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I don't understand the difference between chemical composition and the amount of phase, why does the chemical composition of the phase not add up to 100%. For example in the image below the chemical composition of liquidus in this composition of Nickel and Copper $C_L=32$% and of the solidus $C_{\alpha}=43$% they don't add up to 100%. and why does $C_{\alpha}$ decrease as we cool does this mean that copper is solidifying faster than nickel and how is that possible if the solidification temperature of nickel is higher i.e. it should solidify more at lower temperatures.

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For example in the image below the chemical composition of liquidus in this composition of Nickel and Copper CL=32% and of the solidus Cα=43% they don't add up to 100%

There's no reason they should. In the liquid region, the same material has a weight percent of nickel of about 35%. This isn't 100% either!

What we need is for the percentages of all constituents (i.e., nickel and copper) to add up to 100%. We also need the weighted percentages of each constituent from all phases (e.g., α and liquid) to equal the total percentage of that constituent of the overall material (i.e., the nickel–copper alloy).

why does Cα decrease as we cool

Because nickel has a higher melting temperature than copper and because the two easily substitute for each other in a mixture, maintaining this trend from pure copper to pure nickel. Therefore, at a lower temperature, we tend to see more nickel as having frozen.

does this mean that copper is solidifying faster than nickel

No; we can't generally conclude anything about rates from an equilibrium phase diagram.

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