Investigating solid solutions: Geometric transformations triggered by germanium incorporation in Cu2ZnGexSn1−xS4

Abstract

Through experimental exploration, diverse phases—tetragonal and orthorhombic—have been observed within the Cu2ZnGexSn1−xS4 region (0 ≤ x ≤ 1), hinting at potential miscibility gaps. To complement these findings, our computational investigation, employing density functional theory (DFT), delves into the Ge substitution-induced phase transition in Cu2ZnGexSn1−xS4. Contrary to a single-phase behavior, our FP-LAPW at zero temperature results reveal a compelling shift from stannite (Sn-rich) to Wurtzite-Stannite (Ge-rich) at xGe ≈ 80%. Negative enthalpy of formation values indicates the inherent stability of these structures. The calculations reveal an estimated 8.884 meV per atom difference in enthalpies of formation between the Stannite and Wurtzite-Stannite phases for Cu2ZnSnS4. For Cu2ZnGeS4, the Wurtzite-Stannite structure emerges as the most stable, closely trailed by the Stannite structure, with enthalpies of formation at − 4.833 eV·atom−1 and − 4.804 eV·atom−1, respectively. Furthermore, our quasi-harmonic Debye model facilitates the analysis of phase transitions triggered by the introduction of germanium. This is achieved by calculating the Gibbs energy, which remains unaffected by variations in temperature and pressure. As the tin cation is replaced by the smaller germanium cation, there is an observable decrease in the cell parameters. The corresponding reduction in cell volume adheres to the principles of Vegard's Law. Exploring the behavior of these materials in diverse conditions can significantly contribute to enhancing the performance and stability of devices built upon Cu2ZnGexSn1−xS4.