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REVIEW 4 major objections 5 minor 39 references

Temperature-dependent hardness of diamond-structured covalent materials

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Temperature-dependent Vickers hardness of diamond, silicon, and germanium is derived from dislocation theory, with a shuffle-to-glide mechanism switch controlling high-temperature softening.

desk verdict A physically motivated dislocation model for temperature-dependent hardness in diamond-structure materials, with a real new descriptor (a^3G), but the headline transition temperatures rest on an unsupported six-orders-of-magnitude choice of mobile dislocation densities. read the letter →

arxiv 1909.11032 v2 pith:WWU565TG submitted 2019-08-28 cond-mat.mtrl-sci physics.class-phphysics.comp-ph

Xing Feng , Jianwei Xiao , Bin Wen , Jijun Zhao , Bo Xu , Yanbin Wang , Yongjun Tian This is my paper · ORCID
classification cond-mat.mtrl-sciphysics.class-phphysics.comp-ph
keywords Vickershardnesstemperaturedependencedislocationtheorydiamondstructurecovalentmaterialsshuffle-setandglide-setdislocationscriticalresolvedshearstresssuperharddesign
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

Building on dislocation theory rather than empirical fitting, this paper derives a temperature-dependent formula for the Vickers hardness of diamond-structured covalent materials and tests it against diamond, silicon, and germanium. The formula states $H_T = 8.5\,\hat{\tau}_T^c$, where $\hat{\tau}_T^c$ is the smaller of the critical resolved shear stresses for the shuffle-set perfect screw dislocation and the glide-set $90^\circ$ partial dislocation. Because thermal activation lowers the shuffle-set stress less than the glide-set stress, the controlling mechanism switches from shuffle to glide as temperature rises, giving a steep hardness drop at high temperature. The model reproduces the measured hardness data and predicts the shuffle-to-glide transition temperatures 1402.6 K, 676.8 K, and 560.2 K, in line with experimental values of 1450 K, 650 K, and 600 K for diamond, Si, and Ge.

What carries the argument

The carrying machinery is the kink-pair nucleation model for a dislocation under stress. The total energy of a kink pair as a function of kink-pair width $x$ includes kink formation energy, migration energy, kink-pair interaction, and the work done by the applied stress; the critical width $x_c$ is found by setting the derivative to zero, which yields an activation energy versus stress relation. Combining that activation energy with the strain-rate–dislocation-mobility relation and Boltzmann thermal activation gives a transcendental equation for the temperature-dependent critical resolved shear stress $\tau_T^c$. For diamond structure, two competing geometries are used: the $1/2\langle110\rangle$ shuffle-set screw perfect dislocation and the $1/6\langle112\rangle$ glide-set $90^\circ$ partial dislocation, and the model takes the minimum of the two stresses. Multiplying by the orientation and hardness–yield-strength prefactors ($3.1$ and $2.74$) gives $H_T=8.5\,\hat{\tau}_T^c$.

What would settle it

Measure the mobile dislocation densities $\rho_m$ for shuffle-set and glide-set dislocations in diamond, Si, or Ge under controlled stress and temperature, and recompute $\tau_T^c$ from Eq. (5); a density ratio different from about $10^6$ would shift the predicted transition temperatures away from 1402.6 K, 676.8 K, and 560.2 K toward or past the experimentally observed 1450 K, 650 K, and 600 K. Alternatively, an atomistic calculation of the kink-pair activation energy for each slip system at the stresses used here would check the central activation-energy input directly.

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Extended reading notes

Core claim

The central claim is that plastic deformation in diamond-structured covalent materials is governed by whichever of two dislocation types can move under the lower resolved shear stress, and that this minimum stress, converted by the product of an orientation factor and a hardness–yield-strength factor, is the Vickers hardness. The paper derives the temperature-dependent critical resolved shear stress for each dislocation type from a kink-pair activation model coupled with the strain-rate relation for dislocation motion and thermal activation. At low temperature the hardness equation collapses to $H_0 = k(\nu)G$ with $k(\nu)\approx 0.18+0.05\nu-0.51\nu^2$; at high temperature the glide-set partial dislocations take over and hardness falls steeply. The authors show that the intrinsic quantity $a^3G$ controls resistance to softening, and that the predicted hardness and shuffle-to-glide transition temperatures for diamond, Si, Ge, cubic BN, SiC, and a range of III–V compounds agree with experiments.

Load-bearing premise

The load-bearing premise is that the mobile dislocation densities for the shuffle-set and glide-set systems are $0.3\times10^8\ \mathrm{m}^{-2}$ and $0.3\times10^{14}\ \mathrm{m}^{-2}$, values taken without independent experimental or computational support; this six-order-of-magnitude ratio sits inside the thermal-activation logarithm and controls where the shuffle-to-glide crossover falls.

Editorial extensions

If this is right

  • At low temperature hardness is controlled mainly by shear modulus and Poisson's ratio; high shear modulus and low Poisson's ratio are the practical targets for superhard materials.
  • For any diamond-structured covalent material, once elastic constants and dislocation geometry are known, the full temperature-dependent hardness curve follows without fitting to hardness data.
  • The parameter $a^3G$ acts as a high-temperature softening index: larger values give a higher shuffle-to-glide transition temperature and slower hardness drop.
  • Microstructure and loading effects—mobile dislocation density, strain rate, grain size—enter the same formula and can be tuned to predict hardness under different conditions.
  • The model's scope includes cubic BN, SiC, and III–V compounds such as BAs, GaP, InP, and AlSb, with predicted 300 K hardness values listed alongside experiment.

Reading between the lines

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

  • The most consequential uncontrolled input is the six-order-of-magnitude ratio between the shuffle-set and glide-set mobile dislocation densities used in Table 1; an independent measurement of these densities would place a direct bound on the predicted crossover temperatures.
  • If the shuffle-to-glide switch is real, in-situ transmission electron microscopy or X-ray topography near the predicted transition temperatures should show the dominant dislocation character change from screw to partial.
  • The model's normalized form $k=H/G$ suggests a possible master curve for all diamond-structured covalent materials as a function of $(T, \nu, a^3G)$; replotting existing hardness data in these coordinates would test the universality.
  • The same kink-pair framework could be extended to nanotwinned diamond or other nanostructured covalent materials by treating twin boundaries and grain boundaries as obstacles that reduce the mean free path $\lambda_b$.
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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 manuscript proposes a temperature-dependent Vickers hardness model for diamond-structured covalent materials. Starting from a kink-pair dislocation activation-energy expression, the authors derive a temperature-dependent critical resolved shear stress for shuffle-set and glide-set dislocations, take the minimum of the two CRSS values as the controlling deformation mechanism, and convert it to hardness through Schmid's and Tabor's laws. The model is applied to diamond, Si, Ge, and several compound semiconductors. The authors report good agreement with room-temperature hardness data, reproduce the drop of hardness with temperature, and predict shuffle-to-glide transition temperatures of 1402.6 K, 676.8 K, and 560.2 K for diamond, Si, and Ge, compared with experimental values of about 1450 K, 650 K, and 600 K. They also propose the quantity a^3G as an intrinsic index of resistance to high-temperature softening.

Significance. If the model is robust, it would be a valuable contribution because it connects hardness measurements to dislocation kink-pair physics in covalent materials and gives a physically motivated explanation for the steep high-temperature softening. The comparison with transition temperatures across three materials is a useful and falsifiable prediction. The authors also include an MD cross-check of the activation-energy crossover and compare with multiple experimental data sets. The main weakness is that the crossover prediction is highly sensitive to the mobile-dislocation densities in Table 1, which are quoted without experimental or simulation support, and no sensitivity analysis is given. Because these densities enter the thermal-activation logarithms linearly, they control the shuffle-to-glide crossover temperature. A revision that provides a basis for these parameters, or a sensitivity analysis showing robustness, is needed before the quantitative claims can be accepted.

major comments (4)
  1. [Eq. (5) and Table 1] The central quantitative success, the shuffle-to-glide transition temperatures, is governed by the difference between the two thermal-activation logarithms in Eq. (5), L_g - L_s = ln[(rho_m,g b_g)/(rho_m,s b_s)] when the other factors are held at the Table 1 values. The manuscript chooses rho_m,s = 0.3 x 10^8 m^-2 and rho_m,g = 0.3 x 10^14 m^-2 without a citation or a supporting argument. This six-order-of-magnitude ratio supplies essentially all of the 13.3 difference between the fixed constants 18.8 and 32.1, and a one-order change in the ratio shifts the difference by ln(10) = 2.3, about 17%. Because the crossover condition is tau_T,s = tau_T,g, this shifts the predicted transition temperature by tens to hundreds of kelvin. The authors should either justify rho_m,s and rho_m,g from experiment or atomistic simulation, or demonstrate through a sensitivity analysis that the reported agreement with 1450 K, 650 K, and 600 K is not simply a consequence of this choice.
  2. [Section on fixed logarithms, Fig. 4 and Fig. S4] The use of the fixed values 18.8 and 32.1 for the second logarithm in Eq. (5) is described as reflecting the 'general range' of rho_m, lambda_b, and epsilon_dot, but no calculation of this range is shown beyond a reference to Fig. S4. Since the crossover depends on the difference of these two numbers, fixing them is equivalent to imposing the crossover temperature rather than predicting it. The authors should report the actual range of ln(rho_m b lambda_b nu_D / epsilon_dot) for the materials studied, and show how the predicted transition temperatures vary when rho_m and lambda_b are varied over physically reasonable ranges.
  3. [Eq. (3) and derivation of activation energy] The derivation of the activation energy in Eq. (3) relies on two explicit approximations: setting R = x_c in Eq. (1) and neglecting W_m when locating the envelope maximum. No estimate of the magnitude of the error introduced by these approximations is provided. The kink-migration energy W_m is expected to contribute to the local oscillations, but it may also bias the envelope when the kink-pair width is small. The authors should quantify the effect of these approximations, for example by comparing Eq. (3) with numerically computed energy barriers for the same dislocation geometries, or with available atomistic calculations.
  4. [Table 2 and Fig. 2] The quantitative comparison mixes Vickers and Knoop hardness values. For example, the experimental hardness for Si in Table 2 is from a Knoop measurement (Ref. [37]) and that for Ge from Ref. [38], while the model predicts Vickers hardness. Knoop and Vickers hardness numbers differ systematically for anisotropic covalent crystals, and no conversion or uncertainty interval is provided for these experimental values. The claimed 'remarkable agreement' therefore mixes two different engineering measures. The authors should either convert the Knoop values to Vickers with a stated conversion factor, or restrict the quantitative comparison to Vickers data and discuss the remaining differences qualitatively.
minor comments (5)
  1. [Throughout] There are typographical issues, including 'shear modules' for 'shear modulus' in the abstract and several garbled equation fragments in the typeset version (notably Eq. (1) and the definitions of A1 and A2). The manuscript should be carefully proofread.
  2. [Eq. (9)] The polynomial k_0(nu) = 0.18 + 0.05 nu - 0.51 nu^2 is a fit to the model's own output over the range 0 <= nu <= 0.3. This should be stated explicitly so that readers do not interpret it as an independent parameter-free result, and the fit range should be respected in applications.
  3. [Table 1] The geometric parameters b, h, r, and beta for the two dislocation types appear without a direct source. The authors should provide a reference or a short derivation for these values, especially for the core radius r, since it enters the fixed constants in Eq. (5).
  4. [Fig. 2] The experimental data in Figs. 2b-d are drawn from several references, but the symbol legend and the temperature ranges are not always clear. Adding a legend and vertical error bars would make the comparison easier to evaluate.
  5. [Reference list] References [20] and [27] appear to refer to the same paper by Xiao et al.; these should be consolidated or distinguished properly in the citation list.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the derivation chain is self-contained, with the disputed dislocation-density ratio entering as an input rather than as a retrofitted prediction.

full rationale

The paper constructs a temperature-dependent hardness model from dislocation kink-pair theory (Eqs. 1–5), converts CRSS to Vickers hardness via standard Schmid/Tabor prefactors (Eq. 6), and takes the minimum of shuffle- and glide-set CRSS (Eq. 7). The headline transition temperatures are outputs of this parameterized model, not quantities used to define the model. The fixed logarithms 18.8 and 32.1 in Eq. (5) are chosen from the assumed mobile-dislocation densities and typical strain-rate/log ranges (Table 1 and Fig. S4); the paper does not tune them against the 1450/650/600 K experimental transition temperatures. Thus the agreement is a genuine, if parameter-sensitive, prediction. The 10^6 ratio between shuffle- and glide-set dislocation densities is unsupported by citation, and the transition temperature will be sensitive to that ratio, but an unjustified or unvalidated input is a correctness/robustness concern, not a circular reduction of the output to the input. Likewise, Eq. (9) is explicitly a fit of the proportionality coefficient k0(ν) to the model's own zero-temperature hardness from Eq. (6); it is a transparent parameterization used for the low-temperature discussion, not an independent prediction, and it is not used to generate the main T_s−g comparison. Existing self-citations (e.g., Refs. [20–22], [27–31]) provide contextual or parameter-evaluation background; none is load-bearing in the sense of importing the paper's target result. No mathematical step is equivalent to its inputs by construction.

Assumptions & free parameters 7 free parameters · 5 assumptions · 1 invented entities

The model rests on standard dislocation theory plus a set of hand-chosen dislocation parameters (rho_m, lambda_b, epsilon, r) and two fixed logarithm constants. These are not fitted to the target hardness data, but they are not derived from first principles either. The low-temperature formula is parameterized by a polynomial fit to the model's own output. The main validation is comparison with published hardness data, which has wide scatter and mixes Vickers and Knoop scales.

free parameters (7)
  • Mobile dislocation density for shuffle-set dislocations (rho_m,s) = 0.3 x 10^8 m^-2
    Chosen in Table 1 as a typical value; it strongly affects the athermal CRSS and the competition between shuffle-set and glide-set control.
  • Mobile dislocation density for glide-set dislocations (rho_m,g) = 0.3 x 10^14 m^-2
    Six orders of magnitude higher than the shuffle-set value; no experimental or simulation source is cited, and this choice is load-bearing for the predicted transition temperature.
  • Mean free path (lambda_b) = 100 nm
    Set as a constant for both dislocation types in Table 1; enters the thermal-activation logarithm.
  • Strain rate (epsilon_dot) = 10^-4 s^-1
    Assumed typical for indentation; enters the same logarithm.
  • Dislocation core radius (r) = 0.9b (shuffle-set), 0.3b (glide-set)
    Chosen values in Table 1; they affect the activation energy in Eq. (3).
  • Fixed logarithm terms for shuffle and glide sets = 18.8 and 32.1
    Estimated from general ranges of rho_m, lambda_b, nu_D, and epsilon; treated as material-independent constants.
  • Coefficients in the k_0(nu) polynomial = 0.18, 0.05, -0.51
    Quadratic fit (Eq. 9) to the model's own computed k_0 values over Poisson ratios from 0 to 0.3.
assumptions (5)
  • standard math The kink-pair energy expression in Eq. (1) with its geometric prefactors is valid for the dislocations considered.
    Taken from standard dislocation theory (Hirth and Lothe), not derived here.
  • domain assumption Orowan's relation connects strain rate to mobile dislocation density, Burgers vector, and dislocation velocity.
    Used to derive the temperature-dependent CRSS equation (Eq. 4).
  • domain assumption Hardness is related to CRSS by fixed Schmid (3.1) and Tabor (2.74) prefactors, giving H = 8.5 tau_c for all temperatures and materials.
    Assumes the prefactor product is universal for diamond-structured polycrystals, including at high temperature and for polar crystals.
  • domain assumption Plastic deformation in diamond-structured covalent materials is dominated by two specific dislocation types: 1/6<112> glide-set 90 degrees partial and 1/2<110> shuffle-set perfect screw.
    Based on refs [26,27]; if other systems contribute, the competition picture changes.
  • ad hoc to paper The approximations R = x_c in Eq. (3) and neglecting W_m when locating the envelope maximum are acceptable.
    Stated in the text as simplifications; not rigorously justified.
invented entities (1)
  • a^3G (lattice parameter cubed times shear modulus) independent evidence
    purpose: Proposed as an intrinsic parameter measuring resistance to high-temperature softening of diamond-structured covalent materials.
    a and G are independently measurable, and the predicted transition temperatures for diamond, Si, and Ge match experiments, providing a falsifiable check. It is a derived combination, not a new physical substance.

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Cite this review

Pith. "Pith review of Temperature-dependent hardness of diamond-structured covalent materials." pith.science (2026). https://pith.science/paper/WWU565TG

@misc{pith2026190911032,
  author       = {Pith},
  title        = {Pith review of: Temperature-dependent hardness of diamond-structured covalent materials},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WWU565TG}},
  note         = {Machine review of arXiv:1909.11032}
}
read the original abstract

Understanding temperature-dependent hardness of covalent materials is not only of fundamental scientific interest, but also of crucial importance for technical applications. In this work, a temperature-dependent hardness formula for diamond-structured covalent materials is constructed on the basis of the dislocation theory. Our results show that, at low temperature, the Vickers hardness is mainly controlled by Poisson's ratio and shear modulus with the latter playing a dominant role. With increasing temperature, the plastic deformation mechanism undergoes a transition from shuffle-set dislocation control to glide-set dislocation control, leading to a steeper drop of hardness at high temperature. In addition, an intrinsic parameter, a3G, is revealed for diamond-structured covalent materials, which measures the resistance to soften at high temperature. Our hardness model shows remarkable agreement with experimental data. Current work not only sheds lights on the physical origin of hardness, but also provides a direct principle for superhard materials design.

Figures

Figures reproduced from arXiv: 1909.11032 by the authors.

Figure 1
Figure 1. Schematic diagram for the computational method used in this study. (a) {110} projection of the diamond-structured lattice. The green and red lines indicate the {111} shuffle and glide planes, respectively. (b) Kink-pair nucleation and motion process under applies stress. Shear stress  acting perpendicularly to a dislocation line parallel to  110 produces a kink pair (I), which expands subsequently (II through V),… view at source ↗
Figure 3
Figure 3. Effect of shear modulus and Poisson’s ratio on hardness of diamond-structured covalent materials at 0 K. (a) Calculated Vickers hardness map as a function of shear modulus and Poisson’s ratio. (b) Effect of shear modulus on materials hardness with different Poisson’s ratio. (c) Effect of Poisson’s ratio on materials hardness with different shear modulus [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗
Figure 4
Figure 4. Temperature effect on Vickers hardness of diamond-structured covalent materials. (a) The effects of temperature, a 3G, and Poisson’s ratio on k. (b) The effect of a 3G and Poisson’s ratio on the transition temperature Ts−g [PITH_FULL_IMAGE:figures/full_fig_p019_4.png] view at source ↗

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Works this paper leans on

39 extracted references · 39 canonical work pages

  1. [37]

    Williams, Occupational & Environmental Medicine 126(7) (1996) 81-84

    M.L. Williams, Occupational & Environmental Medicine 126(7) (1996) 81-84

    work page 1996

  2. [38]

    Szymanski, J.M

    A. Szymanski, J.M. Szymanski, Materials science monographs 49 (1989)

    work page 1989

  3. [1]

    Gilman, Chemistry and Physics of Mechanical Hardness, John Wiley & Sons2009

    J.J. Gilman, Chemistry and Physics of Mechanical Hardness, John Wiley & Sons2009

    work page

  4. [2]

    Liu, M.L

    A.Y . Liu, M.L. Cohen, Science 245(4920) (1989) 841-842

    work page 1989

  5. [3]

    Teter, MRS bulletin 23(1) (1998) 22-27

    D.M. Teter, MRS bulletin 23(1) (1998) 22-27

    work page 1998

  6. [4]

    X.-Q. Chen, H. Niu, D. Li, Y . Li, Intermetallics 19(9) (2011) 1275-1281

    work page 2011

  7. [5]

    Jiang, J

    X. Jiang, J. Zhao, X. Jiang, Computational materials science 50(7) (2011) 2287-2290

    work page 2011

  8. [6]

    F. Gao, J. He, E. Wu, S. Liu, D. Yu, D. Li, S. Zhang, Y . Tian, Physical Review Letters 91(1) (2003) 015502

    work page 2003

Show all 39 references
  1. [7]

    Šimůnek, J

    A. Šimůnek, J. Vackář, Physical Review Letters 96(8) (2006) 085501

    2006

  2. [8]

    K. Li, X. Wang, F. Zhang, D. Xue, Physical Review Letters 100(23) (2008) 235504

    2008

  3. [9]

    X. Guo, L. Li, Z. Liu, D. Yu, J. He, R. Liu, B. Xu, Y . Tian, H.-T. Wang, Journal of Applied Physics 104(2) (2008) 023503

    2008

  4. [10]

    Weidner, Y

    D.J. Weidner, Y . Wang, M.T. Vaughan, Science 266(5184) (1994) 419-422

    1994

  5. [11]

    Novikov, Y .V

    N. Novikov, Y .V . Sirota, V . Mal'Nev, I. Petrusha, Diamond Related Materials 2(9) (1993) 1253- 1256

    1993

  6. [12]

    Suzuki, T

    T. Suzuki, T. Ohmura, Philosophical Magazine A 74(5) (1996) 1073-1084

    1996

  7. [13]

    Trefilov, Y .V

    V . Trefilov, Y .V . Mil'Man, Soviet Physics Doklady 8 (1964)

    1964

  8. [14]

    Gerk, Philosophical Magazine 32(2) (1975) 355-365

    A.P. Gerk, Philosophical Magazine 32(2) (1975) 355-365

    1975

  9. [15]

    Mukhanov, O.O

    V .A. Mukhanov, O.O. Kurakevych, V .L. Solozhenko, Philosophical Magazine 89(25) (2009) 2117-2127

    2009

  10. [16]

    Ceder, Science 280(5366) (1998) 1099-1101

    G. Ceder, Science 280(5366) (1998) 1099-1101

    1998

  11. [17]

    Peierls, Proceedings of the Physical Society 52(1) (1940) 34

    R. Peierls, Proceedings of the Physical Society 52(1) (1940) 34

    1940

  12. [18]

    Nabarro, Proceedings of the Physical Society 59(2) (1947) 256

    F. Nabarro, Proceedings of the Physical Society 59(2) (1947) 256

    1947

  13. [19]

    Nabarro, M.S

    F.R. Nabarro, M.S. Duesbery, Dislocations in solids, Elsevier2002

  14. [20]

    J. Xiao, H. Yang, X. Wu, F. Younus, P. Li, B. Wen, X. Zhang, Y . Wang, Y . Tian, Science advances 4(9) (2018) eaat8195

    2018

  15. [21]

    B. Wen, B. Xu, Y . Wang, G. Gao, X.-F. Zhou, Z. Zhao, Y . Tian, npj Computational Materials 5(1) (2019) 117

    2019

  16. [22]

    J. Xiao, B. Wen, B. Xu, X. Zhang, Y . Wang, Y . Tian, npj Computational Materials 6(1) (2020) 119

    2020

  17. [23]

    Hirth, J

    J.P. Hirth, J. Lothe, T. Mura, Theory of Dislocations (2nd ed.), Wiley1983

  18. [24]

    Tabor, The hardness of metals, Oxford university press2000

    D. Tabor, The hardness of metals, Oxford university press2000

  19. [25]

    Kolar, J

    H. Kolar, J. Spence, H. Alexander, Physical Review Letters 77(19) (1996) 4031

    1996

  20. [26]

    Blumenau, M.I

    A.T. Blumenau, M.I. Heggie, C.J. Fall, R. Jones, T. Frauenheim, Physical Review B 65(20) (2002) 205205

    2002

  21. [27]

    J. Xiao, H. Yang, X. Wu, F. Younus, P. Li, B. Wen, X. Zhang, Y . Wang, Y . Tian, Science Advances 4(eaat8195) (2018)

    2018

  22. [28]

    H. Yang, J. Xiao, Z. Yao, X. Zhang, F. Younus, R. Melnik, B. Wen, Diamond and Related Materials 88 (2018) 110-117

    2018

  23. [29]

    T. Shao, B. Wen, R. Melnik, S. Yao, Y . Kawazoe, Y . Tian, Journal of Applied Physics 111(8) (2012) 083525

    2012

  24. [30]

    B. Wen, T. Shao, R. Melnik, Y . Kawazoe, Y . Tian, Journal of Applied Physics 113(10) (2013) 103501

    2013

  25. [31]

    X. Feng, J. Xiao, R. Melnik, Y . Kawazoe, B. Wen, The Journal of Chemical Physics 143(10) (2015) 104503

    2015

  26. [32]

    Sekhar, S

    A.P. Sekhar, S. Nandy, K.K. Ray, D. Das, Hardness-Yield Strength Relation of Al-Mg-Si Alloys, IOP Conference Series: Materials Science and Engineering, IOP Publishing, 2018

    2018

  27. [33]

    Stoller, S.J

    R.E. Stoller, S.J. Zinkle, Journal of Nuclear Materials 283-287(00) (2000) 349-352

    2000

  28. [34]

    Basinski, Philosophical Magazine 4(40) (1959) 393-432

    Z.S. Basinski, Philosophical Magazine 4(40) (1959) 393-432

    1959

  29. [35]

    Siethoff, Journal of Applied Physics 94(5) (2003) 3128-3134

    H. Siethoff, Journal of Applied Physics 94(5) (2003) 3128-3134

    2003

  30. [36]

    Brazhkin, A.G

    V .V . Brazhkin, A.G. Lyapin, R.J. Hemley, Philosophical Magazine A 82(2) (2002) 231-253

    2002

  31. [39]

    C.-M. Sung, M. Sung, Materials Chemistry and Physics 43(1) (1996) 1-18. Table 1. Geometric parameters for 1 1126  glide-set 90° partial and 1 1102 shuffle-set perfect dislocations. Dislocation type  b h r m (m-2) b (nm)  (s-1) 1 1102 shuffle-set 0° 22a 64a 0.9b 0.31...

    1996

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