Grain Boundary Diffusion Parameter Research Articles

ATOMISTIC SIMULATION OF SELF- DIFFUSION AND DIFFUSION Co ALONG SYMMETRIC TILT GRAIN BOUNDARIES [2¯1 ¯1 0] IN α-Ti

The structure, point defects, self-diffusion, and diffusion of Co for four energetically preferred grain boundaries (GB) with the tilt axis [21 1 0] in α-Ti are being investigated by computer modeling methods. The structure and energies of the boundaries and the energies of the formation of point defects in GB, were calculated by molecular static modeling. The dependencies of point defect formation energies on the distance from the grain boundary plane are demonstrated. The coefficients of grain boundary self-diffusion are calculated by the method of molecular dynamics. The results of self-diffusion modeling are compared with the available experimental data. The simulation of grain boundary diffusion of the impurity Co in titanium is also performed. It is shown that the structure of GB affects the parameters of grain-boundary diffusion both in the case of self-diffusion and in the case of impurity diffusion, and the coefficients of grain-boundary diffusion may differ by several orders of magnitude depending on the structure.

Two-dimensional model of grain boundary diffusion and oxidation

The grinding of the structure of materials is accompanied by a change in the physical and mechanical properties. This occurs largely due to the accumulation of energy and defects in the structure, which activates the diffusion of impurities contained in the material. The increase in the number of grain boundaries and joints can cause the inelastic behavior of the material, its additional chemical activation. For some metals and alloys this leads to strengthening, while for others it leads to rapid degradation of mechanical properties. Grain boundary diffusion in such materials is the main mechanism of transport of alloying components or harmful impurities, so its study is important. This paper presents a two-dimensional model of grain boundary diffusion in a material with an explicit structure assignment. The model takes into account the presence of chemical transformations that can determine the corrosion mechanisms under operating conditions. For simplicity of calculation the material structure is taken symmetrical and contains two phases: grains and a boundary phase. Diffusion and kinetic parameters of the phases may differ. The model is represented in dimensionless form so that the distances between neighboring grains or the widths of the boundary phase are the same and the grain sizes can vary. Depending on the ratio of phase sizes we can speak about micro- and nanocrystalline structure. The problem was solved numerically using implicit difference scheme and coordinate splitting. Diffusion and kinetic parameters, which are close to the parameters of oxygen grain boundary diffusion in titanium and titanium oxidation, respectively, were taken for the calculations. Integral concentrations reflect the dynamics (kinetics) of oxygen and oxides accumulation over the calculation area. Results showing the role of changes in the oxidation kinetics due to changes in the reaction constants in the phases and the phase size ratio are presented. The model can be useful for assessing the degree of influence of grain boundary diffusion on the oxidation process and the accompanying change in properties, as well as for setting up appropriate experiments.

Phase-field model of grain boundary diffusion in nanocrystalline solids: Anisotropic fluctuations, anomalous diffusion, and precipitation

The anisotropic phase-filed model of grain boundary diffusion and precipitation of solute in nanocrystalline solids has been developed. In this model, the Cahn–Hilliard equation is generalized for the anisotropic phase-field diffusion of solute and anisotropic compositional fluctuations. It is found that dynamics of solute concentration profile demonstrates the anomalous diffusion behavior with scaling parameters depending on the mobility ratio and microstructure of a solid solution. It is noteworthy that the increase in source concentration can slow down the concentration front propagation due to uphill diffusion or formation of a new phase. Parameters of grain boundary diffusion control the precipitation dynamics. In particular, a decrease in transverse diffusion coefficient is responsible for longer incubation time, and lower rates of nucleation and nuclei growth in comparison with the case of isotropic solute transport near grain boundaries. Transport properties of boundary and bulk are responsible for the formation of the bimodal size distribution function of second phase particles and specific kinetics of average radius and number density.

Математическое моделирование диффузионно-контролируемых процессов эволюции структуры приповерхностного слоя псевдосплава W-Cu при воздействии высокотемпературным газовым потоком

The article presents the results of mathematical modeling of copper leakage from a near-surface layer with a thickness of about 30 microns of experimental samples of W-18% Cu composite (VD-MP brand) as a result of exposure to a high-temperature (1500 K) gas flow caused by the diffusion along the boundaries of tungsten grains (GB) from copper particles located in the volume and on the tungsten GB. The parameters of grain-boundary diffusion in the studied composite in the temperature range, when copper particles are in a liquid state, were evaluated. Using the known experimental data, the value of the high-temperature coefficient of grain-boundary diffusion of copper in the polycrystalline tungsten matrix of the composite under study is calculated within the framework of the constructed computer model. The value of the obtained coefficient D = 7∙10-10 m2/s turned out to be close to the corresponding one for diffusion in liquid copper.

РАЗРАБОТКА МЕТОДИКИ ПОСЛОЙНОГО РАДИОМЕТРИЧЕСКОГО АНАЛИЗА МЕТОДОМ ЭЛЕКТРОЛИТИЧЕСКОГО СНЯТИЯ СЛОЕВ ДЛЯ ОПРЕДЕЛЕНИЯ ПАРАМЕТРОВ ЗЕРНОГРАНИЧНОЙ ДИФФУЗИИ КОБАЛЬТА В ПОЛИКРИСТАЛЛИЧЕСКОМ НИКЕЛЕ

A technique for layer-by-layer radiometric analysis using electrolytic layer stripping to determine the parameters of grain-boundary diffusion of cobalt in polycrystalline nickel has been developed. The aim of the work is to develop a complete technological cycle of layer-by-layer radiometric analysis, to select the optimal electrolyte composition for nickel and the conditions for conducting an experiment to remove metal layers with their thickness of 20–200 nm. The studies have been carried out on nickel of nominal purity of 99,98 %. The stabilizing heat treatment of the samples is carried out at a pressure of 10–5 Pa for 2 hours at a temperature of 1273 K. Diffusion annealing is carried out at a pressure of 10–9 Pa in the temperature range of 623–1173 K for 5–30 hours. Concentration profiles have been measured by parallel stripping of layers, which are obtained by electrolytic polishing in a solution based on nickel sulfamate, followed by weighing the sample on a high-precision analytical balance. The difference in weight before and after removal of the layers is used to further calculate the thickness of the removed layers and, as a consequence, the penetration depth of the diffusing. The residual activity of the sample is measured using a digital gamma spectrometer with a NaI (Tl) detector. Before carrying out the experiments, a reference source with a previously known activity has been made to take into account the correction factor due to the radioactive decay of 57Co. The specific layer activity is calculated from the integral remainder of the 122,14 keV line using the Gruzin method. Based on the proposed technique, it is possible to determine the parameters of grain boundary diffusion, such as the diffusion coefficient of grain boundary, triple product and segregation coefficient.

Application of Nuclear Gamma-Resonance Spectroscopy for Determination of Grain-Boundary Diffusion Characteristics and the State of Grain Boundaries

Capabilities of application of Mössbauer spectroscopy for determination of grain-boundary diffusion parameters in coarse-grained and ultrafine-grained materials have been analyzed. Application of this method for revealing of non-equilibrium state of grain boundaries in ultrafine-grained materials obtained by severe plastic deformation is demonstrated.

Determination of Grain Boundary Diffusion Parameters Based on Specified Model of Grain Boundary Diffusion and Combined Analysis of Radiotracer and Mössbauer Spectroscopy Data

The classical Fisher model of grain-boundary diffusion and the traditional method of determination of grain-boundary diffusion parameters by radiotracer technique combined with the serial-sectioning method are analyzed. The Fisher model specification based on the data of the emission Mössbauer spectroscopy is considered, and the additional information which can be extracted from the Mössbauer studies is discussed. The possibility of determination of grain-boundary diffusion parameters based on the combined analysis of the radiotracer technique and Mössbauer spectroscopy with the application of the specified Fisher model of grain-boundary diffusion is considered. This approach is demonstrated by an example of determination of grain-boundary diffusion of Co in W and Mo.

Modeling and simulation of the TiC reaction layer growth during active brazing of diamond using DICTRA

The growth kinetics of the TiC reaction layer during active brazing of diamond with Cu–Sn–Ti and Ag–Cu–Ti based filler alloy has been investigated by kinetic simulations and comparing with available experimental data. First, to obtain a reliable mobility database, the atomic mobilities of C and Ti in fcc (face-centered cubic) TiC are assessed using software DICTRA based on available diffusion data from literatures. Then, to carry out simulations for GB (Grain Boundary) diffusion in TiC, the bulk activation energy multiplier is determined by evaluating the available GB diffusion data. With the obtained mobility data, the TiC growth for Cu–Sn–Ti–Zr filler as a function of brazing temperature and time is simulated using various possible GB diffusion parameters. Afterwards, the determined GB diffusion parameters are validated by simulating the TiC growth for various Cu–Sn–Ti or Ag–Cu–Ti brazing alloys and comparing the simulated results with experimental data. Based on the optimized GB diffusion parameters, the influence of brazing temperature, filler alloy composition, and braze layer thickness on growth kinetics of TiC are simulated and discussed. Finally, the experimentally observed segregation of Cu at the interface between diamond and TiC layer during brazing of diamond using Cu–Sn–Ti or Ag–Cu–Ti filler is analyzed by diffusion simulations.

Early Solar System hydrothermal activity in chondritic asteroids on 1–10-year timescales

Chondritic meteorites are considered the most primitive remnants of planetesimals from the early Solar System. As undifferentiated objects, they also display widespread evidence of water-rock interaction on the parent body. Understanding this history has implications for the formation of planetary bodies, the delivery of water to the inner Solar System, and the formation of prebiotic molecules. The timescales of water-rock reactions in these early objects, however, are largely unknown. Here, we report evidence for short-lived water-rock reactions in the highly metamorphosed ordinary chondrite breccia Villalbeto de la Peña (L6). An exotic clast (d = 2cm) has coexisting variations in feldspar composition and oxygen isotope ratios that can only result from hydrothermal conditions. The profiles were modeled at T = 800 °C and P(H(2)O) = 1 bar using modified grain-boundary diffusion parameters for oxygen self-diffusion and reaction rates of NaSiCa(-1)Al(-1) exchange in a fumarole. The geochemical data are consistent with hydrothermal activity on the parent body lasting only 1-10 y. This result has wide-ranging implications for the geological history of chondritic asteroids.

Grain-boundary diffusion of germanium in copper and Cu-Ge and Cu-Fe alloys

The grain-boundary diffusion (GBD) of germanium in copper and its alloys Cu-2% Ge and Cu-0.5% Fe is investigated in the temperature range of 500–590°C by means of electron-probe microanalysis. The GBD parameters (triple product P = sδDGB and effective activation energy E) are found. The temperature dependence of the triple product for germanium GBD in pure copper can be described by equation P = 3 × 1015exp[−80 kJ mol−1/(RT)] m3 s−1. It is shown that the addition of Ge has almost no effect on the GBD parameters in copper, while doping with iron leads to a considerable reduction in the triple product.

Determination of Grain Boundary Diffusion Parameters Based on Combined Analysis of Radiotracer Technique and Mössbauer Spectroscopy Data

A method of grain boundary diffusion characterization has been suggested based on combined analysis of radiotracer serial-sectioning technique and Mössbauer spectroscopy data and a specified model of grain boundary diffusion. Its application for determination of parameters of Co grain boundary diffusion in W is demonstrated.

Grain-boundary diffusion parameters inferred from grain-size variation of quartz in cherts from a contact metamorphic aureole

Grain-boundary diffusion parameters inferred from grain-size variation of quartz in cherts from a contact metamorphic aureole

Determination of the parameters of grain-boundary diffusion and segregation of Co in W using an improved model of grain-boundary diffusion

Based on the recently proposed model of grain-boundary diffusion, the available research data on grain-boundary diffusion of Co in W, and on emission Mossbauer studies of grain boundaries in polycrystalline W have been analyzed in detail. Using joint processing of primary data for tracer analysis and Mossbauer studies, all the parameters of grain-boundary diffusion of Co in W have been determined: the coefficient of grain-boundary segregation, coefficient of grain-boundary diffusion, and the diffusion width of the grain boundary.

Model of grain-boundary diffusion with allowance for near-boundary layers of equilibrium composition

Fisher model of intercrystalline diffusion is refined based on an analysis of previously obtained results of emission Mossbauer studies of grain boundaries. It is shown that under conditions of dominating intercrystalline diffusion, the existence of monatomic near-boundary layers of equilibrium composition should be taken into account. It has been found that the allowance for these layers does not change the expressions for the distribution of the concentration of the diffusing impurity in a polycrystal in the case of a type-B kinetic regime, whereas in the type-C regime the corresponding expressions change somewhat. The technique that was used previously for the determination of parameters of grain-boundary diffusion and segregation, which is based on the results of emission Mossbauer investigations of grain boundaries, has been modified; the application of the new approach has been demonstrated on the example of processing data of Mossbauer investigations of grain boundaries in polycrystalline Nb at 119mSn nuclei.

Diffusion and Segregation in Bulk Nanomaterials and Thin Layers

The data are presented for Ni selfdiffusion and Au heterodiffusion in nanocrystalline Ni. Volume diffusion coefficients are much greater than those for a coarse – grained polycrystals extrapolated from high temperatures. Interface diffusion parameters were calculated based on the assumption that B – kinetic regime is realized at temperature range more than 448 K, while C – kinetic regime is realised at temperatures less than 423 K. The consistency of obtained results with the proposed cluster diffusion model is discussed. Diffusion in Au – Cu thin films (from several tens to several hundreds nanometers) was studied with the use of the Rutherford Back Scattering, RBS, under the kinetic regime B (448 – 523 K). The RBS spectra were transformed in the concentration depth profiles for both volume and grain boundary (GB) diffusion. The triple products Pn = snδDn (sn is the enrichment coefficient, while δ is the nanograin boundary width) were calculated using Whipple model. As a result of this analysis the s – value for Cu – Au system was determined to be of the order of unity. The paper is focused on a difference between GB diffusion parameters in nano – and coarse grained materials.

Relations between the parameters of grain-boundary diffusion of zinc in aluminum

Experimental results on the grain-boundary diffusion of zinc in aluminum bicrystals containing 〈100〉 and 〈111〉 tilt boundaries at normal and high hydrostatic pressures have been considered. A comparison of the diffusion activation energies and the activation volumes for grain boundaries having the same crystallographic parameters has revealed a linear relation between these kinetic constants. The diffusion activation energy is found to increase with the activation volume. This relation is shown to correspond to the compensation effect well-known in diffusion theory.

Diffusion of iron in Cr2O3: polycrystals and thin films

Chromia protective layers are formed on many industrial alloys to prevent corrosion by oxidation. The role of such layers is to limit the inward diffusion of oxygen and the outward diffusion of cations. A number of chromia-forming alloys contain iron as a major component, such as the stainless steels. To check if chromia is a barrier to the outward diffusion of iron in these alloys, iron diffusion in chromia was studied in both polycrystals and oxide films formed by oxidation of Ni–30Cr alloy in the temperature range 700–1100 ◦ C at an oxygen pressure equal to 10 −4 atm. An iron film of about 80 nm thick was deposited on the chromia surface, and after the diffusing treatment, iron depth profiles were established by secondary ion mass spectrometry (SIMS). Two diffusion domains appear whatever the nature of the chromia material, polycrystals or films. In the first domain, using a solution of the Fick’s second law for diffusion from a thick film, effective or bulk diffusion coefficients were determined. With the second domain, Le Claire’s and Hart’s models allowed both the bulk diffusion coefficient and the grain-boundary diffusion parameter (αDgbδ) to be obtained. Iron bulk and grain-boundary diffusion does not vary significantly according to the microstructure of chromia. The activation energy of grain-boundary diffusion is at least equal or even greater than the activation energy of bulk diffusion, probably on account of segregation phenomena. Iron diffusion was compared to cationic self-diffusion in the bulk and along grain boundaries and related to the protective character of chromia. © 2004 Elsevier B.V. All rights reserved.

Grain Boundary Diffusion in Polycrystalline Ferrites with Different Intergranular Potential Barrier

Using the method of layer-by-layer measurements of the electrical conductivity activation energy, an investigation is performed of grain-boundary diffusion of oxygen in polycrystalline Li–Ti-ferrites in the range of temperatures 873–1073 K. A correlation relation is established between the value of the intergranular potential barrier and the parameters of grain-boundary diffusion of oxygen in polycrystalline ferrites. An increase in this value gives rise to a growth in the diffusion activation energy. The grain-boundary diffusion coefficient increases with the value of the intergranular potential barrier.

Motion of 〈1 0 0〉-tilt grain boundaries

The motion of planar symmetrical 〈1 0 0〉-tilt boundaries in high-purity aluminum was investigated in situ under the influence of an external mechanical stress field. It was observed that the motion of planar 〈1 0 0〉-tilt boundaries could be activated by an applied shear stress which acts perpendicular to the grain boundary plane. The motion of the grain boundaries is thermally activated so that we could derive the activation parameters for the motion from the in situ data of the mobility at different temperatures. A sharp transition between low angle grain boundaries and high angle grain boundaries was observed for the planar tilt boundaries at 8.6° which was apparent from a step change in the activation enthalpy for the stress induced grain boundary motion. The observed activation parameters for the stress-induced motion can be correlated to the activation parameters of self-diffusion for the motion of low angle boundaries and to the activation parameters of grain boundary diffusion for the motion of high angle grain boundaries. From these correlations, it seems obvious that the motion of planar low and high angle grain boundaries under the influence of a mechanical stress field can be attributed to the movement of the grain boundary dislocations which comprise the structure of the boundary.

Grain Boundary Diffusion and Mechanisms of Creep of Nanostructured Metals

Comparative investigations of diffusion in coarse-grained (d = 20 μm), nanocrystalline (d = 0.04 μm) and nanostructured nickel (d = 0.3 μm) have been carried out in a temperature interval of 0.2–0.3 melting temperature. The reasons for difference of parameters of copper grain-boundary diffusion in the above materials are discussed. The effect exerted by grain boundary state and grain boundary diffusion fluxes of impurity on creep mechanisms of nanostructured nickel and copper in the temperature interval of 373–473 K have been studied. Significant change in the apparent creep activation energy under copper grain boundary diffusion fluxes is described as a consequence of different contribution of grain boundary sliding to overall deformation.