2134/28203 V. Heinonen V. Heinonen C.V. Achim C.V. Achim Tapio Ala-Nissila Tapio Ala-Nissila Long-wavelength properties of phase-field-crystal models with second-order dynamics Loughborough University 2018 untagged Mathematical Sciences not elsewhere classified 2018-01-19 14:48:47 Journal contribution https://repository.lboro.ac.uk/articles/journal_contribution/Long-wavelength_properties_of_phase-field-crystal_models_with_second-order_dynamics/9388568 © 2016 American Physical Society. The phase-field-crystal (PFC) approach extends the notion of phase-field models by describing the topology of the microscopic structure of a crystalline material. One of the consequences is that local variation of the interatomic distance creates an elastic excitation. The dynamics of these excitations poses a challenge: pure diffusive dynamics cannot describe relaxation of elastic stresses that happen through phonon emission. To this end, several different models with fast dynamics have been proposed. In this article we use the amplitude expansion of the PFC model to compare the recently proposed hydrodynamic PFC amplitude model with two simpler models with fast dynamics. We compare these different models analytically and numerically. The results suggest that in order to have proper relaxation of elastic excitations, the full hydrodynamical description of the PFC amplitudes is required.