Hexagonal Close-packed Structure Research Articles

Tensor Representation Method Applied to Magnesium Alloys

The tensor representation method (TRM) offers tensorial tools suitable for streamlining the development of constitutive models. The TRM reduces the empiricism of phenomenological descriptions and provides physics-based justifications for the tensorial construction of material models. The method is presented in a stepwise manner, thus giving the reader an opportunity to appreciate the details of the concept. The selected material is magnesium alloy AZ31B (wt% composition: Mg 95.8, Al 3.0, Zn 1.0, and Mn 0.2), and the choice is not coincidental. The hexagonal close-packed (hcp) structure of rolled sheets exhibits highly directional plastic flow, while the crystallographic reorientations add to the complexity of the material’s behavior. A generic structure of the deformation mechanisms is determined first. In the next step, the TRM tools enable the coupling of the mechanisms with proper stimuli. Lastly, the thermo-mechanical flow rules for plasticity and twinning complete the constitutive description. The model predictions for Mg AZ31B have been compared with experimental data, demonstrating a desirable level of predictability.

Unveiling deformation twin nucleation and growth mechanisms in BCC transition metals and alloys

Twinning provides critical stress-relieving and flaw tolerance in body-centred cubic (BCC) transition metals (TMs) when dislocation plasticity is suppressed. Twin nucleation and growth mechanisms have been studied for over half a century without a consensus. Here, we use a reduced-constraint slip method to unveil the path to twin nucleation, growth and associated energy barriers in the entire BCC TM family. Twinning is surprisingly but essentially controlled by a normalized energy difference η between the hexagonal close-packed (HCP) and BCC structures in elemental TMs, and can be effectively tuned and quantitatively predicted by first-principles calculations in TM alloys. Fracture mechanics theory with η-based barriers enables predictions of critical solute concentrations to activate twinning and reverse ductile-to-brittle transitions in BCC TMs, as demonstrated in WRe alloys. The computational approach provides a unified and quantitative method to predict twinning and a practical tool for rapid screening of alloy compositions ensuring ductile behaviour.

Identify the Micro-Parameters for Optimized Discrete Element Models of Granular Materials in Two Dimensions Using Hexagonal Close-Packed Structures.

The widely used simple cubic-centered (SCC) model structure has limitations in handling diagonal loading and accurately representing Poisson's ratio. Therefore, the objective of this study is to develop a set of modeling procedures for granular material discrete element models (DEM) with high efficiency, low cost, reliable accuracy, and wide application. The new modeling procedures use coarse aggregate templates from an aggregate database to improve simulation accuracy and use geometry information from the random generation method to create virtual specimens. The hexagonal close-packed (HCP) structure, which has advantages in simulating shear failure and Poisson's ratio, was employed instead of the SCC structure. The corresponding mechanical calculation for contact micro-parameters was then derived and verified through simple stiffness/bond tests and complete indirect tensile (IDT) tests of a set of asphalt mixture specimens. The results showed that (1) a new set of modeling procedures using the hexagonal close-packed (HCP) structure was proposed and was proved to be effective, (2) micro-parameters of the DEM models were transit form material macro-parameters based on a set of equations that were derived based on basic configuration and mechanism of discrete element theories, and (3) that the results from IDT tests prove that the new approach to determining model micro-parameters based on mechanical calculation is reliable. This new approach may enable a wider and deeper application of the HCP structure DEM models in the research of granular material.

A first-principles method to calculate fourth-order elastic constants of solid materials

A first-principles method is presented to calculate elastic constants up to the fourth order of crystals with the cubic and hexagonal symmetries. The method relies on the numerical differentiation of the second Piola-Kirchhoff stress tensor and a density functional theory approach to calculate the Cauchy stress tensor for a list of deformed configurations of a reference state. The number of strained configurations required to calculate the independent elastic constants of the second, third, and fourth order is 24 and 37 for crystals with the cubic and hexagonal symmetries, respectively. Here, we present conceptual aspects of our method, we provide technical details of its implementation and use, we assess its accuracy, and we discuss several applications. In particular, this method is applied to five crystalline materials with the cubic symmetry (diamond, silicon, aluminum, silver, and gold) and two metals with the hexagonal close packing structure (beryllium and magnesium). Our results are compared to available experimental data and previous computational studies. Calculated linear and nonlinear elastic constants are also used in the context of nonlinear elasticity theory to predict values of volume and bulk modulus over an interval of pressures. These predictions are compared to results obtained from density functional theory calculations to assess the reliability of our method.

Enabling high ionic conductivity in yttrium-based lithium halide electrolytes by composition modulation for all-solid-state batteries

Chloride electrolytes have again become a focus of research in recent years due to the oxidative stability at high potential. Y-based chlorides such as Li3YCl6 have a considerable ionic conductivity of ∼10−4 S/cm. The ionic conductivity of a solid-state electrolyte (SSE) is closely related to its crystal structure. Low lithium concentration composition is beneficial for lithium-ion conduction structure. Due to the presence of more free octahedral sites, the crystal structure with Pnma space group has a better ion diffusion compared to the crystal structure with P-3m1 space group with hexagonal close-packed structure (hcp). In addition to this, the doping of cations with higher valence states results in more lithium vacancy compensation in the crystal structure, which is a significant modification to improve the ionic conductivity of the chloride. Herein, ab initio molecular dynamics (AIMD) simulations were performed to investigate the effects of the lithium-deficient state configuration and the cation Nb5+ doping modification on the ion conduction of LiaYClb solid-state electrolytes. The lithium-deficient state composition structure has shifted the material space group structure from P-3m1 to Pnma, which facilitates the diffusion of lithium ions. The Nb5+ doping has increased the chance of lithium ion co-diffusion and disordered the lithium ion sites near the Y(Nb) cation site, resulting in a lower ab-plane diffusion barrier and a significant improvement of lithium ion migration. A series of lithium-deficient state compositions and Nb-doped chlorides were synthesized. Li2.31Y0.98Nb0.02Cl5.31 is obtained by solid sintering preparation with an ionic conductivity close to 1.0 × 10−3 S/cm and high electrochemical stability. The full cell of Li2.31Y0.98Nb0.02Cl5.31 matched with bare LiCoO2 maintains stability for 100 cycles.

A novel type of core-shell structured secondary phase particles in Ge-addition modified Zircaloy-4 alloy subjected to β-phase region solution treatment

Secondary phase particles (SPPs) in a Ge-addition modified Zircaloy-4 alloy subjected to β-phase region solution treatment was investigated in detail by transmission electron microscopy to acquire a better understanding on the microstructure of this new zirconium alloy. Result revealed that a novel type of SPPs with core-shell structure were frequently observed in this alloy, in which the “core” and “shell” structures were separately identified as primitive tetragoanl Zr3Ge phase and Zr(Fe,Cr)2 Laves phase with a hexagonal close-packed (HCP) structure. The orientation relationship between the Zr3Ge core, Zr(Fe,Cr)2 shell structures and the surrounding matrix were investigated and can be approximately described as [115]Zr3Ge||[112¯6¯]Zr(Fe,Cr)2||[112¯3]α−Zr. It was strongly suggested that the gradient of Ge concentration occurred during the subsequent β-phase region annealing affected the phase stability of Zr(Fe,Cr,Ge)2 nanophase in the as-cast Ge-addition modified Zr-4 alloy, thereby causing the formation of Zr3Ge/core-Zr(Fe,Cr)2/shell microstructures. The knowledge attained from this study, shedding new lights on the formation mechanism of these novel core-shell SPPs, would also greatly benefit the understanding on the formation of similar composite precipitates in other alloys.

Unveiling the Alloying-Processing-Microstructure Correlations in High-Formability Sheet Magnesium Alloys

Designing magnesium sheet alloys for room temperature (RT) forming is a challenge due to the limited deformation modes offered by the hexagonal close-packed crystal structure of magnesium. To overcome this challenge for lightweight applications, critical understanding of alloying-processing–microstructure relationship in magnesium alloys is needed. In this work, machine learning (ML) algorithms have been used to fundamentally understand the alloying-processing–microstructure correlations for RT formability in magnesium alloys. Three databases built from 135 data collected from the literature were trained using 10 commonly used machine learning models. The accuracy of the model is obviously improved with the increase in the number of features. The ML results were analyzed using advanced SHapley Additive exPlanations (SHAP) technique, and the formability descriptors are ranked as follows: (1) microstructure: texture intensity > grain size; (2) annealing processing: time > temperature; and (3) alloying elements: Ca > Zn > Al > Mn > Gd > Ce > Y > Ag > Zr > Si > Sc > Li > Cu > Nd. Overall, the texture intensity, annealing time and alloying Ca are the most important factors which can be used as a guide for high-formability sheet magnesium alloy design.

High-performance rechargeable metal–air batteries enabled by efficient charge transport in multielement random alloy electrocatalyst

The integration of bifunctionally active sites of multielement random alloy catalysts with other metal oxide electrocatalysts is a promising strategy for efficient electrochemical reactions. In this study, a novel combination of virtual crystal approximation and hydrothermal synthesis was used to investigate the composition-dependent structure and electrical property in a Ag1−xNix catalyst. The combination showed that a hexagonal closed-packed structure of Ag1−xNix with a compositional ratio of 6:4 (Ag:Ni) had electrical conductivity of ∼2 × 107 S∙cm−1 and an ionization potential of − 5.4 eV. Furthermore, the bifunctional oxygen electrocatalytic efficiencies of Ag0.6Ni0.4 were improved by forming a heterointerface with the CoNb2O6 electrocatalyst, resulting in a discharge-charge voltage gap of 0.81 V over 587 h, peak power density of 178.9 mW∙cm−2, and specific capacity of 806.8 mA∙h∙g−1 in a zinc–air battery. This approach was applied to pouch-type zinc–air batteries, resulting in long-term stability of over 158.6 h at 10 mA∙cm−2.

Twinning in Hexagonal Close-Packed Materials: The Role of Phase Transformation

Twinning is a major mechanism of plastic deformation in hexagonal close-packed (hcp) structures. However, a mechanistic understanding of twin nucleation and growth has yet to be established. This paper reviews the recent progress in the understanding of twinning in hcp materials—particularly the newly discovered phase transformation-mediated twinning mechanisms—in terms of crystallographical analysis, theoretical mechanics calculations, and numerical simulations. Moreover, the relationship between phase transformation-mediated twinning mechanisms and twinning dislocations are presented, forming a unified understanding of deformation twinning. Finally, this paper also reviews the recent studies on transformation twins that are formed in hcp martensite microstructures after various phase transformations, highlighting the critical role of the mechanical loading in engineering a transformation twin microstructure.

Structure and magnetism of rhodium particles as a size effect

The magnetic properties of Rh clusters with face-centered-cubic (FCC) and hexagonal-closed-packed (HCP) structures were studied by first-principles calculations. The results show that both the structure and magnetic properties have size effects. Bulk Rh exists as a FCC structure. However, as the size of Rh particles shrinks, the FCC and HCP structures have comparable energies, consistent with the coexistence of the two structures experimentally observed previously. Although the bulk Rh is nonmagnetic, the nanoparticles or clusters of Rh in both the FCC and HCP structures are magnetic. The average magnetic moment gradually increases as the clusters shrink. The origin of the magnetism of Rh clusters can be attributed to the reduction of coordination number, other than the lattice expansion. The findings provide insights for understanding the magnetic properties of noble metal clusters.

Formation mechanism of co-axial grain boundaries in a Mg alloy

Due to the insufficient slip systems in hexagonal close-packed structure, twinning is frequently activated to support stable plastic deformation of Mg alloy. In this work, we found four typical twin-like interfaces with misorientations of 102°, 109°, 142° and 149°, respectively, which had not only a shared [11 2 ¯ 0] zone axis of neighboring grains, but also overlapped diffraction spots similar to twins. However, high-resolution transmission electron microscope (HRTEM) analysis revealed that the interfaces in real space deviated from the supposed twinning planes in reciprocal space, i.e. their overlapped diffraction spots. We clarified that the incoherent interfaces were co-axial grain boundaries (CGBs). Additionally, a special angle of θ , close to 90°, between the interface and one side of basal plane, was frequently formed in CGBs. We proposed that interaction of multiple twinning contributes to the formation of CGBs, and the θ is formed due to alternative tensile and compression twinning under a uniaxial loading.

Texture-dependent bending behaviors of extruded AZ31 magnesium alloy plates

The relatively insufficient knowledge of the deformation behavior has limited the wide application of the lightest structure material-Mg alloys. Among others, bending behavior is of great importance because it is unavoidably involved in various forming processes, such as folding, stamping, etc. The hexagonal close-packed structure makes it even a strong texture-dependent behavior and even hard to capture and predict. In this regard, the bending behaviors are investigated in terms of both experiments and simulations in the current work. Bending samples with longitudinal directions inclined from the transverse direction by different angles have been prepared from an extruded AZ31 plate, respectively. The moment-curvature curves and strain distribution have been recorded in the four-point bending tests assisted with an in-situ digital image correlation (DIC) system. A crystal-plasticity-based bending-specific approach named EVPSC-BEND was applied to bridge the mechanical response to the microstructure evolution and underlying deformation mechanisms. The flow stress, texture, twin volume fraction, stress distribution, and strain distribution evolve differently from sample to sample, manifesting strong texture-dependent bending behaviors. The underlying mechanisms associated with this texture dependency, especially the occurrence of both twinning and detwinning during the monotonic bending, are carefully discussed. Besides, the simulation has been conducted to reveal the moment-inclination angle relation of the investigated AZ31 extruded plate in terms of the polar coordinate, which intuitively shows the texture-dependent behaviors. Specifically, the samples with longitudinal directions parallel to the extruded direction bear the biggest initial yielding moment.

Atomic-scale analysis of deformation behavior of face-centered cubic nanocrystalline high-entropy alloys with different grain sizes at high strain rates

In the present study, the microscopic deformation mechanism and tensile properties of Al0.1CoCrFeNi nanocrystalline high-entropy alloys (HEAs) during uniaxial tension were studied through molecular dynamics simulation, and the dependence of mechanical properties on grain size and strain rate has been explored. As the tensile strain increases from 0 to 0.1, the atoms undergo a phase transformation from the face-centered cubic (FCC) structure into the hexagonal close-packed (HCP), body-centered cubic (BCC) and amorphous structure, and the dislocation density increases gradually due to dislocation annihilation and interaction. HEA grains undergo the transformation of the inverse Hall-Petch (H–P) relation into the H–P relation after exceeding one critical size of 14.77 nm at a strain rate of 5 × 107/s, and this critical size increases with increasing strain rate. The microscopic deformation mechanism of the H–P relation is that the accumulation of dislocations at the grain boundaries leads to an increase in the strength of HEAs. In contrast, the inverse H–P relation is caused by the migration of grain boundaries, and the rotation and merging of HEA grains. The increase of strain rate positively affects the tensile properties of nanocrystalline HEAs, and the flow stress and yield strength exhibit sensitive dependence on the extremely high strain rates. In addition, the amorphization of atoms has become an important way for HEAs to deform plastically at high strain rates.

Migration of lattice oxygen during chemical looping dry reforming of methane with Ca2Fe2O5/Zr0.5Ce0.5O2 oxygen carrier

Ca2Fe2O5/Zr0.5Ce0.5O2 exhibits excellent reactivity in chemical looping dry reforming of methane. The migration of lattice oxygen is crucial to the cyclic stability of oxygen carrier, but the lattice oxygen migration in Ca2Fe2O5/Zr0.5Ce0.5O2 were not extensively explored. This work explored the lattice oxygen migration of Ca2Fe2O5/Zr0.5Ce0.5O2 during redox process. During the reduction process, the lattice oxygen reacted with the hydrogen radical, resulting in the decrease of lattice oxygen content and the increase of oxygen vacancy. As the lattice oxygen released, the spatial structure of Ca2Fe2O5 was destroyed and transferred into Fe8Ca8O20 with oxygen defects due to lattice distortion. The exothermic reaction between H2 and Ca2Fe2O5 promoted the formation of FeH with hexagonal close-packed structure. After reduction for 160 min, the unstable FeH completely converted into FeC with stable structure and the complete reduction was reached. As for the oxidation process, Fe and CaO reacted with the oxygen radical to form Ca2Fe2O5, leading to the complete recovery of lattice oxygen within 40 min. However, crystalline phase transformation could lead to the spatial structure instability and sintering after multiple redox cycles. Overall, the migration of oxygen during redox process is clarified in detail, providing a reference for improving the cyclic stability of Ca2Fe2O5/Zr0.5Ce0.5O2.

X-Ray Diffraction of Ramp-Compressed Silicon to 390GPa.

Silicon (Si) exhibits a rich collection of phase transitions under ambient-temperature isothermal and shock compression. This report describes insitu diffraction measurements of ramp-compressed Si between 40 and 389GPa. Angle-dispersive x-ray scattering reveals that Si assumes an hexagonal close-packed (hcp) structure between 40 and 93GPa and, at higher pressure, a face-centered cubic structure that persists to at least 389GPa, the highest pressure for which the crystal structure of Si has been investigated. The range of hcp stability extends to higher pressures and temperatures than predicted by theory.

Chemical interactions that govern the structures of metals.

Most metals adopt simple structures such as body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed (HCP) structures in specific groupings across the periodic table, and many undergo transitions to surprisingly complex structures on compression, not expected from conventional free-electron-based theories of metals. First-principles calculations have been able to reproduce many observed structures and transitions, but a unified, predictive theory that underlies this behavior is not yet in hand. Discovered by analyzing the electronic properties of metals in various lattices over a broad range of sizes and geometries, a remarkably simple theory shows that the stability of metal structures is governed by electrons occupying local interstitial orbitals and their strong chemical interactions. The theory provides a basis for understanding and predicting structures in solid compounds and alloys over a broad range of conditions.

Corrosion resistance and mechanical properties of electrodeposited Co-W/ZrO2 composite coatings

Co-W/ZrO2 composite coatings were prepared on copper substrate by electrodeposition technology, and the effect of the concentration of ZrO2 particles in the plating solution on the content of ZrO2 particles in the composite coating, the corrosion resistance, and mechanical properties of the composite coating were studied. The results show that as the concentration of ZrO2 particles in the plating solution increases from 3 g/L to 26 g/L, the content of ZrO2 particles in the composite coating first increases and then decreases, and the grains shape and compactness of the composite coating change significantly, resulting in differences in the corrosion resistance, hardness, wear resistance and tensile strength. Appropriate amount of ZrO2 particles in the plating solution can increase the content of ZrO2 particles in the composite coating, which may cause a greater degree of lattice distortion and dislocation leading to compact surface morphology and better mechanical properties. The composite coating prepared when the concentration of ZrO2 particles in the plating solution is 18 g/L is composed of face-centered cubic structure Co, close-packed hexagonal structure Co and Co3W phases with 7.35% ZrO2 particles. The composite coating has many densely arranged elongated structures, and exhibits the best corrosion resistance and mechanical performance with charge transfer resistance of 7056 Ω·cm2, low-frequency impedance of 6960 Ω·cm2 and phase angle of 66.5°, hardness of 573.2 HV0.05 and tensile strength of 206.8 MPa, which are all higher than Co-W alloy coating.

Visible-light induced photocatalytic degradation of estrone (E1) with hexagonal copper selenide nanoflakes in water

Steroid hormones, being potent endocrine-disruptors, are a menace to human health and aquatic life. Herein, visible-light induced photocatalytic degradation of estrone (E1) by hexagonal copper selenide (CuSe) nanoflakes has been reported. CuSe was synthesised by a facile and low-temperature (100 oC) co-precipitation method and was characterised. The nanocrystals were of stoichiometric Cu:Se ratio with Se2- and Cu in the + 1/+ 2 mixed-valence state and exhibited laminar, flake-like morphology with a preferred hexagonal close-packed structure (P63/mmc) having average particle size and thickness of 0.229 ± 0.146 µm and 0.05 ± 0.02 µm, respectively. The adsorption isotherms of E1 were linear and the adsorption process was exothermic. The reactivity of E1 under aqueous suspensions of CuSe exposed to visible light exhibited pseudo-first-order kinetics with a rate constant, k, that varied with initial E1 concentration, light power, catalyst dose, and pH. Particularly, k was almost constant over the range pH5–9 but substantially increased as pH rose to 11, while light power and catalyst dose increased k up to a maximum, and the initial concentration reduced k. Surprisingly, CuSe oxidised E1, even in the absence of light, and leached species that were identified and their time-dependency was determined. We concluded that the disappearance of E1 by CuSe is attributed to synergetic effects of adsorption, oxidation by CuSe, and photocatalytic degradation. Supported by liquid-mass spectrometry analysis and molecular chemistry calculations, we also suggested a possible mechanism for E1 degradation. Thus, hexagonal CuSe nanocrystals can be a promising candidate for the treatment of endocrine-disrupting chemicals (EDC)-contaminated wastewaters.

A computational map of the probe CO molecule adsorption and dissociation on transition metal low Miller indices surfaces

The adsorption and dissociation of carbon monoxide (CO) have been studied on 81 Transition Metal (TM) surfaces, with TMs having body centred cubic (bcc), face centred cubic (fcc), or hexagonal close-packed (hcp) crystalline structures. For each surface, CO, C, and O adsorptions, and C+O co-adsorptions were studied by density functional theory calculations on suited slab models, using the Perdew-Burke-Ernzerhof functional with Grimme’s D3 correction for dispersive forces. CO dissociation activation and reaction energies, ΔE, were determined. The values, including zero point energy, were used to capture chemical trends along groups, d-series, and crystallographic phases concerning CO adsorption and dissociation, while simulated infrared (IR) spectroscopies and thermodynamic phase diagrams are provided. Late fcc TMs are found to adsorb CO weakly, perpendicularly, and are IR-visible, opposite to early bcc TMs, while hcp cases are distributed along these two extremes. The d-band centre, εd, is found to be the best descriptor for CO adsorptions and C + O co-adsorptions, ΔE, and activation energies. The implications of the found trends and descriptors are discussed on processes requiring CO dissociation, such as the Fischer-Tropsch.

Superconducting state of the van der Waals layered PdH2 structure at high pressure

We report structural and superconducting transitions in layered van der Waals (vdW) palladium dihydride (PdH2) calculated under high-pressure compression. PdH2 has a Hexagonal Closed-Packed (HCP) structure with a space group of P63mc, and has a superconducting transition temperature of 24 K at ambient pressure. At 15 GPa, the crystalline to vdW layered structural transition occurs, while the superconductivity remains. On compressing from 15 to 50 GPa, the Tc increased abnormally by 3.5 K. It is found that the superconducting critical temperature of P63mc PdH2 is determined by the out-of-plane interlayer breathing vibrational mode. As a vdW layered metal hydride superconductor, PdH2 provides a platform to study hydride superconductivity in such kinds of materials.