Solids: Thermodynamics and Bonding

· The behavior of the Gibbs function with temperature may be understood from the thermodynamic relationship: dg = - s dT + v dp
· The slope of the g(T) curve, (dg/dT)_p = -s and, since s is positive, the slope is negative. The entropy also increases as T increases.
· The curvature of the g(T) curve may be related to the specific heat capacity of the material: (d²g/dT²)_p = - (ds/dT)_p = - (c_p / T). The specific heat is a positive quantity and, hence, the curvature is negative and decreases as T increases.
· For iron, the specific heat of the bcc phase (a,d zones) is larger than the specific heat of the fcc phase (g) and, hence, the g(T) curve for bcc iron has more curvature than that of fcc iron at any given temperature.
· The greater curvature of the bcc curve causes it to have two intersections with the fcc curve between room temperature and the melting point. The lowest Gibbs function gives the equilibrium phase and so two phase changes occur as T increases from room temperature.