Browsing by Author "Achim, C. V."

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Bcc crystal-fluid interfacial free energy in Yukawa systems
(2013) Heinonen, V.; Mijailovic, A.; Achim, C. V.; Ala-Nissilä, Tapio; Rozas, R. E.; Horbach, J.; Löwen, H.
School of Science | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
We determine the orientation-resolved interfacial free energy between a body-centered-cubic (bcc) crystal and the coexisting fluid for a many-particle system interacting via a Yukawa pair potential. For two different screening strengths, we compare results from molecular dynamics computer simulations, density functional theory, and a phase-field-crystal approach. Simulations predict an almost orientationally isotropic interfacial free energy of 0.12k B T/a 2 (with k B T denoting the thermal energy and a the mean interparticle spacing), which is independent of the screening strength. This value is in reasonable agreement with our Ramakrishnan-Yussouff density functional calculations, while a high-order fitted phase-field-crystal approach gives about 2−3 times higher interfacial free energies for the Yukawa system. Both field theory approaches also give a considerable anisotropy of the interfacial free energy. Our result implies that, in the Yukawa system, bcc crystal-fluid free energies are a factor of about 3 smaller than face-centered-cubic crystal-fluid free energies.
Bcc crystal-fluid interfacial free energy in Yukawa systems
(2013-01-28) Heinonen, V.; Mijailović, A.; Achim, C. V.; Ala-Nissilä, Tapio; Rozas, R.E.; Horbach, J.; Löwen, H.
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
We determine the orientation-resolved interfacial free energy between a body-centered-cubic (bcc) crystal and the coexisting fluid for a many-particle system interacting via a Yukawa pair potential. For two different screening strengths, we compare results from molecular dynamics computer simulations, density functional theory, and a phase-field-crystal approach. Simulations predict an almost orientationally isotropic interfacial free energy of 0.12kBT/a2 (with kBT denoting the thermal energy and a the mean interparticle spacing), which is independent of the screening strength. This value is in reasonable agreement with our Ramakrishnan-Yussouff density functional calculations, while a high-order fitted phase-field-crystal approach gives about 2-3 times higher interfacial free energies for the Yukawa system. Both field theory approaches also give a considerable anisotropy of the interfacial free energy. Our result implies that, in the Yukawa system, bcc crystal-fluid free energies are a factor of about 3 smaller than face-centered-cubic crystal-fluid free energies.
Consistent Hydrodynamics for Phase Field Crystals
(2016-01-15) Heinonen, V.; Achim, C. V.; Kosterlitz, J. M.; Ying, See-Chen; Lowengrub, J.; Ala-Nissilä, Tapio
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
We use the amplitude expansion in the phase field crystal framework to formulate an approach where the fields describing the microscopic structure of the material are coupled to a hydrodynamic velocity field. The model is shown to reduce to the well-known macroscopic theories in appropriate limits, including compressible Navier-Stokes and wave equations. Moreover, we show that the dynamics proposed allows for long wavelength phonon modes and demonstrate the theory numerically showing that the elastic excitations in the system are relaxed through phonon emission.
Dynamical transitions and sliding friction of the phase-field-crystal model with pinning
(2010) Ramos, J. A. P.; Granato, E.; Ying, S. C.; Achim, C. V.; Elder, K. R.; Ala-Nissilä, Tapio
School of Science | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
We study the nonlinear driven response and sliding friction behavior of the phase-field-crystal (PFC) model with pinning including both thermal fluctuations and inertial effects. The model provides a continuous description of adsorbed layers on a substrate under the action of an external driving force at finite temperatures, allowing for both elastic and plastic deformations. We derive general stochastic dynamical equations for the particle and momentum densities including both thermal fluctuations and inertial effects. The resulting coupled equations for the PFC model are studied numerically. At sufficiently low temperatures, we find that the velocity response of an initially pinned commensurate layer shows hysteresis with dynamical melting and freezing transitions for increasing and decreasing applied forces at different critical values. The main features of the nonlinear response in the PFC model are similar to the results obtained previously with molecular dynamics simulations of particle models for adsorbed layers.
Glassy phases and driven response of the phase-field-crystal model with random pinning
(2011) Granato, E.; Ramos, J. A. P.; Achim, C. V.; Lehikoinen, J.; Ying, S. C.; Ala-Nissilä, Tapio; Elder, K. R.
School of Science | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
We study the structural correlations and the nonlinear response to a driving force of a two-dimensional phase-field-crystal model with random pinning. The model provides an effective continuous description of lattice systems in the presence of disordered external pinning centers, allowing for both elastic and plastic deformations. We find that the phase-field crystal with disorder assumes an amorphous glassy ground state, with only short-ranged positional and orientational correlations, even in the limit of weak disorder. Under increasing driving force, the pinned amorphous-glass phase evolves into a moving plastic-flow phase and then, finally, a moving smectic phase. The transverse response of the moving smectic phase shows a vanishing transverse critical force for increasing system sizes.
Long-wavelength properties of phase-field-crystal models with second-order dynamics
(2016-05-09) Heinonen, V.; Achim, C. V.; Ala-Nissilä, Tapio
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
The phase-field-crystal (PFC) approach extends the notion of phase-field models by describing the topology of the microscopic structure of a crystalline material. One of the consequences is that local variation of the interatomic distance creates an elastic excitation. The dynamics of these excitations poses a challenge: pure diffusive dynamics cannot describe relaxation of elastic stresses that happen through phonon emission. To this end, several different models with fast dynamics have been proposed. In this article we use the amplitude expansion of the PFC model to compare the recently proposed hydrodynamic PFC amplitude model with two simpler models with fast dynamics. We compare these different models analytically and numerically. The results suggest that in order to have proper relaxation of elastic excitations, the full hydrodynamical description of the PFC amplitudes is required.
Modeling buckling and topological defects in stacked two-dimensional layers of graphene and hexagonal boron nitride
(2021-03-12) Elder, K. R.; Achim, C. V.; Heinonen, V.; Granato, E.; Ying, S. C.; Ala-Nissila, T.
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
In this paper, a two-dimensional phase field crystal model of graphene and hexagonal boron nitride (hBN) is extended to include out-of-plane deformations in stacked multilayer systems. As proof of principle, the model is shown analytically to reduce to standard models of flexible sheets in the small deformation limit. Applications to strained sheets, dislocation dipoles, and grain boundaries are used to validate the behavior of a single flexible graphene layer. For multilayer systems, parameters are obtained to match existing theoretical density functional theory calculations for graphene/graphene, hBN/hBN, and graphene/hBN bilayers. More precisely, it is shown that the parameters can be chosen to closely match the stacking energies and layer spacing calculated by Zhou et al. [Phys. Rev. B 92, 155438 (2015)PRBMDO1098-012110.1103/PhysRevB.92.155438]. Further validation of the model is presented in a study of rotated graphene bilayers and stacking boundaries. The flexibility of the model is illustrated by simulations that highlight the impact of complex microstructures in one layer on the other layer in a graphene/graphene bilayer.
Modeling self-organization of thin strained metallic overlayers from atomic to micron scales
(2013) Elder, K. R.; Rossi, G.; Kanerva, P.; Sanches, F.; Ying, S-C.; Granato, E.; Achim, C. V.; Ala-Nissilä, Tapio
School of Science | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
A computational study of the self-organization of heteroepitaxial ultrathin metal films is presented. By means of a continuum complex field model, the relationship of the equilibrium surface patterns of the film to the adsorbate-substrate adhesion energy, as well as to the mismatch between the adsorbate and the substrate bulk lattice parameters, are obtained in both the tensile and the compressive regimes. Our approach captures pattern periodicities over large length scales, up to several hundreds of nm, retaining atomistic resolution. Thus, the results can be directly compared with experimental data, in particular for systems such as Cu/Ru(0001) and Ag/Cu(111). Three nontrivial, stable superstructures for the overlayer, namely, stripe, honeycomb, and triangular, are identified that closely resemble those observed experimentally. Simulations in nonequilibrium conditions are performed as well to identify metastable structural configurations and the dynamics of ordering of the overlayer.
Nonlinear driven response of a phase-field crystal in a periodic pinning potential
(2009) Achim, C. V.; Ramos, J. A. P.; Karttunen, M.; Elder, K. R.; Granato, E.; Ala-Nissilä, Tapio; Ying, S. C.
School of Science | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
We study numerically the phase diagram and the response under a driving force of the phase field crystal model for pinned lattice systems introduced recently for both one- and two-dimensional systems. The model describes the lattice system as a continuous density field in the presence of a periodic pinning potential, allowing for both elastic and plastic deformations of the lattice. We first present results for phase diagrams of the model in the absence of a driving force. The nonlinear response to a driving force on an initially pinned commensurate phase is then studied via overdamped dynamic equations of motion for different values of mismatch and pinning strengths. For large pinning strength the driven depinning transitions are continuous, and the sliding velocity varies with the force from the threshold with power-law exponents in agreement with analytical predictions. Transverse depinning transitions in the moving state are also found in two dimensions. Surprisingly, for sufficiently weak pinning potential we find a discontinuous depinning transition with hysteresis even in one dimension under overdamped dynamics. We also characterize structural changes of the system in some detail close to the depinning transition.
Patterning of Heteroepitaxial Overlayers from Nano to Micron Scales
(2012) Elder, K. R.; Rossi, G.; Kanerva, P.; Sanches, F.; Ying, S-C.; Granato, E.; Achim, C. V.; Ala-Nissilä, Tapio
School of Science | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Thin heteroepitaxial overlayers have been proposed as templates to generate stable, self-organized nanostructures at large length scales, with a variety of important technological applications. However, modeling strain-driven self-organization is a formidable challenge due to different length scales involved. In this Letter, we present a method for predicting the patterning of ultrathin films on micron length scales with atomic resolution. We make quantitative predictions for the type of superstructures (stripes, honeycomb, triangular) and length scale of pattern formation of two metal-metal systems, Cu on Ru(0001) and Cu on Pd(111). Our findings are in excellent agreement with previous experiments and call for future experimental investigations of such systems.
Phase diagram and commensurate-incommensurate transitions in the phase field crystal model with an external pinning potential
(2006) Achim, C. V.; Karttunen, M.; Elder, K. R.; Granato, E.; Ala-Nissilä, Tapio; Ying, S. C.
School of Science | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
We study the phase diagram and the commensurate-incommensurate transitions in a phase field model of a two-dimensional crystal lattice in the presence of an external pinning potential. The model allows for both elastic and plastic deformations and provides a continuum description of lattice systems, such as for adsorbed atomic layers or two-dimensional vortex lattices. Analytically, a mode expansion analysis is used to determine the ground states and the commensurate-incommensurate transitions in the model as a function of the strength of the pinning potential and the lattice mismatch parameter. Numerical minimization of the corresponding free energy shows reasonable agreement with the analytical predictions and provides details on the topological defects in the transition region. We find that for small mismatch the transition is of first order, and it remains so for the largest values of mismatch studied here. Our results are consistent with results of simulations for atomistic models of adsorbed overlayers.
Phase diagram of pinned lattices in the phase field crystal model
(2008) Achim, C. V.; Karttunen, M.; Elder, K. R.; Granato, E.; Ala-Nissilä, Tapio; Ying, S. C.
School of Science | A4 Artikkeli konferenssijulkaisussa
We study the phase diagram and the commensurate-incommensurate phase transitions of a two-dimensional phase field crystal model for adsorbed layers. The model allows for both elastic and plastic deformations on atomic and diffusive time-scales, and provides a continuum description of lattice systems, such as adsorbed atomic layers or two-dimensional vortex lattices. Analytically, mode expansion analysis and numerical minimization of the free energy are used to determine the ground states as a function of the pinning potential and lattice mismatch parameter. The results show a rich phase diagram with several different types of commensurate and incommensurate phases.
Phase-field-crystal models and mechanical equilibrium
(2014) Heinonen, V.; Achim, C. V.; Elder, K. R.; Buyuddagli, S.; Ala-Nissilä, Tapio
School of Science | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Phase-field-crystal (PFC) models constitute a field theoretical approach to solidification, melting, and related phenomena at atomic length and diffusive time scales. One of the advantages of these models is that they naturally contain elastic excitations associated with strain in crystalline bodies. However, instabilities that are diffusively driven towards equilibrium are often orders of magnitude slower than the dynamics of the elastic excitations, and are thus not included in the standard PFC model dynamics. We derive a method to isolate the time evolution of the elastic excitations from the diffusive dynamics in the PFC approach and set up a two-stage process, in which elastic excitations are equilibrated separately. This ensures mechanical equilibrium at all times. We show concrete examples demonstrating the necessity of the separation of the elastic and diffusive time scales. In the small-deformation limit this approach is shown to agree with the theory of linear elasticity.
Striped, honeycomb, and twisted moiré patterns in surface adsorption systems with highly degenerate commensurate ground states
(2017-11-29) Elder, K. R.; Achim, C. V.; Granato, E.; Ying, S. C.; Ala-Nissila, T.
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Atomistically thin adsorbate layers on surfaces with a lattice mismatch display complex spatial patterns and ordering due to strain-driven self-organization. In this work, a general formalism to model such ultrathin adsorption layers that properly takes into account the competition between strain and adhesion energy of the layers is presented. The model is based on the amplitude expansion of the two-dimensional phase field crystal (PFC) model, which retains atomistic length scales but allows relaxation of the layers at diffusive time scales. The specific systems considered here include cases where both the film and the adsorption potential can have either honeycomb (H) or triangular (T) symmetry. These systems include the so-called (1×1), (3×3)R30â, (2×2), (7×7)R19.1â, and other higher order states that can contain a multitude of degenerate commensurate ground states. The relevant phase diagrams for many combinations of the H and T systems are mapped out as a function of adhesion strength and misfit strain. The coarsening patterns in some of these systems is also examined. The predictions are in good agreement with existing experimental data for selected strained ultrathin adsorption layers.
Thermal fluctuations and phase diagrams of the phase-field crystal model with pinning
(2008) Ramos, J. A. P.; Granato, E.; Achim, C. V.; Ying, S. C.; Elder, K. R.; Ala-Nissilä, Tapio
School of Science | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
We study the influence of thermal fluctuations in the phase diagram of a recently introduced two-dimensional phase field crystal model with an external pinning potential. The model provides a continuum description of pinned lattice systems allowing for both elastic deformations and topological defects. We introduce a nonconserved version of the model and determine the ground-state phase diagram as a function of lattice mismatch and strength of the pinning potential. Monte Carlo simulations are used to determine the phase diagram as a function of temperature near commensurate phases. The results show a rich phase diagram with commensurate, incommensurate, and liquidlike phases with a topology strongly dependent on the type of ordered structure. A finite-size scaling analysis of the melting transition for the c(2×2) commensurate phase shows that the thermal correlation length exponent ν and specific heat behavior are consistent with the Ising universality class as expected from analytical arguments.
Thermodynamics of bcc metals in phase-field-crystal models
(2009) Jaatinen, A.; Achim, C. V.; Elder, K. R.; Ala-Nissilä, Tapio
School of Science | A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
We examine the influence of different forms of the free-energy functionals used in the phase-field-crystal (PFC) model, and compare them with the second-order density-functional theory (DFT) of freezing, by using bcc iron as an example case. We show that there are large differences between the PFC and the DFT and it is difficult to obtain reasonable parameters for existing PFC models directly from the DFT. Therefore, we propose a way of expanding the correlation function in terms of gradients that allows us to incorporate the bulk modulus of the liquid as an additional parameter in the theory. We show that this functional reproduces reasonable values for both bulk and surface properties of bcc iron, and therefore it should be useful in modeling bcc materials. As a further demonstration, we also calculate the grain boundary energy as a function of misorientation for a symmetric tilt boundary close to the melting transition.