Dislocation Climb Research Articles

On Dislocation Climb as an Important Deformation Mechanism for Planetary Interiors

An understanding of the rheological behavior of the solid Earth is fundamental to provide a quantitative description of most geological and geophysical phenomena. The continuum mechanics approach to describing large-scale phenomena needs to be informed by a description of the mechanisms operating at the atomic scale. These involve crystal defects, mainly vacancies and dislocations. This often leads to a binary view of creep reduced to diffusion creep or dislocation creep. However, the interaction between these two types of defects leading to dislocation climb plays an important role, and may even be the main one, in the high-temperature, low strain rate creep mechanisms of interest to the Earth sciences. Here we review the fundamentals of dislocation climb, highlighting the specific problems of minerals. We discuss the importance of computer simulations, informed by experiments, for accurately modeling climb. We show how dislocation climb increasingly appears as a deformation mechanism in its own right. We review the contribution of this mechanism to mineral deformation, particularly in Earth's mantle. Finally, we discuss progress and challenges, and we outline future work directions. ▪Dislocations can be sources or sinks of vacancies, resulting in a displacement out of the glide plane: climb.▪Dislocation climb can be a recovery mechanism during dislocation creep but also a strain-producing mechanism.▪The slow natural strain rates promote the contribution of climb, which is controlled by diffusion.▪In planetary interiors where dislocation glide can be inhibited by pressure, dislocation climb may be the only active mechanism.

Dislocation Climb in AlN Crystals Grown at Low-Temperature Gradients Revealed by 3D X-ray Diffraction Imaging

The dislocation evolution in a cross-section a-plane cut through a sublimation-grown aluminum nitride (AlN) crystal grown with low-temperature gradients and subsequent low thermal stress is investigated with different X-ray diffraction imaging methods. Exploiting the so-called weak-beam contrast using monochromatic X-rays in combination with suitable three-dimensional (3D) interpretation and reconstruction allows the identification of individual dislocations as well as tracing their progression in the crystal volume, even in the considerably strained interface region. It is particularly striking that the laterally grown crystal volume is dislocation-free. The dislocation densities in the seed and the bulk volume are similar (1 × 103 cm–2), but while the dislocations in the seed are randomly arranged, the dislocations in the bulk volume show a uniform line shape, indicating a common mechanism of dislocation movement. Since the dislocation slings in the bulk do not lie in slip planes, it can be concluded that the lateral movement does not result from dislocation glide, but from impurity-driven climb of dislocations during growth. The absence of slip can be explained by the low-temperature gradients and the subsequent low thermal stress below the critical resolved shear stress (CRSS).

Partial Dislocation Climb in Nitride Semiconductors

Partial Dislocation Climb in Nitride Semiconductors

Constructing a Three-Dimensional Histogram Describing Dislocation Viscous Glide and Climb Mechanisms

Creep is the process by which material occurs at high temperatures and its slow deformation process. -2 since the slow...

Solute Softening and Vacancy Generation by Diffusion-Less Dislocation Climb in Magnesium Alloys

Active room temperature diffusion-less climb of the edge dislocations in model Mg-Al alloys was observed using molecular dynamics simulations. Dislocations on prismatic and pyramidal I planes climb through the basal plane to overcome solute obstacles. This out-of-plane dislocation motion softens the high resistance pyramidal I glide and significantly reduces the anisotropy of dislocation mobility, and could help improve the ductility of Mg. The flow stress scales linearly with solute concentration, cAl . Dislocations climb predominantly in the negative direction, with climb angle on the order of 0.01 cAl , producing very high vacancy concentration on the order of 10-4 .

High-Temperature Dislocation Climb in the γ′ Rafts of Single-Crystal Superalloys: The Hypothesis of a Control by Dislocation Entry into the Rafts

The good mechanical resistance to high-temperature creep of [001] oriented single-crystal superalloys is due to the properties of the rafts, i.e., platelets of the L12 γ′ phase embedded in a γ matrix. At temperatures higher than 900 °C, the plastic strain of the rafts results from the climb of dislocation pairs with a total $$ a \cdot \left\langle {100} \right\rangle $$ Burgers vector and/or from the climb at the γ/γ′ interfaces of $$ a/2 \cdot \left\langle {110} \right\rangle $$ dislocation segments. This climb motion involves the exchange of vacancies between these dislocations and vacancy sinks such as pores and the specimens’ surfaces. In this paper, we suggest that the entry of $$ a \cdot \left\langle {100} \right\rangle $$ dislocations into the rafts requires the overcoming of a threshold stress and show that this hypothesis gives a natural explanation to some of the most salient aspects of their mechanical behavior.

Large-Strain Softening of Aluminum in Shear at Elevated Temperature: Influence of Dislocation Climb

This communication complements an earlier publication in this journal by the authors describing the basis for large-strain softening in aluminum under pure shear at elevated temperatures. Earlier work by the authors and the materials community only considered changes in the dislocation glide stress with the evolving texture as an explanation for the softening. New analysis finds that changes in the dislocation climb stress with texture development can explain the softening trends.

An Efficient High Order Method for Dislocation Climb in Two Dimensions

We present an efficient high order method for dislocation dynamics simulation of vacancy-assisted dislocation climb in two dimensions. The method is based on a second kind integral equation (SKIE) formulation that represents the vacancy concentration via the sum of double layer potentials and point sources located at each dislocation, where the climb velocity of each dislocation (or the strength of each point source) is proportional to the integral of the unknown density on the boundary of each dislocation. The method discretizes the interfaces only. Unlike previously used formulations, the proposed method avoids the need for introducing additional unknowns or integrating kernels with logarithmic singularity, and the boundary integrals in the formulation are easily discretized via the trapezoidal rule with spectral accuracy. Thus, the number of unknowns in the linear system to achieve certain accuracy is optimal for typical settings in dislocation dynamics. We compare three different methods for solving r...

Transition from Superplastic Behavior - Viscous Glide - Dislocation Climb - Power-Law Break down Regimes in Friction Stir Processed AA5083

5083 Al alloy was friction stir processed (FSP) at room temperature under various experimental conditions. Two rotational speeds of 430 and 850 rpm with a single traverse feed of 90 mm/min (430-90, 850-90) were used, to investigate the effect of rotation speed. Also, another feed rate of 140 mm/min was used with a rotational speed of 430 rpm (430-140), to investigate the effect of feed rate. The processing conditions resulted in three different grain sizes of 0.95, 1.6 and 2.6 μm depending on the FSP parameters. The deformation behavior of the FSP samples was investigated at 250 C at three strain rates of 10-4, 10-3 and 10-2 s-1. The values of strain rate sensitivity, m was determined, as a function of grain size, and it decreased from 0.45 to 0.33 to 0.18 with increasing the grain size. True activation energy was calculated as 63, 95, 157 kJ/mole for the grain sizes of 0.95, 1.6 and 2.6 μm, respectively. These calculated values are comparable to grain boundary sliding of magnesium in aluminum (69 – 78 kJ mol-1), magnesium in aluminum (~115 kJ mole-1) and aluminum lattice diffusion (~143 kJ mol-1 ). The change in the deformation mechanism with grain size was discussed in some details.

Hot Forming of Mg AZ31B Alloy Sheet Processed by Warm Rolling

Mg alloy AZ31B is of interest for hot forming because it can achieve a superplastic response at high temperatures and slow strain rates. As temperature decreases and forming rate increases, its strain-rate sensitivity decreases and significant plastic anisotropy can arise. These effects are the result of a transition in deformation mechanisms from grain-boundary-sliding (GBS) to dislocation-climb (DC) creep. However, sheet production using warm rolling can produce a material with a smaller grain size and weaker basal texture. These microstructural changes promote GBS creep and decrease the degree of anisotropy under DC creep. Microstructural and tensile data are presented to show these effects at 350 and 450C through comparisons to a similar material having a more usual microstructure.

Coble, Orowan Strengthening, and Dislocation Climb Mechanisms in a Nb-Modified Zircaloy Cladding

Biaxial creep tests on HANA-4 tubes, Nb-added Zircaloy-4 were conducted using internal pressurization of closed-end tubes to investigate the rate-controlling mechanisms over a range of hoop stresses, \( 8.38 \times 10^{ - 5} E - 2.87 \times 10^{ - 3} E \), at three different temperatures 673 K, 723 K, and 773 K (400 °C, 450 °C, and 500 °C). The mechanistic creep parameters such as stress exponent (n) and activation energy (Q C) were then determined from steady-state creep rates. Based on the variance in stress exponent with respect to the applied stress, three regimes have been identified: a stress exponent close to 1 at low stresses that increased to 3 at the intermediate stresses, which became 4.5 at high stresses. An activation energy value of 226 kJ/mol was evaluated for the n = 3 and n = 4.5 regimes, which lies close to the activation energy for self-diffusion (Q L) in α-Zr alloys. Further, TEM analyses of crept microstructures and comparison of experimental results with standard models were undertaken to find out the rate-controlling mechanisms. Coble creep, climbing of dislocations to bypass β-Nb precipitates, and dynamic recovery by edge dislocation climb are proposed as the rate-controlling mechanisms in the n = 1, n = 3, and n = 4.5 regimes of HANA-4, respectively.

A mechanism-dependent material model for the effects of grain growth and anisotropy on plastic deformation of magnesium alloy AZ31 sheet at 450 °C

Utilization of wrought magnesium sheet alloys for structural components in transportation industries has been severely limited by poor room-temperature formability, a result of the slip behaviors inherent to Mg’s hexagonal close-packed crystal structure. Today, the only production technology to clearly overcome this limitation uses hot forming to activate additional (non-basal) slip systems in Mg alloy sheet. The absence of an accurate material constitutive model that captures the complex mechanical response of Mg sheet alloys at elevated temperatures has been a persistent barrier to accurate forming simulations. This study addresses that issue using experimental measurements and mechanism-based modeling. The mechanisms of plastic deformation in a Mg AZ31 wrought alloy sheet at 450°C across strain rates from 10−4 to 10−1s−1 are identified as grain-boundary-sliding (GBS) creep and five-power dislocation-climb (DC) creep. GBS creep is subject to hardening from grain growth, and DC creep produces texture-dependent plastic anisotropy. Based on these mechanisms, a new material constitutive model for Mg AZ31 at 450°C is constructed to predict plastic response under general multiaxial loading. A unique aspect of this new model is that it accounts for hardening and plastic anisotropy by linking these effects to the two mechanisms controlling deformation. The model is validated against independent experimental data and provides accurate predictions for hot forming of a simple test shape. The new material model is the first for Mg AZ31 sheet that accurately predicts deformation at an elevated temperature under both uniaxial and biaxial stress states.

The microstructure and impression creep behavior of cast AZ80 magnesium alloy with yttrium additions

The effects of 0.5, 1.0 and 2.0wt.% Y additions on the microstructure and creep behavior of the as-cast AZ80 alloy were investigated by impression tests. The tests were performed at temperatures in the range 423–523K, under punching stress in the range 150–650MPa. At low temperatures up to 473K, the AZ80+0.5Y alloy had the highest creep resistance among all materials tested, whereas with increasing temperature from 473K to 523K, the AZ80+1.0Y alloy had a better performance. This can be attributed to the fact that at low temperatures the presences of β-Mg17Al12 and Al2Y phases together with solid solution hardening effects of Al in the Mg matrix strengthen the AZ80+0.5Y alloy. At higher temperatures, AZ80+1.0Y with a higher volume fraction of the more thermally stable Al2Y and lower amounts of the less stable β-Mg17Al12 exhibits better creep behavior. The stress exponents and activation energies were almost the same for all alloy systems studied, 6.0–8.8 and 90–119kJ/mol, respectively. The observed decreasing trend of creep-activation energy with stress suggests that two parallel mechanisms of lattice and pipe-diffusion-controlled dislocation climb are competing. Climb of dislocations with an additional particle strengthening effect controlled by dislocation pipe diffusion is dominant at high stresses, whereas climb of dislocations is the controlling mechanism at low stresses.

Predicting Dislocation Climb and Creep from Explicit Atomistic Details

Here we report kinetic Monte Carlo simulations of dislocation climb in heavily deformed, body-centered cubic iron comprising a supersaturation of vacancies. This approach explicitly incorporates the effect of nonlinear vacancy-dislocation interaction on vacancy migration barriers as determined from atomistic calculations, and enables observations of diffusivity and climb over time scales and temperatures relevant to power-law creep. By capturing the underlying microscopic physics, the calculated stress exponents for steady-state creep rates agree quantitatively with the experimentally measured range, and qualitatively with the stress dependence of creep activation energies.

The Role of Dislocation Climb across Particles at Creep Conditions in 9 to 12 Pct Cr Steels

The influence of a distribution of particles on creep strength is analyzed. The time it takes for dislocations to climb across the particles is the basis for a model that can describe the effect of particle size distribution, particle area fraction, stress, and temperature on the creep rate. The degradation of microstructure through coarsening is taken into account. The particle size distributions for M23C6 carbides and MX carbonitrides in a 9 pct Cr steel are accurately represented by an exponential function. Coarsening coefficients and phase fractions for MX and M23C6 particles are predicted using thermodynamic modeling, and show good fit to experimental data. The size distributions are used to determine the amount of dislocations, which can either climb across particles or make Orowan loops. The dislocation climb model is integrated into a creep rate prediction model and is used to reproduce experimental creep data for P92 steel.

Molecular Dynamics Simulation of Ga Penetration along Grain Boundaries in Al: A Dislocation Climb Mechanism

Many systems where a liquid metal is in contact with a polycrystalline solid exhibit deep liquid grooves where the grain boundary meets the solid-liquid interface. For example, liquid Ga quickly penetrates deep into grain boundaries in Al, leading to intergranular fracture under very small stresses. We report on a series of molecular dynamics simulations of liquid Ga in contact with an Al bicrystal. We identify the mechanism for liquid metal embrittlement, develop a new model for it, and show that is in excellent agreement with both simulation and experimental data.

Glide and Climb of Dislocations in Ultra-Thin Metal Films

Glide and Climb of Dislocations in Ultra-Thin Metal Films

The deformation behavior of Sn62Pb36Ag/sub 2/ and its implications on the design of thermal cycling tests for electronic assemblies

The introduction of new packages as well as the ongoing miniaturization in SMT make the evaluation of the reliability of solder joints a permanent task. Since solder joints fail due to low cycle fatigue caused by cyclic thermomechanical stress passive thermal cycling is an important test to evaluate the lifetime of solder joints. Since a reliability prediction with the thermal cycle encountered in reality would take years to complete the tests, methods to accelerate the test cycle are to be used. However, due to the viscoplastical deformation behavior of tin-lead solder it is mandatory to take the metallurgical behavior of the solder into account when designing accelerated tests. Two different deformation mechanisms occur, depending on the temperatures of the test as well as the temperature gradient: grain boundary sliding (GBS) and dislocation climb (DC) each one having its own influence on the damage occurring in the solder. Therefore, one is not free in choosing the parameters of a test cycle. In this paper the deformation behavior of tin lead solder is explained, A constitutive equation extracted from experiments is presented, describing the deformation behavior of Sn62Pb36Ag2. Results of simulations of the deformation behavior of Sn62Pb36Ag2 on the base of the constitutive equation are shown. Suggestions for the design of accelerated lifetime tests for solder joints are given.

Climb of dislocations in GaAs by irradiation

Climb of dislocation dipoles within GaAs during electron beam irradiation has been observed by high resolution transmission electron microscopy. In particular, 90° Shockley partials of α - and β -type forming part of a faulted dipole climbed through absorption of interstitials, with the β -partial showing a greater extent of climb for the same conditions of irradiation. Dislocation climb initiated with the formation of perfect dislocation loops located on the partial dislocations.

Atomistic simulation of void nucleation in aluminium lines

Abstract The formation of voids in aluminium interconnects in integrated circuits was studied atomistically with emphasis on nucleation. Input computational cells included different levels of concentrations of vacancies and stresses together with the typically observed structural defects (grain boundaries and dislocations) in metal lines. The input cells were relaxed using Monte Carlo (atom transpose) and static energy minimization (strain relaxation) techniques concurrently. Besides agglomeration of vacancies in unstrained crystals, the formation of vacancies in crystals under tension was found to be a main contributor to void nucleation. Climb and glide of dislocations were observed atomistically during the formation of voids. Compressive stresses in the metal lines, on the other hand, prevented the formation of voids.