A 65 wt % Ni-35 wt% Cu alloy is heated to a temperature within the α+ liquid-phase region. If th

step 1 All right, so here in this problem in part A, we are given that the mass fractions of alpha and

A 65 wt % Ni-35 wt% Cu alloy is heated to a temperature...

A 65 wt $\%$ Ni-35 wt$\% $Cu alloy is heated to a temperature within the $\alpha+$ liquid-phase region. If the composition of the $\alpha$ phase is 70 wt$\%$ $\mathrm{Ni}$, determine: (a) The temperature of the alloy (b) The composition of the liquid phase (c) The mass fractions of both phases

A 65 wt $\%$ Ni-35 wt$\% $Cu alloy is heated to a temperature within the $\alpha+$ liquid-phase region. If the composition of the $\alpha$ phase is 70 wt$\%$ $\mathrm{Ni}$, determine:
(a) The temperature of the alloy
(b) The composition of the liquid phase
(c) The mass fractions of both phases

Key Concepts

Binary Phase Diagrams

Binary phase diagrams graphically depict the equilibrium phases present in a two-component system as functions of temperature and composition. They show the boundaries between different phase fields, and provide essential information regarding phase stability, solubility limits, and the compositions of coexisting phases at given conditions.

Two-Phase Equilibrium

Two-phase equilibrium refers to the state in which two distinct phases coexist in equilibrium under specific conditions of temperature and overall composition. In a phase diagram, this is represented by regions where a tie-line connects the compositions of the two coexisting phases, ensuring that the overall composition is a weighted average of the respective phase compositions.

Lever Rule

The lever rule is a quantitative tool used in phase diagrams to determine the mass fractions of the phases in a two-phase region. By treating the phase diagram as a lever with the two phase compositions as the fulcrum points, the mass fraction of each phase is calculated by measuring the relative distances on the composition axis from the overall alloy composition to the phase boundaries.

Tie-Line

A tie-line is a horizontal line drawn at a constant temperature within a two-phase region of a phase diagram that connects the equilibrium compositions of the coexisting phases. It enables the direct reading of phase compositions and is critical for the application of the lever rule to obtain the phase fractions.

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