RanTcin and Wright — Ternary System Ca 0-Al 2 O s -Si 2 . 1 7 



u A theorem by Yan Rijn van Alkemade serves as a very 

 effective guide in regard to temperature changes in the interior 

 of the triangle. If the two points in the triangle which cor- 

 respond to the composition of two solid phases be connected 

 by a line, the temperature at which these same two phases can 

 be in equilibrium with solution and vapor rises as the boundary 

 curve approaches this line, becoming a maximum at the inter- 

 section, though the boundary curve often ceases to be stable 

 before this point is reached. When the two solid phases are 

 two of the components, the line connecting their compositions 

 is one of the sides of the triangle. ' It is, therefore, clear that 

 the temperature must always rise in passing along a boundary 

 curve to the side of the triangle if the theorem of van 

 Alkemade be right."* 



The usefulness of the theorem of van Alkemade will be 

 more apparent when applied in the study of the different 

 types of three component systems. 



TYPICAL THREE-COMPONENT SYSTEMS. 



Six simple representative types of three-component systems, 

 in which no solid solutions occur, are given to illustrate some 

 of the general principles ; they are represented by diagrams in 

 fig. 4. 



The simplest type (1) is that in which the three components 

 are the only solid phases. A, B and G are the three compo- 

 nents, whose respective melting points are represented by the 

 apices of the triangle, the sides of which represent the melting 

 temperatures for the binary mixtures, A-B, B-G and G-A. 

 The arrows on the sides of the triangle indicate the direction 

 of falling temperature and the points 1, 2 and 3 are the quadru- 

 ple points at which each pair of components, G-A, B-G and 

 A-B respectively, are in equilibrium with solution and vapor. 

 If, as in the present case, the quadruple points are the lowest 

 melting temperatures for each two-component system, they are 

 known as eutectic points. 



Inside of the triangle there is for each component a definite 

 area (field) in which it is in equilibrium with solution and 

 vapor ; in other words, there is a definite field which represents 

 the melting temperatures of one component in mixtures con- 

 taining the other two components. The lines 1-4, 2-4, 3-4 

 separating these fields are known as boundary curves, each of 

 which represents a condition of 4-phase equilibrium between 

 two components, liquid and vapor ; that is, a boundary curve 

 represents the melting temperatures of mixtures of two com- 

 ponents containing varying proportions of the third component. 

 * Bancroft, " The Phase Rule," p. 149. 



Am. Jour. Sci.— Fourth Series, Vol. XXXIX, No. 229. -January, 1915. 

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