Chapter 12, Problem 12.74P

Interpretation Introduction

(a)

Interpretation:

To determine eutectoid temperature, the composition of phase, amount of each phase of ZrO₂-CaO.

  

Concept Introduction:

The graphical representation of the physical state of a substance which is under various conditions of pressure and temperature is known as phase diagram. A phase diagram has temperature on the x-axis and pressure on the y-axis. It is a type of chart which is used to demonstrate conditions at which thermodynamically different phases takes place and coexist at equilibrium.

Answer to Problem 12.74P

The percentage of monoclinic and cubic is $\text{18\%}$ and $\text{82\%}$.

Explanation of Solution

  

Sketch a horizontal line at ${\text{900}}^{\text{0}}\text{C}$ which goes through the different structure of CaO as shown in the diagram.

  ${\text{Tetragonal}}_{\text{12\% CaO}}\to {\text{Monoclinic}}_{\text{3\% CaO}}\to {\text{Cubic}}_{\text{14\% }\text{}\text{CaO}}$

Therefore, from the graph mentioned above, the percentage of Monoclinic,

  $\text{\% Monoclinic= }\frac{14-12}{14-3}\times 100$

  $\begin{array}{l}\text{\% Monoclinic=18\%}\\ \text{\% Cubic=100-18}\\ \text{\% Cubic=82\%}\end{array}$

Interpretation Introduction

(b)

Interpretation:

To determine the eutectoid temperature, composition and amount of phase in Cu-Al at $\text{11}\text{.8\% Al}$.

  

Concept Introduction:

The graphical representation of the physical state of a substance which is under various conditions of pressure and temperature is known as phase diagram. A phase diagram has temperature on the x-axis and pressure on the y-axis. It is a type of chart which is used to demonstrate conditions at which thermodynamically different phases takes place and coexist at equilibrium.

Answer to Problem 12.74P

The percentage of composition obtained are $\text{\% α}$ and $\text{\% β}$ are $\text{61}\text{.3\%}$ and $\text{38}\text{.7 \%}$ respectively.

Explanation of Solution

  

Draw a horizontal line that passes through $\text{11}\text{.8\% Al}$ and intersects the temperature axis at.

At this particular temperature, β phase transforms to a phase, as shown in the diagram above.

Therefore,

  ${\text{β}}_{\text{11}\text{.8\%AL}}\to {\text{α}}_{\text{9}\text{.4\%Al}}\to {\text{γ}}_{\text{15}\text{.6\%Al}}$

  $\begin{array}{l}\text{Percentage α=}\frac{\text{15}\text{.6-11}\text{.8}}{\text{15}\text{.6-9}\text{.4}}\text{×100}\\ \text{Percentage α=61}\text{.3\%}\\ \text{\% β=100-61}\text{.3}\\ \text{\% β=38}\text{.7\%}\end{array}$

Interpretation Introduction

(c)

Interpretation:

To determine the eutectoid temperature, composition and amount of each phase in $\text{Cu-Zn at 47 \%Zn}\text{. }$

  

Concept Introduction:

The graphical representation of the physical state of a substance which is under various conditions of pressure and temperature is known as phase diagram. A phase diagram has temperature on the x-axis and pressure on the y-axis. It is a type of chart which is used to demonstrate conditions at which thermodynamically different phases takes place and coexist at equilibrium.

Answer to Problem 12.74P

The percentage composition of a and that of $\text{γ}$ phase are 52.5% and $\text{47}\text{.8\%}$ respectively.

Explanation of Solution

  

Draw a vertical line from 47 weight percent of Zinc that meets a point A. Further, from A draw the meeting point B and C, these points are in equilibrium with α and γ phases, weight percentages at these points are $\text{36\%}$ and $\text{59\%}$.

Therefore,

  $\begin{array}{l}\text{\% α=}\frac{\text{59-47}}{\text{59-36}}\text{×100}\\ \text{\% α=52}\text{.5\%}\\ \text{\% γ=100-52}\text{.5}\\ \text{\% γ=47}\text{.8\%}\end{array}$

Interpretation Introduction

(d)

Interpretation:

To determine the eutectoid temperature amount and composition of each phase in Cu-Be.

  

Concept Introduction:

The graphical representation of the physical state of a substance which is under various conditions of pressure and temperature is known as phase diagram. A phase diagram has temperature on the x-axis and pressure on the y-axis. It is a type of chart which is used to demonstrate conditions at which thermodynamically different phases takes place and coexist at equilibrium.

Answer to Problem 12.74P

The percentage composition of the a phase and γ phase is obtained as 51.6% and 48.3%

Explanation of Solution

  

Sketch a vertical line from 6 weight percent of beryllium that meets a point A. Further, from A draw line meeting point B and C, these points are in equilibrium with phase $\text{α}$ and phase $\text{γ}$. Weight percentages at these points are 1.5 and $\text{10}\text{.8\%}$.

  $\begin{array}{l}\text{\% α=}\frac{\text{10}\text{.8-6}}{\text{10}\text{.8-1}\text{.5}}\text{×100}\\ \text{\% α=51}\text{.6\%}\\ \text{\% γ=100-51}\text{.6}\\ \text{\% γ=48}\text{.38\%}\end{array}$