314 BELL SYSTEM TECHNICAL JOURNAL 



Since the edge P2 (thickness direction) is the normal to the major face 

 of the plate, its .Y, F, Z components (second horizontal row) give the 

 orientation of the major face of the plate in terms of A', Y, Z axes of the 

 mother crystal. 



For example, suppose the orientation of the major face of an A^T plate 

 is desired in terms of the A', F, Z axes. The shop rotation angles for an 

 NT plate are 



Ax = 99°25' 



Ai = 49°25' 



As = -12°20' 



Substituting these values in the above matrix gives 



/ .99027 ~.13917\ 



r'" = ( - .64279 - . 10662 - . 75852 ) (3.9) 



\-. 76604 .08946 .63653/ 



the second row of which gives the components (direction cosines) of the 

 unit normal to the plate surface on the A', F, Z axes: 



X = .64279 

 F = .10662 

 Z = .75852 



(B) Discovery of the plane whose orientation and X-ray properties 

 are most suitable for use with the face to be checked. 



The first requisite for the atomic plane to be used is that it shall make 

 as small an angle 8 as possible with the face to be checked. This is desirable 

 because (1) 8 must be smaller than 6; (2) if 8 is small the same plane can be 

 used for correction around Pi as around P3 since the j8 angle will be small. 

 If 8 is very small the difference between g and 6 may be within the required 

 limits of error so that the 6 value may be used without correction; (3) if 5 

 is large, the difference between ge and gf will be large and if the plate is 

 placed in the goniometer in such a way that ge is the larger angle the re- 

 flected ray may be too weak to register on the ionization chamber meter. 



By plotting the stereographic projection of the normal to the plate face 

 on Fig. 3.7 the most promising planes may be found quickly. On this chart 

 each concentric circle connects all points with the same Z direction-cosine; 

 each arc that crosses the X axis connects all points with the same AT direc- 

 tion-cosine; each arc that crosses the F axis connects all points with the 

 same F direction-cosine. 



For example, the normal to the major face of the NT cut is plotted as 

 follows: 



.64 units are marked off in a positive direction (down) on the A' axis (to 



