584 Sir William Bragg [May 19 r 



Institution some time ago.* We may call it the principle of radii 

 of combination. The distance between the centre of one atom and 

 the centre of a neighbour in many cases can be measured with great 

 accuracy ; we can compare these distances when substitutions are 

 made in isomorphous compounds. The replacement of fluorine by 

 chlorine, chlorine by bromine, bromine by iodine in a series of salts 

 produces changes in the distances which imply that the radius of 

 any one of the atoms mentioned may be treated as a constant within 

 the range of the substitution considered. The accuracy is amply 

 sufficient to give useful assistance in crystal analysis. It would not 

 be true, however, to say that each atom has an invariable radius, 

 and indeed the original statement of the principle purposely 

 refrained from going so far. It is not right to speak of the 

 radius of an atom ; it is better to speak of a radius of combina- 

 tion. We may take an illustration from the behaviour of arsenic* 

 antimony, and bismuth. The crystals of these substances are trigonal 

 in form,'t plainly showing that the properties of each atom are not 

 the same in all directions within the crystal ; in fact, analysis shows 

 that each atom is fastened to three on one side of it by much 

 closer bonds than to three atoms on the other side. One 

 bonding resembles more closely that of the diamond, the other 

 that of a metal where free electrons keep the atoms together by 

 electrostatic attraction. It may be said that the atom behaves as a 

 metal on one side and a non-metal on the other. At any rate, there 

 are two radii of combination varying with the nature of the bond. 

 The metallic bond is the weak one, and the cleavage plane cuts only 

 through such bonds. It seems very likely that in this way we can 

 understand the formation of crystals of different type when these- 

 elements enter into their composition. For example, in the cubic 

 form of senarmontite (Sb 2 3 ) the atoms of antimony are completely 

 separated ; each touches six atoms of oxygen, while each oxygen 

 touches four atoms of antimony. Antimony is here behaving as a 

 metal only, so that we represent it in a model as a sphere, and the 

 uniform spheres of antimony and of oxygen naturally build into a 

 simple crystal. It is a cube in which the atoms of antimony occupy 

 the corners and centres of the faces, while the six oxygen atoms lie 

 at the centres of six of the eight small cubes into which the large 

 one can be divided. 



There is, however, an alternative form of Sb 2 3 known as valen- 

 tinite, which is ortho-rhombic. Analysis, so far as it has gone, 

 though it is not yet complete, points emphatically to the conclusion 

 that here atoms of antimony are pairing, the bonds between the 

 members of a pair being of the stronger variety already referred to. 



* See Phil. Mag., Aug. 1920. 



+ James and Tunstall\ Phil. Mag., Aug. 1920 and July 1921 ; Ogg, PhiL 

 Mag., July 1921. 



