Abstract
Deviations of local structure and chemistry from the average crystalline unit cell are increasingly recognized to have a significant influence on the properties of many technologically important materials. Here, we present the vector pair correlation function (vPCF) as a new real-space crystallographic analysis method, which can be applied to atomic-resolution scanning transmission electron microscopy (STEM) images to quantify and analyze structural order/disorder correlations. Our STEM-based vPCFs have several advantages over radial PCFs and/or 3D pair distribution functions from x-ray total scattering: vPCFs explicitly retain crystallographic orientation information, are spatially resolved, can be applied directly on a sublattice basis, and are suitable for any material that can be imaged with STEM. To show the utility of our approach, we measure partial vPCFs in Ba5SmSn3Nb7O30 (BSSN), a tetragonal tungsten bronze (TTB) structured complex oxide. Many TTBs are known to be classical or relaxor ferroelectrics, and these properties have been correlated with the presence of superlattice ordering. BSSN, specifically, exhibits relaxor behavior and an incommensurate structural modulation. From the vPCF data, we observe that, of the cation sites, only the Ba (A2) sublattice is structurally modulated. We then infer the local modulation vector and reveal a marked anisotropy in its correlation length. Finally, short-range correlated polar displacements on the B2 cation sites are observed. This work introduces the vPCF as a powerful real-space crystallography technique, which enables direct, robust quantification of short-to-long range order on a sublattice-specific basis and is applicable to a wide range of complex material types.
Highlights
The manner in which local structure and chemistry deviate from the average crystalline unit cell has a great influence on the properties of many functional materials
We present the vector pair correlation function as a new real-space crystallographic analysis method, which can be applied to atomic-resolution scanning transmission electron microscopy (STEM) images to quantify and analyze structural order/disorder correlations
We present a two-dimensional vector pair correlation function (vPCF) applied to atomic-column locations in a STEM image, in principle, the method could be applied to 3D atomic position data, resulting in a 3D vPCF
Summary
The manner in which local structure and chemistry deviate from the average crystalline unit cell has a great influence on the properties of many functional materials This is true for technologically important material categories, such as classical and relaxor ferroelectrics. These are often fully occupied, though many “unfilled” TTBs exist, which have a large fraction of vacancies, primarily on the A1 sites. Other observed deviations from the high symmetry tetragonal structure result in an orthorhombic unit cell due to symmetry breaking from octahedral tilts, displacements of the A2 sites along the [110] type directions, and a small (4 pm) lattice parameter difference between the a and b axes. In modulated TTBs, the true c lattice parameter is doubled from the prototype cell, primarily as a result of alternating octahedral tilts along that axis. Other observed deviations from the high symmetry tetragonal structure result in an orthorhombic unit cell due to symmetry breaking from octahedral tilts, displacements of the A2 sites along the [110] type directions, and a small (4 pm) lattice parameter difference between the a and b axes.
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