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We address a three-dimensional, coarse-grained description of dislocationnetworks at grain boundaries between rotated crystals. The so-called amplitudeexpansion of the phase-field crystal model is exploited with the aid of finiteelement method calculations. This approach allows for the description ofmicroscopic features, such as dislocations, while simultaneously being able todescribe length scales that are orders of magnitude larger than the latticespacing. Moreover, it allows for the direct description of extended defects bymeans of a scalar order parameter. The versatility of this framework is shownby considering both fcc and bcc lattice symmetries and different rotation axes.First, the specific case of planar, twist grain boundaries is illustrated. Thedetails of the method are reported and the consistency of the results withliterature is discussed. Then, the dislocation networks forming at theinterface between a spherical, rotated crystal embedded in an unrotatedcrystalline structure, are shown. Although explicitly accounting fordislocations which lead to an anisotropic shrinkage of the rotated grain, theextension of the spherical grain boundary is found to decrease linearly overtime in agreement with the classical theory of grain growth and recentatomistic investigations. It is shown that the results obtained for a systemwith bcc symmetry agree very well with existing results, validating themethodology. Furthermore, fully original results are shown for fcc latticesymmetry, revealing the generality of the reported observations.

Defects at grain boundaries: A coarse-grained, three-dimensional description by the amplitude expansion of the phase-field crystal model