W0190

Constraints and Caveats on Tensor Coefficients for Bulk Physical Properties. Yvon Le Page¹, John S. Tse¹, Dennis D. Klug¹ and John R. Rodgers², ¹Natl Research Council of Canada, Ottawa, Canada K1A0R6, ²Toth Information Systems Inc., Ottawa, Canada

Fueled by sustained progress in both algorithms and computing speed, the progress in speed and accuracy of quantum modelling of technologically important crystalline phases has been spectacular in recent years. All bulk physical properties of pure phases can in principle be extracted from the calculated wave function resulting from this modelling.

Physical properties of materials are described in a Cartesian reference system related to their crystallographic reference system by the "IRE rules" [Transactions of the Institute of Radio Engineers (1949) 1378- 1395]. Since Curie's work on the symmetry of physical properties [J. De Physique (1894), vol 5 pp 393-415], it has been well known that the point-group symmetry of crystalline materials controls the characteristics or existence of their bulk properties, while atomic structure controls the magnitudes. With time, this refined into Neumann's principle, tensor analysis of physical properties, and tabulation of constraints on given physical properties. The manual derivation of constraints on coefficients for low-order polar or axial properties is a simple exercise. That for high-order properties is by no means trivial. As a result, all such printed Tables of constraints known to the authors are incomplete and/or incorrect.

The algebra for derivation of symmetry constraints on coefficients for bulk physical properties, and its programming, will be explained in simple terms. Computer generation of those constraints, based on the Altwyk approach to the interpretation of Hermann-Mauguin symbols for alternate settings of space-groups will be available at URL http://ylp.icpet.nrc.ca/Altcon/ beginning of July 1998. Details about corresponding IRE rules and appropriate caveats about selection of the physical reference system in the presence of such pitfalls as merohedry or enantiomorphism, are also generated from the input of the Hermann-Mauguin symbol for the structure study.