16 Rankin and Wright — Ternary System CaO-Al 2 0^-SiO^ 



phases are necessary. There are two possible such systems, 

 S-S-S- V and S-S-L- V. In order that the system be bivari- 

 ant three phases are necessary. There are two possible such 

 systems, #-#-Fand S-L-V. The solid phases may be com- 

 ponents, binary or ternary compounds. 



From the general conditions of equilibrium as deduced from 

 the phase rule for three component systems under the condi- 

 tions we have mentioned it is now possible to ascertain some- 

 thing of the nature of such systems. 



The equilibrium relations in a three component system are 

 most easily grasped if the compositions are plotted on an 

 equilateral triangle ; the same scale is taken for the binary 

 systems on the sides of the triangle as for the ternary system 

 in the interior. On such a diagram* the pure components are 

 given by the apices of the triangle, the invariant systems by 

 points (quintuple points), the univariant systems by lines 

 (boundary curves) and divariant systems by fields included 

 within the triangle. All compositions will be given here in 

 percentage weights of the components. 



The effects of the change of the variable-temperature- 

 are more obvious if a solid model is made by erecting, at each 

 point in the plane of the triangular diagram, lines perpendi- 

 cular to that plane, the length of each being proportional to the 

 equilibrium temperature at that composition. f For our pres- 

 ent purpose, however, projection of ternary curves on the 

 plane of the triangle will be used. 



* Eoozeboom, Zs. physik. Chem., xv, 13, 1894 ; Bancroft, J. phys. Chem., 

 i, 403, 1897. 



f An ingenious method for the construction of a solid concentration- 

 temperature model has been devised by Mr. England of this laboratory. 

 This model represents accurately concentrations and the corresponding 

 temperatures for a three component system. — On a flat piece of well-seasoned 

 wood is securely fastened a piece of sheet tin, which serves as a base for the 

 solid model. On the surface of the sheet tin is drawn an equilateral triangle, 

 on which are represented the compositions of the compounds (binary and 

 ternary), the quadruple and quintuple points, and the boundary curves, 

 which define the limits of the various ternary fields, as lines. The concen- 

 tration-temperature diagram for each binary system (not only the binary 

 systems of which the sides of the triangle give the compositions but also 

 the binary systems included within the ternary system) and each, boundary 

 curve is cut from a piece of sheet tin. The lowest temperature for each 

 concentration-temperature diagram must necessarily be a common tem- 

 perature, which is that represented by the plane of the base of the model. 

 Each of the concentration -temperature diagrams is placed along its parti- 

 cular concentration line on the triangular base, perpendicular to the plane 

 of this base, and is then soldered in place. The resulting figure is a skeleton, 

 form which represents the compositions and corresponding temperatures of 

 the compounds, quadruple points, quintuple points and boundary curves. 

 If now we fill in each space in the skeleton with plaster of Paris, which is 

 surfaced to conform to the slopes of the curves surrounding each space, we 

 have produced a solid model, points on the surface of which represent com- 

 positions and the corresponding melting temperatures of ternary mixtures. 

 Changes which take place in solid ternary crystalline mixtures, of course can 

 not be represented in this solid model. 



