Interplay Between Surface In-Plane Ordering and Roughening

This thesis is intended to present a detailed theoretical study of some of the above mentioned scenarios, both for the unreconstructed and for the reconstructed (110) surfaces, by means of Monte Carlo simulations performed on a suitably chosen Hamiltonian. It is organized as follows. Chapter 1 is roughly divided in two parts. The first leads into the structural and geometrical aspects of the surfaces examined in the thesis and introduces the Solid-On-Solid (SOS) description appropriate for them, since the model adopted for the study of the fee (110) phenomenology belongs to the SOS class of Hamiltonians. A section is dedicated to the deconstruction transition (of the reconstructed surfaces), with particular regards to its critical behaviour, and another to the roughening transition. The latter, after some historical review, presents some important results characterizing the transition, especially from the point of view of the universal features shared by the various models thus far proposed. Amongst them, a position of outstanding importance is attached to the BCSOS model, of which a detailed description is given in connection with the six vertex model. The section is concluded by some phenomenological argument about the vanishing of the step free energy (and of the corresponding facet in the equilibrium crystal shape) at the roughening transition. The second part of the chapter is dedicated to scattering. It is in fact essential to introduce the main concepts concerning this important experimental tool, since many investigations on surfaces are performed by means of scattering experiments. An introductory section tries to clarify the sometimes confusing scattering terminology, then the most relevant physical quantities, such as the scattering intensities, are introduced and discussed both for atom and X-ray scattering (in the kinematic approximation). Decomposition into coherent and incoherent scattering is presented in connection with critical behaviour near a second order surface phase transition. Extraction of information about the physics of the surface under consideration is finally implemented by the ~tudy of scattering from a rough surface, since its features strongly differ both from those of an ordered surface and from those of a randomly disordered one. The aim of Chapter 2 is to offer a concise but comprehensive review of the phenomenology of the (110) surfaces, both reconstructed and unreconstructed, from the point of view of their low temperature symmetries and their thermal phase transitions. Each section is devoted to a particular metal and a final section tries to summarize the general most relevant features in an overview. In Chapter 3 a review is presented of the most recent and relevant theoretical models of the phase transitions which can occur on the fcc(llO) surfaces: preroughening on the unreconstructed surface, deconstruction for the reconstructed ones, and roughening. The presence on the "hot" surface of many kinds of defects, from vacancies and adatoms to bound or free arrays of steps, may lead to an intriguing interplay between the various transitions which gives rise to the formulation of different disordering scenarios. The main source is represented by the work by Marcel den Nijs, starting from the idea of a preroughening transition on a model for a simple cubic (100) surface, then evolving into the study of the connections between deconstruction and roughening for (2 x 1) reconstructed fcc(llO) surfaces. On this second line, important contributions have been provided by the works of Villain and Vilfan (and, very recently, of Balents and Kardar), all of these comprehensively reviewed in a "global" paper by Bernasconi, who presents some new ideas and puts forward new possible scenarios; their detailed description will be the main subject of Chapter 3. In Chapter 4 the model from which all the new results of the thesis are drawn is presented. Two different real systems, the (2 x 1) reconstructed surface of gold and the (1 x 1) unreconstructed surface of silver, are chosen for investigation of their low temperature symmetries and their high temperature critical behaviour, while particular emphasis is given to the physical motivations underlying the structure of the model itself as well as to the choice of the energy parameters adopted to describe what will be henceforth called "gold" and "silver" (110). Then, a short account of the Monte Carlo algorithm set up in order to study the properties of the chosen Hamiltonian is provided, together with a list of the relevant quantities which have been examined for understanding the physics embodied by the model. Particular stress is given to the definition and significance of surface order parameters. Chapter 5 is dedicated to the study of the roughening transition on the BCSOS model. Its aim is threefold. First, it can be seen as a check for the techniques and, in general, for the global simulation procedure against an exactly solvable model. Secondly, an important concept like that of sublattice order parameter is introduced and studied in connection with known exact results. Lastly, a deeper insight into a quantity which has remained hitherto unexplored, the staggered susceptibility, is provided. In Chapter 6 the results of the Monte Carlo simulation for Au(llO) are presented. Evidence for a second order Ising-like phase transition and of a distinct (separated in temperature) roughening transition is given, in accordance with the most recent experimental results. Scattering calculations are able to reproduce a temperature dependent shift in the half integer order peaks, a feature which provides a deep insight into the nature of the flat but disordered phase between the two transitions. A discussion follows where one of the scenarios proposed in Chapter 3 for the two transitions is chosen and its nature and occurrence on the simulated surface justified. Chapter 7 provides results for the unreconstructed fcc(llO) surface which has been called "silver". Data analysis runs parallel to that in the preceeding Chapter, also form the point of view of the scattering calculation. For the first time in a Monte Carlo simulation, a new transition, apart form roughening, is found and characterized. It can be ascribed to the class of preroughening transitions introduced (in Chapter 3) by theoretical analysis, though up to now no direct experimental evidence has been clearly detected it on a real surface. An Appendix shows the exact relations between order parameters and scattering intensities, while the final section summarizes the situation of the fcc(llO) surfaces arisen from the present Monte Carlo simulations.