Self-diffusion Coefficients Of Iron Research Articles

A comparative study on hot deformation behaviours of low-carbon and medium-carbon vanadium microalloyed steels

Carbon is an essential element in steel, but there are still discrepancies regarding its effect on steel hot deformation behaviours. In this research, isothermal compression tests were carried out for a low-carbon (0.05 C) and a medium-carbon (0.38 C) vanadium microalloyed steel with deformation temperatures of 900−1050 °C and strain rates of 0.01−30 s−1. It was found that carbon causes a softening effect at low strain rates (0.01−1.0 s−1), while a hardening effect at high strain rates (10.0−30 s−1). Through constitutive analysis, the hot deformation activation energy for 0.05 C steel is 305.9 kJ/mol in the whole strain rate range, while for 0.38 C steel, the activation energy is 292.3 kJ/mol in the low strain rate range (0.01−1 s−1) and 475.0 kJ/mol in the high strain rate range (10−30 s−1). It was proposed that the addition of carbon decreases the deformation activation energy at low strain rates (0.01−1 s−1), due to its positive influence on the self-diffusion coefficient of iron, which increases the rates of dislocation climb and recovery. On the other hand, carbon lowers the stacking fault energy of austenite, which could make partial dislocation collapse more difficult than dislocation climb and thus becomes the rate-controlling mechanism for 0.38 C steel at high strain rates (10−30 s−1). This gives rise to the higher activation energy and work hardening rate of 0.38C steel at high strain rates. Comparing the power-dissipation-efficiency maps, two peak domains were found in those of 0.38 C steel, while only one peak domain exists in those of 0.05 C steel.

Effect of Irradiation on Interdiffusion in Fe–Cr System

A method for calculating diffusion coefficients DFe and DCr and interdiffusion coefficient $$\tilde {D}$$ in an irradiated Fe–Cr alloy is proposed. The substitution of the values of the self-diffusion coefficient of iron into Darken’s equation refined by Manning, which are determined with allowance for the radiation enhanced diffusion and the formation of vI and iI complexes (v is a vacancy, i is a self-interstitial atom, and I is an impurity atom), makes it possible to obtain the temperature and concentration dependences of DFe, DCr, and D at various rates of generation of radiation point defects (dpa/s).

Properties of iron under Earth’s core conditions: Molecular dynamics simulation with an embedded-atom method potential

Using an earlier proposed embedded-atom method potential, we have performed molecular dynamics simulations of the thermodynamic, structural, and diffusional properties of iron under Earth’s core conditions (temperatures of up to 5000 K and densities of up to 12.5 g/cm3). The results attest to spontaneous crystallization of liquid iron at certain parameters of state. We have derived equations of state for the liquid and solid phases and have calculated their heat capacities at constant pressure and temperature, thermal expansion coefficients, isothermal and adiabatic bulk moduli, and sound velocities under various conditions. In addition, we have calculated the heat of fusion of iron and the change in its molar volume on melting. The results agree with literature data. The self-diffusion coefficient of iron decreases linearly with increasing density, vanishes at the densities corresponding to the liquid-solid phase boundary, and is a roughly linear function of temperature.

Thermodynamic and Structural Properties for the FeO–SiO<SUB>2</SUB> System by using Molecular Dynamics Calculation

Molecular dynamics (MD) simulation has been widely used as a very useful method for the calculation of thermodynamic, structural and transport properties for the molten slags and fluxes at high temperatures. In this study, MD simulation using the Born-Mayer-Huggins type pairwise potential with partial ionic charges has been used to calculate the thermodynamic, structural and transport properties for the FeO–SiO2 system. The calculated structural properties such as pair distribution functions and fractions of bonding types of oxygen (bridging, non-bridging and free oxygen) with silicon atoms in FeO–SiO2 melts were in good agreement with previously measured and estimated results, and also the self-diffusion coefficients of iron, silicon and oxygen have been calculated at various temperatures and compositions. The enthalpy, entropy and Gibbs energy of mixing for the FeO–SiO2 system were calculated based on the thermodynamic and structural parameters obtained from MD simulation. The phase diagram for the FeO–SiO2 system estimated by calculated Gibbs energy of mixing shows good agreement with observed result in the range from pure iron to fayalite, and the liquid–liquid immiscibility region in the FeO–SiO2 system has also been assessed by MD calculation.

Creep behavior of Fe–C alloys at high temperatures and high strain rates

The creep behavior of Fe–C alloys (1–1.8%C) has been studied at high temperatures (0.7–0.9 T m) and high strain rates (1–100 s −1). The dominant deformation resistance has been found to be climb-controlled dislocation creep and thus the creep rates are a function of elastic modulus, lattice diffusivity and stacking fault energy. The self-diffusion coefficient of iron in austenite was found to be solely a function of T m/ T and to vary as D=6.8×10 −6 exp(−17 T m/ T) m 2 s −1. The Fe–C alloys were observed to have a high stacking fault energy which was unaffected by carbon and manganese. The stacking fault energy was observed to decrease with increasing concentrations of silicon, aluminum and chromium. At high stresses, deviation from power law behavior was accounted for by considering the contributions to diffusivity by dislocation pipe diffusion. The results have been used to develop a rate equation for these steels of varying composition that depends on only three material characteristics – alloy melting temperature, elastic modulus and stacking fault energy.

Self-diffusivity of polyvalent ions in silicate liquids

Self-diffusion coefficients of tin, lead, arsenic, antimony, bismuth, vanadium, chromium, manganese, iron, nickel, cobalt, zinc, cadmium, copper and cerium were measured as a function of temperature in a borosilicate glass liquid. Self-diffusion coefficients of iron were also measured in some alkali–magnesia–silicate, alkali–lime–silicate and alkali–lime–alumosilicate liquids. The method used was the square-wave voltammetry, a fast potentiostatic pulse method. In the temperature range of 700–1500°C, a linear correlation between log D and 1/ T in which D is the diffusivity and T is sample temperature is observed for all polyvalent elements and compositions studied. The self-diffusion coefficients of Cu + are up to six orders of magnitude larger than those of Cr 6+. Self-diffusion coefficients of iron in liquids possessing larger alkali content and hence smaller viscosity were larger. At all temperatures studied, the self-diffusion coefficients of iron decrease from lithium to cesium. However, if liquids of constant viscosity are compared, the self-diffusion coefficients of iron decrease with decreasing size of the alkali cation, increasing alkali concentration and decreasing alumina content. This decrease is explained by a structural model for the incorporation of iron.

Self-diffusivity of iron in alkali–lime–alumosilicate glass melts

Self-diffusion coefficients of iron were measured in glass melts with the basic mol% composition of 16 R 2O, 10 CaO, x Al 2O 3 and (74 − x) SiO 2 with x=0, 5, 10, 15 and R=Li, Na, K and Cs in the temperature range of 900–1300°C using square-wave voltammetry. All diffusion coefficients had an Arrhenian dependence which depended on the type of alkali present and the Al 2O 3-concentration. Larger alkali cations, e.g. Cs +, as well as an increase in the Al 2O 3-content led to a decrease in the diffusion coefficients and also to an increase in viscosity. Within one glass composition, the Stokes–Einstein equation is fulfilled with respect to the dependence of the diffusivity upon viscosity. At constant viscosity, however, increasing size of the alkali cation and increasing Al 2O 3-content led to larger iron diffusion coefficients.

Self-diffusion of iron in alkali–magnesia–silica glass melts

Alkali–magnesia–silica glass melts with lithium (74 SiO 2, 16 Li 2O, 10 MgO), sodium ((90− x) SiO 2, x Na 2O, 10 MgO ( x=10, 15, 20, 25)), potassium ((90− x) SiO 2, x K 2O, 10 MgO ( x=10, 15, 20, 25)) and caesium (74 SiO 2, 16 Cs 2O, 10 MgO) (all compositions given in mol%) doped with 0.2 mol% Fe 2O 3 were studied by means of square-wave voltammetry. Decreasing Na 2O- and K 2O-contents lead to a decrease in the self-diffusion coefficients of iron and an increase in the viscosities of the liquids. A comparison of diffusivities of different alkali ions shows that at constant temperature, the self-diffusion coefficients decrease from lithium to caesium. Within the error limits, in most of the glasses studied, the Stokes–Einstein equation is fulfilled with respect to the dependence of the diffusivity on the viscosity. At constant viscosity, i.e., mobility of the glass network, the self-diffusion coefficients decrease with increasing alkali concentrations and decreasing size of the alkali cation. These effects are discussed using a structural model for the incorporation of iron into alkali containing glasses.

Isothermal transport properties of Fe 1−δO from a polarization method

We report chemical diffusion coefficient D̃ and effective charge number Z ∗ measurements for various deviations from stoichiometry in Fei 1−δO and at various temperatures. The results are compared with available data, and correlation factors ⨍ for Fe 1−δO are deduced from the comparison of our D̃ values with available self-diffusion coefficients of iron D ∗ Fe ⨍ is shown to be mostly invariant with temperature and nonstoichiometry. Its value lies in the range 0.54–0.62. The charge of the moving cations is Z ∗ = 2 . These two results indicate that iron diffusion in Fe 1−δO is mediated by a vacancy mechanism from octahedral to octahedral positions within regions where the number of first Fe neighbours of a vacancy is much lower than 12.

Sulfidation of iron at high temperatures and diffusion kinetics in ferrous sulfide

The kinetics and mechanism of iron sulfidation have been studied as a function of temperature (950–1200 K) and sulfur pressure (10−3-0.065 atm). It has been stated that a compact Fe1−yS scale on iron grows according to the parabolic rate law as a result of outward lattice diffusion of metal ions through cation vacancies. The activation energy of sulfidation increases with sulfur pressure and the 1/n exponent increases with temperature. This nontypical dependence of iron sulfidation kinetics on temperature and pressure results from the analogous effect of both these parameters on defect concentration in ferrous sulfide. The chemical diffusion coefficients,∼DFeS, and diffusion coefficients of defects, Dd, in ferrous sulfide have been calculated on the basis of parabolic rate contacts of iron sulfidation and deviations from stoichiometry in ferrous sulfide. It has been shown that∼DFeS is practically independent of cation vacancy concentration whereas the diffusion coefficient of defects depends strongly on that parameter. A comparison of self-diffusion coefficients of iron in Fe1−yS calculated from the kinetics of iron sulfidation to those obtained from radioisotopic studies indicates that within the range studied of temperatures and sulfur vapor pressures the outward diffusion of iron across the scale occurs preferentially along the c axis of columnar ferrous sulfide crystals.

Defect structure and diffusion in nonstoichiometric ferrous sulphide

The self-diffusion coefficient of iron in ferrous sulphide has been determined from the kinetics of iron sulphidation as a function of temperature (943–1223 K) and sulphur vapour pressure (5.9 × 10 -4 -0.65 atm) and calculated from other date. The chemical diffusion coefficients and deviations from stoichiometry of ferrous sulphide have also been studied as a function of the same parameters by means of equilibration measurements. It has been proved that the self-diffusion coefficient of iron in ferrous sulphide is a function of sulphur vapour pressure analogous to that of deviation from stoichiometry and it cannot be described by a simple equation typical of transition metal oxides. Empirical equations are given for both quantities. It has been stated that the chemical diffusion coefficient of Fe 1- y S practically does not depend on sulphur vapour pressure and is a function of temperature. It has been shown that the Libowitz model, which assumes strong repulsive interactions between statistically distributed cation vacancies describes correctly the defect structure in ferrous sulphide over a wide range of temperatures and sulphur vapour pressure.

The relationships between the different rate constants and the diffusion properties of the oxides in the parabolic oxidation of a metal or a lower oxide to multilayer scales: application to the oxidation of iron

The various rate constants involved in the parabolic oxidation of a pure metal to form multilayer scales, as well as those intervening in the oxidation of a previously formed oxide to higher oxides in the absence of the metal phase, are correlated with the rate constants expressing directly the diffusion properties of each phase. The theory is then applied to the experimental results on the oxidation of iron and FeO to magnetite and haematite, and it is shown that it leads to consistent results when the experimental rate constants are compared to those calculated from the application of Wagner's theory for both FeO and Fe 3O 4 on the basis of the known self-diffusion coefficients of iron in these compounds.

Analysis of diffusion in ferromagnets

The depression of the self-diffusion coefficient of iron upon magnetic ordering is compared with similar effects which occur in order-disorder alloys. A treatment which uses the basic assumptions of the Bragg-Williams description of order-disorder alloys is used to develop an equation giving the temperature dependence of the diffusion coefficient of iron both above and below the Curie temperature as a function of the activation energy of diffusion in the paramagnetic range and a magnetic ordering term. This equation fits recently published diffusion data in iron-base systems.

Self-diffusion of iron in α-phase of iron and Fe-Cr alloys

In the present paper the self-diffusion coefficients of iron in α-iron and in Fe-Cr alloys in the temperature range 660–890°C and in the concentration interval 0–11.8 wt.% Cr were determined. The residual activity method has been applied using the isotope 59Fe. Special attention was payed to the close neighbourhood of the Curie temperature. The obtained data confirmed the effect of ferromagnetic ordering on the iron self-diffus ion in pure Fe and in all the investigated Fe-Cr alloys. An empiric relation was found between the excess free activation enthalpy of diffusion and the spontaneous magnetization that yields a picture about the magnetic ordering of the used materials.

Self-Diffusion of Iron in Molten Fe-C Alloys

Self-diffusion coefficients of iron in molten Fe-C alloys have been measured by using the capillary method. In addition, the samples have been autoradiographed and sectioned to insure that no significant convection has occurred during the diffusion. The results can be represented by the equation D = 4.3×10−3 exp (—12.200/RT) for carbon = 4.6 pct and T = 1513° to 1633°K; and D = 1.0×10−2 exp (—15,700/RT) for carbon = 2.5 pct and T = 1613° to 1673°K. The D values are higher and the heat of activation for diffusion lower in alloys containing more carbon. Calculation based on the Einstein-Stokes equation indicates that the diffusing species is iron ion.