330 weight: crystals and crystal forces 



crimination in problems which are essentially vectorial in char- 

 acter, as are problems involving differences in directional crystal 

 forces. A large number of the minerals which occur in nature 

 are of the monotropic type and many of the reactions are exam- 

 ples of thermodynamically false equilibria and yet these may 

 exist for geologic ages without change. In applying thermo- 

 dynamical reasoning to problems of equilibria between crystals, 

 it is essential that the individuality of the crystals be considered, 

 especially as this introduces factors which may be superior in 

 magnitude to the thermodynamical tendencies toward equi- 

 librium, i.e. a configuration for which at the given temperature 

 the total energy content is a minimum. Thus, to speak of the 

 lack of crystallization in a volcanic obsidian because of an ex- 

 ceedingly slow rate of reaction, does not describe the situation 

 adequately, because in the volcanic glass the internal friction at 

 ordinary temperatures is so high that it is superior to the crystal 

 forces and completely inhibits effective action on their part; 

 the viscosity serves as a brake and may bring the crystallizing 

 tendencies to a stop. Similar conclusions apply to the general 

 application of thermodynamical equations to problems involving 

 the elastic properties of crystals, especially to the deformation 

 of a crystal under load. 



In the treatment of problems of this nature which involve 

 crystallization it is important to realizje that the influence of 

 certain forces which are grouped under the term " individuality" 

 of the crystal may exceed in importance the thermodynamical 

 tendencies toward equilibrium. In crystal as in other systems 

 thermodynamical relations are fundamental, but equally funda- 

 mental are the vectorial and polar force-relations which hereto- 

 fore have been little regarded because of the difficulty of defin- 

 ing and of measuring them satisfactorily. Many of the prob- 

 lems of crystal equilibria are of such a nature that in order to 

 effect a complete solution neither thermodynamics alone is ade- 

 quate, because of its inherent inability to treat vectorial and 

 polar properties properly, nor is crystallography alone adequate, 

 because it considers chiefly the single crystal. Progress can best 

 be made by bringing to bear on the problem both thermody- 



