X-RAYS AND ORIENTATION OF OVARTZ CRYSTALS 



325 



is so simple (See section ,v6, h) that the above procedure need not Ije 

 followed. 



P'or such plates the complete transformation is an .I2 rotation around .V: 



/I ^ 



•'" = [0 cos .I. -sin /1 2 



V) sin /1 2 cos /1 2/ 



(3.38) 



The planes used for checking these plates are of the type fO^-O so that, 

 from equations (3.13) and (3.14) 



whence 



r"'N = 



N = l2k/V's]-^ 



\ f/\A I ^^ 







2 ( 



k cos .42 — j- sin A'. 



(3.39) 



V3 

 2 



( 



/= k sin .42 + 7-r cos ^2 

 . V 3 1.1 



1 



(3.40) 



but 



2K 



VWs^ ''''''"'■' '"'^ Li V3 = '°' "'^-^ 



where 7 = the angle between the normal to the atomic plane and the Z axis 

 (note that for 7 angles on the negative side of the Z axis the value given 

 in Table I should be subtracted from 180°, as in the case of the AT cut 

 given below). 



Thus (3.40) may be written 



/ .0 ^ 



TV = I sin (7 - A'i) 

 \cos (7 - A2), 



(3.41) 



and (3.25) becomes 



gi= e - 8[ where 8[ = 90° + .42 - 7 (3.42) 



(Note that where. 42 is positive 7 will be on the negative side of theZ axis) 



whence gi = d -{- y - 90° - Ai (3.43) 



g3 = 90° + ^ + .42- 7 (3.44) 



For position 2, equation (3.40) applied to equation 3.27 gives 



sin Q = sin (7 — .42) sin ,^2 



