Hcp Zr Research Articles

Tight-binding calculations of the elastic constants and phonons of hcp Zr: Complications due to anisotropic stress and long-range forces

We have calculated the phonons and elastic constants of zirconium in the hexagonal-close-packed (hcp) crystal structure using the Naval Research Laboratory (NRL) empirical tight-binding (TB) approach; the tight-binding parameters are obtained by fitting to ab initio density-functional theory--generalized gradient approximation energy bands and total energies for many different structures and volumes. We address difficulties involved with the fitting procedure and give results for elastic constants, force constants, quasiharmonic phonons, and specific heat. Because the predicted TB lattice constants at the zero-temperature energy minimum are slightly different from those experimentally observed at room temperature, our TB model has an anisotropic stress at the experimental lattice constants. We correct for these stresses in our calculations of the elastic constants and sound speeds. Such techniques are also useful for calculating such properties for arbitrary $c∕a$. Our phonon calculations were done by the direct-force method in real space using calculated force constants; these fall off quite slowly with distance, which causes problems with the calculated phonon spectrum due to the slow convergence with increasing supercell size. This long-range behavior could play a large role in determining the unusually anharmonic and anomalous physical properties of Zr. We show that similar, although less severe, problems should arise for other metals. These considerations suggest that the direct-force method for calculating phonons may be problematic for many metals.

Modified embedded-atom method interatomic potentials for Ti and Zr

Semiempirical interatomic potentials for hcp elements, Ti and Zr, have been developed based on the MEAM (modified embedded-atom method) formalism. The new potentials do not cause the stability problem previously reported in MEAM for hcp elements, and describe wide range of physical properties (bulk properties, point defect properties, planar defect properties, and thermal properties) of pure Ti and Zr, in good agreement with experimental information. The applicability of the potentials to atomistic approaches for investigation of various materials behavior (slip, irradiation, amorphous behavior, etc.) in Ti or Zr-based alloys is demonstrated by showing that the related material properties are correctly reproduced using the present potentials and that the potentials can be easily extended to multicomponent systems.

Irradiation-Enhanced Second-Phase Precipitation in Zr-Fe Nanocrystalline Thin Films

AbstractIn situ observations in a transmission electron microscope (TEM) were used to study ion-beam enhancement of second-phase precipitation in Zr-Fe nanocrystalline thin films. The free-standing films were prepared by co-sputter deposition with an Fe content of 1.2 at%. TEM diffraction analysis showed that only the hcp Zr crystal structure was present in the as-deposited films. No second phases were detected, although Rutherford Backscattering Spectroscopy (RBS) confirmed a Fe content beyond the solubility limit of Fe in Zr (of the order of ppm). This means the thin films were Zr solid solutions supersaturated with Fe. Heat treatment in the absence of irradiation was observed to cause precipitation of the Zr2Fe intermetallic phase, but only above 673 K. The same second-phase precipitation can occur at lower temperatures in the presence of ion irradiation. Samples were irradiated in-situ at the Intermediate Voltage Electron Microscope (IVEM) at Argonne National Laboratory with Kr ions to fluences in excess of 1016 ion/cm2, at temperatures ranging from 50 to 573 K. Second phase precipitation was detected by electron diffraction patterns and by dark field imaging comparing regions exposed to the beam with regions protected from the beam by the TEM support grid. Precipitation of Zr2Fe intermetallic phase was observed at all irradiating temperatures above room temperature. In the bulk, this phase is thermodynamically metastable in the range of temperatures investigated (relative to the orthorhombic Zr3Fe intermetallic phase). The kinetics of the irradiation-enhanced second-phase precipitation was followed by recording the diffraction patterns at regular intervals. The dose to precipitation was found to decrease with increasing irradiation temperature.

Long-term behaviour of irradiated hcp Zr using Monte Carlo simulations

Kinetic Monte Carlo (kMC) modelling has been used to study the diffusion of defects produced under irradiation in alpha-zirconiun. Database of displacement cascades created by recoils from 10 to 25keV obtained by molecular dynamics (MD) simulations have been used as initial damage state in the metal. These cascades have been annealed for times of hours at a fixed temperature of 600K. The number of freely migrating defects, the recombination ratio between vacancies and interstitials, the surviving defects in the bulk as well as the average cluster size for these remaining defects have been obtained.

Phase stability of bcc Zr in Nb/Zr thin film multilayers

A change in phase stability from hcp Zr to bcc Zr occurs in Nb/Zr multilayers when the bilayer thickness is reduced to the nanometer scale. This phase stability in these multilayers has been described using a model based on classical thermodynamics. Using a previously reported experimental observation of hcp to bcc transformation in these multilayers, a phase stability diagram (referred to as the biphase diagram) has been proposed. Subsequently, a range of multilayers with varying volume fractions and bilayer thicknesses have been sputter deposited. The crystal structures in these multilayers have been determined using X-ray and electron diffraction. The hcp and bcc Zr phases within the Nb/Zr multilayers are in agreement with the predictions afforded by the proposed biphase diagram. The sequence of the Zr bcc phase stability was accomplished by forming its β-Zr (high temperature bcc phase) prior to forming a bcc coherent interface with Nb. First approximations of the structural and chemical contributions to the interfacial energy accompanying the changes in hcp to bcc phase stability for Zr have been evaluated.

Modeling of Surface Diffusion in hcp Zr and Ti

The statics and dynamics of vacancies and adatoms on different surface orientations in two hcp materials are studied by using static relaxation techniques and many-body potentials. Formation and migration energies and entropies as well as attempt frequencies are evaluated and used in the random walk approach to obtain correlation factors and diffusivities. It is found that the main features of surface diffusion are dominated by jumps on and between a few atomic layers, so that a consistent comparison between the two mechanisms is feasible. The activation energies and the diffusivities for different environments, namely, bulk Q b, D b, symmetric grain boundaries Q gb, D gb, and surfaces, Q s, D s, calculated using the same simulation technique and interatomic potentials, fulfil the expected relationships Q s < Q gb < Q b and D s > D gb > D b. It is also found that generally adatoms are faster surface diffusers than vacancies.

Oxidation characteristics of basal ( [formula omitted]) plane and prism ( [formula omitted]) plane in HCP Zr

The oxidation characteristics of (0 0 0 2) basal plane and (1 1 2 ̄ 0) prismatic plane of an unalloyed Zr were investigated. From the Zr crystal bar, the specimen representing a single crystal was prepared to be coarse enough to have its grain be 4×4×1 mm 3 in size. After identifying the crystallographic orientations and planes by X-ray diffraction (XRD), the samples were cut out in such a way as the cutting planes could correspond to the desired crystallographic planes. Oxidation tests were carried out in water at 360 °C. The oxidation rate of the (1 1 2 ̄ 0) prismatic plane was faster than that of the (0 0 0 2) basal plane. The analysis of oxide using the synchrotron XRD revealed that the oxide grown at the basal plane had the preferred (2 0 0) plane in mono-ZrO 2, while the oxide at the prismatic plane grew at both the (2 0 0) and (0 0 2) planes of mono-ZrO 2. In addition, the oxide layer that had formed at the basal plane having only one preferred growth plane exhibited a high fraction of columnar oxide and a relatively wide range of protective barrier layer. These results mean that the characteristics of the preferred planes of mono-ZrO 2 play an important role on the oxidation rate of Zr single crystal.

Experimental and Thermodynamic Assessment of the Fe-Gd-Zr System

Abstract The phase equilibria in the ternary system Fe-Gd-Zr at 1073 K have been investigated by X-ray diffraction and electron probe microanalysis. The isothermal section consists of terminal solution phases bcc (Fe), hcp (Zr), and hcp (Gd) (bcc = body-centred cubic, hcp = hexagonal close-packed), binary compounds FeZr2 and FeZr3, quasibinary compounds (Fe, Zr)17Gd2, Fe17(Gd, Zr)2, Fe23(Gd, Zr)6, Fe3(Gd, Zr), and Laves phase Fe2(Gd, Zr). No ternary compounds were detected. The isomorphous phases Fe23Gd6-Fe23Zr6 and Fe2Gd-Fe2Zr do not form continuous solid solutions. The Fe3(Gd, Zr) phase shows the largest homogeneity region (0–12 at.% Zr). In the compound Fe17Gd2, Zr atoms can substitute for both Gd and Fe atoms. This results in the formation of two distinct phases (hexagonal and rhombohedral), respectively. The experimental results have been used to obtain a self-consistent thermodynamic description of the ternary system Fe-Gd-Zr.

Development of a tight-binding potential for bcc Zr: Application to the study of vibrational properties

We present a tight-binding potential based on the moment expansion of the density of states, which includes up to the fifth moment. The potential is fitted to bcc and hcp Zr and it is applied to the computation of vibrational properties of bcc Zr. In particular, we compute the isothermal elastic constants in the temperature range $1200 \mathrm{K}&lt;T&lt;2000 \mathrm{K}$ by means of standard Monte Carlo simulation techniques. The agreement with experimental results is satisfactory, especially in the case of the stability of the lattice with respect to the shear associated with ${C}^{\ensuremath{'}}.$ However, the temperature decrease of the Cauchy pressure is not reproduced. The $T=0$ K phonon frequencies of bcc Zr are also computed. The potential predicts several instabilities of the bcc structure, and a crossing of the longitudinal and transverse modes in the (001) direction. This is in agreement with recent ab initio calculations in Sc, Ti, Hf, and La.

A first-principles study of the theoretical strength and bulk modulus of hcp metals

A first-principles method based on the local-density approximation using discrete variational clusters has been used to study the electronic structure of the hcp metals, Be, Mg, Sc, Y, Ti, Zr, Co, Zn and Cd. The binding energy of these metals was calculated in relation to the volume of a unit cell. The variation in the binding energy with the unit cell volume was obtained by means of a polynomial fit. The theoretical tensile strength and bulk modulus of these metals were estimated from the electronic structure and binding energy calculations. The predicted bulk moduli for these metals are in good agreement with experimental findings and other available theoretical data. A linear relationship between the calculated and the experimental strengths is observed.

Crystallographic and morphological properties of magnetron sputtered Ti and Zr thin films

ABSTRACTCrystallographic and surface morphological characteristics of polycrystalline hcp Ti and Zr thin films were studied as a function of the homologous substrate temperature TS/TM and the thickness t of the films (28 nm ≤ t ≤ 380 nm). TS is the substrate temperature during deposition and TM is the melting point of the film's material. For the whole range of considered temperatures (0.14 ≤ TS/TM ≤ 0.48) Zr films presented a {0002} crystallographic orientation. As TS/TM increased, Ti films suffered a transition from a columnar grain structure with {0002} preferential crystallographic orientation to a cone-like-shape grain structure with {1011} preferential crystallographic orientation. Our results suggest that Zr films suffer a structural transition from Zone T to Zone II at temperatures similar to those predicted by Thornton's Structure Zone Model for thick films while Ti films do not have a microstructure typical of Zone II even for relatively high values of TS/TM, presenting a transition from Zone I to Zone T in the studied range of temperatures.

Pressure and temperature effects on the [formula omitted] and N-phonons in zirconium

The effective potentials for the E2g-phonon at the Γ point of the Brillouin zone of hcp Zr and the transverse N phonon of bcc Zr are calculated for different pressures by the frozen-phonon method. The temperature and pressure dependences of the phonon frequencies are studied within the framework of a modified pseudo-harmonic approximation. The results obtained are in good agreement with the experimental ones. The change observed in the behavior of frequencies with increasing temperature and pressure may be attributed to the peculiarities of the phase diagram of zirconium.

Atomic Scale Simulation of the Effect of Hydrogen on Dislocations in Zr

AbstractIn nuclear power plants, Zr–based cladding is corroded by the primary coolant. Concomitantly, it undergoes hydrogen pick–up which induces modifications of its mechanical properties, especially creep and recrystallization rates. Below 600K, the deformation in hcp Zr is partially controlled by screw dislocations, which due to their intricate core structure have reduced intrinsic mobility. Here, we address the possible hydrogen induced modifications of the core structure of screw dislocations. We used first–principle calculations based on the density functional theory to evaluate the interaction between hydrogen and screw dislocation cores and also to evaluate the hydrogen induced modifications of the prismatic and basal gamma surfaces. We show that the presence of hydrogen results in significant reductions of the stacking fault energies.

High pressure and temperature behaviour of electrical resistivity of hcp metals Ti, Zr and Gd

High pressure measurements of electrical resistivity of polycrystalline Ti, Zr and Gd have been performed in the temperature range 22-1000 °C and in the pressure range 4-48 kbar. The pressure and temperature coefficients of electrical resistivity of the hcp phase have been determined and new measurements of the boundaries into hcp-neighbouring phases are presented. All three metals show typical pressure and temperature dependences of resistivity behaviour in the hcp region, with Gd displaying the greatest sensitivity to pressure due to its high compressibility.

Mössbauer spectroscopy of the Zr-rich region in Zr–Nb–Fe alloys with low Nb content

Intermetallic phases and solid solutions in the Zr-rich region of the Zr–Nb–Fe system with low Nb content are studied by Mossbauer spectroscopy complemented with X-ray diffraction, optical and scanning electron microscopy and electron microprobe analysis. The phases found in each sample were those expected from the corresponding binary Zr–Fe system. Furthermore, one of the samples showed a ternary cubic Ti2Ni type phase with a similar stoichiometry to the tetragonal Zr2Fe compound. Mossbauer parameters were suggested to this phase (IS: - 0.12 mm/s, QS: 0.30 mm/s), to the bcc Zr(β) phase (IS: (-0.11 α 0.01) mm/s, QS: (0.23 α 0.02) mm/s), and to the hcp Zr(βT) phase (IS: (-0.24 α 0.02) mm/s, QS: (0.45 α 0.02) mm/s).

Pressure effect on the transverse Γ-point optical phonon in hcp Zr

Pressure effect on the transverse Γ-point optical phonon in hcp Zr

Allotropic phase formation in Ti/Zr multilayers

Abstract The presence of face centered cubic Ti and Zr in Zr/Ti multilayers in specimens prepared for transmission electron microscopy is noted. X-ray diffraction shows that in the as-deposited state the multilayers contain the equilibrium hcp Ti and Zr phases, implying that a transformation occurs during thinning of specimens for TEM study.

Electron structure and activation energy of hydrogen in α-Zr using nonlinear response theory

The electron structure of hydrogen in hcp Zr is calculated by using self-consistent nonlinear screening theory. The host-ion contribution is included through the spherical solid model potential (SSMP). The resulting charge density and scattering phase shifts are used to calculate the activation energy and residual resistivity of hydrogen in α-Zr matrix. The calculated activation energy 0·285 eV is found in reasonably good agreement with experimental value 0·3 eV. The estimated residual resistivity 0·53 μΩ cm/at% for Zr-H system using the scattering phase shifts agrees reasonably well with the observed value 0·27 μΩ cm/at%. The calculated configurational energy shows that hydrogen prefers tetrahedral(T)-sites over octahedral(O)-sites in α-Zr. The strong binding energy of electron-proton suggests that hydrogen forms zirconium hydride.

LEED crystallographic analysis for the structure formed by 2 ML of O at the Zr(0001) surface

A tensor LEED analysis is reported for the Zr(0001)-(1 × 1)-O surface which involves oxygen at a total coverage of 2 monolayers. The structure is indicated to have two layers of O: one forms an overlayer in which the O atoms bond to hollow sites of three-fold coordination on the regular metal surface, while the other layer has the O atoms in tetrahedral hole sites between the first and second metal layers. The stacking sequence, designated as (C)B(A)AB... corresponds to the first three layers of anion-terminated cubic ZrO 2, although some lateral compression is needed for superposition on the regular hcp Zr structure. The absorption of O in the tetrahedral holes results in a significant expansion in the first-to-second ZrZr interlayer spacing to about 3.44 Å from the bulk vaue of 2.57 Å. The OZr bond lengths are estimated to equal 2.07 Å for the overlayer O atoms, and 2.21 Å for the O atoms in tetrahedral hole sites. Comparisons are made with the structures of the corresponding 0.5 and 1 ML surfaces formed by the O Zr(0001) system.

Diffusion-Governed-Asymmetric Growth of Amorphous Layer Under Solid-State Reaction in Ni-Zr Multilayers

ABSTRACTA molecular-dynamics simulation with an n-body potential was performed to study solid-state amorphization in the Ni-Zr system upon annealing at medium temperatures ranging from 300 to 600 °C. The models for simulation were a Zr-Ni-Zr sandwich consisting of both hcp Zr and fcc Ni (001) atomic planes and a bilayer with a thin preset disordered interfacial layer, respectively, for revealing the detailed amorphization process and the growing kinetics of an amorphous layer upon solid-state reaction. Our simulation results demonstrated, for the first time, that the atomic process proceeded through first diffusion, then alloying and eventually amorphization. In other words, amorphization was controlled by a diffusion-limited reaction and the growth kinetics of the amorphous layer followed exactly a t1/2 law. Another interesting finding was that the growing speeds of the amorphous layer exhibited an asymmetric behavior, i.e. the amorphous layer extended faster towards Ni lattice than that directed to Zr side. Besides, it was also found that an initiation of amorphization upon annealing was dependent to the interfacial textures, i.e. amorphization could take place when the interfaces were composed of the more open atomic planes, whereas it was suppressed if the interfaces were constructed with the close-packed planes of both lattices.