Rankin and Wright — Ternary System CaO-Alfi 3 -SiO„. 53 



" From the deductions of Alkemade, it is known that the 

 temperatures fall along the sides of the triangle toward the 

 binary eutectics and, so far as this diagram is concerned, toward 

 the ternary eutectic."* The direction of falling temperature 

 is indicated in the diagram by arrows ; fig. IT is, of course, a 

 projection of the solid model on the horizontal plane. 



When a saturated solution, whose composition is represented 

 by any point within triangle S-CS-CAS^ is cooled and a 

 solid crystallizes, the concentration of the solution changes by 

 the amount of the separated phase. In other words, the differ- 

 ence between the number of kilograms of #, CS and CAS n \n 

 the original solution and the number of kilograms of S, OS, 

 and CAS 2 in the residual solution is the number of kilograms 

 of solid crystallized. Now if one starts with any solution 

 and cools, the composition of the residual solution after partial 

 crystallization lies on a straight line which passes through the 

 point giving the composition of the solid separating and the 

 point giving the composition of the initial solution. Such a 

 change of concentration along a straight line through the 

 initial solution and the solid crystallized constitutes the funda- 

 mental principle of phase separations. Thus in fig. 17, on 

 cooling a solution which has a composition represented by the 

 point d, on the side of the triangle CS-S, the component S 

 will crystallize, while the solution itself will change concentra- 

 tion in the opposite direction along the line OS-S, and at some 

 temperature, lower than that of the original solution, there 

 exists, in equilibrium with S, a new solution e. 



By means of the diagram one can compute the amount of S 

 which has separated from the solution and also the amount of 

 S retained in the solution e. The ratio of the line de to the line 

 Se is the percentage of the total composition of the solution d 

 which has separated as S in cooling from d to e. The ratio of 

 Sd to Se is the percentage of the total composition correspond- 

 ing to d which remains in the solution e. For example, let 

 the composition of d be 80 kilograms of S and 20 kilograms of 

 OS, and that of e be TO per cent S and 30 per cent OS. The 

 number of kilograms that have separated is found by the ratio 



de 10 



— - X 100 =— X 100 = 33 1/3 percent. 



Thus 33 1/3 kilograms have separated as S, and 66 2/3 kilo- 

 grams of & and OS remain in solution at e. The solution d 

 contains 80 kilograms of S. 80-33 1/3 = ±6'6 kg. of S remain 



* Geer, ibid., p. 259. 



f It is, of course, understood that the process of cooling is slow enough to 

 secure the continuous attainment of equilibrium. 



