Because of their unique properties, the 111-V substitutional alloys have become firmly established as useful semiconductors whose field of applications is constantly widening /l/. The thermodynamic properties of those alloys a r e generally
A calculation of many physical properties of crystals requires the integration of the corresponding properties over the Brillouin zone. Examples include calculations of the valence electron charge density in solids, the total crystal energy, the selfconsistent crystalline potential, etc. The important method of integration has been introduced by Baldereschi /1/ and developed by Cohen et al. /2 to 4/. These authors have shown that the sum over a large number of uniformly distributed points in the Brillouin zone can be approximated quite well by using a very small number of carefully chosen representative points. Phillips /5/ has argued that these points may have physical significance over and above their mathematical significance a s "meanvalue" points.
,The formalism required to derive the Baldereschi points is a s follows. We denote by f( k) the periodic function whose integral is of interest, and express this integral a s the Brillouin-zone volume times the average value of f ( k):
Internal Strain Parameter in Diamond-Type Crystals BY V.K. BASHENOV, D.I. MARVAKW, andA.M. MUTALWhen a crystal lattice is macroscopically strained, there is a relative displacement between the sublattices which is linear with macroscopic strain /l/.In diamond-type crystals this sublattice displacement can be described in terms of a single quantity, the internal strain parameter c , which is the ratio of the internal base strains with and without noncentral forces /2/. It has been pointed out /3/ that a direct measurement of 0 would be extremely difficult so that one must rely on theoretical values only.There are several attempts to calculate the internal strain parameters for crystals having diamond o r zincblende structure /4 to 6 / . Keating /4/ has considered this problem using the method of homogeneous strain. A suitable form of the strain energy density for a diatomic crystal is given by 4 , whereC! is the unit cell volume, Bmnmlnl a r e the short-range force constants, and crystal C si Ge Sn K 9 J a. B if t P /a "1 T # O r=o ; y # O r=o 130.4 84.8 -0.33 0.213 0.208 0.650 0.655 49.4 13.8 -0.31 0.565 0.557 0.279 0.285 53 3 11.6 -4.59 0.666 0.546 0.217 0.294 56.3 6.44 -10.3 0 . 8 2 4 /5/ R.M. MARTIN, Phys. Rev. B 1, 4005 (1970). / 6 / P. LAWAETZ, phys. stat. sol. (b) 57, 535 (1973). /7/ K. KUNC, M. BALKANSKI, and M.A. NUSIMOVICI, phys. stat. sol. (b) 7 % 229 (1975). /8/ A . SEGMULLER and H . R . NEYER, Phys. kondens. Mater. 4, 63 (1965).
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