The role of the alkali and chalcogen atoms on the stability of the layered chalcogenide $A_2{M}^{II}{M}_3^{IV}{Q}_8$ (A  =  alkali-metal; M  =  metal-cations; Q  =  chalcogen) compounds: a density functional theory investigation within van der Waals corrections

There is a great interest to design two-dimensional (2D) chalcogenide materials, however, our atomistic understanding of the major physical parameters that drive the formation of 2D or three-dimensional (3D) chalcogenides is far from satisfactory, in particular, for complex quaternary systems. To address this problem, we selected a set of quaternary 2D and 3D chalcogenide compounds, namely, ${\text{A}}_2\text{ZnS}{\text{n}}_3{\text{Q}}_8$ (A  =  Li, K, Cs; Q  =  S, Se, Te), which were investigated by density functional theory calculations within van der Waals (vdW) corrections. Employing experimental crystal structures and well designed crystal modifications, we found that the average atomic radius of the alkali-metal, A, and chalcogen, Q, species play a crucial role in the stability of the 2D structures. For example, the 2D structures are energetically favored for smaller $(R<1.5\mathring{\text{A}})$ and larger $(R>1.8\mathring{\text{A}})$ average atomic radius, while 3D structures are favored at intermediate average atomic radius. Those results are explained in terms of strain minimization and Coulomb repulsion of the anionic species in the structure framework. Furthermore, the equilibrium lattice parameters are in excellent agreement with experimental results. Thus, the present insights can help in the design of stable quartenary 2D chalcogenide compounds. (paper)