Chapter 10, Problem 10.57P

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.

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

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

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

Percentage of a component in a ceramic is calculated as:

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