ON THE CHEMICAL COMPOUNDS CONTAINED IN ALLOYS. 



139 



Fig. 7. 



region below the eutectic angle to solid conglomerates of separate crystals 

 of A and B. The range of temperature between the first appearance of 

 crystals in a liquid alloy and its complete solidification is measured by the 

 vertical line drawn from a point on the curve to the level of the eutectic point. 



Let us now suppose that the two metals, which we will still call a and 

 B, can form mixed crystals in all proportions. According to Roozeboom 

 there will be no angle of intersection of the two curves, but the freezing- 

 points of A and B will be joined by a continuous curve, the points on 

 which cori-espond to exactly saturated liquids. He calls this the ' L ' or 

 ' liquid ' curve. But also starting from the freezing-points of A and b, 

 and lying under the ' l ' curve, a continuous curve can be drawn giving 

 the composition of the mixed crystals that form at each temperature. He 

 calls this the ' s ' or ' solid ' curve. The case is represented in fig. 7, 

 which, together with figs. 8 and 9, is taken from his paper. To find what 

 happens at a particular temperature, draw a horizontal line cutting the 

 ' L ' curve in 7i and the s curve in o. These two points of intersection 

 give the composition of the two phases that can exist together at the 

 temperature of the horizontal line. In fig. 7 n gives the composition of 

 the liquid that when it begins to freeze deposits 

 mixed crystals of the percentage o. 



The complete process of freezing can now 

 be stated. Draw through n a vertical line 

 mnqz cutting the L curve in n and the s curve 

 in q. Then n and all points above it correspond 

 to uniform liquid, q and all points below it to a 

 uniform mass of mixed crystals (not, as in fig. 1, 

 to a conglomerate of crystals of A and b). The 

 temperature range during freezing is n q, and 

 during the process, if perfect equilibrium is 

 ensured, the solids formed undergo continuous 

 transformation from the composition o to that 

 of q, while the liquid remaining at any moment 

 changes from n to p, where p is the intersection 

 of|L by a horizontal through q. Thus all the areas shaded vertically repre- 

 sent homogeneous states — above l of a liquid, below s of homogeneous 

 crystals. The part between l and s, shaded horizontally, represents states, 

 in which a solid is mixed with a liquid. 



The L and s curves may have a maximum or a minimum, in both of 

 which cases they touch each other at the maximum or minimum point, as 

 in figs. 8 and 9. 



The liquid whose composition is that of the maximum or minimum 

 will solidify completely at one temperature. Hence in the case of the 

 maximum one might mistake the solid for a definite chemical compound, 

 and in the case of a minimum for a eutectic mixture. One must remember 

 that the diagram need not stand for the whole freezing-point curve 

 of two elements, but for the horizontal space between the two points 

 corresponding to compounds, and we can treat the compounds themselves 

 as the components of the mixed crystals. Our copper-tin curve probably 

 shows such a case in the region between Cu^Sn and Cu^Sn. 



These considerations point to a great danger in the interpretations of 

 the minor details in complicated freezing-point curves such as those of 

 Kurnakov, Gautier, and our AuAl curve. Given perfect equilibrium 

 transformations during cooling, it should be fairly easy by appropriate 





z 

 Cone 



