A discussion of the structure and behaviour of dipole walls in cyclic plasticity

Assuming that cross-slip by thermally activated migration of jogs can cause annihilation of screw dislocation dipoles without macroscopic crystallographic confinement of cross-slip to the cross-slip plane, an attempt is made to re-derive earlier equations for the saturation stress and the plastic strain amplitude in persistent slip bands. These equations had been based on the assumption that cross-slip could occur only on a cross-slip plane making an obtuse angle with the slip plane, an assumption which limits the mean free path of screw dislocations. The key new assumption is that the walls of edge dislocation dipoles which dominate the structure of persistent slip bands are penetrable obstacles, which increases the mean free paths of the mobile dislocations. Agreement with experiment is obtained if the penetration probability in cyclic saturation is on average one third, a value for which there is a simple rationalization. Estimates can be made of the wall width, which is independent of temperature, in agreement with recent observations by Tippelt et al. However, the main unresolved difficulty is the role of the very fine dipoles, particularly the faulted dipoles, in the walls. A further weakness in the theory is that it ignores the cutting of dipoles by the cross-slipping screw dislocations. Despite these problems, the distribution of dipole heights can be worked out and is found to be in reasonable agreeement with experiment.     

铝-镁合金的高温变形机构

用变温变速的拉伸试验,研究了Al-3％Mg和Al-6％Mg合金的高温变形行为,求得各温度下的激活能、激活体积和频率因子等。证明在250—400℃温度范围内,铝-镁合金变形机构可能是带割阶的螺位错作非保守性运动,变形方程为ε=Nι_jb²zAνexp{-(△H_s-ι_jb²τ)/(kT)}。然后计算得到两种合金在不同温度下的割阶间距ι_j,运动位错密度ρ=Nι_j,割阶密度N以及位错速度等数值。     

Ordinary dislocation configurations in high Nb-containing TiAl alloy deformed at high temperatures

Abstract

High Nb-containing TiAl (Nb–TiAl) alloys possess mechanical properties at elevated temperatures superior to conventional TiAl alloys. However, the strengthening mechanisms induced by Nb addition have been discussed controversial for a long time. In the present study, the dislocation structures in a polycrystalline high Nb–TiAl alloy after tensile tests at 700 and 900 °C were investigated by transmission electron microscope (TEM) observation. The results show that abundant double cross slip of ordinary dislocations is activated in the samples deformed at 700 °C. The dislocations are pinned at the jogs and numerous dipoles are observed. Debris can be commonly observed in the vicinity of screw dislocations. Trace analysis shows that the cross-slip plane is (1?1?0)γ at 700 °C but (1?1?1)γ octahedral plane at 900 °C. Three-dimensional (3D) dislocation structures, caused by cross-slip and annihilation of ordinary dislocations, were observed along the screw orientation. The dipoles and debris produced by high-temperature cross slip can be important for the strengthening of high Nb–TiAl alloys.     

Structure factors that influence the stability of plastic strain of bcc metals under tensile load

The effect of the Peierls stress on the ultimate tensile stress and uniform strain prior to the formation of a neck during stretching of metals and alloys with bcc structure is theoretically analyzed. The analysis is based on the equation for the variation of the dislocation density with deformation; this equation determines the shape of the work-hardening curve for a bcc material and the effect of the Peierls stress on the parameters of this equation (the annihilation coefficient for screw dislocations). Using the Considére condition for plastic instability of the neck type, the ultimate tensile stress and the magnitude of uniform strain are found theoretically as a function of the Peierls stress at different temperatures below 0.15T _m , where T _m is the melting temperature of the bcc metal. Theoretical results are illustrated with experimental data on the temperature dependences of the annihilation coefficients for screw dislocations and of the magnitude of uniform strain in molybdenum and Armco iron.     

Dislocation dynamics in doped NaCl single crystals determined by pulsed NMR between RT and 300°C

The mean free path of mobile dislocations is measured by determination of the spin-lattice relaxation rate of deforming NaCl single crystals as a function of temperature and of the concentration of Ca⁺⁺ impurities. The latter may influence the magnitude of the mean free path but this depends to a large extent on the point defect configuration. The degree of association and the mobility of the point defects is studied by measuring the spin-lattice relaxation rate without deforming the samples. On the other hand the distribution of dislocations varies also with temperature and this affects the mobility of dislocations too. The work-hardening rate of the crystals is compared with the mean free path as a function of temperature and it is shown that both quantities have extremes under the influence of competitive mechanisms such as an enhanced thermal activation of dislocations at obstacles, an increasing mobility of point defects, and increasing number of intersections of mobile dislocations with dislocation dipoles.     

Hydrogen diffusion in the elastic fields of dislocations in iron

The effect of dislocation stress fields on the sink efficiency thereof is studied for hydrogen interstitial atoms at temperatures of 293 and 600 K and at a dislocation density of 3 × 10¹⁴ m^–2 in bcc iron crystal. Rectilinear full screw and edge dislocations in basic slip systems 〈111〉{110}, 〈111〉{112}, 〈100〉{100}, and 〈100〉{110} are considered. Diffusion of defects is simulated by means of the object kinetic Monte Carlo method. The energy of interaction between defects and dislocations is calculated using the anisotropic theory of elasticity. The elastic fields of dislocations result in a less than 25% change of the sink efficiency as compared to the noninteracting linear sink efficiency at a room temperature. The elastic fields of edge dislocations increase the dislocation sink efficiency, whereas the elastic fields of screw dislocations either decrease this parameter (in the case of dislocations with the Burgers vector being 1/2〈111〉) or do not affect it (in the case of dislocations with the Burgers vector being 〈100〉). At temperatures above 600 K, the dislocations affect the behavior of hydrogen in bcc iron mainly owing to a high binding energy between the hydrogen atom and dislocation cores.     

Low temperature electron transport in phosphorus-doped ZnO films grown on Si substrates

Low temperature magneto-transport properties and electron dephasing mechanisms of phosphorus-doped ZnO thin films grown on (1 1 1) Si substrates with Lu₂O₃ buffer layers using pulsed laser deposition were investigated in detail by quantum interference and weak localization theories under magnetic fields up to 10 T. The dephasing length follows the temperature dependence with an index p≈1.6 at higher temperatures indicating electron–electron interaction, yet becomes saturated at lower temperatures. Consistent with photoluminescence measurements and the multi-band simulation of the electron concentration, such behavior was associated with the dislocation densities obtained from x-ray diffraction and mobility fittings, where charged edge dislocations acting as inelastic Coulomb scattering centers were affirmed responsible for electron dephasing. Owing to the temperature independence of the dislocation density, the phosphorus-doped ZnO film maintained a Hall mobility of 4.5 cm² V⁻¹ s⁻¹ at 4 K.     

Atomistic simulation of the interaction between mobile edge dislocations and radiation-induced defects in Fe-Ni-Cr austenitic alloys

The classical molecular dynamics method is employed to simulate the interaction of edge dislocations with interstitial Frank loops (2 and 5 nm in diameter) in the Fe-Ni₁₀-Cr₂₀ model alloy at the temperatures T = 300–900 K. The examined Frank loops are typical extended radiation-induced defects in austenitic steels adapted to nuclear reactors, while the chosen triple alloy (Fe-Ni₁₀-Cr₂₀) has the alloying element concentration maximally resembling these steels. The dislocation-defect interaction mechanisms are ascertained and classified, and their comparison with the previously published data concerning screw dislocations is carried out. The detachment stress needed for a dislocation to overcome the defect acting as an obstacle is calculated depending on the material temperature, defect size, and interaction geometry. It is revealed that edge dislocations more efficiently absorb small loops than screw ones. It is demonstrated that, in the case of small loops, the number of reactions accompanied by loop absorption increases with temperature upon interaction with both edge and screw dislocations. It is established that Frank loops are stronger obstacles to the movement of screw dislocations than to the movement of edge ones.     

Electrically stimulated movement of edge dislocations in silicon in the temperature range 300–450 K

The movement of edge dislocations and the related acoustic emission of Si (111) carrying a direct current of density 0.5?5×10⁵ A/m² in the [110] direction are studied in the temperature range T=300–450 K. It is shown that the basic mechanism of dislocation movement is the electric wind determining the magnitude of the effective charge (per atom of the dislocation line) Z _eff=0.06 (n-Si) and ?0.01 (p-Si). Matching theory with experimental data has made it possible to determine the main contribution of edge dislocations to the acoustic-emission response of the silicon samples under investigation. The characteristic transition frequencies of dislocations in n-and p-Si from one metastable state into another are found to be f _max=0.1–0.5 Hz. The numerical values of the diffusion coefficient for atoms in the dislocation impurity atmosphere are estimated as 3.2×10^?18 m²/s (n-Si) and 1.5×10^?18 m²/s (p-Si).     

Theory of electrical resistance of multivalley semiconductors with screw dislocations

The diffusion theory of electrical resistance in multivalley semiconductors of Si-type with screw dislocations is developed. Intervalley electron transitions are taken into account. The effect of the inhomogeneous dislocation distribution on the electrical resistance of the crystal is considered.It is shown that randomly distributed dislocations having the mean density 10¹⁰ cm–2 contribute some percents to the electrical resistance at room temperature. Intervalley transitions make this contribution much lower (by one order or more). The inhomogeneity of dislocation distribution enhances the electrical resistance several orders as compared with randomly distributed dislocations.     

Dislocation mobility in C<Subscript>60</Subscript> fullerite crystals

The dependences of the path of leading dislocations in indentation rosette rays on the load, the loading time, and the indentation temperature in the range 260 < T ≤ 373 K were studied for C₆₀ fullerite crystals. The dislocation mobility parameters are estimated: the exponent m characterizing the stress dependence of the dislocation velocity depends on the structural perfection of the crystal and ranges from 2.3 to 24.5, the activation energy for dislocation motion ΔH ₀ ? (0.4–0.5) eV, and the velocity of leading dislocations in indentation rosette rays v _l ? 10^?5?10^?4 cm/s. The data from micro-and macromechanical experiments are shown to agree with each other. The dislocation mobility is assumed to be controlled by the dislocation interaction with local barriers.     

Mobility of edge and screw dislocations in γ-irradiated LiF crystals

The free path lengths of ensembles of edge and screw dislocations in the stress field of a concentrated load are studied in γ-irradiated LiF crystals. The relative mobility of edge and screw dislocations is found to depend substantially on the irradiation dose and temperature. The results obtained are discussed in the context of additional retardation of screw dislocations with dislocation debris that appears during double cross slip.     

The interaction of dislocation loop and γ' precipitate in nickel based alloys

The nucleation and growth of interstitial loops during irradiation has a : ontrolling effect on the subsequent swelling behaviour of metals. In nickel based alloys containing ordered γ' precipitate (Ni₃Al, Ti), interactions occur between the nucleated loops and γ' particles. This effect has been studied in two nickel based alloys using a High Voltage Electron Microscope.

For the case of Nimonic 80A alloy containing 18% volume fraction : gamma;' precipitate, dislocation loop-particle interactions obeyed the developed isotropic elasticity theory.²'³'¹² Consequently, rather low dislocation densities were developed and the swelling resistance was high during electron irradiation. In Nimonic 115A alloy, loop nucleation and growth was dependent on the availability of interfacial dislocation surrounding the γ' particles.

With regard to the swelling behaviour of γ' hardened alloys, it : s concluded that several mechanisms contribute to make these materials resistant.

Coherency strains at the γ' particles reduce the density of : limbing dislocations.

The γ' precipitate affects the climb efficiency of the : ucleated dislocations by:

pinning the dislocation line, thus introducing a line tension force : hich opposes dislocation climb and reduces swelling;

reducing the available volume of material in which dislocation loops : an nucleate and grow.     

Molecular dynamic simulation of the CsCl–Al2O3 interface

The interface between solid cesium chloride and α-aluminum oxide was simulated by molecular dynamics technique. It was shown that due to a misfit between lattices of the components the interfacial contact may be presented as a small-angle boundary saturated with dislocations. Also a domain structure is formed. The dislocations and interdomain boundaries act as a source of defects and give rise to the total ionic mobility along the interface and boundaries. According to the calculation at a temperature of nearly 70% of the melting point, the diffusion coefficients of ions along misfit dislocation cores and domain walls, ∼ 10^– 6 cm²/s, are only an order of magnitude lower than the corresponding values for molten salts.     

Equilibrium and passing properties of dislocation dipoles

Static and dynamic properties of dislocation dipoles are investigated under isotropic and anisotropic elasticity. In elastically isotropic systems for a dislocation character between 35 and 40°, a dipole assumes the same stress-free equilibrium angle of 90° as the screw dipole. This can be affected by elastic anisotropy, as in Cu where the equilibrium angle assumed by a screw dipole (≈59°) is unchanged up to a dislocation character of 22°. In contrast, the static properties of near-edge dislocation dipoles are little influenced by elastic anisotropy. Certain dipole passing properties, not the passing stress however, are also modified by elastic anisotropy. For large heights and/or in the case of undissociated dislocations, the minimum passing stress corresponds to a dipole character of ～60° and it exhibits a sharp maximum in screw orientation. Reasonably moderate dislocation reorientations should facilitate the passing of near-screw dislocations in fatigue channels. Within a certain range of applied stresses, the passing of dipoles, comprised of unlike attractive dislocations, is accompanied by the sweeping of one dislocation by the other over a limited distance. Dissociation plays a prominent role in determining both static and dynamic properties for dipole heights less than a few times the dissociation distance of an isolated dislocation.     

Effect of temperature on the dislocation structure of the ordered alloy Ni3(Fe,Cr)

Transmission electron microscopy is used to study the dislocation structure of ordered polycrystalline Ni₃(Fe, Cr) alloy after deformation at temperatures of 293, 473, 673, and 773°K. The flow stress σ is plotted as a function of the density of dislocations ρ. It is observed that there is a direct proportionality between σ and ρ^1/2, which indicates that the relation τ= αGbρ^1/2 is satisfied, where τ is the shear stress, G is the shear modulus, b is the Burgers vector, and α is a coefficient weakly dependent on the density of dislocations. The values of α are found for different deformation temperatures from the slope of the lines. It is found that α decreases with increasing deformation temperature. When the temperature is increased from 293 to 773°K the reduction in α is about 20% in agreement with estimates of the resistance to motion by superdislocations caused by nonconservative drag of dislocation jogs.     

Structural properties of 10 μm thick InN grown on sapphire (0001)

The structural properties of a 10 μm thick In-face InN film, grown on Al₂O₃ (0001) by radio-frequency plasma-assisted molecular beam epitaxy, were investigated by transmission electron microscopy and high resolution x-ray diffraction. Electron microscopy revealed the presence of threading dislocations of edge, screw and mixed type, and the absence of planar defects. The dislocation density near the InN/sapphire interface was 1.55×10¹⁰ cm⁻², 4.82×10⁸ cm⁻² and 1.69×10⁹ cm⁻² for the edge, screw and mixed dislocation types, respectively. Towards the free surface of InN, the density of edge and mixed type dislocations decreased to 4.35×10⁹ cm⁻² and 1.20×10⁹ cm⁻², respectively, while the density of screw dislocations remained constant. Using x-ray diffraction, dislocations with screw component were found to be 1.2×10⁹ cm⁻², in good agreement with the electron microscopy results. Comparing electron microscopy results with x-ray diffraction ones, it is suggested that pure edge dislocations are neither completely randomly distributed nor completely piled up in grain boundaries within the InN film.     

Evidence from numerical modelling for 3D spreading of [001] screw dislocations in Mg2SiO4 forsterite

Computer simulations have previously been used to derive the atomic scale properties of the cores of screw dislocations in Mg₂SiO₄ forsterite by direct calculation using parameterized potentials and via the Peierls–Nabarro model using density functional theory. We show that, for the [001] screw dislocation, the parameterized potentials reproduce key features of generalized stacking fault energies when compared to the density functional theory results, but that the predicted structure of the dislocation core differs between direct simulation and the Peierls–Nabarro model. The [001] screw dislocation is shown to exhibit a low-energy non-planar core. It is suggested that for this dislocation to move its core may need to change structure and form a high-energy planar structure similar to that derived from the Peierls–Nabarro model. This could lead to dislocation motion via an unlocking–locking mechanism and explain the common experimental observation of long straight screw dislocation segments in deformed olivine.     

The peierls energy and kink energy in fcc metals

In fcc crystals, dislocations are dissociated on the {111} glide plane into pairs of partial dislocations. Since each partial interacts individually with the Peierls potential and is coupled to its neighbour by a stacking fault, periodic variations in the separation distance d of the partials occur when dislocations running along closed packed lattice directions are displaced. This can drastically reduce the effective Peierls stress. By using the Peierls model the structure of 0°, 30°, 60° and 90° dislocations in a typical fcc metal with the elastic properties of Cu and a stacking-fault energy γ₀ in the interval 0.04?≤?γ₀?≤?0.05?J/m² was studied, and the magnitude of the Peierls energy ΔE _P and the resulting kink energies E _K were determined. Since the energies involved are of the order of 10^?3?eV/b or less, their magnitude cannot be asserted with high confidence, considering the simplifying assumptions in the model. The difference in the changes of the core configuration during displacement of dislocations of different orientations should, however, be of physical significance. It is found that a dissociated 60° dislocation generally has a higher effective Peierls energy than a screw dislocation, but the reverse is true for the kink energy, at least in Cu.     

铁磷合金中的Snoek-Kê-K?ster峰

用真空葛氏摆,研究了Fe-C+N-P合金系冷加工试样内耗。发现置换式固溶元素磷,强烈减低铁的S-K-K内耗(Q^-1)、降低内耗峰温度(T_p)和明显减小其弛豫激活能(H)。在铁中磷的固溶限度以下,内耗峰高度(Q_h^-1)随合金中磷浓度的三分之二次方(即位错线上磷浓度平方)C_p^2/3增加而线性减低。实验结果符合Schoeck理论。本文还讨论了内耗机制,认为它是非螺(包括刃)位错段拖曳Cottrell气团间隙溶质原子移动产生的。位错段运动以弯曲的方式进行。 关键词：