Explain the use of physico-chemical principles in metallurgy.

(N/A) Some basic concepts of thermodynamics help in understanding the principles of metallurgical transformations.
In pyrometallurgy,the interpretation of which element is suitable for the reduction of a given metal oxide $(M_xO_y)$ at a specific temperature is done using Gibbs energy. The criterion for easy thermal reduction is that the value of the Gibbs energy change $(\Delta G)$ must be negative at the given temperature.
The change in Gibbs energy at a given temperature is represented by the following equation:
$\Delta G = \Delta H - T \Delta S$
Where $\Delta H = \text{enthalpy change}$,$\Delta S = \text{entropy change}$.
Any reaction will proceed only when the value of $\Delta G$ in the above equation is negative.
$(i)$ Increasing temperature $T$: If $\Delta S$ is positive,then increasing temperature $(T)$ will increase the value of $T \Delta S$ $(\Delta H < T \Delta S)$,and subsequently,$\Delta G$ will become negative.
If the overall reaction resulting from the coupling of two reactions,i.e.,oxidation and reduction,results in a negative value of $\Delta G$,then the final reaction occurs easily. This type of coupling can be easily understood through a plot of Gibbs energy $(\Delta_r G^{\ominus})$ versus $T$ for the formation of oxides.
This plot is for the free energy change when one gram mole of oxygen is consumed.
$(ii)$ Ellingham diagrams: The graphical representation of Gibbs energy was first used by $H.J.T. Ellingham$ and provides a sound basis for calculating the choice of reducing agent in the reduction of oxides. This is known as the Ellingham diagram.