Empirical Evidence for A‐Site Order in Perovskites

Abstract

Models for composition–structure relationships are useful in both the lab and industry, yet few exist for perovskites-containing extrinsic defects or cation ordering. In this work, an empirical model is used to predict the existence of A-site cation ordering. Specifically, four compositions in the Na(1−3x)/2La(1+x)/2TiO3 system (x = 0.0, 0.0533, 0.1733 and 0.225) were synthesized using a conventional solid-state mixed-oxide method. The structure of the x=0 end-member (Na0.5La0.5TiO3) has been reported in various space groups, but always with a random distribution of Na+ and La3+ on the A site; however, empirical modeling suggests that it is not only ordered but also that a small volume increase accompanies the ordering process. While no evidence of long-range A-site ordering is observed in this composition via X-ray or neutron diffraction, electron-diffraction data indicate short-range ordering of Na+ and La3+ ions, with the degree of cation ordering decreasing (but the scale of ordered domains and degree of vacancy ordering generally increasing) with increasing x. First-principles calculations via density functional theory support both conclusions that short-range ordering in Na0.5La0.5TiO3 is stable and that it results in a volume increase with respect to the disordered analog. A similar analysis has been conducted for the Li(1−3x)/2La(1+x)/2TiO3 and Na(1−3x)/2La(1+x)/2(Mg0.5W0.5)O3 solid solutions. These systems provide additional validation of the accuracy and versatility of the empirical modeling method used

Empirical models for layered A‐site ordering in perovskite titanates

“…The ordering of cations on either A or B sites in a complex perovskite clearly has structural implications. It has also recently been established using this model and verified via both density functional theory (DFT) and Rietveld refinements that, while rock salt ordering of the B site results in a decrease in the unit‐cell volume with respect to the disordered state, A‐site layered ordering can result in an increase in the unit‐cell volume. This counterintuitive expansion was later explained crystalochemically by the fact that ordering in perovskites causes more efficient packing—and so shrinkage— within ordered planes but an expansion of bonds perpendicular to them.…”

“…In addition, the x = 0.2233 composition showed similar ordering. Knapp and Woodward also studied Na 0.5 La 0.5 TiO 3 ( x = 0) and observed no long‐range cation ordering on the A site; however, the NLT system was recently re‐examined by Tolman et al using electron diffraction, and short‐range cation ordering was observed for x = 0 and attributed to the existence of ordered nanodomains, which explains why the ordering is not observed via X‐ray diffraction (XRD). Furthermore, both (Na 0.5 La 0.5 )TiO 3 and (Na 0.5 Tb 0.5 )TiO 3 were later studied via neutron diffraction; and while the latter was observed in orthorhombic space group Pbnm , the former crystallized in trigonal space group R c .…”

“…This result could have implications for functional properties, especially ionic conduction. Specifically, large negative errors (−1% to −2%) in both and , caused by an underestimation of the A–X bond length, are indicative within this model of so‐called layered A‐site ordering . In such systems, errors can be corrected by introducing a Δ r A correction term, which is a way of quantifying the degree of order as a function of composition.…”

“…Interestingly, while no evidence of long‐range A‐site ordering has been observed in the NLT system via x‐ray or neutron diffraction, this model clearly shows the pattern of errors leading to the conclusion of order. In fact, electron diffraction shows that the structure consists of nanodomains of order (short‐range order); thus, even short‐range order can be quantified with this model. Indeed, such regions of short‐range order may be a more common phenomenon than is widely realized, as similar regions have also been found within long‐range disordered spinel and pyrochlore structures.…”

Correlative models for perovskites with rock salt B‐site ordering

“…In other words, bonds which lie in or near the ordering planes will contract whereas those more perpendicular will tend to expand. For this reason, a strong indicator of rock salt B‐site ordering within this model is an overestimation of B‐X bond length, which results in large positive errors (1%‐3%) in both and . In these cases, a negative Δ r B correction term can be introduced to effectively correct for these errors.…”