Direct mapping of spatially modulated octahedral tilting and coupled in-plane strain in the (3+2)-D modulated, Li1/2-3xNd1/2+xTiO3 system and its underlying crystal chemistry

R. Withers1, Y. Zhu2, L. Bourgeois2, C. Dwyer2, J. Etheridge2

1Research School of Chemistry, The Australian National University, Canberra, Australia

2Monash Centre for Electron Microscopy (MCEM) and Department of Materials Engineering, Monash University, Melbourne, Australia.

Ray.Withers@anu.edu.au

A remarkably complex, typically long period, (3+2)-dimensional, incommensurately modulated structure occurs in the layered perovskite, Li1/2-3xNd1/2+xTiO3 (LNT), ~0.02 <= x <= ~0.12, solid solution system [1-3]. The metric symmetry and typically long period of the overall structure is compositionally dependent (i.e. dependent upon x) with e.g. tetragonal metric symmetry and, on average, ~ 27-28ap x ~27-28bp basal plane, parent perovskite (subscript p) unit cell dimensions at low x (= 0.04) by comparison with orthorhombic metric symmetry and ~ 20ap  ~13bp  repeat dimensions at high x (= 0.095). The overall structure at any one composition appears to result primarily from competition between 00c+ and a-a-c0 tilting of TiO6 octahedra (in Glazer notation), leading to spatially variable a-b-c+ octahedral tilting and parent perovskite unit cell shape and size.

In this contribution, a special atomic-resolution BF-STEM imaging condition is used to quantitatively measure the spatially modulated 00c+ component of the oxygen octahedral tilting in LNT, parent unit cell by unit cell. A rigorous dynamical calculation is used to determine detector collection angles that filter out the heavy Nd columns and enable TiO6 octahedra to be imaged sensitively and robustly over a large range of specimen thicknesses, up to 150 nm. Using these calculations, the image of each octahedral column can be converted to a direct measurement of the corresponding octahedral-tilt angle (see Fig.1).

Figure 1. A quantitative mapping of the magnitude of the spatially modulated 00c+ octahedral tilt angle for an LNT, x = 0.04 sample.

 

In this way, the [001] octahedral-tilt angles in LNT, for x = 0.04 and 0.095 samples, have been quantitatively mapped and the mathematical equations in superspace describing the 2D ordered octahedral tilt pattern determined as well as the absolute magnitude of the maximum [001] octahedral-tilt angle. In this manner, it is shown that the x = 0.04 sample requires higher order modulation wave harmonics in order to fit the observed anharmonic octahedral tilt distributions whereas the x = 0.095 sample can be adequately described by only first order harmonic terms.

Simultaneously, the heavy atom positions have been imaged and measured using conventional annular dark-field (ADF) STEM, enabling us to correlate, cell-by-cell, changes in local parent perovskite lattice parameters with octahedral tilting and, in turn, with the overall superstructure. The observed strain variation is found to be surprisingly large (~ 2-3%) and largely localised to within 2 parent unit cells of the octahedral tilt twin boundaries associated with the a-b- octahedral tilting.

Bond valence sum calculations were also carried out using the recently reported average and modulated crystal structures of an x = 0.1167 sample [3] to investigate the local crystal chemistry of LNT. Remarkably, it is found that the stabilising drop in the square of the global instability index, GII2, associated with a0a0c+ tilting is almost the same as it is for and a-a-c0 tilting strongly suggesting that the origin of the overall LNT modulated structure is indeed the competition between a0a0c+ and  a-a-c0 tilting.

1. A. D. Robertson, S. Garcia-Martin, A. Coats, A. R. West, J. Mater. Chem., 5(9), (1995), 1405.

2. R. L. Withers, L. Bourgeois, A. Snashall, Y. Liu, L. Norén, C. Dwyer, J. Etheridge, Chem. Materials, 25, (2013), 190.

3. A. M. Abakumov, R. Erni, A. A. Tsirlin, M. D. Rossell, D. Batuk, G. NĂ©nert, G van Tendeloo, Chem. Materials, 25, (2013), 2670.