Contribution a la theorie atomique de la diffusion chimique

Here we present an analysis and a development of the atomic theory of chemical diffusion as proposed by Manning for a binary system a/b.The general expression for the flux of a tracer in a concentration gradient is first established. This expression of the flux is identified with that deduced in the phenomenological theory. Thus a relationship between the partial correlation factors of vacancies with each of the a and b species is obtained.The effect of “vacancy flow” can be described in terms of these correlation factors. Thus the vacancy flow on species A leads to a correlation of the vacancy jumps with species B and vice versa.We shall see that the Nernst-Einstein equation can be extended to the case of chemical diffusion and that the ratio of the intrinsic diffusion coefficients is equal to the ratio of the mean jump frequencies W_A and W_B.Also, the activation energies of intrinsic diffusion coefficients are related very simply to the activation enthalpies of atomic jumps.In conclusion, we shall see that chemical diffusion in a binary system a/b can be completely described if either the thermodynamic factor and the coefficients of self diffusion, or the thermodynamic factor and the coefficients of intrinsic diffusion are known as functions of the concentration.     

Isothermal transport properties of Fe1−δO from a polarization method

We report chemical diffusion coefficient D̃ and effective charge number Z¹ measurements for various deviations from stoichiometry in Fei_1−δO and at various temperatures. The results are compared with available data, and correlation factors ⨍ for Fe_1−δO are deduced from the comparison of our D̃ values with available self-diffusion coefficients of iron D¹_Fe ⨍ is shown to be mostly invariant with temperature and nonstoichiometry. Its value lies in the range 0.54–0.62. The charge of the moving cations is $\text{Z}{}^1\text{= 2}$. These two results indicate that iron diffusion in Fe_1−δO is mediated by a vacancy mechanism from octahedral to octahedral positions within regions where the number of first Fe neighbours of a vacancy is much lower than 12.     

Entropy and enthalpy of formation and migration of lattice defects in Na(I)

The self-diffusion coefficients of Na⁺ and I^?, as well as the ionic conductivity, are measured in Na(I) single crystals, pure and doped with Ca²⁺ ions. The computer analysis of the whole set of data shows that the atom transport in Na(I) is ensured essentially by the free vacancies with a very small contribution (～4%) of the vacancy pairs. The thermodynamic parameters of vacancy formation and migration are derived by taking the long range interactions into account (activity coefficients on the concentrations and relaxation factors on the mobilities). The respective entropies of Schottky defect formation, cation migration and anion migration are equal to 7.64, 3.23 and 2.91 k while the corresponding enthalpies are equal to 2.00, 0.58 and 0.77 eV.     

Ion beam mixing and liquid interdiffusion

Abstract

A characteristic of ion mixing in the low temperature portion of the thermally assisted ion mixing regime is that the activation energy obtained from most experiments is in the range of 0.1 to 0.3 eV. These values are typically a factor of 4 to 10 lower than the vacancy migration energy of most elements. This discrepancy is maintained even when the ion mixing data is contrasted to the more comparable data from concentrated homogeneous alloys. It appears that an explanation of the ion mixing activation energy is not possible by radiation enhanced diffusion (RED) where, at the low temperature end of RED, defect annihilation is by direct vacancy-interstitial recombination and the predicted activation energy is Q = 0.5 E^M _v

In an attempt to understand the origin of the low activation energies obtained during ion mixing we have performed calculations of the mutual diffusion coefficients in binary liquid mixtures. A hard sphere fluid model based on the kinetic gas theory of Enskog was used. The model was corrected to agree with molecular dynamic calculations of liquid state diffusion and included thermodynamic driving forces. The calculations resulted in temperature dependent mixing curves which are in good agreement with ion mixing experiments and suggested that the temperature rise in the thermal spike approximately ranged between 1000 and 4000 K.     

Monte Carlo simulation of phosphorus diffusion in α-iron via the vacancy mechanism

Monte Carlo simulations of the vacancy and phosphorus (P) atom diffusion in body centred cubic (bcc) iron are presented. The input parameters for the calculations, namely the activation energies of atomic jumps, have been obtained using a potential set developed recently for a dilute Fe–P alloy using ab initio data. The diffusion coefficients entering equations for the fluxes of vacancies and solute atoms are evaluated. The results show that, in the temperature range of practical importance for P segregation, P atoms move down the vacancy gradient; hence, under irradiation conditions, vacancies should drag P atoms towards sinks of point defects. This is because of the high binding energy between a P atom and a vacancy in the first and second nearest neighbour sites from each other, which allows a vacancy to move around a P atom without loss of bonding and, hence, co-migrate with it.     

Finite temperature properties of a supersolid: a RPA approach

We study in random-phase approximation the newly discovered supersolid phase of ⁴He and present in detail its finite temperature properties. ⁴He is described within a hard-core quantum lattice gas model, with nearest and next-nearest neighbour interactions taken into account. We rigorously calculate all pair correlation functions in a cumulant decoupling scheme. Our results support the importance of the vacancies in the supersolid phase. We show that in a supersolid the net vacancy density remains constant as function of temperature, contrary to the thermal activation theory. We also analyzed in detail the thermodynamic properties of a supersolid, calculated the jump in the specific heat which compares well to the recent experiments.     

Diffusion coefficients of hydrogen and deuterium in highly concentrated palladium hydride and deuteride phases

Fick's diffusion coefficients for hydrogen and deuterium were determined in palladium hydride and deuteride in the pressure range of gaseous hydrogen and deuterium from 10¹–10⁴ bar and the temperature range from 208 to 338K. This corresponds to the concentration range H, D/Pd from about 0.8 to near stochiometry. An electrical resistance relaxation method was used experimentally. Einstein's diffusion coefficients were calculated and the activation volumes and energies were evaluated. An attempt is made to interpret the anomalous behaviour of the diffusion coefficient in the low temperature range. The results are presented in terms of a compact formula.     

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.     

Palladium-vacancy pairs in p-type and n-type germanium

Time differential perturbed angular correlation spectroscopy was performed for n-type and p-type germanium samples that had been recoil-implanted with the probe ¹⁰⁰Pd/¹⁰⁰Rh. Two different measurements with the detectors aligned along <100> and <110> crystallographic directions of germanium confirm that the palladium probe pairs with the nearest neighbour vacancy and not a dopant. The pairs interact with a coupling constant of υ _Q = 10.7(2) MHz and this agrees with what has been observed in undoped Ge. This further suggests that the palladium pairs with a vacancy in germanium, doped or un-doped. It was also observed that there are more Pd-V pairs in Ga-doped than there are in Sb-doped Ge. DFT calculations of the binding energies of the Pd-defect complexes support the experimental observations.     

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^?.     

Investigation of Diffusion of Magnesium in Lithium Fluoride Crystals by the SIMS Method

Using secondary ion mass spectroscopy, diffusion of magnesium impurity in lithium fluoride is investigated. A temperature dependence of the magnesium diffusion coefficients within the temperature interval 870–1073 K is established, which is described by an expression of the following type: D = 2.8·10^–3·exp(–1.5/kT). Combining the data on self-diffusion of cations with the results of the ion conductivity measurements, estimation is made of the thermodynamic parameters characterizing the jump of a diffusant. The calculated frequencies of the impurity ion jump to the cation vacancy are reported.     

Localized diffusion of helium atoms around indium impurities in aluminium observed by means of perturbed angular correlations

The behaviour of He atoms implanted in ¹¹¹In doped Al has been investigated by means of perturbed angular correlation (PAC) measurements. The onset of He mobility was found to be at about 250K, probably due to vacancy-assisted migration. Mobile helium is effectively trapped at In impurities in small vacancy clusters that accomodate at most 11 He atoms. The PAC spectra taken at temperatures from about 510 K to 670 K exhibit a relaxation effect that is ascribed to hopping of He atoms from one vacancy to another, the saddle-point energy for this localized diffusion being 0.67(5) eV. A tentative model of the cluster is given.     

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.     

Fast diffusion of cs+, a large alkali ion,in silver chloride

The diffusion of Cs⁺ tracer in AgCl has been measured in the temperature range 327–447°C. The unexpectedly small activation energy of 0.83 eV and tracer diffusivities larger than those of substitutional Ag⁺ have been interpreted in terms of local strain in the lattice, caused by the large radius of cesium, with a concomitant strong binding of a cation vacancy.     

Activation volumes for formation and motion of defects in crystalline solids

By consideration of the factors that affect the activation volume for formation, ΔV_F, and for motion, ΔV_M, of a diffusing species, it is suggested that the sign dependence of the activation volume for self-diffusion, ΔV_D, can be predicted. Our predictions are based on the assumption that (1) interstitial diffusion is associated with an abnormally low activation energy for diffusion, (2) vacancy diffusion is present where normal activation energies are observed, and (3) a disordered, liquid-like region is produced when the diffusing species moves into the activated state. Several examples are presented to illustrate our proposed model.     

Oxygen permeability and stability of Ba0.5Sr0.5Co0.8Fe0.2O3−δ as an oxygen-permeable membrane at high pressures

Oxygen permeation fluxes across the dense Ba_0.5Sr_0.5Co_0.8Fe_0.2O_3−δ (BSCFO) membrane disks were measured under an air/helium oxygen partial pressure gradient at high pressures (up to 10 atm) and various temperatures (973–1123 K). The fabricated BSCFO membrane exhibited good oxygen permeability with a high oxygen permeation flux of 2.01 ml min^− 1cm^− 2 (thickness: 1.37 mm) at 1123 K and 10 atm. Oxygen permeation results were analyzed theoretically using the surface exchange current model. The dependences of the oxygen permeation fluxes on the oxygen partial pressure gradient, suggested that the bulk oxygen ionic diffusion was the rate-limiting step for the overall oxygen permeation process across the BSCFO membrane. The ambipolar diffusion coefficients (D_a), the oxygen vacancy diffusion coefficients (D_v) and the oxygen ionic conductivities (σ_i) of the BSCFO material at different temperatures (973–1123 K) were calculated. It was found that BSCFO possessed high oxygen diffusion coefficients and ionic conductivities, which resulted in the good oxygen permeability of BSCFO. In addition, the BSCFO membrane exhibited good stability of oxygen permeation at 1123 K, while the deterioration of oxygen permeation stability was observed at 1098 K due to structural changes occurring at the surface of the BSCFO membrane disk as demonstrated by XRD.     

First principles calculations of alloying element diffusion coefficients in Ni using the five-frequency model

The diffusion coefficients of several alloying elements(Al,Mo,Co,Ta,Ru,W,Cr,Re) in Ni are directly calculated using the five-frequency model and the first principles density functional theory.The correlation factors provided by the five-frequency model are explicitly calculated.The calculated diffusion coefficients show their excellent agreement with the available experimental data.Both the diffusion pre-factor(D 0) and the activation energy(Q) of impurity diffusion are obtained.The diffusion coefficients above 700 K are sorted in the following order:DAl>DCr>DCo>DTa>DMo>DRu>DW>D Re.It is found that there is a positive correlation between the atomic radius of the solute and the jump energy of Ni that results in the rotation of the solute-vacancy pair(E 1).The value of E 2-E 1(E 2 is the solute diffusion energy) and the correlation factor each also show a positive correlation.The larger atoms in the same series have lower diffusion activation energies and faster diffusion coefficients.