We derive a generalized model for isotropic as well as anisotropic crystal lattice systems of arbitrary Poisson ratio within the framework of the continuum phase-field crystal (PFC) approach (Elder and Grant 2004 Phys. Rev. E 70 051606). To this end we extend the simplest PFC model defined by a free energy functional, which is based upon the Swift-Hohenberg model of pattern formation (Swift and Hohenberg 1993 Phys. Rev. A 15 851) to a conservative, anisotropic Langevin equation. By studying heterogeneous nucleation of ellipsoidal colloids at a wall, we demonstrate the capacity of our approach to contribute to the more precise understanding of condensed matter systems built up from non-spherical units at the atomic scale. In particular we address the question of how (a) the orientation of the ellipsoids as well as (b) the interaction potential with the wall determine the resulting contact angle.

Vein microstructures in the Earth's crust contain a wealth of information on the physical conditions of crystal growth, but correct interpretation requires an improved understanding of the processes involved. In this paper the processes involved in the formation of veins are briefly reviewed, and the possibilities of modelling these processes using the phase-field method are discussed. This technique, which is established in the computational materials science community to investigate crystallization processes, is shown to be a powerful tool to describe processes during vein formation and other geological processes involving crystal growth.

We contribute to the more detailed understanding of the phase-field crystal model recently developed by Elder et al (2002 Phys. Rev. Lett. 88 245701), by focusing on its noise term and examining its impact on the nucleation rate in a homogeneously solidifying system as well as on successively developing grain size distributions. In this context we show that principally the grain size decreases with increasing noise amplitude, resulting in both a smaller average grain size and a decreased maximum grain size. Despite this general tendency, which we interpret based on Panfilis and Filiponi (2000 J. Appl. Phys. 88 562), we can identify two different regimes in which nucleation and successive initial growth are governed by quite different mechanisms.

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