Stability of self-interstitial atoms in hcp-Zr

Journal of Nuclear Materials

We investigate the effect of the axial ratio (c/a) on the stability of self-interstitial atoms (SIAs) in hexagonal close-packed crystal structures, using hcp-zirconium as a prototype, through density functional theory based ab initio calculations. The axial ratio is found to dominate the relative stability of SIAs over volumetric strains. We observe that below the ideal value of 1.633, the basal octahedral configuration is the most stable. Above the ideal value, the off-plane SIAs are more stable than in-plane ones.

Scientific Reports

The self-interstitial atoms (SIAs) mediate the evolution of micro-structures which is crucial in understanding the instabilities of hexagonal close packed (HCP) structures. Taking zirconium as a prototype, we investigate the pressure effect on the stabilities of SIAs using first-principles calculations based on density-functional theory. We found that the pressure greatly affects the stability of the SIAs. The SIAs in basal planes are more stable under pressure. The SIA configuration of the lowest formation energy changes from basal octahedral (BO) to octahedral (O) at a pressure of 21 GPa. The lowest formation enthalpy configuration switches from BO to S (split-dumbbell) at the pressure of 30 GPa. The formation volumes of SIAs decrease monotonically in response to an increase in pressure. Our results reveal that it is important to take pressure effects into account when predicting the micro-structural evolution of HCP structures.

Acta Materialia, 2002

Bulk properties of the Zr-H system were studied in the framework of the density functional theory. The local density approximation (LDA) is found to be insufficient for a proper description of interactions between Zr and H atoms and the generalized gradient approximation (GGA) is required. In αZr, H atoms preferentially occupy tetrahedral (T) sites at low temperatures, and can be regarded as being independent of each other up to very short distances, except for repulsive interactions between dumbbells in the same interstitial site. The Zr density of electronic states is perturbed by the presence of H, which induces the emergence of localized states. H diffusion occurs along the c → axis preferentially in octahedral (O) sites, and in the basal plane by alternate jumps into T and O sites. In the γ(ZrH), δ (ZrH 1.5) and ε(ZrH 2) hydrides, H-H interactions cannot be neglected, the nearly equal formation energies of these compounds indicate that their relative stabilities probably depend on mechanical and thermal contributions to free energies, and in fcc Zr, H atoms tend to adopt planar arrangements for compositions close to ZrH.

2012

Journal of Solid State Chemistry, 1998

The new quasi-binary Zr 2.7 Hf 11.3 P 9 was synthesized by arcmelting of Zr, Hf, Co, and HfP in a ratio corresponding to the initial composition ''Zr 2.25 Hf 6.75 Co 2 P 4 ''. Zr 2.7 Hf 11.3 P 9 crystallizes in the Zr 14 P 9 structure type, which is unknown in the binary Hf/P system. The ideal orthorhombic lattice dimensions (space group Pnnm (No. 58), Z ‫؍‬ 4) were refined to a ‫؍‬ 16.640 A s s 3 . The structure consists of three-dimensional condensed one-, two-, and threecapped trigonal (Zr, Hf ) 6 P prisms, occurring with numerous short M-M bonds (M ‫؍‬ Zr, Hf ). Each of the 15 metal sites is statistically occupied by a mixture of Zr and Hf, which varies significantly from site to site. The Hf/Zr ratio in a given site depends on the M-M and M-P interactions. The systematic increase of this ratio with increasing total bond order, as evaluated via Mulliken overlap populations and Pauling bond orders, can be understood based on the trend that Hf forms stronger M-M and M-P bonds than Zr. As expected for a metal-rich phosphide, band structure calculations for the hypothetical ''Hf 14 P 9 '' carried out with the extended Hu¨ckel approximation result in a significant density of states at the Fermi level.

Journal of Alloys and Compounds, 2009

Density-functional formalism is applied to study the phase equilibria in the U-Zr system. The obtained ground-state properties of the (bcc) and ı (C32) phases are in good agreement with experimental data. The decomposition curve for the -based U-Zr solutions is calculated. Our calculations confirm that experimentally observed "partial" ordering of the alloy components in the ı-UZr 2 (AlB 2 ) phase, in which Zr atoms occupy the "Al" position and the two "B" sites are randomly shared by the U and Zr atoms, is the most energetically favorable within the C32 structure. We argue that stabilization of the ı-UZr 2 phase relative to the˛-Zr (hcp) structure is due to an increase of the Zr d-band occupancy that occurs when U is alloyed with Zr. A comparison with stabilization of the ω-phase (also C32) in Zr under compression is made.

Physical Review B, 2006

We have calculated the phonons and elastic constants of zirconium in the hexagonal-close-packed ͑hcp͒ crystal structure using the Naval Research Laboratory ͑NRL͒ empirical tight-binding ͑TB͒ 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.

Journal of Nuclear Materials, 2008

The role of Fe in the hcp Zr diffusion process is analyzed, given its ultra-fast diffusion (up to nine orders of magnitude higher than the self-diffusion in the temperature range 779-1128 K) and the enhancement observed in the self and substitutional diffusion induced by its unavoidable presence as impurity. Ab-initio calculations using SIESTA and WIEN2K codes were performed in order to find the actual Fe minimum energy configuration within the hcp Zr matrix and its interaction with vacancies. Several off-centre quasi-interstitial positions with energies similar to substitutional Fe were encountered. The comparison with diffusion coefficient measurements and Mö ssbauer experiments allows us to discard the substitutional position of the Fe atom as well as to affirm that its presence creates a considerable lattice distortion together with an increment in the number of vacancies. The above effects could be responsible for the enhancement in the self and substitutional diffusion, whereas the large amount of quasi-interstitial positions for Fe could be, at least partially, responsible for the ultra-fast Fe diffusion.

Intermetallics, 2019

The intermetallic compounds Zr 2 Pd and ZrPd 2 have been investigated by perturbed angular correlation (PAC) spectroscopy considering anomalies in their hydrogen absorption properties. It is known that both these compounds have same crystal structure, but Zr 2 Pd forms an excellent hydride while ZrPd 2 does not, even at high pressure. From PAC measurement at room temperature in annealed ZrPd 2 sample, this phase is found as a minor component (∼27%) while the dominating phase is identified to be the ZrPd 3 (∼73%). In Zr 2 Pd, this phase has been found to be predominant (∼86%) along with a minor phase (∼14%) due to ZrPd. In ZrPd 2 , unlike Zr 2 Pd, a weak temperature dependence of electric field gradient (EFG) has been found from present PAC measurements. Also, site occupancies for both Zr and Pd atoms by the Ta-probe atoms have been found in ZrPd 2 and ZrPd 3 (formed in ZrPd 2). In ZrPd 3 , Pd site occupancy by the probe is found to be maximum while a small fraction for Zr site occupancy has been found. But, in case of Zr 2 Pd and ZrPd, no Pd site occupancy of the probe is observed. Calculation of electric field gradients at 181 Ta impurity atom for different phases have been performed by density functional theory based on the all electron full potential linearized augmented plane wave plus local orbitals (FP-(L)APW + lo) method to assign the different components observed from PAC measurements. Measurements by XRD have also been carried out to confirm the presence of component phases in the samples.

Chemical Physics Letters, 1997

Geometries and energy separations of low-lying electronic states of Zr 5 with different structures have been investigated by complete active space multi-configuration self-consistent field method followed by large-scale multi-reference singles + doubles configuration interaction computations that included up to 3 million configurations. Three nearly degenerate electronic states, namely 3A 2 (C2,.) with a distorted tetragonal pyramid structure and J,~ and 57~ (C~) with distorted edge capped tetrahedral geometries were found as the candidates for the ground state of Zr 5. The atomization and dissociation energies have been calculated and compared with smaller clusters. © 1997 Elsevier Science B.V.