Subsurface Laboratory Methods 235 



the unit-cell data with the powder-diffraction data is accomplished by 

 application of the reciprocal-lattice concept. A complete explanation of 

 this concept is, of course, beyond the scope of this section and the reader 

 is referred to other sources.*^ *^ ^^ However, it can be shown that the re- 

 lationship between the true lattice (real space) and the reciprocal lattice 

 (reciprocal space) can be expressed by the equation, 



, RX 

 d = , 



d* ' 



where d is the interplanar distance in the true lattice, c?* the interplanar 

 distance in the reciprocal lattice, A the wave length of the radiation used, 

 and R a constant called the "magnification factor" applied to convert 

 the dimensions in reciprocal space to such a magnitude that the reciprocal 

 lattice or net can be plotted easily in cm.-units. If the unit-cell dimensions 

 are not much over 10 A., the value 7? = 10 will produce a reciprocal net 

 of convenient dimensions. If the unit cell has dimensions between 10 and 

 30 A., a value of 7? = 20 should be chosen. Briefly, the procedure is the 

 following: the a, b, and c dimensions of the unit cell are converted into 

 reciprocal-cell dimensions by means of the equation above and the result- 

 ing three-dimensional net plotted in one plane by folding the vertical planes 

 down into the horizontal plane (See fig. 99). Thereupon, the experiment- 

 ally determined powder-diffraction data are also converted into reciprocal 

 dimensions by the same equation and the results (rings representing the 

 ends of reciprocal space vectors free to turn about the origin) are super- 

 posed on the reciprocal net of the unit cell. If the unit cell fits' the experi- 

 mentally determined powder-diffraction data, there will be a net intersection 

 at the end of each vector ; i.e., the rings derived from the powder data will 

 all pass through one or more intersections of the three-dimensional recip- 

 rocal-unit cell net. 



A mixture of minerals which are frequently difficult to differentiate 

 by optical examination, especially when examined in the form of a rather 

 fine powder, has been chosen to illustrate this method. Owing to the nature 

 of these minerals, the mixture could be identified as a single homogeneous 

 substance. A diffraction-powder pattern, however, will definitely show it 

 to be a mixture. With the methods described above, one constituent can 

 readily be identified as quartz from these powder data. This identification 

 is further verified by direct comparison with a standard quartz pattern 

 (See pi. 7). 



Assuming that powder data are not available for the other constituent 

 of the mixture, it would then be impossible to identify this constituent 

 with the aid of the card index. However, if now through more thorough 

 optical examination, further data can be obtained to limit the number of 

 possible compounds to be checked to a reasonable number, identification 



** Clark, G. L., op. cit. 

 *«Davey, W. P., op. cit. 

 « Bunn, C W., op. cit. 



