Chapter 10, Problem 10.70P

Interpretation Introduction

(a)

Interpretation:

The liquidus temperature, solidus temperature and freezing range for the given Nb-Walloy are to be determined.

Concept Introduction:

The formula to calculate the wt% from the given volume for an alloy containing components $1\text{ and }2$ is:

  ${\left(\text{wt\%}\right)}_1=\frac{\left[V_1\times {\rho }_1\right]}{\left[V_1\times {\rho }_1+V_2\times {\rho }_2\right]}\times 100$ ...... (1)

Here, $V_1\text{ and }{V}_2$ are the volumes of the components present in the alloy, and ${\rho }_1\text{ and }{\rho }_2$ are the densities of the components.

On the temperature-composition graph of analloy, 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 analloy, beyond which the alloy is completely in solid phase. The temperature at this curve is minimum known as solidus temperature at which the crystals in the alloy can coexist with its melt in the thermodynamic equilibrium.

Freezing range for analloy is the difference of the liquidus and the solidus temperature of analloy. In this range, the alloy melt starts to crystallize at liquidus temperature and solidifies when reaches solidus temperature.

Interpretation Introduction

(b)

Interpretation:

The phases present, their compositions and their amounts for given Nb-W alloy are to be determined.

Concept Introduction:

On the temperature-composition graph of analloy, 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 analloy, 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)