**1. Introduction**

Clogging of mold nozzles, also called submerged entry nozzles (SEN), disrupts the steel casting process, affecting the caster's productivity. The nozzle clogging produces inconsistent flow and temperature variations, steel level fluctuations in the mold, impairment of steel quality, and the steel casting's abrupt interruption. Clogging starts when solid compounds, mainly steel skull and non-metallic inclusions, are non-uniformly deposited at the inner nozzle wall, at some typical preferential zones characterized for neighboring dead flow conditions [1–5]. These inclusions have as primary sources: (1) The reaction between the dissolved oxygen with the deoxidizers [6–9]; (2) re-oxidation in the tundish or the nozzle [10, 11]; and (3) the entrainment of slag or refractory particles [11–14]. Researchers who have worked on the determination of inclusions sources and clogging recognize that the deposited inclusions at the nozzle wall are mainly alumina inclusions [7–9, 15, 16]. Steel re-oxidation occurs due to possible air aspiration under the flow control valves (slide gate) to maintain the entry flow to the molds [17–19]. Besides, regardless of the refractory nozzle composition (alumina-graphite, zirconia, and magnesia), the steel melt infiltrates the refractory and removes the protective surface [11, 20], allowing the entrapment of refractory particles and inclusion attachment at the nozzle wall.

Δ*GV* ¼ *RTln*

*The Physical Chemistry of Steel Deoxidation and Nozzle Clogging in Continuous Casting*

<sup>¼</sup> *<sup>h</sup><sup>x</sup> Mh y O* � � *hx Mh y O* � � *E*

> 2 *σPL* þ

¼ �*RTln <sup>S</sup>*<sup>0</sup>

KMO is the solubility product of the oxide. The free energy balance for the nucleation of an oxide precipitated in the homogeneous melt includes the volumetric free energy and the surface energy opposing to the stabilization and growth of the nucleus,

Making zero the derivative of the free energy (**Table 1** [26, 27] reports the molar Gibbs free energy of deoxidation reactions of iron melts) allows the calculation of

4 3 � �*π<sup>r</sup>* 3

<sup>¼</sup> <sup>2</sup>*σPLVO RTlnS*<sup>0</sup>

<sup>¼</sup> <sup>16</sup>*πσ*<sup>3</sup>

16*πσ*<sup>3</sup> *PLV*<sup>2</sup> *O*

" #

3*kBR*<sup>2</sup> *T*3

frequency factor, VO is the oxide**'**s molar volume, *σPL* is the interfacial tension

**Reaction log Keq. (at 1873 K)** Al2O3 (s) = 2 Al + 3 O �55.76 (= 11.80–62790/T) ZrO2 (s) = Zr + 2 O �36.24 (= 21.76–57000/T) MgO (s) = Mg + O �32.85 (= 12.45–38050/T) SiO2 (s) = Si + 2 O �19.39 (= 11.58–30400/T) MnO (s) = Mn + O �5.55 (= 6.70–15050/T) CaO (s) = Ca + O �42.76 (= 7.77–33700/T)

*PLV*<sup>2</sup> *O*

<sup>¼</sup> *Aexp* �16*πσ*<sup>3</sup>

3*kBR*<sup>2</sup> *T*3

3ð Þ *RTlnS*<sup>0</sup>

ð Þ *ln SO* 2

, is the Boltzmann constant, A = 10<sup>32</sup> m�<sup>3</sup> s

*V*<sup>0</sup>

<sup>¼</sup> ½ � %*<sup>M</sup> <sup>x</sup>*

½ � %*<sup>M</sup> <sup>x</sup>* ½ � %*<sup>O</sup> <sup>y</sup>* f g*<sup>E</sup>*

½ � %*<sup>O</sup> <sup>y</sup>*

Δ*GV* (6)

<sup>2</sup> (8)

*PLV*<sup>2</sup> *O*

" #

ð Þ *ln S*<sup>0</sup> 2 (4)

(5)

(7)

(9)

(10)

�<sup>1</sup> is the

*Q KE*

and S0 is the supersaturation ratio given by,

<sup>¼</sup> *KMO KE*

Δ*G* ¼ 4*πr*

the critical radius for the onwards growth of the nucleus, obtaining,

<sup>Δ</sup>*<sup>G</sup>* <sup>¼</sup> <sup>16</sup>*πσ*<sup>3</sup>

*rc* <sup>¼</sup> �2*σPL* Δ*GV*

The free energy required for the nucleation is obtained by substituting this

*PL* 3Δ*G*<sup>2</sup> *V*

*exp* �Δ*<sup>G</sup> kBT* � �

*<sup>S</sup>*<sup>0</sup> <sup>¼</sup> *<sup>Q</sup> KE*

*DOI: http://dx.doi.org/10.5772/intechopen.95369*

radius in Eq. (6),

*I* ¼ *exp*

**Table 1.**

**89**

*Equilibrium constants [26, 27].*

The nucleation rate is [26, 28],

3*kBR*<sup>2</sup> *T*3

where kB = 1.38X10�<sup>23</sup> J K�<sup>1</sup>

16*πσ*<sup>3</sup> *PLV*<sup>2</sup> *O*

" #

ð Þ *ln SO* 2

*A* ¼ *exp*

The non-metallic inclusions come from the steelmaking process; several researchers have focused on studying the variables that induce the inclusion deposition at the inner nozzle wall producing the clogging phenomena [1, 11–14, 16, 21–22]. Steel chemistry and, in particular, steel grades containing titanium, like Ti-SULC, (Ti Stabilized Ultra-Low Carbon Steels), steels enhance the nozzle clogging due to the surface tension properties of this element in liquid steel [23–25]. The wetting of inclusions, rich in Ti oxide, assists in the clustering and compaction of particles. When the ratio Ti/Al is above a threshold, dictated by thermodynamics, the wettability of complex oxides of Ti and Al works intensifying the nozzle's clogging under the presence of oxygen. This series of papers provides an insight into the clogging phenomena while casting these steel grades.

In the present chapter, the authors deal with the physical–chemical aspects of the nozzle-clogging problem by inclusions originated through the deoxidation reactions of steel. Hence, to understand the fundamentals of the problem first, these particle's nucleation and growth are considered using non-equilibrium thermodynamics principles. Second, the influence of the steel refining processes on the deoxidation particle morphology and the relation with their further growth through aggregation and clustering mechanisms is under scrutiny. The analysis continues with studying the thermodynamics related to the oxide particle's adherence to the refractory. Finally, a dynamic analysis lets the establishment of balance among drag, buoyancy, adherence, and lift forces leading to a detachment criterion for an inclusion forming part of a first layer of the clogging. After this work, conclusions and recommendations are provided.

## **2. Non-equilibrium thermodynamics**

#### **2.1 Nucleation and growth rates of oxide inclusions**

The nucleation of a foreign phase in an originally homogeneous solution, in the present case an oxide particle in a liquid solution of iron, is driven by the free energy of the reaction.

$$\mathbf{x}[\mathbf{M}] + \mathbf{y}[\mathbf{O}] = \mathbf{M}\_{\mathbf{x}} \mathbf{O}\_{\mathbf{y}} \tag{1}$$

$$
\Delta G\_m = \Delta G\_m^0 + RTln \frac{a\_{M\_xO\_y}}{h\_M^x h\_O^y} = \Delta G\_m^0 + RTlnQ \tag{2}
$$

where Q is the activity quotient, in the thermodynamic equilibrium *ΔGm* ¼ 0 and the Eq**.** (2) changes to,

$$
\Delta G\_m^0 = -RTlnK\_E \tag{3}
$$

where KE is the equilibrium constant, which depends only on the temperature. Combining Eqs. (2) and (3), dividing the result between the molar volume of the oxide results in,

*The Physical Chemistry of Steel Deoxidation and Nozzle Clogging in Continuous Casting DOI: http://dx.doi.org/10.5772/intechopen.95369*

$$
\Delta G\_V = RTln
$$

$$
\frac{Q}{K\_E} = -RTln\frac{S\_0}{V\_0}\tag{4}
$$

and S0 is the supersaturation ratio given by,

the deposited inclusions at the nozzle wall are mainly alumina inclusions [7–9, 15, 16]. Steel re-oxidation occurs due to possible air aspiration under the flow control valves (slide gate) to maintain the entry flow to the molds [17–19]. Besides, regardless of the refractory nozzle composition (alumina-graphite, zirconia, and magnesia), the steel melt infiltrates the refractory and removes the protective surface [11, 20], allowing the entrapment of refractory particles and inclusion

The non-metallic inclusions come from the steelmaking process; several researchers have focused on studying the variables that induce the inclusion deposition at the inner nozzle wall producing the clogging phenomena [1, 11–14, 16, 21–22]. Steel chemistry and, in particular, steel grades containing titanium, like Ti-SULC, (Ti Stabilized Ultra-Low Carbon Steels), steels enhance the nozzle clogging due to the surface tension properties of this element in liquid steel [23–25]. The wetting of inclusions, rich in Ti oxide, assists in the clustering and compaction of particles. When the ratio Ti/Al is above a threshold, dictated by thermodynamics, the wettability of complex oxides of Ti and Al works intensifying the nozzle's clogging under the presence of oxygen. This series of papers provides an insight into the clogging

In the present chapter, the authors deal with the physical–chemical aspects of the nozzle-clogging problem by inclusions originated through the deoxidation reactions of steel. Hence, to understand the fundamentals of the problem first, these particle's nucleation and growth are considered using non-equilibrium thermodynamics principles. Second, the influence of the steel refining processes on the deoxidation particle morphology and the relation with their further growth through aggregation and clustering mechanisms is under scrutiny. The analysis continues with studying the thermodynamics related to the oxide particle's adherence to the refractory. Finally, a dynamic analysis lets the establishment of balance among drag, buoyancy, adherence, and lift forces leading to a detachment criterion for an inclusion forming part of a first layer of the clogging. After this work, conclusions

The nucleation of a foreign phase in an originally homogeneous solution, in the

*aMxOy hx Mh y O*

where Q is the activity quotient, in the thermodynamic equilibrium *ΔGm* ¼ 0

where KE is the equilibrium constant, which depends only on the temperature. Combining Eqs. (2) and (3), dividing the result between the molar volume of the

<sup>¼</sup> <sup>Δ</sup>*G*<sup>0</sup>

*x M*½ �þ *y O*½ g ¼ *MxOy* (1)

*<sup>m</sup>* ¼ �*RTlnKE* (3)

*<sup>m</sup>* þ *RTlnQ* (2)

present case an oxide particle in a liquid solution of iron, is driven by the free

*<sup>m</sup>* þ *RTln*

Δ*G*<sup>0</sup>

attachment at the nozzle wall.

phenomena while casting these steel grades.

*Casting Processes and Modelling of Metallic Materials*

and recommendations are provided.

energy of the reaction.

and the Eq**.** (2) changes to,

oxide results in,

**88**

**2. Non-equilibrium thermodynamics**

**2.1 Nucleation and growth rates of oxide inclusions**

<sup>Δ</sup>*Gm* <sup>¼</sup> <sup>Δ</sup>*G*<sup>0</sup>

$$\mathbf{S}\_{0} = \frac{\mathbf{Q}}{\mathbf{K}\_{E}} = \frac{\mathbf{K}\_{\text{MO}}}{\mathbf{K}\_{E}} = \frac{\begin{bmatrix} h\_{M}^{\text{x}} h\_{O}^{\text{y}} \end{bmatrix}}{\begin{bmatrix} h\_{M}^{\text{x}} h\_{O}^{\text{y}} \end{bmatrix}\_{E}} = \frac{[\text{@M}]^{\text{x}}[\text{@O}]^{\text{y}}}{\{ [\text{@M}]^{\text{x}} [\text{@O}]^{\text{y}} \}\_{E}} \tag{5}$$

KMO is the solubility product of the oxide. The free energy balance for the nucleation of an oxide precipitated in the homogeneous melt includes the volumetric free energy and the surface energy opposing to the stabilization and growth of the nucleus,

$$
\Delta G = 4\pi r^2 \sigma\_{PL} + \left(\frac{4}{3}\right) \pi r^3 \Delta G\_V \tag{6}
$$

Making zero the derivative of the free energy (**Table 1** [26, 27] reports the molar Gibbs free energy of deoxidation reactions of iron melts) allows the calculation of the critical radius for the onwards growth of the nucleus, obtaining,

$$r\_c = \frac{-2\sigma\_{PL}}{\Delta G\_V} = \frac{2\sigma\_{PL}V\_O}{RTl nS\_0} \tag{7}$$

The free energy required for the nucleation is obtained by substituting this radius in Eq. (6),

$$
\Delta G = \frac{\mathbf{1} \mathsf{6} \pi \sigma\_{PL}^3}{\mathbf{3} \Delta G\_V^2} = \frac{\mathbf{1} \mathsf{6} \pi \sigma\_{PL}^3 V\_O^2}{\mathbf{3} (RT \ln S\_0)^2} \tag{8}
$$

The nucleation rate is [26, 28],

$$I = \exp\left[\frac{16\pi\sigma\_{\rm PL}^3 V\_O^2}{3k\_B R^2 T^3 \left(\ln S\_O\right)^2}\right] \exp\left(\frac{-\Delta G}{k\_B T}\right) = A \exp\left[\frac{-16\pi\sigma\_{\rm PL}^3 V\_O^2}{3k\_B R^2 T^3 \left(\ln S\_0\right)^2}\right] \tag{9}$$

$$A = \exp\left[\frac{\mathbf{1}\mathfrak{K}\pi\sigma\_{\rm PL}^3 V\_O^2}{\mathfrak{B}k\_B\mathcal{R}^2T^3(\ln S\_O)^2}\right] \tag{10}$$

where kB = 1.38X10�<sup>23</sup> J K�<sup>1</sup> , is the Boltzmann constant, A = 10<sup>32</sup> m�<sup>3</sup> s �<sup>1</sup> is the frequency factor, VO is the oxide**'**s molar volume, *σPL* is the interfacial tension


**Table 1.** *Equilibrium constants [26, 27].* between liquid iron and an oxide particle, R is the gas constant, and T is temperature. The critical supersaturation *S*� *<sup>O</sup>* is the minimum one to nucleate one nucleus m�<sup>3</sup> s 1 . Hence, making I = 1 m�<sup>3</sup> s �<sup>1</sup> in Eq**.** (9) implies *S*� *<sup>O</sup>* ¼ *S*0, and gives,

$$S\_0 = \exp\left[\frac{V\_0}{RT}\sqrt{\frac{16\pi\sigma\_{PL}^3}{3k\_B T l n A}}\right] \tag{11}$$

The nucleation process consumes short times of the order of microseconds [26, 29, 30], as shown schematically by **Figure 2.** The fluctuations of concentrations in the liquid structure, after the de-oxidant addition, require a critical supersaturation reached in the point (a) of this figure. Once reached the critical supersaturation, the embryo starts with a group of M-O dimers that develop into metastable structures becoming into a nuclei, and as the thermodynamic and kinetic conditions permit it, evolves in alumina with time, as seen in **Figure 3**. After stabilizing the nuclei, the local supersaturation decreases by diffusion process [31], due to the local consumption of M and O, to the point (b) in **Figure 2** where the nucleation kinetics overlaps with the diffusion process. The supersaturation continues decreasing and the

*Supersaturations of alumina close and far away from surfaces with finite and infinite curvature radius.*

*The Physical Chemistry of Steel Deoxidation and Nozzle Clogging in Continuous Casting*

*DOI: http://dx.doi.org/10.5772/intechopen.95369*

*Evolution of supersaturations with time during nucleation and initial growths by diffusion and Ostwald*

**Figure 1.**

**Figure 2.**

**91**

*ripening mechanisms.*

The supersaturation of iron melts in contact with different oxides was measured through electrochemical methods [29]. The critical supersaturation, *S*� *<sup>O</sup>*, depends on the oxide's nature and surface tension, as seen in the precedent equation. The experimental results provide the inclusions sizes'statistical dispersion directly in the sense that the larger surface tensions, contributing to the opposing free surface energy to the nucleation, lead to larger size dispersions [26]. **Table 2** shows the experimental results of supersaturation experiments reported in Ref. [26] using different metal deoxidizers. The second and third columns are the molar volume and the interfacial tension between the oxide and the melt, the fourth and fifth, the experimental and calculated critical supersaturations through Eq. (11). The sixth and seventh columns include the experimental and corrected supersaturations, respectively. Revision of these data shows that the magnitudes of the calculated critical supersaturations are larger than the experimental critical supersaturations. The other observations are the small magnitudes of the experimental supersaturation. The large differences behind the critical supersaturations are due to the experimental data's nature as they correspond to the metal bulk property. On the other hand, the other magnitude (the corrected supersaturations) is theoretically related to the nuclei's curvature, as is schematized in **Figure 1**. The curvature raises the gradients of concentration of all solutes, M (Al, Si, Mn, Mg, Ti, Zr, Ca) and O in the nuclei's tip and, consequently, the critical supersaturations are larger in the proximities of the tip than in the metal bulk. The curvature, given by *r*�<sup>1</sup> *<sup>C</sup>* is calculated through Eq. (7) and matching its magnitude by considering an embryo formed by two or three pairs of M-O dimers, (consulting for that purpose the atomic radius of the involved elements of the corresponding oxides in the Periodic Table).

The correction of the experimental supersaturations is possible through the Gibbs–Thomson's Equation which gives the ratio between both types of supersaturations as,


$$\left[\mathbf{S}\_{0,corr}\right]\_{r=r} = \left[\mathbf{S}\_{0,exp}\right]\_{r=\infty} \exp\left[\frac{V\_0}{RT}\frac{2\sigma}{r\_c}\right] \tag{12}$$

**Table 2.**

*Experimental, calculated and corrected critical supersaturation degree for precipitation of oxides [26].*

*The Physical Chemistry of Steel Deoxidation and Nozzle Clogging in Continuous Casting DOI: http://dx.doi.org/10.5772/intechopen.95369*

The nucleation process consumes short times of the order of microseconds [26, 29, 30], as shown schematically by **Figure 2.** The fluctuations of concentrations in the liquid structure, after the de-oxidant addition, require a critical supersaturation reached in the point (a) of this figure. Once reached the critical supersaturation, the embryo starts with a group of M-O dimers that develop into metastable structures becoming into a nuclei, and as the thermodynamic and kinetic conditions permit it, evolves in alumina with time, as seen in **Figure 3**. After stabilizing the nuclei, the local supersaturation decreases by diffusion process [31], due to the local consumption of M and O, to the point (b) in **Figure 2** where the nucleation kinetics overlaps with the diffusion process. The supersaturation continues decreasing and the

**Figure 2.**

*Evolution of supersaturations with time during nucleation and initial growths by diffusion and Ostwald ripening mechanisms.*

between liquid iron and an oxide particle, R is the gas constant, and T is tempera-

*V*<sup>0</sup> *RT*

4

the oxide's nature and surface tension, as seen in the precedent equation. The experimental results provide the inclusions sizes'statistical dispersion directly in the sense that the larger surface tensions, contributing to the opposing free surface energy to the nucleation, lead to larger size dispersions [26]. **Table 2** shows the experimental results of supersaturation experiments reported in Ref. [26] using different metal deoxidizers. The second and third columns are the molar volume and the interfacial tension between the oxide and the melt, the fourth and fifth, the experimental and calculated critical supersaturations through Eq. (11). The sixth and seventh columns include the experimental and corrected supersaturations, respectively. Revision of these data shows that the magnitudes of the calculated critical supersaturations are larger than the experimental critical supersaturations. The other observations are the small magnitudes of the experimental supersaturation. The large differences behind the critical supersaturations are due to the experimental data's nature as they correspond to the metal bulk property. On the other hand, the other magnitude (the corrected supersaturations) is theoretically related to the nuclei's curvature, as is schematized in **Figure 1**. The curvature raises the gradients of concentration of all solutes, M (Al, Si, Mn, Mg, Ti, Zr, Ca) and O in the nuclei's tip and, consequently, the critical supersaturations are larger in the proxim-

2 s

The supersaturation of iron melts in contact with different oxides was measured

*S*<sup>0</sup> ¼ *exp*

ities of the tip than in the metal bulk. The curvature, given by *r*�<sup>1</sup>

through Eq. (7) and matching its magnitude by considering an embryo formed by two or three pairs of M-O dimers, (consulting for that purpose the atomic radius of

The correction of the experimental supersaturations is possible through the

� �

**O (exp.) S\***

MgO 1.10E-05 1.8 8.4 280 3.6 � 7.2e4 280.224 1801440 ZrO2 1.01E-05 1.63 4.5 85 48 � 68 84.825 1093.3 Al2O3 8.60E-06 2.11 14.7 529 37 � 60 530.229 1803.5

CaO-Al2O3 1.47E-05 1.3 3.6 92 8.5E+04 90.936 2147100

MnO-SiO2 1.36E-05 1 1.7 18 1.5 18.598 16.41

*Experimental, calculated and corrected critical supersaturation degree for precipitation of oxides [26].*

*<sup>r</sup>*¼<sup>∞</sup> *exp*

*V*<sup>0</sup> *RT* 2*σ rc* � �

**<sup>O</sup> (cal.) SO S\***

the involved elements of the corresponding oxides in the Periodic Table).

Gibbs–Thomson's Equation which gives the ratio between both types of

*<sup>S</sup>*0,*corr* ½ �*<sup>r</sup>*¼*<sup>r</sup>* <sup>¼</sup> *SO*,*exp*

through electrochemical methods [29]. The critical supersaturation, *S*�

�<sup>1</sup> in Eq**.** (9) implies *S*�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 16*πσ*<sup>3</sup> *PL* 3*kBTlnA*

*<sup>O</sup>* is the minimum one to nucleate one nucleus

3

*<sup>O</sup>* ¼ *S*0, and gives,

5 (11)

*<sup>C</sup>* is calculated

**O (exp.) corr SO corr.**

(12)

*<sup>O</sup>*, depends on

ture. The critical supersaturation *S*�

. Hence, making I = 1 m�<sup>3</sup> s

*Casting Processes and Modelling of Metallic Materials*

m�<sup>3</sup> s 1

supersaturations as,

**OXIDE Vo [m3**

**Table 2.**

**90**

**. Mol**�**<sup>1</sup>**

**]** *σ*PL **[J. m<sup>2</sup> ] S\***

CaO 1.65E-05 1.17 3.4 83

SiO2 1.13E-05 1.24 1 27

diffusion overlaps with the particle growth through the Ostwald ripening process summarized by the following expression [32],

$$
\dot{r}^3 - \acute{r}\_0^3 = a\Bbbk\_d t \tag{13}
$$

The main obstacle of a particle to born is the creation of a new surface preceding the formation of a small volume in a hosting matrix, as is seen in **Figure 3**, with a different structure. Those particles requiring larger supersaturations would, eventually, nucleate smaller populations of particles with a broader size distribution once their first step of development ends. The precipitates characterized by high and low supersaturations are schematized in **Figure 5a** and **b**, respectively, showing the period for each one of them. The first case will yield numerous small particles with limited growth as the supersaturation decays providing a narrow size distribution. The longer times lead to larger diffusion and growth time scales yielding broader size distributions in the second case. The time scales change to exponentially larger ones when the precipitates of solid-state transformations take place. For example, steel aging by nitrogen diffusion consumes long times as the diffusion coefficients of this interstitial element are very small in ferrite or austenite phases at 300°C [32, 33] compared with its diffusion coefficient at 1600°C [34], as is schematized in **Figure 5c** and **d.** Hence, the interfacial tension between the melt and the nuclei governs the nucleation rate, as seen in **Figure 6**. Alumina has one of the lowest nucleation rates as its interfacial tension is large, and its crystals will have a

*The Physical Chemistry of Steel Deoxidation and Nozzle Clogging in Continuous Casting*

*DOI: http://dx.doi.org/10.5772/intechopen.95369*

broad spectrum of sizes after the nucleation and the diffusion end.

Alumina may acquire a wide diversity of morphologies depending on the concentrations of oxygen and the deoxidant. Accordingly, the initial supersaturation ratio influences the morphology of alumina. **Figure 7** shows a scheme of the relation between oxygen concentrations and the deoxidant with the particle morphology [35]. In oxidized melts, the inclusions are rounded spheroids, as the oxygen activity decreases the surface roughness develops reaching the stage of dendritic precipitation. With further deoxidation the morphology changes to faceted, disks and

The heterogeneous nucleation of alumina particle also yields characteristic morphologies. Other foreign particles catalyze alumina's nucleation in the melt, such as those of metastable iron oxide precipitated in the steelmaking furnace and manganese silicates in the refining ladle [36]. A catalyzed nucleation process means that

*Schematics of nucleation rate evolution with time. (a) High nucleation rates at low supersaturation in liquid state, (b) high nucleation rates in solid state, (c) low nucleation rates at high supersaturation in liquid state,*

**2.2 Alumina morphology**

crystalline rhomboids.

**Figure 5.**

**93**

*(d) low nucleation rates in solid state.*

$$k\_d = \frac{2\sigma D\_O V\_O C\_O}{RT(C\_P - C\_O)}\tag{14}$$

where CO and CP are the concentrations of dissolved oxygen and oxygen content in the oxide, respectively, and DO is the diffusion coefficient of oxygen. Further growth phenomena of the particles, in industrial vessels, includes Stokes collisions, collisions among particles driven by turbulent flows deriving in aggregates of particles and clusters. Grown particles are easily floated out thanks to the bottom stirring with argon of steel ladles which carries these particles through their contact with gas bubbles, and melt convection making them contact the slag facilitating their absorption in this phase.

**Figure 4a** and **b** show the effect of the supersaturation on the nucleation kinetics on the nucleation rates of different oxides recalculated from reference [26]. There are two important differences, the first is that the nucleation rates are considerably lower than those reported in Ref. [26] and the second is the larger supersaturations required to precipitate the MgO shown in **Figure 4b**. Another important feature is the small supersaturations required for the precipitation of silica and manganese silicate. Therefore, those particles requiring small or relatively small supersaturations yield the largest nucleation rates meaning, physically, the fast generation of million of nuclei distributed inside the reaction and diffusion boundaries.

**Figure 3.** *Nucleation of an alumina lattice from the union of Al-O dimers.*

**Figure 4.**

*Effect of supersaturation ratios on nucleation rate at 1600°C, (a) various metal deoxidizers, (b) with magnesium.*

## *The Physical Chemistry of Steel Deoxidation and Nozzle Clogging in Continuous Casting DOI: http://dx.doi.org/10.5772/intechopen.95369*

The main obstacle of a particle to born is the creation of a new surface preceding the formation of a small volume in a hosting matrix, as is seen in **Figure 3**, with a different structure. Those particles requiring larger supersaturations would, eventually, nucleate smaller populations of particles with a broader size distribution once their first step of development ends. The precipitates characterized by high and low supersaturations are schematized in **Figure 5a** and **b**, respectively, showing the period for each one of them. The first case will yield numerous small particles with limited growth as the supersaturation decays providing a narrow size distribution. The longer times lead to larger diffusion and growth time scales yielding broader size distributions in the second case. The time scales change to exponentially larger ones when the precipitates of solid-state transformations take place. For example, steel aging by nitrogen diffusion consumes long times as the diffusion coefficients of this interstitial element are very small in ferrite or austenite phases at 300°C [32, 33] compared with its diffusion coefficient at 1600°C [34], as is schematized in **Figure 5c** and **d.** Hence, the interfacial tension between the melt and the nuclei governs the nucleation rate, as seen in **Figure 6**. Alumina has one of the lowest nucleation rates as its interfacial tension is large, and its crystals will have a broad spectrum of sizes after the nucleation and the diffusion end.

#### **2.2 Alumina morphology**

diffusion overlaps with the particle growth through the Ostwald ripening process

*kd* <sup>¼</sup> <sup>2</sup>*σDOVOCO RT C*ð Þ *<sup>P</sup>* � *CO*

where CO and CP are the concentrations of dissolved oxygen and oxygen content in the oxide, respectively, and DO is the diffusion coefficient of oxygen. Further growth phenomena of the particles, in industrial vessels, includes Stokes collisions, collisions among particles driven by turbulent flows deriving in aggregates of particles and clusters. Grown particles are easily floated out thanks to the bottom stirring with argon of steel ladles which carries these particles through their contact with gas bubbles, and melt convection making them contact the slag facilitating

**Figure 4a** and **b** show the effect of the supersaturation on the nucleation kinetics on the nucleation rates of different oxides recalculated from reference [26]. There are two important differences, the first is that the nucleation rates are considerably lower than those reported in Ref. [26] and the second is the larger supersaturations required to precipitate the MgO shown in **Figure 4b**. Another important feature is the small supersaturations required for the precipitation of silica and manganese silicate. Therefore, those particles requiring small or relatively small supersaturations yield the largest nucleation rates meaning, physically, the fast generation of

million of nuclei distributed inside the reaction and diffusion boundaries.

*Effect of supersaturation ratios on nucleation rate at 1600°C, (a) various metal deoxidizers, (b) with*

*Nucleation of an alumina lattice from the union of Al-O dimers.*

<sup>0</sup> ¼ *αkdt* (13)

(14)

´*r* <sup>3</sup> � ´*<sup>r</sup>* 3

summarized by the following expression [32],

*Casting Processes and Modelling of Metallic Materials*

their absorption in this phase.

**Figure 3.**

**Figure 4.**

*magnesium.*

**92**

Alumina may acquire a wide diversity of morphologies depending on the concentrations of oxygen and the deoxidant. Accordingly, the initial supersaturation ratio influences the morphology of alumina. **Figure 7** shows a scheme of the relation between oxygen concentrations and the deoxidant with the particle morphology [35]. In oxidized melts, the inclusions are rounded spheroids, as the oxygen activity decreases the surface roughness develops reaching the stage of dendritic precipitation. With further deoxidation the morphology changes to faceted, disks and crystalline rhomboids.

The heterogeneous nucleation of alumina particle also yields characteristic morphologies. Other foreign particles catalyze alumina's nucleation in the melt, such as those of metastable iron oxide precipitated in the steelmaking furnace and manganese silicates in the refining ladle [36]. A catalyzed nucleation process means that

#### **Figure 5.**

*Schematics of nucleation rate evolution with time. (a) High nucleation rates at low supersaturation in liquid state, (b) high nucleation rates in solid state, (c) low nucleation rates at high supersaturation in liquid state, (d) low nucleation rates in solid state.*

**Figure 6.** *Nucleation rate as a function of surface tension between the particle and the melt at 1600°C.*

#### **Figure 7.**

*Evolution of the growth shapes of oxide inclusions as a function of the local oxygen activity (solid line) and deoxidizer activity (dashed line) according to Steinmetz [35].*

the foreign particle decreases the supersaturation required by the precipitation process of the particle through a decrease of the free energy according to [32],

$$
\Delta \mathbf{G}\_{het} = \left\{ \frac{-4}{3} \pi r^3 \Delta \mathbf{G}\_v + 4 \pi r^2 \sigma\_{PL} \right\} \mathbf{S}(\theta) \tag{15}
$$

2½ �þ *Al* 3ð Þ¼ *FeO* ð Þþ *Al*2*O*<sup>3</sup> 3½ � *Fe* (18)

The interfacial tension between the alumina and silicate particles is reduced due to the chemical reaction, a layer of alumina, (it is initially nucleated and the alumina layer grows by the reaction), surrounds the particle of silicate making sluggish the diffusion of aluminum through the alumina layer to continue the reaction. During the process, some particles of Mn and Si precipitate as products of the reaction (17). No dendrites were observed and there is the presence of needle like clusters with disk type terminations indicating a growth under small supersaturations, once the oxygen content decreases. Iron oxide suffers a rapid reduction by aluminum, reaction (18) and the product is an alumina particle without other phases. Other alumina particles nucleate heterogeneously on the original alumina particles and

*The Physical Chemistry of Steel Deoxidation and Nozzle Clogging in Continuous Casting*

After concluding the nucleation and growth by diffusion and Ostwald ripening,

and the probability of collision under the action of turbulent eddies is expressed

In Stokes regime, the highest collision probability is observed when the inclusions have large size differences as seen in **Figures 9** and **10** indicates that collisions of silicate inclusions smaller than ten μm, have low probabilities for collisions under turbulent flow conditions and those with large dimensions have higher collision probabilities. **Figure 11** shows the corresponding collision probabilities for alumina inclusions and particles as small as three μm yield the highest probabilities for a collision. Therefore, alumina inclusions grow from microscopic inclusions to large aggregates and clusters by collisions among small particles forming aggregates [40].

j j *R*<sup>1</sup> � *R*<sup>2</sup> ð Þ *R*<sup>1</sup> þ *R*<sup>2</sup>

3

<sup>3</sup> (19)

f g *Noexp*ð Þ �*αR*<sup>1</sup> *Noexp*ð Þ �*αR*<sup>2</sup> *=*2

(20)

the inclusions continue their growth through direct collision. In a Stokes flow regime, the probability for collision among inclusions of sizes R1 and R2 is [37],

*<sup>ε</sup>=<sup>ν</sup>* <sup>p</sup> <sup>¼</sup> <sup>7</sup>*:*2j j *<sup>R</sup>*<sup>1</sup> � *<sup>R</sup>*<sup>2</sup> ð Þ *<sup>R</sup>*<sup>1</sup> <sup>þ</sup> *<sup>R</sup>*<sup>2</sup>

*ws* <sup>¼</sup> <sup>2</sup> 9 *g* Δ*ρ μ*

*Heterogeneous nucleation of alumina on iron oxide and silicate particles [36].*

*DOI: http://dx.doi.org/10.5772/intechopen.95369*

yield dendritic morphologies.

**2.3 Further growth of inclusions**

by the Saffman's Equation as [38],

<sup>3</sup> ffiffiffiffiffiffiffi

*<sup>π</sup>* <sup>p</sup> ð Þ *<sup>R</sup>*<sup>1</sup> <sup>þ</sup> *<sup>R</sup>*<sup>2</sup>

*<sup>w</sup>* <sup>¼</sup> <sup>1</sup>*:*<sup>3</sup> ffiffiffi

**95**

**Figure 8.**

where

$$S(\theta) = \frac{(2 + \cos \theta)(1 - \cos \theta)^2}{4} \tag{16}$$

Note that except for factor S(θ) this expression is the same as that obtained for homogeneous nucleation, Eq. (6). S(θ) has a numerical value ≤1 dependent only on θ, i.e. contact angle and the nucleus's shape. A catalyzed alumina particle will have a morphology depending on the oxide's nature over which it nucleates as shown in **Figure 8** [36]. If the foreign o catalyzer particle is a silicate, already existent given its high nucleation rate, a chemical reaction intervenes,

$$2[\text{Al}] + (\text{MnO} \bullet \text{SiO}\_2) = (\text{Al}\_2\text{O}\_3) + [\text{Mn}] + [\text{Si}] \tag{17}$$

if the particle is iron oxide, then

*The Physical Chemistry of Steel Deoxidation and Nozzle Clogging in Continuous Casting DOI: http://dx.doi.org/10.5772/intechopen.95369*

**Figure 8.** *Heterogeneous nucleation of alumina on iron oxide and silicate particles [36].*

$$\mathfrak{Z}[Al] + \mathfrak{Z}(FeO) = (Al\_2O\_3) + \mathfrak{Z}[Fe] \tag{18}$$

The interfacial tension between the alumina and silicate particles is reduced due to the chemical reaction, a layer of alumina, (it is initially nucleated and the alumina layer grows by the reaction), surrounds the particle of silicate making sluggish the diffusion of aluminum through the alumina layer to continue the reaction. During the process, some particles of Mn and Si precipitate as products of the reaction (17). No dendrites were observed and there is the presence of needle like clusters with disk type terminations indicating a growth under small supersaturations, once the oxygen content decreases. Iron oxide suffers a rapid reduction by aluminum, reaction (18) and the product is an alumina particle without other phases. Other alumina particles nucleate heterogeneously on the original alumina particles and yield dendritic morphologies.

#### **2.3 Further growth of inclusions**

After concluding the nucleation and growth by diffusion and Ostwald ripening, the inclusions continue their growth through direct collision. In a Stokes flow regime, the probability for collision among inclusions of sizes R1 and R2 is [37],

$$
\Delta w\_s = \frac{2}{9} \text{g} \frac{\Delta \rho}{\mu} |R\_1 - R\_2| (R\_1 + R\_2)^3 \tag{19}
$$

and the probability of collision under the action of turbulent eddies is expressed by the Saffman's Equation as [38],

$$\Delta w = 1.3\sqrt{\pi}(R\_1 + R\_2)^3 \sqrt{e/\nu} = 7.2|R\_1 - R\_2|(R\_1 + R\_2)^3 \{ \text{Nocxp}(-aR\_1) \text{Nocxp}(-aR\_2) \}/2 \tag{20}$$

In Stokes regime, the highest collision probability is observed when the inclusions have large size differences as seen in **Figures 9** and **10** indicates that collisions of silicate inclusions smaller than ten μm, have low probabilities for collisions under turbulent flow conditions and those with large dimensions have higher collision probabilities. **Figure 11** shows the corresponding collision probabilities for alumina inclusions and particles as small as three μm yield the highest probabilities for a collision. Therefore, alumina inclusions grow from microscopic inclusions to large aggregates and clusters by collisions among small particles forming aggregates [40].

the foreign particle decreases the supersaturation required by the precipitation process of the particle through a decrease of the free energy according to [32],

*Evolution of the growth shapes of oxide inclusions as a function of the local oxygen activity (solid line) and*

Δ*Gv* þ 4*πr*

*<sup>S</sup>*ð Þ¼ *<sup>θ</sup>* ð Þ <sup>2</sup> <sup>þ</sup> *cos<sup>θ</sup>* ð Þ <sup>1</sup> � *cos<sup>θ</sup>* <sup>2</sup>

Note that except for factor S(θ) this expression is the same as that obtained for homogeneous nucleation, Eq. (6). S(θ) has a numerical value ≤1 dependent only on θ, i.e. contact angle and the nucleus's shape. A catalyzed alumina particle will have a morphology depending on the oxide's nature over which it nucleates as shown in **Figure 8** [36]. If the foreign o catalyzer particle is a silicate, already existent given

2 *σPL*

2½ �þ *Al* ð Þ¼ *MnO*∙*SiO*<sup>2</sup> ð Þþ *Al*2*O*<sup>3</sup> ½ �þ *Mn* ½ � *Si* (17)

*S*ð Þ*θ* (15)

<sup>4</sup> (16)

<sup>3</sup> *<sup>π</sup><sup>r</sup>* 3

*Nucleation rate as a function of surface tension between the particle and the melt at 1600°C.*

<sup>Δ</sup>*Ghet* <sup>¼</sup> �<sup>4</sup>

*deoxidizer activity (dashed line) according to Steinmetz [35].*

*Casting Processes and Modelling of Metallic Materials*

its high nucleation rate, a chemical reaction intervenes,

if the particle is iron oxide, then

where

**94**

**Figure 6.**

**Figure 7.**

#### **Figure 9.**

*Comparison of the collision probability (Stoke's model) with the radius of the inclusions. Miki Y, Kitaoka H, Sakuraya T, Fujii T. mechanism for separating inclusions from molten steel stirred with a rotating electro-magnetic field. ISIJ Int. 1992;32:142–149. DOI: 10.2355/isijinternational.32.142. Reproduced with permission [39].*

**2.4 Bond strength among particles**

*DOI: http://dx.doi.org/10.5772/intechopen.95369*

**Figure 11.**

**Figure 12.**

**97**

*Geometries of the gas cavity of different contact types [42].*

Another important aspect of inclusions growth is the stability of aggregates and clusters, forming large particles that float out of the bath faster as larger are their sizes. Strong bond strengths are desirable as once the particles form aggregates or clusters, their integrity must prevail, avoiding the generation of smaller particles, by breaking processes due to turbulence, which may bring on floatation slowness. The variety of bonds among inclusions with a wide spectrum of morphologies is simpli-

*Prediction of the collision probability (Saffman's model) for alumina inclusions. Miki Y, Kitaoka H, Sakuraya T, Fujii T. mechanism for separating inclusions from molten steel stirred with a rotating electro-magnetic field. ISIJ Int. 1992;32:142–149. DOI: 10.2355/isijinternational.32.142. Reproduced with permission [39].*

*The Physical Chemistry of Steel Deoxidation and Nozzle Clogging in Continuous Casting*

fied into three basic cases, sphere-sphere, sphere-plate and plate-plate, see

*x*5

**Figure 12**. According to thermodynamic calculations of surface tensions, the plateplate geometry yields the largest bond strength, as suggested by **Figure 13** [42]. The bond strength, eventually, will increase by the thickenings of the neck formed by the union of two particles of alumina through diffusion processes according to,

*<sup>R</sup>*<sup>2</sup> <sup>¼</sup> *<sup>K</sup>*1*σPPV*<sup>0</sup>

*RT DVt* (21)

#### **Figure 10.**

*Comparison of the collision probability (Saffman's model) with the radius of the inclusions. Miki Y, Kitaoka H, Sakuraya T, Fujii T. mechanism for separating inclusions from molten steel stirred with a rotating electro-magnetic field. ISIJ Int. 1992;32:142–149. DOI: 10.2355/isijinternational.32.142. Reproduced with permission [39].*

Roughly speaking, in the turbulence regions, in a bottom stirred ladle, the ratio between Stokes and Safmann's regimes is approximately 6X10<sup>4</sup> . Thereby, deoxidation during steel tapping in bottom stirred ladles is the most indicated step to deoxidize and grow inclusions by turbulent collisions. This is particularly applicable to the growth of alumina particles. Indeed, vigorously stirred melts at tapping times, lead to cleaner steel heats [41]. In the secondary refining of steel, where the turbulence levels are considerably smaller, this ratio decreases and is the highest in the argon-plume regions, while in the top layer of the bath, the Stokes regime dominates.

*The Physical Chemistry of Steel Deoxidation and Nozzle Clogging in Continuous Casting DOI: http://dx.doi.org/10.5772/intechopen.95369*

#### **Figure 11.**

*Prediction of the collision probability (Saffman's model) for alumina inclusions. Miki Y, Kitaoka H, Sakuraya T, Fujii T. mechanism for separating inclusions from molten steel stirred with a rotating electro-magnetic field. ISIJ Int. 1992;32:142–149. DOI: 10.2355/isijinternational.32.142. Reproduced with permission [39].*

#### **2.4 Bond strength among particles**

Another important aspect of inclusions growth is the stability of aggregates and clusters, forming large particles that float out of the bath faster as larger are their sizes. Strong bond strengths are desirable as once the particles form aggregates or clusters, their integrity must prevail, avoiding the generation of smaller particles, by breaking processes due to turbulence, which may bring on floatation slowness. The variety of bonds among inclusions with a wide spectrum of morphologies is simplified into three basic cases, sphere-sphere, sphere-plate and plate-plate, see **Figure 12**. According to thermodynamic calculations of surface tensions, the plateplate geometry yields the largest bond strength, as suggested by **Figure 13** [42]. The bond strength, eventually, will increase by the thickenings of the neck formed by the union of two particles of alumina through diffusion processes according to,

$$\frac{\omega^5}{R^2} = \frac{K\_1 \sigma\_{PP} V\_0}{RT} D\_V t \tag{21}$$

**Figure 12.** *Geometries of the gas cavity of different contact types [42].*

Roughly speaking, in the turbulence regions, in a bottom stirred ladle, the ratio

*Comparison of the collision probability (Saffman's model) with the radius of the inclusions. Miki Y, Kitaoka H, Sakuraya T, Fujii T. mechanism for separating inclusions from molten steel stirred with a rotating electro-magnetic field. ISIJ Int. 1992;32:142–149. DOI: 10.2355/isijinternational.32.142. Reproduced with permission [39].*

*Comparison of the collision probability (Stoke's model) with the radius of the inclusions. Miki Y, Kitaoka H, Sakuraya T, Fujii T. mechanism for separating inclusions from molten steel stirred with a rotating electro-magnetic field. ISIJ Int. 1992;32:142–149. DOI: 10.2355/isijinternational.32.142. Reproduced with permission [39].*

*Casting Processes and Modelling of Metallic Materials*

tion during steel tapping in bottom stirred ladles is the most indicated step to deoxidize and grow inclusions by turbulent collisions. This is particularly applicable to the growth of alumina particles. Indeed, vigorously stirred melts at tapping times, lead to cleaner steel heats [41]. In the secondary refining of steel, where the turbulence levels are considerably smaller, this ratio decreases and is the highest in the argon-plume regions, while in the top layer of the bath, the Stokes regime

. Thereby, deoxida-

between Stokes and Safmann's regimes is approximately 6X10<sup>4</sup>

dominates.

**96**

**Figure 10.**

**Figure 9.**

**Figure 13.**

*Attractive force for different contact types. Zheng L, Malfliet a, Wollants P, Blanpain B, Guo M. effect of alumina morphology on the clustering of alumina inclusions in molten iron. ISIJ Int. 2016;56:926–935. DOI: 10.2355/isijinternational.ISIJINT-2015-561. Reproduced with permission [42].*

In this equation, DV = 1*:*3*X*10 *exp* �<sup>110000</sup> *RT* [43], *<sup>σ</sup>pp* <sup>¼</sup> <sup>1</sup> *<sup>J</sup> <sup>m</sup>*<sup>2</sup> is the interfacial tension between alumina particles K1 = 10–100 [43]. **Figure 14** shows the mechanism of diffusion of vacancies in the alumina lattice to form the bond [44]. The bond strength reaches the order of MPa due to the interdiffusion between alumina particles [45].
