Volumes

Shmueli, U.

doi:10.1107/97809553602060000549

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

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International Tables for Crystallography (2006). Vol. B. ch. 1.1, pp. 3-4 | 1 | 2 |

Section 1.1.3.2. Volumes

U. Shmueli^a ^*

^aSchool of Chemistry, Tel Aviv University, 69 978 Tel Aviv, Israel
Correspondence e-mail: ushmueli@post.tau.ac.il

1.1.3.2. Volumes

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The reciprocal relationship of V and $[ {V}^{*}]$ follows readily. We have from equations (1.1.3.2), (1.1.3.3) and (1.1.3.4) $[ {\bf c}\cdot {\bf c^{*}} = {({\bf a} \times {\bf b})\cdot ({\bf a}^{*} \times {\bf b}^{*})\over {VV}^{*}} = 1.]$ If we make use of the vector identity $[({\bf A} \times {\bf B})\cdot ({\bf C} \times {\bf D}) = ({\bf A}\cdot {\bf C}) ({\bf B}\cdot {\bf D}) - ({\bf A}\cdot {\bf D}) ({\bf B}\cdot {\bf C}), \eqno(1.1.3.5)]$ and equations (1.1.3.1) and (1.1.3.2), it is seen that $[ {V}^{*} = 1/{V}]$ .

References

International Tables for Crystallography (2006). Vol. B. ch. 1.1, pp. 3-4