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A Graphical Method of Evaluating Trigonometric Functions Used in Crystal Structure Analysis. Parts I and II

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1 Author(s)
Grenville‐Wells, H. J. ; Laboratory for Insulation Research, Massachusetts Institute of Technology, Cambridge, Massachusetts

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A graphical method is described for evaluating structure factors of the form

F(hk0)=
n
0
fr(hk0) cossin2π(hxr+kyr)
and electron density expressions of the form ρ(X,Y)=Σ Σ F(hk0) cossin2π(hX+kY). The method depends upon the fact that if, in a [001] projection of a unit cell the normal to the planes (hk0) is graduated with the appropriate sine or cosine function giving the phases of points along the normal, then a circle with its center at (½x,½y), passing through the origin, will cut the normal to F(hk0) at the value of cossin2π(hx+ky). Part I contains the basic principles and a standard chart, and Part II cites examples of the use of the method and the accuracy to be expected in structure factor calculations, and of its application to least-squares refinements.

Published in:

Journal of Applied Physics  (Volume:25 ,  Issue: 4 )