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A note on crystallographic calculations

Published online by Cambridge University Press:  14 March 2018

Max H. Hey
Max H. Hey*
Affiliation:
Department of Mineralogy of the British Museum
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Extract

In the course of work on the Barker index of determinative crystallography, a number of interesting problems have arisen owing to the selection by a few workers of unusual sets of fundamental angles for their computations. Most of these problems have been of no general application, but One appears to have a wider interest and may prove of practical value in dealing with crystals having curved or striated faces that only admit of accurate measurements along one zone.

This problem was to compute the angles and elements of a monoclinic crystal, using as fundamentals the angles from b(010) to any three faces e, f, g (of known indices) not in the zone [010], and no pair of which are co-zonal with b(fig. 1).

Type
Research Article
Information
Mineralogical magazine and journal of the Mineralogical Society , Volume 25 , Issue 169 , June 1940 , pp. 534 - 537
Copyright
Copyright © The Mineralogical Society of Great Britain and Ireland 1940

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References

page 534 note 1 τ (101), m (110), q (011), R (101̄).

page 535 note 1 It may perhaps be noted here that if be, bg′, eg′ (fig. 2) are given as fundamentals, the most direct solution is given by the relation

cot De+cot eg′ = cos bg′/cos be.sin eg′.

page 536 note 1 The measurement of ammonium cobalticyanide by Lang, V. von (Sitzungsber. Akad. Wias. Wien, 1862, vol. 45, Abt. II, p. 107) includes so few angles that the only available fundamentals are of this type.Google Scholar The same selection of fundamentals was made for hydrobromcinchene by Muthmann, W. (Zeits. Kryst. Min., 1889, vol. 15, p. 391).Google Scholar

page 536 note 2 Where the given angles are DW, uW, vW (fig. 4), solution is possible by drawing zone-circles through u and v to cut [DWb] at right angles; the final solution is sec DŴu = 2 cot DW/(cot uW—cot vW). Unless the angle DŴu differs considerably from 90° this selection of fundamentals is very unfavourable, but was used for potassium cobalticyanide by Topsøe, H., Sitzungsber. Akad. Wiss. Wien, 1872, vol. 66, Abt. II, p. 43.Google Scholar

page 537 note 1 Exemplified by 3:3-dimethyl-2-(α-oximinoethyl)-pseudoindol (Boeris, G., cited by Groth, P., Chem. Kryst., 1919, vol. 5, p. 552).Google Scholar