ISSN:
1600-5724
Source:
Crystallography Journals Online : IUCR Backfile Archive 1948-2001
Topics:
Chemistry and Pharmacology
,
Geosciences
,
Physics
Notes:
The description of n-dimensional space by a basis of (n + 1) vectors, ai (i = 1, . . . , n + 1), is discussed, with particular reference to the Miller–Bravais system of indexing hexagonal crystals. It is shown that if a hyperplane with normal h makes intercepts hi−1 on the ai and a vector u has components ui relative to the ai, then h. u = Σhiui without any further restrictions on the hi or ui. Furthermore, it is possible to find a basis a†i(i = 1, . . . , n + 1) for reciprocal space such that h = Σhia†i is always true and indeed there are n degrees of freedom available for choosing such a basis. Criteria which may lead to a unique choice of a†i are discussed.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1107/S0567739470001353
