[Paper Review] Thermodynamics of point defects and diffusion mechanisms in B2-ordered compounds

Michael Leitner|arXiv (Cornell University)|Mar 12, 2015

Metallurgical and Alloy Processes1 references3 citations

TL;DR

This paper develops a thermodynamic framework for point defects in B2-ordered compounds using two key energy parameters to classify defect behavior. It identifies the waltzing-step mechanism and 4+2-jump cycles as dominant diffusion pathways—challenging the long-held assumption that six-jump cycles or triple-defect mechanisms prevail—especially in off-stoichiometric conditions.

ABSTRACT

The point defect thermodynamics in a general family of binary compounds, including B2 compounds as a specific representative, are classified by way of two non-trivial energy parameters. The scheme is applied to published ab initio defect formation energies, and the variety of resulting phenomena is demonstrated. Further, by introducing model assumptions the consequences for the active diffusion mechanisms are deduced. It is shown that particularly for the off-stoichiometric case, the assumed prevalence of either the six-jump cycle or the triple-defect mechanism has to be reconsidered, as a number of qualitatively different mechanisms emerge as likely candidates for the dominant effect. Two of those, the 4+2-jump cycles and the waltzing-step mechanism, are introduced here.

Motivation & Objective

• To classify point defect thermodynamics in B2-ordered compounds using two non-trivial energy parameters derived from ab initio calculations.
• To re-evaluate conventional assumptions about dominant diffusion mechanisms in off-stoichiometric B2 systems.
• To propose and analyze new diffusion mechanisms, including the waltzing-step mechanism and 4+2-jump cycles, as plausible alternatives to established models.
• To compare theoretical predictions with experimental diffusivity data in NiAl and CoGa, resolving discrepancies in prior interpretations.

Proposed method

• Applies a grand-canonical theory of defect concentrations to model point defect equilibria in binary B2 compounds, accounting for constitutional and thermal defects.
• Re-parametrizes ab initio defect formation energies into two effective energy parameters to classify defect stability and phase transitions.
• Enumerates all possible nearest-neighbor vacancy migration mechanisms, including six-jump cycles, divacancy, triple-defect, and the newly proposed waltzing-step mechanism.
• Evaluates diffusion activation energies under two models: non-interacting defects and nearest-neighbor pair interactions, to assess mechanism dominance.
• Uses percolation theory to determine thresholds for anti-site and vacancy bridge mechanisms in clustered defect configurations.
• Compares model predictions with experimental diffusion data from NiAl and CoGa to validate mechanism dominance.

Experimental results

Research questions

• RQ1 Which defect mechanisms dominate self-diffusion in off-stoichiometric B2 compounds, and how do they differ from the conventional six-jump cycle or triple-defect model?
• RQ2 How do the thermodynamic parameters of point defect formation influence the phase diagram of dominant defect types in B2-structured intermetallics?
• RQ3 What is the role of the waltzing-step mechanism in minority-element diffusion, and why is it expected to dominate over six-jump cycles in systems like NiAl?
• RQ4 Why do experimental diffusivity trends in NiAl and CoGa not show a clear percolation threshold for the anti-structure bridge mechanism, and what does this imply about the dominant mechanism?
• RQ5 To what extent do the predictions of non-interacting and interacting defect models agree in identifying dominant diffusion pathways?

Key findings

• The waltzing-step mechanism is predicted to dominate minority-element diffusion across a wide range of B2 compounds, challenging the assumption that six-jump cycles are primary.
• Six-jump cycles are shown to predominantly proceed as 4+2-jump cycles in strongly asymmetric systems, particularly in transition metal-group III compounds like NiAl.
• The divacancy mechanism is less relevant in asymmetric systems, where the triple-defect mechanism becomes more favorable, especially at low temperatures.
• Model predictions for diffusion activation energies based on non-interacting and nearest-neighbor pair interactions show strong qualitative agreement, supporting the robustness of the mechanism classification.
• Experimental diffusivity data in NiAl and CoGa are better explained by the vacancy bridge mechanism and waltzing-step pathway than by the anti-structure bridge or six-jump cycle, especially in Ga-rich or Co-rich compositions.
• The absence of a clear percolation threshold for the anti-structure bridge mechanism in CoGa is attributed to high intrinsic disorder, which suppresses long-range defect correlations and favors faster, less correlated diffusion pathways.