_ 71 A 



~ 2 sin 



with the powder pattern recorded on cylindrical film the Bragg angle in degrees 

 is obtained from the relationship, 



\ K / £ir 7rK 



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 in Bragg's law 

 we obtain (Clark, 1955) 



, n A 



a = — 



sin 



/ 90a \ 

 \ *R ) 



In some commercial cameras available today, the diameters have been so chosen 

 that one millimeter film distance is equivalent to 1° or 2°, 8 angle. 



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

 ated. 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 usually can see all the details in 

 a pattern that can be detected with a densitometer. Relative intensities of lines 

 in a well-exposed pattern are different 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 

 (Hellman, 1944). If a particular constituent is to be determined, the writer has 

 found it advisable to prepare a series of underexposed patterns of the con- 

 stituent 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 demon- 

 strate why rather strong lines of the patterns of minor constituents frequently 

 cannot be found in the pattern of the mixture. Such a series of patterns can 

 also be used by semiquantitative estimation (see page 173). 



IDENTIFICATION OF If X-ray diffraction data have been obtained 



MINERALS AND from single-crystal rotation patterns and unit- 



COMPONENTS OF cell dimensions calculated, the identity of the 



MIXTURES compound usually can be determined, directly 



by means of suitable tables (Donnay, 1954). 



If the X-ray diffraction data were obtained from powder patterns, the 



164 



