Chapter 10, Problem 10.68P

Interpretation Introduction

(a)

Interpretation:

The temperature when first solid nucleus is formed when $\text{Bi-60 wt\% Sb}$ alloy is cooled is to be determined.

Concept Introduction:

On the temperature-composition graph of an alloy, the curve above which the alloy exist in the liquid phase is the liquidus curve. The temperature at this curve is maximum known as liquidus temperature at which the crystals in the alloy can coexist with its melt in the thermodynamic equilibrium.

Interpretation Introduction

(b)

Interpretation:

The composition of the phases present, and their amounts for $\text{Bi-60 wt\% Sb}$ at ${450}^{\circ }\text{C}$ are to be determined.

Concept Introduction:

On the temperature-composition graph of an alloy, the curve above which the alloy exist in the liquid phase is the liquidus curve. The temperature at this curve is the maximum temperature at which the crystals in the alloy can coexist with its melt in the thermodynamic equilibrium.

Solidus curve is the locus of the temperature on the temperature composition graph of an alloy, beyond which the alloy is completely in solid phase.

Between the solidus and liquidus curve, the alloy exits in a slurry form in which there is both crystals as well as alloy melt.

Solidus temperature is always less than or equal to the liquidus temperature.

Amount of each phase in wt% is calculated using lever rule. At a particular temperature and alloy composition, a tie line is drawn on the phase diagram of the alloy between the solidus and liquidus curve. Then the portion of the lever opposite to the phase whose amount is to be calculated is considered in the formula used as:

  $\text{Phase wt\%}=\frac{\text{opposite arm of lever}}{\text{total length of the tie line}}\times 100$ ...... (2)

Interpretation Introduction

(c)

Interpretation:

The temperature when last liquid is solidified when $\text{Bi-60 wt\% Sb}$ alloy is cooled is to be determined.

Concept Introduction:

On the temperature-composition graph of an alloy, the curve above which the alloy exist in the liquid phase is the liquidus curve. The temperature at this curve is maximum known as liquidus temperature at which the crystals in the alloy can coexist with its melt in the thermodynamic equilibrium.

Solidus curve is the locus of the temperature on the temperature composition graph of an alloy, beyond which the alloy is completely in solid phase.

Between the solidus and liquidus curve, the alloy exits in a slurry form in which there is both crystals as well as alloy melt.

Solidus temperature is always less than or equal to the liquidus temperature.