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

International Tables for Crystallography (2013). Vol. D, ch. 3.4, p. 535


V. Janoveca* and J. Přívratskáb

aInstitute of Physics, Academy of Sciences of the Czech Republic, Na Slovance 2, CZ-18221 Prague 8, Czech Republic, and bDepartment of Mathematics and Didactics of Mathematics, Technical University of Liberec, Hálkova 6, 461 17 Liberec 1, Czech Republic
Correspondence e-mail:


Transmission electron microscopy (TEM) image of the incommensurate triangular ([3-q] modulated) phase of quartz. The black and white triangles correspond to domains with domain states [{\bf S}_1] and [{\bf S}_2 ], and the transition regions between black and white areas to domain walls (discommensurations). For a domain wall of a certain orientation there are no reversed domain walls with the same orientation but reversed order of black and white; the walls are, therefore, non-reversible. Domain walls in regions with regular triangular structures are related by 120 and 240° rotations about the z direction and carry parallel spontaneous polarizations (see text). Triangular structures in two regions (blocks) with different orientations of the triangles are related e.g. by [2_x] and carry, therefore, antiparallel spontaneous polarizations and behave macroscopically as two ferroelectric domains with antiparallel spontaneous polarization. Courtesy of E. Snoeck, CEMES, Toulouse and P. Saint-Grégoire, Université de Toulon.