In this dissertation the study of Si and Si-Ge systems is conducted to provide answers to both statistical mechanics and material science questions. The compress- ible Ising model provides a general framework for describing phase transitions in alloys where the ordering is accompanied by a displacive structural change. Its behavior in the case of ferromagnetic interactions and constant volume conditions is investigated here using a model of binary alloys driven by elastic interactions. Clas- sical Monte Carlo simulations in the semi-grand-canonical ensemble are utilized, and the two species composing the alloy are modeled by Si and Ge interacting via the Stillinger-Weber potential. A volume much closer to pure Ge than to pure Si is chosen to introduce a significant diference between the two species. The phase diagram con- tains a closed first order line which divides a \phase-segregated" (\ordered") phase from a disordered one. In the \ordered" phase the most unfavorable species (Si in this case) congregates forming planes in-between which the other species is located. When interested in the study of technological important materials, few, if any, are more relevant than Si and Ge. In this work a classical, hybrid MC-MD algorithm is introduced for the study of surface phenomena (2D island stability or step-edge evolution) on (001) Si or Ge surfaces. This method is very general and can be easily expanded to other semiconductors and diferent surfaces. With respect to previously developed algorithms, this presents the advantage of working off-lattice and uti- lizing bulk-fitted potentials. It is based on the introduction of collective moves, such as dimer jumps, into the MC algorithm. MD-driven local relaxations are considered as trial moves for the MC. Results on early stages of island formation, island stability versus temperature and system size, and step-edge evolution are obtained in good qualitative agreement with experimental results.