The influence of radiation-induced vacancy on the formation of thin-film of compound layer during a reactive diffusion process

A theoretical approach is developed that describes the formation of a thin-film of AB-compound layer under the influence of radiation-induced vacancy. The AB-compound layer is formed as a result of a chemical reaction between the atomic species of A and B immiscible layers. The two layers are irradiated with a beam of energetic particles and this process leads to several vacant lattice sites creation in both layers due to the displacement of lattice atoms by irradiating particles. A- and B-atoms diffuse via these lattice sites by means of a vacancy mechanism in considerable amount to reaction interfaces A/AB and AB/B. The reaction interfaces increase in thickness as a result of chemical transformation between the diffusing species and surface atoms (near both layers). The compound layer formation occurs in two stages. The first stage begins as an interfacial reaction controlled process, and the second as a diffusion controlled process. The critical thickness and time are determined at a transition point between the two stages. The influence of radiation-induced vacancy on layer thickness, speed of growth, and reaction rate is investigated under irradiation within the framework of the model presented here. The result obtained shows that the layer thickness, speed of growth, and reaction rate increase strongly as the defect generation rate rises in the irradiated layers. It also shows the feasibility of producing a compound layer (especially in near-noble metal silicide considered in this study) at a temperature below their normal formation temperature under the influence of radiation.     

Autodiffusion dans les alliages concentres fer-palladium

Measurements of the diffusion coefficients of ³⁹Fe and ¹⁰³Pd in various iron-palladium alloys (between 0 and 100at.% iron) between 1100 and 1250°C, have shown that the activation energies for selfdiffusion for the two tracers are practically equal, independent of composition.The values obtained are very close to those corresponding to the activation energy of chemical diffusion. This result is in good agreement with the fact that the thermodynamic activities of iron and palladium have small temperature dependance and that the vacancy flow, as calculated with the model of Manning, is rather small.In spite of a strong ordering tendency in the solid solution of Fe-Pd, as indicated by a thermodynamic calculation, this model allows to calculate, with the aid of the measured self-diffusion coefficients, various parameters, such as the correlation factors for both iron and palladium, the vacancy correlation factors, and the atomic jump frequencies.     

Atom transport in random two sublattice structures: analogue of the random alloy sum rule

A simple and often used model of atom transport by the vacancy mechanism on two physically distinct interpenetrating sublattices assumes that each atom–vacancy exchange frequency depends only on the species of the atom and the sublattice from which it jumps. In the kinetic theory of this model, the phenomenological coefficients can be expressed as sums of partial correlation functions, each labelled by the sublattices associated with the atoms making the first and last jumps in the sequence of correlated jumps which it represents. A sum rule, a set of exact relations among these partial correlation functions, is derived for the model, assuming arbitrary vacancy content and any number of chemical species. It reduces to a widely used sum rule for the random lattice gas [L.K. Moleko and A.R. Allnatt, Phil. Mag. A 58 677 (1988)] in the limit that atom jump frequencies are made independent of sublattice. For the two sublattice model at very low vacancy contents, a more powerful sum rule is also derived; it is essentially the same as that of Belova and Murch [Defect Diffus. Forum 194/199 547 (2001)]. The efficiencies of the three sum rules are briefly compared. The low vacancy concentration sum rule is illustrated by numerical simulations for a binary two sublattice system.     

Phase diagram calculations in glass-forming systems—I: Theory

The theory of regular associated solutions is assumed to deal with the formation of molecular species or chemical complexes of general formula A_pB_q, in a liquid phase. Two approximate treatments are developed, depending on the association strength, in order to treat binary and ternary systems. The solid-liquid equilibrium equations for a ternary system containing A_pB_q and A_rC_s complexes are calculated. The success of these treatments for glass-forming liquids is discussed.     

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.     

Possible preferential order-disorder in A15(β-W type) compounds

A possible existence of preferential disorder in the B sites in A₃B(β-W type) compounds is demonstrated. This appears to support the “A-chain integrity” recognized in these compounds. Therefore, the correlation between the order-disorder parameters and the superconducting critical temperatures, investigated in the past, should be reexamined.     

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.     

Self-diffusion at grain boundaries with a disordered atomic structure

A change in the free energy of a grain boundary is analyzed in the case when lattice vacancies come to the boundary and are then delocalized in its disordered atomic structure. It is shown that the free energy of the boundary is minimized at some excess atomic volume Δv _b =Δv _b ^* , whose value depends on the energy of vacancy formation in the crystal lattice and the boundary energy. The formation of a metastable localized grain-boundary vacancy as a result of thermal fluctuations of the density in a group of n ₀=\gM_v/Δv _b atoms (\gM_v is the vacancy volume), followed by the jump of an adjacent atom into this vacancy, is taken as an elementary event of grain-boundary diffusion. Expressions for the activation energy of diffusion and the diffusion coefficient are derived for equilibrium (Δv _b =Δv _b ^* ) and nonequilibrium (Δv _b >Δv _b ^* ) boundaries.     

Relationship between triple and pair correlations in an A y B 1 − y solid solution with a planar hexagonal lattice

An analytical relationship is found between triple correlations and nearest neighbor pair correlations in an A _y B _{1 ? y} solid solution with a planar hexagonal lattice (plane group p6mm). The range of variations in the triple correlation is determined as a function of the composition of the A _y B _{1 ? y} solid solution and the value of the pair correlation. It is assumed that periodically ordered planar hexagonal and square island nanostructures can be considered as solid solutions A _1/4□_3/4 with vacancy sites □ and sites occupied by nanoparticles A. In this case, an ordered distribution of nanoparticles over the planar-lattice sites occurs because the nearest neighbor pair correlation is negative and has a maximum magnitude.     

Analysis of interdiffusion via isolated vacancies in strongly ionic crystals

In this paper, we analyse chemical interdiffusion in strongly ionic crystals for diffusion couples AY _m –BY _m , where A and B have the same charge numbers. We employ the exact sum rule given by Moleko and Allnatt relating the phenomenological coefficients for diffusion in the multicomponent random alloy via the agency of monovacancies. It is shown that the ratio of the intrinsic diffusivities can be expressed very simply in terms of the atom–vacancy exchange frequencies without correlation terms. For the case of an immobile anion sublattice and making use of a highly accurate diffusion kinetics theory due to Moleko et al., it is shown that the interdiffusivity is principally proportional only to the off-diagonal phenomenological coefficient relating the two cations.     

Superconducting critical temperature, Tc, and phase equilibrium diagram of A3B β-W) type compounds

A correlation between the superconducting critical temperature, T_c, and solid solution range (SSR) appearing in the phase equilibrium diagram of A₃B (β-W) type compounds has been observed. Among the compounds of incongruent melting (peritectic or peritectoid) type, the T_c is directly proportional to the solid solution range. Further, in the low temperature range, the solid solution range invariably is found on the A element-rich side of the stoichiometric composition (75 at. % A: 25 at. % B), suggesting a fundamental importance in the “A-chain integrity,” viz., an A element can substitute for a B element which is not a part of the chain, but a B element cannot replace an A element which forms a part of the chain) which is believed to be a key to superconductivity.     

How chaotic is a state of a quantum system?

A concept related to the entropy is studied. Let A and B be two density matrices, with eigenvalues a₁, a₂,… and b₁, b₂,…, arranged in decreasing order and repeated according to multiplicity. Then A is said to be “more mixed”, or “more chaotic”, than B, if a₁?b₁, a₁+a₂?b₁+b₂,…,a₁+…+a_m?b₁+…+b_m,…; It turns out that if A is more mixed than B, then the entropy of A is larger than the entropy of B. However, more generally, let v be an arbitrary concave function, ?0, and vanishing at 0. Then, if A is more mixed than B, trv(A)?trv(B). It is shown that also the converse is true. Furthermore, a variety of other characterizations of the relation “A is more mixed than B” is obtained, and several applications to quantum statistical mechanics are given.     

Connections between thermodynamic quantities and vacancy and diffusion characteristics in binary metallic solid solutions

With the use of the similarity of interatomic potentials relations concerning vacancy and diffusion characteristics in disordered regular solid solutions have been derived. It has been shown that the vacancy concentration is constant along ifT_c(x) = T_A + (T_B ? T_A)x + 2ΔT_x(1?x), (T_A and T_B are the melting points of pure components A and B respectively, and ΔT is proportional to the excess enthalpy of mixing, x is the concentration of the atoms B) which is proportional to the binding energy of the crystal. The validity conditions of several empirical rules known in the literature are also analyzed. It has been found that the generalization of the well-known rule for self- and impurity diffusion in pure metals has the following form In $\text{D}{}_0{}^{\mathrm{z}}\text{(x) ～ p}\text{Q}{}^{\mathrm{z}}\text{(x)}\text{T}{}_{\mathrm{c}}\text{(x)}$ (Z = AorB) where p is a constant for alloys having identical structures (D₀^z(x) and Q^z(x) denote the preexponential factors and the activation energies respectively). The results calculated from the relations derived were compared with experimental data for tracer diffusion in the systems AgAu, CuNi (having slight deviation from regularity), Pb-Tl (showing ordering phenomena) and AlZn (clustering effects) and a good agreement was found.     

Short-range order and pair correlations in a binary solid solution with a square lattice

Using the example of a disordered A _y B _{1 ? y} solid solution whose atoms are distributed over squarelattice sites, it is shown that correlations in the first coordination shell inevitably cause correlations in the second and more distant coordination shells. These induced correlations decay with distance extending to the ninth coordination shell in a square lattice. The induced correlations are calculated as a function of the correlation in the first coordination shell for binary solid solutions with various compositions. This dependence is described by a third-degree polynomial in the first-shell correlation to within the computational accuracy. The coefficients of the polynomial calculated in this paper using computer simulation can be useful in developing short-range order theory and in calculating the phase diagrams of binary solid solutions.     

NMR study of hydrogen diffusion in uranium hydride

The diffusion of hydrogen in uranium hydride is studied employing the NMR technique. From measurements of spin-spin relaxation time T₂, the activation energy for hydrogen diffusion in β-UH₃ is determined to be $\text{E}{}_{\mathrm{a}}\text{= (19.25 ± 0.4)}\text{kcal}\text{mole}$ and the preexponential factor to be A₀ ≈ 5 × 10¹⁴ Hz. It is shown that these results are in fair agreement with spin-lattice relaxation time T₁ data. Assuming that hydrogen diffusion proceeds via vacancies whose concentration is temperature dependent, it is concluded that E_a is the sum of the energies of vacancy formation and barrier height, and that A₀ contains an entropy change factor. Using vacancy concentration data calculated by Libowitz, we estimate the barrier height energy to be E_b ≈7 kcal/mole. Using a value for the frequency of hydrogen vibration v₀ determined from inelastic neutron scattering by Rush et al., we estimate the entropy change due to vacancy formation and the hydrogen atom jump to be about $\text{S}\text{k}{}_{\mathrm{B}}\text{≈3}$. Similar measurements on samples containing less hydrogen than is needed to compose stoichiometric UH₃, show that the rate of diffusion is enhanced by the presence of excess metal in the sample. The jump frequency at 500°K in UH₃ is found to be approximately 10⁶ Hz while for the two-phase samples of H/U = 2.8 and 2.5, it is larger by a factor of about 3 and 3.5, respectively.     

Correlation between the refractive index and average energy gap for simple and complex binary compounds

An empirical correlation between refractive index and corresponding average energy gap, proposed by Reddy et al, has been examined for different solids and it has been shown that the validity of such a relation is highly questionable. A new theoretical correlation is established instead of empirical correlation which is found applicable to a large number of binary A^NB^8-N type solids as well as for complex binary A₂B, AB₂, A₃B and A₃B₂ semiconductors.     

Silicon diffusion in molybdenum disilicide: correlation effects

Correlation factors for silicon diffusion by a vacancy mechanism in the silicon sublattice of the tetragonal MoSi₂ structure have been calculated by combining an analytical and a Monte Carlo approach. The ratio of the silicon diffusivity perpendicular to the tetragonal axis to that parallel to the tetragonal axis is also deduced. An effect of forward correlation of tracer atom jumps in the silicon sublattice with the corresponding partial correlation factor of 1.5 appears at small frequencies of silicon atom jumps along the tetragonal axis with respect to the jump frequencies in the silicon layer perpendicular to the tetragonal axis of the MoSi₂ structure. The anisotropy of silicon diffusion in MoSi₂ measured by Salamon et al. is explained in terms of correlation effects of silicon diffusion on its own sublattice.     

Electrical conductivity and chemical diffusion in Perovskite-type proton conductors in H2-H2O gas mixtures

The electrical conductivities of SrZr_0.9Y_0.1O_3-δ (SZY10) and BaCe_0.95Y_0.05O_3-δ(BCY5) were measured as a function of hydrogen partial pressure P(H₂), oxygen partial pressure P(O₂), steam partial pressure P(H₂O) and temperature. Their relaxation processes were analyzed using the solution of Fick's diffusion equation to determine the chemical diffusion coefficients and surface reaction rate constants. There were the differences in chemical relaxation kinetics and the conductivity dependence on P(H₂O) between the both oxides. The chemical diffusion coefficients depend on temperature but are essentially independent of P(H₂), P(O₂) and P(H₂O). The ambipolar diffusion treatment can explain the temperature dependence of chemical diffusion coefficients quantitatively. The chemical diffusion coefficients of SZY10 is one or two order of magnitude smaller than those of BCY5 at low temperature. The sluggish conductivity relaxation in SZY10 was due to considerably small oxygen vacancy diffusion coefficients at low temperatures. The total conductivity depends on P(H₂O) in the case of SZY10, but not for BCY5. This different dependence on P(H₂O) is caused by the difference in the ratio between proton mobility and oxide-ion mobility.     

Infrared dispersion of lead phosphate at room temperature

Infrared reflection spectra [15–4000 cm^-1] along the b (binary axis) and c axes (A_u and B_u-type modes) are reported at room temperature as obtained with a Fourier-transform scanning interferometer. The spectra are analyzed with the factorized form of the dielectric function and the infrared-active mode parameters are reported.     

Reordering kinetics of disordered A15 compounds

The study of reordering in A15 compounds gives valuable information about atomic processes in this structure. This information is relevant to diffusion and solid-state compound growth, as well as to recovery from radiation damage. It also offers further valuable insight into the nature of radiation damage in these materials, complementing the results obtained by X-ray studies, electron microscopy, and the measurement of superconducting and normal-state properties. The extreme sensitivity of superconducting critical temperature T_c to the degree of order in the A15 compounds allows the former property to be used to monitor the reordering- process. The recovery of T_c in A15 compounds disordered thermally and by neutron irradiation has been achieved by annealing, and the data analyzed in terms of a theory of reordering due to Welch. From this analysis, it is possible to make estimates of the activation energies for atomic migration and vacancy formation in A15 compounds.