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Phase equilibrium is a fundamental concept in physics and chemistry, described by the phase rule deduced by J. Willard Gibbs. It relates the number of phases (solid, liquid, gas) in a system at thermodynamic equilibrium to the number of chemical components and the degrees of freedom (variables like temperature and pressure).1

The phase rule is mathematically expressed as (F = C - P + 2), where (F) is the number of degrees of freedom, (C) is the number of components, and (P) is the number of phases. For example, a single-component system with one phase has two degrees of freedom, meaning both temperature and pressure can vary. However, with one component and three phases (like ice, water, and vapor at the triple point), there are no degrees of freedom, and temperature and pressure are fixed.1

Phase diagrams visually represent these relationships, showing the conditions under which different phases can coexist in equilibrium. These diagrams are crucial in understanding mineral associations in rocks and optimizing industrial processes.23

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