Determination of low temperature volume diffusion coefficients in an Al-Zn alloy

Low temperature volume diffusion coefficients relating to Zn diffusion in aluminium have been measured by monitoring the composition gradients across grain boundaries, developed during ageing [6]. The composition profiles were measured using STEM X-ray microanalysis and were consistent with the model of Aaron and Aaronson[7] as were the low temperature diffusion coefficients with extrapolated high temperature data.     

Grain boundary self-diffusion of tracer <Superscript>18</Superscript>O atoms in nanocrystalline oxide LaMnO<Subscript>3 + δ</Subscript>

Diffusion coefficients of tracer ¹⁸O atoms at boundaries of nanograins of LaMnO_{3 + δ} oxide have been measured in the temperature range of 400–500°C. The samples of the nanocrystalline oxide are prepared with the use of the shockwave loading method. The concentration profile of the tracer atoms after diffusion annealing is measured with the use of the nuclear microanalysis method. The activation energies of the grain boundary diffusion amounts to about 2 eV and the boundary width is ～0.05 nm. The measured coefficients of the grain boundary diffusion at 500°C exceed the corresponding coefficients of the volume diffusion by seven orders of magnitude.     

Electronic conductivity and chemical diffusion in n-conducting barium titanate ceramics at high temperatures

The electronic conductivity as well as the chemical diffusion coefficient of barium titanate ceramics doped with Y and Mn (donor-doped and acceptor co-doped) have been determined by application of conductivity relaxation experiments. The equilibrium values of the electronic conductivity of n-conducting BaTiO₃ have been analyzed by application of a defect chemical model involving electrons and cation vacancies as the predominant defect species at oxidizing conditions (fairly high oxygen partial pressures). The relaxation curves of the electronic conductivity yield the chemical diffusion coefficient of the bulk by employing a spherical grain model where the appropriate diffusion length is the radius of grains (average grain size). The conductivity relaxation experiments have been performed as a function of temperature ranging from 1100 to 1250 °C at oxygen partial pressures between 0.01 and 1 bar. The kinetics of the oxygen exchange process can be interpreted in terms of extremely fast diffusion of oxygen via oxygen vacancies along the grain boundaries and slow diffusion of Ti (cation)-vacancies from the grain boundaries into the grains. The Ti-vacancy diffusion coefficients were extracted from the chemical diffusion coefficients as a function of temperature. Typical values for the Ti-vacancy diffusivity are around 10^− 15 cm² s^− 1 with an activation energy of 3.9 ± 0.7 eV.     

Short-Circuit Diffusion in Ceramics

This article discusses grain boundary diffusion in ceramics. It gives a brief review of the experimental data available for ionic oxides and the problems of interpretation associated with it. The fundamental differences between grain boundary diffusion in metals and ceramics are noted. Calculations of the segregation of defects and impurities to grain boundaries are discussed together with methods of calculating diffusion coefficients in these boundaries. New results for alumina and chromia are presented. The problem of defining a grain boundary width is discussed with respect to new calculations on nickel oxide.     

Energies of formation and structures of point defects at tilt grain boundaries in molybdenum

The structure and formation energy of vacancies and interstitials at symmetrical tilt grain boundaries in molybdenum have been investigated by means of classical molecular dynamics. The dependence of the formation energy of these boundaries on the grain misorientation angle has been calculated. The structures of defects, energies of their formation, and diffusion mechanisms have been determined for the most stable grain boundaries.     

Cobalt Modification of Thin Rutile Films Magnetron-Sputtered in Vacuum

Using X-ray phase analysis, atomic force microscopy, and secondary ion mass-spectrometry, the phase formation and component distribution in a Co–TiO₂ film system have been investigated during magnetron sputtering of the metal on the oxide and subsequent vacuum annealing. It has been found that cobalt diffuses deep into titanium oxide to form complex oxides CoTi₂O₅ and CoTiO₃. A mechanism behind their formation at grain boundaries throughout the thickness of the TiO₂ film is suggested. It assumes the reactive diffusion of cobalt along grain boundaries in the oxide. A quantitative model of reactive interdiffusion in a bilayer polycrystalline metal–oxide film system with limited solubility of components has been developed. The individual diffusion coefficients of cobalt and titanium have been determined in the temperature interval 923–1073 K.

     

Diffusion through a polycrystalline thin film

Analytical solutions to Fick’s second law of diffusion have been simultaneously derived without the restrictions of parabolic profiles along the x-axis in grain boundaries and expressed in a series for both grain interior and grain boundary diffusing through a polycrystalline thin film. The analysis takes segregation of diffusion species at grain boundaries into account. The analytic solutions lead to the concentration profiles in the grain interior and in the grain boundary, to the average-integrated amount of diffusion species at the exit surface, and to the time lag, which can be technologically used for depth profile studies and kinetic accumulation measurements.     

Molecular dynamics investigation of the diffusion permeability of triple junctions of tilt and mixed-type boundaries in nickel

The diffusion permeability of triple junctions of high-angle tilt boundaries 〈111〉 and 〈100〉 and mixed-type boundaries in nickel has been investigated using the molecular dynamics method. It has been shown that the diffusion permeability of equilibrium triple junctions does not exceed the permeability of the grain boundaries forming them. The effective diffusion radius of the considered triple junctions and the width of the grain boundaries are determined.     

Surface exchange reactions and diffusion in composite materials: A finite element approach

A two-dimensional square grain model has been applied to model oxygen exchange processes between a gas phase and a ceramic composite consisting of two randomly distributed phases of equal grain size (side length of squares). Both average diffusion profiles for thin films and the time dependence of the total amount of exchanged oxygen (relaxation curves) have been calculated numerically by means of the finite element method. The boundary conditions refer to an instantaneous change of the oxygen partial pressure in the surrounding gas phase, which gives rise to surface exchange reactions as well as to diffusion in the composite. Both local equilibrium at the interface between different phases (host phase and inclusions) and blocking heterophase boundaries have been taken into account. The numerical results are compared with the analytical solution for diffusion in a homogeneous medium introducing effective diffusion and surface exchange coefficients. When the relaxation time for effective medium diffusion is considerably shorter than that for the transport process from the host phase into the inclusions, relaxation curves with two separate time constants are predicted. Based on analytical approximations, relaxation times for various limiting cases are given.     

Solid–state diffusion–controlled growth of the phases in the Au–Sn system

The solid state diffusion-controlled growth of the phases is studied for the Au–Sn system in the range of room temperature to 200 °C using bulk and electroplated diffusion couples. The number of product phases in the interdiffusion zone decreases with the decrease in annealing temperature. These phases grow with significantly high rates even at the room temperature. The growth rate of the AuSn₄ phase is observed to be higher in the case of electroplated diffusion couple because of the relatively small grains and hence high contribution of the grain boundary diffusion when compared to the bulk diffusion couple. The diffraction pattern analysis indicates the same equilibrium crystal structure of the phases in these two types of diffusion couples. The analysis in the AuSn₄ phase relating the estimated tracer diffusion coefficients with grain size, crystal structure, the homologous temperature of experiments and the concept of the sublattice diffusion mechanism in the intermetallic compounds indicate that Au diffuses mainly via the grain boundaries, whereas Sn diffuses via both the grain boundaries and the lattice.     

Theory of grain boundary motion during high-temperature DIGM

A theory of diffusion induced grain boundary migration (DIGM) is presented for high temperatures where volume diffusion of solute atoms out of the grain boundary is important. It is shown that due to the presence of a gradient term in the expression for the free energy of solid solution, even a relatively small discontinuity in the solute distribution across the gain boundary provides enough driving force for grain boundary migration. From the expression obtained for the grain boundary velocity the coefficient for the Ni diffusion across the grain boundaries in a Cu(Ni) polycrystal has been estimated.     

Grain-boundary diffusion in nanocrystals with a time-dependent diffusion coefficient

A solution to the equation of grain-boundary diffusion is obtained under conditions where migration of the diffusant from the boundaries into the grains is absent and the diffusion coefficient decreases with time from an increased value to a value characteristic of equilibrium grain boundaries. The specific features of the grain-boundary diffusion in nanocrystals are qualitatively analyzed in terms of this solution.     

Monte Carlo simulation of the kinetics of decomposition and the formation of precipitates at grain boundaries of the general type in dilute BCC Fe–Cu alloys

The kinetics of decomposition of a polycrystalline Fe–Cu alloy and the formation of precipitates at the grain boundaries of the material have been investigated theoretically using the atomistic simulation on different time scales by (i) the Monte Carlo method implementing the diffusion redistribution of Cu atoms and (ii) the molecular dynamics method providing the atomic relaxation of the crystal lattice. It has been shown that, for a small grain size (D ~ 10 nm), the decomposition in the bulk of the grain is suppressed, whereas the copper-enriched precipitates coherently bound to the matrix are predominantly formed at the grain boundaries of the material. The size and composition of the precipitates depend significantly on the type of grain boundaries: small precipitates (1.2–1.4 nm) have the average composition of Fe–40 at % Cu and arise in the vicinity of low-angle grain boundaries, while larger precipitates that have sizes of up to 4 nm and the average composition of Fe–60 at % Cu are formed near grain boundaries of the general type and triple junctions.     

Plasma-stimulated penetrability of hydrogen as a tool for studying phase transitions at grain boundaries

It is well known that the diffusion of hydrogen atoms through the intrinsic defects of a crystal lattice has characteristics different from those of bulk diffusion and, at certain parameters for some polycrystalline metals, ensures the determining contribution to the transfer of hydrogen atoms through the material. Grain boundaries (and dislocations) are the most important and shortest paths, the diffusion through which is much faster than bulk diffusion through a crystal lattice. It is particularly important to take into account this diffusion in materials with grains having sizes of about several nanometers. The possibility of using the method of the plasma-stimulated penetrability of hydrogen to analyze phase transitions at the grain boundaries is demonstrated on the example of polycrystalline niobium foils. In contrast to the existing methods, this method proposed for studying grain-boundary diffusion and phase transitions is simple and ensures control over the surface. The temperature characteristics of the diffusion of hydrogen atoms through niobium grain boundaries have been measured.     

On the micromechanical modelling of the effective diffusion coefficient of a polycrystalline material

This study focuses on calculation of the effective diffusion coefficient of a polycrystalline material accounting for the grain size and shapes. Polycrystal is modelled as a composite consisting of a matrix with high diffusivity (grain boundaries and triple junctions) and inhomogeneities with low diffusivity (bulk grains including crystal defects like dislocations). The segregation at the grain boundaries is accounted for. Typical micromechanical models are re-written for diffusivity assuming that the grains have the shape of ellipsoids of revolution (spheroids). The results are compared with (1) numerical results for hydrogen diffusion in an imaginary polycrystalline material and (2) experimental results for diffusion of hydrogen in nickel polycrystal available in the literature. The approach can be used for extraction of information on diffusivity along the grain boundaries.     

Effect of the wetting of grain boundaries on the formation of a solid solution in the Al-Zn system

Phase transitions in the bulk and at grain boundaries in the (Al-20 wt % Zn) alloy have been studied by means of differential scanning calorimetry and transmission electron microscopy. Polycrystals with a high specific area of grain boundaries have been obtained using severe plastic deformation (high-pressure torsion). It has been shown that the Zn-based solid phase completely wets the grain boundaries in aluminum at a temperature of 200°C. The position of the grain boundary solvus line (solubility line), which is above the bulk solvus by 40?C45 K, has been determined.     

Misorientation Dependence of the Grain Boundary Energy in Magnesia

Geometric and crystallographic data obtained from a well annealed magnesia polycrystal have been used to specify the five macroscopic degrees of freedom for 4665 grain boundaries. The results indicate, that for this sample, the five parameter grain boundary character space is fully occupied. A finite series of symmetrized spherical harmonics has been used to approximate the misorientation dependence of the relative grain boundary energy. Best fit coefficients for this series were determined by assuming that the interfacial tensions at each triple junction are balanced. The grain boundary energy function shows Read-Shockley behavior at small misorientations and a broad minimum near the 3 misorientation. Furthermore, misorientations about the ‹100› axis create boundaries with relative energies that are less than those created by misorientations about the ‹110› or ‹111› axes.     

Low temperature diffusion in thin-film couples of polycristalline silver and gold

Limited diffusion spaces which may be easily traversed by atoms diffusing along grain boundaries generally cause thin-film diffusion to differ from common bulk diffusion. These peculiarities were studied in Ag−Au thin-film couples by means of electrical resistance measurements. Diffusion coefficients were found to decrease with annealing time mainly as a consequence of recrystallisation and recovery in the films during the diffusion anneal. It is shown that the rate of homogenisation is fairly independent of the film thickness thus giving evidence that diffusion into the crystallites occurs out of the grain boundary network rather than directly through the couple interface. Effective diffusion coefficients determined between 150 and 250° C ranged from 10⁻¹⁴ to 10⁻¹⁶ cm² s⁻¹ revealing an activation energy of 25 kcal mol⁻¹.     

Comparison between the EBIC and XBIC contrasts of dislocations and grain boundaries

The X-ray-beam-induced current (XBIC) method is used to calculate the contrasts of dislocations and grain boundaries perpendicular to a surface as a function of the diffusion length of minority charge carriers and the X-ray probe width. The results are compared with the contrasts of the same defects determined via the electron-beam-induced current (EBIC) techniques. It is demonstrated that the XBIC contrasts of grain boundaries and dislocations can be several times greater than those obtained in the EBIC mode in the case of a rather narrow X-ray beam. The XBIC contrast always exceeds that of EBIC in semiconductors with a large diffusion length even if the X-ray beam is rather wide.     

Diffusion of nickel in single- and polycrystalline Cr2O3

Chromia protective layers are formed on many industrial alloys to prevent corrosion by oxidation. Their role is to limit the inward diffusion of oxygen and the outward diffusion of cations. A number of chromia-forming alloys contain nickel as a component, such as steels, FeNiCr and NiCr alloys. To ascertain if chromia is a barrier to outward diffusion, nickel diffusion in chromia was studied in both single crystals and polycrystals in the temperature range 900–1100°C at an oxygen pressure of 10^?4 atm (argon + 100 ppm O₂). A nickel film of ～35 nm thick was deposited on the chromia surface and, after diffusing treatment, nickel penetration profiles were established by secondary ion mass spectrometry (SIMS). Two diffusion domains appear in polycrystals, the first domain is assigned to bulk diffusion and the second is due to diffusion along grain boundaries. For the bulk diffusion domain and diffusion in single crystals, using a solution of Fick's second law for diffusion from a thick film, bulk diffusion coefficients were determined at 900 and 1000°C. At the higher temperature, a solution of Fick's second law for diffusion from a thin film could be used. For the second domain in polycrystals, Le Claire's model allowed the grain boundary diffusion parameter (αD _gb δ) to be established. Nickel bulk diffusion does not vary significantly according to the microstructure of chromia. The activation energy of grain boundary diffusion is slightly greater than the activation energy of bulk diffusion, probably on account of segregation phenomena. Nickel diffusion was compared with cationic self-diffusion and with literature data on Fe and Mn heterodiffusion in the bulk and along grain boundaries. All results were analyzed in relation to the oxidation process of stainless steel.