Dislocation-Mediated SRO Evolution

• Dislocation-mediated SRO evolution is defined as the transformation of local atomic arrangements driven by dislocation motion during thermomechanical processing.
• A kinetic model quantifies the competing rates of motif creation and annihilation, linking processing conditions to measurable nonequilibrium SRO states.
• Enhanced dislocation mobility at high temperatures accelerates chemically biased motif selection, enabling tailored alloy design beyond equilibrium limits.

Dislocation-mediated short-range order (SRO) evolution refers to the transformation and control of local atomic, compositional, or defect arrangements in crystalline materials as driven by the dynamics and interactions of dislocations. Dislocations—line defects in the crystal lattice—alter local microstructures, chemical environments, and defect distributions both by transporting atoms and by inducing elastic fields that reshape local order. Advances in atomistic simulation, kinetic modeling, and information-theoretic quantification have enabled direct connections between processing conditions, dislocation kinematics, and the resultant SRO states, particularly in chemically complex alloys subjected to thermomechanical processing (Islam et al., 19 Aug 2025).

1. Fundamentals of Dislocation-Mediated SRO Evolution

During thermomechanical processing (TMP), metals and alloys are plastically deformed at elevated or room temperature, inducing large-scale dislocation motion through the lattice. As dislocations glide and multiply, they locally break and re-form chemical bonds, shuffle atomic configurations, and generate new motifs in their cores and along slip planes. This process simultaneously destroys existing equilibrium SRO—characterized by preferred atomic pairings or short-range chemical motifs—and creates new nonequilibrium SRO, whose properties depend on the kinetic and energetic biases imparted by the dislocation trajectories and the surrounding chemical landscape (Islam et al., 23 Sep 2024).

Two competing processes determine the evolution of SRO:

• Creation rate (Γ): The rate at which dislocation motion introduces or selects new local motifs, driven by energetic preference for specific compositions or atomic arrangements encountered by dislocation lines.
• Annihilation rate (λ): The rate at which the ongoing shuffling randomizes the local order, destroying preexisting SRO either by overprinting it with new motifs or by facilitating transitions to less ordered states through atomic mixing.

This competition shapes the steady-state SRO attained after sufficient plastic deformation, resulting in far-from-equilibrium states that cannot be produced by equilibrium annealing (Islam et al., 19 Aug 2025).

2. Kinetic Model for SRO Evolution: Competing Rates

The evolution of dislocation-mediated SRO in TMP is quantitatively described by a kinetic model in terms of strain (ε) or time (t), with the SRO magnitude measured via a rigorous information-theoretic metric such as the Jensen–Shannon divergence $D_\mathrm{SRO}$ between the observed motif population and that of a random solid solution (Islam et al., 19 Aug 2025, Islam et al., 23 Sep 2024):

• Kinetic equation with respect to strain:

$$\frac{dD_\mathrm{SRO}}{d\epsilon} = \Gamma - \lambda D_\mathrm{SRO}$$

The solution for finite strain $\epsilon$ is

$$D_\mathrm{SRO}(\epsilon) = (D_\mathrm{SRO}^0 - \frac{\Gamma}{\lambda}) e^{-\lambda \epsilon} + \frac{\Gamma}{\lambda}$$

where $D_\mathrm{SRO}^0$ is the initial SRO before deformation, $\Gamma$ is the creation (bias) rate, and $\lambda$ is the annihilation (randomization) rate.

• Steady-state SRO:

$$D_\mathrm{SRO}^{\mathrm{ss}} = \frac{\Gamma}{\lambda}$$

Given this, the final SRO is determined by the ratio of creation to annihilation rates, each of which depends sensitively on temperature, strain rate, dislocation density, and dislocation character.

3. Temperature, Strain Rate, and Dislocation Character Effects

Low-Temperature Regime

At lower temperatures (e.g., $300\,\mathrm{K}$–$1100\,\mathrm{K}$), the dislocation density is high and dislocation mobility is limited; cross-kinks and vacancies are prevalent, impeding cooperative motion. In this regime:

• The chemical bias introduced by dislocation motion is suppressed.
• Both $\Gamma$ and $\lambda$ show weak dependence on strain rate and temperature.
• A modest amount of athermal SRO is created, dominated by the dense network of dislocation-induced defects.

High-Temperature Regime

At higher temperatures (above $\sim1300\,\mathrm{K}$):

• Dislocation density drops, freeing dislocations for more selective motion.
• The fraction of screw dislocations increases, with the edge-to-screw ratio $R$ (defined as $$R = [\sum_i |\sin\theta_i| L_i]/[\sum_i |\cos\theta_i| L_i]$$) decreasing, where $\theta_i$ is the line-Burgers angle and $L_i$ is segment length.
• Screw dislocations sample chemically favorable kink-pair configurations that amplify the rate of SRO creation.
• $\Gamma$ increases exponentially with temperature and further with decreasing strain rate due to increased opportunity for dislocations to explore low-energy atomic pathways.
• $\lambda$ increases linearly with temperature—although SRO destruction is accelerated, the far faster growth of $\Gamma$ ensures that steady-state SRO rises overall.

Accordingly, the magnitude and chemical character of the SRO that develops are strongly processing-dependent.

4. Quantification of Nonequilibrium SRO

SRO is quantified using information-theoretic metrics—specifically, the Jensen–Shannon divergence ($D_{\mathrm{SRO}}$) between motif population distributions $P$ (measured in simulation) and the population $P_\mathrm{RSS}$ of a random solid solution (Islam et al., 19 Aug 2025, Islam et al., 23 Sep 2024):

• $$D_{\mathrm{SRO}} = D_{\mathrm{JS}}(P || P_\mathrm{RSS})$$, where higher values indicate stronger deviation from random order.

This metric enables direct comparison not only between nonequilibrium and equilibrium SRO states, but also characterizes the chemical specificity (e.g., Ti-Ta-V cluster abundance) of the emergent order. Steady-state SRO is often far-from-equilibrium and cannot be reproduced by any thermal treatment in the absence of dislocations (Islam et al., 19 Aug 2025).

5. Mechanisms of Chemically Biased Dislocation Motion

At the atomistic level, dislocation motion is biased by the local chemical environment. Particularly for screw dislocations, motion proceeds via kink-pair nucleation and cross-slip, both strongly sensitive to site energy fluctuations induced by chemical complexity. As dislocations traverse the crystal, selection for low-energy pathways stabilizes chemically preferred motifs, generating SRO even as ongoing motion continues to disrupt established arrangements. These effects are amplified in alloys where atomic size mismatch or species-specific interaction energies exist across slip planes. The resultant SRO is an emergent product of local motif selection and randomization processes (Islam et al., 19 Aug 2025).

6. Processing-Controlled SRO: Predictive Links and Far-From-Equilibrium States

The direct mechanistic and predictive link between processing parameters (temperature, strain rate) and SRO evolution is established via simultaneous atomistic simulation (with machine learning interatomic potentials) and analytics (Islam et al., 19 Aug 2025):

• At low temperature/high strain rate, SRO formation is limited by constrained dislocation motion.
• At higher temperature and lower strain rate, amplified chemical bias and reduced dislocation hindrance drive rapid formation of far-from-equilibrium SRO states.
• These SRO states are characterized both by increased magnitude and by distinct motif populations, reflecting the interplay between dislocation kinetics and atomic interactions.

Furthermore, steady-state SRO produced by TMP cannot be reached by isothermal annealing; the accessible SRO “design space” is systematically expanded by exploiting the competing kinetic rates and character of dislocation motion.

7. Broad Impact and Design Implications

Dislocation-mediated SRO evolution sets a tunable pathway for the microstructural refinement of metallic alloys. By controlling temperature, strain rate, and deformation regime, it becomes possible to engineer the magnitude and chemical form of SRO, targeting mechanical properties such as yield strength, ductility, or phase stability according to the desired application. The integration of kinetic rate models, information-theoretic metrics, and atomistically validated interatomic potentials (Islam et al., 19 Aug 2025) establishes a foundation for systematic alloy design leveraging dislocation-driven SRO manipulation, expanding the domain of achievable material properties beyond thermal equilibrium constraints.

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In summary, dislocation-mediated SRO evolution during thermomechanical processing is governed by the competition between chemically biased creation and randomizing annihilation rates. These rates are highly sensitive to processing conditions and dislocation microstructure, producing steady-state SRO that is often far from equilibrium and inaccessible via purely thermal routes. This predictive framework enables rational design of alloy microstructures through control of plastic deformation kinetics, atomic-scale dislocation dynamics, and chemical motif selection.