Premelting (also surface melting) refers to a quasi-liquid film that can occur on the surface of a solid even below the bulk material's melting point ( T m {\displaystyle T_{m}} ). The thickness of the film is temperature ( T {\displaystyle T} )-dependent. This effect is common for all crystalline materials. Premelting shows its effects in frost heave, and, taking grain boundary interfaces into account, maybe even in the movement of glaciers. Considering a solid-vapour interface, complete and incomplete premelting can be distinguished. During a temperature rise from below to above T m {\displaystyle T_{m}} , in the case of complete premelting, the solid melts homogeneously from the outside to the inside; in the case of incomplete premelting, the liquid film stays very thin during the beginning of the melting process, but droplets start to form on the interface. In either case, the solid always melts from the outside inwards, never from the inside.
History The first to mention premelting might have been Michael Faraday in 1842 for ice surfaces. He compared the effect which holds a snowball together to that which makes buildings from moistured sand stable. Another interesting thing he mentioned is that two blocks of ice can freeze together. Later Tammann (1910) and Stranski (1942) suggested that all crystals might, due to the reduction of surface energy, start melting at their surfaces. Frenkel strengthened this by noting that, in contrast to liquids, no overheating can be found for solids. After extensive studies on many materials, it can be concluded that it is a common attribute of the solid state that the melting process begins at the surface.
Theoretical explanations There are several ways to approach the topic of premelting, the most figurative way might be thermodynamically. A more detailed or abstract view on what physics is important for premelting is given by the Lifshitz and the Landau theories. One always starts with looking at a crystalline solid phase (fig. 1: (1) solid) and another phase. This second phase (fig. 1: (2)) can either be vapour, liquid or solid. Further it can consist of the same chemical material or another. In the case of the second phase being a solid of the same chemical material one speaks of grain boundaries. This case is very important when looking at polycrystalline materials.
Thermodynamical picture for solid gas interface
In the following thermodynamical equilibrium is assumed, as well as for simplicity (2) should be a vaporous phase. The first (1) and the second (2) phase are always divided by some form of interface, what results in an interfacial energy γ 1 − 2 {\displaystyle \gamma _{1-2}} . One can now ask whether this energy can be lowered by inserting a third phase (l) in between (1) and (2). Written in interfacial energies this would mean:
If this is the case then it is more efficient for the system to form a separating phase (3). The only possibility for the system to form such a layer is to take material of the solid and "melt" it to a quasi-liquid. In further notation there will be no distinction between quasi-liquid and liquid but one should always keep in mind that there is a difference. This difference to a real liquid becomes clear when looking at a very thin layer (l). As, due to the long range forces of the molecules of the solid material the liquid very near the solid still "feels" the order of crystalline solid and hence itself is in a state providing a not liquid like amount of order. As considering a very thin layer at the moment it is clear that the whole separating layer (l) is too well ordered for a liquid. Further comments on ordering can be found in the paragraph on Landau theory. Now, looking closer at the thermodynamics of the newly introduced phase (l), its Gibbs energy can be written as:
where T {\displaystyle T} is the temperature, P {\displaystyle P} the pressure, d {\displaystyle d} the thickness of (l) corresponding to the number or particles N {\displaystyle N} in this case. n l {\displaystyle n_{l}} and μ l {\displaystyle \mu _{l}} are the atomic density and the chemical potential in (l) and γ t o t a l = γ 1 − l + γ l − 2 {\displaystyle \gamma _{total}=\gamma _{1-l}+\gamma _{l-2}} . Note that one has to consider that the interfacial energies can just be added to the Gibbs energy in this case. As noted before d {\displaystyle d} corresponds N {\displaystyle N} so the derivation to d {\displaystyle d} results in:
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