X-RAYS AND ORIENTATION OF QUARTZ CRYSTALS 329 



changes in temperature and humidity, measurements are made from two 

 spots about equally removed from the center but on opposite sides. 



If all three errors exist simultaneously they may still be measured in this 

 way provided they are small. 



Given e( , e^, and et for plates containing the .V axis the errors in .li , A2 

 and A3 can be computed by the formulae 



Error in Ai = e,:,/cos A2 



Error in .42 = e( 



Error in A3 — et — e^ tan A^ 



Consider, for example, the negative (Fig. 3.24) for a BT plate. The row 

 of spots (01-4), (01-3), (01-2), (03-4), (01-1), etc., results from reflections 

 from the group of planes parallel to the -Y axis (see Fig. 3.8). (Such a 

 group of planes all parallel to a given line is called a zone.) In the BT cut 

 the -lo angle results from rotation around the A' axis. The effect of such a 

 rotation on the photograph (Fig. 3.24) is a shift of the spots of the (0^-/) 

 atomic planes along the line on which they lie. Therefore, to measure the 

 Ai angle from Fig. 3.24, we choose two spots along this hne about equi- 

 distant from the center of the film such as (01 • 1) and (01 -2) and measure 

 the angular distance a between the incident X-ray beam and the reflected 

 ray causing each spot by measuring the distance between the center of the 

 film and each spot using the specially calibrated scale. 



By "center of the film" is meant the point through which the center of 

 the X-ray beam passed. This point is located as follows. When the film 

 is in place in the camera, two reference points are pricked in it by pins built 

 into the camera. These points may be seen in Fig. 3.24 as small white 

 circles near the center of the right and left edges of the picture. The center 

 of the X-ray beam is at the center of a line between these two points. 



When the negative is to be measured it is placed on a glass plate engraved 

 as shown in Fig. 3.26 with the reference points at P, P. The intersection A' 

 then marks the center of the film. 



If T2 is the plate angle around the A' axis from the Z axis and 7 is the 

 angle between the atomic plane normal and the Z axis and a is the angle 

 measured between the center of the film and the spot, then 



A2 - 90° - ynk-t + ochk-t (3.46) 



For the two spots chosen for measurement of the BT plate of Fig. 3.24, 



Ai. = 90° — 7012 — «oi 2 (Rotation from the BT cut to the 01-2 plane 



is a negative rotation) 

 A2 = 90° — 701. 1 + aoii 



4 — 00° — "Yoi-^ ~i~ To il 1 «oii ~ «oi-2 

 . - 2 "^ 2 



