Grain Boundary Width Research Articles

Determination of the chemical width of grain boundaries of boron- and carbon-doped hot-pressed β-SiC by HAADF imaging and ELNES line-profile

A residue of sintering additives is often found at the grain boundaries in sintered ceramics. This can be used to determine the macroscopic properties of the sintered polycrystalline materials. A combination of both high-angle annular dark-field (HAADF) imaging and energy-loss near edge-structure (ELNES) line-profile methods was carried out to measure the chemical width of grain boundaries using the sintering additives. Application of both HRTEM and HAADF imaging methods for boron- and carbon-doped hot-pressed SiC leads to the identification of the structural differences either within the matrix or at the grain boundaries very clearly. Additionally, EELS analysis was also carried out to identify the chemistries and bondings at the grain boundaries. The segregation of both boron and nitrogen is clearly shown, as well as the chemical width measured at the grain boundaries by the ELNES line-profile method. Incorporation of nitrogen within the grain interior was also detected by ELNES analysis.

Grain boundaries of nanocrystalline materials – their widths, compositions, and internal structures

Nanocrystalline materials contain many atoms at and near grain boundaries. Sufficient numbers of Mossbauer probe atoms can be situated in grain boundary environments to make a clear contribution to the measured Mossbauer spectrum. Three types of measurements on nanocrystalline materials are reported here, all using Mossbauer spectrometry in conjunction with X-ray diffractometry, transmission electron microscopy, or small angle neutron scattering. By measuring the fraction of atoms contributing to the grain boundary component in a Mossbauer spectrum, and by knowing the grain size of the material, it is possible to deduce the average width of grain boundaries in metallic alloys. It is found that these widths are approximately 0.5 nm for fcc alloys and slightly larger than 1.0 nm for bcc alloys.

Structural and Chemical Widths of General Grain Boundaries: Modification of Local Structure and Bonding by Boron-Doping in β-Silicon Carbide

Using a hot-isostatic-pressed boron-doped silicon carbide (SiC) material as an example, we demonstrate that the structural width and the chemical width of general boundaries may be quite different. The high-resolution electron microscopy (HREM) observation did not detect the existence of ∼1 nm thick amorphous film at such grain boundaries (GB). There is only a core structure of 1–2 atomic planes at GB. The chemical width of GB, obtained by the spatially-resolved electron energy-loss spectroscopy (EELS) analysis, is visibly wider than the core region. Furthermore, the spatially-resolved energy-loss near-edge structures (ELNES) analysis not only revealed the chemical bonding between boron and carbon, oxygen and silicon, but also distinguished an extended GB region with chemical bonding modified from that of the grain interiors. Such ELNES analysis defines an ELNES width that is even wider than the chemical width. The three GB widths of different scale construct a comprehensive picture of general boundaries that is remarkably different from general boundaries with amorphous film. Instead of a film confined by the two atomically sharp grain surfaces, there is only one interface, the rough GB core having most of the B–C and Si–O bonds, and the extended grain surface layers, to form such general GB in B-doped SiC.

TEM, XPS and SIMS Analyzes on Grain Boundary of Lanthanum Chromites

The morphological characteristics, chromium valence state, and cation transport in the vicinity of grain boundary in La1-xCaxCrO3 were investigated by using TEM/EDS, XPS and SIMS techniques. The width of grain boundary was around 1 nm where anomalous enrichment of calcium was observed. Higher valence state of chromium such as Cr6+(d0) was detected in the grain boundaries whereas Cr3+(d3) and Cr4+(d2) were dominant in the bulk. Very fast interdiffusion of alkaline earths was observed in the Sr2+-La0.75Ca0.25CrO3 system. All observed phenomena were correlated by assuming the A-site vacancy which may be induced by the formation of Cr6+ at grain boundaries.

Iron grain boundary diffusion in pure and in Cr, Fe and Zr-doped Ni3Al alloys

Abstract The grain-boundary diffusion (GBD) of 59 Fe in pure and in Cr-, Fe- and Zr-doped Ni 3 Al alloys was studied at temperatures between 873 and 1273 K using the serial sectioning method. The grain-boundary diffusivities P ( P is a product of grain-boundary width δ , and the diffusion coefficient in the grain-boundary D b ) were obtained from the penetration profiles using both the Le Claire’s analysis and direct fit of Suzuoka’s solution. The activation enthalpies of 59 Fe GBD were somewhat lower in comparison with analogous values for 51 Cr GBD, reported in our previous paper.

Nickel and selenium grain boundary solute diffusion and segregation in silver

For the first time, the grain boundary (GB) solute diffusion of Ni and Se in Ag polycrystals was investigated systematically by the radiotracer serial sectioning technique using 63Ni and 75Se isotopes. Measurements in the temperature ranges 589–989 K for Ni and 371–877 K for Se were carried out in Harrison's type B regime at high temperatures and in type C regime at low temperatures. In the B regime, the product sδD GB was determined ( s being the solute GB segregation factor, δ the GB width, D GB the GB diffusion coefficient), while in the C-regime D GB values were measured directly. The solid solubility of both solutes, Ni and Se, in Ag is very small. The equilibrium phase diagrams, however, are quite different: Se forms an intermetallic compound whereas Ni does not form any compound with Ag, which indicates dominating Se–Ag and Ni–Ni bonds, respectively. Comparing the solute D GB values with C regime measurements of GB self-diffusion in Ag, a drastic decrease of the Ni diffusivity and an increased activation enthalpy of Ni diffusion, H GB Ni, in Ag GBs is observed. This behaviour is discussed in terms of repulsive Ni-vacancy interactions and decreased jump frequencies of the Ni atoms which are mainly located at low energy positions in the GB. The measured D GB values of Se, on the other hand, are comparatively close to GB self-diffusion, whereas H GB Se is again larger than H GB Ag of GB self-diffusion. This behaviour is explained in terms of the formation of “embryos” of two-dimensional phases at high energy GB sites. Combining the obtained sδD GB and D GB values and assuming δ=0.5 nm, the GB segregation factors and segregation enthalpies of Ni ( H s Ni=−39.7 kJ/mol) and Se ( H s Se=−21.4 kJ/mol) in Ag were evaluated.

Grain-boundary diffusion of chromium in Ni3Al intermetallic modified by Fe, Cr and Zr

Tracer grain-boundary diffusion (GBD) of chromium Cr-51 in slightly hypostoichiometric (xAl < 25 at%) Ni3Al alloys containing several at. pct of Fe, Cr and Zr was studied using both serial sectioning and residual activity methods. Measurements of the product of the diffusion coefficient in grain boundary and the width of grain boundary, P, were carried out in the temperature interval from 773 to 1273 K. It was found that the addition of Fe and Cr up to about 6 at% does not alter the diffusion characteristics of Cr grain-boundary diffusion. The addition of a small amount of Zr, on the other hand, tends to increase the activation enthalpy and pre-exponential factor of Cr grain-boundary diffusion.

Thermodynamics of Vacancies and Impurities at Grain Boundaries

The thermodynamics of vacancy and impurity adsorption at interfaces and grain boundaries (GBs) in solids is considered. Theoretical expressions are derived for the GB/interface free energy change caused by various levels of vacancy or impurity adsorption. This information is used to predict the behavior of vacancies at interfaces and GBs in a stress gradient and to forecast the effect of impurities on GB fracture strength. The latter predictions provide an interpretation of intergranular fracture behavior in terms of impurity adsorption and GB structural parameters such as GB width and Σ value.

Grain boundary self-diffusion in Cu polycrystals of different purity

The temperature dependence of grain boundary (GB) self-diffusion in Cu polycrystals was systematically investigated using the 64Cu radiotracer and the serial sectioning technique. Two different high-purity Cu materials were used: 99.9998% Cu and 99.999% Cu. The difference in impurity content was checked by time-of-flight secondary-ion mass spectrometry (SIMS). The two materials were studied in the temperature ranges 1066-720 K (99.9998% Cu) and 973-784 K (99.999% Cu). A significant dependence of the GB self-diffusion on the material purity was observed, resulting in a different Arrhenius behaviour of the diffusivity δD GB where δ is the GB width and D GB is the GB diffusion coefficient. The Arrhenius parameters are 3.89 × 10 −16 m 3/s and 72.47 kJ/mol for the highest purity material, and 1.16 × 10 −15 m 3/s and 84.75 kJ/mol for the high purity material. The differences in GB diffusion coefficients and activation enthalpies are explained in terms of strong impurity-Cu atom bonds in the boundary. In the present investigation sulphur is the dominant impurity. Remarks are made relating the impurity segregation and the reduction of the GB diffusivity to the lifetimes of thin film metallic interconnects determined by electromigration effects in GBs. Using a semi-empirical relation of Borisov et al. the GB energy, γ GB, of large angle boundaries and its temperature dependence were determined from the self-diffusion data of Cu. The resulting values of γ GB (e.g. 650 mJ/m 2 at 1000 K) are in good agreement with GB energy measurements and model calculations for Cu.

The Determination of the Grain Boundary Width of Ultrafine Grained Copper and Nickel from Electrical Resistivity Measurements

The grain size distribution of copper and nickel processed by severe plastic deformation was studied by transmission electron microscopy. The temperature dependence of electrical resistivity in the temperature range from 20 to 300 K is presented. The tunnel model of electrical resistivity of grain boundaries is discussed. The width of the potential barrier at grain boundaries in copper and nickel is determined. Larger values of potential barriers are noted in ultrafine grained materials in comparison to the crystallographic width of grain boundaries.

Temperature and orientation dependences of the grain-boundary diffusion coefficient of antimony in copper bicrystals

An investigation is made of the diffusion of antimony through the bulk and along grain boundaries in copper bicrystals containing a symmetric 〈100〉 misorientation boundary with misorientation angles from 20 to 37.2°. The bicrystals are grown by the method of horizontal zone recrystallization. The temperature range for these studies is 480–580 °C, where the solubility of Sb in Cu is about 6 atomic % and practically temperature-independent. The concentration profiles are obtained by x-ray spectral microanalysis, and the grain-boundary diffusion parameters are computed by the method of Whipple and Suzuoka. The orientation dependence of the triple product P=sδD b (where s is the segregation coefficient, δ the width of the grain boundary, and D b the grain-boundary diffusion coefficient) is nonmonotonic, with a maximum for the special ∑5 misorientation boundary (36.9°). The effective activation energy for grain-boundary diffusion ranges from ∼70 kJ/mol for ∑5 to140 kJ/mol for general boundaries.

Microstructural analysis of a uniaxially deformed sandstone—Evidence of intergranular microcrack growth

Abstract This study is aimed at revealing the mechanism of microcrack growth in a sandstone subjected to a uniaxial stress state. Next to direct observation of microcracks in our SEM study, we have determined width of grain boundaries by means of a manually controlled image processing procedure. By comparing deformed with undeformed rock, we have found strong evidence that, in the well cemented sandstone that we have studied, inter granular crack growth is the main change in the microstructure that occurs during pre-failure deformation. It requires further research to determine the precise underlying micromechanism of deformation.

Development of a polyester-based pumpable grout

This study is aimed at revealing the mechanism of microcrack growth in a sandstone subjected to a uniaxial stress state. Next to direct observation of microcracks in our SEM study, we have determined width of grain boundaries by means of a manually controlled image processing procedure. By comparing deformed with undeformed rock, we have found strong evidence that, in the well cemented sandstone that we have studied, inter granular crack growth is the main change in the microstructure that occurs during pre-failure deformation. It requires further research to determine the precise underlying micromechanism of deformation.

Nickel Self-Diffusion along Grain Boundaries in Ni&lt;sub&gt;3&lt;/sub&gt;Al-Base Intermetallic Alloys

{sup 63}Ni self-diffusion along grain boundaries (GBs) in intermetallic alloys Ni-25.2Al, Ni-24.9Al-4.8W, Ni-24.2Al-4.7Cr, Ni-19.3Al-4.5Hf and Ni-27.6Al-4.9Co (at.%) has been investigated by the radiotracer technique. The usual darkening in the positions of GBs on the autoradiographs obtained on the parallel and inclined sections of the specimens was observed. The diffusion penetration profiles were measured by the serial sectioning technique. Using the near-surface parts of the profiles which characterize lattice diffusion, the volume diffusion coefficients D were estimated. For pure Ni{sub 3}Al the agreement of the measured high temperature values of D with those of Bronfin et al. is good. By using the D-values and processing the tails of the measured profiles the GB diffusivity P (P = D{prime}{delta}, where D{prime} is the GB diffusion coefficient, {delta} the GB width) was calculated. The obtained P values followed an Arrhenius dependence at high temperatures: Ni-Al, T = 1,273--1,073 K, Q{prime} = 195 kJ/mol, P{sub 0} = 1 {times} 10{sup {minus}12}m{sup 3}/s; Ni-Al-Hf, T = 1,373--1,023 K, Q{prime} = 219 kJ/mol, P{sub 0} = 6.4 {times} 10{sup {minus}12}m{sup 3}/s; Ni-Al-W, T = 1,373--1,023 K, Q{prime} = 217 kJ/mol, P{sub 0} = 3.3 {times} 10{sup {minus}12}m{sup 3}/s; Ni-Al-Co, T = 1,273--1,023 K, Q{prime} = 189more » kJ/mol, P{sub 0} = 6.8 {times} 10{sup {minus}13}m{sup 3}/s; Ni-Al-Cr, T = 1,323--1,023 K, Q{prime} = 265 kJ/mol, P{sub 0} = 1.8 {times} 10{sup {minus}9}m{sup 3}/s. By using the obtained D and P values the GB energy {gamma} in Ni{sub 3}Al and its alloys was estimated by the Borisov et al. semiempirical relationship. The {gamma}-values calculated exhibit a strong positive temperature dependence, which is usually revealed in metallic alloys containing elements with a strong tendency to GB segregation.« less

Monte carlo simulation of the EBIC grain boundary contrast in semiconductors

The electron beam induced current (EBIC) recombination contrast of grain boundaries (GB) is calculated by means of a Monte Carlo simulation algorithm. After considering a pointlike generation source, a three-dimensional distribution of pointlike sources is simulated and used to calculate the EBIC profiles across the grain boundary. In both cases, we observe a saturation of the maximum EBIC contrast as the carrier lifetime within the GB decreases. The results show, for a three dimensional electron probe, a linear dependence of the contrast on the GB width. In addition, extrapolated values of the maximum contrast obtained for a zero width GB are in good agreement with that calculated by analytical models.

Nickel self-diffusion along grain boundaries in Ni3Al-base intermetallic alloys

63Ni self-diffusion along grain boundaries (GBs) in intermetallic alloys Ni25.2Al, Ni24.9Al4.8W, Ni24.2Al4.7Cr, Ni19.3Al4.5Hf and Ni27.6Al4.9Co (at. %) has been investigated by the radiotracer technique. The usual darkening in the positions of GBs on the autoradiographs obtained on the parallel and inclined sections of the specimens was observed. The diffusion penetration profiles were measured by the serial sectioning technique. Using the near-surface parts of the profiles which characterize lattice diffusion, the volume diffusion coefficients D were estimated. For pure Ni3Al the agreement of the measured high temperature values of D with those of Bronfin et al. is good. By using the D-values and processing the tails of the measured profiles the GB diffusivity P (P = D′δ, where D′ is the GB diffusion coefficient, δ the GB width) was calculated. The obtained P values followed an Arrhenius dependence at high temperatures:NiAl, T = 1273-1073K, Q′ = 195kj/mol, P0= 1 × 10−12m3/SNiAlHf, T = 1373-1023K, Q′ = 219kj/mol, P0= 6.4 × 10−12m3/SNiAlW, T = 1373-1023K, Q′ = 217kj/mol, P0= 3.3 × 10−12m3/SNiAlCo, T = 1273-1023K, Q′ = 189kj/mol, P0= 6.8 × 10−13m3/SNiAlCr, T = 1323-1023K, Q′ = 265kj/mol, P0= 1.8 × 10−9m3/SBy using the obtained D and P values the GB energy γ in Ni3Al and its alloys was estimated by the Borisov et al. semiempirical relationship. The γ-values calculated exhibit a strong positive temperature dependence, which is usually revealed in metallic alloys containing elements with a strong tendency to GB segregation.

Segregation effect on grain-boundary diffusion in thin metallic films

The diffusion in AuCu and PtCu thin films has been studied by Rutherford backscattering sperctrometry (RBS) under the kinetic regimes B (within the temperature interval of 175–290 °C) and C (room temperature). The 1.5–2.0 MeV He + RBS spectra were taken using 14–18 keV resolution. The RBS spectra were changed to depth-concentration profiles for both bulk and grain boundary (GB) diffusion. Under kinetic regime C the absolute values of GB diffusion coefficients were obtained. Under kinetic regime B the triple products δKD b (δ is the GB width, D b is the GB diffusion coefficient, K is the enrichment ratio) were obtained using the Whipple and Gilmer-Farrell models. The activation energies for GB diffusion of Au into Cu films and Cu into Au films are close to 0.95–0.98 eV atom −1, whereas the activation energy for GB diffusion of Pt into Cu films is equal to 1.25 eV atom −1. The comparison between the data on the GB diffusion for kinetic regime B extrapolated to room temperature and the data on the GB diffusion for kinetic regime C enables one to derive the product δK and to separate the contribution of segregation to the parameters of GB diffusion for the systems under study.

Study of Pt diffusion in thin copper films under two kinetic regimes

The diffusion of platinum in thin copper films has been studied by Rutherford backscattering spectrometry (RBS) under the kinetic conditions B (within the temperature range of 200–290 °C) and C (room temperature). The RBS spectra were modified to concentration curves for both bulk and grain boundary (GB) diffusion. Under the kinetic regime B the triple products KδDb (Db is the GB diffusion coefficient, δ is the GB width, K is the enrichment ratio) were obtained using Whipple’s model. Under the kinetic regime C the absolute value of the GB diffusion coefficient of Pt in Cu films was obtained. A comparison between the data on GB diffusion for the kinetics B extrapolated to room temperature and the data on GB diffusion for the kinetics C enables one to derive the product Kδ and to separate the contribution of segregation into the GB diffusion of Pt in Cu films.

Unusual thickness dependence of the magnetic critical-current density for granular high-Tc films.

The magnetic critical-current density ({ital J}{sub {ital c}{ital m}}) in the low-field limit (where grains are essentially electromagnetically coupled) is found to increase with film thickness for granular YBa{sub 2}Cu{sub 3}O{sub 7{minus}{ital x}} films, which is quite an opposite trend in comparison to the variation of the transport {ital J}{sub {ital c}} ({ital J}{sub {ital c}{ital t}}) with film thickness. To explain the thickness dependence of {ital J}{sub {ital c}{ital m}}, theoretical estimation of the several microstructural parameters, e.g., grain-boundary width, thickness, etc., and their variation with the film thickness is attempted. Though such estimation does provide information regarding the sample characteristics, it cannot throw light on the observed discrepancy between {ital J}{sub {ital c}{ital t}} and {ital J}{sub {ital c}{ital m}} over the entire thickness regime. To accommodate the discrepancy it has been proposed that in addition to the microstructural parameters, the trapping of extra vortex chains---in the case of magnetic measurement---between two oppositely directed current loops is also governing the {ital J}{sub {ital c}{ital m}} significantly. The trapped extra flux varies with film thickness and is smaller in case of thinner films ({lt}25 {mu}m). However, in the thinner regime the geometric factor plays a dominant role in controllingmore » the {ital J}{sub {ital c}{ital t}} while it does not have any influence on {ital J}{sub {ital c}{ital m}}.« less

Diffusivity of ions in pore water as a quantitative basis for rock deformation rate estimates

A systematic treatment of diffusion of ions in rock pore water is presented in order to provide data suitable for quantitatively addressing water-rock interaction problems including the influence of fluids on rock deformation. Diffusivity of ions in water-saturated, high-porosity sediments is primarily controlled by total porosity ø tot and grain size. Diffusivity of ions in water-saturated, medium-porosity rocks ( ø tot = 0.005 to 0.5) is mainly controlled by the transport porosity ø tra (> 5 nm), but is influenced by the tortuosity difference between fast pathways through interconnected micropores and slow pathways including nanopores (less than 25 nm). The effective diffusivity D e vs. ø tot relations obtained are potentially useful for the prediction of diffusion coefficients in rocks and also their time-dependence during water-rock interactions. Based on the above and literature data, the value ranges at 25°C of “pore-water diffusion” coefficients ( D pw) and of “grain-boundary diffusion” coefficients ( D gb) are evaluated. Comparison of these with recent higher temperature data suggests low activation energies estimated for both D pw and D gb (15 kJ mol −1). Representative D gb value trends thus obtained yield “wet” grain-boundary diffusion coefficients D gb of the order of 10 −14 m 2 s −1 at 150–350°C. An example calculation of strain rates in fluid-assisted rock deformation such as pressure solution is given based on the method of Shimizu using the above D gb values. The strain rates at 350°C with typical grain size ( d = 0.1 mm), differential stress (σ = 100 MPa) and typical grain-boundary width of about 1–10 nm are estimated to be very fast around 10 −11 to 10 −9 s −1 via diffusion through “wetted” grain boundaries. Very slow strain rates of about 10 −17 s −1 are estimated for “non-wetted” deformation. Wetting characteristics of grain boundaries and the nature of aqueous fluid films have a significant role in the enhancement of rock deformation, especially for low-porosity rocks.