Ab initio heat capacity and atomic temperature factors of chalcopyrites

Using first-principles calculations and phonon direct method, thermodynamical properties such as heat capacities and anisotropic and isotropic temperature factors as well as temperature dependence of characteristic Debye temperatures of $\mathrm{Ag}\mathrm{Ga}{\mathrm{S}}_2$, $\mathrm{Ag}\mathrm{Ga}{\mathrm{Se}}_2$, $\mathrm{Ag}\mathrm{Ga}{\mathrm{Te}}_2$, $\mathrm{Cu}\mathrm{In}{\mathrm{S}}_2$, $\mathrm{Cu}\mathrm{In}{\mathrm{Se}}_2$, and $\mathrm{Zn}\mathrm{Sn}{\mathrm{P}}_2$ chalcopyrite compounds have been calculated in harmonic approximation. Obtained results agree quite well with available experimental data taken from literature. From comparison of heat capacities calculated at constant volumes with those measured at constant pressures, we estimate temperature range of harmonic approximation applicability.

Figure 1

(Color online) Calculated (solid line) heat capacity of $\mathrm{Cu}\mathrm{In}{\mathrm{S}}_2$. The experimental data are taken from Ref. 30 (filled squares) and Ref. 31 (open circles). Inset: low-temperature range.

Figure 2

(Color online) Comparison of heat capacity calculated for $\mathrm{Ag}\mathrm{Ga}{\mathrm{S}}_2$ with experimental data taken from Ref. 30 (filled squares), Ref. 7 (open circles), and Ref. 8 (dashed line). Inset: low-temperature range.

Figure 3

(Color online) Comparison of experimental [open circles (Ref. 9) and dashed line (Ref. 8)] $C_p$ of $\mathrm{Ag}\mathrm{Ga}{\mathrm{Se}}_2$ with calculated $C_{Vh}$ (solid line) and fitted $C_p$ (dotted line) using relation (8).

Figure 4

(Color online) Calculated elastic Debye temperatures for $\mathrm{Ag}\mathrm{Ga}{\mathrm{S}}_2$ (circles), $\mathrm{Ag}\mathrm{Ga}{\mathrm{Se}}_2$ (squares), $\mathrm{Ag}\mathrm{Ga}{\mathrm{Te}}_2$ (diamonds), $\mathrm{Cu}\mathrm{In}{\mathrm{S}}_2$ (up triangles), $\mathrm{Cu}\mathrm{In}{\mathrm{Se}}_2$ (left triangles), and $\mathrm{Zn}\mathrm{Sn}{\mathrm{P}}_2$ (down triangles).

Figure 5

(Color online) Temperature dependence of elastic Debye temperature of $\mathrm{Ag}\mathrm{Ga}{\mathrm{S}}_2$. Experimental data (filled squares) are taken from Ref. 30.

Figure 6

(Color online) Temperature dependence of elastic Debye temperature of $\mathrm{Cu}\mathrm{In}{\mathrm{S}}_2$. Experimental data (filled circles) are taken from Ref. 30.