n6 



NA TURE 



[July 



1922 



carried out in a second of these ways, the relative 

 numbers of neighbours being four to two. It is the 

 lightest and most open of the 2 to 1 structures, and is 

 consistent with the low specific gravity of ice and with 

 the possibility of compressing the substance into denser 

 forms : at the same time it shows the six -pointed 

 arrangement and the featheriness of the snow crystal. 2 



The earlier results at the same time showed that in 

 the diamond we had a construction of very different 

 properties and nature. Here the atoms are electrically 

 neutral and are bound to one another, not by electrical 

 attraction from centre to centre, but by a more intimate 

 process which probably consists in some way of a 

 sharing of structural electrons. The diamond is on 

 this account the hardest of known substances. 



These considerations amount to a recognition that 

 the bonds between the atoms may be of very- 

 different characters though it may be difficult to draw 

 hard and fast lines between them. We can say that 

 there is a very strong electron sharing bond of which 

 the diamond is typical, and that there are ionic bonds 

 in polar compounds which in general are of a weaker 

 character, as, for example, in rocksalt, though on the 

 other hand they may be strong when, as in the ruby, 

 the ionic charges are large. 



Lastly, there is a third type, which is found in the 

 organic crystal, where it would appear that the separate 

 molecule can be distinguished. The atoms in each 

 molecule are strongly tied together, but the forces that 

 bind molecule to molecule may be described as residual. 

 They would appear to be weak fields concentrated at 

 definite points on the molecule, the positive and 

 negative charges to which they are due lying 

 within it. 



The second principle which emerged fairly early in 

 the experiments was described by my son in an address 

 which he gave in this Institution some time ago. 3 We 

 may call it the principle of radii of combination. The 

 distance between the centre of one atom and the centre 

 of a neighbour can in many cases 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 con- 

 sidered. 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 prin- 

 ciple 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 combination. We may take an 

 illustration from the behaviour of arsenic, antimony, 

 and bismuth. The crystals of these substances are 

 trigonal in form, 4 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 



! Proc. Phys. Soc, London, vol. xxxiv. pt. 3, p. 98. 



3 See Phil. Mag., Aug. 1920. 



4 James and Tunstall, Phil. Mag., Aug. 1920 and July 1921 ; Ogg, Phil. 

 Mag., July 1921. 



NO. 2751, VOL. I io] 



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 valentinite, 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 

 antimonv are pairing, the bonds between the members 

 of a pair being of the stronger variety already referred 

 to. We now have an elementary body of a dumb-bell 

 shape which, when forming part of the crystal structure, 

 will naturally cause a deviation from a simple cube. 



Yet again, there are principles which are barely 

 established as yet, though it seems probable that they 

 will be found of material assistance in analysis. The 

 greater expansion of some crystals in certain directions 

 than in others seems to depend upon the nature of the 

 bonds. Bismuth expands more along the axis than 

 across it, as we might expect from the fact that in the 

 one expansion the weak bonds alone can be operative. 

 In the same way diamond has an extremely small 

 expansion co-efficient because all the bonds are of the 

 strongest kind, but in graphite, on the other hand, the 

 expansion along the axis may be described as enormous. 

 Mr. Backhurst finds an increase in length of 3 per cent, 

 for a rise of 900 C. At the same time, so far as can 

 be inferred, the expansion across the axis is still quite 

 small. In one case weak bonds only are concerned, 

 in the other, strong bonds of the same kind as in the 

 diamond. 



It is when all these considerations are taken 

 into account that it seems possible to make an 

 attempt upon the structure of the organic crystals. 

 They are, of course, very complex ; naphthalene 

 contains 10 atoms of carbon and 8 atoms of hydrogen, 

 and our ability to interpret X-ray evidence, that is to 

 say, the relative intensities of reflection by the different 

 planes in different orders, is not sufficiently advanced 

 to enable us to place so many atoms in their proper 

 position in the cell from this evidence alone. We can 

 readily find the size of the unit cell, show that there 

 are two molecules in it, and that the points, each of 

 which represents a whole molecule, are to be placed as 

 is shown in Fig. 1, but without some further help we 

 can frame no hypothesis on which to proceed. 



Suppose now that we compare the structures of 

 diamond and graphite. As my son showed long ago, 



