Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals

Elder, K. R.; Grant, Martin

doi:10.1103/physreve.70.051605

Cited by 773 publications

(1,163 citation statements)

References 79 publications

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“…For most of the present analysis the precise form of the higher order nonlinearities is not important, as they enter the expressions for the interface interaction only as prefactors in terms of matching constants. However, to complete the model, we use here amplitude equations which are derived via a multiscale expansion 42 from the three-dimensional phase-field-crystal model 28,29 ,…”

Section: Amplitude Equationsmentioning

confidence: 99%

“…Several continuum descriptions have been pushed forward, including those based on phase field models [24][25][26][27] with either an orientational order parameter 24,25 or multiorder parameter models 26,27 ; these order parameters are needed to distinguish between the different grain orientations. More recently, the phase field crystal (PFC) method has been introduced 28,29 , allowing to describe the atomic structure and thus the local lattice orientation via the crystal density field. GB premelting studies using these models have been performed in Refs.…”

Section: Introductionmentioning

confidence: 99%

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Structural short-range forces between solid-melt interfaces

Spatschek

Adland

2013

Phys. Rev. B

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We predict the structural interaction of crystalline solid-melt interfaces using amplitude equations which are derived from classical density functional theory or phase-field-crystal modeling. The solid ordering decays exponentially on the scale of the interface thickness at solid-melt interfaces; the overlap of two such profiles leads to a short range interaction, which is mainly carried by the longest-range density waves, which can facilitate grain boundary premelting. We calculate the tail of these interactions, depending on the relative translation of the two crystals fully analytically and predict the interaction potential, and compare it to numerical simulations. For grain boundaries the interaction is predicted to decay twice faster as for two crystals without misorientation.

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Section: Amplitude Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Structural short-range forces between solid-melt interfaces

Spatschek

Adland

2013

Phys. Rev. B

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“…In this paper, we investigate GB premelting and shearing and their relationship using the PFC method [40][41][42][43][44][45][46] . We use the simplest PFC model 40,41 with the same freeenergy function as the Swift-Hohenberg model of pattern formation 47 , which favors hexagonal and bcc ordering in two and three dimensions (2D and 3D), respectively.…”

Section: Introductionmentioning

confidence: 99%

“…We use the simplest PFC model 40,41 with the same freeenergy function as the Swift-Hohenberg model of pattern formation 47 , which favors hexagonal and bcc ordering in two and three dimensions (2D and 3D), respectively. This model can be interpreted 43 as a considerably simplified version of classical density function theory (DFT) [48][49][50][51][52][53] where the crystal density field is dominated by the set of primary reciprocal lattice vectors.…”

Section: Introductionmentioning

confidence: 99%

Phase-field-crystal study of grain boundary premelting and shearing in bcc iron

et al. 2013

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We use the phase-field-crystal (PFC) method to investigate the equilibrium premelting and nonequilibrium shearing behaviors of [001] symmetric tilt grain boundaries (GBs) at high homologous temperature over the complete range of misorientation 0 < θ < 90 • in classical models of bcc Fe. We characterize the dependence of the premelted layer width W as a function of temperature and misorientation. In addition, we compute the thermodynamic disjoining potential whose derivative with respect to W represents the structural force between crystal-melt interfaces due to the spatial overlap of density waves. The disjoining potential is also computed by molecular dynamics (MD) simulations, for quantitative comparison with PFC simulations, and coarse-grained amplitude equations (AE) derived from PFC that provide additional analytical insights. We find that, for GBs over an intermediate range of misorientation (θmin < θ < θmax), W diverges as the melting temperature is approached from below, corresponding to a purely repulsive disjoining potential, while for GBs outside this range (θ < θmin or θmax < θ < 90 • ), W remains finite at the melting point. In the latter case, W corresponds to a shallow attractive minimum of the disjoining potential. The misorientation range where W diverges predicted by PFC simulations is much smaller than the range predicted by MD simulations when the small dimensionless parameter ǫ of the PFC model is matched to liquid structure factor properties. However it agrees well with MD simulations with a lower ǫ value chosen to match the ratio of bulk modulus and solid-liquid interfacial free-energy, consistent with the amplitude-equation prediction that θmin and 90 • − θmax scale as ∼ ǫ 1/2 . The incorporation of thermal fluctuations in PFC is found to have a negligible effect on this range. In response to a shear stress parallel to the GB plane, GBs in PFC simulations exhibit coupled motion normal to this plane or sliding. Furthermore, the coupling factor exhibits a discontinuous change as a function of θ that reflects a transition between two coupling modes. Sliding is only observed over a range of misorientation that is a strongly increasing function of temperature for T /TM ≥ 0.8 and matches roughly the range where W diverges at the melting point. The coupling factor for the two coupling modes is in excellent quantitative agreement with previous theoretical predictions [J. W. Cahn, Y. Mishin, and A. Suzuki, Acta Mater. 54, 4953 (2006)].

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“…On the other hand, recent numerical simulation tools have been developed for physical models of grain formation and grain dynamics on the atomistic scale. Concerning such simulations, we refer to numerical results obtained from a phase field crystal (PFC) model [10] derived from the density function theory (DFT) of freezing [23]. Its methodology describes the evolution of the atomic density of a system according to dissipative dynamics driven by free energy minimization.…”

Section: Introductionmentioning

confidence: 99%

Identification of Grain Boundary Contours at Atomic Scale

Berkels

Rätz

Rumpf

et al.

Lecture Notes in Computer Science

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Abstract. Nowadays image acquisition in materials science allows the resolution of grains at atomic scale. Grains are material regions with different lattice orientation which are typically not in equilibrium. At the same time, new microscopic simulation tools allow to study the dynamics of such grain structures. Single atoms are resolved in the experimental and in the simulation results. A qualitative study of experimental images and simulation results and the comparison of simulation and experiment requires the robust and reliable extraction of mesoscopic properties from these microscopic data sets. Based on a Mumford-Shah type functional, grain boundaries are described as free discontinuity sets at which the orientation parameter for the lattice jumps. The lattice structure itself is encoded in a suitable integrand depending on the local lattice orientation. In addition the approach incorporates solid-liquid interfaces. The resulting Mumford-Shah functional is approximated with a level set active contour model following the approach by Chan and Vese. The implementation is based on a finite element discretization in space and a step size controlled gradient descent algorithm.

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Modeling elastic and plastic deformations in nonequilibrium processing using phase field crystals

Cited by 773 publications

References 79 publications

Structural short-range forces between solid-melt interfaces

Structural short-range forces between solid-melt interfaces

Phase-field-crystal study of grain boundary premelting and shearing in bcc iron

Identification of Grain Boundary Contours at Atomic Scale

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