Critical roughening temperature

At elevated temperatures, due to thermal fluctuations, singular faces acquire a surface roughness manifested by the formation of adatoms and surface vacancies, di- or polyatomic surface clusters, and vacancies and steps with kinks as shown in Figure 1. The surface roughness becomes appreciable only above a critical roughening temperature T,. The theoretical value of Tr for a simple cubic crystal lattice, T, = where i(fx denotes the... 

For liquid-vapor interfaces, the correlation length in the bulk is of t he order of atomic distance unless one is close to the critical point Hence the concept of local equilibrium is well justified in most practical circumstances For. solid surfaces above the roughening temperature, the concept also makes sense. Since the surface is rough adding (or removing) an atom to a particular part of the surface docs not disturb the local equilibrium state very much, and this sampling procedure can be used to determine the local chemical potential. This is the essence of the Gibbs-Thomson relation (1). 

As remarked above, surface science has come to be partitioned between chemists, physicists and materials scientists. Physicists have played a substantial role, and an excellent early overview of surface science from a physicist s perspective is by Tabor (1981). An example of a surface parepisteme that has been entirely driven by physicists is the study of the roughening transition. Above a critical temperature but... 

This surface tension /int(T, H) is singular at the roughening transition temperature 7r, as well as at the bulk critical temperature Tc of the Ising model. 

Fig. 36. Schematic temperature variation of intcrfacial stiffness kn I K and interfacial free energy, for an interface oriented perpendicularly to a lattice direction of a square a) or simple cubic (b) lattice, respectively. While for tl — 2 the interface is rough for all non zero temperatures, in d — 3 il is rough only for temperatures T exceeding the roughening transition temperature 7r (see sect. 3.3). For T < 7U there exists a non-zero free energy tigT.v of surface steps, which vanishes at T = 7 r with an essential singularity. While k is infinite throughout the noil-rough phase, k Tic reaches a universal value as T - T . Note that k and fml to leading order in their critical behavior become identical as T - T. ...

Substrate Ad. Entropy critical temperature triple roughening Remark Ref... 

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