150 BELL SYSTEM TECHNICAL JOURNAL 



but in this case exposures are long enough to record the "white" radiation 

 reflected from both the small-angle disturbed and undisturbed material. If 

 reflections from material misoriented by more than a few minutes were re- 

 corded on the Aim the lines from the reflected X-rays would be broader than 

 they are. 



In the undisturbed material there is one wave length from a ray traveling 

 in a given direction that will satisfy the Bragg equation for a given set of 

 atomic planes. Most of these "usable" X-rays are reflected by the hrst thin 

 layer of undisturbed crystal they meet and therefore very little reflection of 

 X-ra}-s of this wave-length from this ray takes place from deeper layers of 

 the undisturbed crystalline material. This removal of the reflectable X-rays 

 by the first thin layer of undisturbed crystal is known as "primar}^ 

 extinction". 



In the disturbed surface layer, on the other hand, regions of dissimilar 

 orientation are superposed. In this case a ray traveling in a given direction 

 will have X-rays of one wave-length subtracted from it by the first crystalline 

 material of a particular orientation it meets in accordance with the Bragg 

 equation; then, beneath this, cr\^stalline material at a different orientation 

 will subtract from it X-rays of a different wave-length and so on so that 

 from each ray a broader range of wave-lengths is diffracted by the disturbed 

 material than by the undisturbed, resulting in a stronger reflected beam from 

 the disturbed material. Since the lapped surfaces of the crystal plate give 

 a stronger reflected beam than the undisturbed interior of the plate, the re- 

 flection of the slit collimated beam from each set of atomic planes appears 

 on the film as a pair of lines. The density of these lines is related to the dis- 

 turbance and their width is related to the depth of the disturbed sur- 

 face layer, as shown diagrammatically in Fig. 10. The four photographs in 

 Fig. 1 1 were taken in this way, all through the same BT quartz plate. Figure 

 11a shows the reflections from the various atomic planes of the 4 mm. -thick 

 BT-cut quartz plate, lapped on one side with coarse abrasive (180 carborun- 

 dum) and on the other with fine abrasive (^303^ emery). As shown in 

 Fig. 10, the coarsely lapped surface was toward the photographic film and 

 therefore the line closer to the line from the direct beam (the single line in 

 the loW'Cr right corner) is the stronger of the tw-o. Figure 1 lb was taken in 

 the same way after the plate had been etched in 48^ hydrofluoric acid for 

 47 hours. The acid was renewed every few hours. The presence of dis- 

 turbed material near the two surfaces is still discernible. Micrometer 

 measurements after etching indicated that the thickness of the plate had 

 been reduced by 0.14 mm. 



Such a measurement is from the peaks of the rugged etched surface on one 

 side of the plate to the peaks on the other side: over most of the plate the 

 etching had proceeded to a greater depth than the .07 mm. indicated by the 



