Low molecular weight materials, such as metals, typically exist as crystals in the solid state. The driving force behind the formation of crystals, which are structures having a long-range periodic order, is the lowering in free energy that accompanies the process of crystallization. Thus, if we were to plot the Gibbs free energy per unit volume, G, of a material in both the solid crystalline and molten forms as a function of temperature, we would get a plot of the type shown in Figure 11.1; the decrease in free energy with increasing temperature for both phases is due to the relative increase in the temperature–entropy term. The point of intersection of the two curves is the equilibrium melting point T m 0 https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429398506/ad7eee93-95b6-469a-9473-882b7f974cbc/content/eq1469.tif"/> , whereas the vertical difference between them represents the free-energy change, ∆Gv , between the two states at any temperature. Note that many materials (such as iron) exhibit polymorphism; that is, they exist in more than one crystalline form. In such a case, each form has its own G versus temperature curve. Variation with temperature of the Gibbs free energy per unit volume. https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9780429398506/ad7eee93-95b6-469a-9473-882b7f974cbc/content/fig11_1.tif"/>