In Situ 3D Neutron Depolarization Study of the Transformation Kinetics and Grain Size Evolution During Cyclic Partial Austenite-Ferrite Phase Transformations in Fe-C-Mn Steels

The kinetics of the austenite-to-ferrite (γ-α) and the ferrite-to-austenite (α-γ) transformations in low-alloyed steels have attracted extensive attention due to their practical importance and scientific challenges.[1‐5] During the austenite-to-ferrite transformation, the ferrite first nucleates at the preferred nucleation sites and subsequently grows into the austenite grains. As observed with synchrotron X-ray diffraction, ferrite nucleation occurs in a certain temperature (or time) range, where new nuclei continuously form until a maximum density is reached.[6] Once nucleated, the growth of a ferritic grain, i.e., the interfacial migration, is controlled by interfacial mobility and diffusion of solute elements in the vicinity of the moving interface. To explore the effect of the alloying elements M (=Mn, Ni, Co, etc.) on interfacial migration in Fe-C-M steels, extensive studies have been performed using conventional isothermal or continuous heating and cooling experiments.[7‐10] However, in such experiments where nucleation and interfacial migration take place simultaneously, the impossibility to determine the nucleation rate during the entire transformation process unavoidably leads to nonnegligible uncertainties in the derivation of the interfacial mobility and investigating the effect of the alloying elements. To avoid the effect of nucleation on the transformation kinetics, the concept of cyclic partial austenite-ferrite transformation, where the temperature is varied cyclically within the γ/α two-phase region, was recently proposed.[11] This cyclic approach has proven to be more informative in studying the effect of interfacial mobility and alloying elements on the rate of the interfacial migration as a result of the (assumed) absence of new nucleation events from the moment of the first inverse transformation cycle. This assumption is physically realistic and has been verified ex-situ by 2D metallographic cross sections.[12] A large number of dilatometric cyclic partial phase transformation measurements[11,12] and various modeling approaches such as DICTRA,[11] 1D mixed-mode modeling,[13] and 1D phase-field modeling[14,15] have been used to study the effect of alloying element M on the austenite decomposition rate and to obtain the interfacial mobility. These cyclic partial phase transformation studies reveal unexpected phenomena such as inverse and stagnant transformations as a result of various degrees of local partitioning of substitutional alloying elements at the moving austenite-ferrite interface. However, the key assumption behind the cyclic partial phase transformation approach that there are no, or only negligible, new nucleation events during cycling has not been verified by in situ experiments yet. To resolve this, we use three-dimensional neutron depolarization (3DND) to simultaneously measure the ferrite fraction and grain size during cyclic partial phase transformations in a low-alloyed construction steel. In the current study, the ferrite number density can be determined in situ during the cyclic partial phase transformation. The 3DND method also allows the in situ determination of the average grain size during the transformation, which can hardly be obtained from other physical in situ characterization techniques.

3DND is a powerful technique to characterize magnetic induction inside bulk materials at (sub)micron scale.[16,17] In a 3DND measurement, polarized neutrons demonstrate Larmor precession around a local magnetic field within a magnetized sample. After transmission through the sample, the mean magnetization causes a net rotation of the polarization vector, while a field variation due to magnetic inhomogeneities results in the decrease of the polarization vector. Therefore, the rotation angle measures the ferromagnetic phase fraction inside bulk materials. The shortening of the polarization vector determines the magnetic correlation length and thereby the mean size of the magnetic regions along the neutron path. A quantitative description of the relation between the correlation and the size of the magnetic particles in 3DND experiments was derived by Rosman and Rekveldt.[16] For the austenite-to-ferrite transformation in steels, the newly formed ferritic grains become magnetic below the Curie temperature (1043 K for pure iron), while the surrounding austenitic matrix remains paramagnetic and thereby effectively non-magnetic. This enables 3DND to determine the key microstructural features of the ferrite phase, i.e., the ferrite volume fraction and the average ferrite grain size. Te Velthuis and coworkers[18] further developed the formulation of the 3DND method and applied it to study the austenite-to-ferrite transformation in medium carbon steels. In a recent study, we computationally analyzed the effect of the size distribution on the 3DND-derived microstructural parameters and found that the 3DND method, under certain conditions, may even yield information on the ferrite grain size distribution.[19] Therefore, the 3DND technique provides a powerful tool to simultaneously measure the ferrite fraction and the grain size within the bulk of steel samples. This technique has been used successfully to study austenite-to-ferrite[20] and austenite-to-pearlite[21] phase transformations in steels under isothermal conditions and during continuous cooling conditions.

In a 3DND measurement, a 3 × 3 depolarization matrix \( \hat{D} \) expresses the relationship between the polarization vector before (\( \vec{P}^{0} \)) and after (\( \vec{P}^{\prime} \)) transmission through the sample by \( \vec{P}^{\prime} = \hat{D}\vec{P}^{0} \).[16,22] The components of the polarization vector are determined by the corresponding intensities detected by a ³He detector parallel or antiparallel to the x, y, and z axis as expressed bywhere i, j = x, y, or z represent the analyzed and initial polarization directions, respectively. P₀ is the degree of polarization of the incoming neutron beam and I_s is the shim intensity, which is given by \( I_{\text{s}} = \left( {I_{zz} + I_{zZ} } \right)/2 \). The capital Z indicates a negative z direction. For the case with a net magnetization along the z axis, the neutron precession is around the plane perpendicular to the magnetization, resulting in a rotation angle of the polarization vector that can be expressed as

This rotation of the polarization vector is related to the mean magnetization of the sample[20,21]where η is a geometric factor that accounts for the stray fields, c = 2.15 × 10²⁹λ² T⁻² m⁻⁴ is a constant with λ the neutron wavelength, L_x is the sample thickness, f is the volume fraction of the ferromagnetic phase, 〈m_z〉 is the average reduced magnetization in the direction of the applied magnetic field (z direction), μ₀ is the permeability of vacuum, and M_s is the saturation magnetization of the ferromagnetic phase. In the current study, ferrite is the only ferromagnetic phase in the temperature range of interest. The 〈m_z〉 value was determined by fitting the magnetization hysteresis curves which were obtained by varying the applied magnetic field at a constant temperature. In the current study, 〈m_z〉 = 1.0 for temperatures above 1022 K (749 °C), 〈m_z〉 = 0.7 for temperatures below 955 K (682 °C), and a linear temperature dependence \( \langle m_{z} \rangle = 1 - 0.3\left( {749 - T} \right)/67 \) with T in degrees Celcius was found between 1022 K and 955 K (749 °C and 682 °C). M_s is calculated using the method proposed by Arrott and Heinrich.[23] η can be expressed as \( \eta = \left( {1 - f} \right)\eta^{P} + \eta^{M} \) with η^P = 0.5 for spherical magnetic particles and \( \eta^{M} = \frac{2}{\pi }{ \arctan }\left( {\frac{{L_{z} }}{{L_{y} }}} \right) \) determined by the sample dimensions perpendicular to the neutron beam.[24] Hence, the ferrite volume fraction can be determined.

The correlation function ξ, which is proportional to the correlation length of \( \left| {\vec{B}\left( {\vec{r}} \right)} \right|^{2} \) along the neutron beam, measures the size of the magnetic particles. Assuming that there are no correlations between \( \Delta {B}_{i} \left( {\vec{r}} \right) \) and \( \Delta {B}_{j} \left( {\vec{r}} \right) \) (i ≠ j) along the neutron path, the relation between the correlation function and the determinant of the depolarization matrix can be expressed as \( \xi = - \frac{{\ln \left( {\det \left( {\hat{D}} \right)} \right)}}{{2cL_{x} }} \). The effective radius of the magnetic particle that characterizes the average particle size δ is related to the correlation function ξ aswhere the constants c₂ and c₃ are calculated according to Reference 18. For a given particle size distribution, the average particle size δ corresponds to \( \delta = \frac{{\langle R^{4} \rangle}}{{\langle R^{3} \rangle}} \) where R is the particle radius.[18] The validity of the analysis was recently evaluated by simulated particle size distribution.[19] The influence of the particle size distribution was characterized in detail. The previous simulations confirm that Eq. [4] provides a reliable estimate for the ferrite grain size. More detailed information about the 3DND theory can be found elsewhere.[16,17,22]

Steel samples for the 3DND measurements with dimensions L_x × L_y × L_z = 1.5 × 15 × 100 mm³ were cut from a cold-rolled steel sheet (1.5 × 150 × 200 mm³) provided by Arcelor Mittal. The middle area (ΔL_y × ΔL_z = 15 × 20 mm²) of the sample plate was thinned down to 0.4 mm by spark wire erosion. The chemical composition of the steel sample is given in Table I. The 3DND experiments were performed on the PANDA instrument at the nuclear reactor at the Reactor Institute Delft using a polarized neutron beam with a fixed wave wavelength of 2.06 Å and a spread of about 2 pct. The degree of polarization of the empty beam is 98 pct. The samples were mounted in a sample holder sandwiched by two BN blocks. Three K-type thermocouples were welded onto the sample with an identical spacing to monitor the temperature homogeneity along the vertical axis of the sample. The sample was mounted into a furnace, which was placed on the PANDA instrument, under a vacuum environment (with a pressure < 10⁻³ Pa). In the current study, neutron beam is in the x direction, and the applied magnetic field B_appl is along the z direction. During the time-dependent 3DND experiments, the applied magnetic field was B_appl = 6.2 mT.

In situ 3DND measurements were carried out to investigate the microstructure evolution in the sample during cycling between T₁ and T₂ in the γ/α two-phase region. The sample was first annealed at 1073 K (800 °C) for at least one hour and subsequently cooled to T₁ at a rate of 3 K min⁻¹. After holding at T₁ for 20 minute in order to reach a (quasi-)equilibrium state, the temperature was raised to T₂ and lowered back to T₁ and cycled between these values at a constant rate. After a preset number of cycles, the sample was cooled down to room temperature. During the test, the temperature difference over the sample region probed by the neutron beam was within 2 K. The cycling temperatures and the corresponding equilibrium ferrite fraction calculated with Thermo-Calc software using the TCFE8 database are given in Table II. The sample composition and the cycling temperatures of the Fe-C-2.06 wt pct Mn alloy are shown in the phase diagram in Figure 1. The cycling temperatures were chosen such that the equilibrium ferrite fraction is not too small to form a significant amount of the ferrite phase and is not too large to avoid extensive hard impingement of the ferrite grains. Therefore, the cycling temperatures were chosen to show an equilibrium ferrite fraction between 0.2 and 0.6. The cycling temperature window was set to be constant ΔT = 20 K. As the ferrite formation in this steel is relatively slow according to previous studies,[2,7] we chose a relatively slow cycling rate to ensure that a sizable variation of the ferrite fraction can be observed. As neutron experiments are rate limited too, this low cycling rate matches the relatively long measurement times required for the 3DND measurements: for the current installation 45 seconds were required to complete the determination of a whole depolarization matrix. Figure 1 shows that the temperature is cycled across the A_e3 under para-equilibrium condition (para-A_e3) for the tests of S740 and S750, while for the other tests, the temperature is cycled below para-A_e3 and above the NPLE/PLE transition temperature between negligible partitioning local equilibrium (NPLE) and partitioning local equilibrium (PLE). The ferromagnetic Curie temperature of the sample is determined from the 3DND measurements as T_C = 1034 K (761 °C). Micrographs of the samples after the multicyclic partial transformation 3DND measurements were taken to evaluate the final ferrite grain size. To corroborate the 3DND results, rectangular samples with dimensions of 1.5 × 1.5 × 10 mm³ were heat treated in a DIL805D/T dilatometer with the same temperature profiles as used in the 3DND experiments, but quenched at various stages during multicycling. The samples were etched with 2 pct nital to distinguish between the ferrite and the martensite that was transformed from the austenite during quenching. Both optical and electron microscopy techniques (JEOL JSM 6500F) were used to examine the microstructures of the quenched samples. The ferrite volume fraction was determined using the point-counting method. The 3D ferrite grain radius R_3D was derived from the 2D spherical equivalent radius R_2D with \( R_{3D} = 4R_{2D} /\pi \).[25]

The evolution of the ferrite fraction and the ferrite grain size during slow partial cyclic austenite-ferrite phase transformations in Fe-0.25C-2.1Mn (wt pct) steel has been studied in detail with 3DND experiments. The number density of the ferrite grains was estimated, and the results demonstrate that during cycling additional nucleation is proven to be negligible or even absent. Hence, the current study provides the experimental evidence that cyclic partial transformations indeed can yield direct information on the actual movement of the austenite-ferrite interface and can be free from the effects of simultaneous nucleation. During cycling, the austenite-ferrite interface migrates into the austenite region and back to the ferrite region in each cycle with a net increase in both ferrite fraction and ferrite grain size over multiple cycles; a feature which cannot be captured by 1D (or fixed geometry) simulations of interfacial mobility during solid state phase transformations. The interfacial migration velocity is of the order of 10⁻³ µm/s during cycling. This low value is attributed to Mn partitioning. The length of the Mn diffusion spike is estimated to be 1–15 nm, indicating a probable coexistence of short-range and long-range diffusions. The intrinsic cyclic behavior of the interfacial migration is visible after subtracting the effect of the progressive interfacial migration into austenite. The closing cyclic loops are reproducible and reveal a stagnant stage.