Carbon In Α-iron Research Articles

Effect of Alloying Elements on Grain Boundary Segregation of Boron and Carbon in α-Iron

To clarify the effect of alloying elements (M) on the grain boundary segregation behavior of boron (B) and carbon (C) in α-iron, the grain boundary segregation of B, C and alloying elements was evaluated thermodynamically for the Fe–B–1.0 at.%M and the Fe–C–1.0 at.%M ternary systems (M: Al, Ti, V, Cr, Mn, Nb, Mo) using the parallel tangent law proposed by Hillert. In this calculation, the Gibbs energies of the liquid phase in the Fe–B–M and Fe–C–M ternary systems were applied to those of the grain boundaries. According to the calculated results, in the Fe–B–M ternary systems, co-segregation of Ti, V, Mn or Nb with B was predicted, while no co-segregation behavior was confirmed in the case of Al, Cr or Mo addition; in the Fe–C–M ternary systems, co-segregation of Ti, V, Nb or Mo with C was predicted, while no co-segregation behavior was confirmed in the case of Al, Cr or Mn addition. These co-segregation tendencies correspond well with the formation tendencies of metal borides or metal carbides. Although the present calculated results were based on the assumption that substitutional elements can diffuse sufficiently in addition to interstitial elements B and C, we proposed an equation for the parallel tangent law under paraequilibrium condition in which no partitioning of substitutional elements occurs.

Impact of Ni alloying on Fe-C martensite ageing: an atomistic investigation

We propose a computational investigation of Ni-alloying impact on Fe-C martensite ageing, at the atomic scale. Using the Climbing Image Nudged Elastic Band technique, we showed the repulsive nature of Ni-C pairwise interactions in α-iron, and demonstrated that Ni alloying lowers the migration energies and force dipole tensor components associated to an interstitial carbon in α-iron. Computed values of pairwise interactions, migration energies and dipole components were used to implement a Kinetic Monte-Carlo approach. We found that Ni alloying: (i) has negligible impact on martensite thermodynamical stability, (ii) accelerates ageing kinetics, by increasing carbon diffusivity.

Phase transformation mechanism and kinetics during step quenching of st37 low carbon steel

Step quenching of st37 low carbon steel was studied for understanding the phase transformation kinetics. During step quenching, the amount of martensite (formerly austenite) decreased by increasing the holding time at the intercritical annealing temperature. Based on the Johnson–Mehl–Avrami–Kolmogorov (JMAK) analysis using the hardness data, Avrami exponents were determined in the range of 0.3 to 0.8, which indicate that the austenite to ferrite transformation in the intercritical temperature region is diffusion controlled. The activation energy of 84.2 kJ mol−1 was obtained, which is close to the activation energy for the diffusion of carbon in α-iron (87.4 kJ mol−1). Consequently, the diffusion of carbon in α-iron was found to be responsible for the microstructure formation via transformation of austenite to ferrite during step quenching. In fact, the grain-boundary ferrite phase grows into the surrounding austenite phase during step quenching while the austenite phase forms in place of pearlite and also nucleates on the ferrite grain boundaries during intercritical annealing of ferrite-pearlite microstructure. Based on these findings, the slower kinetics of the microstructure formation during step quenching (as compared to the conventional intercritical annealing) was related to the atomic diffusion mechanisms, where the diffusion of carbon in α-iron was calculated to be slower than that in γ-iron at 850 °C.

Solubility of Carbon in Nanocrystalline α-Iron

ABSTRACTBy using a thermodynamic model of nanocrystalline alloys the grain size effect on the solubility of carbon in α-iron is calculated. More specifically the enrichment at grain boundaries is predicted to result in a solubility enhancement. An experimental setup is devised to measure carbon solubility in nanocrystalline iron powder in equilibrium with graphite. At 390 °C a solubility of 0.514 at% is determined for nanocrystalline iron with a grain size of 23 nm.

Solubility of carbon in α-iron under volumetric strain and close to the Σ5(3 1 0)[0 0 1] grain boundary: Comparison of DFT and empirical potential methods

The solubility of carbon in α-Fe as a function of lattice strain and in the vicinity of the ∑5(310)[001] symmetrical tilt grain boundary is calculated with ab initio methods based on density-functional theory (DFT). The results are compared to four different empirical potentials: the embedded-atom method (EAM) potentials of Lau et al. [1], Ruda et al. [2] and Hepburn et al. [3], and the modified embedded-atom method (MEAM) potential of Lee [4]. The results confirm that the solubility of carbon in body-centered-cubic (bcc) Fe increases under local volume expansion and provide quantitative data for the excess enthalpy to be used in thermodynamic databases. According to our study the excess enthalpy obtained from DFT is more strain-sensitive than the ones obtained from the tested empirical potentials. The comparison of the applied methods furthermore reveals that among the empirical potentials the MEAM is most appropriate to describe the solubility of C in bcc Fe under strain. The differences between the four empirical potentials stem from different parameterizations of the EAM potentials and, in the case of the MEAM, from the altogether different formalism that also includes angular dependent terms in the binding energy.

Carbon diffusion in α-iron: Evidence for quantum mechanical tunneling

Recent experimental data on the diffusion coefficient of carbon in α-iron below the liquid nitrogen temperature (LNT) question the classical approach to the observed temperature dependence. As the temperature is lowered below the LNT, the diffusion constant tends toward a nearly temperature-independent value rather than continuing its activated trend. The low-temperature branch is apparently characteristic of a quantum mechanical process dominated by tunneling in the ground state. Concomitantly, we apply an occurrence-probability approach to describing the overall temperature dependence as a single continuous rate. Within the adiabatic approximation, the electronic eigen value, depending parametrically on the nuclear coordinates, is taken to be the potential energy to control the motion of the nuclei. The resulting rate involves all horizontal-tunneling energy-conserving elastic transitions at the quantized energy levels of the migrating atom. A small though not negligible slope in the temperature dependence as the temperature is raised below 100 K is dealt with by complementing for the rate of a parallel one-phonon inelastic-tunneling process in excess of the basic elastic-tunneling rate. Our combined approach agrees well with the experimental data. In particular, the frequency of the coupled vibration is obtained virtually identical to the carbon vibrational frequency from inelastic neutron scattering data. The migrational barrier is also found to be within the limits expected for α-iron.

Effect of dissolved small molecules on the mechanical relaxation behavior of polycarbonate

After sorption of gas molecules (CO 2, C 2H 4) in polycarbonate, a new damping peak appears and the intrinsic γ-relaxation is depressed. The new peak increases in intensity and shifts to lower temperature with increasing gas concentration. This relaxation could be attributed to jumps of the gas molecules inside the polymer matrix similar to the Snoek relaxation of carbon in α-iron.

Diffusion Equation for Solute Atoms under a Temperature Gradient

By combining Wirtz's equation and the phenomenological diffusion equation for carbon under a temperature gradient, J C =-(D C N C /RT)[⊇(μ C ) τ + * Q C ⊇T/T], Shewmon proposed the relation, * Q C =-e m C , where, * Q C and e m C are the heat of transfer and the migration enthalpy of carbon in α-iron. In this paper, it is pointed out that (1) the vector space in which Wirtz's and the phenomenological diffusion equation are defined is not the same, (2) hence, it is not allowed theoretically to combine directly these two equations to obtain the relation, * Q C =-e m C . Showing a correct equation to be combined with Wirtz's equation, the correct diffusion equation for solute atoms under a temperature gradient is derived.

Heat of Transfer for Carbon in Iron-Carbon System

The implications of the phenomenological diffusion equation for solute atoms under a temperature gradient are examined. It is pointed out that the quantity which can be derived from the steady state distribution of the solute atoms under a temperature gradient is, in principle, not the heat of transfer for the solute atoms but the partial molar enthalpy of the solute atoms less the heat of transfer for the solute atoms in the system. And it is shown that the reported value of the heat of transfer for carbon in α-iron agrees well with the value of the partial molar enthalpy for carbon in α-iron calculated using the thermodynamic database SGTE with THERMO-CALC. Correspondingly, it is concluded that the carbon distribution observed experimentally is not the result of the thermal diffusion of carbon but the distribution of carbon in equilibrium under a temperature gradient. The calculated value of the partial molar enthalpy of carbon in γ-iron, however, does not meet with the experimental value of the reduced heat of transfer for carbon in γ-iron. It is pointed out that the reported value of the reduced heat of transfer for carbon in γ-iron may have large experimental errors.

Comparative study of solubilities of hydrogen, nitrogen and carbon in ?-iron

Solubility data of hydrogen, nitrogen and carbon in α-iron are analysed on the basis of statistical thermodynamics. Present analysis appears to yield realistic values for the enthalpy term of the solutions of these interstitial elements into α-Fe, while the entropy terms remain ambiguous. During the course of this analysis a parameter θ x, which refers to the solubility limit of the specific interstitial element X (X=hydrogen, nitrogen or carbon), is also estimated; θ H< θ N< θ C. This order of θ X values appears to be in accord with the observation that, under normal conditions, the solubility of carbon is the highest and that of hydrogen the lowest in α-Fe, while the atomic size increases with the order hydrogen<nitrogen<carbon.

Calculation of the lattice distortion due to carbon inα-iron

A method for calculating the static displacements of lattice atoms near a defect atom is presented and applied to carbon occupying the octahedral site in α-iron. The interaction between lattice atoms and the defect is assumed to extend to second neighbors, but a defect-lattice atom interatomic potential is neither assumed nor constructed. Instead the displacements of the first and second neighbors of the defect atom are treated as adjustable parameters, which can be determined experimentally, and the displacement field is calculated as a function of these parameters. A central, two-body Morse potential is used to describe the interaction of lattice atoms, and the lattice atom displacements are calculated for both harmonic and anharmonic (quartic) approximations of the potential. The latter calculation requires an iterative procedure that obtains self-consistent anharmonic displacements without sacrificing the convenience of the matrix inversion technique that is used to solve the harmonic problem.

On the electronic structure of carbon in α-iron

Abstract The electronic structure of carbon atom in a ferromagnetic transition metal is computed in a Hartree-Fock scheme, taking full account of the Friedel sum rule. The atomic ‘p’ levels of the carbon atom are expected to fall within the ‘d’ part of the band structure of the transition metal. It appears possible to screen the additional charge arising from the carbon atom without perturbing potentials on the neighbouring crystal sites of the carbon but these results are not completely consistent with the available experimental results. Taking into account an extended perturbation up to second-nearest neighbours, reasonable agreement with saturation magnetization and hyperfine fields can be obtained.

Electromigration of carbon in α-iron

Electromigration of carbon in α-iron has been investigated by the steady-state method to determine the effective charge number Z* of carbon as functions of the electric current density and the temperature in the ranges 97–867 A/cm2 and 550–850 °C, respectively. It has been found that the drift velocity of carbon is proportional to the electric current density, that is, Z* is independent of the electric current density, and Z* decreases from +12.2 to +3.6 with increasing temperature from 550 to 850 °C, showing larger temperature dependence in the ferromagnetic α-iron. This is explained in terms of the spin-disorder scattering model. Z* estimated from the electrical resistivity data depends on temperature in a way similar to that determined from the electromigration. From the dependence of Z* on the resistivity increment in α-iron due to solution of carbon, the true charge number of carbon has been determined to be about zero. Thus, it is concluded that the carbon ion is subjected not to the electrostatic force but to the drag force from the current carriers during electromigration.

An Auger Electron Spectroscopic Study of the Diffusion of Sulfur and Carbon in α-Iron

Auger electron spectroscopy has been employed to study the diffusion of sulfur and carbon in α-iron. In the temperature range 25 to 500°C carbon preferentially segregates to the surface. From 400 to 700°C sulfur segregates to the surface while carbon is thermally desorbed. An Arrhenius analysis of the sulfur diffusion data yields an activation energy of 14.5 kcal/mol, which is consistent with a grain boundary diffusion process. The kinetics of carbon migration is complicated by the thermal desorption which makes Arrhenius analysis impossible.

帯域純化した鉄中の過飽和Cの析出

In order to separate the effect of impurities from the inherent process in the precipitation of super saturated carbon in α-iron, super-purity iron specimens were made by zone refining, carburized to 0.009 wt% carbon, and used in the quench aging experiment. The results were compared with the specimens from the same sources (Puron 99.9% and Johnson-Matthey) but not zone refined.The precipitation process was followed by measuring the electrical resistivity and internal friction and by the direct observation with the transmission electron microscope. All of the measurements showed appreciable differences between the super-purity specimens and lower purity specimens, as are summarized in the following.(1) The precipitation process consisted of two steps, as previously reported(1), showing the formation of a meta-stable phase before that of the cementite phase. For the fact that clear and explainable differences were observed in the first step while they were not always well-interpreted in the second step, only the former step was dealt with in this report.(2) The internal friction measurement revealed that for purer specimens the time necessary for the precipitation is shorter. As most of the impurity atoms were considered to be oxygen and no difference in the density of precipitation nuclei was found by electron microscopy, it was quite conceivable that the oxygen atoms do not give rise to the decrease of the nucleation rate but temporarily trap the migrating carbon atoms to make the process delayed.(3) In the lower purity iron the aging curves obtained by the electrical resistivity measurement were in fairly good accordance with those by the internal friction measurement, while in the zone melted super-purity iron the resistivity decreased in the order of ten times slower than the C-Snoek peak decay in the first step. It was suggested that in super-purity iron were formed a special configuration of precipitates with a large capacity of scattering the conduction electrons which brings about a considerably large resistivity increase.It was concluded that the precipitation phenomena of interstitial elements so far reported in pure iron are not characteristic of the pure state but mostly arise from the impurity effect.

The mechanical damping of iron from room temperature to 400°c at 7 megacycles/sec

The pulse-echo method has been used to measure the Snoek damping peaks of nitrogen and carbon in α-iron at 6.65 Mc/sec. The diffusion peaks occurred at 326° ± 2° C for nitrogen and at 353° ± 4° C for carbon. The diffusion coefficient of nitrogen so determined was in good agreement with a determination by other workers at nearly the same temperature by a bulk desorption method. The carbon diffusion coefficient so determined fell on the Arrhenius line extrapolated upward from the low temperature data, but the present data accentuates the anomaly reported by both Smith and Homan. Consideration of all the available diffusion data for nitrogen in α-iron (and also δ-iron) shows that the diffusion coefficient can be represented from −50° to 1470°C by a single Arrhenius relation, namely: D = 4.88 × 10 −3 exp[ −(18,350) RT ] cm 2/ sec . The diffusion coefficient of carbon may be represented from −40° to at least 350°C by: D = 3.94 × 10 −3 exp[ −(19,160) RT ] cm 2/ sec . This new value for carbon removes the discrepancy between D 0 for carbon and nitrogen and according to the ideas of Zener, shows that the strain energy is only a part of the total activation free energy for diffusion. The work on the carbon Snoek peak indicates that supersaturated solutions of carbon in α-iron may be quite persistent around 350°C. This could possibly account for the discrepancy between the heat of solution of cementite as measured by equilibria and by internal friction methods. The orientation dependence of the nitrogen Snoek peak height was observed with longitudinal waves propagated in the [100], [110] and [111] directions in single crystals, with results confirming Polder's theory. The tem perature dependence of this relaxation in single crystals gives a possible indication that nitrogen atoms resist martensite-type ordering to a great extent in dilute iron-nitrogen alloys. Magnetic damping peaks due to carbon and nitrogen, similar to those observed by Maringer near 1 c/s, have been observed at 6.65 Mc/sec. The small nitrogen Maringer peak, however, occurs at a lower temperature than the corresponding Snoek peak.

Calculation of the energy and migration characteristics of carbon in martensite

A model previously used for the calculation of the energy and migration characteristics of carbon in α-iron has been extended to simulate martensite. Iron atoms near a carbon interstitial are treated as individual particles interacting with a nearest and next-nearest neighbor two-body central force, and the remainder of the lattice is treated as an elastic continuum. A two-body central force is also used for the carbon-iron interaction. Computer experiments are performed by inserting a carbon atom into a perfect body-centered tetragonal lattice of iron atoms with the lattice parameters adjusted for a given carbon concentration. The carbon migration energy was found to increase with carbon concentration, e.g. from 0.86 eV in α-iron to 1.00 eV for motion in the plane perpendicular to c axis and 1.09 eV for motion parallel to the c axis for 1 wt. % carbon in martensite. The di-carbon binding energy shows a little change and the carbon-vacancy binding energy decreases with increasing carbon concentration, and no carbon reorientation internal friction peak is predicted by this model for martensite.

Directional Order and Diffusion Aftereffect

If an anisotropic local atomic configuration is produced in some way or other, the magnetization is stabilized in a direction related to this anisotropy, causing an additional uniaxial magnetic anisotropy. This kind of an anisotropy in the atomic configuration is called a directional ordering. This may be an anisotropic distribution of constituent atoms in substitutional ferromagnetic alloys, of interstitial atoms in a body centered cubic lattice, or of different atoms or ions on the B sites of mixed ferrites, etc. A brief explanation of the phenomena is given in each case. Also because of the coupling between the atomic arrangement and the direction of the magnetization, a relaxation phenomenon may be observed in the magnetization process which depends on the diffusion of atoms. The magnetic aftereffect arising from a small amount of carbon in α-iron is explained in detail.

A method for the measurement of elastic relaxation, and its use for determination of the solubility of carbon in α-iron

A new method is developed for measuring elastic relaxation. The samples are in the form of spirals, which are twisted through a certain angle and then released. The course of creep is registered photographically, and thus the magnitude of the elastic after-effect is found. The method is applied to the determination of the solubility of carbon in α-iron. The specimens are made so large that the carbon in solution can be determined directly by weighing, which is a considerable advantage of the method. First, the relation between carbon content and after-effect was determined. Supersaturated samples were then quenched from different temperatures, and thus the solubility limit was obtained between 400 and 700°C. The results deviate both from earlier investigations using the torsional pendulum method, and also considerably from the results obtained by calorimetric methods. The latter need correction, partly because of the recently discovered precipitation of Fe 2C at lower temperatures. The equilibrium between this carbide and carbon in solution is also discussed.

Influence of grain boundaries on the behaviour of carbon and nitrogen in α-iron

The internal friction has been studied as a function of the concentration of carbon or nitrogen in α-iron at two different grain sizes and upon quenching from various temperatures. It is found that grain boundaries reduce the mobility of the interstitial atoms and that carbon probably is enriched in grain boundary films with rather high carbon content, both phenomena decreasing the internal friction. The solubility of carbon in α-iron increases the smaller the grain size. The influence of 0.08 per cent of manganese contained in the test material is briefly discussed, and a calculation of the influence of preferred orientation on the internal friction is given.