Relation between the Elastic Constants of the Hexagonal and Cubic Polytypic Modifications of Zinc Sulphide

Abstract

Patrick (2) has assumed that the phonon spectrum in the axial direction is one f the physical properties common to all polytypes. Feldman et al. (3) have reported ie joint dispersion curve for Sic polytypes making use of the above assumption. In ur earlier study (1) we have analysed the joint dispersion curve for silicon carbide olytypes and have established two unique relationships between the elastic constants f the cubic and the hexagonal polytypic modifications. The relations a r e C C C H Cll -C12 + c44 = 3c44 7 C C C H Cll + 2C12 + 4CM = 3 c 33 , rhere the superscripts c and H stand for cubic and hexagonal types. The elastic onstants C44 and CH can be determined by calculating the sound velocity from I'e slopes of the acoustic branches of the dispersion curves. The above two relations an be tested against the calculated values of the elastic constants of hexagonal form I the elastic constants of the cubic form a r e known. Unfortunately in the case of Sic,o experimental data of elastic constants of the cubic form a r e available, hence reourse was taken to theoretical data for the purpose of verification. As the theoretica lastic constants are liable to some uncertainties, the verification of these relations annot be taken to be very decisive. It is, however, possible to verify these relations )r the ZnS polytypes for which the complete precise data needed a r e now available.Very recently Schneider and Kirby (4) have published the joint dispersion curves H 33 )r zinc sulphide polytypes by their measurements of the Raman spectra of 2H and H polytypes. By determining the sound velocity from the slopes of the dispersion urves, we have calculated the elastic constants C and C : 3 which come out to be H 44