316 BELL SYSTEM TECHNICAL JOURNAL 



3.8 Determination of the Orientation of an Atomic Plane ^VITH 



Respect to the Plate-Edges, Given its 



Miller-Bravais Indices 



Since the indices (hk-i) are the reciprocals of the intercepts of the atomic 

 plane on the quartz crystallographic axes (See Section 3.5) of which the 

 vertical axial unit is 1.09997 times that of the others, the intercepts on axes 

 which were all divided into the same length unit would be 



11 ,1.1 



(If 1.1 is substituted for 1.09997 the error introduced is never greater than 

 one minute.) 



The intercepts on the orthogonal axes may be derived as indicated in 

 Fig. 3.17. They are: 



1 Vs U 

 A ' h -\- 2k' ( 



These intercepts may be taken as the lengths of 3 vectors whose com- 

 ponents on the .V, Y and Z axes are as follows: 



/1//A 



ix{X axis vector) = I 1 (3.10) 



i,{Y axis vector) = | jf^^ | (3.11) 



/ \ 



73(Z axis vector) = (3.12) 



Now the two vectors (13 - k) and {h - 12) lie in the plane {hk • () (See 

 Fig. 3.18), and therefore their vector product is the vector normal to the 

 plane hk • I 



