Phase field crystal modeling as a unified atomistic approach to defect dynamics

Berry, Joel; Provatas, Nikolas; Rottler, Jörg; Sinclair, Chad W.

doi:10.1103/physrevb.89.214117

Cited by 61 publications

(47 citation statements)

References 71 publications

(109 reference statements)

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“…The currently-implemented PFC methods addressing the evolution of distributed defects from point defect diffusion [21,31,32] lack an accurate description of the true atomic-scale point defects, with neither defect structures, energies, nor transition rates, computed accurately [33]. Related to the application here, while "climb" processes have been simulated, the nucleation processes are not captured with true atomistic fidelity and climb mechanisms that do not rely on double kink nucleation are reported [21]. The DMD method combines a classical density functional approach for the free energy with a Master Equation-type diffusion model to follow the evolution of defects over "diffusive" time scales [24,30].…”

Section: Discussion and Summarymentioning

confidence: 99%

“…Thus, this preliminary application is not a full study of the problem of dislocation climb. There is a long-standing theoretical framework for double-jog nucleation [16,17,18,19,20] but, because of the huge range of spatial and temporal scales involved, only a few recent attempts have been made to model the climb process at the atomistic scale [21,22,23,24]. We discuss our simulations with respect to theory and earlier models in the discussions sections.…”

Section: Application: Edge Dislocation Climb In Aluminummentioning

confidence: 99%

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Multiscale diffusion method for simulations of long-time defect evolution with application to dislocation climb

Baker

Curtin

2016

Journal of the Mechanics and Physics of Solids

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In many problems of interest to materials scientists and engineers, the evolution of crystalline extended defects (dislocations, cracks, grain boundaries, interfaces, voids, precipitates) is controlled by the flow of point defects (interstitial/substitutional atoms and/or vacancies) through the crystal into the defect. Precise modeling of this behavior requires fully atomistic methods in and around the extended defect, but the flow of point defects entering the extended defect region can be treated by coarse-grained methods. Here, a multiscale algorithm is presented to provide this coupling. Specifically, direct accelerated molecular dynamics (AMD) of extended defect evolution is coupled to a diffusing point defect concentration field that captures the long spatial and temporal scales of point defect motion in the presence of the internal stress fields generated by the evolving defect. The algorithm is applied to study vacancy absorption into an edge dislocation in aluminum where, under a sufficient driving stress and vacancy supersaturation, vacancy accumulation in the core leads to nucleation of a double-jog that then operates as a sink for additional vacancies; this corresponds to the initial stages of dislocation climb modeled with explicit atomistic resolution. The method is general and so can be applied to many other problems associated with nucleation, growth, and reaction due to accumulation of point defects in crystalline materials.

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Section: Discussion and Summarymentioning

confidence: 99%

Section: Application: Edge Dislocation Climb In Aluminummentioning

confidence: 99%

Multiscale diffusion method for simulations of long-time defect evolution with application to dislocation climb

Baker

Curtin

2016

Journal of the Mechanics and Physics of Solids

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“…PFC has been used to model complex defect structures and kinetics, like dislocation dynamics 23,24,[30][31][32] , structural phase changes 44 , grain boundary energies and evolution 8,26,27,[33][34][35] , and vacancy diffusion 61 . In some cases, the results for some complex problems show qualitative trends consistent with basic models and direct molecular simulations 26,27,62 .…”

Section: Discussionmentioning

confidence: 99%

“…Recent work has applied the PFC method to study dislocations and their motion in face centered cubic (FCC) crystals 23,24 . Because the PFC models can be tuned to achieve a desired lattice constant and elastic constants, the long-range elastic fields of a dislocation can be captured in PFC models because those fields only depend on the Burgers vector (a primitive lattice vector) and the elastic constants.…”

Section: Introductionmentioning

confidence: 99%

Assessment of phase-field-crystal concepts using long-time molecular dynamics

Baker

2015

Phys. Rev. B

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The ability of the phase-field-crystal (PFC) model to quantitatively predict atomistic defect structures in crystalline solids is addressed. First, general aspects of the PFC model are discussed within the context of obtaining quantitative results in solid materials. Then a specific example is used to illustrate major points. Specifically, accelerated molecular dynamics is used to compute the oneparticle probability density, ρ (1) (r), in a complex atomistic defect consisting of a Lomer dislocation with an equilibrium distribution of vacancies in the core, and the results are considered within the general framework of the PFC model. As expected, ρ (1) (r) shows numerous spatially localized peaks with integrated densities smaller than unity, as would arise in a PFC computation. However, the ρ (1) (r) actually corresponds to a time-averaged superposition of a few well-defined atomic configurations each having a well-defined energy. The deconvolution of ρ (1) (r) to obtain the actual distinct atomic configurations is not feasible. Using a potential energy functional that accurately computes the energies of distinct configurations, the potential energy computed using ρ (1) (r) differs from the actual average atomistic energy by ∼50 eV divided among approximately 46 atoms in the core of the defect. Attempts to rectify this deviation by introducing correlations can not significantly reduce this error. The simulations show that energy barriers between distinct configurations varying by up to 0.5 eV, indicating that the simple kinetic evolution law used in PFC cannot accurately capture the true time evolution in this problem. Overall, these results demonstrate, in one non-trivial case, that the PFC model is probably unable to predict atomistic defect structures, energies, or kinetic barriers, at the quantitative levels needed for application to problems in materials science.

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“…Both conservative and nonconservative dislocation evolution processes are captured for arbitrary crystal structure, orientation, morphology, and applied stress [25][26][27][28][29][30][31] . PFC simulations of diffusion-accommodated plastic flow under creep conditions may therefore reveal previously inaccessible information about the atomistic mechanisms that control diffusional and power law creep.…”

Section: Pfc Approachmentioning

confidence: 99%

Atomistic study of diffusion-mediated plasticity and creep using phase field crystal methods

et al. 2015

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The nonequilibrium dynamics of diffusion-mediated plasticity and creep in materials subjected to constant load at high homologous temperatures is studied atomistically using Phase Field Crystal (PFC) methods. Creep stress and grain size exponents obtained for nanopolycrystalline systems, m 1.02 and p 1.98, respectively, closely match those expected for idealized diffusional NabarroHerring creep. These exponents are observed in the presence of significant stress-assisted diffusive grain boundary migration, indicating that Nabarro-Herring creep and stress-assisted boundary migration contribute in the same manner to the macroscopic constitutive relation. When plastic response is dislocation-mediated, power law stress exponents inferred from dislocation climb rates are found to increase monotonically from m 3, as expected for generic climb-mediated natural creep, to m 5.8 as the dislocation density ρ d is increased beyond typical experimental values. Stress exponents m 3 directly measured from simulations that include dislocation nucleation, climb, glide, and annihilation are attributed primarily to these large ρ d effects. Extrapolation to lower ρ d suggests that m 4 − 4.5 should be obtained from our PFC description at typical experimental ρ d values, which is consistent with expectations for power law creep via mixed climb and glide. The anomalously large stress exponents observed in our atomistic simulations at large ρ d may nonetheless be relevant to systems in which comparable densities are obtained locally within heterogeneous defect domains such as dislocation cell walls or tangles. The tendency of a solid material to gradually and irreversibly deform or even flow under low loads at high temperatures is termed creep deformation 1-6 . Low loads and high temperatures in this context are σ σ y and T T m /2, respectively, where σ y is the yield stress and T m is the equilibrium melting temperature of the material. This type of slow plasticity not only alters material microstructure, shape, and properties over extended time periods, but is also a primary cause of mechanical failure in materials such as gas turbine blades that operate in high temperature load bearing environments 1-3 .The plastic flow that occurs during creep can involve conservative defect evolution mechanisms, such as dislocation glide and grain boundary sliding, but is generally facilitated by thermally activated defect motion along local stress and/or chemical potential gradients, and is therefore inherently diffusive in nature. Vacancy diffusion in particular tends to be a central facilitator of deformation, either directly during diffusional creep or indirectly during dislocation or power law creep, as discussed further in the following. Moreover, it is the collective evolution of different defect populations over multiple length and time scales that leads to the observed diverse macroscopic phenomenology of creep. If the characteristic time scales associated with the diffusion of individual defects are almost entirely inaccessible to most at...

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Phase field crystal modeling as a unified atomistic approach to defect dynamics

Cited by 61 publications

References 71 publications

Multiscale diffusion method for simulations of long-time defect evolution with application to dislocation climb

Multiscale diffusion method for simulations of long-time defect evolution with application to dislocation climb

Assessment of phase-field-crystal concepts using long-time molecular dynamics

Atomistic study of diffusion-mediated plasticity and creep using phase field crystal methods

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