ISIJ International
Online ISSN : 1347-5460
Print ISSN : 0915-1559
ISSN-L : 0915-1559
Fundamentals of High Temperature Processes
Role of Interfacial Properties in the Evolution of Non-metallic Inclusions in Liquid Steel
Lichun ZhengAnnelies MalflietBaiqiang YanZhouhua Jiang Bart BlanpainMuxing Guo
著者情報
ジャーナル オープンアクセス HTML

2022 年 62 巻 8 号 p. 1573-1585

詳細
Abstract

The evolution of non-metallic inclusions in liquid steel involves a series of processes, including nucleation, growth by diffusion and Ostwald ripening, growth by collisions, floating up and removal of relatively large inclusions, as well as pushing and engulfment of remaining inclusions during solidification. All the evolution processes occur uniquely at the interface between inclusions and liquid steel. Therefore, interfacial properties between inclusions and liquid steel, such as interfacial energy and contact angle, play a crucial role in the evolution of inclusions, thus determining the inclusion characteristics. To effectively control the inclusion characteristics, the role of interfacial properties in the evolution processes of non-metallic inclusions is systematically reviewed in this work, based on theoretical analysis and published experimental results. In the early and middle stages of deoxidation, inclusions should have as high interfacial energy or contact angle as possible to enhance inclusion removal. In the later stage, however, the interfacial energy should be decreased as much as possible to weaken the clustering and pushing of inclusions, favoring the formation of small-sized and uniformly-distributed inclusions. To optimize the characteristics of Al2O3 inclusions, which are the most common in steel, several control strategies are proposed.

1. Introduction

Deoxidation of liquid steel is an essential process during steelmaking, and is usually carried out during tapping by adding into the ladle appropriate amounts of Fe–Mn, Fe–Si, Al or other special deoxidizers. Due to high affinity towards oxygen and relatively low price, Al deoxidizer is most commonly used in steelmaking. Deoxidation removes excessive dissolved oxygen in liquid steel, but it also causes the formation of non-metallic inclusions, i.e., deoxidation products. Depending on their characteristics, residual inclusions either positively or negatively affect steel properties. Large inclusions with irregular morphology are especially harmful to steel properties, such as ductility, toughness, fatigue strength and corrosion resistance.1,2) On the contrary, small inclusions with suitable composition can serve as heterogeneous nucleation sites for phase transformation and precipitation, improving steel properties.3) Therefore, controlling the inclusion characteristics is of great importance for the production of high-quality steel.

Starting from the addition of deoxidizers, non-metallic inclusions evolve following a series of processes. When supersaturation degree reaches a critical value, nucleation of inclusions starts, followed by rapid growth by diffusion, Ostwald ripening and collisions including Brownian collisions, Stokes collisions, gradient collisions and turbulent collisions.4) After substantial growth, floating up of inclusions becomes significant, removing large inclusions to the top slag. During solidification of liquid steel, residual inclusions are either engulfed or pushed by the advancing solid-liquid interface, resulting in a homogeneous or inhomogeneous distribution of inclusions in the steel matrix.5) A schematic diagram on the evolution of non-metallic inclusions is given in Fig. 1 as an example. Note that these processes are not separated in time.4) The evolution of inclusions determines their characteristics, such as number, size distribution, morphology and spatial distribution.

Fig. 1.

Schematic diagram on the evolution of non-metallic inclusions.4,5,6,7,8) SO and S O * are supersaturation degree and critical supersaturation degree, respectively. (Online version in color.)

Theoretically, all the above evolution processes occur uniquely at the interface between inclusions and liquid steel. Therefore, interfacial properties, such as interfacial energy and contact angle, play a crucial role in the evolution of inclusions, thus determining the inclusion characteristics. The interfacial properties between liquid steel and different types of inclusions vary significantly, and have been extensively measured by many researchers. The contact angle of inclusions in molten iron decreases in the order Al2O3 (144°) > MgO (125°) > ZrO2 (122°) > Ti2O3 (121°) > SiO2 (115°) > Ce2O3 (105°) > TiO2 (84°) > CaO–Al2O3 (54–65°) > CaO–SiO2 (~30°).9,10,11) Moreover, liquid steel contains a variety of impurity elements. Some are strongly surface active, such as oxygen (O), sulfur (S), nitrogen (N), selenium (Se), tellurium (Te) and titanium (Ti). Trace amounts of these elements lead to a significant decrease of the interfacial energy between inclusions and liquid steel.11,12,13,14) Regarding the contact angle, it is a little complicated. Taking Al2O3 inclusions as an example (Fig. 2), O, P and Ti decrease the contact angle, while Te, Se and S increase it.13,14)

Fig. 2.

Effect of surface-active elements on the contact angle between Al2O3 inclusions and molten iron at 1873 K. Solid-lines show the results by Nogi and Ogino.13) Dashed-lines show the results by Karasangabo and Bernhard.14)

Nakashima and Mori,9) and Olette15) systematically reviewed the interfacial properties of various phases involved in steelmaking, including inclusions, liquid steel and molten slag. Olette15) also briefly analyzed the effect of interfacial properties on various interfacial phenomena in steelmaking, such as slag foaming, clogging of submerged entry nozzles (SENs), and inclusion removal. In this work, to effectively control the inclusion characteristics, we give a condensed review of the evolution of non-metallic inclusions in liquid steel, focusing on the effect of interfacial properties and the presence of surfactants.

2. Nucleation of Non-metallic Inclusions

Nucleation is the first step in the formation of non-metallic inclusions, denoted as MmOn. In the classical homogeneous nucleation theory,16) non-metallic nuclei only form when the supersaturation degree SO exceeds a critical value S O * , so as to overcome the barrier of interfacial energy. SO, S O * and nucleation rate I are expressed in Eqs. (1), (2), (3), respectively.4)   

S O = a M m/n a O ( a M m/n a O ) eq = a M m/n a O K eq (1)
  
S O * =exp( V O RT 16π γ pl 3 3 k B Tln A f ) (2)
  
I= A f exp( - 16π γ pl 3 V O 2 3 k B R 2 T 3 (ln S O ) 2 ) (3)
where aM and aO are the activities of deoxidizer and oxygen, respectively, Keq is the equilibrium constant, VO is the molar volume of the oxide per mole of oxygen, γpl is the interfacial energy between inclusions and liquid steel, R is the universal gas constant, T is the absolute temperature, Af is the frequency factor, and kB is the Boltzmann constant.

Both S O * and I are functions of γpl. Suito and Ohta4) calculated the relationship between I and γpl for various types of inclusions (Fig. 3). The value of I increases significantly when decreasing γpl, indicating that small γpl promotes nucleation. Nucleation and growth by diffusion proceed simultaneously. For the case of rapid nucleation, nucleation and growth of inclusions last a shorter time, favoring more uniform size distribution. This was observed by Suito and Ohta4) after plotting the curve between γpl and ln σ, where σ is the geometric standard deviation of inclusion size (Fig. 4). MnO–SiO2 inclusions have the most uniform size distribution, whereas Al2O3 inclusions have the least uniform size distribution. Therefore, to obtain a narrow size distribution, deoxidizers with low interfacial energy between their oxides and liquid steel should be used, such as Si, Mn and Ti.4) These deoxidizers, however, have relatively weak deoxidizing power, compared with Ca, Mg, Al and Zr, failing to meet the requirement of clean steel.

Fig. 3.

Relationship between interfacial energy and nucleation rate for various inclusions.4)

Fig. 4.

Relationship between interfacial energy and ln σ for various inclusions.4)

Surfactants in liquid steel, such as O, S and Te, can significantly lower the interfacial energy γpl, thus influencing the inclusion characteristics. Van Ende et al.17) examined the effect of O content on Al2O3 inclusion characteristics in the very initial stage of deoxidation by bringing a piece of Al into contact with molten iron, and observed that the inclusion size tended to decrease with increasing O content. Specifically, the inclusion size was about 2.1 μm at 160 and 450 ppm O, and decreased to below 1 μm when increasing the O content to 780 ppm. Also, the number density of Al2O3 inclusions became much higher at high O contents. A similar phenomenon was also reported by Wakoh and Sano.18) The nucleation rate affects the size and number density of the inclusions. High O contents increase the nucleation rate of Al2O3 inclusions not only by increasing the supersaturation degree, but also by decreasing the interfacial energy.

More directly, Tanabe and Suito19) measured the equilibrium O content at a given Al level in molten iron under different Te contents, and found that Te decreased the critical supersaturation degree S O * for Al2O3 formation. Besides Te, other alloying elements C, Mn, Si and Cr also have a similar effect, as reported by Li and Suito.20) Nogi and Ogino13) found that Te decreased the size of Al2O3 and ZrO2 inclusions by around half. Zheng et al.21) further studied the effect of Te addition on the characteristics of Al2O3 inclusions in molten iron. When the melt was not stirred after Al addition, Te decreased the size of the Al2O3 inclusions and narrowed the size distribution in the early stage of deoxidation by promoting Al2O3 nucleation. On the contrary, when the melt was stirred for 30 s after Al addition, the size of the Al2O3 inclusions increased with increasing Te addition from 0 to 250 ppm, thereafter decreased with further Te addition (Fig. 5). Most surfactants are impurity elements in steel. Therefore, control of non-metallic inclusions by adding surfactants is rarely used in steelmaking.

Fig. 5.

Evolution of Al2O3 size at different Te contents.21)

3. Growth by Diffusion and Ostwald Ripening

Once stable nuclei are formed, non-metallic inclusions start to grow by diffusion. Growth by diffusion is usually controlled by the diffusion of O atoms.6,7,18) The growth rate can be expressed using Wert and Zener’s formula22) as:   

dr dt = D O r ( C O - C eq ) ( C p - C eq ) (4)
where r is the radius of inclusions at time t, DO is the diffusion coefficient of O atoms in liquid steel and CO, Ceq and Cp are the O contents in the bulk of liquid steel, at equilibrium in liquid steel, and in inclusions, respectively. The time required for the volume of inclusions to reach 90% of the equilibrium volume can be expressed as:22)   
t 90 = 1 D O ( C p - C eq ) ( C O,i - C eq ) r ¯ 2 (5)
where CO,i is the initial O content in liquid steel before adding deoxidizer and r ¯ is the mean radius of inclusions. Ohta and Suito7) calculated the relationship between t90 and r ¯ for MgO inclusions (Fig. 6). Within 1 s, the mean radius r ¯ reaches over 1 μm. This indicates that deoxidation of liquid steel proceeds very fast, as demonstrated by experiments17,18,23) and modellings.6,8,24)
Fig. 6.

Relationship between t90 and mean radius of MgO inclusions grown by diffusion.7)

Inclusion growth by diffusion ends up with numerous nano-sized inclusions, when the supersaturation degree SO reaches unity. The nano-sized inclusions are thermodynamically unstable due to the high interfacial energy associated with the large interfacial area. Therefore, the nano-sized inclusions will grow up to lower the interfacial energy as much as possible. Further growth of inclusions occurs via Ostwald ripening, i.e., large inclusions grow and small inclusions dissolve. Overall, the average size increases with time, when neglecting floating up and adsorption by the top slag. Growth of inclusions by Ostwald ripening can be described as:6)   

r ¯ 3 = r ¯ 0 3 + 4 9 2 γ pl D O V O C O RT( C p - C O ) t (6)
where r ¯ 0 is the mean radii of inclusions at the start of Ostwald ripening. Theoretical calculations by Lindborg and Torssell6) show that inclusion growth by Ostwald ripening is very slow, mainly arising from low dissolved O content. For example, it takes about 30 min for SiO2 inclusions to grow from 0 to 2.5 μm. This growth mechanism, however, contributes to inclusion growth for a long period of time. Kluken and Grong,25) Suzuki et al.,26) and Ohta and Suito7) reported that under no fluid flow, growth of inclusions is mainly attributed to Ostwald ripening. Besides dissolved O content, the size distribution of inclusions also affects their growth by Ostwald ripening. A broader size distribution results in a faster growth.7)

4. Growth by Collisions

When growth by diffusion finishes, growth by collisions, including Brownian collisions, gradient collisions, Stokes collisions and turbulent collisions, starts to play the most important role. Collisions between two inclusions lead to the formation of a single inclusion or a cluster, depending on the size and type of inclusions.27) Brownian collisions occur due to random motion of fine inclusions suspended in liquid steel. The Brownian collision rate can be expressed as:28)   

W b = 2 k B T 3η ( r i + r j )( 1 r i + 1 r j ) (7)
where ri and rj are the radii of inclusions i and j, respectively, and η is the viscosity of the melt. Note that all collision rates mentioned in this section represent the growth rate of particles due to collisions and thus have the unit of m3·s−1. Based on mathematical modelling, Zhang and Lee8) reported that Al2O3 inclusion growth by Brownian collisions becomes dominant from 1.0 μs after nucleation to 2.0 s, when the inclusion size reaches around 0.4 μm in diameter. Van Ende et al.17) observed that the size of most single Al2O3 inclusions in clusters was much smaller than 1 μm at the onset of deoxidation (Fig. 7). As the deoxidation time was only several seconds, Al2O3 clusters were possibly formed due to Brownian collisions. Söder et al.29) as well as Zhang and Pluschkell24) made a similar conclusion that Brownian collisions are significant only when inclusion size is below 1 μm in diameter. This growth mechanism is neglected in most inclusion growth models, where inclusion nucleation is not incorporated.30)
Fig. 7.

Overview of Al2O3 inclusions at the onset of deoxidation (5 s) in molten iron containing 1800 ppm O.17)

Gradient collisions occur when inclusions are moving along different streamlines under laminar flow conditions. The gradient collision rate can be expressed as:6)   

W g = 4 3 ( r i + r j ) 3 du dx (8)
where du/dx is the local velocity gradient in the melt. The larger the velocity gradient, the higher the collision rate. Since laminar flow mainly appears in the regions close to the reactor wall, inclusion growth by gradient collisions is limited in practice. Therefore, this growth mechanism is also not considered in most inclusion growth models.29,30)

Non-metallic inclusions tend to float up due to their smaller mass density compared with liquid steel. Large inclusions float up fast. Therefore, large inclusions can catch up with small inclusions and collide with them, known as Stokes collisions. The Stokes collision rate can be expressed as:6)   

W s = 2π( ρ L - ρ P )g 9η ( r i + r j ) 3 | r i - r j | (9)
where ρL and ρP are the mass density of the melt and the inclusions, respectively, and g is the gravitational acceleration. The larger the size difference between two inclusions, the higher the collision rate. Extremely, when there is no size difference, the collision rate becomes zero. Therefore, growth by Stokes collisions is significant only when the size distribution of inclusions becomes wide, which happens usually in the later stage of deoxidization.8,30,31)

In stirred steel bath, inclusions grow rapidly via turbulent collisions, arising from small eddies. Saffman and Turner32) derived the collision rate equation between two particles in turbulent eddies. Later, Nakanishi and Szekely33) modified the collision rate equation by introducing an effective collision coefficient. The turbulent collision rate can be expressed as:   

W t =1.30 α t ( r i + r j ) 3 ( ρε η ) 0.5 (10)
where ε is the turbulent dissipation rate, and αt is the effective collision coefficient. The contribution of turbulent collisions to inclusion growth becomes significant when the mean diameter of the inclusions reaches around 1.0 μm.8,24,34) Nakanishi and Szekely33) predicted the effective collision coefficient αt between 0.27 and 0.63 for Al2O3 inclusions in liquid steel by comparing measured and calculated O contents. Higashitani et al.35) later theoretically derived the expression of αt, considering hydrodynamic and van der Waals interactions between two particles. The effective collision coefficient αt can be expressed as:   
α t =-0.24log( 6π ( r i + r j ) 3 4ε / 15πη A H ) +0.047 (11)
where AH is the Hamaker constant. As well known, inclusions unwetted by liquid steel have a much higher tendency of growing via turbulent collisions. However, such a phenomenon cannot be seen from the effective collision coefficient αt in Eq. (11). Nakajima et al.36) proposed a new expression of the Hamaker constant by introducing the interfacial energy between inclusions and liquid steel, as:   
A H =24π a 2 γ pl (12)
where a is the ionic radius. Compared with the other three growth mechanisms by collision, inclusion growth by turbulent collisions is usually dominant with the presence of turbulence.8,29,30,31) Collisions and subsequent agglomeration between inclusions lead to the formation of clusters consisting of several individual inclusions, significantly accelerating inclusion growth. This phenomenon is known as clustering, and is commonly observed in steelmaking, especially among inclusions unwetted by liquid steel. Nakajima et al.36) found that the Hamaker constants for Al2O3, MgO and Ti2O3 inclusions in molten iron are 6.7~11.8 × 10−18 J, 4.2~9.6 × 10−18 J and 8.3~9.3 × 10−18 J, respectively. Based on Eq. (12), Chen et al.37) calculated the relative effective collision coefficients for Al2O3, MgO and MgAl2O4 inclusions, considering the effect of steel compositions (Fig. 8). Clearly, Al2O3 inclusions have the largest Hamaker constant and effective collision coefficient. However, the difference is insignificant, being unable to explain why the clustering tendency of Al2O3 inclusions is much higher than other inclusions, such as MgO and Ti2O3.
Fig. 8.

Comparison of relative coagulation coefficients of three types of inclusions in five kinds of steel matrix.37) (Online version in color.)

Clusters, due to their large size, can float up more rapidly to the top slag. They are, however, very detrimental to steel properties if they remain in solidified steel. Mechanisms of inclusion clustering will be further reviewed in section 7.

5. Floating up and Removal

Non-metallic inclusions in liquid steel are subjected to floating up due to buoyancy force, followed by crossing the slag-metal interface and dissolving in the slag phase. The rising velocity of inclusions can be expressed with the Stokes’ law:   

u P = 2 9 ( ρ L - ρ P ) η g r 2 (13)

The rising velocity depends on the mass density difference between the inclusions and the liquid steel as well as on the inclusion size. Therefore, light and large inclusions, e.g., Al2O3 clusters, are easier to be removed by floating up. The rising velocity of an Al2O3 inclusion with a radius of 10 μm is estimated at 4.8 × 10−5 m·s−1. Still, this velocity is negligible compared with the ladle depth of several meters. Therefore, many approaches have been developed to improve inclusion removal. Gas injection is a particularly effective one, which is commonly used in ladle and tundish metallurgy.38) Injected gas transforms into bubbles, interacting with inclusions. Consequently, inclusions either attach on bubbles or rebound away from bubbles.39) Once attached on bubbles, inclusions can float up more rapidly. Attachment of inclusions on bubbles depends on the wettability of liquid steel on inclusions. The poorer the wettability, the easier it is for inclusions to attach on bubbles.40) This relationship has been observed in steelmaking, and also demonstrated by cold model experiments.41,42,43) An example is shown in Fig. 9, where the removal rate constant of particles sharply increases once the contact angle exceeds around 90°.43)

Fig. 9.

Particle removal rate constant as a function of contact angle in water at agitation speed of 6.7 s−1.43)

When transported to the slag-metal interface, inclusions have to cross the interface first before dissolution into the slag phase. Thermodynamically, inclusions have a lower interfacial energy in the molten slag phase than in the liquid steel. Therefore, inclusions with a high interfacial energy in the liquid steel correspondingly have a high tendency to enter the molten slag phase. However, to cross the slag-metal interface, inclusions should overcome an energy barrier, which is related to the break of the liquid steel film between the inclusions and the molten slag. Lee et al.44) studied the passage rate of inclusions through the slag-metal interface with the aid of confocal scanning laser microscope (CSLM), and observed that Al2O3 inclusions passed through the interface rapidly without residence. On the contrary, liquid MnO–SiO2–Al2O3 inclusions took up to 7 s to cross the interface, and were not captured by the slag at all in some cases. Nogi and Ogino13) studied the effect of Te on the deoxidation of molten iron with Al, and observed that white Al2O3 powders, which accounted for around 60% of total Al2O3 inclusions, covered the top surface of the solidified ingot containing Te. This phenomenon was not observed in the ingot without Te addition. Clearly, Te promoted the passage of Al2O3 inclusions through the steel-gas interface. Te as a strong surfactant decreases the interfacial energy of Al2O3 inclusions in molten iron, but increases the contact angle.13) The contact angle is closely related to the interfacial energy via the Young’s equation. Therefore, essentially, it is the contact angle not the interfacial energy that determines the passage rate of inclusions through the slag-metal interface. Normally, solid inclusions have a much larger contact angle than molten inclusions.9) Therefore, solid inclusions pass through the slag-metal interface much more rapidly than molten inclusions, as observed by Lee et al.44) and Zhou et al.45)

Ca treatment is often a necessary operation in steelmaking to alleviate SEN clogging caused by accretion of Al2O3 inclusions. After adding proper amounts of Ca, solid Al2O3 inclusions are modified into molten CaO–Al2O3 inclusions. Moreover, soft Ar stirring is commonly used to accelerate the floating up and removal of inclusions. To more efficiently remove inclusions, the moment when Ca is added is critical. Due to the larger contact angle, solid inclusions are more easily trapped by Ar bubbles and separated from the slag-metal interface, compared with molten inclusions. Therefore, it is better to carry out Ca treatment in the later stage of soft Ar stirring.

6. Pushing and Engulfment during Solidification

During solidification of liquid steel, non-metallic inclusions interact with the advancing solid-liquid interface. Inclusions are either engulfed or pushed by the interface. This phenomenon has been in situ observed on the surface of liquid steel using CSLM.46,47,48) Inclusions engulfed by the advancing solid-liquid interface will stay in the grains. On the contrary, inclusions pushed by the interface will be located at grain boundaries or inter-dendritic regions. Therefore, engulfment leads to a homogeneous distribution of inclusions, while pushing results in segregation of inclusions, causing decreased steel properties.

6.1. Critical Velocity for Pushing-engulfment Transition

The phenomenon of particle engulfment and pushing plays a crucial role in a wide range of physical processes, such as ceramic particle-reinforced metal-matrix composites49,50,51) and solidification of monotectics.52) Numerous theoretical models have been proposed since the early work of Uhlmann et al.53) in 1964. These models can be divided into three broad categories: thermodynamic criterion models,53,54) thermal properties criterion models55,56) and kinetic models.57,58,59) The first two of these models do not consider process variables, such as solidification rate and particle size. Therefore, they are of limited value as a predictive tool in practice.

A large body of experiments reveal that there is a critical value of interface velocity, termed as critical velocity, below which particles are pushed and above which particles are engulfed. Kinetic models consider the process variables to predict the critical velocity. When a particle stays ahead of an advancing solid-liquid interface, several forces act on the particle, including viscous drag force FD, interfacial force FI, gravity force Fg, and lift force FL, as schematically illustrated in Fig. 10. The viscous drag force and interfacial force are usually primary forces. The viscous drag force arises from solidification induced liquid flow. The interfacial force arises from the variation of interfacial energy among the particle, the solid phase and the liquid phase with the particle-interface distance. The viscous drag force is always attractive, while the interfacial force is mostly repulsive.

Fig. 10.

Sketch of the forces acting on a particle in the vicinity of the solid-liquid interface. VS is the velocity of the solid-liquid interface. (Online version in color.)

Shangguan et al.58) considered the viscous drag force and interfacial force, and derived the critical velocity Vcr as:   

V cr = a 0 3ηφ(n-1) Δ γ 0 r ( n-1 n ) n (14)
where a0 is the interatomic distance, φ is the thermal conductivity ratio, and Δγ0 is the change of interfacial energy at minimum particle-interface distance. n can vary between 2 and 7. Currently, due to the lack of reliable data for Δγ0 and the indeterminate value of n, it is almost impossible to accurately predict the critical velocity with Eq. (14). However, the equation indicates that the critical velocity Vcr is inversely proportional to the particle radius r, suggesting large particles are easier to be engulfed.

Shibata et al.46) in situ observed the engulfment and pushing of inclusions with CSLM, and found that Vcr (μm/s) = 60/r (μm) for solid Al2O3 clusters, whereas Vcr = 23/r for liquid globular inclusions, showing that liquid inclusions are easier to be captured. By analyzing the spatial distribution of inclusions over a micro-segregation domain, Ohta and Suito60) reported that Al2O3 inclusions have a higher tendency of being pushed, compared with MgO and ZrO2 inclusions. The reason is that Al2O3 inclusions have the highest interfacial energy in liquid steel among the three types of inclusions, leading to the highest critical velocity.

6.2. Effect of Solutes and Surfactants

Solutes rejected by the solid phase during solidification will accumulate at the gap between the particles and the solid-liquid interface, thus changing the interface shape from planar to concave due to constitutional undercooling. Therefore, the presence of solutes decreases the critical velocity, thus favoring particle engulfment.59) Such a phenomenon has been observed in ceramic particle-reinforced metal-matrix composites.61,62,63)

In liquid steel, however, the presence of surface-active solutes causes completely different phenomena. Ohta and Suito64,65) and Zheng et al.5) reported that surfactants O, S and Te facilitate pushing of Al2O3, ZrO2, MgO and MnO–SiO2 inclusions via analyzing their distribution homogeneity. Such a phenomenon was directly observed on the surface of liquid steel by several researchers using CSLM, and was explained with the Marangoni flow caused by thermal and concentration gradients.47,48) The Marangoni flow, however, disappears in the bulk of liquid steel.

Mukai and Lin66) proposed that a solute gradient built-up in front of the solid-liquid interface may produce an interfacial energy gradient extending from the interface to the liquid phase, yielding an additional attractive force acting on a bubble (particle) ahead of the interface. The attractive force Fσ can be expressed as:   

F σ =- 8 3 π r 2 K (15)
where K is the interfacial energy gradient. Shibata et al.46) reported that the attractive force Fσ is comparable in magnitude with the viscous drag force and interfacial force in Al2O3/molten Fe–S system. This theory could well explain why in steel billets the surface defect of blowholes, which is related to the capture of Ar bubbles by the solidifying shell in continuous casting of steel, is more severe at high S contents.67,68,69) This theory treats particles and bubbles equally. However, it fails to explain why the presence of surfactants facilitates pushing of inclusions in liquid steel.

Zheng et al.5) treated the liquid gap confined by an advancing solid-liquid interface and a particle (bubble) as an asymmetric thin liquid film (Fig. 11). Assuming that the film is flat, parallel and of equal area, the authors derived a thermodynamic description of the film as:   

d( γ pl + γ sl )=- D dh-( Γ s pl + Γ s sl )d μ s (16)
where γsl is the interfacial energy of the solid-liquid interface, h is the particle-interface distance, Γ s pl and Γ s sl are the surface excesses of the solute at particle-liquid and solid-liquid interfaces, respectively, μs is the chemical potential of the solute, and ΠD is the disjoining pressure. ΠD relates to the interfacial force FI. If ΠD > 0, a repulsive force develops, favoring particle pushing. If ΠD < 0, an attractive force develops, favoring particle engulfment.
Fig. 11.

Sketch of an asymmetric thin liquid film confined by an advancing solid-liquid interface and a particle (bubble). Reprinted from Ref. [5] with permission from Elsevier. (Online version in color.)

According to Eq. (16), a Maxwell relation can be derived, as shown in Eq. (17). The equation correlates the changes of the surface excesses of a solute Γ s pl + Γ s sl , the chemical potential μs, the disjoining pressure ΠD and the particle-interface distance h. The equation describes how Γ s pl + Γ s sl varies with h. There are two possibilities. First, Γ s pl + Γ s sl will decrease with decreasing h, if ΠD increases when raising μs. This statement can be described using Eq. (18). The interfacial force FI becomes more repulsive or less attractive, when raising μs, depending on the nature of the force. This applies to the case of particle-interface interactions. Second, Γ s pl + Γ s sl will increase with decreasing h, if ΠD decreases when raising μs, as formulated in Eq. (19). The interfacial force FI becomes more attractive or less repulsive, when raising μs. This applies to the case of bubble-interface interactions. The opposite changes of Γ s pl + Γ s sl for particles and bubbles are possibly due to their different interfaces.   

( D μ s ) h,T = ( ( Γ s pl + Γ s sl ) h ) μ s ,T (17)
  
Δ μ s >0 Δ Π D >0 Δh<0 }d( Γ s pl + Γ s sl )<0 (18)
  
Δ μ s >0 Δ Π D <0 Δh<0 }d( Γ s pl + Γ s sl )>0 (19)

The asymmetric thin liquid film theory could well explain the behaviors of inclusions and bubbles at the advancing solid-liquid interface, when surfactant is present. However, a quantitative description of surface excesses Γ s pl + Γ s sl versus distance h is not available at present. Therefore, accurate prediction of the critical velocity with the theory is still not possible. More work is necessary on this aspect.

7. Clustering of Non-metallic Inclusions

Clustering of non-metallic inclusions arises from collisions and subsequent agglomeration. In the early stages of deoxidization, the clusters are loose and individual inclusions in the clusters are clearly distinguishable. With increasing time, the clusters become more compact due to sintering. Clustering is commonly observed in steelmaking among inclusions unwetted by liquid steel, such as Al2O3, CeS and TiN,23,70,71) suggesting the existence of strong attractions between non-wetting inclusions.

7.1. Clustering on Melt Surface

With the aid of CSLM, the clustering behavior of inclusions on the surface of liquid steel can be in situ observed, and has been well understood. Non-wetting inclusions were observed to move to each other, followed by collisions and agglomeration.44,72,73,74,75,76) Such a behavior, however, was not observed between wetting inclusions. The attractive force is considered to arise from the capillary force, which is due to the deformation of the melt surface around inclusions,75,77) as schematically shown in Fig. 12. Great mass density difference between inclusions and liquid steel, poor wettability, and large surface tension of liquid steel all increase the strength of the capillary force.75,77)

Fig. 12.

Schematic diagram of capillary interaction between non-wetting inclusions in liquid steel. (Online version in color.)

Yin et al.74) reported that the attractive force was above 10−16 N, and the acting length reached over 10 μm for Al2O3 particles larger than 3 μm. On the contrary, such long-range attraction was not observed between liquid CaO–Al2O3, Al2O3–SiO2 or CaO–Al2O3–SiO2 inclusions, all containing less than 60 wt.% Al2O3. Similar results also have been observed by other researchers.44,72,73,74,75,76,78)

Regarding the effect of surface-active elements in liquid steel, Yin et al.74) found that S, within the content range 0.002–0.021%, had little effect on the long-range attraction among Al2O3 inclusions. S decreases the surface tension of liquid steel, but increases the contact angle of the Al2O3 inclusions.13) Possibly, the two effects cancel each other to make the capillary force insensitive to the presence of S.

By comparing CSLM observations with industrial investigation, Kang et al.72) concluded that inclusions on the surface of liquid steel have the same behavior as in the bulk of liquid steel even though clustering of inclusions in the bulk of liquid steel cannot be explained with the capillary force, simply because the force does not exist in the bulk.

7.2. Clustering in the Bulk of the Liquid Melt

7.2.1. Van der Waals Force

Regarding the origin of the strong attractive force between non-wetting inclusions in the bulk of liquid steel, extensive studies have been carried out in the past few decades. The van der Waals force, a relatively weak electric force, exists between all particle pairs. Initially, the van der Waals force was considered as the main attractive force for the clustering of all kinds of inclusions. As seen in Eq. (11), the van der Waals force is involved in the effective collision coefficient αt, which is a critical parameter in calculating the turbulent collision rate in Eq. (10). Zhang et al.79) calculated the effective collision coefficient αt versus inclusion radius. The value of αt is around 0.05 for 10 μm inclusions. This theoretical value is far smaller than the actual value of 0.27–0.63 for Al2O3 inclusions in liquid steel.33) Moreover, according to the work by Nakajima et al.,36) no significant difference in magnitude of the van der Waals force was observed among severe non-wetting inclusions (such as Al2O3) and slightly non-wetting inclusions (such as MgO). Therefore, the van der Waals force is not responsible for the strong attraction between non-wetting inclusions.

7.2.2. Liquid Bridge Force

By observing the behavior of Al2O3–Fe2O3 mixtures on the surface of liquid steel, Sasai and Mizukami80) found that the clustering tendency of Al2O3 inclusions was promoted when molten FeO was present in the liquid steel (Fig. 13), and concluded that molten FeO formed a liquid bridge between the Al2O3 inclusions in the bulk of liquid steel and served as a binder during the clustering. Such a conclusion was also obtained by Mizoguchi et al.81) after comparing the Fe content in Al2O3 inclusions sampled from liquid steel after RH-degassing and from a cast slab. Molten FeO may locally exist in the bulk of liquid steel due to reoxidation of liquid steel. However, molten FeO is thermodynamically unstable in Al-killed steel.

Fig. 13.

Morphologies of Al2O3 particles on the surface of liquid steel with Fe2O3 addition during electron beam melting. (a) 0 wt.% Fe2O3–1 wt.% Al2O3-Fe; (b) 0.4 wt.% Fe2O3–1 wt.% Al2O3-Fe.80)

7.2.3. Cavity Bridge Force

Understanding the clustering mechanism of particles is of crucial importance not only for the metallurgical field but also for other fields, such as colloidal science and mineral processing. The interactions between non-wetting particles in aqueous solutions have been extensively studied, revealing the existence of very strong and long-range attractive forces between the particles.82,83,84) Yaminsky et al.85,86) proposed that liquid may be spontaneously expelled from the region between two approaching particles unwetted by the liquid, and a gas cavity forms around the contact zone (Fig. 14), resulting in a strong attractive force. This mechanism has been validated experimentally.82,83)

Fig. 14.

Sketch of a cavity between two identical particles unwetted by the liquid. Rp is the radius of the particles, θ is the contact angle and α is the filling angle. (Online version in color.)

According to the spontaneous cavitation theory, when two particles unwetted by liquid phase are approaching each other, formation of a cavity becomes favorable in thermodynamics. This is because the replacement of a particle-liquid interface by a particle-vapor interface leads to a negative change of Gibbs free energy, following Young’s equation:   

γ pv - γ pl = γ lv cosθ (20)
where θ is the contact angle, γ is the interfacial energy. The subscripts p, l and v refer to the particle, liquid phase and vapor phase, respectively. Once the gas cavity is formed, an attractive force, termed as cavity bridge force, develops between the particles. The cavity bridge force is the summation of the forces due to surface tension of the liquid phase and pressure drop across the liquid-vapor interface, as expressed in Eq. (21).87)   
F C =2π γ lv l+π l 2 ΔP (21)

ΔP is the pressure drop, which can be calculated with the Laplace-Young equation:   

ΔP= γ lv (1/r -1/l ) (22)
where r is the radius of the cavity, and l is the half-width of the cavity at the neck. The two parameters are schematically illustrated in Fig. 14. These two parameters determine the profile of the liquid-vapor interface. When the cavity is in equilibrium with the liquid phase, its shape can be obtained by minimizing the Gibbs free energy:88)   
G= P o V-N k B TlnV+ γ lv A lv +( γ pv - γ pl ) A pv (23)
where Po is the pressure in the liquid phase, V is the volume of the cavity, N is the number of gas molecules inside the cavity, Alv is the liquid-vapor interfacial area, and Apv is the particle-vapor interfacial area. The liquid-vapor interface can be optimized using the Laplace-Young equation at constant pressure drop86) or approximated by an arc with radius r.87,89) The latter method is known as the toroidal approximation.

Thermodynamic calculations by Yushchenko et al.86) revealed that the cavity nucleates spontaneously when the two particles come into contact. After separation, the cavity connecting the two particles becomes metastable and finally unstable with increasing the separation distance. Once the cavity ruptures, the attractive force disappears. Theoretically, the attractive force FC is a function of the surface tension of the melt, the wettability and the particle size and shape.

The spontaneous cavitation theory has been adopted to interpret the clustering phenomena of non-wetting inclusions in liquid steel. By using a newly established experimental method, Sasai90,91,92) directly measured the attractive force between two Al2O3 cylinders in molten iron. Figure 15 shows the cross sections of two Al2O3 cylinders at different distances in solidified steel ingots. The cavity started to form when the distance was decreased to 0.4 mm. When further decreasing the distance, the cavity grew rapidly. At complete contact, the half-width of the cavity neck was 1.35 mm. Figure 16 shows that with increasing the diameter of the Al2O3 cylinders, the attractive force between the cylinders also increases. Assuming the pressure drop of the cavity is 3.86 × 10−3 Pa, the calculated attractive force between the Al2O3 cylinders is in good agreement with the measured force. Moreover, Sasai90) compared the cavity bridge force with the buoyant force and drag force exerted on Al2O3 inclusions with a diameter in the range of 1–10 μm , and found that the cavity bridge force (3.50 × 10−6~3.51 × 10−5 N) is much larger than the buoyant force (1.56 × 10−14~1.56 × 10−11 N) and the drag force (1.24 × 10−7~2.32 × 10−6 N). This explains why clustered Al2O3 inclusions cannot be easily separated even under turbulent flow of liquid steel.

Fig. 15.

States of cavity bridge formation between Al2O3 cylinders with diameter 8 mm in solidified steel ingots at different separation distances (0.5, 0.4, 0.3 and 0.1 mm).91)

Fig. 16.

The attractive force between Al2O3 cylinders versus cylinder diameter in Al-killed liquid steel.90)

Sasai92) further measured the attractive force between two Al2O3 cylinders in liquid steel at different O and S contents (Fig. 17). O reduces the attractive force more significantly than S. This is because both O and S affect the surface tension of the liquid steel and the contact angle of Al2O3, but the effect of O is much more significant. Therefore, Sasai92) concluded that the presence of O in liquid steel can greatly decrease the clustering tendency of Al2O3 inclusions.

Fig. 17.

Effect of O and S contents in liquid steel on the attractive force between two identical Al2O3 cylinders.92)

Zheng et al.93) quantitatively measured the clustering degree of Al2O3 inclusions with different morphologies in molten iron, and found that the clustering degree increases in the order of spherical, dendritic, plate-like and faceted inclusions (Fig. 18). To explain this, the cavity bridge force between two Al2O3 particles with different shape combinations, i.e., sphere-sphere (S-S), sphere-plane (S-P), plane-plane (P-P) was calculated (Fig. 19). The attractive force is influenced significantly by the particle shape. The S-S type has the smallest attractive force and the shortest acting length. The P-P type has the largest attractive force and the longest acting length. Further, the authors investigated the effects of surface tension of liquid steel and contact angle on the energy required to rupture the cavity between two identical spherical inclusions (Fig. 20). The larger the rupture energy, the more difficult it is to separate inclusions in contact with each other. The rupture energy increases linearly with increasing surface tension of the melt. The rupture energy increases slowly with increasing contact angle to around 120°, thereafter increasing sharply. Regarding the effect of contact angle, Wang et al.94) obtained similar results.

Fig. 18.

Clustering degree of Al2O3 inclusions versus their morphologies in molten iron.93)

Fig. 19.

Calculated cavity bridge force versus separation distance for different contact types.93) (Online version in color.)

Fig. 20.

Effects of surface tension and contact angle on the rupture energy between two identical spherical Al2O3 particles of 10 μm in diameter.93)

Currently, for simplicity, the liquid-vapor interface of the cavity is described with an arc with radius r in all the above theoretical calculations. The toroidal approximation approach can cause great errors, especially for very small inclusions.95) Moreover, to more accurately predict the clustering behavior of non-wetting inclusions, it is necessary to modify the effective collision coefficient αt in Eq. (11) by replacing the van der Waals force with the cavity bridge force or taking both forces into account.

8. Control Strategies of Non-metallic Inclusions in Steel

The above review clearly indicates that the interfacial energy or contact angle significantly affects the inclusion characteristics. Figure 21 schematically shows the relationship between the interfacial energy, the evolution processes and the inclusion characteristics. Decreasing the interfacial energy promotes the nucleation and engulfment of inclusions, while it prevents the clustering and removal of inclusions. A high nucleation rate and a low clustering tendency favor the formation of inclusions with small and uniform size. A high engulfment tendency leads to a uniform spatial distribution of inclusions. However, a low removal rate of inclusions is unfavorable for the production of clean steel. When increasing the interfacial energy, all the above trends will reverse. This is the root cause why it is difficult to control the inclusion characteristics to a satisfactory level, i.e., extremely low amount, small and uniform size, uniform spatial distribution, etc. Surfactants have some beneficial effects in promoting nucleation and removal of inclusions. However, most of them are impurity elements, which are harmful to steel properties. Therefore, surfactants are rarely used in steelmaking.

Fig. 21.

Schematic diagram of the relationship between the interfacial energy, the evolution processes and the inclusion characteristics. (Online version in color.)

From the perspective of clean steel production, deoxidizers with strong affinity for oxygen are the premise. Moreover, in the early and middle stages of deoxidation, non-metallic inclusions should have as high interfacial energy as possible to enhance inclusion removal. In the later stage, however, the interfacial energy should be decreased as much as possible to weaken the clustering and pushing of inclusions, favoring the formation of small-sized and uniformly-distributed inclusions. As the interfacial energy of inclusions intrinsically depends on their composition, the composition must be modified in the later stage of deoxidation. As aforementioned, Al deoxidizer is widely used in steelmaking. However, residual Al2O3 inclusions are usually large in size and irregular in morphology. Ca treatment is commonly adopted after Al deoxidation to modify Al2O3 inclusions into liquid CaO–Al2O3 inclusions. Nevertheless, liquid CaO–Al2O3 inclusions tend to grow into large-sized inclusions by collisions. Besides, Ca treatment is inhibited in some steel grades, such as bearing steel. Therefore, to obtain small-sized, uniformly-distributed and spherical inclusions, Al2O3 inclusions should be modified into solid or semi-solid inclusions with lower interfacial energy in the later stage of deoxidation. For this purpose, some control strategies of Al2O3 inclusions are proposed on the basis of Ca treatment, as schematically presented in Fig. 22.

Fig. 22.

Schematic diagram of control strategies for Al2O3 inclusions. (Online version in color.)

8.1. Partial Ca Treatment

Traditional Ca treatment modifies Al2O3 inclusions into fully liquid CaO–Al2O3 inclusions to prevent SEN clogging. Decreasing Ca addition, termed as partial Ca treatment, can modify Al2O3 inclusions into semi-liquid inclusions with a solid core. Such a structure can substantially increase the merging time after collisions.96) Therefore, contacted semi-liquid inclusions may separate again due to hydrodynamic effects, favoring small inclusion sizes. Abdelaziz et al.97) reported that the size of semi-liquid CaO–Al2O3 inclusions is much smaller than fully liquid inclusions. Also, semi-liquid CaO–Al2O3 inclusions can effectively prevent SEN clogging.97,98)

8.2. Ca→RE Treatment

After Ca treatment, fully liquid CaO–Al2O3 inclusions could be further treated with rare earth (RE) elements, changing the inclusions into solid or semi-solid CaO–Al2O3–RE2O3 inclusions, depending on the RE2O3 content. Also, the CaO–Al2O3–RE2O3 inclusions may inherit the initial spherical morphology. According to the CaO–Al2O3–La2O3 phase diagram reported by Li et al.,99) the presence of several percentages of La2O3 could transform liquid CaO–Al2O3 inclusions into solid state. Currently, interfacial properties between CaO–Al2O3–RE2O3 inclusions and liquid steel have not been reported in the open literature. Nevertheless, the interfacial energy of CaO–Al2O3–RE2O3 inclusions should be substantially lower than pure Al2O3 inclusions, considering that CaO and RE2O3 oxides have lower interfacial energies than Al2O3.9,10) Note that, if excessive RE is added, pure RE2O3 inclusions, which have a strong tendency of clustering,70) can be generated.

8.3. Ca→Mg Treatment

Similar to RE, Mg can also modify liquid CaO–Al2O3 inclusions into solid or semi-solid CaO–Al2O3–MgO inclusions, depending on the MgO content. Zhang et al.100) reported that Mg addition modified liquid CaO–Al2O3 inclusions into solid spherical CaO–Al2O3–MgO inclusions containing around 25% MgO. Also, the size was decreased from over 5 μm to around 2 μm. Note that, if initial CaO–Al2O3 inclusions are solid and irregular in morphology, the obtained CaO–Al2O3–MgO inclusions are also irregular.

Thermodynamically, the liquid fraction in CaO–Al2O3, CaO–Al2O3–RE2O3 and CaO–Al2O3–MgO inclusions depends on both temperature and their chemical compositions. To obtain optimal characteristics of the above inclusions, their compositions should be optimized. Furthermore, relevant thermodynamic relationships need to be studied in depth.

9. Conclusions

(1) Non-metallic inclusions with low interfacial energy (or contact angle) have a high nucleation rate and low clustering tendency, thus possessing a narrower size distribution. The deoxidation products of Si, Mn, Ti and other deoxidizers have relatively low interfacial energy. But these deoxidizers also have weak deoxidizing power, failing to meet the requirement of clean steel.

(2) Inclusions unwetted by liquid steel, thus with high interfacial energy, not only are more easily trapped by rising Ar bubbles, but also can more rapidly cross the slag-metal interface. Solid inclusions have much larger contact angles than molten inclusions. To more efficiently remove Al2O3 inclusions, it is better to carry out Ca treatment in the later stage of soft Ar stirring.

(3) Inclusions unwetted by liquid steel have a higher tendency of being pushed into grain boundaries or inter-dendritic regions during solidification of liquid steel. The presence of surfactants favors the pushing of inclusions. The root cause is that the surface excesses of surfactants at the particle-liquid and solid-liquid interfaces decrease with decreasing the particle-interface distance.

(4) Inclusions unwetted by liquid steel have a higher tendency of clustering. On the surface of liquid steel, the capillary force is responsible for the clustering. In the bulk of liquid steel, the cavity bridge force is the root cause. The cavity bridge force increases with increasing surface tension of liquid steel and contact angle of inclusions. The inclusion morphology also affects the clustering tendency by affecting the cavity bridge force. Spherical inclusions have the least clustering tendency. The influence of surfactants on the clustering of inclusions depends on the type of surfactants.

(5) Surfactants have some beneficial effects in promoting nucleation, floating up and removal of inclusions. However, most of them are impurity elements in steel. Therefore, they are rarely used to control the inclusion characteristics.

(6) For Al-killed steel, to obtain small-sized, uniformly-distributed and spherical inclusions, Al2O3 inclusions should be modified into solid or semi-solid spherical inclusions with lower interfacial energy in the later stage of deoxidation. Partial Ca, Ca→RE and Ca→Mg treatments may be effective strategies to achieve the above purpose.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (51904067, 52174309).

References
 
© 2022 The Iron and Steel Institute of Japan.

This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs license.
https://creativecommons.org/licenses/by-nc-nd/4.0/
feedback
Top