230 Subsurface Geologic Methods 



The process of measuring the powder pattern is the same regardless of 

 how the measurements are to be used. The diameters (or radii) of all 

 lines in the pattern are measured and recorded in centimeters or milli- 

 meters. If the X-ray pattern is recorded on flat film, the Bragg angle is 

 obtained from the tangent relationship, namely, 



line radius 

 tan 26=- 



sample to film distance 



With the Bragg angle 6 known, the interplanar distances, d, can then be 

 readily calculated by means of Bragg's law. 



a=- 



2 sin 9 



With the powder pattern recorded on cylindrical film the Bragg angle in 

 degrees is obtained from the relationship, 



, „ ^360 90a 



2^=(-iTlTr- or e = —^ 



_/a\360 

 ~\r) 2tt 



where a is the line radius on the film in millimeters and R is the film 

 radius (camera radius) in millimeters. Substituting this value of 6 in 

 Bragg's law we obtain ^^ 



nX 

 d = 



o . /90a\ 



In addition to this calculation, the relative line intensities must be 

 evaluated. The intensities are expressed in some system, for example 

 as V.V.S. to V.V.W. (very, very strong through various gradations to 

 very, very weak), or on a numerical basis ranging from 10 to 1 or 1 to 

 0.01. Visual approximation of intensity is sufficient, as a trained operator 

 can see all the details in a pattern that can be detected with a densi- 

 tometer. As has been suggested previously (See fig. 97), relative intensi- 

 ties of lines in a well-exposed pattern are diff'erent from those in an 

 underexposed pattern. Differences in exposures not only result from 

 changes in exposure time from specimen to specimen, but also occur within 

 a single pattern representing a mixture containing both large and small 

 proportions of the several ingredients.^'^ If a particular constituent is to 

 be determined, the writer has found it advisable to prepare a series of 

 underexposed patterns of the constituent in pure form with exposure 

 times of 1 percent, 2.5 percent, 5 percent, etc., of that used in obtaining 

 the pattern of the mixture. This procedure will demonstrate why rather 



^ Clark, G. L., op. cit., p. 279. 



'"' Hellman, N. N., and Jackson, M, L., Photometric Interpretation of X-ray Diffraction Patterns for 

 Quantitative Estimation of Minerals in Clays: Soil Sci. Soc. Am, Proc, vol. 8, pp. 135 ff., 1944. 



