Grain Boundary Segregation Behavior and Thermodynamic Analysis Based on CALPHAD Method for B Added High Carbon Steel

Abstract

Segregation behaviors on the prior austenite grain boundaries for the B-doped high C case hardening steel (Fe-0.82C-0.22Si-0.86Mn-0.02P-1.1Cr-0.21Mo-0.005B (mass%)) were evaluated using a three-dimensional atom probe (3DAP). Results revealed the intense segregation of C, Mo, Cr, and B on the grain boundaries. Findings also confirmed suppression of the segregation of P, known as a strong segregation element for steel. Thermodynamic analysis based on the parallel tangent law by McLean–Hillert was conducted to validate the segregation of each element. To evaluate the chemical potentials while taking interaction with multiple elements into account, the Calculation of Phase Diagram (CALPHAD) method was used, where liquid phase was adopted to estimate the Gibbs free energy of grain boundaries. The calculation results represent the segregation tendencies obtained from 3DAP. Detailed investigations of the interaction effects of C, B, and Mo on the other elements were also conducted. Results showed the suppression of P segregation by increasing the B content, therefore demonstrating the efficiency of the segregation prediction method which implemented CALPHAD for the B-added high C steels.

 

This Paper was Originally Published in Japanese in J. Japan Inst. Met. Mater. 87 (2023) 193–199. Figure 6 was slightly modified.

1. Introduction

Addition of a small amount of B is well known to improve the hardenability of steels because of the lowered grain boundary energy of austenite (γ). Strong grain boundary segregation of B retards the heterogeneous nucleation of ferrite (α) on γ grain boundaries during cooling.^1–4) Because reduction of the grain boundary energy also increases the grain boundary strength, improved fatigue and impact strengths of structural steels by doping B have been reported because of grain boundary crack suppression.^5–7)

Improvement of hardenability by doping B varies along with materials’ production conditions and alloy compositions. Earlier reports have described that segregation of B on γ grain boundaries is influenced strongly by metallurgical phenomena in hot deformation: recrystallization generating new grain boundaries, diffusion of B to segregate on the newly generated grain boundaries, and formation of M₂₃(C,B)₆ precipitates on the grain boundaries. These findings suggest that designing an appropriate process is necessary to obtain the desired high strength by direct quenching process after hot rolling in B-added steels.⁸⁾ Regarding the effects of alloying elements on the grain boundary segregation in steels, an increase in C content reportedly tends to suppress the grain boundary segregation of P.^9,10) It has also been reported that addition of B suppresses the grain boundary segregation of P.¹¹⁾ Some reports have described that addition of Mo, B, V, Mn, and Si showed no apparent influences on the grain boundary segregation of P.^10,12) Because multiple elements including unavoidable impurities are included in commercial structural steels, it is important to understand interactions between B and other elements for the alloy design and process control of B-added high-strength steels.

Many studies of grain boundary segregation behavior of solute B in the A–B binary system have been reported, based on the grain boundary phase model proposed by McLean and Hillert,¹³⁾ taking the parallel tangent law, where the chemical potential differences between elements A and B in the matrix and the grain boundary phases are equal. The theory has been extended to ternary systems: Guttmann analyzed grain boundary segregation behaviors in a ternary system based on the McLean–Hillert model, considering interactions between the two segregated elements.¹⁴⁾ However, because of a lack of experimentally obtained data for grain boundary segregation energies and interactions among the alloying elements, applying the model to multicomponent systems such as commercial structural steels is difficult.

The Calculation of Phase Diagram (CALPHAD) method enables thermodynamic calculations for multicomponent systems with an extensive database of thermodynamic parameters including interaction parameters among various elements. Applying the CALPHAD method for the McLean–Hillert model is expected to enable the thermodynamic calculation of grain boundary segregation behaviors in multicomponent systems. Takahashi et al. analyzed grain boundary segregation behavior of B and Mo in an Fe-Mo-B ternary system with the McLean–Hillert model, applying the CALPHAD method with their assessed thermodynamic parameters.¹⁵⁾ Ohnuma showed the segregation tendencies of P and S on grain boundaries in Cu-based alloys using thermodynamic calculation based on the McLean–Hillert model applying the CALPHAD method.¹⁶⁾ Motomura et al. reported grain boundary segregation behavior of N in α phase steel¹⁷⁾ and Tokunaga et al. demonstrated the effects of alloying elements on the grain boundary segregation of B in α phase steel¹⁸⁾ with thermodynamic calculations based on the McLean–Hillert model using the CALPHAD method. Usually, the Gibbs free energy of the liquid phase is used for the free energy of the grain boundary phase in the McLean–Hillert treatment, regarding the grain boundary phase as the supercooled liquid phase with the random atomic structure.¹⁹⁾ No report has described a theoretical study examining grain boundary segregation behavior in multicomponent commercial steels, based on the McLean–Hillert model and using the CALPHAD method.

For this study, segregations of B and other elements on prior γ grain boundaries were investigated using a three-dimensional atom probe (3DAP) in B-added case-hardened steel containing high C of 0.82 mass%, which has similar C content to that of carburized steels. Thermodynamic calculations of grain boundary segregation were conducted based on the McLean–Hillert model using the CALPHAD method. Good agreement obtained between the experimentally obtained and calculated results showed the effectiveness of the calculation method for estimating grain boundary segregation in multicomponent steels. Changes in the grain boundary segregation with the alloy composition in multicomponent steels have also been discussed based on thermodynamic calculations applying the CALPHAD method.

2. Experimental

2.1 Sample preparation

Table 1 shows the chemical composition of the sample, as analyzed using inductively coupled plasma atomic emission spectroscopy (ICP). The sample is equivalent to SCM420, however contained high C of 0.82 mass%, which was equivalent C content to that of a carburized steel, and a small amount of B of 0.0050 mass%. The sample was prepared using induction melting with soft magnetic iron (SUY; JIS C 2504), electrolytic pure iron, graphite, pure Si, pure Mn, ferromolybdenum, and ferroboron under Ar atmosphere. The melt was cast into a metal mold. Consequently, a 1.8 kg ingot was obtained. The ingot was deformed to a 9 mm diameter bar through high temperature rolling and swaging processes. The bar was heated to the γ phase region of 950°C for 30 min with subsequent oil quenching to ambient temperature. A cylindrical test piece of 7 mm diameter and 11 mm height was machined from the bar. After it was heated to 950°C with the heating rate of 10°C/s and held at the temperature for 300 s, it was quenched to ambient temperature using He gas. The heat treatment was done using a thermomechanical treatment simulator (Thermecmastor Z; Fuji Electronic Industrial Co. Ltd.). The heating temperature of 950°C was chosen to simulate the carburization process. The average grain size of the prior γ grains was 22 µm.

Table 1 Chemical composition obtained from ICP and equilibrium matrix composition of the sample at 950°C.

2.2 3DAP analysis for elemental segregation on grain boundary

A fine needle sample for 3DAP, containing the prior γ grain boundary, was taken from the heat-treated sample using the focused ion beam (FIB) process. The scanning transmission electron microscopic image confirmed that the sample contained the prior γ grain boundary (Fig. 1). Then 3DAP analysis was conducted using an ultraviolet (UV) laser-assisted atom probe (LEAP 4000XSi; Cameca SAS), under 30 pJ pulse energy, 50 K sample temperature, 90 mm flight length, and a less than 0.1%/pulse evaporation rate.

Fig. 1

The microstructure for 3DAP specimen observed by STEM. The black arrow indicates the prior austenite (γ) grain boundary (GB).

2.3 Thermodynamic calculation for grain boundary segregation

The grain boundary segregation coefficient of the solute B, k_B^GB, in the A–B binary system is given by the following equation:

  

\begin{equation} k_{\text{B}}^{\text{GB}} = \exp\left(\frac{\Delta\varepsilon_{\text{B}}^{\text{GB}}}{kT}\right) \approx \frac{X_{\text{B}}^{\text{GB}}}{100 - X_{\text{B}}^{\text{GB}}}\bigg/\frac{X_{\text{B}}^{\text{MAT}}}{100 - X_{\text{B}}^{\text{MAT}}}, \end{equation} (1)

where X_B^GB, X_B^MAT, Δε_B^GB, and k respectively denote the compositions of the solute B on the grain boundaries and in the matrix (both in mol%), the grain boundary segregation energy, and Boltzmann’s constant.

The grain boundary phase model proposed by McLean and Hillert was applied to analyze grain boundary segregation. In this model, the chemical potential differences between the elements A and B in the matrix and the grain boundary phases were assumed to be equal under equilibrium segregation (the parallel tangent law),¹³⁾ as represented in the following equation.

  

\begin{equation} \mu_{\text{A}}^{\text{MAT}} - \mu_{\text{A}}^{\text{GB}} = \mu_{\text{B}}^{\text{MAT}} - \mu_{\text{B}}^{\text{GB}} \end{equation} (2)

Therein, μ_X^MAT and μ_X^GB respectively denote the chemical potentials of the element X (X = A or B) in the matrix and grain boundary phases. The chemical potentials of μ_A^MAT, μ_A^GB, μ_B^MAT and μ_B^GB are shown schematically in the Gibbs free energy-composition diagram for the A–B binary system (Fig. 2(a)). In this figure, X_B^MAT and X_B^GB respectively show the chemical compositions of the matrix and grain boundary phases; also, G^MAT and G^GB are the respective Gibbs free energies of the matrix and grain boundary phases. As given in eq. (1), the grain boundary segregation coefficient k_B^GB is calculable using X_B^MAT and X_B^GB, which satisfy eq. (2).

Fig. 2

Schematic of chemical compositions (X_B,C^MAT and X_B,C^GB) and chemical potentials (μ_A–C^MAT, μ_A–C^GB) for grain boundary segregation for (a) A–B binary alloy and (b) A–B–C ternary alloy.

The model can be expanded to ternary systems. Figure 2(b) represents the schematic Gibbs free energy–composition diagram for the A–B–C ternary system, showing the equilibrium grain boundary segregation. The chemical potentials of the elements A, B, and C in the matrix phase (μ_A^MAT, μ_B^MAT, μ_C^MAT) are given by the tangent plane of the Gibbs free energy surface contacted at the matrix composition: X_B,C^MAT. The chemical potentials of elements A, B, and C in the grain boundary phase (μ_A^GB, μ_B^GB, μ_C^GB) are given by the plane, which is parallel to the matrix plane, and contacted with the Gibbs free energy surface for the grain boundary phase. The contacted point gives the composition of grain boundary phase: X_B,C^GB. Equation (2) can be extended to the ternary system, as given in eq. (3).

  

\begin{equation} \mu_{\text{A}}^{\text{MAT}} - \mu_{\text{A}}^{\text{GB}} = \mu_{\text{B}}^{\text{MAT}} - \mu_{\text{B}}^{\text{GB}} = \mu_{\text{C}}^{\text{MAT}} - \mu_{\text{C}}^{\text{GB}} \end{equation} (3)

Equation (3) can be transformed to the following equations.

  

\begin{equation} \mu_{\text{A}}^{\text{MAT}} - \mu_{\text{B}}^{\text{MAT}} = \mu_{\text{A}}^{\text{GB}} - \mu_{\text{B}}^{\text{GB}} \end{equation} (4-1)

  

\begin{equation} \mu_{\text{A}}^{\text{MAT}} - \mu_{\text{C}}^{\text{MAT}} = \mu_{\text{A}}^{\text{GB}} - \mu_{\text{C}}^{\text{GB}} \end{equation} (4-2)

The composition of the grain boundary phase X_B,C^GB and the grain boundary segregation of the elements B and C are obtainable by the condition satisfying both eqs. (4-1) and (4-2).

Furthermore, the model can be extended to multicomponent systems of Fe–Y (Y = B, C, D, …). The chemical potentials of Fe and the elements Y (Y = B, C, D, …) in the matrix (γ) and grain boundary phases (μ_Fe^γ, μ_Fe^GB, μ_Y^γ, μ_Y^GB) satisfy

  

\begin{equation} \mu_{\text{Fe}}^{\gamma} - \mu_{\text{Y}}^{\gamma} = \mu_{\text{Fe}}^{\text{GB}} - \mu_{\text{Y}}^{\text{GB}} = \Delta\mu_{\text{Fe,Y}}, \end{equation} (5)

where Δμ_Fe,Y is the difference in the chemical potentials of Fe and the elements Y (Y = B, C, D, …) in the γ and grain boundary phases.

Therefore, Δμ_Fe,Y is calculable with the chemical potentials of Fe and the elements Y (Y = B, C, D, …) in the γ phase with the matrix composition X_Y^γ. The chemical composition in the grain boundary phase, X_Y^GB (Y = B, C, D, …), is calculable with the chemical potentials of the elements Y (Y = B, C, D, …) in the grain boundary phase and Δμ_Fe,Y, satisfying the eq. (5) for each element.

For this study, Δμ_Fe,Y was calculated in the multicomponent Fe-base alloy containing the elements Y (Y = C, Si, Mn, P, Cr, Mo, B) with the chemical potentials of Fe and the elements Y (Y = C, Si, Mn, P, Cr, Mo, B) in the γ phase, applying the CALPHAD method. Then, the chemical composition in the grain boundary phase, X_Y^GB (Y = C, Si, Mn, P, Cr, Mo, B), was calculated with the chemical potentials of the elements Y (Y = C, Si, Mn, P, Cr, Mo, B) in the grain boundary phase and Δμ_Fe,Y, satisfying eq. (5). The Gibbs free energy of the liquid phase was applied to estimate the Gibbs free energy of the grain boundary phase, as proposed by Ohtani et al.¹⁹⁾ The advantage of the analysis model is that it allows the use of the assessed thermodynamic databases. However, it assumes random grain boundaries, therefore the model is not applicable to low energy grain boundaries such as a twin boundary.

Because the sample contains Mo, B, and C, the borocarbide phase is expected to be formed.²⁰⁾ The calculated phase diagram for the Fe-0.82%C-0.22%Si-0.86%Mn-1.1%Cr-0.21%Mo-B (mass%) system is depicted in Fig. 3. The borocarbide phase, M₂₃(C,B)₆, is regarded as formed at 950°C in the sample containing 0.0050%B. Therefore, the calculated equilibrium composition of the γ phase at 950°C shown in Table 1 was used for the matrix composition, X_Y^γ. A commercially available thermodynamic solver (Thermo-Calc ver. 2022a; Thermo-Calc Software) and a database for iron and steels, TCFE7, were used for the thermodynamic calculations and analysis.

Fig. 3

Calculated phase diagram of Fe-0.82C-0.22Si-0.86Mn-1.1Cr-0.21Mo-xB system.

3. Results

3.1 3DAP measurement and analysis

The atomic distribution mapping obtained by 3DAP in the sample containing the prior γ grain boundary is portrayed in Fig. 4(a). The dark line, indicated by the black arrow in the figure, was confirmed to be the prior γ grain boundary by comparison with the STEM image presented in Fig. 1. The segregated elements appeared to be distributed uniformly on the grain boundary without forming coarse borocarbide particles.

Fig. 4

The results of 3DAP analysis. (a) 3DAP image (atomic distribution) (b) Chemical composition profiles.

The chemical composition profiles along the red arrow in Fig. 4(a), which is perpendicular to the prior γ grain boundary, are portrayed in Fig. 4(b). Grain boundary segregations of C, Cr, B, and Mo were clearly recognized. The amount of C in the matrix was found to be in the range of 2–3 mol%, which is low compared with the calculated C content of 3.6 mol% in the γ phase at 950°C (Table 1). Actually, M₂₃(C,B)₆ is formed at 950°C based on the calculated phase diagram (Fig. 3). However, formation of the borocarbide seems not to be the reason for the difference in the calculated and observed C contents because the borocarbide amount is extremely small. The chemical composition analysis results obtained using 3DAP include statistical errors. The statistical errors for the C content were calculated in the range of ±0.3–0.4 mol%, in the confidence range of ±2 σ (σ: standard deviation). The difference between the calculated and observed C contents (0.5–1 mol%) remained larger than the calculated statistical errors. Reportedly, the preferential and delayed evaporation in 3DAP are possible causes for the differences between the detected and actual composition.^21,22) Although the 3DAP results include statistical and experimental errors, the effects of errors are expected to be limited in this study because analysis of the grain boundary segregation has been conducted in terms of the grain boundary excess while integrating the concentration profiles across the grain boundary obtained using 3DAP, as described later.

Considerable grain boundary segregation of B as high as 2 mol% was observed as shown in Fig. 4(b). A very high grain boundary segregation coefficient for B was expected because the detected amount of B in the matrix was extremely low. Grain boundary segregations of Cr and Mo were also observed in Fig. 4(b). However, no grain boundary segregation was recognized for Mn and Si. The amount of Si was apparently even smaller on the grain boundary than that in the matrix.

The concentration profile for B appeared to be symmetrical and widely distributed across the grain boundary compared to those for Mo and Cr. The C and Cr profiles were apparently asymmetrical. Depleted zones were observed near the grain boundary, as indicated by red arrows in Fig. 4(b).

3.2 Thermodynamic calculation for grain boundary segregation

Thermodynamic calculation results for the chemical compositions of matrix and grain boundaries at 950°C (X_Y^γ, X_Y^GB) and the grain boundary segregation coefficient (k_Y^GB) are shown in Table 2. The extremely high value of the grain boundary segregation coefficient for B (k_B^GB), as high as 2600, shows significant grain boundary segregation tendency of B. The calculated grain boundary segregation coefficient for C (k_C^GB) was 3.2. Although the value of k_C^GB is much smaller than that of k_B^GB, the segregated amount of C on the grain boundary is expected to be much larger than that of B because the sample contains a large amount of C (3.6 mol%) compared to that of B (0.0029 mol%). The calculated values of grain boundary segregation coefficient for Cr and Mo were, respectively, 2.5 and 12, suggesting positive grain boundary segregation. The value for Mn was 0.97, which was almost equal to 1.0, suggesting no grain boundary segregation. The value for Si was a very low 0.19, suggesting negative grain boundary segregation.

Table 2 Thermodynamic calculation results of grain boundary segregation.

4. Discussion

4.1 Comparisons between the 3DAP and thermodynamic calculation results

The grain boundary segregations of C, B, Cr, and Mo were observed, although no grain boundary segregation for Mn and a negative grain boundary segregation for Si were recognized by 3DAP, as portrayed in Fig. 4(b). Similar trends were obtained using the thermodynamic calculations, as shown in Table 2. For comparison between the 3DAP and thermodynamic calculation results, the atom number per unit area on the grain boundary should be used^12,23) because the grain boundary had its own thickness depending on the grain boundary structure. Moreover, the concentration profiles showed distributions of the elements across the grain boundary.

The grain boundary excess obtained by 3DAP, denoted as N_3DAP^GB, is calculable by integrating the concentration profiles along the thickness direction of the grain boundary (Fig. 4(b)).¹⁵⁾ Actually, N_3DAP^GB is given as

  

\begin{equation} N_{\text{3DAP}}^{\text{GB}} = \int_{-w/2}^{-w/2}(n_{3\textit{DAP}}(z) - n_{0})dz,\quad (\text{atom/m$^{2}$}) \end{equation} (6)

where z denotes the distance perpendicular to the grain boundary, w represents the grain boundary thickness, n_3DAP is the concentration profile obtained by 3DAP, and n₀ is the concentration in the matrix. The molar volume of the γ phase (7 × 10⁻⁶ m³/mol) and the Avogadro number (6.023 × 10²³) were used to convert from the measured value (mol%) to the atom number per unit area.

The grain boundary excess obtained using the thermodynamic calculation, denoted as N_TC^GB, is described by eq. (7) as a function of the molar fraction (x_TC), the average molar fraction (x₀), and the atomic density of the grain boundary (D_GB). The value of D_GB was reported as 48 atom/nm².¹²⁾

  

\begin{equation} N_{\text{TC}}^{\text{GB}} = (x_{\text{TC}} - x_{0})D^{\text{GB}} \end{equation} (7)

Figure 5 presents the integration results for B, based on eq. (6), using the concentration profile for B portrayed in Fig. 4(b). A significant increase near the grain boundary is presented in Fig. 5, confirming the strong grain boundary segregation of B.

Fig. 5

Integral B content obtained from 3DAP results.

Calculated N_3DAP^GB values for C, Si, Mn, P, Cr, and Mo along with B are shown as blue bars in Fig. 6. The values are the average of two separate measurements by 3DAP. Calculated N_TC^GB values based on eq. (7) are also shown as orange bars in Fig. 6. The N_3DAP^GB value for B was 4.7 atom/nm², which corresponds to the reported data.^12,23) The N_TC^GB value for B was low: 3.4 atom/nm².

Fig. 6

The segregations amount of C, Si, Mn, P, Cr, Mo, and B obtained from 3DAP analysis and thermodynamic calculation at 950°C. Note: Segregation amount of B (N_BG^B) obtained from the calculation method using eq. (1) and Δε_BG^B = 0.65 eV is indicated by the dashed line.

The grain boundary excess of B (N_B^GB), without considering interactions between B and other elements, was calculated as 0.66 atoms/nm² based on eqs. (1) and (7), where Δε_B^GB = 0.65 eV^12,24) was used. The value was much smaller than the experimentally obtained value of 4.7 atom/nm². The grain boundary excess obtained using the thermodynamic calculation (N_TC^GB) was smaller than the experimentally obtained value (N_3DAP^GB). However, it was much closer to the experimental obtained value, than the one without considering interactions to other elements (N_B^GB). Some factors can be pointed out for the smaller value of N_TC^GB compared to that of N_3DAP^GB, for example, using thermodynamic data for the liquid phase to calculate the average grain boundary energy even through the grain boundary energy shows the structural dependency. Additionally, non-equilibrium segregation at elevated temperatures because of the large amount of vacancies can result in more segregation than the equilibrium amount.^12,23)

The 3DAP results for other elements (C, Si, Mn, P, Cr, and Mn) showed an identical tendency to that found with the thermodynamic calculation results, as depicted in Fig. 6, although the value of N_TC^GB for Cr was apparently smaller than that of N_3DAP^GB. Good agreement between N_3DAP^GB and N_TC^GB values for Mn and Si, respectively indicate no grain boundary segregation and negative segregation.

The observed similar asymmetric profiles for C and Cr and the depleted zones as shown in Fig. 4(b) are possibly formed by the solute-drag of Cr during grain growth of γ,²⁵⁾ because C and Cr reduce their mutual activities. Furthermore, Da Rosa et al. reported that depleted zones of B formed near the grain boundaries in the quenched sample with a cooling rate of 500°C/s.²⁶⁾ For this study, because the maximum cooling rate was about 100°C/s in gas quenching by He, it was possible that the diffusion of C during quenching was not suppressed perfectly. This lack of suppression is another possible mechanism for the asymmetric profile of C.

The thermodynamic calculation results obtained for the grain boundary segregation behaviors based on the CALPHAD method, considering interactions among the elements, showed overall good agreement with experimentally obtained data from 3DAP. These results strongly suggest that the thermodynamic calculation applying the CALPHAD method is applicable for alloy design to use grain boundary segregation, such as B-added multicomponent high strength steels.

4.2 Investigation of elemental interaction of grain boundary segregation behavior

Effectiveness of thermodynamic calculations applying the CALPHAD method to elucidate the grain boundary segregation behavior in the B-doped steels was presented in the preceding section, considering interactions among the alloying elements. In this section, changes in the grain boundary segregation with the alloy composition are discussed based on thermodynamic calculations.

Figure 7(a) shows changes in the grain boundary segregation coefficient for each element with the C content in Fe-C-0.42Si-0.85Mn-0.0035P-1.14Cr-0.12Mo-0.0025B (mol%) alloys. The segregation coefficient for B decreased gradually with an increase in the C content. However, the coefficient remained at a high value of over 1 × 10³ at the high C content of 6 mol%. The segregation coefficient for Si, having a smaller value than 1, also decreased with increased C content, suggesting strong negative segregation at the high C contents. The segregation coefficient for Mn was also smaller than 1 at 0% C. However, the segregation coefficient became greater than 1 over approximately 4 mol%C, suggesting that the segregation of Mn changed from negative to positive with increased C contents from 0 to 6 mol%. The segregation coefficient for P decreased slightly with an increase in the C content from 0 to 3 mol%. It was almost unchanged in the C content over 3 mol%. The obtained trend apparently corresponds to the reported results^9,27) indicating that the addition of C suppressed the grain boundary segregation of P in the Fe-C-P alloys. In high-C steels, as in the sample examined for the present study (3.6 mol%), the effect of C on the grain boundary segregation of P appeared to be limited. Because the grain boundary segregation of Mn is changed from negative to positive with an increase in the C content as portrayed in Fig. 7(a), the existence of Mn on the grain boundaries might influence the grain boundary segregation of P in the high C region. The calculated segregation coefficient for P at the composition of 5 mol%C-0Mn (Fe-5.0C-0.42Si-0Mn-0.0035P-1.14Cr-0.12Mo-0.0025B (mol%) alloy) was 7.35, which was almost equal to the value of 7.00 for Fe-5.0C-0.42Si-0.85Mn-0.0035P-1.14Cr-0.12Mo-0.0025B (mol%) alloy. Therefore, the effect of grain boundary segregation of Mn in the high-C region (Fig. 7(a)) on the segregation of P appears to be limited.

Fig. 7

Segregation tendencies at 950°C calculated by CALPHAD method as a function of (a) C content, (b) B content, (c) Mo content.

Figure 7(b) shows changes in the grain boundary segregation coefficient for each element with the B content in Fe-3.69C-0.42Si-0.85Mn-0.0035P-1.14Cr-0.12Mo-B (mol%) alloys. The segregation coefficients for Cr and Mo increased, whereas those for C, Si, Mn, and P decreased with an increase in the B content. For example, the grain boundary segregation coefficient for P decreased from 14 to 7, with an increase in the B content from 0 to 0.0029B (mol%). Reportedly, compared to increasing C content, the addition of B was much more effective for suppressing the grain boundary segregation of P.^11,27) The calculation results agree well with the reported trend. The calculation results also agree with the trend reported by Kuzmina,⁶⁾ showing that addition of B to the steel containing 9%Mn (mass%) was effective at suppressing the grain boundary segregation of Mn.

Figure 7(c) presents changes in the grain boundary segregation coefficient for each element with the Mo content in Fe-3.69C-0.42Si-0.85Mn-0.0035P-1.14Cr-Mo-0.0025B (mol%) alloys. Although the effects of Mo content on the segregation coefficients of other elements were nearly negligible, slight decreases in the segregation coefficient for Si and P with an increase in the Mo content were noted. This finding suggests that addition of Mo to B-added steels is effective at suppressing the grain boundary segregation of P. The near lack of an effect on the segregation of B with increased Mo content agrees with trends reported earlier by Takahashi.¹²⁾

Thermodynamic calculations applying the CALPHAD method are effective for predicting the grain boundary segregation behavior in B-added multicomponent steels like those described above. Alloy design with control of grain boundary segregation of multiple alloying elements is possible through thermodynamic calculation, although the model treats only the equilibrium condition. Thermodynamic calculations applying the CALPHAD method are expected to be useful for alloy design and process control related to the grain boundary segregation, for example, using grain boundary segregation of microalloying elements such as B, or suppressing grain boundary segregation of P and other impurities.

5. Conclusions

For the present study, segregation on the prior γ grain boundaries in B-added multicomponent steel (Fe-0.82C-0.22Si-0.86Mn-0.02P-1.1Cr-0.21Mo-0.005B (mass%) alloy) was analyzed using thermodynamic calculations based on the grain boundary phase model proposed by McLean–Hillert, applying the CALPHAD method to examine interactions among the alloying elements. The Gibbs free energy for the liquid phase was applied to the Gibbs free energy for the grain boundary phase. Segregation on the prior γ grain boundaries in the B-added steel was also observed using 3DAP experimentation. Comparisons between the experimentally obtained and calculation results were made to ensure the effectiveness of the thermodynamic calculation method. The obtained results were the following.

1. (1)    The 3DAP results showed positive grain boundary segregation for B, C, Cr and Mo, but almost no segregation for Mn and P, and negative grain boundary segregation for Si.
2. (2)    The thermodynamic calculation results obtained by applying the CALPHAD method showed positive grain boundary segregation for B, C, Cr, and Mo, which corresponded to the experiment results obtained using 3DAP.
3. (3)    Effects of alloying elements on the grain boundary segregation behavior in the alloy composition base used for this study were discussed based on the thermodynamic calculation applying the CALPHAD method. The calculation results indicated similar trends to the reported results, for example, suppression of grain boundary segregation of P with increasing in the B and C contents, and a significant effect by B addition to suppress grain boundary segregation compared to that by increasing C content. Thermodynamic calculations applying the CALPHAD method are expected to be useful to understand, to predict, and to analyze grain boundary segregation behavior in multicomponent alloys such as B-added high-strength steels.

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