Transient convective instabilities in directional solidification

We study the convective instability of the melt during the initial transient in a directional solidification experiment in a vertical configuration. We obtain analytically the dispersion relation, and perform an additional asymptotic expansion for large Rayleigh number that permits a simpler analytical analysis and a better numerical behavior. We find a transient instability, i.e. a regime in which the system destabilizes during the transient whereas the final unperturbed steady state is stable. This could be relevant to growth mode predictions in solidification.Comment: 28 pages, 5 figures. The following article has been accepted for publication in Physics of Fluids. After it is published, it will be found at http://pof.aip.or

Localized Instabilities and Spinodal Decomposition in Driven Systems in the Presence of Elasticity

We study numerically and analytically the instabilities associated with phase separation in a solid layer on which an external material ux is imposed. The first instability is localized within a boundary layer at the exposed free surface by a process akin to spinodal decomposition. In the limiting static case, when there is no material ux, the coherent spinodal decomposition is recovered. In the present problem stability analysis of the time-dependent and non-uniform base states as well as numerical simulations of the full governing equations are used to establish the dependence of the wavelength and onset of the instability on parameter settings and its transient nature as the patterns eventually coarsen into a at moving front. The second instability is related to the Mullins- Sekerka instability in the presence of elasticity and arises at the moving front between the two phases when the ux is reversed. Stability analyses of the full model and the corresponding sharp-interface model are carried out and compared. Our results demonstrate how interface and bulk instabilities can be analysed within the same framework which allows to identify and distinguish each of them clearly. The relevance for a detailed understanding of both instabilities and their interconnections in a realistic setting are demonstrated for a system of equations modelling the lithiation/delithiation processes within the context of Lithium ion batteries.Comment: 8 figures, 19 page

Complex dynamics in double-diffusive convection

The dynamics of a small Prandtl number binary mixture in a laterally heated cavity is studied numerically. By combining temporal integration, steady state solving and linear stability analysis of the full PDE equations, we have been able to locate and characterize a codimension-three degenerate Takens-Bogdanov point whose unfolding describes the dynamics of the system for a certain range of Rayleigh numbers and separation ratios near S=-1.Comment: 8 pages, 5 figure

Thin-film electrodes for high-capacity lithium-ion batteries: Influence of phase transformations on stress

In this study we revisit experiments by Sethuraman et al. [J. Power Sources, 195, 5062 (2010)] on the stress evolution during the lithiation/delithiation cycle of a thin film of amorphous silicon. Based on recent work that show a two-phase process of lithiation of amorphous silicon, we formulate a phase-field model coupled to elasticity in the framework of Larché-Cahn. Using an adaptive nonlinear multigrid algorithm for the finite-volume discretization of this model, our two-dimensional numerical simulations show the formation of a sharp phase boundary between the lithiated and the amorphous silicon that continues to move as a front through the thin layer. We show that our model captures the nonmonotone stress loading curve and rate dependence, as observed in experiments and connects characteristic features of the curve with the stucture formation within the layer. We take advantage of the thin film geometry and study the corresponding one-dimensional model to establish the dependence on the material parameters and obtain a comprehensive picture of the behaviour of the system

Thin-film electrodes for high-capacity lithium-ion batteries: Influence of phase transformations on stress

In this study we revisit experiments by Sethuraman et al. [J. Power Sources, 195, 5062 (2010)] on the stress evolution during the lithiation/delithiation cycle of a thin film of amorphous silicon. Based on recent work that show a two-phase process of lithiation of amorphous silicon, we formulate a phase-field model coupled to elasticity in the framework of Larch'e-Cahn. Using an adaptive nonlinear multigrid algorithm for the finite-volume discretization of this model, our two-dimensional numerical simulations show the formation of a sharp phase boundary between the lithiated and the amorphous silicon that continues to move as a front through the thin layer. We show that our model captures the non-monotone stress loading curve and rate dependence, as observed in experiments and connects characteristic features of the curve with the stucture formation within the layer. We take advantage of the thin film geometry and study the corresponding one-dimensional model to establish the dependence on the material parameters and obtain a comprehensive picture of the behaviour of the system

Sharp-interface formation during lithium intercalation into silicon

In this study we present a phase-field model that describes the process of intercalation of Li ions into a layer of an amorphous solid such as a-Si. The governing equations couple a viscous Cahn-Hilliard-Reaction model with elasticity in the framework of the Cahn-Larch'e system. We discuss the parameter settings and flux conditions at the free boundary that lead to the formation of phase boundaries having a sharp gradient in ion concentration between the initial state of the solid layer and the intercalated region. We carry out a matched asymptotic analysis to derive the corresponding sharp-interface model that also takes into account the dynamics of triple points where the sharp interface in the bulk of the layer intersects the free boundary. We numerically compare the interface motion predicted by the sharp-interface model with the long-time dynamics of the phase-field model

H2-dependent attachment kinetics and shape evolution in chemical vapor deposition graphene growth

Experiments on graphene growth through chemical vapor deposition (CVD) involving methane (CH4) and hydrogen (H2) gases reveal a complex shape evolution and a nonmonotonic dependence on the partial pressure of H2 (pH2). To explain these intriguing observations, we develop a microkinetic model for the stepwise decomposition of CH4 into mobile radicals and consider two possible mechanisms of attachment to graphene crystals: CH radicals to hydrogen-decorated edges of the crystals and C radicals to bare crystal edges. We derive an effective mass flux and an effective kinetic coefficient, both of which depend on pH2, and incorporate these into a phase field model. The model reproduces both the non-monotonic dependence on pH2 and the characteristic shapes of graphene crystals observed in experiments. At small pH2, growth is limited by the kinetics of attachment while at large pH2 growth is limited because the effective mass flux is small. We also derive a simple analytical model that captures the non-monotone behavior, enables the two mechanisms of attachment to be distinguished and provides guidelines for CVD growth of defect-free 2D crystals

Oscillatory Instabilities in Directional Solidification with Solutal Convection. Transient Regime

Peer ReviewedPostprint (published version

Thin-film electrodes for high-capacity lithium-ion batteries: Influence of phase transformations on stress

In this study we revisit experiments by Sethuraman et al. [J. Power Sources, 195, 5062 (2010)] on the stress evolution during the lithiation/delithiation cycle of a thin film of amorphous silicon. Based on recent work that show a two-phase process of lithiation of amorphous silicon, we formulate a phase-field model coupled to elasticity in the framework of Larché-Cahn. Using an adaptive nonlinear multigrid algorithm for the finite-volume discretization of this model, our two-dimensional numerical simulations show the formation of a sharp phase boundary between the lithiated and the amorphous silicon that continues to move as a front through the thin layer. We show that our model captures the non-monotone stress loading curve and rate dependence, as observed in recent experiments and connects characteristic features of the curve with the stucture formation within the layer. We take advantage of the thin film geometry and study the corresponding one-dimensional model to establish the dependence on the material parameters and obtain a comprehensive picture of the behaviour of the system

A blue sky catastrophe in double-diffusive convection

A global bifurcation of the blue sky catastrophe type has been found in a small Prandtl number binary mixture contained in a laterally heated cavity. The system has been studied numerically applying the tools of bifurcation theory. The catastrophe corresponds to the destruction of an orbit which, for a large range of Rayleigh numbers, is the only stable solution. This orbit is born in a global saddle-loop bifurcation and becomes chaotic in a period doubling cascade just before its disappearance at the blue sky catastrophe.Comment: 4 pages, 6 figures, REVTeX, To be published in Physical Review Letter