Electronic structure, phase stability, and transport properties of the AlTiVCr lightweight high-entropy alloy: A computational study

TL;DR

This study uses a multi-scale, first-principles workflow to understand ordering, phase stability, and transport in the AlTiVCr high-entropy alloy. By combining KKR-CPA electronic structure, a concentration-wave analysis (S^{(2)}) to predict ordering tendencies, and atomistic Monte Carlo simulations with recovered Bragg–Williams pair interactions, the authors predict a high-temperature B2 (CsCl) chemical ordering driven by strong Al–Ti site separation, with V and Cr showing weaker preferences. The predicted B2 ordering increases the residual resistivity due to a DOS reduction at the Fermi level, while subsequent low-temperature Monte Carlo simulations reveal a fully ordered ground state with vanishing resistivity. The work validates the KKR-CPA and concentration-wave framework for HEA thermodynamics and links atomic-scale ordering to measurable transport, suggesting that electronic transport measurements could serve as order-detection tools and pointing to future DMFT extensions and high-throughput alloy design applications.

Abstract

We investigate the thermodynamics and phase stability of the AlTiVCr lightweight high-entropy alloy using a combination of ab initio electronic structure calculations, a concentration wave analysis, and atomistic Monte Carlo simulations. In alignment both with experimental data and with results obtained using other computational approaches, we predict a $\textrm{B2}$ (CsCl) chemical ordering emerging in this alloy at comparatively high temperatures, which is driven by Al and Ti moving to separate sublattices, while V and Cr express weaker site preferences. The impact of this $\textrm{B2}$ chemical ordering on the electronic transport properties of the alloy is investigated within a Kubo-Greenwood linear response framework and it is found that, counter-intuitively, the alloy's residual resistivity increases as the material transitions from the $\textrm{A2}$ (disordered bcc) phase to our predicted $\textrm{B2}$ (partially) ordered structure. This is understood to result primarily from a reduction in the density of electronic states at the Fermi level induced by the chemical ordering. At low temperatures, our atomistic Monte Carlo simulations then reveal subsequent sublattice orderings, with the ground-state configuration predicted to be a fully-ordered, single-phase structure with vanishing associated residual resistivity. These results give fresh, insight into the atomic-scale structure and consequent physical properties of this well-studied, technologically relevant material.

Figures (9)

• Figure 1: Illustrations---for an equiatomic binary alloy---of the disordered bcc structure, Strukturbericht designation A2, and the ordered CsCl structure, Strukturbericht designation B2. Panel (a) shows a supercell representation of the A2 structure, while panel (b) shows a representation of the unit cell where half-coloured spheres indicate partial lattice site occupancies. Panel (c) then shows a supercell representation of the B2 structure, while panel (d) shows a representation of the unit cell. Such chemically-ordered structures can emerge in an alloy if it is annealed below its disorder-order transition temperature. In panels (b) and (d), lattice sites are given their Wyckoff labels. Images generated using Vestamomma_vesta_2011.
• Figure 2: Schematic illustration of a particular concentration wave modulating partial atomic lattice site occupancies in a toy, one-dimensional $A_2BC$ alloy. In order, the chemical species are coloured blue, orange, and red. The first state of the alloy, shown in panel (a), is homogeneous, with all lattice site occupancies equal. The second state of the alloy, shown in panel (b) is obtained by modulating the occupancies of panel (a) with a concentration wave of wave vector $k=\frac{\pi}{a}$ and (normalised) chemical polarisation $\Delta c_\alpha = \frac{1}{\sqrt{6}}(2, -1, -1)$.
• Figure 3: Bloch spectral function (a 'bandstructure' for the disordered alloy) and species-resolved electronic DOS around the Fermi energy, $E_\textrm{F}$ for the AlTiVCr high-entropy alloy as described within the KKR-CPA for the A2 (disordered bcc) phase. A degree of hybridisation between the $sp$-like states of Al and the $3d$ states of the transition metals is indicated by the localised peaks/troughs in the species-resolved DOS for Al at energies where there are peaks/troughs in the DOS associated with the narrow $3d$ bands of the transition metals.
• Figure 4: Plots of data associated with the concentration wave analysis performed using the alloy $S^{(2)}$ theory khan_statistical_2016woodgate_compositional_2022woodgate_modelling_2024. Panel (a) shows the raw $S^{(2)}_{\alpha \alpha'}(\mathbf{k})$ data plotted along selected high-symmetry lines of the IBZ of the bcc lattice, while panel (b) shows the eigenvalues of the chemical stability matrix along those same high-symmetry directions. That the minimum eigenvalue lies at $H$ in panel (b) indicates that a B2 chemical ordering is favoured.
• Figure 5: Calculated real-space atom-atom effective pair interactions for the AlTiVCr high-entropy alloy recovered from the ab initio concentration wave analysis. A negative value of $V^{(n)}_{\alpha,\alpha'}$ indicates that is is energetically favourable to find the pair $\alpha$-$\alpha'$ on coordination shell $n$, while a positive value of $V^{(n)}_{\alpha,\alpha'}$ indicates the opposite. It can be seen that the strongest interactions are between Al-Al, Al-Ti, and Ti-Ti pairs, and also that interactions tail off quickly with increasing distance.