508 Dr. L. Vegard on 



Arrangement of Oxygen Atoms. 



§ 3. As far as the Y and P atoms are concerned, we have 

 assumed a lattice of the Zircon type. The first question we 

 shall put is : Can such an arrangement of the oxygen atoms 

 as that found for zircon explain the spectra of xenotime ? 



The spectra of the faces (100), (110), (101), might be 

 accounted for by a proper choice of the parameters, and the 

 test will be whether the zircon lattice can explain the 

 peculiar spectrum of the face (111), in other words, explain 

 the fact that the first three spectra are too weak to be 

 detected. With regard to the determination of the intensities 

 I shall only refer to my previous paper (II. p. 84). 



The functions/, (n) and f 2 (n), which determine the strength 

 of the spectrum of order n, are for the (111) face of an 

 arbitrary lattice of the Zircon type given by the expressions 

 (II. eq. 12) 



/ l (n) = N 1 +(-l)N 2 + (N 1 + N 2 + 4N 3 )cosn| 



+ 2N 3 (cos nu x -f ( — l) n cos na 2 ), 

 / 2 (?2)=(N 1 -N 2 )sinn- 



1T 



N 3 is the atomic number of oxygen ; N T , N 2 those of the 

 two other elements. In our case we have to put Nj = 39, 

 N, = 15, N 3 = 8. 



We can, however, prove that there is no value of the 

 parameters which can give a distribution of intensities in 

 accordance with observations. Thus it is impossible to make 

 the first order spectrum sufficiently small as compared with 



the fourth. 



Bemembering that the amplitude A n = v / / 1 (n) 2 + t / 2 (n) 2 , 

 we shall find that the smallest value of A x is 24, and the 

 largest value of A 4 is 172. This would mean that the first 

 order spectrum should be at last half as strong as that of 

 the fourth order, and the spectra of the second and third 

 orders would not be sufficiently weak at the same time. 



Now the maximum observed was not very strong, but we 

 should easily have detected a peak equal to J of that observed 

 for the fourth order spectrum. We can then safely conclude 

 that the oxygen atoms in xenotime cannot be arranged in a 

 lattice of the Zircon type. 



If in the lattice proposed for the Y and P atoms of 

 xenotime, both sorts of atoms were replaced by atoms of the 

 same reflecting power, the first three orders of the face (111) 

 would vanish. Then we must arrange the oxygen atoms so 



