Development and Validation of Interatomic Potential for Sc and Al-Sc Alloys: Thermodynamics, Solidification, and Intermetallic Ordering

TL;DR

This work develops and validates a second-nearest-neighbor MEAM potential for Sc and Al--Sc alloys, capturing cohesive energetics, defect properties, melting, and solidification within a single transferable framework. The Sc potential faithfully reproduces 0 K properties and a melting point near $T_m \approx 1814$ K, while the Al--Sc binary is anchored to the L1$_2$ Al$_3$Sc reference with formation enthalpies, lattice parameters, and elastic constants in close agreement with first-principles and calorimetric data. High-temperature liquid behavior is characterized by exothermic mixing with a minimum near $x_{Sc} \approx 0.49$ and strong Al--Sc association, validated against IAS and CALPHAD models. MD simulations reveal how Sc modulates solidification: in pure Al rapid nucleation and growth, whereas Al--Sc exhibits longer incubation due to solute drag and supports early L1$_2$-ordered Al$_3$Sc embryos, linking thermodynamics to microstructural evolution. The resulting potential enables large-scale nucleation studies and multicomponent alloy design, providing a quantitative tool to explore intermetallic ordering and processing-structure relationships in Al--Sc systems.

Abstract

We present a second-nearest-neighbor Modified Embedded Atom Method (2NN--MEAM) potential for Scandium (Sc) and Aluminum-Scandium (Al--Sc) alloys that unifies cohesive, thermodynamic, and solidification behavior within a single transferable framework. The Sc component accurately reproduces cohesive energy, lattice constants, defect energetics, and the experimental melting point obtained from two-phase coexistence, demonstrating reliable description of both hcp and liquid phases. The Al--Sc binary interaction parameters were fitted using the L1$_2$--Al$_3$Sc reference and benchmarked against first-principles and calorimetric data. The potential reproduces the strong negative formation enthalpy of Al$_3$Sc (--0.45~eV~atom$^{-1}$), correct relative stability of competing phases, and realistic elastic properties. Mixing enthalpies of the liquid alloy agree with ideal-associated-solution and CALPHAD models, confirming that the potential captures exothermic Al--Sc association in the melt. Molecular-dynamics simulations of solidification reveal the expected temperature and composition dependence of homogeneous nucleation. Pure Al crystallizes readily, while Al--1~at.\%~Sc exhibits a longer incubation and slower growth at the same absolute temperature due to reduced undercooling and solute drag. Within the alloy, ordered Al$_3$Sc-type L1$_2$ embryos appear spontaneously, with Sc atoms occupying cube-corner (B) sites surrounded by twelve Al neighbors. Energy--volume trajectories confirm that the potential links thermodynamics to microstructural evolution. Overall, the developed 2NN--MEAM potential provides a quantitatively grounded basis for modeling melting, solidification, and intermetallic ordering in Sc and Al--Sc systems, enabling future multicomponent alloy design and large-scale nucleation studies.

Figures (8)

• Figure 1: Radial distribution function $g(r)$ of scandium at different temperatures obtained from 2NN--MD simulations. The potential correctly captures the disappearance of long-range order near the melting point ($T_m \approx 1814$ K) and the emergence of liquidlike short-range correlations at 2200 K, demonstrating reliable solid–liquid transferability of the potential.
• Figure 2: Formation enthalpy ($\Delta H$) of Al--Sc intermetallic compounds as a function of scandium atomic fraction. The black line with open circles represents values computed using the present 2NN--MEAM potential, while the brown dashed line with filled squares corresponds to zero-temperature ab initio (VASP) calculations from Asta et al. asta2001structural. Blue open diamonds denote experimental calorimetry data from Jung et al., Meschel and Kleppa, and Cacciamani et al.cacciamani1999thermodynamicjung1991standardmeschel1994standard. The 2NN--MEAM results closely follow the experimental trend, accurately reproducing the strong stabilization of Al$_3$Sc and Al$_2$Sc.
• Figure 3: Partial (a) and integral (b) mixing enthalpies of liquid Al–Sc alloys compared with available experimental and thermodynamic data. Panel (a) shows the partial molar enthalpies of aluminum ($\Delta \bar{H}_{\mathrm{Al}}$) and scandium ($\Delta \bar{H}_{\mathrm{Sc}}$) obtained from 2NN-MD simulations at 1873 K (orange lines) and compared with the ideal associated solution (IAS) model (black solid and dashed lines). The present results reproduce the strong asymmetry between $\Delta \bar{H}_{\mathrm{Al}}$ and $\Delta \bar{H}_{\mathrm{Sc}}$, with a minimum around $x_{\mathrm{Sc}} \approx 0.5$, consistent with calorimetric measurements and IAS fitting reported by Shevchenko et al.shevchenko2014thermodynamic. Literature data from Batalin et al. (1720 K) Batalin1985, Litovskii et al. (1873 K) litovskii1986enthalpies, Zviadadze et al. (1500–1800 K) zviadadze1982thermodynamics, and Kang et al. (1873 K evaluation) kang2008 are shown for reference. Panel (b) compares the integral enthalpy of mixing ($\Delta H_{\mathrm{mix}}$) predicted by 2NN-MD over 1500–1873 K with the IAS model and prior evaluations by Cacciamani et al.cacciamani1999thermodynamic, showing excellent agreement near the experimentally observed minimum of $-32.7~\mathrm{kJ/mol}$ at $x_{\mathrm{Sc}} \approx 0.49$. The trends confirm that the 2NN-MD approach accurately reproduces the exothermic nature of mixing in the Al–Sc melt and the strong deviation from ideal-solution behavior observed experimentally.
• Figure 4: Snapshots of nuclei formation and growth during solidification of Sc for two isothermal processes. Fcc atoms are shown in green, while hcp atoms are shown in red; amorphous atoms are omitted for clarity. (a) 500 K, (b) 850 K, and (c) 850 K with fcc atoms highlighted. For comparison, the nucleation and stacking-fault evolution observed here closely follow similar trends reported for Al by Mahata et al.mahata2018understanding.
• Figure 5: Time evolution for pure Sc at fixed temperature: (a) potential energy per atom (eV/atom) and (b) volume per atom (Å$^{3}$/atom). Curves at 500--850 K show sharp drops at crystallization, whereas 900--1000 K remain flat, indicating no nucleation within $\sim$0.5 ns. (c) Critical nucleus diameter$d^{\ast}$ from capillarity-based CNT using $V_m(T)$ from panel (b): Hoffman--Turnbull ($\Delta g_v = \Delta H_m V_m^{-1} T \Delta T / T_m^2$) and Turnbull linear ($\Delta g_v = \Delta H_m V_m^{-1} \Delta T / T_m$), together with MD diameters. (d) Isothermal TTT summary (time to first nucleus vs. temperature); dashed lines mark $T_m / 2$ ($\approx$907 K) and 300 K. Parameters: $\sigma_{SL} = 129$ mJ m$^{-2}$, $\Delta H_m = 16.1$ kJ mol$^{-1}$, $T_m = 1814$ K.