Dynamics and thermodynamics of tetragonal zirconia determined by 111In/Cd TDPAC

For several years this research group has been using ¹¹¹In/Cd TDPAC to study oxygen vacancies in pure and lightly doped zirconia powders at temperatures up to 1400°C. This paper includes a brief survey of important results from those studies and some recent results. In particular, our new measurement showing negligible relaxation due to vacancy hopping above 600°C provides a major breakthrough in our ability to analyze PAC data and to determine accurately hopping and trapping rates and enthalpies for vacancies in tetragonal zirconia. This revised version was published online in August 2006 with corrections to the Cover Date.     

PAC analysis of defect motion by Blume's stochastic model forI=5/2 electric quadrupole interactions

Using Blume's stochastic model and the approach of Winkler and Gerdau, we have computed time-dependent effects on perturbed angular correlation (PAC) spectra due to defect motion in solids in the case ofI=5/2 electric quadrupole interactions. We report detailed analysis for a family of simple models: “XYZ+Z” models, in which the symmetry axis of an axial EFG is allowed to fluctuate among orientations alongx, y, andz axes, and a static axial EFG oriented along thez axis is added to the fluctuating EFGs. When the static EFG is zero, this model is termed the “XYZ” model. Approximate forms are given forG ₂(t) in the slow and rapid fluctuation regimes, i.e. suitable for the low and high temperature regions, respectively. Where they adequately reflect the underlying physical processes, these expressions allow one to fit PAC data for a wide range of temperatures and dopant concentrations to a single model, thus increasing the uniqueness of the interpretation of the defect properties. Application of the models is illustrated with data from a PAC study of tetragonal zirconia.     

Investigation of cadmium-hydrogen complexes in silicon

Formation, stability and electric properties of (In-H) and (Cd-H) complexes in Si are studied by the perturbed angular correlation spectroscopy (PAC). The trapping of hydrogen at the acceptors results in three different defect specific electric field gradients (EFGs), which are studied as function of temperature, doping concentration and annealing time. Two of the three observed hydrogen-related EFGs are identified as different charge states of one (Cd-H) acceptor. Within the framework of a model, which takes into account the dynamics of charge fluctuations and Shockley, Read and Hall statistics, the energy level of this (Cd-H) acceptor at E = E_V + 60 meV is deduced. Furthermore, the dynamical behavior of the hydrogen atom within the (Cd-H) complexes is studied. From the relaxation of the PAC signal the hopping rate of the hydrogen atom is extracted. This rate is thermally activated with an activation energy of E = 0.20 eV.     

Site occupation of indium and jump frequencies of cadmium in FeGa<Subscript><Emphasis Type="Bold">3</Emphasis></Subscript>

Perturbed angular correlation (PAC) measurements using the In-111 probe were carried out on FeGa₃ as part of a broader investigation of indium site occupation and cadmium diffusion in intermetallic compounds. One PAC signal was observed with hyperfine parameters ω ₁= 513.8(1) Mrad/s and η= 0.939(2) at room temperature. By comparison with quadrupole frequencies observed in PAC measurements on isostructural RuIn₃, it was determined that indium occupies only the 8j site in the FeGa₃ structure, denoted Ga(2) below because two out of the three Ga sites have this point symmetry. PAC spectra at elevated temperature exhibited damping characteristic of electric field gradients (EFGs) that fluctuate as Cd probes jump among Ga(2) sites within the lifetime of the excited PAC level. A stochastic model for the EFG fluctuations based on four conceivable, single-step jump-pathways connecting one Ga(2) site to neighboring Ga(2) sites was developed and used to fit PAC spectra. The four pathways lead to two observable EFG reorientation rates, and these reorientation rates were found to be strongly dependent on EFG orientation. Calculations using density functional theory were used to reduce the number of unknowns in the model with respect to EFG orientation. This made it possible to determine with reasonable precision the total jump rate of Cd among Ga(2) sites that correspond to a change in mirror plane orientation of site-symmetry. This total jump rate was found to be thermally activated with an activation enthalpy of 1.8 ±0.1 eV.     

Stochastic Model of PAC Nuclear Relaxation Caused by Defects Hopping on a Simple Cubic Lattice

A stochastic model is used to obtain an analytic approximation for the perturbation function caused by quadrupole interaction that applies when there is a fixed concentration of defects hopping on a simple cubic lattice, with the probe atom located at center of one of the cubes. A realization of this model is jumping of structural vacancies on one sublattice in the CsCl structure, with the probe atom on the other sublattice. PAC spectra obtained for Pd-poor PdIn using ¹¹¹In/Cd probes are refitted with the model perturbation function to obtain the vacancy jump frequency as a function of temperature. This revised version was published online in September 2006 with corrections to the Cover Date.     

PAC perturbation factor for spin 5/2 nuclei subject to a rapidly fluctuating EFG1

We report numerical computations of the PAC perturbation factor G₂(1) for spin 5/2 nuclei subject to a static EFG symmetric about the z-axis and an additional axially-symmetric EFG whose symmetry axis fluctuates randomly among the x, y, z directions. For sufficiently large fluctuation rates, the numerical results are described by the expression for the static interaction alone with the addition of relaxation terms. Results of applying this model to¹¹¹Cd TDPAC measurements on tetragonal ZrO₂ are described briefly. The model allows one to evaluate the probability that oxygen vacancies are trapped. the energy of association of vacancy-metal pairs, and the vacancy activation energy of motion. Supported in part by USDOE contract DE-FG06-85ER45191     

Time differential perturbed angular correlation studies of hafnium hydrides

The dependence of the electric field gradients (EFG) in Hafnium-Hydride systems as a function of the composition H/Hf in the cubic δ and tetragonal ε phases were investigated using the time-dependent perturbed angular correlation (TDPAC) technique, with¹⁸¹Ta as the nuclear probe. Two EFGs were found in the ε phase, indicating the existence of two major symmetries surrounding the Ta probe. The results indicate that the trend of the EFGs, in the ε phase, are due to the changes in the lattice parametersa _o,c _o as hydrogen is added to the Hf-H system. In the δ phase, only one major symmetry was found. Both phases are characterized by broad frequency distributions and large anisotropies.     

Fe-Hydroxysulphates from Bacterial Fe2+ Oxidation

The perturbed angular correlation method (PAC) was applied to investigate the lattice location of implanted ¹¹¹In probe ions in Hf₂Ni and Zr₂Ni intermetallic compounds. It is concluded that the ¹¹¹In/¹¹¹Cd probe nuclei experiencing the highly asymmetric electric field gradient (EFG) occupy the unique hafnium or zirconium 8(h) sites in the investigated phases. Above room temperature, the EFGs decrease linearly with temperature. The results are compared with that of previous PAC measurements with ¹⁸¹Ta probes.     

Electric field gradients at Ta in Zr and Hf inter-metallic compounds

Here we calculate the electric field gradient (EFG) at the nucleus of the substitutional Ta impurity site in Zr₂T and Hf₂T (T=Cu, Ag, Au, and Pd) C11_b inter-metallic compounds. We use the ab initio FP-LAPW method as embodied in the Wien97 code in a super-cell approach and include lattice relaxations around the impurity. Our results are compared with EFG values inferred from measurements of the quadrupole coupling constants at the ¹¹¹Ta probe in these compounds performed with the time differential perturbed angular correlation (TDPAC) technique. We also performed EFG calculations for the pure inter-metallic compounds. Through the comparison of theoretical and experimental EFGs in these cases, we elucidate the role played by the Ta probe in the TDPAC measurements of Hf and Zr compounds. Our results show that, although the EFGs at the Hf site are very similar to the EFGs at the Ta impurity, there is no direct correlation between the Zr and Ta EFGs.     

Hopping motion of chlorine atoms on Si(1 0 0)-(2 × 1) surfaces induced by carrier injection from scanning tunneling microscope tips

Injection of tunneling electrons and holes from the probe tips of a scanning tunneling microscope was found to enhance the hopping motion of Cl atoms between neighboring dangling-bond sites of Si dimers on Si(1 0 0)-(2 × 1) surfaces, featured by the rate of hopping linearly dependent on the injection current. The hopping rate formed peaks at sample biases of V_S∼+1.25 and −0.85 V, which agree with the peaks in the local density of states spectrum measured by scanning tunneling spectroscopy. The Cl hopping was enhanced at Cl-adsorbed sites even remote from the injection point. The Cl hopping by hole injection was more efficiently enhanced by sweeping the tip along the Si dimer row than by tip-sweeping along the perpendicular direction. Such anisotropy, on the other hand, was insignificant in the electron injection case. All of these findings can be interpreted by the model that the holes injected primarily into a surface band originated from the dangling bonds of Si dimers propagate quite anisotropically along the surface, and become localized at Cl sites somehow to destabilize the Si-Cl bonds causing hopping of the Cl atoms. The electrons injected into a bulk band propagate in an isotropic manner and then get resonantly trapped at Si-Cl antibonding orbitals, resulting in bond destabilization and hopping of the Cl atoms.     

On the nature of trapped states in an MoS2 two-dimensional semiconductor with sulfur vacancies

ABSTRACT

Molybdenum disulfide (MoS₂) is a common two-dimensional semiconductor that has been highly studied as an emerging material for catalysis and electronics. The most common material defects in MoS₂ are sulfur vacancies. In order to reveal the nature of the trapped states induced by sulfur vacancies, we perform Density Functional Theory (DFT) combined with quantum dynamics calculations. According to our model, we find that the sulfur vacancies create trap states in the original band gap of monolayer MoS₂ that disrupt charge transmission through the monolayer. In addition, we did not find any resonance states among the shallow states in the conduction band continuum.     

Inhomogeneous broadening of PAC spectra with V zz and η joint probability distribution functions

The perturbed angular correlation (PAC) spectrum, G ₂(t), is broadened by the presence of randomly distributed defects in crystals due to a distribution of electric field gradients (EFGs) experienced by probe nuclei. Heuristic approaches to fitting spectra that exhibit such inhomogeneous broadening (ihb) consider only the distribution of EFG magnitudes V _zz , but the physical effect actually depends on the joint probability distribution function (pdf) of V _zz and EFG asymmetry parameter η. The difficulty in determining the joint pdf leads us to more appropriate representations of the EFG coordinates, and to express the joint pdf as the product of two approximately independent pdfs describing each coordinate separately. We have pursued this case in detail using as an initial illustration of the method a simple point defect model with nuclear spin I?=?5/2 in several cubic lattices, where G ₂(t) is primarily induced by a defect trapped in the first neighbor shell of a probe and broadening is due to defects distributed at random outside the first neighbor shell. Effects such as lattice relaxation are ignored in this simple test of the method. The simplicity of our model is suitable for gaining insight into ihb with more than V _zz alone. We simulate ihb in this simple case by averaging the net EFGs of 20,000 random defect arrangements, resulting in a broadened average G ₂(t). The 20,000 random cases provide a distribution of EFG components which are first transformed to Czjzek coordinates and then further into the full Czjzek half plane by conformal mapping. The topology of this transformed space yields an approximately separable joint pdf for the EFG components. We then fit the nearly independent pdfs and reconstruct G ₂(t) as a function of defect concentration. We report results for distributions of defects on simple cubic, face-centered cubic, and body-centered cubic lattices. The method explored here for analyzing ihb is applicable to more realistic cases.     

Electric Field Gradients of Fluorides Calculated by the Full Potential KKR Green's Function Method

We report on the calculation of electric field gradients (EFGs) of MgF₂, MnF₂, CoF₂, NiF₂ and ZnF₂. EFGs were calculated by the full potential Korringa–Kohn–Rostoker (KKR) Green's function method in the framework of the density functional theory. While EFG calculation of these fluorides are rather difficult in the muffin-tin-potential model, due to its sensitivity to the muffin-tin radius, no difficulties arise in the present full potential treatments. EFGs calculated by this method well reproduce experimental data.     

Investigation of hyperfine interactions in RMO 3 (R = La, Nd; M = Cr, Fe) antiferromagnetic perovskite oxides using PAC spectroscopy

Because of its sensitivity to point defects atomically close to probe nuclei, it is reasonable to expect that perturbed angular correlation (PAC) spectroscopy has the potential to assist in the identification of diffusion mechanisms. It is of interest to characterize under what conditions diffusing defects are visible and how the defects affect relaxation in PAC spectra. This was investigated using a stochastic model to simulate PAC spectra for the special case of non-impurity PAC probes diffusing via a simple vacancy mechanism on the Cu-sublattice in Cu₃Au-structured compounds.     

次近邻电子跳跃对孤子的电子束缚态和孤子附近局域模的影响

从SSH模型出发,考虑电子次近邻跳跃的影响,研究了聚乙炔中孤子的电子束缚态和孤子附近的局域振动模。结果发现:1.电子能谱中的电子-空穴对称性消失;2.孤子的电子束缚态的数目和位置发生了变化,且与孤子的类型有关;3.孤子附近出现了一个新的局域振动模G₆;4.次近邻电子跳跃改变了局域模的频率,增强了局域模的局域性。 关键词：     

Electric field gradients in Hf2Fe

Perturbed Angular Correlations (PAC) technique was applied to measure the electric field gradients (EFG) at ¹⁸¹Ta sites in Hf₂Fe. The compound has the cubic structure of the Ti₂Ni prototype with two non‐equivalent crystallographic sites for Hf atoms. EFGs for the two sites were measured as a function of the temperature. In addition, one more EFG was observed, which was assigned to the presence of defects in the lattice. The ratio of the measured EFG at the regular lattice sites has been used to assign charges to the ions through a simple calculation using the point charge model and it is shown that the lattice symmetry can explain the very different EFG at both sites. This revised version was published online in August 2006 with corrections to the Cover Date.     

Vacancy encounter model for stochastically fluctuating electric field gradients in the Cu3Au crystal structure

A class of experimental techniques known as hyperfine methods can be used to measure electric field gradients (EFGs) through the hyperfine interaction experienced by tracer nuclei. When EFGs fluctuate at rates comparable to the inverse characteristic timescale of the hyperfine method, there is a loss of signal coherence that can be used to determine EFG fluctuation rates. This has been used to measure, for example, EFG fluctuations accompanying atomic jumps of radiotracers using perturbed angular correlation spectroscopy (PAC). Nominally, there is a one-to-one correspondence between EFG fluctuation and tracer jump, but when tracer jumps are mediated by a vacancy diffusion mechanism, a subset of multiple tracer-vacancy exchanges will not affect spectra when they occur much faster than the hyperfine timescale, leading to an underestimate of underlying tracer jump rate if this correlated random-walk effect is not taken into consideration. The present work calculates the factor by which EFG fluctuation rate differs from tracer jump rate based on a time-dependent, random-walk analysis of tracer displacement probabilities in a vacancy encounter model for the special case of self-diffusion in the L1₂ crystal structure.     

Molecular dynamics simulation of zirconia melting

The melting point for the tetragonal and cubic phases of zirconia (ZrO₂) was computed using Z-method microcanonical molecular dynamics simulations for two different interaction models: the empirical Lewis-Catlow potential versus the relatively new reactive force field (ReaxFF) model. While both models reproduce the stability of the cubic phase over the tetragonal phase at high temperatures, ReaxFF also gives approximately the correct melting point, around 2900 K, whereas the Lewis-Catlow estimate is above 6000 K.     

Hyperfine interactions in ZrO2–5 wt.% Al2O3 ceramics

Two powder samples of ZrO₂-5 wt.% Al₂O₃ derived from precursor solutions of different pH – 2 for sample (C) and 4 for sample (D) – were prepared by the precipitation method. They were studied using PAC between RT and 1150oC and XRD after heating at increasing temperatures. According to XRD, the addition of Al₂O₃ causes the complete stabilization of tetragonal zirconia in both samples. At a nanoscopic level, however, they present different interactions and thermal evolutions. Sample (C) exhibits predominantly the t₁- and dynamic t₂-forms already reported for pure and yttria-doped stabilized tetragonal zirconias. On the other hand, sample (D) exhibits a novel nanoconfiguration depicted by a totally asymmetric and dynamic EFG whose population achieves 86% at 1150oC and which has been associated to aluminium solubility in zirconia. Upon cooling gradually to RT from the highest temperature, (C) transforms completely to m-ZrO₂ and (D) remains 65% in the metastable tetragonal phase. This revised version was published online in August 2006 with corrections to the Cover Date.     

Structure and electrical behavior in air of TiO2-doped stabilized tetragonal zirconia ceramics

2 -doped YTZP ([%mol]3 Y₂O₃) compositions sintered in the temperature range of 1300 to 1450 °C, the tetragonal zirconia solid solutions field for the ZrO₂-Y₂O₃-TiO₂ system was established. The solubility of TiO₂ in YTZP was found to be about 12–[%mol]14 at 1450 °C. Structural characterization of the Ti-YTZP tetragonal zirconia solid solutions was carried out using X-ray absorption spectroscopy (EXAFS and XANES) to provide information on the environment of Ti atoms. The electrical behavior in air of the TiO₂-doped tetragonal zirconia solid solutions was studied by impedance spectroscopy in the temperature range of 300 to 800 °C, and it was found that the ionic conductivity decreases with increasing titania content. EXAFS and XANES results show that as the Ti⁴⁺ ions dissolve into the tetragonal zirconia YTZP matrix, a displacement of Ti ions from the center of symmetry takes place, leading to a non-random substitution of Ti⁴⁺ ions on Zr⁴⁺ lattice sites. Ti-O bond distances derived from EXAFS indicate that the Ti ion can be in a square-pyramidal arrangement, i.e., fivefold oxygen-coordinated. As a consequence two kinds of cation–oxygen vacancy associations are created; the high-mobility oxygen-vacancy–eightfold-coordinated cation (Zr⁴⁺) and the low-mobility oxygen-vacancy–fivefold-coordinated cation (Ti⁴⁺). This results in a decrease in the global concentration of moving oxygen vacancies and, therefore, in a decrease of the electrical conductivity. Received: 1 April 1998/Accepted: 28 September 1998