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A method of calculating the integral breadths of Debye-Scherrer lines: generalization to non-cubic crystals

Published online by Cambridge University Press:  24 October 2008

A. R. Stokes  and
A. J. C. Wilson
A. R. Stokes
Affiliation:
Cavendish LaboratoryCambridge
A. J. C. Wilson
Affiliation:
Cavendish LaboratoryCambridge
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Extract

Stokes and Wilson(1,2) have shown that the integral breadths of the Debye-Scherrer lines produced by small or imperfect crystals of the cubic system are given by

or, what is the same thing, that the apparent particle sizes are given by

In these equations λ is the X-ray wave-length, θ is the Bragg angle, Vt is the volume common to the crystal and its ‘ghost’ shifted a distance t in the hkl direction(1), and Jt is the mean value of the product FF of the structure amplitudes of two cells separated by a distance t in the hkl direction (2). The purpose of this note is to outline an argument which establishes the same result for crystals of any symmetry.

Type
Research-Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 40 , Issue 2 , June 1944 , pp. 197 - 198
Copyright
Copyright © Cambridge Philosophical Society 1944

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References

REFERENCES

(1)Stokes, A. R. and Wilson, A. J. C.Proc. Cambridge Phil. Soc. 38 (1942), 313.CrossRefGoogle Scholar
(2)Wilson, A. J. C.Proc. Roy. Soc. A, 181 (1943), 360.Google Scholar
(3)Wilson, A. J. C.Proc. Roy. Soc. A, 180 (1942), 277.Google Scholar
(4)Patterson, A. L.Phys. Rev. 56 (1939), 978.CrossRefGoogle Scholar