Chapter 11, Problem 11.46P

Interpretation Introduction

(a)

Interpretation:

The phase diagram of the Ag-Ge system needs to be draw $\text{7}$ n and the phases present in each region of the diagram needs to be labeled.

Concept Introduction:

The initial two phases near the eutectic point are known as −

  $\text{α}$ = Primary solid solution of Ag

  $\text{β}$ = Primary solid solution of Ge

An intermediate phase is observed denoted by $\text{ζ}$, having closed packed hexagonal structure and having axial ratio values near to the ideal value.

Based on the result of in situ observations and experiment of high-pressure quenching, the possible all phase diagram of the two alloys is drawn at pressure GPa.

The phase of Ag-Ge $\left(111\right)$ drawn in the region is called as sub monolayer region.

Answer to Problem 11.46P

The phase of Ag-rich and Ge-rich composition is represented as follows:

  

Explanation of Solution

From the phase diagram of Ag-Ge system as shown below:

  

Ge - rich solid phase denoted by $\text{β}$

Ag - rich solid phase denoted by $\text{α}$

L − Liquid phase

Interpretation Introduction

(b)

Interpretation:

The compositions and the amounts of the phases present in Ag-Ge system needs to be determined.

Concept Introduction:

Phase diagram of Ag-Ge system is as given below:

  

Initial two phases near the eutectic point are observed as −

  $\text{α}$ = Primary solid solution of Ag

  $\text{β}$ = Primary solid solution of Ge

An intermediate phase is observed denoted by $\text{ζ}$, having closed packed hexagonal structure and having axial ratio values near to the ideal value.

Based on the result of in situ observations and experiment of high-pressure quenching, the possible all phase diagram of the two alloys is drawn at pressure $\text{7}$ GPa.

The phase drawn of Ag-Ge region is called as the sub monolayer region.

Answer to Problem 11.46P

The composition of the phase diagram Ag-Ge is made up of $21$ % and $79$ % of alloy of Ag and Ge respectively.

Explanation of Solution

Given:

Ge = $80$ %

Ag = $20$ %

Temperature T= $700$ K

Calculation:

From the given figure, we get to know that,

At $700$ K temperature, the alpha composition is $5$ % of Ag and beta composition is $100$ % of Ge

Hence, we want to determine the amount of all phase of $80$ % Ge −

Consider −

a = $5$ % Ag

b = $100$ % Ag

c = $80$ % Ag

X = amount of Ge present in alloy

  $\begin{array}{l}{\text{X}}_{\alpha }\text{=}\frac{\text{80-100}}{\text{5-100}}\text{×100}\\ \end{array}$

  ${\text{X}}_{\alpha }\text{ = 21}$ % and ${\text{X}}_{\beta }\text{ = 79}$ %

Hence, at $700$ K in Ag-Ge alloy, $\text{α}$ and $\text{β}$ are found to be $21$ % and $79$ % respectively.

Interpretation Introduction

(c)

Interpretation:

The transformation in phases that occur on solidification from the melt at the point marked with a circle needs to be explained and the special name needs to be given to this transformation.

Concept Introduction:

Solidification is also called as the process of freezing. The freezing point of liquid is higher than the temperature of liquid changed into the solid state which is called as freezing. Internationally, freezing is solidification where change of liquid phase or liquid content occurs because of the cooling effect.

For a greater number of substances, the freezing and melting temperature is available at the same temperature whereas some substances having different transition temperature of liquid-solid state.

Answer to Problem 11.46P

The marked point in the figure is known as the eutectic point.

Explanation of Solution

Given Information:

  

From the given figure, the marked point is the eutectic point as a transformation from the liquid state to the solid state is occurring.

The eutectic reaction for the eutectic point is

  $\text{L}\to \text{α}\left(\text{Solid}\right)\text{+β}\left(\text{Solid}\right)$

Here, L= liquid phase

  $\text{α}$ = Solid phase

  $\beta$ = Solid phase

Hence during solidification, the liquid phase is converted into the liquid phases at the eutectic points.

Interpretation Introduction

(d)

Interpretation:

A schematic diagram illustrating the final microstructure of $15$ % Ge ( $85$ % Ag) cooled slowly to $300$ K from the liquid state needs to be drawn.

Concept Introduction:

Phase diagram of Ag-Ge system is represented as follows:

  

Initial two phases near the eutectic point are given as −

  $\text{α}$ = Primary solid solution of Ag

  $\text{β}$ = Primary solid solution of Ge

An intermediate phase is observed denoted by $\text{ζ}$, having closed packed hexagonal structure and having axial ratio values near to ideal value.

Based on the result of in situ observations and experiment of high-pressure quenching, the possible all phase diagram of the two alloys is drawn at pressure $\text{7}$ GPa.

The phase drawn of Ag-Ge region is called as sub monolayer region

Answer to Problem 11.46P

The composition of $15$ % Ge is present at $300$ K temperature and the phase is present at $\left(\text{α + β}\right)$.

Explanation of Solution

From the phase diagram of Ag-Ge, we get to know that composition of $15$ % Ge is present at $300$ K temperature and the phase is present at $\left(\text{α + β}\right)$.

  

Thus, the composition of $15$ % Ge is present at $300$ K temperature and the phase is present at $\left(\text{α + β}\right)$

Interpretation Introduction

(e)

Interpretation:

The stronger sample from the two given samples at room temperature in Ag-Ge system needs to be determined.

Concept Introduction:

Phase diagram of Ag-Ge system is represented as follows:

  

Initial two phase near the eutectic point are given as −

  $\text{α}$ = Primary solid solution of Ag

  $\text{β}$ = Primary solid solution of Ge

An intermediate phase is observed denoted by $\text{ζ}$, having closed packed hexagonal structure and having axial ratio values near to the ideal value.

Based on the result of in situ observations and experiment of high-pressure quenching, the possible all phase diagram of the two alloys is drawn at pressure $\text{7}$ GPa.

The phase drawn of Ag-Ge region is called as the sub monolayer region.

Answer to Problem 11.46P

Ag- $2$ % Ge is stronger than the Ag element.

Explanation of Solution

The micro-hardness of material has a direct relationship with the strength of the material and the wear resistance of compositions. Hence, for determination of the properties of the material, this micro-hardness measurement is to be considered. When there is a use of different microstructures and compositions, then the properties of the materials get varied.

In compositions, $\text{α}$ denotes inhibit dislocation hence, Ag- $2$ % Ge is stronger than Ag element.

  $\text{α}$ and $\beta$ phase boundaries also denote inhibit dislocations and this leads the material to be stronger.

Thus, Ag- $2$ % Ge is stronger than the Ag element.