An extended Cahn-Hilliard model for interfaces with cubic anisotropy


Autoria(s): Abinandanan, TA; Haider, F
Data(s)

01/10/2001

Resumo

For studying systems with a cubic anisotropy in interfacial energy sigma, we extend the Cahn-Hilliard model by including in it a fourth-rank term, namely, gamma (ijlm) [partial derivative (2) c/(partial derivativex(i) partial derivativex(j))] [partial derivative (2) c/(partial derivativex(l) partial derivativex(m))]. This term leads to an additional linear term in the evolution equation for the composition parameter field. It also leads to an orientation-dependent effective fourth-rank coefficient gamma ([hkl]) in the governing equation for the one-dimensional composition profile across a planar interface. The main effect of a non-negative gamma ([hkl]) is to increase both sigma and interfacial width w, each of which, upon suitable scaling, is related to gamma ([hkl]) through a universal scaling function. In this model, sigma is a differentiable function of interface orientation (n) over cap, and does not exhibit cusps; therefore, the equilibrium particle shapes (Wulff shapes) do not contain planar facets. However, the anisotropy in the interfacial energy can be large enough to give rise to corners in the Wulff shapes in two dimensions. In particles of finite sizes, the corners become rounded, and their shapes tend towards the Wulff shape with increasing particle size.

Formato

application/pdf

Identificador

http://eprints.iisc.ernet.in/39504/1/An_extended_Cahn-Hilliard.pdf

Abinandanan, TA and Haider, F (2001) An extended Cahn-Hilliard model for interfaces with cubic anisotropy. In: Philosophical Magazine A & B, 81 (10). pp. 2457-2479.

Publicador

Taylor and Francis Group

Relação

http://www.tandfonline.com/doi/abs/10.1080/01418610110038420

http://eprints.iisc.ernet.in/39504/

Palavras-Chave #Materials Engineering (formerly Metallurgy)
Tipo

Journal Article

PeerReviewed