Hcp Metals Research Articles

Identifying deformation mechanisms in molecular dynamics simulations of laser shocked matter

In this paper we demonstrate a new post-processing technique that allows straightforward identification of deformation mechanisms in molecular dynamics simulations. We utilise reciprocal space methods by calculating a per-atom structure factor (PASF) to visualise changes in volume, orientation and structure, thus allowing unambiguous discrimination between key deformation/relaxation mechanisms such as uniaxial strain, twinning and structural phase transformations. The full 3-D PASF is reduced to a 2-D representation by taking only those points which lie on the surface of an ellipsoid passing through the nearest reciprocal lattice points. Projecting this 2-D representation onto the set of spherical harmonics allows for a numerical characterisation of the system state that easily captures various plastic deformation mechanisms that have been historically difficult to identify. The technique is used to successfully classify high temperature twinning rotations in shock compressed tantalum and to identify the α to ω phase transition in group-IV hcp metals.

Non-dislocation-mediated basal stacking faults inside [formula omitted] twins

Anomalous basal stacking faults have frequently been observed inside 101−2 twins in deformed hcp metals. In this work, we report transmission electron microscopy observation of basal stacking faults inside 101−1 twins. These stacking faults present similar characteristics to those inside 101−2 twins. To reveal the formation mechanism, we performed atomistic simulations. The results show that the stacking faults are not mediated by partial dislocations. Lattice transformation analysis based on classical twinning theory shows that very large atomic shuffles (~0.16nm) perpendicular to the twinning shear are required for twinning and responsible for the formation of these stacking faults.

Beyond initial twin nucleation in hcp metals: Micromechanical formulation for determining twin spacing during deformation

Capturing twin nucleation in full-field crystal plasticity is a long-standing problem in materials science modeling. Pronounced efforts have been deployed to understand the nucleation event at the atomic level. Yet, it remains very challenging to appropriately scale up the inherently discrete mechanisms to the continuum scale. However, of significant implications for modeling of hardening and damage is not the embryonic/lamellar nucleation of an individual twin per say, but the spacing of the twins and their concomitant interactions with each other and active defects in the lattice. Thus, knowing when and where the next twin would nucleate or grow is certainly of significant consideration to crystal plasticity and would have been perhaps the primary goal of any model which would capture early site-specific nucleation. In this study, we develop an analytical model based on a micromechanical formulation, which is able to pinpoint where a second twin nucleates in an idealistic scenario in a homogeneous material. The model was probed with a three-point bending boundary value problem and predictions were compared to in-situ bending tests of an AZ31 Mg alloy. The alloy was chosen because it exhibited sharp textures which tend to develop twin patterns similar to single crystals. The analytical expression for the stress field was obtained for an ellipsoidal twin in an isotropic half-space. We show that the twin spacing depends primarily upon the height of the twin band, and the stress relaxation from twinning depends primarily upon the thickness of the twin domain. The solution compared well to experimental results.

The balance between the energies of the symmetric [formula omitted] twin boundaries and asymmetric basal/prismatic interfaces in hcp metals

The energies of grain boundaries with different inclination of the boundary plane for a misorientation close to 90° about the [12¯10] axis in hexagonal close packed metals are discussed. On the basis of large scale computer simulations with an empirical potential for magnesium, it can be illustrated that the basal/prismatic interfaces possess special properties.

Stacking faults and mechanisms strain-induced transformations of hcp metals (Ti, Mg) during mechanical activation in liquid hydrocarbons

The evolution of the structure and substructure of metals Ti and Mg with hexagonal close-packed (hcp) lattice is studied during their mechanical activation in a planetary ball mill in liquid hydrocarbons (toluene, n-heptane) and with additions of carbon materials (graphite, fullerite, nanotubes) by X-ray diffraction, scanning electron microscopy, and chemical analysis. The temperature behavior and hydrogen-accumulating properties of mechanocomposites are studied. During mechanical activation of Ti and Mg, liquid hydrocarbons decay, metastable nanocrystalline titanium carbohydride Ti(C,H) x and magnesium hydride β-MgH2 are formed, respectively. The Ti(C,H) x and MgH2 formation mechanisms during mechanical activation are deformation ones and are associated with stacking faults accumulation, and the formation of face-centered cubic (fcc) packing of atoms. Metastable Ti(C,H)x decays at a temperature of 550°C, the partial reverse transformation fcc → hcp occurs. The crystalline defect accumulation (nanograin boundaries, stacking faults), hydrocarbon destruction, and mechanocomposite formation leads to the enhancement of subsequent magnesium hydrogenation in the Sieverts reactor.

Modeling microstructure evolution in magnesium: Comparison of detailed and reduced-order kinematic models

The inelastic behavior of hcp metals, such as magnesium (Mg) and its alloys, is dominated by the shortage of available slip systems and the resulting competition between dislocation slip and deformation twinning to accommodate large, irreversible deformation. A variety of models exist to describe the material behavior to varying degrees of accuracy and efficiency. Specifically, detailed crystal plasticity models account for the full set of slip and twin systems, thereby providing detailed microstructural insight at high computational costs. By contrast, reduced-order models aim to describe the same material response by a contracted set of phenomenological internal variables, resulting in significant efficiency gains at the cost of accuracy. Here, we contrast two such approaches for the example of pure Mg and apply those to model texture and yield surface evolution in applications including cold rolling and uniaxial compressions on textured Mg polycrystals. For the latter, we also compare simulated stress–strain predictions to experimental data. We highlight common features and key differences between the two models and compare their levels of accuracy and efficiency for the chosen applications. Our findings demonstrate that the efficient model agrees well with the full-detail calculations at lower levels of strain but shows deviations at large strains due to the missing account of lattice misorientation. We thus show that formulations employing differing kinematic assumptions can predict similar macroscopic behavior by altering material parameters (i.e., using a more detailed model to inform coarse-scale models).

Anisotropic hydrogen diffusion in \u03b1-Zr and Zircaloy predicted by accelerated kinetic Monte Carlo simulations

This report presents an accelerated kinetic Monte Carlo (KMC) method to compute the diffusivity of hydrogen in hcp metals and alloys, considering both thermally activated hopping and quantum tunneling. The acceleration is achieved by replacing regular KMC jumps in trapping energy basins formed by neighboring tetrahedral interstitial sites, with analytical solutions for basin exiting time and probability. Parameterized by density functional theory (DFT) calculations, the accelerated KMC method is shown to be capable of efficiently calculating hydrogen diffusivity in α-Zr and Zircaloy, without altering the kinetics of long-range diffusion. Above room temperature, hydrogen diffusion in α-Zr and Zircaloy is dominated by thermal hopping, with negligible contribution from quantum tunneling. The diffusivity predicted by this DFT + KMC approach agrees well with that from previous independent experiments and theories, without using any data fitting. The diffusivity along <c> is found to be slightly higher than that along <a>, with the anisotropy saturated at about 1.20 at high temperatures, resolving contradictory results in previous experiments. Demonstrated using hydrogen diffusion in α-Zr, the same method can be extended for on-lattice diffusion in hcp metals, or systems with similar trapping basins.

Shock compression and release of a-axis magnesium single crystals: Anisotropy and time dependent inelastic response

To gain insight into inelastic deformation mechanisms for shocked hexagonal close-packed (hcp) metals, particularly the role of crystal anisotropy, magnesium (Mg) single crystals were subjected to shock compression and release along the a-axis to 3.0 and 4.8 GPa elastic impact stresses. Wave profiles measured at several thicknesses, using laser interferometry, show a sharply peaked elastic wave followed by the plastic wave. Additionally, a smooth and featureless release wave is observed following peak compression. When compared with wave profiles measured previously for c-axis Mg [Winey et al., J. Appl. Phys. 117, 105903 (2015)], the elastic wave amplitudes for a-axis Mg are lower for the same propagation distance, and less attenuation of elastic wave amplitude is observed for a given peak stress. The featureless release wave for a-axis Mg is in marked contrast to the structured features observed for c-axis unloading. Numerical simulations, using a time-dependent anisotropic modeling framework, showed that the wave profiles calculated using prismatic slip or (101¯2) twinning, individually, do not match the measured compression profiles for a-axis Mg. However, a combination of slip and twinning provides a good overall match to the measured compression profiles. In contrast to compression, prismatic slip alone provides a reasonable match to the measured release wave profiles; (101¯2) twinning due to its uni-directionality is not activated during release. The experimental results and wave profile simulations for a-axis Mg presented here are quite different from the previously published c-axis results, demonstrating the important role of crystal anisotropy in the time-dependent inelastic deformation of Mg single crystals under shock compression and release.

Atomic self-diffusion anisotropy of HCP metals from first-principles calculations

A plane wave pseudo-potential method based on density functional theory is employed to calculate the migration energy barrier for the atomic self-diffusion in HCP metals including Mg, Zn, Ti, Zr, and Hf. The influences of some key factors (plane-wave cutoff energy, k-mesh, supercell size, and geometric optimization scheme) on the calculated migration energy barrier and its anisotropy are systematically investigated. We show that the supercell size affects heavily the migration energy barrier and its anisotropy for the metals with valence d electrons (Ti, Zr, and Hf) but not for the ones with only valence s metals (Mg). In general, the anisotropy of the migration energy barrier reduces with increasing size of the supercell especially for Ti, Zr, and Hf. The optimization of the shape and volume of the supercell matters for the migration energy barrier calculated with the small size supercell but not for that calculated with the large supercell. With the calculated migration energy barrier, the self-diffusion coefficients are evaluated based on the transition state theory and compared with other first-principles calculations and the experimental measurements.

Subsequent Yield Behavior of Hexagonal Metal with Rolling Texture

The subsequent yield surface of a rolling textured polycrystalline hexagonal metal sheet is computed using homogenization-based crystal plasticity. Hexagonal metals, such as magnesium and titanium, generally shows poorer formability compared to than cubic metals. The subsequent yielding behavior of a polycrystalline metal strongly affects the formability. The abrupt strain path change method is used to evaluate the direction of plastic flow, allowing the non-normality effect of the hexagonal metal to be quantitatively determined. The homogenization-based crystal plasticity model is used for representing the polycrystalline behavior of a HCP metal. The role of each slip system in the subsequent yield behavior is investigated. The mechanism of subsequent yielding of the HCP metal, which induces the non-normality effect, is discussed.

A multi-state modified embedded atom method potential for titanium

The continuing search for broadly applicable, predictive, and unique potential functions led to the invention of the multi-state modified embedded atom method (MS-MEAM) (Baskes et al 2007 Phys. Rev. B 75 094113). MS-MEAM replaced almost all of the prior arbitrary choices of the MEAM electron densities, embedding energy, pair potential, and angular screening functions by using first-principles computations of energy/volume relationships for multiple reference crystal structures and transformation paths connecting those reference structures. This strategy reasonably captured diverse interactions between atoms with variable coordinations in a face-centered-cubic (fcc)-stable copper system. However, a straightforward application of the original MS-MEAM framework to model technologically useful hexagonal-close-packed (hcp) metals proved elusive. This work describes the development of an hcp-stable/fcc-metastable MS-MEAM to model titanium by introducing a new angular function within the background electron density description. This critical insight enables the titanium MS-MEAM potential to reproduce first principles computations of reference structures and transformation paths extremely well. Importantly, it predicts lattice and elastic constants, defect energetics, and dynamics of non-ideal hcp and liquid titanium in good agreement with first principles computations and corresponding experiments, and often better than the three well-known literature models used as a benchmark. The titanium MS-MEAM has been made available in the Knowledgebase of Interatomic Models (https://openkim.org/) (Tadmor et al 2011 JOM 63 17).

Accounting of the Elasticity Modules Anisotropy in HSP Metals for X-Ray Investigations of Dislocation Structure

A calculation of X-ray diffraction on the dislocation structure of polycrystalline materials with the biaxial anisotropy of the crystal lattice has been carried out. The task was reduced to definition of the field of lattice distortion in this neighborhood applied to edge dislocations of the «c» type in condition of anisotropy of elastic modules of a crystal. As a result of general solution of this task, a parameter of spatial anisotropy of the distortion field was defined from elastic modules and further included into tensors of transformation of both initial isotropic model of this field and its coordinates. According to this principle a modified mathematical model of the field of elastic atomic displacements in the neighborhood of an edge dislocation has been built. The final result shows that this anisotropy entirely reflects onto dislocation specific parameters of distortion that can be obtained by an XRD method for determination dislocation distributions and density. It is noted that for hcp metals widely used, accounting of this anisotropy would be reduced to small corrections of parameters.

Intrinsic Behaviour of Mode II and Mode III Long Fatigue Cracks in Zirconium and the Ti-6Al-4V Alloy

This work is focused on experimental study of micromechanisms of mode II and mode III fatigue cracks in metallic materials in the near-threshold regime. The resistance to fatigue crack growth can be divided to an intrinsic component (ahead of the crack tip) and an extrinsic component (shielding, closure), which is significantly higher than the intrinsic one. Fracture surfaces from the Ti6Al4V alloy and pure zirconium were observed in three dimensions. Experiments were conducted using a special device for simultaneous crack loading in modes II and III. Additionally, pure mode II and pure mode III experiments were done using CTS and torsion specimens, respectively. At the beginning of all experiments, crack closure was eliminated due to precracks generated under cyclic compressive loading. A common mechanism of local mode II advances was observed in both modes II and III. The results were similar to those of pure titanium. The hcp metals exhibit a transition behaviour between materials with coplanar shear-mode crack propagation and materials with a high tendency to deflect to the opening mode I.

Grain neighbour effects on twin transmission in hexagonal close-packed materials.

Materials with a hexagonal close-packed (hcp) crystal structure such as Mg, Ti and Zr are being used in the transportation, aerospace and nuclear industry, respectively. Material strength and formability are critical qualities for shaping these materials into parts and a pervasive deformation mechanism that significantly affects their formability is deformation twinning. The interaction between grain boundaries and twins has an important influence on the deformation behaviour and fracture of hcp metals. Here, statistical analysis of large data sets reveals that whether twins transmit across grain boundaries depends not only on crystallography but also strongly on the anisotropy in crystallographic slip. We show that increases in crystal plastic anisotropy enhance the probability of twin transmission by comparing the relative ease of twin transmission in hcp materials such as Mg, Zr and Ti.

Thermally activated deformation and the rate controlling mechanism in CoCrFeMnNi high entropy alloy

The nature of obstacles to dislocation motion in CoCrFeMnNi alloy was analyzed using the thermally activated deformation analyses at low temperatures. The strong temperature dependence of yield stress and small activation volume in CoCrFeMnNi favor the dislocation glide over the obstacles with high friction stress. The activation volume of CoCrFeMnNi alloy (10–100 b3) in this study is much smaller than those of conventional FCC metals (102~103 b3), but close to those observed in BCC metals (8–100 b3) and HCP metals (5–100 b3). The increase of the activation volume with strain supports overcoming the nanoscale inhomogeneity such as co-clusters and/or short range orders as the rate controlling mechanism. The transition of dislocation structure from planar array to cell structure at 20% strain in CoCrFeMnNi reported in the literature can be attributed to the prevalent shearing of nanoscale inhomogeneity with strain.

Jump to contact of hcp nanowires

Exploiting molecular dynamics simulations, we have investigated jump to contact (JC) at the recontact of broken Mg and Cd nanowires. We observed frequent JCs for junctions of these soft hcp metals, as previously reported for soft fcc metals [C. Untiedt et al., Phys. Rev. Lett. 98, 206801 (2007)]. Thus, the crystal structure matters little for JC, and the high rate of JC should be a common characteristic of soft metal junctions. Recontacts of broken nanowires also lead to the frequent formation of single-atom contacts (SACs). For comparison, we have also studied JC and the SAC formation for tip–sample junctions of Pb.

Effect of β-stabilizer elements on stacking faults energies and ductility of α-titanium using first-principles calculations

The effect of W, Mo, V, Ta, and Nb, five common β-stabilizing substitutional elements, on α-Ti stacking fault energy has been studied using first principle calculations. The generalized stacking fault energy (GSFE) curves have been determined for different concentrations of β-stabilizers at the fault plane using supercells with up to 360 atoms. Both basal and prismatic slip systems with the stable (γSF) and unstable (γUSF) stacking faults and twinning fault energies were determined. All the alloying elements reduce the stacking fault energy for Ti for both basal and prismatic slip. At higher concentration of 25 at. % of V, Ta, and Nb at the slip plane, the basal slip becomes more favorable than the prismatic slip in Ti. Ti-Mo and Ti-W systems also show a significant shift in the GSFE curve towards a higher shear deformation strain along 〈011¯0〉 due to the change in bond character between Ti and those two elements. Using Rice criterion, which employs γS/γUSF ratio to estimate ductility, we show that all the alloying elements likely improve the ductility of α-Ti with Ti-25 at. % Nb exhibiting the most ductile behavior. However, according to the Tadmor and Bernstein model, all the alloying elements considered here do not improve the partial dislocation emission or the twinning propensity in spite of decreasing the stacking fault energies for α-Ti and. Hence, a better empirical model that incorporates changes in the character of directional bonding upon alloying is needed to estimate how alloying influences ductility in hcp metals.

Comprehensive first-principles study of stable stacking faults in hcp metals

The plastic deformation in hcp metals is complex, with the associated dislocation core structures and properties not well understood on many slip planes in most hcp metals. A first step in establishing the dislocation properties is to examine the stable stacking fault energy and its structure on relevant slip planes. However, this has been perplexing in the hcp structure due to additional in-plane displacements on both sides of the slip plane. Here, density functional theory guided by crystal symmetry analysis is used to study all relevant stable stacking faults in 6 hcp metals (Mg, Ti, Zr, Re, Zn, Cd). Specially, the stable stacking fault energy, position, and structure on the Basal, Prism I and II, Pyramidal I and II planes are determined using all-periodic supercells with full atomic relaxation. All metals show similar stacking fault position and structure as dictated by crystal symmetry, but the associated stacking fault energy, being governed by the atomic bonding, differs significantly among them. Stacking faults on all the slip planes except the Basal plane show substantial out-of-plane displacements while stacking faults on the Prism II, Pyramidal I and II planes show additional in-plane displacements, all extending to multiple atom layers. The in-plane displacements are not captured in the standard computational approach for stacking faults, and significant differences are shown in the energies of such stacking faults between the standard approach and fully-relaxed case. The existence of well-defined stable stacking fault on the Pyramidal planes suggests zonal dislocations are unlikely. Calculations on the equilibrium partial separation further suggests 〈c + a〉 dissociation into three partials on the Pyramidal I plane is unlikely and 〈c〉 dissociation on Prism planes is unlikely to be stable against climb-dissociation onto the Basal planes in these metals.

Nonstoichiometric molybdenum hydride

The molybdenum-hydrogen system was studied in a diamond anvil cell at high hydrogen pressure up to 30 GPa at room temperature by X-ray diffraction. At pressure around 4 GPa a phase transformation was observed of a bcc metal to a hydride with a hcp metal lattice and H/Mo ≈ 1.1. Further hydrogen pressure increase resulted in a continuous increase of the hydrogen content of the hydride. At about 15 GPa the hydrogen content reached saturation, and no further hydrogen absorption occured up to the maximal reached pressure. The saturation composition H/Mo = 1.35 (10) was estimated from volumetric considerations.

Self-interstitials structure in the hcp metals: A further perspective from first-principles calculations

We study the structure of several standard and non-standard self-interstitial configurations in a series of hcp metals, by using Density Functional Theory as embodied in the computer codes SIESTA and WIEN2k. The considered metals include Be, Mg, Ti, Zr, Co, Zn, and Cd, thus spanning the whole range of experimental c/a ratios, different kinds of bonding, and even magnetism (Co). The results show the importance of low symmetry configurations, closely related to the non-basal crowdion, in order to rationalize the experimental data on self-interstitial structure and migration.