Shear, dilation, and swap: Mixing in the limit of fast diffusion

Brassart, Laurence; Liu, Qihan; Suo, Zhigang

doi:10.1016/j.jmps.2016.06.013

Cited by 11 publications

(11 citation statements)

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“…The latter also provides a justification to phenomenological models which do not rely on the chemical equilibrium assumption at macroscopic scale, see e.g. (Brassart and Suo, 2013) (coupled diffusion and elasto-plasticity) and (Brassart et al, 2016 (coupled diffusion and viscoplasticity).…”

Section: Resultsmentioning

confidence: 95%

“…In response to a jump in chemical potential, the local concentration does not immediately adjust, but rather evolves towards its equilibrium value according to a kinetic model with relaxation time τ . The latter could represent for example the kinetics of breaking and reforming chemical bonds or creep relaxation associated with volume change due to species insertion (Brassart et al, 2016). In the context of supercooled liquids (Li et al, 2014), the theory assumes fast diffusion through regions of high mobility and creep-limited species insertion dominated by regions of low mobility.…”

Section: Introductionmentioning

confidence: 99%

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Effective transient behaviour of heterogeneous media in diffusion problems with a large contrast in the phase diffusivities

Brassart

Stainier

2019

Journal of the Mechanics and Physics of Solids

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This paper presents a homogenisation-based constitutive model to describe the effective transient diffusion behaviour in heterogeneous media in which there is a large contrast between the phase diffusivities. In this case mobile species can diffuse over long distances through the fast phase in the time scale of diffusion in the slow phase. At macroscopic scale, contrasted phase diffusivities lead to a memory effect that cannot be properly described by classical Fick's second law. Here we obtain effective governing equations through a two-scale approach for composite materials consisting of a fast matrix and slow inclusions. The micro-macro transition is similar to first-order computational homogenisation, and involves the solution of a transient diffusion boundary-value problem in a Representative Volume Element of the microstructure. Different from computational homogenisation, we propose a semi-analytical mean-field estimate of the composite response based on the exact solution for a single inclusion developed in our previous work [Brassart, L., Stainier, L., 2018. Effective transient behaviour of inclusions in diffusion problems. Z. Angew Math. Mech. 98, 981-998]. A key outcome of the model is that the macroscopic concentration is not one-to-one related to the macroscopic chemical potential, but obeys a local kinetic equation associated with diffusion in the slow phase. The history-dependent macroscopic response admits a representation based on internal variables, enabling efficient time integration. We show that the local chemical kinetics can result in non-Fickian behaviour in macroscale boundary-value problems.

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Section: Resultsmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Effective transient behaviour of heterogeneous media in diffusion problems with a large contrast in the phase diffusivities

Brassart

Stainier

2019

Journal of the Mechanics and Physics of Solids

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“…are reached [1][2][3]. In this case, as is known [4,5], the near-contact regions and metal-semiconductor contacts may heat up to temperatures over the melting points for eutectics of relatively fusible systems (Al-Si, Ag-Si, Au-Si; the melting point for Au-Si eutectic Te = 370°C).…”

Section: Introductionmentioning

confidence: 96%

The Formation and Migration of Molten Inclusions in Silicon

Скворцов¹

2017

New Research on Silicon - Structure, Properties, Technology

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The mechanisms of formation and migration of molten inclusions in silicon are described. Consideration of them is necessary for development of technological approaches to formation of conducting regions (characteristic sizes of 10 μm-30 nm) and doped conducting channels in silicon. The problem of formation of local conducting regions is topical, e.g., for single electronics. It is known that sizes of a "Coulomb island" (about 10 nm) present difficulties to modern technologies. That is why the development of alternative procedures to form a "Coulomb island" (in particular, those based on electromigration of molten regions in semiconductor bulk) is a topical problem. Besides, high heat loads on the "classical" silicon structures, owing to specific character of their work ( operating current densities may be as high as j ~ 10 9 -10 10 A/m 2 ), promote their active degradation. The appearing molten regions coagulate into drops and are displaced by a current along the electric field lines. Therefore, a detailed analysis of the mechanisms of inclusions formation and migration in silicon will make it possible to predict more accurately the "critical" modes of silicon structures operation (e.g., in power electronics). The main mechanisms of molten inclusions formation (contact melting in a metal-semiconductor system, decomposition of supersaturated solid solutions in heavily doped semiconductors) are considered, as well as the procedures to form and control mobility of such objects: electric current, temperature gradient, structural inhomogeneities, etc. The problems of molten inclusions migration in silicon single crystals occurring in electric field with contact melting electric transport of melt components and thermoelectric effects at interphase boundaries are considered in detail. The molten region is moving along the electric field lines, thus enabling to exert control over the trajectory of its motion. The results of author's original investigations on formation and migration of molten silver-and aluminum-based inclusions in silicon are presented, as well as the experimental data by other authors. The main migration mechanisms related to melting-crystallization processes at © 2017 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.interphase boundaries and components diffusion through the melt region are discussed in detail. The problems to defect formation in silicon after crystallization of inclusions are also considered.Keywords: silicon single crystals, contact melting, crystallization, melt inclusion, formation of molten regions in a metal-semiconductor system, electromigration of inclusions by the melting-crystallization mechanism, diffusion in the melt, gradients of concentration and temperature, formation of structural defects in silicon single crystals with inclu...

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“…We call such an idealized solution a molecularly incompressible solution. In our previous work (Brassart et al (2016)), we have identified that the homogeneous state of a molecularly incompressible solution of two molecular species can evolve in three modes:…”

Section: Introductionmentioning

confidence: 99%

“…The idea was first proposed by Suo (2012, 2013)) in the context of chemically reactive host-guest systems. In our previous work (Brassart et al (2016)), we presented a thermodynamic theory of mixing in a body small enough so that diffusion is taken to be infinitely fast. We now generalize our theory into a theory that couples flow and diffusion.…”

Section: Introductionmentioning

confidence: 99%

Mixing by shear, dilation, swap, and diffusion

Brassart

Liu

Suo

2018

Journal of the Mechanics and Physics of Solids

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This paper presents a theory of poroviscosity for binary solutions. Subject to mechanical forces and connected to reservoirs of molecules, a binary solution evolves by concurrent flow and diffusion. Our theory generalizes the classical theory of interdiffusion by decoupling the molecular processes for flow and diffusion. We further remove the assumption of local chemical equilibrium, so that the insertion of molecular into a material element, accompanied by a change in volume, is treated as nonequilibrium process and is put on the same footing as the process of shear deformation by viscous flow. The theory of poroviscosity has an intrinsic length scale, called the poroviscous length, below which the homogenization of a composition heterogeneity is limited by viscous flow, rather than by diffusion. The theory has implications for the analysis of interdiffusion in systems that display a decoupling between flow and diffusion, such as supercooled liquids, glasses, and physical gels. We illustrate the theory with numerical examples of a layered structure and a spherical particle. We discuss the results for feature sizes below and above the poroviscous length.

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Shear, dilation, and swap: Mixing in the limit of fast diffusion

Cited by 11 publications

References 45 publications

Effective transient behaviour of heterogeneous media in diffusion problems with a large contrast in the phase diffusivities

Effective transient behaviour of heterogeneous media in diffusion problems with a large contrast in the phase diffusivities

The Formation and Migration of Molten Inclusions in Silicon

Mixing by shear, dilation, swap, and diffusion

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