Grain refinement in solidification of undercooled Fe₂B intermetallic compound alloy Open Access

Solidification is a crucial transformation process wherein a substance changes from a liquid state to a solid state. It is widely recognized as one of the most effective methods for material manufacturing.¹ The solidification process can be influenced by various factors, including the alloy composition and the chosen processing technology. One important factor is the melt undercooling prior to nucleation. The solidification at significant undercooling gives rise to a wide range of intriguing phenomena, including the formation of metastable phases,^2–4 transitions from regular to anomalous eutectics,^5,6 spontaneous grain refinement,⁷ and solute trapping.⁸ The manifestation of these phenomena is contingent upon the composition and nature of the alloy under investigation.

Grain refinement is primarily observed during the solidification of undercooled solid-solution alloys. After its initial discovery in the nickel melt by Walker,⁹ it was observed in various systems, including Ni–Cu,¹⁰ Fe–Ni,¹¹ and Fe–Co.¹² As a result, it was once believed that this phenomenon of grain refinement was inherent to solid solution alloys and pure metals. Grain refinement is considered to be beneficial for enhancing the overall mechanical properties of most materials.¹³ The underlying physics has thus been attracting much attention during past decades. For solid solution alloys with a certain crystallization temperature interval, grain refinement has been found to occur not only with large undercooling but also within a range of moderate undercoolings. Based on a quantitative assessment of the superheating degree of primary solid during the temperature recalescence induced by rapid solidification, Li et al. attributed the grain refinement at moderate undercoolings to the remelting of primary solid, while that at large undercooling was attributed to the post-solidification recrystallization.^14,15 Although some researchers linked the grain refinement at large undercooling with massive homogeneous nucleation,¹⁶ or the solid/liquid interface energy-induced break-up,^17,18 the theory of recrystallization was more widely recognized.^14,15,19

Intermetallic compounds can be classified into two types according to their compositions: non-stoichiometric and stoichiometric intermetallic compounds. For the formers such as Ni₃Ge and CoSi whose compositions can change within a certain range, the solidification within a range of moderate undercoolings as well as at large undercoolings also results in grain refinement.^20,21 Besides chemical superheating, the solid instability from disorder trapping at large undercooling was thought to be another reason for grain refinement.²⁰ For stoichiometric intermetallic compounds that solidify without solute trapping, it was impossible for remelting to take place in the primary solid. The grain refinement at large undercooling is probably linked with the stress-induced dendrite fragmentation.^22,23 However, the investigations performed so far have been mainly focused on single-phase solid solution alloys. Experiments with undercooled stoichiometric intermetallic compounds are very limited, and the evidence for the grain refinement mechanism in this type of alloy is far from sound.

Fe–B binary alloys are drawing attention for their special magnetic properties, glass forming ability, and the role as basic components in many multi-component alloys.^24,25 In the phase diagram, there are three stable phases: α-Fe, Fe₂B, and FeB. Fe₃B and Fe₂₃B₆ were occasionally reported as metastable phases in the solidification of some Fe–B alloys.^26–29 As a stoichiometric intermetallic compound, Fe₂B is an ideal model alloy for investigating solidification theories and understanding fundamental aspects of phase transformations. To our knowledge, there has not been any report on the solidification of undercooled Fe₂B alloy. In this paper, the alloy with a nominal composition of Fe₂B was solidified at different undercoolings, and grain refinement was detected at high undercooling. Solidification stress-induced recrystallization was thought to be the reason for the grain refinement.

The Fe₂B alloy ingot was synthesized by arc melting a mixture of high purity Fe (99.999 wt. %) and B (99.999 wt.  %) blocks under a high purity argon atmosphere in a water-cooled copper crucible. It was remelted several times and turned over after each melting operation to ensure chemical homogeneity.

The alloy ingot was then crushed into small pieces. In each undercooling experiment, about 3 g of the alloy and a small quantity of B₂O₃ glass flux were put together into a fused silica crucible inserted in the induction-heating coil. After evacuating the vacuum chamber to a pressure of 2 × 10⁻³ Pa, ultra-high purity argon was filled back into the chamber, followed by induction melting the alloy. Covered by the molten flux, the alloy was cyclically superheated and cooled by adjusting the input power until a desired undercooling was obtained. Nucleation occurred spontaneously without any manual triggering. All the samples solidified in natural cooling. An infrared pyrometer with an accuracy of ±1 K and a response time of 1 ms was utilized to monitor the thermal history of the alloy. The temperature data were recorded in a computer.

Each solidified sample was sectioned, polished, and etched with a mixture of 8% nitric acid and alcohol. The solidification microstructure was analyzed using an optical microscope (OM), and the phase constitution was determined using a Rigaku SmartLab x-ray diffractometer (XRD) with monochromatic Co K_α radiation. Electron backscattered diffraction (EBSD) measurements were performed to reveal the crystal orientation relationship using AZtecHKL and Channel 5 software. After the focused ion beam (FIB) thinned, the sample was analyzed in an FEI Talos F200X transmission electron microscope (TEM).

Typical cooling curves of the Fe₂B samples are illustrated in Fig. 1(a). Defining the melt undercooling to be the difference between the equilibrium liquidus temperature T_l and the nucleation temperature T_N, a maximum undercooling of up to 336 K was achieved in the present experiment. From Fig. 1(a), it can be seen that there is only one temperature recalescence event on each cooling curve. As undercooling increases, the highest recalescence temperature and the duration of solidification decrease.

The recalescence rate, i.e., the ratio of the recalescence degree (the maximum recalescence temperature minus the nucleation temperature) to recalescence time, reflects the speed of temperature change over time. It can be calculated from the cooling curves, and the results in Fe₂B alloy are shown in Fig. 1(b). As undercooling increases, the recalescence rate increases monotonically. The maximum recalescence rate reaches 3000 K/s at 336 K undercooling.

Figure 2 shows the XRD patterns of the Fe₂B alloy solidified at different undercoolings. The solidification products are all single Fe₂B stable phases. According to the phase diagram, the Fe₂B alloy should solidify through a peritectic reaction L + FeB → Fe₂B, taking FeB as the primary phase. Due to the limited atomic diffusion in the solid state, peritectic reactions can often be incomplete. In this case, part of the primary phase will be preserved in the final solidification structure. For the Fe₂B alloy, if the Fe₂B phase is formed through the peritectic reaction, the FeB phase should be detected by XRD. To clarify this point, the alloy ingot was also examined by XRD. As shown in Fig. 2, the FeB phase did not also form as a primary phase. The temperature interval from the liquidus to peritectic line for Fe₂B alloy is quite narrow, due to which the alloy melt is very easily undercooled below the peritectic temperature in the solidification and the precipitation of FeB as the primary phase is suppressed. Hence, Fe₂B directly precipitated from the melt. Metastable phases, such as Fe₃B and Fe₂₃B₆, did not precipitate because their compositions deviate significantly from the alloy’s composition.

Figure 3 shows the typical microstructures of the Fe₂B alloy. At low undercooling, the alloy solidifies into coarse dendrites of the faceted Fe₂B phase [Fig. 3(a)]. The dendritic morphology is more visible in the surface micrograph shown in Fig. 3(e). As the undercooling increases, Fe₂B crystals change from a faceted into non-faceted profile. Grain refinement begins to occur from an undercooling of 48 K, and fully refined equiaxed grains are obtained as the undercooling reaches 92 K. The grain size at different undercoolings was estimated from the microstructure by the method of drawing lines. As shown in Fig. 4, the average grain diameter reaches several millimeters at low undercoolings. As the grain refinement occurs, the grain size decreases sharply as the undercooling increases. The grain size is only about 8 µm at the maximum undercooling of 336 K.

Two representative samples, solidified at 48 and 221 K undercooling, respectively, were analyzed by EBSD, and the results are shown in Fig. 5. From the inverse pole figure (IPF) maps and the {001} pole figures, it can be seen that the dendrite arms are well oriented at low undercooling [Figs. 5(a) and 5(b)] but the refined grains are randomly oriented at large undercooling [Figs. 5(d) and 5(e)]. The misorientation angle distribution shown in Fig. 5(f) further illustrates that the refined grains are characterized by high-angle and flat boundaries and random crystal orientations.

As the undercooling increases, the rise of growth velocity is more significant than the nucleation rate in a binary alloy. As a result, it is often observed that the alloy solidifies through a single nucleation site at large undercooling. The presence of abundant nucleation has been excluded as one of the reasons for grain refinement in deeply undercooled alloys. As a stoichiometric compound, the Fe₂B phase solidifies without any solute trapping. It is also impossible for chemical superheating to trigger the grain refinement at large undercooling. However, under high crystal growth velocities, some atoms may occupy wrong lattice sites of the compound, i.e., resulting in so-called disorder trapping. Severe chemical disorder in crystals can lead to their destabilization and eventual break up. On the other hand, it has been shown that disorder trapping is easier to occur in non-stoichiometric than in stoichiometric intermetallic compounds.³⁰ In this sense, the grain refinement in Fe₂B alloy is mostly independent on disorder trapping. The microstructural evolution should be ascribed to other reasons.

The interfacial atomic arrangement is related to the entropy of fusion ∆S_f. According to Jackson’s rule, if the dimensionless entropy ∆S_f/R < 2 (R is the gas constant), a rough interface will be favored. Otherwise a smooth interface will be favored.^31,32 The entropy of fusion of Fe₂B is about 16.09 J/mol,²⁷ corresponding to a ∆S_f/R of 1.94. Therefore, the solidifying interface of the Fe₂B intermetallic compound is in a critical state. When the phase grows slowly at low undercooling, the interface is smooth in a microscopic scale, and the solid develops into a faceted morphology. At larger undercooling, it grows into a non-faceted interface due to the kinetic effect.^33–35 

The transition from a liquid to a solid phase can be associated with either a volume contraction or expansion. When crystals grow rapidly in melts, a stress generates in the solid because the volume change cannot be fed in time,³⁹ due to which the dendrite skeleton is deformed as the yield strength of the solid at elevated temperature is very low. In the subsequent cooling process, recrystallization takes place in the dendrite, driven by the deformation energy,¹⁹ which refines the grains. So far, the investigation activities on the recrystallization-induced grain refinement have been mainly focused on solid solution alloys. There are still doubts about whether this type of grain refinement can take place in intermetallic compounds considering the significant difference in the crystal structure between a solid solution and an intermetallic compound. To clarify the mechanism underlying the grain refinement in the Fe₂B phase, the solidification microstructure of the highly undercooled Fe₂B samples was further examined by TEM, and surviving un-recrystallized structures were detected at the grain boundaries. Figure 7(a) shows a TEM image of this structure at an undercooling of 221 K, where the dense drapes reflecting stacking faults can be clearly observed. The HRTEM image (indicated by a white arrow) and the clusters of diffraction spots shown in the SAD pattern [Figs. 7(b) and 7(c)] also reveal the formation of stacking faults in the primary Fe₂B phase. With abundant crystal defects, the rapidly solidified solid is unstable. New crystals surely nucleate and grow into the deformed solid, releasing the stored deformation energy until the grain boundaries meet each other.^40,41 As shown Fig. 5, the random nucleation in the recrystallization results in a non-oriented distribution of the refined grains. As the time for the sample to hold at elevated temperatures was very short under the present experimental condition, some deformation structures survived from the recrystallization, as shown in Fig. 7(a), which provides us with clear and sound evidence to judge the origin of grain refinement.

The recrystallization degree in a sample can be revealed by EBSD measurement.^42,43 Figure 8 shows the proportions of various microstructures in the samples undercooled by 48 and 221 K. According to the internal average misorientation angle (IAMA), three types of grains were distinguished: deformed grains with IAMAs above 10°, substructured grains with IAMAs between 1° and 10°, and recrystallized grains with IAMAs below 1°. As the undercooling increases from 48 to 221 K, the recrystallization proportion increases from 58.3% to 87.1%. It can be inferred that the greater the undercooling, the higher the degree of recrystallization. The stress states in grains were analyzed using the kernel average misorientation (KAM), and the results are shown in Fig. 9. The larger the KAM value, the higher the stored energy. It can be seen that the sample undercooled by 48 K has more regions of high KAM values than that undercooled by 221 K. This is consistent with the analysis results of the recrystallization degree. It is further confirmed that the grain refinement in Fe₂B alloy occurs via recrystallization.

To verify the hypothesis of recrystallization for the grain refinement, a temperature incubation experiment was carried out using a set of samples solidified around 210 K undercooling. In each experiment, the sample was solidified at about 210 K. When it was naturally cooled to 1600 K (the liquidus temperature of Fe₂B alloy is 1696 K), the power was switched on immediately and the input power was adjusted to hold the sample at 1600 K for a predetermined duration of time. Then the power was turned off, and the sample was cooled to room temperature. The microstructures of the samples with different holding times are shown in Fig. 10. It can be seen that the grain size increases with the prolonging holding time. Figure 11 shows the relationship between the grain size and the holding time. The grains grow quickly at the initial annealing treatment. The microstructures annealed for 20 and 40 min do not show any obvious difference. Note that the substructures in a solidification dendrite, i.e., its various dendrite arms, are quite stable due to their similar crystal orientations and difficult to coarsen through annealing the sample at a high temperature for a short time. The experimental result presented in Fig. 10 supports the argument that the grain refinement in highly undercooled Fe₂B alloy is induced by recrystallization.

In summary, Fe₂B alloy has been solidified at various undercoolings, and the solidification microstructure evolution with undercooling was investigated. The conclusions are as follows:

1. For Fe₂B alloy, the equilibrium peritectic reaction L + FeB → Fe₂B is very easy to suppress. Only Fe₂B is there to form, regardless of whether the alloy solidifies in a water-cooled copper crucible or in a fused silica crucible at various undercoolings.

2. As the undercooling increases, the Fe₂B phase transits from a faceted to non-faceted morphology. The solidification with an undercooling larger than 92 K results in remarkable grain refinement.

3. When a sample solidified at large undercooling is annealed at elevated temperatures, the grains is coarsened quickly. In combination with the deformation structure survived in the solidification structure, it is suggested that the grain refinement in Fe₂B alloy occurs via recrystallization.

This work was supported by the National Natural Science Foundation of China (Grant Nos. 51771116, 52231002, 51620105012, and 51821001).

The authors have no conflicts to disclose.

Changsong Ma: Data curation (lead); Investigation (equal); Visualization (lead); Writing – original draft (lead). Lin Yang: Investigation (equal); Methodology (lead); Validation (equal). Jinfu Li: Conceptualization (lead); Funding acquisition (lead); Project administration (lead); Resources (lead); Supervision (lead); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.