Papers by Keyword: Mean Field

Abstract: The zircon polymorph of GdCrO₄ has a large magnetocaloric effect over a wide temperature range, with |ΔS_T| > 20 J/kg·K from 6 K to 34 K, for a magnetic field of 9 T. This unusual behaviour is very interesting on magnetic refrigeration applications, for liquefying H₂ or natural gas. The mean-field approach explains that it is due to the weaker Gd-Cr magnetic exchange relative to the Cr-Cr one, while the Gd-Gd exchange is negligible. This possibility has not been sufficiently studied and opens an interesting strategy to design more efficient materials for magnetic refrigeration.

Abstract: Propagation of elastic waves in heterogeneous linear 1-D media is considered. The scalar wave equation is transformed by the Liouville substitution and the Dyson integral equation is applied for a statistically homogeneous field of heterogeneities. The result is the mean wave field which is analysed in detail for the exponential correlation functions. The general case of the random elastic medium with an arbitrary heterogeneity of small scale is considered and simple closed form expressions for the mean field and attenuation are derived.

Abstract: Quantitative prediction of grain size and recrystallized volume fraction is still a real challenge for many alloys, and even for simple materials when subjected to complex thermal/mechanical histories, as in multi-pass (industrial) processing. A first step is therefore taken in the direction of multiscale modelling of recrystallization, by considering digital polycrystalline microstructures. These synthetic mesoscopic microstructures are meshed adaptively and anisotropically, with refinement close to the grain boundaries. Crystal plasticity finite element (CPFEM) simulations are combined with a level set framework to model primary recristallization, following plastic deformation. In the level set method, the kinetic equation describing interface motion uses the calculated stored energy field provided by CPFEM calculations, and works on the same mesh. Discontinuous dynamic recrystallization can be modelled within the same approach, effectively coupling plastic deformation with nucleation and growth processes. Parallel to the finite element approach, a mean field model is developed in the general context of multi-pass processing. The model considers categories of grains based on two state variables : grain size and total dislocation density. As opposed to the finite element approach, there is no crystallographic or topological information. It is computationally much cheaper and therefore suitable for direct coupling at the scale of forming processes, for industrial applications. The parameters of the model can be identified from inverse analysis, using experimental stress-strain curves, recrystallized volume fractions, and grain sizes. Mean field and finite element models are compared, and it is shown that the detailed information provided by finite element simulations can be used to calibrate or optimize the mean field method.

Abstract: A Self-Consistent Mean Field (SCMF) kinetic theory including an explicit description ofthe vacancy diffusion mechanism is developed. The present theory goes beyond the usual local equi-librium hypothesis. It is applied to the study of the early time spinodal decomposition in alloys. Theresulting analytical expression of the structure function highlights the contribution of the vacancydiffusion mechanism. Instead of the single amplification rate of the Cahn-Hillard linear theory, thelinearized SCMF kinetic equations involve three constant rates, first one describing the vacancy re-laxation kinetics, second one related to the kinetic coupling between local concentrations and paircorrelations and the third one representing the spinodal amplification rate. Starting from the same va-cancy diffusion model, we perform kineticMonte Carlo simulations of a Body Centered Cubic (BCC)demixting alloy. The resulting spherically averaged structure function is compared to the SCMF pre-dictions. Both qualitative and quantitative agreements are satisfying.

Abstract: The continuum theory of dislocations, as developed predominantly by Kröner and Kosevich, views each dislocation as a source of incompatibility of strains. We show that this concept can be employed efficiently in the Landau free energy functional to develop a mean-field mesoscopic model of materials with dislocations. The order parameters that represent the distortion of the parent phase (often of cubic symmetry) are written in terms of elastic strains which are themselves coupled by incompatibility constraints. Since the “strength” of the incompatibility depends on the local density of dislocations, the presence of dislocations affects the evolution of the microstructure and vice versa. An advantage of this formulation is that long range anisotropic interactions between dislocations appear naturally in the formulation of the free energy. Owing to the distortion of the crystal structure around dislocations, their presence in multiphase materials causes heterogeneous nucleation of the product phase and thus also shifts of the transformation temperature. This novel field-theoretical approach is very convenient as it allows to bridge the gap in studying the behavior of materials at the length and time scales that are not attainable by atomistic or macroscopic models.

Abstract: We research under what condition the mean-field approximation can be applied to study ordered phases of quasi-one-dimensional metal. It is shown that the mean-field treatment is indeed permissible provided that it is applied not to the microscopic Hamiltonian (subject to severe one-dimensional high-energy fluctuations), but rather to effective Hamiltonian derived at the dimensional crossover scale. The resultant mean-field phase diagram has three ordered phases: spin density wave, charge density wave, and superconductivity. The density wave orders win if the Fermi surface nests well. Outcome of competition between the intra-chain and inter-chain electron repulsion determines the type (spin vs. charge) of the density wave. The ground state becomes superconducting (with unconventional order parameter) when the nesting is poor. The superconducting mechanism relies crucially on the one-dimensional fluctuations.