Phase field crystal dynamics for binary systems: Derivation from dynamical density functional theory, amplitude equation formalism, and applications to alloy heterostructures

摘要

The dynamics of phase field crystal (PFC) modeling is derived from dynamicaldensity functional theory (DDFT), for both single-component and binary systems.The derivation is based on a truncation up to the three-point directcorrelation functions in DDFT, and the lowest order approximation using scaleanalysis. The complete amplitude equation formalism for binary PFC is developedto describe the coupled dynamics of slowly varying complex amplitudes ofstructural profile, zeroth-mode average atomic density, and systemconcentration field. Effects of noise (corresponding to stochastic amplitudeequations) and species-dependent atomic mobilities are also incorporated inthis formalism. Results of a sample application to the study of surfacesegregation and interface intermixing in alloy heterostructures and strainedlayer growth are presented, showing the effects of different atomic sizes andmobilities of alloy components. A phenomenon of composition overshooting at theinterface is found, which can be connected to the surface segregation andenrichment of one of the atomic components observed in recent experiments ofalloying heterostructures.