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. 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