Accurate ab initio modeling of solid solution strengthening in high entropy alloys

Abstract

High entropy alloys (HEA) represent a class of materials with promising properties, such as high strength and ductility, radiation damage tolerance, etc. At the same time, a combinatorially large variety of compositions and a complex structure render them quite hard to study using conventional methods. In this work, we present a computationally efficient methodology based on ab initio calculations within the coherent potential approximation. To make the methodology predictive, we apply an exchange-correlation correction to the equation of state and take into account thermal effects on the magnetic state and the equilibrium volume. The approach shows good agreement with available experimental data on bulk properties of solid solutions. As a particular case, the workflow is applied to a series of iron-group HEA to investigate their solid solution strengthening within a parameter-free model based on the effective medium representation of an alloy. The results reveal intricate interactions between alloy components, which we analyze by means of a simple model of local bonding. Thanks to its computational efficiency, the methodology can be used as a basis for an adaptive learning workflow for optimal design of HEA.

Figures (15)

• Figure 1: Comparison of the experimental and calculated atomic volume and bulk modulus for disordered paramagnetic and nonmagnetic alloys. ($\times$ red): LDA with XC pressure-correction (LDA-XPC). ($+$ blue): PBE. Phonon contributions to the thermal expansion are included in all cases. Magnetic entropy is considered for the paramagnetic alloys.
• Figure 2: Comparison of experimentally measured and calculated apparent, misfit ($\times$,$+$,$\star$) and equilibrium volumes ($-$). Dash-dotted line indicates the experimental equilibrium volume. Ref (1): Volumes extracted from experimental measurements Yin2020b. DLM Ref (2): CPA-DLM calculations Yin2020b. SQS Ref (3): SQS calculations Yin2020b. For our calculations, results of applying successively finite-temperature effects and exchange-correlation corrections are displayed. [LDA-0] and [XPC-0]: CPA-DLM with LDA calculation at 0 K without and with applying the exchange-correlation correction. [XPC-300]: Applying finite-temperature phonon contributions within the Debye-Grüneisen model at 300 K. [XPC-300-LSF]: Additionally adding LSF. [GGA-300-LSF]: Conventional PBE calculation combined with DLM-LSF and phonon contributions at 300 K for comparison.
• Figure 3: Comparison of CRSS $\Delta \tau$ from calculations and experiments versus temperature of NiCoCr (A), FeNiCoCr (B) and FeMnNiCoCr (C). [Poly. Exp.]: Experimental polycrystalline measurements with subtracted Hall-Petch contribution Wu2016otto2013. [Sing. Exp.]: Experimental single-crystalline measurements Uzer2018Wu2015okamoto2016Abuzaid2017Kawamura20211. [DFT]: Theoretical CRSS with all material parameters calculated for the given temperature and uncertainties (filled curves) due to deviations from experiment. [DFT 0 K] (dashed lines): Theoretical CRSS with all material parameters calculated once for 0 K and then used for the whole temperature range.
• Figure 4: Comparison of misfit volumes of the individual components for the (A) NiCoCr, (B) FeNiCoCr and (C) FeMnNiCoCr alloy versus temperature.
• Figure 5: Comparison of the main parameters of the VC model from calculations and experiments versus temperature of (A) NiCoCr, (B) FeNiCoCr and (C) FeMnNiCoCr. A: Calculated and experimental (Yin2020b) misfit parameter $\delta$. B: Calculated Voigt-averaged shear modulus and experimental values of the shear modulus Jin2017wu2014Wagner2022Laplanche2020Haglund2015. C: Calculated results for energy barrier $\Delta E_{b}$.