Hexagonal Close-packed Research Articles

Three-dimensional shape and stress field of a deformation twin in magnesium

While the three-dimensional (3D) shape and stress field of a twin in hexagonal close-packed (HCP) metals have attracted considerable interest in recent years due to their substantial impact on internal stress and mechanical properties, a detailed understanding of their variation with twin size is still lacking. An analytical model that is not restricted by spatial scale is developed in this work by considering the effects of anisotropic twin boundary energy, elastic strain energy and plastic relaxation to predict the 3D shape with the minimum energy, and the stress field, of an isolated ellipsoidal twin of different sizes. The model is applied to Mg with a focus on the {101¯2} twin type. The analytical calculation results show that the nucleation of the nano-sized twin embryos is facilitated by the stress field near structural defects such as dislocations. During the expansion of this nano-sized twin embryo, the interplay between the elastic strain energy and interfacial energy changes the length of the twin along the twin shear (forward) direction from being shorter to longer than that along the lateral direction. In contrast to the current understandings, the maximum shear stress on the twin plane along the twin shear direction occurs at the lateral, rather than the forward, side of the twin. At the forward side, the maximum shear stress occurs at a distance ahead of the twin tip and this distance increases with increasing twin thickness.

Deformation-induced grain rotation and grain boundary formation achieved through dislocation-disclination reactions in polycrystalline hexagonal close-packed metals

Grain boundary mediated plasticity (e.g., grain rotation and grain boundary sliding) plays a critical role in determining the deformation behavior of polycrystals, which is especially important for nanocrystalline metals or plastic deformation at elevated temperatures. However, due to the lack of a theoretical framework, the mechanism of deformation-induced grain rotation has not been well understood. By introducing a disclination-based description, we show that crystal rotation can be captured conveniently through the characteristic rotational vector of a disclination (i.e., the Frank vector). Under the framework of topological defect theory, grain boundary mediated plasticity can be treated as topological reactions between dislocations and disclinations, leading to rigorous predictions of grain/subgrain rotation through a pseudo-inverse solution for the reformulated Frank-Bilby equation. Systematic classifications of grain/subgrain rotation and grain boundary formation are raised for hexagonal close-packed (HCP) metals, which has been validated by Electron-Backscattered Diffraction characterizations in Mg alloys. Our work not only suggests a theoretical approach to investigate grain/subgrain rotation based on the topological correlation between dislocations and disclinations, but also provides a new insight into the plastic behaviors of polycrystalline HCP metals.

Investigation on the Microstructure and Mechanical Properties of the Ti-Ta Alloy with Unmelted Ta Particles by Laser Powder Bed Fusion

Titanium-tantalum (Ti-Ta) alloy has excellent biomechanical properties with high strength and low Young's modulus, showing great application potential in the biomedical industry. In this study, Ti-Ta alloy samples were prepared by laser powder bed fusion (LPBF) technology with mixed pure 75 wt.% Ti and 25 wt.% Ta powders as the feedstock. The maximum relative density of Ti-Ta samples prepared by LPBF reached 99.9%. It is well-accepted that four nonequilibrium phases, namely, α', α″ and metastable β phase exist in Ti-Ta alloys. The structure of α', α″ and β are hexagonal close-packed (HCP), base-centered orthorhombic (BCO) and body-centered cubic (BCC), respectively. X-ray Diffraction (XRD) analysis showed that the α' phase transformed to the α″ phase with the increase of energy density. The lamellar α'/α″ phases and the α″ twins were generated in the prior β phase. The microstructure and mechanical properties of the Ti-Ta alloy were optimized with different LPBF processing parameters. The samples prepared by LPBF energy density of 381 J/mm3 had a favorable ultimate strength (UTS) of 1076 ± 2 MPa and yield strength of 795 ± 16 MPa. The samples prepared by LPBF energy density of 76 had excellent ductility, with an elongation of 31% at fracture.

Polymorph Stability and Free Energy of Crystallization of Freely-Jointed Polymers of Hard Spheres.

The free energy of crystallization of monomeric hard spheres as well as their thermodynamically stable polymorph have been known for several decades. In this work, we present semianalytical calculations of the free energy of crystallization of freely-jointed polymers of hard spheres as well as of the free energy difference between the hexagonal closed packed (HCP) and face-centered cubic (FCC) polymorphs. The phase transition (crystallization) is driven by an increase in translational entropy that is larger than the loss of conformational entropy of chains in the crystal with respect to chains in the initial amorphous phase. The conformational entropic advantage of the HCP polymer crystal over the FCC one is found to be ΔschHCP-FCC≈0.331×10-5k per monomer (expressed in terms of Boltzmann's constant k). This slight conformational entropic advantage of the HCP crystal of chains is by far insufficient to compensate for the larger translational entropic advantage of the FCC crystal, which is predicted to be the stable one. The calculated overall thermodynamic advantage of the FCC over the HCP polymorph is supported by a recent Monte Carlo (MC) simulation on a very large system of 54 chains of 1000 hard sphere monomers. Semianalytical calculations using results from this MC simulation yield in addition a value of the total crystallization entropy for linear, fully flexible, athermal polymers of Δs≈0.93k per monomer.

Strengthening of CoCrNi medium entropy alloy with gadolinium additions

A series of (CoCrNi)100–xGdx (x = 0/0.1/0.3/0.5/1.0) medium entropy alloys (MEAs) was fabricated by high-vacuum arc melting. The effects of rare-earth element, Gd, additions on the evolution of microstructures and mechanical properties of CoCrNi MEAs were studied. The phase and microstructure were examined using X-ray diffraction, scanning electron microscope and transmission electron microscope. The tensile properties were measured by material testing system (MTS) and the hardness was measured by both Vickers indenter and nanoindentation. As the Gd concentration increased, the phase transformed from face-centered cubic (FCC) to hexagonal close-packed (HCP) precipitates in FCC matrix. Compared to the single phase CoCrNi MEA with the yield strength of 400 MPa and fracture strength of 880 MPa, CoCrNi99.5Gd0.5 MEA exhibited a much higher yield strength of 751 MPa and ultimate tensile strength of 1216 MPa, while the ductility still maintained a high value of ∼55%. The enhanced mechanical properties were ascribed to solid solution, precipitation and grain refinement strengthening mechanisms. The relations among compositions, microstructures and mechanical properties of (CoCrNi)100–xGdx MEAs were discussed.

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.

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.

Does Zn mimic diffusion of Al in the HCP Al-Sc-Hf-Ti-Zr high entropy alloys?

The presence of Al in the hexagonal close-packed (HCP) Al-Sc-Hf-Ti-Zr high-entropy-alloy system was previously found to be a primary reason for partial D019 ordering. Since tracer measurements of Al self-diffusion are extremely challenging due to the absence of a suitable radioisotope, in this work, diffusion of Zn as a solute element is investigated for two HCP Al-Sc-Hf-Ti-Zr alloys. The experimental results on diffusion of the 65Zn radioisotope are benchmarked against Al diffusion rates predicted by kinetic Monte Carlo simulations using ab initio-informed calculations of the vacancy formation and migration energies. Furthermore, the partitioning of Zn and the mechanism of Zn diffusion are evaluated. Similarities between Zn and Al diffusion in the investigated HCP Al-Sc-Hf-Ti-Zr alloys are traced back to correlations between the corresponding chemically resolved site substitution energies and migration barriers.

Selective Catalytic Behavior Induced by Crystal-Phase Transformation in Well-Defined Bimetallic Pt-Sn Nanocrystals.

The Pt-Sn bimetallic system is a much studied and commercially used catalyst for propane dehydrogenation. The traditionally prepared catalyst, however, suffers from inhomogeneity and phase separation of the active Pt-Sn phase. Colloidal chemistry offers a route for the synthesis of Pt-Sn bimetallic nanoparticles(NPs) in a systematic, well-defined, tailored fashion over conventional methods. Here, the successful synthesis of well-defined ≈2nm Pt, PtSn, and Pt3 Sn nanocrystals with distinct crystallographic phases is reported; hexagonalclosepacking(hcp) PtSn and fcc Pt3 Sn show different activity and stability depending on the hydrogen-rich or poor environment in the feed. Moreover, facecentredcubic(fcc) Pt3 Sn/Al2 O3 , which exhibited the highest stability compared to hcp PtSn, shows a unique phase transformation from an fcc phase to an L12 -ordered superlattice. Contrary to PtSn, H2 cofeeding has no effect on the Pt3 Sn deactivation rate. The results reveal structural dependency of the probe reaction, propane dehydrogenation, and provide a fundamental understanding of the structure-performance relationship on emerging bimetallic systems.

Microstructural design and deformation behavior of a TRIP/TWIP tri-phase heterogeneous high-entropy alloy

In this study, a tri-phase heterogeneous high-entropy alloy (HEA) (Al9(Fe50Mn30Co10Cr10)91, at. %) exhibiting transformation- and twinning-induced plasticity (TRIP-TWIP) that overcomes the strength-ductility trade-off. The current HEA was systematically investigated the microstructure and mechanical properties under different thermo-mechanical processing (TMP). The HEA had a hierarchical microstructure of face-centered cubic (FCC), body-centered cubic (BCC), and a small content of hexagonal close-packed (HCP) phases after TMP. As regards the mechanical properties, after introducing recrystallized zone of ∼14.5 vol%, the HEA showed a strength of 1.15 GPa with total elongation of 10%. When the recrystallized fraction increased to ∼69.9 vol%, the HEA exhibited a combination of yield strength ∼489 MPa and tensile strength ∼704 MPa, while a satisfactory uniform elongation of 37% was maintained. The deformation activated multiple strengthening mechanisms, including dislocation slip, stacking faults, TRIP-TWIP effects, etc. led to a significant increase of work hardening rate in the intermediate stage of the strain. Additionally, the phase distribution and recrystallized grains morphology were characterized and the relationship between their results and the strength-ductility synergy were discussed. These findings provide a new method to tune the mechanical behavior of HEAs.

Grain Refinement and Phase Transformation of Pure Titanium Foils During Asymmetrical Rolling

Ultrafine‐grained microstructure and face center cubic (FCC) phase are produced in the pure titanium foils through asymmetrical rolling (ASR) to explore the mechanical properties of pure titanium foils with different thicknesses. Herein, the grain refinement process and phase transformation behavior are systematically investigated. The grain refinement process can be described as: 1) coarse equiaxed grains are elongated along RD due to the compressive strain and shear strain caused by the ASR process. 2) elongated grains are split into thin laths and subgrains by dislocation walls under greater strain. 3) thin laths and subgrains are further refined and ultrafine‐grained microstructures are obtained. In addition, hexagonal close‐packed (HCP)‐FCC phase transformation is also discovered during the ASR process. The orientation relationship between the HCP and FCC phases is determined as [0001]HCP//[001]FCC, (100)HCP//(20)FCC and the phase transformation is caused by Shockley partial dislocation with Burgers vector 1/6[110] gliding on each (100) plane. Uniaxial tensile tests on heat‐treated pure titanium foils of different thicknesses show a size effect on tensile properties. As the thickness decreases, tensile strength and elongation are reduced, with fewer/single‐layer equiaxed grains at the section of the specimen.

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.

First-Principles Calculation and Kink-Dislocation Dynamics Simulation on Dislocation Plasticity in TiZr-Based Concentrated Solid-Solution Alloys

The dislocation plasticity of TiZr-based hexagonal close-packed (HCP) concentrated solid-solution alloys (CSAs) is investigated using a multiscale simulation approach combining the first-principles calculation and Frenkel–Kontonova kink-dislocation model. The first-principles calculation reveals that dislocation-mediated slip is significantly enhanced by the additions of Y and Sc in TiZrHf CSAs. The dislocation kinetics is simulated using the kink-dislocation model at mesoscopic scales, and the predicted mechanical strength of CSA is found to be consistent with experimental results. In addition to predicting the mechanical properties of CSAs accurately, the multiscale simulation approach elucidates the deformation mechanisms in CSAs at atomic scales, suggesting that the approach is robust in modeling the dislocation plasticity of CSAs.

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.

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.

Dislocation behavior in initial stage of plastic deformation for CoCrNi medium entropy alloy

The effects of crystal orientation on the plastic deformation behavior for typical CoCrNi medium entropy alloy under tensile and compressive loading were investigated by molecular dynamics simulations. The Lomer-Cottrell (L-C) structure and parallel hexagonal close packed (HCP) bands are produced in the [111] and [11̅0] orientations at the initial stage of tensile deformation, respectively. However, perfect dislocations and two types of non-slip dislocations (Hirth and Stair-rod) are generated in the [111] and [11̅0] orientations during compressive deformation, respectively. The L-C structure produced by tensile loading in the [111] orientation and Hirth/Stair-rod dislocations produced in the [11̅0] orientation under compression act as a dislocation pinning and limit the continued glide of the dislocations. The dislocation reactions under various conditions were analyzed, which is helpful to understand the plastic deformation mechanism of CoCrNi alloy.

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.

Atomic-scale insight into interaction mechanism between screw dislocation and HCP phase in high-entropy alloy

The face-centered cubic (FCC)/hexagonal close-packed (HCP) dual-phase structure is a new design strategy proposed in recent years to achieve high strength and excellent plasticity of high-entropy alloys (HEAs). Here, the effect of HCP phase thickness, strain rate, and temperature on the interaction mechanism between screw dislocation and the HCP phase in the FCC structured CoCrFeMnNi HEAs is investigated by molecular dynamics simulation. The results show that there are two types of interaction modes between dislocations and the HCP phase: one is the dislocation passing through the HCP phase, that is, the penetration mechanism, and the other is the dislocation being absorbed by the HCP phase, that is, the absorption mechanism. The generation of these two mechanisms mainly depends on the relative ability of the HCP phase to prevent dislocation slip, which is closely related to the HCP phase thickness, strain rate, and temperature. When the relative ability of the HCP phase to block dislocation is large, the interaction between dislocations and the HCP phase presents an absorption mechanism; otherwise, it presents a penetration mechanism. The research can provide theoretical guidance for the development and design of new high-performance HEAs to achieve high strength and high ductility of materials.

Advancing strength and counteracting embrittlement by displacive transformation in heterogeneous high-entropy alloys containing sigma phase

Metallic alloy design for room temperature applications typically aims at avoiding undesired brittle intermetallic phases. In transition metal alloys, the sigma phase is particularly known as a harmful phase leading to serious embrittlement. Here, we develop a novel strategy that utilizes displacive transformation and heterogeneous structures to mitigate the embrittlement of sigma phase particles in high-entropy alloys (HEAs). A careful study of the deformation behavior reveals that the displacive transformation from face-centered cubic (FCC) to hexagonal close packed (HCP) phase can effectively suppress the propagation of microcracks originated in these brittle sigma particles (310±52 nm) and contributes to high work hardening behavior during tensile deformation. This is achieved by tuning the stacking fault energy of the FCC matrix by reducing the Ni content to promote transformation induce plasticity (TRIP) around the sigma phase in a non-equiatomic Fe34Mn20Co20Cr20Ni6 (at. %) HEA. Such TRIP effect can be optimized in various heterogeneous structures with bimodal grain sizes via simple cold-rolling (∼60%) and subsequent annealing (30 min at 700 or 800 °C). The heterogeneously structured HEAs containing brittle sigma particles exhibit ultimate tensile strengths as high as ∼1.2 GPa while maintaining a ductility up to ∼50%. This is mainly attributed to the transformation induced stress-relaxation around the regions containing brittle sigma particles. The insights provide a new design strategy of combining TRIP effect and heterogeneous structures for developing strong and ductile alloys.