Related papers: Closing the gap between atomic-scale lattice defor…
We formulate a model for a point defect embedded in a homogeneous multilattice crystal with an empirical interatomic potential interaction. Under a natural, phonon stability assumption we quantify the decay of the long-range elastic fields…
We present a mesoscale field theory unifying the modeling of growth, elasticity, and dislocations in quasicrystals. The theory is based on the amplitudes entering their density-wave representation. We introduce a free energy functional for…
Elastic interactions arising from a difference of lattice spacing between two coherent phases can have a strong influence on the phase separation (coarsening) of alloys. If the elastic moduli are different in the two phases, the elastic…
Amplitude representations of a binary phase field crystal model are developed for a two dimensional triangular lattice and three dimensional BCC and FCC crystal structures. The relationship between these amplitude equations and the standard…
The dynamics of phase field crystal (PFC) modeling is derived from dynamical density functional theory (DDFT), for both single-component and binary systems. The derivation is based on a truncation up to the three-point direct correlation…
Change in the interatomic spacing of a two-atom system under tension and compression has been modelled by the elastic deformation of atoms. The critical elastic strain of atoms before separation or cracking from tension was estimated by the…
Material properties controlled by evolving defect structures, such as mechanical response, often involve processes spanning many length and time scales which cannot be modeled using a single approach. We present a variety of new results…
We present a phase-field crystal (PFC) model for solidification that accounts for thermal transport and a temperature-dependent lattice parameter. Elasticity effects are characterized through the continuous elastic field computed from the…
Atomically thin 2-dimensional heterostructures are a promising, novel class of materials with groundbreaking properties. The possiblity of choosing the many constituent components and their proportions allows optimizing these materials to…
We precisely and rigorously characterise the decay of elastic fields generated by dislocations in crystalline materials, focusing specifically on the role of multilattices. Concretely, we establish that the elastic field generated by a…
In this paper we provide a proof of the multiplicative kinematic description of crystal elastoplasticity in the setting of large deformations, i.e. $\mathbf{F}=\mathbf{F}^e\mathbf{F}^p$, for a two dimensional single crystal. The proof…
The inherent inconsistency in identifying the phase field in the phase field crystal Theory with the material mass and, simultaneously, with material distortion is discussed. In its current implementation, elastic relaxation in the phase…
We investigate connections between the continuum and atomistic descriptions of deformable crystals, using certain interesting results from number theory. The energy of a deformed crystal is calculated in the context of a lattice model with…
The phase-field crystal model in its amplitude equation approximation is shown to provide an accurate description of the deformation field in defected crystalline structures, as well as of dislocation motion. We analyze in detail the…
We report on a novel extension of the recent phase-field crystal (PFC) method introduced in [Elder et al., Phys. Rev. Lett., Vol. 88, 245701:1-4 (2002)], which incorporates elastic interactions as well as crystal plasticity and diffusive…
The mechanisms of void growth and coalescence are key contributors to the ductile failure of crystalline materials. At the grain scale, single crystal plastic anisotropy induces large strain localization leading to complex shape evolutions.…
We examine the atomistic scale dependence of material's resistance-to-failure by numerical simulations and analytical analysis in electrical analogs of brittle crystals. We show that fracture toughness depends on the lattice geometry in a…
Using the density functional formalism we derive expression for the distortion free energy for systems with continuous broken symmetry and use it to derive expression for the elastic constants of smectic phases in which director is tilted…
We derive a phase field crystal model that couples the diffusive evolution of a microscopic structure with the fast dynamics of a macroscopic velocity field, explicitly accounting for the relaxation of elastic excitations. This model…
Continuum models of plasticity fail to capture the richness of microstructural evolution because the continuum is a homogeneous construction. The present study shows that an alternative way is available at the mesoscale in the form of truly…