November 24, 1923] 



NATURE 



773 



Cohesion and Molecular Forces. 



T N opening a joint discussion on cohesion and mole- 

 -•^ cular forces between Sections A, B, and G of the 

 British Association at its recent meeting at Liverpool, 

 Sir Wilham Bragg emphasised the change of point of 

 view which the analysis of crystal structure by 

 X-rays has brought about. The older view, in which 

 atoms and molecules were pictured as centres of 

 force exerted in all directions, and governed by some 

 power law of the distance between them, has had 

 some measure of success in explaining the principal 

 features of surface tension and some of the departures 

 from perfection in a gas. But in a solid, except 

 possibly in the case of polar compounds, no satis- 

 factory results have accrued. On the newer view we 

 consider, not the aggregate, but the individual, atom 

 or molecule. 



It appears to be necessary to say that the very 

 strong forces between atom and atom, molecule and 

 molecule, are limited in their effective range of action 

 to distances much smaller than we have hitherto 

 supposed. Small, it may even be, compared to the 

 distances between the centres of atoms as they lie 

 side by side in a crystal. A crystal conforms so 

 exactly to rules respecting its angular dimensions 

 that it seems impossible to imagine its form to be 

 merely the result of an average of tendencies. The 

 forces of adjustment cannot, therefore, be thought 

 of as a force between two points each representing 

 one of the molecules. On the contrary, it is nearer 

 the truth to think that the adjustment is made so as 

 to bring together certain points on one molecule and 

 certain points on the other. In considering, there- 

 fore, the binding of the individual molecules of a 

 solid, the analogy of the electrostatic attraction of 

 two charged spheres is imperfect, and should be 

 replaced by that of two members of a girder structure 

 adjusted until the rivets can be dropped into the holes 

 brought into true alignment. This is seen well in 

 the recent work by Muller and Shearer, and by Piper 

 and Grindley on the structure of the organic fatty 

 acids and their salts. There is no doubt that the 

 ultimate flakes of the crystals of these fatty acids 

 are the monomolecular films investigated by Lang- 

 muir and by Adam, and it would appear that in 

 passing from one acid to a homologue of greater 

 molecular weight, each addition in thickness of the 

 ultimate flake is made in complete independence of 

 the previous length, as if the only thing that mattered 

 was the nature of the attachment of one carbon atom 

 to the next. There is no influence of the ends upon 

 the atoms in the middle. Again, we have the forces 

 different at different parts of the atomic surface, as 

 in the case of bismuth and its homologues, in which 

 the atom is attached to three neighbours on one side 

 by bonds differing from those which attach it to its 

 three neighbours on the other. 



With regard to the nature of these binding forces 

 three types may be recognised. First, there is the 

 effect set up by the sharing of a pair of electrons by 

 two contiguous atoms, leading to strong and directed 

 attachment. Next, there arc actions of a different 

 and generally weaker type manifested in the binding 

 of molecule to molecule in a crystal. We may be 

 sure that this type plays an important part in metals 

 and alloys. Lastly, there are the pure electro- 

 statical central actions. In the case of the polar 

 crystal Born and Land^ have made some progress in 

 calculating the effect of this. 



One well-known fact in crystal growth is that the 

 faces have different rates of growth, indicating that 

 there may be great differences in the ease with which 

 molecules slip into their places. Into this the 



NO. 2821, VOL. I I 2] 



element of time may enter, because a molecule may 

 come nearly into its right place and be held there 

 sufficiently long to get settled in by thermal agitation 

 or otherwise. We may suppose that the formation 

 of the crystal begins correctly enough, but that 

 errors of adjustment creep in until the surface 

 becomes somewhat disordered, and the growth ceases 

 because fresh molecules cannot find their proper 

 places to slip into. Without a more detailed knowledge 

 of the active forces localised at various points of atoms 

 and molecules we cannot build up a complete theory 

 of cohesion. 



Dr. Rosenhain, who followed, dealt with the simple 

 monatomic bodies — the metals — in which the develop- 

 ment of strength and ductility is so pronounced. 

 In his opinion it has now become possible to sketch 

 certain principles from which a general theory of the 

 nature of alloys may arise. The first is that the 

 atoms of two metals in solid solution are built on a 

 simple space lattice, the atoms of the solute metal 

 taking the places of a corresponding number of atoms 

 of the solvent metal, the lattice remaining essentially 

 unaltered. The presence of a " stranger " atom 

 produces a certain amount of distortion which is 

 responsible for the changes in the hardness, strength, 

 melting point, and other properties of the metal. The 

 second principle is that the inter-atomic distance 

 through which interatomic cohesion is appreciable 

 is strictly limited. When increased by any means — 

 thermal expansion, mechanical stress, or " stranger " 

 atoms — a limit is soon reached when the lattice 

 breaks down suddenly with the formation of another 

 phase. On heating, such a change is simply melting ; 

 on straining, it is the breakdown of elastic behaviour ; 

 and on alloying, we have the limit of solid solubility 

 resulting in the formation of crystals of a new type. 

 In many metals cohesion phenomena are complicated 

 by the occurrence of intra-crystalline slip, which 

 results in plastic deformation under stress by the 

 process of slip along certain planes within the crystal. 

 At the surface of slip there must be a rapid exchange 

 of partners without loss of continuity of bonding. 

 It is interesting that the phenomenon is confined to 

 metals crystallising in the two most symmetrical 

 systems, in which, presumably, the distribution of 

 atoms is sufficiently uniform to permit the passing on 

 of bonds to take place. 



The mechanism of ductility by means of slip is 

 intimately connected with diffusion in solid cnk-'stals. 

 In Dr. Rosenhain's opinion the process of diffusion of 

 one metal into another, the structure of which is 

 already that of closely packed lattices, may be due 

 to movement or slip of atoms in rows, the requisite 

 stress, which at high temperatures need not be great, 

 being provided by the lattice distortion arising from 

 a concentration of " stranger " atoms in a solid 

 solution of non-uniform concentration. On this 

 view ductile metals should allow diffusion far more 

 readily than brittle. It is well known that brittle 

 metals, like antimony and bismuth, show, no appreci- 

 able diffusion until quite near the melting point. 

 Moreover, it is known that nickel and copper — two 

 very similar atoms — exhibit extremely slow diffusion 

 as compareti with zinc and copper. This fits with the 

 above view and is at the same time not to be expected 

 on the view that metallic diffusion is a kinetic 

 phenomenon similar to that of liquids and gases. On 

 the same principles, a crude picture of the constitution 

 of an amorplious solid fitting the facts in a general 

 way may also be formed. 



With refjard to the method of binding of two 

 crystal lattice systems growing towards one another, 



