Complex order parameter phase-field models derived from structural phase-field-crystal models

Ofori-Opoku, Nana; Stolle, Jonathan; Huang, Zhi Feng; Provatas, Nikolas

doi:10.1103/physrevb.88.104106

Cited by 34 publications

(52 citation statements)

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“…These goals are part of a larger effort to exploit the novel features of the PFC approach within traditional areas of materials science, including crystal plasticity, structural phase transformations, and microstructure evolution [21][22][23][24][25][26]. Some initial groundwork covering fundamental dislocation properties in FCC materials was reported by the present authors in Ref.…”

Section: Introductionmentioning

confidence: 92%

“…The larger length scales described by DDD and PF models cannot currently be reached by PFC, though one may imagine using PFC simulations to generate input parameters for such models or numerically coupling PFC with DDD or PF. Coarse-grained complex amplitude PFC models also provide an interesting means of self-consistently reaching larger length scales [16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2014

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Material properties controlled by evolving defect structures, such as mechanical response, often involve processes spanning many length and time scales which cannot be modeled using a single approach. We present a variety of new results that demonstrate the ability of phase field crystal (PFC) models to describe complex defect evolution phenomena on atomistic length scales and over long, diffusive time scales. Primary emphasis is given to the unification of conservative and nonconservative dislocation creation mechanisms in three-dimensional FCC and BCC materials. These include Frank-Read-type glide mechanisms involving closed dislocation loops or grain boundaries as well as Bardeen-Herring-type climb mechanisms involving precipitates, inclusions, and/or voids. Both source classes are naturally and simultaneously captured at the atomistic level by PFC descriptions, with arbitrarily complex defect configurations, types, and environments. An unexpected dipole-to-quadrupole source transformation is identified, as well as various new and complex geometrical features of loop nucleation via climb from spherical particles. Results for the strain required to nucleate a dislocation loop from such a particle are in agreement with analytic continuum theories. Other basic features of FCC and BCC dislocation structure and dynamics are also outlined, and initial results for dislocation-stacking fault tetrahedron interactions are presented. These findings together highlight various capabilities of the PFC approach as a coarse-grained atomistic tool for the study of three-dimensional crystal plasticity.

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Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

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

et al. 2014

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“…t v Mnφ k 0/1 ξ 1/2 A0,1 ωB α2,4 1 1 1 0.05 2π, √ 22π (1, 1) (1, 1) 1 (-0.001, 0) [20] and chosen to maximize the energetic difference between square and triangular phase. i = 1, 2, respectively.…”

Section: Model and Numerical Approachmentioning

confidence: 99%

Magnetically induced/enhanced coarsening in thin films

Backofen

Voigt

2020

Phys. Rev. Materials

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External magnetic fields influence the microstructure of polycrystalline materials. We explore the influence of strong external magnetic fields on the long time scaling of grain size during coarsening in thin films with an extended phase-field-crystal model. Additionally, the change of various geometrical and topological properties is studied. In a situation which leads to stagnation, an applied external magnetic field induces further grain growth. The induced driving force due to the magnetic anisotropy defines the magnetic influence of the external magnetic field. Different scaling regimes are identified dependent on the magnetization. At the beginning, the scaling exponent increases with the strength of the magnetization. Later, when the texture becomes dominated by grains preferably aligned with the external magnetic field, the scaling exponent becomes independent on the strength of the magnetization or stagnation occur. We discuss how the magnetic influence change the effect of retarding or pinning forces, which are known to influence the scaling exponents. We further study the influence of the magnetic field on the grain size distribution (GSD), next neighbor distribution (NND) as well as grain shape and orientation. If possible, we compare our predictions with experimental findings. arXiv:1909.00527v4 [cond-mat.mtrl-sci]

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“…The system sizes required to describe typical experimentally-relevant dislocation densities, though not yet accessible, may be realizable within the next decade or potentially sooner with further development of computationally efficient, coarse grained complex amplitude expansions of PFC models [39][40][41][42] . Potential points of shorterterm study include investigation of fully 3D systems with more realistic microstructures and a distribution of dislocation source activation stresses, as well as development of constant stress deformation methods that impose fewer constraints on the shape of the polycrystalline domain.…”

Section: Discussionmentioning

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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Complex order parameter phase-field models derived from structural phase-field-crystal models

Cited by 34 publications

References 50 publications

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

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

Magnetically induced/enhanced coarsening in thin films

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

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