Neutron Total Scattering Studies of Group II Titanates (ATiO3, A2+ = Mg, Ca, Sr, Ba)

Abstract

neutron total scattering measurements were conducted on Mgtio 3 , catio 3 , Srtio 3 , and Batio 3 to simultaneously investigate the local and average structure of these materials. the local structures of Mgtio 3 , catio 3 , and Srtio 3 were well modelled using the refined average structural models: trigonal R3, orthorhombic Pbnm, and cubic Pm3m respectively. However the local structure for Batio 3 , at both temperatures where the average structure is orthorhombic Amm2 and tetragonal P4mm, was best described by the rhombohedral R3m model. only the R3m model was able to account for the observed displacement of titanium in the [111] direction. Furthermore, box-car type refinements were conducted. These refinements show that the coherence length of the rhombohedral distortion is around 10 Å, at larger r-ranges the local distortions become misaligned and average out to Amm2 and P4mm.

Effect of Ligand Polarity on the Internal Dipoles and Ferroelectric Distortion in BaTiO3 Nanocubes

“…Figure 3 and Figure S7 compare the refinement results of variable r ‐range refinements and phase dominant regimes for bulk BaTiO 3 and the differently sized nanoparticles in this study. For the bulk, the R 3 m structure model fits the data best below 9 Å (approximately the length of two unit cells), which is consistent with the 10 Å coherence length of local rhombohedral distortions previously ascribed to order‐disorder behavior in bulk BaTiO 3 [4b,15] . The calculated R wp difference in Figure 3(a) confirms the P 4 mm structure provides the best description at higher r max in bulk, as expected.…”

“…This suggests that nanoparticle size stabilizes increased dipole‐dipole correlation, in this case resulting in Amm 2‐like coherence at intermediate (several nanometers) length‐scales. This is a marked departure from the more directionally‐averaged dipole‐dipole correlations manifest in the intermediate length‐scale P 4 mm structure of the bulk phase [15] …”

Total scattering and the pair distribution function in crystallography

“…To account for this in scenarios where the local structure is very different from the average and where the PDF fit is only effective over a limited range of pair distances, PDFgui can be used to fit the data over different r-ranges or over a rolling small range of distances (a "box-car" compromise approach) to show how the local structure slowly morphs into the average (e.g. [120,141]).…”

“…RMCProfile is more demanding in terms of the data and the time and effort required to obtain good results, but is more generally applicable. Increasingly general Rietveld refinement codes will offer PDF fitting options, indeed they are already available within the TOPAS software [182] (see [141] where TOPAS was used for Rietveld refinement of the Bragg powder pattern and for small-box modelling of the PDF) and may soon be incorporated within GSAS-II [183], the modern incarnation of the original GSAS-EXPGUI [98,99] version of Rietveld refinement software; RMCProfile has very recently been made available from within GSAS-II [184]. The RMCProfile code has also recently been optimised for speed in order to increase the size of models that can be refined [175] as has the related EPSR code for liquid and amorphous materials [44].…”

Recovery of harmonic-like behaviour of the polar mode in BaTiO$_3$ at high pressure

“…Clearly, the investigation of the temperature-induced phase transitions of BaTiO 3 has been extensive, and a wide range of techniques have been utilised to investigate the average and local structure of the perovskite material 19 . However, challenges associated with in situ high pressure measurements have perhaps limited investigation of the local structure of BaTiO 3 in other regions of the phase diagram.…”