International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shumeli © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. B, ch. 3.1, p. 349
Section 3.1.7. Components of vector product^{a}Department of Chemistry, University of Kentucky, Chemistry–Physics Building, Lexington, Kentucky 40506-0055, USA |
As is shown in Sands (1982a), the components of the vector product are given by where again is a reciprocal basis vector (some writers use to represent the reciprocal axes). A special case of (3.1.7.1) is which may be taken as a defining equation for the reciprocal basis vectors. Similarly, which completes the characterization of the dual vector system with basis vectors and obeying In (3.1.7.4), is the Kronecker delta, which equals 1 if , 0 if . The relationships between these quantities are explored at some length in Sands (1982a).
References
Sands, D. E. (1982a). Vectors and tensors in crystallography. Reading: Addison Wesley. Reprinted (1995) Dover Publications.