Study of cation tracer diffusion in NaF

Cation tracer diffusion coefficients were measured in pure NaF crystals in the intrinsic ionic conductivity range (876–970 °C). The results can be rationalized satisfactorily in terms of contributions to the observed Na tracer diffusivities arising from both free vacancies and neutral vacancy pairs, the latter contribution amounting to about 53 per cent of the total Na diffusion at the highest measuring temperature. The best-fit defect parameters derived in an earlier conductivity study [21] from this laboratory on similar NaF crystals give for the free vacancy contribution D_v^*(Na) = 4·25 exp (?2·21 eV/kT) cm²s^?1. A combination of these D_v^*(Na) values with the present diffusion data yields for the vacancy-pair contribution D_p^*(Na) = 1·15 × 10⁸exp (?4·04 eV/kT) cm²s^?1. Comparison of the present findings with published values of the anion tracer diffusion coefficient in NaF showed that D_p^* (F) is 2·3 to 4·4 times larger than D_p^*(Na) over the temperature range of our observations, the difference between the two contributions increasing with decreasing temperature. When approximate account is taken of the temperature-dependence of the two pair correlation factors, this last result indicates that the anion jumps into the vacancy pair occur with a higher frequency, and increasingly so at lower temperatures, than do those involving the cations.     

Energy of migration of monovalent ions in NaCl: An experimental and theoretical study

Experimental diffusion measurements show that migration enthalpies of Cl^?, Br^? and I^? in NaCl are comparable, while that of F^? is considerably lower. Earlier studies had shown that migration enthalpies of Na⁺, K⁺, Rb⁺ and Cs⁺ in NaCl were similar. The polarised point ion model predicts migration energies of ions (by vacancy mechanism) to monotonically increase with ion size, contrary to experiment. Inversely, the shell model calculations rightly predict the variation of migration energies with ionic size. Thus, migration energies by vacancy mechanism do not vary significantly for ions larger than the host ions. However, in the case of the small ions, Li⁺ and F^?, the migration energies by vacancy mechanism are much lower and in good agreement with experiment for F^?.     

Self-diffusion of potassium in potassium azide

The tracer sectioning technique was used to study the diffusion of potassium ions in melt grown single crystals of potassium azide. The temperature dependence of the diffusion coefficients in the range 85–254°C can be represented by D=(0·19±0·03) exp [(?0·80±0·06) eV/kT] cm²/sec. It appears that the cations are the predominant mobile species and that they diffuse by a vacancy mechanism with an enthalpy of migration of 0·80±0·06 eV.     

Cation diffusion,semiconductivity and nonstoichiometry in (Co,Ni)O crystals

The diffusivities of ⁶⁰Co and ⁵⁷Ni, and the electrical semiconductivity in (Co,Ni)O crystals have been determined as a function of temperature and composition in an air atmosphere. Both ⁶⁰Co and ⁵⁷Ni diffuse by a vacancy mechanism. Their diffusivities increase exponentially with an increase cation fraction of cobalt in the mixed oxides at a constant temperature. Using Manning's model of diffusion in a random alloy, the relative extent of off-stoichiometry and, therefore, the concentration of cation vacancies relative to NiO as a function of c in (Co_cNi_1?c)O were evaluated from the diffusion data. The change in enthalpy of formation of a cation vacancy as a function of the cation composition in mixed oxides has also been deduced from the experimental results. From a comparison of the cation composition dependency characteristic of the electrical semiconductivity with that of the cation vacancy cocentration, it was deduced that the apparent number of effective negative charge on a cation vacancy varies almost linearly from two in NiO to almost unity in CoO. Interdiffusion experiments show that a net flow of cations in one direction in a CoO?NiO diffusion couple will produce a gradient in the oxygen activity that can alter the diffusion behavior of the sample.     

Spinodal method of vacancy diffusion study in ionic mixed crystals at room temperature

Some aspects of the spinodal method of deducing diffusion coefficients are considered. The decomposition kinetics yield the interdiffusion coefficient which is, however, not an intrinsic property of ionic crystals at low temperatures since it depends on the nonequilibrium vacancy concentration. Comparing, though, the spinodal kinetics in crystals doped with aliovalent impurity and undoped crystals enables one to obtain the vacancy diffusion coefficient which is an intrinsic property. The spinodal decomposition has been studied in nominally pure and Ca²⁺-doped mixed crystals of NaCl-KCl by the thermal gradient method and the cation vacancy diffusion coefficient D_v = 2 × 10⁻¹²cm²s⁻¹ at room temperature.     

Ab initio study of formation, migration and binding properties of helium-vacancy clusters in aluminum

Ab initio calculations based on density functional theory have been performed to study the dissolution and migration of helium, and the stability of small helium-vacancy clusters He_nV_m (n, m=0-4) in aluminum. The results indicate that the octahedral configuration is more stable than the tetrahedral. Interstitial helium atoms are predicted to have attractive interactions and jump between two octahedral sites via an intermediate tetrahedral site with low migration energy. The binding energies of an interstitial He atom and an isolated vacancy to a He_nV_m cluster are also obtained from the calculated formation energies of the clusters. We find that the di- and tri-vacancy clusters are not stable, but He atoms can increase the stability of vacancy clusters.     

The kinetics of vacancy annihilation and short range order formation in Ni 11.4 at % Cr

In Ni-Cr alloys annealing after quenching from high temperatures leads to an increase of electrical resistivity which is attributed to a short range order state often denoted as K-state. Here the kinetics of the formation of the K-state in a Ni 10% Cr alloy is investigated by resistivity measurements for different quenching and annealing temperatures. The measurements are analyzed by an extended Schulze-Lücke method [22] which assumes that the rate of resistivity change is proportional to the vacancy concentration and that this rate as well as the rate of vacancy annihilation is described by a chemical rate equation.This analysis allowed a quantitative determination of the parameters determining the kinetics of short range order formation under different vacancy concentrations as well as the kinetics of annealing out of the quenched-in surplus vacancies. Among other quantities this treatment yielded the activation energies for vacancy formation H_F = 1.16 eV, for vacancy migration H_M = 1.56 eV and, as an independent cross check, for self diffusion H_D = 2.73 eV in good agreement with H_F + H_M = 2.72 eV.     

Diffusion of 22Na and 45Ca and ionic conduction in two standard soda-lime glasses

The tracer diffusivities of ²²Na and ⁴⁵Ca in two high-quality silica glasses produced by the Deutsche Glastechnische Gesellschaft as standard glasses I and II have been measured in the temperature range between 473 K and 783 K. The temperature dependences of the tracer diffusion coefficients in both glasses follow Arrhenius laws. The diffusion of ²²Na is more than six orders of magnitude faster than the diffusion of ⁴⁵Ca. The ionic conductivity was determined by frequency-dependent impedance spectroscopy and the conductivity diffusion coefficient D_σ was deduced from the dc conductivity via the Nernst–Einstein relation. The temperature dependences of D_σ for both glasses follow also Arrhenius functions. The activation parameters and pre-exponential factors for tracer diffusion and for conductivity diffusion were determined. The activation enthalpy of ²²Na and the activation enthalpy of the dc conductivity are equal, showing that the conductivity of standard glasses is due to the motion of Na ions. The viscosity diffusivities D_η were determined from available viscosity data using the Stokes–Einstein relation. They are considerably slower than both tracer diffusivities. The Haven ratios H_R are temperature independent for both glasses. The diffusivities of ²²Na and ⁴⁵Ca in soda-lime glasses increase with increasing Na₂O content.     

Positron studies of hydrogen-defect interactions in proton irradiated molybdenum

Molybdenum single crystals are irradiated at 20 K with 6 MeV protons. The radiation damage and lattice defect annealing is studied by positron lifetime spectroscopy in the temperature range from 15 to 720 K. Loss of vacancies due to recombination with mobile interstitials is observed at 40 K (Stage I) in agreement with resistivity measurements. This is the first time Stage I is observed by positrons below 77 K. The implanted hydrogen decorates the vacancies around 100 K, which is consistent with a hydrogen migration energy in molybdenum:E _M ^H = 0.3–0.4 eV. Clustering of spatially correlated vacancies takes place in a wide temperature region below the usual vacancy clustering stage (Stage III). Stage III is observed at rather low temperatures (400–480 K) due to the very high vacancy concentration. Hydrogen bound to vacancies and vacancy clusters is released above 540 K, which puts an upper limit to the hydrogen binding energy:E _B ^H 1.4 eV. The present work emphasizes the advantage of employing a vacancy sensitive technique to study hydrogen in metals, where its intrinsic solubility is low. In such metals (as molybdenum) both the effective solubility and the effective mobility of hydrogen are strongly influenced by the presence of vacancies.     

Intrinsic polyatomic defects in Sc2(WO4)3

The intrinsic formation of polyatomic defects in Sc₂(WO₄)₃-type structures is studied by Mott Littleton calculations and Molecular Dynamics simulations. Defects involving the WO₄²⁻ tetrahedron are found to be energetically favorable when compared to isolated W and O defects. WO₄²⁻ Frenkel and (2Sc³⁺, 3WO₄²⁻) Schottky defects exhibit formation energies of 1.23 eV and 1.97 eV, respectively and therefore may occur as intrinsic defects in Sc₂(WO₄)₃ at elevated temperatures. WO₄²⁻ vacancy and interstitial migration processes have been simulated by classical Molecular Dynamics simulations. The interstitial defect exhibits a nearly 10 times higher mobility (with a migration energy of 0.68 eV), than the vacancy mechanism (with a slightly higher migration energy of 0.74 eV) and thus should dominate the overall ionic conduction. Still both models reproduce the experimental activation energy (0.67 eV) nearly within experimental uncertainty.     

Oxygen vacancy formation and migration in Sr- and Mg-doped LaGaO3: a density functional theory study

Oxygen vacancy formation and migration in La0.9Sr0.1Ga0.8Mg0.2O3-5 （LSGM） with various crystal symmetries （cubic, rhombohedral, orthorhombic, and monoclinic） are studied by employing first-principles calculations based on density functional theory （DFT）. It is shown that the cubic LSGM has the smallest band gap, oxygen vacancy formation energy, and migration barrier, while the other three structures give rise to much larger values for these quantities, implying the best oxygen ion conductivity of the cubic LSGM among the four crystal structures. In out calculations, one oxygen vacancy migration pathway is considered in the cubic and rhombohedral structures due to all the oxygen sites being equivalent in them, while two vacancy migration pathways with different migration barriers are found in the orthorhombic and monoclinic symmetries owing to the existence of nonequivalent O1 and 02 oxygen sites. The migration energies along the migration pathway linking the two 02 sites are obviously lower than those along the pathway linking the O1 and 02 sites. Considering the phase transitions at high temperatures, the results obtained in this paper can not only explain the experimentally observed different behaviours of the oxygen ionic conductivity of LSGM with different symmetries, but also predict the rational crystal structures of LSGM for solid oxide fuel cell applications.     

阳离子空位和吸附氧的协同作用对Na0.5Bi0.5TiO3(100)表面磁性影响的第一性原理研究

The combination effect of cation vacancies and O₂ adsorption on ferromagnetism of Na_0.5Bi_0.5TiO₃(100) surface is studied by using density functional theory.An ideal Na_0.5Bi_0.5TiO₃(100) surface is non-magnetic and the cation vacancy could induce the magnetism.By comparing the formation energies for Na,Bi and Ti vacancy,the Na vacancy is more stable than the others.Therefore,we focus on the configuration and electric structure for the system of O₂ molecule adsorption on the Na_0.5Bi_0.5TiO₃(100) surface with a Na vacancy.Among the five physisorption configurations we considered,the most likely adsorption position is Na vacancy.The O₂ adsorption enhances the magnetism of the system.The contribution of spin polarization is mainly from the O 2p orbitals.The characteristics of exchange coupling are also calculated,which show that the ferromagnetic coupling is favorable.Compared with the previous calculation results,our calculations could explain the room-temperature ferromagnetism of Na_0.5Bi_0.5TiO₃ nanocrytalline powders more reasonably,because of taking into account adsorbed oxygen and cation vacancies.Moreover,our results also show that adsorption of O₂ molecule as well as introduction of cation vacancies may be a promising approach to improve multiferroic materials.     

Vacancy diffusion in Cu∑ = 5[0 0 1] twist grain boundary

Both the formation energies and the diffusive activation energy of a single vacancy migrating intra- and inter-layer in the first four atomic planes near Cu∑ = 5[0 0 1] twist GB have been investigated by means of MD in conjunction with MAEAM. The effects of the GB on the vacancy formation and migration are only to the third layer. The vacancy is favorable to be formed on the un-coincident site in the first, second and third layers near the GB plane and this case is enhanced successively following the third, second and first layers. A single vacancy either on un-coincident site or on coincident site in the forth, third and second layers is favorable to migrate to un-coincident site (its first-nearest-neighbor) in its adjacent layer near the GB. But for the first layer, the favorable migration path of the vacancy on the un-coincident site is between un-coincident sites of the first layer or to its nearest-neighbor of the first layer in the rotating grain, which is not the case for the vacancy on the coincident site ‘1’ that is migrated difficultly. So, there are collective tendency of the vacancy in the GB.     

Measurement of the lattice parameter of sodium by neutron-back-scattering

We report high precision results (δa/a ≈ 3 x 10^-6) of the lattice parameter of high purity sodium (99.99%) in the temperature region from 32°C up to the melting point. Data of the crystal quality are also given: the half width of the angular mosaic spread amounts to about 4'. Preliminary results on vacancy formation energy and entropy, using literature data of volume expansion, are 0.35 ± 0.02 eV and (3.7 ± 0.5) k_B resp. for a single vacancy.     

Ionic conductivity and point defects in pure and doped MnF2 and MgF2 single crystals

Conductivity, σ, of MnF₂ and MgF₂ single crystals, pure and doped (with Li⁺, Na⁺, Y³⁺, Gd³⁺), has been measured, from room temperature to 500°C. Further, some crystals were contaminated with O^2? as an additional impurity. These tetragonal (rutile structure) crystals both behave like typical ionic conductors. Of particular interest is the existence of a large anisotropy, σ being largest when measured parallel to the c-axis. Study of the conductivity isotherms and anisotropy as functions of impurity concentration allows identification of the conduction mechanism in terms of the migration of two mobile defects: the fiuorine-ion vacancy, V_F, and interstitial, F_i. A value of 1.44 eV was obtained for the enthalpy of formation of the intrinsic anion Frenkel defect, 0.80 eV for the migration enthalpy of a V_F and 0.88 eV for an F₁ in MnF₂ parallel to the c-axis. Similar values were obtained for MgF₂. This work shows that more information about point defects can be obtained from conductivity measurements in non-cubic cyrstals than in cubic ionic crystals, because of the additional information from conductivity anisotropy.     

Elucidating hydrogen assisting vacancy formation in metals: Mo and Nb as examples

Impurity H is inclined to be trapped by some defects with more space such as vacancy and grain boundary when it dissolves in a metal. Inversely, H can also enhance formation of large amount of vacancies even if there are few vacancies in intrinsic metals initially. Using first-principles simulation combined with statistical model, Mo and Nb as examples, we quantitatively calculate the concentration of vacancies including pure vacancy and H _n -vacancy (H _n V) complexes. The concentrations of vacancies in the form of H _n V notably increase due to the decrease of effective formation energy of vacancy from H stimulation. Our finding solves a long-standing puzzle on the atomistic mechanism underlying H assisting vacancy formation in some metals.     

Vacancies in transition metals: Formation energy and formation volume

This work describes a calculation of the formation energy and volume for a vacancy in transition metals. One uses a tight-binding scheme for the d band and a Born-Mayer type potential to account for the repulsive part of the energy at small distances. The results show that the relaxation energy is small in all cases, less than 0.1 eV. This seems to be coherent with the good agreement obtained for the theoretical and experimental values of the formation energy E_f^v of the vacancy, without including relaxation. The center of the transitional series is found to give a contraction (formation volume of order ?0.4 at. vol.) whereas the edges are found to produce dilatations.