In this thesis we study thermal properties and melting behavior of crystals using Monte Carlo simulations. The Monte Carlo method is very difficult to implementfor melting investigation, unlike for problems where particles (such as spins) are localized on lattice sites. However, once it is well conceived, it is among themost efficient numerical techniques, to be able to study melting.We have created a high-performance algorithm based on an optimized Verlet procedure, which allowed us to investigate thermalproperties up to the melting. This optimization was necessary for treating an important number of atoms in very long runsto have good statistics, without prohibitive CPU time.We applied our algorithm to rare-gas crystals using the Lennard-Jones potential with parameters given by Bernardes which are widely used in the literature since 1958.Our results, thanks to their precision, show that we should modify these parameters in order to have a good agreement with experimental data.We studied melting of bulk semiconductors and metals by considering the case of Si and Ag. These materials have been chosen to serve our project about Silicene. Silicon has a diamond structure, and silver has the FCC lattice structure, both of them have been well experimentallystudied with well-known experimental melting temperatures. In spite of this, no good simulations have been done. For Si, one of the major problems is thechoice of a potential which stabilizes the diamond structure at finite temperatures. We have applied our algorithm to these materials using the multi-body Stillinger-Weber and Tersoff potentials for Si and the Gupta and EAM(embedded atom method) potentials for Ag. We obtained results much more precise than in early simulations and in good agreement with experiments.We also studied the Ag(111) surface trying to elucidate the long-standing controversy whether or not there is the ''anomalous'' thermal expansion whichhappens, for certain metals, when the inter-layer distances between the topmost atomic planes changes from a contracted situation to an expansion with respect tothe bulk distance. We showed that, depending on the potential, the anomalous crossover exists and the surface melting can occur at a temperature very far belowthat of the bulk melting. This is the case of EAM potential, but not the Gupta potential where surface melting occurs just belowbulk the melting.Finally, we studied the thermal stability of a stand-alone silicene sheet. Silicene is the Si counterpart of 2D carbon sheet called ''graphene". Siliceneattracts the attention of many researchers, because of its electronic and thermal properties which seem to be comparable to those of graphene which is actually oneof the most studied materials, due to its unusual properties susceptible for revolutionary device applications. Furthermore, because it is a Si-based material, thecompatibility, with the actual Si-based electronic industry, is expected to be better than for graphene. We show that, using the Tersoff potential with twosets of parameters (the original and the modified ones), the silicene 2D honeycomb structure is stable up to high temperatures without buckling. We have tested the Stillinger-Weberpotential: it yields a buckled honeycomb sheet at low temperatures but the 2D structure is destroyed in favor of a tri-dimensional structureat the melting. Discussion on this point is given.A general conclusion with some open perspectives is given at the end.
| Identifer | oai:union.ndltd.org:CCSD/oai:tel.archives-ouvertes.fr:tel-00949404 |
| Date | 16 December 2013 |
| Creators | Bocchetti, Virgile |
| Publisher | Université de Cergy Pontoise |
| Source Sets | CCSD theses-EN-ligne, France |
| Language | English |
| Detected Language | English |
| Type | PhD thesis |
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