position of Kp lines can be calculated and the lines disregarded in the interpre- 

 tation of the data. However, the Kp radiation should be removed when making 

 patterns of mixtures, as such patterns are always very complex and the presence 

 of Kp lines serves only to cause errors and confusion. 



MEASUREMENT OF LINES The X-ray pattern usually must be measured 

 IN PATTERN AND and the data used to determine interplanar 



CONVERSION TO d VALUES spacings or the unit-cell dimensions. Conse- 

 quently, all precautions must be taken in the 

 processing of the film to avoid film shrinkage or to reduce it to negligible 

 amounts. Film shrinkage can usually be kept to a minimum and often to the 

 point where it is negligible by rigidly following a processing procedure which 

 keeps all times in the procedure to the minimum required. Film shrinkage has 

 been found to increase with washing time, especially if prolonged and the 

 shrinkage is not uniform throughout the entire film (Claassen, 1946). Develop- 

 ing procedures can be checked for film shrinkage by exposing, or marking, on 

 the film fixed lengths before processing. Correction for shrinkage is also 

 frequently made through the use of an internal standard such as NaCl the line 

 positions of which are accurately known, the pattern for NaCl being superposed 

 directly on the pattern of the unknown. 



A number of measuring devices are offered by manufacturers of X-ray 

 apparatus with which either the diameters or radii of the powder rings can be 

 rapidly and accurately measured in units of length, usually centimeters. These 

 devices could be calibrated directly in KX or A, units {A. = 1.00202 KX units) , 

 but calibration in this way restricts their use to a single type of camera with a 

 fixed radius. Consequently, the measurements in centimeters must be converted 

 into interplanar spacings or the unit-cell dimensions by calculation or calibra- 

 tion curves indicating ring diameters or radii (in centimeters or millimeters) as 

 a function of interplanar spacing (in angstrom units). For rapid and approxi- 

 mate measurements, a direct-reading scale on transparent plastic can be prepared 

 from calculated or plotted data, interplanar distances equivalent to each ring 

 being read directly when the scale is superimposed on the pattern. 



If single-crystal-rotation patterns taken perpendicular to each of the three 

 crystallographic axes are available, one dimension of the unit cell can be 

 calculated from each of the three patterns. For cylindrical patterns the angle 

 u„, is caculated from the tangent function of the distance measured on the 

 pattern between the and nth layer line and the film radius. For flat patterns 

 it is calculated from the distance measured between the layer and the apex of 

 the n^-layer-line hyperbola and the sample-to-film distance (fig. 9-8). This 

 value is then substituted in the equation: 



162 



