Chapter 11, Problem 11.30P

Interpretation Introduction

(a)

Interpretation:

In the given phase diagram, whether the alloy Al-4% Si is hypo-eutectic or hyper-eutectic needs to be determined.

Concept Introduction:

An alloy is a mixture of metals or the mixture of non-metals with another metal. A metallic bonding character defines alloys. For practical applications, the alloy constituents are generally evaluated by mass proportion and for fundamental science studies in the atomic fraction. Alloys are generally categorized as a replacement or interstitial alloys, based on the alloy's nuclear structure.

Answer to Problem 11.30P

The alloy is hypo-eutectic because its composition lies between eutectic reaction and eutectic composition.

Explanation of Solution

The phase diagram given is as follows:

From the phase diagram oftheAl-Si alloy system,

The alloy is hypo-eutectic because the composition is between eutectic reaction and the eutectic composition, and it lies between 1.65% and 12.6%Si.

Thus, from the phase diagram of the Al-Si alloy system, this alloy is hypo-eutectic because the composition lies between eutectic reaction and eutectic composition.

Interpretation Introduction

(b)

Interpretation:

The composition of the first solid to form during solidification needs to be determined.

Concept Introduction:

An alloy is a mixture of metals or the mixture of non-metals with another metal. A metallic bonding character defines alloys. For practical applications, the alloy constituents are generally evaluated by mass proportion and for fundamental science studies in the atomic fraction. Alloys are generally categorized as a replacement or interstitial alloys, based on the alloy's nuclear structure.

Answer to Problem 11.30P

The composition of the first form during solidification is 1%.

Explanation of Solution

Given:

It is given that % of Al=96%,wt. of Si=4gm, molar mass of Si=63.54 g/mol, molar mass of Al=26.891g/mol.

Calculations:

The formula for finding the composition of the first solid to form during solidification is,

  $\%S\text{i=}\frac{\frac{\text{wt}\text{.}\text{of}\text{Si}}{\text{molar}\text{mass}\text{of}\text{Si}}}{\text{(}\frac{\text{wt}\text{.}\text{of}\text{Si}}{\text{molar}\text{mass}\text{of}\text{Si}}\text{)+(}\frac{\text{\%}\text{of}\text{Al}}{\text{molar}\text{mass}\text{of}\text{Al}}\text{)}}\text{×100}\%$

Putting the values,

  $=\frac{\frac{4g}{63.54g/mol}}{\frac{4}{63.54}+\frac{96}{23.981}}\times 100\%$

Thus,

%Si $=1\%$

Therefore, from the formula, the composition of first solid to form during solidification is 1%.

Interpretation Introduction

(c)

Interpretation:

The amounts and compositions of each phase at $578°C$ needs to be determined.

Concept Introduction:

An alloy is a mixture of metals or the mixture of non-metals with another metal. A metallic bonding character defines alloys. For practical applications, the alloy constituents are generally evaluated by mass proportion and for fundamental science studies in the atomic fraction. Alloys are generally categorized as a replacement or interstitial alloys, based on the alloy's nuclear structure.

Answer to Problem 11.30P

The amounts and compositions of each phase at $578°C$ is $78.5\%$ and $21.5\%$ respectively.

Explanation of Solution

Given Information:

The given phase diagram is as follows:

The above-given diagram is the phase diagram of the Al-Si alloy system for the eutectic temperature of $578°C$

Calculations:

The eutectic reaction of the Al-Si alloy is in the form of $\alpha +L$. The amount and composition of each phase at $578°C$ is calculated with $\alpha =1.65\%$ and $L=12.6\%$.

  $\%\alpha =\frac{C_L-C_0}{C_L-C_{\alpha }}\times 100\%$

  $=\frac{12.6-4}{12.6-1.65}\times 100\%$

  $=78.5\%$

Thus, the liquid phase composition is

  $\begin{array}{l}\text{\%liquid}\text{phase}=100-78.5\\ =21.5\%\end{array}$

Thus, from the given phase diagram of Al-Si the amount and composition is $578°C$ is $78.5\%$ and $21.5\%$ respectively.

Interpretation Introduction

(d)

Interpretation:

The amounts and compositions at each phase and each micro-constituent at $576°C$ needs to be determined.

Concept Introduction:

An alloy is a mixture of metals or the mixture of non-metals with another metal. A metallic bonding character defines alloys. For practical applications, the alloy constituents are generally evaluated by mass proportion and for fundamental science studies in the atomic fraction. Alloys are generally categorized as a replacement or interstitial alloys, based on the alloy's nuclear structure.

Answer to Problem 11.30P

The amounts and compositions of each phase at $576°C$ are $97.6\%$ and $2.4\%$ respectively and the composition of each micro-constituent is $78.5\%$ and $21.5\%$ respectively.

Explanation of Solution

GivenInfromation:

The below diagram is the phase diagram of the Al-Si alloy system of eutectic temperature at $576°C$.

Calculation:

For the Al-Si alloy, the eutectic phase reaction is in the form of $\alpha +\beta$. At $576°C$, the amount and composition of each phase is calculated with $\alpha =1.65\%$ and $\beta =99.83\%$.

  $\%\alpha =\frac{C_{\beta }-C_0}{C_{\beta }-C_{\alpha }}\times 100\%$

  $=\frac{99.83-4}{99.83-1.65}\times 100\%$

  $=97.6\%$

Therefore, the solid phase is calculated as,

  $\begin{array}{l}\%\text{solid}\text{phase}=100-97.6\\ =2.4\%\end{array}$

The Al-Si alloy contains two stages. Therefore, the Al-Si alloy micro-constituent is primary and eutectic. Solid forming before an alloy is cooled to eutectic temperature is known as the primary micro-constituent and the strong forming is known as eutectic after the cooling temperature. The structure of micro-constituents is the primary $\alpha$ or 78.5% and the eutectic is 21.5%.

Thus from the phase diagram of Al-Si, the amounts and compositions of each phase at $576°C$ is $97.6\%$ and $2.4\%$ respectively and the composition of each micro-constituent is $78.5\%$ and $21.5\%$ respectively.

Interpretation Introduction

(e)

Interpretation:

The amounts and compositions at each phase $25°C$ needs to be determined.

Concept Introduction:

An alloy is a mixture of metals or the mixture of non-metals with another metal. A metallic bonding character defines alloys. For practical applications, the alloy constituents are generally evaluated by mass proportion and for fundamental science studies in the atomic fraction. Alloys are generally categorized as a replacement or interstitial alloys, based on the alloy's nuclear structure.

Answer to Problem 11.30P

The amounts and compositions of each phase at $25°C$ is $96\%$ and $4\%$ respectively.

Explanation of Solution

Given Information:

The above diagram is the phase diagram of the Al-Si alloy system of eutectic temperature at $25°C$.

Calculation:

For the Al-Si alloy, the eutectic phase reaction is in the form of $\alpha +\beta$. At $25°C$, the amount and composition of each phase is calculated with $\alpha =0\%$ and $\beta =100\%$.

  $\%\alpha =\frac{C_{\beta }-C_0}{C_{\beta }-C_{\alpha }}\times 100\%$

  $\begin{array}{l}=\frac{100-4}{100-0}\times 100\%\\ =96\%\end{array}$

Therefore, the solid phase is calculated as,

  $\begin{array}{l}\%\text{solid}\text{phase}=100-96\\ =4\%\end{array}$

Thus from the phase diagram of Al-Si the amounts and compositions of each phase at $25°C$ is $96\%$ and $4\%$ respectively.