Thermal/kinetic study of the formation mechanism of NbC-Fe composite layer on the surface of GCr15 prepared by hot pressure diffusion

In this study, an NbC-Fe composite layer is in situ prepared on the surface of GCr15 bearing steel. The formation mechanism of the composite layer was investigated in terms of thermodynamics, dynamics, and crystal structure transformation processes during the in situ reaction. According to computational thermodynamics, the reaction at 1150 °C–1200 °C allows NbC, Fe3C, Cr3C2, Cr7C3, and Cr23C6 phases to spontaneously react and stabilize in the Fe-C-Nb-CR system. The functional relationship between the growth thickness, time, and temperature of the NbC-Fe composite layer was obtained experimentally and via computational dynamics. Particularly, the growth activation energy, Q, of the NbC-Fe composite layer was calculated to be 367.06 kJ mol−1. The combination of computational thermodynamic/kinetic research and experimental observation of crystal transformation data revealed that the formation mechanism of NbC in the NbC-Fe layer on the surface of GCr15 caused the C atoms in the bearing steel diffuse into the Nb plate and occupy the octahedral gap of the Nb unit cell to form NbC. In the formation mechanism of the NbC-Fe composite layer, C and Fe atoms partially migrated from the pearlite and diffused towards the direction of the Nb plate to form the NbC-Fe composite layer.


Introduction
In view of the problems of low surface hardness, poor wear resistance, and corrosion resistance of steel materials, surface strengthening technology is widely used to prepare surface carbide reinforced composite layers to prolong the service life of the workpieces [1,2]. The current methods for producing surface carbide reinforcement layers include spraying [3,4], surfacing [5,6], vapor deposition [7][8][9], laser cladding [10,11], and vacuum dipping infiltration casting [12,13]. However, all the above methods still possess structural or functional shortcomings such as difficulty in obtaining high-volume fraction ceramic reinforced dense layers, poor interfacial bonding between the reinforced layer and the matrix, laboriousness of the process, long cycle, and high cost. The preparation process of the in situ reaction is simple, and the preparation cycle is short. Moreover, the composite layer and the steel matrix have a pure and impurity-free binding interface with a strong interfacial binding strength. This technique has been applied to the synthesis of carbide/iron surface composites [14][15][16], and the surface comprehensive mechanical properties of the obtained steel matrix composites were found to exceed those obtained via other surface technologies.
Common ceramic particle reinforcement phases include NbC, M 7 C 3 , WC, Al 2 O 3 , etc Amongst these phases, NbC possesses theoretical hardness and elastic modulus that can attain values of 23.5 GPa and 338 GPa, respectively. As strengthening phases, NbC and Fe have good wettability, resistance to interfacial reactions, and good semi-coherence between them [17,18]. When NbC is formed in situ in steel, it generally exhibits spherical, hemispherical, or nearly square sugar-like rounded structure in the nano, submicron, and micron scale.
Compared with M 7 C 3 complex phase in high chromium cast iron or coarse WC grains with sharp corners and edges, NbC does not easily fall off or crack under wear stress. In that regard, it can effectively protect the matrix and serve as an anti-wear phase. For certain composites, thermodynamic analysis is used to simulate the possible reactions under given conditions and to assess the stability of reaction products prior to experiments. For instance, the thermodynamic study of the growth law during the in situ formation of the reinforcement layers can reveal their formation mechanism and verify the accuracy of the experimental results. For example, M Labonne [19] et al calculated the grain growth constant KD of NbC by evaluating the NbC particle size in cemented NbC-12vol% Ni carbide after sintering at 1360°C Fan [20] et al described the growth kinetics of vanadium carbide coatings on steel surfaces during thermal reactive deposition/diffusion (TRD) by deriving the following mathematical model. Zhong [21] et al reported the preparation of tungsten carbide reinforced ironbased surface composites by in situ solid-phase diffusion method, and analyzed the dynamics of the tungsten carbide-iron layer by measuring its thickness variation with heat treatment time and temperature. The thickness of the pure tungsten carbide layer followed a parabolic relationship with heat treatment time, and the activation energy of this layer was 184.06 kJ mol −1 .
In this work, NbC-Fe composite layers with micro/nanostructures were prepared on the surface of a GCr15 bearing steel via in situ reaction. Rolled niobium sheet and GCr15 bearing steel matrix were used as raw materials to achieve the surface strengthening of the bearing steel matrix. Thermodynamic methods were applied to evaluate the feasibility of spontaneous reactions from left to right under given conditions, and to assess the stability of reaction products. The growth rate constant K and the activation energy Q of the NbC-Fe composite layer were calculated based on the cross-sectional thickness of the reinforcement layer using classical kinetic parabola theory and Arrhenius law. Also, the functional dependences of the growth thickness of the NbC enhanced layer on the holding time and reaction temperature were established. Finally, the grain growth mechanism and transformation in crystal structure associated with the in situ preparation of reinforcement layer of niobium plate/bearing steel were discussed.

Materials and methods
The raw material used to fabricate the bearing steel was GCr15 steel and the niobium (Nb) plate was rolled. The chemical compositions of the bearing steel and the niobium plate are listed in table 1. The specific preparation process is shown in figure 1. The bearing steel and Nb metal plate were cut with an electric spark molybdenum wire cutting machine to the dimensions required for the sample preparation. Among them, the specification size of bearing steel was 10 × 10 × 5 mm, and the size of Nb metal plate was 10 × 5 × 1 mm. To remove oxides from the contact surfaces of the cut pieces, the cut samples were ground in a stepwise manner using 120-to-2000mesh sandpapers. The treated niobium plate was then placed directly on the bearing steel and the assembled specimen was placed into a graphite crucible. Finally, the crucible with the sample was kept in a horizontal tube furnace for heating, heat preservation, and cooling treatment, and argon gas was supplied in, at a rate of 15 ml min −1 to prevent oxidation. The sample was heated up from room temperature to the specified temperature at a heating rate of 4°C min −1 , then cooled within the furnace to room temperature at the same rate.
The sample was sectioned longitudinally by wire EDM. The sample surface was initially ground with 120-2000 mesh sandpaper and subsequently polished with 1.5 μ and 0.5 μ diamond polishing agents on fine flannel cloth for 1 h and 30 min to remove scratches, respectively. During the polishing process, the samples were subjected to ultrasonic cleaning in a concentrated ethanol solution for 10 min intermediately. Afterward, 4% nitric acid alcohol was used to etch the polished surface of the sample. The microstructure and morphology of the gradient composites were observed using a Zeiss Merlin Compact field emission scanning electron microscope (FESEM), and the composite layer thickness was measured and counted in combination with Smile View software. A wire cutting machine was used to cut the composite layer from the center to obtain a cylindrical plate with a diameter of Φ3 mm and a thickness of 1 mm. NbC ceramic particles in the composite layer and the NbC-NbC interface were characterized using a JSM-3010 transmission electron microscope (TEM).

Results and discussion
3.1. Thermodynamics of Fe-C-Nb-Cr system The NbC-Fe composite layer was formed in situ at the interface between the metal Nb plate and the steel matrix. During this process, Nb atoms were released and migrated from the high-purity niobium plate, whereas the GCr15 steel matrix provided the reaction with Fe and C atoms. As a result, the Fe-C-Nb-Cr reaction system was produced in the interface micro-reaction zone. In this research, the potential function method was used to calculate the Gibbs free energy of the Fe-C-Nb-Cr system, which was characterized with several chemical reactions. Based on phase diagram analysis and standard thermodynamic calculations [22,23], the possible products in this reaction process include NbC, Nb 2 C, Fe 3 C, Cr 3 C 2 , Cr 7 C 3 , Cr 23 C 6 , and other phases. The standard Gibbs free energy ΔG θ is the criterion for determining whether a reaction can occur in the direction under the conditions of the standard state ( = = q P P T K 105 a, 298 ). However, this characteristic does not reflect the parameters of the real system because the thermodynamic function in real solutions is calculated using the activity (effective concentration) instead of the actual concentration. The mass fraction of each component in the Fe-C-Nb-Cr system can be determined according to the maximum solubility of each alloy element in iron [24]. In particular, the maximum solubility of Nb in Fe is 2.0%, the corresponding values of C in α-Fe and γ-Fe are 0.02% and 2.1%, respectively, and that of Cr in Fe is 4.5%. The activity coefficients of Nb, C, and Cr components introduced into the Fe-C-Nb-Cr system at 1873 K are =lgf 1.029; respectively. The interaction coefficients at different temperatures can be obtained separately from the handbook of metallurgical thermodynamics [25]. At the in situ reaction temperature of 1150°C (1423 K), the activity coefficients of each component in the system are respectively. The reaction Gibbs free energy results of reaction products that may exist in the Fe-C-Nb-Cr system are calculated by the thermodynamic potential function method as follows: Figure 2 displays the Gibbs free energies of NbC, Nb 2 C, Fe 3 C, Cr 3 C 2 , Cr 7 C 3 , and Cr 23 C 6 reaction products in the Fe-C-Nb-Cr system as functions of temperature. According to the plots, the Gibbs free energies of NbC, Fe 3 C, Cr 3 C 2 , Cr 7 C 3 , and Cr 23 C 6 are all below zero, within the temperature range under consideration. This implies that resultant phases can spontaneously be formed through the in situ reaction. However, in GCr15 steel, Cr exists in the form of carbides, which are mainly composed of Cr elements dissolved in Fe 3 C to form (Fe, Cr) 3 C composites [26]. Meanwhile, the Cr carbides in the Fe-C-Nb-Cr system do not participate in the reaction. Therefore, the formation of NbC in the composite structure might be possible at this test temperature.

Calculation of growth kinetics of NbC-Fe composite layer
The formation of the NbC-Fe composite layer at the interface of the niobium plate-steel matrix system was dominated by the in situ chemical reaction between various atoms. In this respect, the growth rate of the composite layer could be affected by many factors, namely, the diffusion rates of Nb, C, Fe, Cr, and other atoms, the rates of chemical reaction between the atoms, the interface properties, as well as the elemental distribution    According to equation (9), the square of thickness, y 2 , of the NbC-Fe composite layer is proportional to the reaction-diffusion time, t. In the experiment, the in situ reaction temperatures were 1150°C, 1175°C, and 1200°C, and the reaction times were 10, 20, 30, and 40 min. The composite layer thickness was measured, and the corresponding results are shown in figures 3-4. The thickness of composite layer increased with the increase in reaction time. In the same reaction time, the higher the temperature, the greater the thickness of composite layer.
The thicknesses of the resultant interfaces, under varying holding temperatures and times, were obtained, as shown in figure 3−4. Figure 5 illustrates the relationship between the interfacial thickness and holding times under varying soaking temperatures. Figure 6 depicts the square of thickness, y 2 , of the NbC-Fe composite layer as a function of growth time, t, under different holding conditions. The plots were fitted according to equation (9), revealing the linear relationship between y 2 and t. The slopes of the fitted lines corresponded to the growth rate constants K of the NbC composite reinforcement layer at different holding temperatures. The fitting correlation coefficients R 2 for the three straight lines in the figure were all above 0.9, which indicated that the growth rate constant K under different temperature conditions was an effective value. For the temperature set in the experiment, the growth rate constants were K 1150°C = 4.95 × 10 -10 m 2 s -1 , K 1175°C = 7.96 × 10 -10 m 2 s -1 , and K 1200°C = 1.42 × 10 -9 m 2 s -1 . At the same temperature, the growth rate constant K of the NbC enhanced layer remained unchanged but increased with the increase in temperature.
The relationship between the diffusion activation energy Q and the growth rate constant K of the NbC-Fe composite layer can be established by taking the natural logarithms of both sides of the Arrhenius equation [29,30]: Figure 7 displays the lnK parameter as a function of 1/T. According to equation (10), the diffusion activation energy, Q, of the NbC-Fe composite layer was 367.06 kJ/mol and the pre-exponential factor, K 0 , was as high as 1.4 × 10 4 . Substituting the values of Q and K 0 into the Arrhenius equation gives: According to equation (11), the diffusion coefficient K of the system can be calculated at any temperature from the temperature range under consideration. Thus, the diffusion coefficients of the NbC-Fe composite layer at the in situ reaction temperatures of 1150°C, 1175°C, and 1200°C were calculated as K 1150calculated = 4.68 ×  10 -10 m 2 s -1 , K 1175calculated = 8.03 × 10 -10 m 2 s -1 , and K 1200calculated = 1.35 × 10 -9 m 2 s -1 , respectively. The experimental data and calculation results are summarized in table 2.
With the substitution of the equation (11) of temperature T and diffusion coefficient K into the expression (9), the relationship between the layer thickness of the NbC-Fe composite layer and the reaction temperature and time can be obtained as follows: where y is the layer thickness of the NbC-Fe composite layer, in m; t is the reaction time, in s; and T is the reaction temperature, in K.

Formation mechanism of NbC-Fe composite layer
The formation mechanism of NbC particles was observed using TEM, which is shown in figures 8(a)-(c). The morphology of NbC ceramic particles in the dense layer mainly appeared as nearly circular, triangular, and quadrilateral, with an average grain size of about 200−500 nm. Figures 8(e)-(g) correspond to the electron diffraction pattern calibration results of the labeled grains in figures 8(a)-(c), respectively. The analysis showed that the NbC ceramic particles with different morphologies were all rock salt face-centered cubic structures of Fm-3m (225). At the initial stage of the in situ reaction of the system, the nucleation rate of NbC is large, and smaller NbC grains are formed, thus forming a dense NbC layer. Extending the holding time, the fine NbC grains in the dense layer become larger according to the Oswald curing mechanism, that is, the smaller grains integrate into bigger grains to form fewer number of grains. The reduction of the interfacial energy of the system provides a driving force for this growth process. The grown NbC grain appeared as a cubic structure and diffused continuously into the bearing steel matrix, thus forming an NbC gradient layer, as shown in figure 8(d). Consequently, the thickness of the NbC gradient layer increased with the extension of the holding time. Figure 9 shows the TEM image of the dense NbC ceramic region. The image was taken from the middle region of the composite layer, and the sample is heated to 1150°C and kept at this temperature for 30 min.  According to figure 6(a), the particles in the NbC composite layer were tightly bound to each other, and their dimensions varied uniformly between 100 and 200 nm. Moreover, the NbC grains had regular polygon shapes with clearly defined grain boundaries without any precipitations. Figure 6(b) depicts the high-resolution TEM micrograph of the grain boundary shown with a white arrow in image (a). The atomic dislocation region at the grain boundary was small, and the grain boundary stress was low. According to the thermodynamic calculation results, the formation of the NbC phase in the Fe-C-Nb-Cr system was spontaneous at the temperatures under consideration and ΔG NbC < 0. Since Nb is a transition metal element and a strong carbide element, and C is a non-metal element, it is easy for Nb to react with C to form NbC in the Fe-C-Nb-Cr system. The C-to-Nb radius ratio is R C /R Nb = 0.91/2.09 = 0.438. According to the Hagg principle, when 0.41 < R C /R Nb < 0.59, C diffuses into Nb to form a simple interstitial phase. Meanwhile, the Nb lattice has a body-centered cubic (bcc) structure with a tetrahedral gap radius of 0.291R Nb , which is not enough  to accommodate C atoms. On the other hand, the octahedral gap radius in the 〈110〉 direction is 0.633 R Nb , therefore, C atoms can fill the space to such a size in the octahedral gap. Figure 10 displays a schematic diagram of the structural transition from a simple Nb unit cell to the composite NbC structure.
During the formation of the NbC-Fe composite layer, C and Fe atoms were partially dissociated from the pearlite and diffused toward the Nb plate due to the existence of the chemical potential gradient. At the same time, the Nb atoms were partially desorbed and dissociated from the surface of the metal Nb plate. The dissociated Nb atoms also diffused toward the steel matrix under the action of the chemical potential gradient, and reacted with C atoms to form NbC, while a few Fe atoms existed in the NbC composite layer. The diffusion process of each atom is shown in figure 11. Since the Nb plate was in direct contact with the substrate, the diffusion distance of C atoms into Nb was the shortest, whereas their diffusion flux was the largest in the initial reaction process. Hence, a submicron NbC dense ceramic region would be formed as the nucleation rate was highest at the initial interface. In the course of the reaction, the reaction interface continued to grow inwardly, and the diffusion flux of carbon atoms gradually decreased, mainly because the diffusion distance increased, and the formed carbide layer acted as a diffusion barrier to hinder further migration of carbon atoms. Therefore, as the reaction progressed and the distance from the initial reaction interface gradually increased, the concentration of C atoms, as well as the nucleation rate of NbC decreased. This enabled the NbC grains to grow  into a gradient NbC composite layer that transitioned from smaller grains to larger grains towards the Nb plate side of the composite layer.

Conclusions
In this paper, NbC-Fe composite layer was prepared on the surface of GCr15 bearing steel by in situ method, based on the strong carbide formation characteristics of Nb, the rapid diffusion of C atoms, adequate melting of contact surfaces, and mass transfer within the steel matrix. The feasibility of in situ reaction and the controlled preparation of the reinforced layer were predicted based on thermodynamics and kinetics, respectively. Moreover, the crystal structure transformation and the formation mechanism of the composite layer during the in situ reaction were analyzed. The following conclusions were drawn: (1) The Gibbs free energy of each reaction product (NbC, Fe 3 C, Cr 3 C 2 , Cr 7 C 3 , and Cr 23 C 6 ) in the Fe-C-Nb-Cr reaction system was calculated using the thermodynamic potential function method. It was found that the above phases could stably exist within the temperature range under consideration.
(2) The growth rate constants of the NbC-Fe composite layer at the relevant temperatures were K 1150calculated = 4.68 × 10 -10 m 2 s -1 , K 1175calculated = 8.03 × 10 -10 m 2 s -1 , and K 1200calculated = 1.35 × 10 -9 m 2 s -1 , which were consistent with the experimental results. The diffusion activation energy of the NbC-Fe composite layer was calculated using the Arrhenius law to be 367.06 kJ/mol. Finally, the functional relationship was established between the thickness of the composite layer, the holding time, and the reaction temperature as =´´y t T 118.32 exp 44149 . ⎛ ⎝

⎞ ⎠
This meant that the in situ growth process of the composite layer conformed to the classical kinetic parabola theory.
(3) The formation of the NbC phase was due to the rapid diffusion of C atoms from the matrix into the Nb plate and their subsequent occupation of the octahedral gaps in the Nb unit cell. At the interface between the Nb plate and the bearing steel matrix, there were relatively more dissolved Nb atoms and abundant C atoms. Moreover, the nucleation rate of NbC was much higher than the growth rate of NbC, leading to the emergence of a submicron, dense ceramic region in the outermost layer, which gradually moved away from the interface. As a result, the concentration of C atoms slowly decreased and the gradient NbC ceramic layer was formed.
(4) In this paper, the controlled preparation of the NbC reinforcement layer on the surface of the steel matrix was achieved. The grain growth and phase transition involved in the in situ preparation of the NbC reinforcement layer were discussed. The determination of the process parameters of developed NbC reinforcement layer on the surface of steel matrix provides a certain theoretical basis for industrial practice. Furthermore, it is suggested that a certain pressure can be introduced in production to improve the efficiency of the in situ reaction and the quality of the composite layer.