Free surfaces roughening transition

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. ...

A predictive theory of heterogeneous catalysis, therefore, should include the prediction of the restructuring phenomena that occur when a catalyst is brought into its reactive phase. This is especially important when surface roughening occurs with the creation of reactive steps and kinks. Surface reconstruction is driven by the surface s desire to minimize its surface energy. Sometimes a surface which is free of adsorbates will reconstruct its bulk terminated surface, as for instance the hexagonal reconstruction of the Pt(lOO) surface. Surface reconstruction of clean surfaces occurs predominantly on transition metals with spatially extended d-valence atomic orbitals and with high electron occupations such as Pt and Au. 

Figure 9.40 Step free energy for single and double steps as function of temperature. Formation energy for single steps vanishes at 1230°C the surface undergoes a roughening transition. (Figure adapted from Ref [73].)...

The step free energies Esa—Ssa T and Fsb—Ssb T with the configurational entropy SsA and Ssb, respectively, decrease with increasing temperature and vanish around 1230 °C as shown in Figure 9.40 [73]. At this temperature, steps are created spontaneously and the surface undergoes a roughening transition. 

The effective increases in the Raman scattering cross sections, or surface enhancement factors (SEE), are typically about lO fold on electrochemically roughened silver, gold, and copper. Few works have been reported on the other free electron metals such as alkali metals. Many transition metals have relatively weak surface enhancements. Their SEE values depend on the nature of the metal, for example, 10 10" for Pt, Rh, Ni, Co, and Fe, and 10 for Pd. 

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