Chapter 11, Problem 11.31P

Interpretation Introduction

(a)

Interpretation:

Whether the alloy is hypoeutectic or hypereutectic needs to be determined.

Concept Introduction:

Eutectic alloy is defined as a mixture of metals having a melting point lower than that of any of components. An alloy which has composition that lies to the left of the eutectic point present on the phase diagram is termed as hypoeutectic alloy. The hyper-eutectic alloy is defined as the alloy which consist of composition that lies to the extreme right of the eutectic point.

Answer to Problem 11.31P

The Ai- $25\%$ Si alloy is hypereutectic.

Explanation of Solution

The Al- $25\%$ Si alloy has a eutectic composition between the range $61.9\%$ to $97\%$ Si.

Therefore, Al- $25\%$ Si alloy is hypereutectic that has its composition between the eutectic reaction.

The hyper-eutectic alloy is defined as the alloy which consist of composition that lies to the extreme right of the eutectic point.

Hence, as per the hyper-eutectic alloy conditions, the given Ai- $25\%$ Si alloy fits into the hypereutectic.

Interpretation Introduction

(b)

Interpretation:

The value of composition of the first solid formed during the solidification process needs to be determined.

Concept Introduction:

Solidification is the method which is also known as freezing process. Solidification process is defined as the phase change of matters. The phase change of matter that results in the production of solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquid takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Answer to Problem 11.31P

The value of composition is $99.9\%$ Si.

Explanation of Solution

During solidification the first solid formed has some amount of composition. The value of composition of the first solid formed during solidification of Al- $25\%$ Si alloy is calculated by the expression given below.

Therefore, composition where the first solid phase occurs as $99.9\%$ Si.

Interpretation Introduction

(c)

Interpretation:

The amount and composition of each phase of temperature of $\text{578°C}$ needs to be determined.

Concept Introduction:

Solidification is the method which is also known as freezing process. Solidification process is defined as the phase change of matters. The phase change of matter that results in the production of solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquid takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Answer to Problem 11.31P

The amount of the phase obtained is $12.6\%$ Si and the composition are $85.8\%$.

Explanation of Solution

The given temperature is $\text{578°C}$. The phases which are present at $\text{578°C}$ are phase and liquid phase. The amount of each phase at $\text{578°C}$ is determined and given below-

  $\begin{array}{l}\text{a=12}\text{.3\%}\\ \text{b=99}\text{.83\%}\\ \text{c=25\%}\end{array}$

  

So, we can calculate the weight percentage of eutectic phase ${\text{X}}_{\text{L}}$ by using lever rule −

  $\begin{array}{l}{\text{X}}_{\text{L}}\text{=}\frac{\text{c-b}}{\text{a-b}}\text{×100}\\ {\text{X}}_{\text{L}}\text{=}\frac{\text{25-99}\text{.83}}{\text{12}\text{.6-99}\text{.83}}\text{×100}\\ {\text{X}}_{\text{L}}\text{= 85}\text{.8\%}\end{array}$

Thus, we obtained the amount and composition of phase from the above standard phase diagram as $85.8\%$ Si and $14.2\%$ Si.

Interpretation Introduction

(d)

Interpretation:

The amount and composition of each phase at temperature of $\text{576°C}$ needs to be determined.

Concept Introduction:

Solidification is the method which is also known as freezing process. Solidification process is defined as the phase change of matters. The phase change of matter that results in the production of solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquid takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Answer to Problem 11.31P

The amount of phase obtained is $76.2\%$ and $23.8\%$ Si.

Explanation of Solution

The given temperature is $\text{576°C}$. phases are present in Al- $25\%$ Si alloy at the given temperature of $\text{576°C}$.

The amount of each phase at $\text{576°C}$ is given as follows;

To calculate the composition of each phase at $\text{576°C}$ apply the lever's rule in the phase and the sketch the tie line in the phase.

To calculate the composition of phase, we have the expression,

  $\begin{array}{l}\text{a=1}\text{.65\%}\\ \text{b=99}\text{.83\%}\\ \text{c=25\%}\end{array}$

So, we can calculate the weight percentage of eutectic phase ${\text{X}}_{\text{L}}$ by using lever rule −

  $\begin{array}{l}{\text{X}}_{\text{α}}\text{=}\frac{\text{c-b}}{\text{a-b}}\text{×100}\\ {\text{X}}_{\text{α}}\text{=}\frac{\text{25-99}\text{.83}}{\text{1}\text{.65-99}\text{.83}}\text{×100}\\ {\text{X}}_{\text{α}}\text{= 76}\text{.2\%}\end{array}$

Interpretation Introduction

(e)

Interpretation:

The amount and composition of each micro constituent at the temperature of $\text{576°C}$ needs to be determined.

Concept Introduction:

Solidification is the method which is also known as freezing process. Solidification process is defined as the phase change of matters. The phase change of matter that results in the production of solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquid takes place in the process of solidification. Solidification can yield metastable product structures high undercooling. The constituents of the metastable products are the result of kinetic competition.

Answer to Problem 11.31P

The amount of eutectic phase and phase is calculated at $85.8\%$ Si and $14.2\%$ Si. The composition of eutectic phase and phase is $12.6\%$ and $99.83\%$ respectively.

Explanation of Solution

The phases present at eutectic phase and phase is calculated as $12.6\%$ Si and $99.83\%$ Si. The composition of eutectic phase and phase is $85.8\%$ and $14.2\%$ respectively.

The phases present at the $\text{576°C}$ are at the temperature of $\text{576°C}$ the microconstituents which are present are primary and eutectic.

From the diagram mentioned above at $\text{576°C}$ the amount of micro-constituent is as follows;

To calculate the composition of eutectic phase at $\text{576°C}$, apply the lever's rule with expression given below,

To calculate the composition of primary phase −

  $\begin{array}{l}\text{a=12}\text{.3\%}\\ \text{b=99}\text{.83\%}\\ \text{c=25\%}\end{array}$

So, the weight percentage of eutectic phase ${\text{X}}_{\text{L}}$ by using lever rule can be calculated as follows:

  $\begin{array}{l}{\text{X}}_{\text{α}}\text{=}\frac{\text{c-b}}{\text{a-b}}\text{×100}\\ {\text{X}}_{\text{α}}\text{=}\frac{\text{25-99}\text{.83}}{\text{12}\text{.6-99}\text{.83}}\text{×100}\\ {\text{X}}_{\text{α}}\text{= 85}\text{.8\%}\end{array}$

Interpretation Introduction

(f)

Interpretation:

The amount and composition of each phase at $\text{25°C}$ needs to be determined.

Concept Introduction:

Solidification is the method which is also known as freezing process. Solidification process is defined as the phase change of matters. The phase change of matter that results in the production of solid phase. Regularly, this occurs when the temperature of the liquid is lowered below the freezing point. Undercooling of liquid takes place in the process of solidification. Solidification can yield metastable product structures at high undercooling. The constituents of the metastable products are the result of kinetic competition.

Answer to Problem 11.31P

The number of phases present in Al- $25\%$ Si alloy are $0\%$ Si and $100\%$ Si. The amount of $\text{α}$ and $\text{β}$ as $75\%$ and $25\%$

Explanation of Solution

The phases present at $\text{25°C}$ are phase and phase.

From the diagram mentioned above the amount of the phases calculated are

To calculate the composition of phase at $\text{25°C}$, apply the lever's rule drawing a tie line in phases, we have the below expression,

  $\begin{array}{l}\text{a=0\%}\\ \text{b=100\%}\\ \text{c=25\%}\end{array}$

So, one can calculate the weight percentage of eutectic phase ${\text{X}}_{\text{L}}$ by using lever rule −

  $\begin{array}{l}{\text{X}}_{\text{α}}\text{=}\frac{\text{c-b}}{\text{a-b}}\text{×100}\\ {\text{X}}_{\text{α}}\text{=}\frac{\text{25-100}}{0-100}\text{×100}\\ {\text{X}}_{\text{α}}\text{= 75\%}\end{array}$