Diffusion Coefficient Of Cr Research Articles

Diffusion processes in multicomponent nickel-base superalloy-nickel system

Optical and scanning electron microscopy, as well as electron microprobe analysis and electron backscatter diffraction, have been used to study diffusion processes that occur in a diffusion pair that consistsof a single-crystal CMSX-10 nickel-base superalloy and polycrystalline nickel, at temperatures of 1050–1250°C. It has been found that, in this system, the distributions of γ-stabilizing elements (Cr, Co, W, and Re) are described by the Boltzmann solution for diffusion between two semiinfinite plates of a binary alloy. The processing of these distributions has shown that the diffusion coefficients of Cr, Co, W, and Re in the multicomponent system are close to those in binary alloys of these elements with Ni. The diffusion redistribution of the elements leads to the dissolution of the γ′ phase in the nickel-base superalloy, growth of nickel grains toward the superalloy constituent of the diffusion pair, and the formation of porosity on both sides of the migrating interface, which is determined from a crystal misorientation of the alloy single crystal and nickel grains.

Sorption of Cr(VI) ions by oxyhydrates of M x Al1−x O y · nH2O composition, where M is Zr(IV), Ti(IV), or Sn(IV)

The equilibrium and kinetics of Cr(VI) ion sorption from acidic (pH 2.5) and alkaline (pH 10.5) aqueous solutions by oxyhydrates of the MxAl1 − xOy · nH2O composition, where M is Zr(IV), Ti(IV), or Sn(IV) and x = 0.0−0.7, are studied. It is shown that the sorption equilibrium can be described using the Langmuir model. The effective diffusion coefficients of Cr(VI) ions calculated from the exchange half-time and specific conductivity of oxyhydrates measured after the sorption of the target component are (0.11–0.28) × 10−11 m2 s−1.

Enhancing the Homogenized Diffusion of Chromium in Alloy Steel Ingot by Forging

AbstractThe effects of forging on the diffusion of chromium (Cr) in alloy steel ingot are studied by diffusion model with finite element method (FEM) and verified by the experimental observations. Calculated results show that forging can enhance the diffusion of Cr in alloy steel ingot during the homogenization treatment, which is attributed to the geometry change and the increased diffusion coefficient caused by recrystallization. The geometry change caused by the forging is a factor to increase the diffusivity (from the high concentration region to the low one) of Cr. But, the diffusion coefficient of Cr in the deformed sample is obviously enhanced, the diffusivity is two orders of magnitude higher than that caused by geometry change. The enlarged diffusion coefficient is originated from the recrystallization, which plays a major role in enhancing the diffusion during the homogenization treatment. The experimental results are confirmed with the calculated predicts, the calculated deviation is less than 7%. It is shown that the effect of recrystallization is a new mechanism of enhancing the diffusion by forging .The theoretical explanations of the diffusion mechanism enhanced by forging are also proposed.

Electrochemical aspects of black chromium electrodeposition from 1-butyl-3-methylimidazolium tetrafluoroborate ionic liquid

The electrochemical behaviour of trivalent chromium (Cr 3+) in 1-butyl-3-methylimidazolium tetrafluoroborate [BMIm][BF 4] ionic liquid solutions was studied by cyclic voltammetry and chronoamperometry. The reduction of Cr 3+ occurs in two steps, Cr 3+ to Cr 2+ and Cr 2+ to Cr 0, respectively. The first step is quasi-reversible with a diffusion coefficient of Cr 3+ in solution of 3.13 × 10 −8 cm 2 s −1 at 303 K and 25.8 × 10 −8 cm 2 s −1 at 358 K, estimated from cyclic voltammetry data. Black chromium films were electrodeposited on copper, stainless steel and carbon steel substrates at a constant potential of −1.5 V vs Pt quasi-reference electrode. The films consist of aggregates of nanosized particles. The coatings in the as-deposited condition present an amorphous structure but after annealing for 4 h, a nanocrystalline Cr 2O 3 phase is formed, with an average crystallite size of 17 nm.

Diffusion of chromium in sapphire: The effects of electron beam irradiation

In this paper, we measured the diffusion of chromium in sapphire (α-Al 2O 3). Sapphires were irradiated with 10 MeV electrons to fluencies of 2×10 17 cm −2 for 1 h. Annealing experiments were performed using the three sapphire samples prepared using the three different diffusion methods at temperatures ranging from 1773 to 1923 K for 200 h under an oxidation condition of 1 atm. The diffusion of chromium in sapphire was profiled using scanning electron microscope-energy dispersive X-ray spectrometry (SEM-EDX). The following Arrhenius equations for the diffusion coefficient of Cr 3+ were obtained over the temperature range of 1773–1923 K: Coated and electron beam-irradiated sapphire samples, D cr = 1 . 8 × 1 0 − 7 exp ( − 385 . 7 ± 18 . 2 kJ mol − 1 / R T ) m 2 s − 1 ; Electron beam-irradiated sapphire samples, D cr = 3 . 3 × 1 0 − 7 exp ( − 4 0 1 .0 ± 14 . 7 kJ mol − 1 / R T ) m 2 s − 1 ; Natural non-irradiated sapphires, D cr = 2 . 8 × 1 0 − 7 exp ( − 4 0 5 . 9 ± 28 . 7 kJ mol − 1 / R T ) m 2 s − 1 These results indicate that chromium penetrated deepest within the coated and electron beam-irradiated sapphire samples.

Determination of diffusion coefficient and analysis of diffusion factors of Cr(VI) ion in clay soil

Some laboratory diffusion tests were conducted with diffusion device to determine the diffusion coefficient of Cr(VI) ion passing through Dalian red clay samples. The concentrations of Cr(VI) at different places of the samples were then measured spectrophotometrically after a standing time of 1 000 d. A one-dimensional solute transport equation was used to simulate the transport of Cr(VI) through clay samples. Back-calculation of diffusion coefficient of Cr(VI) was made with finite difference method. Parametric analysis was conducted to simulate variations in soil dry density, temperature, pH and standing time. The results show that the method used in this paper is simple and effective. The diffusion coefficient of Cr(VI) in Dalian red clay varies from 1.50×10−7 cm2/s to 2.08×10−7 cm2/s. After 1 000 d diffusion, the concentration of the source solution drops down to 1.27 mg/L from 62.5 mg/L, and the diffusion distance is only 3.5 cm. Under the assumption that diffusion coefficient is constant, the diffusion effect becomes more obvious with lower density, lower temperature, higher pH value, and much more time.

Electrochemistry of Cr(III) in the Molten System NaF–AlF3–(Al2O3) at 900°C

The diffusion coefficient of Cr(III) determined by chronopotentiometry in the molten system NaF–AlF3–CrF3 was found to be D(Cr(III)) = (5.28 ± 0.14) × 10−5 cm2 s−1. The molar ratio CR = n(NaF)/n(AlF3) was 1.4, which allowed us to perform measurements at 900°C. When oxygen anions were present in the melt, chromium was deposited simultaneously with aluminium at the cathode, and the apparent diffusion coefficient related to Cr(III) was too high by two orders of magnitude. This may be explained by the formation of oxofluoro complexes of chromium and aluminium. The solubility of Cr2O3 was studied in the above-mentioned melt at 900°C by two methods: chemical analysis of solidified samples and by chronopotentiometry. It was found that saturation was achieved after several hours, and the concentration of chromium was (177 ± 6) ppm, corresponding to (258 ± 9) ppm Cr2O3.

Study on transport of Cr(VI) through the landfill liner composed of two-layer soils

A new landfill liner system composed of two-layer soils was proposed. The upper soil layer composed of 90% raw clay plus 10% lime contributes significant to bearing capacity of liners, and the lower soil layer containing 3 or 6% granular activated carbon (GAC) or 3 or 6% acid-activated bentonite contributes to adsorption capacity of liners. The results from unconfined compressive strength tests showed that the method of adding lime into liner soil material was effective measure to improve compressive strength of liners. The batch test results indicated that GAC and acid-activated bentonite were two potential materials for use as adsorptive amendments for trapping heavy metal ions in liners. To investigate the transport of Cr(VI) through the new liner system, laboratory column tests were performed. The column tests results indicated that the lower soil layer containing adsorptive amendments prevented effectively the transport of Cr(VI). The diffusion coefficients of Cr(VI) for liner soil materials were back-calculated by a one-dimensional numerical transport program. The diffusion coefficient of Cr(VI) was 4.64 × 10 −8 m 2/s on average for the upper soil layer. The diffusion coefficient of the lower soil layer was 5.4 × 10 −10 m 2/s to 7.0 × 10 −10 m 2/s. The differences of diffusion coefficients may be due to different grain size distributions and moulding density between these soils.

Transport of Cr(VI) through clay liners containing activated carbon or acid-activated bentonite

The potential of clays containing 3 or 6% granular activated carbon (GAC) or 3 or 6% acid-activated bentonite was assessed for use as a landfill liner-soil material. Permeability, batch adsorption and column tests were performed to evaluate the seepage properties, the Cr(VI) adsorption capacity and transport parameters of the soils. All soil specimens had a hydraulic conductivity of < 1 × 10 −7 cm/s at a certain range of moulding water content. The Cr(VI) adsorption was much larger than adsorption by the raw clay. The improved clay prevented effectively the transport of Cr(VI). The diffusion coefficient of Cr(VI) for liner-soil materials was back-calculated by a one-dimensional nonlinear advection–dispersion–reaction numerical transport program. This coefficient for the clay or the improved clay was 2.2 × 10 −10 to 8.3 × 10 −10 m 2/s. The improved clay may be used as a good barrier material to attenuate contamination of Cr(VI) in landfills.

10.1007/s11453-008-2022-9

Diffusion of Cr into epitaxial GaAs in an open system in the temperature range of 750–850°C was studied. Temperature dependences of the diffusion coefficient and solubility of Cr in GaAs were determined. Temperature dependences of the diffusion coefficient and solubility of Cr are described by the Arrhenius equation with the parameters D 0 = 1.9 × 109 cm2/s and E = 4.1 ± 0.2 eV for the diffusion coefficient and N 0 = 2.3 × 1024 cm−3 and E 0 = 1.9 ± 0.4 eV for solubility. The effect of protective SiO2 filmon the Cr diffusion coefficient and morphology of the GaAs surface after diffusion was studied.

Influence of the crystal field effect on chemical transport in Earth's mantle: Cr 3+ and Ga 3+ diffusion in periclase

Experiments were performed to determine concentration-dependent diffusion coefficients of Cr 3+ and Ga 3+ in periclase at temperatures of 1563–2273 K. Diffusion profiles measured in the quenched samples are consistent with a theoretical model in which the mobile species is a bound M 3+-vacancy pair, and each profile was fitted to determine the binding energy and diffusion coefficient of the pair. Trivalent chromium-vacancy pairs diffuse more slowly than Ga 3+-vacancy pairs, and with higher migration energy, 237 kJ/mol vs. 190 kJ/mol. Cation vacancies also bind less tightly to Cr 3+ than to Ga 3+, with average binding free energies of −22 and −83 kJ/mol, respectively. At all concentrations and temperatures, Cr 3+ diffuses much more slowly than Ga 3+, by up to two orders of magnitude. The differences between Cr 3+ and Ga 3+ cannot be explained by differences in ionic radius or dipole polarizability, but are consistent with the influence of the crystal field on the partially occupied 3d orbitals of Cr 3+. The crystal field splitting stabilizes Cr 3+ on the octahedral cation site, increasing the energy required for Cr 3+ to exchange positions with an adjacent vacancy. It also makes Cr 3+-vacancy pairs less favorable, with the presence of a nearest-neighbor vacancy disrupting the symmetry of the octahedral site, thus diminishing the crystal field stabilization. Trends in the diffusion of first-row divalent transition metals in periclase can also be explained by the crystal field effect. High-spin to low-spin transitions in Fe 2+, Co 2+ or Mn 2+ would significantly enhance their crystal field stabilization in periclase, and if such spin transitions occur in the deep mantle, they would be expected to slow the diffusivity of these ions significantly, perhaps by several orders of magnitude.

Diffusion and solubility of Cr in WC

Although no detailed study on the Cr solubility in WC exists the compilation on the various C–Cr–W phase diagrams [1] suggests this behaviour. In order to prove this and to estimate the diffusivity of Cr in WC we prepared diffusion couples of the type Cr3C2–WC by joining and annealing polished fully dense counterparts of the two carbides (temperature range 1550–1750 °C). After thermal treatment the diffusion couples were cut, polished and investigated by metallography. For the measurement of the diffusion profiles the couples were subjected to WDS-EPMA (Cameca SX 100 microprobe). W, Cr, and C concentration profiles were obtained from line scans performed perpendicular to the interface. The analysis of diffusion couples of WC contacted to other carbides used for doping of hardmetals (VC, TaC, NbC, and TiC) did not yield perceptible solubility of the respective metals in WC with respect to the detection limit of EPMA. From the Cr diffusion profiles a diffusion coefficient of Cr in WC of approximately D = 1.70–2.20 × 10−11cm2/s and an activation energy of EA = 0.75 eV was estimated. In addition the composition of the ternary phase (W,Cr)2C in equilibrium with WC and Cr3C2 could be measured. For example, in couples annealed at 1750 °C the composition reaches from (W0.5Cr0.5)2C (in equilibrium with WC) to (W0.2Cr0.8)2C (in equilibrium with Cr3C2). With the results obtained from the analysis of diffusion couples, the Cr uptake of WC powder as a function of grain size, time and temperature was calculated. Cr saturation in idealised spherical particles of 1 μm occurs only within a few minutes.

Electrode processes in the course of Cr(III) and Cr(II) reduction/oxidation in KCl melt

A hypothesis about formation of a polynuclear chromium complex is made on the basis of a voltammetric study of the processes of trivalent and divalent chromium reduction within complex chloride ions in a potassium chloride melt. The effect of the reaction of Cr2Cl73− formation on deviation of theoretical dependences from the experimentally obtained dependences under the terms of linear voltammetry is shown. Models are suggested for the complex chromium ions, quantum-chemical calculations of the bond lengths in them are performed and steric energies of ions are determined. Diffusion coefficients of Cr(III) and Cr(II) are calculated, diffusion activation energies are determined.

Electrochemical properties of Cr doped V 2O 5 between 3.8 V and 2.0 V

Cr 0.1V 2O 5.15 was prepared by an oxalic acid assisted sol–gel method. X-ray diffraction showed that Cr doping induced a slight expansion (ΔV/V ≈ 2.3%) in the crystal lattice of V 2O 5. The electrochemical properties of Cr 0.1V 2O 5.15 in the potential range of 3.8–2.0 V were studied by cyclic voltammetry, galvanostatic charge–discharge cycling and potentiostatic intermittent titration technique. Cyclic voltammetry showed that the irreversible phase transition of V 2O 5 during the first cycle was effectively prevented by Cr doping. This caused the good charge–discharge cycling performance of the doped material. The discharge capacities were recorded to be 200, 170 and 120 mAhg − 1 after fifty cycles at the C/10, C/2 and 1C rates, respectively. However, ex-situ X-ray diffraction showed that the crystal structure of the material was destroyed after long-term cycling. The lithium diffusion coefficient of Cr 0.1V 2O 5.15 varied between 10 − 11 and 10 − 12 cm 2 s − 1 , which was larger than that of crystalline V 2O 5, and was close to those of metal doped V 2O 5 in previous reports. The improvement in lithium diffusion kinetics was regarded as an important reason for the good electrochemical performance of Cr 0.1V 2O 5.15.

Diffusion of hexavalent chromium in chromium-containing slag as affected by microbial detoxification

An electrochemical method was used to determine the diffusion coefficient of chromium(VI) in chromium-containing slag. A slag plate was prepared from the original slag or the detoxified slag by Achromobacter sp. CH-1. The results revealed that the apparent diffusion coefficient of Cr(VI) was 4.4 × 10 −9 m 2 s −1 in original slag and 2.62 × 10 −8 m 2 s −1 in detoxified slag. The results implied that detoxification of chromium-containing slag by Achromobacter sp. CH-1 could enhance Cr(VI) release. Meanwhile, the results of laboratory experiment showed that the residual total Cr(VI) in slag decreased from an initial value of 6.8 mg g −1 to 0.338 mg g −1 at the end of the detoxification process. The Cr(VI) released from slag was also reduced by Achromobacter sp. CH-1 strain since water soluble Cr(VI) in the leachate was not detected after 4 days. Therefore, Achromobacter sp. CH-1 has potential application for the bio-detoxification of chromium-containing slag.

The Effect of Water Vapor on High Temperature Oxidation of Fe-Cr Alloys at 1073 K

The effect of water vapor on high temperature oxidation was studied based on Wagner's theory of binary alloy oxidation. The oxidation of Fe-Cr alloys was carried out at 1073 K in dry and humid conditions. The oxidation was conducted in a closed apparatus at 1073 K and the oxygen partial pressure of 1.1 x 10 -14 Pa, which was fixed by a Fe/FeO buffer. To prepare the humid condition, Ar-5% H 2 gas mixture of 3 x 10 4 Pa was filled in the apparatus, which provided the water vapor pressure of 3.3 x 10 2 Pa. The transition of internal and external oxidation was observed in Fe-8Cr in the dry condition and in Fe-12Cr in the humid condition. Interdiffusion experiment of Fe/Fe-16Cr diffusion couples in dry and humid environments showed that the diffusion coefficient of Cr was not influenced by dissolved hydrogen. The oxygen permeability in α-Fe was determined by means of internal oxidation of Fe-5Cr alloy at 1073 K and the oxygen partial pressure of 1.1 x 10 -14 Pa in a dry and two humid conditions with water vapor of 1.1 x 10 2 Pa and 3.3 x 10 2 Pa. The oxygen permeability in humid condition increases by a factor of 1.4. Dissolved hydrogen increases the oxygen permeability, thus increases the minimum concentration of Cr to form external scales in humid conditions. The presence of dissolved hydrogen changes the oxide shape from discrete spherical particle to spike-like precipitates, which enhances the oxygen transport along the metal/oxide precipitates interface.

ELECTRO-DEIONIZATION OF Cr (VI)-CONTAINING SOLUTION. PART II: CHROMIUM TRANSPORT THROUGH INORGANIC ION-EXCHANGER AND COMPOSITE CERAMIC MEMBRANE

Cr (VI) transport through a composite ceramic membrane containing an ion-exchange component, namely xerogel of hydrated zirconium dioxide, was investigated. The diffusion coefficient of Cr (VI) species through the membrane, which has been determined under open circuit conditions, is 1.80 × 10−10 m2 s−1. The transport number of Cr (VI) species through the ceramic membrane was found to rise with increasing voltage and reached 0.17 under “over-limiting current” conditions. On the other hand, the transport of chromate ions through hydrogel of hydrated zirconium dioxide becomes more intensive with a decrease in potential drop through the system involving ion-exchanger bed and ceramic membrane due to decrease in the membrane resistance. The diffusion coefficient of Cr (VI) ions in hydrogel of the inorganic ion exchanger was estimated as 4.36 × 10−12 m2 s−1. A possibility of Cr (VI) removal from a weakly acidic diluted solution using an electro-deionization method was shown: the degree of solution purification was found to reach 50%. The transport of species is realized through both the solution and the ion exchanger.

Cr and Al diffusion in chromite spinel: experimental determination and its implication for diffusion creep

Diffusion coefficients of Cr and Al in chromite spinel have been determined at pressures ranging from 3 to 7 GPa and temperatures ranging from 1,400 to 1,700°C by using the diffusion couple of natural single crystals of MgAl2O4 spinel and chromite. The interdiffusion coefficient of Cr–Al as a function of Cr# (=Cr/(Cr + Al)) was determined as D Cr–Al = D 0 exp {−(Q′ + PV*)/RT}, where D 0 = exp{(10.3 ± 0.08) × Cr#0.54±0.02} + (1170 ± 31.2) cm2/s, Q′ = 520 ± 81 kJ/mol at 3 GPa, and V* = 1.36 ± 0.25 cm3/mol at 1,600°C, which is applicable up to Cr# = 0.8. The estimation of the self-diffusion coefficients of Cr and Al from Cr–Al interdiffusion shows that the diffusivity of Cr is more than one order of magnitude smaller than that of Al. These results are in agreement with patterns of multipolar Cr–Al zoning observed in natural chromite spinel samples deformed by diffusion creep.

Effect of the state of vacancy equilibrium on diffusion of chromium impurity in gallium arsenide

The results of studying the diffusion of Cr impurity in GaAs according to electrical measurements are reported. Dependences of the diffusion coefficient and limiting solubility of electrically active Cr atoms in GaAs on temperature (at fixed pressures of As vapors) and on the pressure of As vapors (at fixed temperatures) are determined. The dependence of the Cr diffusion coefficient in GaAs on the ratio between the volume of the sample under study to the volume of the cell in the case of pronounced deviation from the crystal’s stoichiometry towards Ga excess is established. The obtained experimental data are analyzed on the basis of concepts concerning the dissociative mechanism of migration of Cr atoms in the GaAs crystal lattice; according to this mechanism, the diffusion coefficient depends heavily on the concentration of Ga vacancies.

Diffusion of chromium into epitaxial gallium arsenide

Diffusion of Cr into epitaxial GaAs in an open system in the temperature range of 750–850°C was studied. Temperature dependences of the diffusion coefficient and solubility of Cr in GaAs were determined. Temperature dependences of the diffusion coefficient and solubility of Cr are described by the Arrhenius equation with the parameters D0 = 1.9 × 109 cm2/s and E = 4.1 ± 0.2 eV for the diffusion coefficient and N0 = 2.3 × 1024 cm−3 and E0 = 1.9 ± 0.4 eV for solubility. The effect of protective SiO2 filmon the Cr diffusion coefficient and morphology of the GaAs surface after diffusion was studied.