Pressure dependent Raman, and conductivity studies of the fast ion conductors Cu2HgI4, Ag2HgI4 and Tl2ZnI4

J. Phys. Chem. Solids Vol. 43, No. 9, pp. 903-909, 1982 Printed in Great Britain.

0022-36971821090903-07503.00[0 Pergamon Press Ltd.

PRESSURE DEPENDENT RAMAN, AND CONDUCTIVITY STUDIES OF THE FAST ION CONDUCTORS Cu2HgL, Ag2HgI4 AND T12ZnI4 J. I. McOMBER,~ D. F. SHRIVERand M. A. RATNER Department of Chemistry and MaterialsResearch Center, Northwestern University, Evanston, IL 60201, U.S.A.

J. R. FERRARO~and P. LABONVILLEWALLING§ Chemistry Division,Argonne National Laboratory, Argonne,IL 60439, U.S.A. (Received 22 October 1981; accepted in revisedform 12 February 1982) Abstract--High pressure Raman, electrical conductivity, and optical microscopicstudies on the ternary fast ion conductor Cu2Hgl~were undertaken to delineatethe pressure-temperaturephase diagram. In addition, comparison of the pressure dependence of Raman shifts in Cu2Hgl4 and TI2ZnI4was used to assist in making vibrational assignments whenever possible.

INTRODUCTION

At somewhat elevated temperatures, the ambient pressure phases of Cu2HgL and Ag2HgL display high Cu+ and Ag+ ion mobility respectively[l]. Because their structures are simpler than most ternary electrolytes, these compounds are excellent candidates for fundamental studies. In this paper we present the ambient temperature variable pressure Raman spectra of Cu2HgL, Ag2HgL and TI2ZnL, and variable pressure and temperature Raman, conductivity and optical measurements for Cu2HgL. The results presented here represent an extension of Greig's investigations[2], to include a broader range of conditions, improved pressure calibration, and conductivity measurements. The purposes of the present work were to determine the P - T phase relationship for Cu2HgL, to correlate the phases of Cu2HgL with other copper and silver iodides, and to tCurrent address: Intel Corp., 3065 Bowers Ave., Santa Clara, California, U.S.A. ~Current address: Department of Chemistry, Loyola University, Chicago,Illinois,U.S.A. §Current position: Private Consultant.

B Ag 2 HgI4

0 Ag"

•

Hg'"

o Cu*

correlate the normal modes of these halides through their pressure dependent anharmonicities. Structures of Ag2HgL and Cu2Hgh based on x-ray powder pattern were proposed by Ketelaar[3] and Hahn[4]. Later Kasper and Browail employed single crystal X-ray crystallography to obtain refined structures for the alpha (disordered)[5] and beta (ordered)[6] phases of AgzHgL. The structures of the high temperature a phase and the low temperature // phases of Ag2Hgh and Cu2HgL are shown in Fig. 1. In the // phases the iodides form a face-centered cubic lattice with the two silver or copper ions and one mercury ion occupying three of the four available tetrahedrai sites, leaving one-quarter of the tetrahedral sites empty. The two salts differ in the relative position of the cations and the empty sites. The primitive Widner-Seitz cell of the copper compound shows higher symmetry (D2d) than that of the silver salt ($4). Above the phase transition the cations disorder to partially occupy all of the tetrahedral sites, and the two compounds become isostructural. The third compound studied here, TI2ZnL[7], belongs to the noncentric space group C22-P2t with two formula units per unit cell. The iodide sublattice consists

Cu2HgI4

c~ Ag2HgI 4 ond Cu2HgI4

( ~ t-

Ag', Cu', ond Hg"+ ("~,-

Fig. 1. Structures of the low temperature E-phases and high temperature a-phase of C u 2 H g I 4 and Ag2Hgl4. 9O3

J. I, MCOMBERet

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of distorted close packed iodide layers with threefold arrays of I and square I arrays associated with nearby T1 ions. The Zn ions lie in tetrahedral sites between layers while the TI ions reside in sites of seven coordination. EXPERIMENTAL

The M2HgL compounds were prepared from reagent grade chemicals by the method of Mensel[8]. Both compounds were analyzed by Galbraith Laboratories, Inc. and found to agree with the theoretical formula. X-Ray powder patterns and Raman spectra of the compounds agreed with previous results[2]. Tl2ZnL was synthesized and analyzed by Ammlung[9]. The 676.4 nm line of a krypton-ion laser was used to illuminate the samples. The monochromator bandpass was 1 cm ~and the laser power was typically between 10 and 100 mW. The scattered radiation was detected by a 0.85 m Spex 1401 double monochromator coupled with a RCA C31034 photomultiplier cooled to ca. -40°C. Raman data was processed and plotted by a digital computer. Samples were observed at high pressures in a diamond anvil cell (DAC)[10] containing Type II diamonds. Near hydrostatic pressure conditions were achieved by enclosing the powdered sample mixed with mineral oil in a platinum gasket 5 mil thick (132 #m) with a hole for the sample 10 mil in diameter (264/zm). A few flecks of finely powdered ruby (0.05% Cr ÷3 doped by weight) were mixed with the sample to provide an internal pressure standard [11]. Pressure calibration was made by following the R~ fluorescence at 694.3nm with pressure[l 1]. The breadth of the R~ fluorescence peak was used as an indication of the pressure gradients over the sample. Raman spectra were determined at successively higher pressure during each run. Samples of Ag2HgL are photosensitive so the sample was changed frequently and shielded from the laser beam when spectra were not being recorded. Smaller diamonds capable of exerting higher pressures were used for the region above 20kbar. To obtain sufficient Raman intensities, gaskets with 10 mil diameter holes were used. In conjunction with the smaller diamonds this led to significant pressure gradients over the sample, causing considerable uncertainty in the high pressure phase boundaries. Elevated sample temperatures were achieved by means of a resistance heater that surrounded the diamond pistons, and temperature was monitored by an iron-constautan thermocouple placed in a hole close to the diamonds. Spectra were run in most cases with constant pressure and variable temperature, but for the low pressure-high temperature phases of Cu2HgL, spectra were obtained at constant temperature as pressure was varied. Pressure and thermal effects on the conductivity of Cu2HgL were studied in a DAC[12I. Pressures were measured by means of a transducer (Sensotec Inc., Columbus, Ohio) which was calibrated on the basis of the area of the diamonds, as well as the known pressure phase transitions of Ag2HgL. Mylar gaskets (10mil thick) were used to support the electrodes. Temperatures were measured using a copper constantan thermocuople

al.

in contact with the diamond anvil. The conductivity measurements in the DAC were made using the two probe techniques of Block and Piermarini[13]. A.C. contributions were measured with an Electro Scientific Inc. Model 252 digital impedance meter operating at l kHz using W (0.002" dia.) ion-blocking electrodes[14]. The use of an ion reversible copper electrode was not possible, owing to the reaction of the copper with the Cu2HgL. Hence the degree of polarization was estimated with W electrodes by comparison of AC to DC resistance values. When the two values were the same, it was inferred that electronic conductivity predominated. The contributions of the bulk, interface and grain boundaries to impedance cannot be separated by single frequency measurements; therefore .the present measurements give the sum of these effects. Shibata et al.[15] have discussed the frequency dependent conductivity of Cu2HgL. Visual observation of phase changes for Cu2HgL with varying temperature and pressure in a DAC was performed using a Leitz Wetzlar light transmission microscope. Due to the non-hydrostatic conditions, more than one phase was observable at a time with the different phases separated by distinct Becke lines[16]. RESULTS

Ambient pressure spectra of Cu2HgL and TI2ZnI4 agreed with those in the literature [2, 9]. A compilation of the pressure dependence of Raman peak positions is given in Table 1. Pressure dependent phase transitions are easily observed in the silver and copper salts. At room temperature, the first phase transition in Ag2HgL occurs above 6.2 kbar, with the Raman spectra showing simplification and broadening; in addition, the band found at ca. 122 cm -t at ambient pressure shifts to lower frequency. The high pressure phase of Cu2HgL is difficult to study owing to the very low intensity of the Raman scattering. Raman spectra of the high temperature a-Cu2HgL display broadening similar to that of the silver salt. For the beta phase all the peaks except one for each salt shift to higher frequency with pressure. The 24cm -t peak in Ag2HgL and the 37cm ~ peak in Cu2HgL show negative shifts with pressure. The frequency shifts with pressure are nearly linear for the three salts as can be seen in Fig. 2 for the Cu2HgL sample. The variable pressure Raman spectra of TI2ZnL reveal the growth of a peak at 22 cm ~ commencing at 2kbar, and a gradual broadening and increase in frequency with increased pressure for other features. As shown in Table 2, optical microscopic observations demonstrate the presence of four phases for Cu2HgL. Constant temperature photomicrographs under nonhydrostatic pressure conditions allowed the simultaneous observation of up to four different phases. The results are summarized in Table 2(b). An approximate phase diagram for Cu2HgL based on 124 spectra and on optical microscopy is presented in Fig. 3. The error bars represent uncertainties in the phase boundaries arising from the non-hydrostatic conditions for experiments conducted above 20kbar. Examples of the Raman spectra for the four phases of

Studies of the fast ion conductors Cu2Hgl4,Ag2HgI4and TIzZnI4

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Table 1. Pressure dependence of Raman peak positions Material

Peak

Cu2UgI 4

37

-0.10

-2.7 x 10 -3

48

0.11

2.3 x 10 -3

85

1.0

12. x 10-3

127

0.51

4.0 x 10-3

24

-.07

-2.9 x 10-3

29

0

Ag2Hgl 4

6"o/Ap cm- t / k b a r

0

34

0.1

2.0 x 10 - 3

81

~0.5

~6 x 10-3

positive

103 122 Tl2ZnI 4

Au/vAP/kbar

? 3.7 x I0-3

0.45

22

none

none

29

1.0 x 10 -2

0.30

48

?

58

0.57

80 127

? 1 x 10 - 2

l.

1 . 2 x 10 - 2

0.62

5 x 10-3

120 _

12

O

O

,o~,/r-

~oo 2 80

s

160

B °

-

0

4

~ c ra°L ~ sloP* 8 .O.l~

8

12 36 crn'l 8

40

16 .

L 200

i I'0

J 20

Pressure Pressure kbor

Fig. 2. Pressure dependence of the frequencies for the principal Raman features of CuzHgI4. The wavenumber values given above each line correspond to frequencies of ambient pressure. the copper salt are seen in Fig. 4 with the peak positions given in Table 3. The relative intensities of the four spectra have been scaled so that the major feature of each spectrum is on scale. Raman scattering from the y and 8 phases was extremely poor. Under high laser power irreversible decomposition of the sample was occasionally observed but all of the phase boundaries in Fig. 3 were determined to be reversible with pressure and temperature.

30

40

in kbor

Fig. 3. Pressure-temperature phase diagram for Cu2HgI4. Error bars represent the range of uncertainties indicated by the various data sets.

Cu2HgL was found to be photoconductive and therefore precautions were taken to keep the sample in the DAC protected from light during conductivity measurements. Several of the conductivity study results are presented in Figs. 5 and 6. AC measurements at I khz at ambient temperature and elevated pressures on the fl, y and ~ phases with W electrodes gave substantially the same conductivity as DC measurements with these same electrodes, indicating that the 8, Y and 8 phases are

906

J. 1. McOMBER et al.

Table 2(a). Characterization of the phases of Cu2HgI4by optical microscopy P (kbar)

T*C

Color

Assigned Phase

25

atm

bright red

B

above 70

atm

dark red

a

25

30

yellow

above 70

30

orange

6

Table 2(b). Optical microscopic observation of Cu2HgI4 phases under nonhydrostatic conditions T *C

Phases observed in order of increasing P

25*

Maximum P

B, T, 6

110"

a,

[tO*

~, ~, y

17

~, ~

28

75"

~, ¥,

36 6

>35

Table 3. Positions of the prominent Raman features in the 4 phases of Cu2Hgl4 Phase

a

Frequency (cm-l) a

Pressure (kbar)

Temp (°C)

36

48

53

127

arm.

70

19

37

48

85 127

arm.

25

Y

(17)

(38)

6

(26)

I17

142

29

25

34

70

aparentheses indicate very weak bands which are close to the noise level and therefore may not be real. The low frequency features in the spectrum of the B phase are somewhat more certain because these data were obtainable on b u l k samples where the signal to noise is more favorable.

predominantly electronic conductors. The AC (1 khz) conductivity at ambient temperature and variable pressure increases in the 3 phase to about - 9 kbar then decreases and levels off at the transition to the 3' phase (Fig. 5a). This dramatic change of slope within a phase is unusual and will be discussed later. Differences are noted between AC and DC conductivity measurements at 75 and 110° with an increase in pressure indicating mixed ionic and electronic conductivity at elevated temperature (see Fig. 5b). However, at pressures approaching 30kbar these differences appear to narrow. Mixed ionic and electronic conductivity in the alpha phase of Cu2Hgh has been noted by several authors[13, 14, 17], and a substantial ionic conductivity is indicated in the present work by the difference begween AC and DC conductivities.

u~

DISCUSSION

1.4S! 0

Fi

4

le$] O 9~!e" "/~0 klFIVENUMI~£R (~ICM~

eprese°ta,ive.amans

ec,ra,romthefour0ha

Cu2Hgl,.

4S!e

e

e~]

o

The variable pressure Raman studies show noticeable frequency shifts as a function of pressure. If the frequency v~ of each mode is considered to be purely a function of volume V, we can write eqn (1)[18]:

'

yl = - V/v,(cgvJOP)r ~-~ r = - ~ \ a P / r

(I)

Studies of the fast ion conductors Cu2HgI4, Ag2HgI4and TI2ZnI4 10-4.

•

~

D~ 11o°C

(b)

%-.

10-~ 75°C

5 5

~

DC

h

o tO 10-5

~

10-6

I

112

I 24

I 15

310

316

Pressure in kbor

Fig. 5. Pressure dependent conductivityof CueHgI4. 40*

~

70

iO0

10-~

o

o

312

I

31o

28

1/T

°K x I0 -3

I

Fig, 6. Temperature dependent conductivity of Cu2HgI4 at ambient temperature. where X is the isothermal compressibility, ~'l is the mode Gruneisen parameter, P is pressure and T is temperature. For the compounds under study, X is unknown but the relative mode Gruneisen parameters for the various modes of a compound can be compared using eqn (2). "r~X= ll v~(~vd aP )r. (2)

907

For a molecular crystal the Gruneisen parameter is larger for modes involving intermolecular motion than for those which are intramolecular in nature[19]. The compounds Ag2HgI4 and Cu2HgI4 are not molecular but some of the modes appear to exhibit localized character. For example, the strong band around 122 cm-: in Ag2HgI4 corresponds closely with the totally symmetric HgI42stretch which has been determined in solution and in salts of HgI42- with large organic cations [2]. Table 1 lists the values of Av/vAP for the major Raman features in the three salts. The pressure range for the/~ phase in Ag2HgL was not large enough to determine easily the pressure shifts of several of the broad peaks so these values are uncertain. A comparison of the values of Av/vAP for Cu2HgI,, and Ag2HgL show some interesting similarities between the two salts. In order to understand these similarities, it is useful to first review results of single crystal Raman studies. Table 4 shows the factor group analysis for Ag2HgL and Cu2HgL as well as the symmetry assignments of the modes from single crystal polarized Raman studies [2, 20]. The physical descriptions of the modes is somewhat artificial in these partially ionic solids but some empirical justification can be made for this approach. As already mentioned, the HgI4-2 symmetric stretch which is prominent in the M2HgL spectra correlates with solution spectra, and, as will be described later, a low frequency feature displays a mass dependence indicating that M + translation is a legitimate assignment. For other modes, the eigenvectors may involve considerable mixing of HgI4-2 motions with those of M +. The single crystal studies of Ag2HgI4 and Cu2HgL which are described in detail elsewhere[20] suffered from use of small crystals which did not provide distinct polarization of some of the Raman features. The symmetry analysis in Table 4 in conjunction with the similar values of A d v A P for the 127cm -m and 122cm -1 features of Cu2HgL and Ag2HgI4 respectively, further substantiate the assignment of the HgL 2- symmetric stretch. The peaks at 85 (Cu2HgL) and 81 cm -1 (Ag2HgL) show larger values of A d v A P and they also show similar temperature dependent damping, from sharply defined peaks at 8°K to very broad features near the a-fl phase transition. In the polarized single crystal Raman study of Cu2HgL[20], it was not possible to distinguish between At and B~ symmetry for the 85 and 48 cm-: features. However, the pressure dependence of the 85 cm -~ peak is the same as that of the 81cm -~ peak in Ag2HgI4. Therefore, the mode associated with the 85 cm -j feature is assigned A: symmetry and the 48 cm -t feature probably has Bt symmetry. Of special interest are the E modes at 24 (Ag2HgL) and 37cm -t (Cu2HgL) which show negative shifts with pressure. This negative shift is also seen in the E2 modes of Agl, CdS, ZnO and ZnS, all of which have the wurtzite structure [21-23]. The ratio of the two frequencies is approximately proportional to the ratio of the square roots of the masses of copper and silver, indicating that these modes involve a large component of Cu and Ag motion. Accordingly, these E symmetry features are assigned as external Cu or Ag

J. 1. MCOMBERet aL

908

Table 4. Symmetryand approximate assignmentsfor the Ramanbands of Ag2HgI4and Cu2HgL at ambientand pressure and temperature Ag2Hgl 4

Space

Group:

Site

Symmetry

Free

Unit

14(S42)

Cu2Hgl 4

z=2

D2dlI(142M)

Hg

in S 4

D2d

Ag

in S 4

Cu

z=2

iu $4

Hg142stretches

A1 + T2

A1 +

deformations

E + T2

E

1' 2

+ T2

cell Hg142-

stretches

A + B + E

A I + B2 + E

Hg142-

deformations

A + 2B + E

A 1 * B I + B2.+

Hg142-

external

A + B + 2E

A 2 + B 2 + 2E

B + E

B2 + E

B + E

B2 + E

M+

lattice

acoustic

modes

modes

modes

E

Assignments* Ag2Hgl 4

Cu2Hgl 4

. F r e q u e n c l e.s

82

3q

34

29

!4

A

B

E

B

E

127

85

53

48

A1

A I or

122

106

A

?

BI

?

A I or B 1

37 E

in cm-I

translational modes in the xy plane. Even though the attempt frequency concept is poorly defined in these compliant solids, it appears that these E symmetry modes can be approximately identified with one of the attempt frequencies for ion transport. An attempt frequency for ion migration need not correspond to a zone-centered normal mode. The geometry of the crystal is such that a combination of x, y and z translation is necessary to carry the ion through the face of the surrounding iodide tetrahedra. Above 70°C at ambient pressure Cu2HgI4 transforms from an ordered electronic conductor into the a phase which displays mixed ionic and electronic conductivity and disorder of the Cu + and Hg2~ ions[l]. In keeping with these properties, the Raman spectrum of the a phase is broad, a characteristic feature of disorder and ionic conduction[2,21,24]. The major feature in the a phase is the broad peak at 127cm -' assigned as the HgI4-2 symmetric stretch. Increasing the pressure at ambient temperature causes the peak at 127 cm-' to shift to higher frequency until the 28 kbar transition is reached and the sharp spectrum transforms to a less intense broad spectrum. The major feature is now the weak peak at 142 cm '. This feature is still thought to be the Hg-I symmetric stretch with the mercury surrounded by a tetrahedron of iodides. The Clausius Clapeyron equation and comparison with similar salts [25] indicate that the/3 to y phase transition involves a volume change with little disordering because the slope of the line separating the phases is near parallel to the temperature axis. In analogy with the high pres-

sure phases of Cui[26], it is possible that the 3' phase of Cu:Hgl4 can approximately be described as a rhombohedrally distorted zinc blende structure or as an "anti" structure to the tetragonal structure of litharge (red PbO). In both structures the cations reside in sites of coordination four. As was previously noted, a conductivity maximum is observed in the ~ phase at ambient temperature as the pressure is increased. The observation of a similar conductivity maximum was made by Weil and Lawson[17] for AgzHgl4 and by Shibata et aL[15] for Cu2HgI4. The occurrence of the conductivity maximum and a faint darkenin~ prompted Weil and Lawson to propose a phase transition at the maximum. Greig[2] observed no change in the Raman spectrum around this pressure. Our Raman studies of Cu2HgL also show no noticeable change when passing through this point. We also observe this conductivity maximum at a higher pressure than Shibata et al.[15] (about 9 kbar vs 1-2 for Shibata et al.), and from the Raman data we believe that the maximum does not correspond to a phase change. The main Raman feature for the ~ phase occurs at 117 cm ' and is similar to the strong peak in the first high pressure phase of Ag2HgI4. The shift of the peak to lower frequency would imply that the mercury is moving to a site of higher coordination number, probably an octahedral site. Salts crystallizing in the zinc blende or wurtzite structure at atmospheric pressure eventually transform to the rock salt structure with increasing pressure[27]. Beta Cu2HgL can be approximated as a zinc blende structure with one quarter of the tetrahedral

Studies of the fast ion conductors Cu2HgI4,Ag2HgI4and TI2ZnI4 sites vacant. Therefore the Raman data along with the above analogies indicate that the 8 phase may be related to the rock salt structure. Extrapolation of the high pressure Raman results indicates that at room temperature the 8 phase should exist above 40 kbar, which is beyond the range which we could explore with our equipment. The high temperature variable pressure conductivity measurements indicate that the 8 phase may be an electronic conductor. This is consistent with a transition to an ordered, closer packed array. Interesting comparisons can be made between the stability of the high pressure phases of Ag2HgL, Cu2HgL, Agl and CuI. The silver salts Ag~HgI4 and AgI go to six coordination at 6.2 and 4 kbar respectively, similarly ca. 40 and 90 kbar are required for the phase transition to six coordination in Cu2HgI4 and CuI. The greater ease of achieving six coordination with Ag+ than Cu + is consistent with simple radius ratio arguments and also with Phillips[28] correlation of optical electronegativities and covalencies.

Acknowledgements--We appreciate informative discussions with D. H. Whitmore, B. Phipps, and C. Chaney. This research was supported by the National Science Foundation Materials Research Laboratory Program through the Northwestern University Materials Research Center (Grant DMR 79-23575)and at Argonne Laboratory by the Department of Energy. REFERENCES 1. Ketelaar J. A. A., Z. Phys. Chem. B26, 327 (1934). 2. Greig D., Shriver D. F. and Ferraro J. R., J. Chem. Phys. 66, 5248 (1979). 3. Ketelaar J. A. A., Z. Krist. 80, 190 (1931). 4. Hahn H., Frank G. and Klingler W., Z. anorg. Chem. 279, 271 (1955).

909

5. Kasper J. S. and Browall K. W., J. Solid St. Chem. 13, 49 (1975). 6. Browall K. W., Kasper J. S. and Wiedemeier H., ]. Solid St. Chem. 10, 20 (1974). 7. AmmlungR. L., Scaringe R. P., Ibers J. A., Shriver D. F. and Whitmore D. H., J. Solid State Chem. 29, 401 (1979). 8. Mensel E. P., Ber. Deutsch Chem. Ges. 3, 123 (1870). 9. AmmlungR. L., Shriver D. F., Kamimoto M. and Whitmore D. H., J. Solid St. Chem. 21, 185 (1977). 10. Ferraro J. R. and Basile L. J., Appl. Spectrosc. 28, 505 (1974). 11. Forman R. A., Piermarini G. J., Barnett J. D. and Block S., Science 176, 284 (1972). 12. LaBonville Walling P. and Ferraro J. R., Rev. Sci. Instr. 49, 1557 (1978). 13. Block S. and Piermarini G. J., Phys. Today 29-9, 44 (1976). 14. Wagner J. B., Electrode Processes in Solid State lonics (Edited by M. Kleitz and J. DuPoy), p. 185. Reidel, Boston (1975). 15. Shibata S., Hoshino H. and Shimoji M., J. Chem. Soc. (London) Faraday Trans. 1409(1974). 16. Weissberger A., Physical Methods of Organic Chemistry, Vol. 1, p. 491. Interscience, New York (1945). 17. Well R. and Lawson A. W., J. Chem. Phys. 41,832 (1964). 18. Mitra S. S., Phys. Stat. Solidi 9, 519 (1965). 19. Zallen R., Phys. Rev. B 9, 4485 (1974). 20. McOmber J. I., Ph.D. Thesis, Northwestern University (1980). 21. Hanson R. C., Fjeldly T. A. and Hochheimer H. D., Phys. Stat. Solidi (B) 70, 567 (1975). 22. Mitra S. S., Brafman O., Daniels W. B. and Crawford R. K., Phys. Rev. lg6, 942 (1969). 23. Ebisuzaki Y. and Nicol M., ./. Phys. Chem. SOc. 33, 763 (1971). 24. Nitzan A., Ratner M. A. and Shriver D. F., J. Chem. Phys. 72, 3320 (1980). 25. Sherman W. F. and Wilkinson G. R., Adv. Infrared Raman Spect. 6, 158 (1980). 26. Meisalo V. and KalliomakiM., High Temp, High Press 5, 663 (1973). 27. Gutmann V. and Mayer H., Structure and Bonding 31, 50 (1977). 28. Phillips J. C., Rev. Mod. Phys. 42, 317 (1970).