arXiv subjects

Mathis Plapp

Publications and source records attributed to Mathis Plapp.

At least 19 recordsLinked to original sources

arXiv2024

Multi-Physics Modeling Of Phase Change Memory Operations in Ge-rich Ge$_2$Sb$_2$Te$_5$ Alloys

One of the most widely used active materials for phase-change memories (PCM), the ternary stoichiometric compound Ge$_2$Sb$_2$Te$_5$ (GST), has a low crystallization temperature of around 150$^\circ$C. One solution to achieve higher operating temperatures is to enrich GST with additional germanium (GGST). This alloy crystallizes into a polycrystalline mixture of two phases, GST and almost pure germanium. In a previous work [R. Bayle et al., J. Appl. Phys. 128, 185101 (2020)], this crystallization process was studied using a multi-phase field model (MPFM) with a simplified thermal field calculated by a separate solver. Here, we combine the MPFM and a phase-aware electro-thermal solver to achieve a consistent multi-physics model for device operations in PCM. Simulations of memory operations are performed to demonstrate its ability to reproduce experimental observations and the most important calibration curves that are used to assess the performance of a PCM cell.

cond-mat.mtrl-sci↗

arXiv2024

Grand-potential phase field simulations of droplet growth and sedimentation in a two-phase ternary fluid

A methodology is built to model and simulate the dynamics of domain coarsening of a two-phase ternary liquid with an arbitrary phase diagram. High numerical performance is obtained through the use of the phase field-method for interface capturing, a lattice Boltzmann method numerical scheme for all the model equations, and a portable, parallel simulation code running on multiple GPUs. The model is benchmarked against an analytic solution for a ternary diffusion couple. It also reproduces the well-known power law for droplet coarsening during Ostwald ripening without fluid flow. Large-scale simulations with flow illustrate the effects of momentum transport and buoyancy, as well as droplet coalescence and sedimentation.

cond-mat.mtrl-sci↗

arXiv2024

Dendrites with corners

A phase-field model for diffusion-limited crystal growth is formulated that is capable of handling highly anisotropic interfaces. It uses a Willmore regularization that yields corners of finite size. An asymptotic analysis reveals that Herring's law is recovered for the advancing surfaces. The model is validated by conducting simulations of dendritic growth for low anistorpies and comparing the results to the data from the literature. The model makes it possible to simulate high anisotropy dendrites for which the standard phase-field models are ill-posed. In this regime, the interplay between a Herring instability on the dendrite flanks and the corner regularization creates zig-zag shaped corrugations and leads to a non-monotonic trend of tip velocity as a function of anisotropy strength.

cond-mat.mtrl-sci↗

arXiv2024

Spinodal decomposition and domain coarsening in a multi-layer Cahn-Hilliard model for lithium intercalation in graphite

During the intercalation of lithium in layered host materials such as graphite, lithium atoms can move within the plane between two neighboring graphene sheets, but cannot cross the sheets. Repulsive interactions between atoms in different layers lead to the existence of ordered phases called "stages", with stage $n$ consisting of one filled layer out of $n$, the others being empty. Such systems can be conveniently described by a multi-layer Cahn-Hilliard model, which can be seen as a mean-field approximation of a lattice-gas model with intra- and interlayer interactions between lithium atoms. In this paper, the dynamics of stage formation after a rapid quench to lower temperature is analyzed, both by a linear stability analysis and by numerical simulation of the full equations. In particular, the competition between stages 2 and 3 is studied in detail. The linear stability analysis predicts that stage 2 always grows the fastest, even in the composition range where stage 3 is the stable equilibrium state. This is borne out by the numerical simulations, which show that stage 3 emerges only during the non-linear coarsening of stage 2. Some consequences of this finding for the charge-discharge dynamics of electrodes in batteries are briefly discussed.

cond-mat.mtrl-sci↗

arXiv2023

A Fully Coupled Multi-Physics Model to Simulate Phase Change Memory Operations in Ge-rich Ge$_2$Sb$_2$Te$_5$ Alloys

A self-consistent model for the simulation of Ge-rich Ge$_2$Sb$_2$Te$_5$ phase change memories is presented. Combining the multi-phase field model and a phase-aware electro-thermal solver, it reproduces the multi-physics behavior of the material. Simulations of memory operations are performed to demonstrate its ability to reproduce experimental observations.

cond-mat.mtrl-sci↗

arXiv2021

Spacing Homogenization in Lamellar Eutectic Arrays with Anisotropic Interphase Boundaries

We analyze the effect of interphase boundary anisotropy on the dynamics of lamellar eutectic solidification fronts, in the limit that the lamellar spacing varies slowly along the envelope of the front. In the isotropic case, it is known that the spacing obeys a diffusion equation, which can be obtained theoretically by making two assumptions: (i) the lamellae always grow normal to the large-scale envelope of the front, and (ii) the Jackson-Hunt law that links lamellar spacing and front temperature remains locally valid. For anisotropic boundaries, we replace hypothesis (i) by the symmetric pattern approximation, which has recently been found to yield good predictions for lamellar growth direction in presence of interphase anisotropy. We obtain a generalized Jackson-Hunt law for tilted lamellae, and an evolution equation for the envelope of the front. The latter contains a propagative term if the initial lamellar array is tilted with respect to the direction of the temperature gradient. However, the propagation velocity of the propagative wave modes are found to be small, so that the dynamics of the front can be reasonably described by a diffusion equation with a diffusion coefficient that is modified with respect to the isotropic case.

cond-mat.mtrl-sci↗

arXiv2019

On topological defects in two-dimensional orientation-field models for grain growth

Standard two-dimensional orientation-field based phase-field models rely on a continuous scalar field to represent crystallographic orientation. The corresponding order parameter space is the unit circle, which is not simply-connected. This topological property has important consequences for the resulting multi-grain structures: (i) trijunctions may be singular; (ii) for each pair of grains, there exist two different grain boundary solutions that cannot continuously transform to one another; (iii) if both solutions appear along a grain boundary, a topologically stable, singular point defect must exist between them. While (i) can, (ii) and therefore (iii) cannot be interpreted in the classical picture of grain boundaries. In addition, singularities cause difficulties, such as lattice pinning in numerical simulations. To overcome these problems, we propose two new formulations of the model. The first is based on a 3-component unit vector field, while in the second we utilise a 2-component vector field with an additional potential. In both cases, the additional degree of freedom introduced make the order parameter space simply-connected, which removes the topological stability of these defects.

cond-mat.mtrl-sci↗

arXiv2019

Nucleation of crystal surfaces with corner energy regularization

The thermodynamics of strongly anisotropic crystalline surfaces is analogous to that of a binary mixture exhibiting phase separation. On a metastable planar surface, formation of stable orientations requires a nucleation process, in which the energy associated with the presence of corners must be considered. In this context, a nucleation event corresponds to the formation of a critical shape for the crystalline surface before the system enters the growth regime. We first derive the Euler-Lagrange equation for crystal surface nucleation, in two dimensions, and show that the saddle-point condition corresponds to a vanishing chemical potential along this critical surface. We then perform numerical simulation of the equation of motion for the crystal surface and show that, as compared with saddle point nucleation, ridge crossing is dynamically favoured.

cond-mat.mtrl-sci↗

arXiv2019

Influence of morphological instability on grain boundary trajectory during directional solidification

The interplay between the diffusion-controlled dynamics of a solidification front and the trajectory of a grain boundary groove at the solid-liquid interface is studied by means of thin-sample directional solidification experiments of a transparent alloy, and by numerical simulations with the phase-field method in two dimensions. We find that low-angle grain boundaries (subboundaries) with an anisotropic interfacial free energy grow tilted at an angle $\theta_t$ with respect to the temperature gradient axis. $\theta_t$ remains essentially equal to its value imposed at equilibrium as long as the solidification velocity $V$ remains low. When $V$ increases and approaches the cellular instability threshold, $\theta_t$ decreases, and eventually vanishes when a steady-state cellular morphology forms. The absence of mobility of the subboundary in the solid is key to this transition. These findings are in good agreement with a recent linear-stability analysis of the problem.

cond-mat.mtrl-sci↗

arXiv2017

Grain coarsening in two-dimensional phase-field models with an orientation field

In the literature, contradictory results have been published regarding the form of the limiting (long-time) grain size distribution (LGSD) that characterizes the late stage grain coarsening in two-dimensional and quasi-two-dimensional polycrystalline systems. While experiments and the phase-field crystal (PFC) model (a simple dynamical density functional theory) indicate a lognormal distribution, other works including theoretical studies based on conventional phase-field simulations that rely on coarse grained fields, like the multi-phase-field (MPF) and orientation field (OF) models, yield significantly different distributions. In a recent work, we have shown that the coarse grained phase-field models (whether MPF or OF) yield very similar limiting size distributions that seem to differ from the theoretical predictions. Herein, we revisit this problem, and demonstrate in the case of OF models [by R. Kobayashi et al., Physica D 140, 141 (2000) and H. Henry et al. Phys. Rev. B 86, 054117 (2012)] that an insufficient resolution of the small angle grain boundaries leads to a lognormal distribution close to those seen in the experiments and the molecular scale PFC simulations. Our work indicates, furthermore, that the LGSD is critically sensitive to the details of the evaluation process, and raises the possibility that the differences among the LGSD results from different sources may originate from differences in the detection of small angle grain boundaries.

cond-mat.mtrl-sci↗

arXiv2016

Lattice Boltzmann simulations of 3D crystal growth: Numerical schemes for a phase-field model with anti-trapping current

A lattice-Boltzmann (LB) scheme, based on the Bhatnagar-Gross-Krook (BGK) collision rules is developed for a phase-field model of alloy solidification in order to simulate the growth of dendrites. The solidification of a binary alloy is considered, taking into account diffusive transport of heat and solute, as well as the anisotropy of the solid-liquid interfacial free energy. The anisotropic terms in the phase-field evolution equation, the phenomenological anti-trapping current (introduced in the solute evolution equation to avoid spurious solute trapping), and the variation of the solute diffusion coefficient between phases, make it necessary to modify the equilibrium distribution functions of the LB scheme with respect to the one used in the standard method for the solution of advection-diffusion equations. The effects of grid anisotropy are removed by using the lattices D3Q15 and D3Q19 instead of D3Q7. The method is validated by direct comparison of the simulation results with a numerical code that uses the finite-difference method. Simulations are also carried out for two different anisotropy functions in order to demonstrate the capability of the method to generate various crystal shapes.

physics.comp-ph↗

arXiv2015

An individual-based model for biofilm formation at liquid surfaces

The bacterium {\em Bacilus subtilis} frequently forms biofilms at the interface between the culture medium and the air. We develop a mathematical model that couples a description of bacteria as individual discrete objects to the standard advection-diffusion equations for the environment. The model takes into account two different bacterial phenotypes. In the motile state, bacteria swim and perform a run-and-tumble motion that is biased toward regions of high oxygen concentration (aerotaxis). In the matrix-producer state they excrete extracellular polymers, which allows them to connect to other bacteria and to form a biofilm. Bacteria are also advected by the fluid, and can trigger bioconvection. Numerical simulations of the model reproduce all the stages of biofilm formation observed in laboratory experiments. Finally, we study the influence of various model parameters on the dynamics and morphology of biofilms.

q-bio.CB↗

arXiv2015

Influence of interphase anisotropy on lamellar eutectic growth patterns

It is well documented in many experiments that crystallographic effects play an important role in the generation of two-phase patterns during the solidification of eutectic alloys. In particular, in lamellar composites, large patches of perfectly aligned lamellae are frequently observed. Moreover, the growth direction of the lamellae often markedly differs from the direction of the temperature gradient (the lamellae are tilted with respect to the main growth direction). Both of these effects cannot be explained either by the standard theory or the available numerical models of eutectic growth, which all assume the interfaces to be isotropic. We have developed a phase-field model in which the anisotropy of each interface (solid-liquid and solid-solid) can be separately controlled, and we have investigated the effect of interface anisotropy on the growth dynamics. We have found that anisotropy of the solid-solid interphase boundary free energy dramatically alters the growth dynamics. Tilted lamellae result from the modified equilibrium condition at the triple lines, in good agreement with a theoretical conjecture proposed recently. In three dimensions, the interphase boundaries tend to align with directions of minimal energy. We have also performed simulations in which two grains with different anisotropies are in competition. In all cases, the grain containing the boundaries with the lowest energies was selected after a transient. These results shed new light on the selection of growth patterns in eutectic solidification.

cond-mat.mtrl-sci↗

arXiv2014

Current Induced Fingering Instability in Magnetic Domain Walls

The shape instability of magnetic domain walls under current is investigated in a ferromagnetic (Ga,Mn)(As,P) film with perpendicular anisotropy. Domain wall motion is driven by the spin transfer torque mechanism. A current density gradient is found either to stabilize domains with walls perpendicular to current lines or to produce finger-like patterns, depending on the domain wall motion direction. The instability mechanism is shown to result from the non-adiabatic contribution of the spin transfer torque mechanism.

cond-mat.mtrl-sci↗

arXiv2012

An orientation-field model for polycristalline solidification with a singular coupling between order and orientation

The solidification of polycrystalline materials can be modelled by orientation-field models, which are formulated in terms of two continuous fields: a phase field that describes the thermodynamic state and an orientation field that indicates the local direction of the crystallographic axes. The free-energy functionals of existing models generally contain a term proportional to the modulus of the orientation gradient, which complicates their mathematical analysis and induces artificial long-range interactions between grain boundaries. We present an alternative model, in which only the square of the orientation gradient appears, but in which the phase and orientation fields are coupled by a singular function that diverges in the solid phase. We show that this model exhibits stable grain boundaries whose interactions decay exponentially with their distance. Furthermore, we demonstrate that the anisotropy of the surface energy can be included while preserving the variational structure of the model. Illustrative numerical simulations of two-dimensional examples are also presented.

cond-mat.mtrl-sci↗

arXiv2012

Thermodynamically consistent description of the hydrodynamics of free surfaces covered by insoluble surfactants of high concentration

In this paper we propose several models that describe the dynamics of liquid films which are covered by a high concentration layer of insoluble surfactant. First, we briefly review the 'classical' hydrodynamic form of the coupled evolution equations for the film height and surfactant concentration that are well established for small concentrations. Then we re-formulate the basic model as a gradient dynamics based on an underlying free energy functional that accounts for wettability and capillarity. Based on this re-formulation in the framework of nonequilibrium thermodynamics, we propose extensions of the basic hydrodynamic model that account for (i) nonlinear equations of state, (ii) surfactant-dependent wettability, (iii) surfactant phase transitions, and (iv) substrate-mediated condensation. In passing, we discuss important differences to most of the models found in the literature.

physics.flu-dyn↗

arXiv2011

Tensorial mobilities for accurate solution of transport problems in models with diffuse interfaces

The general problem of two-phase transport in phase-field models is analyzed: the flux of a conserved quantity is driven by the gradient of a potential through a medium that consists of domains of two distinct phases which are separated by diffuse interfaces. It is shown that the finite thickness of the interfaces induces two effects that are not present in the analogous sharp-interface problem: a surface excess current and a potential jump at the interfaces. It is shown that both effects can be eliminated simultaneously only if the coefficient of proportionality between flux and potential gradient (mobility) is allowed to become a tensor in the interfaces. This opens the possibility for precise and efficient simulations of transport problems with finite interface thickness.

cond-mat.mtrl-sci↗

arXiv2011

Unified derivation of phase-field models for alloy solidification from a grand-potential functional

In the literature, two quite different phase-field formulations for the problem of alloy solidification can be found. In the first, the material in the diffuse interfaces is assumed to be in an intermediate state between solid and liquid, with a unique local composition. In the second, the interface is seen as a mixture of two phases that each retain their macroscopic properties, and a separate concentration field for each phase is introduced. It is shown here that both types of models can be obtained by the standard variational procedure if a grand-potential functional is used as a starting point instead of a free-energy functional. The dynamical variable is then the chemical potential instead of the composition. In this framework, a complete analogy with phase-field models for the solidification of a pure substance can be established. This analogy is then exploited to formulate quantitative phase-field models for alloys with arbitrary phase diagrams. The precision of the method is illustrated by numerical simulations with varying interface thickness.

cond-mat.mtrl-sci↗