Abstract: In this paper, we show how lattice–based random walks of virtual particles directed by
Monte Carlo methods (Lattice Monte Carlo) can be used to address a variety of complex
phenomenologically mass diffusion problems. Emphasis is put on the practical details of doing the
calculations. It is shown how concentration depth profiles can be determined: this is exemplified
with diffusion in the presence of isolated dislocation pipes, grain boundary slabs, and oxygen
segregation at interfaces in metal-ceramic oxide composites. It is also shown how effective
diffusivities can be determined in materials. We also show how temperature profiles and the
effective thermal conductivity can be determined for the thermal diffusion analogue of mass
diffusion. A detailed comparison is made in one case with the results of the Finite Element method.
Abstract: The mass transport in the presence of stress, electrical, mechanical and chemical potential
gradients in multicomponent solid solution is analyzed. The method bases on the Darken concept
and the calorimetric equation of state. We effectively coupled the conservation of the mass
(continuity equations), energy, momentum and Gauss equations. The diffusion fluxes of the
components are given by the Nernst-Planck formulae and take into account the electro-chemical
and mechanical potentials.
We simulate the deformation field during the diffusion caused by the gradients of the chemical
potential of all elements in non-ideal Fe-Cu-Ni alloy. The simulations show that the model is
compatible with experimental results, and can be effectively used for modelling the energy,
momentum and mass transport problems in compressible multicomponent solid solutions. The
numerical problems and methods of solution are presented.
Abstract: A kinetic Monte Carlo (KMC) model for surface diffusion on a 2D lattice is proposed.
An equivalent continuum cellular automaton (CA) model is derived from this. These models are
shown to produce similar results at high temperatures. A hybrid KMC-CA model is derived which
consistently allows material to transfer between a deterministic CA model and a stochastic KMC
model concurrently embedded within it. The quality of the model is demonstrated by simulating the
flattening of a sinusoidal surface profile and the evolution of an elliptical body into a circular one.
Abstract: An investigation of the application of a multi scale CAFE model to prediction of the
strain localization phenomena in industrial processes, such as extrusion, is presented in this work.
Extrusion involves the formation of a strong strain localization zone, which influences the final
product microstructure and may lead to a coarse grain layer close to the surface. Modelling of the
shape of this zone and prediction of the strain magnitude will allow computer aided design of the
extrusion process and optimisation of the technological parameters with respect to the
microstructure and properties of the products. Thus, the particular objective of this work is
comparison of the FE and CAFE predictions of strain localization in the shear zone area in
extrusion. Advantages and disadvantages of the developed CAFE model are also discussed on the
basis of the simulation results.
Abstract: The thermodynamic and kinetic properties of Fe-Cu alloys are studied by ab initio
calculations, in the framework of a multiscale modeling of precipitation kinetics. The configuration
energies at various compositions, the solute migration and binding energies, as well as the vacancy
formation and binding energies are computed. The effects of the local copper distribution on the
migration barriers are considered. We show that a simple diffusion model with effective interactions
on a rigid lattice, which includes a description of the saddle-point configurations, captures the main
features of the energetic landscapes explored by the vacancy during its diffusion in dilute and
Abstract: A kinetic Monte Carlo method has been developed for the simulation of interface
controlled solid-state transformations to overcome timescale limitations associated with other
atomistic simulation methods. In the simulation method the atoms can take place on sites from
(at least) two intertwining crystal lattices. To enable the atoms to also take positions between
the ideal lattice sites, a collection of randomly placed sites can be included. These ‘random
sites’ have a realistic chance to be occupied at the location of the transformation interface and
thus allow for irregularities in the atomic structure of the transformation interface. The atoms
move by independent, thermally activated jumps. The activation energy for the atomic jumps
can be determined for every jump separately based on the arrangement of the neighbouring
atoms. The simulation method has been used to study the interface mobility in the austenite to
ferrite transformation in iron for different interface orientations. The results obtained indicate
that the excess volume associated with the interface plays a key role for the activation enthalpy
for the interface mobility. The rate controlling process is the rearrangement of free space at the
interface by series of (unfavourable) jumps by different atoms to create a path from the parent
to the product phase.
Abstract: The aim of this paper is to give a short review on cluster dynamics modeling in the field
of atoms and point defects clustering in materials. It is shown that this method, due to its low
computer cost, can handle long term evolution that cannot, in many cases, be obtained by Lattice
Kinetic Monte Carlo methods. Indeed, such a possibility is achieved thanks to an important
drawback that is the loss of space correlations of the elements of the microstructures. Some
examples, in the field of precipitation and irradiation of metallic materials are given. The limitations
and difficulties of this method are also discussed. Unsurprisingly, it is shown that it goes in a very
satisfactory way when the objects are distributed homogeneously. Conversely, the source term
describing the primary damage under irradiation, by nature heterogeneous in space and time, is
tricky to introduce especially when displacement cascades are produced.