Low-Temperature Thermal Expansion of Zinc Oxide. Vibrations in Zinc Oxide and Sphalerite Zinc Sulfide

New measurements of the linear thermal-expansion coefficients α_∥ and α_⊥ in the c and a crystallographic axis directions of ZnO are reported between 90 and 260 ^∘{}K. Gr\"uneisen parameters γ_∥ and γ_⊥, defined for strain coordinates parallel and perpendicular to the c axis, respectively, have been calculated from the present thermal-expansion coefficients and related data. Similar calculations have been performed for ZnS, with modifications appropriate to cubic symmetry, using earlier experimental results for specific heat, thermal expansion, and elastic constants. The Gr\"uneisen parameters fall from positive values at room temperature to negative values at low temperatures, and in the case of zinc oxide, interpolation has been employed to obtain the mean low-temperature limiting value of γ₀ calculated from the pressure dependence of the elastic constants. A quasiharmonic approximation has been applied to calculate the characteristic temperatures θ(n) corresponding to the maximum frequencies ωD(n) of the Debye distributions having the same nth moments 〈ωⁿ〉 as the specimens for -3<~n<~6. In the case of zinc oxide, the similarity of the dimensional dependences of the moments, defined by γ(n)=ΣγⱼωⱼⁿΣωⱼⁿ corresponding to γ_∥(n) and γ_⊥(n), indicates a low degree of crystal anisotropy, while their variations with n suggest that transverse modes of vibration predominate among the low-frequency modes, and longitudinal modes predominate among the high-frequency modes. The account concludes with calculations of the rms displacements of the atoms in both compounds considered as functions of temperature between 0 and 300 ^∘{}K.