Variable jump barriers in Monte Carlo simulations

Monte-Carlo simulation is one of the most widely used tools for the investigation of atom configuration kinetics. The objective of the proposed project is to introduce a decisive improvement in the calculation of jump barriers for atoms exchanging places with a vacancy. The two main advantages of Monte Carlo simulation are flexibility to describe various homogeneous and heterogeneous situations, and to be free of most restrictive assumptions entering in other kinetic models. The assumptions which still remain merit therefore special attention. In the classical treatments jump frequencies (jump probabilities per unit time) are used according to the tenets of transition state theory. They are proportional to an attempt frequency times a Boltzmann factor with an energy barrier which is the difference in Gibbs free energy of the saddle point state and the initial equilibrium state. The energy of the initial state is computed as the binding energy necessary to remove the atom from its equilibrium position, employing a suitable bonding model. The energy of the saddle point G S traditionally has been receiving much less attention, mostly assuming it to be a constant. In the meantime, it has been recognized especially in irregular atom environments as on surfaces that this simplification is not justified and leads to unrealistic results. Any reasonable estimate of the effect of varying atom environment on saddle point energy will thus be a clear improvement against not accounting for this effect at all. Preliminary calculations performed in our workgroup of ordering kinetics in L12 ordered intermetallics have shown the great sensibility of the kinetic rates to the assumption of a variable jump barrier. In this project, an extended series of jump profile calculations by ab initio density functional theory in the framework of the nudged elastic band method shall serve to study the influence of various atomic neighborhoods on barrier height. As it is not possible to treat all occupational variants, careful explorations of various dependences will be made in order to arrive at a manageable (but still large) representative set. A statistical method will be developed which allows to make use in real time - when running a Monte Carlo simulation - of the information gathered by ab initio calculations. The improved simulation method shall be implemented first for the L12 ordered structure and then transferred to the L10 and B2 structure. Various order-order/disorder transformations will be modeled and compared with experimental results and simulations with previous algorithms. The kinetic behavior in situations of reduced symmetry as in thin films, surfaces and nanostructures will be studied with the new, improved algorithm.

Monte-Carlo simulation is one of the most widely used tools for the investigation of atom configuration kinetics. The objective of the proposed project is to introduce a decisive improvement in the calculation of jump barriers for atoms exchanging places with a vacancy. The two main advantages of Monte Carlo simulation are flexibility to describe various homogeneous and heterogeneous situations, and to be free of most restrictive assumptions entering in other kinetic models. The assumptions which still remain merit therefore special attention. In the classical treatments jump frequencies (jump probabilities per unit time) are used according to the tenets of transition state theory. They are proportional to an attempt frequency times a Boltzmann factor with an energy barrier which is the difference in Gibbs free energy of the saddle point state and the initial equilibrium state. The energy of the initial state is computed as the binding energy necessary to remove the atom from its equilibrium position, employing a suitable bonding model. The energy of the saddle point G s traditionally has been receiving much less attention, mostly assuming it to be a constant. In the meantime, it has been recognized especially in irregular atom environments as on surfaces that this simplification is not justified and leads to unrealistic results. Any reasonable estimate of the effect of varying atom environment on saddle point energy will thus be a clear improvement against not accounting for this effect at all. Preliminary calculations performed in our workgroup of ordering kinetics in L12 ordered intermetallics have shown the great sensibility of the kinetic rates to the assumption of a variable jump barrier. In this project, an extended series of jump profile calculations by ab initio density functional theory in the framework of the nudged elastic band method shall serve to study the influence of various atomic neighborhoods on barrier height. As it is not possible to treat all occupational variants, careful explorations of various dependences will be made in order to arrive at a manageable (but still large) representative set. A statistical method will be developed which allows to make use in real time - when running a Monte Carlo simulation - of the information gathered by ab initio calculations. The improved simulation method shall be implemented first for the L12 ordered structure and then transferred to the L10 and B2 structure. Various order-order/disorder transformations will be modeled and compared with experimental results and simulations with previous algorithms. The kinetic behavior in situations of reduced symmetry as in thin films, surfaces and nanostructures will be studied with the new, improved algorithm.