Thermodynamic Criteria for Grain-Boundary Melting: A Molecular-Dynamics Study

Broughton, Jeremy Q.; Gilmer, G. H.

doi:10.1103/physrevlett.56.2692

Cited by 132 publications

(79 citation statements)

References 15 publications

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“…(29), whereas the lines were computed by integration of Eqs. (30), (31) and (32). The excellent agreement between the two calculations confirm the correctness and accuracy of our methodology.…”

Section: Tension and Compression Parallel To The Gb Planesupporting

confidence: 66%

“…Over the entire temperature range studied here, γ decreases from 0.905 J/m 2 at 0 K to 0.660 J/m 2 at 900 K. The trend for γ to decrease with temperature is consistent with previous simulations. 32,33 C. Cu-Ag alloys at finite temperatures Fig. 16 shows MC snapshots of the simulation block with the grain compositions of 0.036%, 0.24% and 0.58% Ag at 800 K. These images demonstrate that Ag strongly segregates to the GB and that the segregated amount and the width of the segregation region both increase with temperature.…”

Section: B Pure Cu At Finite Temperaturesmentioning

confidence: 99%

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Thermodynamics of coherent interfaces under mechanical stresses. II. Application to atomistic simulation of grain boundaries

Frolov

Mishin

2012

Phys. Rev. B

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The thermodynamic theory of coherent interfaces developed in Part I of this work is applied to grain boundaries (GBs) subject to non-hydrostatic elastic deformations. We derive expressions for the GB free energy as the reversible work of GB formation under stress. We also present a generalized adsorption equation whose differential coefficients define the GB segregation, GB stress tensor, GB excess volume, and GB excess shear. The generalized adsorption equation generates a set of Maxwell relations describing cross-effects between different GB properties. The theory is applied to atomistic simulations of a symmetrical tilt GB in Cu and Cu-Ag alloys.Using a combination of molecular dynamics and Monte Carlo methods, we compute a number of GB excess quantities and their dependencies on the applied stresses, temperature and chemical composition in the grains.We also test several Maxwell relations and obtain excellent agreement between the theory and simulations.

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Section: Tension and Compression Parallel To The Gb Planesupporting

confidence: 66%

Section: B Pure Cu At Finite Temperaturesmentioning

confidence: 99%

Thermodynamics of coherent interfaces under mechanical stresses. II. Application to atomistic simulation of grain boundaries

Frolov

Mishin

2012

Phys. Rev. B

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“…The difference between the coupling functions (18) and (20) is that the first is quartic in the amplitude variations in the bulk states and the latter linear. From this we immediately conclude that in the first case it is not necessary to take the tilt term into account for the solution of the linearized equations in the liquid region, as it is of higher order, and it appears there only effectively through the energy shift as the value of the Hamiltonian.…”

Section: Appendix A: Linear Temperature Couplingmentioning

confidence: 99%

“…On the theoretical side we mention in particular discrete lattice models 17 as well as molecular dynamics (MD) simulations [18][19][20][21][22][23] . 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.…”

Section: Introductionmentioning

confidence: 99%

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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“…Theoretical approaches include discrete lattice models 17 and molecular dynamics (MD) simulations [18][19][20][21][22][23] , as well as conventional phase-field models [24][25][26][27] , which either exploit an orientational order parameter 24,25 or multiple phase-fields 26,27 to distinguish between grains, and the phase-field-crystal (PFC) method 28,29 , which resolves the crystal density field on an atomic scale and hence naturally models crystal defects such as isolated dislocations and GBs.…”

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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Thermodynamic Criteria for Grain-Boundary Melting: A Molecular-Dynamics Study

Cited by 132 publications

References 15 publications

Thermodynamics of coherent interfaces under mechanical stresses. II. Application to atomistic simulation of grain boundaries

Thermodynamics of coherent interfaces under mechanical stresses. II. Application to atomistic simulation of grain boundaries

Structural short-range forces between solid-melt interfaces

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

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