On the energetics of cation ordering in tungsten-bronze-type oxidesElectronic supplementary information (ESI) available: Derivation of thermodynamic equations, energetics data in tabular form and data on crystal structures. See DOI: 10.1039/c5cp05119c

Oxides with the tetragonal tungsten bronze (TTB) structure are well-known ferroelectrics that show a large flexibility both with respect to chemical composition and cation ordering. Two of the simplest compounds in this family are lead metaniobate (PbNb 2 O 6 or PN) and strontium barium niobate (Sr x Ba 1− x Nb 2 O 6 or SBN). While PN is a classical ferroelectric, SBN goes from ferroelectric to relaxor-like with increasing Sr content, with a polar direction different from that in PN. The partially occupied sublattices in both systems give the possibility for cation order-disorder phenomena, but it is not known if or how this influences the polarization and ferroelectricity. Here, we use density functional theory (DFT) calculations to investigate how cation and cation vacancy ordering influences the energetics of these compounds, by comparing both the energy differences and the barriers for transition between different cation configurations. We extend the thermodynamic model of O'Neill and Navrotsky, originally developed for cation interchange in spinels, to describe the order-disorder phenomenology in TTB oxides. The influence of order-disorder processes on the functional properties of PN and SBN is discussed. The energetics of order-disorder of cations in tungsten-bronze-type oxides investigated by ab initio calculations and thermodynamic modelling.