addenda and errata\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

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The transformation matrices (distortion, orientation, correspondence), their continuous forms and their variants. Corrigenda

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aLaboratory of ThermoMechanical Metallurgy (LMTM), PX Group Chair, Ecole Polytechnique Fédérale de Lausanne (EPFL), Rue de la Maladière, 71b, Neuchâtel, 2000, Switzerland
*Correspondence e-mail: cyril.cayron@epfl.ch

Edited by A. Altomare, Institute of Crystallography - CNR, Bari, Italy (Received 7 June 2019; accepted 28 June 2019; online 30 August 2019)

Appendices B4 and B5 of Cayron [Acta Cryst. (2019), A75, 411–437] contain equations involving the point group and the metric tensor in which the equality symbol should be substituted by the inclusion symbol.

In Appendices B4 and B5 of Cayron (2019[Cayron, C. (2019). Acta Cryst. A75, 411-437.]), we confused different notations related to the point groups, Laue groups and lattice groups. We denote the point group by [{\bb G}] and the metric tensor by [{\cal M}]. As the symmetries preserve the norms and the angles, it is correct to write that [{g^{\rm{t}}}{\cal M}g = {\cal M}] for any symmetry matrix g. However, the reciprocal is not always true. For example, a non-centrosymmetric crystal has its metric preserved by the inversion, but the inversion is not an element of [{\bb G}]. Consequently, equation (53)[link] is incorrect and should be substituted by

[{\bb G}\subseteq \{g \in \pm {\rm SL}(N, {\bb Z}), g^{\rm t}{\cal M}g={\cal M}\}.\eqno(53)]

Equation (55) should also be modified by replacing the first equals sign in each line by ` [\subseteq] ', and equation (56) no longer holds. The confusion is inexcusable, but fortunately it does not affect all the other results presented in the paper.

Note: there is also a typographical error in Section 7.7. The lattice parameter [{a^{\gamma }}] should not appear in the value of the shear amplitude: s = [(1/ r) - r ].

References

First citationCayron, C. (2019). Acta Cryst. A75, 411–437.  CrossRef IUCr Journals Google Scholar

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