Hexagonal Close-packed Crystals Research Articles

Crystal Plasticity Modeling of Grey Cast Irons under Tension, Compression and Fatigue Loadings

The study of the micromechanical performance of materials is important in explaining their macrostructural behavior, such as fracture and fatigue. This paper is aimed, among other things, at reducing the deficiency of microstructural models of grey cast irons in the literature. For this purpose, a numerical modeling approach based on the crystal plasticity (CP) theory is used. Both synthetic models and models based on scanning electron microscope (SEM) electron backscatter diffraction (EBSD) imaging finite element are utilized. For the metal phase, a CP model for body-centered cubic (BCC) crystals is adopted. A cleavage damage model is introduced as a strain-like variable; it accounts for crack closure in a smeared manner as the load reverses, which is especially important for fatigue modeling. A temperature dependence is included in some material parameters. The graphite phase is modeled using the CP model for hexagonal close-packed (HCP) crystal and has a significant difference in tensile and compressive behavior, which determines a similar macro-level behavior for cast iron. The numerical simulation results are compared with experimental tensile and compression tests at different temperatures, as well as with fatigue experiments. The comparison revealed a good performance of the modeling approach.

Atomistic structures of 〈0001〉 tilt grain boundaries in a textured Mg thin film.

Nanocrystalline Mg was sputter deposited onto an Ar ion etched Si {100} substrate. Despite an ∼6 nm amorphous layer found at the interface, the Mg thin film exhibits a sharp basal-plane texture enabled by surface energy minimization. The columnar grains have abundant 〈0001〉 tilt grain boundaries in between, most of which are symmetric with various misorientation angles. Up to ∼20° tilt angle, they are composed of arrays of equally-spaced edge dislocations. Ga atoms were introduced from focused ion beam milling and found to segregate at grain boundaries and preferentially decorate the dislocation cores. Most symmetric grain boundaries are type-1, whose boundary planes have smaller dihedral angles with {21̄1̄0} rather than {101̄0}. Atomistic simulations further demonstrate that type-2 grain boundaries, having boundary planes at smaller dihedral angles with {101̄0}, are composed of denser dislocation arrays and hence have higher formation energy than their type-1 counterparts. The finding correlates well with the dominance of type-1 grain boundaries observed in the Mg thin film.

Impact of free energy of polymers on polymorphism of polymer-grafted nanoparticles.

Colloidal crystals have gathered wide attention as a model material for optical applications because of their feasibility in controlling the propagation of light by their crystal structure and lattice spacing as well as the simplicity of their fabrication. However, due to the simple interaction between colloids, the colloidal crystal structures that can be formed are limited. It is also difficult to adjust the lattice spacing. Furthermore, colloidal crystals are fragile compared to other crystals. In this study, we focused on polymer-grafted nanoparticles (PGNP) as a possible solution to these unresolved issues. We expected that PGNPs, composed of two distinct layers (the hard core of a nanoparticle and the soft corona of grafted polymers on the surface), will demonstrate similar behaviors as star polymers and hard spheres. We also predicted that PGNPs may exhibit polymorphism because the interaction between PGNPs strongly depends upon their grafting density and the length of the grafted polymer chains. Moreover, we expected that crystals made from PGNPs will be structurally tough due to the entanglement of grafted polymers. From exploration of crystal polymorphs of PGNPs by molecular dynamics simulations, we found face-centered cubic (FCC)/hexagonal close-packed (HCP) and body-centered cubic (BCC) crystals, depending on the length of the grafted polymer chains. When the chains were short, PGNPs behaved like hard spheres and crystals were arranged in FCC/HCP structure, much like the phase transition observed in an Alder transition. When the chains were long enough, the increase in the free energy of grafted polymers was no longer negligible and crystals were arranged in BCC structure, which has a lower density than FCC/HCP. When the chains were not too short or long, FCC/HCP structures were first observed when the volume fraction of system was small, but a phase transition occurred when the system was further compressed and the crystals arranged themselves in a BCC structure. These results most likely have laid strong foundations for future simulations and experimental studies of PGNP crystals.

Unconventional Deformation Twinning Mechanisms in Magnesium at High Strain Rates

Despite 150 years of research, there is still a lack of experimental evidence on how deformation twinning in hexagonal‑close‑packed (HCP) metals evolves at different strain rates. Here, we present a systematic investigation of {10-12} extension twinning mechanism in single crystal magnesium micropillars deformed over seven orders of magnitude of strain rate, from 10 ‑4 to 500 s ‑1 , revealing how the accommodation of newly formed twins depends on the kinetic compatibility of interfacial processes when high deformation rates are imposed. This work shows that deformation twinning is not only stress- but also strongly time‑controlled. Away from quasi‑static conditions, simple considerations of twinning shear do not suffice to describe unconventional twin morphologies, requiring the competition between dislocations and lattice distortions. Under shock compressions, the basal/prismatic transformation establishing a lattice misorientation of 90° governs the parent-twin conversion. The results illustrated here demonstrate that some of the recent interpretations deduced by particular twin morphologies are not universally valid. This work aims at closing the gap between currently reported modelling and macroscale high strain rate results, broadening the fundamental understanding of twinning in HCP crystals.

Investigation of the anharmonic EXAFS oscillation of distorted HCP crystals based on extending quantum anharmonic correlated Einstein model

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

Variable precipitation behaviors of Laves phases in an ultralight Mg-Li-Zn alloy

Precipitation habits plays a decisive role in strengthening materials, especially for Mg alloys the non-basal plane precipitation is necessary but very limited. Generally, the precipitates would nucleate and grow up in a specific habit plane owing to the constraint of free-energy minimization of the system. Herein, in an aged ultralight Mg-Li-Zn alloy, we confirmed that the precipitates dominated by C15 Laves structure could form in a variety of habit planes, to generate three forms of strengthening-phases, i.e., precipitate-rod, precipitate-lath, and precipitate-plate. Among which, the precipitate-plates are on basal plane as usually but precipitate-rods/laths are on non-basal plane, and such non-basal precipitates would transform into the basal (Mg, Li)Zn2 Laves structure with prolonged aging. These findings are interesting to understand the precipitation behaviors of multi-domain Laves structures in hexagonal close-packed crystals, and expected to provide a guidance for designing ultralight high-strength Mg-Li based alloys via precipitation hardening on the non-basal planes.

Effect of the non-ideal axial ratio c/a on anharmonic EXAFS oscillation of h.c.p. crystals.

The temperature and wavenumber dependence of the extended X-ray absorption fine-structure (EXAFS) oscillation of hexagonal close-packed (h.c.p.) crystals have been calculated and analyzed under the effect of the non-ideal axial ratio c/a. The anharmonic EXAFS oscillation is presented in terms of the Debye-Waller factor using the cumulant expansion approach up to the fourth order. An effective calculation model is expanded and developed from the many-body perturbation approach and correlated Debye model using the anharmonic effective potential. This potential, depending on the non-ideal axial ratio c/a, is obtained from the first-shell near-neighbor contribution approach. A suitable analysis procedure is performed by evaluating the influence of EXAFS cumulants on the phase shift and amplitude reduction of the anharmonic EXAFS oscillation. The numerical results for crystalline zinc are found to be in good agreement with those obtained from experiments and other theoretical methods at various temperatures. The obtained results show that the present theoretical model is essential and effective in improving the accuracy for analyzing the experimental data of anharmonic EXAFS signals of h.c.p. crystals with a non-ideal axial ratio c/a.

Analysis of Nanoscratch Mechanism of C-Plane Sapphire with the Aid of Molecular Dynamics Simulation of Hcp Crystal.

In this study, single groove nanoscratch experiments using a friction force microscope (FFM) with a monocrystalline diamond tip were conducted on a c-plane sapphire wafer to analyze the ductile-regime removal and deformation mechanism including the anisotropy. Various characteristics, such as scratch force, depth, and specific energy for each representative scratch direction on the c-plane of sapphire, were manifested by the FFM, and the results of the specific scratch energy showed a trend of six-fold symmetry on taking lower values than those of the other scratch directions when the scratch directions correspond to the basal slip directions as . Since this can be due to the effect of most probably basal slip or less probably basal twinning on the c-plane, a molecular dynamics (MD) simulation of zinc, which is one of the hexagonal close-packed (hcp) crystals with similar slip/twining systems, was attempted to clarify the phenomena. The comparison results between the nanoscratch experiment and the MD simulation revealed that both the specific scratch energy and the burr height were minimized when scratched in the direction of the basal slip. Therefore, it was found that both the machining efficiency and the accuracy could be improved by scratching in the direction of the basal slip in the single groove nanoscratch of c-plane sapphire.

Nonlocal hcp kernel functions based on ab initio calculations: Pertinent dislocation problems revisited

Eringen's nonlocal theory and an accurate determination of the nonlocal kernel functions for hexagonal close-packed (hcp) crystals are of interest. The kernel functions are closely related to the anisotropy as well as any crystalline symmetries. To this end, five new distinct nonlocal kernel functions which have the characteristics of discrete atomistic Green's functions in the stress space are obtained through consideration of the nonlocal dispersion relations associated with certain directions combined with ab initio Density Functional Perturbation Theory (DFPT) calculations of the pertinent phonon frequencies. This is the first work which provides the nonlocal hcp kernel functions pertinent to each component of the elastic moduli tensor of Eringen's nonlocal continuum theory based on quantum mechanical considerations. Moreover, the nonzero components of the classical elastic moduli as well as the equilibrium lattice parameters associated with the hcp crystals of Mg, Cd, Ti, and Zn have been computed using ab initio Density Functional Theory (DFT) and compared with the available experimental data. In order to show the importance of the anisotropy of the kernel functions, the nonlocal stress field of a straight screw dislocation and a straight edge dislocation inside an infinitely extended hcp medium have been examined for the case where the dislocation lies in the basal plane. Within this theory the unrealistic singular behavior of the classical stresses at the dislocation core is eliminated. In contrast to the classical anisotropy theory that predicts singular shear stress on the slip plane at the core of the dislocation, the corresponding nonlocal shear stress component predicted by the present theory is zero at the dislocation core. It is noteworthy to mention that the normalized nonlocal shear stress distribution and its maximum value are greatly influenced by the anisotropy of the crystalline solids.

In situ microbeam surface X-ray scattering reveals alternating step kinetics during crystal growth

The stacking sequence of hexagonal close-packed and related crystals typically results in steps on vicinal {0001} surfaces that have alternating A and B structures with different growth kinetics. However, because it is difficult to experimentally identify which step has the A or B structure, it has not been possible to determine which has faster adatom attachment kinetics. Here we show that in situ microbeam surface X-ray scattering can determine whether A or B steps have faster kinetics under specific growth conditions. We demonstrate this for organo-metallic vapor phase epitaxy of (0001) GaN. X-ray measurements performed during growth find that the average width of terraces above A steps increases with growth rate, indicating that attachment rate constants are higher for A steps, in contrast to most predictions. Our results have direct implications for understanding the atomic-scale mechanisms of GaN growth and can be applied to a wide variety of related crystals.

A finite element formulation for deformation twinning induced strain localization in polycrystal magnesium alloys

Deformation twinning induces shear strain localization in hexagonal close-packed crystals and is critical for the material’s ductility and failure. Cracks often occur at twin-twin or twin-grain boundary intersections and propagate along twin bands. However, most crystal plasticity models for deformation twinning are based on a “pseudo-slip” approach and do not capture the localized deformation associated with the formation of each discrete twin band. The few exceptions are discrete twin models that involve very complex numerical algorithms and are often compromised in accuracy due to the numerical convergence. These factors make the discrete twin models hard to adopt. This paper proposes a modification to the conventional finite element weak form, to fully incorporate a twin-induced heterogeneous deformation that does not depend on the “pseudo-slip” assumption. The model starts by splitting the deformation gradient into elastic-slip-twinning components. The twin-induced deformation gradient component is computed separately by solving a microstructural evolution problem and then implemented into finite element weak form by constructing a global “twin-force” vector. The constitutive update (e.g., in the user-defined material subroutine, or UMAT, for ABAQUS) therefore avoids dealing with the twinning and recovers to the form of a regular slip-based crystal plasticity model. The results indicate that the twin-induced strain localization and the associated stress-reversal phenomena near the twin band were naturally captured in the model, which was validated against an in-situ synchrotron X-ray micro-diffraction experiment.

Formation of one-dimensional quantum crystals of molecular deuterium inside carbon nanotubes

Crystallization under stringent cylindrical confinement leads to novel quasi-one-dimensional materials. Substances with strong cohesive interactions can eventually preserve the symmetries of their bulk phase compatible with the restricted geometry, while those with weak cohesive interactions develop qualitatively different structures. Frozen molecular deuterium (D2), a solid with a strong quantum character, is structurally held by weak dispersive forces. Here, the formation of one-dimensional D2 crystals under carbon nanotube confinement is reported. In contradiction with its weak cohesive interactions, their structures, scrutinized using neutron scattering, correspond to definite cylindrical sections of the hexagonal close-packed bulk crystal. The results are rationalized on the grounds of numerical calculations, which point towards nuclear quantum delocalization as the physical mechanism responsible for the stabilization of such outstanding structures.

Solid−solid phase transition of tungsten induced by high pressure: A molecular dynamics simulation

Abstract The phase transition of tungsten (W) under high pressures was investigated with molecular dynamics simulation. The structure was characterized in terms of the pair distribution function and the largest standard cluster analysis (LSCA). It is found that under 40−100 GPa at a cooling rate of 0.1 K/ps a pure W melt first crystallizes into the body-centred cubic (BCC) crystal, and then transfers into the hexagonal close-packed (HCP) crystal through a series of BCC−HCP coexisting states. The dynamic factors may induce intermediate stages during the liquid−solid transition and the criss-cross grain boundaries cause lots of indistinguishable intermediate states, making the first-order BCC−HCP transition appear to be continuous. Furthermore, LSCA is shown to be a parameter-free method that can effectively analyze both ordered and disordered structures. Therefore, LSCA can detect more details about the evolution of the structure in such structure transition processes with rich intermediate structures.

Twin nucleation from a single dislocation in hexagonal close-packed crystals

Twinning plays an important role in governing the balance between strength and ductility in hexagonal-close-packed (HCP) metals. Here, we report a combined experimental and theoretical study of twin nucleation from a single <c+a> dislocation in HCP crystals. Specifically, high-resolution transmission electron microscopy has been used to identify {112¯1} twin nuclei in HCP rhenium, providing evidence of their nucleation from a <c+a> dislocation. The favorability of this dislocation-based nucleation mechanism is rationalized by an anisotropic elasticity model of <c+a> dislocation dissociation, parametrized by density functional theory calculations, which suggests the conditions for disconnection nucleation and propagation, under which this {112¯1} twinning mechanism is expected to be effective. The analysis serves to advance our understanding of the origin of the unique predominance of {112¯1} twinning in rhenium, which correlates with the high strength and ductility featured by this metal. It also provides new insights into design strategies that may be effective in activating this twinning mode and enhancing the balance between strength and ductility in HCP alloys more broadly.

Twin Nucleation From a Single (c+a) Disclocation in Hexagonal Close-packed Crystals

Twinning plays an important role in governing the balance between strength and ductility in hexagonal-close-packed (HCP) metals. Here, we report a combined experimental and theoretical study of twin nucleation from a single

On the nucleation of deformation twins at the early stages of plasticity

Understanding the deformation mechanisms of hexagonal close-packed (HCP) polycrystals at the grain scale is crucial for developing both macro and micro scale predictive models. Slip and twinning are the two main deformation mechanisms of HCP polycrystals at room temperature. In this paper, the development of grain-level stress tensors during nucleation and growth of twins is investigated. A pure zirconium specimen with HCP crystals is deformed in-situ while the centre-of-mass, orientation, elastic strain, and stress of individual grains are measured by three-dimensional synchrotron X-ray diffraction (3D-XRD). The observed microstructure is subsequently imported into a crystal plasticity finite element (CPFE) model to simulate the deformation of the polycrystal. The evolution of stress in twin-parent pairs at the early stages of plasticity, further into plasticity zone, and unload is studied. It is shown that twins do not relax very much at the nucleation step, but the difference between the measured stress in the twin and parent increases further into plastic zone where twins relax. While at the early stages of plasticity all six twin variants are active, a slightly better estimation of active variants is obtained using the measured grain-resolved stress tensors.

Direct observation of dual-step twinning nucleation in hexagonal close-packed crystals

Design and processing of advanced lightweight structural alloys based on magnesium and titanium rely critically on a control over twinning that remains elusive to date and is dependent on an explicit understanding on the twinning nucleation mechanism in hexagonal close-packed (HCP) crystals. Here, by using in-situ high resolution transmission electron microscopy, we directly show a dual-step twinning nucleation mechanism in HCP rhenium nanocrystals. We find that nucleation of the predominant {1 0 −1 2} twinning is initiated by disconnections on the Prismatic│Basal interfaces which establish the lattice correspondence of the twin with a minor deviation from the ideal orientation. Subsequently, the minor deviation is corrected by the formation of coherent twin boundaries through rearrangement of the disconnections on the Prismatic│Basal interface; thereafter, the coherent twin boundaries propagate by twinning dislocations. The findings provide high-resolution direct evidence of the twinning nucleation mechanism in HCP crystals.

Magnetostrictive properties of Tb0.2Gd0.8 single crystal in high magnetic fields

Temperature and field dependencies of the magnetostriction of the Tb0.2Gd0.8 single crystal were measured in strong magnetic fields up to 14 T in a temperature range of 4.2–300 K. The temperature dependencies of five magnetostriction constants λ1α,0, λ2α,0, λ1α,2, λ2α,2 and λγ,2 were determined, using Clark's theory for rare-earth hexagonal close-packed single crystals. Giant values of linear and volume magnetostriction due to forced magnetostriction were found in the Tb0.2Gd0.8 single crystal (λbc = 1.6 × 10−3) in the region of the Curie temperature (near room temperatures). It is shown that giant values of forced magnetostriction are caused by the sharp dependence of exchange interactions on interatomic distances along the hexagonal the c axis.

Phase-field modeling of complex dendritic structures in constrained growth of hexagonal close-packed crystals.

We perform the phase-field modeling to investigate the growth pattern selections of the complex dendritic structures in constrained growth with different solidification and orientation conditions. The results show that hexagonal close-packed (hcp) crystals emerge as dendritic and cellular arrays in different planes, originating from the specific hcp anisotropy that allows different growth preferences between the basal and cylindrical planes. A morphological transition of the titled dendrites to tip-splitting dendrites arises reflecting the competition between the preferred orientation induced primary growth and the misorientation induced sidebranching formation. Furthermore, the dendritic patterns exhibit sharper tips and the more significant sidebranches, while the cellular pattern is changed from the symmetric cells to the tip-splitting cells, and to seaweeds with the increase of anisotropy strength, indicating the competitive mechanism of the in-plane anisotropy induced growth promotion and the out-plane anisotropy induced growth restriction. We expect to understand the growth competition, the morphology selection, as well as the orientation dependence of the complex dendritic structures in the three-dimensional (3D) constrained growth.

Molecular Dynamics Simulations of Ti Crystallization with Solid–Liquid Configuration Method

The computation models were created with the solid-liquid configuration method. The molecular dynamics simulations were performed to exhibit the crystallization process of liquid pure Ti to hexagonal close packed (HCP) and face-centered cubic (FCC) structure crystals. The results showed that both HCP and FCC crystallizations start from the solid–liquid interfaces and develop toward the middle. The system energy sharply falls at the beginning of crystallization, then is reduced slowly, and finally has a sudden down jump at the end of crystallization. The first peak of RDF is increased significantly with time and some new secondary peaks occur, which is consistent with configuration evolution. The HCP crystal has a longer crystallization process but lower stable energy than the FCC crystal.