Hcp Crystals Research Articles

Formation and slip of pyramidal dislocations in hexagonal close-packed magnesium single crystals

Slip of pyramidal 〈c+a〉 dislocations in hexagonal close-packed (hcp) crystals is a requisite for accommodation of homogeneous c-axis deformation. However, fundamental aspects of the formation and slip of pyramidal dislocations, including the formation mechanism, dissociation, core structure and slip features, are still poorly characterized. In this study, large-scale molecular dynamics simulations reveal that the formation of 〈c+a〉 dislocations in magnesium single crystals during c-axis loading occurs by sequential nucleation of leading and trailing partial dislocations on pyramidal I planes, owing to their lower lattice resistance to shear compared with pyramidal II planes. Local shuffling on pyramidal I planes was also found to be a mediating mechanism for nucleation and slip of pyramidal I 〈c+a〉 dislocations. Subsequent transition of pyramidal I slip to pyramidal II planes is achieved either by cross-slip of screw-segments or by cooperative slip of edge-segments on two equal and alternative pyramidal I planes. Consequently, at moderate strains, slip occurs predominantly on pyramidal II planes, in excellent agreement with experimental observations. Climb was also observed for both pyramidal I and pyramidal II 〈c+a〉 dislocations even at very low temperatures. This results in production of an abundance of interstitials and vacancies in the crystal. Formation of pyramidal I 〈a〉 dislocations by reaction of two pyramidal I 〈c+a〉 dislocations was also observed. These findings uncover unique features of pyramidal slip in low-symmetry hcp magnesium crystals and have important implications for understanding their distinct mechanical behavior and also for improving their performance.

Elastic properties and lattice dynamics of ruthenium at high pressures

The elastic properties and structural stability in ruthenium under pressure are investigated. The analysis is performed in the framework of Landau theory and nonlinear elasticity. For this purpose the definition of effective elastic constants (EC) of n-th (n≥2) order characterizing elastic properties of loaded crystal and the relations between effective EC and corresponding EC of Bragger type for hcp crystals is given. The conditions of hcp lattice stability to the uniform shear strain under the pressure P are expressed in terms of the second order effective EC. The method of effective EC calculations for hcp crystals under hydrostatic pressure is presented. The equation of state and EC of second and third order and phonon dispersion relations in high-symmetry directions in the pressure range of 0 – 600 GPa are calculated in the framework of the density functional theory (DFT) and the density functional perturbation theory (DFPT) respectively. EC are in the good agreement with available experimental data and increase monotonically with pressure, no softening or stability condition violation are observed. Softening of phonon frequencies near the Brillion zone center is also not observed.

Smooth cubic commensurate oxides on gallium nitride

Smooth, commensurate alloys of ⟨111⟩-oriented Mg0.52Ca0.48O (MCO) thin films are demonstrated on Ga-polar, c+ [0001]-oriented GaN by surfactant-assisted molecular beam epitaxy and pulsed laser deposition. These are unique examples of coherent cubic oxide|nitride interfaces with structural and morphological perfection. Metal-insulator-semiconductor capacitor structures were fabricated on n-type GaN. A comparison of leakage current density for conventional and surfactant-assisted growth reveals a nearly 100× reduction in leakage current density for the surfactant-assisted samples. HAADF-STEM images of the MCO|GaN interface show commensurate alignment of atomic planes with minimal defects due to lattice mismatch. STEM and DFT calculations show that GaN c/2 steps create incoherent boundaries in MCO over layers which manifest as two in-plane rotations and determine consequently the density of structural defects in otherwise coherent MCO. This new understanding of interfacial steps between HCP and FCC crystals identifies the steps needed to create globally defect-free heterostructures.

Radiation growth of hcp crystals driven by discrete breathers

A new mechanism of radiation growth (RG) of hexag-onal close pack (hcp) crystals is proposed, which is based on the radiation-induced creation of moving ‘discrete breathers’ (DBs), i.e. large amplitude anharmonic lattice vibrations, which can propagate and transfer energy along close-packed crystallographic directions within the basal planes of and excite atoms at prismatic faces/edges. Ac-cordingly, the DB-induced vacancy emission from pris-matic faces is enhanced as compared to that from the basal faces, at which only thermally activated vacancy emission takes place. This should result in the vacancy diffusional flow from prismatic to basal faces leading to expansion along the a-directions and to contraction along the c-axis, i.e. to the radiation-induced growth. The RG rate driven by this mechanism is evaluated in the framework of a rate theory modified with account of the DB-induced vacancy emission.

Mechanism of polyol assisted ccp to hcp crystal phase conversion of nickel particles

The effect of different chain length glycols on the conversion of ferromagnetic ccp nickel nanoparticles to antiferromagnetic hcp structure was investigated. To be an effective crystal phase tuner, the glycol molecule must have both an ether fragment and a linear chain structure. The phase conversion was studied at reaction times up to 100 hours and temperatures between 200 and 275 °C. Under selected conditions nickel particles of pure or mixed crystal structure could be generated.

Probe–impurity interaction in dilute alloy ZrxHf1−x (x~0.98): Results from perturbed angular correlation measurements

Time-differential perturbed angular correlation measurements have been performed in Zr metal with ~2at% Hf to understand the results of previous measurements. From present measurements at different temperatures two interaction frequencies have been found. One of these produces an asymmetry parameter η=0 as expected for a hcp crystal while the other one gives a non-zero value of η. The component with η=0 gives a value of quadrupole frequency ωQ=47.4(3)Mrad/s at 298K while the second component produces values of ωQ=49.5(2)Mrad/s, η=0.22(1) at room temperature. The component with η=0 has been attributed to a configuration where all the 12 nearest neighbor (NN) to the probe has Zr atoms while the non-zero η component arises due to the presence of 1 NN Hf. The site fractions for these two components depend on temperature and it is found that with increase in temperature, the ratio f/(1−f) decreases following the Arrhenius behavior, f is the component fraction for the probe–impurity interaction. The entropy of formation and binding energy for the probe–impurity pair have been determined in the present report.

High-resolution infrared spectroscopy of atomic bromine in solid parahydrogen and orthodeuterium

This work extends our earlier investigation of the near-infrared absorption spectroscopy of atomic bromine (Br) trapped in solid parahydrogen (pH2) and orthodeuterium (oD2) [S. C. Kettwich, L. O. Paulson, P. L. Raston, and D. T. Anderson, J. Phys. Chem. A 112, 11153 (2008)]. We report new spectroscopic observations on a series of double transitions involving excitation of the weak Br-atom spin-orbit (SO) transition ((2)P(1/2) ← (2)P(3/2)) in concert with phonon, rotational, vibrational, and rovibrational excitation of the solid molecular hydrogen host. Further, we utilize the rapid vapor deposition technique to produce pH2 crystals with a non-equilibrium mixture of face centered cubic (fcc) and hexagonal closed packed (hcp) crystal domains in the freshly deposited solid. Gentle annealing (T = 4.3 K) of the pH2 sample irreversibly converts the higher energy fcc crystal domains to the slightly more stable hcp structure. We follow the extent of this conversion process using the intensity of the U1(0) transition of solid pH2 and correlate crystal structure changes with changes in the integrated intensity of Br-atom absorption features. Annealing the pH2 solid causes the integrated intensity of the zero-phonon Br SO transition to increase approximately 45% to a value that is 8 times larger than the gas phase value. We show that the magnitude of the increase is strongly correlated to the fraction of hcp crystal domains within the solid. Theoretical calculations presented in Paper II show that these intensity differences are caused by the different symmetries of single substitution sites for these two crystal structures. For fully annealed Br-atom doped pH2 solids, where the crystal structure is nearly pure hcp, the Br-atom SO transition sharpens considerably and shows evidence for resolved hyperfine structure.

Hexatic-to-Disorder Transition in Colloidal Crystals Near Electrodes: Rapid Annealing of Polycrystalline Domains

Colloids are known to form planar, hexagonal closed packed (hcp) crystals near electrodes in response to electrohydrodynamic (EHD) flow. Previous work has established that the EHD velocity increases as the applied ac frequency decreases. Here we report the existence of an order-to-disorder transition at sufficiently low frequencies, despite the increase in the attractive EHD driving force. At large frequencies (~500 Hz), spherical micron-scale particles form hcp crystals; as the frequency is decreased below ~250 Hz, however, the crystalline structure transitions to randomly closed packed (rcp). The transition is reversible and second order with respect to frequency, and independent measurements of the EHD aggregation rate confirm that the EHD driving force is indeed higher at the lower frequencies. We present evidence that the transition is instead caused by an increased particle diffusivity due to increased particle height over the electrode at lower frequencies, and we demonstrate that the hcp-rcp transition facilitates rapid annealing of polycrystalline domains.

Stacking Principle and Magic Sizes of Transition Metal Nanoclusters Based on Generalized Wulff Construction

Nanoclusters with extra stability at certain cluster sizes are known as magic clusters with exotic properties. The classic Wulff construction principle, which stipulates that the preferred structure of a cluster should minimize its total surface energy, is often invoked in determining the cluster magicity, resulting in close-shelled Mackay icosahedronal clusters with odd-numbered magic sizes of 13, 55, 147, etc. Here we use transition metal clusters around size 55 as prototypical examples to demonstrate that, in the nanometer regime, the classic Wulff construction principle needs to be generalized to primarily emphasize the edge atom effect instead of the surface energy. Specifically, our detailed calculations show that nanoclusters with much shorter total edge lengths but substantially enlarged total surface areas are energetically much more stable. As a consequence, a large majority of the nanoclusters within the 3d-, 4d-, and 5d-transition metal series are found to be fcc or hcp crystal fragments with much lower edge energies, and the widely perceived magic size of 55 is shifted to its nearby even numbers.

Molecular dynamics simulation on microstructure evolution during solidification of copper nanoparticles

The effect of cooling rate on the microstructure evolution of liquid Cu nanoparticles during their solidification process is investigated by using a molecular dynamics simulation based on the embedded atom method (EAM) potential developed by Foiles et al.. The potential energy analysis, the pair distribution function and the common neighbor analysis have been used. The results show that the solidification point increases with decreasing cooling rate and that the solidification of the microstructure of Cu nanoparticles varies with the cooling rate. The microstructure consists of fcc, hcp and bcc crystals or mixtures, though the fcc structure dominates, except in the amorphous state. An amorphous structure was obtained when the cooling rate reached 1.0 × 1013 K/s or higher while crystallization degree increased with decreasing cooling rate, and the total content of crystal structures reached to 95% when the cooling rate dropped to 4.0 × 1011 K/s, which was nearly a perfect crystal structure. The results also indicate that a single-crystal nanoparticle will not be obtained by quenching the liquid metal under various cooling rates.

The strength of binary junctions in hexagonal close-packed crystals

A comparative study of non-coplanar binary dislocation junctions in magnesium (Mg) and beryllium (Be) is presented to examine the effects of elastic properties and active Burgers vectors on junction formation and destruction in hexagonal close-packed (hcp) crystals via discrete dislocation dynamics simulations. Two junction configurations formed at intersecting prismatic (011¯0)/basal(0001) planes and type-II pyramidal (2¯112)/prismatic(011¯0) planes are studied using Burgers vectors of varying magnitudes. The equilibrium junctions are created from two intersecting straight gliding dislocations, and their subsequent strengths are evaluated under uniform applied stresses. The relative junction strengths between Mg and Be are consistent with their relative elastic stiffness, i.e., the modulus of elasticity for Mg is approximately one order of magnitude smaller than that of Be, and their junction strengths are similarly one order of magnitude apart. In general, the yield surfaces for junctions in Be are larger than those in Mg after normalization with the respective elastic moduli and Poisson’s ratios. All yield surfaces exhibit a strong symmetry. However, the size and shape of the yield surfaces depend on the slip systems, especially the active Burgers vectors. The yield surfaces of hcp crystals can resemble those of face-centered cubic or body-centered cubic crystals when the active Burgers vectors of the dislocations involved in the junction are of type 〈a〉, namely 13〈112¯0〉, and are distinct when Burgers vectors of different types are used: for instance, a type 〈a+c〉, namely 13〈112¯3¯〉, interacting with a type 〈a〉. It was also found that junctions with more edge part exhibit more elongated yield surfaces than those with more screw part, and slip systems involved with 〈a〉 Burgers vectors result in smaller yield surfaces. These results demonstrate that junction strengths for hcp crystals are largely determined by elastic properties and Burgers vectors. The work aims to assess the effects of intrinsic material properties and dislocation slip systems on the strength of different binary dislocation junctions for general hcp structures.

Anisotropic Diffusion Behavior of Al in Mg: Diffusion Couple Study Using Mg Single Crystal

In this study, the anisotropic diffusion behavior of Al in hcp Mg was for the first time experimentally investigated using the diffusion couple technique with single crystal Mg at the temperatures ranging between 638 K and 693 K (365 °C and 420 °C). The diffusion coefficients derived from Al profiles in single crystal hcp Mg are D ⊥(a-axis) = 3.1 × 10−3 (m2/s) exp(−152154/RT) and D ║(c-axis) = 8.7 × 10−3(m2/s) exp(−159221/RT). The diffusion coefficient of Al within the basal plane is about 1.3 times greater than that along normal direction of the basal plane at the experimental temperatures. The interdiffusion coefficients of Mg17Al12 and Mg2Al3 solid solutions were also derived, and the values are similar to the previous studies.

Structure analysis of Ni thin films epitaxially grown on bcc metal underlayers formed on MgO(100) substrates

Ni thin films are prepared on Cr, V, and Nb underlayers with bcc structure formed on MgO(100) single-crystal substrates by molecular beam epitaxy. The growth behavior and the crystallographic properties are investigated by in-situ reflection high-energy electron diffraction and pole-figure X-ray diffraction. Cr(100) and V(100) single-crystal underlayers grow epitaxially on the substrates, whereas an Nb epitaxial_underlayer consisting of two bcc(110) variants is formed on the MgO(100) substrate. Metastable crystals nucleate on the Cr and the V underlayers, where the metastable hcp structure is stabilized through heteroepitaxial growth. With increasing the film thickness, the hcp structure starts to transform into more stable fcc structure by atomic displacement parallel to the hcp(0001) close-packed plane. The resulting films are consisting of mixtures of hcp and fcc crystals. On the other hand, only the formation of fcc crystal is recognized for the Ni film grown on Nb(110) underlayer.

Effects of a 3He impurity on the Elastic Anomalies of 4He at T=0

Effects on the elastic constants of a system formed from 4He atoms with a 3He impurity concentration of 0.14 % are investigated in a range of densities varying from 0.029 to 0.035 A−3. A model wave function of the shadow class is used to compute elastic constants and quantities defined through relations satisfied by them. The linear compressibility assumes the isotropic character expected for an hcp crystal with a constant value of the structure axis ratio c/a. This is in contrast with bulk 4He where an anisotropic behavior is observed.

On the Order–Disorder Surface Phase Transition and Critical Temperature of Pure Metals Originating from BCC, FCC, and HCP Crystal Structures

The excess surface Gibbs energy and surface tension of pure liquid metals (originating from bcc, fcc, and hcp solid metals) of ordered and disordered surface structures are compared in this paper. It is shown that at a special temperature T* an order–disorder surface phase transition is expected in all liquid metals from a low-temperature ordered surface state to a high-temperature disordered surface state. This surface phase transition is similar to the first-order bulk solid–liquid phase transition (melting). The values of T* appear in the temperature interval between the melting point and the critical point of metals. Critical temperatures of metals are estimated from the equation for high-temperature disordered surfaces.

The structure of Fe‐Ni alloy in Earth's inner core

The crystal structure of Fe‐10%Ni was investigated up to 340 GPa and 4700 K, corresponding to the Earth's inner core conditions by synchrotron X‐ray diffraction measurementsin‐situat ultrahigh pressure and temperature in a laser‐heated diamond‐anvil cell. The results show that hexagonal closed‐packed (hcp) structure is stable throughout the experimental conditions investigated with no evidence for a phase transition to body‐centered cubic (bcc) or face‐centered cubic (fcc) phases. The axialc/a ratio of the hcp crystal obtained around 330 GPa has a small temperature dependence similar to the axial ratio of pure Fe. Iron alloy with less than 10% Ni crystallizes to an hcp structure with c/a ratio of ∼1.61 at inner core conditions, although the effect of small amount of light elements remains to be examined by experiments.

Atomic Structures of $$ [0\bar{1}10] $$ Symmetric Tilt Grain Boundaries in Hexagonal Close-Packed (hcp) Crystals

Abstract Molecular dynamics simulation and interface defect theory are used to determine the relaxed equilibrium atomic structures of symmetric tilt grain boundaries (STGBs) in hexagonal close-packed (hcp) crystals with a $$ [0\bar{1}10] $$ tilt axis. STGBs of all possible rotation angles θ from 0 deg to 90 deg are found to have an ordered atomic structure. They correspond either to a coherent, defect-free boundary or to a tilt wall containing an array of distinct and discrete intrinsic grain boundary dislocations (GBDs). The STGBs adopt one of six base structures, $$ P_{B}^{(i)} $$ , i = 1, …, 6, and the Burgers vector of the GBDs is related to the interplanar spacing of the base structure on which it lies. The base structures correspond to the basal plane (θ = 0 deg, $$ P_{B}^{(1)} $$ ); one of four minimum-energy, coherent boundaries, $$ (\bar{2}111),\;(\bar{2}112),\;(\bar{2}114) $$ , and $$ (\bar{2}116)\;\left( {P_{B}^{(2)} - P_{B}^{(5)} } \right) $$ ; and the $$ \left( {11\bar{2}0} \right) $$ plane (θ = 90 deg, $$ P_{B}^{(6)} $$ ). Based on these features, STGBs can be classified into one of six possible structural sets, wherein STGBs belonging to the same set i contain the same base boundary structure $$ P_{B}^{(i)} $$ and an array of GBDs with the same Burgers vector $$ b_{\text{GB}}^{(i)} $$ , which vary only in spacing and sign with θ. This classification is shown to apply to both Mg and Ti, two metals with different c/a ratios and employing different interatomic potentials in simulation. We use a simple model to forecast the misorientation range of each set for hcp crystals of general c/a ratio, the predictions of which are shown to agree well with the molecular dynamics (MD) simulations for Mg and Ti.

Crystal plasticity analysis of micro-deformation, lattice rotation and geometrically necessary dislocation density

A gradient-enhanced crystal plasticity model is presented that explicitly accounts for the evolution of the densities of geometrically necessary dislocations (GNDs) on individual slip systems of deforming crystals. The GND densities are fully coupled with the crystal slip rule. Application of the model to two distinct and technologically important crystal types, namely hcp Ti and ccp Ni, is given. For the hcp crystals, slip is permitted with a -type slip directions on basal, prismatic and pyramidal planes and c + a -type slip directions on pyramidal planes. First, a single crystal under four-point bending is simulated as the uniform strain gradient expected in the central span provides a good validation of the code. Then, uniaxial deformation of a model near- α Ti polycrystal has been analysed. The resulting distributions of GND densities that develop on the various slip system types have been compared with independent experimental observations. The model predicts that GND density on the c + a systems is approximately an order of magnitude lower than that for a -type systems in agreement with experiment. For the ccp case, slip is considered to take place on the <110>{111} slip systems. Thermal loading of a single-crystal nickel alloy sample containing carbide particles of size approximately 30 μm has been analysed. Detailed comparisons are presented between model predictions and results of high-resolution electron backscatter diffraction (EBSD) measurements of the micro-deformations, lattice rotations, curvatures and GND densities local to the nickel–carbide interface. Qualitatively, good agreement is achieved between the coupled and decoupled model elastic strains with the EBSD measurements, but lattice rotations and GND densities are quantitatively well predicted by the coupled crystal model but are less well captured by the decoupled model. The GND coupling is found to lead to reduced lattice rotations and plastic strains in the region of highest heterogeneity close to the Ni matrix/particle interface, which is in agreement with the experimental measurements. The results presented provide objective evidence of the effectiveness of gradient-enhanced crystal plasticity finite element analysis and demonstrate that GND coupling is required in order to capture strains and lattice rotations in regions of high heterogeneity.

Universal relationships for the phonon spectra in BCC, FCC, and HCP crystals with a short-range interatomic interaction

The frequencies of the phonon branches that correspond to the vibrations of the close-packed atomic planes in bcc, fcc, and hcp crystals with short-range interatomic interaction are shown to be described by a universal relationship, which only contains two parameters for each branch, for any polarization λ. These phonon branches correspond to the (ξ, ξ, 0) direction in bcc crystals, the (ξ, ξ, ξ) direction in fcc crystals, and the (0, 0, ξ) direction in hcp crystals. This universal relationship can only be violated by long-range interactions, namely, the interactions outside the sixth coordination shell in a bcc crystal, the fifth coordination shell in an fcc crystal, and the eleventh or tenth coordination shell in an hcp crystal. The effect of these long-range interactions for each phonon branch can be quantitatively characterized by certain parameters Δnλ, which are simply expressed in terms of the frequencies of three phonons of the branch. The values of these parameters are presented for all bcc, fcc, and hcp metals whose phonon spectra are measured. In most cases, the proposed relationships for the frequencies are found to be fulfilled accurate to several percent. In the cases where the Δnλ parameters are not small, they can give substantial information on the type and scale of long-range interaction effects in various metals.

Atomic structures of symmetric tilt grain boundaries in hexagonal close packed (hcp) crystals

Using molecular dynamics (MD) simulations, the dislocation structures of symmetric tilt grain boundaries (STGBs) in hexagonal close packed (hcp) crystal structures are studied. STGBs over the entire range of possible rotation angles θ from 0° to 90° are found to have an ordered atomic structure. Formation energy calculations reveal four local minimum-energy boundaries that correspond to coherent grain boundaries (GBs). Deviations in tilt from the basal plane (θ = 0°, , prismatic plane (θ = 90°, , or one of these four minimum-energy boundaries, , result in the formation of a tilt wall (edge-type grain boundary dislocations, GBDs) superimposed on the nearest GB structure in θ-space. As θ deviates far from the rotation angle of one and draws closer to that of an adjacent , an abrupt transition in STGB base boundary structure and GBD Burgers vector occurs. For all θ, the sign and spacing of GBDs depend on θ, and their Burgers vector is either one or two times the interplanar spacing of PB. We present a simple model that generalizes the results to other c/a ratios. Subsequent MD simulations show that (1) the model forecasts the STGB structure to first-order and (2) STGBs with two distinct atomic structures can have remarkably different responses when interacting with basal lattice dislocations originating from the adjoining crystals.