Effect of Impurity Te on the Morphology of Alumina Particles in Molten Iron

Abstract

Surface active elements in liquid steel may affect the morphology of non-metallic particles during deoxidation. The effect of Te on the morphology of alumina particles was therefore studied by adding Te to molten iron before Al deoxidation at 1873 K. Dendritic, spherical, faceted, plate-like and clustered particles were identified in all samples. Te, however, considerably changes the relative frequencies of the morphologies, decreasing the amount of dendritic and spherical particles whereas increasing the amount of faceted and plate-like particles. This effect is closely related with the supersaturation degree, stirring, and Te content. The way Te influences the morphology of the alumina particles and the factors influencing Te effectiveness are discussed.

1. Introduction

Non-metallic particles in liquid steel are generated during deoxidization. Complete removal of these particles is difficult and expensive in practice. Mostly, non-metallic particles are considered to be detrimental to the mechanical properties of steel due to their different properties than the steel matrix, such as plasticity. Compared with spherical particles, hard non-deformable particles of irregular shape are more prone to initiate cracks due to local concentration of internal stresses, which can considerably decrease steel mechanical properties, such as ductility, toughness and fatigue strength.^1,2,3,4) Moreover, soft particles of irregular shape, such as sheet-like and rod-like MnS particles, are more deformable during hot rolling, which can result in reduced mechanical properties especially in the transverse direction.^4,5,6) Therefore, the morphology of non-metallic particles in steel products should be controlled.

The morphology of a crystal is intrinsically determined by its internal crystal structure.⁷⁾ However, external factors, such as supersaturation degree, holding time, temperature, stirring, impurities and solvent, can change the growth rates of individual faces and hence modify the morphology.⁷⁾ In Al-killed steel, alumina particles exhibit various morphologies, such as dendritic, spherical, faceted, plate-like, and clustered.⁸⁾ Moreover, faceted alumina particles show irregular, octahedral and truncated octahedral morphologies, largely deviating from the rhombohedral morphology expected from the crystal structure. This suggests that the morphology of alumina particles is affected by external factors during deoxidation. Studies of factors influencing the morphology of alumina particles show that: (1) faceted particles are formed at low supersaturation degree, whereas spherical and dendritic particles are formed at high supersaturation degree;^{8,9,10,11,12,13,14,15)} (2) stirring can modify the form of dendritic particles by changing the directions of supersaturation gradient, making them coral-like;¹⁶⁾ (3) stirring and long holding time favor the clustering of alumina particles;⁸⁾ (4) sintering and densification of clusters proceed with holding time, forming large polyhedral particles.^8,16) The formation mechanisms of different morphologies of alumina particles in liquid steel have been reviewed by Dekkers et al.¹⁶⁾ However, the origin of some morphologies, such as octahedral and plate-like, is still not fully understood.

Liquid steel is usually impure, containing strong surface active elements, such as O, S, N, and others. Solvent Fe itself is also an impurity from the viewpoint of crystal growth. Due to their surface active nature, these elements adsorb at the interface of non-metallic particles and liquid steel. This may affect the growth of the particles, thus modifying the morphologies. In aqueous solutions, the effect of impurities and solvent on crystal morphology has received great attention.^17,18) In the field of metallurgy, however, such studies are limited. The formation of flake graphite in cast iron is believed to be related to the adsorption of surface active elements, such as O, S, and Te, on the prism plane of high interfacial energy.^19,20,21) Besides, Te was reported to have the effect of spheroidizing manganese sulfide particles.^22,23) Studies of how impurities affect the morphology of alumina particles in liquid steel, however, are not reported.

This paper aims at studying the effect of Te on the morphology of alumina particles in molten iron. For this purpose, Te, which is a strong surface active element in molten iron, was added to the molten iron before Al deoxidization at 1873 K. The morphologies of alumina particles extracted from the iron matrix were examined with a high resolution SEM. Moreover, the way Te influences the morphology of the alumina particles and the factors influencing Te effectiveness are discussed.

2. Experimental Methods

2.1. Procedure

The experiments were carried out in a vertical tube furnace (heating element MoSi₂) under purified Ar atmosphere (flowrate 0.5 L/min, Po₂<10⁻²⁰ atm). 80 g of electrolytic iron (99.99 mass%, Mairon SHP, Toho Zinc Co. Ltd.) together with reagent grade Fe₂O₃ powder used to adjust the initial oxygen content was melted in a magnesia crucible (27 mm ID and 50 mm H), which was put into the furnace before heating up. After homogenizing for 30 min at 1873 K, Te (99.999 mass%) was added through a quartz tube (8 mm ID), followed by stirring for 30 s with an alumina rod. 3 min later, Al (99.99%) was added in the same way, followed by stirring for 0 or 30 s. Thereafter, the melt was held at 1873 K. Iron samples were taken with a quartz tube (6 mm ID) at 1, 3, and 10 min after Al addition and rapidly quenched in water. The experimental conditions are listed in Table 1. In the tests without Fe₂O₃ addition, the total oxygen content in the molten iron was measured to be around 150 ppm. Additions of 3.2, 20 and 80 mg Te correspond to 40, 250 and 1000 ppm Te in the melt, respectively. For the purpose of reproducibility, sampling was always done close to the crucible bottom.

Table 1. Details of the experimental conditions.

Test No.	Fe2O3	Te	Al	Stirring
	(g)	(mg)	(g)	(s)
L1	0	0	0.08	0
L2		80
LS1	0	0	0.08	30
LS2		80
HS1	0.11	0	0.13	30
HS2		3.2
HS3		20
HS4		80

2.2. Observation of Alumina Morphologies

0.1 g of iron sample was dissolved in an acid solution (HCl/HNO₃/H₂O = 10/1/10) at 90°C. After complete dissolution (4 h), the solution was filtered on a polycarbonate membrane with 0.2 μm pore size. Then, the membrane was washed, dried and coated with Au–Pd. Alumina particles on the membrane were subjected to SEM (Philips XL 30 FEG) observation. Successive micrographs were taken at a magnification of 5000 to have a dataset of at least 500 particles with an equivalent diameter larger than 0.8 μm. Only samples taken at 1 min after Al addition were analyzed as long holding time tends to make individual alumina particles in clusters undistinguishable due to sintering and densification processes.

2.3. Measurement of Impurity Content in Alumina Particles

The impurity content in alumina particles in a polished cross section of the iron samples was analyzed with an electron probe microanalysis (FEG-EPMA JXA-8530F), equipped with WDS and EDS spectrometers. The analysis starts with a wavelength spectral scan to identify possible impurity elements. Then the impurities were measured quantitatively at 10 kV voltage and 15 nA current. The depth x and width y of interaction volume in α-alumina matrix were calculated as 0.80 μm and 0.62 μm, respectively, using the following empirical formulas.²⁴⁾ Therefore, to minimize matrix interference, the analysis was performed on particles with an equivalent diameter larger than 2 μm. For each sample, impurity contents were averaged from more than 10 particles.   

$$x=\frac{0.1E_0^{1.5}}{\rho }$$(1)

  

$$y=\frac{0.077E_0^{1.5}}{\rho }$$(2)

where E₀ is the accelerating voltage (kV), and ρ is the density of the sample (g/cm³).

3. Experimental Results

3.1. Overview of Alumina Morphologies

During SEM observation, dendritic, spherical, faceted, plate-like and clustered alumina particles were identified in all samples. The classification in the present work follows that of Braun et al.⁸⁾ Dendritic particles develop with a typical multi-branching form; spherical particles are singular and have the shape of a sphere; faceted particles have well-developed crystal faces and are three-dimensional in character; plate-like particles also have well-developed crystal faces but appear as two-dimensional, showing a platy {222} form; clustered particles consist of two or more individual particles of the above mentioned morphologies. Examples of the various morphologies are shown in Fig. 1.

Fig. 1.

Alumina morphologies after acid extraction: spherical (S), dendritic (D), faceted (F), plate-like (PL) and clustered (C).

3.2. Effect of Te on the Morphology Distribution of Alumina Particles under Different Conditions

Alumna particles show various morphologies. To evaluate the morphological modification by Te, the morphology distribution of alumina particles in samples taken 1 min after Al addition was analyzed and shown in Fig. 2. The morphology distribution represents the relative frequencies of the different morphologies. The distribution includes four morphologies: dendritic, spherical, plate-like and faceted. Alumina particles existing in clusters are also considered.

Fig. 2.

Effect of Te on the morphology distribution of alumina particles at low supersaturation degree and unstirred (a), low supersaturation degree and stirred (b) and high supersaturation degree and stirred (c).

3.2.1. Low Supersaturation Degree and Un-stirred Conditions

In tests L1 and L2, the supersaturation degree S_o expressed as $(a_{\text{Al}}^{2/3}\cdot a_{\text{O}})/{(a_{\text{Al}}^{2/3}\cdot a_{\text{O}})}_{\text{eq}}$ is low, around 47.1 (calculated with FactSage 6.4 software using FSstel and FToxide database), and the melt was not stirred after Al addition. The morphology distributions of alumina particles in samples L1 and L2 are shown in Fig. 2(a). Te decreases sharply the percentage of spherical particles from 68.0% in sample L1 to 33.9% in sample L2, whereas it increases both the percentage of faceted and plate-like particles from 21.6% to 32.1% and from 8.8% to 30.5%, respectively. This shows that Te strongly modifies the morphology of alumina particles, making them more faceted, even plate-like. This supports the proposal that plate-like alumina particles in liquid steel are due to the presence of impurities.^16,25) However, in sample L1 without Te addition, plate-like particles were also frequently observed. This implies that the presence of impurities is not the only reason for the formation of plate-like particles. The solvent Fe itself can also trigger the formation of plate-like particles, as explained in section 4.2.

Faceted and plate-like alumina particles are the result of stable growth, whereas dendritic and spherical particles result from unstable growth. The higher percentages of faceted and plate-like alumina particles show that Te can stabilize alumina growth. The stability of crystal growth depends on the rate-determining process: surface kinetics or volume diffusion of growth units.²⁶⁾ The experimental results suggest that Te, to a large extent, changes the rate-determining growth process from volume diffusion to surface kinetics. This is because Te adsorbs at the interface of alumina particles and molten iron and occupies preferential growth sites, such as ledges, steps and kinks.¹⁷⁾ Removing Te slows down the deposition rate of incoming growth units. As a result, the rate-determining growth process changes.

3.2.2. Low Supersaturation Degree and Stirred Conditions

In tests LS1 and LS2, the supersaturation degree is the same as in tests L1 and L2 but the melt was stirred for 30 s after Al addition. The morphology distributions of alumina particles are shown in Fig. 2(b). It seems that stirring makes alumina particles more faceted, even plate-like, regardless of the presence of Te. Comparing samples L1 and LS1, stirring greatly decreases the percentage of spherical particles from 68.0% to 23.7%, whereas it increases the percentages of faceted and plate-like particles from 21.6% to 55.4% and from 8.8% to 16.7%, respectively. Such an obvious effect was also observed between samples L2 and LS2 with 1000 ppm Te addition. This shows that stirring can also stabilize the growth of alumina particles possibly for the following reasons: (1) stirring decreases the inhomogeneity of the supersaturation degree, suppressing alumina growth adhesively; (2) stirring increases the volume diffusion rate, causing a transition from volume diffusion-controlled to surface kinetics-controlled growth. On the other hand, stirring strengthens the effectiveness of Te on the morphological modification of alumina particles. As seen in Fig. 2(b), with stirring, Te decreases both the percentages of spherical and faceted particles considerably from 23.7% to 4.0% and from 55.4% to 43.2%, respectively. Consequently, the percentage of plate-like particles increases sharply from 16.7% to 46.6%. This shows that stirring favors the formation of plate-like alumina particles, as observed in aqueous solutions.²⁷⁾

3.2.3. High Supersaturation Degree and Stirred Conditions

In tests HS1 to HS4, the supersaturation degree is high, around 209.0, and the melt was stirred for 30 s after Al addition. The morphology distributions of alumina particles are shown in Fig. 2(c). Faceted particles are dominant in all samples. With increasing the addition of Te, the percentage of faceted particles first increases rapidly, thereafter decreases gradually. A maximum percentage of 78.2% is obtained in sample HS2 with 40 ppm Te addition. Plate-like particles are the second dominant morphology, except in sample HS1. With increasing the addition of Te from 0 to 1000 ppm, the percentage of plate-like particles increases gradually from 11.2% to 20.6%. This value is much lower than that in sample LS2, showing that the effectiveness of Te on the morphological modification of alumina particles is weakened at high supersaturation degree. A similar trend was observed for spherical particles, which increase from 3.1% to 8.3%. Moreover, the addition of 40 ppm Te sharply decreases the percentage of dendritic particles from 19.7% to 4.7%. Further increasing the addition of Te has no obvious effect. From this viewpoint, the addition of 40 ppm Te is sufficient to significantly modify the morphology of alumina particles.

In summary, Te considerably modifies the morphology of alumina particles. Generally, Te tends to make the morphology of alumina inclusions evolve from dendritic and spherical, via faceted, to plate-like. The effectiveness of Te closely relates to the growth conditions, i.e., stirring, supersaturation degree and Te content. Specifically, stirring strengthens the effectiveness of Te, whereas increasing the supersaturation degree weakens the effectiveness of Te. Moreover, the addition of 40 ppm Te is sufficient to strongly modify the morphology of alumina particles in the samples with high supersaturation degree.

3.3. Effect of Te on the Morphology of Polyhedral Alumina Particles

Growth conditions influence the growth rates of crystal faces, making them more or less morphologically important. This was observed on polyhedral alumina particles in the present work.

Figure 3 shows the different forms of faceted alumina particles grown under different conditions. In sample L1 without Te addition, both octahedral and truncated octahedral particles (Fig. 3(a)) were frequently observed. The addition of Te changes, to a large extent, truncated octahedral to octahedral particles (Fig. 3(b)). The size of octahedral particles is smaller than that of truncated octahedral particles, implying that octahedral particles are formed under conditions where the growth rates of relevant faces are slower. This can also be observed from the fewer crystallographically important faces. Stirring also favors the formation of octahedral particles, as shown in Fig. 3(c). In sample HS1 with high supersaturation degree and without Te addition, the edges of faceted particles are quite blunt (Fig. 3(d)). The addition of 40 ppm Te makes the edges of the faceted particles sharp again (Fig. 3(e)). Further increasing the addition of Te to 1000 ppm has no obvious effect on the morphology of the faceted particles (Fig. 3(f)).

Fig. 3.

Morphologies of faceted alumina particles after acid extraction. (a) L1, (b) L2, (c) LS1, (d) HS1, (e) HS2 and (f) HS4. O: octahedral; TO: truncated octahedral.

Figure 4 shows the various forms of plate-like alumina particles under different conditions. In sample L2 with low supersaturation degree and no stirring, plate-like particles are small and thick (Fig. 4(a)). Stirring makes plate-like particles grow dendritically, forming large and thin plate-like particles (Fig. 4(b)); At high supersaturation degree, small and very thick plate-like particles (Fig. 4(c)) were frequently found, besides large and thin particles of hexagonal form (Fig. 1(b)).

Fig. 4.

Morphologies of plate-like alumina particles in samples with 1000 ppm Te addition at different conditions. (a) L2, (b) LS2, and (c) HS4.

4. Discussion

4.1. Formation Mechanisms of Various Alumina Morphologies

The morphology of a crystal is determined by the relative normal growth rates of its faces. As a general rule, faces which grow slowly appear as large developed faces.⁷⁾ The growth rates are determined by the interface roughness, the growth mechanism and the driving force, as illustrated schematically in Fig. 5.²⁸⁾ The interface roughness, i.e., atomic structure, can be analyzed with the Hartman-Perdok’s periodic bond chain (PBC) theory, in which crystal faces are classified as either F (flat), S (stepped), or K (kinked) faces according to the number of PBCs in a slice of thickness d_hkl.²⁹⁾ An F face contains at least two PBCs, whereas an S face contains only one PBC and a K face contains no PBC. In α-Al₂O₃, six F faces were recognized as {011}, {01-1}, {121}, {021}, {222} and {200}.²⁵⁾ S and K faces are rough at atomic level and grow adhesively, whereas F faces are smooth and grow layer-wise. Therefore, F faces grow slower and determine the morphology of actual crystals.²⁸⁾ Based purely on the structural analysis, a polygonal crystal bounded by F faces is predicted.^25,30) Yet, various morphologies are observed in practice. This is because the growth mechanism of a crystal evolves from spiral growth, via 2D nucleation growth, to adhesive growth, with increasing the driving force, which is related to the supersaturation degree for crystals grown from vapor, solution, or melt. This is known as kinetic roughening.²⁸⁾ Consequently, the morphology of the crystal changes from polyhedral, via hopper, to spherical and dendritic due to interface instability. Polyhedral and hopper crystals both consist of flat faces. Their surface topographies, however, are featured with macrosteps (Fig. 1(b)) and island-like patterns, respectively.³¹⁾ Spherical crystals are formed under uniform conditions of high supersaturation degree. When the size of a spherical crystal exceeds a critical value, complex shapes, such as dendritic, develop, due to the Mullins-Sekerka instability.³²⁾ This explains why the size of spherical alumina particles is usually smaller than that of dendritic particles. Besides supersaturation degree, the morphology of alumina particles is also affected by the presence of impurities in molten iron, as shown in the present work.

Fig. 5.

Relationship of different morphologies of crystals with growth rate versus driving force in three growth mechanisms. Curve (a) spiral growth, (b) 2D nucleation growth, and (c) adhesive growth.²⁸⁾

4.2. Incorporation of Impurities in Alumina Particles

During crystal growth, adsorbed impurities may be incorporated into the crystal. Analyzing the content of impurities in a crystal provides the key to understand which impurities affect the growth of the crystal and thus modify the morphology.³¹⁾ Impurities in alumina particles were identified and analyzed quantitatively in the present work. Here the word “impurities” refers to all other elements except Al and O.

Figure 6 shows the results of wavelength dispersive spectrometry from an alumina particle in sample L2. The original x-axis unit mm (L-value, peak position) was converted into keV. A clear Fe spectrum was identified. Te spectrum was not observed clearly, indicating the Te content is very low. Therefore, only the Fe content was measured quantitatively. The average Fe content in more than 10 alumina particles is 2.15 ± 0.22 wt.%. A wavelength spectral scan was also performed for alumina particles in sample HS4 and similar results were obtained. The average Fe content in more than 10 alumina particles is 1.78 ± wt.0.21%. T-test shows that the difference of the measured Fe content in the two samples is highly significant. Fe content in sample HS4 is 0.37% smaller than in sample L2. This implies that the Fe content in alumina particles is inversely related to the supersaturation degree.

Fig. 6.

Identification of Fe and Te in alumina particles from sample L2. (a) SEM image, (b) Fe spectrum and (c) Te spectrum.

Due to the same crystal structure of rhombohedral lattice, α-Al₂O₃ can dissolve a large amount of α-Fe₂O₃ to form a solid solution. According to the equilibrium phase diagram Fe₂O₃–Al₂O₃,³³⁾ the equilibrium solubility of Fe₂O₃ in Al₂O₃ is 12.8 wt.% at 1873 K. In molten iron, however, the equilibrium solubility of α-Fe₂O₃ in α-Al₂O₃ depends on the oxygen activity. To clarify how Fe is incorporated into alumina particles, thermodynamically or kinetically, the equilibrium Fe content in α-Al₂O₃ is calculated using FactSage 6.4 software (FSstel and FToxide database), based on reaction (3).   

$$2[\text{Fe}]+3[\text{O}]\mathrm{\hspace{0.17em} }={({\text{Fe}}_{\text{2}}{\text{O}}_{\text{3}})}_{\alpha -{\text{Al}}_2{\text{O}}_{\text{3}}}$$(3)

The calculated result is plotted in Fig. 7. The calculated Fe content increases with the [O] content in the molten iron, but is almost two orders of magnitude smaller than the measured content, which decreases with the supersaturation degree. This suggests that Fe is kinetically incorporated during alumina growth because of the strong adsorption of Fe at the surface of the alumina particles. Due to the competitive adsorption of Fe, Al and O on the faces of alumina particles, the probability that Fe is adsorbed and then incorporated into alumina particles is higher at low supersaturation degree. The higher Fe content in alumina particles implies that alumina growth is more susceptible to the influence of solvent Fe. This is consistent with the more sharp edges of faceted alumina particles at low supersaturation degree.

Fig. 7.

Relationship of [O] content in molten iron and Fe content in α-Al₂O₃ at 1873 K.

Te adsorbs at the surface of the alumina particles due to its surface active nature. The low content of Te in alumina particles shows that Te is desorbed before the deposition of growth units due to its relatively weak adsorption energy at crystal faces, as seen from the bond strength in Table 2. Therefore, we can conclude that the growth of alumina particles is influenced not only by Te, but also by the solvent Fe.

Table 2. Bond dissociation energies in diatomic molecules at 298 K.³⁴⁾

Bond types	Values/kJ·mol−1
O–Te	377.0 ± 21.0
O–Fe	407.0 ± 1.0
O–Al	501.9 ± 10.6

4.3. Impurity Action on Alumina Morphology

Crystal growth occurs uniquely at the solid-liquid interface. Impurities adsorbing at the interface modify the crystal morphology by changing the growth rates of some crystallographically important faces.¹⁷⁾ Thermodynamically, adsorbed impurities should promote crystal growth as they decrease the surface free energy, which favors the 2D nucleation. Kinetically, however, they suppress crystal growth as they impede the deposition of incoming growth units. Mostly, impurities decrease crystal growth rate even at ppm level, as observed in the present work.

The way impurities suppress crystal growth rate depends on the crystal growth mechanisms and on the preferential adsorption sites: kinks, steps or ledges.^31,35) Impurities adsorbing at kinks decrease spiral growth rate as the number of available kinks for deposition of growth units is reduced. Immobile impurities adsorbing at steps decrease crystal growth with a 2D nucleation growth mechanism as step advancement is pinned. During crystal growth, the supersaturation degree decreases continuously due to the consumption of growth units, causing a transformation of the growth mechanism from 2D nucleation growth to spiral growth. Consequently, mechanisms of impurity action evolve from step pinning to kink occupation.

Impurities adsorb on the faces of a crystal, and thus modify the morphology of the crystal, implying that growth of crystal faces with strong tendency to adsorption is more prone to be suppressed. A high density of unsaturated bonds in a crystal face usually indicates strong adsorption of impurities. The unsaturated bonds in the upmost layer of six F faces of α-alumina are listed in Table 3.

Table 3. Unsaturated bonds for O and Al atoms at different F faces of α-alumina.²⁵⁾

Crystal faces	Multiplicity	Al2O3 molecules per layer	Unsaturated bonds for each O						Unsaturated bonds for each Al				Total unsaturated bonds per Al2O3
{011}	6	2	1	1	0	0	0	0	1	1	0	0	2
{01-1}	6	2	2	1	1	0	0	0	1	1	1	1	4
{121}	6	2	1	1	1	1	0	0	2	2	0	0	4
{021}	12	2	1	1	1	1	1	0	3	1	1	0	5
{222}	2	1	1	1	1	–	–	–	3	0	–	–	6
{200}	6	1	2	1	0	–	–	–	2	1	–	–	6

As seen, {222} and {200} have the largest density of unsaturated bonds, indicating the strongest tendency to adsorb impurities. Therefore, it is reasonable to conclude that growth rates of {222} and {200} should be decreased greatly when impurities are present. Assuming that α-alumina is bounded only by {222} and {200} growing at the same growth rate, a regular octahedral form is predicted using a Wulff plot,³⁶⁾ as shown in Fig. 8(a). Combination of {222} with {011} or {121} can also form octahedral shapes. However, these octahedrons are irregular, as shown in Fig. 8(b), and deviate considerably from the observed octahedral alumina particles. Moreover, theoretical calculations based on attachment energy model show that the growth rate of {200} is smaller than that of {011} and {121},³⁷⁾ suggesting that {200} is more morphologically important. When the growth rate of {222} becomes smaller than that of {200} at certain conditions, a platy form is predicted. An example is shown in Fig. 8(c), where the growth rate of {222} is one-fifth of {200}. This explains how octahedral and plate-like alumina particles are formed.

Fig. 8.

Shapes of α-alumina bounded by different faces. (a) R₂₂₂=R₂₀₀, (b) R₂₂₂=0.6R₁₁₀ and (c) R₂₂₂=0.2R₂₀₀.

4.4. Influencing Factors on Te Effectiveness

Several kinetic models have been proposed to study the effect of impurity adsorption on crystal growth rate, based on different adsorption sites.^35,38,39,40) Kubota and Mullin⁴⁰⁾ assumed that step advancement on a crystal face is hindered by impurities adsorbing on the step lines at kink sites following the Langmuir adsorption isotherm. The relative growth rate of a crystal face is described by:   

$$v/v_0=1-\alpha \theta$$(4)

  

$$\alpha =\gamma a/kT\sigma L$$(5)

  

$$\theta =Kc/(1+Kc)$$(6)

where v/v₀ is the relative growth rate, α is the impurity effectiveness factor, θ is the equilibrium coverage of adsorption sites by impurities, K is the Langmuir constant, c is the impurity content, γ is the edge free energy, a is the size of a growth unit, k is the Boltzmann constant, σ is the relative supersaturation and L is the average distance between active growth sites.

According to Eq. (5), α is inversely proportional to the relative supersaturation σ. A high relative supersaturation will result in a low effectiveness factor. As the values of the parameters α and K in the present work are unknown, effect of the supersaturation degree and the Te content on the relative growth rate of alumina particles can only be discussed qualitatively. Figure 9 shows the relationship between relative growth rate and impurity content at different values of α. In principle, the decrease in growth rate of a crystal face reflects the extent of morphological modification of the crystal face by impurities. Clearly, the larger α is, the faster the relative growth rate decreases. This explains why Te modifies the morphology of alumina particles in sample LS2 much more obviously than in sample HS4. It should be mentioned that the kinetic model proposed by Kubota and Mullin⁴⁰⁾ does not consider the competition between growth units and impurities for preferential adsorption sites. This can be seen in Eq. (6). In practice, the competition will surely occur. Therefore, increasing supersaturation degree decreases not only the impurity effectiveness factor α but also the equilibrium coverage θ. They together make the effect of impurities on growth rate less obvious at high supersaturation degree. Moreover, at a given value of α, the relative growth rate decreases sharply at low impurity contents. Further increasing the content of impurity has no obvious effect on the growth rate. A similar tendency in the variation of the relative amount of dendritic alumina particles was observed in samples HS1 to HS4. As seen in Fig. 2(c), 40 ppm Te addition sharply reduces the amount of dendritic particles. Further increasing Te addition even up to 1000 ppm has little effect on the amount of dendritic alumina particles. Therefore, we can conclude that decreasing supersaturation degree improves Te effectiveness in morphological modification of alumina particles, whereas increasing Te addition does not result in a comparable increase of Te effectiveness.

Fig. 9.

Relationship of relative growth rate with dimensionless impurity concentration at varying impurity effectiveness factors.⁴⁰⁾

5. Conclusions

The effect of Te on the morphology of alumina particles in molten iron has been studied. The results are summarized as follows:

(1) Dendritic, spherical, faceted, plate-like and clustered alumina particles were observed in all samples. The different growth morphologies originate from different growth mechanisms.

(2) Te addition considerably modifies the morphology of alumina particles. Stirring increases the effectiveness of Te on the modification of alumina particles, whereas increasing supersaturation degree decreases the effectiveness of Te. Moreover, the addition of 40 ppm Te is sufficient to strongly modify the morphology of alumina particles.

(3) The quantitative measurement of the impurity contents in alumina particles indicates that the solvent Fe also affects the morphology of alumina particles.

(4) How impurities affect the morphology of alumina particles depends on both alumina growth mechanisms and preferential adsorption sites. Due to the highest density of unsaturated bonds in {222} and {200}, growth of these faces are more prone to be suppressed by the adsorption of impurities, leading to the formation of octahedral and plate-like alumina particles.

(5) The effectiveness of Te on the morphological modification of alumina particles was discussed with a kinetic model, which can qualitatively explain why Te effectiveness is weakened at high supersaturation degree and why low content Te can be very effective on the morphological modification of alumina particles in the samples with high supersaturation degree.

Acknowledgement

The authors thank the China Scholarship Council (CSC) for financial support (File No. 201206080011). The authors are also grateful to the financial support from the Hercules Foundation (Project No. ZW09-09) for the FEG-EPMA system.

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