International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

© International Union of Crystallography 2006
International Tables for Crystallography (2006). Vol. C. ch. 9.8, p. 912

Section 9.8.1.4.4. Generalized nomenclature

T. Janssen,a A. Janner,a A. Looijenga-Vosb and P. M. de Wolffc‡

a Institute for Theoretical Physics, University of Nijmegen, Toernooiveld, NL-6525 ED Nijmegen, The Netherlands,bRoland Holstlaan 908, NL-2624 JK Delft, The Netherlands, and cMeermanstraat 126, 2614 AM, Delft, The Netherlands

9.8.1.4.4. Generalized nomenclature

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In Section 9.8.4[link], the theory is extended to structures containing d modulations, with [d \, \ge \, 1]. In this case, each point-group transformation in internal space is given by [R_I] and the associated internal translation by the (d-dimensional) vector [{\bf v}_I]. Thus, [g_s=\{(R,R_I)|({\bf v},{\bf v}_I)\}.]The transformations R and [R_I] are represented by the matrices [\Gamma_E(R)] and [\Gamma_I(R)], respectively. In the following discussion, this nomenclature (but with vI rather than vI) is sometimes also applied for the (3 + 1)-dimensional case. The usual formulae are obtained by replacing RI by ɛ and vI by Δ.








































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