510 Dr. L. Vegard on 



Hence we conclude that the arrangement (a) must be 

 excluded. 



We shall then consider the second possibility (6), which 

 gives the spacings represented in fig. 2 for the four faces 



Fig. 2. 

 Xenotime 



tun 



! • 



i 



i 





i 



Y 



P0 2 



1100) 



PO z 



YP 



2ot 



H 



YP 



fllO) 



•2ct 



■2«C 



y/»^ 



ffOl) 



I! 

 II 



!! 



II 



K/> 



Ob 



YP 



examined. The amplitudes are determined by the following 

 expressions : 



(111) A„ = [2-44 + (-l) n (l'94+ cos n*)] cos 



nir 



(110) A w =4-37+ cos2n«, 



(100) A„=l'69 + cos 2na, 



(101) A„=l'69 + cosn*. 



(3) 



If I is the distance from an oxygen atom to the central 



P atom : 



4tt I 

 u= — -=— , 



V2 a 



The equation for the amplitude of (111) shows that the 

 second order spectrum will disappear for all values of a. 

 The first order spectrum will vanish for a =60°, and for this 

 value the ratio of the intensity of the third to that of the 

 fourth order spectrum will be 1 : 7 and the third order 

 spectrum might well be so weak as not to be detected. 



In order to get the best possible agreement between 



