POLYMORPHISM AT HIGH PRESSURES. 181 



certain critical distance. Thus Griineisen,^^ who has succeeded in 

 correlating many of the thermodynamic properties of solids by assum- 

 ing the atoms to be the centers of attractive and repulsive forces uni- 

 form in all directions, finds that the repulsive force must vary at least 

 as the inverse twelfth power of the distance, while the attraction varies 

 as the square. So rapid an increase of the repulsive force means a 

 close approach to the phenomena of a definite boundary. As for 

 regarding the atom (or unit) as possessing a definite geometrical shape 

 other than spherical, we cannot well do otherwise, for the very exist- 

 ence of crystals shows that the field of force about an atom is not 

 uniform in every direction. It has perhaps been more usual to regard 

 the crystal unit as a rigid sphere with localized centers of attractive 

 force. But this seems to be an unnecessary and unjustifiable restric- 

 tion. From the point of view of the field of force, this is equivalent 

 to saying that the attractive forces are unsymmetrically deposed, 

 whereas the repulsive forces are symmetrically directed toward all 

 sides. 



The atom or molecule need not be thought of as absolutely rigid. 

 It must of course be deformable to a certain extent, and there is experi- 

 mental evidence (the increase of energy of a liquid if isothermal com- 

 pression is carried beyond a certain point *^) that such an effect is 

 actually of importance. Furthermore, the temperature agitation in a 

 solid is doubtless largely a matter of internal agitation of the mole- 

 cules, rather than of motion of the molecules as wholes. 



One of the puzzles of polymorphic change is offered by substances 

 like benzol, in which the transition has no latent heat, but the internal 

 energy of the phase of smaller volume is the greater. If the forces 

 between the molecules are on the whole attractive, then we should 

 expect the potential energy to be decreased when the molecules are 

 brought closer together, instead of increased. An increase of energy 

 would be expected only if the approach of the molecules took place 

 against an average repulsive force. But if the force is on the average 

 repulsive, it is difficult to see why the molecules become unstable 

 and assume a new arrangement. However, if the atoms ha\'e proper- 

 ties like those above, this becomes understandable. Figure 34 shows 

 schematically what may be the arrangement in the phase of larger 

 volume. The molecules assume such an arrangement that the local- 

 ized centers of force approach as closely as possible. This is the 



41 E. Gruneisen, Ann. d. Phys., 39, 257 (1912). 



42 G, p. 95. 



