Nonequilibrium chemical short-range order in metallic alloys

TL;DR

Metallic alloys experience nonequilibrium processing that biases chemical short-range order (SRO), which is not captured by equilibrium thermodynamics. The authors combine large-scale atomistic simulations with a minimal nonequilibrium Monte Carlo model to quantify SRO via Jensen-Shannon divergence, define an effective temperature T_eff and an effective distance D_eff, and show that processing can produce remnant SRO states far from equilibrium. They find that solidification yields far-from-equilibrium SRO inherited from the liquid, while thermomechanical deformation yields quasi-equilibrium SRO along a common trajectory, with SRO dynamics following dD_sro/dt = lambda D_sro + Gamma and remnant D_sro = -Gamma/lambda. The framework reveals a broad nonequilibrium SRO diagram, implying that manufacturing routes can be designed to access SRO states beyond the equilibrium design space, enabling co-design of SRO with microstructure and composition.

Abstract

Metallic alloys are routinely subjected to nonequilibrium processes during manufacturing, such as rapid solidification and thermomechanical processing. It has been suggested in the high-entropy alloy literature that chemical short-range order (SRO) could offer a new knob to tailor materials properties. While evidence of the effect of SRO on materials properties accumulates, the state of SRO evolution during alloy manufacturing remains obscure. Here, we employ high-fidelity atomistic simulations to track SRO evolution during the solidification and thermomechanical processing of alloys. Our investigation reveals that alloy processing can lead to nonequilibrium steady-states of SRO that are different from any equilibrium state. The mechanism behind nonequilibrium SRO formation is shown to be an inherent ordering bias present in nonequilibrium events. These results demonstrate that conventional manufacturing processes provide pathways for tuning SRO that lead to a broad nonequilibrium spectrum of SRO states beyond the equilibrium design space of alloys.

Figures (4)

• Figure 1: Remnant SRO after nonequilibrium materials processing. a) CrCoNi is annealed at $1000\,\text{K}$ before undergoing uniaxial tensile deformation at room temperature ($300\,\text{K}$) under a constant strain rate of $10^9 \text{s}^{-1}$. Dislocation network shown in green. b) Stress-strain curve shows strengthening plateau. c) Evolution of SRO ($D_\text{sro}$) reveals that mechanical deformation leads to an ultimate steady-state with finite SRO. d) Solidification of CrCoNi at $\Delta T = 1\,\text{K}$ undercooling ($\Delta T = T_\text{m} - T$, where $T_\text{m} = 1661\,\text{K}$ is the melting temperature). e) Growth rate of the solid under various undercooling temperatures. f) The amount of remnant SRO in the as-cast alloy has a mild dependence on the undercooling temperature. The reported $D_\text{sro}$ values of as-cast alloy correspond to the final solidified structure.
• Figure 2: A simple physical model for nonequilibrium SRO. a) The model has only two possible dynamical events, which are enough to capture the effect of nonequilibrium processes on SRO. Thermal events guide the alloy towards equilibrium SRO at temperature $T$, while athermal events drive the alloy towards random chemical mixing. Athermal events are periodically introduced with frequency $\gamma$. b) Monte Carlo simulations demonstrate that this simple physical model captures the emergence of remnant SRO. c) Spectrum of remnant SRO as a function of the model's temperature and nonequilibrium driving force $\gamma$. The highlighted state at $600\,\text{K}$ and $\gamma = 0.04 \; \text{step}^{-1}$ has nearly the same amount of SRO ($D_\text{sro}$) as an alloy in equilibrium at $800\,\text{K}$.
• Figure 3: Physical framework for nonequilibrium SRO. a) The remnant SRO state (brown circle) has the same amount of SRO (i.e., $D_\text{sro}$) as the equilibrium state (dark red circle). $D_\text{eff}$ measures how far the remnant SRO is from the equilibrium spectrum of SRO states. b) Diagram of nonequilibrium SRO states as function of materials processing conditions (temperature and driving force). The effective temperature $T_\text{eff}$ of a remnant SRO state (indicated by the contour lines) is the temperature of the equilibrium SRO state closest to it. Quasi-equilibrium SRO states are physically indistinguishable from their effective equilibrium states. Far-from-equilibrium SRO states do not correspond to any equilibrium state. The far-from-equilibrium region (orange) comprises states whose $D_\text{eff}$ values exceed the expected $D_\text{eff}$ under equilibrium. These states do not possess a physically meaningful $T_\text{eff}$. c) Illustration of how nonequilibrium processes lead to the three states shown in fig. \ref{['figure_3']}. $T_\text{m} = 1661\,\text{K}$ is the melting temperature.
• Figure 4: Nonequilibrium SRO during materials processing. The remnant SRO states created during a) solidification (fig. \ref{['figure_1']}) are far-from-equilibrium, while b) thermomechanical processing (fig. \ref{['figure_1']}) leads to quasi-equilibrium states. The reported $D_\text{eff}$ values correspond to the final snapshots of the simulations. The boundary between quasi-equilibrium (green) and far-from-equilibrium (orange) regimes is defined by calculating the expected value of $D_\text{eff}$ in equilibrium. c) Most of the Warren-Cowley parameters ($\alpha_{AB}$) of the as-cast alloy ($\Delta T = 1\,\text{K}$ undercooling) are closer to the liquid phase than to the solid phase, suggesting that a large portion of the far-from-equilibrium SRO is inherited from the liquid. The grey shaded region denotes the range of $\alpha_{AB}$ values between the solid and liquid equilibrium states. d) Evolution of the amount of SRO ($D_\text{sro}$) during mechanical deformation of samples prepared using different thermal treatments. The predictive model for $D_\text{sro}$ (inset equation and dashed lines) is derived from the observed linear behavior of the e) entropy-production rate on $D_\text{sro}$.