Hexagonal Close-packed Crystals Research Articles

Ab initio investigation of electronic structure and magnetic transformation during the bcc to hcp transition in Fe induced by pressure

The pressure-induced structural transition from a body-centered cubic (bcc) to a hexagonal close-packed (hcp) crystal in Fe is studied through ab initio electronic structure calculations, combining with the thermodynamic and kinetic phase-transition methods. According to the energy-volume relationship and thermodynamic criterion, the reasonable phase transition pressure is calculated to be about 13.88 GPa. The SSNEB method is employed to examine kinetic structural and barrier changes along bcc-hcp transition under various pressures. The transformation path involves the deformation of (110)bcc into the tightly packed (0001)hcp, accompanied by the relative slip of (110)bcc along the [1̅10]bcc direction, leading to the formation of the hcp structure. Our results indicate a reduction in the transition barrier of bcc-hcp with increasing pressure. Under the thermodynamic phase transition pressure, the bcc-hcp phase transition barrier is still as high as 140 meV, implying that pure hydrostatic pressure is not a sufficient condition to drive the phase transition. In addition, different from the continuous change of volume, the magnetism of the structure undergoes a magnetic mutation at the transition state, and the phase transition process involves complex magnetic transitions.

In situ observation of the atomic shuffles during the {112¯1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{11}}\\bar{{{2}}}{{1}}$$\\end{document}} twinning in hexagonal close-packed rhenium

Twinning, on par with dislocations, is critically required in plastic deformation of hexagonal close-packed crystals at low temperatures. In contrast to that in cubic-structured crystals, twinning in hexagonal close-packed crystals requires atomic shuffles in addition to shear. Though the twinning shear that is carried by twinning dislocations has been captured for decades, direct experimental observation of the atomic shuffles, especially when the shuffling mode is not unique and does not confine to the plane of shear, remains a formidable challenge to date. Here, by using in-situ transmission electron microscopy, we directly capture the atomic mechanism of the 112¯1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left\\{11\\bar{2}1\\right\\}$$\\end{document} twinning in hexagonal close packed rhenium nanocrystals. Results show that the 112¯1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left\\{11\\bar{2}1\\right\\}$$\\end{document} twinning is dominated by the (b1/2, h1/2) twinning disconnections. In contrast to conventional expectations, the atomic shuffles accompanying the twinning disconnections proceed on alternative basal planes along 1/6 11¯00\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left\\langle 1\\bar{1}00\\right\\rangle$$\\end{document}, which may be attributed to the free surface in nanocrystal samples, leading to a lack of mirror symmetry across the 112¯1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left\\{11\\bar{2}1\\right\\}$$\\end{document} twin boundary.

Data-driven texture design for reducing elastic and plastic anisotropy in titanium alloys

Polycrystalline titanium alloys exhibit anisotropic elastic and plastic properties, which hinder their extensive application as structural components. Overcoming this anisotropy via texture control is challenging due to the anisotropy intrinsic to the titanium single crystal. We propose a theoretical framework to derive textures that minimize anisotropy while maximizing Young’s modulus or flow stress. The workflow integrates data-driven methods, convex optimization theory, and computational crystal plasticity, using measured elastic constants and the alloy’s three slip modes. Optimization constraints are applied to predict textures that satisfy an anisotropy-reducing texture-property relationship. Examples include minimizing both elastic and plastic anisotropy while maximizing stiffness or flow stress, maximizing both stiffness and flow stress, and minimizing the number of distinct orientations. Deformation crystal plasticity simulations of 3D polycrystal microstructure realizations of the example textures demonstrate the achievement of target properties. We show that uniformly distributed (or no) textures or textures designed to purely reduce elastic anisotropy are accompanied by reduced moduli. Counterintuitively, the analysis reveals that appropriate fractions of a relatively small number of select orientations can reduce elastic or plastic anisotropy. Moreover, we derive anisotropy-reducing textures constrained to achieve similarity to those from common metal forming processes like rolling. Finally, we show that anisotropy-reducing textures from this framework can be effectively used for minimizing anisotropy in other Ti alloys, without the need to repeat the data-collection and optimization processes. This study offers new insights into the link between microstructure texture and structural properties, providing a novel approach to designing materials of anisotropic hexagonal close-packed crystals.

An assessment of polarized light microscopy as a characterization method for crystal plasticity simulations

Polarized light microscopy is a large-area, high-resolution, high-throughput microstructural characterization method for polycrystalline materials comprised of hexagonal close-packed crystals. Due to the fact that polarized light microscopy only determines the orientation of a crystal’s c axis, it is necessary to assess the applicability of this new characterization modality for use in integrated computational materials engineering workflows for simulating the deformation response of polycrystalline materials. We present a computational study in which the effect of this orientation ambiguity on the predictions of crystal plasticity finite element simulations is quantified. We focus on an idealized polycrystalline sample with random texture, from which a number of c axis-similar samples are generated, each with random rotations about each constituent crystal’s c axis. We scrutinize the differences in stress field predictions between the reference sample and the randomly altered samples during monotonic tensile tests, as well as the spatial differences in predictions. Our findings indicate that differences are lowest in the elastic regime, and increase dramatically during the macroscopic elastic–plastic transition. We further find that results do not exhibit a strong spatial dependence, indicating that orientation and neighborhood are the primary causes of differences in stress field predictions.

Low-temperature anomalies in solid 4He (Review article)

The thermodynamic and mechanic anomalies within the region 0.1–0.5 K experimentally observed in hexagonal close-packed solid 4He crystal are discussed and interpreted on the basis of a polytypic HCP structure (close-packed stack of 2D crystalline planes on the triangular lattice). It elucidated the principal role of the stacking faults and Shockley’s partial dislocations in the quite unexpected low-temperature behavior of the solid 4He.

Densest-known packings and phase behavior of hard spherical capsids.

By mostly using Monte Carlo numerical simulation, this work investigates the densest-known packings and phase behavior of hard spherical capsids, i.e., hard infinitesimally thin spherical caps with a subtended angle larger than the straight angle. The infinitely degenerate densest-known packings are all characterized by hard spherical capsids that interlock and can be subdivided into three families. The first family includes crystalline packings that are constructed by suitably rotating and stacking layers of hexagonally arranged and suitably tilted hard spherical capsids; depending on the successive rotations, the crystalline packings of this family can become the face-centered cubic crystal, the hexagonal close-packed crystal, and their infinitely degenerate variants in the hard-sphere limit. The second family includes crystalline packings that are characterized by rhombic motifs; they all become the face-centered cubic crystal in the hard-sphere limit. The third family includes crystalline packings that are constructed by suitably shifting and stacking layers in which hard spherical capsids are arranged in tightly packed, straight or zigzag, columns; depending on the successive shifts, the crystalline packings of this family can become the face-centered cubic crystal, the hexagonal close-packed crystal, and their infinitely degenerate variants in the hard-sphere limit. In the plane number density vs subtended angle, the phase diagram of hard spherical capsids features a hexagonal columnar liquid-crystalline phase, toward the hard-hemispherical-cap limit, and a plastic-crystalline phase, toward the hard-sphere limit, in addition to the isotropic fluid phase and crystalline phases. On departing from the hard-sphere limit, the increasing propensity of hard spherical capsids to interlock progressively disfavors the plastic-crystalline phase while favoring auto-assemblage into mostly dimeric interlocks in the denser isotropic fluid phase so that a purely entropic isotropic-fluid-plastic-crystal-isotropic-fluid re-entrant sequence of phase transitions is observed in systems of hard spherical capsids with a subtended angle intermediate between the straight angle and the complete angle.

Modeling Thermoelasticity of HCP single crystals using a nonlocal discrete approach

This paper presents full-field modeling Thermoelasticity of hexagonal close-packed (HCP) single crystals using reformulations of conventional continuum theories based on a novel nonlocal lattice particle method (LPM). In LPM, grain domain is modeled as an assembly of regularly packed material particles according to the atomic lattice. The interaction between material particles is nonlocal, e.g., for mechanical problems, a material particle interacts with neighboring material particles up to certain distance via bonds and the interaction between two material particles depends on the deformation states of not only the two material particles but also all their neighbors. To determine the nonlocal interaction between material particles, a top-down approach based on the classical continuum theories is developed. Equivalency assumptions of energy, heat transfer rate and thermal strain between LPM and its continuum counterpart are made to consistently determine the material particle interaction for mechanical, thermal, and thermal–mechanical coupling problems, respectively. To capture the crystallographic orientation, a lattice rotation scheme that is equivalent to the coordinate transformation used in the classical continuum theories is adopted. Numerical studies regarding validity of the proposed nonlocal discrete reformulation and accuracy of the model prediction are conducted for all three types of analysis. Good agreements are observed between the results from the developed reformulations and the conventional continuum theories.

A New Anti-Alias Model of Ab Initio Calculations of the Generalized Stacking Fault Energy in Face-Centered Cubic Crystals

The anti-alias model is an effective method to calculate the generalized stacking fault energy of the hexagonal close-packed crystals, but it has not been applied to the face-centered cubic crystals due to two different stacking faults occurring in the supercell during the sliding process. Based on the symmetry of these two stacking faults and the existing single analytic formula of the generalized stacking fault energy, we successfully extend the anti-alias model to compute the generalized stacking fault energy of face-centered cubic crystals, and the common fcc metals Al, Ni, Ag and Cu are taken as specific examples to illustrate the computational details. Finally, the validity of the proposed model is verified by data comparison and analysis. It is suggested that the anti-alias model is a good choice for the researchers to obtain more accurate generalized stacking fault energy of face-centered cubic metals.

Thermal plasma sintering of forsterite ceramics

To date, new synthesis methods of forsterite (Mg2SiO4) ceramics are being searched for refractory industry. The limiting factor of Mg2SiO4 synthesis is its high melting point of 1890 °C, which makes it difficult to conduct experimental studies.The paper proposes a new method of forsterite synthesis based on thermal plasma. The plasma source is an effective medium for heating and melting refractory materials. For the Mg2SiO4synthesis, such initial materials are used as natural and sub-standard raw materials (silica sand sifting, microsilica, magnesite). The degree of crystallinity varies from 10 to 98 %, which allows studying the formation of the phase composition at different parameters.According to powder X-ray diffraction patterns, at a MgO/SiO2stoichiometric ratio of 1.34, the obtained melting products consist up to 90 % Mg2SiO4and the X-ray amorphous phase content varies from 5 to 12 %. After isothermal exposure, the amorphous phase is represented by silicon dioxide in the polymorphic modification of cristobalite. According to scanning electron microscopy observations, the formation of hexagonal close-packed crystals occurs on the surface of the ceramic sample, with the size ranging from 180 to 250 µm. The elemental composition of the crystal consists of ~ 38.60 wt. % O, ~ 28.54 wt. % Mg, ~ 26.92 wt. % Si, which matches the theoretical composition of Mg2SiO4. A detailed analysis of a single crystal shows that the surface structure consists of acicular microcrystals arranged symmetrically, but at the same time overlapping each other, thereby forming a lattice structure. The growth angle between the cubic microcrystals tends to ~87–94 degrees.

White Laue and powder diffraction studies to reveal mechanisms of HCP-to-BCC phase transformation in single crystals of Mg under high pressure

Mechanisms of hexagonal close-packed (HCP) to body-centered cubic (BCC) phase transformation in Mg single crystals are observed using a combination of polychromatic beam Laue diffraction and monochromatic beam powder diffraction techniques under quasi-hydrostatic pressures of up to 58 ± 2 GPa at ambient temperature. Although experiments were performed with both He and Ne pressure media, crystals inevitably undergo plastic deformation upon loading to 40–44 GPa. The plasticity is accommodated by dislocation glide causing local misorientations of up to 1°–2°. The selected crystals are tracked by mapping Laue diffraction spots up to the onset of the HCP to BCC transformation, which is determined to be at a pressure of 56.6 ± 2 GPa. Intensity of the Laue reflections from HCP crystals rapidly decrease but no reflections from crystalline BCC phase are observed with a further increase of pressure. Nevertheless, the powder diffraction shows the formation of 110 BCC peak at 56.6 GPa. The peak intensity increases at 59.7 GPa. Upon the full transformation, a powder-like BCC aggregate is formed revealing the destructive nature of the HCP to BCC transformation in single crystals of Mg.

Resolving local microstructure variations in Zr-2.5Nb CANDU pressure tubes using high spatial resolution electron backscatter diffraction and imaging

The alloy Zr-2.5Nb is used for manufacturing the pressure tubes installed in the core of Canada Deuterium Uranium (CANDU) nuclear reactors. This alloy consists of α-zirconium with hexagonal close-packed (HCP) crystals and a minor β-zirconium phase with body centered cubic (BCC) crystals that are mainly located in between the α-grains. Due to the significant elastic and plastic anisotropy of HCP crystals as well as the development of strong textures during manufacturing, these tubes exhibit significant mechanical anisotropy. However, both local microstructure and texture can change, affecting the local patterning of stress fields and the subsequent hydrogen embrittlement rate. Resolving the local microstructure variation of Zr-2.5Nb is challenging due to the development of nano-sized grains during manufacturing. This paper focuses on developing a procedure for the consistent characterization of such local variations using high spatial resolution electron backscatter diffraction (EBSD) and imaging. Microstructure variations along the radial and transverse directions of the transverse-radial plane, as well as along the axial direction of the transverse-axial and radial-axial planes are studied. It is shown that microstructure variations are non-negligible. For the locations that the transverse-radial planes are studied, pole figures rotate, and Kearns factors decrease along the radial direction. In addition, the morphologies of both α- and β-crystals change significantly along the radial direction. With the procedure used for characterization, some β-crystals are indexed and their orientation relationship with their neighboring α-grains are examined.

Local and Global Order in Dense Packings of Semi-Flexible Polymers of Hard Spheres.

The local and global order in dense packings of linear, semi-flexible polymers of tangent hard spheres are studied by employing extensive Monte Carlo simulations at increasing volume fractions. The chain stiffness is controlled by a tunable harmonic potential for the bending angle, whose intensity dictates the rigidity of the polymer backbone as a function of the bending constant and equilibrium angle. The studied angles range between acute and obtuse ones, reaching the limit of rod-like polymers. We analyze how the packing density and chain stiffness affect the chains' ability to self-organize at the local and global levels. The former corresponds to crystallinity, as quantified by the Characteristic Crystallographic Element (CCE) norm descriptor, while the latter is computed through the scalar orientational order parameter. In all cases, we identify the critical volume fraction for the phase transition and gauge the established crystal morphologies, developing a complete phase diagram as a function of packing density and equilibrium bending angle. A plethora of structures are obtained, ranging between random hexagonal closed packed morphologies of mixed character and almost perfect face centered cubic (FCC) and hexagonal close-packed (HCP) crystals at the level of monomers, and nematic mesophases, with prolate and oblate mesogens at the level of chains. For rod-like chains, a delay is observed between the establishment of the long-range nematic order and crystallization as a function of the packing density, while for right-angle chains, both transitions are synchronized. A comparison is also provided against the analogous packings of monomeric and fully flexible chains of hard spheres.

Single-orientation colloidal crystals from capillary-action-induced shear.

We study the crystallization of colloidal dispersions under capillary-action-induced shear as the dispersion is drawn into flat walled capillaries. Using confocal microscopy and small angle x-ray scattering, we find that the shear near the capillary walls influences the crystallization to result in large random hexagonal close-packed (RHCP) crystals with long-range orientational order over tens of thousands of colloidal particles. We investigate the crystallization mechanism and find partial crystallization under shear, initiating with hexagonal planes at the capillary walls, where shear is highest, followed by epitaxial crystal growth from these hexagonal layers after the shear is stopped. We then characterize the three-dimensional crystal structure finding that the shear-induced crystallization leads to larger particle separations parallel to the shear and vorticity directions as compared to the equilibrium RHCP structure. Confocal microscopy reveals that competing shear directions, where the capillary walls meet at a corner, create differently oriented hexagonal planes of particles. The single-orientation RHCP colloidal crystals remain stable after formation and are produced without the need of complex shear cell arrangements.

A model of porous plastic single crystals based on fractal slip lines distribution

The ductile failure of crystalline materials is strongly linked to the growth of intragranular voids. The estimation of the overall yield criterion thus requires to take into account the anisotropic plastic behavior of the single crystal. In the framework of the kinematic limit-analysis approach, this problem has been considered up to now with Gurson-type isotropic trial velocity fields. In the present work, a different class of piecewise constant velocity fields is proposed based on a detailed analysis of FFT numerical results on the strain localization in porous single crystals with periodic distributions of voids. This original approach is implemented for the model 2D problem of a square or hexagonal array of cylindrical voids in a hexagonal close-packed single crystal with in-plane prismatic slip systems. For equibiaxial loadings, the assumption of discontinuous velocity field provides a good approximation of the smooth jumps observed in the numerical results. Consistently, this new proposal leads to a significant improvement on the macroscopic yield stress with respect to the estimate based on an isotropic velocity field. Our theoretical estimate almost coincides with the FFT numerical results for all the unit-cells and crystalline orientations considered.

Surface Characterization and Optimization of Porous Zinc Anodes to Improve Cycle Stability by Mitigating Dendritic Growth

Zinc-based batteries are a scalable and safe alternative to Lithium-ion batteries due to the nature of abundance, low cost and easy to process. In this work, we have successfully synthesized porous zinc electrodes (PZEs) via a gel-binder method that can stably charge and discharge for over 700 h at 1 mA cm−2 before showing signs of failure. We compared PZEs synthesized from small (60 nm), intermediate (10 μm), and large (150 μm) zinc particles to determine which surface features are best suited to mitigate dendritic growth and to improve electrolyte stability. The zinc deposits on the large PZE shows a stable and flat morphology, which does not form the hexagonal close-packed (HCP) crystal structure that is typically seen on planar zinc anodes. The intermediate PZE has an increased affinity to deposit onto the glass microfiber separator leading to a decrease of active material on the anode that causes instability during galvanostatic cycling. Both planar zinc and small PZE show HCP deposits that are normal to the surface, which result in very poor electrochemical performance. As the particle size increases, the deposits transition from HCP crystals to flat amorphous metal deposits, increasing cyclic stability.

Nucleation and growth of [formula omitted] compression twin in Mg single crystals

The {101¯1} compression twin is more commonly observed under a-axis tension rather than c-axis compression in hexagonal close-packed (hcp) Mg single crystals both in experiments and atomistic simulations. In this work, molecular dynamics simulations are applied to investigate the nucleation and growth of {101¯1} twin in Mg single crystal, which is crucial for a comprehensive understanding of the plasticity of hcp metals. A {101¯1} twin embryo with 4-layer height is found to be naturally nucleated at the free surface via 〈a〉 dislocation slip in Mg single crystal. The nucleation of the {101¯1} twin embryo involves the cross-slip of the nucleated prismatic 〈a〉 dislocation onto pyramidal {101¯1} plane, which is achieved by slip of 〈a〉 dislocation and shear along the 〈101¯2〉 direction. Basal stacking faults (SFs) forms in twin embryo and grows with the migration of {101¯1} twin boundary. The formation of basal SFs in {101¯1} twin embryo can greatly reduce the required atomic shuffling in 〈12¯10〉 direction, thus facilitate the development of a {101¯1} twin embryo. The basal SFs inside {101¯1} twin are anomalous SFs without dislocation activities involved, thus the {101¯1} twinning shear is not influenced by the existence of basal SFs, which is consistent with the irrational shear of 2-layer twinning dislocation.

Study of HCP (Hexagonal Close-Packed) Crystal Structure Lattice through Topological Descriptors.

Chemical graph theory is a multidisciplinary field where the structure of the molecule is analyzed as a graphical structure. Chemical descriptors are one of the most important ideas employed in chemical graph theory; this is to associate a numerical value with a graph structure that often has correlation with corresponding chemical properties. In this paper, we investigate another very important closed-packed usual crystal structure defined as HCP (Hexagonal Close-Packed) crystal structure and its lattice formed by arranging its unit cells in a dimension for topological descriptors based on a neighborhood degree, reverse degree, and degree. Furthermore, we classify which descriptor is more dominating.

Crystallization of Flexible Chains of Tangent Hard Spheres under Full Confinement.

We present results from extensive Monte Carlo simulations on the crystallization of athermal polymers under full confinement. Polymers are represented as freely jointed chains of tangent hard spheres of uniform size. Confinement is applied through the presence of flat, parallel, and impenetrable walls in all dimensions. We analyze crystallization as the summation of two contributions: one that occurs in the bulk volume of the system (bulk crystallization), and one on the wall surfaces (surface crystallization). Depending on volume fraction initially amorphous (disordered) hard-sphere chain packings transit to the stable crystal phase. The established ordered morphologies consist primarily of hexagonal close-packed (HCP) crystals in the bulk volume and of triangular (TRI) crystals on the surface. As in the case of athermal packings in the bulk (without confinement), a structural competition is observed between the 5-fold local symmetry and the formation of close-packed crystallites. Effectively, the full confinement inside a cube favors the growth of the HCP crystal, as the FCC one is quite incompatible with the imposed spatial constraints. Consequently, we observe the formation of noncompact ordered motifs which grow from the surface to the inner volume of the simulation cell. We further compare the 2D and 3D crystals formed by monomeric hard spheres under the same simulation conditions. Significant differences are observed at low densities that tend to diminish as concentration increases.

Temperature-Dependent EXAFS Debye–Waller Factor of Distorted HCP Crystals

In this paper, an efficient theoretical model has been developed to calculate and analyze the extended X-ray absorption fine structure (EXAFS) Debye–Waller factor (DWF) of distorted hexagonal close-packed (HCP) crystals with non-ideal axial ratio c/a in the temperature dependence. The analysis procedure is performed by evaluating the influence of temperature on the amplitude reduction and phase shift of EXAFS oscillation that is expressed in terms of EXAFS DWF using EXAFS cumulants in the cumulant expansion approach. The calculation model of the temperature-dependent EXAFS cumulants is expanded from the correlated Einstein model using the classical statistical theory and the anharmonic effective potential that depends on non-ideal axial ratio c/a of distorted HCP crystals. The numerical results for crystalline zinc agree well with those obtained from other theoretical methods and experiments at various temperatures. The obtained results show the present theoretical model is necessary to analyze and evaluate the temperature-dependent experimental EXAFS signals of distorted HCP crystals under the effect of non-ideal axial ratio c/a.

Laser shock peening-induced misfit dislocation at interfaces between HCP and BCC crystals of Ti6Al4V alloy and the corresponding dislocation patterns in two phases

Understanding of laser shock peening (LSP)-generated microstructural characteristics at the interfaces between hexagonal close-packed (HCP) and body-centered cubic (BCC) crystals and dislocation patterns could provide useful insights into designing the interface between both phases of dual- or multi- phase metallic materials, which is a key information for higher properties. Herein, with a severe plastic deformation process of LSP, a systematic work of the mechanism behind misfit dislocations at different grain size has been carried out. It demonstrates that, as the grain gradually is refined, extrusion and torsion of the lattice are important contributions to the modified d-spacing and quantity of misfit dislocation. Hence, the growth orientation and the style of bicrystal interface between HCP and BCC crystals are affected. Furthermore, the size effect of the LSP-generated dislocation pattern has a significant attribution to the stress of misfit dislocation originating from neighboring interfaces.