324 ANDERSEN: PROPERTIES OF PYROPHOSPHATES 



and structure as revealed by the chemical formula, the axial 

 ratios and the properties of cohesion (cleavage). 



It is seen that the two compounds form monoclinic crystals 

 whose axial ratio a : b and angle 13 are very nearly of the same 

 magnitude. As to the ratio b : c nothing can be said owing to 

 the lack of a sufficient number of angles in the manganese pyro- 

 phosphate cry^als. The agreement in internal structure of the 

 crystals is evident from the presence of cleavage along the same 

 faces. Both kinds of crystals have a perfect cleavage along the 

 prisim z and in both there is a cleavage parallel to c though not 

 equally good in both. It may also be worth mentioning that 

 there is agreement in other physical properties. The hardness 

 is the same and the specific gravity of the same order of magni- 

 tude in the two substances: Altogether it seems on the basis 

 of the chemical composition and the crystallographic properties, 

 entirely justified to rank the two substances together as iso- 

 morphous. 



Isomorphism is, however, sometimes defined so as to imply 

 miscibility in the solid state (solid solution, mix-crystals). In 

 order to examine whether the two phosphates here considered 

 were isomorphous also in this extended sense a few experiments 

 were carried out: 



Three intermediate mixtures containing 76, 50 and 25 per cent 

 Mn2P207 (and a corresponding amount of jMg2P207) were pre- 

 pared. With these mixtures heating curves were run and the 

 substances were examined under the microscope. The results 

 are listed in Table 3, where also the melting points and refrac-, 

 tive indices of the pure compounds are given for comparison. 



It is plainly seen that there is a gradual transition from one 

 component to the other, both in ''melting point"^ and mean 

 refractive index. The heating curves showed no breaks other 

 than those corresponding to the melting points and the micro- 

 scopic examination proved that only one solid phase was formed 

 by crystallization of the melts. 



^ The breaks on the heating curves of the mixtures correspond to points be- 

 tween the liquidus and the solidus. In the present case these points probably 

 fall very near the liquidus. This may be inferred from the sharpness of the 

 breaks. 



