Nucleation of Al3Zr and Al3Sc in aluminum alloys: from kinetic Monte Carlo simulations to classical theory

Zr and Sc precipitate in aluminum alloys to form the compounds Al3Zr and Al3Sc which for low supersaturations of the solid solution have the L12 structure. The aim of the present study is to model at an atomic scale this kinetics of precipitation and to build a mesoscopic model based on classical nucleation theory so as to extend the field of supersaturations and annealing times that can be simulated. We use some ab-initio calculations and experimental data to fit an Ising model describing thermodynamics of the Al-Zr and Al-Sc systems. Kinetic behavior is described by means of an atom-vacancy exchange mechanism. This allows us to simulate with a kinetic Monte Carlo algorithm kinetics of precipitation of Al3Zr and Al3Sc. These kinetics are then used to test the classical nucleation theory. In this purpose, we deduce from our atomic model an isotropic interface free energy which is consistent with the one deduced from experimental kinetics and a nucleation free energy. We test di erent mean-field approximations (Bragg-Williams approximation as well as Cluster Variation Method) for these parameters. The classical nucleation theory is coherent with the kinetic Monte Carlo simulations only when CVM is used: it manages to reproduce the cluster size distribution in the metastable solid solution and its evolution as well as the steady-state nucleation rate. We also find that the capillary approximation used in the classical nucleation theory works surprisingly well when compared to a direct calculation of the free energy of formation for small L12 clusters.Comment: submitted to Physical Review B (2004

A parsimonious oscillatory model of handwriting

International audienceWe propose an oscillatory model that is theoretically parsimonious, empirically efficient and biologically plausible. Building on Hollerbach’s (Biol Cybern 39:139–156, 1981) model, our Parsimonious Oscillatory Model of Handwriting (POMH) overcomes the latter’s main shortcomings by making it possible to extract its parameters from the trace itself and by reinstating symmetry between the x and y coordinates. The benefit is a capacity to autonomously generate a smooth continuous trace that reproduces the dynamics of the handwriting movements through an extremely sparse model, whose efficiency matches that of other, more computationally expensive optimizing methods. Moreover, the model applies to 2D trajectories, irrespective of their shape, size, orientation and length. It is also independent of the endeffectors mobilized and of the writing direction

Web ensemble averages for retrieving relevant information from rejected Monte Carlo moves

We study the relevance of including information about rejected Monte-Carlo moves in path-sampling computations of free energies. For this purpose, we define webs as sets of paths linked by the path-sampling scheme and introduce an associated statistical ensemble. Within this web ensemble, we derive and test several statistical averages enabling to include information about configurational and path quantities belonging to the unselected trial moves. We numerically observe that retrieving this information does not always result in variance reduction, as theoretically predicted by Delmas and Jourdain. To explain the possible detrimental effect of information-retrieving from web sampling, an action for the webs is introduced. The behaviour of the statistical variance is observed to correlate to an overlapping area of a web action histogram. This area represents the probability that a generated web is such that the difference of its action between the targeted and reference ensembles is lower than the corresponding difference of free energy. Variance reductions are numerically observed for increased areas, as it is the case for the residence weight method proposed previously. More generally, web ensembles yield a rigorous framework for rationalizing existing methods and also for deriving potentially new methods enabling to retrieve relevant information from rejected trial moves

A path-sampling scheme for computing thermodynamic properties of a many-body system in a generalized ensemble

We propose to compute the thermodynamic properties of many-body systems using a path-sampling Monte Carlo scheme implemented in a generalized path ensemble. Trial paths are generated through an expanded ensemble using a reversible discretization of Langevin's equation of motion. We also show how the systematic errors resulting from the use of a finite time step can rigorously be taken into account in the path-sampling scheme. We find that the degree of convergence of the estimated thermodynamic quantity towards the exact value correlates with the mean acceptance rates of the path-sampling scheme. An application of the path method for simulating glassy systems is finally suggested

Web ensemble averages for retrieving relevant information from rejected Monte Carlo moves

We study the relevance of including information about rejected Monte-Carlo moves in path-sampling computations of free energies. For this purpose, we define webs as sets of paths linked by the path-sampling scheme and introduce an associated statistical ensemble. Within this web ensemble, we derive and test several statistical averages enabling to include information about configurational and path quantities belonging to the unselected trial moves. We numerically observe that retrieving this information does not always result in variance reduction, as theoretically predicted by Delmas and Jourdain. To explain the possible detrimental effect of information-retrieving from web sampling, an action for the webs is introduced. The behaviour of the statistical variance is observed to correlate to an overlapping area of a web action histogram. This area represents the probability that a generated web is such that the difference of its action between the targeted and reference ensembles is lower than the corresponding difference of free energy. Variance reductions are numerically observed for increased areas, as it is the case for the residence weight method proposed previously. More generally, web ensembles yield a rigorous framework for rationalizing existing methods and also for deriving potentially new methods enabling to retrieve relevant information from rejected trial moves

Monte Carlo Simulation of Simultaneous Ordering and Precipitation in BCC Lattice

Fe-Al system quenched into its two-phase field undergoes a phase separation leading to the coexistence of A2 and B2 phases. Using transmission electron microscopy, three different decomposition behaviours have been reported with increasing aluminium concentration : nucleation-growth of B2 inside a disordered matrix, decomposition of interconnected ordered phases which was attributed to spinodal decomposition, and nucleation-growth of A2 inside B2 domains. This work presents the first Monte Carlo simulations of simultaneous phase separation and ordering in a two-phase A2/B2 domain. Calculations were performed using an Atomistic Kinetic Model ; one vacancy allows atomic diffusion and a residence time algorithm is used. The three experimentally observed morphologies of evolution are reproduced. Moreover decomposition kinetics is compatible with the classical Lifshits-Slyosov-Wagner coarsening theory