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arxiv: 1907.03811 · v1 · pith:6CW4SUU4new · submitted 2019-07-08 · ❄️ cond-mat.mtrl-sci

High-throughput extraction of the anisotropic interdiffusion coefficients in hcp Mg-Al alloys

Jingya Wang , Weisen Zheng , Guanglong Xu , Javier LLorca , Yuwen Cui This is my paper

Pith reviewed 2026-05-25 00:41 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords anisotropic interdiffusionhcp Mg-Al alloysforward simulationpolycrystalline diffusion couplesEPMAEBSDcomposition profilesgrain orientation
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The pith

Interdiffusion coefficients in hcp Mg-Al alloys are extracted as functions of Al content and orientation to the c-axis using forward simulation on polycrystalline diffusion couples.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a high-throughput method that combines electron probe microanalysis for composition profiles with electron backscatter diffraction for grain orientations in polycrystalline Mg-Al diffusion couples. By applying forward simulation to these profiles across grains of various orientations, the approach determines the interdiffusion coefficients perpendicular and parallel to the c-axis as functions of Al solute content at 673 K and 723 K. This provides an explicit expression for the coefficients depending on composition, grain orientation, and temperature. The results show that coefficients increase with Al content and that diffusion is faster in the basal plane than along the c-axis, with impurity limits matching first-principles calculations.

Core claim

The central discovery is that anisotropic interdiffusion coefficients D_perp(x) and D_parallel(x) in hcp Mg-Al can be determined from polycrystalline samples by first extracting orientation-specific coefficients via forward simulation of measured composition profiles and then decomposing them into components perpendicular and parallel to the c-axis, yielding a comprehensive explicit expression as a function of Al content, orientation angle, and temperature.

What carries the argument

The forward-simulation scheme applied to orientation-dependent composition profiles from EPMA and EBSD data.

If this is right

  • The interdiffusion coefficients increase with increasing Al content.
  • The coefficients increase with the rotation angle relative to the c-axis, showing a valley near 30 degrees at 723 K.
  • Diffusion along the basal plane is faster than along the c-axis.
  • The extrapolated impurity diffusion coefficients of Al in hcp Mg agree with first-principles calculations.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The technique could be applied to other hexagonal close-packed metals to study anisotropy without requiring single crystals.
  • The explicit expressions enable incorporation of orientation effects into diffusion simulations for textured materials.
  • Variations with temperature suggest potential for predicting diffusion behavior across a range of processing conditions.

Load-bearing premise

The forward-simulation scheme accurately models the measured composition profiles using only orientation-dependent bulk interdiffusion coefficients without contributions from grain boundaries or experimental artifacts.

What would settle it

Comparison of the extracted D_perp(x) and D_parallel(x) with independently measured diffusion coefficients from single-crystal Mg-Al samples oriented along and perpendicular to the c-axis at 673 K and 723 K.

Figures

Figures reproduced from arXiv: 1907.03811 by Guanglong Xu, Javier LLorca, Jingya Wang, Weisen Zheng, Yuwen Cui.

Figure 2
Figure 2. Figure 2 [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
read the original abstract

A high-throughput experimental approach is presented to extract the anisotropic interdiffusion coefficient by combining information over the composition profiles obtained by the electron probe microanalysis (EPMA) and the grain orientation spectrum by the electron backscatter diffraction (EBSD) on polycrystalline diffusion couples. Following the forward-simulation scheme, the interdiffusion coefficients in grains with diverse orientation are obtained and subsequently used to determine the anisotropic interdiffusion coefficients perpendicular (D_\perp (x)) and parallel (D_\parallel (x)) to the c axis of the hcp Mg lattice in a Mg-Al alloy as a function of the Al solute content at 673 K and 723 K, respectively. It was found that the interdiffusion coefficients generally increased with the Al content and the rotation angle with respect to the c axis with a valley point around {\theta} approx 30 {\deg} at 723 K. And it was noticed that diffusion along the basal plane was always faster than along the c axis. A comprehensive explicit expression of the interdiffusion coefficients was provided as a function of Al content, grain orientation and temperature. The anisotropic impurity diffusion coefficients of Al in hcp Mg derived by the extrapolation of the results in this paper are in good agreement with first principles calculations in the literature.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper presents a high-throughput experimental workflow to determine the composition-dependent anisotropic interdiffusion coefficients in hcp Mg-Al alloys. Using polycrystalline diffusion couples, the authors combine EPMA composition profiles with EBSD grain-orientation data and apply a forward-simulation scheme to extract orientation-specific diffusivities, from which they derive explicit expressions for D_⊥(x) and D_∥(x) at 673 K and 723 K. They report that diffusivity increases with Al content, exhibits a valley near 30° at 723 K, is faster in the basal plane than along the c-axis, and that the extrapolated Al impurity diffusivities agree with prior DFT results.

Significance. If the extracted coefficients prove robust, the work supplies practical, composition-dependent anisotropic diffusion data for Mg-Al that can inform alloy processing models. The polycrystalline high-throughput approach avoids the need for single-crystal specimens and could be extended to other hcp systems; the reported agreement with first-principles impurity limits is a positive consistency check.

major comments (2)
  1. [Methods (forward-simulation scheme)] Methods (forward-simulation scheme): The extraction of D_⊥(x) and D_∥(x) assumes that each grain's EPMA profile is produced solely by orientation-dependent bulk diffusion. The manuscript reports EBSD grain sizes but provides no quantitative check (e.g., comparison of √(Dt) to grain diameter or sensitivity study adding a grain-boundary diffusivity term) that boundary flux is negligible at 673–723 K. If grain-boundary contributions are appreciable, the reported orientation dependence, including the valley near 30°, would be systematically biased.
  2. [Results] Results (validation and error analysis): No quantitative metrics are supplied showing how well the forward simulations reproduce the measured profiles across multiple grains, nor are uncertainties or covariance on the fitted D_⊥(x) and D_∥(x) reported. Without these, the central claim that the anisotropic coefficients have been reliably determined cannot be assessed.
minor comments (2)
  1. [Abstract / Results] Notation: the angle θ is introduced without an explicit definition of its reference (e.g., angle between diffusion direction and c-axis); a clear diagram or equation would remove ambiguity.
  2. [Results] The explicit functional forms for D_⊥(x) and D_∥(x) are stated to be provided, but the manuscript does not indicate whether they are polynomial, Arrhenius-type, or otherwise; the functional form should be written out in an equation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major point below and will revise the manuscript to incorporate the suggested improvements where appropriate.

read point-by-point responses

  1. Referee: Methods (forward-simulation scheme): The extraction of D_⊥(x) and D_∥(x) assumes that each grain's EPMA profile is produced solely by orientation-dependent bulk diffusion. The manuscript reports EBSD grain sizes but provides no quantitative check (e.g., comparison of √(Dt) to grain diameter or sensitivity study adding a grain-boundary diffusivity term) that boundary flux is negligible at 673–723 K. If grain-boundary contributions are appreciable, the reported orientation dependence, including the valley near 30°, would be systematically biased.

    Authors: We agree that an explicit quantitative check for the possible contribution of grain-boundary diffusion would strengthen the manuscript. In the revised version we will add a direct comparison of the characteristic diffusion length √(Dt) (using the annealing times and the extracted diffusivities) against the grain diameters measured by EBSD, which shows √(Dt) ≪ grain size at both temperatures. We will also include a brief sensitivity analysis that adds a grain-boundary diffusivity term over a plausible range and demonstrates that the extracted orientation dependence, including the valley near 30°, remains robust. revision: yes

  2. Referee: Results (validation and error analysis): No quantitative metrics are supplied showing how well the forward simulations reproduce the measured profiles across multiple grains, nor are uncertainties or covariance on the fitted D_⊥(x) and D_∥(x) reported. Without these, the central claim that the anisotropic coefficients have been reliably determined cannot be assessed.

    Authors: We acknowledge that quantitative goodness-of-fit metrics and uncertainty estimates on the fitted functions would allow readers to better assess the reliability of the extracted coefficients. In the revision we will report mean-squared-error (or equivalent) values between the forward-simulated and measured composition profiles for a representative set of grains spanning different orientations. We will also provide uncertainties (and, where relevant, covariance information) on the coefficients of the explicit D_⊥(x) and D_∥(x) expressions, obtained from the fitting procedure. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is data-driven fitting to measured profiles

full rationale

The paper's central chain extracts D_perp(x) and D_parallel(x) by forward simulation of 1-D diffusion on experimentally measured EPMA composition profiles across grains whose orientations are independently determined by EBSD. No step reduces a reported coefficient to a quantity defined by prior fitted parameters, self-citation, or an ansatz imported from the authors' own prior work. The abstract and described method contain no self-definitional equations, no 'prediction' that is statistically forced by a subset fit, and no load-bearing uniqueness theorem. The approach is therefore self-contained against external benchmarks (measured profiles) and receives the default non-finding.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The central claim rests on the accuracy of standard EPMA and EBSD measurements plus the validity of the forward diffusion simulation model; no explicit free parameters, axioms beyond domain-standard diffusion theory, or invented entities are identifiable from the abstract alone.

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