ISIJ International
Online ISSN : 1347-5460
Print ISSN : 0915-1559
ISSN-L : 0915-1559
Steelmaking
Crystallization Control for Fluorine-free Mold Fluxes: Effect of Na2O Content on Non-isothermal Melt Crystallization Kinetics
Qifeng Shu Jeferson Leandro KlugSamuel Lucas Santos MedeirosNestor C. HeckYang Liu
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2020 Volume 60 Issue 11 Pages 2425-2435

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Abstract

There are increasing demands for developing fluorine-free mold fluxes for continuous casting of steel. When removing fluorine from mold flux composition, it is necessary to replace it with oxides, which must maintain the technological parameters, related to viscosity, melting characteristics, and crystallization behavior. For industrial developments in the CaO–SiO2–Na2O–Al2O3–TiO2–B2O3–MgO (with basicity = 1, Al2O3 = 7%, TiO2 = 5%, B2O3 = 3%, MgO = 2%) slag system, it is necessary to know the effect of Na2O concentration regarding crystallization kinetics. This is especially important for fluorine-free mold fluxes for peritectic steel slab casting. In this work, the crystals´ precipitation sequence for this system during cooling was determined, combining Differential Scanning Calorimetry (DSC), X-Ray Diffraction (XRD), and Scanning Electron Microscopy (SEM). The Friedman differential isoconversional method was applied for determining the effective activation energy for non-isothermal crystallization, since it gives relevant information without knowing the form of the kinetic equation. A modified Avrami model was used to calculate the n values; it was found that they are near 2.5, for all analyzed samples, which means that it is related to the crystallization mode diffusion controlled, with constant nucleation rate and three-dimensional growth. This agrees with the SEM micrographs, where dendritic structure is observed for all crystalline samples. Additionally, structural information got from Raman spectroscopy, for the samples in vitreous state, was used to interpret crystallization tendency, i.e., the fact that crystallization was enhanced by increasing Na2O content, due to slag depolymerization. Moreover, computational thermodynamics was used to analyze mold fluxes crystallization behavior.

1. Introduction

Mold flux has two main functions during continuous casting of steel. The first one, lubrication, prevents sticking. The second one is the control of horizontal heat transfer rate. It is well known that these functions are strongly dependent on crystallization behavior of mold flux.1) Crystallization happens in two different ways, since crystals precipitate from liquid slag and from glassy phase. The other functions are to protect steel against oxidation, to absorb inclusions, and thermal insulation.2)

Fluorine is usually part of commercial mold fluxes composition, because it is relevant for mold flux performance. This element in traditional CaO–SiO2–CaF2 mold fluxes is important to control their technological parameters, such as: mold slag viscosity, characteristic temperatures, and crystallization kinetics. On the other hand, fluorine in mold fluxes is disadvantageous due to environmental and health concerns. Furthermore, it causes the corrosion of the continuous casting machine, because hydrofluoric acid is generated from mold flux; it increases dramatically the corrosion rate especially below the mold where there is a high amount of water accelerating the process.3,4,5,6,7) This context makes the elimination of fluorine of mold fluxes composition a very important industry demand.

When developing fluorine-free mold fluxes, the technological parameters should be similar when using alternative raw materials. Besides, the cost for these materials must be observed; Li2O-bearing raw materials, for example, are very expensive. Some oxides as alternatives to replace CaF2 have been tried, mainly TiO2, B2O3 and Na2O.7) For billet casting, steelmakers frequently use high viscosity mold fluxes to overcome problems such as slag entrapment and submerged entry nozzle (SEN) erosion. In this case, crystallization kinetics does not need to be addressed when developing fluorine-free mold fluxes, since crystallization rate is very low; increase in Na2O content is a good choice to compensate for fluorine removal.8) For low carbon steel slab casting, B2O3 can be used as alternative, since crystallization tendency is low for this case. B2O3 addition decrease crystallization ability of slags; this was not a problem for industrial tests with a B2O3-bearing F-free mold flux.9)

However, when it is necessary to reduce horizontal heat transfer rate (mild cooling), crystallization kinetics becomes a very important parameter. For peritectic steel (0.09–0.16 wt% C) slab casting, the crystalline fraction of the solid slag layer along the mold must be high to avoid longitudinal cracking, which in turn happens because of the 4% mismatch in the steel thermal shrinkage coefficients for the δ and γ phases. Regarding crystallization behavior for CaO–SiO2–CaF2 mold slags, the precipitation of cuspidine (3CaO.2SiO2.CaF2) is related to heat transfer control. Although the mechanism for heat transfer control has not yet been determined, two ideas have been proposed. An idea is that radiation heat flux decreases by scattering at the boundary between the crystalline and the liquid layers during crystallization from slag. Another idea is that the total heat flux can be decreased by the large thermal resistance of the air gap formed because of the solidification shrinkage of the solidified slag layer, which occurs due to crystallization from glass. In both cases, crystallization of cuspidine happens. When comparing crystallization from melt and crystallization from glass, the first one should be more important, because crystallization from liquid is faster. The heat transfer control function starts to work a few seconds from the casting, therefore crystallization from melt brings the great effect on heat transfer control.10) Thus, the first crystal should have a special role.

Nakada and Nagata10) suggested it is worth to investigate the effect of Na2O addition in CaO–SiO2–TiO2 slags, considering the possibility of using this slag system for tailoring fluorine-free mold fluxes. These slags are expected to have the lubrication function because liquidus temperatures and viscosities are similar to slags in the CaO–SiO2–CaF2 system. This suggestion was followed by another work, in which the effect of Na2O on crystallization kinetics was evaluated with Time-Temperature-Transformation (TTT) and Continuous-Cooling-Transformation (CCT) diagrams, which were built using the Single Hot Thermocouple Technique (SHTT).11) It was found that addition of Na2O in CaO–SiO2–TiO2 slags dramatically shortens the crystals’ incubation times to the range of seconds, with a clear effect of the Na2O content on the critical cooling rate. Thus, it is possible to control crystallization kinetics in CaO–SiO2–TiO2 slags by changing the Na2O content. In this study, five samples were analyzed, with binary basicity in the range 0.6–0.8, TiO2 15.2–18.1 wt%, and Na2O 0.0–7.1 wt%.11)

Based on plant trials, Wen et al.12) proposed the following composition range for TiO2-bearing F-free mold fluxes for peritectic steel slab casting: basicity 0.95–1.15, TiO2 4.0–7.0 wt%, Na2O 5.0–8.0 wt%, Li2O 1.0–2.0 wt%, MnO 3.0–5.0 wt%, and B2O3 4.0–8.0 wt%. They reported that the laboratory technological parameters were like the corresponding traditional F-bearing mold flux. Besides, the industrial trials indicated that the F-free mold flux effectively controlled heat transfer, due to rapid precipitation of perovskite (CaO.TiO2), which replaced cuspidine. In terms of crack index, slab surface quality became even better.

In a previous laboratory work,13) non-isothermal melt crystallization kinetics for CaO–Al2O3–B2O3 F-free mold fluxes, for continuous casting of high aluminum steels, through modified Avrami analysis and Friedman differential isoconversional method, was studied. Crystallization mechanisms and effective activation energy of crystallization were determined for different compositions, for the first crystal, which precipitates from melt (Ca3Al2O6). It was found for all compositions that effective activation energy is negative, showing anti-Arrhenius behavior, because crystallization is controlled by thermodynamic driving force for nucleation.

Another way to analyze crystallization from melt is from structural data of glasses, considering that structure of quenched glass should be like parent melt. In this way, it is possible to find correlations between structure of quenched glass and crystallization tendency, for different compositions. In a previous work,14) the effect of TiO2 content on structure of the glassy CaO–SiO2–CaF2–TiO2 system, which is related to the mold slag for continuous casting of titanium-stabilized stainless steel, was investigated through two techniques: Raman spectroscopy, and Nuclear Magnetic Resonance with Magic Angular Spinning spectroscopy (MAS-NMR). It was observed that Q2 is the predominant silicate species for the studied samples, and that Ti4+ mainly exists in the form of [TiO4] in silicates, forming TiO2-like clusters with Ti4+ in tetrahedral coordination, not changing degree of polymerization of the silicate network. Moreover, it was concluded that a small amount of Ti enters the silicate network as the role of network formation, enhancing degree of polymerization of the silicate network. Three samples were studied, with TiO2 contents of 0, 5, and 10 wt.%, basicity (wCaO)/(wSiO2) ~1,3 and CaF2 content ~10 wt.%.

Thus, it is important to understand crystallization from mold slag to improve performance of continuous casting process. The objective of the present work is, therefore, to investigate non-isothermal melt crystallization kinetics for F-free TiO2-bearing mold fluxes, considering the first crystal, which precipitates during cooling, using the model-free Friedman differential isoconversional method, and modified Avrami analysis. Three samples with different Na2O contents were studied through Differential Scanning Calorimetry (DSC). Besides, structural information got from Raman spectroscopy was used to interpret crystallization behavior for these samples. Moreover, a thermodynamic analysis was carried out considering the effect of Na2O addition on thermodynamic driving force for the precipitation of Ca2SiO4 during cooling.

2. Experimental

2.1. Preparation of Glassy Samples

Slags were synthesized from reagent grade MgO, Al2O3, Na2CO3, CaO, TiO2, SiO2 and H3BO3. Composition (wt.%) of the samples investigated in the present work are shown in Table 1. CaO was prepared by decomposition of CaCO3 at 1000°C overnight. Reagent powders were mixed in an agate mortar and held in a platinum crucible placed in a MoSi2 furnace at 1400°C for 2 hours in air. After melting, the samples were quenched in water to obtain glassy cullets. X-Ray Diffraction (XRD) confirmed the glassy state, according to Fig. 1.

Table 1. Chemical composition of the samples investigated in the present work.
SampleComposition (wt%)
CaOSiO2Al2O3MgONa2OTiO2B2O3Basicity
135.535.57212531
236.5036.507210531
337.537.5728531
Fig. 1.

XRD pattern for Sample 2, which was quenched in water after melting at 1400°C for 2 hours. All the samples investigated in the present work were prepared in this way. The pattern confirms glassy structure.

2.2. DSC Measurements

Glassy cullets were pulverized and subjected do DSC analysis. The runs were performed using a thermal analyzer STA 449 F3 Jupiter from the manufacturer Netzsch-Gerätebau GmbH, with argon acting as purge gas at dynamic conditions. Calibration for the apparatus was performed using alfa-Al2O3 as the reference material, building a temperature calibration curve and a sensitivity calibration curve with pure substances. After calibration, the glassy samples were heated up to 1400°C with a heating rate of 20°C/min, and then cooled with different rates (15, 20, 25, and 30°C/min). Platinum crucibles with platinum lids were used to minimize the loss of volatile substances. A new baseline was generated for each heating rate using an empty platinum crucible.

From DSC data, CCT diagrams were built, and characteristic temperatures (liquidus, crystallization temperature, and undercooling) were determined for each sample.

2.3. SEM-EDS and XRD Analyses

In order to determine the sequence of crystal precipitation in DSC runs, the following thermal cycle was applied, using muffle furnace. Glassy cullets were heated from room temperature to 1400°C, with the rate of 5°C/min, and then cooled to target temperatures with the rate of 5°C/min. Then, the slags were quenched in water. The composition, morphology, and nature of crystallization products were identified by Scanning Electron Microscopy with Energy Dispersed Spectroscopy analysis (SEM-EDS), with the working voltage of 25 kV, and by XRD analysis, which was performed with a 18 kW X-ray diffractometer (RIGAKU TTRIII), using Cu–Kα radiation. With this procedure, the sequence of crystal precipitation from melt can be determined.

2.4. Raman Spectroscopy

Raman spectra were recorded at room temperature in the frequency range of 100–2000 cm−1 using a laser confocal micro-Raman spectrometer, LabRAM HR-Evolution (Horiba, Japan). Data collection were performed in room temperature using excitation wavelength of 532 nm and the light source He-Cd laser with power of 100 mW. The spectra were fitted by assuming Gaussian line shapes for peaks of different structural units. Abundances of structural units were calculated in terms of area fraction of peaks.

2.5. Computational Thermodynamic Analysis

The computational thermodynamic tool FactSage 7.3 was used, with FACT oxide database (FToxide) providing the data for solution and stoichiometric solid and liquid oxide phases. In this way, the effect of Na2O addition on activities of slag components was determined, considering crystallization behavior.

3. Results and Discussion

3.1. Crystals Precipitation Sequence

Figure 2 shows DSC results for Sample 1 (12 wt.% Na2O), which has the highest content of Na2O. The thermograms show that the higher the cooling rate is, the bigger the exothermic peaks become. The crystals related to the peaks are indicated in Fig. 2; they were identified by XRD. Samples were prepared according to the thermal cycle which was adopted to identify the sequence of crystal precipitation.

Fig. 2.

DSC results for Sample 1 (12 wt% Na2O) at different cooling rates from 1400°C: 15, 20, 25 and 30°C/min. (Online version in color.)

Figure 3 shows XRD diffraction patterns for Sample 1. The thermal cycle to determine the sequence of crystal precipitation is: (i) heating glassy cullets from room temperature up to 1400°C, with a heating rate of 5°C/min; (ii) cooling down to the target temperatures (1175°C, 1091°C, and 1015°C, and room temperature) with a rate of 5°C/min; and water quenching (except for room temperature). Diffraction peaks of CaTiO3 and Ca2SiO4 are found in the patterns quenched at 1015°C and 1091°C, while only diffractions peaks of Ca2SiO4 are found in the pattern quenched at 1175°C. When cooling to room temperature the crystal NaAlSiO4 was found in diffraction pattern, together with CaTiO3 and Ca2SiO4. Thus, the first crystal for Sample 1 is Ca2SiO4, followed by CaTiO3, and finally NaAlSiO4, as slag is gradually cooled.

Fig. 3.

XRD diffraction patterns for Sample 1 (12 wt% Na2O), after going through the thermal cycle which was adopted to identify the sequence of crystal precipitation. (Online version in color.)

The sequence of crystal precipitation for Sample 1 was also confirmed by SEM-EDS. For the sample quenched from 1175°C, Fig. 4(a) shows some dark grey crystals, whose elemental composition corresponds to Ca2SiO4, indicated by number 1. When quenching from 1091°C, Fig. 4(b) shows grey crystals (Ca2SiO4) and some light grey crystals, indicated by number 2 (CaTiO3); moreover, the Ca2SiO4 crystals are bigger because quenching temperature is lower. Figure 4(c) shows that the number and size of Ca2SiO4 and CaTiO3 crystals increase further when quenching from 1015°C. For the sample cooled down to room temperature at the rate 5°C/min, in addition to crystals of Ca2SiO4 and CaTiO3, which are still bigger, there are also NaAlSiO4 crystals, according to Fig. 4(d). Thus, the SEM-EDS results confirms the XRD results, regarding precipitation sequence.

Fig. 4.

SEM micrographs for Sample 1 (12 wt% Na2O), after going through the thermal cycle which was adopted to identify the sequence of crystal precipitation. Phases: 1 - Ca2SiO4, 2 - CaTiO3, and 3 - NaAlSiO4. (a) quenching from 1175°C, (b) quenching from 1091°C, (c) quenching from 1015°C, and (d) cooling down to room temperature at the rate 5°C/min. (Online version in color.)

For Sample 2 (10 wt.% Na2O), DSC results are in Fig. 5. The thermogram shows two peaks, one for Ca2SiO4, and the other for NaAlSiO4. XRD diffraction patterns and SEM micrographs are in Figs. 6 and 7, respectively. The analyzed samples were also submitted to the same thermal cycle: heating glassy cullets up to 1400°C with a heating rate of 5°C/min, then cooling down to the target temperatures at 5°C/min–990°C and 950°C for this sample –, followed by water quenching. Even with these relatively low target temperatures, only Ca2SiO4 was found. Thus, the first crystal is Ca2SiO4, and it should be related to the first peak of the thermograms. For Sample 2 the precipitation sequence is the same: Ca2SiO4, CaTiO3, and NaAlSiO4, as slag is cooled. Besides, it can be observed, when comparing Sample 1 (12 wt.% Na2O) with Sample 2 (10 wt.% Na2O), that crystallization temperature decreased.

Fig. 5.

DSC results for Sample 2 (10 wt% Na2O) at different cooling rates: 15, 20, 25 and 30°C/min. (Online version in color.)

Fig. 6.

XRD diffraction patterns for Sample 2 (10 wt% Na2O), after going through the thermal cycle which was adopted to identify the sequence of crystal precipitation. Quenching temperatures: 990°C and 950°C. (Online version in color.)

Fig. 7.

SEM micrographs for Sample 2 (10 wt% Na2O), after going through the thermal cycle which was adopted to identify the sequence of crystal precipitation. Quenching temperatures: (a) 990°C, and (b) 950°C. Phases: 1 - glass, 2 - Ca2SiO4. (Online version in color.)

For Sample 3 (8 wt.% Na2O), which has the lowest content of Na2O, Fig. 8 shows DSC results. Only one peak can be seen for all the cooling rates in the thermograms, in the range ~1000–1150°C. According to SEM and XRD data, Figs. 9 and 10, it is assumed that this peak is related to the primary crystallization of Ca2SiO4. A possible explanation for the absence of the other peaks is the fact that the sample with lower Na2O content will have lower tendency to crystallization, and consequently lower thermal effect, because reduction of the Na2O content increases slag viscosity. It was reported in a previous study, with the Single Hot Thermocouple Technique, that it is possible to control crystallization kinetics in CaO–SiO2–TiO2 slags by changing the Na2O content.11) It was observed that the incubation time for crystallization for CaO–SiO2–TiO2–Na2O slags is dramatically shortened by Na2O addition; however, in that case, the analyzed slags had different TiO2 and Na2O contents, and lower basicity.

Fig. 8.

DSC results for Sample 3 (8 wt% Na2O) at different cooling rates: 15, 20, 25 and 30°C/min. (Online version in color.)

Fig. 9.

XRD diffraction patterns for Sample 3 (8 wt% Na2O), after going through the thermal cycle which was adopted to identify the sequence of crystal precipitation. (Online version in color.)

Fig. 10.

SEM micrographs for Sample 3 (8 wt% Na2O), after going through the thermal cycle which was adopted to identify the sequence of crystal precipitation. Quenching temperatures: (a) 996°C, (b) 905°C. Phases: 1 - glass, 2 - Ca2SiO4, 3 - CaTiO3, 4 - NaAlSiO4. (Online version in color.)

The glassy samples were submitted to the same adopted thermal cycle, with the target temperatures 996°C and 905°C, and then water quenching. At 996°C (end of precipitation according to Fig. 8), Ca2SiO4 and CaTiO3 were found. At 905°C, NaAlSiO4 was detected, but the thermal effect was not enough to form a peak in DSC curve.

The SEM images (Figs. 4, 7, and 10) show that the primary crystal – Ca2SiO4 – precipitates as dendrite. This reflects the fact that growth of Ca2SiO4 is controlled by diffusion from bulk slag to slag-crystal interface.15)

The diffusion coefficient of ions in a slag can be calculated from its viscosity according to the Stokes-Einstein equation:16)   

D= k B T 6πrη (1)
where D is the diffusion coefficient of the ion in the slag, kB is the Boltzmann constant, T is the absolute temperature, r is the radius of the ion in the slag, and η is the viscosity.

Viscosity for CaO–SiO2–Na2O melts was measured;17) it was found that increase of Na2O content leads to a gradual decrease of viscosity. A similar conclusion was got when studying crystallization kinetics in CaO–SiO2–TiO2 slags, i.e., increase of Na2O content decreases viscosity; besides, it was experimentally found that increase of Na2O content decreases incubation times in TTT diagrams, and also raised the critical cooling rate.11) Moreover, in another work,18) in which the fluorine-free system CaO–SiO2–Na2O–B2O3–Al2O3–TiO2–MgO–Li2O was studied, for a fixed CaO/SiO2 ratio and nearly constant values of B2O3, Al2O3, TiO2, MgO and Li2O, the content of Na2O varied in the range 5.0–11.0 wt%; then, the effect of Na2O content on crystallization behavior was discussed. It was found that the increase of Na2O content raised the critical cooling rate and shortened the incubation time in TTT diagrams, promoting in this way the crystallization tendency for the analyzed slags.

3.2. Characteristic Temperatures

Crystallization temperatures and liquidus temperatures for the studied slags were got from thermograms. Crystallization temperature is defined as the onset temperature of the first exothermic peak, during cooling. With these temperatures, CCT curves were built and shown in Fig. 11. The higher the cooling rate is, the lower the crystallization temperature becomes; this fact can be explained considering that nucleation and growth rate of crystals are functions of viscosity (kinetics) and undercooling (thermodynamics). At higher cooling rate, more time is needed for initiating nucleation and subsequent crystal growth. Therefore, the crystallization temperature correspondingly decreases.19) Sample 1 has the highest crystallization temperatures for any cooling rate. It can be seen that crystallization temperature decreases when decreasing Na2O content.

Fig. 11.

CCT curves for the investigated samples. (Online version in color.)

Liquidus temperatures were also determined from the thermograms, considering the peak temperature for the last endothermic peak when heating the samples. Moreover, undercooling for onset crystallization (ΔT) was calculated; it is defined as the difference between liquidus temperature (TL) and crystallization temperature (TC). The characteristic temperatures and undercooling values are in Table 2, for the higher cooling rate.

Table 2. Characteristic temperatures and undercooling values at the cooling rate of 30 K/min for the investigated samples. TL: liquidus temperature, Tc: crystallization temperature, ΔT: undercooling.
TL (°C)TC (°C)ΔT (°C)
Sample 11155.31125.929.4
Sample 21132.71102.230.5
Sample 31137.81003.7134.1

Undercooling for Sample 1 and Sample 2 are similar; this result indicates that the crystallization ability for them is near. However, undercooling for Sample 3 is much higher; this sample presents the lowest crystallization ability.

3.3. Relative Crystallinity of Ca2SiO4 as a Function of Temperature

To investigate the non-isothermal melt crystallization kinetics, the heat released during crystallization was measured through DSC. The first crystal of the precipitation sequence should have a special role related to heat transfer control, during continuous casting of steel. Because of that, crystallization kinetics of Ca2SiO4 was considered in the following part. Values of relative crystallinity as a function of temperature, α(T), were obtained from the thermograms through the Eq. (2). The kinetic curves for the investigated samples, at different cooling rates, are shown in Fig. 12.   

α(T)= T 0 T (dH/dT)dT T 0 Te (dH/dT)dT (2)
where T, T0, and Te are the instantaneous, onset, and end crystallization temperatures, respectively, and dH/dT is the heat flow rate determined by DSC.
Fig. 12.

Relative crystallinity of Ca2SiO4 as a function of temperature for the investigated samples, at different cooling rates. (a) Sample 1 (12 wt% Na2O), (b) Sample 2 (10 wt% Na2O), and (c) Sample 3 (8 wt% Na2O). (Online version in color.)

3.4. Effective Activation Energy for Crystallization of Ca2SiO4

In Avrami equation, which holds for isothermal transformation, the crystallization rate constant has the overall nature because the macroscopic crystallization rate is generally determined by the rates of two processes, nucleation and nuclei growth. Because these two processes are likely to have different activation energies, the temperature dependence of the overall rate constant k can rarely be fit by a single Arrhenius equation, like Eq. (3), in a wide temperature range:   

k=A   exp( -E RT ) (3)
where R is the gas constant, A is the preexponential factor, and E is the activation energy.

Nevertheless, Eq. (3) should hold reasonably well for a relatively narrow temperature interval that permits estimating the effective value of the activation energy. Therefore, by splitting the temperature region of non-isothermal crystallization into smaller regions, it is possible to determine the temperature dependence of the effective activation energy for non-isothermal crystallization.20)

The differential isoconversional method recommended by Brown et al.,21) which was originally proposed by Friedman,22) was employed to obtain the effective activation energy for crystallization (Eα) of Ca2SiO4, at a given crystallization fraction, through the following equation:   

ln ( dα dt ) α =- E α R T α +C (4)
where (dα/dt)α is the instantaneous crystallization rate at the relative crystallinity α, Tα is the temperature at the relative crystallinity α, and C is a constant.

Plotting ln(dα/dt) against 1/Tα should give a straight line with slope -Eα/R. The relation between relative crystallinity and Eα of Ca2SiO4 is shown in Fig. 13. By this method, Eα can be determined without knowing the form of the kinetic equation.

Fig. 13.

Effective activation energy for crystallization (Eα) of Ca2SiO4 as a function of relative crystallinity for the investigated samples. (Online version in color.)

The Eα values for all samples and all crystalline fractions are negative, indicating that crystallization becomes slower with increasing temperature. That is to say, the crystallization of Ca2SiO4 during cooling follows anti-Arrhenius behavior, which was found in crystallization of polymers,20) traditional mold fluxes,23) and F-free mold fluxes.13)

For Sample 1, the one with the highest Na2O content, Eα takes greater negative values at lower values of relative crystallinity, corresponding to temperatures closer to liquidus. The Eα increases as the extent of conversion rises and the temperature decreases. A physical explanation could be given in terms of the nucleation theory proposed by Turnbull and Fisher.24) According to this theory, the temperature dependence of the nucleation rate is given by   

I=A   exp( - E D k B T )    exp   ( - Δ G * k B T ) (5)
where I is the nucleation rate i.e. the number of nuclei per unit volume formed per unit time, A is the pre-exponential factor, ED is the activation energy for diffusion across the phase boundary, and ΔG* is the thermodynamic barrier to nucleation.

The ED and ΔG* exponential terms have opposing effects on the nucleation rate. The value of ΔG* is inversely proportional to the degree of undercooling as follows:   

Δ G * 1 ( T L -T) 2 (6)

At temperatures close to liquidus, ED is nearly constant and ΔG* can be very high. In this situation, the overall crystallization rate is determined by the nucleation rate, and its temperature dependence is determined by Eq. (6).20) Once ΔG* drops, the nucleation rate becomes controlled by the transport process, whose temperature dependence is determined by the ED exponential term. This reasoning explains the increase of Eα with relative crystallinity for Sample 1.

For Sample 2, Eα values also increases as the extent of conversion rises and the temperature decreases. This sample has intermediate content of Na2O (10%), intermediate values of Eα, and presents undercooling value 1.1°C higher than Sample 1. Thus, ΔG* for Sample 2 should be lower than that for Sample 1.

Regarding Sample 3, the one with the lowest Na2O content and the highest undercooling, Eα values remain nearly constant with relative crystallinity. Due to the very high undercooling this sample has relatively low value of ΔG*, according to Eq. (6), thus the nucleation rate should be controlled mainly by the transport process. Assuming ED as approximately constant, this would explain the shape of the curve for Sample 3.

Another expression for the nucleation rate I is the Eq. (7), which shows that the lower the viscosity is, the higher the nucleation rate becomes. Equation (8) states a similar dependence, since the crystal growth rate U is also inversely proportional to the viscosity η.25) Thus, by decreasing viscosity (through Na2O addition for example), I and U increase.   

I= Ah 3π λ 3 η exp( -W* k B T ) (7)
where λ is the atomic jump distance, and h is Planck´s constant.   
U=( k B T 3π a 0 2 η ) [ 1-exp( ΔG k B T ) ] (8)
where a0 is the interatomic separation distance, and ΔG is the thermodynamic barrier to crystal growth.

3.5. Modified Avrami Equation

Crystallization kinetics for isothermal transformations is described by the Avrami equation26) in double logarithm form (see Eq. (7)). Values of n corresponding to different nucleation and growth mechanisms can be seen in Table 3.   

ln(-ln(1-α))=ln Z t +nlnt (9)
where α is the relative crystallinity, t is the crystallization time, Zt is the crystallization rate constant, and n is the parameter which indicates crystallization mechanism.

Table 3. Values of n for different nucleation and growth mechanisms.40)
Crystallization Mode
Diffusion controlledInterfacial reaction controlled
Constant nucleation rate
 Three-dimensional growth2.54
 Two-dimensional growth23
 One-dimensional growth1.52
Instantaneous nucleation
 Three-dimensional growth1.53
 Two-dimensional growth12
 One-dimensional growth0.51
Surface nucleation11

However, Avrami equation cannot be directly used for non-isothermal crystallization. The parameter related to crystallization kinetics is corrected according to Eq. (10).   

ln Z c =ln Z t /β (10)
where β is the cooling rate.

This correction, which is based on the approximate theory formulated by Ziabicki (apud Jeziorny27)), enables the characterization of non-isothermal crystallization kinetics, since Zc should be constant for each material. Thus, the modified Avrami equation becomes Eq. (11).   

ln(-ln(1-α))=βln Z c +nlnt (11)

Half crystallization time (t1/2) is calculated using Zc and n according to Eq. (12). The calculated Zt, Zc, n and t1/2 values for the analyzed samples are in Table 4.   

t 1/2 = ( ln2 Z c ) 1/n (12)

Table 4. Modified Avrami analysis results.
SampleCooling ratenZtZct1/2 (min)
Sample 115°C/min2.640.480.950.89
20°C/min2.760.410.960.89
25°C/min2.231.211.010.85
30°C/min2.321.401.010.85
Sample 215°C/min2.821.451.030.87
20°C/min2.481.521.020.86
25°C/min2.822.791.040.87
30°C/min2.164.011.050.83
Sample 315°C/min2.780.050.820.94
20°C/min2.510.100.900.90
25°C/min2.600.210.940.89
30°C/min2.300.350.970.87

As already mentioned in section 3.1, the SEM images show that the primary crystal precipitates as dendrite; this reflects the fact that growth of Ca2SiO4 is controlled by diffusion from bulk slag to slag-crystal interface. Therefore, the crystals grow three-dimensionally. From Table 3, the n value of 2.5 is related to the crystallization mode diffusion controlled, for constant nucleation rate and three-dimensional growth. It can be seen in Table 4 that the calculated values are near the value of 2.5.

3.6. Mold Slags Structure

Raman spectra for the investigated glassy samples are in Fig. 14. It is assumed that the structure for the vitreous samples at room temperature is like the structure of the molten mold slags. Before deconvolution, spectra backgrounds were subtracted. Then, for bands in the range 600–1200 cm−1, Gaussian deconvolution was applied, using a method proposed in literature,28,29) with correlation coefficient r2 ≥ 0.999. The envelope in the range 600–1200 cm−1 is fitted by considering six Gaussian peaks. Deconvolution results are in Fig. 15.

Fig. 14.

Raman spectra for Sample 1 (12 wt.% Na2O), Sample 2 (10 wt.% Na2O), and Sample 3 (8 wt.% Na2O). All the samples in glassy state and room temperature. (Online version in color.)

Fig. 15.

Deconvolution results for the analyzed samples (glassy state and room temperature). (a) Sample 1 (12 wt% Na2O), (b) Sample 2 (10 wt% Na2O), and (c) Sample 3 (8 wt% Na2O). (Online version in color.)

The band around 700 cm−1 reflects the deformation vibration of O–Ti–O bonds and vibration of [TiO6] structural units.30,31,32,33) The band in the range 826–836 cm−1 is attributed to the vibration of monomer or chainlike [TiO4] unit.30,31,32) The bands around 860 cm−1, 910 cm−1, 960 cm−1 and 1050 cm−1 reflect the vibration of Q0 monomer unit (SiO44−), Q1 dimer unit (Si2O76−), Q2 chain unit (SiO32−), and Q3 sheet unit, respectively.28,29,30,31,32,33,34,35) Assignments for the Raman bands are summarized in Table 5.

Table 5. Assignments for Raman bands for the analyzed samples.
Raman shift (cm−1)Raman assignments
~700mixing of the [TiO6] structure unit and O–Ti–O deformation
~870 Si O 4 4- stretching in monomer structure unit (Q0), or Q4(4Al) structure unit
830–860Vibration of monomer or chainlike [TiO4] unit
~860 Si O 4 4- stretching with no bridging oxygen in monomer structure unit (Q0)
~910Si2O76− stretching with one bridging oxygen in dimer structure unit (Q1)
~960SiO32− stretching with two bridging oxygen in chain-like structure unit (Q2)
~1050stretching with three bridging oxygen in sheet-like structure unit (Q3)

The molar fraction of a silicate structural unit Qi is estimated in the following way:   

X Q i = A Q i i=0 3 A Q i (13)
where X Q i is the molar fraction of Qi, and A Q i is the area of the Gaussian peak which corresponds to Qi.

Molar fractions of Qi for the investigated slags are in Table 6. Molar fractions of Q0 and Q1 increases and molar fractions of Q2 and Q3 decreases with increase of Na2O content in slag, indicating that the degree of polymerization decreases with increase of Na2O content.

Table 6. Distribution of structural units Qn (n = 0, 1, 2, and 3) for Sample 1 (12 wt.% Na2O), Sample 2 (10 wt% Na2O), and Sample 3 (8 wt% Na2O).
wt.% Na2Ox(Q0)x(Q1)x(Q2)x(Q3)Q
120.1100.2720.5520.0661.574
100.0960.2350.5980.0701.641
80.0760.1980.6060.1211.773

The average number of bridging oxygen per silicate tetrahedron (Q) can be used to quantify the degree of polymerization of slags. The value of Q is also shown in Table 6; it is calculated with Eq. (14).   

Q= i=0 4 X Q i i (14)

Thus, the value for Q decreases with increase of Na2O content.

The role of Na2O in borosilicate melts varies with chemical composition. When Na2O/B2O3 molar ratio is less than 0.5, Na2O act as a charge compensator to BO4 tetrahedron.38,39) When Na2O/B2O3 molar ratio is larger than 0.5, Na2O would behave as a network modifying oxide and enter into the silicate and borate network causing the depolymerization of silicate and borate network.38,39)

Since Na2O/B2O3 content in the present fluxes is larger than 2, additional Na2O should act in a role of network modifying oxide. Accordingly, the increase of Na2O content in slag would lead to the decrease of degree of polymerization and lead to more simple structural units such as Q0 and Q1.

As discussed in previous sections, crystallization for the investigated samples was controlled mainly by diffusion from bulk slag to the slag-crystal interface. The increase of Na2O content decreases the degree of polymerization, facilitating ions diffusion. Accordingly, crystallization was enhanced when adding Na2O.

3.7. Computational Thermodynamic Analysis

For the simplified CaO–SiO2–Al2O3–Na2O system, which includes the main components of the mold fluxes samples of Table 1 (in this simplification, mass of each component not included in the system was not considered in the calculations), the calculated CaO and SiO2 activities are shown in Table 7.

Table 7. Results for the simplified system CaO–SiO2–Al2O3–Na2O, for Sample 1, Sample 2, and Sample 3 (analyzed compositions in Table 1), at 1250°C.
Sample number1 (12% Na2O)2 (10% Na2O)3 (8% Na2O)
CaO activity in slag (aCaO)2.03 E-31.48 E-31.35 E-3
SiO2 activity in slag (aSiO2)1.04 E-21.95 E-22.27 E-2
(aCaO)2aSiO24.28 E-74.27 E-84.137 E-8

For rising Na2O levels (up to 12 wt.%) an increase in CaO activity in the liquid slag phase is noticed while SiO2 activity is simultaneously reduced. The precipitation reaction for Ca2SiO4 could be represented as:   

2(CaO)+(Si O 2 )=C a 2 Si O 4 (15)

where parentheses mean the component in slag. Accordingly, the thermodynamic driving force for Ca2SiO4 crystallization ∆G should be represented by supersaturation Π :41)   

ΔG=RT( a CaO 2 a SiO2 1 K ) (16)
where aCaO and aSiO2 denote the activity of CaO and SiO2 respectively; K is the equilibrium constant for reaction (15); R is gas constant; K is temperature in Kelvin.

Therefore, the value of (aCaO)2aSiO2 could be calculated to investigate the thermodynamic driving force for Ca2SiO4 precipitation. As seen in Table 7, the value of (aCaO)2aSiO2 increases as Na2O content rises. Accordingly, the thermodynamic driving forces for Ca2SiO4 precipitation increase with increase of Na2O content in slag. From viewpoint of thermodynamics, the addition of Na2O would be beneficial to the nucleation and growth of Ca2SiO4 crystals.

4. Conclusions

Non-isothermal melt crystallization kinetics for F-free TiO2-bearing mold fluxes was investigated, for three samples, with wt.% Na2O of 12% (Sample 1), 10% (Sample 2), and 8% (Sample 3). The following conclusions can be drawn:

(1) During continuous cooling from melt, the crystals´ precipitation sequence is Ca2SiO4, followed by CaTiO3, and finally NaAlSiO4, as slag is gradually cooled.

(2) The effective activation energy for non-isothermal crystallization Eα, as a function of relative crystallinity, for the first crystal which precipitates (Ca2SiO4), was experimentally determined with the Friedman differential isoconversional method. This method, which can be used without knowing the form of the kinetic equation, shows that the higher the Na2O content is, the lower the Eα values become i.e. crystallization is enhanced.

(3) With the modified Avrami equation, the n value near 2.5 was calculated for all samples; this value is related to the crystallization mode diffusion controlled, with constant nucleation rate and three-dimensional growth. It agrees with the SEM micrographs, where dendritic structure is observed.

(4) Raman spectra study for the samples in glassy state shows that the increase of Na2O content decreases the degree of polymerization, facilitating ions diffusion. This confirms the fact that crystallization was enhanced when adding Na2O.

(5) For the simplified CaO–SiO2–Al2O3–Na2O base system, thermodynamic analysis shows that Na2O addition causes an increase in CaO activity in the liquid slag while SiO2 activity is reduced; The value of (aCaO)2aSiO2 increases with addition of Na2O, which indicates that the thermodynamic driving force of Ca2SiO4 increases. From the viewpoint of thermodynamics, the addition of Na2O would promote the precipitation of Ca2SiO4 crystals.

Acknowledgements

Financial supports from the Academy of Finland for Genome of Steel Grant (No. 311934), from the National Natural Science Foundation of China (NSFC No. 51774026), and from the Coordination for the Improvement of Higher Education Personnel of Brazil (CAPES, Finance Code 001) are gratefully acknowledged.

References
 
© 2020 The Iron and Steel Institute of Japan.

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