Relation between the activation parameters of low-temperature slip and the mean-square amplitude of atomic vibrations in cubic metals

The available data on various activation parameters of low-temperature slip in 9 body-centred cubic and 5 face-centred cubic elements have been examined as a function of a single microscopic parameter, namely mean-square amplitude of atomic vibrations <u ²>, specific to the material. It is found that for a given crystal structure, the microscopic parameters of the unit activation process of yielding, e.g. the initial length of dislocation segment, the critical height of the kink-pair nucleated, the associated activation volume, the binding energy per interatomic spacing along the glide dislocation on the slip plane etc. correlate well with the mean-square amplitude of atomic vibrations <u ²> through a power regression formula.     

Kinetics of flow stress in crystals with high intrinsic lattice friction

A relatively simple theoretical model, based on the concept of kink-pair mode of escape of screw dislocations trapped in Peierls valleys, has been developed to account for the observed temperature dependence of the critical resolved shear stress (CRSS), τ, and of the associated activation volume, v, in crystals with high intrinsic lattice friction at rather low temperatures. In this model, the CRSS varies with temperature T as τ^1/2?=?A–BT, and the associated activation volume v depends on temperature T as v ^?1?=?C–DT, where A, B, C and D are positive constants. Moreover, the activation volume v is found to be a function of τ such that vτ^1/2 is constant for a given slip system. Data analysis of the temperature dependence of the CRSS of W, α-Fe, Cr and V metal crystals shows excellent agreement between theory and experiment in both regime III (low temperature or high stress) and regime II (intermediate temperature/stress). However, the predicted temperature and stress dependence of the activation volume are borne out by experiment in regime II, but lack quantitative agreement in regime III. On the other hand, the CRSS of CdTe crystals at low temperatures (T?≤?200?K) is determined by the Peierls mechanism, whereas the weak temperature dependence of the CRSS above 200?K is probably governed by the breakaway of edge dislocation segments from arrays of pinning points due to localized defects in the crystal.     

Dislocation structure and dynamics govern pop-in modes of nanoindentation on single-crystal metals

ABSTRACT

There are two types of pop-in mode that have been widely observed in nanoindentation experiments: the single pop-in, and the successive pop-in modes. Here we employ the molecular dynamics (MD) modelling to simulate nanoindentation for three face-centred cubic (FCC) metals, including Al, Cu and Ni, and two body-centred cubic (BCC) metals, such as Fe and Ta. We aim to examine the deformation mechanisms underlying these pop-in modes. Our simulation results indicate that the dislocation structures formed in single crystals during nanoindentation are mainly composed of half prismatic dislocation loops. These half prismatic dislocation loops in FCC metals are primarily constituted of extended dislocations. Lomer–Cottrell locks that result from the interactions between these extended dislocations can resist the slipping of half dislocation loops. These locks can build up the elastic energy that is needed to activate the nucleation of new half dislocation loops. A repetition of this sequence results in successive pop-in events in Al and other FCC metals. Conversely, the half prismatic dislocation loops that form in BCC metals after first pop-in are prone to slip into the bulk, which sustains plastic indentation process after first pop-in and prevents subsequent pop-ins. We thus conclude that pop-in modes are correlated with lattice structures during nanoindentation, regardless of their crystal orientations.     

Kinetics of Plastic Deformation in CuBr Single Crystals at Low Temperatures

Single crystals of CuBr with zincblende structure, deformed in compression at a strain rate 2×10^-4 s^-1 between room and liquid-nitrogen temperatures, exhibit two well-defined regions in the critical resolved shear stress (CRSS) versus temperature relationship. At rather low temperatures in the range from 78 to 150 K, the slope d ln /dT of the straight line fitted to the data points plotted in log-linear coordinates is found to be 2.9 times greater than that at temperatures between 150 and 300 K. Similar behaviour is also observed in the case of temperature dependence of activation volume associated with the CRSS. Data analysis in terms of the kink-pair nucleation model of plastic flow shows that stress-assisted thermally-activated escape of screw dislocations trapped in Peierls troughs induces slip below about 150 K. At temperatures above 150 K, CRSS is determined by the unpinning of edge-dislocation segments from groups of randomly dispersed point defects, e.g. residual gaseous and metallic impurities, deformation-induced defects formed during the pre-yield stage etc.     

Face-centred cubic to body-centred cubic phase transformation under [1 0 0] tensile loading

Molecular dynamics simulation was used to verify a speculation of the existence of a certain face-centred cubic (FCC) to body-centred cubic (BCC) phase transformation pathway. Four FCC metals, Ni, Cu, Au and Ag, were stretched along the [1?0?0] direction at various strain rates and temperatures. Under high strain rate and low temperature, and beyond the elastic limit, the bifurcation of the FCC phase occurred with sudden contraction along one lateral direction and expansion along the other lateral direction. When the lattice constant along the expansion direction converged with that of the stretched direction, the FCC phase transformed into an unstressed BCC phase. By reducing the strain rate or increasing the temperature, dislocation or ‘momentum-induced melting’ mechanisms began to control the plastic deformation of the FCC metals, respectively.     

Analysis of temperature and concentration dependence of flow stress in KCl–KBr single crystals with special reference to solute distribution

Available data on the temperature and concentration dependence of critical resolved shear stress (CRSS) of KCl–KBr solid-solution crystals containing 9, 17, 27 and 45?mol% KBr in the temperature range 77–230?K have been analyzed within the framework of the kink-pair nucleation model of plastic flow in solid- solution crystals. It is found that CRSS τ decreases with increasing temperature T in accordance with the model relation lnτ?=?A???BT, where A and B are positive constants. The CRSS τ at a given temperature depends on solute concentration c as τ?∝?c^p , where exponent p has a value between 0.33 and 0.57 as temperature T rises from 0 to 230?K. The model parameter W _o, i.e. binding energy between the edge-dislocation segment L _o involved in the unit activation process and the solute atoms close to it (T?→?0?K), which is inversely proportional to B, increases with solute concentration c monotonically as W _o?∝?c ^0.33 up to a critical value c _m?=?35?mol% KBr, which is in reasonable agreement with the model prediction W _o?∝?c ^0.25. However, W _o decreases with an increase in c beyond c _m, which indicates somewhat ordered distribution of solute in the host lattice of concentrated KCl–KBr solid solutions with c?>?c _m.     

On low temperature glide of dissociated 〈1 1 0〉 dislocations in strontium titanate

An elastic interaction model is presented to quantify low temperature plasticity of SrTiO₃ via glide of dissociated 〈1 1 0〉{1 1 0} screw dislocations. Because 〈1 1 0〉 dislocations are dissociated, their glide, controlled by the kink-pair mechanism at T < 1050 K, involves the formation of kink-pairs on partial dislocations, either simultaneously or sequentially. Our model yields results in good quantitative agreement with the observed non-monotonic mechanical behaviour of SrTiO₃. This agreement allows to explain the experimental results in terms of a (progressive) change in 〈1 1 0〉{1 1 0} glide mechanism, from simultaneous nucleation of two kink-pairs along both partials at low stress, towards nucleation of single kink-pairs on individual partials if resolved shear stress exceeds a critical value of 95 MPa. High resolved shear stress allows thus for the activation of extra nucleation mechanisms on dissociated dislocations impossible to occur under the sole action of thermal activation. We suggest that stress condition in conjunction with core dissociation is key to the origin of non-monotonic plastic behaviour of SrTiO₃ at low temperatures.     

Evaluating the effects of loading parameters on single-crystal slip in tantalum using molecular mechanics

This study is aimed at developing a physics-based crystal plasticity finite element model for body-centred cubic (BCC) metals, through the introduction of atomic-level deformation information from molecular dynamics (MD) investigations of dislocation motion at the onset of plastic flow. In this study, three critical variables governing crystal plasticity mediated by dislocation motion are considered. MD simulations are first performed across a range of finite temperatures up to 600K to quantify the temperature dependence of critical stress required for slip initiation. An important feature of slip in BCC metals is that it is not solely dependent on the Schmid law measure of resolved shear stress, commonly employed in crystal plasticity models. The configuration of a screw dislocation and its subsequent motion is studied under different load orientations to quantify these non-Schmid effects. Finally, the influence of strain rates on thermal activation is studied by inducing higher stresses during activation at higher applied strain rates. Functional dependence of the critical resolved shear stress on temperature, loading orientation and strain rate is determined from the MD simulation results. The functional forms are derived from the thermal activation mechanisms that govern the plastic behaviour and quantification of relevant deformation variables. The resulting physics-based rate-dependent crystal plasticity model is implemented in a crystal plasticity finite element code. Uniaxial simulations reveal orientation-dependent tension–compression asymmetry of yield that more accurately represents single-crystal experimental results than standard models.     

Atomic modeling of irradiation-induced hardening

We review recent results obtained by Molecular Dynamics (MD) simulations on the elementary interaction mechanisms between dislocations and irradiation defects, with the aim to obtain a fundamental understanding of plasticity in irradiated metals. The reactions obtained included defect shear, drag and absorption in edge and screw dislocations. We present the state of the art in both FCC and BCC metals and discuss the challenges faced by MD simulations, in particular in BCC metals in order to realistically simulate the thermally-activated glide of screw dislocations in the presence of obstacles. To cite this article: D. Rodney, C. R. Physique 9 (2008).     

On the investigation of magnetic critical phenomena in ferromagnets by μSR and PAC

On the basis of current theoretical views on the critical phenomena in isotropic Heisenberg ferromagnets the power temperature behavior Λ=c(τ)λ₀τ^-w has been derived for the muon spin relaxation rate Λ as π-T _c ⁻¹ (T-T _c ) → 0⁺. It is shown that the crossover from an exchange critical regime to a dipolar one is accompanied not only with the change in the critical exponentw in the above law, but also with the reduction of the coefficientc(π). A comparison with the temperature behaviour of the inverse nuclear relaxation timet _R ⁻¹ measured in the PAC experiment is carried out.     

Evolution of dislocation structure during deformation of γ-irradiated LiF crystals

The effect of γ irradiation on the mechanical characteristics and dislocation structure of slip bands in LiF crystals is studied at doses D⩽7.3×10⁸ R. Irradiation causes a substantial increase (up to a factor of 30) in the yield stress τ _y of the crystals, with τ _y ∝ D ^0.4 in the first approximation. The deformation shear increases in the slip bands of irradiated crystals, as do the densities of the screw and edge dislocation components, while the dislocation mean free paths decrease. Irradiation also raises the probability of twinning cross slip for screw dislocations. The observed effects are assumed to be related to the formation of a different kind of defects in the irradiated crystals, primarily clusters of implanted atoms. Fiz. Tverd. Tela (St. Petersburg) 39, 1072–1075 (June 1997)     

Elastic shape memory effect in In-Pb alloys in the temperature range 0.48–180 K

Pseudoelasticity caused by pseudotwinning in short-range ordered In-Pb alloys (6, 8 and 11.6 at. % Pb) is studied in the temperature range 0.48–180 K. The mechanical hysteresis parameters, namely, the thermodynamic stress τ _T which provides the reversibility of plastic deformation and the frictional stress τ _f which characterizes the resistance offered by crystal lattice and its defects to twin boundaries motion are estimated. It is found that athermal processes determine the reversible deformation: the mechanical parameters τ _T and τ _f do not depend on temperature and strain rate. The stress τ _T increases and the stress τ _f decreases with increasing Pb content. One of the main conditions of the exhibition of superelasticity is the fulfillment of the inequality τ _T >τ _f .     

Thermopower of Al1−x Six solid solutions in vicinity of lattice instability

The thermopower coefficient as a function of temperature, S(T), has been measured in nonequilibrium superconductors, such as Al_1−x Six substitutional solid solutions and Al-Si alloys on various decay stages. When aluminum is substituted with silicon, the contribution to the thermopower due to phonon-drag effects, which are dominant in pure aluminum at low temperatures, is suppressed, and low-temperature anomalies in S(T) detected in compositions near lattice instability limit are determined by the diffusion component of the thermopower. The low-temperature anomalies in the thermopower and the notable increase in the coefficient in front of the linear term in S(T) are attributed to effects of thermopower renormalization due to the electron-phonon interaction enhancement with “soft modes” in the face-centered cubic (FCC) lattice of Al_1−x Six solid solutions. The nature of these anomalies in S(T) is analyzed in terms of the Kaiser and Reizer-Sergeev models. Zh. éksp. Teor. Fiz. 113, 339–351 (January 1998)     

Size effects under plastic deformation of microcrystals and nanocrystals

A theoretical analysis of size effects in plastically deformed crystals with transverse sizes in micro and nanometer ranges has been performed in the framework of the dislocation-kinetic approach. The analysis is based on the evolution equation of the dislocation density in these crystals and takes into account the generation of dislocations from surface dislocation sources and the escape of dislocations from the crystal through the crystal surface. It has been established that the generation of dislocations from the sources leads to a strong strain hardening of the crystal and that the escape of dislocations through the crystal surface results in a fast equilibration of these two kinetic processes. As a result, there occurs a strong “exhaustion” of strain hardening of thin crystals at the early stage of their plastic deformation in accordance with experiments. According to the theory, the flow stresses σ and transverse sizes D of microcrystals and nanocrystals are related by the expressions σ ∼ D ⁻ⁿ (n = 0.625–1.0), which are in agreement with the experiment.     

Deformation of Cd-based alloys single crystals at very low temperatures

The temperature dependence of the critical resolved shear stress — CRSS on Cd-Ag andCd-Zn single crystals was studied at very low temperatures 1·5–80 K. The deformation experi-ments were made by a creep technique. The CRSS for Cd-Ag alloys was determined from re-constructed shear stress — shear strain curves, while the method of one sample was applied tothe determination of ₀-T dependence for Cd-Zn alloys. The difference in the temperaturedependences of ₀ for both Cd-based alloys can be caused by different methods for determiningthe CRSS.     

Longitudinal field relaxation measurements in monocrystalline DyAl2

Longitudinal μSR measurements were performed on a single crystal sphere of DyAl₂ in the range 4K≤T≤300 K (i.e. both in the ferromagnetic and paramagnetic phases). Contrary to previous reports the dynamic depolarization rate does not diverge near T_C≌65 K. Rather a well defined peak in the depolariation rate is observed around 95 K with 1/T₁ (95 K)∼4 μsec⁻¹. The depolariztion rate above T_C is field independent in the range 0≤B_ext≤2.5 kG. The observed behavior may be accounted for by assuming that the effective correlation time τ is given by τ⁻=τ _4f ⁻¹ +τ _diffusion ⁻¹ . The field independence requires that τ_eff<2·10⁻¹¹. The peak in 1/T₁ could then reflect a slowing down in μ⁺.     

(T1u+T1g)⊗(hg+τ1u)vibronic interaction and superconductivity in C 60 n− fullerides

The closeness of low-lying T_1u and T_1g levels of C ₆₀ ⁻ could enable their mixing under an odd parity vibration of (T_{1 u} + T_{1 g} ⊗ (h_g + τ_{1 u})type. In addition, the two levels are susceptible to Jahn-Teller interaction due to five-fold degenerate h_g vibrations. This complex problem of (T_1u+T_1g)⊗(h_g+τ_1u) vibronic interaction is transformed to a form similar to T_2g ⊗ (ε_g + τ_2g) vibronic problem of octahedral symmetry. The problem is analysed in an infinite coupling model and compared with the experimental spectroscopic results for the C ₆₀ ⁻ radical. The resulting parameters are used to calculate the pair-binding energy and superconducting transition temperature in C ₆₀ ⁿ⁻ fullerides. Vibronic mixing with the T_1g level is found to be responsible for maximising the pair-binding energy at the doping level n=3. It is also found to be an important source of T_c enhancement.     

Plastic-strain localization in barium fluoride single crystals at elevated temperatures

The strain distribution is studied in BaF₂ crystals subjected to compression tests along [110] and [112] at a constant strain rate in the temperature range T = (0.22–0.77)T _m. At T > 0.5T _m, the plastic strain in deformed samples is found to be strongly localized in narrow bands, where the shear strain reaches several hundred percent. The degree of localization increases with temperature. Localized-shear microbands are shown to be oriented along {001}〈110〉 slip systems. The phenomenon of serrated yielding is detected, and stress jumps (serrations) are established to correlate with the formation of shear zones.     

Vortex structure in FeTeSe single crystals

Vortex structure in FeTe_0.66Se_0.44 and FeTe_0.6Se_0.4 single crystals with T _c ∼ 11.7 and 14.5 K, respectively, has been studied using the decoration technique. It has been found that in single crystals with the simplest crystalline structure of 11-family iron-containing superconductors (without interlayers), no regular vortex lattice is observed, similar to the case of the previously studied 122 and 1111 families. Using transmission electron microscopy, the dislocation structure with a density of ∼10⁹ cm⁻² has been observed. The problem of pinning in iron-containing superconductor single crystals is discussed.