Chapter 10, Problem 10.58P

Interpretation Introduction

Interpretation:

The amount of MgO in grams that must be added to NiO is to be calculated to give a ceramic of desired properties.

Concept Introduction:

On the temperature-composition graph of a ceramic, the curve above which the ceramic 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 ceramic can coexist with its melt in the thermodynamic equilibrium.

Solidus curve is the locus of the temperature on the temperature composition graph of a ceramic, beyond which the ceramic is completely in solid phase. The temperature at this curve is minimum known as solidus temperature at which the crystals in the ceramic can coexist with its melt in the thermodynamic equilibrium.

Amount of each phase in mol% 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:

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

The formula to calculate the wt% from the given mol% for a ceramic containing components $1\text{ and }2$ is:

  ${\left(\text{wt\%}\right)}_1=\frac{\left[{\left(\text{mol\%}\right)}_1\times \left({\text{M}}_1\right)\right]}{\left[{\left(\text{mol\%}\right)}_1\times \left({\text{M}}_1\right)+{\left(\text{mol\%}\right)}_2\times \left({\text{M}}_2\right)\right]}\times 100$ ...... (2)

Here, ${\left(\text{mol\%}\right)}_1\text{ and }{\left(\text{mol\%}\right)}_2$ are the mole percent of the components present in the ceramic, and ${\text{M}}_1{\text{ and M}}_2$ are the molecular weights of the components.

Percentage of a component in a ceramic is calculated as:

  $\%M_i=\frac{x_i}{{\displaystyle \sum _i{x}_i}}\times 100\%$ ...... (3)