## Related questions with answers

An Al-Si alloy contains $15 \%$ primary $\beta$ and $85 \%$ eutectic microconstituent immediately after the eutectic reaction has been completed. Determine the composition of the alloy. (See Figure 11-19.)

Solution

VerifiedSince the constituents present are the primary-$\beta$ and eutectic, the reaction occurs at a hypereutectic composition. The Al-Si alloy freezing range occurred at the $\beta+L$ region and after it cools past the eutectic temperature of $577^o\text{C}$, transformed into $\alpha+\beta$ with a primary-$\beta$ and eutectic constituents.

We will use the tie line at the hypereutectic region. The $\%\beta$ will already be the relative amount of primary-$\beta$ present, while the amount of $L$ will be the one that will transform into the eutectic constituent. We let $X$ to be the composition of the alloy.

$\%\beta:\frac{X-12.6}{99.83-12.6}=0.15\%\text{ primary-}\beta$

$X=\boxed{\text{Al-}25.68\%\text{Si}}$

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