In the case of an isotropic material both surface tension and diffusivity are independent of the crystalline orientation and are given by and , say. This evolution equation becomes

(6)

where . No analytic solutions are known for equation (6) (Cahn & Taylor, 1994). Mullins (1957) assumed the surface slope was everywhere small, which gives the linearised equation

. (7)

Tritscher (1996a) showed that (7) was also an integrable form of the governing equation (5) for a class of anisotropic materials with behaviour similar to a liquid crystal and constitutive relations

(8)

where *C*1 and *C*2 are arbitrary constants and is the solution of the Herring equation (Herring, 1951)

(9)

By use of symmetry recursion operators applied to the linearizable nonlinear diffusion equation Broadbridge & Tritscher (1996) derived a further linearizable form of the evolution equation

(10)

where are weights for the surface diffusivity and surface tension and *b* is an arbitrary parameter which orients the crystalline lattice relative to the coordinate axis. The constitutive relations for equation (10) are (Tritscher, 1996)

The constitutive functions show degeneracy and for values of *b *less than around the evolution equation satisfactorily models an isotropic material.