Stress In Single Crystals Research Articles

Mineral inclusions as models to characterize deviatoric stress in single crystals

Mineral inclusions as models to characterize deviatoric stress in single crystals

Potential of using inert gas flows for controlling the quality of as-grown silicon single crystal

We have improved the well-known Czochralski single crystal silicon growth method by using two argon gas flows. One flow is the main one (15–20 nl/min) and is directed from top to bottom along the growing single crystal. This flow entrains reaction products of melt and quartz crucible (mainly SiO), removes them from the growth chamber through a port in the bottom of the chamber and provides for the growth of dislocation-free single crystals from large weight charge. Similar processes are well known and have been generally used since the 1970s world over. The second additional gas flow (1.5–2 nl/min) is directed at a 45 arc deg angle to the melt surface in the form of jets emitted from circularly arranged nozzles. This second gas flow initiates the formation of a turbulent melt flow region which separates the crystallization front from oxygen-rich convective flows and accelerates carbon evaporation from the melt. It has been confirmed that oxygen evaporated from the melt (in the form of SiO) acts as transport agent for nonvolatile carbon. Commercial process implementation has shown that carbon content in as-grown single crystals can be reduced to below the carbon content in the charge. Single crystals grown with two argon gas flows have also proven to have highly macro- and micro-homogeneous oxygen distributions, with much greater lengths of single crystal portions in which the oxygen concentration is constant and below the preset limit. Carbon contents of 5–10 times lower than carbon content in the charge can be achieved with low argon gas consumption per one growth process (15–20 nl/min vs 50–80 nl/min for conventional processes). The use of an additional argon gas flow with a 10 times lower flowrate than that of the main flow does not distort the pattern of main (axial) flow circumvention around single crystal surface, does not hamper the “dislocation-free growth” of crystals and does not increase the density of microdefects. This suggests that the new method does not change temperature gradients and does not produce thermal shocks that may generate thermal stresses in single crystals.

Crystal plasticity FE modeling of Ti alloys for a range of strain-rates. Part I: A unified constitutive model and flow rule

The deformation and failure response of many polycrystalline metallic materials is strongly dependent on the strain-rate. For an applied strain-rate, different points in the material microstructure can undergo strain-rates that differ by orders of magnitude depending on location and deformation history. Dislocation motion in metals is governed by the thermally-activated and drag-dominated processes under low and high rates of deformation, respectively. Commonly used flow rules, e.g the phenomenological power law or the linear viscous drag models are generally applicable to a limited range of strain-rates, without transcending these rates. To enable this transition in a seamless manner, this two part paper develops a unified constitutive model and an image-based crystal plasticity finite element model for polycrystalline hcp metals. The first part develops a dislocation density-based crystal plasticity constitutive relation with a unified flow rule by combining the thermally-activated and drag-dominated stages of dislocation slip, suitable for modeling deformation at a wide range of strain-rates. The model is explicitly temperature-dependent, making it appropriate for simulating high rate deformations, where temperature increases locally with plastic deformation due to the adiabatic heating. The unified model is used to study rate-sensitivity of flow stress in single crystal and polycrystalline titanium alloy, Ti-7Al. An elastic overshoot, followed by a stress relaxation is observed at high strain-rates in single crystals. For the polycrystalline simulations, the model effectively captures the increase in rate sensitivity at high strain-rates.

Deformation behaviour of nano-twinned single crystals of an Fe–19Cr–16Ni austenitic alloy

The deformation behaviour of an Fe–19Cr–16Ni austenitic alloy was studied by micro-tensile testing of small-scale single crystals. A detailed comparison of specimens with and without nano-twins was conducted. The study revealed that the deformation behaviour depends strongly on the crystallographic orientation of the parent crystal and the spacing between nano-twin bundles. Although the yield stress in single crystals without nano-twins was governed by Schmid's law, the slip transfer inhibition by twin boundaries contributed significantly to the strengthening in nano-twinned samples. With the parent crystal oriented favourably for single-slip, the dislocations in the parent crystal glided by cross-slip onto the primary plane in the twinned crystal. For the hard-oriented parent crystal with dense nano-twins, dislocation accumulated and led to necking at an early stage. For the same orientation but with sparse nano-twins, twin growth and nucleation was promoted by dislocation reactions with the twin boundaries. These findings suggest that control of the nano-twin structure can allow the desired deformation behaviour to be tuned.

Modeling and simulation of microcrack propagation behavior under shear stress using phase-field-crystal

Phase-field-crystal (PFC) method is applied to simulate the propagation behavior of microcrack under shear stress in single crystal, which is seldom touched before. The microscopic mechanism is explored through the center precast microcrack on the (111) crystal plane in face-centered cubic (FCC) crystal. The influence of different factors on the crack propagation behavior is analyzed. Results show that the crack shape has influence on the occurrence of propagation. Propagation occurs earlier if the crack contains sharper inner angles, otherwise occurs later. Moreover, crack shape also affects the direction of propagation. The rate of applied shear stress can produce effect on the propagation speed, without altering the specific process of crack propagation. Improving shear rate can accelerate propagation. The initial orientation angle of solid phase has a great influence on the propagation mode and morphology of crack. Curves of change in free energy obtained in this work all monotonically ascend. We can divide the curves into five stages, corresponding to different shear strain stages. When simulation area is slightly small or shear rate is relatively large, the curve contains only three stages. Through this research, the PFC simulation is proved to be an effective means to study microcrack propagation behavior under applied shear stress.

Studying the character and mechanisms of thermal hardening for single crystals of alloys with L12 structure

This work discusses mechanisms of temperature dependence of the yield stress of single crystals with L12 superstructure, a feature of which is an anomalous multistage increase in yield stress with temperature. The description of the observed dependences is based on the superpositioning of six different mechanisms of thermal hardening and softening.

Influence of incomplete shape memory deformation on the generation of reactive stresses in single crystals of the Cu-Al-Ni alloy

The influence of preliminary incomplete shape memory (SM) deformation on the generation of reactive stresses in single crystals of the Cu-13.6 wt % Al-4.0 wt % Ni alloy under conditions of constrained SM deformation has been studied. It has been found that, with an increase in the deformation, the value of reactive stresses increases linearly with increasing stress of preliminary deformation of the alloy.

Influence of annealing on the character of structural-phase mismatch in single crystals of heat-resistant nickel alloys

The lattice parameter mismatch between the γ and γ′ phases (γ/γ′ misfit) in single crystals of heat-resistant nickel alloys (HRNAs) ZhS32 and VZhM4 after annealing of varying duration at 900 to 1100°C was studied by X-ray diffraction. It was established that relaxation of coherent stresses in single crystals of HRNAs is accompanied by removal of tetragonal splitting of the matrix (004) γ reflection, and the relaxation dynamics depends on the heat resistance of the single crystal and is determined by the level and duration of temperature exposure. A qualitative change in the profile of the matrix X-ray reflection from the VZhM4 single crystal after long-term annealing at a temperature of 1100°C was revealed.

Dislocation annihilation in plastic deformation: I. Multiscale irreversible thermodynamics

Irreversible thermodynamics is employed as a framework to describe plastic deformation in pure metals and alloys. Expressions to describe saturation stress in single crystals and nanocrystals are employed over wide ranges of temperature, strain rate and grain size. The importance of the roles played by vacancy self-diffusion in dislocation climb and in plasticity is shown. Equations to describe the stress–strain response of single crystals and ultrafine-grained metals are derived. The activation energy for dislocation annihilation plays a central role in the mechanical response of the systems. Succinct formulations for predicting hot deformation behaviour and relaxation of industrial alloys are presented; the influence of composition in the activation energy for dislocation annihilation is shown. All formulations describing stress–strain relationships can be reduced to Kocks–Mecking classical formulation, but incorporating grain size and compositional effects. The importance of the recovery term in such formulation is established, as well as the need to obtain it employing more fundamental approaches.

Accumulation and relaxation of internal stresses in single crystals during high-temperature creep with hindered dislocation slip

The relationship between the kinetics of the initial high-temperature creep of KCl and NaCl single crystals and the internal stresses induced during deformation is examined. The influence of the external stresses and temperature on the internal stresses is established. The possible mechanisms of the accumulation and relaxation of internal stresses that govern deformation kinetics are experimentally established and analyzed.

Asymmetry of the yield strength in single crystals of titanium nickelide

Based on the results of the experimental studies of the temperature dependence of the yield stress of single crystals of TiNi alloys and of the mechanism of the mechanical twinning of the B2 phase as a martensite-type local reversible phase transformation, the asymmetry of the mechanical behavior of these materials during tension and compression in the [001] direction has been investigated. It is shown that a specific feature of this mechanism is the fact that the critical mode of distortion which determines stresses during mechanical twinning is a homogeneous deformation of transformation of the Bain-deformation type. To analyze the asymmetry of these stresses during tension and compression, a concept of the factor of normal stresses reduced to the principal axes of the tensor of the homogeneous deformation of transformation is introduced. It is shown that this factor can be used for analyzing the asymmetry of the mechanical behavior of single crystals of TiNi alloys.

Contribution of point defects to the temperature anomaly of the yield stress in single crystals of the Ni3Ge alloy

The temperature dependence of the yield stress τ* Ni 3 Ge single crystals is studied. The temperature dependence τ*(T) in the high-temperature region (above 420 K) is found to be conditioned by thermally activated accumulation of the density of non-screw components of superdislocations. Interaction of point defects with edge dislocations and its effect on the temperature anomaly of the yield stress in Ni 3 Ge single crystals are analyzed. The calculated results are found to agree with experimental data.

Effect of orientation on the peak temperature of the yield-stress anomaly in single crystals of the Ni3Ge alloy

Temperature dependence of the yield stress τc(T) and shear stresses, as well as the orientation dependence of the peak temperature Tp of the yield-stress anomaly have been studied on single crystals of the Ni3Ge alloy. The peak temperature Tp corresponds to the maximum in the τc(T) dependence. Profiles of the Tp isolines have been determined based on the equality of the values of the yield stress in the octahedral and cube planes of cross slip. It is shown that in the case of the above equality it is possible to describe the orientation dependence of the peak temperature Tp of the temperature anomaly of the yield stress in single crystals of Ni3Ge.

Crystal Lattice Effects on the Orientation and Orbital Degeneracy of Nitric Oxide Trapped in Nitramine Single Crystals

The orientation, structure, and location of nitric oxide (NO) generated by low-temperature photolysis in single crystals of two nitramines, RDX and HNIW, have been investigated by EPR spectroscopy. Following low-temperature photolysis of single crystals of RDX and of the α- and /?-polymorphs of HNIW, various NO species were observed after annealing up to 300 K. The orientation and orbital degeneracy of NO trapped in crystal lattices of these nitramines were inferred from its g tensor. These data illustrate the use of NO as a probe of reaction-generated stress in single crystals. In addition, analyses of α- and β-HNIW crystal packing and of the orientation and structural differences of NO trapped therein, were used to locate the NO within the α-HNIW crystal lattice, where it is shown to be trapped in intermolecular cavities and to survive storage for over 2 years at ambient temperature.

The relationship between mechanical stresses and optical anomalies in germanium and paratellurite

Optical interference and x-ray analysis methods are used to determine the mechanical stresses in single crystals of germanium and paratellurite, which cause local distortions of the wavefronts due to the photoelastic effect. The dislocation structure of the crystals close to optical anomalies is studied. The effect of high-temperature annealing on stress relaxation in germanium and paratellurite is investigated. © 2005 Optical Society of America

Thermodynamic calculation of the oriented internal stress in single crystals of Ni52Mn24Ga24

The internal stress in single crystals of Ni52Mn24Ga2 4 has been calculated based on the balance equation and the experimental data on transformation strains with or without bias field. It was found that the residual oriented internal stress caused by the directional solidification during the crystal growth plays an important role in achieving the reorientation of the variants, and resulting in a large transformation strain.Furthermore, according to Maxwell equation and Ullako's thermal dynamic model, the theoretical value of magnetic-field-induced strains and internal stress at different temperatures in martensite was calculated based on a best fitting of the strain curves versus the bias field. Compared with the experimental observation, the availability of various models has been discussed.

Investigation of the influence of directional internal stress on the arrangement of martensitic variants

Microstructure and magnetic measurements were performed to reveal the distribution of the internal stress in single crystals of Ni2MnGa.It was suggested that due to the existence of the directional internal stress in the growth direction of single crystals results in the perfect arrangement of martensitic variants along the growth direction.Furthermore,the influence of such a perfect arrangement of variants on the formation of magnetic domain was studied in this paper.

X-Ray Intergranular Stresses Analysis in a Cast Duplex Stainless Steel

Polycrystalline approaches are more and more used to characterise the mechanical behaviour of material with the interest to take into account the mechanical properties of the material constituants. In this case; for a better understanding of the polycrystalline material mechanical response, mesoscopic and microscopic parameters must be clearly identified. Our purpose is also to characterise the mechanical behaviour of a cast duplex stainless steel, containing 30% ferrite and 70% austenite, using X-ray diffraction. The mechanical state can be determined using X-ray diffraction technique which enables to measure strains in each phase separately. The measurements are performed at the grain scale because the studied material exhibits coarse grains of up to one millimeter. In this case, only few crystals are irradiated by the incident X-ray beam and the classical sin 2 ψ method for stress determination can not be applied to this material. An adaptation of the single crystal measurement method to large grains materials is used Stresses so determined correspond to second order stresses. The measurement in each phase has successfully been applied to follow the stress state evolution during an in-situ tensile test. Several grains, with different crystallographic orientations were studied. For each one, the stress tensor was determined in the two phases under different macroscopic loading in elastic and plastic domains, different A modelling of the mechanical single crystal behaviour is developed and our pourpose is to identify the parameters of the single crystal behaviour law using X-ray single crystal stress analysis during in situ tensile test.

Dislocation core effects on plasticity

The structure and/or the state of dislocation core often play a significant role in the glide process of the dislocation and hence control the plasticity of the crystal. We show various examples in this paper. (1) The yield stress of single crystals controlled by the Peierls mechanism for screw dislocation does not obey the Schmid law. (2) A narrow dissociation of the core can produce a plateau in the τy- T relation. (3) Duality of the core structure can produce «yield stress anomaly». (4) Multiphonon emission at the core of dislocation in semiconducting crystals by non-radiative recombination of electron-hole pairs enhances drastically the dislocation mobility.

Ferroelastic domain switching behaviour of single crystals

We investigated ferroelastic domain switching due to stress in single crystals grown by a slow evaporation method. The ferroelastic domain switching stress due to the saturation effect is about 0.9 MPa. The temperature dependence of the stress-strain hysteresis was also studied. From this result, it was determined that the single crystal undergoes a phase transition near K. In other words, the phase transition due to an external mechanical stress applied to crystals causes a transformation from the ferroelastic to the paraelastic phase. From these results, it was confirmed that crystals have ferroelastic characteristics below .