In rare-earth steel continuous casting, researchers examined the role of cerium oxide (CeO₂) in mold slag crystallization. Using single hot thermocouple technique (SHTT) and Raman spectroscopy, they investigated the CaO–SiO₂–Al₂O₃–Na₂O–CaF₂–(CeO₂) slag system. The CeO₂ was found to reduce structural polymerization, increase substance migration rates, and promote slag crystallization. Applying Johnson-Mehl-Avrami (JMA) and modified JMA models revealed distinct crystallization behaviors. In isothermal conditions, the crystal growth mechanism transitioned from one-dimensional to three-dimensional as temperature increased. Non-isothermal analysis consistently showed three-dimensional crystal growth. The models quantified how CeO₂ content influences crystallization kinetics, demonstrating altered growth patterns. As CeO₂ increased to 3%, the isothermal crystallization activation energy rose from 153.59 to 302.58 kJ/mol, indicating enhanced crystallization drive. Under non-isothermal conditions, with cooling rates of 1 to 20°C/s, the apparent activation energy ranged from −288.44 to −941.97 kJ/mol. The negative values suggest that accelerated cooling and increased CeO₂ concentration reduce crystallization process inhibition.

An increase in the CeO₂ content in the continuous casting mold slag results in alterations to crystallization, which may result in sticking breakout.^1,2,3) However, if the mold slag has a high SiO₂ content, the oxidation of Ce in the steel is inevitable.^4,5) Meanwhile, some researchers have investigated the effect of CeO₂ on crystallization. Cai et al.^2,6) found that the addition of CeO₂ increases the crystallization and solid slag thickness, which leads to a decrease in the heat transfer coefficient. Zhao et al.⁷⁾ investigated the solidification behaviour of slags containing CeO₂ using a confocal laser scanning microscope (CLSM). Zhou et al.⁸⁾ found that the addition of CeO₂ to blast furnace slag changed the two-dimensional crystallization mechanism into a three-dimensional crystallization mechanism, which improved the stability of the foamed glass-ceramics glass phase. However, the crystallization process has not been sufficiently analysed in those study. By analysing the crystallization process, it is possible to provide a reference for not only continuous casting production but also slag recycling.⁷⁾

In the realm of crystallization kinetics, researchers have grappled with the complexities of analysing thermal transformation processes. Research in this field has historically centered on the utilization of differential thermal analysis (DSC/DTA) methodologies and the Kissinger formula.^9,10) However, the maximum cooling rate available for DSC/DTA experiments is about 50°C min⁻¹, which is insufficient for simulating the continuous casting process. The single hot thermocouple technique (SHTT), as an in-situ observation method that can directly observe the cooling crystallization process, has been widely used in the slag crystallization analysis process.^11,12) However, it should be noted that SHTT records crystallization data at 1 s intervals. Furthermore, the Kissinger formula requires time and temperature data at a fixed crystallization fraction.¹³⁾ Consequently, the Kissinger formula is not applicable to SHTT crystallization data analysis.

To analyse the isothermal crystallization kinetics of the SHTT data, Zhou and Wang et al.^14,15) used the Johnson–Mehl–Avrami (JMA) model to investigate isothermal crystallization, yet the field lacks a systematic approach to cooling crystallization kinetics. And the current analytical methods for SHTT crystallization remain insufficient and controversial. Notably, researchers¹⁶⁾ have developed analytical methods based on the JMA rate equation without thoroughly validating its fundamental accuracy. Paradoxically, despite potential theoretical limitations, these methods often demonstrate remarkable agreement with more precise analytical techniques. This unexpected consistency suggests that the JMA rate equation inherently captures many critical properties of exact solutions. A breakthrough came from Farjas et al.,¹⁷⁾ who proposed a minor yet significant correction that extends the JMA transformation rate equation to non-isothermal conditions. This advancement addresses the previous methodological constraints.

In this work, the effect of CeO₂ on structure and crystallization of the mold slag was analysed through the utilization of the SHTT method. Additionally, the isothermal and non-isothermal crystallization kinetics were investigated by JMA and modified JMA model. This study provides theoretical support for the continuous casting production and recycling of cerium-containing steel slag.

To study the effect of CeO₂ on crystallization, different amounts of CeO₂ were added to the same base mold slag. The sample preparation process began with carefully selected reagent-grade powders from Macklin, with Na₂CO₃ substituting for Na₂O and CaO obtained through precise calcination of calcium carbonate at 1000°C for 6 hours. 5 g powder mixtures in a platinum crucible, which were then heated to 1500°C for approximately 10 minutes under argon. This critical step ensured complete decomposition of Na₂CO₃ and thorough mixing of slag components. The premelted slags were analysed by X-ray fluoroscopy, and the results were listed in Table 1. The evaporative loss of F was around 2 pct that was consistent with Zhou et al.¹⁴⁾ and Li et al.¹⁶⁾

The molten slag at 1500°C underwent a controlled cooling process, stabilizing at 1200°C and 1400°C for 10 minutes before rapid cooling to room temperature. To observe the crystalline phase, the samples sintered at 1200°C were characterized using XRD (Rigaku SmartLab SE) and scanning electron microscopy (SEM). In contrast, microstructure analysis of the 1400°C molten slag samples were performed using Raman spectroscopy (Horiba LabRam HR Evolution), which was employed once XRD analysis confirmed the amorphous state of these samples.

The SHTT served as the primary investigative method, combining advanced computerised image observation and thermocouple technology. This approach allowed for unprecedented precision in temperature control and crystallization monitoring, with cameras capturing crystallized images at one-second intervals. And image analysis is realized by the Image-Pro Plus software.

The experiments were conducted comprehensive across two primary conditions: isothermal crystallization at 50°C intervals ranging from 900 to 1400°C, and non-isothermal crystallization at varied cooling rates of 1, 3, 5, 10, and 20°C/s. The experimental temperature profile is illustrated in Fig. 1.

Fig. 1. Temperature settings for isothermal and non-isothermal crystallization. (Online version in color.)

Figure 2 shows the XRD pattern of the mold slag rapidly cooled at 1400°C and 1200°C. The XRD at 1400°C has no significant crystallization peaks, indicating that the slag sample is in an amorphous state. The main crystalline phase is larnite (Ca₂SiO₄) at 1200°C, and the type of crystalline phase is consistent with previous studies.¹⁸⁾ SEM was used to examine the slag phase. As illustrated in Fig. 3, the white ellipsoidal crystals are embedded in the grey amorphous glass phase. Furthermore, the EDS analysis corroborates the identification of the crystals as Ca₂SiO₄, which match the XRD results. It can be observed that the addition of CeO₂ increases the crystal size of the slag samples, indicating enhanced crystal growth in the mold slag.

Fig. 2. XRD patterns of the slag samples at 1400°C (a) and 1200°C (b). (Online version in color.)

Fig. 3. SEM diagrams of slags crystalized at 1200°C. (Online version in color.)

The effect of CeO₂ on the Raman spectra of mold slag is illustrated in Fig. 4. The spectral investigation focuses on multiple frequency regions, each representing distinct structural characteristics of the slag. In the Raman spectra range of 800–1200 cm⁻¹, the Qⁿ is prominently displayed, with specific bands corresponding to different bridging oxygen configurations. Following the established classifications by McMillan¹⁹⁾ and Mysen^20,21)et al., the bands are precisely categorized: 850–880 cm⁻¹ represents Q⁰, 900–930 cm⁻¹ represents Q¹, 950–1000 cm⁻¹ represents Q², and 1030–1060 cm⁻¹ represents Q³, each indicating progressively complex silicate tetrahedral structures. The mid-frequency region (620–750 cm⁻¹) presents a complicated scientific debate, with researchers offering competing interpretations. Some scholars argue this region represents bending vibrations of Si–O bridging oxygen bonds,^22,23) while alternative perspectives suggest these frequencies correspond to stretching vibrations of Al–O⁰ in [AlO4]⁻tetrahedral units.²⁴⁾ The low-frequency region (550–620 cm⁻¹) is crucial, representing Si–O–Si bond vibrations.²⁵⁾ Notably, as CeO₂ content increases, the Raman peak at 570 cm⁻¹ demonstrates a consistent reduction in height.

Fig. 4. Raman spectra of different CeO₂ contents. (Online version in color.)

The Raman spectroscopic analysis employed Gaussian split peaks for fitting the spectra, with background subtraction ensuring accurate representation of the data. The fitting coefficients (R²) exceeded 0.999, indicating a high degree of reliability in the results, which are illustrated in Fig. 5.

Fig. 5. The peak area ratio obtained from the Raman spectra. (Online version in color.)

Notable changes in the silicate structure of the continuous casting mold slag were observed with increasing CeO₂ content in Fig. 5. Specifically, the relative areas of the Q³ and Q² structures decreased, while the Q¹ and Q⁰ structures increased. This transformation signifies a shift from chain and lamellar structures to monomeric and dimeric configurations. Additionally, the decreasing Q³/Q² ratio suggests a reduction in the degree of structural polymerization,^26,27) indicating CeO₂’s role as a network modifier that promotes the depolymerization of the silicate network. Furthermore, the peak height of the Raman peak at 570 cm⁻¹ continues to decrease, indicating a progressive decrease in Si–O–Si bond configurations as CeO₂ content rises. Overall, the reduction in polymerization leads to decreased diffusion resistance, facilitating enhanced crystallization of the slag.

As shown in the Fig. 6, the isothermal crystallization process of slag has complex morphological changes in different temperature ranges. Initially, the slag appears completely transparent at 1500°C, signifying total liquefaction and homogeneous thermal state (Figs. 6(a), 6(b)). As the temperature progressively declines, a crystallization phenomenon emerges, as evidenced by the white regions observed in the images. The crystalline fraction is quantified through image analysis techniques, measuring the crystal area ratio relative to the total slag image area.

Fig. 6. Sample images at 1500°C of (a) Ce2; (b) Ce3. Crystallization images of spherical shape: (c) at 1200°C of Ce2; (b) at 1150°C of Ce3, square shape: (e) at 1100°C of Ce0; (f) at 1100°C of Ce1, and needle-like or flocculent shapes: (g) at 1000°C of Ce1; (h) at 1000°C of Ce3. (Online version in color.)

Three distinctive crystallization modes are systematically documented, each manifesting unique structural characteristic. Spherical crystallization, predominant above 1150°C, demonstrates a consistent nucleation rate and spherical morphology, as illustrated in Figs. 6(c), 6(d). In contrast, square crystallization, typically occurring below 1150°C, exhibits a markedly different behavior—characterized by low nucleation rates and crystals originating from thermocouple edges with a fixed directional growth pattern. These square crystallizations are illustrated in Figs. 6(e), 6(f). The lower temperature range reveals needle-like crystallization, distinguished by high nucleation rates and the formation of fine, elongated crystal structures. And this needle-like crystallizations are illustrated in Figs. 6(g), 6(h).

Based on the crystallization incubation time (τ_p) during isothermal crystallization, the Time-Temperature-Transformation curve (TTT) of CeO₂ can be plotted as shown in Fig. 7. The addition of CeO₂ demonstrates a profound impact on crystallization behavior, elevating the crystallization temperature to 1400°C while increasing the crystallization temperature. At CeO₂ concentrations exceeding 2%, a remarkable phenomenon emerges where crystallization occurs instantaneously when temperature reduce to the holding temperature, indicating accelerated nucleation of CeO₂.

Fig. 7. TTT curve of the slag. (Online version in color.)

Further investigation into the impact of cooling rates on crystallization was conducted, leading to the development of the Continuous Cooling Transformation (CCT) curve, depicted in Fig. 8. The findings demonstrate that increased cooling rates result in shorter τp and lower crystallization temperatures. Conversely, lower cooling rates necessitate longer crystal incubation times, attributed to the reduced subcooling of slag samples. In conditions of low subcooling, the process of nucleation necessitates a larger critical nucleation radius, which increases the energy required for nucleation, thereby prolonging the time needed for crystallization to initiate.

Fig. 8. CCT curve of the slag. (Online version in color.)

With increasing of CeO₂ content, the crystals appeared at a higher temperature and shorter time at the same cooling rate. This suggests that CeO₂ addition promotes crystal nucleation and reduces the crystallization gestation time. In addition, it should be mentioned that after cooling to room temperature at a rate of 20°C/s, Ce0 and Ce1 were not fully crystallized, while Ce2 and Ce3 were fully crystallized. This suggests that CeO₂ promotes the crystallization of slag and increases the critical cooling rate.

Overall, CeO₂ is demonstrated to facilitate the depolymerization of long-chain silicate anionic groups, resulting in the formation of monomers or dimers, which enhances structural reorganization during crystallization. Additionally, the reduced polymerization lowers the slag’s viscosity, increasing the migration rate of substances within it. Together, these effects lead to faster and easier crystallization of the slag.

The JMA crystallographic kinetic model can be used to analyse the crystal growth mechanism during the isothermal cooling process.²⁸⁾

The relationship between Crystallisation ratio (X) and crystallization time (τ_c) can also be expressed in a linear form as follows:

where n represents the Avrami index, K represents the effective total reaction rate, influenced by both the nucleation rate and the growth rate. The curves of Eq. (2) are shown in Fig. 9 and the fitting results are shown in Table 2. The ln[ln(1/1−X)] and lnτ_c have a good linear correlation (R²>0.95).

Fig. 9. Relation of volume fraction of crystals (X) and crystallization time (τ_c). (Online version in color.)

Fig. 10. Variation of lnK with 1/T. (Online version in color.)

Avrami index n relates to the nucleation and growth mechanism. At high temperatures (T > 1100°C), the value of n in the slag is around 1.5, with spherical crystallization. Combined with the crystal images, the number of slag nuclei is fixed, with the nuclei growing in three dimensions and diffusion controlling the crystallization rate.¹⁴⁾ Below 1100°C, the crystallization shape changes to the square. In Ce0 slag, the n value is around 1 from 1000 to 1100°C, and the number of crystal nuclei is fixed and grows in a two-dimensional manner. In other slag, the n value is around 2 from 1000 to 1100°C, which also indicates that the number of crystal nuclei is fixed and crystallization grows in a two-dimensional manner. The difference in n values may be due to adding CeO₂ to the slag, which alters the control mechanism from diffusion to interfacial reactions. When the crystallization temperature continues to decrease, the crystallization growth mode changes to one-dimensional and the shape becomes needle-like or flocculent. In this case, when n approaches 1.5, the continuous casting mold slag nucleates at a constant rate; when n approaches 1, the number of nuclei remains fixed.

In general, a larger K means that the crystal crystallizes faster, and there is a relationship between it and temperature:

The lnK was further fitted using Eq. (3). The E_c of the samples Ce0, Ce1, Ce2 and Ce3 were 153.59, 158.63, 201.96, and 302.58 kJ/mol, respectively. E_c represents the activation energy of the isothermal crystallization process, and the higher value represents the higher driving force. Consequently, with the increase of CeO₂, the driving force for crystallization increases, thereby facilitating the crystallization process.

In non-isothermal processes, the JMA equation no longer works, and K in the equation cannot represent the crystallization rate. Furthermore, the crystallization conversion rate does not depend only on temperature (via K) and conversion fraction. Melts with different thermal histories (e.g., cooling rate β) will correspond to different states. Therefore, the JMA model is corrected using parameters Z_c, as shown in the following formula:

Crystallization kinetics were analysed according to Eq. (4) and the results are shown in Fig. 11 and Table 3. It can be seen that in most cases 2.3 < n < 3.0. Combined with the crystallographic images, this crystallographic parameter represents the slag growing in a three-dimensional manner with constant rate nucleation and diffusion controlling. At lower crystallization rates, the n value lies around 1.5, which indicates a change from a constant rate to a constant number of nuclei. This may be due to the fact that the low supercooling makes the crystal nucleation more difficult and inhibits the nucleation.

Fig. 11. Relation of ln[ln(1/1−X)] and lnt in non-isothermal crystallization. (Online version in color.)

However, the activation energy of crystallization for non-isothermal processes has to be calculated in a different way. The overall activation energy is defined as:^29,30)

Where n′ is the Avrami index of non-isothermal crystallization process and can be calculated by Eq. (4), E_N and E_G represent the activation energies for nucleation and growth, respectively.

It is possible to propose distinct scenarios based on the relationship between E_N and E_G.¹⁷⁾ The JMA rate equation is applicable to non-isothermal cases, provided the transformation rate depends only on temperature and the degree of transformation,³¹⁾ not on thermal history. This condition is met in specific situations like “site saturation”, where nucleation occurs before crystal growth,^31,32) or in singular isokinetic situation.²⁸⁾ The crystal growth by fixed nuclei is consistent with this condition when n ≈ 1.5. Under these special conditions, E_N = E_G and the Eq. (6) can be used directly, where the constant C can be neglected. When E_N ≠ E_G, E c ′ /K_BT≫ 1 in the experiment. Farjas et al.¹⁷⁾ used an approximate first term based on the JMA isothermal formula transformation resulting in Eq. (6):

Where k₀ is a constant affected by the shape of the crystals and the mode of growth, K_B is the Boltzmann constant. C is a constant that depends on n’, E_N and E_G, C=[ ( n ′ )! E n ′ ∏ i=0 n ′ -1 ( E N +i E G ) ] .

In the derivation, for simplicity of representation, the definition of the p(x)= ∫ x ∞ exp(-u) u 2 du . The plot of ln(p(y)) versus y shows a linear trend: ln(p(y))≈−5.2813−1.051y (20 < y < 60).³³⁾ Equation (6) can write as:

A similar plot of ln[ln 1/(1−X)] versus 1/T based on three-dimensional crystalline growth was obtained by Matusita et al.:³⁴⁾

However, some scholars^9,35) have proposed that the Matusita formula may give rise to erroneous values of activation energy if they are used for studying crystallization during cooling. Thus, the activation energy of crystallization was analysed according to Eq. (7) and the results are shown in Fig. 12 and Table 4.

Fig. 12. Relation of ln[ln(1/1−X)] and 1/T in non-isothermal crystallization. (Online version in color.)

It is noteworthy that the activation energy of the isothermal crystallization process is positive, representing the driving force for crystallization. In contrast, the activation energy of the non-isothermal crystallization process is negative, representing as the hindering force for crystallization. The greater the absolute value of the activation energy, the greater the resistance to the crystallization process. It can be seen that the absolute value of the activation energy decreases as the cooling rate increases. There is a tendency for the absolute value of the activation energy to decrease as the CeO₂ content increases. The data demonstrate that an accelerated cooling rate, coupled with an elevated CeO₂ content, results in a reduction in the hindrance of crystallization.

The influence of CeO₂ on the crystallization of continuous casting mold slag reveals significant insights into the crystallization kinetic under varying conditions. During isothermal crystallization, it was observed that at high temperatures (above 1100°C), the crystals exhibit a three-dimensional growth pattern and take on a spherical shape. As the temperature decreases, the growth morphology transitions to two-dimensional square shapes and eventually to one-dimensional needle-like structures. Notably, increasing the CeO₂ content to 3% results in a substantial rise in the crystallization activation energy, from 153.59 to 302.58 kJ/mol, indicating that higher CeO₂ concentrations enhance the driving force for isothermal crystallization.

In the context of non-isothermal crystallization, the addition of CeO₂ leads to a decrease in crystallization incubation time and an increase in crystallization temperature. The kinetics of this process can be analysed using the modified JMA model, which suggests that crystallization is primarily governed by constant rate nucleation and three-dimensional growth. At lower cooling rates, the crystallization occurs with a constant number of nuclei, demonstrating a stable nucleation process. The apparent crystallization activation energy ranges from −288.44 to −941.97 kJ/mol, depending on the cooling rates (1 to 20°C/s) and CeO₂ content (0 to 3 mass%). This range indicates that both the acceleration of the cooling process and the increase in CeO₂ concentration effectively reduce the inhibition of the crystallization process, facilitating more efficient crystal formation in the continuous casting mold slag.

The authors declare no conflicts of interest regarding this manuscript.

The authors are grateful for the financial support of this work from the National Natural Science Foundation of China (No. 52274406), the Foreign Expert Project (G2023405011L), the Fundamental Research Funds for the Central Universities (FRF-BD-23-02), and the Key Research and Development Program in Shanxi Province (202202050201019).

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