22 Allen, etc. — Diopside and its Relations 



This formula holds approximately for concentrated solutions. 

 When Cj = C 2 , i. e., when the concentration of the solid solu- 

 tion is not changed by the process of inversion, there will 

 evidently be no change in the inversion point; when C X >C W 

 the temperature will fall, but if C 2 , the concentration below 

 the freezing point, is greater, then A will have the opposite 

 sign, and the freezing point will be higher than that of the 

 pure substance. 



The same conclusion is reached by a graphic method.* In 

 fig. 6 let AB represent the vapor pressure curve of the pure 

 solid below the inversion point, BC the vapor pressure above 

 it, and T the inversion temperature. Now if this solid forms 

 a solid solution, the vapor pressure of the former will be 

 lowered according to the concentration of the solution. Sup- 

 pose that this is the same above and below the inversion point, 

 and that the vapor pressures are lowered to the same degree in 

 both. It is evident that the new curves DE and EF will inter- 

 sect at the same temperature and the inversion temperature is 

 therefore unchanged. 



In fig. 7 let us suppose that the concentrations of the two 

 solid solutions are unequal, the one below the inversion point 

 being the more dilute. The curve AB will be lowered to DE 

 and BC will fall to EF by reason of the greater concentration 

 of the second solution. DE and EF now intersect at E, at a 

 temperature lower than T . By similar reasoning we conclude 

 that when the solid solution below the inversion point is the 

 more concentrated the inversion point will be raised. (See 

 fig 8.) Apparently the lower concentrations of diopside in 

 wollastonite remain the same when the mix-crystals invert, 

 for about 1-2 per cent MgSi0 3 is dissolved by the pseudo- 

 wollastonite. In these cases, "therefore, the inversion point 

 theoretically should not change. These solutions, however, are 

 unquestionably less changed at the same temperature than 

 wollastonite is. We therefore conclude that the solution of 

 diopside has increased the intermolecular friction of the crys- 

 tals. It is also possible that these solutions of wollastonite- 

 diopside which are more concentrated than 1-2 per cent 

 MgSiOg really have a higher inversion point than 1190°. 

 If the crystals saturated at this temperature remain more con- 

 centrated in diopside than the pseudo-wollastonite is, this must 

 be true. A decision cannot be reached until we have some 

 sure method of establishing equilibrium. Day and Shepherd 

 found that solid solutions of lime or silica in calcium metasili- 

 cate inverted to wollastonite on cooling. Since the pure rneta- 

 silicate does not behave so, we naturally conclude that the 

 internal friction was lessened by the lime or silica. Magnesium 



* Bodlander, Neues Jahrb. Min., Beilage Bd. xii, p. 52. 



