First-principles study of the order-disorder transition and its effects on the optoelectronic property of ABiS2 ( A=Na , K)

Using first-principles methods, we have studied structural and electronic properties of ternary sulfide $A\mathrm{Bi}{\mathrm{S}}_{2}$ ($A=\mathrm{Na},\phantom{\rule{0.16em}{0ex}}\mathrm{K}$) compounds for low cost and environmentally friendly optoelectronic applications. We find that the most stable crystal structure of these compounds at low temperature forms a 1 \ifmmode\times\else\texttimes\fi{} 1 rocksalt based ${\mathrm{Bi}}^{3+}$ and ${A}^{+}$ superlattice along the [111] direction. The ordered phase will transform to the disordered phase at high temperature, with the calculated order-disorder transition temperature for $\mathrm{K}\mathrm{Bi}{\mathrm{S}}_{2}$ (${T}_{c}=\ensuremath{\sim}1200\phantom{\rule{0.16em}{0ex}}\mathrm{K}$), higher than that for $\mathrm{Na}\mathrm{Bi}{\mathrm{S}}_{2}$ (${T}_{c}=\ensuremath{\sim}900\phantom{\rule{0.16em}{0ex}}\mathrm{K}$) due to the larger size mismatch between K and Bi than between Na and Bi. The disordered phase has higher optical absorption than the ordered one with the light absorption threshold at 1.33 and 1.57 eV, respectively, for $\mathrm{Na}\mathrm{Bi}{\mathrm{S}}_{2}$ and $\mathrm{K}\mathrm{Bi}{\mathrm{S}}_{2}$. The good agreement between our calculated properties such as x-ray diffraction and light absorption of the partially disordered phase and the experimental observations suggests that the partially disordered phase, instead of the ordered phase, was formed in experimental samples. Our study provides theoretical insights into the order-disorder transition and the corresponding variation of the crystal and electronic structures of rocksalt based $A\mathrm{Bi}{\mathrm{S}}_{2}$ ($A=\mathrm{Na},\phantom{\rule{0.16em}{0ex}}\mathrm{K}$) compounds, which is helpful for future synthesis and applications of these materials.