International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shumeli

International Tables for Crystallography (2010). Vol. B, ch. 3.1, p. 405   | 1 | 2 |

## Section 3.1.7. Components of vector product

D. E. Sandsa*

aDepartment of Chemistry, University of Kentucky, Chemistry–Physics Building, Lexington, Kentucky 40506–0055, USA
Correspondence e-mail: sands@pop.uky.edu

### 3.1.7. Components of vector product

| top | pdf |

As is shown in Sands (1982a), the components of the vector product are given bywhere again is a reciprocal basis vector (some writers use to represent the reciprocal axes). A special case of (3.1.7.1) iswhich 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 obeyingIn (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.