Diffusion Coefficient Of Carbon Research Articles

Phase composition and numerical model of low-pressure pulse carburized layer in 15Cr14Co12Mo5Ni2W steel

Aerospace engine gear steel, 15Cr14Co12Mo5Ni2W steel, requires carburizing heat treatment to achieve operational performance. However, predicting the carbon concentration during the vacuum carburizing process poses significant challenges. This paper aims to design and establish a predictive model for the carbon concentration during the vacuum carburizing process of 15Cr14Co12Mo5Ni2W steel. Given the complex phase transformations during the vacuum carburizing process caused by the ultra-high alloy content of 15Cr14Co12Mo5Ni2W steel, vacuum short-term intense carburization and diffusion experiments were designed. Characterization methods such as XRD, scanning electron microscopy, electron probe microanalysis, EBSD, and FIB+TEM were used to study the microstructure, phase composition, phase constituents, and distribution of element concentrations during the vacuum carburizing process. Subsequently, a carbon concentration distribution calculation model considering carbide changes during the vacuum carburizing process of 15Cr14Co12Mo5Ni2W steel was established. Boundary conditions for carbon absorption during the intense carburization process of 15Cr14Co12Mo5Ni2W steel were proposed, and the relationship between surface carbon concentration and boundary conditions was determined through experiments. Using the method of forward calculation with least squares fitting of experimental data, the diffusion coefficient of carbon in the austenite of 15Cr14Co12Mo5Ni2W steel and the rate of carbon exchange between carbides and the matrix were derived, providing a more precise predictive tool for optimizing the vacuum carburizing process of 15Cr14Co12Mo5Ni2W steel.

Effect of Controlling Nb Content and Cooling Rate on the Microstructure, Precipitation Phases, and Mechanical Properties of Rebar.

Seismic anti-seismic rebar, as materials for supporting structures in large buildings, need to have excellent mechanical properties. By increasing the Nb content and controlling the cooling rate, the microstructure and precipitation behavior of the steel are adjusted to develop seismic anti-seismic rebar with excellent mechanical properties. Scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), transmission electron microscopy (TEM), and a universal tensile testing machine were used to characterize the microstructure, precipitation phases, and mechanical properties of the experimental steels. The results show that the ferrite grain size, pearlite lamellae layer (ILS), and small-angle grain boundaries (LAGB) content of the high-Nb steels decreased to 6.39 μm, 0.12 μm, and 48.7%, respectively, as the Nb content was increased from 0.017 to 0.023 wt.% and the cooling rate was increased from 1 to 3 °C·s-1. The strength of the {332}<113>α texture is the highest in the high-Nb steels. The precipitated phase is (Nb, Ti, V)C with a diameter of ~50 nm, distributed on ferrite, and the matrix/precipitated phase mismatch is 8.16%, forming a semicommon-lattice interface between the two. The carbon diffusion coefficient model shows that increasing the Nb content can inhibit the diffusion of carbon atoms and reduce the ILS. The yield strength of the high-Nb steel is 556 MPa, and the tensile strength is 764 MPa.

Influence of V on the Microstructure and Precipitation Behavior of High-Carbon Hardline Steel during Continuous Cooling.

High-carbon hardline steels are primarily used for the manufacture of tire beads for both automobiles and aircraft, and vanadium (V) microalloying is an important means of adjusting the microstructure of high-carbon hardline steels. Using scanning electron microscopy (SEM), X-ray diffraction (XRD), and transmission electron microscopy (TEM), the microstructure and precipitation phases of continuous cooled high-carbon steels were characterized, and the vanadium content, carbon diffusion coefficient, and critical precipitation temperature were calculated. The results showed that as the V content increased to 0.06 wt.%, the interlamellar spacing (ILS) of the pearlite in the experimental steel decreased to 0.110 μm, and the carbon diffusion coefficient in the experimental steel decreased to 0.98 × 10-3 cm2·s-1. The pearlite content in the experimental steel with 0.02 wt.% V reached its maximum at a cooling rate of 5 °C·s-1, and a small amount of bainite was observed in the experimental steel at a cooling rate of 10 °C·s-1. The precipitated phase was VC with a diameter of ~24.73 nm, and the misfit between ferrite and VC was 5.02%, forming a semi-coherent interface between the two. Atoms gradually adjust their positions to allow the growth of VC along the ferrite direction. As the V content increased to 0.06 wt.%, the precipitation-temperature-time curve (PTT) shifted to the left, and the critical nucleation temperature for homogeneous nucleation, grain boundary nucleation, and dislocation line nucleation increased from 570.6, 676.9, and 692.4 °C to 634.6, 748.5, and 755.5 °C, respectively.

Enhanced carburization efficiency and performance of vacuum carburized layers by La2O3-doped supersonic fine particle bombardment

In this work, the fabrication of supersonic fine particle bombardment (SFPB)-doped rare-earth pretreatment modified vacuum carburized layers were applied. The SFPB-doped La2O3 pretreated vacuum carburized reinforced layer was explored by common testing methods such as XRD, XPS, SEM, and TEM, focusing on the effects of La2O3-doped SFPB pretreatment on the decomposition, adsorption and diffusion of active carbon atoms and the diffusion mechanism. The composite carburizing behavior of La2O3-doped SFPB pretreatment modified layer under the action of thermal coupling is explored, and the influence law of rare earth modified carburizing and nano-modified carburizing on the thickness, residual stress, impact toughness, tribological properties of the carburized layer were clarified. The mechanism of mass transfer under the coupling role of pre-set surface defects and rare earth pinning was revealed. The case depth of the LSPC layer was increased by 14.3%, and the residual stress was significantly higher. The carbon diffusion coefficients of LSPC were 1.31 times superior to that of the vacuum carburizing layer, which is mainly attributed to the formation of a large number of nanocrystals with high-angle grain boundaries (HAGBs) by the rare-earth doped nanosized pretreatment, and the multiple synergistic strengthening effects of rare-earth oxides and nanocrystals.

Effects of gas to water ratio and nano-Cu dosage on CH4 hydrate growth: A combined molecular simulation and experimental study

Natural gas hydrate (NGH) is a highly promising alternative for gas storage and transportation. Nevertheless, the artificial generation of gas hydrates faces considerable obstacles for large-scale commercial implementation, primarily due to its slow formation rate and inadequate storage density. This study delves into the effects of gas to water ratios and metal nanoparticle dosages on the synthesis of NGH. Molecular dynamics (MD) simulations were employed to examine the formation of CH4 hydrate under varying gas to water ratios and metal nanoparticle concentrations. The investigation assessed critical parameters of the gas–water system, such as radial distribution function, carbon storage ratio, hydrate cages, potential energy, diffusion coefficient, and thermal conductivity. For the first time, Pearson's correlation coefficient analysis was utilized to discern the interrelationships among these factors. The results demonstrated that medium gas to water ratios led to increased carbon storage, a higher number of cages, and augmented energy consumption. The nano-Cu dosage impacted the stability of hydrates and the thermal conductivity of the gas–water system, particularly at elevated gas to water ratios. Drawing on the MD simulation findings, a design factor was introduced to appraise the performance of the multicomponent system, which in turn, informs the development of a high-performance NGH formation system. The effectiveness of the design factor was corroborated through laboratory experiments, revealing its robust potential for designing high-performance NGH systems. This research paves the way for the practical realization of efficient hydrate-based production in real-world applications.

Properties of carbon up to 10 million kelvin from Kohn-Sham density functional theory molecular dynamics.

Accurately modeling dense plasmas over wide-ranging conditions of pressure and temperature is a grand challenge critically important to our understanding of stellar and planetary physics as well as inertial confinement fusion. In this work, we employ Kohn-Sham density functional theory (DFT) molecular dynamics (MD) to compute the properties of carbon at warm and hot dense matter conditions in the vicinity of the principal Hugoniot. In particular, we calculate the equationof state (EOS), Hugoniot, pair distribution functions, and diffusion coefficients for carbon at densities spanning 8 g/cm^{3} to 16 g/cm^{3} and temperatures ranging from 100 kK to 10 MK using the Spectral Quadrature method. We find that the computed EOS and Hugoniot are in good agreement with path integral Monte Carlo results and the sesame database. Additionally, we calculate the ion-ion structure factor and viscosity for selected points. All results presented are at the level of full Kohn-Sham DFT-MD, free of empirical parameters, average-atom, and orbital-free approximations employed previously at such conditions.

Measurements of Carbon Diffusivity and Surface Transfer Coefficient by Electrical Conductivity Relaxation during Carburization: Experimental Design by Theoretical Analysis

The diffusion coefficient (D) and surface transfer coefficient (β) of carbon are important parameters governing the kinetics of carburization, and some other heat treatment processes accompanied by redistribution of carbon in steel. Here, we propose to use an electrical conductivity relaxation (ECR) method for the in situ measurement of D and β of carbon. The feasibility of the method is discussed by the theoretical modeling of carburization for an infinitely long rectangular sample. The synthetic ECR data for the carburization is simulated by tracking the relaxation of electrical conductivity upon a sharp or a gradual change of carbon potential. Then, by Fourier transform, the synthetic ECR data is transformed to an impedance spectroscopy, which is used for estimation of D and β by fitting with a one-dimensional equivalent circuit model. The effects of the width-to-thickness ratio of the sample and the duration of carbon potential buildup on the accuracy of the estimated D and β are studied. The feasibility of the ECR method is verified, and rational guidance for experimental design is proposed.

Development of a statistical model for calculating the carbon diffusion parameters in iron and steels

Carbon diffusion in metals has received a lot of attention and has been the subject of intensive theoretical investigations in recent years. The purpose of this work is development a simple statistical model of the carbon atoms diffusion in the crystal lattice of metals and its application for calculating the diffusion coefficients of carbon atoms in iron and steel. The relationship between the diffusion flux of atoms and the gradient of their chemical potential, as required by non-equilibrium thermodynamics, is obtained from the basic principles of statistical thermodynamics. For a real solid solution of impurity atoms in a metal, an expression is found for the diffusion coefficient, the value of which depends on physical constants, the atomic weight of the solute, the square of the temperature and activity i-element in solid solution. The calculations have a good agreement with the known experimental data on the diffusion of carbon atoms in iron and steels and is higher than in classical atomic diffusion models. The activation energy of carbon diffusion in γ- phase of various steels has values close to 120 kJ. Proposed formula well describes the deviation of the carbon diffusion coefficient from the Arrhenius law at medium and high temperature.

Hierarchical microstructure growth in a precursor‐derived SiOC thin film prepared on silicon substrate

AbstractSilicon oxycarbide film deposited on a silicon substrate has shown superior electrical conductivity relative to its monolithic counterpart. In this work, the evolution of different microstructures detected on the SiOC film reveals its hierarchical microstructure. The existence of sp2‐hybridized carbon domains has been unambiguously confirmed by means of Raman spectroscopy and transmission electron microscopy corroborated with electron energy loss spectroscopy. The diffusion coefficient of carbon in silica and its dependence on temperature were studied by assessing energy‐dispersive X‐ray spectroscopy profiles taken from the cross‐sections of samples annealed at temperatures in the range from 1100°C to 1400°C. The activation energy for diffusion of carbon in silica was determined to be approximately 3.05 eV, which is significantly lower than the values related to the self‐diffusion of silicon and oxygen. The microstructural evolution of precursor to SiCnO4‐n and SiC serves as migration path of sp2‐hybridized carbon to the SiOx layer. With increasing temperature, the formation of microscale carbon‐rich segregation is promoted while the SiOC film becomes thinner.

Strengthen Synergistic Effect of Soft Carbon and Hard Carbon Toward High-Performance Anode for K-Ion Battery.

Synergistic effect of soft carbon and hard carbon has been proven to be useful for obtaining excellent anode materials for potassium ion battery, which is determined by the mixing degree of precursors. Inspired by the formation of proteins in biology, peptide bonds are used to connect the precursors of the two sort of carbon to prepare soft-hard hybrid carbons with stronger synergistic effects. The hard carbon domain with nanometer size is so highly distributed in the soft carbon that the synergistic effect between two sorts of carbon is significantly enhanced. After the optimization, the diffusion coefficient of as-prepared hybrid carbon (CSHC3-6-1200) is 10 times larger than that of corresponding carbon synthesized by physical method. Consequently, CSHC3-6-1200 can maintain a specific capacity of 71.6 mAh g-1 at a high current density of 1600 mA g-1. It is believed that this new preparation route may bring a new perspective to the development of soft and hard composite carbon material anodes with high power density and ultralong service life.

Mesoporous Carbon as Conductive Additive to Improve the High‐Rate Charge/Discharge Capacity of Lithium‐Ion Batteries

The infiltration ability of electrolytes in to the electrode is vital to the high‐rate charge/discharge capacity of lithium‐ion batteries (LIBs). Herein, mesoporous carbon is used with abundant and continuous mesoporous channels as the conductive additive in LIBs to enhance the infiltration of electrolytes. The Li+ diffusion coefficient of the mesoporous carbon is 1.65 × 10−9 cm s−1, much higher than that of carbon nanotubes (2.5 × 10−10 cm s−1) and carbon black (1.6 × 10−10 cm s−1). It is demonstrated that LiFePO4 cathode‐based LIBs using mesoporous carbon as the conductive additive exhibit excellent high‐rate charge/discharge capacities of 121 mAh g−1 at 5 C and 54 mAh g−1 at 30 C. When the compaction density of the LiFePO4 electrode increases from 0.7 to 1.3 g cm−3, the LIBs can still deliver a capacity of 101 mAh g−1 at 3 C. This work paves a new route to facilely improve the quick charge/discharge performance of LIBs.

Microstructure of Ultrafine Acicular Bainite and Mechanical Properties of 3Cr2MnNiMo Mold Steel during Austempering

Herein, the effect of austempering treatment on martensite/bainite multiphase microstructure evolution and mechanical properties of 3Cr2MnNiMo mold steel are investigated, and the mechanical properties are compared with the conventional quenching and tempering (QT) treatment. It indicated that the morphology of martensite/bainite can be effectively tailored by changing the austempering temperature. With the increase of temperature from 280 to 360 °C, the microstructure changes from tempered martensite + bainite + blocky retained austenite (RA) to martensite + coarse bainite plate + blocky RA and irregular martensite/austenite (M/A) island. When the temperature reaches 420 °C, the martensite content reaches the maximum. The bainite morphology is surprisingly transformed from coarse bainite plate to ultrafine acicular shape owing to the reduction of the bainitic driving force and the sharp increase of carbon diffusion coefficient. Moreover, blocky RA and M/A islands disappear and are replaced by nanoscale filmy RA. The alternating distribution of variants has a refinement effect on the microstructure and the effective grain size reaches a minimum value. Compared with the conventional QT treatment, the tensile strength of austempering at 420 °C increased by 702 MPa, but the toughness and ductility levels are almost the same.

Improving mechanical properties in high-carbon pearlitic steels by replacing partial V with Nb

The effects of combined addition of niobium (Nb) and vanadium (V) on the transformation, microstructure and mechanical properties of high-carbon pearlitic steels were investigated. In-situ observations on a high-temperature laser scanning confocal microscope (LSCM) were conducted to study the pearlitic transformation, the results from which indicate that single V or combined Nb and V addition led to higher transformation temperature and more pearlitic nucleation sites. But the growth rate of pearlite was significantly impeded due to the smaller diffusion coefficient of carbon, resulting in the refinement of the interlamellar spacing and nodule size of pearlite. In addition, compared to the base steel, single V addition in high carbon pearlitic steels was beneficial to the increase of strength, but it deteriorated the toughness, whereas the composited addition of Nb and V resulted in the increase of strength without the expense of the toughness. It is concluded that replacing part V with similar content of Nb is very promising since the impact toughness of the Nb + V steel is increased by 21% without the expense of the strength compared to the V-microalloyed steel. Nb and V strengthened pearlitic steels primarily due to the precipitation of M(C,N), thinner pearlite interlamellar spacing and smaller pearlite nodule size. Compared to the V steel, the improvement of toughness in Nb + V steel was mainly attributed to the smaller nodule size and more uniform grain size distribution. In summary, under the premise of similar microalloying element amount in high-carbon (∼0.77 wt%) pearlitic steels, replacing part V with Nb is beneficial to obtain the finest microstructure and the best comprehensive mechanical properties.

Glucosamine derived hydrothermal carbon electrodes for aqueous electrolyte energy storage systems.

Nitrogen-doped porous hard carbons are synthesized by hydrothermal carbonization method (HTC) using glucosamine as biosource and treated at different carbonization temperatures in nitrogen environment (500, 750, 1000 °C). The electrochemical performances of hard carbons electrode materials for aqueous electrolyte sodium ion batteries are examined to observe the effect of two different voltage ranges (-0.8-0.0) V and (0.0-0.8) V in 1.0 M Na2SO4 aqueous electrolyte. The best electrochemical performances are acquired for the 1000 °C treated glucosamine (GA-1000) porous carbon sample that provides ~96 F/g capacitance value in the negative voltage range (between -0.8 and 0.0) V. The sodium diffusion coefficient of the GA-1000 carbon calculated by electrochemical impedance measurements is found to be 1.5 × 10-14 cm2/s.

Diffusion coefficients of carbon, oxygen and nitrogen in silicon melt

The carbon, oxygen and nitrogen are very important light impurities affecting the quality of silicon crystal used in photovoltaic and semiconductor industry. The diffusion coefficients are key parameters in determining the impurity distribution in the melt and crystal. Unfortunately, these parameters are rarely measured by experiments due to challenges of high temperature and complex flow in the melt during crystal growth. Nonetheless, the liquid diffusion coefficients exist as necessary input parameters in the continuum modelling work of mass transport. Here, we first reviewed the liquid state diffusion coefficients used in the continuum models and found out that they are far from consistency. Then, molecular dynamics simulations are employed to calculate the diffusion coefficients and migration barriers of the carbon, nitrogen and oxygen impurities in silicon melt based on various empirical interatomic potentials. The nitrogen diffusivity in silicon melt is reported for the first time. The calculated diffusion coefficients are generally lower than the values used in most continuum models although consistent across different potentials. This discrepancy is discussed in detail.

Effect of molecular structure on low-temperature properties of bitumen based on molecular dynamics

Low-temperature cracking is one of the most prevalent distress in asphalt pavement, closely related to the bitumen low-temperature properties. However, the molecular mechanism of low-temperature properties of bitumen is still ambiguous. This paper focuses on studying the effects of molecular structure on the low-temperature properties of bitumen by molecular dynamics (MD) simulation. The low-temperature viscoelasticity and glass transition temperature of bitumen were measured by dynamic shear rheometer (DSR) and differential scanning calorimeter (DSC) experiment. The MD models containing 20 kinds of molecules were constructed to represent the bitumen and validated by density, shear modulus and glass transition temperature. Furthermore, the effects of molecular structure on the low-temperature properties were analyzed by relative density, mean square displacement (MSD), radial distribution function (RDF), and potential energy. The DSR and DSC results showed that the low-temperature properties ranking of the bitumen is HY90 > LH50 > LH90 > LH70. The relative density and RDF curves showed that the increasing aromatic carbons in resins and aromatics reduce the asphaltenes aggregation degree and improve the low-temperature properties by promoting the formation and dispersion of asphaltene-resin aggregates. The MSD curves indicated that the bitumen with a high average diffusion coefficient has good low-temperature properties. The increase of aromatic carbons improves the diffusion coefficient by forming molecules with low molecular mass. Moreover, non-bond energy positively correlates with the low-temperature properties of bitumen. The low-temperature properties of bitumen can be optimized by increasing the resins and aromatics, or adding molecules with high aromatic carbon content and diffusion coefficients.

Experimental determination of carbon diffusion in liquid iron at high pressure

Abstract The transport properties of liquid iron alloys at high pressure (P) and temperature (T) are essential for understanding the formation, composition, and evolution of planetary cores. Light alloying elements (e.g., Si, O, S, C, N, H) in liquid iron are particularly relevant due to the density deficit of Earth’s core, yet high P-T experimental diffusion studies involving such alloys remain scarce, with large uncertainties on the P and T dependence required for extrapolation to core conditions. In this study, we measured the chemical diffusion of carbon in liquid iron over a P-T range of 3–15 GPa and 1700–2450 K using a multi-anvil apparatus. Diffusion couples consisting of pure Fe and Fe-2.5 wt%C cylinders were placed end-to-end in an MgO capsule in a vertical orientation. Carbon concentration profiles were measured by electron microprobe and modeled numerically to correct for non-isothermal diffusion that occurred prior to reaching the peak temperature. Carbon diffusion coefficients range from 6 × 10−9 m2·s−1 to 2 × 10−8 m2·s−1, with global Arrhenian fit parameters D0 = 1.4 ± 0.5 × 10−7 m2·s−1, ΔE = 43 ± 6 kJ/mol, and ΔV = −0.06 ± 0.19 cm3·mol−1. A negligible P effect is consistent with previous studies of oxygen diffusion in liquid iron and high-T calculations but differs from larger ΔV values previously reported from carbon self-diffusion experiments for liquid Fe3C and simulations for an Fe-Ni–C alloy. Carbon diffusion coefficients determined here are approximately three times faster than those reported from Fe-Ni-C liquid simulations, which highlights the potential significance of compositional effects on mass transport properties of liquid iron alloys and the need for expanding the P-T experimental diffusion data set currently available in the literature to more complex and geologically relevant compositions.

Turbulent transport of impurities in 3D devices

The evidence of a large diffusive turbulent contribution to the radial impurity transport in Wendelstein 7-X (W7-X) plasmas has been experimentally inferred during the first campaigns and numerically confirmed by means of gyrokinetic simulations with the code stella. In general, the absence of strong impurity accumulation during the initial W7-X campaigns is attributed to this diffusive term. Given the large variety of possible stellarator configurations, in the present work the diffusive contribution is also calculated in other stellarator plasmas. In particular, a numerical cross-device comparison is presented, where the diffusion (D) and convection (V) coefficients of carbon and iron impurities produced by ion-temperature-gradient (ITG) turbulence are obtained. The simulations have been performed for the helias W7-X, the heliotron LHD, the heliac TJ-II and the quasi-axisymmetric stellarator NCSX at the radial position r/a = 0.75. The results show that, although the size of D and V can differ across the four devices, inward convection is found for all of them. For W7-X, TJ-II and NCSX the two coefficients are comparable and the turbulent peaking factor is surprisingly similar. In LHD, appreciably weaker diffusive and convective impurity transport and significantly larger turbulent peaking factor, in comparison with the other three stellarators, are predicted. All this suggests that ITG turbulence, although not strongly, would lead to negative impurity density gradients in stellarators. Then, considering mixed ITG/trapped electron mode (TEM) turbulence for the specific case of W7-X, it has been quantitatively assessed to what degree pellet fueled reduced turbulence scenarios feature reduced turbulent transport of impurities as well. The results for trace iron impurities show that, although their turbulent transport is not entirely suppressed, a significant reduction of the convection and a stronger decrease of the diffusion term are found. Although the diffusion is still above neoclassical levels, the neoclassical convection would gain under such conditions a greater specific weight on the dynamics of impurities in comparison with standard ECRH scenarios without pellet fueling.

Structure and mechanical properties of WC interlayers between iron substrate and thin tungsten plate

To improve the mechanical properties of cast iron (Fe) surface, tungsten carbide (WC) interlayers were fabricated by the in-situ reaction at 1050 °C and 1100 °C for different heat-treatment times. The structure and phase composition of the layer were investigated via scanning electron microscopy, transmission electron microscopy and X-ray diffraction analyses. The effect of vacuum atmosphere temperature on the interfacial structure of sample was discussed. The results indicate that the thickness of the layer, consisting of a dominant WC phase, has a range of 11.12 ± 1.32 to 51.51 ± 1.36 μm obtained at 1050 °C. Based on growth kinetics, the diffusion coefficient of carbon in the WC layer is calculated to be 1.57×10−9 cm2/s. Furthermore, under the load of 100 mN, nanoindentation tests demonstrate that values of hardness and elastic modulus of the layer are approximately 25.09–39.74 GPa and 649.54–834.17 GPa, which are 2.4–3.8 times and 3.5–4.4 times larger than that of the substrate, respectively. By means of Vickers indentation mode using the available equation for Palmqvist crack system, the value of the calculated fracture toughness for the layer changes in a range from 2.55 ± 0.14 to 6.34 ± 0.54 MPa⋅m1/2, and the value decreases with the increasing load. This result may be caused by the reason that the fracture resistance also strongly depends on the applied load.

Modeling and simulation of dissolution process of bulk carbide in Fe–1C–1.44Cr low-alloy steel

Because of the complex morphology of bulk carbides in the core of as-cast bearing steel, their dissolution process is complicated to model, since it is difficult to rationally simplify the bulk carbides using a simple geometric shape. In this study, a metallographic image of an actual bulk carbide is transformed into a two-dimensional physical model. A dissolution model for such bulk carbides is established using thermodynamic and kinetic methods, where the diffusion coefficients for carbon and chromium in austenite and the solute concentrations at the phase interface are calculated assuming local equilibrium conditions. The calculation results from the model are compared with the experimental values, after the bearing steel was soaked at 1150 °C, 1175 °C and 1200 °C, the difference between the measured area of bulk carbides in the core and the model calculation results was 65 μm2, 12 μm2 and 30 μm2, respectively.