A Monte-Carlo Study of B2 Ordering and Precipitation on a Bcc Lattice
- PDF / 1,570,230 Bytes
- 6 Pages / 414.72 x 648 pts Page_size
- 23 Downloads / 169 Views
Since ordering requires only local permutation of atoms while evolution of the composition field requires long range transport of atoms, quenches into a two-phase field below the ordering spinodal are expected to result in a rapid congruent ordering followed by decomposition
of the composition field. One main limitation of these approaches lies in the fact that the vacancy driven diffusion mechanism is not taken into account, as stressed by Allen and Cahn [lklore] realistic simulations can therefore be performed by explicitly including vacancies in the simulations. 545 Mat. Res. Soc. Symp. Proc. Vol. 398 01996 Materials Research Society
Following the approach of Abinandanan et al [8] who have addressed the problem of precipitation and L1 2 ordering, we present here a kinetic Monte-Carlo study of precipitation and B2 ordering on a BCC lattice for a model binary alloy. Evolutions of microstructures for two average compositions after a quench in the two-phase field are presented and discussed. Finally, we put special emphasis on the early stages where congruent ordering may take place; a new effect of the atomic mobility on the kinetic path of the system is presented. ATOMISTIC KINETIC MODEL AND PHASE DIAGRAM A rigid BCC lattice is considered, with periodic boundary conditions; for computer efficiency atomic positions are given in a rhombohedral frame with one atom per unit cell and N = L' lattice sites (L = 64 or 128). The binary alloy consists of NA A atoms, NB B atoms and one vacancy V, with N = NA + NB + 1. Interaction energies are taken as pair energies E•y between nearest and next nearest-neighbour sites, where X,Y equals A or B and i=1,2 for first and second nearest neighbours, respectively. 2 If one introduces the ordering energies, ei = E6A +6BB- EA and the asymmetrical energies i - (BB then the activation energy for an X - V exchange is calculated using a broken bond model. The following symmetrical form is used: AE17xv = _i=1,2 (cin- uinn ) where X ý Y, and n and n' are the numbers in the ith-shell of neighbours of X-type and Y-type around the site occupied by the X atom to be exchanged with the vacancy. According to rate theory, the frequency of the X - V exchange is Fxv = v exp{- kT-, ,wee where v ith is the attempt frequency. The phase diagram of a model system is constructed by standard equilibrium Monte-Carlo simulations in a grand canonical ensemble. For this phase diagram to exhibit a A2-B2 twophase field, Ist and 2 n' nearest neighbour interactions are required [9]. We have chosen c = 0.03eV, 62 = -0.04eV: the corresponding phase diagram is displayed in fig. (la) (the asymmetrical energies does not change the equilibrium properties). The critical temperature T, at A50 B50 composition is 1175 K and the tricritical temperature is Ttr = 690 + 10K. Because the vacancy concentration is small, one assumes that this equilibrium phase diagram is still valid for the ternary system A-B-V used in the kinetics. The asymmetrical energies ui will be varied so as to check their effect on the kinetics: for simpl
Data Loading...
