428 Andersen — System Anorthite-Forsterite-Silica. 



tions and temperatures of the remaining liquid are expressed 

 by the points on the curve a b m. 



Phase relations. — The composition of a crystallizing liquid 

 (see fig. 4) is always expressed by a point on the straight line, 

 which joins the composition point of the solid phase (A) and that 

 of the initial liquid (a) from which the solid has separated. This 

 rule also holds true in the case of separation of two solid 

 phases, for instance A and C crystallizing between b and m. 

 The straight line mentioned then goes through the point which 

 indicates the mean composition of the solid separated, and this 

 mean composition is expressed by a point (b') on the line (AC) 

 joining the composition points of the two solid phases. If, 

 therefore, two solid phases have separated on cooling a liquid 

 between two given temperatures the mean composition of the 

 solid is expressed by the point of intersection between the line 

 joining the composition points of the liquids which correspond 

 to the two given temperatures'* and the line joining the com- 

 position points of the two solid phases.* In fig. 4 the crystal- 

 lization curve of a melt a between the temperatures a and b is 

 the straight line a b, the prolongation of which goes through A. 

 This means that the solid phase A only has separated between 

 a and b. At b the phase C also begins to separate and A and 

 C now ciystallize together along the boundary curve b m. 

 The mean composition of the solid separated between b and m 

 is given by the point b', which indicates a mixture of A and C 

 in the proportion b'C : b 1 A. and the mean composition of the 

 total solid separated between a and m (before eutectic crystal- 

 lization at m begins) is a'. The composition of the solid crys- 

 tallizing at any point, &,+ on a boundary curve is indicated by 

 a point on the tangent to the boundary curve at the point b. 

 This tangent intersects the line A C at the point b' 1 ', which 

 point, therefore, is the composition point of the solid crystal- 

 lizing at b. When the point m is reached the eutectic crystal- 

 lization, with simultaneous separation of A, B and C, begins. 

 During this eutectic crystallization the composition and 

 temperature of the liquid are unchanged while the composition 

 of the total solid changes from a' to a, reaching the latter 

 point at the moment the crystallization is complete and the last 

 of the liquid disappears. 



The amount of solid of composition A separated between a 



and b is equal to 100 x -r-= per cent of the initial composition 



a, and the amount of remaining liquid of composition b is 



a A 



equal to 100 x -r-r- per cent of a. In the same way it is seen 



* Or the prolongation of such a line. 



f That means through an infinitely small temperature range including b. 



