Reflexion of X Rays by Crystals. 



895 



Fig. 8. 



reflexion obtained was complete ; if the crystal had been 

 thicker the reflexion might have been stronger. The point 

 therefore arises as to how the defect is to be calculated. 



Let us denote the space absorption co- 

 efficient of the rays in the diamond by A . 

 Let the primary rays enter along AB 

 (fig. 8), and the intensity at B be e~* x , 

 where «# = AB and the primary rays are 

 supposed to have been of unit intensity 

 when they entered. Let kSx . e~ Xx be the 

 amount reflected while x is increasing to 

 x + 8x. The reflected rays are diminished 

 in the ratio 1 to e~ Kx while traversing the 

 distance BO. Thus the intensity of the 

 reflected pencil is 



J kSx . e~ 2 ^ = gvC 1 -^" 2 ^), 



where x 1 is the distance which the primary 

 rays move through the crystal. If the 

 crystal is so thick that \xi is large, the 

 intensity of reflexion is k/2\. If we compare the intensities 

 of reflexion for two different orders, the X divides out, and 

 the absorption coefficient need not be determined or taken 

 account of. This idea was originally employed by investi- 

 gators of the scattering which X rays undergo when passing 

 through ordinary materials *. But if the crystal has a thick- 

 ness £, and the glancing angle is 0, and if \t cosec 0( = \xi) 

 is not large, then the reflected pencil has an intensity 



J»(\ g—2\t eosee &\ 



If we compare the intensities of reflexion in two different 

 orders for which has different values, the absorption 

 coefficient does not disappear. We must find the value of 

 the factor containing the experimental term before we can 

 obtain a true value for the intensity. 



The diamond which I have used was very kindly lent to 

 me by Prof. S. P. Thompson. It is a slip about 6 mm. 

 square and 0*4 mm. thick, its two main faces being cleavage 

 planes. Experiment shows that Xt is equal to *081. This 

 makes (1 — e~ 2Mcosec9 ) = 0'6$ nearly for the first order and 

 0-33 for the third. 



Consequently the true ratio of the intensities of the first 

 and third order reflexions should not be 8*95 to 1, but only 

 half this quantity. 



This seems most unlikely, since in the case of all the other 

 * For example, by Barkla, Phil. Mag. Feb. 1911. 



