Role of dimensionality on thermodynamic properties in layered sulfides

Understanding thermal expansion of materials helps in assessing the capability, performance, and lifetime of materials operating in variable thermal conditions. Previously Ca₃Ti₂O₇ with the layered Ruddlesden-Popper (RP) structure (n=2 member of A_n+1B_nO_3n+1) was found to exhibit pressure-tunable negative thermal expansion (NTE) and a pressure-independent softening of the bulk modulus due to a quasi-two-dimensional vibration [Huang et al, Phys. Rev. Lett. 117, 115901 (2016)], whereas RP strontium titanates did not exhibit NTE [Huang et al, Chem. Mater. 30, 7100 (2018)]. Here, we evaluate structural, lattice dynamical, and thermodynamic properties of the barium zirconium sulfide family with layer thickness n=1,2, and ∞ using the self-consistent quasi-harmonic approximation within density functional theory. We formulate layer thickness dependent models of the anharmonic lattice properties and discuss how they may be used for design of thermal expansion coefficients in other chemistries.