306 BELL SYSTEM TECHNICAL JOURNAL 



the more important atomic planes of quartz, identified by their indices. 

 Its usefulness in quartz work will be pointed out in Section 3.7B. 



In many cases the reflecting power of an atomic plane dififers from that 

 of the symmetrical plane on the other side of the Z axis. (See, for example 

 01-1 and 01 -I). When this difference is very great as with 04-4 and 04-4 

 the planes are useful in determining whether a plate is cut at a positive or 

 negative angle from the Z axis. The intensities of planes that have been 

 found useful for this purpose are circled in Fig. 3.8. 



3.6 X-Ray Goniometry 



Since the angles 6 and the intensities / are different for different planes 

 we can use them to identify these planes, that is, to orient the crystal by 

 measuring angles between recognized atomic planes and plate surfaces. 

 Figure 3.9 is a diagrammatic representation of an X-ray goniometer where 



T is the tube target shown with its intensity pattern, 

 6*5 are slits that pass only a narrow beam, 

 C is the crystal, 



c 

 Fig. 3.9 — Simplified diagram of X-ray goniometry 



I is the ionization chamber 



M is the meter that measures the ionization current. 



The ionization chamber is placed at an angle 26 to the incident beam, 

 where 6 is the Bragg angle for the atomic plane being used, and is not 

 moved while reflections are being taken from that atomic plane. If C 

 is then rocked about the vertical axis P (normal to the plane of the paper) 

 the ionization chamber registers an electric current when an atomic plane 

 is at the proper angle for reflection. 



(a) Atomic plane parallel to plate-face. 



Let us examine a simple case, that for which the existing face is parallel 

 to an atomic plane (Fig. 3.10). The crystal is held against the reference 

 points by a coil spring. The crystal holder is free to rotate about the 

 vertical axis P (with respect to the X-rays) and the angle of rotation is 

 read on the graduated scale. If the entering angle (the angle between 

 the entering beam and the plate-face) is one that satisfies the equation 

 n\ = 2d sin 6, we will have a reflected ray which is at a leaving angle 

 of d. Also the reflected ray is always deviated from the line of the original 



