Interfacial free energy adjustable phase field crystal model for homogeneous nucleation

Abstract

To describe the homogeneous nucleation process, an interfacial free energy adjustable phase-field crystal model (IPFC) was proposed by reconstructing the energy functional of the original phase field crystal (PFC) methodology. Compared with the original PFC model, the additional interface term in the IPFC model effectively can adjust the magnitude of the interfacial free energy, but does not affect the equilibrium phase diagram and the interfacial energy anisotropy. The IPFC model overcame the limitation that the interfacial free energy of the original PFC model is much less than the theoretical results. Using the IPFC model, we investigated some basic issues in homogeneous nucleation. From the viewpoint of simulation, we proceeded with an in situ observation of the process of cluster fluctuation and obtained quite similar snapshots to colloidal crystallization experiments. We also counted the size distribution of crystal-like clusters and the nucleation rate. Our simulations show that the size distribution is independent of the evolution time, and the nucleation rate remains constant after a period of relaxation, which are consistent with experimental observations. The linear relation between logarithmic nucleation rate and reciprocal driving force also conforms to the steady state nucleation theory.

Controlling the energy of defects and interfaces in the amplitude expansion of the phase-field crystal model

“…Thus, the approach proposed in Ref. [36] cannot be directly considered within our framework. However, similar information is directly gathered from A 2 , which is a measure of the crystalline order, and from its variation in space.…”

“…Within the range of β's used, a relative scaling factor of up to ∼ 1.6 can be achieved, and no restrictions are present for larger values. This can be used in order to match the solid-liquid interface energies from experiments or first-principles approaches, while they are typically underestimated in classical PFC methods [36]. Negative values of β, even small ones, lead to instabilities in the solid phase.…”

“…An additional term in the free energy is considered, which is nonvanishing when the order of the solid phases changes. A similar approach has been recently proposed for the PFC model in order to include phase transition [35] and to introduce an adjustable interface energy [36]. Here we propose a suitable formulation to account for these effects in APFC models, exploiting an order parameter directly connected to the amplitude functions.…”

Quantitative phase-field crystal modeling of solid-liquid interfaces for FCC metals

“…MD calculations [33,35]. Alternatively, extra parameters [36] or even extra terms [37] can be added into the free energy of the model in order to exactly fit to the interface free energy; however, a careful attention must be devoted to not compromise the advantageous features of the model.…”

Phase-field crystal model for heterostructures

“…In this work we introduce spatially smoothed atomic density fields coupled to the atomic density fields n i that enables well-controlled phase separation and, therefore, facilitates modelling heterostructures and composite materials. Smoothed densities have been employed in PFC modelling recently for introducing a vapor phase 28 and arXiv:1908.05564v1 [cond-mat.mes-hall] 15 Aug 2019 for controlling liquid/solid interface energies 29 . Here we apply this modelling approach to 2D heterostructures composed of multiple elements.…”