Magnesium Single Crystals Research Articles

Stage B work‐hardening of magnesium single crystals

AbstractThe change in microstructure during tensile deformation of magnesium single crystals by basal slip was studied with electron backscatter diffraction in the scanning electron microscope. Two samples were plastically deformed up to shear strains of 0.37 and 1.28 belonging to work‐hardening stages A and B, respectively. The results show that the local misorientations resulting from rotations around the <10$ \bar 1 $0> axis strongly increase the work‐hardening coefficient in stage B. The mechanism of work‐hardening in stage B is discussed with respect to subgrain formation. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

New crystal plasticity constitutive model for large strain deformation in single crystals of magnesium

A new rate-dependent elastic–viscoplastic crystal plasticity constitutive model (CPCM) to simulate the large strain deformation in magnesium alloys is presented. The observed intragranular plastic deformation mechanisms of primary extension, primary contraction, and secondary extension (double) twinning are accounted for. The basal and non-basal slip systems in the parent grain, primary and double twins were also incorporated in the model. The crystallographic planes and directions of various slip and twinning systems are calculated. The slip-induced shear in the parent grain, as well as primary and secondary twinned regions are simulated. The twinning-induced shear from the primary and secondary twinned regions are also computed. In the model the texture evolution in the parent, as well as primary and secondary twinned regions are tracked. Separate resistance evolution functions for all the slip and twinning systems were considered. The interactions between various slip and twinning systems are accounted for in a comprehensive manner. Using the proposed CPCM, the plastic deformation in a magnesium single crystal in simple shear strain path is simulated. The contributions of various plastic deformation mechanisms to the macroscopic plastic deformation of the magnesium single crystal in this strain path are presented. The importance of identifying the active plastic deformation in a given strain path on a magnesium single crystal for a reliable model prediction was shown with an example.

The structure, composition and reactivity of clean and ambient-exposed polycrystalline and monocrystalline Mg surfaces

The present article recounts results from studies on the structure, composition and reactivity of polycrystalline and single-crystal magnesium surfaces, previously exposed to the environment and regenerated to pristine conditions in ultrahigh vacuum. Experimental measurements relied on electron spectroscopy, temperature-programmed mass spectrometry and atomic force microscopy. Reaction-chemistry investigations were primarily with gas-phase reagents although selected treatments in aqueous or ethereal electrolyte were also undertaken. The results obtained have relevance in the description of the corrosion characteristics of this industrially important metal. The more significant observations: (i) Air-exposed Mg is invariably encrusted with a surface film composed predominantly of magnesium hydroxide but with a detectable quantity of magnesium bicarbonate. (ii) The exposure of a clean Mg(0001) surface to gradually increased dosages of O 2(g) initially yielded a (1 × 1) oxygen layer that suffered surface disorder at the incipient stages of metal–oxide formation; eventually, an epitaxial MgO(100)-on-Mg(0001) adlattice was generated. (iii) Exposure of Mg(0001) to H 2O (g), regardless of the dosage applied, resulted in a non-ordered hydroxylated surface. (iv) Upon exposure of a clean Mg(0001) surface to CO 2(g), an ordered carbonaceous oxide film was initially found; at much higher dosages, the pseudomorphic adlayer was transformed into a totally disordered film. (v) Exposure of an oxide-coated Mg(0001) surface to H 2O (g) yielded a disordered hydroxylated surface. (vi) With pertinence to Grignard chemistry, treatment of the oxided metal with either gaseous or (anhydrous) ethereal HCl enforced an acid–base reaction that led to a substantial reduction in the amount of surface oxide and the concomitant accumulation of a metal-chloride film.

Atomistic Simulation of Deformation Behavior at a Crack Tip in Magnesium Single Crystal

The mechanisms of low-temperature deformation around a crack tip in a hexagonally closed-packed (hcp) magnesium single crystal have been studied by molecular dynamics simulations. In our simulation a {1010} < 12 10 > model I (opening model) crack is selected. The results indicate that slip on the basal plane is activated due to the shear stress at the crack tip. Thus shear banding caused by a successive slip of the basal planes is the main deformation way for this type of crack.

Transient 3D Simulation of a Submerged-Arc Furnace for Production of MgO Single Crystal

High quality magnesium oxide (MgO) single crystals have been grown by an arc-fusion method. Due to the hostile environment for observing the process occurring in the inner zone of the furnace, direct measurements on the arcs by conventional diagnostic method are practically impossible. Moreover, it has been proved that the control of the temperature field of the whole system is crucial to grow high-purityMgO single crystals with large and super-large sizes. However, very few studies have been carried out to investigate the correlation between the thermal behavior and MgO single crystal growth in the furnace. In present study, a transient 3D finite element model has been developed to depict melt/crystal interface and to find out the determining factors that affect the crystal growth rate and the growth direction. It is shown that the model gave a good description of the bath shape which agrees well with that of the solidified MgO in experiments. By the transient analysis, the trend and time delay of the temperature variation on the shell were also predicted.

OS2011 Mg単結晶における変形機構の結晶方位依存性(OS20-2 マグネシウムの変形挙動,OS-20 HCP金属の実験力学と計算力学)

It is important to clarify deformation mechanisms, such as slip and twin, for understanding deformation behavior of crystalline materials. In hcp metals, there are many deformation mechanisms related to the crystal structure. In this study, magnesium single crystals were s stretched in [112^^-0] and compressed in [0001] in various directions in the range of 77K to 573K to investigate the deformation behavior by non-basal slips and twins. In both case, {112^^-2} <<11>^^^-23> second order pyramidal slip is activated in all magnesium and magnesium alloy single crystals, and its yield stress shows anomalous temperature dependence in the range from 77K to 293K, however, the yields stress decreased rapidly with increasing temperature over 293K. In [112^^-0] compression and [0001] tensile test, {101^^-2} twin occurred at 5-10MPa in both case. These results indicate that deformation behavior of magnesium single crystal strongly depends on the loading orientation.

Temperature dependency of slip and twinning in plane strain compressed magnesium single crystals

This study aims to characterize the critical resolved shear stresses (CRSSs) of slip and twinning in magnesium crystals, as a function of temperature, under conditions of imposed strains. Several crystal orientations have been deformed by plane strain compression in a channel die from room temperature to 450 °C. The deformed microstructure and microtextures are characterized by systematic electron backscatter diffraction orientation maps giving unequivocal primary and secondary twin determinations. In parallel, a crystal plasticity code based on the CRSS and the Schmid law is used to compare model predictions with the active slip and twinning systems and the flow stress. It is shown that tensile twinning and basal slip are only slightly temperature-dependent but that the other systems (compressive twinning, prismatic and pyramidal II ( c + a) slip) possess CRSS values which decrease substantially with temperature.

A phase field model of deformation twinning: Nonlinear theory and numerical simulations

A continuum phase field theory and corresponding numerical solution methods are developed to describe deformation twinning in crystalline solids. An order parameter is associated with the magnitude of twinning shear, i.e., the lattice transformation associated with twinning. The general theory addresses the following physics: large deformations, nonlinear anisotropic elastic behavior, and anisotropic phase boundary energy. The theory is applied towards prediction of equilibrium phenomena in the athermal and non-dissipative limit, whereby equilibrium configurations of an externally stressed crystal are obtained via incremental minimization of a free energy functional. Outcomes of such calculations are elastic fields (e.g., displacement, strain, stress, and strain energy density) and the order parameter field that describes the size and shape of energetically stable twin(s). Numerical simulations of homogeneous twin nucleation in magnesium single crystals demonstrate fair agreement between phase field solutions and available analytical elasticity solutions. Results suggest that critical far-field displacement gradients associated with nucleation of a twin embryo of minimum realistic size are 4.5%–5.0%, with particular values of applied shear strain and equilibrium shapes of the twin somewhat sensitive to far-field boundary conditions and anisotropy of twin boundary surface energy.

Microstructure and Texture of Magnesium Single Crystals Processed by ECAP

Equal channel angular pressing (ECAP) is a promising severe plastic deformation technique for production of ultrafine-grained bulk metals with face centered cubic (fcc) structure. However, the process is often complicated in hexagonal close packed (hcp) metals such as magnesium due to its low forming capability. In this contribution, magnesium single crystals were processed by ECAP through a single pass in order to reveal processes taking place in hcp lattice during severe plastic deformation. The microstructure and texture were investigated by SEM-EBSD. The deformed microstructure contains shear bands, recrystallized regions and mechanical twins. Activity of twinning systems and texture formation are discussed regarding different initial orientation of the single crystals.

Atomistic modeling of crack growth in magnesium single crystal

The analysis of crack growth in magnesium single crystal was performed using molecular dynamics simulation with Embedded Atom Method (EAM) potentials. The twinning process at the crack tip was analyzed. Four specimens with increasing sizes were used to investigate the influences of material length scale on crack growth of magnesium single crystals. Furthermore, the effects of temperature, and the loading strain rate were also verified. The specimens were subjected to uniaxial tension strain up to the total strain level of 0.2 with a constant strain rate. In the simulation of each specimen, the averaged stress strain curve was monitored. The simulation results show that the specimen size, loading strain rate, and temperature strongly influence the peak stress point at which the twin nucleated and subsequently the crack grew. The initial slope of the averaged stress strain curve is independent of the loading strain rate and temperature. Moreover, high temperatures induce increased atomic mobility, and thereby atom reorganization, which, in turn, releases the stress at the crack tip.

Characteristics of coincident site lattice grain boundaries developed during equal channel angular pressing of magnesium single crystals

Distributions of near-coincidence grain boundaries that occur during equal channel angular pressing in magnesium single crystals at 503 K are investigated. The coincidence boundaries with the [0 0 0 1] misorientation axis are frequent in the sample after passage of the shear plane and recrystallization. In contrast, twin boundaries dominate in the end parts of the samples. Existence of a 30° peak in the misorientation angle distribution is explained by a relatively high frequency of Σ13a boundaries and partially by the appearance of Σ15a boundaries.

On the coupling of plastic slip and deformation-induced twinning in magnesium: A variationally consistent approach based on energy minimization

The present paper is concerned with the analysis of the deformation systems in single crystal magnesium at the micro-scale and with the resulting texture evolution in a polycrystal representing the macroscopic mechanical response. For that purpose, a variationally consistent approach based on energy minimization is proposed. It is suitable for the modeling of crystal plasticity at finite strains including the phase transition associated with deformation-induced twinning. The method relies strongly on the variational structure of crystal plasticity theory, i.e., an incremental minimization principle can be derived which allows to determine the unknown slip rates by computing the stationarity conditions of a (pseudo) potential. Phase transition associated with twinning is modeled in a similar fashion. More precisely, a solid–solid phase transition corresponding to twinning is assumed, if this is energetically favorable. Mathematically speaking, the aforementioned transition can be interpreted as a certain rank-one convexification. Since such a scheme is computationally very expensive and thus, it cannot be applied to the analysis of a polycrystal, a computationally more efficient approximation is elaborated. Within this approximation, the deformation induced by twinning is decomposed into the reorientation of the crystal lattice and simple shear. The latter is assumed to be governed by means of a standard Schmid-type plasticity law (pseudo-dislocation), while the reorientation of the crystal lattice is considered, when the respective plastic shear strain reaches a certain threshold value. The underlying idea is in line with experimental observations, where dislocation slip within the twinned domain is most frequently seen, if the twin laminate reaches a critical volume. The resulting model predicts a stress–strain response in good agreement with that of a rank-one convexification method, while showing the same numerical efficiency as a classical Taylor-type approximation. Consequently, it combines the advantages of both limiting cases. The model is calibrated for single crystal magnesium by means of the channel die test and finally applied to the analysis of texture evolution in a polycrystal. Comparisons of the predicted numerical results to their experimental counterparts show that the novel model is able to capture the characteristic mechanical response of magnesium very well.

Numerical formability assessment in single crystals of magnesium

In this paper a rate-sensitive elastic–viscoplastic crystal plasticity constitutive model (CPCM) together with the Marciniak–Kuczynski (M–K) approach have been used to assess the formability of a magnesium single crystal sheet by simulating the forming limit diagrams (FLDs). Sheet necking is initiated from an initial imperfection in terms of a narrow band. A homogeneous deformation field is assumed inside and outside the band, and conditions of compatibility and equilibrium are enforced across the band interfaces. Thus, the CPCM only needs to be applied to two regions, one inside and one outside the band. The FLDs have been simulated under two conditions: (a) the plastic deformation mechanisms are basal, pyramidal 〈 c + a〉, and prismatic slip systems, and (b) the plastic deformation mechanisms are basal, pyramidal 〈 c + a〉, and prismatic slip systems, as well as extension and contraction twinning systems. The FLDs have been generated for two grain orientations. In the first orientation pyramidal 〈 c + a〉 and extension twinning systems, and in the second orientation basal and pyramidal 〈 c + a〉 slip systems, as well as contraction twinning systems have favourable orientation for activation. The effects of shear strains outside the necking band, strain rate sensitivity, and c/ a ratio on the simulated FLDs in the two grain orientations have been individually explored.

Atomistic simulation of tension deformation behavior in magnesium single crystal

Atomistic simulation of tension deformation behavior in magnesium single crystal

A fundamental study of the high temperature deformation mechanisms of magnesium

Single crystals of Magnesium have been deformed in plane strain compression from room temperature to 450 °C. The deformed crystals have been analysed by EBSD to identify the operative twin variants and parent rotations for comparison with the expected systems. In parallel with these experiments, we have developed a crystal plasticity model based on Taylor principles and the Schmid law, to compute the activated systems together with the twin reorientations and the lattice rotations for large strains. The CRSS values are determined by an iterative procedure that best correlates the experimental data with the numerical simulations for each orientation. From the measured stress/strain data the CRSS for twinning and some slip systems are given over this wide temperature range.

Deformation Behavior of Magnesium Single Crystal in &lt;i&gt;c&lt;/i&gt;-Axis Compression and &lt;i&gt;a&lt;/i&gt;-Axis Tension

In general, deformation behavior of magnesium in compression is different from tensile. To investigate deformation behavior of magnesium single crystals by non-basal slips and twins, c-axis compression and a-axis tension tests were performed in the range of 77K-573K. The crystals were yielded by second order pyramidal slip, and the yield stress shows anomalous temperature dependence (increased with increasing temperature) between 203K and 293K. Yield stress of c-axis compression was bigger than that of a-axis tensile. In compression, fracture surface were (11 4) under 293K and were {30 4} above 373K, and fracture strain was smaller than the case of tension test. {10 1}-{10 2} double twin were activated at higher temperature and the crystal, therefore, fractured along the twin interface.

Molecular dynamics simulations of void growth and coalescence in single crystal magnesium

The growth and coalescence of voids in magnesium single crystals at the nanoscale have been investigated using molecular dynamics simulations and the embedded atom method. One void and two void specimens with identical initial void volume fractions were utilized to study the mechanism of void growth and coalescence. In order to study the influences of material length scale on void evolution in single crystals four specimen sizes with the same initial volume fraction of voids were considered. Investigations of the effects of temperature and strain rate were also performed. Uniaxial stress–strain curves were monitored during increasing employed strain. The simulation results show that the specimen size, loading strain rate and temperature had apparent influences on the twin or dislocation pattern, void evolution shape and uniaxial stress–strain responses, but negligible effects on the initial slopes of the uniaxial stress–strain curves. Furthermore, the nucleation stress of twin bands in orientation A – x[0 0 0 1]– y[ 1 2 ¯ 1 0 ]– z[ 1 0 1 ¯ 0 ] was much higher than that of plastic deformation in orientation B – x[ 1 2 ¯ 1 0 ]– y[ 1 0 1 ¯ 0 ]– z[0 0 0 1].

Damage recovery and optical activity in europium implanted wide gap oxides

In this study we compare and discuss the defects and optical behaviour of sapphire and magnesium oxide single crystals implanted at room temperature with different fluences (1 × 10 15–1 × 10 16 cm −2) of europium ions. Rutherford backscattering channelling shows that for fluences above 5 × 10 15 cm −2 the surface disorder level in the Al-sublattice reaches the random level. Implantation damage recovers fast for annealing in oxidizing atmosphere but even for the highest fluence we recover almost completely all the damage after annealing at 1300 °C, independently of the annealing environment (reducing or oxidizing). Annealing above 1000 °C promotes the formation of Eu 2O 3 in the samples with higher concentration of Eu. The optical activation of the rare earth ions at room temperature was observed after annealing at 800 °C by photoluminescence and ionoluminescence. In Al 2O 3 lattice the highest intensity line of the Eu 3+ ions corresponds to the forced electric dipole 5D 0 → 7F 2 transition that occurs ∼616 nm. For the MgO samples the Eu 3+ optical activation was also achieved after implantation with different fluences. Here, the lanthanide recombination is dominated by the magnetic dipole 5D 0 → 7F 1 transition near by 590 nm commonly observed for samples were Eu 3+ is placed in a high symmetry local site. The results clearly demonstrate the possibility to get Eu incorporated in optical active regular lattice sites in wide gap oxides.

An investigation of the onset of elastoplastic deformation during nanoindentation in MgO single crystal (0 0 1) and (1 1 0) planes

Nanoindentation was performed in the (0 0 1) and (1 1 0) planes of magnesium oxide single crystal. The results showed that pop-in events were observed in both cases, which were accompanied by acoustic emissions. The energy released in a pop-in event was related to the acoustic emission energy. The pop-in indicated the onset of plastic deformation. Using the Hertzian contact theory and the measured pop-in load, the critical shear stresses for slipping on the (0 0 1) and (1 1 0) planes were estimated. The stress value for the (0 0 1) plane was about 17% higher than that of the (1 1 0) plane.

Fatigue crack growth in magnesium single crystals under cyclic loading: Molecular dynamics simulation

The fatigue crack propagation behavior of magnesium single crystal was analyzed using molecular dynamics simulation. The inter-atomic potential used in this investigation is Embedded Atom Method (EAM) potentials. The studies of the mechanism of fatigue crack growth in different crystal orientation were performed using Center Crack (CC) specimens while Edge Crack (EC) specimens were employed to investigate the effects of strain rate and temperature. For CC specimen, the periodic boundary conditions were assigned in the x and z direction, while for EC specimen, only z direction was allowed periodic boundary conditions. In order to study the orientation dependence of fatigue crack growth mechanism, 10 crystal orientations of initial crack were analyzed and the simulation results reveal that the fatigue crack growth rate and the crack path vary significantly with the crystallographic orientations of initial crack. The growth rate of orientation D is the highest and the resistance of fatigue crack growth of orientation B is the highest. The analysis of the influences of strain rate was carried out on the orientation F and the results revealed that the growth rate of fatigue crack decreasing with increasing strain rate. The fatigue crack growth rates of different orientation decrease with increasing temperature.