Molecular dynamics simulation on generalized stacking fault energies of FCC metals under preloading stress

Molecular dynamics(MD) simulations are performed to investigate the effects of stress on generalized stacking fault(GSF) energy of three fcc metals(Cu, Al, and Ni). The simulation model is deformed by uniaxial tension or compression in each of [111], [11-2], and [1-10] directions, respectively, before shifting the lattice to calculate the GSF curve. Simulation results show that the values of unstable stacking fault energy(γusf), stable stacking fault energy(γsf), and unstable twin fault energy(γutf) of the three elements can change with the preloaded tensile or compressive stress in different directions.The ratio of γsf/γusf, which is related to the energy barrier for full dislocation nucleation, and the ratio of γutf/γusf, which is related to the energy barrier for twinning formation are plotted each as a function of the preloading stress. The results of this study reveal that the stress state can change the energy barrier of defect nucleation in the crystal lattice, and thereby can play an important role in the deformation mechanism of nanocrystalline material.     

Behavior of an Extended Dislocation near an Elliptical Blunt Crack

The behavior of an extended dislocation near an elliptical blunt crack is investigated. The equilibrium separation between Shockley partials and the critical value of stacking fault energy for the formation of extended dislocations by dissociation reaction as well as the extended dislocation emission criterion are developed. The results show that the equilibrium separation increases as the extended dislocation tends to the blunt crack. If the stacking fault energy is comparable to the critical energy for dissociation in a perfect medium, complete dislocations can dissociate to form extended dislocations near the blunt crack. The critical stress intensity factor （SIF） for extended dislocation emission increases with the stacking fault energy and the curvature radius of the blunt crack tip. Moreover, the critical SIF for extended dislocation emission is far lower than the critical SIF for edge dislocation emission.     

Atomistic simulation of kink structure on edge dislocation in bcc iron

Based on the general theory of dislocation and kink, we have constructed the three kink models corresponding to the 1/2 （111）{011} and 1/2 （111）{112} edge dislocations （EDs） in bcc Fe using the molecular dynamics method. We found that the geometric structure of a kink depends on the type of ED and the structural energies of the atom sites in the dislocation core region, as well as the geometric symmetry of the dislocation core and the characteristic of the stacking sequence of atomic plane along the dislocation line. The formation energies and widths of the kinks on the 1/2 （111）{011} and 1/2 （111）{112} EDs are calculated, the formation energies are 0.05eV and 0.04eV, and widths are 6.02b and 6.51b, respectively （b is the magnitude of the Burgers vector）. The small formation energies indicate that the formation of kink in the edge dislocation is very easy in bcc Fe.     

Dislocation formation and twinning from the crack tip in Ni3Al: molecular dynamics simulations

The mechanism of low-temperature deformation in a fracture process of L12 Ni3Al is studied by molecular dynamic simulations.Owing to the unstable stacking energy,the [01ˉ1] superdislocation is dissociated into partial dislocations separated by a stacking fault.The simulation results show that when the crack speed is larger than a critical speed,the Shockley partial dislocations will break forth from both the crack tip and the vicinity of the crack tip;subsequently the super intrinsic stacking faults are formed in adjacent {111} planes,meanwhile the super extrinsic stacking faults and twinning also occur.Our simulation results suggest that at low temperatures the ductile fracture in L12 Ni3Al is accompanied by twinning,which is produced by super-intrinsic stacking faults formed in adjacent {111} planes.     

Dislocation energy and calculation from Peierls stress： a rigorous the lattice theory

In the classical Peierls--Nabarro (P-N) theory of dislocation, there is a long-standing contradiction that the stable configuration of dislocation has maximum energy rather than minimum energy. In this paper, the dislocation energy is calculated rigorously in the context of the full lattice theory. It is found that besides the misfit energy considered in the classical P-N theory, there is an extra elastic strain energy that is also associated with the discreteness of lattice. The contradiction can be automatically removed provided that the elastic strain energy associated with the discreteness is taken into account. This elastic strain energy is very important because its magnitude is larger than the misfit energy, its sign is opposite to the misfit energy. Since the elastic strain energy and misfit energy associated with discreteness cancel each other, and the width of dislocation becomes wide in the lattice theory, the Peierls energy, which measures the height of the effective potential barrier, becomes much smaller than that given in the classical P-N theory. The results calculated here agree with experimental data. Furthermore, based on the results obtained, a useful formula of the Peierls stress is proposed to fully include the discreteness effects.     

Energetics and electronic structure of refractory elements in the dislocation of NiAl

Using DMol and the discrete variational method within the framework of the density functional theory,we study the alloying effects of Nb,Ti,and V in the [100](010) edge dislocation core of NiAl.We find that when Nb(Ti,V) is substituted for Al in the center-Al,the binding energy of the system reduces 3.00 eV(2.98 eV,2.66 eV).When Nb(Ti,V) is substituted for Ni in the center-Ni,the binding energy of the system reduces only 0.47 eV(0.16 eV,0.09 eV).This shows that Nb(Ti,V) exhibits a strong Al site preference,which agrees with the experimental and other theoretical results.The analyses of the charge distribution,the interatomic energy and the partial density of states show that some charge accumulations appear between the impurity atom and Ni atoms,and the strong bonding states are formed between impurity atom and neighbouring host atoms due mainly to the hybridization of 4d5s(3d4s) orbitals of impurity atoms and 3d4s4p orbitals of host Ni atoms.The impurity induces a strong pinning effect on the [100](010) edge dislocation motion in NiAl,which is related to the mechanical properties of the NiAl alloy.     

Dislocation Dissociation Strongly Influences on Frank-Read Source Nucleation and Microplasticy of Materials with Low Stacking Fault Energy

The influence of dislocation dissociation on the evolution of Frank-Read （F-R） sources is studied using a three- dimensional discrete dislocation dynamics simulation （3D-DDD）. The classical Orowan nucleation stress and recently proposed Benzerga nucleation time models for F-R sources are improved. This work shows that it is necessary to introduce the dislocation dissociation scheme into 3D-DDD simulation, especially for simulations on micro-plasticity of small sized materials with low stacking fault energy.     

Brittle-ductile behavior of a nanocrack in nanocrystalline Ni: A quasicontinuum study

The effects of stacking fault energy, unstable stacking fault energy, and unstable twinning fault energy on the fracture behavior of nanocrystalline Ni are studied via quasicontinuum simulations. Two semi-empirical potentials for Ni are used to vary the values of these generalized planar fault energies. When the above three energies are reduced, a brittle-to-ductile transition of the fracture behavior is observed. In the model with higher generalized planar fault energies, a nanocrack proceeds along a grain boundary, while in the model with lower energies, the tip of the nanocrack becomes blunt. A greater twinning tendency is also observed in the more ductile model. These results indicate that the fracture toughness of nanocrystalline face-centered-cubic metals and alloys might be efficiently improved by controlling the generalized planar fault energies.     

Modification of the Peierls–Nabarro model for misfit dislocation

For a misfit dislocation, the balance equations satisfied by the displacement fields are modified, and an extra term proportional to the second-order derivative appears in the resulting misfit equation compared with the equation derived by Yao et al. This second-order derivative describes the lattice discreteness effect that arises from the surface effect. The core structure of a misfit dislocation and the change in interfacial spacing that it induces are investigated theoretically in the framework of an improved Peierls–Nabarro equation in which the effect of discreteness is fully taken into account. As an application, the structure of the misfit dislocation for a honeycomb structure in a two-dimensional heterostructure is presented.     

Effects of twin and stacking faults on the deformation behaviors of Al nanowires under tension loading

The effects of twin spacing and temperature on the deformation behavior of nanotwinned Al under tensile loading are investigated using a molecular dynamic(MD) simulation method.The result shows that the yield strength of nanotwinned Al decreases with the increase of twin spacing,which is related to the repulsive force between twin boundary and the dislocation.The result also shows that there is no strain-hardening at the yield point.On the contrary,the stress is raised by strain hardening in the plastic stage.In addition,we also investigate the effects of stacking fault thickness and temperature on the yield strength of the Al nanowire.The simulation results indicate that the stacking fault may strengthen the Al nanowire when the thickness of the stacking fault is below a critical value.     

Fe中<100>{010}刃位错芯结构的各向异性修正

在位错晶格理论基础上,采用改进的Peierls-Nabarro方程研究了Fe中<100>{010}刃位错在各向异性近似下的芯结构和Peierls应力. 各向异性近似下的晶格离散效应、切变模量和能量因子的表达式都已确切给出. 在这三个各向异性因素中,晶格离散效应和能量因子可以使位错宽度变窄,切变模量可以使位错宽度变宽. 相比于各向同性近似,各向异性近似下的位错宽度变窄了近20%,并且各向异性近似下的位错宽度与数值计算的结果相一致. 更为重要的是,各向异性使位错的Peierls应力数值几乎加倍,数量级也由 变成了 ,而这些都会显著影响位错的运动机制. 因此,各向异性对于位错来说非常重要,在研究位错芯结构以及运动机制时需要考虑各向异性的影响.     

Glide of dislocations in <1 1 1>{3 2 1} slip system: an atomistic study

Atomistic calculations are performed to investigate plastic slip in the <1?1?1>{3?2?1} system in body-centred cubic iron. Several modern interatomic potentials, developed over the last decade, are applied to compute the stacking fault γ-line energy in the {3?2?1} plane and the results are compared with the ab initio prediction. The applied potentials have shown strong deviations, but several potentials acquired good qualitative agreement with the ab initio data. Depending on the applied potential, the lowest value of the Peierls stress for the edge dislocation (ED) is 50 MPa (Ackland and Bacon from 1997) and the highest is 550 MPa (Dudarev and Derlet from 2005), while for the screw dislocation it is much higher, in the range 1–2 GPa. At finite temperature, however, the flow stress of the ED is found to decrease exponentially reaching a negligible value at about 200 K, irrespective of the applied potential. On the basis of the data obtained using Ackland–Mendelev potential from 2004, we conclude that the slip resistance of the <1?1?1>{3?2?1} system is in between the resistance of the <1?1?1>{1?1?0} and <1?1?1>{1?1?2} slip systems.     

Peierls–Nabarro model for dislocations in MgSiO3 post-perovskite calculated at 120 GPa from first principles

We present here the first numerical modelling of dislocations in MgSiO₃ post-perovskite at 120?GPa. The dislocation core structures and properties are calculated through the Peierls–Nabarro model using the generalized stacking fault (GSF) results as a starting model. The GSFs are determined from first-principle calculations using the VASP code. Dislocation properties such as planar core spreading and Peierls stresses are determined for the following slip systems: [100](010), [100](001), [100](011), [001](010), [001](110), [001](100), [010](100), [010](001), ½[110](001) and ½[110](110). Our results confirm that the MgSiO₃ post-perovskite is a very anisotropic phase with a plasticity dominated by dislocation glide in the (010) plane.     

Dislocation modeling in bcc lithium: A comparison between continuum and atomistic predictions in the modified embedded atoms method

In this study, the modified embedded-atom method (MEAM) was applied to compare the predictions of dislocation core properties obtained by molecular statics with the continuum predictions obtained in the framework of the simplified 1D-Peierls–Nabarro model. To this end, a set of four fictive Li potentials in the MEAM framework was proposed with the condition that all four potentials reproduce the same elastic constants, the same transition energies between bcc and fcc crystal structures, and between bcc and hcp crystal structures, while the unstable stacking fault energy on the plane {110} in the direction <111> was varied around the value predicted by first-principles. Within these potentials, direct atomistic calculations were performed to evaluate dislocation core properties such as dislocation half width and Peierls stress and the results were compared with continuum predictions. We found that the trends predicted by the Peierls–Nabarro model, i.e. (i) a decrease of the dislocation half width with increasing unstable stacking fault energy, and (ii) an increase of the Peierls stress with increasing the magnitude of the unstable stacking fault energy, were recovered using atomic calculations in the MEAM framework. Moreover, the magnitude of the dislocation half width and the Peierls stress calculated in the MEAM framework are in good agreement with the Peierls–Nabarro predictions when the dislocation half width is determined using a generic strategy. Specifically, the dislocation half width is defined as the distance for which the disregistery is included between b/4 and 3b/4. It was, therefore, demonstrated herein that the set of fictive potentials could be parameterized in the MEAM framework to validate or to disprove the continuum theory using atomistic methods.     

Three-loop on-shell charge renormalization without integration:\Lambda _{QED}^{\overline {MS} } to four loops

Using algebraic methods, we find the three-loop relation between the bare and physical couplings of one-flavourD-dimensional QED, in terms of Γ functions and a singleF ₃₂ series, whose expansion nearD=4 is obtained, by wreath-product transformations, to the order required for five-loop calculations. Taking the limitD→4, we find that the \(\overline {MS} \) coupling \(\bar \alpha (\mu )\) satisfies the boundary condition $$\begin{gathered} \frac{{\bar \alpha (m)}}{\pi } = \frac{\alpha }{\pi } + \frac{{15}}{{16}}\frac{{\alpha ^3 }}{{\pi ^3 }} + \left\{ {\frac{{11}}{{96}}\zeta (3) - \frac{1}{3}\pi ^2 \log 2} \right. \hfill \\ \left. { + \frac{{23}}{{72}}\pi ^2 - \frac{{4867}}{{5184}}} \right\}\frac{{\alpha ^4 }}{{\pi ^4 }} + \mathcal{O}(\alpha ^5 ), \hfill \\ \end{gathered} $$ wherem is the physical lepton mass and α is the physical fine structure constant. Combining this new result for the finite part of three-loop on-shell charge renormalization with the recently revised four-loop term in the \(\overline {MS} \) β-function, we obtain $$\begin{gathered} \Lambda _{QED}^{\overline {MS} } \approx \frac{{me^{3\pi /2\alpha } }}{{(3\pi /\alpha )^{9/8} }}\left( {1 - \frac{{175}}{{64}}\frac{\alpha }{\pi } + \left\{ { - \frac{{63}}{{64}}\zeta (3)} \right.} \right. \hfill \\ \left. { + \frac{1}{2}\pi ^2 \log 2 - \frac{{23}}{{48}}\pi ^2 + \frac{{492473}}{{73728}}} \right\}\left. {\frac{{\alpha ^2 }}{{\pi ^2 }}} \right), \hfill \\ \end{gathered} $$ at the four-loop level of one-flavour QED.     

Singular $$ \mathcal{R}$$ -Matrices and Drinfeld's Comultiplication

We compute the $\mathcal{R}$ -matrix which intertwines two dimensional evaluation representations with Drinfeld comultiplication for ${\text{U}}_q \left( {\widehat{{\text{sl}}}_{\text{2}} } \right)$ . This $\mathcal{R}$ -matrix contains terms proportional to the δ-function. We construct the algebra $A\left( \mathcal{R} \right)$ generated by the elements of the matrices L^±(z) with relations determined by $\mathcal{R}$ . In the category of highest-weight representations, there is a Hopf algebra isomorphism between $A\left( \mathcal{R} \right)$ and an extension $\overline {\text{U}} _q \left( {\widehat{{\text{sl}}}_{\text{2}} } \right)$ of Drinfeld's algebra.     

Structure and optical property changes of Nb_{2}O_{5} particles by Q-switched laser pulses in water

Monoclinic H-type Nb $_{2}$ O $_{5}$ powders subjected to Q-switched laser pulses in water were characterized by X-ray/electron diffraction and optical spectroscopy to have a significant optical property change with accompanied transformation into orthorhombic T-, pseudohexagonal TT-type and an amorphous phase. The T-Nb $_{2}$ O $_{5}$ nanoparticles were (100), (010), (001) and ( $\overline{2} $ 01) faceted and commonly in oriented intergrowth with TT-type or amorphized domains retaining the polymerized block units of the relic H-type. Such multiple-phase nanoparticles were hydrogenated and densified to modify Raman and FTIR bands and to show visible absorptions corresponding to a broad minimum band gap of 2.3–2.8 eV for potential opto-catalytic and electrochromic applications.     

Three-loop relation of quark\overline {MS} and pole masses

We calculate, exactly, the next-to-leading correction to the relation between the \(\overline {MS} \) quark mass, \(\bar m\) , and the scheme-independent pole mass,M, and obtain $$\begin{gathered} \frac{M}{{\bar m(M)}} \approx 1 + \frac{4}{3}\frac{{\bar \alpha _s (M)}}{\pi } + \left[ {16.11 - 1.04\sum\limits_{i = 1}^{N_F - 1} {(1 - M_i /M)} } \right] \hfill \\ \cdot \left( {\frac{{\bar \alpha _s (M)}}{\pi }} \right)^2 + 0(\bar \alpha _s^3 (M)), \hfill \\ \end{gathered} $$ as an accurate approximation forN _F?1 light quarks of massesM _i <M. Combining this new result with known three-loop results for \(\overline {MS} \) coupling constant and mass renormalization, we relate the pole mass to the \(\overline {MS} \) mass, \(\bar m\) (μ), renormalized at arbitrary μ. The dominant next-to-leading correction comes from the finite part of on-shell two-loop mass renormalization, evaluated using integration by parts and checked by gauge invariance and infrared finiteness. Numerical results are given for charm and bottom \(\overline {MS} \) masses at μ=1 GeV. The next-to-leading corrections are comparable to the leading corrections.     

Neutral meson oscillations and equivalence principle for particles and antiparticles

Oscillations of neutral meson (K ⁰-$ \overline {K^0 } $ \overline {K^0 } , D ⁰-$ \overline {D^0 } $ \overline {D^0 } , and B ⁰-$ \overline {B^0 } $ \overline {B^0 } are extremely sensitive to the meson and antimeson energies at rest. This energy is determined as mc ²—with the corresponding inertial mass—and as the energy of gravitational interaction. Assuming that the CPT theorem is correct for inertial masses and estimating the gravitational potential for which the largest contribution originates from the field of the galaxy center, we obtain the estimate from experimental data on K ⁰-$ \overline {K^0 } $ \overline {K^0 } oscillations:

Mixing and CP violation: fromB^0 - \overline {B^0 } to T^0 - \overline {T^0 }

We extend from \(B^0 - \overline {B^0 } to T^0 - \overline {T^0 } \) the study of neutral pseudoscalar mesons with respect to mixing and CP violation. The possibility of a quite large top quark mass necessitates a more careful computation of the box diagram amplitude. Our result is that, while in \(B^0 - \overline {B^0 } \) systems CP violation is expected to be very small (～10^?6) and mixing quite large (10–20% or more), precisely the opposite occurs for \( T^0 - \overline {T^0 } \) . In particular, CP violation in the \( T_u^0 - \overline {T_u^0 } \) system could be of the same order of magnitude as in the \(K^0 - \overline {K^0 } \) system (～10^?3) while the mixing is totally negligible.