J. Appl. Cryst. (2000). 33, 909±914 M. Geday et al.  Birefringence imaging 909 research papers Journal of Applied Crystallography ISSN 0021-8898 Received 12 November 1999 Accepted 14 February 2000 # 2000 International Union of Crystallography Printed in Great Britain ± all rights reserved Birefringence imaging of phase transitions: application to Na 0.5 Bi 0.5 TiO 3 M. Geday, a J. Kreisel, a A. M. Glazer a *² and K. Roleder b a Physics Department, Clarendon Laboratory, University of Oxford, Parks Rd, Oxford OX1 3PU, England, and b Institute of Physics, Silesian University, Uniwersytecka 4, 40-007 Katowice, Poland. Correspondence e-mail: glazer@physics.ox.ac.uk In recent years a number of imaging techniques to determine the optical properties of materials, either in re¯ection or in transmission, have been developed. Here the use of an imaging version of the so-called rotating-polarizer method in the study of phase transformations in crystals is demonstrated. This method creates false-coloured images representing the light transmission I 0 , the extinction angle ' (orientation of the optical indicatrix) and |sin |, a function of the retardation resulting from the birefringence (and a measure of the magnitude of optical anisotropy). When combined with a computer-controlled heating stage, this method provides an opportunity to create separate moving images of orientation and magnitude of optical anisotropy, showing the dynamics of twinning and domain-wall behaviour during temperature changes. It is believed that this is the ®rst time that quantitative imaging of changes in birefringence has been used in this way to describe phase transitions. Two-phase transitions in a crystal of Na 0.5 Bi 0.5 TiO 3 (NBT) are presented as examples of the use of the system. 1. Introduction The study of phase transitions is an important ®eld of condensed-matter physics, not only in its own right, but also for its importance in industrial applications. Consequently, reliable methods to characterize phase transitions are of interest. Observation by eye of the birefringence of crystals in a polarizing microscope has for a long time been known to be an ef®cient technique for identifying twins and their associated domain walls. However, recently the increase in computer power and the development of charge-coupled device (CCD) cameras have allowed collection of microscope images and their analysis to be carried out rapidly. A limited number of methods for doing this both qualitatively and quantitatively have been developed, such as that by Oldenbourg & Mei (1995) and the microscope imaging system developed by Glazer et al. (1996). The aim of the present work is to illustrate the versatility and use of this imaging technique in phase- transition studies by taking as an example Na 0.5 Bi 0.5 TiO 3 (NBT). NBT is an extremely rare type of perovskite because it is a compound, i.e. it has a chemical formula with its constituents in ®xed stoichiometric ratios, in which there is a 50:50 substi- tution at the A site of the structure. It therefore occupies a rare niche in the wide and important ®eld of perovskite structural science. NBT was discovered by Smolenskii et al. (1961) and many of its structural and dielectric characteristics have been investigated (e.g. Suchanicz & Ptak, 1990; Suchanicz & Kwapulinski, 1995; Tu et al., 1994). There is considerable disagreement in the literature as to the structures of the different phases and the exact nature of their transitions. Before the present work, the consensus was that below 473 K NBT is found in a ferroelectric rhombohedral phase and becomes cubic above 803 K. Between these temperatures, a coexistence of phases with tetragonal and rhombohedral symmetry has been reported (e.g. Suchanicz & Kwapulinski, 1995). It is worth noting that below 543±553 K, polar prop- erties have been observed. In recent work by Jones & Thomas (2000) it has been con®rmed that the material undergoes a phase transition from phase III with rhombohedral symmetry (R3c) to phase II with tetragonal symmetry (P4bm) and then to the high-tempera- ture cubic prototype phase I of symmetry Pm3 Å m. The phases in the nomenclature of Tole  dano et al. (1998) are given by: III | <573 K | R3c (161) | Z = 6 | ferroic | four ferroelectric, four ferroelastic variants; II | 413±833 K | P4bm (100) | Z = 2 | ferroic | three ferro- electric, three ferroelastic variants; I | >803 K | Pm3 Å m (221) | Z = 1 | non-ferroic | paraelectric, paraelastic. The temperatures listed here are those found in the present work. Phase III is characterized by having [111] p cation displacements (where the subscript p refers to pseudo-cubic ² Also af®liated to Oxford Cryosystems, 3 Blenheim Of®ce Park, Lower Road, Long Hanborough, OX8 8LN, England.