Instituut Lorentz Rijksuniversiteit Leiden,
Nieuwsteeg 18 Leiden, The Netherlands
Department of Physics, University of Washington,
Seattle, Washington 98195-1560
Crystal facets can undergo several types of phase transitions. Surface reconstruction, surface roughening, and surface melting are the best known examples [1-4]. For each phenomenon a complete theoretical description has been developed during the last two decades. However, until recently the theory did not address the interplay between the three. This competition does not play a role when the characteristic temperatures are well separated; for example when a reconstructed surface first looses its reconstruction order, then roughens at a higher temperature, and finally surface melts just below the bulk melting temperature. Surface phase transitions can be studied in much more detail than possible before because of recent improvements in experimental resolution and surface preparation. The experimental evidence indicates that these three phenomena often compete. This competition results in new types of phases, such as disordered flat phases [5,6], and new types of phase transitions such as roughening induced simultaneous deconstruction transitions  and preroughening transitions [5,6]. The purpose of this overview is to present the recent theoretical progress.
Besides their practical applications these new types of phases and phase transitions are also of fundamental importance to the theory of critical phenomena. Surface phase transitions are realizations of two dimensional (2D) critical phenomena. During the last two decades our understanding of the scaling properties of 2D phase transitions has deepened considerably, with the development of renormalization transformations , the study of exactly soluble models , the development of the so-called Coulomb gas method [10,11] and the theory of conformal invariance . From this emerges the notion that the scaling properties of all 2D critical phenomena are exactly known by now. In particular the theory of conformal invariance gives the impression to include all universality classes. Whether this is really true needs to be tested. Phase transitions in crystal surfaces and adsorbed monolayers, might provide examples that fall outside the established universality classes. The interplay between surface roughening and surface reconstruction is very intriguing from this perspective. The most simple types of reconstructions, such as the 1x2 missing row structure, already lead to novel behaviour.
The first half of this overview, sections 1-7, is focussed on deconstruction transitions that do not involve step excitations, where the competition with surface roughening is absent. The scaling properties of these phase transitions are well understood. The theory is the same as for phase transitions in adsorbed monolayers . Still it is important to discuss this, because of the emerging experimental realizations of such deconstruction transitions, and because it sets the stage for the second half of this overview.
Section 8 contains general remarks about geometric aspects of critical phenomena, in particular the connection with fractals. A brief overview of the conventional surface roughening theory is presented in section 9.
The last three sections are focussed on the interplay between surface roughening and surface deconstruction. Roughening induced simultaneous deconstruction transitions in missing row reconstructed FCC(110) facets are discussed in section 10. The properties of disordered flat phases and preroughening transitions are reviewed in sections 11 and 12.