pith. sign in

arxiv: 2604.09329 · v1 · submitted 2026-04-10 · ❄️ cond-mat.mtrl-sci

On the origin of superlattice stacking faults nucleation via climb of Frank partial in CoNi-based superalloys

Zhida Liang , Yinan Cui , Li Wang , Xin Liu , Bin Liu , Yong Liu , Fengxian Liu This is my paper

Pith reviewed 2026-05-10 17:54 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords superlattice stacking faultsFrank partial climbCoNi-based superalloysL12 gamma primehigh-temperature deformationHRTEM observationsolute segregationnon-conservative climb
0
0 comments X

The pith

Frank partial climb nucleates both intrinsic and extrinsic superlattice stacking faults in CoNi superalloys at 850°C.

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

The paper establishes that non-conservative climb of a/3<111> Frank partials supplies a general, kinetically viable route for superlattice intrinsic and extrinsic stacking fault formation inside the L12 gamma-prime phase. High-resolution imaging shows these partials originate at gamma/gamma-prime interfaces from Shockley-mixed dislocation reactions, then climb inward under compression, producing SISFs by positive climb and SESFs by negative climb. Solute segregation lowers the stacking-fault energy enough to sustain the climb, while mobility calculations place vacancy-controlled Frank climb on equal footing with solute-drag-limited Shockley glide at this temperature. If correct, the mechanism unifies fault nucleation pathways that were previously attributed only to conservative glide.

Core claim

Non-conservative climb of a/3<111> Frank partials constitutes a general and kinetically viable pathway for both SISF and SESF formation in the L12 structure of CoNi-based superalloys during compression at 850°C. Frank partials form at gamma/gamma-prime interfaces through reactions between a leading 30° Shockley partial and a 60° mixed dislocation on conjugate planes; positive climb expands SISFs while negative climb expands SESFs. Energetic and kinetic analyses show that solute-segregation-induced reduction of stacking-fault energy supplies the dominant driving force, enabling sustained climb and fault expansion at rates comparable to Shockley glide under solute drag.

What carries the argument

Non-conservative climb of a/3<111> Frank partials that form at gamma/gamma-prime interfaces and move into the L12 precipitate.

If this is right

  • Both SISFs and SESFs can expand via Frank partial climb under high-temperature compression.
  • Solute segregation to the fault plane supplies the sustained driving force for climb.
  • At 850°C the mobility of vacancy-diffusion-controlled Frank climb becomes comparable to solute-drag-controlled Shockley glide.
  • Climb-assisted nucleation supplies a single mechanism that accounts for observed fault populations in the gamma-prime phase.

Where Pith is reading between the lines

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

  • Creep models for these alloys should treat vacancy-mediated climb as a first-order contributor to fault formation rather than a secondary process.
  • The negative-climb route for SESFs may operate in other L12 alloys under similar temperature and stress conditions.
  • Varying the rate of solute diffusion or applying controlled vacancy injection could test whether climb remains competitive with glide.

Load-bearing premise

The HRTEM images show true climb motion rather than glide or post-deformation relaxation, and solute segregation supplies the main energetic drive without large unmodeled contributions from local stress or interfaces.

What would settle it

Direct observation of the same Frank partials remaining immobile or reversing direction when solute segregation is suppressed or when vacancy supersaturation is eliminated at 850°C.

read the original abstract

High-temperature deformation in superalloys is governed by the cooperative glide-climb motion of dislocations. Superlattice stacking faults (SFs) in the gamma prime phase are predominantly interpreted as nucleating via conservative Shockley partial glide. Here, we demonstrate that non-conservative climb of a/3<111> Frank partials constitutes a general and kinetically viable pathway for both superlattice intrinsic (SISFs) and extrinsic stacking faults (SESFs) formation in the L12 structure of CoNi-based superalloys during compression at 850 Celsius. High-resolution transmission electron microscopy reveals that Frank partials form at gamma/gamma prime interface can climb into the gamma prime phase, generating SISFs via positive climb and SESFs via negative climb. Importantly, the negative climb-assisted nucleation of SESFs is experimentally confirmed for the first time, and the observed positive climb-assisted SISF configuration differs fundamentally from previously reported mechanisms. We show that these Frank partials originate from the reaction between a leading 30 degree Shockley partial and a 60 degree mixed dislocation on conjugate {111} planes, producing energetically stable configurations that promote subsequent climb. Energetic and kinetic analyses demonstrate that solute segregation induced reduction of SF energy provides a dominant contribution to Frank partial climb, enabling sustained climb and consequent SF expansion. Quantitative comparisons further indicate that, at elevated temperatures, solute drag-controlled Shockley glide can achieve mobilities comparable to vacancy diffusion-controlled Frank climb. These findings establish climb-assisted SF formation as a unified deformation mechanism in gamma prime phase, and that both SISF and SESF expansion can proceed through Frank partial climb.

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 manuscript claims that non-conservative climb of a/3<111> Frank partials nucleating at the γ/γ' interface provides a general and kinetically viable pathway for both SISF and SESF formation in the L1₂ γ' phase of CoNi-based superalloys during 850°C compression. HRTEM imaging is presented as direct evidence that Frank partials climb into the γ' phase (positive climb generating SISFs, negative climb generating SESFs), originating from reactions between 30° Shockley partials and 60° mixed dislocations on conjugate {111} planes. Energetic analyses attribute the driving force primarily to solute-segregation-induced reduction in stacking fault energy, with kinetic comparisons indicating that vacancy-diffusion-controlled Frank climb can compete with solute-drag-controlled Shockley glide at elevated temperatures.

Significance. If the mechanistic interpretation holds, the work establishes climb-assisted superlattice fault nucleation as a unified deformation process in γ' phases, extending beyond the conventional emphasis on conservative Shockley glide. The experimental identification of negative climb for SESFs is novel, and the mobility comparisons supply a concrete basis for incorporating non-conservative mechanisms into high-temperature constitutive models. The HRTEM configurations supply atomic-scale evidence that strengthens the case for sessile partial involvement, while the attempt to quantify kinetic viability via segregation energetics is a constructive step toward falsifiable predictions.

major comments (2)
  1. [HRTEM results section] HRTEM results section (likely §3 and associated figures): The static post-deformation images capture final atomic configurations of Frank partials and associated faults inside the γ' phase but do not directly demonstrate the direction or mechanism of motion. Alternative pathways—such as conservative Shockley glide on {111} followed by relaxation into a sessile a/3<111> configuration or different dislocation reactions—cannot be ruled out without Burgers vector mapping across multiple zone axes or in-situ observations.
  2. [Energetic and kinetic analyses] Energetic and kinetic analyses (likely §4–5): The claim that solute-segregation-induced SF energy reduction provides the dominant driving force for sustained Frank partial climb lacks reported modeling details, parameter sensitivities, error bars, or quantitative partitioning against other contributions such as local applied stress or γ/γ' interface misfit. This renders the assertion of kinetic viability at 850°C difficult to evaluate and weakens the quantitative mobility comparison to Shockley glide.
minor comments (2)
  1. Define positive versus negative climb directions explicitly in the text and ensure consistent labeling in all figures and captions.
  2. Clarify the precise Burgers vector reaction sequence (30° Shockley + 60° mixed dislocation) with vector diagrams to facilitate reproduction of the proposed nucleation geometry.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review of our manuscript. The comments have helped us to better articulate the strengths and limitations of our experimental and modeling approaches. We have made revisions to the manuscript to address the major concerns, as detailed in the point-by-point responses below. We believe these changes strengthen the paper and clarify the interpretation of our results.

read point-by-point responses

  1. Referee: [HRTEM results section] HRTEM results section (likely §3 and associated figures): The static post-deformation images capture final atomic configurations of Frank partials and associated faults inside the γ' phase but do not directly demonstrate the direction or mechanism of motion. Alternative pathways—such as conservative Shockley glide on {111} followed by relaxation into a sessile a/3<111> configuration or different dislocation reactions—cannot be ruled out without Burgers vector mapping across multiple zone axes or in-situ observations.

    Authors: We agree that the post-deformation HRTEM images provide static snapshots and do not capture the dynamic evolution of the dislocations. The interpretation of climb is based on the final configurations, the determined Burgers vectors, and the specific fault types (SISF for positive climb and SESF for negative climb) that match the expected outcomes of non-conservative motion from the γ/γ' interface. To strengthen this, we have added a new subsection discussing potential alternative mechanisms, including conservative Shockley glide followed by core relaxation, and explain why these are inconsistent with the observed sessile partials originating at the interface and the absence of trailing partials expected in glide mechanisms. Additional Burgers vector analysis using different diffraction conditions has been included where available. However, in-situ TEM at 850°C under load is experimentally challenging and was not performed in this study. revision: partial

  2. Referee: [Energetic and kinetic analyses] Energetic and kinetic analyses (likely §4–5): The claim that solute-segregation-induced SF energy reduction provides the dominant driving force for sustained Frank partial climb lacks reported modeling details, parameter sensitivities, error bars, or quantitative partitioning against other contributions such as local applied stress or γ/γ' interface misfit. This renders the assertion of kinetic viability at 850°C difficult to evaluate and weakens the quantitative mobility comparison to Shockley glide.

    Authors: We appreciate this point and have revised the energetic and kinetic analyses sections to provide greater transparency. The revised manuscript now includes: (i) detailed description of the modeling approach, including the sources of segregation energies (from atomistic simulations and experimental APT data), (ii) sensitivity analysis to variations in key parameters such as vacancy formation energy and diffusion coefficients, (iii) error bars on the calculated driving forces and mobilities, and (iv) a quantitative partitioning table comparing the contributions from SF energy reduction, applied stress, and interface misfit. These additions demonstrate that segregation-induced SF energy lowering is indeed the dominant term under the studied conditions, supporting the kinetic viability comparison at 850°C. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper's core argument rests on post-deformation HRTEM imaging showing a/3<111> Frank partials and associated SISFs/SESFs inside the L1₂ phase, interpreted as evidence of non-conservative climb from the γ/γ' interface. Energetic and kinetic analyses attribute the driving force to solute-segregation-induced SF energy reduction and compare mobilities to Shockley glide, but these steps invoke independent physical models and experimental data rather than redefining fitted parameters or prior results as predictions by construction. No self-definitional loops, fitted-input predictions, or load-bearing self-citation chains appear in the abstract or described content; the derivation remains self-contained against external benchmarks like direct imaging and standard dislocation theory.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The claim relies on standard dislocation theory in FCC/L12 crystals and TEM contrast interpretation; the energetic analysis introduces at least one fitted or calculated quantity (SF energy reduction by solute segregation) whose value is not independently measured in the provided abstract.

free parameters (1)
  • SF energy reduction by solute segregation
    Invoked as the dominant driving force for sustained Frank partial climb; value is either fitted or computed from separate models not shown in the abstract.
axioms (1)
  • domain assumption Dislocation reactions on conjugate {111} planes produce stable a/3<111> Frank partials whose subsequent climb is governed by vacancy diffusion and local chemical potential
    Used to explain the origin of the observed Frank partials and to justify the kinetic comparison with Shockley glide.

pith-pipeline@v0.9.0 · 5614 in / 1429 out tokens · 51980 ms · 2026-05-10T17:54:53.306240+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

62 extracted references · 62 canonical work pages

  1. [1]

    C” layers are absent. This pair of intrinsic faults is crystallographically equivalent to an extrinsic fault because the repeated “AB|AB

    Discussion Based on the above experimental analyses, we identified two new SISF and SESF configurations characterized by Frank leading partials, which differ fundamentally from previously reported SF configurations in both the origin of the LPD and the non-conservative mode of SF expansion, as elaborated in Section 2. In contrast to the well-established m...

    work page

  2. [2]

    slow dislocation

    [37] SESF energy, 𝜸𝑺𝑬𝑺𝑭 89 𝑚𝐽/𝑚2 [46] Energy reduction for SESF (solutes segregation), 𝜟𝜸𝑺𝑬𝑺𝑭 − 71 𝑚𝐽/𝑚2 [29] SISF energy, 𝜸𝑺𝑰𝑺𝑭 68 𝑚𝐽/𝑚2 [46] Energy reduction for SISF (solutes segregation), 𝜟𝜸𝑺𝑬𝑺𝑭 − 58 𝑚𝐽/𝑚2 [29] 5.3.4 Effect of local defect interactions on Frank partial climb To illustrate the potential role of local defect interactions, we evaluate th...

    work page

  3. [3]

    Notably, the nucleation of SESF via the negative climb of a Frank partial was firstly confirmed by experiment

    Conclusion In this work, a new mechanism for SISF and SESF formation in CoNi -based superalloys was identified, involving the positive and negative climb of a Frank partial dislocation ( 𝑎/3〈111〉), respectively. Notably, the nucleation of SESF via the negative climb of a Frank partial was firstly confirmed by experiment. The main conclusions are as follow...

    work page 1987

  4. [4]

    The climb component of the Peach-Koehler force, 𝑓cl, due to the elastic field, 𝑓cl = 𝒇PK ⋅ 𝒏 (A. 17) 44 where 𝒇PK = 𝒇app + 𝒇self + 𝒇inter is the total Peach -Koehler force, arising from the externally applied stress, the dislocation self -stress and elastic interactions with other defects such as other dislocations and interfaces. The climb direction is 𝒏...

    work page

  5. [5]

    For an edge dislocation, the osmotic force per unit length is given as [39], 𝑓os = − 𝑘𝑇𝑏F Ωf ln( 𝑐𝑣𝑐 𝑐𝑣0) (A

    The so -called osmotic force, 𝑓os, arising from the change of free energy due to creation or annihilation of vacancies during climb. For an edge dislocation, the osmotic force per unit length is given as [39], 𝑓os = − 𝑘𝑇𝑏F Ωf ln( 𝑐𝑣𝑐 𝑐𝑣0) (A. 20) where 𝑘 is the Boltzman constant, 𝑇 is the absolute temperature. Ωf is the vacancy formation volume

    work page

  6. [6]

    This term is often negligible compared to the previous two forces [39]

    The drag force, 𝑓dr, opposes dislocation climb and is associated with the change in the free energy of the vacancies due to the evolving local stress field of a climbing dislocation. This term is often negligible compared to the previous two forces [39]. In the present configuration, however, an additional drag force arises from the energy cost of expandi...

    work page

  7. [7]

    Reed, R. C. (2008). The superalloys: fundamentals and applications. Cambridge university press

    work page 2008

  8. [8]

    Yokokawa, H

    T. Yokokawa, H. Harada, K. Kawagishi, T. Kobayashi, M. Yuyama, Y. Takata, Advanced alloy design program and improvement of sixth -generation Ni-base single crystal superalloy TMS -

    work page

  9. [9]

    122-130)

    In Superalloys 2020: Proceedings of the 14th International Symposium on Superalloys (pp. 122-130). Springer International Publishing

    work page 2020

  10. [10]

    Freund, O.M

    L.P. Freund, O.M. Messé, J.S. Barnard, M. Göken, S. Neumeier, C.M. Rae, Segregation assisted microtwinning during creep of a polycrystalline L12 -hardened Co -base superalloy. Acta Mater.123 (2017) 295-304

    work page 2017

  11. [11]

    León-Cázares, F

    F.D. León-Cázares, F. Monni, C.M.F. Rae, Stress orientation dependence for the propagation of stacking faults and superlattice stacking faults in nickel -based superalloys. Acta Mater . 199 (2020) 209-224

    work page 2020

  12. [12]

    Smith, R.R

    T.M. Smith, R.R. Unocic, H. Deutchman, M.J. Mills, Creep deformation mechanism mapping in nickel base disk superalloys. Materials at High Temperatures, 33(4-5) (2016) 372-383

    work page 2016

  13. [13]

    F. Leon Cazares, On the plastic deformation behaviour of nickel -based superalloys: low cycle fatigue and stress orientation effects (Doctoral dissertation, University of Cambridge), (2020)

    work page 2020

  14. [14]

    León-Cázares, R

    F.D. León-Cázares, R. Schlütter, F. Monni, M.C. Hardy, C.M. Rae, Nucleation of superlattice intrinsic stacking faults via cross -slip in nickel -based superalloys. Acta Mater . 241 (2022) 118372

    work page 2022

  15. [15]

    Barba, T.M

    D. Barba, T.M. Smith, J. Miao, M.J. Mills, R.C. Reed, Segregation -assisted plasticity in Ni - based superalloys. Metall. Mater. Trans. A 49 (2018) 4173-4185

    work page 2018

  16. [16]

    Vorontsov, L

    V.A. Vorontsov, L. Kovarik, M.J. Mills, C.M.F. Rae, High-resolution electron microscopy of dislocation ribbons in a CMSX -4 superalloy single crystal. Acta Mater . 60(12) (2012) 4866- 4878

    work page 2012

  17. [17]

    M. Lenz, M. Wu, E. Spiecker, Segregation-assisted climb of Frank partial dislocations: An alternative route to superintrinsic stacking faults in L1 2-hardened superalloys. Acta Mater. 191 (2020) 270-279

    work page 2020

  18. [18]

    B.H. Kear, A. Giamei, J. Silcock, R.K. Ham, Slip and climb processes in gamma prime hardened nickel-base alloys, Scr. Metall. 2 (1968) 287-293. 47

    work page 1968

  19. [20]

    Kolbe, The high temperature decrease of the critical resolved shear stress in nickel -base superalloys, Mater

    M. Kolbe, The high temperature decrease of the critical resolved shear stress in nickel -base superalloys, Mater. Sci. Eng. (2001) 383

    work page 2001

  20. [21]

    Zhang, Y

    Z. Zhang, Y. Ma, M. Yang, P. Jiang, H. Feng, Y. Zhu, X. Wu, F. Yuan, Improving ductility by coherent nanoprecipitates in medium entropy alloy. Int. J. Plast. 172 (2024) 103821

    work page 2024

  21. [22]

    Bezold, J

    A. Bezold, J. Vollhüter, N. Karpstein, M. Lenz, A.P. Subramanyam, C.H. Zenk, S. Neumeier, Segregation-induced strength anomalies in complex single -crystalline superalloys. Commun. Mater. 5(1) (2024) 8

    work page 2024

  22. [23]

    Leverant, B.H

    G.R. Leverant, B.H. Kear, J.M. Oblak, Creep of precipitation-hardened nickel-base alloy single crystals at high temperatures, Metall. Trans. 4 (1) (1973) 355-362

    work page 1973

  23. [24]

    Kear, J.M

    B.H. Kear, J.M. Oblak, A.F. Giamei, Stacking faults in gamma prime Ni 3(Al,Ti) precipitation hardened nickel-base alloys, Metall. Trans. 1 (9) (1970) 2477

    work page 1970

  24. [25]

    B. Kear, S. Copley, F. VerSynder, Strengthening of Nickel-base Superalloy Crystals. Proc. Int. Conf. Strength Met. Alloys, Tokyo (1967), pp. 672-680

    work page 1967

  25. [26]

    Condat, B

    M. Condat, B. Décamps, Shearing of γ′ precipitates by single 𝑎/2〈110〉 matrix dislocations in a γ/γ′ Ni-based superalloy. Scripta metall. 21(5) (1987) 607-612

    work page 1987

  26. [27]

    X. Wu, A. Dlouhy, Y.M. Eggeler, E. Spiecker, A. Kostka, C. Somsen, G. Eggeler, On the nucleation of planar faults during low temperature and high stress creep of single crystal Ni-base superalloys. Acta Mater.144 (2018) 642-655

    work page 2018

  27. [28]

    Borovikov, M.I

    V.V. Borovikov, M.I. Mendelev, T.M. Smith, J.W. Lawson, Stability of high energy superlattice faults in Ni-based superalloys from atomistic simulations. Int. J. Plast. 184 (2025) 104199

    work page 2025

  28. [29]

    Smith, B.D

    T.M. Smith, B.D. Esser, B. Good, M.S. Hooshmand, G.B. Viswanathan, C.M.F. Rae, M. J. Mills, Segregation and phase transformations along superlattice intrinsic stacking faults in Ni -based superalloys. Metall. Mater. Trans. A 49(9) (2018) 4186-4198

    work page 2018

  29. [30]

    B.H. Kear, A. Giamei, J. Silcock, R.K. Ham, Slip and climb processes in gamma prime hardened nickel-base alloys, Scr. Metall. 2 (1968) 287-293

    work page 1968

  30. [31]

    Smith, B.D

    T.M. Smith, B.D. Esser, N. Antolin, G.B. Viswanathan, T. Hanlon, A. Wessman, M.J. Mills, Segregation and η phase formation along stacking faults during creep at intermediate temperatures in a Ni-based superalloy. Acta Mater. 100 (2015) 19-31

    work page 2015

  31. [32]

    Barba, E

    D. Barba, E. Alabort, S. Pedrazzini, D.M. Collins, A.J. Wilkinson, P.A.J. Bagot, R.C. Reed, On the microtwinning mechanism in a single crystal superalloy. Acta Mater. 135 (2017) 314-329

    work page 2017

  32. [33]

    Kovarik, R.R

    L. Kovarik, R.R. Unocic, J. Li, P. Sarosi, C. Shen, Y. Wang, M.J. Mills, Microtwinning and other shearing mechanisms at intermediate temperatures in Ni -based superalloys. Prog. Mater. Sci. 54(6) (2009) 839-873. 48

    work page 2009

  33. [34]

    Kovarik, R.R

    L. Kovarik, R.R. Unocic, J. Li, M.J. Mills, The intermediate temperature deformation of Ni - based superalloys: importance of reordering, JOM 61 (2009) 42-48

    work page 2009

  34. [35]

    Karpstein, M

    N. Karpstein, M. Lenz, A. Bezold, M. Wu, S. Neumeier, E. Spiecker, Reliable identification of the complex or superlattice nature of intrinsic and extrinsic stacking faults in the L12 phase by high-resolution imaging. Acta Mater. 260 (2023) 119284

    work page 2023

  35. [36]

    Liang, F

    Z. Liang, F. Liu, X. Liu, Y. Li, Y. Cui, F . Pyczak, (2025). Segregation -driven cross -slip mechanism of Shockley partials in the gamma prime phase of CoNi -based superalloys. arXiv preprint arXiv:2508.17085

    work page arXiv 2025

  36. [37]

    Knowles, Q.Z

    D.M. Knowles, Q.Z. Chen, Superlattice stacking fault formation and twinning during creep in γ/γ′ single crystal superalloy CMSX-4. Mater. Sci. Eng. A 340(1-2) (2003) 88-102

    work page 2003

  37. [38]

    (2018) GPA - geometrical phase analysis software

    Du, H. (2018) GPA - geometrical phase analysis software

    work page 2018

  38. [39]

    Messé, J.S

    O.M. Messé, J.S. Barnard, E.J. Pickering, P.A. Midgley, C.M.F. Rae, On the precipitation of delta phase in ALLVAC® 718Plus. Philos. Mag. 94(10) (2014) 1132-1152

    work page 2014

  39. [40]

    Edington, Practical Electron Microscopy in Materials Science., Voan Nostrand, New York, 1975

    J.W. Edington, Practical Electron Microscopy in Materials Science., Voan Nostrand, New York, 1975

    work page 1975

  40. [41]

    D. B. Williams, C. B. Carter, The transmission electron microscope, Springer, New York, 1996

    work page 1996

  41. [42]

    Rae, R.C

    C.M.F. Rae, R.C. Reed, Primary creep in single crystal superalloys: Origins, mechanisms and effects. Acta Mater. 55(3) (2007) 1067-1081

    work page 2007

  42. [43]

    Bürger, A

    D. Bürger, A. Dlouhý, K. Yoshimi, G. Eggeler, How nanoscale dislocation reactions govern low-temperature and high -stress creep of Ni -base single crystal superalloys. Crystals, 10(2) (2020) 134

    work page 2020

  43. [44]

    Theory of dislocations[M]

    Anderson P M, Hirth J P, Lothe J. Theory of dislocations[M]. Cambridge University Press, 2017

    work page 2017

  44. [45]

    Karunaratne, S

    M.S.A. Karunaratne, S. Kyaw, A. Jones, R. Morrell, R.C. Thomson, Modelling the coefficient of thermal expansion in Ni -based superalloys and bond coatings. J. Mater. Sci. 51(9) (2016) 4213-4226

    work page 2016

  45. [46]

    Gao, and A.C.F

    Y. Gao, and A.C.F. Cocks, Thermodynamic variational approach for climb of an edge dislocation. Acta Mech. Solida Sin. 22(5) (2009) 426-435

    work page 2009

  46. [47]

    Liu, A.C.F

    F. Liu, A.C.F. Cocks, E. Tarleton , Dislocation climb driven by lattice diffusion and core diffusion. J. Mech. Phys. Solids (2023) 176

    work page 2023

  47. [48]

    Janotti, M

    A. Janotti, M. Krčmar, C.L. Fu, R.C. Reed, Solute diffusion in metals: larger atoms can move faster. Phys. Rev. Lett. 92(8) (2004) 085901

    work page 2004

  48. [49]

    Neumeier, H.U

    S. Neumeier, H.U. Rehman, J. Neuner, C.H. Zenk, S. Michel, S. Schuwalow, M. Göken, Diffusion of solutes in fcc Cobalt investigated by diffusion couples and first principles kinetic Monte Carlo. Acta Mater. 106 (2016) 304-312

    work page 2016

  49. [50]

    Mishin, J.W

    Y. Mishin, J.W. Cahn, Thermodynamics of Cottrell atmospheres tested by atomistic simulations. Acta Mater. 117 (2016) 197-206. 49

    work page 2016

  50. [51]

    Sills, W

    R.B. Sills, W. Cai, Free energy change of a dislocation due to a Cottrell atmosphere. Philos. Mag. 98(16) (2018) 1491-1510

    work page 2018

  51. [52]

    Tucker, Solute -Vacancy Interactions in Nickel

    J.D. Tucker, Solute -Vacancy Interactions in Nickel. MRS Online Proceedings Library 1645 (2014) 808

    work page 2014

  52. [53]

    Eurich, P.D

    N.C. Eurich, P.D. Bristowe, Segregation of alloying elements to intrinsic and extrinsic stacking faults in γ′-Ni3Al via first principles calculations. Scripta Mater. 102 (2015) 87-90

    work page 2015

  53. [54]

    Titus, A

    M.S. Titus, A. Mottura, G.B. Viswanathan, A. Suzuki, M.J. Mills, T.M. Pollock, High resolution energy dispersive spectroscopy mapping of planar defects in L12-containing Co-base superalloys. Acta Mater. 89 (2015) 423-437

    work page 2015

  54. [55]

    Makineni, A

    S.K. Makineni, A. Kumar, M. Lenz, P. Kontis, T. Meiners, C. Zenk, S. Zaefferer, G. Eggeler, S. Neumeier, E. Spiecker, D. Raabe, B. Gault, On the diffusive phase transformation mechanism assisted by extended dislocations during creep of a single crystal CoNi -based superalloy. Acta Mater. 155 (2018) 362-371

    work page 2018

  55. [56]

    Smith, Y

    T.M. Smith, Y. Rao, Y. Wang, M. Ghazisaeidi, M.J. Mills, Diffusion processes during creep at intermediate temperatures in a Ni-based superalloy. Acta Mater. 141 (2017) 261-272

    work page 2017

  56. [57]

    X. Wu, S.K. Makineni, C.H. Liebscher, G. Dehm, J. Rezaei Mianroodi, P. Shanthraj, D. Raabe, B. Gault, Unveiling the Re effect in Ni-based single crystal superalloys. Nature Commun.11(1) (2020) 389

    work page 2020

  57. [58]

    Cottrell, M.A

    A.H. Cottrell, M.A. Jaswon, Distribution of solute atoms round a slow dislocation. Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 199(1056) (1949) 104-114

    work page 1949

  58. [59]

    T. H. Courtney, Mechanical behavior of materials. Waveland Press (2005)

    work page 2005

  59. [60]

    Mishima, S

    Y. Mishima, S. Ochiai, M. Yodogawa, T. Suzuki, Mechanical properties of Ni3Al with ternary addition of transition metal elements. Trans. Jpn. Inst. Met. 27(1) (1986) 41-50

    work page 1986

  60. [61]

    Smith, N.A

    T.M. Smith, N.A. Zarkevich, A.J. Egan, J. Stuckner, T.P. Gabb, J.W. Lawson, M.J. Mills, Utilizing local phase transformation strengthening for nickel-base superalloys. Commun. Mater. 2(1) (2021) 106

    work page 2021

  61. [62]

    Smith, B.D

    T.M. Smith, B.D. Esser, N. Antolin, A. Carlsson, R.E.A. Williams, A. Wessman, M.J. Mills, Phase transformation strengthening of high -temperature superalloys. Nature Commun. 7(1) (2016) 13434

    work page 2016

  62. [63]

    Egan, N.H

    A.J. Egan, N.H. Gunda, L. Feng, M. Ghazisaeidi, Y. Wang, S. Tin, M.J. Mills, Stress-dependent χ phase transformation in a Ni-based superalloy. Commun. Mater. 6(1) (2025) 180

    work page 2025