Liquids

Liquids have more order than gases but much less than crystals. When a material freezes, its entropy and enthalpy decrease. The enthalpy difference between the liquid and solid states is the latent heat of fusion, Δ Hf, that is released to the surroundings. Similarly, when a metal vapor condenses, the latent heat of vaporization, Δ Hv, is released. For most metals Δ Hv is 20 to 30 times as great as Δ Hf. The difference is because on vaporization all near-neighbor bonds are broken, whereas melting statistically breaks only a fraction of a bond per atom. For coordination numbers of 8 and 12, vaporization breaks four and six bonds per atom. Assuming that both Δ Hf and Δ Hv are proportional to the number of near-neighbor bonds broken, melting must break only a fraction of a bond per atom. The entropy change on melting, Δ Sf = Δ Hf/Tm, is about 10 MJ/mol K and the entropy change on vaporization, Δ Sv = Δ HV/ Tb, is about 10 times larger, as shown in Table 10.1.

Most materials contract when they freeze. For most metals the contraction is between 1 and 6%, as shown in Table 10.2 Materials for which packing in the solid is not dense (e.g., Si, Ge, Bi, Ga, and H2O) actually expand when they solidify.

Homogeneous nucleation

The formation of a tiny sphere of solid in a liquid (Figure 10.1) requires an increase of free energy.