8 Prof. W. L. Bragg and Messrs. James and Bosanquet : 

 Effect of Imperfection in the Crystal. 



5. The effect of irregularity in the crystal is discussed 

 very fully by Darwin (Phil. Mag. April 1914, p. 685). 



When X-rays are passing through a homogeneous element 

 or the crystal at the correct angle for reflexion, the reflected 

 beam is in its turn again reflected by the crystal. The beam 

 which has undergone this double reflexion is parallel to the 

 transmitted beam, but its phase differs from it by 7r, so that 

 it tends to diminish it. The absorption of the transmitted 

 beam is therefore greater than the normal absorption, for 

 lays going through at any other angle. The greater the 

 depth of the homogeneous element traversed by the X-rays, 

 the greater is the increase in the effective absorption- 

 coefficient. It is this which gives rise to the diminution 

 of the transmitted beam when a crystal is set so as to reflect 

 the rays. (See fig. 2.) 



If the homogeneous elements in a composite crystal are 

 small, so that the X-rays traverse a few planes only in 

 each homogeneous fragment, the increase in the absorption- 

 coefficient at the reflecting angle will be inappreciable. 

 In this case the formula? (3) and (4) will hold good for 

 reflexion by a face and through a plate, jjb being the normal 

 coefficient of absorption. On the other hand, if the homo- 

 geneous fragments are so large that the increase in the 

 absorption-coefficient is appreciable, the intensity of re- 

 flexion will be thereby diminished. The upper layers of 

 each homogeneous element cut down the transmitted beam 

 to an abnormal extent, so that the lower layers do not 

 contribute so much to the total reflected beam. The more 

 irregular the crystal, the stronger we should expect to rind 

 the reflected beam. 



Darwin (loc. cit. p. 6S6) shows that, in a perfect crystal, 

 all the radiation that can be reflected, is so, long before the 

 depth is reached at which rays at a different angle are 

 appreciably absorbed. Over a small range of angles 

 reflexion is complete, the normal absorption-coefficient 

 playing no part in diminishing the intensity. He takes 

 the case of a crystal composed of homogeneous layers, 

 each of sufficient depth to give the maximum possible 

 amount of reflexion of the X-rays. The orientation of 

 these successive layers is slightly different, so that the 

 lower layers do contribute to the reflected beam when 

 the X-rays fall on the crystal face at the angle which is 

 appropriate to them, since rays reflected at them are 

 able to pass through the upper layers. 



