Interaction of Alloying Elements with Migrating Ferrite/Austenite Interface

Abstract

Alloying elements greatly influence phase transformation kinetics in steel due to local partitioning and interfacial segregation to migrating interface and quantitative understanding of the alloying effects is a key for tailoring mechanical properties of modern high strength steels. Energy dissipation for interface migration is an important concept to understand the alloying effects and also to control carbon enrichment in untransformed austenite in multiphase high strength TRIP or DP steels. In this review, possible sources causing energy dissipation for interface migration are introduced and the energy dissipation for interface migration in formations of grain boundary ferrite (α), Widmanstatten α and bainitic α investigated in various systems are summarized.

1. Introduction

A variety of phase transformations, such as ferrite, pearlite, bainite and martensite, have been widely utilized to tailor mechanical properties of steel products. In development of modern high strength steel, sophisticated control of transformation microstructure is required for better strength and ductility/toughness balance. In addition to fraction, size and distribution of constituent phases, local enrichment of carbon (C) and substitutional elements (M) during phase transformations is also a key factor in development of dual phase and TRIP steels which are typical modern high strength steels. Therefore, quantitative understanding of alloying effects on phase transformation kinetics in Fe–C system becomes increasingly important.

Since C diffusivity is several orders magnitude larger than that of M, those phase transformation takes place without macroscopic partitioning of M and interface migration is basically controlled by C diffusion in austenite (γ). On the other hand, M diffusion in nm scale could accompany with interface migration, e.g. formation of spike or interfacial segregation, and exert friction force against interface migration and eventually slower the interface velocity. Such interaction between alloying element and migrating interface have been extensively discussed in terms of so-called energy dissipation in series of international meetings, Alloying Element Effects on Migrating Interfaces, (ALEMI), see following reviews.^1,2)

In the recent decades, novel sophisticated methods have been developed to elucidate interaction of alloying elements with migrating interface and allow us to understand alloying effects on interface migration quantitatively. Furthermore, it becomes recognized that α/γ interface character has significant influence on the interaction. In this article, possible factors which may arise energy dissipation during interface migration are introduced and interaction of alloying elements with grain boundary ferrite (α), Widmanstatten α and bainitic α with γ interface are reviewed.

2. Various Sources of Energy Dissipation for Interface Migration

2.1. Intrinsic Mobility

There are various ‘frictions’ on the interphase boundary migration exerted from various components of the microstructure as represented in Fig. 1.³⁾ Atomic displacement at the interface for rearrangement of crystal lattice causes intrinsic friction ($\mathrm{\Delta }{G}_m^{diss}$), which would be active even in a pure element. $\mathrm{\Delta }{G}_m^{diss}$ is related to velocity (v) and intrinsic mobility of interface (M^int) as follows;   

$$\mathrm{\Delta }{G}_m^{diss}=v/M^{int}$$(1)

Fig. 1.

Schematic illustration of microstructure components causing energy dissipation in interface migration.³⁾ (Online version in color.)

Dissipation by intrinsic mobility plays an important role in massive transformation where transformation is accompanied with only short-range diffusion and interface migration rate is fast. A lot of effort has been placed to clarify the intrinsic mobility in various binary and ternary alloys.^4,5,6,7,8,9) It is clear that M^int decreases with lowering temperature while the intrinsic mobilities reported in literature scatters by orders of magnitude. Recently intrinsic mobility is reported to be nearly independent on transformation direction, e.g. γ → α and α → γ, and alloying element.⁹⁾

2.2. Element Partitioning

Local partitioning of alloying element is another source for energy dissipation. Figure 2 illustrates isothermal section of Fe–M–C phase diagram. Substitutional element is much slower diffuser than C, and thus α transformation without macroscopic partitioning of M takes place in general transformation condition.^10,11,12,13)

Fig. 2.

Isothermal section of Fe–M–C phase diagram, (a) PE, (b) NPLE/PLE. In regions highlighted by blue in (a) and red in (b), α growth is possible under PE or NPLE mode, respectively. (Online version in color.)

Para equilibrium (PE) shown in Fig. 2(a) is one of the extreme case where M diffusion does not occur at all, and α growth is accompanied with only C diffusion. The blue region in Fig. 2(a) displays (α+γ) two phase region and tie line in PE connects points a and b, whose site fractions of M are equal to the nominal content, $y_M^0$. Point b is the upper limit for α transformation in PE, which will be called as A_e3(PE) hereafter. Another extreme case is negligible partitioning local equilibrium (NPLE), where M is redistributed locally as indicated by points c and d in Fig. 2(b), to maintain local equilibrium at the interface. Partitioning of M leads to the formation of so-called ‘spike’ in γ in front of the interface. Interface migration in NPLE mode is also controlled by C diffusion in γ. Iso-activity line of C passing through point d and C component ray at $y_M^0$ is crossed at point e, and this is the upper limit of α transformation in NPLE mode. Above this composition, macroscopic M partitioning is needed for α growth and this mode is called partitioning local equilibrium (PLE). The point e is referred to as NPLE/PLE transition. C content at NPLE/PLE transition is lower than that at A_e3(PE) regardless of alloying element. This is proved by $a_C^b=a_C^a\ge a_C^c=a_C^d=a_C^e$, where $a_C^i$ is C activity at point-i. $a_C^c$ is lower than $a_C^a$ because two phase region in full equilibrium always includes that in PE. Figure 3 shows NPLE/PLE transition and A_e3(PE) with various energy dissipations (ΔG^diss) calculated using ThermoCalc with TCFE9 database in Fe-2mass%Mn-C alloy (alloy composition without specification will indicate mass%C, hereafter). The gap between NPLE/PLE transition and A_e3(PE) increases at lower temperature and is regarded as energy dissipation due to partitioning of M ($\mathrm{\Delta }{G}_{part}^{diss}$) or in other words, energy dissipation to form spike. Equation (2) approximately represents $\mathrm{\Delta }{G}_{part}^{diss}$ under the assumption of ideal solid solution¹⁴⁾   

$$\begin{array}{l}\mathrm{\Delta }{G}_{part}^{diss}=RT\left[y_M^{0}ln\left(\frac{y_M^0}{y_M^{\gamma }}\right)+\left(1-y_M^0\right)ln\left(\frac{1-y_M^0}{1-y_M^{\gamma }}\right)\right]\\ \hspace{1em}\hspace{1em}\hspace{1em}=RT\left[y_M^{0}ln\left(\frac{1}{k_M^{}}\right)+\left(1-y_M^0\right)ln\left(\frac{1/y_M^0-1}{1/y_M^0-k_M^{}}\right)\right]\end{array}$$(2)

where T and $k_{M }^{}\left(=y_M^{\gamma }/y_M^{\alpha }\right)$ are temperature and partitioning coefficient, respectively. $\mathrm{\Delta }{G}_{part}^{diss}$ is zero at k_M=1 and increases by deviating k_M from unity. k_Mn increases with lowering temperature, which results in increment of $\mathrm{\Delta }{G}_{part}^{diss}$ at lower temperature shown in Fig. 3.

Fig. 3.

A_e3(PE) and NPLE/PLE transition in Fe-2%Mn-C systems calculated. Dotted lines represent A_e3(PE) calculated with various energy dissipations (ΔG^diss).

2.3. Solute Drag Effect Due to Element Segregation

Segregation of alloying elements at interface exerts a drag force against interface migration, which is called as solute drag effect (SDE). By extension of grain boundary segregation model¹⁵⁾ to interphase boundary segregation,¹⁶⁾ element profile within interphase boundary can be calculated by assuming quasi-steady state. Figure 4(a) shows an example of interaction potential profile within interface used in the analysis.¹⁷⁾ E⁰ and 2ΔE indicate a binding energy between interface and alloying element, and partitioning energy of alloying element between α and γ, respectively. At faster interface velocity, diffusion of alloying element cannot catch up with interface migration and segregation is reduced whereas segregation is promoted at slower interface velocity. Two different concepts have been proposed to estimate energy dissipation by SDE and they give identical dissipation when quasi steady-state and ideal solid solution are assumed (see Appendix).   

$$\mathrm{\Delta }{G}_{SDE-PB}^{diss}=-{\int }_{-\delta }^{\delta }\frac{dE}{dx}\left(y_M-y_M^0\right)dx$$(3) ¹⁶⁾

  

$$\mathrm{\Delta }{G}_{SDE-H}^{diss}=-\frac{V_m}{v}{\int }_{-\infty }^{\infty }{J}_M\frac{d\left(\mathrm{\Delta }\mu \right)}{dx}dx$$(4) ¹⁴⁾

where E, Δμ and J_M are interaction potential between solute and interface, inter-diffusion potential and diffusion flux, respectively. δ and V_m are half thickness of interface and molar volume, respectively. It should be noted that Eqs. (3) and (4) include energy dissipation due to partitioning (Details will be shown in Appendix). With no partitioning (ΔE=0), energy dissipation approaches zero at fast and slow interface velocity and becomes maximum at intermediate velocity (Fig. 4(b)). The maximum energy dissipation increases with increase in the binding energy. Partitioning of M adds further energy dissipation (Fig. 4(c)) and energy dissipation approaches $\mathrm{\Delta }{G}_{part}^{diss}$ at slower velocity.

Fig. 4.

(a) interaction potential and composition profiles across α/γ interface, and energy dissipation in Fe-1at% M system as a function of normalized interface velocity (=vδ/D_M) (b) 2ΔE=0 kJ/mol, (c) 2ΔE =−10 kJ/mol. Other parameters used in the calculation are binding energy to interface, E⁰=−5, −10, −15 kJ/mol and temperature T=973 K.¹⁷⁾ (Online version in color.)

2.4. Effects of Interface Character on Energy Dissipation

Grain boundary allotriomorphic α (GBF) usually holds near Kurdjumov-Sachs (K-S) orientation relationship (OR) ((111)_γ // (011)_α, [-101]_γ // [-1-11]_α), [1-21]_γ // [2-11]_α) with one side of γ and deviates from K-S OR with the other side of γ.^18,19,20,21) GBF tends to grow into γ with which α has non K-S OR while the interface with near K-S OR is less mobile.²⁰⁾ By lowering transformation temperature, acicular or plate-shaped Widmanstatten α (WF) or bainitic α (BF) forms, which holds near K-S OR with γ into which they grow.

As shown in Fig. 5, α/γ interface without near K-S OR (non K-S interface) mainly consists of disordered structure while α/γ interface having near K-S OR (near K-S interface) is semi-coherent. Atomic movement at those interfaces should be different, and thus they have different intrinsic mobility. Migration of semi-coherent interface is supposed to give rise to shape change due to uni-directional atomic displacement at migrating interface (Fig. 5(b)) unlike random atomic jump at disordered interface (Fig. 5(a)). The shape change in transformation should be accommodated by elastic and/or plastic deformations, which exert additional energy dissipation during growth. Furthermore, different interface structure between incoherent and semi-coherent interfaces in terms of thickness, interfacial diffusivity and binding energy with solute element will result in different energy dissipation due to element partitioning and SDE. However, understanding of energy dissipation during migration of semi-coherent interface is limited compared to that at disordered interface.

Fig. 5.

Atomic movement at migrating interface and resultant shape strain for (a) reconstructive interface motion corresponding to non K-S interface, (b) displacive interface motion corresponding to near K-S interface. (Online version in color.)

2.5. Relation between Energy Dissipation and Driving Force in Interface Migration

Total energy dissipation caused from various sources described above, $\mathrm{\Delta }{G}_{total}^{diss}$, is balanced by driving force (ΔG^drv) at migrating interphase.   

$$\mathrm{\Delta }{G}_{}^{drv}+\mathrm{\Delta }{G}_{total}^{diss}=0$$(5) ²²⁾

Here, ΔG^drv ≤ 0 and $\mathrm{\Delta }{G}_{total}^{diss}$ ≥ 0. It should be noted that ΔG^drv is determined by local compositions of α and γ near the interface and does not represent overall driving force for transformation. Figure 6 shows C partitioning between α and γ in Fe–C system. The same situation can be imagined for the (Fe, M)-C pseudo-binary case in PE. If no energy is dissipated for interface migration, ΔG^drv is zero and two phases are in equilibrium at the interface as indicated by the common tangent. When a finite energy is dissipated during interface migration, ΔG^drv should be negative. ΔG^drv corresponds to the gap between ${\mu }_{Fe,M}^{\alpha }$ and ${\mu }_{Fe,M}^{\gamma }$;   

$$G_{}^{drv}={\mu }_{Fe,M}^{\alpha }-{\mu }_{Fe,M}^{\gamma }={\sum }_{i=Fe,M}{y}_i^0\left({\mu }_i^{\alpha }-{\mu }_i^{\gamma }\right)$$(6)

where ${\mu }_{Fe,M}^j$, ${\mu }_C^j$ and $y_i^0$ are mean chemical potential for substitutional atoms in j-phase, C potential in j-phase and nominal site fraction of i, respectively. In Eq. (6), energy difference is evaluated at nominal content, $y_i^0$, therefore G^drv represents undercooling from A_e3 in PE. With increasing energy dissipation, C content both in α and γ nearby interface deviates to lower C content. Here C potentials in α and γ are assumed to be the same because of large C diffusivity. Lower C content in γ reduces C gradient in front of the interface, and thus slower interface velocity (Fig. 6(b)).

Fig. 6.

(a) free energy curves showing local equilibrium and constraint C equilibrium in (Fe–M)–C pseudo binary system, (b) corresponding C content profile across migrating α/γ interface. (Online version in color.)

3. Experimental Analysis of Element Interaction with Migrating α/γ Interface

3.1. Growth of Grain Boundary Ferrite

It was reported that growth rate of GBF is slower than that predicted by C-diffusion controlled rate even in Fe–C binary system, this was ascribed to a presence of less mobile and coherent portion of allotriomorphs interfaces.²³⁾ Later this effect was quantitatively explained by a finite intrinsic mobility of α/γ interface.⁵⁾

In Ni or Si added ternary alloys, local equilibrium model, namely NPLE and PLE, give generally better accounting for the growth rate of GBF than PE model.^24,25) Similarly, upper limit of zero-partitioning growth of α in Fe–Mn–C and Fe–Ni–C alloys is remarkably below A_e3(PE) but only slightly above NPLE/PLE transition.²⁶⁾ On the other hand, growth rates of GBF in Fe–Mo–C and Fe–Cr–C are obviously slower than NPLE prediction, and SDE by Mo and Cr was considered to cause the growth delay.^24,25)

In the last decade, novel experimental methods have been proposed to accurately investigate alloying effects on migrating interface. Cyclic partial phase transformation during heating and cooling within (α+γ) two phase region, proposed by van der Zwaag and Chen,²⁷⁾ is an elegant method to investigate kinetics of interface migration by excluding the nucleation effect. They successfully showed the transformation stagnant stage appearing during cyclic partial phase transformation of Fe–Mn–C alloys is induced by development of spike of alloying element at migrating interface. Controlled decarburization experiment proposed by Purdy, Hutchinson and Zurob^28,29) is another method to elucidate alloying effects on interface migration kinetics without an influence of nucleation. In the controlled decarburization experiment, α grows from the specimen surface with keeping α/γ interface nearly parallel to the surface. This simple geometry allows very high precision measurement of migration kinetics of incoherent interface. They reported that α growth rates in Mn-added alloys are relatively close to NPLE prediction while those in Si, Cr, Mo added alloys are slower than the NPLE prediction and systematically evaluate a binding energy between those elements and interface.

As described in the previous section, energy dissipation can be directly quantified when C content in γ in front of α/γ interface is known. Therefore the present authors have focused on C content in γ and its measurement using FE-EPMA. Figure 7 displays an example of calibration curves and C profiles across grain boundary α/γ interfaces in Fe-2%Mn-C alloy.³⁰⁾ As shown in Figs. 7(b) and 7(c), C depletion in α and enrichment in γ are clearly seen. C content in γ is slightly higher than NPLE/PLE transition and C composition gradient disappears at longer holding time.³⁰⁾ It should be noted that spatial resolution of FE-EPMA is as poor as a few hundred nm so that apparent C content at the interface in the profile does not represent C content on the interface but that in γ and α near the interface.

Fig. 7.

(a) example of calibration line for FE-EPMA measurement, C content profiles in Fe-1.5%Mn-0.11%C alloy transformed at 973 K for (a) 300 s, (b) 10.8 ks.³⁰⁾ (Online version in color.)

Figure 8 summarizes C content in γ in Fe–Mn–C alloys with different Mn content.³¹⁾ At higher transformation temperatures, C content is much lower than A_e3(PE) but close to NPLE/PLE transition. While C content in γ deviates further to lower C content by lowering transformation temperature, suggesting additional energy dissipation at lower transformation temperature.

Fig. 8.

C content in γ in α transformation in Fe–Mn–C systems.³¹⁾ (Online version in color.)

In addition to temperature and alloy composition, energy dissipation also varies during isothermal transformation because of variation of interface velocity with time. Figures 9(a) and 9(b) show time evolution of energy dissipation in Fe-1.5%Mn-0.11%C and Fe-0.5%Mo-0.4%C alloys, respectively. In Fe-1.5%Mn-0.11%C alloy (Fig. 9(a)), energy dissipation is slightly higher than the $\mathrm{\Delta }{G}_{part}^{diss}$ in the early stage of transformation and slowly decreases with time at all the temperatures.³⁰⁾ Therefore, NPLE model is good approximation for energy dissipation in Fe–Mn–C system although SDE plays an important role especially in the early stage of transformation.³²⁾ In contrary, Mo partitioning tendency is weaker than Mn, (e.g. partitioning coefficient is 1.1 for Mo in contrast to 3.8 for Mn at 973 K), and $\mathrm{\Delta }{G}_{part}^{diss}$ in Fe-0.5%Mo-C system is less than 0.5 J/mol at 973 K. However, energy dissipation in Fe-0.5%Mo-0.4%C alloy is much higher than $\mathrm{\Delta }{G}_{part}^{diss}$ and exceeds 100 J/mol (Fig. 9(b)).¹⁷⁾ The large energy dissipation by Mo addition stems from SDE. Energy dissipation in Fe–Mo–C alloy decreases rapidly with time in contrast to large dissipation remained after long holding time in Fe–Mn–C alloy (Fig. 9(a)). Figures 4(b), 4(c) qualitatively explains this difference as follows; energy dissipation decreases rapidly at slower velocity when partitioning is weak while $\mathrm{\Delta }{G}_{part}^{diss}$ remains even at v=0 for strong partitioning tendency. Decarburization experiment and first principles calculation also suggest that the binding energy of Mn to α/γ interface, −2.5 kJ/mol²⁸⁾ or −9.6 kJ/mol,³³⁾ are smaller than that of Mo, −15 kJ/mol²⁸⁾ or −14.5 kJ/mol.³³⁾ It should be noted that K-S interface is assumed in the first principles calculation³³⁾ while migration of disordered α/γ interface is observed in decarburization experiment.²⁸⁾

Fig. 9.

Time evolution of energy dissipation in (a) Fe-1.5%Mn-0.11%C,³⁰⁾ (b) Fe-0.5%Mo-0.4%C.¹⁷⁾ (Online version in color.)

Development of advanced nano-scale characterization techniques, e.g. microanalysis using scanning transmission electron microscopy (STEM) or three dimensional atom probe (3DAP), gives us direct evidence of alloy distribution at migrating interface.^{17,32,34,35,36,37,38,39,40)} Figure 10 shows Mo segregation at GBF/γ interface characterized using 3DAP in Fe-0.5%Mo-0.4%C alloy transformed at 973 K. Clear Mo segregation is detected at non K-S α/γ interface (Fig. 10(a)) while Mo segregation is not obvious at near K-S interface (Fig. 10(b)). Similar OR dependence of V segregation at α/γ interface was reported.³⁹⁾ It is well recognized that grain boundary segregation depends on boundary structure and segregation is retarded at a boundary with good coherency.⁴¹⁾ Therefore, weaker segregation at near K-S interface than non K-S interface suggests that a binding energy or site density for segregation is less at near K-S interface than that at non K-S interface. Atomic structures of the α/γ interfaces with near K-S and non K-S ORs needs to be studied in more detail in order to clarify the effects of interface character on SDE.

Fig. 10.

Segregation of Mo at α/γ interface in Fe-0.5%Mo-0.4%C alloy transformed at 973 K for 600 s measured using 3DAP, (a) at non K-S interface, (b) near K-S interface. Color maps represent orientation map showing interface character measured with EBSD, three dimensional C and Mo atom maps, respectively. Δθ shown in the orientation maps indicate deviation angles from the exact K-S OR.¹⁷⁾ (Online version in color.)

In order to understand SDE quantitatively, interface thickness, interfacial diffusivity and binding energy of a solute element with an interface shown in Fig. 4(a) are important physical parameters while direct measurement of those parameters are very challenging. At α/γ boundary having K-S OR, a binding energy and interface structure were evaluated using first principles calculation for various elements.³³⁾ It was shown that Nb has by far the largest binding energy followed by Mo, Mn, and Si, whereas Cr and Ni show marginal binding to the α/γ interface. However, it would take long time until theoretical evaluation of those parameters at incoherent and dynamically migrating interface becomes possible.

Instead, the present authors proposed that those parameters can be estimated from multi-aspects characterization, e.g. velocity, amount of segregation and energy dissipation at migrating interface, through comparison with theoretical SDE model. Namely, velocity of interface and energy dissipation can be measured based on variations in GBF thickness and C content in γ using FE-EPMA, respectively. Furthermore, amount of element segregation is quantified as interfacial excess, which is the number of excess solute atoms per unit area of interface, expressed as follows;   

$$\mathrm{\Gamma }=\frac{1}{V_a}{\int }_{-\delta }^{\delta }\left(y_M-y_M^0\right)dx$$(7)

where V_a is atomic volume. Γ can be estimated from composition profiles across α/γ interfaces in experiment (e.g.Fig. 10) and calculation (e.g.Fig. 4(a)). Figures 11(a), 11(b) and 11(c) compare experimental results with SDE model calculated with optimized parameters, i.e. interface thickness and the binding energy are fitted to 2δ = 2 nm and −30 kJ/mol, respectively, and interfacial diffusivity of Mo used is the same as that in α.¹⁷⁾ Such multi-aspects characterization at migrating interface is helpful to understand the interaction of alloying element quantitatively and should be proceeded further in another system.

Fig. 11.

Comparison of solute drag at non K-S α/γ interface between measurement and calculation in Fe-0.5%Mo-0.4%C transformed at 973 K, (a) energy dissipation vs velocity, (b) energy dissipation vs Mo segregation, (c) Mo segregation vs velocity.¹⁷⁾ (Online version in color.)

Recently, Mn interaction with α/γ interface is also being investigated in the present author’s group. Figure 12 shows Mn profiles across GBF/γ interface in Fe-1.5%Mn-0.11%C alloy transformed at 973 K measured with 3DAP.⁴²⁾ Similar to the Mo segregation described in the previous section, clear Mn accumulation is detected at non K-S α/γ interface while Mn accumulation is not detected at near K-S interface (Figs. 12(a), 12(b)). Mn enrichment observed at non K-S interface is ascribed to transition from segregation to partitioning by comparison with theoretical SDE model.⁴²⁾ It is frequently observed that GBF grows preferentially into γ with which α does not hold K-S OR, namely γ2 in Fig. 13(a) and α/γ1 interface is nearly immobile. Since Mn enrichment is not observed at near K-S interface, immobility of near K-S interface should be attributed to energy dissipation other than SDE or partitioning, e.g. small intrinsic interface mobility or large transformation strain. Interestingly, C enrichment at mobile non K-S interface (α/γ2) and immobile near K-S interface (α/γ1) are similar regardless of large difference of migration distance (Fig. 13(b)). This fact suggests that C diffusion in α from non K-S to near K-S interfaces takes place as suggested by Hillert.⁴³⁾ Therefore, C diffusion in α whose effect is generally ignored, should be taken into account in the analysis of thickening kinetics of GBF.

Fig. 12.

Mn accumulation at α/γ interface in Fe-1.5%Mn-0.11%C transformed at 973 K for 60 s, (a) non K-S interface, (b) near K-S interface. Multiple measurement data are plotted together by different colors.⁴²⁾ (Online version in color.)

Fig. 13.

Comparison of C enrichment in γ at non K-S and near K-S interfaces in Fe-1.5%Mn-0.11%C transformed at 973 K for 60 s, (a) Orientation map, (b) C profile across two α/γ interfaces.⁴²⁾ (Online version in color.)

Figure 14(a) summarizes energy dissipation measured in various alloys.^{17,30,44,45,46)} In a given Fe–M–C system, energy dissipation increases with lowering transformation temperature and at larger amount of alloying element. Two broken lines represent $\mathrm{\Delta }{G}_{part}^{diss}$ calculated in Fe-1.5%Si-C and Fe-1.5%Mn-C alloy. Even though amount of alloy addition in atomic percent is nearly double (3at%Si vs 1.5at%Mn), $\mathrm{\Delta }{G}_{part}^{diss}$ for Fe-1.5%Si-C alloy is smaller than that for Fe-1.5%Mn-C alloy due to weak partitioning tendency of Si. Relatively good agreement with $\mathrm{\Delta }{G}_{part}^{diss}$ and observed energy dissipation in Fe-1.5%Si-C and Fe-1.5%Mn-C alloys indicates that partitioning of Si and Mn is a major source of energy dissipation in those systems. On the other hand, energy dissipation of Mo-contained alloys show larger energy dissipation than Mo-free alloys. This is more obvious in Fig. 14(b) where energy dissipation with respect to NPLE/PLE transition is shown. ΔG with respect to NPLE/PLE transition in Fe-(Mn, Si)-C alloys is small meanwhile that in Mo-added systems is much larger, indicating that SDE of Mo exert energy dissipation in those systems.

Fig. 14.

Temperature dependence of energy dissipation estimated from C content in γ, reference is taken at (a) A_e3(PE), (b) NPLE/PLE.^{17,30,44,45,46)} (Online version in color.)

Interaction of alloying element with migrating incoherent α/γ interface has been clarified experimentally and theoretically as explained so far. However less effort has been placed to clarify the effects of co-segregation of C and M although its importance has been recognized.^47,48) C, a strong segregant to grain boundary, has attractive interaction with carbide forming elements (e.g. Mn, Cr, Mo, V, Nb etc.), therefore C segregation to α/γ interface could enhance SDE. It is shown that amount of segregation and SDE of Mn in Fe–Mn–N alloy is less than those in Fe–Mn–C alloy.^49,50) This difference implies weaker binding energy of N with interface than that of C. Namely, Mn interacts weakly itself with the interface while strong binding energy between C and α/γ interface and between Mn and C promote Mn segregation. Recent SDE model calculation in a Fe–Mo–C system suggests that Mo–C attractive interaction and enrichment of Mo and C due to interface segregation induces uphill diffusion of Mo and C in the interface.¹⁷⁾ Eventually Mo and C enriched region is produced, and this might trigger interphase precipitation of Mo carbide at α/γ interface. Therefore, co-segregation of substitutional and interstitial elements at migrating α/γ interface needs to be explored further.

3.2. Growth of Widmanstatten α and Bainitic α

At relatively lower transformation temperature, acicular or plate-shaped α is nucleated from GBF and grow into γ, which is called as α side plate or Widmanstatten α (WF). WF holds near K-S OR with respect to γ into which it grows and are accompanied with surface relief, indicating its displacive transformation nature.⁵¹⁾ Interface structure of lath martensite or bainitic α (BF), typical displacive transformation products in steel, with γ matrix is similar, and consists of transformation dislocation leading to stacking sequence change and accommodation disconnection (lattice defects) as shown in Fig. 5(b).⁵²⁾ Those defects in the interface should interact with various compenent in the γ matrix, e.g. solute atoms, dislocations, second phase particles and so on, during growth and exert energy dissipation. C content in γ in front of the growth tip of WF evaluated from lengthening rate in Fe–C alloy deviates to lower C content from A_e3 composition.⁵³⁾ Similarly, upper limit for the formation of WF in Fe–M–C alloys is lower than the A_e3(PE).⁵⁴⁾

Further reduction in transformation temperature, typically lower than 873 K, gives rise to the formation of lath-shaped bainitic α (BF) nucleated at γ grain boundary. BF formation is accompanied with surface relief,⁵⁵⁾ C enrichment into γ and occasionally carbide precipitation.^56,57) Although it is widely accepted that C diffusion takes place during nucleation of BF, there have been extensive debates on the transformation mechanism whether BF growth is diffusional or diffusionless.^58,59) One of the points for discussion is the mechanism of transformation stasis or incomplete transformation (ICT), where bainite transformation ceases temporally before reaching equilibrium transformation fraction. Suppression of carbide precipitation is one of the requirement for the occurrence of ICT because carbide precipitation prevents from C enrichment in γ and thus from reduction of driving force for bainite transformation. However, ICT with carbide precipitation is reported in Fe–Si–C⁶⁰⁾ or Fe–Ni–C alloys⁶¹⁾ while the mechanism of ICT with carbide precipitation is not clear.

On a basis of the diffusional growth mechanism, BF growth is controlled by C diffusion in γ and WF and BF are categorized into the same transformation. Hillert²²⁾ analyzed the energy dissipation for BF and WF growth and reported that energy dissipation is basically a function of transformation temperature and independent to Mn and Si content while Mo and Cr increases the energy dissipation. Recently, alloying effects on the energy dissipation for bainite transformation have been explicitly considered by taking SDE into account.^62,63) On the other hand, in diffusionless growth mechanism, supersaturated C in BF is rejected into surrounding γ instantaneously after the growth of BF. Bhadeshia⁶⁴⁾ proposed that ICT occurs when C content in γ reaches T₀’, which is a composition with additional 400 J/mol undercooling from T₀.

Figure 15(a) shows C content in γ in front of the interface in an Fe-3%Si-0.4%C alloy.^3,46,60) As described in the previous section, C content in γ at GBF/γ interface agrees well with NPL/PLE transition, while those for WF is lower than NPLE/PLE transition. For BF, the deviation is much larger than for GBF and WF but C enrichment is still higher than the T₀ line. The estimated energy dissipation from PE exceeds over 300 J/mol for WF and 1500 J/mol for BF (Fig. 15(b)). This result clearly indicates that interface coherency causes the friction in boundary migration. Very recently, energy dissipations for interface migration were compared between WF and GBF by the present author’s group. It was found that larger energy dissipation for WF growth than GBF growth is originated from smaller intrinsic interfacial mobility and strain energy associated with WF/γ interface.⁶⁵⁾

Fig. 15.

(a) C content in γ in WF and BF formation in Fe-3%Si-0.4%C alloys, (b) corresponding energy dissipation.^3,46,60) (Online version in color.)

Energy dissipation from A_e3(PE) for WF and BF formation in Fe–C,^22,66) Fe–N,⁶⁷⁾ Fe-1.5%Mn-C(-(0.3-1.0%)Mo),⁶⁸⁾ Fe-(1.5, 3%)Si-C,⁶⁰⁾ Fe-2%Mn-1.5%Si-C,⁶⁹⁾ nano bainite(Fe-1.5%Si-2%Mn-1.3%Cr-0.3%Mo-0.1%V-C),⁷⁰⁾ Fe-9%Ni-C⁷¹⁾ are compiled and plotted as a function of transformation temperature in Fig. 16. Even though the wide range of alloying element and composition used in this analysis, energy dissipation shows similar trend and increases rapidly with lowering transformation temperature. Although $\mathrm{\Delta }{G}_{part}^{diss}$ by NPLE/PLE model is in good agreement with the dissipation observed in the Fe-1.5Mn-C alloy, large deviation of $\mathrm{\Delta }{G}_{part}^{diss}$ for Fe-1.5Si-C alloy indicates that element partitioning is not a major source for energy dissipation of BF transformation. Furthermore, finite energy dissipation even in Fe–C or Fe–N alloys as well as relatively small fluctuation of energy dissipation with respect to alloying element suggest that contribution of SDE is minor in the energy dissipation for BF/WF transformation. Large energy dissipation especially at lower temperature is probably originated from shear strain energy with less plastic accommodation as well as larger volumetric misfit at lower temperature. Further study will be needed to understand the origin of energy dissipation of WF and BF formation.

Fig. 16.

Energy dissipation for BF and WF transformations in various systems.^{22,65,66,67,68,69,70)} (Online version in color.)

Even though alloying element has minor effects on the energy dissipation compared with large effects of transformation temperature, bainite transformation is affected by Mo addition as shown in Fig. 17.⁶⁸⁾ With increment of Mo content, C enrichment in γ during ICT is suppressed (Fig. 17(a)), and thus energy dissipation increases (Fig. 17(b)). Figure 18(a) also shows that ICT is manifested by Mo addition.³⁷⁾ However, STEM/EDX analysis at BF/γ interface reveals that Mo segregation is not detected in the beginning of ICT and Mo atoms gradually accumulate at BF/γ interface during ICT (Figs. 18(b)–18(e)). Less Mo segregation at BF/γ interface than incoherent GBF/γ interface was also reported using 3DAP.¹⁷⁾ Therefore, SDE cannot explain the increment of energy dissipation by Mo addition and other possibilities needs to be explored further. So far, energy dissipation for interface migration is focused on meanwhile nucleation is generally supposed to dominate martensite transformation kinetics therefore alloying effects on nucleation of BF also needs to be considered as pointed out previously.³¹⁾ In martensite nucleation theory, interfacial friction depends on amount of alloying element in solution and influence Ms temperature.⁷²⁾ Likewise, individual solute atom in solution could interact with BF in nucleation and exert energy dissipation.

Fig. 17.

(a) C content in γ in transformation stasis of Fe-1.5%Mn-0.15%C-Mo alloys, (b) effect of Mo content on energy dissipation for bainite transformation.⁶⁷⁾ (Online version in color.)

Fig. 18.

(a) Transformation kinetics curve, (b) Mn and Mo segregation at BF/γ interface and Mn and Mo composition maps in Fe-1.5%Mn-0.5%Mo-0.15%C alloy transformed at 823 K for (c) 10 s, (d) 60 s, (e) 1.8 ks.³⁷⁾ (Online version in color.)

Figure 19 schematically summarizes variations in driving force for interface migration (G^drv) and energies dissipated by partitioning ($\mathrm{\Delta }{G}_{part}^{diss}$), solute drag ($\mathrm{\Delta }{G}_{SDE}^{diss}$), intrinsic mobility ($\mathrm{\Delta }{G}_m^{diss}$) and transformation strain ($\mathrm{\Delta }{G}_{strain}^{diss}$) as a function of transformation temperature. |G^drv| and $\mathrm{\Delta }{G}_{part}^{diss}$ increase by lowering transformation temperature (Fig. 19(a)). G^drv is balanced with $\mathrm{\Delta }{G}_{part}^{diss}$ at NPLE/PLE transition temperature while |G^drv| increases more rapidly than $\mathrm{\Delta }{G}_{part}^{diss}$ so that the gap becomes larger at lower temperature. When driving force for interface migration is small at high temperature, interface migration rate is generally slow and thus $\mathrm{\Delta }{G}_{SDE}^{diss}$ is marginal (Fig. 19(b)). By lowering transformation temperature which, in general, is accompanied by acceleration of interface migration rate, $\mathrm{\Delta }{G}_{SDE}^{diss}$ reaches maxima. Further reduction in transformation temperature leads to decrement in $\mathrm{\Delta }{G}_{SDE}^{diss}$ because solute diffusion cannot catch up with interface migration. As shown in Fig. 19(c), $\mathrm{\Delta }{G}_{strain}^{diss}$ increases monotonously by lowering transformation temperature as shown in Fig. 16. $\mathrm{\Delta }{G}_m^{diss}$ also increases at lower temperature due to smaller intrinsic mobility. Therefore, in transformation at relatively high temperature, $\mathrm{\Delta }{G}_{part}^{diss}$ and $\mathrm{\Delta }{G}_{SDE}^{diss}$ tend to dominate growth kinetics meanwhile growth kinetics is largely affected by $\mathrm{\Delta }{G}_m^{diss}$ and $\mathrm{\Delta }{G}_{strain}^{diss}$ at lower transformation temperature.

Fig. 19.

Schematic illustrations of variations of driving force for interface migration and energy dissipations as a function of transformation temperature, (a) G^drv and $\mathrm{\Delta }{G}_{part}^{diss}$, (b) $\mathrm{\Delta }{G}_{SDE}^{diss}$, (c) $\mathrm{\Delta }{G}_m^{diss}$ and $\mathrm{\Delta }{G}_{strain}^{diss}$. Constant migration rate is assumed in (c). (Online version in color.)

4. Concluding Remarks

In this paper, interaction of alloying elements with grain boundary α, WF and BF/γ interfaces have been reviewed in terms of energy dissipation during interface migration. It is clear that local partitioning and interfacial segregation exerts large energy dissipation and retard interface migration and those interactions strongly depend on interface character. Meanwhile there are still many points to be clarified, such as energy dissipation due to strain accommodation, co-segregation of elements and interfacial properties (diffusivity, thickness, binding energy etc.). Systematic and quantitative understanding of alloying effects on migrating interface contributes not only to deepening physical metallurgy in phase transformation in metallic materials but also to further advances in the development of novel high strength steels.

Acknowledgements

This work was financially supported by the Innovative Structural Materials Project funded by the New Energy and Industrial Technology Development Organization and CREST Basic Research Program “Creation of Innovative Functions of Intelligent Materials on the Basis of Element Strategy” funded by Japan Science and Technology Agency, Japan and JST “Collaborative Research Based on Industrial Demand” Grand Number JPMJSK1613, Japan. Partial support from JSPS Grant-in-Aid for Scientific Research (B) No. 23360316 (2011–2013), (A) No. 17H01330 (2017–2019) and (B) No. 19H02473 (2019–2021) funded by Japan Society for the Promotion of Science are also gratefully acknowledged.

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Appendix

Comparison of Energy Dissipation in Solute Drag between Eqs. (3) and (4)

Two different equations, Eqs. (3) and (4), have been proposed to estimate SDE. Although only interface region is integrated in Eq. (3), SDE calculated by Eq. (3) includes energy dissipation of spike in γ, which frequently evokes confusion. Based on the papers by Hillert,^14,73) two equations will be compared in this appendix.

Here an Fe–M binary system are considered and chemical potentials of the Fe and M within α/γ interface region are represented in ideal solid solution assumption as follows;   

$${\mu }_{Fe}=RT\mathrm{\hspace{0.17em} }\text{ln}\left(1-y_M\right)$$(A1a)

  

$${\mu }_M=RT\mathrm{\hspace{0.17em} }\text{ln}\left(y_M\right)+E_M\left(x\right)$$(A1b)

where y_M, R and T are a mole fraction of M, a gas constant and temperature, respectively. E_M(x) is the binding energy between M and α/γ interface at the coordinate x as shown in Fig. 4(a). $E_M^0$ is the segregation energy of M, 2ΔE_M is the potential difference of the solute element in α and γ, and 2δ is the interfacial thickness. In other words, the binding energy (E_M(x)) is superposition of the segregation energy to the interface and the potential difference between α and γ.

Diffusion fluxes of Fe and M is given by⁷³⁾   

$$-J_{Fe}=J_M=-\frac{D_M}{RT{V}_m}{y}_M\left(1-y_M\right)\frac{\text{d}\mathrm{\Delta }\mu }{\text{d}x}$$(A2)

where Δμ, V_m and D_M are interdiffusion potential of Fe and M, molar volume and interfacial diffusivity of M, respectively. From Eqs. (A1a) and (b), Δμ is expressed as   

$$\mathrm{\Delta }\mu ={\mu }_M-{\mu }_{Fe}=RTln\left(y_M/\left(1-y_M\right)\right)+E_M\left(x\right)$$(A3)

Hillert⁷³⁾ derived energy dissipated due to diffusion in the whole system, $\mathrm{\Delta }{G}_{SDE-H}^{diss}$, as   

$$\mathrm{\Delta }{G}_{SDE-H}^{diss}=-\frac{V_m}{v}{\int }_{-\infty }^{\infty }{J}_M\frac{d\left(\mathrm{\Delta }\mu \right)}{dx}dx\mathrm{\hspace{0.17em} }\text{(}=\text{Eq}\text{.}\mathrm{\hspace{0.17em} }\text{4)}$$(A4)

where v and J_M represent interface velocity and diffusion flux, respectively. Under steady state assumption, Eq. (A4) is transformed as follows⁷³⁾   

$$\begin{array}{l}\mathrm{\Delta }{G}_{SDE-H}^{diss}=-{\int }_{-\infty }^{\infty }\left(y_M-y_M^0\right)\frac{d\left(\mathrm{\Delta }\mu \right)}{dx}dx\\ =-{\int }_{-\infty }^{\infty }\left(y_M-y_M^0\right)\left[\frac{d\left(E_M\left(x\right)\right)}{dx}+\frac{RT}{\left(1-y_M\right)y_M}\frac{d{y}_M}{dx}\right]dx\end{array}$$(A5)

In steady state, compositional gradient in a product phase diminishes, therefore, integration in α region in Eq. (A5) can be neglected. Integration in γ, $\mathrm{\Delta }{G}_{SDE}^{\gamma }$, in Eq. (A5) is represented by;   

$$\mathrm{\Delta }{G}_{SDE}^{\gamma }=RT\left[y_M^{0}ln\left(\frac{y_M^0}{y_M^{\gamma -int}}\right)+\left(1-y_M^0\right)ln\left(\frac{1-y_M^0}{1-y_M^{\gamma -int}}\right)\right]=\mathrm{\Delta }{G}_{part}^{diss}$$(A6)

$\mathrm{\Delta }{G}_{SDE}^{\gamma }$ is identical to the energy dissipation due to partitioning, $\mathrm{\Delta }{G}_{part}^{diss}$, in Eq. (2). By integrating the energy gradient within interface in Eq. (A5), the energy dissipation by SDE is described by the following equation,   

$$\begin{array}{l}\mathrm{\Delta }{G}_{SDE}^{int}=-{\int }_{-\delta }^{\delta }\frac{d\left(E_M\left(x\right)\right)}{dx}\left(y_M-y_M^0\right)dx\\ \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}+RT\left[y_M^{0}ln\left(\frac{y_M^{\gamma -int}}{y_M^0}\right)+\left(1-y_M^0\right)ln\left(\frac{1-y_M^{\gamma -int}}{1-y_M^0}\right)\right]\end{array}$$(A7)

The first term of Eq. (A7) is identical to the equation proposed by Purdy and Brechet (Eq. (3)) and second term is equal to −$\mathrm{\Delta }{G}_{part}^{diss}$.

Therefore,   

$$\mathrm{\Delta }{G}_{SDE}^{int}=\mathrm{\Delta }{G}_{SDE-PB}^{diss}-\mathrm{\Delta }{G}_{part}^{diss}$$(A8)

Finally Eq. (A9) is obtained in the steady state.   

$$\mathrm{\Delta }{G}_{SDE-PB}^{diss}=\mathrm{\Delta }{G}_{SDE}^{int}+\mathrm{\Delta }{G}_{SDE}^{\gamma }=\mathrm{\Delta }{G}_{SDE-H}^{diss}$$(A9)

It should be noted that $\mathrm{\Delta }{G}_{SDE-H}^{diss}$ is not equal to $\mathrm{\Delta }{G}_{SDE-PB}^{diss}$ in non-steady state.