950 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



more twin-related orientations and is probably twin-boundary material, 

 whereas crystal 6 is a bent crystal. 



The evidence for this interpretation lies in the facts that (1) the streaks 

 in Fig. 5 A converge at the reflections from the various (101) planes which 

 are twin planes, whereas those in Fig. 5B do not; (2) the streaks in Fig. 5B 

 show only that variation in length which is due to the use of a flat film 

 whereas those in Fig. 5 A show greater variation; and, finally, (3) the 

 streaks in Fig. 5B are of nearly uniform intensity throughout, whereas 

 those in Fig. 5A are faint streaks between strong end points. These three 

 points are discussed in the following section. 



Distinction between Twin-Boundary and Other Inhomogeneous 

 Strains in Crystals 



The spots on a back-reflection Laue photograph may be considered as 

 the intersections of the film with normals to atomic planes in the crystal, 

 modified by a non-linear scale factor. The position of any spot is inde- 

 pendent of the wave-length of the x-rays producing it and dependent only 

 on the orientation of the reflecting plane. 



When the x-ray beam falls on a twin boundary two families of twin- 

 related spots appear on the fihn. In barium titanate twin-related spots from 

 equivalent planes are close to each other. If the two spots of such a pair are 

 joined by a line these lines will all converge toward the spot from the (101) 

 plane which is the twin plane, the plane across which reflection of the struc- 

 ture would produce the twin configuration. (See Fig. 6, a back-reflection 

 Laue photograph of a barium titanate crystal with only 2 twin-related 

 orientations.) That this must be so will be clear from Fig. 7. With the 

 exception of the twinning plane the planes in this figure represent zonal 

 planes, planes containing two or more atomic-plane normals. The zonal 

 planes on the two sides of the twin plane represent the zonal plane orienta- 

 tions in the two parts of the twin. The only zonal plane directions common 

 to both parts of the twin are those normal to the twin plane since these are 

 the only directions not changed by reflection across the twinning plane. 

 The one direction common to all these unchanged zonal planes is the nor- 

 mal to the twin plane. Thus the zonal arcs on the plane photograph which 

 are common to spots from both parts of the twin intersect in the reflection 

 from the twin plane. 



Referring now to Parts A and B of Fig. 5, we see that the streaks in Fig. 5A 

 lie along the zonal arcs common to both parts of any given twin pair and 

 are intermediate between the spots of the twin pair. They are therefore 

 reflections from material transitional in orientation between the two twin 

 orientations. The streaks in Fig. 5B, however, do not converge toward a 



