Physical properties and crystal structure of a new semiconducting I-III-VI2 compound, CuScS2

J. Ph~s.

C’l~rrn.

Solids

Pergamon

Press

I97 I. Vol.

32. pp. 9 13-922.

Printed

in Great

Britain.

PHYSICAL PROPERTIES AND CRYSTAL STRUCTURE OF A NEW SEMICONDUCTING I-III-VI, COMPOUND, CuScS, J. P. DISMUKES* RCA

Laboratories.

and

Princeton,

R. T. SMITH N. J. 08540,

U.S.A.

and J. G. WHITE Department

of Chemistry.

(Receiued

Fordham

13 July

University.

1970;

ill reuisedfortn

New

York.

N. Y.

3 1 AURNS/

104.58

U.S.A.

1970)

Abstract-The compound C&c& has been prepared for the first time. and single crystals have been grown by chemical transport reaction with I?. The crystals are trigonal with a = 3.7333 kO.0005 A, c = 6.098 & 0.001 A, and are non-centrosymmetric with space group P 3m I. The crystal structure has been determined by single crystal X-ray methods and is based on a hexagonally close packed arrangement of sulfur atoms, with one formula unit per cell. The scandium atoms occupy octahedral sites and the copper atoms tetrahedral sites giving a new structure type intermediate between the structures of NiAs and hexagonal ZnS. The compound is a semiconductor and optical absorption measurements show two band gaps, one at 2.30 eV representing a direct transition and the other at1.8? 1 eV representing an indirect transition. Doping experiments with Zn produced low resistivity n-type material, but attempts to prepare p-type material were unsuccessful.

2. EXPERIMENTAL

1. INTRODUCTION

(a) Preparation, crystal gronlth and doping Copper scandium sulfide, CuScS,, was prepared by heating a stoichiometric mixture of Cu and SC.& powders at 1050°C in an evacuated quartz ampule for 16 hr in the presence of the required stoichiometric amount of sulfur. The scandium sulfide, SC,&,, was prepared by reacting Sc,O,, contained in a carbon boat, with a helium stream saturated with CS, for 24 hr at 1050°C. X-ray diffraction powder photographs of CuScS, showed no evidence of the starting materials or of sulfides of copper. Copper and scandium were determined by complexometric titration with EDTA [5,6] and sulfur was determined using the idometric method for hydrogen sulfide[7]. Anal. Calcd. for CuScS,: Cu, 36.8%; SC, 26.1%; S, 37.1%. Found: Cu, 37.0 5 0.3%; SC, 25.9 20.2%; S, 37.3 +0*3%. Copper scandium sulfide is stable at room temperature in air and water, and reacts slowly with strong acids. Single crystals of CuScS, for X-ray crystal

TERNARY semiconducting compounds of the general type I-III-VI, having the chalcopyrite structure[ I] have been known for many years, where I = Cu, III = Al, Ga, In and VI = S, Se, or Te. The energy gaps for these materials have been summarized in a recent paper[2]. A series of monoclinic I-III-VI1 compounds [3,4] have been reported. where I = Cu, III = a rare earth element and VI = S, Se. However, only limited data are available on their crystallography and physical properties. In this paper we report the synthesis and crystal growth of the new semiconducting I-III-VI, compound, CuScS,, the X-ray determination of its crystal structure, optical measurement of the energy gap, and investigation of doping behavior.

*Laboratories Zurich, Switzerland.

RCA

Ltd,

569

Badenerstrasse.

8048 91

914

J. P. DISMUKES,

R. T. SMITH

structure determination, for optical measurements, and for investigation of doping behavior were prepared by chemical transport reaction[8], using I2 in a sealed, evacuated quartz ampule. Single crystal platelets up to 1 cm2 in area, and with the c axis perpendicular to the platelet, were transported from hot to cold using an I2 concentration of about 2 mg/cm3 in a temperature gradient of 1050-950°C. A series of experiments was conducted to determine whether CuScS, could be readily doped n- and p-type by simple chemical substitution for Cu, SC, or S. N-type doping was attempted both by annealing chemically transported crystals in 4 atmosphere Zn vapor at 900°C for 16 hr, and by chemically transporting CuScS, with additions of Zn. P-type doping was attempted both by annealing chemically transported crystals in + atmosphere of P, vapor at 9OO”C, and by chemically transporting CuScS, with additions of P or Ca.

and J. G. WHITE

ties, respectively. This procedure neglects reflection, but still gives sufficiently accurate values of (Yin the spectral region near the band edge where (Yis large. (c) X-ray measurements

The crystal system was found to be trigonal from Laue and Weissenberg photographs. Accurate cell dimensions, a = 3.7333 _+ -0005 A, c=6.098 -+ a001 A,wereobtainedfrom the powder diffraction pattern given in Table 1. Ni-filtered CuKa radiation was used and the pattern was taken at 23°C with a 114.6 mm dia. camera. The cell volume gives a calculated density of 3.90 g-cmp9 for one formula weight per unit cell. The measured density value, 3.79? 0.15 g-cm-“, obtained on a 13 mg crystal agrees with the calculated value to within experimental uncertainty. The crystals originally prepared were very thin, and distorted on cutting. For the collection of single crystal intensity data a naturally occurring flake elongated along the b axis and (b) Physical measurements with an approximately constant cross section The density of single crystal CuScS, plate- of 0.26 X O-05 mm was used. The integrated lets was determined by the method of hydrointensities of the hO1, h 11, and h21 levels were static weighing [9], employing Archimedes’ measured on a Buerger single crystal diffractoprinciple and using water as the immersion meter using Zr-filtered MoKL~ radiation. Befluid. cause of the high absorption (CL= 107.1 cm-‘) Electrical resistivityof CuScS, crystal plate- and the rather unsuitable crystal shape, ablets was measured by the four-point probe sorption corrections were made by the method technique [ IO]. The CuScS, crystals were also of Albrecht [ 121. The residual absorption ertested for conductivity type using a simple rors are mainly due to departure of the actual thermal probe technique capable of detecting crystal shape from the idealized shape asconductivity type of silicon with resistivity sumed. A set of F values was obtained for each less than 100 ohm-cm. level after application of Lorentz and polarizaOptical absorption measurements at 300°K tion factors and the three sets were brought in the spectral range 2.0-0.48~ were taken to a single scale by means of the common with a Cary Model 14 Spectrometer on chem- reflections. ically transported CuScS, platelets with a From the three dimensional Patterson funcgrown thickness in the range 100-230 CL, tion it was immediately clear that the atoms and on mechanically thinned specimens in were located in the following special positions the range 10-20~. The thickness t was deter- of the space group P3ml: SC in (a) O,O,z with mined by interferometry, and the optical ab- z= 0; Cu in (b) 4, 3, z with z - 2; S(1) sorption coefficient (Ywas calculated from the in (b) Q, Q, z with z - a; S(2) in (c) Q, 4, simple relation [ 1 I], (Y= (l/t) In (1,/I,), where z with z - 4. Refinement was carried out I, and I, are the initial and transmitted intensi- _ first by difference Fourier synthesis and

PHYSICAL

PROPERTIES

AND

Table 1. Calculated and observed lattice spacings and intensities for CuScS, (CuKa radiation)

001 100 002 101 102 003 110 111 103 200 112 201 004 202 113 203 005 211 114 105 212 300 213 115 205 106 214 220 116 311 304 215 312 313 305 401 324 117 216

6.10 3.23 3.049 2.857 2.218 2.033 1.867 1.785 I.721 1.617 1.592 1.563 1.525 I.428 1.375 1.265 1.219 1.1982 1.1808 1.1412 1.1343 I.0777 1 +I73 1.0210 0.9736 0.9696 0.9535 0.9333 0.8926 0.8872 0.8800 0.8633 0.8603 0.8204 0.8076 0.8017 0.7960 0.7895 0.7814

6.10 3.23 3.046 2.856 2.218 2.032 1.864 1.783 I.720 1.615 1.592 1.563 1.523 1.427 1.376 1.265 1.220 1.1986 1.1803 I.1404 1.1339 I.0774 I.0471 1.0209 0.9733 0.9693 0.953 1 0.9336 0.8927 0.8873 0.8805 0.8632 0.8604 0.8204 0.8076 0.8016 0.7962 0.7894 0.78 14

us = very strong, s = strong, medium, w = weak, VW = very uvw = very, very weak.

m+ sm+ us s w s w s w m m U”W m m m w m mw m mm mvvw w vvw w vvw w VW w mmw vvw vvw vvw mm =

weak,

then by full matrix least squares methods [ 131. Attempts to refine using anisotropic thermal parameters led to physically unreasonable results, presumably because of incomplete correction for absorption. Since the isotropic temperature factors refined independently for each atom did not differ signifi-

CRYSTAL

STRUCTURE

915

cantly from each other, the number of variables was further reduced by refining only a single isotropic temperature factor, the scale factor, and the z parameters for Cu, S(l), and S(2). The weighting scheme used set w = l/a* where u was based on the counting statistics for each reflection. Convergence was obtained to a conventional R of 0.087 for 91 independent reflections. The final calculated and observed values of F are given in Table 2. The scattering factors used are those given in the International Tables [ 141 corrected for anomalous dispersion [ 151. The choice between hkl and hkl was made on the basis of the set giving better agreement with the calculated values. Since the anomalous dispersion effect is quite small the result is not absolutely clear cut. The direction of intensity change from I hk, to Ii;i;i is in agreement with that calculated for 27 pairs and is in the opposite direction for 16 pairs. 3. RESULTS AND DISCUSSION

(a) Crystal structure The crystal structure found for CuScS, is shown in Fig. 1. The structure is essentially a hexagonally close packed array of sulfur atoms in which the copper atoms occupy tetrahedral and the scandium atoms octahedral interstices. Consequently, the two sulfur atoms in the unit cell are differentiated physically as well as crystallographically. The atom S ( 1) is tetrahedrally coordinated to one copper and three scandium atoms while S(2) is octahedrally coordinated to three copper atoms and three scandium atoms. The structure thus belongs to a new basic structure type intermediate between the structures of NiAs and ZnS (wurtzite). This relationship is illustrated in Fig. 2 where all the structures shown are based on hexagonal close packing of the anions with two anions per unit cell. The bond distances found in CuScS, are given in Table 4 and the bond angles in Table 5. The SC-S bonds average 2.60 8, almost identical with the value of 2.59 A found in SC&

-1

-1

-1

-1

-1

-1

10

10

10

10

10

00 0 00 0 00 0 00 0 00 0 00 10

hk

-3

-4

-5

0

0

0

0

0

0

0

0

-5

-4

-3

-2

--I

-2

0

0

-1

0

1

5

4

3

2

6 0 0 1

5

4

3

2

I IFcI 27.8 32.1 53.5 55.2 46.0 48.4 38.7 33.3 58.6 59.2 32.4 46.7 47-6 86.3 81.6 88.2 90.8 44.7 43.9 35.8 37.0 26.0 31.1

IFA

31.8 36.8 55.1 65.6 449 494 35.6 39.7 51.6 59.9 33.0 55.1 54.9 79.5 86.4 76.1 91.3 40.1 45.5 30.0 34.4 23.3 26.1 1

1

1

1

1

1 - 1 3 2 -2 2 -2 2 -2 2 -2 2 -2

-1

-1

-1

-1

-1

h 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

k

-5

-4

-3

-1

-6

-5

-4

5

4

3

6 0 0 0 1

5

4

3

6 -6 - 1 -:

1 38.7 36.6 43.7 39.7 86.0 79.3 30.2 23.5 43.7 38.9 41.3 47.8 63.8 36.0 35-6 27.1 28.3 67.4 76.9 21.5 24.1 39.3 38.3

IFol 45.9 41.8 38.4 38.6 90.2 92.7 29.6 21.5 43.5 42.9 40.6 38.9 72.8 36.2 35-3 30.3 30.1 15.8 73.4 22.5 24.5 37.4 38.1

IFA

2

2

2

2 1 1 1 - 1 I --I 1 -1 1 -1 1 - 1 2

-1

-2

2

-2

-2

-2

h

1 - 1 1 -1 1 -1 1 -1 1 - 1 1

-1

8 0 0 0 1 1

0 0 0 0

k

Table 2. Observed and calculated structure factors for CuScS, (MoKa

- 1 1 -2 2 -3 3 -4 4 -5 0 1 -1 2 -2 3 -3 4 -4 5 -5 6 -6 0

1 66.6 61.7 73.9 65.8 36.6 32.8 27.3 22.7 22.9 99.0 23.9 24.7 39.7 45.1 34.4 39.7 33.2 37.9 49.4 58.9 25.7 27.1 26.7

IF01

radiation).

59.2 63.7 70.4 67.9 36.6 37.3 30.0 28.6 21.8 105.9 20.8 24.4 40.3 41-9 35.9 38.1 33.1 27.9 50.4 51.0 28.8 26.5 29.0

IF4

-2

-2

-2

-2

-2

-2 -:

-2

-2

-2

-2

2 2

2

2

2

2

2

2

2

2

h

1

1

1

1

1

1 - 1 1 -1 1 -1 I -1 2 2 -2

-1

-1

-1

-1

-1

-1

k

F, for one formula

-1

-5

-4

-3

-5 -1

-4

-3

-2

-1

5 0 1

4

3

1

5

4

3

2

0 1

1

26.9 56.9 58.9 63.8 68.4 27.3 31.6 20.6 23.9 23.3 24.9 18.6 18.8 72.1 65.0 19.8 16.6 36.0 29.8 68.6 13.0 13.4

If.01

29.1 53.3 48.8 56-9 59.5 32.4 31.7 24.2 25.6 20.3 25.3 23.0 23.3 63.3 65.6 21.1 19.0 33.8 33.1 64.5 11.2 14.8

IFCI

unit, F, scaled to F,

PHYSICAL

PROPERTIES

AND

CRYSTAL

STRUCTURE

917

Fig. 1. The crystal structure of CuScSz, showing one unit cell outlined by axes (a), (b). and cc). The one Cu atom, one SC atom, and two crystallographically independent sulfur atoms. S(I) and S(2) in the unit cell are indicated. CENTROSYMMETRIC

I

NON-CENTROSYMMETRIC TETRAHEDRAL

SITES1

cu IN I TETRAHEDRAL SITE SC IN I OCTAHEDRAL SITE

CdI&Cd

INI

OCTAHEDRAL

SITEI

l I

Fig. 2. The relationship between the CuScS, structure and the other basic structure types based on hexagonal close packing of anions. All the structures shown contain two anions per unit cell. The distribution of the cations per cell between octahedral and tetrahedral sites is also indicated.

[ 163. The Cu-S bonds as measured differ considerably among themselves. However, it should be noted that the length of the Cu-S bond parallel to the c axis has a much higher standard deviation than the others since the free parameters for both atoms are in the bond

direction. The average Cu-S distance is 2*325 A, which is much smaller than the sum of the ionic radii, 2.80 A[17], and indicates considerab!e covalent character. The bond angles are fairly regular for the coordination groups of sulfur atoms surrounding the central metal

J. P. DISMUKES,

918

R. T. SMITH

Table 3. Structural

parameters for CuScS,

x

Y

SC

0.0

0.0

CU S(1)

0.3333 0.3333 0.6667

06667 06667 0.3333

Atom

S(2)

Atoms

1

cu-S( 1)

3 3 3

CwS(2) SC-S( 1) SC-S(2)

B

Z

!126(28) 0.7760(41) 0.2542(36)

0.31(14) 0.31 0.31 0.31

shortest Cu-SC distance is 3.31 A, compared with the sum of the metallic radii, 2.92A. Metal-metal bonding between Cu and SC is unlikely to occur because Cu’+ has a completely filled d-shell and Sc3+has acompletely empty d-shell. In a very recent paper published after the completion of this work, Gorter[ 191

Table 4. Bond distances in CuScS, Number of bonds

and J. G. WHITE

Distance (A) 2.216(30) 2.361(13) 2.552(13) 2.655(13)

Table 5. Bond angles in CUSCS, Coordination

group

Number of angles

Atoms

Angle (“)

Cu-centered tetrahedron

3 3

S( I)-cu-S(2) S(2)-cu-S(2)

114.1 104.5

S( I)-centered tetrahedron

3 3

SC-S( I)-SC cu-S(l)-SC

94.0 122.4

SC-centered octahedron

3 3 6

S(I)-SC-S( 1) S(2)-SC-S(2) S( 1)-SC-S(2)

94.0 89.4 88.3

S(2)-centered octahedron

3 3 6

cu-S(2)-cu SC-S(Z)-SC cu-S(2)-SC

atoms. However, for the coordination of the sulfur atoms by the metal atoms there is considerable distortion in order to accommodate the rather different Cu-S and SC-S bond distances. The occurrence of the CuScS, structure type is probably restricted to pairs of metal atoms one of which has a very strong tetrahedral site preference and the other a very strong octahedral site preference as is the case with Cu’+ and Sc3+. The structure of CuCrS, [18] has Cu’+ in tetrahedral sites and W+ in octahedral sites. However, the sulfur atoms are cubic close packed, and the structure is believed to be stablized by d-electron interactions between Cu and Cr, resulting in short (2.77A) Cu-Cr distances. In CuScS, the

104.5 89.4 82.4

discussed three possible structures for the then unknown compound CuScS,. These are: (I) the structure of CuCrS2, (II) the structure of CuScS2 which we have determined and (III) a more complex structure in which regions of cubic and hexagonal close packing are interleaved, resulting in a twelve layer sulfur stacking sequence. Of these, Gorter prefers structure (III) since it minimizes repulsive forces between second nearest neighbors. The fact that CuScS, has structure (II) based on simple hexagonal packing of sulfur atoms, is apparently the consequence of its largely covalent character. * Since the chemistry of the rare earth elements is similar to that of SC, one might expect compounds of the general formula CURS,,

PHYSICAL

PROPERTIES

2.30 1 A.4

AND

CRYSTAL

STRUCTURE

eV

I 0.5

0.7

Fig. 3. The dependence of the optical cient (a) of CuScS, upon wavelength sured on a 15 p-thick crystal. Values (2.30eV) and of indirect bandgap indicated.

0. 6

absorption coeffi(A) at 300°K meaof direct bandgap (1.8kO.l eV) are

0 hu(eV)

Fig. 4. The dependence of the square of the optical absorption coefficient (a*) of CuScS, at 300°K upon photon energy (/IV) in the range 2.25-2.55 eV. Data are taken from Fig. 3.

919

J. P. DISMUKES,

920

R. T. SMITH

where R = a rare earth element, to form with the CuScS, structure. Compounds*of the type CURS, have been reported[3], but only for the elements from La through Tb. However, the compounds do not have the CuScS, structure, but rather form monoclinic crystals of an unknown structure. Probably these rare earth elements have too large atomic radii to permit close packing of sulfur atoms required for the existence of the CuScS, structure. A series of nonstoichiometric copper rare earth sulfides (nCu,S.R,S,, with n > 1 and R = Tb to Lu) have been reported by Ballestracci and Bertaut [20]. These compounds have a structure in which rare earth and sulfur atoms occupy approximately the same relative positions as do SC and S in CuScS,. However, the copper atoms are distributed at random between the two tetrahedral sites,+, 3, z, with z - 8, giving a centrosymmetric

20

and J. G. WHITE

structure. As n increases and the occupancy of tetrahedral sites by Cu also increases, the rare earth occupancy of the octahedral sites must decrease to maintain charge balance. It appears that the stability of this nonstoichiometric phase is favored by the incomplete site occupancy which relieves some of the strain which would occur in a stoichiometric CURS, phase due to the disparate size of the metal atoms. (b) Optical energy gap Figure 3 shows a representative plot of optical absorption coefficient (Y of CuScSz as a function of wavelength A at 300°K. There is a sharp absorption edge at 2.30 eV and a shallow absorption edge at 1.8 + 0.1 eV. The absorption coefficient in a semiconductor is known to vary with photon energy as (hv - E,)“[ 11,211, where Eg is the energy gap,

I cuscsp 300*K

15

-y E 2 IO -4

u

5

2. hv(eV)

Fig. 5. The dependence of the square root of the optical absorption coefficient (al’*) of CuScSr at 300°K upon photon energy (hv) in the range 1.75-2.1 eV. Data were taken on a 230 p-thick crystal.

PHYSICAL

PROPERTIES

AND

n = f for a direct, symmetry allowed transition, and n = 2 for an indirect transition. Therefore, plots of (Y” vs. hv were constructed from the data in Fig. 3. The linear relation between (Y’ and hv in Fig. 4 indicates that the energy gap at 2.30 eV is direct. We believe the shallow edge at l-8 r+O*l eV represents an intrinsic, indirect energy gap in CuScS, rather than an extrinsic effect such as impurity band tailing, since measurements on a 230 CLthick crystal, for which the shallow edge covered the full range of the spectrometer, indicated the linear relation between (YI” and hv shown in Fig. 5. The quoted uncertainty is typical for a room temperature measurement of an indirect energy gap. The direct bandgap of CuScS,(2*30 eV) lies in the range expected for CuGaSp by interpolation between CuAIS, (3.35 eV)z and CuInS, (1.2 eV)[22]. However, more detailed and quantitative comparisons of the optical energy gaps of I-III-VI, compounds are not possible at this time, since data on their band structure are almost entirely lacking. (c) Doping experiments

The electrical resistivity of undoped CuScS, crystals was about 2 x 10” ohm-cm as measured by the four-point probe technique, but their conductivity type could not easily be determined since the thermal probe showed no deflection. No further measurements were attempted on these very high resistivity crystals, since the principal objective in this work was to achieve heavily doped (c IO-’ ohmcm) material, both n- and p-type. The tetrahedral coordination of Cu and the octahedral coordination of SC in CuScS, suggested that p- and n-type doping of this compound could be achieved by taking advantage of the tetrahedral site preference of Zn, for n-type doping, and of the octahedral site preference of Ca, for p-type doping. Ptype doping was also attenpted by substituting P for S. Crystals of CuScS, annealed in Zn vapor at 900°C became highly conducting n-type, with resistivity about 1Op3ohm-cm.

CRYSTAL

STRUCTURE

921

Small crystallites of CuScS, chemically transported in the presence of Zn were also highly n-type. The n-type doping appears to be due to substitution of Zn for Cu, as anticipated, since emission spectrographic analysis indicated the presence of Zn in concentrations of 100 ppm for chemically transported specimens and of 1000 ppm for specimens annealed in Zn vapor. Crystals of CuScS, annealed in P, vapor, or in vapors of P, plus Sp remained high resistivity. Likwise, chemical transport of CuScS, in the presence of Ca or P failed to give P-type crystals. Emission spectrographic analysis indicated the incorporation of these impurities in concentrations of several hundred ppm. Thus, neither calcium nor phosphorus, the most obvious impurities which would be expected to give p-type doping, readily give CuScS, with p-type conductivity. Acknowledgemenrs-The authors thank R. J. Ulmer for chemical syntheses and optical measurements, B. J. Goydish for chemical analyses, and R. J. PafT for X-ray powder photographs. REFERENCES HAHN H., FRANK G., KLINGLER W., MEYER A. and STORGER G.. 2. anorg. c~llg. Chem. 271, 153 (1953). 2. HONEYMAN W. N., J. Phys. Chem. Solids 30, 1935 (1969). 3. BALLESTRACCI R. and BERTAUT F., Bull. Sot. franc. Min. -Crist. 88,575 (1965). 4. JULIEN-POUZOL M., GUITTARD M. and ADOLPHE M. C., Cotnpt. rend. 267,823 (1968). 5. CHENG K. L.,Ana/.Chem.33,761(1961). 6. CHENG K. L., Anal. Chem. 34, 1392 (1962). 7. KOLTHOFF I. M. and ELVING P. J.. Treatise on Analytical Chemistry, Part II, Vol. 7,‘~. 75. John Wiley,New York (1961). 8. SCHAFER H., Chemical Transport Reactions, p. 5. Academic Press, New York (1964). 9. SMAKULA A. and SILS V., Phys. Rev. 99, 1744 (1955). IO. VALDES L., Proc. I.R.E. 42,420 (1954). II. MCLEAN T. P., in Progress in Semiconductors, Vol. 5. D. 73. John Wilev. New York (1960). 12. ALBI&HT G.. R;s. scienf Inifrum 10, 221 (1939). 13. BUSING W. R., MARTIN K. 0. and LEVY H. A., A Fortran Crystallographic Least Squares Program. Oak Ridge National Laboratory, Oak Ridge, Tennessee, Report TM-305 (I 964).

922

J. P. DISMUKES,

R. T. SMITH

14. lntemational Tables for X-Ray Crystallography, Kynoch Press, Birmingham, Vol. III (1962). 15. DAUBEN C. H. and TEMPLETON D. H., Acra crysfallogr. 8,841 (1955). 16. DISMUKES J. P. and WHITE J. G., Inorg. Chem. 3, 1220 (1964). 17. PAULING L., The Narure of rhe Chemical Bond, 3rd Edition, Cornell University Press, Ithaca, N. Y. (1960). 18. BONGERS P. F., VAN BRUGGEN C. F., KOOPSTRA J., OMLOO W. P. F. A. M., WIEGERS G.

19. 20.

21. 22.

and J. G. WHITE

A. and JELLINEK F., J. Phys. Chem. Solids 29, 977 (1968). GORTER E. W., J. SolidState Chem. 1,279 (I 970). BALLESTRACCI R. and BERTAUT E. F., Proceedings of the International Conference on the Thermodynamic, Physical, and Structural Properties of Semimetals, p. 4 I, Centre National de la Recherthe Scientifique, Paris ( 1967). DRESSELHAUS G., Phys. Rev. 105, 135 (1957). AUSTIN I. G., GOODMAN C. H. L. and PENGELLY A. E., J. electrochem. Sot. 103,609 (1956).