International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. D. ch. 3.3, pp. 411-412

Section 3.3.6.13. BaTiO3 transformation twins

Th. Hahna* and H. Klapperb

a Institut für Kristallographie, Rheinisch–Westfälische Technische Hochschule, D-52056 Aachen, Germany, and bMineralogisch-Petrologisches Institut, Universität Bonn, D-53113 Bonn, Germany
Correspondence e-mail:  hahn@xtal.rwth-aachen.de

3.3.6.13. BaTiO3 transformation twins

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The perovskite family, represented by its well known member BaTiO3, is one of the technically most important groups of dielectric materials, characterized by polar structures which exhibit piezoelectricity, pyroelectricity and, most of all, ferro­electricity.

BaTiO3 is cubic and centrosymmetric (paraelectric) above 393 K. Upon cooling below this temperature it transforms in one step (first-order transformation with small [\Delta H]) into the ferroelectric tetragonal phase with polar space group [P4mm]. This transition is translationengleich of index [[i]=6]. Hence there are domains of six possible orientation states at room temperature. The transformation can be theoretically divided into two steps:

  • (i) Translationengleiche symmetry reduction cubic [Pm{\bar 3}m\,\,\longrightarrow] tetragonal [P4/mmm] of index [[i_1]=3], leading to three sets of ferroelastic `90° domains', related by the (lost) cubic {110} twin mirror planes or the (lost) cubic threefold axes. These three pseudo-merohedral orientation states point with their tetragonal c axes along the three former cube axes [100], [010] and [001], thus including angles of nearly 90°.

  • (ii) Each of these centrosymmetric domains splits into two antiparallel polar ferroelectric `180° domains', whereby the space group [P4/mmm] is translationsgleich reduced to [P4mm] of index [[i_2]=2]. The total index is: [[i]=[i_1]\cdot [i_2]=6].

The beautiful polysynthetic twin structure of BaTiO3 is shown in the colour micrograph Fig. 3.4.1.1[link] in Chapter 3.4[link] of this volume.








































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