (communicated) 1n response to comments made informally by Dr. Haeberlen I would like to remark that the frequency of the highest order transition of an isolated molecule is determined by the sum of the chemical shifts of the spins involved and is unaffected by the dipolar couplings. The powder pattern or rotation pattern of this transition will reflect the sum of the chemical shift tensors which is itself some new second rank tensor.The principal components of the sum tensor depend on the relative orientations of the individual spin tensors and their principal components. If these individual principal components are known from a multiple pulse powder spectrum then the principal components of the sum tensor obtained from a multiple quantum powder spectrum provide information on the relative orientation of the individual spin tensors. In favourable cases this would provide the tensor orientations in the molecular franie without a need for a single crystal. This approach would have the additional advantage of insensitivity to pulse im- perfections. This would make its use over a wide temperature range much simpler.Analysis of the lower order powder spectra would involve consideration of both dipolar and chemical shift terms and could in principle provide additional information on the tensor orientations since the dipolar terms have an obvious relation to the molecular frame. If a multiple pulse line narrowing sequence were applied during the evolution period the spectra of all orders would be free of dipolar terms but would be sensitive to a variety of linear combinations of individual spin tensors providing a wealth of information on the relative orientations of these tensors. This approach would have the additional advantage of removing intermolecular dipolar broadening. Dr. A. N. Garroway (Washi17gton)(conmunicated) For the three glassy polymers studied Dr.Stejskal finds that the spin-lattice contribution to the average carbon rotating frame relaxation rate (Tl,l(C)i-' is relatively constant ranging from 81 to 85 (x(his table 1). Yet the local fields are quite different due to motional averaging. What is the origin of this clustering near 80 >< spin-lattice contribution? Dr. E. 0. Stejskal (St. Louis) (communicated) The local fields are determined primarily by the strength of the proton interactions and only secondarily by motional averaging. On the other hand TPLis directly determined by molecular motion. Thus the two quantities are free to vary independently and the apparent clustering is fortuitous. Furthermore no particular importance should be placed on the fact that these numbers are so close together.The data analysis was not intended to be more than semi-quantitative. Mr. E. M. Menger (Nijmegen) said As a comment to Dr. Stejskal's paper we GENERAL DISCUSSION would like to report I3C TI,measurements on polyoxymethylene (Delrin) performed at 45 MHz using a 13Cr.f. field of 25 kHz. For samples rotating at the magic angle a clear double-exponential decay of the 13Cmagnetization prepared by 500 /is H-13C cross-polarization as a function of the hold time T was observed. A typical T, measurement at a sample rotation fre- quency of 2.1 kHz is shown in fig. 3(a). The I3Cspectrum of a stationary sample consisting of a motionally narrowed line (x800 Hz) with a short TI (~3.0ms) superimposed on a broad chemical shift powder pattern with a much longer TI (z17.5 ms) convinced us that the polymer was partly amorphous and partly crystalline r cn 0 E 0.01' I I I 1 I I 1 0 5 10 15 20 25 30 35 hold time r/ms 0 5 10 15 20 25 30 35 hold time r/ms Flci.3.-W TI/)measurements on Delrin see text.(N) I3Cmagnetization prepared by 'H-I3C cross-polarization (i) TI/);t 1.5 ms (amorphous part); (ii) TI/>% 17.5 ms (crystalline part). (6) I3C magnetization prepared by a 90 pulse TI/]x 17.5 ms (crystalline part). GENERAL DISCUSSION the amorphous part having the short TI and the crystalline part the relatively long TlP. A noticeable dispersion of relaxation rates due to anisotropy was not observed for stationary samples neither for the crystalline part nor for the amorphous part.T, experiments on samples rotating at the magic angle where the 13Cmagnetiza-tion is prepared by a 13C 90" pulse rather than cross-polarization reveal a single- exponential decay of the l3C spin locked magnetization as a function of the hold time T if the repolarization time is short (1 s) the T, being z 17.5 ms. A double exponen- tial decay is observed if the repolarization time is long (30 s) indicating a short Tl for the crystalline part and a relatively long T for the amorphous part. A typical experi- ment using a repolarization time of 1 s is shown in fig. 3(6). Experiments at various magic angle spinning frequencies showed that the TIPof' the crystalline part which is thought to be dominated by spin-spin contributions as suggested by Stejskal et ul.as well as the dipolar relaxation time T,, are virtually independent of the spinning frequency. The TI of the amorphous part however thought to be dominated by spin lattice relaxation showed a marked dependence on the spinning frequency as shown in fig. 4. \ \\ \ I I I I I I 123456 magic angle spinning frequency/ kHz FIG.4.-Variation of the TIPof the amorphous part of Delrin with the magic angle spinning frequency. Another interesting observation can be made by studying the width of the 13C n.m.r. line as a function of the spinning frequency. Since the crystalline and amor- phous parts have quite different relaxation times Tl and TI,we were able to record spectra where both the crystalline and amorphous parts contribute to the linewidth for exaniple by performing a standard cross-polarization experiment and spectra where the linewidth is completely determined by the crystalline part for example by performing a standard cross-polarization experiment followed by a long spin lock pulse T (T >?> TI,of the amorphous part) or by preparing the 13Cmagnetization by a 90 " pulse using a repolarization time which is much shorter than the 7',of the amor- phous part.At relatively low spinning frequencies (say 2 kHz) the composite linewidth is GENERAL DISCUSSION somewhat larger than the linewidth determined by the crystalline material alone. At the highest spinning frequencies we could reach (~5.5 kHz) a considerable line broadening of the composite line was observed while the linewidth of the crystalline material remained the same.This seems real evidence that at high spinning frequencies stress in the material increases the chemical shift dispersion in the amorphous part while this has no effect on the chemical shift dispersion of the crystalline material. Dr. E. 0.Stejskal (St.Louis) said We have made a few cross-polarization measure- ments on polyoxymethylene with a 13C r.f. field of 25 kHz. In particular our r, data at that r.f. field are quite similar to those shown in fig. 3(a)of the previous remark. However we feel that a 'H r.f. field of 25 kHz is marginal for both spin locking and dipolar decoupling in the more rigid regions of polyoxymethylene and may distort their representation in the 13C spectrum.For materials with such strong proton interactions we prefer r.f. fields of at least 30 kHz. We disagree with a few aspects of the interpretation of the data in this comment namely the assignment of the short-TI long-TI, phase as the crystalline part. To test this assignment Dr. M. D. Sefcik of our group has obtained non-spinning spectra of polyoxymethylene (f.t. at 15 MHz with 36 kHz pulsed dipolar decoupling during data acquisition and without C.W. proton saturation for n.0.e. at other times) for 1 and 30 s repolarization times. The spectrum with the shorter repolarization time has a smaller (but not negligible) contribution from the more rigid component. Furthermore the T, associated with the short-T phase is too long for an r.f.field so close to the local field. Since the basis for assigning this phase is the behaviour of the line shape in a non- spinning T, experiment we must question that behaviour. In our spectra we can clearly see the amorphous phase as distinct from the central maximum in the well defined chemical shift anisotropy pattern of the crystalline phase [fig. 17 in our ref. (15)]. It is much too narrow (5-10 p.p.m.) to correspond to the portion of the spectrum referred to in this comment ( FZ 800 Hz or z 18 p.p.m.) which suggests that far too much of the spectrum has been interpreted as due to the amorphous phase. Perhaps we are looking at samples with different thermal histories (we have seen a line-shape dependence on thermal history) or perhaps the marginal decoupling has reduced the resolution.Incidentally fig. 3(a) would seem to suggest that the initial slope of this decay curve has been assigned to a particular phase. In fact in a multiple-phase system the initial slope yields a relaxation rate corresponding to a weighted average of all the relaxation rates of all the phases present. The spinning dependence of TIPshown in fig. 4 of the previous remark is not unexpected. There are many ways that spinning may modulate the interactions responsible for relaxation as we note in the discussion section of our paper. Stress effects are also possible although we have looked for and have been unable to detect their existence in other polymers. Probably the sharp initial drop in TI is due to the collapse of the dispersion of relaxation rates due to orientation relative to the labora- tory field.In summary polyoxymethylene is a complex system involving at least two phases each of which is far from homogeneous in its relaxation behaviour. It does not enjoy the advantage of clearly defined chemical shift differences to aid in its interpretation. Dr. A. N. Garroway (Washington) said An r.f. field of 25 kHz is very low for GENERAL DISCUSSION rather rigid materials and I would expect to see a substantial spin-spin contribution to rotating frame relaxation with a time constant of the order of 1 ms. The observed drop by a factor of two to three in the reported Tlpon spinning could possibly reflect an averaging over different orientations.This averaging would occur for both spin-spin and spin-lattice contributions. Dr. Stejskal may be able to com- ment further on that aspect. The increase in linewidth at the high spinning rate of 5.5 kHz may indicate mole- cular motions at the spinning frequency which are subverting the averaging of the anisotropy pattern by magic angle rotation. Further as the spinning also removes the dipolar interactions one effect of high speed spinning is to put 5.5 kHz sidebands on the decoupler frequency of 25 kHz. Hence the spinning may reduce the efficiency of the carbon-proton dipolar decoupling and lead to increased broadening. Varying the r.f. field strength would be useful. Dr. P. Mansfield (Nottingharn) said All the double resonance studies of 13Chave been performed by what is now known as the direct method.In assisting in the extrication and separation of TI and cross-coupling relaxation effects would not observation of the proton spins be of value? An intriguing possibility might also be to remove the I-S dipolar interaction during the 13C hold period in the T,,(C) measurements. This can be achieved by a large spin stirring pulse H, which severely violates the Hahn condition. A string of short 90" pulses will also achieve the same end so long as the mean r.f. field again violates the Hahn condition. Dr. E. 0.Stejskal (St.Louis) said No doubt there are cases where changes in the proton polarization could be used to estimate the magnitude of the spin-spin coupling to the 13C spins in the T,,(C) experiment.For instance after a Tlp(C)experiment in which the spin-locked carbon polarization is not achieved by cross-polarization but rather by a conventional spin-locking procedure following thermal equilibration (without any irradiation of the protons) there should be order in the proton dipolar field observable by means of adiabatic remagnetization into the rotating frame as a consequence of any spin-spin relaxation mechanism. (Alternation of the carbon spin temperature will facilitate detection of this polarization.) However since most of the systems we have studied are dominated by spin-lattice relaxation with T,, Tlp(H) and T,,(C) much shorter than T,,(ADRF) this experiment will not necessarily be an improvement over the direct method. Furthermore since there is no spin diffusion among the carbons the direct method permits relaxation of chemic- ally distinguishable carbons to be studied independently.Spin diffusion among the protons would tend to average the various relaxation rates even if some kind of proton line-narrowing technique were able to identify the protons attached to different carbons. Indeed in those systems where spin diffusion among the protons does not average Tlp(H) to a single value we prefer to determine that relaxation parameter by means of the carbon signal in a cross-polarization experiment via eqn (7) of our paper because of the clearer connection between relaxation and chemical structure. Dr. K. J. Packer (East Anglia) said Both Dr. Garroway and Dr. Stejskal are con- cerned with distinguishing spin-spin from spin-lattice processes when measuring TI for a magnetically dilute spin system (e.g.13C) in the presence of an abundant spin system (e.g. 'H). This complication arises because in the absence of a de- coupling field at the proton frequency there is the possibility that the cold rotating frame Zeeman reservoir of the I3C spins may be heated by cross-relaxation to the GENERAL DISCUSSION 179 proton dipolar reservoir and thence coupled to the lattice. I would like to ask what I suspect is a naive question which relates to the method of measurement. Would it not be possible to carry out the T, measurement for the 13Cspins in the presence of a proton decoupling field but one that is severely mis-matched with respect to the Hartmann-Hahn condition.In principle it would seem that this might allow an isolation of the pure 13C spin-lattice processes from the spin-spin processes. Dr. E. 0.Stejskal (St.Louis) said Because I3Cis a rare spin TPLis determined by fluctuating magnetic fields arising from the motion of nearby protons the abundant spin. The T,,(C) experiment as defined is performed in the absence of irradiation of the protons. To irradiate the protons strongly will modulate the magnetic field giving rise to TpLand hence change it. In fact it is necessary to replace TQLin eqn (7) and (8) of our paper with TpL’to take the presence of the proton r.f. field into account. The TpLmeasured in the severely mis-matched experiment would not be the one desired.Dr. A. N. Garroway (Washington) said Under proton irradiation proton dipolar order is still present but in the rotating frame dipolar reservoir and spin fluctuations still persist in general. What may well prove useful is to suppress proton spin fluctuations by off-resonant proton irradiation so that the effective proton field is at the magic angle as in the Lee and Goldberg experiment. Because of the exponential dependence of the carbon-proton spin-spin processes on proton fluctuation time z,, the magic angle need not be well set. Dr. W. S. Veeman (Nijmegen) said Preliminary results of TI measurements on polyoxymethylene (Delrin) via the r.f. pulse sequence 90z-z-45;-t-45; on the proton spins with magic angle spinning of the sample are shown in fig.5 (p. 180) for three different spinning rates. Although these results are somewhat complicated by the fact that both the amorphous and crystalline part of the sample contribute to the signal we find for the FID amplitude as a function oft an oscillation with frequency equal to the spinning frequency superimposed on a more or less exponential decay. The amplitude of this oscillation seems to decrease at the highest spinning frequency of 5450 Hz. Does not this imply that spinning the sample at a few kHz still should be considered as an adiabatic variation of the local field‘ and how does this agree with T, measure-ments at lower spinning frequencies? Dr. A. N. Garroway (Washington) said These are very intriguing results. I have not looked in detail at the fate of dipolar order under high speed magic angle spinning; for the purpose at hand I only wish to establish that dipolar order decays due to spinning.As pointed out by Pourquie [ref. (27) of our paper] the decay of dipolar order under slow perpendicular spinning does indeed contradict the supposi- tion that the dipolar system follows slow motions perfectly adiabatically. The TI experiment under high speed magic angle spinning poses some conceptual problems. The dipolar hamiltonian is modulated at f2 and 2f2 and there is no time independent dipolar hamiltonian to define clearly the dipolar reservoir. Similarly spin diffusion is reduced slowing internal thermalization and coinplicating the estab- lishment of dipolar order by the two pulse method. I think the oscillation in dipolar order that you observe represents the substantially non-adiabatic nature of the evolu- M.Goldman Spin Temperature and Nuclear Magnetic Resonance in Solids (Clarendon Press Oxford 1970). GENERAL DISCUSSION I I I 500 1000 1500 t/ps 0 (b) 0 oooooo 00 00 0 00 O00 t/ps ooo 00 00 3t O0 0 I I I 500 1000 1500 t Ips FIG.5.-TID measurements on Delrin at various magic angle spinning frequencies see text (a)550 (b)2800 and (c) 5450 Hz. tion the short correlation time limit of QT < 1 is no longer valid. The " sudden " approximation may be more suited at high speed. Indeed this behaviour may be analogous to the experiment discussed by Jenner et al. [ref. (19) of our paper] in which a dipolar ordered state is irradiated with a large r.f.field. After the field is turned off the spins thermalize with the new dipolar hamiltonian and so the oscillation of the observed magnetization reflects oscillation of the local field; in that case the oscillation is at 2 wl where coI = yB,. Dr. R. K. Harris (Norwich) said The observed peak widths of the spectra in fig. 3 of Dr. Garroway's paper vary widely presumably partly due to heterogeneity of the local environment (both intra- and inter-molecular) and partly due to lifetime broaden- ing. The former effect is of considerable chemical interest. What qualitative or quantitative conclusions can be drawn from the data regarding this heterogeneity? The sharpness of the signal for the central quaternary carbon of DGEBA has its parallel for the similar carbon of amorphous polycarbonate as confirmed by observa- tions in our own laboratory.Dr. A. N. Garroway (Washington) said The lifetime broadening in the spectra GENERAL DISCUSSION arises from molecular motion at the decoupler frequency wlH,for which decoupling is inefficient. Hence the motional contribution to the carbon Tl provides an esti- mate of this broadening because in general the proton decoupling and carbon spin locking frequencies are comparable c'llH E wIc. At room temperature for this epoxy I find that the lifetime broadenings inferred from TI,,,range for the various lines from about 10 to 35% of the measured widths at a carbon frequency of 15 MHz and decoupler field of 55 kHz.The carbon methyl line broadens and indeed disappears around 150 K. This is qualitatively consistent with the extrapolated temperature dependence of the methyl carbon Tip. Near the glass temperature 1 have some indication that all the lines broaden. For highest resolution one should work at as high a temperature as possible up to the point of TI,,lifetime broadening. High temperature also can average out some chemical shift broadening due to conformational interconversion. For polymers distribution of chemical shifts appears to be the dominant broadening mechanism. The quaternary carbon is well buried in the molecule and so rather oblivious to other conformations and hence yields the narrowest line in the polymer. Dr. E. 0.Stejskal (St.Louis) said 1s it necessary to wait as long as 500 ,us before the beginning of data acquisition in a 13C TIPexperiment? Dr. A. N. Garroway (Washington) said A delay of 500 ps is rather conservative. In the first 50 or 100 ps any transient oscillation certainly vanishes. To ignore pos- sible complications of dipolar ordering created during the spin lock process 1 allow more time for the dipolar order to decay; an additional few hundred /is is probably adequate. Dr. K. J. Packer (Norwich) said Eqn (9a) of the paper by Garroway et al. de-scribes the contribution of macroscopic sample spinning to the dipolar spin-lattice relaxation rate (TID)-'. It appears to have the form of a typical " secular " (T2)-l contribution under motional averaging conditions in which the angular spinning rate plays the role of the modulated second moment with zD being the correlation time.Is this apparent similarity concidence and if not is it possible to see simply how the spinning rate acts as the effective second moment for this relaxation process? Dr. A. N. Garroway (Washington)said Recall the simple BPP picture. A local field jumps between the values *BLwith correlation time z. The magnetization per- pendicular to BLrotates with instantaneous frequency yBL,but as the process is phase- interrupted at z the relaxation rate involves the random walk step length uLz. Hence TT' cc cot7 x M(')z where is a second moment. Here the fast correla- tion time approximation has been assumed coLz < 1. Similarly for slow perpendicu- lar mechanical spinning at R,the time dependent dipolar hamiltonian oscillates at R.Dipolar spin fluctuations change the instantaneous local field with a correlation time 7D. The local field then executes a random walk with step length RzDwhich is super- posed on the coherent precession at R. The local field then loses phase coherence at the rate T;b' cc ~(RT,)= R2 zD. There is a parallel to the self-decoupling of an I-S dipolar interaction by rapid 1-1 spin flips; in the spinning case spin flips "de-couple " the dipolar system from the mechanical motion. It is no coincidence that R' plays the role of the second moment M@). Another way to see this which is incorrect but helpful is to suppose that all the spins with instantaneous local field smaller than 3R cannot follow the motion adia- batically while those seeing larger local fields can.The fraction which cannot follow adiabatically is cc RT cc Rz and that fraction dephases over about one period of GENERAL DISCUSSION revolution. By spin diffusion this " hole " diffuses outward and other fresh spins move in. Hence the dipolar reservoir is fractionally reduced by Qzs every Q-l seconds and so the net relaxation is Ti; cc Q22,. Dr. J. H. Strange (Canterbury)said Have measurements of the proton relaxation times been made as a function of temperature in this cured resin? Such measurements could probably help to check the interpretation of the data and confirm values obtained for the activation energy of methyl group motion and for segmental mobility.For example measurements of proton relaxation times in DGEBA cured with methylene dianiline' gave TI and T, minima attributed to methyl group motion at z 190 and 150 K respectively. An activation energy of 23 kJ mol-' was obtained from the position of these minima which is much higher than found in these experi- ments. It would seem possible that too low a value of activation energy might have been obtained here as the temperature dependence of T, in these high resolution measurements would be reduced if there were a wide distribution of correlation times for the motion. The proton relaxation measurements' also provided an insight into the curing kinetics. Is it likely that these elegant 13C high resolution measurements would provide significantly more information ? Dr.A. N. Garroway (Washington)said Analysis of the temperature dependence of the proton relaxation times would certainly complement the 13C data. As you observe and your proton data show for a similar epoxy system the activation energy inferred from the slope of the T, against temperature data will undervalue the activa- tion energy determined from the frequency dependence of the relaxation minima if there is a distribution of relaxation times. 1 did not follow the methyl relaxation to the TIPminimum. The advantages of I3C TI,seem to lie in the determination of very particular kinds of motion without the complications of spin diffusion. While proton relaxation measurements are far more straightforward than their 13C analogues it requires very good data and perhaps a model to peel off the methyl rotation contribution in order to look at say details of the backbone motion.This is especially true for motions with low activation energies and when the glass point Tgis not sufficiently remote from the methyl relaxation minimum. I hasten to add that these interesting details are certainly not obvious in the very limited range of data presented here. Furthermore the 13C T, measurement may become impractical near very sharp TIPminima. As mentioned in the paper and also in ref. (26) Tlpestimates the life- time broadening of the line. The 13C resonance lines broaden and may disappear when there is substantial molecular motion at the decoupling frequency. Prof. W. M. Ritchey has already found high resolution 13C spectra very useful in suggesting the cure chemistry in a polyimide system.The 13C relaxation data should test further the possible models of curing. However to the extent that average proton properties faithfully reflect the kinetics of the cure the proton relaxation will be very attractive . Mr. S. Brosnan (Oxford) said 1 direct my comment to Prof. Brown. We are interested in the size of the r.f. field H used in your experiments because of the line broadening effects of high power irradiation. We have recently calculated that di- polar coupling between oxygen-17 nuclei and neighbouring protons will give a com- ' D. W. Larsen and J. H. Strange J. Polynzer Sci. 1973 11 449. D. W. Larsen and J. H. Strange J. Polynzer Sci. 1973 11 1453.GENERAL DISCUSSION 183 posite line due to the 0-H system. Several transitions are possible and these may be split by up to 60 kHz the exact splitting depending on the particular quadrupole transition the field gradient parameters the bond lengths and bond angles with the field gradient axes. Have you considered the possibility of using smaller r.f. fields to try to resolve such splitting? Prof. T. L. Brown (Urbana) said The optimal cross-relaxation rate at resonance in the zero-field spin mixing experiment is attained when ysaH, 2 yHHL. There is in effect a resonance interaction in the rotating frame when coo -Q the offset from the pure quadrupole resonance is zero. In principle it should be possible to observe a doublet structure in the 170 spectra with lines at offsets from coo given by [(w -0))' + (ys~Hl,)']t21 YHHL by using sufficiently low level Hls.l In practice the cross-relaxation rates are too low under these conditions.We normally employ an HISin the "0 work on the order of 20 G based on 0.5 of the peak-to-peak applied r.f. voltage. Dr. C. P. Cheng has noted that in certain cases (e.g. 2,5-dichlorobenzoquinone) application of a static magnetic field H' of 4 to 6 x T produces a doublet splitting in the "0line. The maxima in cross-relaxation rates in this case occur at [(o) -cu)' -+(ysaH,,)']t E yH[HE+ H"]*. Because H' is large relative to H, the splitting varies approximately as yHH'. For H' > 257 x T the lines are broadened due to the effects of H' on the I7Ospin levels.Dr. W. S. Veeman (Nijmegen) said In relation to one of the previous comments about the possibility of doing quadrupole-proton double resonance in a magnetic field I would like to mention a technique to transfer polarization between a quadrupolar nucleus and the dipolar reservoir.' By sweeping through a quadrupole resonance line of a powder in a magnetic field the dipolar reservoir is polarized and this polarization can be transferred to the proton Zeeman reservoir by adiabatically applying a r.f. field to the protons. 1 wonder if this technique can be used for double resonance in a magnetic field. Prof. T. L. Brown (Urbana) (communicated) 1 wish to make a considered re- sponse to two remarks made informally by Prof. Hahn and Dr. Haeberlen. Prof.Hahn asked about our experience with Tl behaviour in various prospective samples. In the field-cycling double resonance methods there is potentially a problem with relaxation of the abundant nuclear spins at either extreme in the range of T1values. Long Tl values result in slow acquisition of the spectra because time must be allowed for sufficient remagnetization following each cycle in the experiment. In samples with very long Tl values for which the 14N n.q.r. spectrum is desired we have irradi- ated samples with y rays from a 139Cssource to generate a very low concentration of paramagnetic damage centres. Reductions in TIon the order of 100-fold are readily achieved. The samples must be maintained at 77 K to prevent the damage from annealing out.The level-crossing experiment is not feasible if TIof the abundant spin is too short in high field. In our experience this is invariably the situation at 77 K with samples containing unpaired spins e.g. transition metal complexes. In addition we have noted short TI values in many low spin complexes of CO~~I, in which there may be a contribution to TI from the temperature-independent paramagnetism. Tl may also S. R. Hartmann and E. L. Hahn Phys. Rev.,1962 128,2042. W. S. Veeman and C. S. Yannoni Cheni. Phys. Letters 1975 32 499. GENERAL DISCUSSION be short as a result of motional effects as in methyl or q5-cyclopentadienyl group rotation or low frequency modes in polymer chains. It is occasionally possible to replace a CH group responsible for short TI by a CD group.In addition the TI values for hydrated samples may be increased by use of DzO. Dr. Haeberlen commented that the field gradient tensor contains five not two pieces of inforniation,and he asked whether one can be confident regarding the orienta- tion of the e.f.g. tensor in the molecular axis system from powder n.q.r.data alone. Whether one regards the orientation of the e.f.g. tensor in the crystallographic axis system as a property of the tensor itself is a matter of semantics. In any event Dr. Haeberlen is certainly correct in arguing that the study of oriented single crystals can provide information in addition to that obtained from powders. In some cases the additional information is essential in defining the orientation of the tensor axes in the molecular axis system or in identifying the direction of the principal tensor com- ponent.At the same time it is also true that for very many quadrupole resonance data the orientation of the e.f.g. tensor is well defined by the molecular symmetry or even the lattice site symmetry. It should be kept in mind that the components of the field gradient tensor are the expectation values of one-electron operators with a r -3 dependence on distance from the nuclear quadrupole to the element of charge distribution of interest. It is thus reasonable to expect that in molecular crystals the non-specific intermolecular inter- actions make only small contributions to the e.f.g. tensor. We thus expect that the e.f.g. tensor at let us say 170 in an organic ketone is dependent almost entirely on the intramolecular charge distribution.However more energetic intermolecular effects such as hydrogen bonding or Lewis acid-base adduct formation do produce noticeable effects; indeed the n.q.r. technique serves well in the study of such interactions as exemplified by several ''N n.q.r. studies of coordinated nitrogen.' The point at issue is in my opinion of considerable importance. If n.q.r. spectro- scopy of light elements such as 14N 170 and 'H is to develop as a technique generally useful to the chemist the sample requirements must not be too restrictive. I believe that much of the work already accomplished demonstrates that the n.q.r. data obtained at lower temperatures on samples that are polycrystalline or liquid at room tempera- ture can reveal important new information regarding charge distribution and bonding.Dr. P. Mansfield (No/tiiigliam) said The point was emphasised by Dr. Edmonds that pure quadrupole double resonance field cycling experiments were relatively cheap to perform and often used " off the shelf" powdered samples. However double resonance experiments in high magnetic fields allow (at least in principle) the deter- mination of the full quadrupolar splitting tensor. Furthermore identification and assignment of the principal tensor components with respect to the crystalline axes is much simplified even with non-equivalent quadrupolar split nuclei. It is accepted that pure quadrupole resonance may be the only way to proceed in cases where single crystals just cannot be grown as in the case of many biological molecules.But many of the organic and inorganic compounds being studied by varisus research groups could one suspects be grown into single crystals. I wonder therefore why so few groups are pursuing what amounts to Hahn and Hartmann's original high field double resonance experiment. Dr. D. T. Edmonds (Oxford)said There are several facets to this comment and I will attempt to reply to them in turn. e.g. see Y.-N. Hsieh G. V. Rubenacker C. P. Cheng and T. L. Brown. J. Amer. Chenr. Sue. 1977,99 1384; C. 1. H. Ashby C. P. Cheng and T. L. Brown J. Anier. Chem. Sue. 1978 100 6057. GENERAL DISCUSSION (1) If n.q.r. is to become a widely used analytical and structural technique in chemistry and biology then it seems to me essential that high resolution spectra be obtainable from frozen liquid and powdered solid specimens and not solely from single crystals.This essentially means that the n.q.r. must be detected in zero or small applied magnetic field. This in turn leads to the use of field cycling techniques to obtain the desired high sensitivity especially at low (<5 MHz) frequencies. (2) If a single crystal specimen is available then it is certainly possible to extract extra information consisting of the directions of the principal axes of the electric field gradient. However this information is easy to obtain with a single crystal using field cycling techniques by applying small steady magnetic fields during the irradiation phase.In fact all the Zeeman techniques developed for conventional continuous wave n.q.r. can be used with field cycling provided a single crystal specimen is em- ployed. (3) If n.q.r. is to mature as has n.m.r. then much of the structural information extracted will not reside simply in the quadrupole line centre frequencies but in the shifts and fine structure of the n.q.r. lines due to the interaction of the quadrupolar nucleus with neighbouring nuclei. We have already reported fine structure due to deuterium-deuterium and deuterium-proton interaction in 'D n.q.r.' and also due to nitrogen-proton 'and nitrogen-deuterium interaction in I4N n.q.r. Recently we have detected fine structure in the n.q.r. spectra of naturally abundant I7O spectra due to oxygen-proton and oxygen-deuterium interaction in OH groups.Such fine structure would not be observed in the presence of a large applied magnetic field. For all these reasons I believe the future of n.q.r. lies in field cycling techniques in which the n.q.r. is detected in zero or small applied magnetic fields. Prof. T. C. Waddington (Durham) said Dr. Edmonds used specimens enriched with 170 while Prof. Brown detects the n.q.r. of "0 in natural abundance. Could the differences between the two techniques be explained please? Dr. D. T. Edmonds (Oxford)said In our experiments we used the technique of double resonance with spin mixing by level crossing (d.r.1.c.) whilst Prof. Brown used double resonance in the laboratory frame (d.r.1.f.). D.r.1.f.is much more sensitive than d.r.1.c. but does require the application of radio-frequency fields of large ampli- tude to attain its high sensitivity. We have always tried to avoid the application of large amplitude radio-frequency fields in the hope of obtaining narrow lines so that any fine structure on the line is made more easily discernible. Recently Mr. Brosnan and I have developed a technique which has a sensitivity comparable to d.r.1.f. for the detection of the n.q.r. of naturally abundant 170 but which does not require large amplitude radio-frequency fields. Using this technique we do detect fine structure on the 170 lines due to oxygen-proton and oxygen- deuteron interaction in OH groups of several compounds. An understanding of such fine structure should enhance n.q.r.as a structure-determining tool. Prof. T. L. Brown (Urhana) said Dr. Edmonds and his co-workers report the 14N n.q.r. data for pyridine hydrogen-bonded to a water molecule. We have de- veloped a model that accounts for the e.f.g. tensor parameters in " coordinated " nitrogen in terms of the extent of electron withdrawal from the nitr~gen.~ The ' D. T. Edmonds and J. P. G. Mailer J. Magtietic ReJotiatice 1978 29,213. ' D. T. Edmonds M. J. Hunt and A. L. MacKay J. Magtietic Resonance 1973 9 66. M. J. Hunt and A. L. MacKay J. Mugiretic Resomtice 1974 15 404. S. G. P. Brosnan and D. T. Edmonds J. Magtietic Resotiatice 1979 to be published. Y.-N. Hsieh G. V. Rubenacker C. P. Cheng and T. L. Brown J. Atuer. C/ieni. Soc. 1977 99 1384.186 GENERAL DISCUSSION extent of charge withdrawal is reflected in the donor orbital occupancy which is 2.0 in the free base. The decrease from this value in the acid-base adduct is a measure of the Lewis acidity of the group to which the pyridine is bound. For L-histidine and imidazole in which there is N-H . . . N hydrogen bonding the donor orbital occu- pancies are 1.93 and 1.92 respectively.’ Application of the I4N data of Davidson Edmonds and White to our previously published correlation for pyridine yields a nitrogen donor orbital occupancy in the pyridine water complex of 1.93. It will be of interest to search for regularities in the derived orbital occupancies in a given nitro- gen base as the hydrogen donor is varied but on the basis of the limited results in hand “N n.q.r.looks like a promising tool for probing hydrogen bonding interactions. Dr. P. Mansfield (Nottinghani)said The spectra shown by Dr. Boden are all ob- tained from quadrupolar echoes produced on resonance. In the Fourier transform- ation therefore only half the spectrum is obtained about the origin and it is valid to reflect the frequency data about the origin only if the quadrupolar line shape is indeed symmetric. My concern is that in general this may not be so even for spin I = 1 systems especially when v + 0. I would therefore make the comment that it would in general be better to make measurements either off resonance or preferably on resonance but using quadrature detection. The second order quadrupolar shift is of the order of v&/vo,where vQ is the first order quadrupolar shift and v0 the Larmor frequency.For first order shifts of up to 100 kHz and a Larnior frequency of 10 MHz second order effects can given resonance shift asymmetries of up to 100 p.p.ni. in half integer spins for example thus vitiating any proposal to measure chemical shifts in such systems. Could this be an important factor in the present experiments where only I= 1 spins are studied? Dr. N. Boden (Lee&) said Dr. Mansfield’s question raises a very fundamental point. I will try to answer it. We have followed the normal practice and assumed that first order theory gives a valid description of deuterium n.m.r. spectra in organic solids. The effects of the second order quadrupole term for v = 0 have been discussed by Cohen and Reif2 and Abragani.3 For 1 = I the first order quadrupole splitting is unaffected but the centre of the spectrum is shifted by an amount proportional to (e2gQ/h)2/iio.Let us consider how this affects say the “rigid lattice’’ powder spectrum of [2H,]ben~ene* measured at 77 K and 10 MHz the singularities are shifted by 233 Hz with respect to the wings of the spectrum which are unaffected. Thus the spectrum will be distorted but by an amount small compared with the dipolar broadening (6.5 kHz) and less than the resolution of our transformed spectra (600 Hz). We do not therefore expect the deuterium frequency spectra obtained from resonant spin echo responses to be measurably distorted. This conclusion is confirmed by the agreement between data obtained in this way and that determined by C.W.methods. Nevertheless quadrature detection would be preferable as you suggest and we are currently constructing equipment for this purpose. Turning to the second question. The second order frequency shift will as you point out make a substantial contribution to the “ apparent ” chemical shift. For C. 1. H. Ashby C. P. Cheng and T. L. Brown J. Anlev. Chetn. Soc. 1978,100,6057. M. H. Cohen and F. Reif SolidSrote Phys. 1957 5 321. A. Abragani Pririciples of Niccleav Mngrietisiii (Oxford University Press Oxford 1961) p. 233. * For [’H6]benzene q f 0 but the corresponding powder pattern has not hitherto been calculated. However is very small for organic solids and its inclusion should not seriously affect the con-clusions reached herein.GENERAL DISCUSSION a homogeneously oriented principal axis system such as may be found in single crystal studies this shift may at least in principle be calculated enabling the chemical shift to be unambiguously obtained. It is not possible to say without further calcula- tion how these second order shifts affect the frequency dependence of the echo maxima for either single crystals or powders. We will have to check this. Mr. D. P. Weitekamp (Berkeley)said 1 would like to comment on the issue of the second order quadrupole term raised by Dr. Mansfield. For a spin one nucleus in an axially symmetric electric-field gradient this term in the energy is an odd function of the Zeeman quantum number and its angular dependence is non-negative.' The effect on the single quantum spectrum will be to shift all components of the powder pattern in the same direction by varying amounts and thus give an angle-dependent artifactual chemical shift.The double quantum powder patterns show the effect clearly as these contain frequencies unaffected by the much larger first order quadrupole term.' I have two questions for Dr. Boden. The first is whether it is accurate to calculate the quadrupole echo dynamics as if the quadrupole Hamiltonian did not act at all on the time scale of the pulses. The second is whether one can ignore the possibility of a change in the static bulk susceptibility during a phase change when determining chemical shift differences between solids and liquids without an internal reference.Dr. N. Boden (Leeds) said The quadrupole echo response obtained with pulses of finite width are identical to those predicted assuming &function pulses corresponding to the mid-points of the actual pukes provided the r.f. amplitude is sufficient. The question is what do we mean by sufficient? We might expect l/ntp >> width of spec-trum would be necessary. However we find the 90"-~-90"~~~ echo response is undistorted for much longer pulses. A similar result obtains in the measurement of FID signal and is well under~tood.~ There will indeed be a small change in the bulk susceptibility associated with the change in density on going from liquid to solid which I suppose we should calculate.Dr. J. W. Emsley (Southampton)said It is interesting to compare the results ob- tained for e2qQ/hand q for deuterobenzene by the study of polycrystalline samples and by deuterium n.m.r. of C6D6 dissolved in a liquid crystal solvent. In the case of a liquid crystal sample the spectrum shows a doublet with a splitting Av given by Av = --e2qQ S(1 A q). 4h The +ve sign before q applies when the 2-axis for Y is perpendicular to the molecular plane and -ve sign when it lies in this plane. The S is the order parameter of the 6-fold rotation axis and is obtained from dipolar coupling. To obtain e2qQ/hit is necessary to know q and the location of the 2-axis. Taking q to be 0.041 and the 2-axis perpendicular to the plane as found by Boden et al. and using the liquid crystal data of Caspary et al.,4then e2qQ/his determined as 186.0 * 4.0 kHz.Choosing the 2-axis to lie in the benzene plane gives 202.0 & 4.0 kHz. Clearly one is tempted to assume that the principal axes for V do not change on going from the solid to liquid crystal solution. There is however a discrepancy in the magnitude of either or both A. Abragam Principles of Nuclear Magtietisni (Oxford University Press Oxford 1961) p. 233. 'J. Murdoch personal communication. D. Barnaal and I. J. Lowe Phys. Rev. Letters 1963 11 258. W. J. Caspary F. Millett M. Reichbach and B. P. Dailey J. Chetn. Phys. 1969 51 623. GENERAL DISCUSSION v and e2qQ/hbetween the two phases but this may reflect the error in measuring S for the case of C6D6. A similar comparison has been made for pyridine e2qQ/h polycrystalline C5ND 178.0 & 1.2 0.039 liquid crystal solution of 4-[’H]pyridine 181.9 jl 1.0 0.039 Comparing data obtained in two different phases has two interesting aspects.First if changes in e2qQ/hand q are small then it is possible to determine the orienta- tion of the principal axes. This method will work when molecular rotation does not take place in the solid and depends only on the magnitude of 7 compared with possible changes in the magnitude of e2qQ/hand q on changing phase. Secondly as more precise data on both phases becomes available it should be possible to detect changes in V on changing phase. Dr. N. Boden (Leeds) said We wanted to show in the paper how the quadrupole coupling tensor for deuterium in an organic molecule could be obtained from a com-parison of the “ rigid lattice ’’ and rotationally averaged* powder spectra.In apply- ing the technique to solid C6D6 we used the values 180.7 & 1.5 kHz and 0.041 & 0.007 for respectively e2qQ/hand 7 as obtained by Barnes and Bloom from C.W. measure- ments at liquid nitrogen temperature. At this temperature TI is inconveniently very long; however by temperature-cycling we have measured the spectrum by the spin echo technique and obtained the values 182.3 & 1.3 kHz and 0.048 & 0.007 which are in excellent agreement with those of Barnes and Bloom. Using our value for v the liquid crystal measurements on C6D6 yield 184.8 kHz for e2qQ/h. The discrepancy between the two values is interesting as it reflects differences in the averaging of the quadrupole splitting by the atomic vibrations.The liquid crystal value is averaged by intramolecular vibrations (the reorientational averaging is contained in S) whilst the molecular crystal value is averaged by intermolecular vibrations (li brations) too. The latter are larger in amplitude than the former and we may to a first approximation assume the molecule vibrates as a rigid body in the crystal and include the averaging by the intramolecular vibrations in the “ molecular ” quadrupole tensor. The liquid crystal value of e2qQ/hmay on this basis be taken as representing the static molecule value. The observed temperature dependence of the quadrupole splitting may then be considered to be entirely due to the averaging of e2qQ/hby the librational motion of the molecule since contributions from changes in the small value of 7 will be negli- gible.The change in e2qQ/h,thus obtained is from 184.8 to 171.0 kHz between 0 and 280 K and ought to be calculable from lattice dynamics. Dr. A. M. Achlama (Rehouot) said The chemical shift tensor of deuterium in single crystals may be detected using straightforward FTNMR at high field. Fig. 6 shows a 2D spectrum of a fully deuterated single crystal of potassium hydrogen maleate. There are two magnetically distinguishable molecules in the unit cell each containing one carboxylic and two olefinic deuterons. Consequently the spec- trum contains six pairs of lines. The line at the centre is due to free water molecules trapped in the crystal while growing and may serve as an internal reference.Note that the midpoints of the different pairs of lines do not coincide due to the different chemical shifts of the corresponding nuclei. ’ R. G. Barnes and J. W. Bloom J. Chetn. Phys. 1972 57 3082. J. W. Emsley J. C. Lindon and J. Tabony J.C.S. Furaduy I/ 1975 71 579. * Alternatively the reorientationally averaged quadrupole splitting measured for the molecule in a nematic solvent could be used as suggested by Emsley. GENERAL DISCUSSION GENERAL DISCUSSION Dr. N. Boden (Leeds) said Deuterium chemical shifts may indeed be extracted from measurements of the mid-point frequencies of quadrupole doublets provided the corresponding second order quadrupole shift can be calculated.Whilst this is possible in principle it is not so easy in practice when q-# 0. Dr. J. R. Brookeman (Gainesville)said 1 would like to ask Dr. van der Klink if in their study of the K Pt C1 type mixed crystals they saw any evidence for relaxation of the host lattice around the point defect sites. In our 1i.q.r. study of mixed isotopic crystals of “N and ”N some years ago we found clear evidence of this lattice relaxation and this enabled us to explain the difference between the calculated temperature independent shift of the n.q.r. frequencies and the smaller experimentally observed shift. Dr. J. J. van der Klink (Lnusanne)said 1 certainly think that effects of the kind you refer to do exist in our mixed crystals.In your analysis’ you consider the case of a 14N-14Nmolecule placed in a pure 15N host and you observe the 14N n.q.r. signal. The analogous experiment in our rhenate crystals would be to observe the 79Br signal from the impurity. LJnfortunately we are not equipped at the moment to ob- serve this resonance that occurs around 200 MHz. In the case of our stannate crystals the situation is different we attribute the additional lines in the cubic phase to NH,-impurity nearest-neighbour chlorine atoms. That these signals are visible at all indicates that local volume defects are less important here as one would expect from the small relative difference (0.6 :{) in lattice parameter between the pure ammonium and the pure potassium salt. Dr. J. H. Strange (Canterbury)(comrnunicated) It seems probable that the reduc- tion that we observed in T, and also in TI was due to SnCli- reorientation although the dipolar interaction between the chlorine and proton nuclei is surprisingly strong presumably because the minimum separating distance becomes small when reorienta- tion occurs.The motion may well be rather complex however as the co; dependence for T, and the ratio for TI to TI were not those predicted for a simple rotational model. It is reassuring to see this other evidence for SnC1’- reorientation in (NH,),SnCI,. Dr. R. K. Harris (NurwicI1) said Although the intramolecular barrier to internal rotation in the anilinium ions is sixfold and therefore very low that for the ethyl- enediammonium ions is of lower symmetry and presumably much higher in magnitude.Are the observed barriers (table 4 Prof. Dunell’s paper) for the bromides and iodides of these two systems therefore of different origin? If so is their remarkable similarity purely coincidental ? Dr. C. I. Ratcliffe and Prof. B. A. Dunell (Vancouuer)said The internal barrier to reorientation of -NH$ in the ethylenediammonium ion should indeed be much larger than that in the anilinium ion. Inelastic neutron scattering measurement on the methylammonium ion’ have indicated an internal barrier of ~9.0 kJ mol-I (750 cm-I) and the internal barrier in the ethylenediammonium ion should not be greatly different. The internal barrier thus appears to account for almost all of the barrier ’ J. R. Brookeman M. M.McEnnan and T. A. Scott Phys. Rev. B 1971,4 3661. C. J. Ludman C. I. Ratcliffe and T. C. Waddington J.C.S. Furcichy 11 1976 72 1759. GENERAL DISCUSSION to reorientation of -NH,+ in ethylenediammonium bromide and iodide and both of Harris’ questions should apparently be answered in the affirmative. If the external barriers to -NH,+ reorientation in ethylenediammonium bromide and iodide are close to zero despite the possibility of hydrogen bonding between the NH,+ group and the halide ions we would rationalize that condition by suggesting that the halide ion environment of the -NH rotor in these two compounds is probably a regular wfold arrangement about the direction of the C-N axis with r? # 3. An answer to the question raised by Dr. Harris as to why the total barriers for the ethyl- enediammonium bromide and iodide should parallel so closely the total barriers for the anilinium salts when their origins are different requires structural information on the ethylenediammonium salts and possibly further experimental work that would separate the internal and external barriers.Prof. T. C. Waddington (Durham) said 1 would like to make some comments on the comparison of energies of activation EAcT,measured from n.m.r. TI data and energies of activation obtained by calculation from measured torsional frequencies of the -NHT group. As the authors point out in order to compare the two types of measurement we have to make an assumption about the form of the potential well 3 v3 V(a)= -2 (1 -cos 3a) + .. . and indeed unless we ignore terms above V3we have a two or more parameter problem and cannot compare the two measurements. What I want to suggest is that the agreement between the two measurements for anilinium chloride is very good even better than the authors indicate but that a fair sized discrepancy remains for the bromide and also exists for the iodide for which we have recently measured the -NH torsional frequency. An explanation for this probably lies in the mismatch of the symmetries of the -NHZ rotor and the external environment of the -NH group. (I) The torsional frequencies are temperature dependent. We do not at the moment have a comparison of the frequencies of the -NH$ group in the anilinium salts at differing temperatures but some recent results for the ethylammonium halides where the -NH$ torsional frequencies are higher indicate that the torsional frequencies decrease by z3 i’,in going from liquid nitrogen to room temperature and this would produce a lowering of the calculated barrier by ~5-6?< over the same temperature range.Percentage shifts in torsional frequencies and therefore in barrier heights appear to increase with lower torsional frequencies. The values of the -NH,f torsions reported in the paper are at 77 K. (2) The barrier heights calculated by the authors assume a moment of inertia appro- priate to a tetrahedral -NH group. In fact the C-N . . . (X = C1- Br-) bond angle is rather less than the tetrahedral bond angle and even though the assumption that the H atoms of the -NH$ group lie along the N .. . C1 directions may be an extremum some distortion of the C-N-H bond angle to values lower than tetrahedral is to be expected. Roughly re-working the calculations in the paper including corrections for (1) and (2) and including a recent i.n.s. determination of the -NH$ torsion in anilinium iodide we find GENERAL DISCUSSION C6HsNH3Cl C6HsNH3Br C6HsNH3T 1""3 + icm- 442 294 230 EACT(i .n.s.) corrected for 39.4 19.3 13.3 (1) and (2)EACT(n.m.r.) AEIoL 37.1 5.8 11.2 42.0 8.5 36.1 Since the iodide is thought to be isostructural with the bromide these rough results do seem to confirm the authors' conclusions. It would be of considerable interest to use the n.m.r. and the i.n.s. results together to calculate the ratio of V3 and the next term for each case.Prof. A. Weiss (Dartmadt)said From X-ray diffraction it is proved that the room temperature phase of anilinium iodide is isotypic to the high temperature phase I of aniliniuni bromide. The space group of C,H,NH:I-(I) is D:E(Pnaa) with a = 1.738 nm b = 0.636 nm c = 0.704 nm 2 = 4 at room temperature.' The trans-formation temperature of the anilinium iodide is TII,,= 241 K.' Preliminary results of a neutron diffraction study3 on C,H,NH:Br-(I) at 343 K show that the Debye-Waller factor of the proton in the para-position is higher than those of the protons in the meta-and orrho-positions. It can therefore be concluded that the vibrations around the axis normal to the benzene ring and the axis in the ring plane and normal to C,, .. . C(l,-N are of importance in the dynamical behaviour of both the anilinium bromide and the anilinium iodide. Dr. E. M.Cashell(Norringham) said (1)TheinferencedrawnfroniProf. Dunell'sfig. 3 that s,O is constant for all the samples is inconsistent with the Eyring4 interpretation for h this factor [T = -ek T exp (-AS/R)]. A useful elaboration of their experiments there- fore would be achieved by making measurements at different frequencies this would gain more data points for their plot of activation energy (E)against the temperature at the T minimum. The linearity of this plot and the significance of the Eyring interpretation for T in the context of these activated processes could then be stated more categorically.(2) A factor of some importance in the Eyring formula is the entropy of activation which is indicative of the differing degrees of order required of the excited state for motion to take place. Taking their values for T" (Prof. Dunell's table 2) I have esti- mated the entropies associated with the activated rotor process for each sample. These are presented below along with the corresponding activation energies AS E sample /kJ K-l x lo3 /kJ mol-I chloride -4.24 37.1 bromide 10.39 11.2 iodide 10.88 8.5 sulphate 4.06 11.2 G. Fecher and A. Weiss unpublished results. ' W. Pies and A. Weiss J. Mcgtr. Res. 1978 30 469; W. Pies M. Schahbazi and A. Weiss Ber. Brrtrsetiges. Phys. Client. 1978 82 594. G. Fecher H. Fuess and A. Weiss unpublished results.S. Glasstone K. J. Laidler and H. Eyring Tlieor'y of Rate Processes (McGraw-Hill N.Y. 1941). GENERAL DISCUSSION One point of significance is the negative entropy change and large activation energy associated with the chloride especially because it is clear when one compares columns two and three that a larger activation energy does not necessarily imply a larger entropy change. Of course a complicating factor is that the activation energy itself possibly changes with temperature' and valid comparison with the associated entropy change should allow for this. Measurement of the TI minimum at different frequencies would facilitate the determination of this effect since the temperature at which the minimum occurs and hence the activation energy (if temperature dependent) shift with frequency.Dr. K. J. Packer (Norwich) said 1 would like to comment on the use of the pulsed field gradient spin echo technique used by Drs. Gordon and Strange. First I would like to say that anyone who has worked with those techniques will appreciate the con- siderable achievement represented by the direct n.m.r. measurement of these self- diffusion coefficients at the very high temperatures involved. Secondly I would like to ask the authors whether they used the stimulated spin echo sequence and if not whether this might have significantly extended the range over which they were able to make their measurements. Dr. J. H. Strange (Canterbury)said The simple spin-echo sequence of 90"-~-180" pulses was used.We had investigated the possibility of using the 90"-~,-90"-z,-90" sequence which can have advantages when TI is significantly longer than T,. In our case we calculated that the increase in range to slower diffusion rates was very limited because the TIto T ratio is not enough at 10 MHz to exploit fully the advantages of the stimulated echo sequence. In response to Dr. Pope's informal inquiry the following information should be added to my paper. "The pulsed magnetic field gradient was achieved using a quadrupolar coil. Since these coils were mounted outside the furnace they were necessarily large and with 100 A being switched through them produced 100 G cm-' at the sample." Mr. W. H. M. Alsem (Groningen) said A mass transport phenomenon which can also be investigated suitably by means of the nuclear spin relaxation technique is the motion of dislocations in crystalline solid^.^>^ Dislocations are line defects charac- terized by their Burgersvector b and the vector 5 along the dislocation line together determining the glide plane (fig.7). Stresses applied on crystals may cause dislocations to move on their glide planes opposed by lattice friction. This motion is assisted by thermal activation; the fric- tion is caused by lattice periodicity [Peierls-Nabarro (PN) force] and strong obstacles ziiz. other dislocations and impurities. If the obstacles exert a much larger counter- force than the PN force the dislocation motion will be stepwise i.e. the dislocation (or dislocation segment) waits at an obstacle during an average time interval z which is much larger than the time zs it actually moves.Consequently the mean velocity of a dislocation is determined by z and the distance L covered in one "jump ". Dislocation motion has been studied by means of the spin-locking technique because the atomic motions involved are in the ultra-slow region. The strong colli- C. Brot. Chetii. Pliys. Letters 1969 3 319. G. Hut A. W. Sleeswyk H. J. Hackeliier H. Selbach and 0. Kanert Pliys. Rec. B 1976 14 921. H. J. Hackeloer H. Selbach 0. Kanert A. W. Sleeswyk and G. Hut Phys. Stat. Sol. (b) 1977 80 235. 194 GENERAL DISCUSSION sion approximation which can be derived from the general theory of Wolf’ applies here. From this follows the dependence of I/Tlp,the spin-lattice relaxation rate in the rotating frame on T.The quadrupolar fluctuations caused by the lattice dis- tortions around moving dislocations dominate the dipolar effects on the relaxation rate. -+ T E=[OOl J (c) (d) FIG.7.-Examples of dislocations on {l lo}and {loo}glide planes in crystals with the NaCl structure and the shear caused by their motion. Using the relation between the plastic deformation rate 6 and the dislocation velocity i = pp,bL; (1) the relaxation rate can be expressed in the form where pmis the mobile dislocation density pt the total dislocation density (including p,) p a factor dependent on the angles between the deformation direction and the slip direction and b the magnitude of the Burgers vector of the moving dislocations.In our experiments the change in the relaxation rate due to dislocation motion has been measured in a1 kali halide single crystals plastically compressed uniaxially as a function of the strain rate E (fig. 8) and the magnitude of the locking field confirm- ing relation (2). In the Rf;(E) curve of pure 23NaC1 single crystals compressed in the {100) direc-tion a maximum occurs which is an indication of the transition from the strong colli- sion to the weak collision region. The position of this maximum at i = 20 s-l represents a mean waiting time T~ = 2.8 x s and from the height of the maxi- mum a mobile fraction of dislocations of pm/pt = 0.22 is derived. From the Rg values in the strong collision region a mean distance between strong obstacles L = I .6 x in could be deduced.Assuming that the dislocations are homogeneously distributed in the crystal this value corresponds to a total dislocation density of pt = ’ D. Wolf Phys. Rev. B 1976 14 932. GENERAL DISCUSSION 105 16$ lo3 lo2 101 1 10 lo2 lo3 i/S' FIG.8.-Dislocation induced part of the relaxation rate Rg as a function of the strain rate i measured on different nuclei in alkali halide single crystals deformed in the <loo) direction. T = 293 K (E) % 3 % Ho /j {IlO). x,23NaCl,H1 = 2.2 G; @ 'jNaF HI = 5.5 G; A,*'RbC1 HI == 2.0 G; 0,Na 35Cl,Hl = 2.2 G. 4 x 10" m-2 which is approximately the same as the values found in pure crystals using other methods. This confirms that for a moving dislocation in a pure crystal the main strong obstacles are the dislocations it intersects.The impurity content of the NaCl single crystals has been varied (fig. 9). The impurities consist of Ca2+ ions which are bound to cation vacancies constituting GENERAL DISCUSSION 16~ 16* 16' loo 'c /S' Frc.10 .-Dislocation induced part of the relaxation rate Rg as a function of i in 23NaC1singlecrystals for different crystal orientations with respect to the deformation axis. T = 295 K HI = 2.2 G. Upper (110) (E)= 4x,cr = 80 MPa; (loo) (E) = 3 % o = 1OMPa; lower (10 9 13>,<E> = 4% cr = 80 MPa; (loo) (E) = 3 % cr = 10 MPa. additional local obstacles for dislocation motion. The mean distance L covered during one dislocation "jump " consequently diminishes and therefore the relaxa- tion rate increases with increasing doping concentration.From the position of the lines in fig. 9 however an impurity concentration is derived which is much smaller than the actual Ca2+ content. This indicates that aggregates of Ca'+-ions have grown in the crystals during their slow furnace-cooling. The orientation of '3NaCI crystals with respect to the deformation direction has been varied as well. For crystals with the (1 10) orientation and crystals orientated near the (1 1 I} direction (i.e. (10 9 13)) the relaxation rates have been compared with the measurements in fig. 8 on (100) orientated crystals; in each case the orienta- tion is parallel to the deformation direction (fig. 10). To understand these relaxation-rate changes one should realise that dislocations can move on different glide-planes.Which one is chosen depends on the orientation of the crystal relative to the compression axis accounted for by the factor q in eqn (l) on the PN force of the glide-planes and on the dislocation density on other planes. Therefore in eqn (2) H, pt q and L change with changing orientation. In c.onclusion one can say that the experimental results supply extensive quantita- tive information on dislocation motion.

ISSN:0301-5696    

DOI:10.1039/FS9781300161

出版商:RSC    

年代:1978

数据来源: RSC

摘要:

AUTHOR INDEX* Achlama A. M. 166 188. Menger E. M. 174. Allen P. S. 133. Moniz W. B. 63. Alsem W. H. M. 193. Morris P. G. 37 167. Boden N. 109 170 186 187 188 190. Mortimer M. 109. Brookeman J. R. 190. Packer K. J. 162 173 178 181 193. Brosnan S. 182. Pelzl J. 124. Brown T. L. 75 183 185. Pines A. 149. Cashell E. M. 192. Pintar M. M. 101. Cheng C. P. 75. Provotorov B. N. 19. Clark L. D. 109. Ratcliffe C. I. 142 190. Davidson M. M. 83. Regelsberger M. 124. Dimitropoulos C. 124. Resing H. A. 63. Drobny G. 49. Rossler K. 124. Dunnell B. A. 142 190. Schaefer J. 56. Edmonds D. T. 83 171 184. Shumm B. A. 19. Emsley J. W. 166 171 187. Sinton S. 49. Erofeev L. N. 19. Steger T. R. 56. Fel’dman E. B. 19. Stejskal E. O. 56 174 177 178 179 181. Garroway A. N. 63 162 174 177 179 180 Strange J. H. 153 182 190 193. 181 182. Tiddy G. J. T. 37 168 170. Gordon R. E. 153. van der Klink J. J. 124 190. Haeberlen U. 31 164 165. Veeman W. S. 183. Hahn E. L. 7 161 172. Waddington T. C. 164 185 191. Hanlon S. M. 109. Weiden N. 93. Harris R. K. 162 180 190. Weiss A. 93 192. Manelis G. B. 19. Weitekamp D. P. 49 171 172 174 187. Mansfield P. 37 161 163 164 169 172 178 Wemmer D. 49 179. 184 186. White A. A. L. 83. Mason J. 165. * The references in heavy type indicate papers submitted for discussion. 197

ISSN:0301-5696    

DOI:10.1039/FS9781300197

出版商:RSC    

年代:1978

数据来源: RSC