Models of crystal surfaces

Nicholas, J. E., An Atlas of Models of Crystal Surfaces. Gordon Breach, New York, 1965. 

Gilman S, Bard AJ, editors. Electroanal5dical chemistry vol 2. London Arnold, 1967. Nicholas JF. An atlas of models of crystal surface. New York Gordon and Breach, 1965. 

In this chapter, we will focus on some of the recent developments in understanding the influence of solution and electrochemical conditions over model single-crystal surfaces. Specifically, we will review work applying electronic structure methods to probe electrocatalytic mechanisms occurring at this complex interface. 

In this chapter, we present a brief background account of recent progress in the application of ab initio methods to elucidating the fundamental physicochemical processes that take place at the electrified aqueous metal interface. Our focus is predominantly on model single-crystal surfaces at lower surface coverages. 

After nearly two decades of controversy, it is now generally accepted that helium crystals are model systems for the general study of crystal surfaces, but also exceptional in having unique quantum properties. Helium crystals exhibit faceting as do ordinary crystals, but no other crystals can grow and melt sufficiently fast to make the propagation of crystallization waves possible at their surfaces. 

There are two layer-spreading models. In these models, the crystal surface is atomically flat except at screw dislocations or steps of a partially grown surface layer. If there are screw dislocations, growth would continue on the screw... 

The notion of nonuniformity of catalytic surfaces has been originally advanced by Langmuir (20) and particularly by Taylor. The physical nature of nonuniformity is insufficiently clarified. To some extent, it results from the difference in properties of crystal faces, from dislocations, and other disturbances of crystal lattice. It is possible that admixtures of some foreign substances is of greater importance. The particles of admixtures change adsorption energy on adjacent surface sites. The model of nonuniform surface probably describes the overall result of the effect of particles of admixtures on adsorbed particles and of the mutual influence of adsorbed particles (i.e., to an approximation the model takes into account not only biographical, but also induced nonuniformity). 

The last topic to comment is the difference between the optimum compositions in Ru of the Pt-Ru alloys for the oxidation of CO (50 at.% Ru) and methanol (10-20 at.% Ru). Gasteiger et al. " proposed an explanation based on a statistical modelization of the surface of an alloy containing x at.% Ru. The stmctural atomic model proposed by these authors needs a maximum number of 3-fold platinum sites for the adsorption of the CH3OH molecule, and adjacent to 1 Ru atom to adsorb the OH species. This would correspond to a surface with 8-14 at.% Ru depending on the orientation of the low index single crystal planes, 8% for (111), 10% for (100)... 

Fleming S, Rohl A, Lee MY, Gale J, Parkinson G (2000) Atomistic modeling of gibbsite surface structure and morphology. J Crystal Growth 209 159-166... 

It is therefore necessary to begin with the warning that one may not be looking at catalysis. Somorjai s approach to catalysis is to adopt the strategy of examining the building blocks and then to assemble them into a model for catalysis. The steps are made up of the study of (/) crystal surfaces and structures plus adsorbed gas, (/7) surface reactions at pressures <10 torr, Hi) reactions at 10 —10 torr, and (zt>) dispersed catalysts. 

All of the above models assuming two-dimensional surface nucleation predict crystal growth rates at low supersaturation which are much lower than those observed in practice. A possible solution to this problem was put forward by Frank (1949), who proposed a self-generating step creation process involving a screw dislocation. The model was further formalized by Burton et al. (1951) and became known as the Burton-Cabrera-Frank (BCF) model of crystal growth. Detailed discussion of the BCF model can be found in Ohara and Reid (1973) and Nyvlt et al. (1985). 

Kardar, M., Parisi, G., and Zhang, Y.-C., Dynamic scaling of growing interfaces, Phys. Rev. Lett, 56, 889, 1986 Villain, J., Continuum models of crystal growth from atomic beams with and without desorption, J. Phys. I France, 1, 19, 1991 Lai, Z.W. and Das Sarma, S., Kinetic growth with surface relaxation Continuum versus atomistic models, Phys. Rev. Lett, 66, 2348, 1991. 

The first step in building a planar model of a surface is cleaving the carefully-optimised bulk crystal to produce a slab with two exposed faces. Both surface orientation and cleavage plane must be selected. Low-index orientations hkt) are parallel to close-packed layers of ions and so can be expected to show little corrugation and minimal surface area. As a result, low-index orientations are often those of lowest surface energy and predominate in experiment. 

---