2012/07/27 by Hervé Henry, Jesper Mellenthin, Mathis Plapp
Earth and Planetary Sciences · Engineering · Materials Science · Mathematics · Physics and Astronomy · #Aluminum Alloy Microstructure Properties #Anisotropy #Condensed matter physics #Coupling (piping) #Crystallite #Field (mathematics) #Geometry #Integral equation #Materials science #Mathematical analysis #Mathematics #Optics #Orientation (vector space) #Phase (matter) #Phase field models #Physics #Quantum mechanics #Singular function #Singular integral #Solidification and crystal growth phenomena #Statistical physics #Surface energy #cond-mat.mtrl-sci #nanoparticles nucleation surface interactions #nlin.PS
paper · pdf · doi:10.1103/physrevb.86.054117
10 figures, submitted to Phys. Rev. B
arxiv created 2012/07/27 · openalex publication_date 2012/08/23 · arxiv updated 2015/06/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The solidification of polycrystalline materials can be modeled by orientation-field models, which are formulated in terms of two continuous fields: a phase field that describes the thermodynamic state and an orientation field that indicates the local direction of the crystallographic axes. The free-energy functionals of existing models generally contain a term proportional to the modulus of the orientation gradient, which complicates their mathematical analysis and induces artificial long-range interactions between grain boundaries. We present an alternative model in which only the square of the orientation gradient appears, but in which the phase and orientation fields are coupled by a singular function that diverges in the solid phase. We show that this model exhibits stable grain boundaries, the interactions of which decay exponentially with their distance. Furthermore, we demonstrate that the anisotropy of the surface energy can be included while preserving the variational structure of the model. Illustrative numerical simulations of two-dimensional examples are also presented.