Peierls Stress

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Shaofeng Wang - One of the best experts on this subject based on the ideXlab platform.

  • The Dislocation Energy, Peierls Barrier and Stress for Zigzag Single-Walled Carbon Nanotubes
    International Journal of Modern Physics B, 2011
    Co-Authors: Hui Li Zhang, Shaofeng Wang
    Abstract:

    The dislocation energy, Peierls barrier and Peierls Stress of pentagon–heptagon (p–h) pair dislocation in zigzag single-walled carbon nanotube (SWCNT) are studied by the improved Peierls–Nabarro (P–N) theory. The contribution of the strain energy is considered in evaluating the dislocation energy and Peierls barrier and Stress. Using the γ-surface obtained from the first-principle calculations, it is found that the misfit energies of p–h pair dislocations are weakly dependent on the perimeters of the SWCNTs, while the strain and total energies have logarithmic behaviors with the perimeters of larger SWCNTs (N>10). For the smaller SWCNTs (N⩽10), the strain and total energies have a little deviation from the logarithmic behaviors due to the curvature and size effects. The calculated Peierls barrier and Peierls Stress are about 4.2–4.8 eV and 0.3μ, respectively. For the (12,0)–(11,0) carbon nanotube with different modification factors, the dislocation energy remains almost invariant (about 18 eV). The Peierls barrier and Peierls Stress increase linearly with the increasing of the modification factor. When modification factor changes from 0.10 to 0.45, the Peierls barrier changes from 3.6 eV to 7.4 eV, and the Peierls Stress changes from 0.2μ to 0.5μ.

  • The theoretical investigations of the core structure and the Peierls Stress of the ½〈1 1 1〉{1 1 0} edge dislocation in Mo
    Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 2010
    Co-Authors: Ruiping Liu, Shaofeng Wang, Rui Wang, Jian Jiao
    Abstract:

    Abstract By using the modified Peierls–Nabarro (P–N) model in which the lattice discrete effect is taken into account, the core structure and the Peierls Stress of the ½〈1 1 1〉{1 1 0} edge dislocation in molybdenum (Mo) have been investigated in the anisotropic elasticity approximation. The coefficient of the lattice discrete correction and the energy coefficient are all calculated in the anisotropic elasticity approximation. By considering the lattice discrete effect, the core width obtained from the modified P–N model is much wider than the results obtained from the P–N model. Because the Peierls Stress of the ½〈1 1 1〉{1 1 0} edge dislocation in Mo moving with the rigid mechanism is smaller than that with the kink mechanism, therefore, through investigating the Peierls Stress of the edge dislocation we obtained with the atomistic simulations, it can be indicated that when the external Stress is loaded on the ½〈1 1 1〉{1 1 0} edge dislocation in Mo, the dislocation may move with the rigid mechanism rather than the kink mechanism or other mechanisms.

  • On Core Structure Properties and Peierls Stress of Dissociated Superdislocations in Aluminides: NiAl and FeAl
    Acta Mechanica Solida Sinica, 2010
    Co-Authors: Shaofeng Wang
    Abstract:

    Abstract The study of dislocation properties in B2 structure intermetallics NiAl and FeAl is crucial to understand their mechanical behaviors. In this paper, the core structure and Peierls Stress of collinear dissociated (111}{110} edge superdislocations in NiAl and FeAl are investigated with the modified P-N dislocation equation. The generalized stacking fault energy curve along (111) direction in {110} slip plane contains two modification factors that can assure the antiphase energy and the unstable stacking fault energy to change independently. The results show that the core width of superpartials decreases with the increasing unstable stacking fault energy, and increases with the increasing antiphase boundary energy. The calculated Peierls Stress of (111}{110} edge superdislocations in NiAl and FeAl are 475 MPa and 3042 MPa, respectively. The values of Peierls Stress in NiAl is in accordance in magnitude with the experimental and the molecular statics simulations results.

  • Peierls Stress for 110 001 mixed dislocation in srtio3 within framework of constrained path approximation
    Acta Mechanica Sinica, 2010
    Co-Authors: Shaofeng Wang, Ruiping Liu
    Abstract:

    The core structure of 〈110〉{001} mixed dislocation in perovskite SrTiO3 is investigated with the modified two-dimensional Peierls–Nabarro dislocation equation considering the discreteness effect of crystals. The results show that the core structure of mixed dislocation is independent of the unstable energy in the 〈100〉 direction, but closely related to the unstable energy in the 〈110〉 direction which is the direction of total Burgers vector of mixed dislocation. Furthermore, the ratio of edge displacement to screw one nearly equals to the tangent of dislocation angle for different unstable energies in the 〈110〉 direction. Thus, the constrained path approximation is effective for the 〈110〉{001} mixed dislocation in SrTiO3 and two-dimensional equation can degenerate into one-dimensional equation that is only related to the dislocation angle. The Peierls Stress for 〈110〉{001} dislocations can be expediently obtained with the one-dimensional equation and the predictive values for edge, mixed and screw dislocations are 0.17, 0.22 and 0.46 GPa, respectively.

  • On the dislocation properties of 60o partial dislocation in silver: core structure and Peierls Stress
    Journal of Atomic and Molecular Sciences, 2010
    Co-Authors: Shaorong Li, Shaofeng Wang, Xiaozhi Wu
    Abstract:

    Two-dimensional modified Peierls-Nabarro dislocation equation concern- ing the discreteness of crystals is reduced to one-dimensional equation to determined the core structure of partial dislocation in Ag. The generalized stacking fault energy along the Burgers vectors of partial dislocation is a skewed sinusoidal force law, which is related to the intrinsic stacking fault energy and the unstable stacking fault energy. A trial solution appropriate for arbitrary dislocation angle is presented within the vari- ational method. The results show that the half core width increases as the increase of dislocation angle. Moreover, the core width decreases with the increase of the unsta- ble stacking fault energy and the intrinsic stacking fault energy. Peierls Stress for 60 - partial dislocation is in agreement with the experimental results. PACS: 61.72.Bb, 61.72.Lk, 61.72.Nn

Ruiping Liu - One of the best experts on this subject based on the ideXlab platform.

  • The theoretical investigations of the core structure and the Peierls Stress of the ½〈1 1 1〉{1 1 0} edge dislocation in Mo
    Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 2010
    Co-Authors: Ruiping Liu, Shaofeng Wang, Rui Wang, Jian Jiao
    Abstract:

    Abstract By using the modified Peierls–Nabarro (P–N) model in which the lattice discrete effect is taken into account, the core structure and the Peierls Stress of the ½〈1 1 1〉{1 1 0} edge dislocation in molybdenum (Mo) have been investigated in the anisotropic elasticity approximation. The coefficient of the lattice discrete correction and the energy coefficient are all calculated in the anisotropic elasticity approximation. By considering the lattice discrete effect, the core width obtained from the modified P–N model is much wider than the results obtained from the P–N model. Because the Peierls Stress of the ½〈1 1 1〉{1 1 0} edge dislocation in Mo moving with the rigid mechanism is smaller than that with the kink mechanism, therefore, through investigating the Peierls Stress of the edge dislocation we obtained with the atomistic simulations, it can be indicated that when the external Stress is loaded on the ½〈1 1 1〉{1 1 0} edge dislocation in Mo, the dislocation may move with the rigid mechanism rather than the kink mechanism or other mechanisms.

  • Peierls Stress for 110 001 mixed dislocation in srtio3 within framework of constrained path approximation
    Acta Mechanica Sinica, 2010
    Co-Authors: Shaofeng Wang, Ruiping Liu
    Abstract:

    The core structure of 〈110〉{001} mixed dislocation in perovskite SrTiO3 is investigated with the modified two-dimensional Peierls–Nabarro dislocation equation considering the discreteness effect of crystals. The results show that the core structure of mixed dislocation is independent of the unstable energy in the 〈100〉 direction, but closely related to the unstable energy in the 〈110〉 direction which is the direction of total Burgers vector of mixed dislocation. Furthermore, the ratio of edge displacement to screw one nearly equals to the tangent of dislocation angle for different unstable energies in the 〈110〉 direction. Thus, the constrained path approximation is effective for the 〈110〉{001} mixed dislocation in SrTiO3 and two-dimensional equation can degenerate into one-dimensional equation that is only related to the dislocation angle. The Peierls Stress for 〈110〉{001} dislocations can be expediently obtained with the one-dimensional equation and the predictive values for edge, mixed and screw dislocations are 0.17, 0.22 and 0.46 GPa, respectively.

  • Peierls Stress for 110{ 001} mixed dislocation in SrTiO3 within framework of constrained path approximation
    Acta Mechanica Sinica, 2009
    Co-Authors: Shaofeng Wang, Ruiping Liu
    Abstract:

    The core structure of 〈110〉{001} mixed dislocation in perovskite SrTiO3 is investigated with the modified two-dimensional Peierls–Nabarro dislocation equation considering the discreteness effect of crystals. The results show that the core structure of mixed dislocation is independent of the unstable energy in the 〈100〉 direction, but closely related to the unstable energy in the 〈110〉 direction which is the direction of total Burgers vector of mixed dislocation. Furthermore, the ratio of edge displacement to screw one nearly equals to the tangent of dislocation angle for different unstable energies in the 〈110〉 direction. Thus, the constrained path approximation is effective for the 〈110〉{001} mixed dislocation in SrTiO3 and two-dimensional equation can degenerate into one-dimensional equation that is only related to the dislocation angle. The Peierls Stress for 〈110〉{001} dislocations can be expediently obtained with the one-dimensional equation and the predictive values for edge, mixed and screw dislocations are 0.17, 0.22 and 0.46 GPa, respectively.

  • the Peierls Stress of the moving formula see text screw dislocation in ta
    Journal of Physics: Condensed Matter, 2009
    Co-Authors: Ruiping Liu, Shaofeng Wang
    Abstract:

    The Peierls Stress of the moving [Formula: see text] screw dislocation with a planar and non-dissociated core structure in Ta has been calculated. The elastic strain energy which is associated with the discrete effect of the lattice and ignored in classical Peierls-Nabarro (P-N) theory has been taken into account in calculating the Peierls Stress, and it can make the Peierls Stress become smaller. The Peierls Stress we obtain is very close to the experimental data. As shown in the numerical calculations and atomistic simulations, the core structure of the screw dislocation undergoes significant changes under the explicit Stress before the screw dislocation moves. Moreover, the mechanism of the screw dislocation is revealed by our results and the experimental data that the screw dislocation retracts its extension in three {110} planes and transforms its dissociated core structure into a planar configuration. Therefore, the core structure of the moving [Formula: see text] screw dislocation in Ta is proposed to be planar.

  • the Peierls Stress of the moving frac 1 2 langle 111 rangle 110 screw dislocation in ta
    Journal of Physics: Condensed Matter, 2009
    Co-Authors: Ruiping Liu, Shaofeng Wang
    Abstract:

    The Peierls Stress of the moving screw dislocation with a planar and non-dissociated core structure in Ta has been calculated. The elastic strain energy which is associated with the discrete effect of the lattice and ignored in classical Peierls?Nabarro (P?N) theory has been taken into account in calculating the Peierls Stress, and it can make the Peierls Stress become smaller. The Peierls Stress we obtain is very close to the experimental data. As shown in the numerical calculations and atomistic simulations, the core structure of the screw dislocation undergoes significant changes under the explicit Stress before the screw dislocation moves. Moreover, the mechanism of the screw dislocation is revealed by our results and the experimental data that the screw dislocation retracts its extension in three {110} planes and transforms its dissociated core structure into a planar configuration. Therefore, the core structure of the moving screw dislocation in Ta is proposed to be planar.

Irene J. Beyerlein - One of the best experts on this subject based on the ideXlab platform.

  • comparative modeling of the disregistry and Peierls Stress for dissociated edge and screw dislocations in al
    International Journal of Plasticity, 2020
    Co-Authors: Shuozhi Xu, Jaber Rezaei Mianroodi, Abigail Hunter, Bob Svendsen, Irene J. Beyerlein
    Abstract:

    Abstract Many elementary deformation processes in metals involve the motion of dislocations. The planes of glide and specific processes dislocations prefer depend heavily on their atomic core structures. Atomistic simulations are desirable for dislocation modeling but their application to even sub-micron scale problems is in general computationally costly. Accordingly, continuum-based approaches, such as the phase-field microelasticity, phase-field dislocation dynamics (PFDD), generalized Peierls–Nabarro (GPN) models, and the concurrent atomistic–continuum (CAC) method, have attracted increasing attention in the field of dislocation modeling because they well represent both short-range cores interactions and long-range Stress fields of dislocations. To better understand their similarities and differences, it is useful to compare these methods in the context of benchmark simulations and predictions. In this paper, we apply the CAC method and different PFDD variants – one of them is equivalent to a GPN model – to simulate an extended (i.e., dissociated) dislocation in Al with initially pure edge or pure screw character in terms of the disregistry. CAC and discrete forms of PFDD are also employed to calculate the Peierls Stress. By conducting comprehensive convergence studies, we quantify the dependence of these measures on time/grid resolution and simulation cell size. Several important but often overlooked differences between PFDD/GPN variants are clarified. Our work sheds light on the advantages and limitations of each method, as well as the path towards enabling them to effectively model complex dislocation processes at larger length scales.

  • First-principles investigation of strain effects on the stacking fault energies, dislocation core structure, and Peierls Stress of magnesium and its alloys
    Physical Review B, 2017
    Co-Authors: S. H. Zhang, Irene J. Beyerlein, Dominik Legut, Zuoguang Zhang, Shun-li Shang, Zi-kui Liu, Timothy C. Germann, Ruifeng Zhang
    Abstract:

    Taking pure Mg, Mg-Al, and Mg-Zn as prototypes, the effects of strain on the stacking fault energies (SFEs), dislocation core structure, and Peierls Stress were systematically investigated by means of density functional theory and the semidiscrete variational Peierls-Nabarro model. Our results suggest that volumetric strain may significantly influence the values of SFEs of both pure Mg and its alloys, which will eventually modify the dislocation core structure, Peierls Stress, and preferred slip system, in agreement with recent experimental results. The so-called "strain factor" that was previously proposed for the solute strengthening could be justified as a major contribution to the strain effect on SFEs. Based on multivariate regression analysis, we proposed universal exponential relationships between the dislocation core structure, the Peierls Stress, and the stable or unstable SFEs. Electronic structure calculations suggest that the variations of these critical parameters controlling strength and ductility under strain can be attributed to the strain-induced electronic polarization and redistribution of valence charge density at hollow sites. These findings provide a fundamental basis for tuning the strain effect to design novel Mg alloys with both high strength and ductility.Web of Science9522art. no. 22410

Huifang Feng - One of the best experts on this subject based on the ideXlab platform.

  • High Pressure Effects on the Properties of 〈110〉 {001} Dislocation in Superconducting ZnCNi3 and MgCNi3 Determined from First Principles Calculations Combined with an Improved Peierls-Nabarro Equation
    Journal of Superconductivity and Novel Magnetism, 2015
    Co-Authors: Zhenya Meng, Lili Liu, Huifang Feng
    Abstract:

    We have employed an improved Peierls-Nabarro (P-N) equation considering the discreteness effect of crystals to study the properties of 1/2 〈110〉 dislocation in the (001) plane in cubic anti-perovskites type superconducting materials ZnCNi3 and MgCNi3 under different pressure. The generalized-stacking-fault energy (GSFE) curves were calculated by using first-principles density functional theory (DFT). The core structures and Peierls Stress of the screw, mixed, and edge dislocation in the pressure range 0–50 GPa have been systematically researched by solving the modified P-N dislocation equation combining with calculation of GSFE curves. With increasing pressure, the Peierls Stress increases, but the core width decreases, and the Peierls Stress of mixed dislocations is in the region between screw and edge dislocations. Finally, the electronic structure further reveals the underlying mechanisms for the effects of dislocation on the electronic properties.

  • The Core Structure and Peierls Stress of 〈112¯0〉 Dislocations in MgB2 with Mg and B Vacancies
    Journal of Superconductivity and Novel Magnetism, 2015
    Co-Authors: Ping Shen, Huifang Feng, Rui Wang
    Abstract:

    The improved Peierls-Nabarro theory is employed to study the core structure and mobility of \(\langle 11\overline {2}0\rangle \) dissociated dislocations of MgB2. The generalized stacking fault energy entering the theory is calculated by using first-principle methods. The effects of Mg and B vacancies on the properties of \(\langle 11\overline {2}0\rangle \) dislocations are also presented. It is found that Mg vacancy can reduce the antiphase boundary energy and unstable stacking fault energy obviously compared with B vacancy. Peierls Stress of MgB2 with Mg vacancy is about 1/4 ∼1/5 of MgB2 and MgB2 with B vacancy.

  • the core structure and Peierls Stress of 112 0 dislocations in mgb2 with mg and b vacancies
    Journal of Superconductivity and Novel Magnetism, 2015
    Co-Authors: Ping Shen, Huifang Feng, Rui Wang
    Abstract:

    The improved Peierls-Nabarro theory is employed to study the core structure and mobility of \(\langle 11\overline {2}0\rangle \) dissociated dislocations of MgB2. The generalized stacking fault energy entering the theory is calculated by using first-principle methods. The effects of Mg and B vacancies on the properties of \(\langle 11\overline {2}0\rangle \) dislocations are also presented. It is found that Mg vacancy can reduce the antiphase boundary energy and unstable stacking fault energy obviously compared with B vacancy. Peierls Stress of MgB2 with Mg vacancy is about 1/4 ∼1/5 of MgB2 and MgB2 with B vacancy.

  • On the generalized stacking energy, core structure and Peierls Stress of the $$\frac{1} {2}\left\langle {110} \right\rangle \left\{ {110} \right\}$$ dislocations in alkali halide
    European Physical Journal B, 2012
    Co-Authors: Lancui Liu, Ronghua Wang, Huifang Feng
    Abstract:

    Using the improved P-N theory in which the lattice discrete effect is taken into account, the core width and Peierls Stress of the \(\frac{1} {2}\left\langle {110} \right\rangle \left\{ {110} \right\}\) dislocations in NaCl structure alkali halide have been investigated with the generalized stacking fault energy calculated by the ab initio calculation. The anisotropic of elasticity are taken into account while calculation the lattice discrete correction coefficient and the energy coefficient for dislocations. The discrete effect leads to a wider dislocation core in the improved P-N theory than that in the P-N theory. The obtained Peierls Stress are in agreement with the existing experimental results. The predicted Peierls Stress for edge dislocations in LiF and NaCl are 0.13 × 10−3 μ and 0.46 × 10−3 μ, respectively. The corresponding experimental values are 0.16 × 10−3 μ and 0.50 × 10−3 μ. It is also found that the Peierls Stress and the anisotropic factor decrease with the increasing radius of the positive ion for the same negative ion in alkali halide.

  • on the generalized stacking energy core structure and Peierls Stress of the frac 1 2 left langle 110 right rangle left 110 right dislocations in alkali halide
    European Physical Journal B, 2012
    Co-Authors: Lancui Liu, Ronghua Wang, Huifang Feng
    Abstract:

    Using the improved P-N theory in which the lattice discrete effect is taken into account, the core width and Peierls Stress of the \(\frac{1} {2}\left\langle {110} \right\rangle \left\{ {110} \right\}\) dislocations in NaCl structure alkali halide have been investigated with the generalized stacking fault energy calculated by the ab initio calculation. The anisotropic of elasticity are taken into account while calculation the lattice discrete correction coefficient and the energy coefficient for dislocations. The discrete effect leads to a wider dislocation core in the improved P-N theory than that in the P-N theory. The obtained Peierls Stress are in agreement with the existing experimental results. The predicted Peierls Stress for edge dislocations in LiF and NaCl are 0.13 × 10−3 μ and 0.46 × 10−3 μ, respectively. The corresponding experimental values are 0.16 × 10−3 μ and 0.50 × 10−3 μ. It is also found that the Peierls Stress and the anisotropic factor decrease with the increasing radius of the positive ion for the same negative ion in alkali halide.

Yao Shen - One of the best experts on this subject based on the ideXlab platform.

  • Quasi-periodic variation of Peierls Stress of dislocations in face-centered-cubic metals
    International Journal of Plasticity, 2017
    Co-Authors: Guisen Liu, Xi Cheng, Jian Wang, Kaiguo Chen, Yao Shen
    Abstract:

    Abstract The Escaig Stress, i.e. the shear Stress perpendicular to the Burgers vector, modulates the stacking fault area between two partials of a full dislocation, in turn, affects the mobility of the dislocation. In this paper, using the newly improved semi-discrete variational Peierls-Nabarro (SVPN) model we studied the variation of Peierls Stress ( τ p ) of dislocations in face-centered-cubic crystals with respect to the Escaig Stress. We found that τ p quasi-periodically oscillates and the oscillation gradually decreases with the increase of Escaig Stress. This quasi-periodic variation of τ p can be mathematically described by the combination of a sinusoidal and an exponential function, and further accounted for by the variation of the stacking fault width (SFW) between two partials during their movement under applied Stress. For the maximum τ p , SFW is about integral multiples of the Peierls period. For the minimum τ p , SFW is around half-integral multiples of Peierls period. The variation of τ p is associated with the oscillation magnitude of SFW from half-integral multiples to integral multiples of the Peierls period and then back to integral multiples of Peierls period caused by the Escaig Stress. Molecular dynamics (MD) simulations further examined quasi-periodic variation of τ p , validating the SVPN model's capability of predicting sophisticated behavior of dislocation under applied Stress.

  • Peierls Stress in face-centered-cubic metals predicted from an improved semi-discrete variation Peierls-Nabarro model
    Scripta Materialia, 2016
    Co-Authors: Guisen Liu, Xi Cheng, Jian Wang, Kaiguo Chen, Yao Shen
    Abstract:

    Abstract In order to quantitatively predict Peierls Stress, a semi-discrete variational Peierls-Nabarro model is improved by incorporating an additional gradient energy term into the energy functional. This gradient energy term is designed to effectively represent the influence of both the discreteness of atoms and the quick variations of the displacement profile in the dislocation core. Using face-centered-cubic metals as a model system for validation, we obtain a more accurate prediction of the displacement profile across the slip plane, and consequent precise Peierls Stress, within a few times the prediction from molecular dynamics calculations.

  • Dislocation movement over the Peierls barrier in the semi-discrete variational Peierls framework
    Scripta Materialia, 2009
    Co-Authors: Yao Shen, Xi Cheng
    Abstract:

    A new method has been developed to calculate the Peierls Stress ( τ p ) in the semi-discrete variational Peierls framework. It provides a physically transparent view of the variation of the dislocation core while overcoming the Peierls barrier, and with a minor extension it can simulate the coordination between leading and trailing partial dislocations. Calculations show that the relaxation of the slip profile reduces the Peierls Stress and the unstable stacking fault energy plays a critical role in determining τ p .