Chapter 10, Problem 10.56P

Interpretation Introduction

Interpretation:

The amount of nickel in grams that must be added to copper is to be calculated to give an alloy of desired properties.

Concept Introduction:

On the temperature-composition graph of an alloy, the curve above which the alloys 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. 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.

Amount of each phase in wt% is calculated using lever rule. At a particular temperature and ceramic composition, a tie line is drawn on the phase diagram of the ceramic 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:

  $\text{Phase wt\%}=\frac{\text{opposite arm of lever}}{\text{total length of the tie line}}\times 100$ ...... (1)

Percentage of a component in an alloy is calculated as:

  $\%M_i=\frac{x_i}{{\displaystyle \sum _i{x}_i}}\times 100\%$ ...... (2)