334 



BELL SYSTEM TECHNICAL JOURNAL 



Two planes determine a zone. The zonal indices are computed by "cross 

 multiplication" of the indices of the planes. The two planes {hiki- (i) and 

 {hiki-ti) determine the zone (^i4 — ^1^2 , hh-i — hili , hiki — kxhi). In 

 practice this is developed by writing the indices of each plane twice; those 

 of one under those of the other, then striking out the two end members of 

 each and taking the difference of the cross products. Whereas plane indices 

 are always enclosed in parentheses ( ), zonal indices are always enclosed in 

 brackets [ ]. For example (0 0-1) and (0 1 -0) are in the zone: 



[1 0.0] 



while (2T-0) and (21-2) are in the zone [24-4], or reducing, in the [12-2] 

 zone. 



This zonal relation is reciprocal in the sense that the plane common to 

 two zones is derived in the same way as were the zonal indices. For example, 

 the plane common to the zones [10-0] and [12- 2] is 



(0 2-2) or, (0 i-i) 



If a given face with indices xyz lies in a zone with the symbol uvw, the 

 following equation, known as "the zonal equation" will be true: 



ux -{- vy -\- wz — Q 



In the Laue photograph of the BT plate, Fig. 3.24, the row of spots (12-2) 

 (13-3) (01-1) (IvS-5) (l3-3) etc. is due to reflections from planes which 

 belong in one zone. Other rows such as (12 -5) (12 '4) (12 '3) etc. cross this 

 row at some spot whose indices can be computed if two spots in each row 

 are known. If the row passes through the center of the film all the spots 

 lie on a straight line. If the row is off center it is curved, convex towards 

 the center. Experience soon shows us how much curvature goes with how 

 great a distance from the center for a series of spots to form a zone. 



3.11 X-Ray Checks of Slabs in the Course of Manufacturing 



Quartz Plate 



In the course of manufacturing a quartz plate it is common practice to 

 X-ray check the first sawn slab and correct the orientation of the quartz 

 with respect to the saw before cutting the remaining slabs. Each of these 

 slabs is then cemented to the head of a barrel jig so built that the orientation 



