PRECIPITATION IN ALLOYS: A KINETIC MONTE CARLO AND CLASS MODEL STUDY David Bombac, Goran Kugler Faculty of Natural Sciences and Engineering, Department of Materials and Metallurgy, Askerceva 12, SI-1000 Ljubljana, Slovenia Introduction Breakthroughs and advances in materials science are closely connected to the basic research to interpret meso-, micro- and nano-scopic mechanisms. Many physical properties of the metals depend on the defects such as vacancies and their concentration in the crystals. Study of the precipitation kinetics from the saturated metastable solid solution can be divided into three regimes: (i) nucleation, (ii) diffusion controlled growth of clusters and (iii) cluster coarsening (Ostwald ripening) and coalescence where larger clusters grow on the expense of smaller. In reality those three idealized regimes often overlap consequentially making the interpretation of obtained results difficult. Dynamic and kinetic development of molecular (atomic) systems using computational materials science is the main focus of this paper. Particular methods used here are a kinetic Monte Carlo (kMC) and a class model. The kMC is based on statistical mechanics [1-5], where development of the system is simulated in real time. The class model is based on classical nucleation and growth theory, [6], where precipitates are distributed in classes of size. These are then used to obtain time evolution of the particle size distribution. Results obtained with class model were compared to kMC simulations at atomic scale which gives precise evolution of precipitation, growth and coarsening in time. Both methods were performed on Fe, 1 at. % Cu alloy isothermally treated at 873 K. Numerical model Kinetic Monte Carlo model Monte Carlo simulations in this work rely on the rigid lattice BCC residence time algorithm model. The vacancy diffusion simulations were performed on binary FeCu alloy with 1 at. % Cu on a fixed size of 80 periodic boundary conditions lattice constants. Evolution of the system is determined by eight first nearest jump probabilities around vacancy. Each probability is given by: exp XV XV X E kT           (1) where X  represent attempt frequencies for particular atom and XV E is the energy difference between stable position and the saddle point position of jumping atom. To calculate activation energies broken bond model was used [1, 2]. The activation energies depend on the saddle point energies and interatomic potentials of the first and second nearest neighbours of the jumping atom, calculated by: XV SpX XX XX XY XY XV XV E e n n n         (2) After calculation of eight possible jump probabilities around vacancy, the independent event is selected on the basis of the random number. The real time is calculated with correlation between vacancy concentration in the simulation box and reality, multiplied by averaged residence time and is given by 8 1 1 Vsim Vreal i i c t c                        (3) Simulation parameters are presented in Table 1. Table 1: Simulation parameters (1) 0.778 FeFe   eV (2) 0.389 FeFe   eV (1) 0.778 CuCu   eV (2) 0.389 CuCu   eV (1) 0.731 FeCu   eV (2) 0.366 FeCu   eV (1) 0.335 FeV   eV (1) 0.335 CuV   eV 9.557 SpFe e  eV 9.098 SpCu e  eV 12 8.7 10 Fe    s -1 12 8.7 10 Cu    s -1 Class model The class model for precipitation aims at describing the quantitative time evolution of the precipitation state, namely the particle size distribution, the volume fraction and the number density of precipitates. The precipitate size distribution is discretized into several size classes. The time evolution of the radius of each class is calculated as a function of temperature, solute content, solubility limit and diffusivity. Nucleation can eventually take place, thus adding new classes of precipitates. Time evolution of precipitates thus depends on diffusion controlled growth. In order to study the kinetics of the precipitation process a simulations for homogeneous precipitation were performed. For the sake of simplicity the model was restricted to spherical precipitates. Other parameters used were as follows; an interfacial energy of precipitates 0.25   Jm -2 , diffusion constant 8 0 6 10 D    m 2 s -1 , activation energy for diffusion 166400 Q  Jmol -1 , and the simulation time used in model with 1 at. % of Cu was 10 6 s. 19th Annual International Conference on Composites or Nano Engineering, July 24th - 30th 2011, Shanghai (China) World journal of engineering, Vol. 8, supp. 1). Toronto: Sun Light Publishing Canada, 2011, p. 129-130