Interfacial free energy and stiffness of aluminum during rapid solidification

Abstract

Using molecular dynamics simulations and the capillary fluctuation method, we have calculated the anisotropic crystal-melt interfacial free energy and stiffness of aluminum in a rapid solidification system where a temperature gradient is applied to enforce thermal non-equilibrium. To calculate these material properties, the standard capillary fluctuation method typically used for systems in equilibrium has been modified to incorporate a second-order Taylor expansion of the interfacial free energy term. The result is a robust method for calculating interfacial energy, stiffness and anisotropy as a function of temperature gradient using the fluctuations in the defined interface height. This work includes the calculation of interface characteristics for temperature gradients ranging from 11~34 K/nm.The captured results are compared to a thermal equilibrium case using the same model and simulation technique with a zero gradient definition. We define the temperature gradient as the change in temperature over height perpendicular to the crystal-melt interface. The gradients are applied in MD simulations using defined thermostat regions on a stable solid-liquid interface initially in thermal equilibrium. The results of this work show that the interfacial stiffness and free energy for aluminum are dependent on the magnitude of the temperature gradient, however the anisotropic parametersremainindependent of the nonequilibrium conditionsapplied in this analysis. The relationships of the interfacial free energy/stiffness are determined to be linearly related to the thermal gradient, and can be interpolated to find material characteristics at additional temperature gradients.

Solid-liquid Interfacial Energy for Fe–Cr Alloy under Temperature Gradient from Molecular Dynamics Simulation

“…The capillary fluctuation method with a modified term is employed to estimate the solid-liquid interfacial energy under temperature gradient. According to Brown and coworkers, 29) the interface stiffness can be estimated from the amplitude of the fluctuation of the solid-liquid interface under temperature gradient on the basis of the following equation, where S is the solid-liquid interfacial stiffness, A(k) is the Fourier amplitude of the interface height profile, k is the wave number, k B is Boltzmann's constant and T eq is the equilibrium temperature at which the solid-liquid interface does not move (i.e., melting point for pure metals and equilibrium temperature for alloys). b and W are the thickness and length of the interface, respectively.…”

“…The brackets represent averages over the number of sampling times. a is additional contributions to the fluctuation spectrum that are independent of stiffness for a stationary solid-liquid interface under temperature gradient, 29) which is derived from Karma's theory on fluctuations in solidification. 38) G is the temperature gradient, γ G0 is the solid-liquid interfacial energy at no temperature gradient (i.e., G = 0), and L is the latent heat at the equilibrium temperature.…”

“…The solid-liquid interface energy of Fe-Cr alloy under temperature gradient is investigated by MD simulations in conjunction with a capillary fluctuation method including the effect of temperature gradient. 29) The simulation methodology basically follows our previous study 27) except for the installation of temperature gradient in the MD simulation. MD simulations are performed by the Large-scale Atomic/ Molecular Massive Parallel Simulator (LAMMPS).…”

“…[24][25][26][27][28] One of the remaining problems is how to treat the effect of temperature gradient on the solid-liquid interfacial energy. Recently, Brown and coworkers 29) proposed a derivation process of the solid-liquid interfacial energy under the large temperature gradient. They modified the formulation of the capitally fluctuation method and applied this method for rapid solidification of Al system.…”

Predictive modeling of solidification during laser additive manufacturing of nickel superalloys: recent developments, future directions

“…MD Simulations can help to estimate the parameters that characterize a solid-liquid interface in AM regime. Recently, MD simulations were performed on a stable aluminum solid-liquid interface under rapid solidification conditions and it was found that the interfacial free energy increased by a factor of 1.25 as the temperature gradient increased by a factor of 3, while the interface anisotropy parameter remained independent of the solidification conditions [40]. The interfacial properties of multicomponent alloys under non-equilibrium conditions need to be calculated in MD for use in the phase-field model.…”