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Why Grain Growth is Not Curvature Flow

T0 review · 4 major / 5 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read The paper shows that grain growth departs from classical curvature flow because grain boundaries shear as they migrate, and the internal stresses this generates, not anisotropy or triple-junction drag, are the main source of the observed…

desk verdict A well-validated mechanism and a strong MD benchmark, but the central quantitative claim leans on an arbitrary scaling factor; still deserves serious review. read the letter →

arxiv 2411.15983 v3 pith:RVHQ7VKC submitted 2024-11-24 cond-mat.mtrl-sci

Caihao Qiu , David J. Srolovitz , Gregory S. Rohrer , Jian Han , Marco Salvalaglio This is my paper · ORCID
classification cond-mat.mtrl-sci
keywords graingrowthshearcouplingmeancurvatureflowvonNeumann-Mullinsrelationphase-fieldsimulationdisconnectionsinternalstressboundarymigration
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that grain growth in polycrystals is not mean curvature flow, and that the failures of the classical description are caused mainly by the shear deformation that accompanies grain-boundary migration. When grain boundaries move, they also shear, and in a constraining polycrystalline network this generates internal stresses that add a mechanical driving force to the usual capillarity force. Using large-scale phase-field simulations built on a disconnection-based model of boundary motion, the authors reproduce the weak velocity–curvature correlation and the breakdown of the von Neumann–Mullins relation seen in experiments on nickel and iron and in atomistic simulations of aluminum. If correct, the result says that predicting microstructure evolution requires coupling mechanics to capillarity, not just anisotropic curvature flow.

What carries the argument

The load-bearing object is the disconnection: a line defect on a grain boundary that carries both a step, so it moves the boundary, and a Burgers vector, so it shears the boundary. The ratio of shear rate to normal migration rate is the shear-coupling factor $\beta = v_\parallel/v_\perp$, assigned by misorientation to each boundary. In a polycrystal, boundaries cannot shear freely, so disconnection flow builds an internal stress field; the machinery is the phase-field discretization of the equation of motion $v = M(\Gamma\kappa + \boldsymbol{\tau}\cdot\boldsymbol{\beta} + \psi)\hat n$, where the elastic term $\boldsymbol{\tau}\cdot\boldsymbol{\beta}$ enters through an added force density $f_{\rm elastic}=\boldsymbol{\tau}\cdot\boldsymbol{\beta}_{ij}|\nabla\eta_j|(\hat n(\eta_i)\cdot\hat n(\eta_j))$. This couples each boundary's velocity to the resolved shear stress from all other boundaries' disconnections, which is what decorrelates velocity from curvature.

What would settle it

Measure the shear-coupling factors of many individual grain boundaries within a growing polycrystal, for example by combining in-situ diffraction mapping of grain rotation and shear with boundary migration tracking during annealing, and use the measured distribution rather than $S=1/30$ in the same model. If the measured coupling is an order of magnitude smaller, the predicted velocity–curvature decorrelation should largely disappear; if it is close to the scaled values, the claim is supported.

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Extended reading notes

Core claim

The central claim is that the well-documented failure of mean curvature flow and the von Neumann–Mullins relation in real grain growth is not an anisotropy or triple-junction drag effect, but the direct consequence of shear-coupled grain-boundary migration. The paper proposes the equation of motion $v = M(\Gamma\kappa + \boldsymbol{\tau}\cdot\boldsymbol{\beta} + \psi)\hat n$ in place of $v = M\gamma\kappa$: the new term $\boldsymbol{\tau}\cdot\boldsymbol{\beta}$ is the elastic driving force exerted by internal shear stresses on the disconnections that mediate boundary motion. Because those stresses are generated by the boundaries' own motion and are spatially and temporally inhomogeneous, boundaries can migrate faster, slower, or even opposite to their curvature. The authors support this with two-dimensional phase-field simulations that, with shear coupling included, reproduce both the scatter in grain size change versus neighbor number and the weak velocity–curvature correlation of experiments and molecular dynamics, while simulations with anisotropic energy, anisotropic mobility, or triple-junction drag alone do not.

Load-bearing premise

The load-bearing premise is that the shear-coupling factors of grain boundaries inside a polycrystal are comparable to the scaled bicrystal values used here, with the scaling factor $S=1/30$ chosen arbitrarily in the paper; if real polycrystalline shear coupling is much weaker, the simulated decorrelation between velocity and curvature would shrink.

Editorial extensions

If this is right

  • The von Neumann–Mullins relation, and its anisotropic and three-dimensional extensions, is not a valid quantitative description of polycrystalline grain growth; grain size changes are not reliably predicted by neighbor count.
  • Grain boundaries should frequently migrate against their local curvature when internal stresses are strong enough, a signature that has been seen experimentally and appears in the simulations only when shear coupling is included.
  • Grain growth proceeds faster with shear coupling (roughly 50 percent faster in the two-dimensional simulations here) and dissipates elastic energy, so stored internal stress is part of the coarsening process itself.
  • Anisotropic grain-boundary energy, anisotropic mobility, and triple-junction drag are real effects but are too weak to explain the observed scatter; quantitative models of microstructure evolution should include mechanical coupling.
  • At sufficiently high temperatures, where multiple disconnection modes weaken net shear coupling, grain growth should approach curvature flow, but most experimentally relevant temperatures are far from that limit.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper, the same mechanism may unify previously separate observations—stress-driven grain growth, grain rotation, and grain-boundary sliding—as different manifestations of one disconnection-mediated, shear-coupled kinetics.
  • Beyond the paper, a direct quantitative test would be to measure the actual distribution of shear-coupling factors of individual boundaries inside a growing polycrystal, for example from in-situ lattice-rotation and strain maps, and feed that distribution into the same model without the arbitrary $S=1/30$ scaling.
  • Beyond the paper, the results imply that microstructure evolution codes for annealing and thermomechanical processing should solve for the internal stress field concurrently with boundary motion; residual stresses are not just a response to grain growth but also a driver of it.
  • Beyond the paper, the prediction could be checked by comparing grain growth in high-modulus and low-modulus materials at the same homologous temperature, since the model predicts weaker velocity–curvature correlation in higher-modulus materials.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper argues that grain growth in polycrystals is not mean curvature flow because shear coupling between GB migration and shear deformation generates internal stresses that add an elastic driving force (τ·β) to the GB equation of motion. Using a diffuse-interface (phase-field) implementation of a disconnection-mediated GB model, the authors simulate 2D polycrystalline grain growth with and without shear coupling, quantify the velocity–curvature correlation (COD), compare it with experimental and MD data for Ni, α-Fe, and Al, and test alternative explanations (anisotropic GB energy/mobility and triple-junction drag). They also validate the model against idealized MD microstructures from Thomas et al. and conclude that internal stresses from shear coupling are the main cause of the observed failure of curvature flow and of the von Neumann–Mullins relation.

Significance. If the central claim is established, this is a significant result: it would imply that classical and weighted mean-curvature descriptions of grain growth are insufficient for real polycrystals and that mechanical driving forces must be included in microstructure evolution models. The paper has notable strengths: the idealized-microstructure MD benchmarks use measured bicrystal shear-coupling factors with no adjustable parameters; the comparison of velocity–curvature scatter across experiments, MD, and the present simulations is systematic; and the paper explicitly tests—and finds wanting—anisotropic energy, anisotropic mobility, and triple-junction drag as alternative explanations. These features make the paper valuable regardless of the quantitative calibration issue discussed below.

major comments (4)
  1. [SI §S-II C, Eq. (S-12)] The polycrystalline simulations assign every GB a shear-coupling factor β = S·β_bicrystal with S = 1/30, introduced as 'chosen arbitrarily.' Because the elastic driving force in Eq. (2) is τ·β and the self-stress in Eq. (S-3) is proportional to β, the entire elastic driving contribution scales as S². A factor-of-three reduction in S therefore reduces the elastic driving force by roughly an order of magnitude, and the predicted velocity–curvature correlation should move substantially back toward the curvature-flow limit. The reported COD values in Figs. 4g,h are thus not a parameter-free prediction but a demonstration conditional on the order of magnitude of S. The manuscript needs either a direct quantitative constraint on polycrystalline shear-coupling factors, a sensitivity analysis in S, or a clearly stated bounds argument showing that the conclusions are robust over the plausible range of S.
  2. [Main text, Discussion (Fig. 5) and SI §S-II D] The MD benchmarks in Fig. 5 use shear-coupling factors measured in bicrystal MD simulations and validate the mechanism in small, idealized microstructures with a small number of GB types. These benchmarks do not constrain the statistical value of S in a 1000-grain polycrystalline network, where constraints from neighboring grains and triple junctions activate additional disconnection modes and reduce the effective coupling. The cited qualitative evidence that polycrystalline coupling is smaller than bicrystal coupling supports the direction of the correction but not the specific factor 1/30. As written, the central quantitative claim rests on this uncalibrated factor.
  3. [Main text, text following Fig. 2] The authors acknowledge that bulk plastic deformation is not included in the simulations and that simulated stresses reach values as large as μ/10, comparable to the theoretical strength. Plastic relaxation in real polycrystals would reduce the internal stresses and hence reduce the elastic driving force τ·β in Eq. (2). This is not a minor detail: it is another mechanism—independent of S—that could lower the effective decorrelation strength. The paper should discuss quantitatively whether the conclusion that shear coupling is the 'main' cause survives when plastic relaxation is present, or whether the claimed dominance should be restricted to microstructures without significant intragranular plasticity.
  4. [Main text, Fig. 3 and accompanying footnote] The comparison between the 2D shear-coupling simulations in Figs. 3b and the 3D SrTiO3 experimental data in Fig. 3d is qualitative rather than quantitative. In 3D the appropriate von Neumann–Mullins-type statement involves the mean width of the grain, not simply the number of neighbors, as the authors themselves note in the footnote. The large scatter in the 3D experiment is suggestive and consistent with the authors' mechanism, but it cannot by itself establish that shear coupling is the cause of the 3D von Neumann–Mullins failure. This comparison should be framed as a qualitative analog, not as a direct validation.
minor comments (5)
  1. [Introduction, first paragraph] The phrase 'quantitively answer' should be 'quantitatively answer.'
  2. [Main text, Eq. (2) and Methods] M is described as an 'intrinsic disconnection mobility tensor,' but throughout the simulations it is used as a scalar mobility. Please clarify whether the tensor character is retained and what off-diagonal components would mean, or state that the isotropic/scalar limit is used.
  3. [Fig. 3 caption and axes] Panels (a,b) plot δR2/δt while panels (c,d) plot δR3/δt, but the axes are labeled identically except for the variable name; the different physical dimensions and scales make direct visual comparison difficult. Please add normalizations or a clearer statement that the two rows are separate quantities.
  4. [SI §S-II C] The sentence introducing S says it is 'chosen arbitrarily' but 'of the correct order of magnitude compared with experimental observations.' If no additional constraint can be provided, at least identify which experimental observations set this order of magnitude and how a factor-of-1/30 estimate was obtained.
  5. [Main text, Fig. 2 panels] In Figs. 2e and 2h the color or line assignment of distributions at different times is not explicitly explained in the caption; the statement 'the lightest and darkest lines are for the initial and final microstructures' should be complemented by a scale or legend for intermediate times.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the shear-coupling mechanism is demonstrated by forward simulation and benchmarked against independent MD; the arbitrary S=1/30 is a robustness caveat, not a circular reduction.

full rationale

The paper's central claim is that shear coupling, through internally generated stresses, is the main cause of the experimentally observed weak velocity-curvature correlation. This is established by forward phase-field simulations that include the elastic driving force tau·beta in the equation of motion (Eq. 2) and then compare the resulting COD values with experimental and MD data. Adding a physical term that is not proportional to curvature will of course weaken the curvature-velocity correlation, but that is a mechanistic demonstration rather than a tautology: the elastic driving force is not fitted to the experimental v-kappa scatter, and the same model is independently benchmarked against MD simulations of idealized microstructures (Fig. 5) using measured bicrystal shear coupling factors, with no adjustable physical parameters in that benchmark. The SI does introduce S = 1/30 as an arbitrarily chosen scaling factor for polycrystal shear coupling factors, and since the elastic driving force scales roughly as S^2, the quantitative strength of the conclusion depends on this choice. This is a genuine robustness limitation and a reason for caution about the strength of the quantitative match, but it is not a circularity: S is not fitted to the target velocity-curvature data, and the central mechanism is supported by externally validated MD comparisons. The model provenance includes several prior papers by the same authors, but those papers contain the independently checkable derivation of the disconnection-mediated equation of motion; the load-bearing validation here is the MD benchmark, not a self-citation chain. Overall, the derivation is not equivalent to its inputs, and no specific circular step can be exhibited.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The model introduces no new physical entities; it uses the existing disconnection framework. The central dependence is on the arbitrary scaling factor S=1/30 and on the assumption that internal stresses are not plastically relaxed.

free parameters (1)
  • Shear coupling scaling factor S = 1/30
    Chosen arbitrarily to account for reduced shear coupling in polycrystals relative to bicrystals; directly sets the magnitude of the elastic driving force and hence the velocity-curvature correlation. See SI S-II C.
assumptions (3)
  • domain assumption The disconnection-mediated continuum model of GB migration, Eq. (S-2) and (2), is the correct sharp-interface equation of motion for curved boundaries in polycrystals.
    The model is taken from the authors' prior work [25-27] and is not re-derived here; the PF implementation assumes this equation captures the microscopic mechanics of disconnection flow.
  • domain assumption Bulk plastic deformation is negligible in the simulated grain growth, so internal stresses are not relaxed by dislocation slip or twinning within grains.
    The paper notes stresses can approach mu/10 near triple junctions and that "the possibility of bulk plastic deformation is not included in these simulations." If plastic relaxation were significant, the stress fields and hence the decorrelation would be reduced.
  • ad hoc to paper Shear coupling factors from bicrystal MD simulations, scaled by S=1/30, apply to boundaries in a polycrystalline network.
    Justified by appeal to prior observations that polycrystalline coupling is smaller, but the specific scaling is arbitrary.

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Cite this review

Pith. "Pith review of Why Grain Growth is Not Curvature Flow." pith.science (2026). https://pith.science/paper/RVHQ7VKC

@misc{pith2026241115983,
  author       = {Pith},
  title        = {Pith review of: Why Grain Growth is Not Curvature Flow},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/RVHQ7VKC}},
  note         = {Machine review of arXiv:2411.15983}
}
read the original abstract

Grain growth in polycrystals is traditionally considered a capillarity-driven process, where grain boundaries (GBs) migrate toward their centers of curvature (i.e., mean curvature flow) with a velocity proportional to the local curvature (including extensions to account for anisotropic GB energy and mobility). Experimental and simulation evidence shows that this simplistic view is untrue. We demonstrate that the failure of the classical mean curvature flow description of grain growth mainly originates from the shear deformation naturally coupled with GB motion (i.e., shear coupling). Our findings are built on large-scale microstructure evolution simulations incorporating the fundamental (crystallography-respecting) microscopic mechanism of GB migration. The nature of the deviations from curvature flow revealed in our simulations is consistent with observations in recent experimental studies on different materials. This work also demonstrates how to incorporate the mechanical effects that are essential to the accurate prediction of microstructure evolution.

Figures

Figures reproduced from arXiv: 2411.15983 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: f where indicated by the arrows. (Increasing time in this microstructure is indicated by the transition of the GB color from blue to red.) Note that, while anisotropic [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. High-fidelity modeling of interface crossing in the diffusion welding process at the polycrystalline scale

    cond-mat.mtrl-sci 2025-07 conditional novelty 6.0 of 10

    Level-set grain-growth simulations of diffusion-welded interfaces introduce two normalized crossing criteria and quantify how grain size and second-phase particle density, shape, and evolution control interface crossing.

Reference graph

Works this paper leans on

52 extracted references · 52 canonical work pages · cited by 1 Pith paper

  1. [1]

    C. S. Smith, Grains, phases, and interfaces: An introduc- tion of microstructure, Transactions of the Metallurgical Society of AIME 175, 15 (1948)

    work page 1948

  2. [2]

    Von Neumann, Metal interfaces, American Society for Metals, Cleveland 108 (1952)

    J. Von Neumann, Metal interfaces, American Society for Metals, Cleveland 108 (1952)

    work page 1952

  3. [3]

    W. W. Mullins, Two-dimensional motion of idealized grain boundaries, Journal of Applied Physics 27, 900 (1956)

    work page 1956

  4. [4]

    R. D. MacPherson and D. J. Srolovitz, The von Neumann relation generalized to coarsening of three-dimensional microstructures, Nature 446, 1053 (2007)

    work page 2007

  5. [5]

    J. E. Taylor, J. W. Cahn, and C. A. Handwerker, Overview no. 98 i—geometric models of crystal growth, Acta Metallurgica et Materialia 40, 1443 (1992)

    work page 1992

  6. [6]

    Kazaryan, Y

    A. Kazaryan, Y. Wang, S. Dregia, and B. Patton, Grain growth in anisotropic systems: comparison of effects of energy and mobility, Acta Materialia 50, 2491 (2002)

    work page 2002

  7. [7]

    Legros, D

    M. Legros, D. S. Gianola, and K. J. Hemker, In situ TEM observations of fast grain-boundary motion in stressed nanocrystalline aluminum films, Acta Materialia 56, 3380 (2008)

    work page 2008

  8. [8]

    Mompiou, D

    F. Mompiou, D. Caillard, and M. Legros, Grain bound- ary shear–migration coupling—i. in situ TEM straining experiments in Al polycrystals, Acta Materialia 57, 2198 (2009)

    work page 2009

Show all 52 references
  1. [9]

    Sharon, P

    J. Sharon, P. Su, F. Prinz, and K. Hemker, Stress-driven grain growth in nanocrystalline Pt thin films, Scripta Ma- terialia 64, 25 (2011)

    2011

  2. [10]

    Harris, V

    K. Harris, V. Singh, and A. King, Grain rotation in thin films of gold, Acta Materialia 46, 2623 (1998)

    1998

  3. [11]

    Farkas, S

    D. Farkas, S. Mohanty, and J. Monk, Linear grain growth kinetics and rotation in nanocrystalline Ni, Physical Re- view Letters 98, 165502 (2007)

    2007

  4. [12]

    Y. Tian, X. Gong, M. Xu, C. Qiu, Y. Han, Y. Bi, L. V. Estrada, E. Boltynjuk, H. Hahn, J. Han, D. J. Srolovitz, and X. Pan, Grain rotation mechanisms in nanocrys- talline materials: Multiscale observations in Pt thin films, Science 386, 49 (2024)

    2024

  5. [13]

    Sch¨ afer and K

    J. Sch¨ afer and K. Albe, Competing deformation mecha- nisms in nanocrystalline metals and alloys: Coupled mo- tion versus grain boundary sliding, Acta Materialia 60, 6076 (2012)

    2012

  6. [14]

    L. Wang, Y. Zhang, Z. Zeng, H. Zhou, J. He, P. Liu, M. Chen, J. Han, D. J. Srolovitz, J. Teng, et al. , Track- ing the sliding of grain boundaries at the atomic scale, Science 375, 1261 (2022)

    2022

  7. [15]

    C. Qiu, M. Punke, Y. Tian, Y. Han, S. Wang, Y. Su, M. Salvalaglio, X. Pan, D. J. Srolovitz, and J. Han, Grain boundaries are brownian ratchets, Science 385, 980 (2024)

    2024

  8. [16]

    Barmak, E

    K. Barmak, E. Eggeling, D. Kinderlehrer, R. Sharp, S. Ta’asan, A. Rollett, and K. Coffey, Grain growth and the puzzle of its stagnation in thin films: The curious tale of a tail and an ear, Progress in Materials Science 58, 987 (2013)

    2013

  9. [17]

    Backofen, K

    R. Backofen, K. Barmak, K. Elder, and A. Voigt, Cap- turing the complex physics behind universal grain size distributions in thin metallic films, Acta Materialia 64, 72 (2014)

    2014

  10. [18]

    Bhattacharya, Y.-F

    A. Bhattacharya, Y.-F. Shen, C. M. Hefferan, S. F. Li, J. Lind, R. M. Suter, C. E. Krill III, and G. S. Rohrer, 11 Grain boundary velocity and curvature are not correlated in Ni polycrystals, Science 374, 189 (2021)

    2021

  11. [19]

    Xu, Y.-F

    Z. Xu, Y.-F. Shen, S. K. Naghibzadeh, X. Peng, V. Mu- ralikrishnan, S. Maddali, D. Menasche, A. R. Krause, K. Dayal, R. M. Suter, et al. , Grain boundary migra- tion in polycrystalline α-Fe, Acta Materialia 264, 119541 (2024)

    2024

  12. [20]

    G. B. Bizana and L. A. Barrales-Mora, Kinetics of grain boundary migration in nanosized Al polycrystals, Acta Materialia 260, 119261 (2023)

    2023

  13. [21]

    C. H. Li, E. H. Edwards, J. Washburn, and E. R. Parker, Stress-induced movement of crystal boundaries, Acta Metallurgica 1, 223 (1953)

    1953

  14. [22]

    J. W. Cahn, Y. Mishin, and A. Suzuki, Coupling grain boundary motion to shear deformation, Acta Materialia 54, 4953 (2006)

    2006

  15. [23]

    J. Han, S. L. Thomas, and D. J. Srolovitz, Grain- boundary kinetics: A unified approach, Progress in Ma- terials Science 98, 386 (2018)

    2018

  16. [24]

    S. L. Thomas, K. Chen, J. Han, P. K. Purohit, and D. J. Srolovitz, Reconciling grain growth and shear-coupled grain boundary migration, Nature Communications 8, 1 (2017)

    2017

  17. [25]

    Zhang, J

    L. Zhang, J. Han, Y. Xiang, and D. J. Srolovitz, Equation of motion for a grain boundary, Physical Review Letters 119, 246101 (2017)

    2017

  18. [26]

    J. Han, D. J. Srolovitz, and M. Salvalaglio, Disconnection-mediated migration of interfaces in microstructures: I. continuum model, Acta Materialia 227, 117178 (2022)

    2022

  19. [27]

    Salvalaglio, D

    M. Salvalaglio, D. J. Srolovitz, and J. Han, Disconnection-mediated migration of interfaces in microstructures: II. diffuse interface simulations, Acta Materialia 227, 117463 (2022)

    2022

  20. [28]

    C. Qiu, M. Salvalaglio, D. J. Srolovitz, and J. Han, In- terface faceting-defaceting mediated by disconnections, Acta Materialia 251, 118880 (2023)

    2023

  21. [29]

    C. Qiu, M. Salvalaglio, D. J. Srolovitz, and J. Han, Disconnection flow–mediated grain rotation, Proceedings of the National Academy of Sciences 121, e2310302121 (2024)

    2024

  22. [30]

    Chen, Phase-field models for microstructure evo- lution, Annual Review of Materials Research 32, 113 (2002)

    L.-Q. Chen, Phase-field models for microstructure evo- lution, Annual Review of Materials Research 32, 113 (2002)

    2002

  23. [31]

    Steinbach, Phase-field models in materials science, Modelling and Simulation in Materials Science and En- gineering 17, 073001 (2009)

    I. Steinbach, Phase-field models in materials science, Modelling and Simulation in Materials Science and En- gineering 17, 073001 (2009)

    2009

  24. [32]

    E. R. Homer, S. M. Foiles, E. A. Holm, and D. L. Olm- sted, Phenomenology of shear-coupled grain boundary motion in symmetric tilt and general grain boundaries, Acta Materialia 61, 1048 (2013)

    2013

  25. [33]

    Bollmann, General geometrical theory of crystalline interfaces, in Crystal Defects and Crystalline Interfaces (Springer, 1970) pp

    W. Bollmann, General geometrical theory of crystalline interfaces, in Crystal Defects and Crystalline Interfaces (Springer, 1970) pp. 143–185

    1970

  26. [34]

    J. P. Hirth and R. W. Balluffi, On grain boundary dislo- cations and ledges, Acta Metallurgica 21, 929 (1973)

    1973

  27. [35]

    Muralikrishnan, H

    V. Muralikrishnan, H. Liu, L. Yang, B. Conry, C. J. Mar- vel, M. P. Harmer, G. S. Rohrer, M. R. Tonks, R. M. Suter, C. E. Krill III, et al. , Observations of unexpected grain boundary migration in SrTiO 3, Scripta Materialia 222, 115055 (2023)

    2023

  28. [36]

    Fullman and J

    R. Fullman and J. Fisher, Formation of annealing twins during grain growth, Journal of Applied Physics22, 1350 (1951)

    1951

  29. [37]

    E. A. Holm and S. M. Foiles, How grain growth stops: A mechanism for grain-growth stagnation in pure materials, Science 328, 1138 (2010)

    2010

  30. [38]

    Hayashi, D

    Y. Hayashi, D. Setoyama, Y. Hirose, T. Yoshida, and H. Kimura, Intragranular three-dimensional stress tensor fields in plastically deformed polycrystals, Science 366, 1492 (2019)

    2019

  31. [39]

    Florez, K

    S. Florez, K. Alvarado, B. Murgas, N. Bozzolo, D. Chatain, C. E. Krill, M. Wang, G. S. Rohrer, and M. Bernacki, Statistical behaviour of interfaces sub- jected to curvature flow and torque effects applied to microstructural evolutions, Acta Materialia 222, 117459 (2022)

    2022

  32. [40]

    Z. Xu, C. M. Hefferan, S. F. Li, J. Lind, R. M. Suter, F. Abdeljawad, and G. S. Rohrer, Energy dissipation by grain boundary replacement during grain growth, Scripta Materialia 230, 115405 (2023)

    2023

  33. [41]

    and (ii) triple junction drag effect [19]. To exam- ine the effect of anisotropic GB energy, we conducted a series of PF simulations that include misorientation and inclination-dependent anisotropic GB energies with- out GB shear coupling (using the GB energy function of Al fr...

    2000

  34. [42]

    V. V. Bulatov, B. W. Reed, and M. Kumar, Grain bound- ary energy function for fcc metals, Acta Materialia 65, 161 (2014)

    2014

  35. [43]

    Zhang, W

    J. Zhang, W. Ludwig, Y. Zhang, H. H. B. Sørensen, D. J. Rowenhorst, A. Yamanaka, P. W. Voorhees, and H. F. Poulsen, Grain boundary mobilities in polycrystals, Acta Materialia 191, 211 (2020)

    2020

  36. [44]

    Gottstein, A

    G. Gottstein, A. King, and L. Shvindlerman, The effect of triple-junction drag on grain growth, Acta Materialia 48, 397 (2000)

    2000

  37. [45]

    Johnson and P

    A. Johnson and P. Voorhees, A phase-field model for grain growth with trijunction drag, Acta Materialia 67, 134 (2014)

    2014

  38. [46]

    K. Chen, J. Han, S. L. Thomas, and D. J. Srolovitz, Grain boundary shear coupling is not a grain boundary property, Acta Materialia 167, 241 (2019)

    2019

  39. [47]

    S. L. Thomas, C. Wei, J. Han, Y. Xiang, and D. J. Srolovitz, Disconnection description of triple-junction motion, Proceedings of the National Academy of Sciences 116, 8756 (2019)

    2019

  40. [48]

    that allows for a more versatile parametrization. Grains forming a microstructure are described via smooth, order parameters {ηi(r)} with r ∈ Ω ⊂ R2, which are 1 in the region corresponding to the i-th grain and 0 elsewhere with a smooth transition in between. Such smooth inte...

  41. [49]

    C. Wei, S. L. Thomas, J. Han, D. J. Srolovitz, and Y. Xi- ang, A continuum multi-disconnection-mode model for grain boundary migration, Journal of the Mechanics and Physics of Solids 133, 103731 (2019)

    2019

  42. [50]

    Steinbach and F

    I. Steinbach and F. Pezzolla, A generalized field method for multiphase transformations using interface fields, Physica D: Nonlinear Phenomena 134, 385 (1999). AUTHOR CONTRIBUTIONS C.Q., J.H. and M.S. designed research; C.Q. and M.S. performed research; C.Q. and M.S. contribut...

    1999

  43. [52]

    anti-curvature

    The mobility Mij at the corresponding grid point (l, m) in Eq. (S-5) is thus set to Mij = M GB ij M TJ ij + exp(−500(ηi + ηj − 1)2)(1 − M TJ ij ) . (S-14) If ηi + ηj = 1 (at GBs), Mij = M GB ij while if ηi + ηj ≪ 1 (at TJs), Mij = M GBM TJ ij . In this work, we choose M TJ = 0...

    2017

  44. [100]

    Grain C has a misori- entation angle of -22.6◦ away from grains A and B

    || ex, [010] || ey and [001] || ez. Grain C has a misori- entation angle of -22.6◦ away from grains A and B. Grain D has a misorientation angle of 28.1 ◦ away from grains A and B. In this sense, the GBs between grains A and C, B and C are Σ13[100] asymmetric tilt GBs, whilst t...

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.