phys. stat. sol. (a) 14, 839 (1972)

Subject classification: 1.1 and 8; 22.8

Solid State Physics Laboratory, Delhi

Variation of Lattice Parameter with Temperature and Thermal Expansion of the Compound Cu,SnSe,

BY B. B. SHARMA and F. R. CIIAVADA

The temperature variation of the lattice parameter of the compound Cu,SnSe, has been studied in the temperature range 30 to 600 "C by X-ray diffraction methods. The linear cmfficient of thermal expansion a t room temperature (30 "C) is 20.4 X deg-J and it is found to decrease with increasing teniperature.

Die Temperaturanderung des Gitterparameters der Verbindung Cu,SnSe, wurde irn 'l'emperaturbereich 30 bis 600 "C durch Rontgenstrahlenbeugungsmethoden untersucht. 1 )er lineare Koeffizient der thermischen Ausdehnung bei Zimmertemperatur (30 "C) betragt 20,4 x grd-1 und nimmt mit steiqender Temperatur ab.

1. Introduction Cu,SnSe, belongs to a group of compounds represented by the general formula

.\fBIVCT1 (superscripts denote group in the periodic table and subscripts the iiumber of atoms). These compounds are ternary analogues of I V group elements having tetrahedral bonding [l]. I n an earlier paper [a] we reported the tempera- ture variation of lattice parameters for another compound, Cu,GeSe,, belonging t o the same group. In this communication we report some results of latticc Itaremeter measurements for Cu,SnSe, in the temperature range 30 to 600 "C.

This compound is known to have a sphalerite type lattice but there is some tlixcrepancy in the reported values of the lattice constant [3, 41. The value of the thermal expansion coefficient a obtained in the present experiment by X-ray diffraction methods is much larger as compared to the reported [ 5 , G ] \ alue obtained by dilatometric methods.

2. Experimental The compound was synthesized from spectroscopically pure elements ob-

tirined from Johnson-Matthey UK. The constituent elements taken in stoichio- nictric ratio were sealed in an evacuated (pressure Torr) quartz capsule nhich was kept a t 1000 "C for 6 h with a continuous vibration mixing arrange- incwt. The ingot obtained after cooling the melt was cut and polished. A micro- wopic examination of the polsihed surface and microhardness test a t different places confirmed that the material is single phase. The microhardness number obtained with a PMT-3 (Russian) instrument is (250 f 10) kp/mm2. This is in good agreement with [ 7 ] . A cooling curve was also drawn and it gavc a sharp freezing point a t 694 "C, in agreement with 141.

For X-ray powder diffraction work a part of the ingot was powdered and passed through a 400 mesh sieve. This powder was annealed at 350 "C for 11)0 h. The lattice constant at room temperature was obtained using a 114.46 mm

640 B. B. SHAHMA and F. K. CHAVADA

diameter Debye-Scherrer camera employing asymmetric mount>ing of the film. High temperature work was done on a 19 cm diameter Unicam camera. The procedure followed for temperature measurement was the same as described earlier [ 2 ] . All experiments were performed with CuK, radiation.

3. Besults

The line quality in the high-angle region of the powder pattern was not very good. Even at room temperature only one a1 a,-doublet occurring at 75" Bragg anlge could be resolved. With increasing temperature the line quality rapidly deteriorated and no line beyond 60" Bragg angle could be measured above 200°C'.

All thelines could be indexed on the base of a cubic unit cell with a = (5.6877 & 1 2 ) A. The lattice parameters were calculated by least squares analysis using all lines beyond 30" Bragg angle. The extrapolation function used was

The probable error in the lattice parameter was estimated in the following way. All the Bragg angles were corrected using the value of the drift constant obtained from least squares analysis. The lattice parameter was then obtained from each individual powder line. The standard deviation of these lattice param- eter values from that obtained from least squares analysis was taken as a measure of the probable error.

Fig. 1 shows a plot of lattice parameter values against temperature. The estimated error has been shown by arrow marks. The observed points in Fig. 1 were fitted to a parabolic curve, equation (l), by least squares analysis :

a7' = 5.6851 (1 + 2.083 x 2' - 6.922 x T2) , (1)

where aT is the lattice parameter a t T "C. The curve in Fig. 1 is actually a plot of equation ( I ) . The linear coefficient of thermal expansion at different tem- peratures was obtained from the relation ciT = (daT/dT)/aT by differentiating equation (1). Fig. 2 shows a plot of 0: versus temperature. The values of latticc

57% I

0 200 400 600 T PCl -

Fig. 1. Variation of lattice coiint~ant a with temperaturc Fig. 2. Variation of a with tenrperaturr

Variation of Lattice Paramet'er with Temperature on Cii,SnSe, 64 1

Fin. 3. Variatioii of unit ccll roliinie with temperature

parameter a and thermal expansion coefficient at room temperature (30 "C) are given below :

a = (5.6877 f 2 ) A ,

= 20.4 x 10-6deg-1.

The reported value of LX determined from dilatometric measurements [5, 61 is 8.9 x 10-6deg-1.

4. Discussion

The results of the present study on Cu,SnSe, are similar to those obtained varlier for Cu,GeSe, [2]. I n both cases LY falls with increasing temperature. For 1 he sake of comparison, the unit-cell volumes of the two compounds (it may be recalled that Cu,GeSe, has a tetragonal symmetry while Cu,SnSe, is cubic) have been plotted as functions of temperature in Fig. 3. The data for Ch,GeSe, have been taken from our earlier work [ 2 ] . I n case of Cu,GeSe,, the decrease of LX with incrcasing temperature was attributed to the possible existence of a superstruc- ture in the lattice, a fact which has since been confirmed [8]. I n the case of ( h,SnSe, also a superstructure has been reported [3] but we did not observe any buperstructure lines in the powder photographs even after prolonged exposures. The density measurements show that the cubic unit cell with a = 5.6877 A con- tains four units with the formula 1/3 (Cu,SnSe,), indicating random distribution of Cu and Sn atoms. Normally 0; is expected t o increase with temperature bc- cause of the increased lattice anharmonicity. However, in many simple tetrahe- dral compounds and elements o, is known to behave anomalously [9] especially a t low temperatures. The ternary compounds investigated by us, also have tetra- hedral bonding but present a very complicated system for theoretical analysis, especially in the absence of sufficient experimental data on their thermal and elastic properties.

No convincing explanation could be found for the very large diference be- t ween the values of LY obtained from X-ray diffraction methods and the values obtained from dilatometric methods reported earlier. A similar discrepancy was reported earlier for Cu,GeSe, [ Z ] .

Arkwo u-ledgemen ts

We are very grateful t o Dr. V. V. Agashe and Dr. A . I<. Sreedhar for many valuable suggestions and to Mr. Hari Singh for his help in measurements. We also express our sincere gratitude to the Director of the Solid State Physics Laboratory for his encouragement during the work and permission to publish it.

6-42 B. B. SHARMA and F. R. CHAVADA: Vttriation of Lattice Parameter

Referoncos

[l] N . A. GORYUNOVA, Chemistry of Dianiond Like Semiconductors, Chapman and Hall,

121 B. B. SHARnL4, phys. stat. sol. (a) 2, K13 (1970). Ltd.. 1965.

[ 3 ] W. €3. PEARSON, Hand Book of Lattice Spacings and Structure of Metals and Alloys,

141 G. K. AVERKIEVA et. al., Soviet Research in New Semiconductiiig Materials, Ed.

[5] 1,. I. BEKGER and A. E. BALENSKAYA, Soviet Phys. - Solid State 6, 1023 (1964). 161 K. A. ANNAMARIEDOV et. a1 ., Chemical Bonds in Semiconductors and Thermodynamics,

171 K. HIHONO and M. KONO, Japan. J. appl. Phys. 7, 54 (1968). [ X I E. PARTIIE and J. GARIX, Monatshefte fur Chemie 102, 1197 (1971). [9] S. I. h’OVrKoV.4. Semiconductors and Semimetals, Vol. 2, Ed. R. K. \VILLARDSOK and

Vol. 2, Pergamon Press, London 1967 (p. 886).

D. N. XASLEDOV and N. A. GORYUNOVA, Consultants Bureau, 1965 (p. 26).

Ed. N. N. SIROTA, Consultants Bureau, 1968 (p. 240).

=\. C. BF~ER, Academic Press, London 1966 (p. 33).

(Received August 18, 1072)