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For studying systems with a cubic anisotropy in interfacial energy ¼, we extend the Cahn±Hilliard model by including in it a fourth-rank term, namely, ®ijlm‰q 2 c=…qxi qx j †Š‰q 2 c=…qxl qx m †Š. This term leads to an additional linear term in the evolution equation for the composition parameter ®eld. It also leads to an orientation-dependent eOE ective fourth-rank coe cient ®hhkli in the governing equation for the one-dimensional composition pro®le across a planar interface. The main eOE ect of a non-negative ®hhkli is to increase both ¼ and interfacial width w, each of which, upon suitable scaling, is related to ®hhkli through a universal scaling function. In this model, ¼ is a diOE erentiable function of interface orientationn n , and does not exhibit cusps; therefore, the equilibrium particle shapes (WulOEshapes) do not contain planar facets. However, the anisotropy in the interfacial energy can be large enough to give rise to corners in the WulOE shapes in two dimensions. In particles of ®nite sizes, the corners become rounded, and their shapes tend towards the WulOEshape with increasing particle size.

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