The derivation for the Gibbs phase rule, provided in physical chemistry text books, often assumes that all the components are present in all the phases coexisting at equilibrium. However, very often we have situations where all the phases at equilibrium do not have all the components, the binary eutectic system being a classic example. The melt (miscible solution of A and B) coexists with pure solid A and pure solid B at the eutectic point. The solid phases are one-component phases, whereas the system itself is binary. How does the phase rule, derived under the above-mentioned assumption, apply to the eutectic point? Using a simple example, we demonstrate that all the components need not be present in all the phases to arrive at the phase rule.

中文翻译：

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吉布斯相位规则：当某些相位缺少某些组件时会发生什么？

物理化学教科书中提供的Gibbs相规则的推导通常假设所有组分都存在于平衡共存的所有相中。但是，在很多情况下，处于平衡状态的所有相都不具有所有组成部分，二元共晶系统就是一个典型的例子。熔体（A和B的混溶溶液）在纯共晶点处与纯固体A和纯固体B共存。固相是单组分相，而系统本身是二元的。在上述假设下得出的相位规则如何适用于共晶点？通过一个简单的示例，我们证明了不必在所有阶段中都包含所有组件才能得出阶段规则。