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BELL SYSTEM TECHNICAL JOURNAL 



vertical axis is an axis of 3-fold symmetry, the major cap-face planes (01 -1), 

 (lO-l) and (11-1) have the same properties and this applies also of course 

 to the parallel crystal faces (same atomic planes) which are, respectively, 

 (Ol-I), (10 -I), and (Il-l). Thus we can choose any one of these symbols 

 to represent this type of plane when speaking of such properties as dis- 

 tance between atomic planes, Q angle, or angle between atomic planes and 

 the Z axis. The symbol that will be used in this paper for this type of 

 plane is (01-1). 



Similar considerations apply to the set of minor cap faces for which the 

 symbol used here is (Ol-I) which is chosen instead of (Ol-l) because it 

 simplifies tabulation, as in Table I and Fig. 3.8. 



The indices {hh • () of all faces or atomic planes with the same X-ray 

 properties as those for any given plane may be derived as follows: First 

 replace the omitted digit / in the indices of the given plane, which may be 



+X +X 



Fig. 3.6 — Indices of cap-faces of right- and left-handed quartz crystals 



determined from the equation i = —{h-\-k). Rotary permutation of 

 the first three indices is then permitted, sls ab c I, c a b f, b c a f. 



The other three of the six equivalent faces are found by interchanging 

 any adjacent two of the first three indices and also changing the sign of f, 

 as a b c f becomes a cbl or b ac L For example: 



12 3 4 3 12 4 



2 3 14 



1324 2134 3214 



We could consider the 2 1 3 4 as derived from cycUc permutation of 

 13 2 4, and 3 2 1 4 as similarly derived from 2134 instead of by inter- 

 change of the sets above them. 



The six symbols derived from the above by changing the sign of only 

 the final digit refer to faces whose 6 X-ray angle is the same as that of the 

 above planes but whose intensity of reflection may be different. 



