Pith. sign in

REVIEW 4 major objections 4 minor 48 references

Activation entropy helps explain anomalous flow stress temperature dependence in copper

T0 review · 4 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Activation entropy alone could explain why copper's flow stress rises with temperature.

desk verdict The main CRSS claim is contradicted by the paper's own Eq. (15) and the Table 5/6 inconsistency; the friction-rate study is salvageable, but the central explanation of the flow stress anomaly fails. read the letter →

arxiv 2504.21246 v2 pith:VDD7ZAK5 submitted 2025-04-30 cond-mat.mtrl-sci physics.atm-clus

Mohammadhossein Nahavandian , Liam Myhill , Enrique Martinez This is my paper · ORCID
classification cond-mat.mtrl-sciphysics.atm-clus
keywords activationentropyflowstressanomalycriticalresolvedsheardislocationdipoleKramersratetheorySchoeckformalismLangevinfrictioncopper
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

This paper claims that activation entropy, not impurities or cross-slip, can explain the long-standing anomaly in which copper's flow stress increases with temperature at low to intermediate temperatures. Using atomistic simulations of edge and screw dislocation dipoles, the authors compute the rate at which dislocations overcome their mutual interaction barrier and compare it with Kramers rate theory. They find that the temperature dependence of the elastic constants makes the activation entropy strongly negative and growing with temperature, so the activation free energy barrier rises with temperature when the enthalpy barrier is small. This entropic effect raises the critical resolved shear stress with temperature, matching the experimentally observed trend. The paper further shows that Langevin friction modifies only the attempt frequency, not the barrier, a result confirmed by molecular dynamics.

What carries the argument

The load-bearing machinery is Schoeck's entropy formalism, which expresses the change in entropy induced by internal strains as $\Delta S = \alpha_V K \int_\Omega V_{ii}\,d\Omega - \frac{1}{2}\int_\Omega \frac{\partial C_{iklm}}{\partial T} V_{ik} V_{lm}\,d\Omega$, in combination with nudged elastic band (NEB) enthalpy profiles along the minimum energy path. This yields the activation free energy $\Delta G = \Delta H - T\Delta S$ at each stress and temperature. The rate is then evaluated with Kramers' expression, whose attempt frequency depends on the curvature of the enthalpy at the initial and saddle points and on the Langevin friction coefficient. The temperature dependence of the elastic constants (and the thermal expansion term, found negligible here) makes the entropy temperature dependent, and that is the mechanism driving the anomalous increase of $\tau_{\mathrm{CRSS}}$ with temperature.

What would settle it

Perform the same dipole-bypass rate calculations with the effective mass extracted from the actual normal mode at the initial and saddle points instead of the total cell mass; if the resulting rates and the temperature dependence of the critical resolved shear stress differ substantially from the paper's predictions, the central claim is falsified.

Watch

Extended reading notes

Core claim

The central discovery is that for both edge and screw dislocation dipoles in face-centered cubic copper, the activation entropy computed with Schoeck's elasticity formalism depends on temperature and stress, is negative, and grows in magnitude with temperature. When this temperature-dependent entropy is inserted into the activation free energy $\Delta G = \Delta H - T\Delta S$, the barrier that a dislocation must overcome increases with temperature, especially at stresses approaching the critical resolved shear stress at 0 K. Consequently, the critical resolved shear stress $\tau_{\mathrm{CRSS}}$ increases with temperature, reproducing the anomalous flow-stress behavior observed experimentally. Kramers' transition state theory, with harmonic prefactors derived from the enthalpy curvature at the minimum and saddle points, reproduces the rates measured by molecular dynamics and correctly captures the effect of Langevin friction, which acts only on the prefactor. The non-Arrhenius rate behavior at high temperature is captured only when the entropy is treated as temperature dependent, not when it is held constant.

Load-bearing premise

The Kramers rate calculation treats the dislocation bypass as a one-dimensional crossing whose attempt frequencies use the total mass of all atoms in the simulation cell, so if the true effective mass along the reaction path differs, every predicted rate and the extracted critical stress change.

Editorial extensions

If this is right

  • Kramers rate theory reproduces the MD-computed rates and their dependence on Langevin friction, so friction enters only through the attempt frequency and leaves the energy barrier unchanged.
  • At stresses near the zero-temperature critical resolved shear stress, the bypass rate can become non-Arrhenius: increasing temperature can reduce the rate, because the entropic barrier grows faster than $k_B T$.
  • The critical resolved shear stress for dislocation dipole bypass in pure copper increases with temperature, matching the direction of the anomaly seen experimentally in Cu and Cu-based alloys.
  • No impurities, cross-slip, or dynamic strain aging are needed to produce the anomalous increase; activation entropy alone is sufficient in the simulated configurations.

Reading between the lines

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

  • If activation entropy is the driver, then alloying or pressure that changes $\partial C_{iklm}/\partial T$ should systematically shift the magnitude and temperature range of the flow-stress anomaly, a prediction that goes beyond the paper's pure-copper dipoles.
  • The same Schoeck-plus-Kramers machinery could be applied to other face-centered cubic metals (Al, Ni, Ag) to test whether the anomaly's magnitude scales with the temperature sensitivity of their elastic constants.
  • A testable extension is to compute the rates with a different thermostat (e.g., Nose-Hoover) or with explicit heat baths of varying coupling; if the friction dependence vanishes or changes sign, the Kramers prefactor identification would need revision.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The manuscript reports atomistic molecular dynamics (MD) and nudged-elastic-band (NEB) calculations of thermally activated edge and screw dislocation dipole bypass in face-centered cubic copper, using the Mishin potential. Rates obtained from 465 MD simulations are compared with Kramers rate theory at several Langevin friction coefficients, temperatures, and shear stresses. The authors also compute activation entropies along the NEB paths using Schoeck's formalism and construct temperature- and stress-dependent activation free energies. The paper's headline claim is that activation entropy produces a critical resolved shear stress (CRSS) that increases with temperature, thereby explaining the low-to-intermediate temperature flow-stress anomaly in copper and other FCC metals.

Significance. If correct, the observation that Langevin friction changes only the Kramers prefactor and not the activation barrier would be a useful contribution, and the entropy-based explanation of the flow-stress anomaly would be significant because it would provide a mechanism distinct from impurities, cross-slip, and dynamic strain aging. The direct MD/Kramers comparison across friction coefficients (Figs. 7 and 8, Table 7) is a genuine strength, and the use of Schoeck's entropy with temperature-dependent elastic constants is methodologically interesting. However, the central CRSS claim is not supported by the manuscript's own equations: the fitted activation free energies in Table 6 are inconsistent with the directly computed barriers in Table 5, and Eq. (15) for the edge dislocation gives a CRSS that decreases with temperature over the anomalous range. The rate-versus-friction portion of the paper is separable and more robust, but the advertised explanation of the anomaly fails in its present form.

major comments (4)
  1. [§4.1, Eq. (15) and Fig. 9] Equation (15) contradicts the stated conclusion of a slight increase of CRSS with temperature. Evaluating the edge expression gives 11.97 MPa at 0 K, 10.54 MPa at 100 K, 7.83 MPa at 200 K, and 4.04 MPa at 300 K, and the expression crosses zero near 387 K. The screw expression, Eq. (16), decreases slightly from 39.71 MPa at 0 K to about 38.6 MPa at 300 K before rising slowly. The average of the edge and screw CRSS is therefore monotonically decreasing over the experimentally anomalous range below 300 K, in direct contradiction to the text and to Fig. 9, which claim that the theoretical CRSS follows the same increasing trend as the experimental flow stress.
  2. [§4.1, Table 5 versus Table 6] Table 6 is internally inconsistent with the directly computed activation free energies in Table 5. For the edge dipole at τ = 100 MPa and T = 0 K, Table 5 gives ΔG_eff ≈ 1.468 eV, whereas the Table 6 expression gives 1.005 − 8.394×10⁻² × 100 = −7.389 eV. At 120 MPa the discrepancy is similar. Since the anharmonic activation free energy ΔG_nh at T = 0 reduces to the activation enthalpy, a negative value is unphysical. The polynomial used to derive Eqs. (15) and (16) therefore does not represent the paper's own NEB/Schoeck data, and the CRSS curves built on it are not a valid prediction.
  3. [§4.1, Table 6 temperature derivatives] The temperature derivatives implied by Table 6 do not support the proposed entropy mechanism. For the edge dipole at 100 MPa, ∂ΔG/∂T at T = 0 is approximately −9.5×10⁻⁵ eV/K, and for the screw dipole at 30 MPa it is approximately −6.6×10⁻⁴ eV/K. Thus the fitted activation free energy decreases with temperature at these conditions, while the text states that negative activation entropy increases the activation free energy and leads to an increasing τCRSS. The fitted polynomials and the qualitative mechanism asserted in Section 4.1 are mutually inconsistent.
  4. [§4.1, CRSS extrapolation] The CRSS is defined by setting the fitted activation free energy polynomial to zero and extrapolating far outside the simulated stress window (30–120 MPa) and to temperatures below those used in the MD and NEB calculations. No uncertainty estimate, validation against direct barrier calculations, or sensitivity analysis is provided for this extrapolation. This is particularly problematic because the polynomial already fails to reproduce the barriers in Table 5 at the stress values on which it is ostensibly based.
minor comments (4)
  1. [Table 5 caption] The caption reads 'Activation free energy per as a function of temperature' and is missing a word; it should say what the free energy is normalized by.
  2. [Tables 3 and 4] The labels '1st jump' and '2nd jump' for the edge dislocation are not defined in the text; please explain what these two barriers correspond to physically.
  3. [Fig. 9] The figure mixes computed CRSS values with experimental flow-stress data from different mechanisms and alloys; the caption should state the plotted quantity, the stress units, and whether the comparison is quantitative or only qualitative.
  4. [§2.4, Eqs. (10) and (11)] The Kramers prefactor uses the total mass of all atoms in the simulation cell as the effective mass along the reaction coordinate; this assumption is not tested or justified, and the text should at least discuss its sensitivity, even though it does not affect the CRSS determination.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the CRSS(T) curve is a derived zero of independently computed free energies; noted self-citations are methodological, not load-bearing.

full rationale

The derivation chain is self-contained: NEB computes enthalpy barriers, Schoeck's formalism computes entropy from elastic constants and strain fields, and Kramers theory combines these into rates that are compared against independent MD waiting-time data (Fig. 7). The MD rates are not used to fit the entropy or the barriers, so the rate comparison is an external check rather than a circular validation. The tau_CRSS(T) curve is obtained by setting the fitted Delta G(T,tau) polynomial in Table 6 to zero, as the paper explicitly states: "The critical resolved shear stress (CRSS) is defined as the stress that zeros the activation free energy. Hence, we can equate to zero the expressions in Table 6 to obtain the dependence of the CRSS with temperature." This is a derived contour of the computed free energy, not a parameter fitted to the experimental flow-stress anomaly; the experimental data enter only in the final comparison. The main self-citation, Ref. [22], is methodological (entropy calculation along an MEP) and the method is described and re-derived in this paper, so it is not load-bearing. The paper also honestly states limitations: single-dipole configurations, potential accuracy, narrow MD temperature windows, and the unvalidated choice of total cell mass in the Kramers prefactor (Eqs. 10-11). Separately, there are internal numerical inconsistencies that are correctness defects rather than circularity: Table 6 at 100 MPa and 0 K gives a negative activation free energy for the edge dipole (-7.389 eV), inconsistent with Table 5 (1.468 eV), and Eq. (15) gives an edge CRSS that decreases from 11.97 MPa at 0 K to 4.04 MPa at 300 K, which contradicts the abstract's claim of an entropically driven increase. These issues undermine the central claim, but they do not constitute a step in which a prediction reduces to its input by construction. Therefore the circularity score is low.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new particles or forces. Its central claim, however, rests on fitted polynomial coefficients for the activation free energy, an arbitrary effective mass in the Kramers prefactor, and temperature-dependent elastic constant fits whose quadratic terms are weakly constrained. These are the quantities that create the predicted CRSS increase, so they carry the explanatory burden.

free parameters (3)
  • Activation free energy polynomial coefficients DeltaG(T,tau) = Table 6 coefficients: edge intercept 1.005 eV, stress coefficient -8.394e-2 eV/MPa; screw and cross terms as listed
    The CRSS(T) result is obtained by zeroing this fitted polynomial, so the central anomaly claim is carried entirely by these fitted numbers.
  • Effective mass in Kramers prefactor = Total mass of the ~600,000 atom simulation cell
    Eqs. (10)-(11) use this mass to convert barrier curvature into angular frequencies; no independent justification is given for treating the total cell mass as the reaction coordinate mass.
  • Second-order elastic constant temperature fits = C11 = 5.263e-6 T^2 - 0.014 T + 168.2; C12 = 1.009e-5 T^2 - 0.004 T + 121; C44 = -4.885e-6 T^2 - 0.003 T + 73.73
    The temperature dependence of the entropy, and hence the non-Arrhenius and CRSS trends, comes from these fits. Appendix A reports R2 values of only 0.27 for C12, so the quadratic term is not strongly constrained.
assumptions (5)
  • domain assumption Schoeck entropy formula Eq. (1) gives the activation entropy of a dislocation dipole bypass.
    The entire entropy analysis relies on this elasticity formalism from Ref. [39].
  • domain assumption The NEB enthalpy path, computed after thermal expansion, is the correct reference for the free energy saddle.
    Section 2.3 assumes the enthalpy maximum along the MEP approximates the free energy barrier; the paper itself notes the true free energy saddle might differ.
  • ad hoc to paper Kramers one-dimensional theory with a single scalar reaction coordinate and total-cell mass applies to dipole bypass.
    Section 2.4; the mass choice is not derived from dislocation dynamics and is structurally load-bearing.
  • domain assumption Mishin EAM potential faithfully captures elastic constant temperature dependence and thermal expansion.
    Appendix A shows computed elastic constants deviate from experiments at high temperature, especially C12.
  • ad hoc to paper CRSS can be defined by setting the fitted activation free energy polynomial to zero and extrapolating outside the simulated window.
    Section 4.1, Eqs. (15)-(16); the fit is based on 30-40 MPa screw and 100-120 MPa edge data, but the zero-crossing stress is outside or at the edge of that range.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Activation entropy helps explain anomalous flow stress temperature dependence in copper." pith.science (2026). https://pith.science/paper/VDD7ZAK5

@misc{pith2026250421246,
  author       = {Pith},
  title        = {Pith review of: Activation entropy helps explain anomalous flow stress temperature dependence in copper},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VDD7ZAK5}},
  note         = {Machine review of arXiv:2504.21246}
}
read the original abstract

Thermal activation of dislocations is critical for predicting the mechanical response of materials under common experimental conditions. According to transition state theory (TST), the rate for the system to overcome free energy barriers depends on an attempt frequency, activation free energy, and temperature. We computed the rate for edge and screw dislocation dipoles to overcome their interaction fields at various temperatures, Langevin friction coefficients, and shear stresses using Molecular Dynamics (MD), Schoecks entropy formalism and compared with Kramers rate theory. Kramers theory matches the rates computed dynamically, which depend on Langevin friction, increasing with weaker friction. Statically, using Schoeck formalism to compute the entropy along the minimum energy path (MEP), we found significant entropic effects that lead to an increase of the critical resolved shear stress with temperature and could help explain the long-standing anomaly observed at low to intermediate temperatures in copper and other metals, where the flow stress increases with temperature.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

48 extracted references · 33 canonical work pages

  1. [1]

    H. A. Kramers, Brownian motion in a field of force and the diffusion model of chemical reactions, physica 7 (4) (1940) 284–304

    work page 1940

  2. [2]

    J. J. Gilman, Influence of dislocation dipoles on physical properties, Discuss. Faraday Soc. 38 (1964) 123–137. doi:10.1039/DF9643800123. URL http://dx.doi.org/10.1039/DF9643800123

    work page doi:10.1039/df9643800123 1964

  3. [3]

    Design Kinetic Parameters for Improved Resilience of Materials under Irradiation

    M. Nahavandian, E. Aydogan, J. Byggm¨ astar, M. A. Tunes, E. Martinez, O. El- Atwani, Design kinetic parameters for improved resilience of materials under ir- radiation, arXiv preprint arXiv:2412.13343 (2024). arXiv:2412.13343. URL https://arxiv.org/abs/2412.13343

    work page Pith review arXiv 2024

  4. [4]

    D. Hull, D. J. Bacon, Introduction to dislocations, Vol. 37, Elsevier, 2011

    work page 2011

  5. [5]

    Parkhomenko, V

    T. Parkhomenko, V. Pustovalov, The low-temperature yield stress anomaly in metals and alloys, Physica status solidi (a) 74 (1) (1982) 11–42

    work page 1982

  6. [6]

    Turnage, M

    S. Turnage, M. Rajagopalan, K. Darling, P. Garg, C. Kale, B. Bazehhour, I. Ad- lakha, B. Hornbuckle, C. Williams, P. Peralta, et al., Anomalous mechanical behavior of nanocrystalline binary alloys under extreme conditions, Nature com- munications 9 (1) (2018) 2699. doi:10.1038/s41467-018-05027-5 . URL https://doi.org/10.1038/s41467-018-05027-5

    work page doi:10.1038/s41467-018-05027-5 2018

  7. [7]

    Schneider, G

    M. Schneider, G. Laplanche, Effects of temperature on mechani- cal properties and deformation mechanisms of the equiatomic crfeni medium-entropy alloy, Acta Materialia 204 (2021) 116470. doi:https: //doi.org/10.1016/j.actamat.2020.11.012. URL https://www.sciencedirect.com/science/article/pii/ S1359645420308879

    work page doi:10.1016/j.actamat.2020.11.012 2021

  8. [8]

    Takeuchi, E

    S. Takeuchi, E. Kuramoto, Temperature and orientation dependence of the yield stress in ni{in3} ga single crystals, Acta metallurgica 21 (4) (1973) 415–425

    work page 1973

Show all 48 references
  1. [9]

    Kuramoto, D

    E. Kuramoto, D. P. P. and, The orientation dependence of the yield stress of cu3au, The Philosophical Magazine: A Journal of Theoretical Experimental and Applied Physics 33 (4) (1976) 675–683. doi:10.1080/14786437608221127. URL https://doi.org/10.1080/14786437608221127 29

    1976 doi

  2. [10]

    Caillard, Yield-stress anomalies and high-temperature mechanical properties of intermetallics and disordered alloys, Materials Science and Engineering: A 319- 321 (2001) 74–83

    D. Caillard, Yield-stress anomalies and high-temperature mechanical properties of intermetallics and disordered alloys, Materials Science and Engineering: A 319- 321 (2001) 74–83. doi:https://doi.org/10.1016/S0921-5093(00)02017-7. URL https://www.sciencedirect.com/science/arti...

    2001 doi

  3. [11]

    Fusenig, E

    K.-D. Fusenig, E. Nembach, Dynamic dislocation effects in precipitation hard- ened materials, Acta Metallurgica et Materialia 41 (11) (1993) 3181–3189. doi:https://doi.org/10.1016/0956-7151(93)90048-W. URL https://www.sciencedirect.com/science/article/pii/ 095671519390048W

    1993 doi

  4. [12]

    Shim, H.-J

    J.-H. Shim, H.-J. L. Voigt, B. D. Wirth, Temperature dependent dislocation bypass mechanism for coherent precipitates in cu–co alloys, Acta Materialia 110 (2016) 276–282. doi:https://doi.org/10.1016/j.actamat.2016.03.027. URL https://www.sciencedirect.com/science/article/pii/ ...

    2016 doi

  5. [13]

    Granato, K

    A. Granato, K. L¨ ucke, Application of dislocation theory to internal fric- tion phenomena at high frequencies, Journal of Applied Physics 27 (7) (1956) 789–805. arXiv:https://pubs.aip.org/aip/jap/article-pdf/27/7/ 789/18315840/789\_1\_online.pdf, doi:10.1063/1.1722485. URL ht...

    1956 doi

  6. [14]

    Granato, K

    A. Granato, K. L¨ ucke, Theory of mechanical damping due to dislocations, Journal of Applied Physics 27 (6) (1956) 583–593. arXiv:https://pubs. aip.org/aip/jap/article-pdf/27/6/583/18315628/583\_1\_online.pdf, doi:10.1063/1.1722436. URL https://doi.org/10.1063/1.1722436

    1956 doi

  7. [15]

    D. V. Churochkin, S. Sahling, V. A. Osipov, Low-temperature internal friction and thermal conductivity in plastically deformed metals due to dislocation dipoles and random stresses, Phys. Rev. B 72 (2005) 014116. doi:10.1103/PhysRevB. 72.014116. URL https://link.aps.org/doi/10...

    2005 doi

  8. [16]

    Grabowski, N

    B. Grabowski, N. Zotov, Thermally-activated dislocation mobility in bcc metals: An accelerated molecular dynamics study, Computational Materials Science 200 (2021) 110804. doi:https://doi.org/10.1016/j.commatsci.2021.110804. 30 URL https://www.sciencedirect.com/science/article...

    2021

  9. [17]

    Bitzek, P

    E. Bitzek, P. Gumbsch, Atomistic study of drag, surface and inertial effects on edge dislocations in face-centered cubic metals, Materials Science and Engineer- ing: A 387-389 (2004) 11–15, 13th International Conference on the Strength of Materials. doi:https://doi.org/10.1016...

    2004 doi

  10. [18]

    Cerrai, M

    S. Cerrai, M. Freidlin, Large deviations for the langevin equation with strong damping, Journal of Statistical Physics 161 (2015) 859–875. doi:10.1007/ s10955-015-1346-2. URL https://doi.org/10.1007/s10955-015-1346-2

    2015 doi

  11. [19]

    D. N. Blaschke, D. J. Luscher, Dislocation drag and its influence on elas- tic precursor decay, International Journal of Plasticity 144 (2021) 103030. doi:https://doi.org/10.1016/j.ijplas.2021.103030. URL https://www.sciencedirect.com/science/article/pii/ S0749641921001054

    2021

  12. [20]

    Jung, D.-G

    I.-C. Jung, D.-G. Kang, B. C. De Cooman, Impulse excitation internal fric- tion study of dislocation and point defect interactions in ultra-low carbon bake- hardenable steel, Metallurgical and Materials Transactions A 45 (2014) 1962–

    2014

  13. [21]

    Galiakhmetova, L

    L. Galiakhmetova, L. Safina, R. Murzaev, J. Baimova, Dynamics of dislocation dipoles in graphene at high temperatures, Diamond and Related Materials 143 (2024) 110896. doi:https://doi.org/10.1016/j.diamond.2024.110896. URL https://www.sciencedirect.com/science/article/pii/ S09...

    2024

  14. [22]

    Nahavandian, S

    M. Nahavandian, S. Sarkar, S. Bagchi, D. Perez, E. Martinez, From anti-arrhenius to arrhenius behavior in a dislocation-obstacle bypass: Atomistic simulations and theoretical investigation, Computational Materials Science 239 (2024) 112954. doi:https://doi.org/10.1016/j.commat...

    2024

  15. [23]

    Y. Wang, W. Cai, Stress-dependent activation entropy in thermally acti- vated cross-slip of dislocations, Proceedings of the National Academy of Sci- ences 120 (34) (2023) e2222039120. arXiv:https://www.pnas.org/doi/pdf/ 10.1073/pnas.2222039120, doi:10.1073/pnas.2222039120. UR...

    2023 doi

  16. [24]

    S. Rao, D. Dimiduk, J. El-Awady, T. Parthasarathy, M. Uchic, C. Woodward, Screw dislocation cross slip at cross-slip plane jogs and screw dipole annihilation in fcc cu and ni investigated via atomistic simulations, Acta Materialia 101 (2015) 10–15. doi:https://doi.org/10.1016/...

    2015 doi

  17. [25]

    Allera, T

    A. Allera, T. D. Swinburne, A. M. Goryaeva, B. Bienvenu, F. Ribeiro, M. Perez, M.-C. Marinica, D. Rodney, Activation entropy of dislocation glide, arXiv preprint arXiv:2410.04813 (2024). URL https://arxiv.org/abs/2410.04813

    2024 arXiv

  18. [26]

    Bagchi, D

    S. Bagchi, D. Perez, Anomalous entropy-driven kinetics of dislocation nucleation, Nature Communications 16 (1) (2025) 912. doi:10.1038/s41467-025-56272-4 . URL https://doi.org/10.1038/s41467-025-56272-4

    2025 doi

  19. [27]

    Ferrando, R

    R. Ferrando, R. Spadacini, G. E. Tommei, Kramers problem in periodic potentials: Jump rate and jump lengths, Phys. Rev. E 48 (1993) 2437–2451. doi:10.1103/ PhysRevE.48.2437. URL https://link.aps.org/doi/10.1103/PhysRevE.48.2437

    1993 doi

  20. [28]

    Guantes, J

    R. Guantes, J. L. Vega, S. Miret-Art´ es, E. Pollak, Kramers’ turnover theory for diffusion of na atoms on a cu(001) surface measured by he scattering, The Journal of Chemical Physics 119 (5) (2003) 2780–

    2003

  21. [29]

    A. T. Frank, I. Andricioaei, Reaction coordinate-free approach to recover- ing kinetics from potential-scaled simulations: Application of kramers’ rate theory, The Journal of Physical Chemistry B 120 (33) (2016) 8600–8605, pMID: 27220565. arXiv:https://doi.org/10.1021/acs.jpcb...

    2016 doi

  22. [30]

    Pollak, R

    E. Pollak, R. Ianconescu, Kramers’ turnover theory: Improvement and extension to low barriers, The Journal of Physical Chemistry A 120 (19) (2016) 3155– 3164, pMID: 26731294. arXiv:https://doi.org/10.1021/acs.jpca.5b11502, doi:10.1021/acs.jpca.5b11502. URL https://doi.org/10.1...

    2016 doi

  23. [31]

    Denton, S

    C. Denton, S. Heredia-Avalos, J. Moreno-Mar´ ın, E. Martinez, M. Caturla, Influence of the distance of a collisional cascade to an edge dipole in α-fe on dislocation mobility and defect production, Nuclear Materials and Energy 39 (2024) 101663. doi:https://doi.org/10.1016/j.nm...

    2024

  24. [32]

    H¨ anggi, P

    P. H¨ anggi, P. Talkner, M. Borkovec, Reaction-rate theory: fifty years after kramers, Rev. Mod. Phys. 62 (1990) 251–341.doi:10.1103/RevModPhys.62.251. URL https://link.aps.org/doi/10.1103/RevModPhys.62.251

    1990 doi

  25. [33]

    Plimpton, Fast parallel algorithms for short-range molecular dynam- ics, Journal of Computational Physics 117 (1) (1995) 1–19

    S. Plimpton, Fast parallel algorithms for short-range molecular dynam- ics, Journal of Computational Physics 117 (1) (1995) 1–19. doi:https: //doi.org/10.1006/jcph.1995.1039. URL https://www.sciencedirect.com/science/article/pii/ S002199918571039X

    1995

  26. [34]

    Hirel, Atomsk: A tool for manipulating and converting atomic data files, Computer Physics Communications 197 (2015) 212–219

    P. Hirel, Atomsk: A tool for manipulating and converting atomic data files, Computer Physics Communications 197 (2015) 212–219. doi:https://doi.org/10.1016/j.cpc.2015.07.012. URL https://www.sciencedirect.com/science/article/pii/ S0010465515002817

    2015 doi

  27. [35]

    Mishin, M

    Y. Mishin, M. J. Mehl, D. A. Papaconstantopoulos, A. F. Voter, J. D. Kress, Structural stability and lattice defects in copper: Ab initio, tight-binding, and embedded-atom calculations, Phys. Rev. B 63 (2001) 224106. doi:10.1103/ PhysRevB.63.224106. URL https://link.aps.org/do...

    2001 doi

  28. [36]

    A. Stukowski, Visualization and analysis of atomistic simulation data with ovito–the open visualization tool, Modelling and Simulation in Materials Science and Engineering 18 (1) (2009) 015012. doi:10.1088/0965-0393/18/1/015012. URL https://dx.doi.org/10.1088/0965-0393/18/1/015012 33

    2009 doi

  29. [37]

    Stukowski, K

    A. Stukowski, K. Albe, Extracting dislocations and non-dislocation crystal defects from atomistic simulation data, Modelling and Simulation in Materials Science and Engineering 18 (8) (2010) 085001. doi:10.1088/0965-0393/18/8/085001. URL https://dx.doi.org/10.1088/0965-0393/18...

    2010 doi

  30. [38]

    Stukowski, A

    A. Stukowski, A. Arsenlis, On the elastic–plastic decomposition of crystal defor- mation at the atomic scale, Modelling and Simulation in Materials Science and Engineering 20 (3) (2012) 035012. doi:10.1088/0965-0393/20/3/035012. URL https://dx.doi.org/10.1088/0965-0393/20/3/035012

    2012 doi

  31. [39]

    Schoeck, The entropy of internal stress fields, physica status solidi (b) 97 (1) (1980) 345–354

    G. Schoeck, The entropy of internal stress fields, physica status solidi (b) 97 (1) (1980) 345–354. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10. 1002/pssb.2220970140, doi:https://doi.org/10.1002/pssb.2220970140. URL https://onlinelibrary.wiley.com/doi/abs/10.1002/pssb. 2220970140

    1980 doi

  32. [40]

    Henkelman, B

    G. Henkelman, B. P. Uberuaga, H. J´ onsson, A climbing image nudged elastic band method for finding saddle points and minimum energy paths, The Journal of Chemical Physics 113 (22) (2000) 9901–9904. arXiv:https://pubs.aip. org/aip/jcp/article-pdf/113/22/9901/19259681/9901\_1\_...

    2000 doi

  33. [41]

    M. R. Gilbert, P. Schuck, B. Sadigh, J. Marian, Free energy generalization of the peierls potential in iron, Phys. Rev. Lett. 111 (2013) 095502. doi:10.1103/ PhysRevLett.111.095502. URL https://link.aps.org/doi/10.1103/PhysRevLett.111.095502

    2013 doi

  34. [42]

    B. L. Mordike, P. H. and, The influence of temperature and strain rate on the flow stress of α-iron single crystals, The Philosophical Magazine: A Journal of Theo- retical Experimental and Applied Physics 7 (75) (1962) 459–474. arXiv:https: //doi.org/10.1080/14786436208212178,...

    1962 doi

  35. [43]

    Beuers, S

    J. Beuers, S. J¨ onsson, G. Petzow, Tem-in situ deformation of beryllium single crystals—a new explanation for the anomalous temperature dependence of the critical resolved shear stress for prismatic slip, Acta Metallurgica 35 (9) (1987) 2277–2287. doi:https://doi.org/10.1016/...

    1987 doi

  36. [44]

    W. v. Meyer, H. Neldel, Relation between the energy constant and the quantity constant in the conductivity–temperature formula of oxide semiconductors, Z. tech. Phys 18 (12) (1937) 588–593

    1937

  37. [45]

    W. C. Overton, J. Gaffney, Temperature variation of the elastic constants of cubic elements. i. copper, Phys. Rev. 98 (1955) 969–977. doi:10.1103/PhysRev.98. 969. URL https://link.aps.org/doi/10.1103/PhysRev.98.969

    1955 doi

  38. [46]

    F. C. Nix, D. MacNair, The thermal expansion of pure metals: Copper, gold, alu- minum, nickel, and iron, Phys. Rev. 60 (1941) 597–605. doi:10.1103/PhysRev. 60.597. URL https://link.aps.org/doi/10.1103/PhysRev.60.597 35

    1941 doi

  39. [1978]

    URL https://doi.org/10.1007/s11661-013-2122-z

    doi:10.1007/s11661-013-2122-z . URL https://doi.org/10.1007/s11661-013-2122-z

    doi

  40. [2791]

    URL https://doi.org/10.1063/1.1587687

    arXiv:https://pubs.aip.org/aip/jcp/article-pdf/119/5/2780/ 19321922/2780\_1\_online.pdf, doi:10.1063/1.1587687. URL https://doi.org/10.1063/1.1587687

    doi

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.