摘要:

76 IONS OF ALKALINE EARTHS THE IONS PRODUCED BY TRACES OF ALKALINEEARTHS IN HYDROGEN FLAMES BY T. M. SUGDEN AND R. C. WHEELER Dept. of Physical Chemistry, University of Cambridge Received 27th January, 1955 The concentration of free electrons produced when traces of the alkaline earth metals were added as salts to various hydrogen -1- air flames has been studied by a resonant cavity method, operating at a wavelength of about 10cm. It has been studied as a function of amount of added metal and of the temperature of the burned gases. Pre- liminary and extensive calibrations were carried out with alkali metals. In particular, comparison of the number of free electrons produced by addition of the same amounts of lithium and of sodium enabled estimates to be made of the concentration of hydroxyl radicals in the various flame gas systems used, by taking into account the known relative stabilities of sodium and lithium hydroxides. This has enabled the concentration of negative hydroxyl ions produced to be calculated.The alkaline earths show a much more complicated variation of electron concentration with amount of metal added, and this has been interpreted in terms of the formation of both positive and negative ions containing one atom of metal each. Analysis of the results suggests that the positive ions are mainly of the type (BaOH)+, and that these are produced in equilibrium amounts. A discussion of the stability of radical-ions of this type is given. The negative ions are considered to arise by combination of hydroxyl ions with molecules of the diatomicT .M . SUGDEN AND R . C. WHEELER 77 oxides. Such ions are shown to be reasonably stable, but the results indicate that they cannot be formed in amounts corresponding with thermal equilibrium. The kinetics of their formation are discussed, and found to be consistent with the observations. A large amount of previous work has shown that when alkali metals are present in flame gases a t high temperature (- 2000" K), the ionization which occurs is explicable on the basis of equilibrium between the metal, its positive ion, and free electrons, provided that reasonable account is taken of the side reactions involving the free hydroxyl radicals of the flame gases to give the hydroxide of the metal and negative hydroxyl ions, also in equilibrium amounts.1 The most obvious expression of this equilibrium is the dependence of the concentration of electrons on the total concentration of metal present (free or combined as hydroxide), which is expressed by over wide ranges of concentration wherc the proportion of free metal ionized is small.KX is a constant for a given flame, and [Ao] the concentration in the flame gases of the total alkali metal present (free or combined). Work on the alkaline earth elements has shown that this simple law is not obeyed,2 and that for very small amounts of metal prescnt in thc flame gases, the electron concentra- tion rather follows a law [el2 == KA+[Ao] Throughout this paper A will be used to represent an alkali mctal, and B an alkaline earth. In the last expression b and c are constant for a given flame, and [Bo] is the total concentration of alkaline earth (free or combined, expressed in terms of atoms or compounds with one atom of alkaline earth).The purpose of the work to be described is the determination of these parameters b and c for various conditions of gas temperature and composition, and to see whether they can be interpreted on an equilibrium basis, and if so, what ions take part with electrons in this equilibrium. It is already known that when alkaline earths are present in the hot gases from flames containing hydrogen and oxygen, the great majority of the metal is prescnt in the form of the diatomic oxide B 0 . 3 ~ 4 In the ranges of temperature and concentration of alkaline earth uscd here, appreciable dimer- ization of this oxide does not occur, so that compounds and ions containing only one atom of R need be taken into account.EXPERIMENTAL The ionization has been studied by measurement of the concentration of free electrons using the resonant cavity method described in the previous paper,s and used previously in work of similar type.6.7 Metered streams of hydrogen and air were mixed, sometimes diluted with excess nitrogen, and burned in a M&ker type of burner of nickel. The metals were added as fine sprays of solutions of salts from an atomizer, which had been calibrated for delivery into the flame gas supply to the flame. This burner, about 2 cm in diameter, was surroundcd by another similar one, supplied with a gas mixture of the same com- position, but without added salt, giving a total diameter of about 4cni.This outer flame shielded the salt-bearing inner gases from cntrainment of outside air, which causes aftcr-burning with the excess hydrogen, and introduccs marked inhomogeneity of tem- perature near the boundaries. Somewhat hydrogen-rich mixturcs were used, since these gave a more clearly defined central column of gas of fairly uniform temperature. The temperatures were measured by the method of sodium D-line reversa1,g which has proved very satisfactory for work of this type, and a series of flames chosen in which the tem- perature of the central column of gases did not vary by more than 9: 10°C over the region used for measurement of electron concentration, i.e. about 12 cm of height. The surface of the burner formed part of the lower face of a cylindrical resonant cavity tuned to resonate in the T E o , ~ , ~ mode at a wavelength of about 10cm.The burned gases from the flame escaped through a hole in the upper end of the cavity, rather larger in diameter than the column of hot gases. This hole was electrically sealed to prevent78 IONS OF ALKALINE EARTHS escape of microwave radiation by a very coarse mesh of about ten strands of stout gauge platinum wire. The burner and exit-hole were offset from the axis of the cavity so that the cross-section of the conducting central column of gas was in a region of more nearly uniform electric field than if it had been concentric with the cavity. The cones of primary combustion (about 3 mm high) were inside the cavity, but being near the end, in a region of low electric field, any ionization in them, which would almost certainly not be thermally equilibrated, had little eifect.This method, which was chosen as the most convenient in operation, gave the same results as when the flame was placed a little below the cavity, with the burned gases entering via a gauze similar to the exit onc. The cavity was excited through an iris aperture by a CV36 klystron, from which it was almost isolated by a large wedge attenuator to reduce coupling. The microwave power transmitted was rectified by a silicon crystal, similarly isolated from the cavity by an attenuator. Measurements of Q, which is decrcased by the losses due to conduction by free electrons, being rather tedious to carry out in large numbers, the transmission of the cavity at fixed frequency was measured when the central column of gases was made conducting by addition of salts, and compared with that of a “ clean ” flame, which was practically non-conducting.This effect was calibrated by using sodium salts in the atomizer, where the proportionality between the square of the electron concentration and that of the sodium added is well established.1 The whole cavity was water-cooled. Fluctuations in the behaviour of the apparatus were eliminated by frequent checks against sodium. An absolute check on the reliability of the system was obtained for sodium by measuring the Q of the cavity, and comparing the concentration of electrons thus measured with the theoretical value (that derived on a basis of calculations of thermodynamic cquilibrium at the measured temperature).As described in the previous paper,s the electrical con- ductivity a is given by where &o and Ql are the Q’s of the cavity in the absence and presence of conducting flame respectively, OJ = 27r (frequency of radiation), and g is a numerical factor relating to the size of the cavity, the size of the column of conducting gases, and its position inside the cavity. This factor is readily calculated. The electrical conductivity is related to the number n of electrons per cm3 and hence to their partial pressure in atmospheres [E], if thermally equilibrated, by ne2 wl where e and m are the electronic charge and mass respectively, and wl is the frequency of collision of an electron with molecules of gas.Using a value 9 of w1 of 8.8 x 1010 sec-1, a value of [E] of 4.4 x 10-8 atm was found in a particular case of sodium added to a hydrogen + air flamc, comparing with a theoretical value for thermal ionization of thc sodium added of 5.9 x 10-8 atm for [el. This supposed only the simple ionization Na + Na+ + E (see below). This agreement is more than satisfactory, in view of the many measurements and assumptions involved, and may involve some cancellation of errors. It is certainly good enough to validate the method as giving a reasonable measure of the absolute concentration of free electrons. Relative measurements of this con- centration under various conditions of flame and added metal are accurate to within f 5 % with respect to each other. The method was capable of dealing with electron concentrations down 108 electrons per cm3 ([E] - 3 x 10-11 atm).(J = -- __- m fd + w12’ RESULTS HYDROXYL CONCENTRATIONS FROM COMPARISON OF LITHIUM AND SODIUM Since it was suspccted that the presence of hydroxyl might affect the ionization of the alkaline earths (as later it will be seen is very probably the case), a short study of the conccntration of free hydroxyl radicals in the flame gases was made by comparing the ionization from lithium and sodium. It appcars that while sodium exists almost entirely as free atoms in the flame gascs from hydrogen -t air flames, lithium is prcscnt to a very large extent as the hydroxide LiOH, in amounts 1 given by the equilibrium LiOH+LiSOH. The ionization of an alkali metal added to a flame is given by an equation due to Saha,loT.M. SUGDEN AND R. C . WHEELER 79 where V is the ionization potential in eV, T is the absolute temperature in OK, and K is the equilibrium constant of the ionization A + A+ + e in atm. The ionization given by the same total concentrations of lithium and sodium added to a flame may be expressed by a modified equation of this type where 4Li = [LiOH]/[Li], the corresponding quantity for sodium being approximately zero, on account of the instability of NaOH. If the equilibrium constant of LiOH + Li + OH is K’, then + ~ i = [OH]/K’. Measurements of the relative electron concentrations for the two metals leads to a value for $ ~ i , and it has been found that K’ is satisfactorily represented 1,11 by K‘= 7.6 x 10s exp (-- 102,0001RT) atm, so that values of [OH] Q) > .- a- Molarity of solution FIG.1.--The variation of electron concentration with total metal added, plotted as [el2 against molarity of solution in the atomizer. Sodium calibration added to show different dilution law for alkaline carths. Flame-gas temperature 2010” K. may be derived. The rcsults are shown in table 1, where they are compared with calculated values. The calculated values were obtained from the equilibrium com- position of the burned gas at the measured sodium D-line reversal temperature, using the data of Lewis and von Elbe 12 for the equilibrium constant of the reaction H20 + OH + 4H2. This gas consists largely of H20, unreacted H2 and N2, with up to about 0.05 % of OH and H, whose concentrations are buffered by the major constituents.The agreement TABLE RESULTS OF HYDROXYL AND HYDROXYL ION TESTS temp. of flame gases C K) k i 21 80 8.7 4.0 x 10-4 5.6 x 10-4 1.2 2109 9.3 2.1 Y Y 3-4 9 , 1.1 2063 14.6 1.7 ,) 2.1 3, 1.3 2010 15.3 9.6 x 10-5 1.2 9, 1.2 1965 18.2 6.3 y y 7.3 x 10-5 1.2 1907 27 3.4 9 , 3-7 $ 9 1.2 1855 31 2.3 9, 2-1 Y9 1.380 IONS OF ALKALINE EARTHS is seen to be good, and it is not unlikely that the experimental values are better than the calculated ones. These hydroxyl radicals are capable of reacting with electrons to give hydroxyl ions, OH- 6 OH + E, and if the equilibrium constant of this reaction is K", then it is given by in atm. This equation is a slightly modified form of the Saha equation to take account of the different statistical weights of the ion and the uncharged molecule.It assumes that the interatomic distance and the frequency of vibration are the same in the hydroxyl radicals and ions, which is not likely to be greatly in error, and in any case has little effect on the value of K". Thus 4' = [OH]/K" = [OH-J/[c] may be calculated if K" is known. d 1907OK /_i_O_ 2 BOOK 0 . 5 [SroJ x IO'atrn FIG. 2.-Plots of the function [Sro]/[c]2 against [Sro] for three temperatures. K" has been calculated from the last equation at the various temperatures used with a value 13 of E, the electron affinity of OH of 2.7 eV (62 kcal). The derived values of +' are given in the last column of table 1, and are seen to be very nearly constant. If the revised value of E = 2.82 eV given by Page14 is used, these values are about doubled, but the constancy is little affected.ELECTRON CONCENTRATIONS FOR ALKALINE EARTHS The electron concentrations for the alkaline earths, calcium, strontium and barium, are com- pared with that for sodium for various amounts of the metals added to a givcn flame in fig. 1. The plots are of relative [€I2 against the concentration of the salt solution in the atomizer (molarities). The chlorides were generally used, but the results were independent of the anion, so that the solution is merely a convenient vehicle for conveying the metal into the flame. It will be seen that the electron con- centration rises much less rapidly than the linear (calibration) result for sodium. Other alkali metals give straight lines like that for sodium.Similar results have been obtained for all the flames used, the error becoming rather large, however, for calcium in thc cooler flames, which gives a very small number of electrons. Wheeler 7 has shown that linear plots can be obtaincd in terms of a relation [el2 = b[Bo]/(l 3- ~[Bo]) by plotting [Bo]/[c]~ against [Bo] with interccpt 1/b on the ordinatc and slope clb. Such plots are shown for three flames in fig. 2. [Bo], the total concentration of alkaline earth B, is obtained from the molarity of the salt solution by calibration of the atomiser (a 1-M solution gave [Bo]==3.5 x 10 - 5 atm). The partial prcssure of electrons [el is obtained from the effects on the transmission of the cavity at resonance as described in outline above. Fig. 2 shows good straight lines, provided that [Bo] does not rise above 10-6 atm (003 M solutions).With barium and strontium at least, [Bo] does not rise above the vapour pressure of the oxides BaO and SrO, as quoted by Claassen and Veenemans,ls so that solid oxide is most unlikely to be present. The cooler flames (< 2000" K) should permit the prescnce of a little solid CaO for the higher levels of [Bo] used, but there was no cvidence of this in the gases insideT. M. SUGDEN AND R , C . WHEELER 81 the cavity in the form of continuous radiation. It can be seen that at very low [Bo], the above equation reduces to [el2 = b[Bo], resembling the expression for alkali metals. Hence the values of b obtained for the various flames may be compared with the cor- responding values of the proportionality constant for sodium, and this is shown plotted against 1/T in fig.3. These parameters plotted in fig. 3 are very closely related to the I / T ( " K ) 16* FIG. 3.--Plots of log b against 1/T for the alkaline earths, with sodium plot added for comparison. equilibrium constants for ionization to positive ions and electrons, and are in fact these equilibrium constants if there are no side equilibria arising from, e.g., the presence of hydroxyl radicals in the gases. They will be examined from this point of view in the next section. The parameters c for the alkaline earths in the various flames are similarly plotted against 1/T in fig. 4. They show little significant variation with temperature, and unlike b, vary in the anomalous order Ba, Ca, Sr. This also will be commented on in the discussion.---------.- 7--- V 0 0- 0 - I / T ( W ~ la4 FIG, 4.-Plots of log c against 1/T. DISCUSSION If the variation of ionization with amount of alkaline earth depends only on an equilibrium B + a-1- -1 E, where B represents a molecule of any substance con- taining only one atom of the alkaline earth B, and if the ionization is sinall com- pared with the total B present ([Bo]), then the situation is the same as with the alkali metals, and a dilution law [el2 E DO] is obtained. This does not coincide with the expcrimental results, which give a less rapid variation of [el with [Bo],82 IONS OF ALKALINE EARTHS and an attempt will be made to explain the observed variation by considering other ionic equilibria which may occw in this case.One way in which the observed results can be explained is to suppose that a negative ion B-, containing one atom of B, can be made. Then putting B + Bi- I- E ; K$ = [B'][€]/[B], [E] -k [B-1 = [B'] (charge balance), [B] - LBO] (small ionization), B - B + E ; KB = [B][E]/[B-], the following equation may be deduced which is of the observed form, with b = K&, and c = l/KB. The formation of hydroxyl ions in equilibrium amount does not affect the form of the dependence. Another explanation of a low rate of variation of [el is to suppose that extensive dimerimtion to unionized moleculcs of type B2 occurs, but the prcssures of alkaline earth available are considered to be too low for this at these temperatures, and in any case this leads to a prediction that [Bo]/[E]~ against [el2 will bc linear, which is not the case.This hypothesis of a positive ion B+ and a negative ion B- will therefore be adopted for the present. The possibilities for the ion Bi- arc the singly ionized metal BI, the ionized oxide (BO)f, and the ionized hydroxide radical (BOH)+. The last two will be essentially electrovaleiit compounds made up of B2+, and 0-, OH- respectively, with highly distorted (polarized) ions. The ion (BOH)+ has constituent ions with a closed shell (inert gas) type of structure, and in this resembles the alkali hydroxides AOH and the alkaline earth oxides BO. The experimental parameters b are the same as the equilibrium constant KB for the ionization to give the positive ion, and hence the corresponding " ioniza- tion potential " may be deduced from them in two ways, using the Saha equation.Firstly, the variation of loglo b with l/Tshould give a straight line of slope -5050 V (second law method), and secondly, the absolute value of b at a given temperature may be used to obtain a valuc of V (third law method). These values, obtained from the results shown in fig. 3, are given in table 2, together with the values for sodium, and the known first ionization potentials of the atoms. Good agrcement TABLE 2.-IONIZATION POTENTIALS first i.p. from i.p. from absolute &%I (eV) 2000' K (eV) slope of fig. 3 value of fig. 3 at metal Na 5.12 5.1 5.1 ca 609 4.16 5-19 Sr 5-65 3.96 4.97 Ba 5.19 3.57 4-75 betwecn thc various methods applies for sodium, but not for the others. The formation of hydroxyl ions has little effect on the results for sodium because 4' is independent of temperature for the flamcs used, and because it is quite small (about 1).The implication of the lack of agreement between the last two columns for the alkaline earths is that the neutral molecule on which the positive ion is based is not the compound of B which is dominant in the flame gases4.e. it is not the oxide BO, which is known to make up well over 90 % of the total B present. Thus thc ion (BO)-l- is ruled out. The positive ion must therefore bc derived from a neutral constituent which is present in different amounts at differcnt temperatures. The free atoms B form such a constituent, but table 2 shows that the observed ionization potentialsT . M . SUGDEN AND R . C .WHEELER 83 are much too low compared with the known ones. Thus the atomic ion Bf may be eliminated as well. The neutral hydroxide radicals BOH will be unstable with respect to the oxides BO, and will be rather like the unstable halide radicals, such as BaF, with which they correspond in electronic structure. The spectra of these radicals have recently been identified in flames of this type 4 and resemble those of the halides.16 These spectra also indicate that BOH is a very minor constituent compared with BO. The ion (BOH)+ may, however, be relatively stable on account of its closed shell electrovalent structure (i.e. the molecules BOH will have low ionization potentials). The ionic equilibria governing it may be set up as follows : with charge balance ignoring the other types of positive ion already rejected, and mass balance [E] + [OH-] = [(BOH)+I, D o 1 = LBO], ignoring neutral constituents other than oxide.This system of equations leads to Kl W2Q"ol +Y1 + $9 ' [€I2 = which is of the same form as the observations when c[Bo] << 1. The parameter b is then K1[H20]/4'(1 + $'). For the flames used the variation of [H20] with temperature is negligible, as is that of 4' (cf. table 1). Hence the temperature coefficient of b should be the same as that of K1. Assuming this to be so, a value of the heat of formation of (BOH)+ from B2+ and OH- may be worked out by combining the results with standard thermodynamic data. This is set out in table 3 . TABLE 3.-REACTION SCHEME FOR HEAT OF FORMATION OF BOH+ AH0 (kcal) reaction Ca Sr Ba BO + HzO --> BOH+ + OH- 96 91 80 B + O +BO -103 -111 -126 B2++ 2~ + B -414 - 384 -349 20H -+ 0 + H20 - 19 - 19 - 19 20H- + 2 0 H + 2 ~ 124 124 124 B2+ + OH- 3 BOH+ - 316 -299 -290 reference present work Brewer 17 Znt.Cuit. Tables 18 Dwyer and Oldenberg 19 Smith and Sugden 13 TABLE 4.-HEATS OF FORMATION FROM IONS (kcal/mole) ht. of ht. of ht. of formation ht. of formation from ions charge on from ions charge on each ion each ion substance formation per unit substance formation per unit substance KOH 125 125 CaOH 316 153 CaO RbOH 123 123 SrOH 299 150 SrO CsOH 120 120 BaOH 290 145 BaO hr. of ht. of formation formation per unit from ions charge on each ion 685 171 663 165 64 1 161 The final figures from table 3 are compared in table 4 with the heats of formation of alkali hydroxides AOH from A+ and OH-, and with those of the alkaline earth oxides from B2+ and 02-. The last column of each set of three gives the energy involved for each pair of unit charges on the two ions, assuming all the molecules to be essentially electrovalent.It will be seen that the values deduced for the84 IONS OF ALKALINE EARTHS radical-ion lie very reasonably between those for the alkali hydroxide and those for the alkaline earth oxide. The steady increase in the heat per pair of unit charges in the series AOH --f (BOH)+ -+ BO is consistent with steady shortening of the interionic distance. The variation of b with temperature is thus consistent with the presence of these ions. The absolute level of b must also be consistent if this is the true explanation.K1 is given in statistical terms by where the q's are the appropriate partition functions, and AH^ is the heat of reaction at absolute zero. The q factor has been evaluated using either known interatomic distances and frequencies of vibration, or reasonable calculated ones. For calcium with AH0 = 96 kcal, a value of K1 = 9 x 1011 is obtained (the q factor is about 3). At 2000" K the components of the burned gas gave [HzO] - 0.3 atm, and $ r = 1.2 (table 1). This data yields a calculated b of 1.4 x 10-11 atm, com- paring with the measured value of 4.5 x 10-12 atm. This three-fold difference is by no means unreasonable in view of the possible errors in AH^, and the assumptions made. There is also some doubt about the statistical weight of the ground electronic state of the oxide.This has been taken as a singlet, but if it were a triplet the agreement would be rather improved. Similar results obtain for strontium and barium. There is thus a very strong case for considering that the ion B+ is in fact of type (BOH)+. Further, the existence of this kind of ion at low concentrations of alkaline earth is quite independent of whatever complications may arise at higher concentrations, i.e. it is not necessarily tied to the formation of ions of type B-. It may readily be equilibrated in the time available by the following scheme of actual processes B + H20 + BO + Hz B + OH +BO + H BO + H + (BOH)+ + E E + H20 + OH- + H. No ternary collisions are involved in any of these. The first two pairs involve heats of reaction of about 20 kcal, and will have low energies of activation.The third pair is 30-50 kcal endothermic in the forward direction, with a back reaction likely to have zero energy of activation. The last reaction is about 50 kcal endothermic in the forward reaction, and again thc energy of activation will not be much greater than this. None of the energies involved is sufficiently high to prevent enough effective collisions for the system to come near equilibrium. The parameter c of the results is much more difficult to deal with. It is approximately independent of tempesature, and decreases in the anomalous order Ba, Ca, Sr. This anomalous order in the alkaline earths has been com- mented on already by Drummond and Barrow20 in connection with some pro- perties of the oxides BO, and there is little doubt that the oxides are important here.There are two negative ions worthy of consideration, viz., the oxide ion (BO)-, and an ion made by attachment of OH- to BO with formula (0BOH)--, and with electrovalent structures B+02- and 02-BZfOH- respectively. The former may be introduced in the equilibrium which leads to c = 1/(1 4- $')K3. Now $ r varies hardly at all with temperature, so the implication of the near constancy of c is that the reaction which K3 describes must have a very small heat change. This is impossible if (B0)- is stable. In the same way, if the other negative ion is used, BO- F+ BO + E ; K3 = [BO][C]/[BO-], (0BOH)- + BO + OH-; K4 = [BO][OH-]/[(OBOH)-]T. M. SUGDEN AND R . C. WHEELER 85 leads to a value of c = $'/(1 + 4')&, and the same objection applies.Hence neither of these two ions is feasible on an equilibrium basis. This conclusion warrants further examination on the basis of stability. The ion (B0)-, which would be electrovalent, would be derived from B+ in a 2 s state, which is a larger ion than that of the singlet state of B2f. Similarly the 0 2 - ion is certainly larger than the 0- ion. Hence (B0)- will be less stable than (BO)+, which has already been rejected as a likely positive ion. The other negative ion, however, is, like (BOH)+, made up of closed shell ions 02-B2+0H-, which will tend to lend it stability. In this connection, Wheeler 2 has found strong evidence of specific interactions in flame gases between the positive ions of alkali metals and molecules of alkaline earth oxides, which are readily explicable by the presence of compound ions of the same type, viz.B2+02-A+. Calculations using the methods of Rittner 21 for one of these, (SrONa)+, lead to a heat of formation from SrO and Na+ of 125 f 20 kcal. This is sufficient to make this compound ion stable with respect to its dissociation products under flame gas conditions. The ion (0BOH)- should have about the same stability with respect to BO and OH-, and thus should appear in our experiments. Further, fragments such as Ba20+ have been observed mass-spectrographically by Aldrich.22 A difficulty arises, however, in the formation of this negative ion from BO and OH- on account of the few collisions between them in the time available, particularly since these may need to be three-body collisions to remove the heat of formation released.The only other ways in which it can be formed involve either the simultaneous production of a positive ion from the flame gases by, e.g., BO + H20 + (0BOH)- + H+, which requires too much energy, or by processes involving collision between two molecules each containing an atom of B, e.g., BO + BOH + (0BOH)- + Bf, which are far too infrequent. The time allowable for a position near equilibrium to be reached is of the order of 10 msec, from leaving the burner, during which the average molecule makes about 107 collisions with other molecules, and an electron about 109 collisions with molecules. The fraction of OH- ions is of the order of 10-7 of the total gases, so that a BO molecule will only collide with one or two OH- ions in the time available.The possibility of equilibrium being established is thus very remote, and large departures from it might be expected. The reactions BO + H20 + (BOH)+ + OH- OH- + OH + E will be reasonably well equilibrated by the reactions quoted previously, which fulfil the necessary collisional conditions, If to this is added d[(OBOH)-Ifdt = k[BO][OH-], where k is essentially the collision frequency (possibly including the concentrations of third bodies), then for the very early stages of the production of the complex negative ion, where its decomposition can be ignored, it may be shown that the concentration of electrons is given by This is of the observed form with c = k$'t/(l + 4') On the basis of bimolecular collisions at 2000" K, k has a value of 5 x 10-10 molecule-1 cm+3 sec-1, assuming a collision diameter of 3 A, which becomes 2 x 109 in atm-1 sec-1.For t = 10-2 sec, therefore, kt$'/(l + 4') - 107 atm-1, which is the same order of magnitude86 IONS OF ALKALINE EARTHS as the coefficients c observed. This will vary very little with temperature. Three- body collisions will be about 1000 times as infrequent as two-body ones, but on the other hand, the collision diameter chosen for a two-body collision between an ion and a large dipole is probably considerably too small. The absolute magnitude and small variation of c with temperature is thus reasonably explained. As has already been pointed out, the order Ba, Ca, Sr is characteristic of many of the properties of the oxides BO of the alkaline earths, and the result obtained here, which is really a measure of the collisional cross-section of the oxides, is in line with this. CONCLUSION The complicated ionization, as evidenced by the variation of electron con- centration with amount of alkaline earth present in hydrogen + air flames, is in strong contrast with the simple case of alkali metal elements.Positive ions are produced, in equilibrium with electrons and hydroxyl ions, and considerations of the amounts of ionization, and their variation with temperature, indicate strongly that these are the hydroxide radical-ions (BaOH)+, (SrOH)+, (CaOH)+. These are thermodynamically probable bodies, the results indicating that they fit well in a series of essentially electrovalent molecules such as CsOH, (BaOH)+, BaO.A full account of the results can be given if, in addition, negative ions containing one atom of alkaline earth are produced, and it is shown that combination of alkaline earth oxide molecules with hydroxyl ions to give, e.g., (0BaOH)- is feasible. The results are, however, inconsistent with thermal equilibrium of these, and it is shown that the time available in the flame system is insufficient for this equilibrium to be brought about by collisions of, in this case, BaO and OH-. Simple kinetic calculations show that the degree of combination which could take place is consistent with the observed results. Although the method used is somewhat indirect, it is difficult to explain the results in any other way, and there are good thermodynamic reasons why the interpretation adopted should be the correct one. Thanks are due to the Imperial Oil Company of Canada for the award of a scholarship to one of us (R. C . W.). 1 Smith and Sugden, Proc. Roy. SOC. A, 1953, 219, 204. 2 Wheeler, Diss. (Cambridge, 1954). 3 Huldt and Lagerqvist, Ark. Fys., 1950, 2, 333. 4 James and Sugden, Nature, 1955,75, 333. 5 Sugden, this Discussion. 7 Sugden and Thrush, Nature, 1951, 168, 703. 8 Gaydon and Wolfhard, Flames, their Structure, Radiation and Temperature (Chap- 9 Belcher and Sugden, Proc. Roy. SOC. A, 1950,201,480. 10 Saha, Phil. Mag., 1920, 40,472. 11 James and Sugden, Proc. Roy. SOC. A, 1955,227, 312. 12 Lewis and von Elbe, Combustion, Flames and Explosions of Gases (Academic Press, 13 Smith and Sugden, Proc. Roy. SOC. A , 1952,211, 31. 14 Page, this Discussion. 15 Claassen and Veenemans, 2. Physik, 1933, 80, 342. 16 Pearse and Gaydon, The Identification of Molecular Spectra (Chapman and Hall, 17Brewer, Chem. Rev., 1953, 52, 1. 18 Int. Crit. Tables (McGraw-Hill, New York, 1929). 19 Dwyer and Oldenberg, J. Chem. Physics, 1944, 12, 351. 20 Drummond and Barrow, Trans. Faraday SOC., 1951, 47, 1275. 21 Rittner, J. Chem. Physics, 1951, 19, 1030. 22 Aldrich, J. Appl. Physics, 195 1 , 22, 1 168. 6 Adler, J. Appl. Physics, 1949, 20, 1125. man and Hall, 1953). Inc., New York, 1951), appendix A. London, 1950).

ISSN:0366-9033    

DOI:10.1039/DF9551900076

出版商:RSC    

年代:1955

数据来源: RSC

摘要:

THE DETERMINATION OF THE ELECTRON AFFINITY OF THE HYDROXYL RADICAL BY MICROWAVE MEASUREMENTS ON FLAMES BY F. M PAGE Dept. of Physical Chemistry, Free School Lane, Cambridge Received 28th January, 1955 An improved method of measuring the direct attenuation of centimetric radio waves has been used to obtain the concentrations of free electrons resulting from ionization of sodium in hot flame gases. By studying the variation of electron concentration with the calculated concentration of hydroxyl radicals in isothermal sets of such gases, resulting from burning different mixtures, the equilibrium constant of the reaction OH- % OH + e is determined. From this the electron affinity of the hydroxyl radical is deduced to be 65 f 1 kcal. This value is discussed in relation to other measurements in flames and to previous estimates.The idea of using the secondary zone of a flame as a high temperature bath in which to study the equilibria between atoms, molecules, ions and electrons was used by Rolla and Piccardi 1 and developed by Sugden and his co-workers. The method is neat and convenient, but suffers from the disadvantage that the flame gases may affect the equilibria being investigated. Further studies have shown that the effects of the flame gases are principally due to hydroxyl, and that if due allowance is made for these effects, experiment and theory can be brought into agreement.aS3 A great drawback to the early attempts to exploit this field was the lack of control of the flame variables of temperature and composition, and the inaccuracy of the techniques for measuring the concentration of electrons.The development of microwave techniques greatly facilitated the work, since measurements are specific to the electron, except where heavy ions exceed the electrons in concentration by several powers of ten, which is not likely to be realized in practice. The ways in which these difficulties have been brought under control has been set out in an earlier paper in this Discussion.4 EXPERIMENTAL The measurement which is required is that of the number of electrons per cm3 in the flame gases. This is made by determining the attenuation per centimetre of K-band radiation when traversing the gases. This attenuation can be related, by electromagnetic theory quoted by Sugden,4 to the number of electrons per cm3. Early measurements using this technique measured directly the attenuation produced by a flame burning in a gap in a waveguide system.In an attempt to achieve greater sensitivity and stability, a double beam system has been set up. It is illustrated schematically in fig. 1. This apparatus was capable of giving measurements of the attenuation of the flame reproducible to 0.005 db between 0.10 and 4.00 db. The crystal outputs were balanced when only one flame was attenuating, and this attenuation, which was entirely due to the presence of alkali metal in the flame, was then replaced by stopping the supply of alkali metal, and adjusting the calibrated resistive attenuator until balance was again reached. The earliest work on equilibria in flames suffered from the disadvantage that it was necessary to alter the temperature of the flame whenever the composition was altered.A number of flames were therefore chosen, such that a set of flames, all at the same temperature, was available in which the burned composition was different in each flame. These flames, produced by burning carefully metered mixtures of oxygen, nitrogen, and hydrogen, were all sheathed by nitrogen, as it has been found that such sheathed flames a788 ELECTRON AFFINITY OF HYDROXYL have a fairly uniform temperature cross-section.2 The gases were burnt on a flat Mkker type burner, 6 cm by 1 cm, the burner top being formed from Kanthal AD heat-resistant alloy. After preliminary experiments to map the temperature-composition contours, sets of four flames were chosen at 100" intervals from 1800°K to 2600°K.These chosen flames were set up, and their temperatures measured by the sodium D-line reversal method, the compositions being adjusted slightly where necessary until the measured reversal temperatures were within 5" of the desired temperature. This represented the limit of the method, and of the calibrated pyrometer on which the method is ultimately based. The temperatures were measured at the level of the waveguide system, that is, about 3 cm above the primary cones. Alkali metal was added to the flame as a salt spray from an atomizer containing a solution of the alkali metal chloride. I SoUARE-WAVE MODULATOR I U POWER ZIx f FLAMES ATTENUATORS CALIBRATED RESISTIVE AT TENU ATOR a+- + t L CRYSTALS f BALANCING RESISTIVE ATTENUATOR 1 PUSH-PULL Po FIG.1. Besides the temperature, the other important flame parameter is the thickness. This was measured at the level of the centre of the waveguide system, by a screw caliper, carrying on each limb a piece of platinum wire. The caliper was closed until the tips of the pieces of wire just glowed. Various other methods have been tried in these laboratories, but none were appreciably better than this simple device, RESULTS Let us consider the equilibria consequent upon the introduction of an easily ionizable metal into a flame. It is known that electrons are produced, some of which form hydroxyl ions, and that the metal hydroxide may be stable. M t s M + + c , OH- % OH + E, MOH % M + OH, All concentration terms are expressed in atm.Introducing equations for conservation of metal, and for charge balance, we have [XI = [MI + [M+] + [MOH], where [XI is the total M introduced into the system, [M+] = [el + [OH-]. Solving these equations by inserting the equilibrium constants, we obtain kI2(1 + [OHI/K2)(1 3- [OH]/&) + KikI(1 + [OH]/K2). KiFI The second term on the right-hand side arises from the finite amount of M+ formed, and may usually be ignored, while for sodium, and to a lesser degree, potassium, the term (1 -I- [OH]/&) may be put equal to unity since NaOH is relatively unstable, and may be neglected.5 Therefore, for the special case of sodium at the temperatures used in these experiments, we may write ~1INaI = [EIW + [OHIIKZ).F. M. PAGE 89 Inserting the attenuation per cni (p), which is proportional to the partial pressure of electrons (p = k[e]), or K1"aI = ( P 2 / W ( 1 + [OHI/K2, 1/82 = (l/K~kWal) + ([oHl/&k2[Nal&).A plot of 1/82 against [OH] should therefore yield a straight line, the ratio of whose slope to intercept is the value of K2, the equilibrium constant of the reaction OH- + OH + e. A typical set of results is given in table 1. The partial pressures of [OH] were cal- culated from the partial pressures of hydrogen and oxygen in the pre-burned gas mixture, and the thermodynamic data given in Lewis and von Elbe.6 TABLE 1 H;h comNPpsitio~z atF$;04 a g . thickness cm dbrcm 1/82 reversal temp. ("K) flame 2000A 62 27 11 4.6 -349 1.45 -241 17.2 1995 2000B 48 41 11 5.7 -313 1.15 -216 21.4 2000 2000C 41 48 11 6.8 -203 0.96 -209 23.2 1995 2000D 33 56 11 9.3 -187 0.95 -193 27.8 2000 Two similar sets of results, obtained at 2200" K, are shown in fig.2, where lip2 is plotted as a function of [OH]. It will be seen that the points do lie on straight lines, whose slope and intercept, though different for the two lines, do bear the same ratio to each other, as required by theory. These slopes and intercepts are given in table 2. 2200°K,NNaCI Two Atomizers 2200°K, N/2 NaHC030ne Atomizer 10 $2 5 I [OH]X 10' atrn /$HI x lo4 atm FIG. 2. Equilibrium constants were measured by this method at 100" intervals from 1900" K to 2200" K. Below this range, the ionization of sodium was insufficient to give a reason- able level of attenuation, The full set of results is given in table 2.TABLE 2 temp. (OK) slope intercept KZ Wm) 1900 1-02 x 105 12.2 1.4 x 10-5 2000 a 2.0 x 105 6.9 3.3 x 10-5 4-5 x 105 16.4 3.6 x 10-5 1.1 x 105 8.6 8.0 x 10-5 8 2200 c( 1.6 x 104 2.4 1.5 x 10-4 P 3.0 x 104 4.1 1.4 x 10-4 2100 The suffices a, /3 refer to experiments with differing values of Kl[Na], either due to a different atomizer, or to a different strength of salt solution in the atomizer.90 ELECTRON AFFINITY OF HYDROXYL At temperatures above this range, it was not possible to obtain a sufficient variation of composition, and an alternative method was adopted, in which, by comparing flames at different temperatures, the various constants of proportionality, the atomizer delivery, and the ionization of the alkali metal could still be eliminated, though their temperature coefficients had to be taken into account.We may write the equation developed in the previous section in the form Ki"a1 = (P2/k2>(1 + EoWK2). The temperature dependent terms in K1, i.e. the thermal ionization constant of sodium, may be estimated from the Saha equation for the ionization of alkali metals ; 7 the con- stant of proportionality between the attenuation, and the partial pressure of electrons (k) also depends on the temperature, and over a wide range of temperature, the change in the burnt gas volume, and the finite ionization of the sodium may also be significant. TABLE 3 temp. ("K) 2300 2400 2500 2600 K2 x lO4(atm) 2.95 5.8 11.1 14.1 All these temperature effects can be calculated readily, and combined into a correction factor with which the observations at high temperatures may be brought into comparison with those at a reference temperature-in the present case 2200" K.When this is done, we may write (1 + [OHI/K2)t = (1 3- [OHlIluz>o(Po/Pt>2f(T> wheref(T) is the correction factor, and the suffix 0 refers to 2200" K and t to the higher temperature. The factor (1 + [OH]/K& is that at 2200" K, and was obtained from the results of the previous section. All the data are available to calculate the values of K2 at the higher temperatures, that is up to 2600"K, from a knowledge of the easily measured attenuations PO and fit. Finally we may consider the possibility of a finite degree of ionization. In the derivation of the equation relating the attenuation to the amount of alkali metal in the flame, the term arising from the ionized alkali metal [M+] was ig- nored. At high temperatures, and with the more readily ionizable alkali metals, this is not valid.Indeed at 2600" K even sodium is 2 % ionized when a N solution is sprayed into the flame, and a more dilute solution of caesium will be almost completely ionized. Under these conditions of com- plete ionization, we may neglect the term arising from the un-ionized metal, while retaining that arising from the ion. The relation then becomes P I = I~l(1 -I- [OH]/&). This can be used to evaluate K2 if the atomizer delivery, and the constant of proportionality (k) are known, or else it can be combined with the expression for the attenuation due to sodium, where the fraction of metal ionized may be neglected, and either the constant of proportionality, or the ionization constants of the alkali metals and the atomizer delivery may be eliminated.If one assumes that the latter two quantities are known accurately, then a value for K2 is obtained (1.3 x 10-3 atm) which is in fair agreement with the otherF . M . PAGE 91 values obtained at this temperature. The importance of this method lies in the support that it gives to the theory behind the previous methods, rather than its value as a separate determination. The various values of K2 obtained during this work are plotted logarithmically as a function of 1/T in fig. 3, and the graph has a slope which corresponds to an electron affinity of 66.1 kcal, or 2.86 eV, in excellent agreement with the mean of the values (2.87 eV) obtained from the separate measurements by applying the Saha equation in the form loglo K2 = (- 5050 V/T) + loglo T - 5.6.The values thus obtained are included with other similar values in table 4. The concord of the values for the electron affinity determined by methods depending on both the second and third laws of thermodynamics is itself strong support for the values so obtained. DISCUSSION The value of the electron affinity of the hydroxyl radical that has been obtained experimentally in this work is in good agreement with other estimates that have been published, based on similar experiments,zS 3 but since these estimates have been criticized recently 8 in comparison with the lower values suggested by theoretical arguments, it is necessary to consider all the methods by which the experimental values have been obtained.These methods are, including the three described above : (a) from the isothermal variation of composition, (b) from the comparison of flames at different temperatures, (c) from the complete ionization of caesium, (d) from the number of heavy ions in a flame. Smith and Sugden 2 studied the dielectric constant of a flame at frequencies about 100 Mcls and deduced the relative numbers of electrons and heavy ions in the flame. From the principle of electrical neutrality, they were able to separate these into potassium and hydroxyl ions, and give two values for the equilibrium constant K2, viz., 4.2 x 10-5 atm at 2050" K and 1.2 x 10-4 atm at 2170" K. (e) From the absolute level of the attenuation of a flame.The same workers 3 showed that though the relative attenuations of sodium and potassium were correct, yet they were both low in comparison with the pre- dictions of the Saha equation, and this was ascribed to the formation of hydroxyl ions, by the same argument as used in the present work. They deduced values for K2 from three flames : 7 x 10-5 atni at 2145" K, 1.2 x 10-4 ,, 2245"K, 3 x 10-4 ,, 2260°K. This method could be applied to the results used in methods (a), (6) and (c), but some additional values were given by the earlier workers in a private com- munication, which it is preferable to consider : temp. ("K) 2060 2097 2137 2195 2243 2291 2291 2257 K2 x lO4(atm) 0.28 0.58 1.0 0.9 1.2 1.7 3.4 2.3 These results were obtained from flames in decreasing order of fuel to air ratios.James and Sugden 9 studied the intensity of the resonance radiation emitted by a flame containing alkali metal, and were able to estimate the value of K2 from the decrease in the intensity of the radiation from caesium with dilution, due to a finite degree of ionization. The value given was 1.2 x 10-4 atm at 2167" K. (g) From the effect of other electron acceptors on the attenuation of (f) From the emission of resonance radiation by a flame. a flame.92 ELECTRON AFFINITY OF HYDROXYL The addition of about 0.1 % of a halogen to a flame containing alkali metal produces a measurable reduction in the attenuation and a theoretical analysis of this reduction, assuming that halogen acid, alkali halide and halide ions are formed, in addition to the hydroxide ions and alkali hydroxide postulated in this paper, and that all are at equilibrium, leads to the expression : [(Po/P)~ - 11(1/[YI) = 1/K4’ + I/&‘ + [Yl/K4’Ks’, where K4’ = K4(1 + e)(l + +), Ks’ = K5(1 + e)(l + +’), [Y] = total concentration of halogen, 8 = [halogen acid]/[halogen atom], fi = [OH]/&, $’ = lOHIK2, K4 = [Hal][metal]/[alkali halide], K5 = [Hal][electron]/[halide ion], halogen, respectively.halogens respectively, can be obtained from the experimental data.10 PO, p = attenuation in the absence and presence of added The values of K4/ and K5’, which come from the effects of alkali halide and Taking the ratio of these effects to eliminate 8, Ks’lK4’ = (Ks/K4)(1 -k $’)/(I -k $1, or 1 + $’ = 1 + [OH]/& = (1 + $)(Ks’K4’1K4‘Ks).The mean value of K2 obtained from the preliminary results on the effect of chlorine, bromine, and iodine on sodium, potassium, rubidium and caesium at a temperature of 2243” K, and using the values of 1 + 4 given by Smith and Sugden (1.0, 1.2, 1.7 and 3.5 for the flame used for Na, K, Rb and Cs respectively) was 2 3 x lO-4atm. (h) From the halogen effect in isothermal sets of flames. It is necessary, when evaluating K2 by method ( g ) , to calculate the equilibrium constants K4 and Ks. The isothermal sets of flames used in the experimental part of this paper enable this calculation to be avoided. The argument used follows that of the previous method in that the halogen acid effect (0) is eliminated by taking the ratio of the salt and ion effects.The attenuation in the absence of halogen is given by the equation derived earlier, which is, using the $-notation : KlEXI = EE12(1 + +)(I + +’I, or 1!P2 = (UK1[XIk2)(1 + +)(l + $0 Combining this with the expression for R, the ratio of the halogen effects, we obtain RIP2 = (Ks/KiK4k2~Xl)(1 + +‘Y. That is, a plot of the square root of R/P2 against [OH] should yield a straight line, from whose slope and intercept the value of K2 can be deduced in the same way as was done in the first method described. This method has been used to determine the value of K2 from a study of the effects of chlorine on the attenuation produced by caesium, and gave a value of 3.1 x lO-5atm at 2000”K, and 1.3 x lO-4atm at 2200°K. The results at 2000” K are illustrated in fig. 4. The extrapolation required is a long one to be made on only three points, but is a fairly easy one to make.These estimates of the electron affinity of the hydroxyl have been quoted at some length since in most cases the estimate was incidental to the main interest of the work from which the data were taken, or else the estimate was assumed andF . M. PAGE 93 the data used to calculate other functions, whose numerical values, determined by other methods, have been used in the present calculations. It is necessary, in order to assess the weight to be attached assumptions on which the various methods are based, how far these assumptions are valid, and how far the different assumptions made in the different methods support each other by the concord of the results. Although the majority of the methods given depend upon the measurement of the attenuation of microwave radiation by the flame, it is significant that an entirely different method (f) gives a result which corresponds closely with the remainder.The attenuation methods all depend on the proportionality of the observed attenuation and the concentration of electrons, but it has been demonstrated many times that under conditions where the only variable is the normality of the salt solution in the atomizer, the attenuation is proportional to the square root of this normality as predicted by Ostwald’s dilution law for small degrees of dissociation. Furthermore, Belcher and Sugden 11 showed that the variation of the attenuation with frequency is entirely compatible with the assumption, to the experimental data, to consider the I 5 I @H) 1oSatm FIG. 4.3 while in a paper by Andrews, Axford and Sugden,l2 the number of electrons in a transient flame was measured by the attenuation, and shown to be the same as the number derived from measurements of the d.c. conductivity. Only in two methods (c), (e) is any assumption made about the exact value of the constant of proportionality; in all others it is enough that such a proportionality exists. Method (d), not being an attenuation method, does not make this assumption, though it does make a comparable appeal to electromagnetic theory. In methods (c) and (e) also, the magnitude of the ionization constant of the alkali metal is obtained from Saha’s equation, while in method (b) this equation is used, though only to obtain the temperature variation of the ionization constant. The thickness of the flame is concerned in all methods except (f) and (g). The possibility that indrawn air may affect the composition, the temperature, or the temperature distribution cannot be important in the regions of the flame where measurements were made; method (f) was used with a flame sheathed by a second flame, a technique used by Sugden and Wheeler in their resonant cavity method,l3 which has produced numerical results for the alkali metals in close agreement with those from the direct attenuation methods.Methods (a), (b), (c), (d), (h) all used a nitrogen sheath to protect the flame, while methods (e) and (8) used an unsheathed flame, though one in which the temperature cross-section was fairly uniform.Finally, sodium was the substrate in methods (a), (b), (c) and ( g ) , potassium in methods (d), (e) and ( g ) , rubidium only in method (g), and caesium in methods The measurement of the temperature of the flame is fundamental to all the methods, and the sodium line reversal method has been used throughout the ( 4 7 (f>7 (9) and (h).94 ELECTRON AFFINITY OF HYDROXYL work. This method is the most appropriate one for the study of equilibria in which atoms of alkali metal are involved. It has been found that similar flames, set up by different workers at different times, gave closely similar results, suggesting that the figures obtained have a real significance, and that the temperatures quoted in this paper form a coherent set.Furthermore, the temperature is involved in the estimation of other equilibrium constants used in methods (b), (e) and (g), and these methods give values in agreement with the remainder. All methods use the values of the hydroxyl concentration in the burned gases at the measured temperature obtained by calculation from the thermodynamic data given ia Lewis and voii Elbe.6 The use of these calculated values is probably satisfactory, since in almost every case the flames were well removed from stoichiometry. The vexed question of whether or not the assumption of thermo- dynamic equilibrium is valid cannot be answered simply. The hot gases of the secondary zone of the flame have a few milliseconds in which to reach equilibrium before reaching the measuring zone, but the possibility that this is insufficient cannot be overlooked.In any case, the flame is not an isolated system, and though the term “ equilibrium constant ” has been loosely used in this paper, it is more proper to consider the flame as a steady state, in which the appropriate concentration products may approach the values of the true equilibrium constants fairly closely. No evidence has yet been found that would suggest unquestionably that any appreciable degree of disequilibrium existed, while the coherence of the results obtained by the various methods is evidence that the assumption of equilibrium is at least a good approximation. In addition, the study of the halogens referred to under method (g), has led to preliminary values for the electron affinities of chlorine, bromine and iodine which agree with the values obtained by completely different methods to within a few kilocalories.These results depend on a much more complicated system of equilibria than do the results for hydroxyl, and yet there is no evidence for any significant deviation from the expected results, due to disequilibrium. Although the criticisms based on the fact that all the methods described use flames to reach the ternperaturcs required apply to all methods, and there must be some doubt about thc hydroxyl concentration, the temperature, and disequi- librium, yet the fact that eight different and distinct methods yield coherent results, and these results cover a range of 700 deg., and as mentioned, other quantities can be evaluated on the basis of these results, which are in good agreement with the accepted values, is strong indication that the experimental value given to the electron affinity is correct.It may be said in passing that the question of whether it is hydroxyl which is in fact responsible for the observed effects has not been answered. No other possible entity has been considered, but such an entity must vary with the flame composition in the same way as does hydroxyl. The flames do contain large quantities of N2, H2 and H20, but these have negligible electron affinities, while of the minor constituents, the hydrogen atom concentra- tion is of the order of that of hydroxyl (lO-4atm) and the oxygen atom con- centration is several powers of ten lower. Neither of these minor constituents can therefore contribute appreciably to the removal of electrons.It has been claimed throughout this paper that the various methods give results that are in good agreement. How good this agreement is, may be judged from table 4, where the electron affinities are calculated from the equilibrium constants by Saha’s equation, and are collected together. Since there appears little doubt that the experimental value is correct, it is now necessary to examine the evidence for the indirect estimates, which lead to a value of about 50 kcal. These methods are : lattice energy calculations, argu- ments based on an analogy with the oxygen atom, and certain extrapolations based on spectra. Of these, the lattice energy calculations are by far the most important, and lead to two very different values, depending on whether or not the dipole moment of the hydroxyl radical is taken into account.F .M . PAGE 95 The arguments by analogy are based on the fact that the oxygen atom and the hydroxyl radical have very nearly the same ionization potential, and that therefore it is reasonable to expect that they would also have thc same electron affinity. Tf this was so, the electron afinity of hydroxyl would be about 53 kcal. However, as James and Sugden 9 mcntion, Mulliken has pointed out that thc valence statc of thc oxygen atom is different in the free atom and in thc hydroxyl radical, and the addition of an electron to thc latter will completc an inert gas shell. An application of bond theory suggests that this will lead to thc electron affinity of the hydroxyl radi- a l bcing about 15 kcal higher than that of the oxygen atom, i.e.about 68 kcal. The methods which arc based on a spectral correlation of the measured clectron affinitics of thc halogcns with the so-called electron-transfer spectra of thc alkali halides, followed by an interpolation to determine the electron affinities of the hydroxyl, and other radicals, are of extremely doubtful value.14 They suggcst a valuc of about 83 kcal which, un- expectedly, is very close to the un- corrected lattice encrgy valuc given by Goubcau.ls This author actually obtained a valuc of 78 kcal, but thc higher figure follows from the use of thc later value of the heat of formation of hydroxyl obtained by Dwyer and Oldenburg.16 Goubeau and Klemm 17 corrected the earlier electron affinity by assuming that the TABLE 4 temp.(OK) 1900 2000 2100 2200 2300 2400 2500 2600 2600 2050 2170 2145 2245 2260 2060 2097 21 37 2195 2243 229 1 229 1 2257 21 67 2243 2000 2200 K2 (atm x 105) 1.4 3.4 8.0 14 29.5 58 110 140 130 4-2 12 7 12 30 2.8 5.8 10 9 12 17 34 23 12 23 13 3.1 VeV 2.80 2.82 2-83 2.88 2.88 2.89 2.89 2.98 3.00 2.86 2.86 2.92 2.99 2.82 2.95 2.88 2-85 2-96 2.98 2.98 2.84 2.87 2-86 2.85 2.85 2.88 The mean value of all detcrminations is 2.87 eV, or 66.2 kcal, with a probable error of the mean of 0.3 kcal. The value derived from a plot of loglo KZ as a function of 1/7 is 69.8 kcal. This must be reduced by about 6 kcal to give the value at 0" K. hydroxyl radical had a dipole moment of 2 D, and from this they estimated that the true valuc of the electron affinity should be somc 29 kcal lowcr, that is, 53 kcal, which is the same as the value deduced, incorrectly, from an analogy with the oxygen atom.While the lattice-encrgy calculations of thesc authors is probably the best so far, the figures thus derived may be in considerable error, since they are obtained as the difference of two large quantities, and furthermore, the dipole correction, which amounts to ovcr one-third of the wholc, may wcll be grcatly in error, and it cannot be said that the value is in any way in disagreement with the value of about 65 kcal which follows from the correct argument by analogy. From this cursory survey, it is apparent that the various indircct estimates arc compatible with any value of the electron affinity bclwcen 45 and 85 kcal, but that the value of 65 kcal can bc supported well, probably better than most.The discrepancy which it has been claimed in a recent review 8 existed betwccll the indircct estimates and thc valuc obtained from a study of flames is sccn to bc illusory, and the two methods are in good accord. Considerable wcight must be attached to the practical determinations outlined in this paper, and the value of the electron affinity of the hydroxyl radical at absolutc zero is put, after con- sidcring all the dcterrninations and cqtirnates, at the mean of the expcrimental96 THEORY OF MOLECULAR OSCILLATOR determinations from the Saha equation (66kcal) and by graphical methods (70 kcal at 2000" K which becomes 64 kcal at 0" K), that is, at 65 kcal i 1 kcal, or 2-82 eV. The author would like to express his indebtedness to his many colleagues, in particular Dr. T. M. Sugden, for continued advice, guidance, and encourage- ment during the progress of this work. 1 RoIla and Piccardi, Atti accad. Lincei, 1925, 2, VI, 29. 2 Smith and Sugden, Proc. Roy. SOC. A, 1952,211, 31. 3 Smith and Sugden, Proc. Roy. SOC. A, 1952, 211, 58. 4 Sugden, this Discussion. 5 Sugden and Smith, Proc. Roy. Soc. A, 1953, 219, 204. 6Lewis and von Elbe, Combustion, Flames and Explosions of Gases (Cambridge 7 Saha, Phil. Mag., 1920, 40, 472. 8 Pritchard, Chem. Rev., 1953, 52, 529. 9 James and Sugden, Proc. Roy. SOC. A , 1955 (in press). 10 Sugden, 5th Int. Symp. on Combustion (Pittsburgh, 1954, in press). 11 Belcher and Sugden, Proc. Roy. SOC. A , 1950, 201,480. 12 Andrews, Axford and Sugden, Trans. Faraday Soc., 1948, 44,427. 13 Sugden and Wheeler, this Discussion. 14 Rabinowitch, Rev. Mod. Physics, 1942, 14, 112. 15 Goubeau, 2. physik. Chem. B, 1936, 34,432. 16 Dwyer and Oldenburg, J. Chem. Physics, 1944, 12, 357. 17 Goubeau and Klemm, 2. physik. Chem, B, 1937,36, 362. University Press, 1938).

ISSN:0366-9033    

DOI:10.1039/DF9551900087

出版商:RSC    

年代:1955

数据来源: RSC

摘要:

96 THEORY OF MOLECULAR OSCILLATOR THE THEORY OF A MOLECULAR OSCILLATOR AND A MOLECULAR POWER AMPLIFIER BY N. G. BASSOV AND A. M. PROKHOROV Lebedev Institute of Physics, Academy of Sciences of the U.S.S.R., MOSCOW, U.S.S.R. Received 4th April, 1955 1. INTRODUCTION A molecular oscillator is the name given to a system using energy connected with transitions among energy levels. A cavity resonator is a circuit of the molec- ular oscillator. The molecules arriving at the cavity are virtually all in the upper states. Back coupling in the molecular oscillator is made through the resonator’s electromagnetic field which, affecting the dipole moments of the molecules, causes induced radiation of the molecules. To create excitation conditions the power of molecular radiation must be higher than that of the losses in the loaded cavity.The saturation effect is the nonlinear character which gives an amplitude of stationary oscillations in the molecular oscillator. A distinctive feature of the molecular oscillator is its great stability of frequency, as the frequency of oscillations depends very little upon exterior conditions and is substantially determined by the frequency of the spectrum line. Therefore, the molecular oscillator can be used as a frequency standard on the one hand, and as a spectroscope with high resolving power, on the other. In conditions under which oscillations are not maintained, the device acts as an amplifier. Such an amplifier may have a noise figure very near unity. In OUT article 1 we pointed to the possibility of building a molecular oscillator.Such an oscillator is reported to have been realized.2N. G. BASSOV AND A . M. PROKHOROV 97 2. THEORY OF THE MOLECULAR OSCILLATOR We shall deduce formulae determining the frequency of the molecular oscillator w using an isolated spectrum line of frequency us. At the same time formulae will be deduced for the amplitude of stationary oscillations of the electric field E inside the cavity. This problem resolves itself into the examination of the behaviour of a cavity filled with a medium with negative losses in the neighbourhood of frequency cog. In solving this problem we disregard the Doppler broadening of the spectrum line, considering that it is possible to take such a type of oscillations in the cavity where there is no Doppler broadening. Let the said medium be characterized by the complex dielectric constant - 1 + hNx, (1) E == - iE" - where x = molecular polarizability, N = density of molecules in the cavity.The value x with the saturation effect taken into account can be written as follows : 3 s 4 where T = Zfi = mean time for molecules to travel through the field, Z = cavity length, 5 = mean velocity of molecules, p i = probability of molecules being at the level k at the moment of arriving at the field inside the cavity. Let NO be the number of active molecules * travelling through the cavity cross-section S per second, then Substituting (2) and (3) in (l), we shall get expres .ions for E' and E". W e shall supposc that the clectric field intensity in the cavity section is uniform.With the field E dependent upon the section co-ordinates, it is necessary to take into account that the saturation effect value differs for different points inside the cavity. Such taking into account, however, can give nothing new but only complicates our expressions. The equation for the electric field intensity in the cavity will be put down as follows : N = No/SG. (3) d2E wodE ~ 0 0 2 - + - - + - E = O , dt2 Q dt E (4) where wo = natural frequency of the cavity without molecules. For a stationary condition E = EO exp (iwt). Substituting expression for E and E in (4), and taking the real and imaginary parts equal to zero, we obtain two equations to determine EO and w : (5) * By the number of active molecules we mean the difference between the numbers of molecules at the high level and at the low level of the given transition.D98 THEORY OF MOLECULAR OSCILLATOR If wo = wg w w and E-+ 0, then we obtain from (6), (I), (2) and (3) the (7) This is the boundary condition of self-excitation we have already arrived at following expression : 4nNo - Im~m,12Q~2-+1. Sh by another way.1 If the approximate expression for stationary amplitude of oscillation will be and the power surrendered by molecules to the cavity is equal to +Nohog. This is the maximum power the molecular oscillator can givc. From (6), (I), (2) and (3) we obtain the following cubic equation for stationary frequency co : Let us put WOL coo2 - wg2 - - Q we get from (7) A = 3wg2 - wo2 + wo2[F + '1 ' Q2 or, as 00 M wg and 007 > 1, As seen from (8) the frequency of stationary oscillations is not equal to the frequency of the spectrum line even when thc natural frequency of the cavity coincides with the frequency of the spectrum line. For a molecular oscillator where cr)oT = 2 x 108, Q = 102, (wg - wo)/wo = 4 x 10-4, 1 we get It follows that in this case the absolute frequency of the spectrum line can be determined with an accuracy of not less than 10-9.p g - - w o - Q -2; 4 x 10-10, ~ = 5 x 10-11. wo 007 Quo7 3. THE MOLECULAR POWER AMPLIFIER If the self-oscillation condition in the molecular oscillator is not fulfilled, such a device can be used as a power amplifier. Let us determine the value of the power amplification ratio of such a device. Instead of the eqn. (4) we shall have the following where B = the amplitude of the external force, which is due to the supplying of power to the cavity,N. G . BASSOV AND A . M . PROKHOKOV We solve cqn. (9) as follows : E = A exp (iwt) 99 For resonance condition B A - 1 4nNo I m,", 1272' - - Q Slh The power amplification ratio is equal to where x is constant for a givqn molecular amplifier. In deducing (10) we consider an amplifier working without saturation effect, i.e., The amplifier pass band is - 2/7. The questions concerning noises in the molec- ular oscillator and amplifier will be discussed in a separate paper. 1 Bassov and Prokhorov, J, Expt. Theor. Physics (U.S.S.R.), 1954, 27, 431. 2 Gordon, Zeiger and Townes, Physic. Rev., 1954, 95, 282. 3 Landau and Lifshitz, Quantum Mechanics, (1948), part 1, pp. 170-172. 4 Karplus and Schwinger, Physic. Rev., 1948, 73, 1020.

ISSN:0366-9033    

DOI:10.1039/DF9551900096

出版商:RSC    

年代:1955

数据来源: RSC

摘要:

N. G . BASSOV AND A . M . PROKHOKOV 99 GENERAL DISCUSSION Prof. A. R. Ubbelohde (Imperial College, S.W.7) said: With regard to the paper by Sugden, it is interesting to inquire at what order of concentrations Saha’s equation for the ionization of alkali metals in the gas phasc will become inadequate. Pursuing thc analogy of solutions of weak electrolytes proposed by Dr. Sugden, the principle of similitude suggests that departures from ideality might be expected at concentrations C where 22.5- (Dgas)3 Csolution (Dso~ution) 3’ since the particles arc subjected to comparable potentials at distances in the ratio Dsolution/Fgas. On this rather crude analogy, if it is appropriate to write for the dielectric constants Dsolution - 80 and Dgas - 1 departure from ideality should be noticeable at about 10-6 of the concentration at which departures from ideality occur in dilute solution.This would seem to be well outside the very low concentrations of electrons calculated by Dr. Sugden, especially since at higher temperatures non-ideal behaviour is shifted to highcr concentrations. However, the Debye-Huckel model of excess ions of the opposite sign surrounding the cation, and vice versa, is not applicable without closer examination when the negative ion is a free electron, since on concentrating elcctron gas around the positive ions quantum effects can intervene. ‘The situation is rather similar to that of the dissociation of a metal vapour at various concentrations in the gas phase. At low concentrations thc metal atoms behave likc any other gas, but at sufficiently1 0 GENERAL DISCUSSION high concentrations overlap effects must intervene between neighbouring atoms.Can Dr. Sugden say if the technique he describes has been tested with metal vapours at various concentrations? Dr. T. M. Sugden (Cambridge University) said : In reply to Prof. Ubbelohde, the experimental results on the variation of the electron concentration with the concentration of alkali metal atoms provide a powerful basis for the conclusion that amounts up to 1012 elcctrons/cm3 do not diverge scriously from ideal be- haviour. The methods used are not suffciently accurate to detect divergences of a few per a n t from ideal behaviour. Work on the ionization of pure metals has only been carried out at lower temperatures where the electron concentra- tion was considerably smaller than some of those used by us, and using lcss accurate methods, but so far as it went supported the ideal behaviour. Mr.R. P. Bell (Oxford University) said: It is of interest to note that the existence of the species CaOHf and BaOHt in aqueous solution is fairly well established by the work oI' C. W. Davies and others, and their stability constants are reasonably accounted for on a purely electrostatic basis. The heats of forma- tion deduced by Sugden and Wheeler for BOH+ in the gas phase are about 300 kcal/mole. If this is divided by 80, the dielectric constant of water, we obtain 3.7 kcal/mole, which is of the right order of magnitude to account for the observed stability in water (e.g. [Ca2+][OH-]/[CaOH+] N 0.03).No exact correspondence would, of course, be expected, since the use of the macroscopic dielectric constant is a very crude way of taking solvation into account. With reference to the point raised by Ubbelohde, I do not think that interionic forces would cause any appreciable deviations from thermodynamic ideality in the systems studied by Sugden and his co-workers. The Debye-Huckel limiting law (which will serve as a rough guide) predicts that the ionic concentrations needed to produce a given departure from ideality are proportional to (DT)3 for different media. For aqueous solutions at room temperature deviations of 10 % occur at concentrations of about 10-2 M. The corresponding concentration for the gas phase will be 10-2 x (80)-3 = 2 x 10-8 M, i.e.about 1013 ions cm-3. This is much greater than the concentrations actually observed : further, as pointed out by Agar, the high temperatures used will also favour ideality. Dr. J. N . Agar (Cambridge University) said: Mr. Bell's conclusion that the Debye-Hiickel type of electrostatic interaction between electrons and ions will not be important at the concentrations of charged particles which OCCLE in Dr. Sugden's experiments is strengthened when one takes into account the high temperatures concerned. The factor governing the activity coefficient a t a given concentration is (DT)* rather than D*. Thus in comparing aqueous solutions at room ternperaturc (D - 80, T - 300" K) with flames (D - 1, T - 2000" K) it is evident that the dccrcasc in D is to a considerable extent compensated by the increase in T.Dr. T. M. Sugden (Cambridge University) (communicated) : The point raised by Prof. Ubbelohde can be resolved into two distinct questions from the theorctical standpoint : (i) whether thcre is sufficicnt interaction betwcen the electrons on account of thcir charge to cause divergence from ideality, and (ii) whether the electrons will diverge from Boltzmann (ideal) statistics in any case. Mr. Bell and Dr. Agar have commented on (i), but it is perhaps useful to add another word here. For thc highest electron conccntrations used in flames (- lOl2/cm3) at 2000" K, where 1/DT is 5 x 10-4, the average interaction between adjacent electrons is - 2.3 x 10-15 ergs, compared with kT - 2.8 X 10-13 ergs. A similar calculation for a millinormal solution of unit chargcs in water at 300" K (where 1/DT-4 x 10-5) gives an interaction of 3 x 10-15 ergs, with kT-4 x 10-14 ergs.Thus on the basis of point chargcs the divergence arising from this typc 1 Srivastava, Proc. Roy. SOC. A, 1940, 175, 23. 2 Srivastava, Proc. Roy. SOC. A , 1940, 176,343.GENERAL DISCUSSION 101 of interaction will be very much less in the flame gases than in millinormal aqueous solution of a uni-univalent electrolyte. The wavelength of the de Broglie waves for free electrons at 2000" K is - 5 x 10-7 cm, compared with an average distance apart of 10-4 cm at lO*2/cm3, so that there is reasonable justification for the point approximation. The second question is readily resolved along these lines. There will be no effective divergence from Boltzmann statistics if nh3/(2nmkT)+ < 1, where n is the number per cm3 of mass m.Using n = lO12/cm3 at 2000" K, we find that the above function becomes -4 x 10-7, which amply fulfils the required con- dition. There is thus no physical reason why the dilute electron gas should not be treated as ideal under our conditions. Dr. E. Warhurst (Manchester University) said : In his introductory remarks, Dr. Sugden mentioned that values for the electron affinities of the halogens could be obtained by admitting sodium halides to the flame zone. In view of the im- portance of Page's values for the electron affinity of the OH radical (and particularly since there is a disagreement with earlier values) I should like to ask whether this method has actually been used for any of the halogens and, if so, what values were obtained for the electron affinities.Mi. F. M. Page and Dr. T. M. Sugden (Cambridge University) said : In reply to Dr. Warhurst, our studies have embraced measurements of the electron-accepting effects of the halogens, a full account of which is to be published shortly, and the results, broadly speaking, support the established values. The analysis of the results is more complicated than for hydroxyl, since in every case the alkali salt is reasonably stable, and since a proportion of the added halogen (an overwhelming one for fluorine and chlorine) is present as the halogen acid. The experimental figures therefore show a number of effects, often difficult to disentangle. Using theoretical values for the dissociation constant of the halogen acid it is found that at lower temperatures (- 1800" K) the electron affinities deduced are about 30 kcal below the commonly accepted ones, but that the effective electron affinities rise with temperature, and smooth out to the following values in the region of C1 = 86 kcal, Br = 82 kcal, I = 76 kcal.It is considered that the deviations at low temperatures arise from some lack of equilibration of the reactions involving halogens, and it is significant that the effective stabilities of the alkali halides show similar variations with temperature, the difference between derived electron affinities and heats of formation of alkali halides being independent of temperature. A semi-quantitative explanation can be obtained by reference to the reaction kinetics of open systems, considering the flame as a steady-state phenomenon.This will be described in the forthcoming paper. No such effect has been found with hydroxyl, possibly because of the presence of a large quantity of water and hydrogen, which help to equilibrate it. The dominant effect found with fluorine was formation of the salt, and it was not possible to evaluate a reasonably accurate value of the electron affinity. Prof. F. S. Dainton (Leeds University) said: A knowledge of the absolute values of the electron affinities of gaseous atoms and radicals provides the key to a great deal of useful data concerning hydration heats of cations and anions of great utility in the study of solution reactions, especially charge transfer reactions.To take a simple example, Mr. Page has shown GH = 65 kcal, and if my memory serves me well, EoH + SOH-, where SOH- is the hydration energy of the hydroxide ion, is about 148 kcal. Hence SOH- is 83 kcal which is placed agreeably between Sw and Scl- as evaluated by Pitzer, Slansky and Latimer just before the war, on tbe assumption that heats and entropies of hydration of simple ions are pro- portional to one another. Perhaps Dr. Page has already considered this and other related consequences of his result in greater detail. If so, it would be very inter- esting to known his conclusions. 2500-2600" K :102 GENERAL DISCUSSION Mr. F. M. Page (Cambridge University) (communicated): In reply to Prof, Dainton, when considering the estimation of thc electron affinity of hydroxyl from solution data, I had cause to examine the various suggested heats of hydration of ions, and the conclusions drawn may be of general interest. The value for the sum of the heat of hydration of the OH- ion and thc electron affinity of OH which is most commonly quoted is that derived by Evans and Uri,l based on a cycle suggested by Baughan, Evans and Polanyi.2 It is, perhaps, not commonly realized that this cycle includes a third unknown quantity, namely, the heat of hydration of the hydrogcn ion, and that the sum of these three unknown quantities is the figurc actually obtaincd when cxpcrimental data are inserted in the cycle.This sum is 429 kcal, and is piobably accurate to within 3 kcal. I have claimed that the electron afiinity of OH is 65 kcal, which leaves the sum of the heats of hydration of the two ions as 364 Similar cycles, involving the halogen acids, were used by Baughan 3 to derive the sums of the heats of hydration of the ions for the four halogens and H 1 , and these sums are, using the experimental values for the electron affinities collcctcd by Fritchard : 4 fluorinc 375 kcal, chlorinc 346 kcal, bromine 338 kcal, iodine 326 kcal, and thcse are also probably coirect to the sanic order of magnitude. Thc great difficulty lies in separating the two hcats of hydration.Baughan used the heats of hydration due to Evans and Eley 5 and estimated the heat of hydration of H to be 280 kcal, which lcads to the heat of solution of OH- suggested by Prof. Dainton. There is, however, a difference of opinion about the accuracy of these heats of hydration of the halide ions, and the latest workers favour much higher values.The heat of hydration of a salt can be derived from the lattice energy and the known heat of solution, and the difference between the heats of hydration of pairs of salts with one common ion, such as the alkali halides and hydroxides are fairly well cstablishcd, and are probably reliable to 2 kcal, the major source of error being the lattice cnergy, which will tend to cancel out. The values given by all workers fall within a very narrow range, and the differences between the other halogens and iodinc are, as the mean of the valucs of Bernal and Fowler,6 Evans and Eley,s Gurney,7 Latimer, Pitzcr and Slansky,8 Goubcau and Klemm,g and Verwey :lo fluorine 48 kcal, chlorine 16 kcal, bromine 10 kcal.The problem of determining the heat of hydration of a given ion then reduces to the problem of apportioning the heat of hydration of a salt between the cation and anion. Bernal and Fowlcr, pointing out that the heat of hydration should be inversely pi oportional to the ionic radius, took as their starting point potassium fluoride, the crystal radii of whose ions are equal (they adjusted their values slightly to take into account their theory of the structure of water). Similar argu- ments were used by Gurney, and by Evans and Elcy, and the results were similar, the heats of hydration of Na+ and I- being 115 and 50 kcal respectively, to the nearest 5 kcal, for each of these papers. Latimer, Pitzer and Slansky did not agree with the use of crystal radii in the study of solutions, and used an cmpirical correction of 0.1 A for negative ions, and 0.85 A for positive ions, and their values 3 kcal. 1 Evans and Uri, Trans.Faraday SOC., 1949, 45, 224. 2 Baughan, Evans and Polanyi, Trans. Faraday Soc., 1941, 37, 377. 3 Baughan, J. Chem. Soc., 1940, 1335. 4Pritchard, Chem. Rev., 1953, 52, 529. 5 Evans and Eley, Trans. Faraday Soc., 1938, 34, 1093. 6Bernal and Fowler, J. Chem. Physics, 1933, 1, 515. 7 Gurney, Ions in Solution (Cambridge, 1936). 8 Latimer, Pitzer and Slansky, J. Chem. Physics, 1939, 7, 108. 9 Goubeau and Klemm, 2. physik. Chem. B, 1937,36,362. 10 Verwey, Rec. trav. chim., 1942,61, 127.GENERAL DISCUSSION 103 are therefore very different to those of the earlier workers : 95 kcal for Na+ and 72 kcal for I-.Almost identical values were proposed independently by Verwey, and it seems probable that these estimates are the best yet. Somewhat earlier, Goubeau and Klemm had quoted results for the heat of hydration of the alkali metal ions " based on the theory of Fajans for the electrical asymmetiy of the H20 molecule " which lead to a value of 98 kcal for Na-1. and 68 kcal for I-. The referee to this paper has added in a footnote : " E. Lange . . . has measured the heat of hydration of Na+ by e.m.f. methods, and finds it to be 101 kcal." Latimer, Pitzer and Slansky also discussed absolute electrode potentials in relation to their heats of hydration for the ions, and their results are used as a basis by Brewcr, Bromley, Gilles and LofLq-en 1 in their compilation of thermodynamic data for aqueous ions.They give, as their considered value, 100 kcal for Na-C- and 61 kcal for I-. When the mean heats of hydration for the halide ions determincd by either of these arguments are fed into the cycle proposed by Baughan, the following values for the heat of hydration of H+ are obtained, and this in turn put into the cycle of Evans and Uri leads to corresponding values for the heat of hydration of OH- : SH+ meanSH+ SOH- Bernal and Fowler 280 282 28 1 279 280 84 Latimer and Verwey 254 259 258 256 257 107 The so-called electron-transfer spectra of the halide ions in the ultra-violet have been discussed by Rabinowitch2 and Parkas and Farkas,3 and though their explanation is not beyond criticism, there does appear to be a strong cor- relation between the absorption maxima and the sum of the electron affinity of the parent radical and the heat of hydration of the ion.It is generally agreed that the relation between v the frcqucncy of the maximum and the energy sum is of the form whcn E is the electron afiity, S the heat of hydration and Q represents the energy gained on transferring an clectron from the ion to a water molecule, and is a positive quantity. N ~ v = E 4- S - Q, We may examinc this relation for the halogens and hydroxyl. ion Cl Br I OH NhV 158 143 127 153 E + S (Latimer and Verwey) 175 161 145 173 E + S (Bernal and Fowler) 150 137 1 20 149 Thus, while both sets of figures give a reasonably constant difference between the energy sum and N / ., the set due to Bernal and Fowler make Q negative. The figures of Latimer and Verwey are therefore to be preferred on these grounds. It is worthy of note that only two values for the heat of hydration of OH- have been given. Goubeau and Klemm suggested that it was approximately 2 kcal less than that of fluorine, on the basis of their lattice energy calculations. The weight of evidence now points to it being 10 kcal farther away from fluorine, and a systematic error of 10 kcal in their lattice energy calculations would increase their value of the electron affinity of OH to 63 kcal, in close agreement with the experimental vahe. Bernal and Fowler give a value of 105 kcal, which is con- siderably higher than any of the halide heats of hydration that they give.This is possibly due to the choice of a low value for the crystal radius of OH-. 1 Brewer, Bromley, Gilles and Lofgren, Utiiv. Calif. Rud. Lab. Reports, 1949, p. 160. 2 Rabinowitch, Rev. Mod. Physics, 1942, 14, 112. 3 Farkas and Farkas, Trans. Faraday Soc., 1938,34, 1 1 13.104 GENERAL DISCUSSION In the absence of any positive experimental evidence by which the heat of hydration of any one ion can be unequivocally fixed the choice of a set of values must remain open, though the balance lies in favour of the set suggested by Latimer and Verwey which indicates 105 kcal for the heat of hydration of the hydroxide ion. Dr. D. J. E. Ingram (University of Southampton) said: Recent experiments carried out at Southampton on the cyclotron resonance of electrons in gas dis- charges 1 suggest that this should prove an alternative and more sensitive method of measuring electron concentrations.These measurements are summarized in the figure where the microwave absorption is plotted against the strength of the qauss FIG. 1. applied magnetic field. The absorption observed in zero magnetic field is similar to that obtained by Dr. Sugden and his co-workers, but if the strength of the applied d.c. magnetic field is increased to the resonance value, given by H = ma&, then microwave energy will also be absorbed as the electrons move in circular orbits such that their frequency of rotation is equal to the microwave frequency. The advantages of employing cyclotron resonance, instead of the zero-field measure- ments, is that a.c. methods of detection and display can be used, with all the techniques normal to paramagnetic resonance absorption.In this way a much more sensitive measurement of the total electron concentration is possible, and additional information can also be obtained from the line width of the resonance absorption. Experiments at Southampton have so far been confined to gas discharges, and the variation of electron concentration and line width with pressure, tem- perature, and ion current ; 1 but since the concentration of electrons in the flames is of the same order of magnitude it seems that this technique should prove very useful in a study of their properties, as well. Prof. C. H. Tomes (Columbia University) said : It may possibly be useful to obtain additional types of experimental measurements of the properties of electrons in the flames studied by Dr.Sugden. For his analysis of chemical equilibrium, three experimental parameters for the electrons are used, the absorption coefficient y, the collision frequency w1 and the electron temperature Te. Dr. Sugden’s experi- ment measures directly y, it measures 01 by using two or more microwave fre- quencies, and it uses TA, the temperature of some alkali atoms, rather than the electron temperature 7’’ which is presumably not very different. The technique involving a magnetic field which was suggested by Dr. Ingram would also measure y, and w l could be rather easily determined from it by a variation of the magnetic field rather than of the microwave frequency. 1 Ingram and Tapley, Physic.Rev., 1955,9,238 ; Research (corr. Dec., 1954), p. 47.GENERAL DISCUSSION 105 It might be interesting to use radiometer techniques with essentially the same experiment, i.e. to measure the microwave energy emitted by electrons in the flame. Such a measurement would give the quantity Te[O - exp (- yL)], where L is the path length. It could also give wl by measurement at two different fre- quencies. However, most importantly, it could be combined with one of the other types of measurements to determine Te directly, Dr. T. M. Sugden (Cambridge University) (partly communicated) : In reply to Dr. Ingram and Prof. Townes, I agree that the methods of cyclotron resonance and of microwave emission might be capable of providing further and more detailed information about the concentration and general behaviour of free electxons in flamc gases.In particular, it would be desirable to measure the effective electron temperature, although what indirect information is available suggests that the electrons are not far removed from thermal equilibrium with the body of the gases. Between the dates of the Discussion and this communication, Mr. P. F. Knewstubb and I have attempted a brief study of cyclotron resonance. Using a heatcd cathode discharge tube containing argon, we have been able to obtain results very similar to those quoted above by Dr. Ingram. We have worked at a wavelength of 8 mm, however, which requires a field of about 16,000 gauss to produce the resonance. In flames at atmospheric pressure, however, no resonance was detected, and it is considered that the reason for this is that one of the necessary conditions is not fulfilled. This condition is that the frequency of rotation of the electrons must be very much greater than their collision frequencies with molecules. In the flame gases, this collision frequency is about 1011 sec-1, whereas the angular frequency of the radiation used is only about twice this-not sufficient to give a detectable effect. It would be necessary to use microwaves of about 2mm wavelength to fulfil the condition, and this would require fields of the order of 60,000 gauss to produce the resonance-i.e. higher fields than we have been able to use. In principle, however, the method is a valid one, although such high fields might interfere seriously with the structure of a con- ducting flame. It probably would be most useful for the study of conduction in low-pressure flames, where the experimental limitations would not be so serious.

ISSN:0366-9033    

DOI:10.1039/DF9551900099

出版商:RSC    

年代:1955

数据来源: RSC

摘要:

m. PARAMAGNETIC RESONANCE INTRODUCTORY PAPER BY J. H. E. GRIFFITHS The Clarendon Laboratory, Oxford Received 10th February, 1955 1. INTRODUCTION Paramagnetic resonance is a branch of spectroscopy which is concerned with the investigation of the absorption spectra of paramagnetic substances in a magnetic field. The spectrum often occurs in the microwave region (1-10cm wavelength) for suitable values of the magnetic field. The substances investigated here have been mainly crystalline salts of the transition and rare earth elements, although measurements have also been made on organic paramagnetic substances and on various types of impurities in diamagnetic substances. The purpose of this paper is to present a brief description of this method and of the theory of the spectra observed in the transition and rare earth compounds, with the emphasis on those features which are of intcrest to chemistry.For more detailed treatments two review articles should be consulted. The first by Bleaney and Stevens 1 gives an account of the theoretical background and dis- cusses the experimental results in relation to this and the second by Bowers and Owen 2 collects together all the available experimental results. The paramagnetic substances described here are characterized by two features : (i) they contain ions which possess permanent magnetic morncnts ; this distinguishes them from diamagnetic substances. These ions therefore have a ground statc which can be split by the application of a magnetic field into two or more sub- states and it is the transitions between these which are observed in paramagnetic resonance.(ii) The energy of interaction, whether magnetic or exchange between these magnetic dipoles is very much smaller than kT at ordinary temperatures; this distinguishes them from ferromagnetic or antiferromagnetic substances. This interaction, although small, is still sufficient to cause broadening of the resonance lines; to minimize this effect, considerable use is made of dilute crystals in which the paramagnetic substance is mixed with an isomorphous diamagnetic substance. This reduces the chance that two paramagnetic ions are close together. Again it is most important to use single crystals as the amount of information obtainable by using polycrystalline material is very limited. 2. EXPERIMENTAL METHODS One commonly used experimental arrangement is as folIows.A small crystal (about 1 or 2 mm in size) is placed at the end of a cavity resonator tuned to the appropriate wavelength which is usually about 1% cm or 3 cm. In this position the crystal is in the greatest oscillatory magnetic field which is what is required for the magnetic dipolar transition to be observed. The resonator is placed in the field of an electromagnet, the two magnetic fields being at right-angles to each other. Conventional methods are used to feed the microwave power from the reflex klystron into the resonator and from thc resonator to thc detector which is a silicon-tungsten crystal rectifier. In taking measurements the frequency is kept constant and the magnetic field varied and when absorption occurs the de- tector current decreases.This may be observed with a galvanometer, but a 106J . H . E . GRIFFITHS 107 more convenient and sensitive method is to modulate the magnetic field by about 100 gauss at 50 c/s by passing alternating current through auxiliary coils on the electromagnet. The signal from the detector is then passed through a low frequency amplifier and displayed on a cathode ray tube. This is a simple method, the only complication in dcsign being duc to the fact that it is often necessary or desirable to cool the substancc to the temperature of liquid air, hydrogen or even helium. There arc two main rcasons for this, firstly, that the interactions between the magnetic dipoles and the lattice vibrations are sometimes so large at room temperature that the linc is very broad or unobscrvable.This interaction de- creases with decrease of tempcrature. Sccondly, the intensity of absorption is usually inversely proportional to the absolute temperature, because it is pro- portional to the difference in population of thc levels concerned, which is given by the Boltzmann factor. There are adjustments to tune the resonator and to rotate the crystal which call for careful dcsign, but thc latter can be dispensed with if the electromagnet can bc rotated. Therc are other methods of greater sensitivity, but of greater complication, which need not be considered here. 3. THE IONIC MODEL Most theories of paramagnetic susceptibility and of paramagnetic resonance use the ionic model as their starting point.In this, it is assumed that the substance is purely ionic and that the effect on the ion of the surrounding atoms or ions can be entirely represented by an electric field of appropriate strength and sym- metry. This electric field may be very large and is produced either by the charges on other (diamagnetic) ions or by the dipole moments of such molecules as H20 or NH3. Before considering the effect of the crystalline electric field on the energy levels of an ion, it is useful to discuss two simple cases to which some actual cases approximate. Thc first is that of a system of independent electron spins of magnetic moment /I (the Bohr magneton). In a magnetic field H there are two energy levcls of each spin with energy f PH, corresponding to the two values of the spin angular momentum, Ms = f - - ' Transitions between these levels can be induced if 2 27r' the frequency v of the radiation is given by numerically this gives HA = 10.7, when H is measurcd in kilogauss and A is the wavelength in cm.This rcsult arises as follows. For a system with total spin S, the magictic quantum numbcr M , can have the values S, (S - 1) . . . (- S), i.e. (2s + 1) values and these states have energy 2M3H in the field H. The selection rule is that Ms can only changc by f 1 and therefore in this case all the allowed transitions have the same frcquency which is given by eqn. (1). The sccond case is that of a system of free ions and neglects the effect of the electric field. Hcre the orbital moment has to bc considered as well as the spin moment.If the ion obeys Russell-Saunders' coupling, there is a total orbital quantum number L and a total spin S which combine to give a resultant J. In a magnetic field there are W + 1 levels corresponding to values of MJ of J, (J- 1) . . . (- J ) and these have energies MJgpH. Again, since the selection rule is that MJ can only change by f 1 , there is only one resonance condition such that Here g is the Land6 splitting factor and has the value unity when there is only an orbital moment and 2 when there is only a spin moment (more accurately the spin only value of g is 2.0023). This factor g is of great importance in paramagnetic resonancc. Many results give a value of g near to 2 and the difference from 2 is interpreted as giving a measure of the contribution of the orbital moment.I ~ v == 2pH; (1) hv = gPH. (2)108 INTRODUCTORY PAPER It is now necessary to consider the effect of the crystalline electric field on the ground state of the ion. There is a general theorem due to Kramers which is very useful in this connection and which states that if there is an odd number of electrons in the system, no electric field can remove all the degeneracy of the states. This means that there are at least two states with the same energy in the electric field and these are split by the application of a magnetic field, so that paramagnetic resonance will usually be observed in these systems. The detailed treatment of the effect of the electric field depends on the strength of this field as compared with the other energy terms.Three cases can be distinguished. (i) SMALL CRYSTAL FIELD.-This is the case of the rare earths where the 4f electrons which are responsible for the paramagnetism are we11 shielded by the closed shells of 5s and 5p electrons. This approximates to the second of the two simple cases considered above. L and S combine to form J which is still a " good " quantum number, but the states of different J z , which is the component of J along the axis of the electric Geld, are split by the electric field, often into pairs of f J z with energy separations between the pairs of the order of 100 cm-1. At the low temperature at which it is usually necessary to make measurements on these salts, only the lowest doubIet is occupied and it is the transition between these levels which is observed.The results on the rare earths are not of great interest to chemistry since the electrons concerned are inner electrons and do not seem to form chemical bonds. The other group in which felectrons occur is the uranium group and this is discussed in the paper by Bleaney. (ii) MODERATE CRYSTAL FIELD.-T~~S is the case of the iron group and approxim- ates to the first of the two simple cases, i.e. that of free spins. The reason for this is as follows. In the case of the rare earths, the energy difference between states of different J z but the same J caused by the electric field is small compared with the energy difference in the free ion between states of different J but the same L and S. In other words, the interaction with the electric field is small compared with the spin orbit coupling.In the iron group this is reversed and therefore J loses its meaning and is no longer a " good " quantum number, but L and S are still " good " quantum numbers. The electric field does not have any direct effect on the spin but splits the 2L + 1 orbital levels with splitting2 of the order of 10,000 cm-1 (see Fig. 1). Transitions between these orbital levels are usually responsible for the characteristic colours of these salts. There are still the 2 s + 1 states belonging to each orbital level and if a single orbital lcvel lies lowest, first- order theory shows that these behave like the spin-only case of eqn. (l), i.e. a single line with g = 2. In the more exact theory it is necessary to consider in some detail the sym- metry of the electric field.It is commonly found in iron groups salts that the ion is surrounded by six H2O molecules which are equally spaced along the three cubic axes (at the corners of an octahedron). This gives a field of cubic symmetry. This arrangement is usually slightly distorted and this distortion produces an additional (small) component of lower symmetry (often uniaxial). When this field is taken into account together with the spin orbit coupling, which has so far been neglected, two new features appear. First, the g values are anisotropic and no longer equal to 2, and secondly, if the spin is greater than 1/2, the spin levels are split with an energy difference usually of the order of 0.1-1 cm-1. Two examples may make this clearer : (i) Cu2+ has nine d electrons (d9) and as a free ion has a 2D state lowest.The five orbital levels are split by a cubic field into a lower doublet and a higher triplet and a field of tetragonal or lower symmetry splits the doublet also (see Fig. 1). Since the spin is 1/2, each of thcse levels is a spin doublet and the single line observed in paramagnetic resonance is the transition between the two spin levels of the lowest orbital level which is the only one populated at ordinary temperatures. In the salt K ~ S O A , CuSO4. 6H2O the g values are found to be gll = 2.4, the value when the magnetic field is parallelJ . H . E. GRIFFITHS 109 to the axis of the electric field and g i = 2.1, the perpendicular value. Theory gives approximately gll = 2[1 - (4A/A)] and g l = 2[1 - @/A)], where A is the spin orbit coupling coefficient (in this case negative) which can be found from optical spectra and A is the energy difference between the lowest level and the higher orbital triplet.This gives a connection between the measured g values and the splitting of the orbital levels. (ii) Cr3+ has three d electrons and 4 F is the lowest state as a free ion. A cubic field splits the orbital levels into a lower singlet with two upper triplets (see diagram). Each of these levels has a spin of 20 4F I I.-. (7 'r" MS CU'+ FIG. 1.-Energy level diagrams (not drawn to scale) for the two cases of Cu2+ and Cr3+ : (a) represents the free ion, (6) shows the splitting of the orbital levels in a cubic electric field, and (c) the lower levels in a field of lower symmetry.On the right of each diagram is represented the splitting in a magnetic field which increases from left to right. The number in parenthesis is the number of orbital states of the same energy. The approximate value of the splitting is given in cm-1- The full lines terminated with arrows indicate the microwave transitions observed. 3/2 and therefore is fourfold degenerate. In a salt such as CsCr(SO&. 12H20 the Cr3-1- ion is surrounded by an arrangement of I 3 2 0 molecules which is nearly octahedral but has a small distortion along the body diagonal of the cubic unit ccll. This electric field splits the spin levels into two doublets of spin f 3/2 and & 1/2 with a separation of 0.13 to 0.18 cm-1 depending on the temperature. The allowed transitions in a magnetic field are still AM, = f 1 and this gives rise to threc lines which are not coincident because of the splitting.This is known as the fine structure and from measurements on these lines the splitting may be determined. Another method of measuring the splitting is from the specific heat anomaly at low temperature (0.2"K) to which it gives rise. The exact behaviour of these four levels is complicated and depends on the angle between the applied magnetic field and the axes of the electric field, but can be worked out in detail. (iii) STRONG ELECTRIC FIELD.-This is the case of the palladium and platinum transition groups and here the field is strong enough to break down the Russell- Saundcrs coupling completely and the effect of the electric field has to be con- sidered before the interactions between the electrons.These electrons are d electrons and a cubic field splits the d state into a lower triplet, generally known as de, and an upper doublet dy, the splitting between which is so large that they can be considered as separate sub-groups. As electrons are added they fill first the de states forming a lowest level of maximum spin consistent with Pauli's prin- ciple (Hund's rule). Thus the spin of the first six ions is respectively 1/2, 1, 13, 1, 1/2, 0, which completes the de sub-group. This contrasts with the normal spin of iron group ions for which the first six have values 112, 1, 1+,2,2+, 2, although110 INTRODUCTORY PAPER some iron group complexes such as cyanides belong to the strong field case.The treatment of the strong field case then proceeds in much the same way as that of the moderate field case. Further discussion is left to the paper by Owen. It must be emphasized that the particular arrangement of splittings of the orbital lcvel depends very much on the symmetry of the electric field and the cases discussed here have predominantly cubic symmetry arising from six neighbours. Other arrangements occur such as with four or eight nearest neighbours and these result in different arrangements of the orbital levels and different results. 4. HYPERFINE STRUCTURE There is a hyperfine structure in those cases in which the magnetic electron is associated with a nucleus that has a magnetic moment. Often this takes a simple form in which there are 21 -l- 1 equally spaced lines to each electronic transition, whcre Z is thc spin of thc nuclcus.This arises in the following way. The effect of the magnetic moment of thc nucleus on the electronic system is the same as that produced by a magnetic field AH. In a transition of this kind the nucleus is not affected so that at constant frequency a resonance line is displaced by AH, and sincc there are 21 + 1 orientations of a nucleus of spin 1 which give equally spaced values of AII, there result 21 -1- 1 equally spaced lines. This gives a method of detcrmining the nuclcar spin in suitable cases and some spins have first bcen determined in this way. The magnitude of the separation of the hyperfine lines often varies with the angle between the applied magnetic field and the axis of the electric field, and there are also effects duc to the quadrupole moment of the nucleus.5. INTERPRETATION OF THE RESULTS There are two stages in thc assembling and interpretation of the results. In the fist it is necessary to detcrmine such quantities as the effective spin, the g- values, the electronic splitting and the hyperfine splittings. Some of these quan- titics vary with the oricntation of the crystal in the external magnetic field and from this variation the directions of the axcs and the symmetry of the electric field may be found. All this information is usually collected together in what is known as a “ spin Hamiltonian ” which expresses the results in the smallest number of constants and from which can be worked out the positions and intensities of thc lines for all orientations and strengths of the external magnetic field by straight- forward quantum mechanical mcthods.This procedure is fully described in the review article by Bowers and Owen.2 The second stagc is to interpret the values of thc constants of the spin Hamiltonian in terms of a model, and here it is necessary to consider also any othcr relevant information such as that obtainable from optical absorption spectra. In this papcr the results have bcen interpreted in terms of an ionic model although even hcre assumptions had to be made about the relative size of thc effects of thc electric ficld and the intcrnal interactions between the elcctrons. The effect of assuming a certain amount of covalent bonding is discussed in the paper by Owcn whcre it is shown that the main obscrvable cffccts arc a reduction of the g-valucs and of thc hyperfinc splitting constant, and in cases where thc nuclei OJ the surrounding atoms have n spin, there may be a hyperfine structure duc to these atoms.6. SCOPE AND LIMITATIONS OF THE METHOD Thc limitations arise mainly from the fact that cven if the substance is para- magnetic it may still be difficult or even impossiblc to observe a resonance. This may be duc to thc following reasons. (i) If the number of electrons in the system is cven thcrc is no Kramcrs’ degeneracy, and the splitting between the spin lcvels may be so large that no rcsonance can be obscrved at the frcquencies and magnctic fields availablc in the laboratory.J . H . E. GRIFFITHS 111 (ii) Even if therc is Kramers' degeneracy, the transition between the two lowest levels may be forbidden and no absorption will be observed unless higher levels are occupied at the temperature used.This probably occurs in some of the rare earths. (iii) The exchange of energy between the spin and the lattice may be so rapid that a very broad line results and this may be too broad to be observable. This effect decreases with decrease of temperature and therefore should be negligible at a sufficiently low temperature, c.g. for CsTi(SO&. 12H20 a temperature of less than 8" K had to be uscd. However, if these limitations are absent and a resonance can be observed in a single crystal, precise information can often be obtaincd about a number of features some of which arc listed herc.(i) The electronic state ofthe ion.-This is often known or can be inferred with reasonable certainty from other evidence, but in the case of the uranium group this is not so and the information obtainable by paramagnetic resonance is discussed in the paper by Bleaney. In other cases it may be a useful method of determining the valency state of an ion wherc this is in doubt. (ii) The crystalline electricjield-As stated abovc, the symrnctry of this field can usually be determincd and from this the arrangerncnt of the immediate surroundings of the ion can often be inferred. Sometimes a small distortion from a regular array can be detected by this means more easily than by X-ray crystallography. (iii) Perhaps the most interesting from the chemical point of view is the in- formation that can be obtained about the amount of covalent bonding which occurs in these compounds.In several cases it has been possible to give a numerical estimate and these are discussed in the following papers. (iv) A spccial case of some intercst is that of cupric acetate. Here the reson- ance results showed that the cupric ions are sufficiently closc togcther in pairs to behave somcwhat like a molecule with the two spins of 1/2 forming a lower diamagnetic lcvcl of S = 0 and upper triplet of S = 1 separated by about 300 cm-1. This arrangement of thc cupric ions was later confirmed by X-ray measurement. (v) Paramagnetic resonance has been observed in a number of organic mole- cules which have an unpaired clcctron. The g-value is very close to 2 but usually a little higher.This seems to be a promising field of investigation particularly if a hyperfine structure can be observed, because from this can be obtained an estimate of the time which the unpaired electron spends attached to the particular nucleus which has a magnctic moment. Some examples arc given in the following papers. (vii) Very small concentrations of impurities can be detected and sometimes identified by this mcthod in suitable cases. There are two types of cases. If the impurity is normally diamagnetic it may become paramagnetic by excitation or by attachment or removal of an electron, this new state being produced by irradi- ation by ultra-violet, X-rays, electrons or neutrons. Several cases have been investigated such as colour centres in alkali halides, quartz irradiated by X-rays in which the spectrum is due to A1 impurity, and neutron irradiated diamond. The second type is when the impurity is paramagnetic such as Mn2+ in phosphors and Fe2f in ZnF2. The possibilities are many and various and the sensitivity is such that a total number of impurity ccntres of the order of 1016 in a sample of about 10-2cm3 can be detected with very straightforward apparatus and this numbcr may well be reduced to 1012 with more refined methods. To conclude this vcry brief review, it seems to be the experience so far that although there are some general categories into which substances may be placed because of the similarity of thcir magnetic behaviour, in fact, most substances present their own problems and yield their own interests, because in each there is a different feature which is important. Thus, if a resonance can be found using a single crystal, the problem of interpreting it is one usually well worth pursuing. * Bleariey and Stevens, Reports Prog. Physics, 1953, 16, 108. 2 Bowers and Owen, Reports Prog. Physics (in press).

ISSN:0366-9033    

DOI:10.1039/DF9551900106

出版商:RSC    

年代:1955

数据来源: RSC

摘要:

PARAMAGNETISM OF THE ACTINIDE GROUP BY B. BLEANEY Clarendon Laboratory, Oxford Received 28th January, 1955 It is well known that the susceptibility of compounds of the 4f group is close to that expected for the free ions, while that of compounds of the 3d group is close to the “ spin- only ” value, the orbital moment being quenched. Susceptibility measurements of Dawson on a number of compounds of uranium and the trans-uranic elements have shown that when there are only one or two magnetic electrons, the susceptibility is close to the spin-only value, while when there are more than three magnetic electrons the be- haviour is similar to that of the rare earths. On this basis he has suggested that in the former case the magnetic electrons are in 6d states, whereas in the latter they are in 5f states, whereas Seaborg from other evidence has postulated that only 5f electrons occur in either case.Independently, Elliott and Pryce have pointed out that in compounds containing the MO2 complex (M = U, Np, Pu, etc.) there is a strong axial crystal field (or strong bonding between M and the oxygens) which modifies the magnetic properties considerably. Pryce and Eisenstein postulate that in a simple a-bond model, the 5fu, 6 4 and 7s valence orbitals of M form highly directional hybrid orbitals bonding with spu orbitals on the oxygens. Thus in U09* the U atom (5f3 6d7s2 in the free state) loses two valence electrons and the other four are used in the (dative) bonding, leaving no magnetic electrons. In Np022+ there is one magnetic electron in the 5f(m == 3) orbital, and in PH0?2+ two electrons in the 5f (m = 3, m = 2) orbitals with their spins parallel.Paramagnetic resonance experiments on the salt Rb(U02)(N03)3 containing small quantities of Np and Pu have confirmed these predictions. The susceptibility of these compounds is also discussed. 1. INTRODUCTION Paramagnetism occurs in well-defined regions of the periodic table, which are associated with the presence of an incomplete electron shell in the paramagnetic ion. The best known of thcse regions are the iron transition group, with an incomplete shell of 3d clectroiis, and the rare earth (lanthanide) series with an incomplete 4f shell. Somewhat less well-defmed are the palladium group (4d shell) and platinum group (5d shell). As early as 1923, Bohr suggested that another paramagnetic group could occur at the top end of the periodic table, where electrons might be in an incomplete 5fshell.The experimental evidence for a long time was inconclusive as to where this shell should begin, suggestions varying from thorium (element 90) to the then hypothetical element 93, When the transuranic elements had been prepared in sufficient quantity for an examina- tion of their properties, the situation became clearer ; in a review of the evidence Seaborg 1 postulated that a second ” rare earth ” 5f series begins with actinium as the analogue of lanthanum, thorium of cerium, etc. The analogy is most complete in the region of elements 95 (americium, analogous to europium) and 96 (curium, analogous to gadolinium), and the beginning of the series was obtained by extra- polation backwards.We are not here concerned with the electron configurations of the elements, and it will suffice to give the number of “ magnetic ” electrons with unpaired spins present in the ions, as shown in table 1. Only the valency states normally obtained are shown, and for convenience all the elements at present known have been included. For the elements above curium it has been assumed that the electrons are in the 5fshel1, so that the numkr of unpaired electron spins shown is (14 - n’), where n’ is the actual number of electrons in the 5fshell. 112n Th Pa U NP Pu Am Cm Bk Cf 99 100 113 5 6 7 B. BLEANEY TABLE 1 0 1 2 3 4 Th4+ (Th3+) (Th2+) Pa5 Pa4+ (Pa3+) u022+ u02+ U4f u3+ NpOzZ+ Np02+ Np4+ Np3 + Pu022+ Pu02+ Pu4+ pu3+ Am022+ ArnOz+ (Am4+) Am3+ ?Am2+ Cm3 + Bk3+ Bk4+ Cf3+ 993 + 1003 + Number n of unpaired electron spins in the actinide ions.( ) indicates observed only in the solid, not in solution. For the ions above curium the number of unpaired spins shown is based on the as- sumption that the electrons are in the Sfishell, so that the number n of unpaired spins is (14-n'), where n' is the number of magnetic electrons. ? doubtful. 2. EVIDENCE FROM SUSCEPTIBILITY DATA In a review of the magnetic data of the actinide compounds Dawsonz has suggested that the magnetic electrons are in 6d states rather than 5fstates in ions with only one or two (or possibly three) magnetic electrons, though they are in 5fstates in ions with more than three electrons. To understand the basis of this suggestion it is necessary to consider briefly the paramagnetic properties of the lower transition groups.Where the magnetic electrons are in the 3 4 4d or 5d shell, their charge clouds reach rather far out and the magnetic electrons are subject to strong interactions with the immediate diamagnetic neighbours of the para- magnetic ion. Such neighbours are either electrically charged negative ions or electric dipoles and the interaction is an electrical one ; the state of lowest energy is the one where the electrons on the paramagnetic ion avoid the regions of high electron density on the diamagnetic neighbours as far as possible, since this reduces the electrostatic energy of their mutual repulsion. The effect of this is to " quench " the orbital angular momentum, so that it makes little or no contribution to the magnetic susceptibility.The reason for this is that the energy of interaction with an external magnetic field (m 1 cm-1 in wave numbers) is insufficient to cause a change in the population of states corresponding to different orientations of the orbit, since a different orientation would bring the electrons closer to the neighbouring ions and require an increase in the energy of 103 to 104 cm-1. The electron spins are virtually unaffected, however, since the electric field of the neighbours has no first-order interaction with the magnetic moment of the spin (there is a second-order interaction through the spin-orbit coupling). Thus the spins are able to make their full contribution to the paramagnetic susceptibility, while the orbit makes vzry little contribution, and the susceptibility has practically the " spin only " value.In the lanthanide group on the other hand, the valency electrons arc in 5d and 6s states, while the magnetic electrons are in the inner 4f shell. This is well inside the electron cloud and its interaction with neighbouring ions is small; the Russell-Saunders coupling of spin and orbit to form a resultant angular momentum is practically undisturbed, and at room temperature the susceptibility of magnetically dilute compounds is roughly the same as for an assembly of free ions. The emphasis on " magnetically dilute " compounds here and later arises from the presence of exchange forces between paramagnetic ions which may be114 THE ACTINIDE GROUP appreciable at distances up to 4 or 5 A, but have little influence at greater di- c tances.Such forces cause the susceptibility to deviate from Curie’s law; in some cases their effect is to produce a Curie-Weiss law, NP2P2 ’= 3k(T- A) where ,8 is the Bohr magneton and p the effective Bohr magneton number ; k is Boltzmann’s constant and A is an empirical “ Weiss constant ”, which may be either positive or negative. The presence of an undetermined Weiss constant makes it useless to determine the value of p2 from a measurement of x at a single temperature, but both p2 and A can be found from measurements over an extended temperature range. This procedure is less reliable than the use of a compound where the magnetic ions are so far apart that the exchange forces can be neglected, siiice departures from Curie’s law from other effects are either masked or lumped into the empirical A.The properties of a dilute compound are conveniently expressed in terms of p2. In the case of spin only paramagnetism, p2 = 4S(S + l), where S is the total spin of the ion, which is (by Hund’s rules) as large as possible, subject to the Pauli exclusion principle. This means that for d electrons the maximum value is S = 5/2 for d5 (a half-filled shell), but for f-electrons the maximum value is S = 7/2, for f7. For rare earth ions, p2 = gZJ(J + l), where g is the Land6 g-factor and J the total angular momentum in the ground state of the ion. The experimental values for the most representative salts (where possible magnetically dilute, or artificially diluted by forming an atomic mixture with an isomorphous diamagnetic compound) are given in table 2.It is clear that the experimental values for four electrons or more follow the theoretical values for rare earth type ions rather closely, and diverge markedly from the spin only values, but for one or two electrons p2 is much closer to the spin only value than the value for L--S coupling to a resultant J. This does not prove that they are d-electrons rather than f-electrons, though quenching of the orbital momentum might be more likely in the former case. In fact close agreement with the spin-only values is fortuitous with the neptunyl and plutonyl compounds, as will now be shown. no. of magnetic compound electrons TABLE 2 (expt.1 p2 (theory.) G - S coupling spin only p2 ~ f-electrons d-electrons f-electrons 1 Na(NpO2) (CZH3 0 2 ) 3 3.4 2F-512 6.4 3 3 Na(Pu02)(CZH302)3 ::;} 3H4 12.8 8 8 2 3 U3f in soln.9.9 41912 13.1 15 15 4 PuF4 in ThF4 8.8 514 7.2 24 24 5 6 AmF3 (conc.) 1.6 7Fo (0) 24 48 7 CmF3 in LaF3 62 *s7/2 63 15 63 UF4 in ThF4 i::} 6&2 0.7 35 35 PuF~ (CO11C.) PuC13 (conc.) Summary of best available data on susceptibility of transuranic compounds. Where possible, the quoted data are for magnetically dilute compounds; they are based on Dawson except for sodium neptunyl acetate, which is based on Gruen and Hutchinson.14 3. PRYCE’S THEORY FOR (U02)2+, (NpO2)2+ AND (Pu02)2+ The actinide elements differ from the lanthanides in their tendency to form compounds with complexes such as the uranyl ion (U02) which are chemically quite stable, and rather more stable than the majority of compounds containing the elementary ion in the case of U, Np and Pu.The U02 ion is linear, and itB . BLEANEY 115 has been suggested 3n4 that its stability is associated with the formation of a bond involving an felectron. The electronic state of the neutral U atom is 5 f 3 6d 782, so that the U2-1- ion may be written as 5f6d 7s2 ; it is postulated 5 that these four electrons are used to form dative or electron transfer covalent bonds with the two oxygen atoms. In a simple model using only a-bonding, a hybrid spz orbital (where the 0-U-0 axis is taken as the z-axis) on each oxygen with its lobe pointing towards the uranium forms the bonding orbital. On the uranium, a-bonding orbitals can be formed by the use of the substates of Sfand 6d which have lz = 0 ; these ate strongly directional, and two hybrid orbitals, each pointing towards one of the oxygen atoms, can be formcd by linear combinations of 5f, 6d and 7s.These hybrid orbitals will have a large overlap with the spz orbitals on the oxygens, and will form a strong bond. This uses up all the electrons on the doubly ionized uranium outside the closed shells, and no electrons are left to produce a normal paramagnetism. The atoms preceding uranium in the periodic table have insufficient electrons to form bonds of this type in a doubly ionized complex (therc is a rather doubtful Pa02-t ion), and so it is natural that the uranyl type of compound is only found from uranium onwards.(NP 02)2+ The neptunyl ion has one electron more than the uranyl ion, and this becomes a magnetic electron. If it is a 5felectron, then the states available for it are those with lz = rrt 3, f 2, & 1, the I, == 0 orbital being uscd in the covalent bonds to the oxygcns. These different orbitals will have different energy bccause of the strong electric field of the bonding electrons, and the state of lowest energy will be that in which the magnetic clcctron avoids the 0-U-0 axis, with its high electron dcnsity, as much as possible. The lowest states will thus be those with I, -= f 3, since for these the electron cloud is concentrated in the equatorial plane, and these probably lie below the Iz = f 2 states by lO4cm-1 or more. When account is taken of the electronic spin s -- 112, the spin-orbit coupling CIS splits the fourfold states with I, f 3, s, = f 1/2 into two doublets with j z = Iz + sz == f 712 and & 512 respectively. The latter of these is lower in energy by 3,000-4,000 cm-1, and is thcrefore the only state populated at room tcmperaturc.This doublet (which we may regard as having an effective spin S’ = 112) is therefore responsible for the paramagnetism, and in this approximation has the anisotropic g-values 611 =- 4, g ~ _ = 0. This result was also obtained indepciidently by Elliott,6 by treating the 0-Np-0 complex as a lincar moleculc. The value of gII is found as follows : I, and s, precess about thc 0-’T-0 axis, and j , = 5/2 corrcsponds to lz -- i 3, sz =_ & 1/2. Hcnce the energy of the two states in a field parallcl to the axis is (I, -I- 2sz)/3H = rlr (3 - l)PH = f 2pH, thc same as for a doublet with an effective spin S’ = 1/2 and gII == 4.The susceptibility should then correspond to a value (2) which is not far from the observed value of 3.4 for sodium neptunyl acctate. p2 =: +S’(S’ -I- l)(g112 -t 2gp) =-- 4, Thc doubly ionized plutonyl ion has two magnetic electrons, and the problem of the ground-state configuration is not quite so straightforward. If a modificd form of Hund’s rules applies, so that the two electrons go into states (i) with their spin parallel, so that Sz has its maximum valuc of 1 ; (ii) states with lz =-= f 3 and & 2 respcctively, so as to make L, as laigc as possible; then we have L, = & 5, Sz = f 1 . Then the spin orbit coupling will split the possible combinations of Lz and Sz and leave a doublet with Jz = - - It.(5- 1) :-- f 4 as the ground states. From This will have a value of g , ; = - = 2(5-2) == 6, and gl F: 0.116 THE ACTINIDE GROUP eqn. (2) the value of p2 is then (1/4)62 = 9. On the other hand, the electrostatic repulsion of the bonding electrons along the axis may give the state with the two electrons (with spins parallel) in states with 1, = + 3 and - 3 a lower energy than that with 1, = + 3 and + 2 (or - 3 and - 2) since the electron cIoud for 1, = & 2 approaches the axial bonding electrons more closely than for IZ = f 3. We should then have a state with S = 1 and no orbital momentum, so that p2 = 8, the spin only value for two electrons. The susceptibility mcasurernents do not distinguish between these two possibilities, since further investigation of the first possibility indicates that the value of 811 may be rather smaller, thus reducing p2.Susceptibility measurements on a single crystal of a compound (other than one with cubic symmetry, i.e., not sodium plutonyl acetate) would show a difference, because the anisotropy would be small in the second case (L = 0) and very large in the first case (L, = 5). 4. PARAMAGNETIC RESONANCE WORK ON NEPTUNYL AND PLUTONYL COMPOUNDS The most suitable compounds for paramagnetic resonance and susceptibility measurements are of the type Rb(U02)(N03)3 ; these form hexagonal crystals with all the magnetic ions identical. Such crystals have been used at Oxford, and resonance has been observed with crystals containing small quantities of neptunium and plutonium, but unfortunately no susceptibility data are available.Detailed susceptibility data are available for compounds of the form Na(U02)(C2H302)3, which form cubic crystals with four molecules in unit cell ; resonance has been detected in the plutonium compound by Hutchinson and Lewis.’ The resonance results enable one to decide immediately between the two possibilities for the (Pu02)2+ outlined in the last section, and these will be dis- cussed first. The transitions observed are of an unusual type in that both the radiofrequency and the steady external magnetic field must be applied along the 0-h-O axis, and arise as follows. The electronic doublet is not a Kramers’ doublet, since in the absence of an external magnetic field the two states can be split by a distortion of the crystal structure which reduces the symmetry.Such distortions also admix the two states of the doublet, and transitions corresponding to the selection rule AJ, = 0 are then allowed, while the usual transitions AJz= &1 are not allowed i f g l = 0. In the rubidium plutonyl nitrate the resonance spectrum shows that the transitions are of the AJ, = 0 type, and the observed g-values,S are gli = 5.32 rt 0.02, gl = 0.0 f 0.4. In the sodium plutonyl acetate the results indicate that 6 11% 5.9, gl = 0. There is thus qualitative agreement with the first-order theory of Pryce, and the resonance results give a natural explanation of the observed susceptibility, giving p2 = 8.7 for the acetate (if anything, the value of 811 given by Hutchinson and Lewis will be slightly too large, owing to the asymmetrical shape of the lines).Neptunium resonance has been reported only in the rubidium neptunyl nitrate.8 This shows a very large hyperfine structure with the nuclear spin I - 5/2 of the isotope 237, which makes accurate measuremcnts of some of thc parameters rather difficult. The spectrum is that of an electronic doublct with effective spin S’ = 1/2, and can be fitted to the Hamiltonian X = g,IPfLS + ~fi(H.xsx + HysJ -1- AStlE + B(S.& + SyZy) + P(ZZ2 - +Z(Z -t- 1)) (3) with the following values of the parameters : grl = 3.413 0.02, gL = 0.21 6 0.02, A = 0.1662 f 0.001 cm--1 = 4983 f 30 Mc/s, B = 0.0175 4: 0.001 cm-1 = 525 -f 30 Mc/s, P = - 0.0302 f 0.001 cm--1 = - 908 f 30 Mc/s.B .BLEANEY 117 The term in P is the interaction with the electric quadrupole moment of the nucleus ; this interaction is large because the 6d electrons of the covalent bond set up a large field gradient at the nucleus; the exact value of this is rather difficult to compute and a tentative estimate 5 of the nuclear electric quadrupole moment is 15 x lO-24cm2. In the nomenclature used in nuclear resonancc, P corresponds to a value of eQq = - 12,080 f 400 Mc/s. These values of glI and gl show that the elementary theory given above must be modified by taking account of the overlap of the wave functions of the magnetic electrons with orbitals located on atoms next to thc actinide ion in thecrystal. In other words we must allow for a certain amount of covalent bonding in addi- tion to the single a-bond assumed earlier.It has been shown by Stevens 10 that this leads to a reduction in the orbital moment of the electrons, but not in the spin moment, an effect which has been observed by resonance measurements in the 4d and 5d groups,lI and to some extent also in the 3d group (for a review, see Owen 12). In our case, the effect of applying a magnetic field H along the axis is to modify the energy by an amount (kLz -/- 2Sr)pH, and the value of 811 for Np and Pu is then given by the expression The full formulae for the g-values are given by Eisenstein and Pryce for neptunium ; with some approximation they can be written as where k is the orbital rcduction factor (k = 1 if there is no reduction) and p is a small coefficient representing the effect of the crystalline electric field.Hence one finds k --- 0.90 ; in the same approximation for plutonium one has g11= 10k- 4, giving k = 0.93 for the isomorphous compound. On the other hand the value of gli for sodium plutonium acetate implies a value of k nearer to unity, and this may be true also for sodium neptunium acetate, for which the measured suscepti- bility implies a rather larger value of (gli2 + 2g12) (see eqn. (2)) than the resonance values give for rubidium neptunyl nitrate. 811 = 2(kLz + 2Sz). 811 = 6k--2, gl = 4P, 5. CONCLUSION The theory seems rather satisfactory in regard to the neptunyl and plutonyl ions, but for other compounds there are insufficient detailed experimental results to form an adequate basis for the construction of a theory.The most desirable information for this purpose is obtained from paramagnetic resonance on a single crystal (preferably one that is magnetically dilute), and from susceptibility measure- ments on a single anisotropic crystal (cubic crystals, such as sodium plutonyl acetate are no better than a powder for this purpose). A programme of sus- ceptibility measurements has been initiated at Oxford, together with a study at A.E.R.E., Harwell, of the optical absorption spectra of single crystals, which will yield information concerning the excited states of the paramagnetic ions. Many attempts to observe resonance have been made on other compounds, but only a few have met with success. In a concentrated powder of UF4 a sym- metrical resonance curve corresponding to a g-value of 2.15 was observed by Ghosh, Gordy and Hill 13 which disappears below room temperature, and so appears to originate from an excited state.The crystal structure of this com- pound is complicated, and the resonance result is not easy to interpret. The same authors report an asymmetrical line in a powder of concentrated UF3, the shape of which suggests an anisotropic g with 811 w 2.8 and g1 w 2.1. Some theoretical results obtained by Miss M. C . M. O’Brien9 show that an 5f3 configuration, subjected to a crystal field of six-fold symmetry about the crystal axis, gives values 811 w 2.6 and g l m 1.8 as a first approximation where the strength of the field is close to that estimated from the known crystal structure. On the other hand, d3 andf2d configurations all lead to values of g l which, in the first approximation,118 MANGANESE IN VARIOUS LATTICES are zero or rather small. Thus the presence of 6d states seems unlikely in this case, as well as for the one and two electron cases, though resonance results on such a concentrated salt should be accepted with some reserve. I am indebted to Prof. M. H. L. Pryce for permission to quote from unpublished work, and to G. R. Hall for assistance in preparing table 1. 1 Seaborg, Nucleonics, 1949, 5, 16. 2 Dawson, Nucleonics, 1952, 10, 35. 3 Glueckauf and McKay, Nature, 1950, 165, 594. 4 Connick and Hugus, J. Arner. Chern. SOC., 1952, 74, 6012. 5 Eisenstein and Pryce, Proc. Roy. SOC. A , 1955,229, 20. 6 Elliott, Physic. Rev., 1953, 89, 659. 7 Hutchinson and Lewis, Physic. Rev., 1954,95,1096. 8 Bleaney, Llewellyn, Pryce and Hall, Phil. Mug., 1954, 45, 773, 991, 992. 9 O’Brien, Proc. Physic. SOC. A , 1955, 68, 351. 10 Stevens, Proc. Roy. SOC. A , 1953, 219, 542. 11 Griffiths, Owen and Ward, Proc. Roy. SOC. A , 1953,219,526. 12 Owen, Proc. Roy. SOC. A , 1955,227, 183. 13 Ghosh, Gordy and Hill, Physic. Rev., 1954, 96, 36. 14 Gruen and Hutchinson, J. Chem. Physics, 1954, 22, 386.

ISSN:0366-9033    

DOI:10.1039/DF9551900112

出版商:RSC    

年代:1955

数据来源: RSC

摘要:

118 MANGANESE IN VARIOUS LATTICES PARAMAGNETIC RESONANCE OF DIVALENT MANGANESE INCORPORATED IN VARIOUS LATTICES BY J. S. VAN WIERINGEN Eindhoven, Netherlands Received 8th February, 1955 Philips Research Laboratories, N. V. Philips’ Gloeilampenfabrieken, Paramagnetic resonance was observed in powder samples containing Mn diluted in various diamagnetic compounds. The measurements were made at 3-2 and 1-25 cm at room temperature. Three effects were found: narrowing of hyperfine splitting by covalent bonding and by exchange, and a g-factor somewhat larger than the free-electron value in ZnSe: MnSe (is. a mixture of ZnSe and a little MnSe) and CdTe: MnTc. Throughout these, and similar, mixtures are written as ZnSe : Mn, CdTe : Mn, etc. The first effect suggests 10-20 %, 30 %, 35 % and 40 % covalent bonding in Mn -I- oxygen compounds, MnS, MnSe and MnTe respectively.In the course of an investigation on paramagnetic resonance in phosphors we studied paramagnetic resonance of small quantities of divalent manganese incorporated in various compounds. All experiments (except for CdTe : Mn) were made with powder samples as no single crystals were available. We shall restrict ourselves to the results obtained with crystals of cubic or nearly cubic symmetry. Some others of lower symmetry were measured (ZnO : Mn, 22x10 . Si02 : Mn, MgF2 : Mn and ZnF2 : Mn) but they showed only one broad absorption line.10 This agrees with theory which predicts an anisotropic para- magnetic resonance spectrum for this case. Such a spectrum is only observable in single crystals.In powder samples it will be smeared out into a broad peak. Cubic crystals, on the other hand, have an isotropic spectrum which can be observed in powders as well. Divalent manganese in a crystalline field of cubic symmetry has a paramagnetic resonance spectrum of 6 lines.2 They originate from the interaction betweenJ . S. VAN WIERINGEN 119 the Mn2+ electron cloud and the Mn55 nucleus of spin 3 I = 8. It was found that the average splitting of these 6 lines was decreased : (i) by covalent bonding (this follows from experiments with different (ii) by exchange interaction with Mn2+ neighbours (this was found in ZnS : Mn Moreover, in ZnSe : Mn and CdTe : Mn with most covalent bonding the 6 lines were shifted to a slightly lower magnetic field (larger g-factor). In this paper experimental results will be given together with a theoretical discussion of the three effects mentioned above.compounds) ; a t different Mn concentrations). EXPERIMENTAL The 3-2cm and 1.25cm microwave apparatus used for the measurements is shown schematically in fig. 1. The sample was placed on the bottom of a cylindrical resonant cavity (TE 11 1 mode). The cavity is fed through a wave guide by a frequency-stabilized klystron and placed between the pole pieces of a magnet (10cm diam.). At magnetic field strengths far from resonance, the cavity is tuned and matched to the wave guide. FIG. 1 .-Microwave apparatus. This is achieved by making the reflected signal zero, the reflected signal being measured by means of a 3 db directional coupler on the wave guide and a superheterodyne detector.At the correct magnetic field strength resonance occurs which is detected by a reflected signal. By modulating the magnetic field the resonance spectrum may be displayed on an oscilloscope as a function of magnetic field. Magnetic fields could be measured with proton resonance in the 3.2cm apparatus. The proton resonance coil was placed in the same field as the cavity. Both resonance signals could be observed simultaneously on the oscilloscope by means of an electronic switch. All spectra were measured at room temperature. RESULTS In the absence of a noncubic crystalline field, an isotropic g-factor and h.f. splitting is to be expected for Mn2+ ions. The Hamiltonian will be 1 %' = gpHS 4- A'IS. (1) Orbital contributions are not given explicitly but incorporated in the g-factor.This is possible because Mn2+ is in a 6s state to a good approximation. In the only " single ' crystal that was investigated, CdTe : Mn, it was checked that the g-factor is isotropic. Taking the axis of the external field as axis of quantization, a first order energy effect (1) will give E(M, m) = gFHM + A'Mm with M, m = & f, -f +, f f . (Z) In a paramagnetic resonance transition AM = f 1, Am = 0, so this leads to a spectru:n (3) of six equally spaced lines. hv = g/3H + A'm.120 MANGANESE IN VARIOUS LATTICES In reality there is a noticeable increase of spacing at the high field side of the spectrum. This is satisfactoriIy described by the next approximation of (2) I I - 1 1 1 .1 . 1 , , , , I , . , , I . . , - 1 . - . 1 I I I 1 I L- - I I I 1 I I _ I I . I I I I . I I I I I I I I - I I I I I I 1 I I , I I I I I I , I Id I 1 I , I t I I I I , I- 1 d. I I I I I In (5) a small term A'2m(2M + 1)/2hV was left out because it gives only a small broadening and no shift of the lines, At 3-2 cm a number of substances showed a 6-line Mn2+ spectrum (fig. 2). The posi- tions of the lines are accurate to about 2 oersteds. All these samples were measured together with the free radical a : a-diphenyl/3-picryl-hydrazyl with a g-factor 4 of 2.0040 (free electron : g = 2.0023). This field marker line is given in all spectra of fig. 2. Details about the preparation of the substances and the best values of the parameters and g are given in table 1. 4 f 1 FIG.2.-Paramagnetic resonance absorption lines of Mn2f in different compounds as a function of magnetic field. In KMgF3 a weak fine structure was found, each of the 6 peaks being split into 5. It proves that this crystal is slightly non-cubic (at least near Mn2+ lattice sites). This non-cubic distortion did not show up in X-ray diffraction and in polarized light. The fine structure splitting was about a quarter of the h.f. splitting (see fig. 2). Therefore the h.f. splitting could be measured well. This is no longer possible if the fine structure is strong. TABLE 1 compound KMgF3 CaF2 CsCaF3 CaO 2Mg0. $A1203 * 6Mg0. As205 * Zn 0.1 . lAl2O3 ZnS CdS ZnSe CdTe MflI204 * approximate [atomic Mn] 0.1 % 0.1 % 0.1 % 0.1 % 0.1 % 0.1 % 0.01 % 0.005 % 0.1 % 0.05 % 0.01 % unknown preparation A (oersted) (f 1) g(d~002S) +h1000"CinNz 98 Y> 99 97 1580" C reducing atmosphere 87 87 2 h 1380" C 87 81 1 h 1OOO" C air and 2 h 1400" C}water vapour Q h 900" C in H2S 69 + h 1050" C in H2S 69 + h 1050" C in H2 65 1100" C in 1 atm Cd 59 14;' C 91 1 h 1250" C in air 2004 2004 2.004 2004 2.004 2004 2.004 2.004 2004 2006 2008 2.W~ *In these phosphors most of the Mn is tetravalent.5 The paramagnetic resonance absorption (caused by M$+) was accordingly weak.3 .S. VAN WIERINGEN 121 For example, in hexagonal ZnS : Mn 1 and CaC03 : Mn,' the fine structure is some- what larger than the h.f. splitting. We found similar results in Mg2TiO4: Mn. We shall not use these results here, because it is difficult to measure the h.f. splitting for this case in powder samples.In hexagonal ZnS : Mn it was of the order of 70 oersteds and in Mg2TiO4 about 85 oersteds. Hershberger reports 93.9 oersteds for CaCO3 : Mn. In cubic ZnS : Mn the resonance spectrum was measured with different Mn concentra- tions at both 3-2 cm and 1.25 cm. The results are shown in fig. 3. Cubic ZnS : Mn 0.005 % was used as field marker. From the experimental results three con- clusions may be drawn. (i) The strength of h.f. splitting A depends strongly on the compound in which Mn2+ is dissolved. The results in fluorides 6 and sulphides show that the lattice parameter is of no importance. Within the groups of fluorides, oxides and sulphides the h.f. split- ting is roughly the same. Hence it is mainly determined by the negative ion neighbours of Mn.Our results can be combined with those of Hurd, Sachs and Hershberger' on CaCO3: Mn and of various workers on aqueous solutions of Mn2+ salts and Mn2+ in crystals containing water of crystallization. This leads to an ordering of neighbours with respect to their influence on h.f. splitting (table 2). It is clear that A depends on covalent bonding: the more covalent the bonding, the smaller the h.f. splitting. (ii) The magnetic moment g,9S has a much less pronounced increase in the same order. It is only in ZnSe : Mn and CdTe : Mn that deviation from the free-electron value is out- side the experimental error. This phenomenon proves that Mn2f is not in a pure 6s state, but that there is some orbital contribution to the magnetic moment. The positive sign of the deviation shows that it is caused by electrons from the second half of an electron shell.-H FIG. 3.-Paramagnetic resonance ab. sorption line shapes of ZnS: Mn at different Mn concentrations as a func- tion of magnetic field ; left at 1.25 cm, right at 3.2 cm ; parameter, atomic Mn concentration. (iii) At increasing concentrations the widths of the 6 lines increase. They merge together so that there is 1 line left of width N 5 A N 350 oersteds. At still higher con- centrations the overall width decreases. We assume that this overall width is mainly TABLE 2 neighbour HzO F- CO32- 0 2 - S2- Sen- Te2- approximate A 98 98 94 80-90 69 65 59 determined by h.f. splitting, Hence the h.f. splitting decreases towards higher Mn2+ concentrations. We will interpret this decrease as an effect of exchange between Mn2+ neighbours.The theory of these three effects will be discussed in the following paragraphs. DISCUSSION NARROWING OF HYPERFINE SPLITTING BY COVALENT BONDING Owing to the symmetry of a half-filled shell a Mn2+ 3 9 3d56S state does not give any hyperfine splitting. Abragam and Pryce3 have indicated how a h.f. splitting of the observed-order of magnitude may be explained by assuming122 MANGANESE IN VARIOUS LATTICES promotion of a 3s electron to a higher s state (e.g. 4s). Because of the high contribution of an s electron to the h.f. splitting, even an admixture of the order of 0.1 % of this excited 3s 4s 3d5 6s state will yield the observed h.f. splitting. Generally this excited state will contain a mixture of 3s 4s triplet and singlet.Calculation shows that 1i.f. splitting arises if the 3s and 4s electrons are in a triplet, but that the effect is zero if the 3s and 4s electrons are in a singlet state. This is plausible because of the continual exchange between the two electrons. From our experiments it is clear that the 3s 4s triplet is perturbed by covalent bonding. If there are covalent bonds, electrons from negative neighbour ions move to the Mn2+ ion, e.g. into 4s 4r3 orbits for tetrahedral cation co-ordination. We will consider the 4s-orbit occupied by an electron coming from some (un- specified) orbit t of the negative ion. This looks plausible because for 4s and t the overlap is larger than for 3s and t. It is clear that this mechanism will hinder the promotion of a 3s electron to a 4s orbit, Comparison with the situation in ionic bonding will show that the situation is much less favourable for h.f.splitting in the presence of covalent bonding. For ionic bonds the ground state is 3s2 3d5 t2 and the excited state is determined by the 35-4s overlap and the promotion energy of a 3s electron to a 4s state. The covalent ground state is 3s2 3d5 1(4s t), the 4s and t electrons being in a spin singlet state. The only plausible excited states for the 3s electron are now 4s, 5s and t. Promotion to 4s leads to 3s 3d5 4s 2t where the covalent bond is lost. This means that the admixture of this excited state is very small. Moreover, the h.f. splitting is less than in the ionic excited state. Promotion to 5s is more difficult because of the higher promotion energy required.It leads to either 3s 3d 55s l(4st) (having a small h.f. splitting) or 3s 3d54s l(5st) (costing most of the covalent exchange energy). Promotion of a 3s electron to a t orbital gives the old ionic excited state 3s 3d5 4st2. This will now involve a considerably higher energy because the CO- valent bond is destroyed. It follows from the foregoing argument that the h.f. splitting is much less (about a factor 10) in the covalent state than in the ionic state. In first approximation the covalent contribution can be neglected. Thus the strength of the h.f. splitting is directly proportional to the amount of ionic bonding. If we assume that in fluorides and in H20 surroundings, the bonding is completely ionic, the percentage of covalent bonding of Mn2+ in oxides, MnS, MnSe and MnTe is 10-20, 30, 35 and 40 respectively.CHANGE OF g-FACTOR IN ZnSe : Mn AND CdTe : Mn In the 6s ground state of Mn2+ only the spin contributes to the magnetic moment. Hence the g-factor is expected to be equal to that of free electrons (g = 2.002). This is in accordance with most measurements. In table 1, how- ever, it appears that in ZnSe: Mn and CdTe: Mn the g-factor differs from the free electron value by more than the experimental error. This shows that there is some interference between the half-filled 3d shell of Mn2+ and the neighbour ions. The covalent state 3d5 l(4st) itself has no influence on the g-factor. It is probable, though, that the 4s electron, being close to Mnz+, tends to orient its spin parallel to the spin of 3d5, i.e.there is a tendency for an admixture of a (non- bonding) state with the 4s spin parallel to the 3d5 spin and t spin antiparallel to it. Spin-orbit coupling will give a (positive) orbital contribution to the g-factor. But another mechanism is energetically equally probable : a t electron goes to a 3d orbit. In the resulting 3d6t state the quenching of the orbital moment is partially lifted. This gives a positive contribution to the g-factor because the 3d shell is more than half-filled. On the other hand the non-compensated t electron that is left behind on the negative ion will give a negative contribution. Both mechanisms are capable of giving an effect of the right order of magnitude. It folIows from the foregoing that they are not a direct result of covalent bonding but that they are favoured by the same phenomenon as covalent bonding, namely,3. S .VAN WIERINGEN 123 by low electron dissociation energy of the anions. Therefore the change in g- factor does not give much information about the state of bonding. DECREASE OF H.F. SPLITTING BY EXCHANGE It is seen in fig. 3 that towards high Mn concentrations the line width is much less than would be expected from dipolar broadening (about 500 oersteds at 10 % and 1000 oersteds at 30 % Mn). Thus there is appreciable exchange narrowing. It can be shown that, even without the complications arising from dipolar broaden- ing, exchange will tend to reduce the h.f. splitting. The h.f. splitting in Mn2f is caused by an interaction between the electron spin S = and the spin 1 =I= of the 55Mn nucleus.If neighbouring Mn2' ions are present, exchange between the electron spins will take place. In coursc of time S jumps from one Mn2+ ion to the next, interacting all the time with different Mn nuclei. Meanwhile the electron spin performs a Larmor precession in the static external magnetic field, applied during the paramagnetic resonance experiment. The frequency of the precession is slightly changed by interaction with Mn nuclei. It may have 21 + 1 values. Thus the precession frequency will change by an amount N A/h when S jumps from one ion to the next. The Fourier spectrum of such a frequency modulated precession consists of 214- 1 peaks if the time between jumps T > h/A but the peaks merge together if T 5 h/A.NOW T is determined by the strength of the exchange energy J, r e k & / J . Thus, narrowing of the lines is expected if J Z A . The same argument may be given by applying the Heisenberg uncertainty principle. It says that spectral lines associated with neighbouring levels (energy difference NA) cannot be split if the life-time T of the levels is too small, i.e. if TA z h . Hence this argument leads again to line narrowing if J L A. The narrowing effect is found in our experiments on ZnS: Mn at different Mn2+ concentrations. The higher the concentration, the stronger the exchange effect and the narrower the line. Mathematically the effect of exchange on h.f. splitting can be found from a calculation of the moments of the paramagnetic resonance spectrum.As in van Vleck's calculation of the effect of exchange on dipolar broadening,lo it will be shown that the 4th moment is increased by exchange. The Hamiltonian is = p H x 'Zl + A ' j 4 + Bkjsksj. (14) i f k > j The first term arises from the external static field W(determining the z-direction). The second gives the interaction with the nuclear moment I (leading to h.f. splitting). The last term describes exchange interaction with other paramagnetic ions. Mathematical difficulties prohibit the direct evaluation of the paramagnetic resonance spectrum of the many electron problem (eqn. (14)). Van Vleck solved the related problem of dipolar broadening 10 by calcuiating the moments of the spec- trum, i.e. v, v2, v3, . . . . In principle the problem can be solved by evaluation of all moments.In practice one cannot go much further than v2 because of mathematical complications. We shall calculate v, v2, 3 and 3 for the whole group of 21 + 1 h.f. lines using the Hamiltonian (eqn. (14)). Zt will be seen that v? is influenced by exchange. The applicability of the method of moments rests on the fact that the moments can be calculated without knowledge of the exact wave function which diagonalizes H (eqn. (14)). The moments are expressed in terms of diagonal sums of matrices which are invariant under transformations from one wave function to another. Hence a simple wave function may be chosen, in particular the representation where all magnetic moments Szj, Izj are quantized individually. - - - - -124 MANGANESE IN VARIOUS LATTICES Before we calculate the successive moments of the resonance line we must make a change in (14), as was discussed by van Vleck.The contribution of Iines near hv = 0, rt 2pH, f 3pH, . . ., must be suppressed by dropping the non-commuting part of the second term of (14). Thus our Hamiltonian reduces to - Sp[(%S, - SxX)(Sx - is,) + (%Sy - SyX)(Sy + isx)] y=------- hSp(Sx2 + Sy2 + Sz) It is seen that we want the commutators (XS, - SxX) and (xSy - Sy%) (21) (22) Their value is - i(Yisx - sxge) = ~ H S , + A 1 SyjIZj, i(xsy - syye) = PEG + A t: sx,Izj , i because Inserting (21) and (22) in (17) the numerator becomes (sxjsyk - syksx~) = 1 (sHsyj - s,,js,j) = i 1 szj = isz etc. (23) jk i and thus all terms containing Iz linearly disappear when the spur is evaluated.J .S. VAN WIERINGEN 125 Similarly S’S, in the denominators of (17), (18), (19) and (20) vanishes. More- over SpSySz = 0. Hence h? = 2pHSpS$/2SpSx2 = pH. (25) Insertion of (21) and (22) in the numerator of (18) gives 2P2ff2SPsy2 -I- ~PHASP z SyjSykIzj 2A2Sp Syjsyk~zj~zk l k i k = 2p2H2SpSy2+ $A2I(I+ 1)SpSy2, (26) as Sp(Xsy - syX)(Xs, - sJe) = 0. It follows that h G = p2H2 + QA2I(I + l ) , (27) or with For the 3rd and 4th moment we need X(%& - &A?) - (XSX - &X>% = P2H2Sx 3- 2pHA and = P2H2Sy + 2PHA x SyjIzj + A2 1 syjIzj2- A z Bkj(S&Syj - sykszj)(Izk- Izj). (31) SxjIzj+A’ z SX Izj2-A 2 Bkj(szksyj- SykSzj)(fZk-Izj), (30) i i k>i A?(XS, - SyX) - (XSy - S,%)c% I j k>j Inserting (39) and ( 3 1 ) in (19) one gets h3~3 = 2Sp[p3H3Sx2 i- pHA2 1 sxj&j2 4- A2 1 sxj2IZj3]SpSx2 j i = p3H3 + pHA2I(I + l), (32) because SpI2 = 0.It follows that m= 0. (33) The numerator of (20) becomes ~ S P [ P ~ H ~ S X ~ + 6,~2H’A2 2 SXj’Izj2 + A4 ~ X j ‘ I q 4 j i A2 Bkj2(szk2,,i2 sXa2sZj2)(Izk2 (34) k>j Now s p ~ ~ 2 1 ~ ~ 4 = { & I ~ ( I + 112 - # ~ I ( I + i))spsx2. ( 3 5 ) i Hence h4v4 = p4H4 + 2p2H2A21(I+ 1) + A4{QIz(I + 1)’ - &I(I + I)) $S(S + I)I(I + 1)A’ Bkj2, (36) k>l and h 4 G = {+P(I + 1)2 - &I(I + l))A4 + &S’(S + l)I(I + 1)A2 Bkj2. (37) It is seen that the absorption line is symmetrical for & = A T = 0. The second moment (27) depends only on the h.f. interaction, but (37) shows that exchange does play a role by changing the 4th moment. From the 2nd and 4th moments alone it is impossible to derive any details about the line shape.k=-/126 MANGANESE I N VARIOUS LATTICES Anyway, the increase of the 4th moment in the presence of exchange shows that part of the absorption is shifted from the centre to the wings of the spectrum. Hence exchange will give an effect like the observed one : at high concentrations where exchange is important, the overall width of the spectrum decreases. How this comes about in detail cannot be made out from the foregoing. There are two alternative mechanisms. Either the splitting between the h .f. lines decreases, or each of the h.f. lines gets extended wings. Anderson's theory of exchange narrowing 19 predicts the former. This is supported by measurements of para- magnetic resonance in aqueous solutions of Mn2+ salts, where narrowing of the individual splittings with increasing concentration has been observed. From our experiments it is impossible to decide between the two mechanisms off hand.At a concentration where exchange becomes important the h.f. lines have merged together because of dipolar broadening.* Under this concentration there is no sign of decreasing h.f. splitting. However, our measurements lend indirect support to the first mechanism. The second mechanism is expected to give, at the position of the outer peaks, an absorption of at least 5-8 of that in the centre. It is seen in fig. 3 that it is much less for Mn concentrations exceeding 5 %. The order of magnitude of B (the Curie tempcrature of MnS, 165" K gives B N 6 cm-1) and A(A N 0.01 cm-1) shows that appreciable narrowing may be expected as soon as a Mn2+ ion has one or more Mn2+ next nearest neighbours. From fig. 3 it follows by extrapolation from high concentrations that exchange affects the h.f. spectrum at concentrations exceeding 1 %. As Mi72 has 6 next nearest %n or Mn neighbours in ZnS: Mn, this means that the effect becomes appreciable if more than 1 out of every 15 Mn ions has next nearest Mn neighbours. The author's thanks are due to MI-. van der Kint for his assistance during the measurehents, to Mr. Zalm and Mr. de Nobel for supplying the samples, and to Dr. Stevens, Dr. Owen (Oxford), Mr. Smit and Mr. Polder for helpful discussions. * The dipole-dipole interaction gives some complications. It contains a term of the exchange type C s i . ~ and thus it mixes the h.f. lines at lower concentrations than exchange i j interaction will do. However, this does not change our rather qualitative conclusions in the following. 1 (a) Hershberger and Leifer, Physic. Rev., 1952, 88, 714 ; (b) Schneider and England, 2 Bleaaey and Stevens, Report Prog. Physics, 1953, 16, 108, 3 Abragam and Pryce, Proc. Roy. SOC. A, 1951,205, 135. 4 Townes and Turkevitch, Physic. Rev., 1950, 77, 148. 5 (a) TravniGek, Kroger, Botden and Zalm, Physica, 1952, 18, 33 ; (b) Kroger, Some 6 Klasens, Zalm and Huysman, Philips Res. Reports, 1953, 8,441. 7 Hurd, Sachs and Hershberger, Physic. Rev., 1954, 93, 373. 8Van Vleck, Physic. Rev., 1948, 74, 1168. 9Anderson, J. Physic. SOC. Japan, 1954 9, 316. Physica, 195 , 17, 221 ; (c) van Wieringen, Physica, 1953, 19, 397. Aspects of the Luminescence of Solids (Elsevier, London, 1948), p. 98.

ISSN:0366-9033    

DOI:10.1039/DF9551900118

出版商:RSC    

年代:1955

数据来源: RSC

摘要:

THE MAGNETIC EVIDENCE FOR CHARGE TRANSFER IN OCTAHEDRAL COMPLEXES BY J. OWEN* Clarendon Laboratory, Oxford Received 25th January, 1955 An account is given of the information about covalent bonding and electron dis- tribution in octahedral complexes containing transition group elements, which is available from paramagnetic resonance measurements. The molecular orbital treatment of u- and n-bonding in these MXg complexes is briefly described ; this suggests that the unpaired electrons responsible for the paramagnetism may be partially transferred from M to x6 in molecular orbits which are usually of antibonding type. From the observed effects in the paramagnetic resonance spectrum (e.g. hyperfine structure from X nuclei, reduction in orbital magnetic moment), the amount of electron transfer can be estimated, and some typical examples are discussed. The results indicate that in hydrated 3d group complexes there are appreciable a-bonds and usually weak or negligible T-bonds, while in the 3d group cyanides and complexes of the 4.d and 5d groups there are strong a-bonds and also appreciable r-bonds.1. 1NTRODUCTION The magnetic properties of MX6 complexes, where M is a transition group element, have long been used as a guide to the nature of the bonding between M and X. Pauling 1 first suggested that the anomalously low magnetic moment and total electronic spin of complexes like [Fe(CN)6]3- was evidence for covalent bonding, and on the basis of this '' spin-criterion ", bonds in many M& complexes have been rather sharply classified as being either ionic or covalent.However, van Vleck2 pointed out that this spin criterion does not directly distinguish between ionic and covalent bonds at all, but only shows whether the bond energy is greater or less than the energy of Russell-Saunders coupling between the d-electrons belonging to M. The only satisfactory way of distinguishing between the bonds requires an estimate of the electron distribution over the complex, and this can only be found by the measurement of properties which give detailed information about the orbits of the electrons, and not by measurement of the total spin. The paramagnetic resonance method is well suited for this purpose, since it gives very precise information both about the orbital magnetic moment of the unpaired d-electrons, and about hyperfine interactions between these electrons and any nuclei with non-zero spin which are included in the orbit.For example, the resonance spectrum of [l[rC16]2- shows 3 that there is a small anomalous reduction in the orbital magnetic moment of the single unpaired d-electron, and that there is hyperfine interaction with Cl as well as with Ir nuclei; these effects can be ascribed to r-bonds in the complex, which involve a partial transfer of the electron from Ir to c16. Subsequent work has given information about (3: and/or r-bonds in many other MX6 complexes, and it is the purpose of this report to collect together some of these results, and to explain how they are obtained from the paramagnetic resonance data. Accordingly, a general discussion of the orbits, energy levels and bonds in MXtj complexes will be given first, and this will be followed by a more specific treatment of the effects of covalent bonding on the magnetic properties of particular complexes.* at present at Department of Physics, University of California, BerkeIey, 127128 OCTAHEDRAL COMPLEXES 2. ORBITS AND ENERGY LEVELS OF MX6 In discussing the orbits and energy levels it is convenient to assume first that the bonds between M and X are ionic, then to consider the effect of introducing covalent cr-bonds, and finally to consider the effect of a-bonds. For the most part, the discussion will follow that of van Vleck,2 Stevens4 and 0wen.S It is assumed throughout that the MX6 complex is a regular octahedron, i.e., that there is cubic symmetry.2.1. IONIC BONDS In this case M is a positive ion with an unfilled 3d, 4dor 5d shell, e.g., Cr3f = 36, Ru3+ = 4d5, Ir4+ == 5d5. The magnetic electrons occupy &orbitals on M, i.e. orbitals of the form d , ~ - ~ 2 , d3z2-r~, dxy, dYz, dzx. The first two orbitals (usually called dy type), if filled with electrons would correspond to negative chargeclouds with lobes pointing towards the attached negative X ions, and consequently are of higher electrostatic energy than the other three orbitals (de type) which have lobes pointing between the attached ions (see fig. 1). This is the origin of the crystal (0) ( b) FIG. 1.-Rough illustration of some atomic orbitals of M and x6. (a) Central dx2-y2 orbital, and 4 of the 6 attached pa orbitals. These are used to construct the molecular orbitals u:2-y2, 0x2-v2 (eqn.(1) and (2)). The admixtures are such that the signs of the central and attached orbitals are all the same (u) or opposite (o*) in the region of overlap. (b) Central dxy orbital, and 4 of the 12 attached pn orbitals. These are used to construct rzy, nxy molecular orbitals (eqn. (3) and (4)). Note that for the corresponding orbitals in the yz plane [p& denotes p&), etc. field splitting between the dy doublet and de triplet energy levels (fig. 2). On the ionic model X can often be treated as a diamagnetic negative ion with a filled p shell; for example, if X = C1- = 3p6 this is literally true, while if X = H20, then as far as M is concerned, X looks something like an 02- ion ' ( 2 ~ 9 . The highest occupied orbital energy levels of x6 can then be approximately represented as in fig.2. The levels are slightly different if X = CN- (see below). On this ionic model the magnetic properties of MX6 depend on the paramagnetic ion M and the crystal field splitting between dy and de levels. 2.2. COVALENT cr-BONDS Using the molecular orbital method one now considers the mixing which can occw when central ndy, (n + 1)s and (n + I)p orbitals, (n = 3, 4 or 5 ) appreciably overlap pa orbitals belonging to &j (cf. fig. 1). In general, s orbitals on X are also involved, and it can be assumed that such s admixtures are included by the symbol pa. The molecular orbitals which can be constructed from linear com- binations of these central and attached atomic orbitals are given by van Vleck.2J .OWEN 129 The*-c arc six bonding and six antibonding Gombinations, of which those involving the magnetic dy orbitals are (neglecting terms containing overlap), * - o3+ y2 = ad3z2-y~ - (1 - a2)'(1/J2)'[2P6 - 2P3 + PI + PZ - P4 - PSI~ 0:2- y2 = ( 4 2 y2 - (1 - a2>* +[P2 + P4 - Pl - PSla, (1) 03~2--r2 ( 1 - a2>"3z2-r2 + a ( 1 / w w 6 - 2p3 + p1 + p2 - p4 - PSI6 032 - y z = (1 - a2)3dx2.-y2 + a4-[p2 + p4 - p1 - psla. (2) In these expressions the suffixes 1, 2, 3, 4, 5 and 6 denote the X at'oms on the x, y , z, - x, - y and - z axes respectively; ~ , Z - ~ Z , etc., denote bonding orbitals and o* antibonding orbitals. (1 - a2)& is the admixture coefficient, which is zero if the bonding is purely ionic. On the other hand, if the bonding is what might be Orbital O r b i t a l O r b i t a l levels of leve I s of levels 01 M tM X61 ' 6 FIG.2.-Diagram showing probable energy order of some of the orbits in an MX6 com- plex, where X is an ion like C1- (see text). The diagram is not drawn to scale. The number of electrons which can be accommodated in each level is shown in brackets, and the available electrons fill these levels in the appropriate energy order ; for examples, see 0 3. called purely covalent, a2 = 1 - a2 = 0.5, corresponding to an equal sharing of electrons between M and X6. If the molecular orbitals involving central s and p orbitals also correspond to equal sharing, one then has, in effect, the d2sp3 bonds of the directed valence-bond method (see van Vleck 2). In practice, one might expect a2 to have some value between these extremes, 1 Z a2 > 03, although, as will be seen below, there is no direct evidence that a2 is never less than 0.5, The probable energy changes resulting from o-bonding are indicated in fig.2 . It will be noted that twelve pa electrons are partially transferred from x6 to M and have their energy lowered, while a small number of dy electrons (not more than three if MX6 is paramagnetic) are partially transferred from M to x6 and have their energy raised. It can be pictured that the net gain in stability results because there is a net transfer of electrons from x6 to M which helps to even out the charge distribution over the complex. The magnetic properties are affected by the a-bonding because (i) the splitting between dy and de levels is increased, and (ii) any unpaired dy electrons are partially transferred from M to x6.E130 OCTAHEDRAL COMPLEXES 2.3. COVALENT n-BONDS In this case one considers the mixing between de orbitals on M and pn orbitals on X. The admixtures would be expected to be smaller than for the o-bonds discussed above, because of the smaller overlap (cf. fig. 1); the experimental evidence, as far as it goes, appears to confirm this. The molecular orbitals which can be constructed are given by Stevens;4 here we will make some slight modifications (see Owen 5) in that terms containing overlap will be neglected, and also the orbitals of the magnetic de electrons are assumed to be antibonding for most cases, rather than bonding. There are then three bonding and three antibonding combinations of the form (cf.fig. 1) (3) (4) and the other combinations, rYz, rrzx, etc., are obtained by cyclic permutation of the suffixes. As in eqn. (1) and (2) the admixture coefficient (1 - P2)* = 0 if there is no n-bonding. The energy changes which result from the v-bonding are indicated in fig. 2, where it is assumed that the orbitals on X which are used for n-bonding are filled with electrons, e.g. X = C1-, H20. Then six pn electrons are partially transferred from Xg to M and their energy is lowered, and the remaining eighteen pn electrons on x6 are non-bonding ; * the magnetic dc electrons on M are partially transferred from M to xfj and their energy is raised. It will be noted that the dc-dy splitting is decreased by the bonding. If X = CN-, on the other hand, the energy levels and eqn.(3) and (4) have to be changed slightly. In this case it seems likely that the orbitals on X available for n-bonding with M look something like Zp, orbitals on C atoms, which are unoccupied and of higher energy than the central de-orbitals, cf. Orgel.6 (The 7r-orbitals on N are assumed not to contribute appreciably because paramagnetic resonance measurements 15 on complexes such as [Cr(CN)#- show that there is at most only an extremely small hyperfine splitting due to the N nuclei, cf. 6 3.2 below.) If this is so the magnetic dc electrons are bonding rather than anti- bonding, their energy is lowered by the transfer from M to Xg, and in eqn. (3) the sign of the admixture coefficient must be changed so that it represents a bonding orbital.There is no electron transfer from xg to M. Thus, with X .-= CN-, it seems likely that n-bonding results in a net transfer of electrons from M to Xg (Pauling 7), and also in an increase of the splitting A between the dc and dy energy levels. For example, in [Fe(CN)g]3-, r-bonds help to increase A, while in [FeF& they tend to decrease A according to the arguments above. We will now consider the magnetic properties of the orbitals discussed above, and show for some cases how these orbitals are related to the observed para- magnetic resonance spectra. 3. THE MAGNETIC PROPERTIES OF MX6 * - n;,v = Pdxy - (1 - B2)wPl + P2 - P4 - PSI, (1 - P2>*dxy 4- P#& 4- P2 - P4 - PSI, r x y The main effects of covalent bonding on the magnetic properties and para- (i) Such bonds may help to cause a reduction in the electronic spin of the (ii) There may be hyperfine interaction between the magnetic electrons and (iii) There may be a reduced orbital magnetic moment.(iv) There may be a reduced hyperfine interaction with the M nucleus. These four effects will be discussed in turn. * Strictly speaking, six of these eighteen electrons may also be weakly bonding through small admixtures of central p to attached pn orbitals. These admixtures are neglected throughout. magnetic resonance spectrum of Mx6 are its follows : ground state. the X nuclei.J . OWEN 131 3.1. THE ELECTRONIC SPIN OF THE GROUND STATE The electronic spin of the ground state depcnds on the number of d-electrons on M, the Russell-Saunders coupling between thcm, and the de-dy splitting A.Covalent bonding affects thc value of the spin mainly because it affects the value of A (fig. 2), but sincc thcre is no obvious way of sorting out the various contribu- tions to A, a knowledgc of the spin-value gives no direct information about covalent bonding, as has already been mentioned abovc.2 When A is small compared with the Russell-Saundcrs coupling cncrgy, the d electrons fill both de and dy orbitals in such a way that there is a maximum number of unpaired electrons, i.e. maximum spin (Hund‘s rule), and, when this condition is fulfilled, a minimum number of electrons occupy the high encrgy dy orbitals. (There are slight cxceptions for the configuration d2 and d7.) Most hydratcd iron s o u p complexes arc in this category. For examplc, the ground state spin and configuration of d-electrons for hydrated complexes of Cr3+ are S = 3/2, (3&)3, for Fe3+, S = 5/2, (3d~)3(3dy)2, and for Ni2+, S == 1, (3&)6(3dy)2.Becausc of the configurations, to a good approximation the transfer of unpaired electrons to (H2O)6 arises in Cr3+ only from n-bonds, in Fe3+ from both (T- and n-bonds, and in Ni2+ onIy from o-bonds. When A is large compared with the Russell-Saunders coupling energy, thc lowcst state of the systcm * is obtained by putting the first six d-electrons into the lower energy de triplet, and the maximum spin is formed consistent with filling this triplet, i.c. as the number of electrons incrcases from d l to d6, the ground state spin has values 1/2, 1, 3/2, 1, 1/2, 0.Thus the spin is anomalously low for d4, d5, and d6. The 3d group cyanides, and all known octahedral complexes of the 4d and 5d groups are in this catcgory. A reduced spin might be expected to occur more frequciitly in the higher transition groups, (i) because the Russcll- Saunders coupling is smaller, and (ii) because the d-wave functions extend farther from the ccntral nucleus thus giving greater overlap and stronger bonding. Since the unpaired electrons are in de orbitals, they are transferred to x6 only because of n-bonding, and magnetic measurements can give no dircct information on (T- bonding in these complexes. 3.2 HYPERFINE STRUCTURE FROM X NUCLEI If an unpaired d-electron from M is partially transferred to an orbit on X, therc may be hyperfine intcraction with the magnetic inomcnt of the X nucleus, whose order of magnitude is the product of the hypcrfinc structure of the free X atom and thc probability of finding the unpaired electron on X.This efiect was fist found in ammonium cliloroiridate.3 Here the [IrC16]2-- complcx is a perfectly regular octahedron, the configuration is Ir4-’- := (5&)5, and there is a single unpaired clcctron, which occupies antibonding n* orbitals (eqn. (3)). This unpaired elcctron is thus approximately 8 2 on Tr and i(1 -- 62) on each C1 atom. Each C1 nucleus, (I :== 3/2 for 35. Wl), then causcs a splitting of each Iinc in the paramagnetic resonance spectrum into 21 4- 1 == 4 components, with separa- tion between adjacent components,4 ( 5 ) In this expression y is the Cl nuclear gyromagnetic ratio, p’ the Bohr magneton, PN thc nuclear magneton, Y the radius of a pn orbit on C1, and 0 is thc angle between thc applied magnetic field and the Ir-Ci direction.(The quantity -$f y p ’ p ~ (m)z3a. where a is the hyperfine structure constant for the 2P312 ground state of a free C1 atom.) The measured splitting, A := 26.5 x 10-4 cm-1, leads to the value 82 = 0.74. The experimentally observed spectrum is complicated by the fact - A cos e := Q (1 - p)[-5s yp’pN(i/r3)1 cos e. * Detailed energy level diagrams showing how a large value of A can bring down a state of low spin below the normal ground level are given by Tanabe and Sugano.8132 OCTAHEDRAL COMPLEXES that two or more C1 nuclei, and also the Ir nucleus, contribute to the structure at the same time.A typical spectrum and reconstruction is shown in fig. 3 ; for details of how to make the reconstruction? and of similar structures in [li-Br6]2-, see Griffiths and Owen.9 Structures from the X nuclei have been found in a few other MX6 complexes, but these have not yet been analyzed in detail. For the majority of complexes which have been measured there are no such structures because X has zero nuclear moment, e.g. X = 02-. However, if a salt containing [cU(&O)6]2' complexes, for example, could be prepared using the isotope 170, a structure at least as large as that in [hC16]3- would be expected due to the magnetic electron transfer arising from a-bonds. 3.3. REDUCTION IN ORBITAL MAGNETIC MOMENT The orbital magnetic moment of an unpaired d-electron on M is in general reduced if this electron is spread out in a molecular orbit over MX6; the spectro- scopic splitting factor (g-value), may then depend on the charge transfer.The theory of this effect was first given by StevensP with particular reference to the anomalously low g-value found in ammonium chloroiridate, where there was direct evidence for electron transfer (see above). We will illustrate the effect with the following three examples, where it is assumed, unless otherwise stated, that the octahedron is regular, i.e., cubic symmetry. (i) [ITCJ6]2-, (5d45, S = 112. As discussed above, there is a single unpaired electron in T* orbitals, which is approximately 82 on the Ir atom and +(l - /32) on each C1 atom. The g-value is 4 (6) Experimentally, g = 1.775 giving 82 = 0.66.9 The difference of this value of /32 from that found from the X hyperfine structure (p2 = 0.74), can probably be attributed to certain simplifying approximations made in the derivation of eqn.(5) and (0, and to the value assumed for (llt-3) when using eqn. (5). For a number of other examples of reduced g-values in this type of complex, see, for example, Griffiths, Owen and Ward.10 (ii) [Ni(H20)6]2+, 3d*, S = 1. The configuration of d-electrons can be written (3d46(3dy)2, and the two unpaired electrons are in a*-antibonding orbitals (eqn. (l)), so that each electron is approximately cc2 on the Ni2+ ion and +(l - cc2) on each H20. Neglecting .rr-bonds, i.e. assuming ,@ = 1, the g-value is 5 where A is the spin-orbit coupling constant, and A is the dc-dy splitting (fig.2) which can be found from optical absorption data. The experimental values of g, X and A lead to a2 = 0.83. (iii) [Cu(H2o)6l2+, 3d9, S = 1/2. If the complex is elongated along the z-axis (in practice, the distortion is usually more complicated), the unpaired electron is in the antibonding orbital a~2-,,2, and is approximately a2 on the Cu2+ ion and +(l - cc2) on each H20 in the xy plane. The g-value measured along the z-axis is then given by eqn. (7), if n-bonds are neglected. The experimental data give a2 = 0.84 (see Bleaney, Bowers and Pryce,ll Owen.5) g = 2 - *(l - 82). - g = 2.0023 - C C ~ ~ X ~ A , (7) 3.4. REDUCED HYPERFINE STRUCTURE FROM M NUCLEUS If the unpaired d-electrons on M are partially transferred to x6, there is a corresponding reduction in the hyperfine interaction with M nucleus. So far, this effect has only been studied quantitatively in [CU(H20)6]2+, 3d9, by Bleaney, Bowers and Pryce.11 The experimentally observed reduction in hyperfine structure gives a2 in fairly good agreement with the value 0.84 deduced from the g-values.J .OWEN 133 For many other complexes there is considerable evidence of variations in the hyperfine structure from a particular M ion, with variations of x6, especially for M = Mn2+. This can certainly be attributed in part to variations in the amount of electron transfer, but no quantitative analysis has yet been published. 4. DISCUSSION OF RESULTS The molecular orbital treatment of covalent bonding in MX6 complexes described above, can be summarized by the following approximate electron transfer scheme, where 1 - a2 and 1 - p2 can be considered to be measures of the amounts of a-bonding and .rr-bonding respectively.(i) Ionic bonds, (a = /3= 1). M has closed shells, plus 1 to 9 d-electrons with configuration ( d ~ ) ~ ( d c ) ~ , where 0 < n < 4, 0 < rn < 6 ; x6 has closed shells plus (usually) 12 cr-el&trons, and (ii) o-bonds, (a < 1). 4(1 - a2) o-electrons 8x o-electrons n(1 - a2) dy-electrons 24 .rrelectrons. x6 -+ M(d2) (bonding), x6 -+ M(sp3) (bonding), M+X6 (antibonding). Magnetic measurements give information about unpaired dy-electrons, and hence, under favourable conditions, the value of a2. They give no information about x, which probably lies in the approximate range 0 < x < - 0.5.either (iii) .n-bonds (p < 1) : .g., x = c1-, .n-electrons x6 -+ M (bonding) m(1 - ,822) deelectrons M -+ X6 (antibonding) or e.g., X = CN-. (b) ?(I 0 p2) deelectrons M -+ & (bonding) n-electrons X6+M Magnetic measurements give information about unpaired deelectrons, and hence, under favourable conditions, the value of 182. They do not distinguish between cases (a) and (b), which requires a measure of the sign of ,8. All of the charge transfers given above are approximate mainly because terms containing the overlap integral have been neglected throughout. This becomes a poor approximation as a2 or /32 become appreciably less than 1. A selection of values of a2 and /32 which can be found from paramagnetic resonance measurements are collected in the table below.These are mostly obtained from g-values only, as described in 3 3, and some of them may be modified slightly by new experimental results and further refinements of the theory (cf. the discrepancies in the results on [IrC16]2-). The values of a2 for (&)5 complexes cannot be found because there are no dy electrons. In these complexes the o-bonding is likely to be stronger, i.e., a2 smaller, than for any hydrated complex, but a2 is not likely to be much less than 0.5, the " pure covalent bond " value (see 5 2) ; thus, very approximately, one might expect - 0.5 .< a2 < -0.7. It should be pointed out that all of the complexes in the table generally occur in crystals as distorted, rather than regular, octahedra, and then the transferred d-electrons are not equally distributed over x6.For some such complexes, details of the exact distribution can be found from paramagnetic resonance measurements, e.g. [IrC16]2-, [IrBr6I2-. The foregoing discussion indicates the type of information about charge- transfer and covalent bonding in MX6 complexes which can be found from para- magnetic resonance measurements. The results show clearly that the same kinds134 OCTAHEDRAL COMPLEXES of bonding occur to a greater or lesser extent in all of these complexes, and that there is no sudden transition from an ionic to a covalent type of complex, as is suggested by the Pauling spin criterion. The results are also of interest because they arc, likely to lead to a better understanding of several other properties of [IrC16]2- [lrBr6]*- configuration (3dc)I ( 3 4 3 (3d€)6(3d# (3 de)6(3 dy) 3 (3d~)5 (4dc)5 (4d+ (5de) 5 (5d45 TABLE 1 reference spin.a2 8 2 112 ? < 0.9 1 2 a2t92 0.63 ((a2 - 0.7, /32 - 0*9)} 1 0.83 1.0 2 1 /2 0.84 1.0 2, 3 1 /2 ? 0.75 4 1 /2 ? 0.90 5 112 ? -0.9 6 7 1 /2 ? 1 /2 ? 3/2 0.66 from g-value 0.74 from h.f.s. 0.66 from g-value 0.74 from h.f.s. 7 References : (1) Bleaney, Bogle, Cooke, Duffus, O’Brien and Stevens, 12 (2) Owen ; 5 (3) Bleaney, Bowers and Pryce; 11 (4) Baker, Bleaney and Bowers; 13 ( 5 ) Griffiths, Owen and Ward ; 10 (6) Owen and Ward (unpublished) ; (7) GriEths and Owen.9 these complexes. For example, anomalies in the optical absorption spectrum of hydrated iron group salts (see Owen 5) can probably be attributed to covalent bonding. Also the mechanism of exchange coupling between neighbouring paramagnetic ions in crystals undoubtedly involves the magnetic electron transfer to the intervening diamagnetic ions (cf. Andersonl4), and an exact knowledge of the transfer is very relevant to this problem. This report has been written during the tenure of a U.S. Foreign Operations Administration Fellowship and a grant from the U.S. Office of Naval Research and the US. Signal Corp, and this support is gratefully acknowledged. 1 Pauling, J. Amer. Chem. SOC., 1931,§3, 1367. 2 van Vieck, J, Chem. Physics, 1935, 3, 807. 3 Owen and Stevens, Nature, 1953,171, 836, 4 Stevens, Proc. Roy. SOC. A, 1953,219, 542. 5 Owen, Proc. Roy. SOC. A, 1955 227, 183. 6 Orgel, 1955 (submitted for publication, J. Chem. Physics). 7 Pauling, Nature of the Chemical Bond (Cornell University Press). 8 Tanabe and Sugano, J. Physic. SOC., Japan, 1954,9, 766. 9 Griffiths and Owen, Proc. Roy. SOC. A, 1954, 226,96. 10 Criffiths, Owen and Ward, Puoc. Roy. SOC. A, 1953, 219, 526. 11 Bleaney, Bowers and Pryce, 1955 (submitted for publication). 12 Bleaney, Bogle, Cooke, Duffus, O’Brien and Stevens, Proc. Physic. Soc. A, 1955, 13 Baker, Bleaney and Bowers, 1955 (submitted for publication). 14 Anderson, Physic. Rev., 1950,79, 350. 15 Bowers, Proc. Physic. SOC. A , 1952, 65, 860. 68, 57.

ISSN:0366-9033    

DOI:10.1039/DF9551900127

出版商:RSC    

年代:1955

数据来源: RSC

摘要:

PARAMAGNETIC RESONANCE IN SOLUTIONS OF ELECTROLYTES BY B. M. KOZYREV Kazan Branch of the Academy of Sciences of the U.S.S.R., Kazan, U.S.S.R. Received 4th April, 1955 Until recently the study of paramagnetic resonance in liquid solutions did not attract much attention, although this effect was discovered by Zavoisky for solu- tions of Mn2+ salts as early as 1944.1 The author of this paper and also his co- workers, N. S . Garifyanov and A. I. Rivkind, carried out studies of electron and proton paramagnetic resonance in a number of solutions of VO2+, Cr3+, Mn2+, Fe3+, Fe2+, Cozf, Ni2+, Cu2+ and Gd3+ salts in water and in other solvents (ethyl alcohol, glycerol, acetone). Measurements at high frequencies (- 10,000 Mc/s) were carried out by the passing wave method using modulation of the magnetic field and at lower frequencies by the grid-current method of Zavoisky.1 A measurable electron paramagnetic effect 2 was found in solutions of salt of VO2+, Cr3+, Mn2+, Cu2+ and Gd3f.Of the ions mentioned, sufficiently dilute aqueous solutions of V02+ and Mn2+ salts exhibit a hyperfine structure of absorption lines at room temperature. Solutions containing the remaining ions yield at room temperature absorption curves with a single maximum. Absorption curves with hyperfine structure will be considered first. Of the solutions of VO2+ salts the sulphate and the chloride solutions were studied by Garifyanov and the author of this paper.3 In these, resolution of the hyperfine line structure begins at V02+ ion concentrations of about 2 to 3 moles/l. The effect is observable up to 0.01 mole/l.The position of the lines of the hyper- fine structure is excellently described by the equation A2 Azm H* = HO - Am - - [I(I + 1) - mz] - - (2M - l), 2HO HO for transitions (M, m % M - 1, m). H* is the resonance value of the static magnetic field H, A the constant of hyperfine splitting, m and M the magnetic quantum numbers of the nucleus and the electron shell of the ion under in- vestigation respectively ; HO = hv/gp. Formula (1) is obtained from the general theory of the line structure of paramagnetic resonance of Abraham and Price4 for an isotropic medium. The best agreement with experimental results for aqueous solutions of vanadyl salts is obtained if A = 116 oersteds and g = 1.962 4 0.002 are used. It is interesting to note that the value of the constant A was found to be some- what dependent on the nature of the solvent.For example, for solutions of VOCI, in acetone containing small percentage of water it was found to equal 110 oersteds, whereas the g-factor was practically constant. The effects for highly supercooled solutions of V02f in organic solvents, investigated by Garifyanov,5 were found to be much more complex. At room temperatures it is not possible to resolve the hyperfine structure in alcohol, glycerol and pure acetone solutions of VOS04 because of the broadness of the lines. Cooling to temperatures of about 90" K makes it possible to obtain resolu- tion. Under such conditions, for solutions whose concentration is not too high, a complex spectrum containing 13 lines is observed. Eight of them, which are considerably narrower and more intense than the others, form a group located 135136 SOLUTIONS OF ELECTROLYTES in the central part of the spectrum and they are satisfactorily described by formula (1) if A is given the value of 76 oersteds and g of 1.960 4 0.003 (for both alcohol and glycerol solutions).The remaining five peaks, which are considerably broader and weaker, lie near the ends of the spectrum, two of thein at the beginning and two at the end. They may be assumed to conform to the second hyperfine structure of the VWf ion with A CL 200 oersteds and g= 1.92. The inter- mediate peaks of this second structure cannot be observed, since they are hidden by the more intense peaks of the first structure.It should be mentioned that within the limits of accuracy of the measurements (which was not very great in this case because of the broadness of the lines) the peaks of the second structure seem to be equally spaced. The complex character of the magnetic radiofrequency spectrum of vanadyl salts and the variability of the value of the A constant should probably be attributed to the molecular nature of the VO2+ ion. In more highly concentrated, supercooled solutions of VO2+ salts along with the hyperhe structure spectrum, a considerable peak due to the partial crystallization of the salt is observed. A number of studies6s7s8s9910 have been made of the hyperfine structure of paramagnetic resonance lines in solutions of Mn2+ salts. Measurements made by Garifyanov and the author of this paper,3 carried out in aqueous solutions of manganese salts at room temperature and at frequencies of - 10,000 Mc/s, were found to be in good agreement with data of England and Schneider,7 and also with those of Tinkham, Weinstein and Kip.* Formula (1) gives a good description of the position of the lines of the hyperfine structure at values of A = 96.5 and At low frequencies (v < 200 Mc/s) and at low Mn2+ concentrations, i.e.in conditions corresponding to the Zeeman effect of the resulting spin F of the nucleus and electron shell of Mn2t in weak fields, the hyperfine structure is represented by the equation g = 2-000 f 0.002. H" = hv/gFp; (2) where and J is the spin of the electron shell. Eqn. (2) gives a single peak with gF = 1 for manganese salts (I = J = 5/2).This was discovered by Altshuler, Salikhov and the author of this paper 6 as early as 1948. Highly concentrated solutions of manganese salts in water, alcohol, glycerol and acetone at room temperature yield an intense and comparatively narrow absorption curve with a single resonance peak corresponding to g = 2-00. (A similar phenomenon is also observed in vanadyl salt solutions of high con- centration, in which case g = 1.96.) It has not been possible to detect a hyperfine structure of the absorption line of the Mn2+ ion in organic solvents at room temperature; even a slight dilution of the solution brings about a severe broadening of the line and the paramagnetic resonance effect becomes unobservable. Cooling narrows the width of these lines; as was shown in the experiments of Garifyanov,s at a frequency of 10,000 Mc/s and at a temperature of 90" K for sufficiently diluted solutions of Mn2+ salts in organic solvents, a spectrum is observed which consists of 6 peaks and which is well described by eqn.(1) if A is given the value of 97 oersteds and g = 2.000 f 0.003. Within the limits of experimental accuracy, the values are the same for solutions of alcohol, glycerol and acetone. Thus the hyperfine splitting constant of the Mn2+ ion, as could be expected, is practically the same in aqueous solutions at room temperature and in organic solvents at low tem- peratures and coincides with the data for ionic crystals containing Mn2+. As was already mentioned above, highly concentrated solutions of VO2+ and Mn2+ salts yield a single, comparatively narrow absorption line which broadens sharply even at very small dilution.For very highly concentrated solutions of Mn(NO3)2. 6H2O, or, to be more exact, for the molten salt, this phenomenonB. M. KOZYREV 137 was observed earlier by Garstens and Liebson,g who explained it as being due to the presence of considerable exchange interactions between the Mn2+ ions in such conditions. For the VO2+ ion, an exchange narrowing accompanied by a dis- appearing of the hyperfine structure is observed at lower concentrations (-5.8 molesll.). As was to be expected, on the basis of experiment with solid salts, exchange interactions were found to be especially intense in solutions containing ions of divalent copper. Experiments with aqueous solutions of Cu(NO3)2 at room temperature and at frequencies of - 10,000 Mc/s showed that: (i) Paramagnetic resonance can be observed to begin at the highest con- ceptrations and down to concentrations of the order of several tenths of a mole/I.(ii) Over the whole measurable range of concentrations, a single resonance peak not having hyperfine structure is observed. (iii) The line width is practically independent of the Cu2+ concentration and is equal to - 140 oersteds, but the intensity decreases rapidly with dilution. These properties of the absorption curve in Cu(NO3)2 solutions were also confirmed by measurements at lower frequencies.” Also in organic solvents a hyperfine struc- ture of the Cu2+ ion absorption line is not found. In all cases a single peak was found, whose g-factor value is somewhat larger than 2 and depends on the immediate surroundings of the Cu2+ ion.Inasmuch as the nuclear spin of both copper isotopes is equal to 3/2 and the hyperfine structure constant, measured in solid salts, is not abnormally small, there seems to be only one possible explanation of the effect observed in solutions of copper salts-it is totally due to those Cu2f ions between which there are con- siderable exchange interactions. This, in turn, points toward the existence in concentrated solutions of copper ions of some sort of a quasi-crystalline structure, the lifetime of microscopical formations containing at least 2 Cu2f ions must at room temperature be not shorter than 10-7 sec. CU~+ ions which do not take part in these microformations, do not give a measurable effect at room tem- perature, evidently as a result of the too short spin-lattice relaxation time corres- ponding to such ions.Garifyanov’s experiments 5 with supercooled solutions of copper salts in organic solvents give proof of this. At 90°K and at con- centrations of 1 mole/l. and lower, these solutions showed besides the ‘‘ exchange ” peak corresponding to a g-factor of 2.091 3: 0.001, four peaks of hyperfine structure, the position of which is well described by eqn. (1) if A is assigned the value of 130 oersteds and g = 2.369 f 0.003. If the temperature is raised, the intensity of the exchange peak loosens rapidly, and at temperatures not far from the boiling point this peak vanishes. This evidently corresponds to the complete destruction of the microcrystalline formations which make the exchange interactions possible.Aqueous solutions of chromium salts of the violet modification, containing [Cr(H20)6]3+ ions, yield intense absorption lines whose width decreases with dilution, down to concentrations of 1 molell. ; further dilution practically does not change this limit width of the order of 200 oersteds. It was not possible to detect an exchange narrowing of the absorption line in solutions of Cr3+ salts. The value of the spectroscopic splitting factor in these solutions is 1.982 f 0-004 and it does not change with dilution. No signs whatsoever of hyperhe structure were discovered in solutions not enriched with the Cr53 isotope. The resonance effect in solutions of chromium salts of the green modification at room temperature is very difficult to observe because of the extreme width of the line.Solutions cf chromium salts of both modification in glycerol at room temperatrue yield very broad lines. Severe cooling 5 narrows them as described for solutions of manganese salts. * Former observations,6 which showed the presence of very weak absorption maxima at low frequencies, attributed to the effect of the spins of the copper nuclei, were not confirmed in later experiments.138 SOLUTIONS OF ELECTROLYTES Salts of trivalent iron, in spite of the fact that its ion is in the same 6S512 basic state as is Mn2*, do not yield a measurable effect in solutions at room temperature. Supercooled solutions 5 in organic solvents made it possible to discover resonance absorption with g N 2.It is interesting to note that when samples containing a partially hydrolyzed Fee13 salt are dissolved in alcohol together with the usual maximum, a second one is observed which corresponds to g = 4.22 f 0.03. An analogous effect occurs if the alcohol solution of FeCl3 is preliminarily heated until its colour changes. This is evidently connected with the special character of magnetism in colloidal hydrolysis products. Ions of Fez+, Ni2+ and Co2+, whose hydrated salts do not yield a measurable effect at room temperatures, like- wise did not show an effect when in solution. Measurements were made in aqueous solutions of gadolinium nitrate as well as with ions of the iron group. These solutions yielded a broad absorption line with a g-factor of about 2.Exchange narrowing of the line was not found. The experimental results briefly surveyed in this paper, show as a whole the existence of a fairly close analogy in some aspects between diluted liquid solutions and the behaviour of polycrystalline solid solutions of the corresponding ions. For example, as a rule, the times of spin-lattice relaxation in liquid solutions in- crease with decreasing temperature just as it does in solids. The presence of exchange effects in concentrated solutions (and for copper even in fairly diluted ones) makes them approximately pure solid paramagnetic substances. All this points with certainty to the existence of a “ near order ” of particle location in solutions at temperatures sufficiently removed from the boiling point.This “ near order ” is sufficiently stable to influence the resonance effects at the fre- quencies used. In developing a theory of electron spin-lattice relaxation for solutions it is essential to take this basic fact into account. Particles located in the immediate vicinity of a paramagnetic ion must, without doubt, have consider- ably less freedom of movement than molecules in pure liquids ; this leads to the similarity of resonance effect with those observed in solids. Experiments with mixed solvents have confirmed that it is not the average correlation time rc of the liquid, but the “ near order ” and the local electrical fields, determined by this order, that are predominant factors in the phenomenon of paramagnetic resonance in solutions.The fifty-fold increase in viscosity obtained by the addition of saccharose to water broadens the line-width of Mn2+ only several times, while the corresponding addition of glycerol completely destroys the resonance effect. The most probable explanation of this is that the molecules of glycerol in these mixed solutions are in the neighbourhood of paramagnetic ions, which is not the case for the molecules of saccharose. Later it was also found necessary to take the “ near order ” into account for proton resonance phenomena in solutions of paramagnetic salts ; this was established by Rivkind.11 He measured the longitudinal TI and transverse T2 proton relaxation times in relative units. Calibration of the values obtained was carried out using the absolute measurements made by Zimmerman 12 for aqueous Mn2+ solutions.In brief, the basic results obtained by Rivkind and the conclusions therefrom drawn by him11 are as follows. In the first place, the “anomalous” ratio of the longitudinal and transverse relaxation times, Tl/T;! > 1, discovered by Zimerman12 in aqueous solutions of manganese salts, were found to occur with several other ions as well. Table 1 serves to illustrate this. Thus the “ anomalous ” broadening of the resonance lines is not an exclusive phenomenon. This can be given only a single explanation-in aqueous solution of salts, the heat correlation time T~ in the vicinity of paramagnetic ions is con- siderably greater than in pure liquids, where r c e 10-11 sec. Because of this, the fluctuating local magnetic field of the ions is less apt to reach an average value during the period of Larmor precession of the nuclear spin, which causes the broadening of the lines in solutions of VO2+, Mn2-J- and Cr3+ of the violet modifi-B .M . KOZYREV 139 cation. Within the limits of a certain radius from a paramagnetic ion, the change of the quantization of electron spin, relative to the external static magnetic field characterized by the electron relaxation time p/2n, is the predominant (as to rate) process. This time should limit the value of the effective correlation time in the vicinity of a paramagnetic ion. Inasmuch as for the first three ions of table 1, the electron relaxation times are long, the ratio Tl/T2 is found to be significantly larger than one.However, for the Cr3+ green modification, Fe3+ and CU2+ * ions, the electron relaxation times are so short that they can effectively limit the correlation time rc; this leads to a " normal " value of Tl/T2. TABLE 1 interval of (moles/l.) concentrations T2N x lo5 TIN X 105 studied (sec mole/l.) (sec mole/l.) T1T2 type of dissolved salt voso4 1.0-1.6 15.5 256 165 MnSO4; MnCl2 - 1.64 14.4 8.8 Cr(N03)3 (violet solutions) 0-3-0.5 5.5 19.3 3.5 (assumed) (assumed) CrCl3 (green solutions) 05-0.6 19.7 23 cuso4 1-0-1-2 94 114 FeNH4@04)2 0.3 11.5 144} 1.2 The above is confirmed in a number of ways. Thus, as was stated above, in alcohol solutions of Mn2+ salts the electron relaxation time is considerably shorter than in aqueous solutions ; correspondingly Tl/T2 for alcohol solutions is close to 1.Furthermore, in Fez+, Co2+ and Ni2+ solutions, for which very short electron relaxation times (p < 10-11 sec) are characteristic, an increase of the viscosity almost a hundred times causes a relatively insignificant change of TI. On the other hand, in solutions of VO2+, Mn2+ and Cu2+ salts, the change is quite significant: TI increases approximately 10 times. Finally, the fact that the parameter Peff., describing the shortening effect 13 of paramagnetic ions on the longitudinal proton relaxation time 7'1, depends on the dimensions of the para- magnetic ions, does not fit into the framework of existing theory. From an investigation of a number of complex Fe3+ ions in aqueous solutions, Rivkind came to the conclusion that P'eff. is approximately proportional to the cube of the ion radius a, whereas the Bbembergen, Purcell, Pound theory does not allow a dependence greater than TI -a.Summarizing, it may be said that experiments in the field of electron and proton paramagnetic resonance confirmed the existence of a " near order " of particle location in solutions of electrolytes and made it possible to study this microstructure of solutions. In conclusion I would like to touch on the problem of studying the formation of complexes in solutions. Rivkind and the author of this paper 14 found that the intensity of the effect of a paramagnetic on the shortening of the longitudinal proton relaxation time T1 in solutions decreases, when the paramagnetic ion forms a complex. The detailed study of this phenomenon undertaken by Rivkindl5 brought about the development by him of a new effective method of investigating the formation of complexes in solutions. By means of measuring proton reson- ance, he studied the following systems of complexes in aqueous solutions: [Cu(NH2CH2C00)]+ and others.It was found possible to determine the co- ordination numbers for them, and in some cases to determine the value of the instability constant of the complex. For stable compounds it was found possible * Here are understood those Cu2+ ions which do not take part in exchange interactions. At the concentrations used, they constitute the predominant fraction. t Glycerol was added to the aqueous solutions to increase the viscosity. "FeF31, [Fe(C204)313-, [Fe(H4c4O6)3l3-, EWNH3)412+, [&(C5H5N)6l2",140 RESONANCE IN PHTHALOCYANINE to obtain curves of pZeff, as a function of the addendum concentration in the solution which clearly show the process of a stepwise formation of complexes.Electron paramagnetic resonance may also be used for studying the formation of complexes; both the width of the absorption lines, as well as the effective spectroscopic splitting factor. change noticeably in a number of cases when the paramagnetic ion becomes complex. Future investigations will without doubt also make it possible to obtain quantitative estimates of values characterizing the formation of complexes from electron resonance data. 1 Zavoisky, Diss. (Institute of Physics of the Academy of Sciences of the U.S.S.R., 2 Kozyrev, Reports A c d . Sci., U.S.S.R. (in press). 3 Garifyanov and Kozyrev, Reports Acad. Sci., U.S.S.R., 1954, 98, 929. 4 Bleaney and Ingram, Proc. Roy. SOC. Arts, 1951,205, 336. 5 Garifyanov, Reports Acad. Sci., U.S.S.R. (in press). 6 Altschuler, Kozyrev and Salikhov, Reports Acad. Sci., U.S.S.R., 1950, 71, 855. 7 England and Schneider, Physica, 1951, 17, 221. 8 Tinkham, Weinstein and Kip, Physic. Rev., 1951, 84, 848. 9 Garstens and Liebson, J. Chem. Physics, 1952,20, 1677. 10 Cohn and Townsend, Nature, 1954, 173, 1090. 11 Rivkind, Reports Acad. Sci., U.S.S.R. (in press), 12 Zimmerman, J. Chem. Physics, 1954,22,950. 13 Bloembergen, PurcelI and Pound, Physic. Reu., 1948,73, 679. 14 Kozyrev and Rivkind, J. Expt. Theor. Physics, 1954, 27, 69. 15 Rivkind, Reports Acad. Sci., U.S.S.R., 1955, 100, 933, Moscow, 1944).

ISSN:0366-9033    

DOI:10.1039/DF9551900135

出版商:RSC    

年代:1955

数据来源: RSC

摘要:

140 RESONANCE IN PHTHALOCYANINE PARAMAGNETIC RESONANCE IN PBHTWO- CUANINE, HAEMOGLOBIIS[, AND OTHER ORGANIC DERIVATIVES. BY D. J. E. INGRAM AND J. E. BENNETT Dept. of Electronics, The University, Southampton Received 4th February, 1955 The results summarized in this paper form the initial section of a general programme designed to study phthalocyanine, chlorophyll, and haemolgIobin derivatives by para- magnetic resonance. The advantages of this method are two-fold in that (i) detailed information concerning the bonding of the central metal atom can be obtained, with no obscuring spectra from the rest of the molecule, and (ii) the techniques are more sensitive and direct than magnetic susceptibility determinations, and hence measurements on single crystals are possible. A brief consideration of the particular experimental problems associated with a study of these organic compounds is first given, the main limitation being that of crystal size, and hence the need to work at high frequencies.The results so far obtained are then summarized, including a detailed analysis of the copper phthalo- cyanine spectra. The relation of these to the bonding derived from susceptibility deter- minations is then discussed; and it is shown that some of the conclusions previously drawn, concerning the binding of the iron atom in haemoglobin derivatives, will have to be altered considerably, in order to explain the paramagnetic resonance results. Finally, a review is given of the future work that is planned, and the information that may be expected from such a line of research.1. INTRODUCTION One of the great advantages of paramagnetic resonance, when used to study problems of chemical binding, is the fact that it can give information on one para- magnetic atom, and its immediate surroundings, with no overlapping or obscuringD . J . E . INGRAM AND J . E. BENNETT 141 spectra from the rest of the molecule. In this respect it differs considerably from infra-red and microwave spectroscopy, as these give information on the energy levels associated with the molecule as a whole, and the bonding of one particular atom can only be derived indirectly. This advantage is especially noticeable with large organic molecules, where very complex spectra are obtained by other forms of spectroscopy; and some of thc most interesting, and biophysically im- portant, compounds that can be studied by such means are the phthalocyanine, chlorophyll and haemoglobin derivatives.These all possess a central metal atoni, surrounded by four nitrogen atoms, and an analysis of the paramagnetic resonance spectra of such complexes should give detailed information on the bonding of this metal atom to its nearest neighbours. Similar, but less precise, data can be obtained from magnetic susceptibility measurements. The resonance experiments have two great advantages over these, however, in that, first, each energy level splitting can be studied separately, no simplifying assumptions being required to interpret the results ; and, secondly, the paramagnetic resonance techniques are more sensitive and allow measurements to be made on single crystals, the maximum size of which is often only 0.0005 cm3 for organic compounds.Since the spectra often vary considerably with the angle between the applied magnetic field and the crystalline axis, measurements on such single crystals enable a large amount of extra information to be obtained. The results reported in this paper form the initial part of a general programme in which it is hoped to study the whole series of metallic phthalocyanine, chloro- phyll and haemoglobin derivatives. Measurements so far have shown that it is possible to observe and analyze the spectra obtained from diluted single crystals of copper phthalocyanine, and, although the sensitivity of the apparatus is not suficient at the moment to give spectra from single crystals of the haemoglobin derivatives, steps are being taken to improve the signal-to-noise ratio substantially, so that such measurements should be possible. In the meantime, considerable information has already been obtained from solutions, or polycrystalline specimens, the spectra often differing markedly from that obtained in normal Fe compounds.2. PARTICULAR EXPERIMENTAL PROBLEMS Only thc particular experimental problems, which arise when these types of compound are studied, will be considered here, as the basic techniques are similar to those of any standard paramagnetic resonance spectroscope.1 The main limitation on the experimental side is the small size of the crystals available, which means that the shortest wavelengths possible must be used, so that the crystal fills a larger proportion of the cavity resonator.Measurements on single crystals havc thereforc been confined to 8 mm and 1.25 cm wavelengths, the 3 cm apparatus only being used to check on g-values of amorphous, or polycrystalline, specimens. The phthalocyanine crystals grow as long needles along the b axis,2 and different typcs of rcsonator must therefore be employed when studying the angular variation of the spectra in diffcrent planes. A cylindrical H111 cavity is used for rotation in the ab and bc planes, with the crystal lying on the cavity bottom; and an Hill resonator is used ibr rotation in the nc plane, the crystal being mounted vertically in the centre. Jn all wscs it has been found best to rotate the magnetic field round the crystals, rather than vice versa.A rectangular H012 resonator was used at 3 cm wavelengths, and a tube containing about 4 ml of the polycrystalline specimens could then be inserted down its centre. Most of the measurements have been made at liquid air or hydrogen tempera- tures, in order to obtain the maximum sensitivity, although the spin-lattice broaden- ing does not usually become appreciable in these compounds, even at room temperature. The use of low temperatures and high field strengths made it neces- sary to reduce the size of the proton resonance coils to 1 mm diameter, and then simultaneous display of the electron and nuclear resonance was always possible.142 RESONANCE IN PHTHALOCYANINE 3. RESULTS (i) PHTHALOCYANINE DERIVATIVES Phthalocyanine and its metal derivatives take the form of planar molecules, with the structure as illustrated in fig.1. It can bc seen that bonds are only directly available from two of the four nitrogen atoms, but as X-ray 3 and other evidence indicate that the four nitrogens are equivalent, a resonating system is envisaged with a sp2d square bond at the centre. Determination of the spectroscopic splitting factors of the different metallic derivatives should give much more information on this central binding, especially if single crystals are available; so that the angular variation can be studied. So far measurements on singlc crystals have been confined to the copper and cobalt derivatives, which are therefore discussed first. a (19.6 FIG. 1 .-Unlabelled positions arc CH groups.FIG. 2.-@ dissimilar ions. The orientation of the planar molecules with respect to the external crystallinc axes is known accurately from the X-ray data,3 and it is therefore possible to correlate all the paramagnetic resonance measurements with the actual directions of the copper-nitrogen bonds.4 The magnetic field was rotated around the crystal in the ab, bc, and ca planes, and then in, and perpendicular to, the plane of the molecules. The direction of 611 was found to be that of an axis through the copper atom, normal to the plane of the molecule, and the value of gl remained constant for all directions in the molecular plane. The width of the absorption line, obtained from concentrated crystals, collapsed to a value of 35 gauss when the riiagnetic iield was in the plane of the molecule, this being smaller than the 200 gauss calculated on normal dipole-dipole broadening,s and suggests a certain amount of exchange interaction.Crystals diluted with zinc phthalocyanine showed four well-rcsolved hyperfine component lines, due to the I = = of the Cu63 and Cu6s nuclei. Their maximum separation was also along the normal to the molecular plane, and the lines came together and formed a complex pattern perpendicular to this, indicating con- siderable electric quadrupole intcraction.6 When correlating these results with the chemical binding of the central coppcr atom, it is to be noted that both divalent ionic copper, and copper in a sp2d bond, have one unpaired electron. There is therefore likely to be a mixture of both types, and this is confirmed by the resonance rneasurcments. The general features of the spectrum are similar to those found for ionically bound copper 6 7 but the smaller g-value variation (61 = 2045 to 611 == 2.165 instead 7 of 2-14 to 2.45) indicates some covalent binding.This would also show up as extra hyperfine component lines due to thc interaction of the unpaired electron with the nitrogen nuclei. The width of the individual hypefine com- ponents is 60 gauss, and a detailed study of this width with dilution should show whether it is due to an interaction of the unpaired electron with the nitrogens. The nearest-neigh- bour copper atoms are the similar ones along the &axis, as can be seen from fig. 2, andD. J . E. INGRAM A N D J . E . BENNETT 143 will produce by far the greatest contribution to the line width. If the width of 60 gauss is produced by dipole-dipolc broadening the crystals must contain at least 50 % Cu, and experiments are now in hand to check this quantitatively, as a constant width with increasing dilution would indicate interaction with the nitrogens, and covalent binding.These results do show, however, that the covalent binding is not as complete as that in the chloroiridate, discussed by Griffiths and Owen.8 Another feature of interest is the fact that the maximum hyperfine splitting is nearly twice that normally observed 6 7 (A = 0.021 cm-1 instead of 0.012 cm-I), which may indicate that thc unpaired electron associated with the sp2d squarc bond of copper is in a 4p rather than a 3d orbital, since the former passes closer to the nucleus.The spectra obtained from single crystals of cobalt phthalocyanine are still being analyzed in detail, but the initial measurements show that each of the two sets of atoms have one line, with a g-value varying froin 2.90 across the free-spin value to 1.98. The line width is smallest when the resonance is in highest fields, as for coppcr, but the change with angle is not so rapid. The full width of 400 gauss remains constant, indepcndent of temperature, from 20" to 290" K indicating a very small spin-lattice broadening. This fact, together with thc g-values observed, shows that the resonance is very different from that normally obtained in ionically bound divalent cobalt,9 where the relation gll+2g~= 13 is obeyed for an ion in a tetragonal field, and spin-lattice interaction is extremely strong.Single crystals, diluted with zinc, gave cight hypefine component lines for each electronic splitting, due to the I = 7/2 of Co59. The width of each component was 60 gauss, inde- pendent of temperature, again confirming the absence of spin-lattice interaction, and the separation between successive lines when in lowest magnetic fields, was 180 gauss (B = 0-025 cm-1) and 185 gauss in highest field position (A = 0.017 cm-1). A detailed analysis of this spectrum is in progrcss, but the large deviation from that of Co2+ salts, already suggests fairly strong covalent binding. Measurements on the other phthalocyanine derivatives have been confined so far to polycrystalline specimens.The g-values observed are listed in table 1, together with the effective magnetic moments obtained from the susceptibility measurements of Klemm.lo TABLE 1 metallic phthalocyanine derivative derivative - g vaIues k f f copper 2045 'to 2.1 65 1.73 cobalt 1.98 to 2-90 2.16 ferrous - 3-96 chloro-ferric 3.8 rfr: 0.05 - manganese 2.0 rt 0.02 4.55 vanadyl 2-0 f 0-02 1.70 Iron phthalocyanine exists as both the ferrous and chloro-ferric derivatives, the ferrous one being of interest as one of thc very few possible instances of two unpaired spins in the Fe orbitals. No resonance has so far been observed from purified polycrystalline samples of the ferrous phthalocyanine, at tempcratures down to 90" K. Binding of an ionic type would only show up at 20" K, however, and measurements at this temperature must bc made before any conclusions arc drawn.On the other hand, the absorption obtained from amorphous chloro-ferric phthalocyanine has an intense maximum at a field corresponding to g == 3.8 at all three wavelengths. Therc may be a variation of g to lowcr values, which would produce a high-field wing in the absorption line, but the maximum intensity occurring at such a high g-value shows that thc binding is very different from that of the normal ferric ion.11 In this way it is similar to haemin, discusscd later, in which a chlorine atom is again attached to the central iron atom. In contrast to this, both the resonance and susceptibility measuremcnts suggest that the binding is mainly ionic in the manganese and vanadyl compounds, each 12, 13 having an isotropic g-value of 20.It will be appreciated that a large number of these determinations are only of a pre- liminary nature, and it is hoped that detailed measurements on single crystals of most of the phthalocyanine derivatives will be made in the near future, thus providing much more prccise information.144 RESONANCE IN PHTNALOCYANINE (ii) CHLOROPHYLL DERIVATIVES Chlorophyll and its derivatives have a similar central structure to the phthalocyanines, the magnesium atom bcing surrounded by the four nitrogens in a square. Copper can be readily substituted for the magnesium, and the paramagnetic resonance spectra of four such coppered chlorophyll dcrivatives have been observed. The samplcs wcre amorphous, and a line of 100 gauss half-width, with a g-value of 2.06 -I- 0.01 was obtained in each case.No low ficld shoulder, similar to that of the amorphous coppcr phthalo- cyaninc, was observed, indicating that the g-value variation is not so large in the chloro- phyll derivatives. It will probably be difficult to obtain more precise information from these, because of the very small size of any single crystals that can be produced. Experi- ments are in hand, however, to see if the excitcd levels of chlorophyll can be detected by paramagnetic resonance, whcn it is irradiated in situ in the cavity. (iii) HAEMOGLOBIN DERIVATIVES Haemoglobin and its derivatives also have a similar central structure to that of the phthalocyanincs, the metal atom always being iron, often with extra radicals attachcd in addition to the four nitrogens.A large number of magnetic susceptibility measurements have been made on these compounds,14~ and cffcctive moments Corresponding to 5, 4, 3 and 1 unpaired electrons have been obtained, suggesting ionic binding in some cases, and covalent octahedral d2sp3 bonds in others. These deductions are based on totally quenched orbital momentum, however, the susceptibility being only measured at one tcmperature in many cases, and then peffequated to [n(n + l)]d., to obtain the number of unpaired electrons. The conclusions thus drawn are therefore likely to be greatly oversimplified. That this is in fact so, is suggested by the initial paramagnetic resonance measurements on polycrystalline haemin (ferriheme chloride). The susceptibility determinations 14 give an effective moment of 5.81 Bohr magnetons, and thus suggest five unpaired electrons, corresponding to normal ionic binding of a ferric ion.If this were so, the paramagnetic resonance expected from such a polycrystalline sample would be a symmetrical absorption line at g = 2.0. No trace of this could be found, but instead a wide absorption line, with its centre corrcsponding to g = 6.0 at all threc wavelengths, was obtained. A spread of this line into higher fields might indicate that thc g-value is anisotropic, falling below 6.0 in some directions, but the position of the maximum at such a very different value from that expected shows that the binding cannot be that of the normal ferric ion, with zero orbital momentum. The general features are the same as those for the chloro- ferric phthalocyanine, and these two appear to be the first in which such a large g-factor, G LOBlN FIG.3. observable at room temperature, has been obtained from Fe deriva- tives. This may be due to only partial quenching of the spin moment by the four nitrogen atoms, and measurements on single crystals should throw considerable light on this problem. More recently measurements have been made on several haemo- globin derivatives themselves, and these have confirmed the somcwhat unexpected results first obtained with haemin. The different deriva- tives can best be classified by the nature of the extra radical attached to the central iron atom. This is illustrated in fig. 3, which represents the central structure of hacmoglobin and its derivatives.The plane of the porphyrin ring, which is very similar to the phthalocyanine molecule, contains the four nitrogens and central metal atom, as before, but the iron atom now has two other radicals attachcd. One of these is the globin molecule, which is usually assumed as attached to the Fe via a nitrogen atom, and the sixth position can be taken by a variety of different radicals. The interesting feature of the haenioglobin molecule is the ease with which this last radical can be replaced, the interchange of oxygen and carbon dioxide being a case in point.D. J . E. INGRAM AND J . E . BENNETT 145 Previous measurements on susceptibility and chemical properties had divided the different haemoglobin derivatives into two main groups, (i) those which were assumed to be " essentially ionically " bound and (ii) those which were assumed to be " essentially covalently " bound.We have made preliminary measurements on derivatives in both groups, and the paramagnetic resonance experiments again show that the binding to the iron atom in the first group is not that of Fe3-1. as in strongly ionic crystals, and the concept of " essentially ionic " bonding thus needs considerable modification. The derivatives studied were the acid-met-ferrihaemoglobin, acid-met-ferrimyoglobin, ferrihaemoglobin fluoride and ferrimyoglobin fluoride. In each case, instead of a g-value of 2.00, a value of 5.90 41 0-05 was obtained. In order to check that this corresponded to a true g-value, the measurements were made over as wide a frequency range as possible, and fig.4 sum- marizes the results. In this, l/y (cm-1) is plotted against the field required for resonant H K - ~ ~ u s s FIG. 4. absorption, the points being those for haemin, and a similar set are obtained for acid-met- haemoglobin. The measurements cover a wavelength range of 3 cm to 6 mm and the slope of the straight line, and the fact that it passes through the origin, indicate that a true g value of 6.0 is being observed. A slight asymmetry in the line shape indicates that the g value falls somewhat below this value in a direction equivalent to 611, but the fact that such a high value i s obtained for g~ shows that the binding of the central iron atom is very different from that in " strongly ionic " ferric salts. In contrast to these measurements, the absorption obtained from ferrihaemoglobin and ferrimyoglobin azide is a wide line corresponding to a g value variation of 2.2 to 2.8. This derivative is one that has been previously classified as " essentially covalently " bound, and the observed g values seem to support the classification in this case.More detailed consideration of these points is to be found in the contribution following this paper. Another type of compound that can also be studied by paramagnetic resonance is illustrated by the nitric-oxide haemoglobin derivatives. In this the unpaired electron is associated with the NO group, and not the Fe atom, and determination of the g-values should give information on the binding of the NO group to the rest of the molecule.The system is thus very similar to the 0 2 - ions of the alkali superoxides, which have g-values varying from 2.00 to 2.17, and these can be used to determine the splitting of the 2II: level, and distortion about the 0-0 axis.18 Prcliminary measurements on the NO derivative give a nearly isotropic g of 2-0, indicating that the N-0 axis is parallel to the plane of the nitrogens. Measurements on several other haemoglobin derivatives are in progress, and a systematic survey of this field is planned ; wherever possible experiments will be carried out with single crystals.146 RESONANCE IN PHTHALOCYANINE 4. CONCLUSIONS AND FUTURE PROGRAMME The initial results reported in this paper indicate that paramagnetic resonance absorption should prove a very powerful method for the detailed investigation of chemical binding in paramagnetic organic compounds.The phthalocyanine and haemoglobin dcrivatives have been selected first, because of the biophysical intercst of the latter, but these techniques can be applied to any other magnetic derivative, and will givc most information when single crystals are available. With the construction of a more scnsitive spectroscope, measurements should be possible on single crystals of all the phthalocyanine and several of the haemoglobin de- rivatives. A detailed analysis of such rcsults should give much more precise information on the elcctronic binding of the central structure than is available by any other method. It may also be remarked, in closing, that it was the study of the phthalocyanine derivatives that led to the discovery of the large free radical concentration in carbonized organic compounds.19 This was first observed as an intense narrow line of g == 2.003 in overheated phthalocyanine residues, and has since been demonstrated as a gcneral property of any organic matter carbonized below 600" C.20 The origin of such a high concentration of trapped free radicals is still in doubt, suggestions including a semi-quinone resonating structure,21 or thc removal of central carbon atoms from the condensed ring system? We would like to thank the Royal Society for a grant towards the cost of the apparatus, and Dr.C. E. Dent and I.C.I. Ltd. for supplying phthalocyanines. We would also like to acknowledge the helpful discussions we have had with Dr. K. W. H. Stevens, and also with Dr. P. George and Mr. J. S. Griffith of the Department of Colloid Science, Cambridge. 1 Bleaney and Stevens, Reports Prog. Physics, 1953, 56, 108. 2 Linstead, Lowe, Dent and Byrne, J. Chem. Soc., 1934, 1016. 3 Robertson, J. Chem. SOC., 1935, 615. 4Bennett and Ingram, Nature, 1955, 175, 130. 5 van Vleck, Physic. Rev., 1948, 74, 1 168. 6 Ingram, Proc. Physic. SOC. A, 1949, 64,664. 7 Bleaney, Bowers and Ingram, Proc. Physic. SOC. A, 1951, 64, 758. 8 Griffiths and Owen, Proc. Roy. Soc. A, 1954,226,96 ; and also this Discussion. 9 Bleaney and Ingram, Proc. Roy. SOC. A, 1951,208, 143. Abragam and Pryce, Proc. Roy. SOC. A, 1951,206, 173. 10Klemm, Senff and Klemm, J. Prakt. Chem., 1935,143,82; 1939,154,73. 11 Bleaney and Trenam, Proc. Physic. SOC. A, 1952, 65, 560. 12Bleaney and Ingram, Proc. Roy. Suc. A , 1951,205, 336. 13Bleaney, Ingram and Scovil, Pruc. Physic. SOC. A, 1951, 64, 601. 14 Pauling and Coryell, Pruc. Nat. Acad. Sci., 1936, 22, 159, 210. 15 Rawlinson, Austral. J. Expt. Biol. Med. Sci., 1940, 18, 185. 16 Coryell, Stitt and Pauling, J. Amcr. Chem. Suc., 1937, 59, 633. 17 Hartree, Ann. Reporfs, 1946, 43, 287. 18 Bennett, Ingram, Symons, George and Griffith, Phil. Mag., 1955, 46, 443. 19 Ingram and Bennett, Phil. Mag., 1954, 45, 545. 20 Ingram, Tapley, Jackson, Bond and Murnagham, Nature, 1954, 174, 797. 21 Garten and Weiss, Aiisfrul. J. Clzem., 1954 (in press). 22 Bennett, Ingram and Tapley, J. Chem. Physics, 1955, 23, 215.

ISSN:0366-9033    

DOI:10.1039/DF9551900140

出版商:RSC    

年代:1955

数据来源: RSC