356 Mr. W. L. Bragg on the 



This was roughly polished, treated with nitric acid to dissolve 

 away the outer layers, and then mounted in the usual way in 

 the X-ray spectrometer *. 



By assuming various arrangements for the copper atoms, 

 we can calculate the spacings o£ various planes of the crystal, 

 starting from the density of copper, 8*96, as a basis. For 

 instance, if the copper atoms are arranged at the corners of 

 cubes, so as to form a simple cubic lattice,, we have the 

 relation 



(d cm y. 8-96 = 63-57. 1-64. 10~ 24 , 



since we know that 



1. Mass of a copper atom =63*57 . (Mass of a hydrogen atom) 



= 63*57. 1-64. 10" 24 gram, 



2. The unit cube of the structure contains one copper atom, 

 This gives the relation 



d am = 2-26. lO" 8 cm. 



The X rays from an anticathode of palladium, such as was 

 used for the purposes of this experiment, have a wave-length 

 of -576 . 10 -s cm. This is reflected from the planes d ( ioo) at 

 an angle given by the equation 



\ = 2 . d ( ioo) . sin 0. 

 Substituting the above values for \ and i(ioo), we find that 



e=r 20'. 



Suppose, on the other hand, that the copper atoms were on 



a face-centred cubic lattice. This lattice has a point at each 



corner of a set of cubes, and one at the centre of each cube 



face. The volume (rf(ioo)) 3 now contains only one-half a 



copper atom. From this it can be calculated that ^( 100) = 



1*80 . 10 -8 cm. So for the other faces ; the results are 



summarized below. 



Smoino- of planes Glancing angle of 



bpacing ot planes. reflexion, ?d rays. 



Face-centred lattice : 



d {m) =l'80 . lO" 8 cm. (1O o) = 9° 13' 



tf (110) = l-27 . lO" 8 cm. 0(uo) = 13° 2 ' 



i au) =2-08 • 10" 8 cm. 0(ui) = 8° 0' 



Simple cubic lattice : 



J ao0 ) = 2-26 . lO" 8 cm. ( ioo) = 7° 20' 



d (110) = l-59 . 10" 8 cm. 0(iio)= 10° 22' 



d (111) =l-30 . lO" 8 cm. ( iu)= 12° 50' 



* For a description of the instrument and its manipulation, see Proc. 

 Roy. Soc. A. vol. lxxxviii. p. 428, and A. vol. lxxxix. p. 468. 



