, Volume 158, Issue 4, pp 471-482

Lattice vibrations and specific heat of zinc blende

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The dispersion relations, frequency distribution function and specific heat of zinc blende have been calculated usingHouston's method on (1) A short range force (S. R.) model of the type employed in diamond bySmith and (2) A long range model assuming an effective charge Ze on the ions. Since the elastic constant data on ZnS are not in agreement with one another the following values were used in these calculations:

$$C_{11} = 10.78; C_{12} = 6.87 and C_{44} = 3.87 in 10^{11} dynes/cm^2 $$
. As compared to the results on the S. R. model, the Coulomb force causes 1. A splitting of the optical branches at (000) and a larger dispersion of these branches; 2. A rise in the acoustic frequency branches the effect being predominant in a transverse acoustic branch along [110]; 3. A bridging of the gap of forbidden frequencies in the S. R. model; 4. A reduction of the moments of the frequency distribution function and 5. A flattening of theΘ- T curve. By plotting (Θ/Θ0) vs.T., the experimental data ofMartin andClusius andHarteck are found to be in perfect coincidence with the curve for the short range model. The values of the elastic constants deduced from the ratio Θ0 (Theor)/Θ0 (Expt) agree with those ofPrince andWooster. This is surprising as several lines of evidence indicate that the bond in zinc blende is partly covalent and partly ionic. The conclusion is inescapable that the effective charge in ZnS is a function of the wave vector\(\vec k\).