Determine the relative amounts (in terms of volume...

Determine the relative amounts (in terms of volume fractions) of the phases for the alloys and temperatures given in Problems $9.10 \mathrm{a}, \mathrm{b}$, and $\mathrm{d}$. The following table gives the approximate densities of the various metals at the alloy temperatures: $$ \begin{array}{ccc} \hline \text { Metal } & \text { Temperature }\left({ }^{\circ} \boldsymbol{C}\right) & \text { Density }\left(\mathrm{g} / \mathrm{cm}^{3}\right) \\ \hline \mathrm{Cu} & 600 & 8.68 \\ \hline \mathrm{Mg} & 425 & 1.68 \\ \hline \mathrm{Pb} & 100 & 11.27 \\ \hline \mathrm{Pb} & 425 & 10.96 \\ \hline \mathrm{Sn} & 100 & 7.29 \\ \hline \mathrm{Zn} & 600 & 6.67 \\ \hline \end{array} $$

Determine the relative amounts (in terms of volume fractions) of the phases for the alloys and temperatures given in Problems $9.10 \mathrm{a}, \mathrm{b}$, and $\mathrm{d}$.
The following table gives the approximate densities of the various metals at the alloy temperatures:
$$
\begin{array}{ccc}
\hline \text { Metal } & \text { Temperature }\left({ }^{\circ} \boldsymbol{C}\right) & \text { Density }\left(\mathrm{g} / \mathrm{cm}^{3}\right) \\
\hline \mathrm{Cu} & 600 & 8.68 \\
\hline \mathrm{Mg} & 425 & 1.68 \\
\hline \mathrm{Pb} & 100 & 11.27 \\
\hline \mathrm{Pb} & 425 & 10.96 \\
\hline \mathrm{Sn} & 100 & 7.29 \\
\hline \mathrm{Zn} & 600 & 6.67 \\
\hline
\end{array}
$$

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Key Concepts

Lever Rule

The lever rule is a graphical method used in phase diagrams to estimate the relative amounts (in terms of mass or mole fraction) of coexisting phases in a two-phase region. By drawing a tie-line across the phases at equilibrium, one can determine the proportion of each phase based on the distances from the overall alloy composition to the phase boundaries.

Density and Mass-to-Volume Conversion

Density is a fundamental physical property that relates mass to volume. In the context of phase analysis in alloys, density values are used to convert mass fractions into volume fractions. Since different phases may have different densities, this conversion is essential to accurately determine the volume proportions of the phases present in an alloy.

Phase Equilibria

Phase equilibria refer to the study of the equilibrium between different phases in a material system. In alloy systems, various phases can coexist at equilibrium at a given temperature and composition. Understanding the phase equilibria allows one to predict the phases present and their compositions under different conditions, which is essential for determining relative amounts of each phase.

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