1424
V6rtes et al.
crystallite distribution and/or “twinning” of the aragonite lattice within the microcrystallites. Twinning on the (110) face is common in mineral aragonite deposit^.^ It is reasonable to expect some crystalline organization with mineralized tissues, but perhaps not as much as in the minerals themselves. We have observed a similar preferencial orientation in the calcitic shells of the barnacle Balanas balanoidesZ3and the mussel Mytilus e d ~ 1 i s . l It ~ is also evident from these Mn(I1) EPR studies, as well as from microscopic examination of the exoskeleton, that some marine organisms have more organization within their exoskeletons than others. It may be possible to examine other more ordered aragonitic exoskeletons to further refine the Mn(I1) EPR parameters and the principal zero-field splitting tensor directions. Acknowledgment. The authors thank the National Science Foundation, Grant No. CHE75-03475 AO1, and the National Institutes of Health, Grant No. GM20194-05, for support of this research. References and Notes (1) F. K. Hurd, M. Sacho, and W. D. Hershberger, Phys. Rev., 93, 373 (1954).
(2) C. Kikuchi, Phys. Rev., 100, 1243 (1955). (3) H. M. McConnell, J. Chem. Phys., 24, 904 (1956). (4) C. Kikuchi and L. M. Matanese, J. Chem. fhys., 33, 601 (1960). (5) J. A. Hodges, J. Chem. Phys., 49, 2857 (1968). (6) V. Lupei, A. Lupei, and I. Ursu, Phys. Rev. B , 6, 4125 (1972). (7) G. E. Barberis, R. Caivo, H. G. Maldonado, and C. E. Zarate, Phys. Rev. B , 12, 853 (1975). (6) G. T. Fonda, J. Phys. Chem., 44, 435 (1940). (9) H. A. Deer, R. A. Howie, and J. Zurrman, “Rock Forming Minerals”, Vol. 5, “Non-Silicates”’, 1963, pp 230-255, 305-315. (10) F. Lippman, “Minerals, Rocks, and Inorganic Materials”, Vol. 6, “Sedimentary Carbonate Minerals”, Springer-Verbg, New York, N.Y., 1973, pp 6-13, 53-66, and references therein. (11) J. P. R. de Villiers, Am. Mineral., 58, 758 (1971). (12) H. Shoji, Z. Kristaliogr., 64, 74 (1932). (13) S. C. Blanchardand N. D. Chasteen, J. phys. Chem., 80, 1362 (1976). (14) A. Abragam and B. Bleaney, “Electron Paramagnetic Resonance of Transition Ions’’, Oxford University Press, London, 1970, pp 186-205. (15) F. Tsay, S. L. Manatt, and S. I. Chan, Chem. Phys. Len., 17, 223 (1972). (16) G. C. Upreti, J. Mag. Reson., 18, 287 (1975). (17) A. Chatelain and R. A. Weeks, J. Chem. Phys., 52, 3758 (1970). (18) G. M. Woltermann and J. R. Wasson, Inow. Chem., 12,2366 (1973). (19) These expresslons are not rigorously true for a rhombic powder pattern, but they give us a good estimate of the zero-field splitting parameters wlthin the listed experimental errors. (20) R. E. Watson and A. J. Freeman, Phys. Rev., 123, 2027 (1961). (21) J. S. Van Wieringen, Discuss. Faraday. Soc., 19, 118 (1955). (22) R. S. Title, Phys. Rev., 136, 623 (1963). (23) S. C. Blanchard and N. D. Chasteen, to be published.
Positron Annihilation Studies on Coordination Compounds. 1. Investigation of Positron Lifetime and Angular Correlation of Annihilation y Photons on the Mixed Complexes of Bis(dimethylglyoximato)cobalt(lll) with Unidentate Ligands K. Burger,+ B. L8vay,t A. Virtes,*$ and 6. VBrhelylN Institute of Inorganic and Analytical Chemistry and rnstitute of Physical Chemistry and Radiology, L. Eotvos University, Budapest, Hungary and Chemistry Department, Babes Bolyai University, Cluj, Roumania (Received August 24, 1976; Revised Manuscript Received December 8, 1976)
Positron annihilation investigation of bis(dimethylglyoximato)cobalt(III)mixed complexes formed with unidentate ligands, compared with ESCA results on the same complexes, suggested that the cobalt(II1)central atom and the nitrogen donor atom of the parent complex have a negligible effect on the change of the positron lifetime. Mainly electrons of halide, pseudohalide, and S-bonded sulfite ion, each coordinated along the 2 axis of the mixed complex, affect the annihilation rate of positrons. The positron lifetime decreasing effect of the unidentate ligands water, ammonia, nitrite, and organic bases was found to be negligible. It has been demonstrated that the positron lifetime decreases parallel to the increasing negative character of the halides I-, Br-, and Cl- and to the increasing n-acceptorability of S- and Se-bound pseudohalides SCN, SeCN. Halides bound in the outer coordination sphere have the effect of decreasing the positron lifetime lower than those in the inner sphere. The positron lifetime of mixed complexes containing one halide ion is longer than those containing two halides. Considering angular correlation data it seems that the localization of positrons on halide ligands decreases (the curves become narrower) in the order C1-, Br-, I-. From this respect pseudohalide ligands lie between C1- and Br- in accordance with their optical electronegativity values. These results suggest the possible role of positron-halide and positron-pseudohalide bound states in the positron annihilation process. Introduction In the course of positron annihilation, generally two photons are produced each with an energy of 8.511 M ~ V corresponding to the rest mass of the electron-positron pair. The angle between the two emitted photons is nearly 180’ to fulfill momentum-conservation requirements. The ‘Institute of Inorganic and Analytical Chemistry, L. Eotvos University. $ Institute of Physical Chemistry and Radiology, L. Eotvos University. .6 Chemistry Department, Babes Bolyai University. The Journal of Physical Chemistw, Vol. 81, No. 14, 1977
deviation from 180° is determined by the momentum of the electron-Positron pair annihilating. Consequently the distribution of electron momenta can be obtained from the distribution curve* Since the probability of positron annihilation depends very much on the electron density a t the site of the positron, the rate of the annihilation process and the angular distribution of the annihilation y photons are closely related to the electronic structure of the substance studied and are influenced very sensitively by changes. Studying the annihilation process one can obtain information about the structure of the material; thus this
Positron Annihilation Studies on Coordination Compounds
method is becoming more widely used.’ The average lifetime of the positrons is a few tenths of a nanosecond in the condensed phase when the “free annihilation” of an electron-positron pair takes place. The annihilation process, however, can be preceded either by the formation of a bound state (e+M)between a positron and an atom or molecule (M), or the formation of the lightest element, the positronium “atom” (Ps), which is a combination of a positron and an electron. When the spins of the electron and positron are parallel orthopositronium (0-Ps) is formed and when the particle spins are opposite parapositronium (p-Ps) is formed. The avs in vacuo, and that of erage lifetime of o-Ps is 1.4 X p-Ps is only 1.25 X 10-los. In the condensed phase the relatively long lifetime of 0-Ps decreases due to different interactions and falls generally into the 0.5-5-ns range. The formation of Ps in the medium is indicated quite often by the long lifetime component of the spectrum. In the case of angular correlation measurements the “narrow” component of the spectra resulting from the annihilation of p-Ps atoms indicates the formation of positronium.’ The fundamental processes of positron annihilation in liquids have been clarified already in many aspects. Mogensen’s “spur” model2 deals with the factors influencing the probability of positronium formation; in addition the rate of the pick-off annihilation of o-Ps atoms can be explained by the bubble model.3 The chemical reactions of Ps atom are elucidated properly, and recently experiments were carried out for studying the chemistry of positrons as In solids (except metals, ionic alkali halides, metal oxides, and polymers) only a few systematic investigations have been made. Positron annihilation measurements carried out so far in solids attempted mainly the study of the correlation with the physical parameters of the substance. The effects of, e.g., vacancies, dislocations or collective imperfections (voids) in metals, F-centers in ionic crystals, the degree of crystallization of polymers, or the granule size of oxide powders on positron annihilation was investigated.’ It was shown that positron annihilation is very sensitive to the changes occurring in the physical state of the environment, and thus the method can be used with good results in an investigation of the physical structure of substances. At the same time the high sensitivity of this method to minor changes in the physical state makes it more difficult to study the chemical structure of the substance. This kind of systematic measurements had not been made yet, and that is why we do not know too much about the correlations between the chemical structure of the substance and the parameters of positron annihilation in solids. The aim of the present work is to study positron annihilation on solid coordination compounds where, if possible, only a few ligands of one parent complex tan be exchanged with chemically considerably different ones in such way that the basic structure of the complex remains practically unchanged. Under such circumstances one can expect that the changes occurring in the parameters of the positron annihilation (lifetime, angular distribution) can be correlated mainly with coordination chemical changes. For the first model system the mixed complexes of bis(dimethylglyoximato)cobalt(III) were chosen, which have already been investigated with different method^.^ Dimethylglyoxime forms square-planar complexes of high stability with transition metals. The two dioxime
1425
ligands are bound to the metal not only with coordinative bonds, but also to each other with H bonds. Thii structure hinders the binding of a third bidentate ligand to the central atom. The square-planar parent complexes are able to coordinate two unidentate ligands along their 2 axis (e.g., hydroxide, halide, pseudohalide, or nitrogen base, etc.).m The nickel complex is an exception in this respect. The cobalt(II1)-dioxime complexes investigated are low spin compounds. To correlate the measured annihilation lifetime or the changes in the parameters of the angular distribution curves with the chemical changes in the coordination sphere, it would be necessary to know the active sites of this complicated molecule where positron annihilation predominantly takes place. To solve this problem the data and experience obtained by other methods with the same complexes can offer some important additional information. The previously determined electron-binding energies measured by the ESCA method on the central cobalt atom and donor atoms provided valuable information on the electronic structure of the complex, and the electron density of the individual atomseg Consequently the interpretation of the results of the positron annihilation investigations was supported by the correlations with the data of ESCA measurements.
Experimental Section The complexes investigated were prepared as described in the l i t e r a t ~ r e ; ~their - l ~ composition was checked by elemental a n a l y ~ i s . ~ Positron lifetime spectra and angular distribution curves were measured by the usual methods. The details of the apparatus have been published el~ewhere.4’~~ The 22Na positron source used for lifetime measurements was evaporated onto an approximately 1mg/cm2 thick Kapton polyimid foil, and was covered with another sheet of the foil. This source was placed between two samples (tablet or powderlike) with a thickness of more than 200 mg/cm2. Lifetime s ectra were evaluated by the POSITRONFIT EXTENDED 1 F Computer program. For the characterization of the angular correlation curves the peak heights normalized to equal areas are given. Results and Discussion I. Lifetime spectra were analyzed for two components but the intensity of the long lifetime component (72 1 ns) was only about 1% for all the compounds investigated. This result indicates that, practically, there is no positronium formation in these compounds. The lifetime data obtained for samples of the original polycrystalline powder form and the ones pressed into pills agreed within the limit of errors. This result indicates the fact that, in the course of high pressure pressing, no new imperfections and positron traps were formed in the substances investigated, consequently they had probably been saturated with them. Thus it would likely not be a great error to assume that the saturation concentration of imperfections were practically the same in chemically different samples. At any rate this uncertainty factor must be considered when explaining the data. 11. In Table I, lifetime data are compared with the previously obtainedg ESCA data, i.e., the electron binding energies on the central cobalt atom, on the nitrogens of the dioxime ligands, and on the iodide coordinated along the 2 axis. The data do not indicate a clear cut correlation between the positron lifetimes and the electron-binding energies on the central cobalt atom and on the nitrogen donor N
The Journal of Physical Chemistry, Voi. 81, No. 14, 1977
VBrtes et al.
1426
TABLE I: Comparison of the Results of Positron Lifetime and ESCA Measurements ESCAC Compd investigateda
PS
co 2p,,,-c
Is
N Is-C IS
13d,,,-C IS -
H[Co(HD)zClzl (1) H[Co(HD),Br,I (11) [Co(HD)2(NH3)2 lcl H[Co(HD)zIzI (IV) H[Co(HD),CNI] ( V ) H[Co(HD),I,I (IV) H[Co(HD),NO,I] (VI) [Co(HD),NH,I] (VII)
334 337 353 368
i
350 368 373 384
%
%
i
i
1: i i
1 1 2 3
495.2 i 0.1 494.75 i 0.1 495.0 i 0.2 494.5 i 0.1
115.6 % 0.1 115.15 1: 0.1 115.0 i 0.1 115.2 i 0.2
2 3 1 1
495.0 = 0.1 494.5 i 0.1 494.5 1: 0.1 494.6 1: 0.2
115.3 i 115.2 1: 115.1 i 115.0 1:
0.1 0.1 0.1 0.1
344.5 % 344.6 i 344.8 i 345.8 i
I
0.1 0.1 0.1 0.1
334 1: 1 495.2 i 0.1 115.6 ~t 0.1 H[Co(HD),C1,1 (1) H[Co(HD),NO,Cl] (VIII) 338 i 1 494.5 1: 0.1 115.9 t 0.2 H[ Co(HD),CNCl] (IX) 348 i 2 495.7 I0.1 115.8 i 0.2 a HD is the dimethylglyoximato ion (with one negative charge). Positron lifetime. Electron bonding energies in eV. The carbon atom of the methyl group of the ligands is taken as reference atom.
atoms, respectively. On the other hand, the ESCA data of the ligands on the 2 axis, e.g., those of iodide in compounds IV-VII, indicate a decreased electronic density with increasing positron lifetime. A similar trend is reflected by the data of compounds XVII and XX in Table 111. Since it can be supposed that the increase of electron density on the given atom decreases the positron lifetime, the comparison of the ESCA data with the positron lifetimes indicate that neither the cobalt nor the oxime ligand are responsible for the change of the positron lifetime but it is caused by the unidentate ligands coordinated along the 2 axis. It is very likely that the coordination of the strong field ligands resulting in the formation of a low spin electronic structure of the central cobalt atom decreased the interaction of the cobalt with the positrons. 111. In most cases angular correlation data are in the expected correlation with the lifetimes. Narrower angular correlation curves with higher peaks indicate a weaker localization and, accordingly, a lesser momentum of positrons while broadened curves show a more pronounced localization of positrons. The annihilation rate of localized positrons increases, that is, their lifetime decreases. This correlation seems to be valid considering the data in Table I1 obtained for complexes containing halides, particularly if the same type of series are compared. Some further relationships can also be deduced from Table 11. 1. Comparing complexes with two halides in their inner coordination sphere it can be seen that the angular distribution curves become narrower in the order of C1-, Br-, I-; consequently the localization of positrons decreases in the same order. This result is in agreement with those of the theoretical c a l c u l a t i ~ n and s ~ ~the ~ ~ ~experimentally found angular correlation for the positron-halide bound state. This facts suggests the possible role of the positron-halide bound state also in our case. The tendency is similar for the halides in the outer coordination sphere. 2. The connection expected can be observed between the lifetime and the peak height of the angular correlation for the complexes containing only a single halide ligand in the inner sphere, too. In this case, however, the angular correlation curves are a bit broader when comparing them with the complexes with two halide ligands or one in the outer sphere. 3. The angular correlation curves of the pseudohalide containing complexes (XIII-XV) were similar to that of the chloride complex (I) indicating that the positronpseudohalide bound state has about the same strength as that formed with the chloride. The angular correlation results for I, 11, IV, XIII, and XV show a trend similar to The Journal of Physical Chemistry, Vol. 81, No. 14, 1977
TABLE 11: Comparison of Lifetime and Angular Correlation Data r1,“ ps
Peak heightb
H[Co(HD),C4 1 (1) H[Co(HD),Br,I (11) H[Co(HD),I,I (IV) [Co(HD),(H,O)BrI (XI
334i 1 3371. 1 368i 3 361 I2
17460 17960 19270 17910
H[Co(HD)*(CN)Il (VI [ CO(HD)z (HzO )I1 (XI 1 [Co(HD),(NH3)I 1 ( V W
350i 2 3732 2 384i 1
18690 18750 18950
[Co(HD)2(NH3)2 lcl [Co(HD),(Py),lBr ( X W
353i 2 373 i 2
18120 19350
Compd investigated
[Co(HD),(H,O)(NCO)] (XIII) 374 i 1 17230 H[Co(HD),(SeCN),] (XIV) 349 i 1 17470 [Co(HD),(SCN)I (XV) 345 i 3 17540 [Co(HD),(H,O)(SCN)] (XVI) 333 i 2 a Lifetime. Angular correlation. The curves are normalized to equal areas. The uncertainties in peak heights are estimated to be about i 100.
that of JBrgensen’s’’ optical electronegativity data for the ions (el-, 3.0; NCO-, 3.0; SCN-, 2.8; Br-, 2.8; I-, 2.5). IV. The following qualitative relationships can be given for the effect of ligands on positron lifetime: 1. The positron lifetime decreasing effect of halide ions decreases in the order of Cl-, Br-, I- irrespective of whether the complex contains one or two halides. Probably this is due to the negative character of the ligands decreasing in the same fashion (Table I and 11). It can be seen that the halide ion plays a decisive role in determining the positron lifetime. The effect of nitrite, ammonia, and coordinated water can be neglected, but cyanide acts like halides and decreases the positron lifetime. Thus it seems likely that the effect of “ h a r d anions on ’positron lifetime is smaller or even negligible in contrast to that of the “soft” polarizable or .Ir-acceptor ligands. Furthermore, an increase in positron lifetime is caused by the exchange of one halide of the dihalide mixed complex for an inert ligand. When comparing chloride and iodide mixed complexes containing cyanide with the appropriate dihalide complexes it is obvious that the positron lifetime decreasing effect of the cyanide is lower than that of the chloride but higher than that of the iodide. Thus in case of the chloridecyanide complex, the positron lifetime is longer, in the iodide-cyanide complex it is shorter than that of the appropriate dihalide. 2. The positron lifetime decreasing effect of the halide depends on the character of the coordination of halide. Such an effect of the halide coordinated in the inner sphere
1427
Positron Annihilation Studies on Coordination Compounds
TABLE 111: P o s i t r o n L i f e t i m e Values of S u l f i t e Complexes a n d t h e E l e c t r o n Binding Energies of S 2p,,, $, Orbitals Lifetime,
C Is-S
r,, ?,I . PS - 2P,,, NH, [Co(HD),H,OSO,] (XVII) 348 i: 2 116.9 f 0.1 rCo(HD),NH,SO,l (XVIII) 348i 2 NH,.[Co(HD),an(SOj)] (XIX) 336 1 NH4[Co(HD),(y-pico1in)SO,1 (XX) 333 f 2 118.3 f 0.1 NH,ICo(HD),(rn-toluidinK30ml (XXI) 336 f 2 NH;[Co(HD)&-fenetidin)SO;] ’(XXII) 334 2 1 Complex
*
is greater than that in the outer sphere. Compare, e.g., the lifetimes of VI11 (338 f 1ps) and I11 (353 f 2 ps), or those of X (361 f 2 ps) and XI1 (373 2 ps). The more pronounced effect of the halide ion in the inner coordination sphere can be explained by the stronger polarization of the halide which makes the electrons of the halide more suitable for the reaction with positrons. It can be also seen from the data that the quality of the halide is more dominant than the nature of its bonding. The chloride, bonded in the outer sphere, is more efficient than the bromide in the inner sphere and the bromide coordinated in the outer sphere is more efficient than the iodide in the inner sphere. (See also VII, 384 1 PS.) 3. The positron lifetime of S- and Se-containing pseudohalides increases in the same way as their ?r-acceptor ability (SCN < SeCN). The N-bonded NCOcomplex showed however a higher positron lifetime than the SCN- and SeCN- compounds. 4. Besides halides and pseudohalides the S-bonded sulfite ion having a great ?r-acceptor ability shows a considerable decreasing effect on the positron lifetime (Table 111). As shown from the data of XVII and XVIII and comparing them with those of VI11 and X, the effect of sulfite is smaller than that of chloride but larger than that of bromide. The identical data of the two sulfite mixed complexes indicate again the negligible effect of coordinated water and ammonia on the positron lifetime (XVII, XVIII). The lifetime data of mixed sulfite complexes XIX-XXII, however, show that the bases substituted with a nucleofil substituent having a relatively loose ?r-electron structure slightly enhance the decreasing effect of the complex on the positron lifetime. 5. The longest lifetimes were obtained in the following p-chloroaniline and p-bromoaniline mixed complexes: [Co(HD),(p-C1-an),]C1O4 (XXIII) 5=394f2ps [ C 0 ( H D ) ~ ( p - B r - a n ) ~ ] C(XXIV) l0~ 5 = 392 f 1 ps
*
*
It is clear from the data that the organic halogens have a negligible effect on positron lifetime. The chlorine atoms of perchlorate positioned in the outer sphere also have little or no effect. Comparing these data with the results of aniline-sulfite and amine-sulfite mixed complexes mentioned previously, it seems that electrophillic halides quench the slight positron lifetime decreasing effect of aniline.
Conclusions Both positron lifetimes and the data obtained by measuring the angular distribution of annihilation y radiation reflect sensitively the changes occurring in the chemical features of bis(dimethylglyoximato)cobalt(III) mixed complexes caused by the coordination of unidentate ligands along their 2 axes. Thus the positron annihilation method seems to be suitable to investigate the chemical structure of the substance even in the solid phase. In our opinion, the changes observed in the course of positron annihilation measurements cannot be attributed simply to random differences in the physical state of the complexes but rather to the changes resulting from different ligands. This is supported by the correlation with the ESCA results and by the similarity of the lifetime data found for the chemically similar groups of compounds (e.g., for XVII-XVIII; XIX-XXII; XXIII-XXIV). Further systematic investigations are planned to obtain a more exact explanation of the connection between annihilation data and chemical structure in the solid phase. Acknowledgment. One of the authors (B.L.) acknowledges the hospitality of the Chemistry Department of the Danish Atomic Energy Commission Research Establishment, Risa, where he had the opportunity to carry out the positron annihilation measurements. He thanks Drs. Ole Mogensen and Peter Jansen for useful discussions and Niels-Jorgen Pedersen for valuable technical assistance. References and Notes (1) J. H. Green and J. Lee, “Posltronlum Chemistry”, Academlc Press, New York, N.Y., 1964; V. I.Gokianskii, At. Energy Rev., 6,3 (1968); R. N. West, A&. Phys., 22, 263 (1973); J. A. Merrlgan, J. H. Green, and S. J. Tao, in “Physical Methods of Chemistry”, Vol. 1. Part IIID, A. Wekberger and B. W. Rosskter, Ed., Wley, New Yak, N.Y., 1972, p 501. (2) 0. E. Mogensen, J. Chem. Phys., 60, 998 (1974). (3) See B. LBvay and A. VBrtes, J. Phys. Chem., 80, 37 (1976), and the references given thereln. (4) 0. E. Mogensen and V. P. Shantarovkh, W m . phys., 6, 100 (1974). (5) K. Burger, “Coordination chemistry: Experimental Methods’ , Butterworths, London, 1973. (6) K. Burger and I. Ruff, Talanfa, 10, 329 (1963). (7) K. Burger and B. Pint&, J. Inorg. Nucl. Chem., 29, 1717 (1967). (8) K. Burger, B. Zelei, 0. Sdnt&HotvBth, and T. T. Binh, J. Inorg. Nucl. Chem., 33, 2573 (1971). (9) K. Burger, E. Fluck, Cs. VBrhelyi, H. Binder, and I.Speyer, 2.Anorg. Allg. Chem., 406, 304 (1974). (10) E. Cambi and C. Coriselli, Gazz. Chim. Ita/., 66, 81 (1936). (11) F. Feigl and H. Rubinstein, Justus Liebigs Ann. Chem., 433, 183 (1923). (12) A. V. Ablov, Bull. SOC. Chim. Fr., (5) 7, 151 (1940). (13) 2. Finta and Cs. VBrhelyi, Acta Chim. Acad. Scl. Hung., submltted for publication. (14) A. K. Babko and V. Korotum, Z. Obscsej Him., 24, 597 (1954). (15) A. V. Ablov. Dokl. Akad. Nauk SSSR, (2) 97, 1019 (1954). (16) Cs. VBrhelyi, I. Genescu, and L. Szotyori, 2. Anorg. A/@. Chem., 366, 232 (1971). (17) M. Eldrup, 0. E. Mogensen, and G. Trumpy, J. Chem. Phys., 57, 495 (1972). (18) P. Kirkegaard and M. Eklrup, Comp. phys. Commun., 3, 240 (1972). (19) P. Cade and A. Farazdel, J. Chem. Phys., in press. (20) A. Farazdei and P. Cade, J. Chem. Phys., In press. (21) 0. E. Mogensen and P. Jansen, Paper G 13, presented at the Forth International Conference on Positron Annihilation, Aug 1978, Helslngijr, Denmark. (22) C. K. Jckgensen, “Modern Aspects of Ligand Field Theory”, North Holland Publishing Co., London, 1971, pp 362-369.
The Journal of Physical Chemlstty, Vol. 81, No. 14, 1977
