On the energetics of cation ordering in tungsten-bronze-type oxides

Abstract

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.

Origin of ferroelectric polarization in tetragonal tungsten-bronze-type oxides

“…Based on this, we suggest that Sr 2+ is able to displace inside the A2 channels under application of an electric field, thereby producing an additional dielectric response which creates a diffuse phase transition for Sr-rich SBN. Sr preferentially occupies the A1 sites in SBN [19,43], but for x > 0.40, Sr must also occupy A2 sites. For x > 0.50, the amount of Sr on A2 is high enough for this displacement effect to be appreciable, and we propose that this induces relaxor behavior.…”

“…The nomenclature describes whether the two vacancies are located on pentagonal A2 sites (P) or on square A1 sites (S), as well as the approximate vector between the vacancies ([100] etc.) [19]. Vacancy ordering lowers the symmetry from the aristotype space group P4/mbm to either tetragonal (SS configurations), orthorhombic (PP) or monoclinic (SP) space group symmetries ( Figure 1b).…”

“…Structural data for BN and SN with TTB structure were taken from our previous work [19] where we calculated the high-symmetry paraelectric structures for the ten distinct cation configurations that can be accommodated in a 1 × 1 × 2 supercell of the aristotype unit cell (Figure 1a). The configurations are shown in Figure 1b, along with their space group symmetries [20] and a label indicating the location of the vacancies.…”

“…We study ten different cation-vacancy configurations, and in each case calculate the structural ground state and its associated spontaneous polarization. Based on the behavior of the end members, we discuss how the Sr/Ba ratio affects the properties of SBN, with particular focus on the ferroelectric mechanism and how it is influenced by different A-site cation size.Structural data for BN and SN with TTB structure were taken from our previous work [19] where we calculated the …”

“…Structural data for BN and SN with TTB structure were taken from our previous work [19] where we calculated the…”