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Title: Multi-phase-field analysis of short-range forces between diffuse interfaces

Journal Article · · Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
 [1];  [2];  [3]
  1. Northeastern Univ., Boston, MA (United States); Northeastern University
  2. Ruhr Univ., Bochum (Germany); Northeastern Univ., Boston, MA (United States)
  3. Northeastern Univ., Boston, MA (United States)
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Here, we characterize both analytically and numerically short-range forces between spatially diffuse interfaces in multi-phase-field models of polycrystalline materials. During late-stage solidification, crystal-melt interfaces may attract or repel each other depending on the degree of misorientation between impinging grains, temperature, composition, and stress. To characterize this interaction, we map the multiphase-field equations for stationary interfaces to a multidimensional classical mechanical scattering problem. From the solution of this problem, we derive asymptotic forms for short-range forces between interfaces for distances larger than the interface thickness. The results show that forces are always attractive for traditional models where each phase-field represents the phase fraction of a given grain. Those predictions are validated by numerical computations of forces for all distances. Based on insights from the scattering problem, we propose a multi-phase-field formulation that can describe both attractive and repulsive forces in real systems. This model is then used to investigate the influence of solute addition and a uniaxial stress perpendicular to the interface. Solute addition leads to bistability of different interfacial equilibrium states, with the temperature range of bistability increasing with strength of partitioning. Stress in turn, is shown to be equivalent to a temperature change through a standard Clausius-Clapeyron relation. The implications of those results for understanding grain boundary premelting are discussed.

Research Organization:
Northeastern Univ., Boston, MA (United States)
Sponsoring Organization:
German Research Foundation (DFG); USDOE Office of Science (SC)
Grant/Contract Number:
FG02-07ER46400
OSTI ID:
1906046
Journal Information:
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics, Journal Name: Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics Journal Issue: 5 Vol. 81; ISSN 1539-3755
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Cited By (3)

Modelling of grain boundary dynamics using amplitude equations journal April 2015
Phase-field modeling of grain-boundary premelting using obstacle potentials journal July 2014
From wetting to melting along grain boundaries using phase field and sharp interface methods preprint January 2014

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36 MATERIALS SCIENCE