Structure and Properties of Slags Used in the Continuous Casting of Steel: Part 1 Conventional Mould Powders

Abstract

The physical properties of mould slags are key to their performance in the continuous casting process. The magnitudes of key properties (viscosity, break temperature, f_cryst and optical properties) are determined by the mould dimensions, casting conditions and the steel grade being cast. However, a range of other properties (e.g. interfacial tension, density) are needed to minimise defects and process problems. The extant data for thermo-physical properties of conventional mould slags are reviewed here and those for specialist powders (e.g. F-free or for casting TRIP steels) are reviewed in Part 2. It was concluded that there is a need for (i) resolution of the huge differences in thermal conductivity of mould slags for T>1050 K obtained with the LP and THW methods (ii) more data for some properties (e.g. C_p and density) and more accuracy for others (viscosity, surface tension) (iii) standardised procedures for the determination of f_cryst and (iv) characterisation of the porosity in slag films. It was also concluded that (i) gaseous convection makes a significant contribution to the heat transfer in the powder bed and (ii) glassy slag films are probably optically-thin.

1. Introduction

The continuous casting of steel (shown in Fig. 1) is a very successful process and the performance of the mould powder is a key factor in this success. In this process, molten steel flows (from the tundish) down a submerged entry nozzle (SEN) into a copper, water-cooled mould which is sealed at the base with a dummy bar. The dummy bar is withdrawn and a steel shell solidifies against the walls of the mould. Two measures are taken to prevent sticking of the shell to the mould (i) the mould is oscillated continuously and (ii) mould powders are fed continuously into the mould and these form a slag film which separates the shell from the mould.

Fig. 1.

Schematic drawings of the continuous casting process (a) showing ladle, tundish and mould and secondary-cooling and (b) of half-section of the mould showing that mould powder added to the top forms a liquid slag pool and a slag film consisting of solid (gray) and liquid (yellow) slag layers between the steel shell and mould. (Online version in color.)

The mould powder heats up as it works its way down the mould. As it proceeds, the powder undergoes the following changes (i) moisture evaporates at ca. 370 K (ii) carbonates decompose at ca. (670–770 K) (iii) sintering occurs between 950 and 1150 K (iv) Carbon particles react with Oxygen to form CO and CO₂ (g) at ca. 770–970 K and finally, (iv) melting of the powder occurs at T>1150 K. Reactions (i) (ii) and (v) are endothermic, whereas carbon combustion (iv) is an exothermic process. The liquid forms a molten pool and molten slag then infiltrates into the channel between the shell and the mould and, subsequently, freezes to form a slag film; this consists of solid (1–2 mm thick) and liquid (ca. 0.1 mm thick) layers. The thickness of the liquid layer (d_l) of the slag film controls the lubrication supplied to the newly-formed shell and the thickness of the solid layer (d_s) controls the rate of heat removal from the shell.¹⁾ Thus the characteristics of the slag film are key to the success of the casting process. The initial, solid slag film is glassy because of the high cooling rate but it tends to crystallise over time. Since the crystal fraction in the slag film takes time to attain a reasonably constant value, studies can be classified as steady state or kinetic investigations; most studies relate to steady state conditions.

The mould powder must carry out the following tasks:

(i) The liquid slag pool must seal off the steel and prevent oxidation.

(ii) The powder bed must provide thermal insulation to prevent the steel from freezing.

(iii) The liquid slag film must provide lubrication to the shell.

(iv) The solid slag film must provide the shell with the optimum heat extraction.

(v) The liquid slag pool must absorb non-metallic inclusions (e.g. Al₂O₃) from the steel.

2. The Need for Slag Property Data

The required properties of mould slags are principally determined by the need to optimise both the lubrication and the heat extraction of the newly-formed shell. However, other mould slag properties must be optimised to minimise problems with defects and process problems (see Table 1). In the past, property values for casting slags have proved very useful in understanding the mechanisms responsible for defect- formation. However, mathematical models of the heat and fluid flow have now developed to the stage where they can reveal these mechanisms and provide reliable predictions of the “in mould ” behaviour. Thus, in the future, the demand for reliable thermo-physical property for slags will come as input data into these models.

Table 1. The properties of mould powders (MP) involved in some defects and process problems encountered during continuous casting:; Lcr=longitudinal cracks; LC crs=longitudinal corner cracks; MP=mould powder; OM=oscillation marks; s=stroke; t_n=negative strip time.

Defect/ Problem	Cause	Casting variables	MP Properties
Lcr; LCcr	Excesssive heat removal from shell	Vc;	Tbr: fcryst; Dcryst optical properties
Sticker breakout	Thin shell & lack of lubrication	Vc:	Tbr; fgl; H2 in slag film:
OM depth (dOM)	Several mechanisms	tn: s;	γmsll: η
Slag entrapment	Metal flow turbulence	Vc; EMBR;	η; γmsl: ρ

3. Lubrication and Heat Extraction from the Shell

The slag film formed between the newly-formed shell and the mould is critical to the casting process since it determines both the lubrication supplied to the shell and the rate of heat removal from the shell.

3.1. Lubrication of the Shell

Analysis of plant data indicates that satisfactory casting is obtained when Q_t.f*≈. 0.48 kg (slag) tonne (steel) ⁻¹ where Q_t is the powder consumption (with units of kg (powder) tonne ⁻¹ (steel)) and f* is the fraction of powder forming slag.²⁾ Powder consumption, Q_s, with units of kg slag m⁻² (of mould) is a measure of the lubrication supplied to the shell and is calculated via Eq. (1) where R*=2(w+t)/wt, i.e. the ratio of (mould surface area/volume) w=width and t=thickness of mould (in m); Q_s, in turn, is related to the melting rate (Q_MR) via Eq. (2). The demand for lubrication increases as the mould width increases (or R* decreases) with slabs> blooms> billets and thin slabs. Thus the required Q_s^req value for satisfactory casting can be calculated from the mould dimensions using Eq. (3).³⁾   

$${\mathrm{Q}}_{\mathrm{s}}=\mathrm{f}*7.6{\mathrm{Q}}_{\mathrm{t}}/\mathrm{R}*\approx 2\hspace{0.17em}600{\mathrm{d}}_l$$(1)

  

$${\mathrm{Q}}_{\mathrm{M}\mathrm{R}}\text{(}\mathrm{k}\mathrm{g}\mathrm{m}\mathrm{i}{\mathrm{n}}^{-1})={\mathrm{V}}_{\mathrm{c}}{\mathrm{Q}}_{\mathrm{s}}.2(\mathrm{w}+\mathrm{t})$$(2)

  

$${\mathrm{Q}}_{\mathrm{s}}{}^{\mathrm{r}\mathrm{e}\mathrm{q}}=2/\left(\mathrm{R}*-5\right)$$(3)

However, Q_s^req is also determined by the casting conditions (principally the casting speed (V_c) but to some degree by s and f.^4,5) Empirical rules based on plant data have shown that the required values of the slag viscosity (η₁₅₇₃^req) at 1573 K can be calculated by Eq. (4).⁶⁾ Thus, values of both Q_s^req (=ρ d_l) and η₁₅₇₃^req are determined by the mould dimensions and the casting conditions.^2,6,7)]   

$${\mathrm{Q}}_{\mathrm{s}}{}^{\mathrm{r}\mathrm{e}\mathrm{q}}=0.55/{\eta }^{\mathrm{0.5.}}{\mathrm{V}}_{\mathrm{c}}$$(4)

3.2. Heat Removal from the Shell

The heat extracted (q_hor) from the shell is primarily controlled via heat transfer across the slag film. The heat transfer mechanism is complicated and involves both lattice (k_lat) and radiation conduction (k_R). The magnitude of heat transfer by lattice conduction increases with (i) decreasing slag film thickness (d_s) (ii) increasing crystallisation (f_cryst) since k_100%cryst≈2 k_glass (iii) decreasing porosity and (iv) decreasing thermal, interfacial resistance (R_int) formed at the slag/Cu interface. Radiation conductivity (k_R) in glassy and liquid slags increases with increasing sample thickness (d)⁸⁾ until the sample becomes optically thick, whereupon, k_R attains a constant value which can be calculated by Eq. (5), where σ=Stefan-Boltzmann constant, n=refractive index and α*=absorption coefficient; (optically thick conditions apply when α*d ≥ 3). Radiation conduction across the slag film can be reduced by (i) absorption of the IR radiation by transition metal oxides e.g. FeO⁹⁾ and (ii) scattering of IR radiation by crystals.^10,11) Thus increasing f_cryst in the slag film results in increased k_lat but decreased k_R; since overall, increased f_cryst reduces the hear flux (q_hor), it is the effect of f_cryst on k_R which is dominant. The effect of adding FeO to the slag is also complicated since the reduction of k_R is partially-offset by the promotion of the glass phase by FeO (i.e. it reduces f_cryst).¹¹⁾ Thus the principal properties of the slag film affecting the heat transfer are (i) the break (or solidification) temperature (T_br or T_sol) since the film thicknesses (d_s and d_l) increase and decrease, respectively, with increasing T_br (ii) f_cryst and (iii) the optical properties of the slag.   

$${\mathrm{k}}_{\mathrm{R}}=16\sigma {\mathrm{n}}^2{\mathrm{T}}^3/3\alpha *$$(5)

Crystallisation of the initially-glassy slag film occurs over time and is accompanied by an increase in density (ρ_cryst>ρ_glass). The resulting shrinkage causes both porosity in the slag film and the formation of an interfacial thermal resistance at the Cu/slag interface (R_int) both of which reduce the horizontal heat flux density (q_hor).

In medium-C (MC) steels the peritectic reaction produces a crumpled shell of variable thickness; the volume changes accompanying the (α-Fe→γ-Fe) transition result in strains which are relieved by longitudinal cracking (Lcr). The cracking levels can be minimised by reducing the horizontal heat flux density (q_hor) so as to produce a thin, uniform shell. In high C (HC) steels the shell is weak and must be strengthened to avoid sticker breakouts and this is done by producing a thicker shell by increasing q_hor. Values of q_hor decrease with increasing T_br and f_cryst but empirical rules (based on the carbon potential and ferrite potential of the stee^2,6,12) only utilise T_br since both factors tend to increase simultaneously with increasing basicity.

3.3. Vertical Heat Transfer

Vertical heat (q_vert) flux covers the heat transfer from the steel meniscus to the atmosphere via the slag pool and the powder bed. It is related to the horizontal heat flux since they both have a common source of heat i.e. the molten steel leaving the SEN. The vertical heat flux contains contributions from (i) k_lat, k_R and convection in the slag pool and (ii) k_lat, and gaseous convection in the powder bed. Thermal insulation of the bed is improved (i.e. q_vert reduced) by (i) better packing of the bed (ii) reduced thermal gradients in the bed using exothermic reactions and (iii) using a deeper powder bed.¹³⁾ Better packing actually increases the thermal conductivity of the bed¹⁴⁾ but the improved insulation arises from the lower permeability of the bed which indicates gaseous convection makes a significant contribution to q_vert.¹⁴⁾

3.4. Steel Flow in the Mould

High casting speeds result in high metal flow velocities which, in turn, cause (i) high heat flux densities and (ii) turbulent metal flow (including standing waves and vortex formation). The latter lead to quality problems such as slag entrapment and enhanced levels of C- pick up. Mould flux properties (e.g. viscosity, or interfacial tension) have been increased, on occasions, to cope with these problems. Electro-magnetic braking (EMBr) is used to reduce metal flow velocity and meniscus fluctuations but has been reported to cause a 30% decrease in q_vert resulting in a decrease in pool depth. Argon bubbling tends to “cushion”^15,16) the metal flow and is reported to reverse the metal flow when the Ar flow rate exceeds 4.5 l min⁻¹.

4. Types of Mould Powders

Conventional mould powders are essentially calcium silicates to which fluxes are added to reduce the melting temperature and viscosity. The basicity (C/S) of these powders varies between 0.6 and 1.5 with viscosity (η₁₅₇₃) ranging from 0.5 dPas (in high speed casting) to 30 dPas (in billet casting). They contain network formers (SiO₂, Al₂O₃) network breakers (CaO, MgO) fluxes (Na₂O, K₂O, Li₂O, CaF₂, and MnO) and may also contain impurities (e.g. FeO and TiO₂). Various types of Carbon particles are added to control the melting rate. In some cases, the powder may also contain (i) exothermic agents (e.g. Ca/Si) and (ii) ZrO₂ additions to minimise SEN wear and to aid nucleation of crystalline phases. However, in recent years, other mould powders have been developed for specialist-use e.g. (i) Fluoride-free^17,18,19) (ii) Non-Newtonian²⁰⁾ (iii) mould powders for casting TRIP steel grades^21,22,23,24) and (iv) C-free (or reduced) powders.²⁵⁾ Part1 of this review is focused solely on Conventional mould powders containing CaF₂ whereas Part 2 compares the properties of powders for specialist- use with those for conventional mould fluxes.

5. The Structure of Silicate Slags

The thermo-physical properties of most silicate slags are dependent upon their structure. The structure is principally defined by (i) the degree of polymerisation of the slag (ii) cation effects and (iii) the physical state of the slag (liquid, glass or crystalline phase and granules or powder when considering the powder bed).

5.1. Polymerisation of Slag

Some properties of silicate slags, like viscosity, are very dependent upon the degree of polymerisation, whereas, in contrast, other properties (e.g. heat capacity) exhibit little dependence on the degree of polymerisation and can be represented by partial molar relations (Eq. (6) where P is the property or parameter and X is the mole fraction of the individual components (1,2 etc.)). The hierarchy of polymerisation dependence on the properties is viscosity>electrical resistivity ≈ diffusivity >thermal conductivity (k)>thermal expansion coefficient (α)>density (ρ)> C_p.   

$$\mathrm{P}=\mathrm{\Sigma }\mathrm{\hspace{0.17em} }{\mathrm{X}}_1{\mathrm{P}}_1+{\mathrm{X}}_2{\mathrm{P}}_2+{\mathrm{X}}_3{\mathrm{P}}_3+$$(6)

5.1.1. Silicate Structure

Much of our knowledge of the structure of silicate melts is based on the spectroscopic work carried out by the geological and glass fraternities.^26,27,28) The standard building block of silicate slags is the Si–O tetrahedron. In pure SiO₂, each Si⁴⁺ ion is surrounded by 4 O⁻ ions and each O⁻ is connected covalently to another Si- tetrahedron (Fig. 2(a)). This results in a 3- dim. polymerised structure. These oxygen ions are referred to as bridging oxygens (BOs). If cations (such as Na⁺, Ca²⁺ or Mg²⁺) are added to pure silica they break the covalent BOs and create ionic O⁻—Na⁺ bonds (referred to as non-bridging oxygens (NBOs). In highly-depolymerised silicate melts, Oxygen ions are formed which are not bonded to any Si⁴⁺ ions, these are denoted as free oxygens (FOs). The Si tetrahedra can be arranged in various forms, rings, chains, 3-dim structures which in turn, affect properties like the viscosity (Fig. 3) diffusion coefficient, electrical and thermal conductivity.

Fig. 2.

Schematic diagram showing structures of the polymeric structures of silicates showing BOs (blue) NBOs (green-maroon) and FOs. (Online version in color.)

Fig. 3.

Viscosity (ln η_{1900 K}) for M₂O–SiO₂ and MO–SiO₂ and alumina-silicate systems as a function of Q (a measure of the degree of polymerisation) showing the progressive development from single tetrahedron to rings, chains, double chains, sheets and 3-dim structures; symbols refer to different systems.³⁰⁾ (Online version in color.)

5.1.2. Alumino-silicate Structure

Most metallurgical slags contain Al₂O₃ and mould powders contain about 5% Al₂O₃ which increases to nearly 10% with alumina pick-up by the slag. These Al³⁺ ions are readily incorporated into the Si⁴⁺ structure but a Na⁺ ion is needed for charge compensation (i.e. to form a {NaAl}⁴⁺ ion). The cations involved in charge-balancing duties are not available for network breaking (i.e. the formation of NBOs).Charge balancing is usually carried out by the cations with lowest field strength;²⁹⁾ in mould slags the charge compensation of Al³⁺ ions is carried out by K⁺ ions, followed by Na⁺ ions. Ions such as Si⁴⁺ and Al³⁺, are referred to as network formers and cations like Na⁺ and Ca²⁺ are denoted as network breakers. The degree of polymerisation increases with increasing SiO₂ and Al₂O₃ contents.

5.1.3. Parameters Used as a Measure of Polymerisation

Several parameters have been used to represent the degree of polymerisation (or de-polymerisation) namely: (i) Basicity (i.e. (C/S)=%CaO/ % SiO₂) or more complicated terms like the basicity index (ii) (NBO/T) which is a basicity term modified for charge compensation (Eq. (7) where X_MO and X_M2O are the mole fractions of CaO and Na₂O etc. respectively) and is a measure of the de- polymerisation (iii) the parameter, Q, a measure of polymerisation calculated from (NBO/T) (Eq. (8)) (iv) Optical Basicity (which is a measure of electron donor power) (v) the number of BOs, NBOs and FOs (sometimes denoted O^o, O⁻, O²⁻, respectively)^31,32) (vi) the concentrations of the various Qⁿ species derived from spectroscopic measurements on the slag,³³⁾ and (vii) the viscosity of the slag.

The parameter, Q, is used here and can be regarded as a mean of the various Qⁿ values, but it should be noted that CaF₂ is ignored in the calculation of Q. The biggest problem with the use of Q is that it does not differentiate between different cations and other terms must be introduced to account for cation effects (e.g. (z/r²)). It can be seen from Fig. 3 that the dramatic increase in Q occurs at Q>3 i.e. when rings chains etc. are replaced by 3-dim.- structures. However, it must be noted that the Al–O bond is weaker than the Si–O bond and this results in a reduction of the viscosity (i.e. η_MS>η_MAS for the same Q value and temperature).³⁴⁾   

$$\mathrm{N}\mathrm{B}\mathrm{O}/\mathrm{T}=\mathrm{\Sigma }2\left({\mathrm{X}}_{\mathrm{M}\mathrm{O}}+{\mathrm{X}}_{\mathrm{M}2\mathrm{O}}-{\mathrm{X}}_{\mathrm{A}\mathrm{l}2\mathrm{O}3}\right)/\left({\mathrm{X}}_{\mathrm{S}\mathrm{i}\mathrm{O}2}+2{\mathrm{X}}_{\mathrm{A}\mathrm{l}2\mathrm{O}3}\right)$$(7)

  

$$\mathrm{Q}=4-\mathrm{N}\mathrm{B}\mathrm{O}/\mathrm{T}$$(8)

5.2. Cation Effects

Cations, such as Ca²⁺, or Na⁺ tend to be arranged octahedrally around the NBO in 6-fold coordination (⁽⁶⁾Ca²⁺) but the coordination number (N_coord) can vary and tends to increase with increasing cation size.^27,28) The size of the cation is important since it affects (i) the strength of the ionic bond formed with the NBO, where the bond strength is usually represented by the cation field strength (z/r²) (ii) the coordination number (N_coord) since N_coord tends to increase with increasing cation size^27,28) and (iii) the movement of cations since large cations tend to move more sluggishly through melts than small cations (leading to lower diffusion coefficients and electrical conductivities). In general, cation effects are smaller than the effects of polymerisation; this can be seen from Fig. 3, where the cation effects are manifested as the scatter of points around the curve.

Increasing cation field strength (K⁺ <Na⁺ <Li⁺ <Ca²⁺ <Mg²⁺) has been reported to cause the following structural changes in slags:^27,28) (i) A wider distribution of polymeric species (Qⁿ) (ii) A lower coordination number (N_coord) which, in turn, affects the numbers of BOs and NBOs present (iii) A more compact distribution of inter-tetrahedral bond angles (Si–O–Si or Si–O–Al in alumino-silicates) which affects the amount of disorder present (i.e. configurational entropy). (iv) An increasing attraction for NBOs (e.g. Mg²⁺>Ca²⁺ etc) and (v) a lower probability of carrying out the charge-balancing duties in alumino-silicates (which are carried out by the cations with lowest (z/r²) i.e. K⁺ or Na⁺ in mould slags).

Transport properties (e.g. diffusion coefficient or electrical conductivity) are also affected by the number of available cations,³⁴⁾ where cations on charge compensation duties are not available for transport. It has been proposed that such properties are affected by which of the following, competing mechanisms is rate-determining, namely, (i) the ability of the cation to free itself from the NBO which increases with decreasing cation field strength (z/r²) and (ii) the ability of the cation to move through the melt which increases with decreasing size (r³).³⁵⁾

5.3. Effects of CaF₂, and TiO₂ on Structure

CaF₂ is a key component in conventional mould slags since it promotes the formation of cuspidine (C₃S₂Fl) crystals. Spectroscopic studies have shown that few Si- F bonds are formed, some Al- F bonds may be formed but F- bonds predominantly with high- field- strength cations like Mg²⁺ and Ca^{2+ 32,33,36,37,38,39,40,41)} and exhibits a coordination number of 4⁴⁰⁾]. In mould slags this is accentuated by the high concentrations of Ca²⁺ (cf. Al³⁺ ions) present. CaF₂ does not alter the concentrations of the various Qⁿ units in the slag³²⁾ i.e. it tends to act as diluent³²⁾ and thus is ignored in the calculation of Q in Eqs. (7) and (8). Additions of F^– ions can be made in two ways (i) where CaO is replaced by CaF₂ and (ii) where CaF₂ is added to the slag. In the first case, F additions reduce the number of available Ca²⁺ ions for network breaking which leads to further polymerisation of the melt. However, although CaF₂ additions act mostly as a diluent, they do result in a decrease in slag viscosity (see Fig. 7); one proposed mechanism is shown in Fig. 4.³⁹⁾

Fig. 7.

The parameter, ln η_{1573 K} as a functions of Q showing dependence on both Q and; X_CaF2; lines represent Q dependence for similar X_CaF2. values, namely (0.025±0.025)=O, +; black line (0.075±0.025)= and red line,; (0.125±0.025)= and green line; (0.175±0.025)=; (0.225±0.025)=; >0.25=.¹¹⁸⁾ (Online version in color.)

Fig. 4.

Proposed mechanism for the addition of CaF₂ to silicate slag.³⁹⁾

TiO₂ is usually present in conventional mould fluxes as an impurity but it has been used as replacement for CaF₂ in F-free powders.¹⁹⁾ It might be expected that additions of TiO₂ to the slag would result in the Ti⁴⁺ ions being incorporated into the Si⁴⁺ network. However, TiO₂ additions have been observed to reduce the slag viscosity.^19,42) The Ti⁴⁺ ions could possibly act as (i) network formers (ii) act as network breakers (i.e. Ti ions adopt 5- (⁽⁵⁾Ti,⁴⁺) or 6- fold coordination²⁷⁾ and (iii) form TiO₂-like clusters (since there is a tendency for Ti⁴⁺ ions to prefer the company of their own kind (i.e. Ti–O–Ti and Si–O–Si are preferred to Ti–O–Si) as witnessed by the tendency for phase separation in the CaO–SiO₂–TiO₂ system).

It can be seen from Fig. 5 that the compositions of mould slags occupy an intermediate position between metallurgical slags (with Q=0 to 2) and those for glasses and minerals (with Q>3). This is not accidental since fast kinetics are promoted by low slag viscosities and processes such as de-sulphurisation (de-S) and de-P are performed using high-basicity, low- viscosity slags; thus metallurgical slags have much higher concentrations of Free Oxygens and NBOs and much fewer BOs than minerals and glasses.

Fig. 5.

Composition ranges for mould slags (CC) metallurgical slags and minerals and glasses shown as a ternary diagram of mole fractions of SiO₂, Al₂O₃ and M_xO* (where X_MxO*=X_MxO-X_Al2O3 =Σ(X_CaO+X_MgO+X_FeO +X_MnO+ X_Na2Oetc. -X_Al2O3) i.e. network breaking oxides after charge-balancing of Al₂O₃; Min=Minerals; BF=blast furnace; Cu=copper-making; Fe/Cr and Fe/Mn=ferro-alloy; SS=secondary steelmaking slags. (Online version in color.)

5.4. Physical State of Slag

The slag film formed in the mould usually contains a mixture of glassy and crystalline phases. In crystalline solids, the ions are in fixed positions and are arranged in a regular manner; thus, in crystals, the disorder and entropy (S), tend to be low. However, in liquids and quenched glasses there is a much higher level of disorder (i.e. the “configurational entropy” is higher than that in the equivalent crystalline phase). Disorder between BOs and NBOs (or disorder between various Qⁿ species) makes significant contributions to the configurational entropy (50% of the total comes from ideal mixing²⁷⁾). Certain slag components promote the formation of the glass phase (e.g. SiO₂, B₂O₃, >4%MnO >7% MgO, Na₂O, FeO) whilst others support the formation of crystalline phases (e.g. CaO, CaF₂). Glasses have lower thermodynamic stability and looser packing than their crystalline equivalents and glasses are promoted by high cooling rates. The initial slag films formed are probably glassy due to the high cooling rates involved but (with the exception of high viscosity slags used for casting billets) they crystallise as the casting proceeds and f_cryst attains a steady state value during the cast.

Increasing temperature results in more agitation of the bonds in the silicate slag and culminates in bonds being broken (with concomitant increases in disorder and configurational entropy). When a glassy mould slag is heated to the glass transition temperature (T_g at ca. 900 K) there is a “step- like” jump in both C_p (Fig. 6) and thermal expansion coefficient (α).^43,44) These increases are associated with the transition of a frozen glass into a supercooled liquid (scl). The scl exists up to the liquidus temperature (T_liq) above which it becomes a liquid. However, crystallisation of the scl occurs at ca. T_g +100 K in many mould slags (see Fig. 6). The temperature range (900–1040 K) tends to be very congested since the deformation temperature (where the scl is unable to support its own weight) also occurs around 1000–1040 K. The values of C_p and α are higher for the scl than for the crystal⁴³⁾ and thus any crystallisation results in a decrease in both C_p and α values but such changes are offset by the fusion of crystal phase at T_liq (i.e. by enthalpy (ΔH^fus) and volume (ΔV^fus) changes on fusion).

Fig. 6.

Heat capacity as a function of temperature for (i) slag film=solid line; glass made from slag film=dash-dot line; ●=estimated C_p value⁴⁴⁾ the downward curves indicate crystallisation (but are not true decreases in C_p but are manifestations of exothermic enthalpy of crystallisation).

When a liquid slag is cooled, if it forms a scl, the viscosity increases smoothly with decreasing temperature until it achieves a value of 10^13.4 (dPas) at T_g. In contrast, if crystals are precipitated on cooling, there is a sharp increase in the viscosity and this temperature is referred to as the break (or solidification) temperature (T_br or T_sol).

In the powder bed, pulverised powders tend to have smaller radii than granules or spherodised mould powders. Consequently, powders (i) pack better (ii) have higher bulk densities (ρ_bulk) (iii) have greater thermal contact area and (iv) have lower permeability (to gaseous convection) than granules.¹⁴⁾

6. Thermophysical Properties

6.1. Limitations in Extant Property Data

It will be seen below that for some thermo-physical properties (e.g. viscosity, T_liq) there are a large number of property data available for mould slags, whereas, for other properties, like density and C_p, there are few published data for mould slags. This is quite surprising since (i) mould fluxes tend to be fairly benign and (ii) there are well-established, accurate techniques available for these measurements. Another common problem is that F and Na can be lost from the sample during experiments on mould slags (such changes will be particularly severe in levitated drop experiments) and can lead to significant composition changes. Few investigators cite the post-measurement composition of the sample. Such limitations affect the accuracy of models of properties which calculate values for mould slags from their chemical compositions; such models are needed as input data for models of heat and fluid flow in the mould.

6.2. Thermo-physical Property Data

The thermo-physical property data reported^{44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139)} for mould slags are summarised in Table 2.

Table 2. Thermo-physical property data for mould slags: Arch=Archimedean: BB=black body; DSC=differential scanning calorimetry; DTA=Differential thermal analysis; LD=Levitated drop; MBP=Maximum bubble pressure; MP=Mould powder; OV=Oscillation viscometer; RD=Ring detachment; RCyl=Rotating cylinder viscometer; SD=Sessile drop; S/F=sink or float; Spectroph=S[ectrophotometer; Trans=Transpiration; XR=X-ray; Chemical formulae B=B₂O₃, C=CaO; Fl=CaF₂: etc. []=tabulated references.

6.2.1. Thermodynamic Data

Gibbs free energies for the formation of cuspidine (C₃S₂Fl) have been reported by several workers and are in good agreement.^45,46) A thermodynamic database has been developed and has been used to elucidate the formation of Al₂O₃ on the mould slag during the continuous casting of high Al, TRIP steels.²⁴⁾ Thermodynamic calculations provide a powerful tool and should prove exceedingly useful in the future.

Values of C_p and (H_T- H₂₉₈) have been determined for a number of glassy mould slags and slag films but these were restricted to temperatures below 1000 K.^{43,44,45,46,47,48)} Reasonable values can be estimated for C_p (see Fig. 6) and the enthalpies of silicate slags using partial molar quantities (Eq. (6)).¹¹⁷⁾ There is a need for further C_p measurements covering the liquid phase and the temperatures between 1000 K and T_br. Estimated values (based on partial molar values, i.e. Eq. (6)) are usually used to calculate C_p for the solid and liquid and the entropy of fusion, (ΔS^fus) but these values need to be validated against experimental values. Experimental data are also needed to differentiate between C_p values for the glass and crystalline phases.

The transition of frozen glass to scl at T_g is accompanied by a step-like increase in C_p of 300–400 JK⁻¹kg⁻¹ (Fig. 6); this transition does not occur in a fully-crystalline slag which maintains its smooth C_p-T relation until fusion occurs and is accompanied by the heat of fusion (ΔH^fus) which is absent from the scl. However, C_p –T relations in the range (T_g- T_liq) are further complicated by crystallisation of the glass which results in a decrease in C_p (but an increase in ΔH^fus). Few experimental C_p and enthalpy data have been published for this temperature range and there are no values for the liquid phase; these data are needed to check the reliability of models to estimate C_p.

6.2.2. Density (ρ) and Thermal Expansion Coefficient (α)

The experimental data for the density^{44,49,50,51,52,53,54,55)} and linear expansion coefficient^43,48) are summarised in Table 2. The densities can be estimated from partial molar relations involving the molar volume (V) but V for the SiO₂ and Al₂O₃ components are expressed as polynomials¹¹⁷⁾ indicating that the structure does have some effect on the density of the slag. There are surprisingly few density data available for solid mould slags. Furthermore, since ρ_cryst> ρ_glass, crystallisation is accompanied by increased porosity and the porosity in slag films has not been quantified, so there are no data available for theoretically-dense, crystalline mould slags at 298 K.

The linear thermal expansion coefficient (α) is given by Eq. (9) where the subscript, _ref, refers to the reference temperature and α is cited for the mean temperature i.e. 0.5 (T+T_ref). At low temperatures the atoms are in fixed positions but as the sample is heated the various bonds vibrate and these vibtations become increasingly asymmetric which results in an increase in α. Increased strength of the bonds tends to reduce both the vibrations and their asymmetry; hence, α will be low in slags which (i) are highly polymerised (i.e. with a high Q value) or (ii) contain cations of high field strength (z/r²).   

$$\alpha =\left({\mathrm{L}}_{\mathrm{T}}–{\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{f}}\right)/{\mathrm{L}}_{\mathrm{r}\mathrm{e}\mathrm{f}}\left(\mathrm{T}–{\mathrm{T}}_{\mathrm{r}\mathrm{e}\mathrm{f}}\right)$$(9)

When a glass transforms to a scl at T_g there is almost a 3-fold increase in α but the sample tends to collapse at the deformation temperature (T_d which occurs about 70–100 K above T_g) making experimental determination difficult for temperatures where T>T_d. Crystallisation occurs in the same temperature region as T_d and is accompanied by a sharp decrease in α.⁴⁸⁾ There are no density values available for mould slags for T>T_d and data are needed.

6.2.3. Viscosity (η) and Break Temperature (T_br)

As can be seen from Table 2 there have been a number of investigations of the viscosities of conventional mould slags.^{43,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77)} The biggest problem lies with the experimental uncertainties associated with viscosity measurements. Six measurements on the same mould slag⁶⁰⁾ resulted in a spread of viscosities (i.e. in a scatter band of ± 25% around the mean). Experimental uncertainties in viscosity can be reduced to about ± 10% with good practice. The principal errors arise from (i) loss of F and Na during the filling of the crucible and during measurements (consequently, post-measurement chemical analysis should be carried out on the sample) and (ii) eccentricities in the rotation of the bob.

The temperature dependencies of the liquid and the supercooled liquids are frequently represented by the Arrhenius and Vogel- Fulcher relations (Eqs. (10) and (11)) respectively, where B_A=E*/R* where R* is the Gas constant and E* is the activation energy for viscous flow. The viscosities (ln η₁₉₀₀) of silicates are very sensitive functions of Q (see Fig. 3) and the parameter B_A also shows a similar, double- exponential relation with Q.³⁴⁾ Mould slags can be regarded as mixtures of alumina-silicates (denoted remaining slag) and CaF₂. It can be seen from Fig. 7 that ln η_{1573 K} for mould slag are affected, simultaneously, by (i) the polymerisation of the remaining slag (i.e. Q calculated using Eqs. (7) and (8) and excluding CaF₂) and (ii) the concentration of CaF₂ (X_CaF2).¹¹⁸⁾ These two factors simultaneously also affect the activation energy term B_A. Inspection of Fig. 7 reveals that ln η_{1573 K} increases with both increasing Q and decreasing X_CaF2. Viscosities of η_{1573 K} vary from 0.5 to 30 dPas (for high speed slab casting to billet casting, respectively); the latter slags probably do not crystallise but form a scl. Thus viscosities of high viscosity, mould slags for casting billets probably refer to the scl state. The largest sources of experimental uncertainty in A_A and B_A arise from (i) restricting the temperature range of measurements (which should be >150 K) and (ii) inclusion of data where the melt contains solidified particles (which increases η and thus increases the apparent B_A).   

$$\mathrm{l}\mathrm{i}\mathrm{q}\mathrm{u}\mathrm{i}\mathrm{d}:\hspace{1em}\mathrm{l}\mathrm{n}{\eta }_{\mathrm{T}}\left(\mathrm{d}\mathrm{P}\mathrm{a}\mathrm{s}\right)={\mathrm{A}}_{\mathrm{A}}+{\mathrm{B}}_{\mathrm{A}}/\mathrm{T}$$(10)

  

$$Scl\hspace{1em}\hspace{1em}\mathrm{l}\mathrm{n}{\eta }_{\mathrm{T}}\left(\mathrm{d}\mathrm{P}\mathrm{a}\mathrm{s}\right)={\mathrm{A}}_{\mathrm{V}}+{\mathrm{B}}_{\mathrm{V}}/\left(\mathrm{T}-{\mathrm{T}}_{\mathrm{o}}\right)$$(11)

Additions of TiO₂ decrease the viscosities of mould slags (η_{1573 K})^19,42) but TiC, TiN¹¹⁹⁾ tend to increase viscosities due to their low solubility in mould slag and the presence of solid particles on the melt viscosity.

6.2.4. Thermal Conductivity (k), Thermal Diffusivity (a)

Transient techniques are used to measure thermal conductivity for both liquid melts and the scl phase since convection can make significant contributions to the apparent conductivity value; two transient methods are widely used to minimise such contributions i.e. the transient hot wire (THW) and the laser pulse or flash (LP) methods. However, heat transfer in semi-transparent media (e.g. glasses) can occur by both lattice (or phonon) conductivity (k_lat) and radiation conductivity (k_R) (see Section 2.2). Heat transfer across a slag sample can be decreased by either absorption of IR (by transition metal oxides in slag) or by scattering and reflection of the IR radiation by crystals. Most slag films contain a mixture of glass and crystalline phases; thus k_R tends to be large for glassy and liquid phases but is significantly reduced by the presence of crystals or transition metal oxides.

6.2.4.1. Powders and Granules

The thermal conductivity (k_THW) values reported for powders and granules (Table 2)^{49,58,80,81,82,83)} have low values which increase with increased bulk density (Eq. (12)) due to both better packing and more points of thermal contact. Values of k_THW also increase with increasing temperature (dk/dT=+10⁻⁴ Wm⁻¹K⁻²). However, in thermal insulation tests (TIT), the values of k_TIT¹⁴⁾ are (i) an order of magnitude higher than k_THW values and (ii) decrease with increasing ρ_bulk i.e. the reverse of Eq. (12). This is probably due to gaseous convection being the dominant heat transfer mechanism in the insulation tests and k_TIT increases with increasing permeability of the bed. The contribution from gaseous convection in k_THW values is unknown but is thought to be small.⁵⁸⁾   

$${\mathrm{k}}_{298}(\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1})=0.10+1.69\times {10}^{-4}{\rho }_{\mathrm{b}\mathrm{u}\mathrm{l}\mathrm{k}}$$(12)

6.2.4.2. Glassy Samples

Thermal conductivity values for glassy mould slags have been reported to have a value of k₂₉₈=1.07 ± 0.03 Wm⁻¹K⁻¹.^57,86) Values of k_THW were found to increase with increasing temperature up to 1040 K (k₁₀₄₀=1.65 Wm⁻¹K⁻¹, Eq. (13)) and then drop dramatically for T>1040 K in the scl region (O, Δ in Fig. 8). Values of k_LP (denoted as □)^49,84,85) are in good agreement with k_THW values for T< 1000 K but k_LP values do not show the dramatic drop in k_THW for T> 1040 K. This difference in behaviour leads to huge discrepancies between k_THW and k_LP for T >1040 K and has been variously attributed to (i) erroneous k values caused by electrical leakage in the THW experiments and (ii) the formation of an interfacial resistance at the Pt/slag interface due to crystallisation and (iii) enhanced contributions from k_R in the k_LP studies, since A_LP ≈ A_THW, where A is the surface area of the probe.   

$$298-1\mathrm{\hspace{0.17em} }040\mathrm{\hspace{0.17em} }\mathrm{K}:\hspace{1em}{\mathrm{k}}_{\mathrm{g}\mathrm{l}\mathrm{a}\mathrm{s}\mathrm{s}}(\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1})=1.07+0.78\times {10}^{-3}\left(\mathrm{T}-298\right)$$(13)

Fig. 8.

Comparison of thermal conductivity THW and LP values for glassy, mould slags as a function of temperature; THW values: o,Δ=^57,59); solid line=Eq. (13); dashed line=values above T_crit;⁵⁷⁾ ●▲=Ozawa;⁸⁶⁾ LP values: □,■=k values calculated from 10⁷a=4.5 and 4 m²s⁻¹, respectively, for glass and liquid; vertical dashed line=T_crit. (Online version in color.)

Values of k₂₉₈ for glassy slags have been reported to increase with (i) increasing polymerisation i.e. Q (or SiO₂ content) and (ii) increasing cation field strength (z/r²).³⁴⁾

6.2.4.3. Partially- crystalline Samples

The thermal conductivities of crystalline and partially crystalline samples are higher than those of glassy samples (k_cryst ≈ 2 k_glass) due to the better packing. The thermal conductivity of some partial-crystalline samples are compared with those for glasses in Fig. 9. For partially – crystalline, mould slags, it was observed that (i) k₂₉₈ values increased with increasing fraction of crystal phase (f_cryst) in the sample⁵⁷⁾ (Eq. (14)) (ii) k_THW=1.65±0.05 Wm⁻¹K⁻¹ at T_crit=1040 K and (iii) k_THW exhibited the same dramatic decrease as the glassy mould slags for T>T_crit (which is due to the collapse of the glass fraction of the sample). One consequence of k_THW=1.65±0.05 Wm⁻¹K⁻¹ is that the sign of the temperature coefficient (dk/dT) between 298 and 1040 K is determined by the magnitude of k₂₉₈, which is, itself, dependent upon f_cryst for the sample (Eq. (14)). However, crystallization results in the formation of pores in the sample which reduce the thermal conductivity. The porosity in slag films and partly- crystalline samples has not been characterized to date, so it is not possible to derive a value for k for a theoretically-dense, mould slag but a value of ca. 2 Wm⁻¹K⁻¹ might be expected. The use of carbon crucibles has been found to lead to extensive porosity in the sample (due to CO(g) formation) and should not be used.⁵⁹⁾   

$${\mathrm{k}}_{298}(\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1})=1.07+0.7\mathrm{\hspace{0.17em} }\mathrm{\hspace{0.17em} }{\mathrm{f}}_{\mathrm{c}\mathrm{r}\mathrm{y}\mathrm{s}}.$$(14)

Fig. 9.

Comparison of thermal conductivity (k_THW) of various phases of mould slags as a function of temperature; Glass :Δ and faint line⁵⁷⁾]; Partially-crystalline; x, + and bold line, dotted line⁵⁷⁾ □=values for a melted powder (with high porosity) on cooling.⁸⁰⁾

6.2.4.4. Liquid Mould Slags

There is a huge discrepancy between thermal conductivity values derived using the THW and LP methods with k_THW=0.1 to 0.3^{57,80,92,93,94)} and k_LP≈1.5 Wm⁻¹K⁻¹,^89,90,91,51) respectively, at 1573 K (calculated from a_LP=4×10⁻⁷ m²s⁻¹). The k values for the liquid have been reported to increase (i) with increasing polymerisation of the silicate network (i.e. Q)³⁴⁾ (ii) decreasing X_CaF2⁹⁴⁾ and (iii) decreasing temperature.

6.2.4.5. Discussion of Thermal Conductivity Results

The discrepancy between k_THW and k_LP values for T>1040 K is huge and must be resolved. Plots of k _THW versus calculated viscosities of the scl for silicates indicated that T_crit corresponds to the temperature where η=10⁶ dPas³⁴⁾ (Fig. 10). This led to the proposal that thermal conductivities of slags are related to the rigidity of the silicate network.³⁴⁾ This view is supported by the observation that k₂₉₈ increases with both increasing Q and increasing cation field strength (z/r²).³⁴⁾ This also suggests that (i) there is a similarity between k and the reciprocal expansion coefficient (1/α) and (ii) T_crit is the equivalent of the deformation temperature (T_d) where the sample cannot support its own weight.

Fig. 10.

Values of thermal conductivity,¹¹⁵⁾ k_THW as a function of calculated, log₁₀ viscosity for M₂O-SiO₂ slags³⁴⁾ ; Δ=NS₄; ♦=NS₃; o=NS₂, ●=KS₂ in the supercooled phase; - - -=T_soft; …..=T_flow. (Online version in color.)

Although significant strides have been made in understanding the extremely complex mechanism of heat transfer across the slag film there is still work to be done in order to calculate the heat flux from fundamental physical and optical property data. Current mathematical models accomplish this by using effective k_eff and R_int values and then calculate d_s values.

6.2.5. Interfacial Resistance (R_int)

Crystallisation results in the formation of a thermal resistance (R_int), or an air gap, at the slag/Cu interface which is sometimes denoted as “surface roughness”. It is usually treated as a series resistance¹²¹⁾ (R_total=R_int+(d/k)_cryst++(d/k)_glass++(d/k)_liq) and where k_R can be treated as a parallel circuit.¹⁰⁴⁾ Values of R_int are shown in Table 2 and it can be seen that R_int values tend to be (i) scattered and (ii) larger in simulation experiments^{98,99,100,101,102,103,104)} than in pilot plant tests.^96,97) The latter finding was attributed to the effect of ferro-static pressure pushing on the shell and reducing R_int.^96,97) Given the complexity of the heat transfer process and the difficulties in simulating, accurately, the heat transfer across the slag film, it is suggested that results of the pilot plant trials be adopted until proved wrong.

6.2.6. Surface (γ_sl ) and Interfacial Tension (γ_msl)

The experimental data for the surface tensions of mould slags are summarised in Table 2.^{51,53,54,68,69,70,71,72,73,105,106,107,108,109)} There is some scatter in the reported values but most of the reported values fall in the range, γ_sl=300–350 mNm⁻¹. Surface tension is a surface property and not a bulk property. Thus, molecules of components with low surface tension (surfactants) tend to accumulate in the surface layers. Mould slags contain several surfactants (e.g. B₂O₃, K₂O, Na₂O and CaF₂) but all the K₂O and most of the Na₂O will normally be required to charge balance the Al³⁺ incorporated into the silicate units. The presence of these surfactants tends to reduce the surface tension of the slag but more accurate surface tension values are needed to identify whether the Na⁺ and K⁺ ions are depleted by charge-balancing duties.

The interfacial tension (γ_msl) can be calculated using Eq. (15) where γ_m is the surface tension of the steel and φ is an interaction coefficient which is dependent on the thermodynamic stability of the component oxides in the mould slag.⁵⁶⁾ The most significant term in Eq. (15) is γ_m since γ_m ≈4 γ_sl and γ_m is very dependent upon the S content of the steel. Values of γ_msl are given in Table 2.^{53,58,87,88,103,104,105,106,107,108,114)}   

$${\gamma }_{\mathrm{m}}={\gamma }_{\mathrm{m}}+{\gamma }_{\mathrm{s}\mathrm{l}}-2\phi {({\gamma }_{\mathrm{m}}.{\gamma }_{\mathrm{s}\mathrm{l}})}^{0.5}$$(15)

6.3. Crystallisation and Fraction Crystalline Phase (f_cryst)

The importance of crystallisation in the slag film lies in its ability to reduce the heat extracted from the shell (q_hor). Crystallisation causes (i) porosity in the slag film (ii) the creation of an interfacial thermal resistance (R_int) and (iii) reflection of IR radiation back to the shell; all three effects lead to a reduction in q_hor. Thus the heat flux is usually manipulated by control of the fraction crystalline phase (f_cryst)⁸⁶⁾ and the size of the crystals^10,122) in the slag film. There is still a debate about whether R_int or the reflection of IR radiation is the dominant mechanism in reducing q_hor; however, the latter mechanism was found to be dominant in the only pilot trials carried out to derive R_int.^96,97)

The initial slag film is probably glassy but crystallises over time and f_cryst probably attains a steady state. Primary crystallisation consists in the precipitation of cuspidine (C₃S₂ Fl) on the shell side,^123,124) and involves the inward diffusion of CaF₂, CaO and SiO₂ and the outward diffusion of Na₂O and Al₂O₃.¹²³⁾ Secondary crystallisation involves the precipitation of other mineralogical phases; the nature of these phases is determined by the chemical composition of the slag.¹²⁵⁾ The mineralogical phase formed has also been reported to affect the lubrication supplied.¹²⁶⁾

Certain constituents promote the glass phase (e.g. SiO₂, Al₂O₃, MnO, FeO, MgO), whereas, others promote the crystalline phase (e.g. CaO, CaF₂). Solid particles such as ZrO₂,¹²⁷⁾ TiO₂^42,128) and Ti(C,N)⁴²⁾ have been reported to act as nucleating agents. A method of calculating f_cryst from chemical composition has been reported.¹²⁹⁾ Given the great importance of f_cryst, there is a need for a standardised method for determining this property and a validation exercise to evaluate the reliability of values obtained with the various methods.

The kinetics of crystallisation have been studied by several workers, mostly through the charting of T-T-t diagrams (e.g.^130,131)). It has been reported that large, equi-axed crystals are formed at high temperature and fine cubic crystals are formed at lower temperatures. The large dendritic crystals have been shown to reflect IR radiation more efficiently.^10,122)

6.4. Optical Properties

The heat transferred across the slag film contains contributions from both k_lat and k_R (see Section 2.2). Heat radiated from the shell can be transmitted (T’), absorbed (A’) or reflected (R’).^10,11) Crystals increase R’ and decrease T’ and A’ whereas FeO additions to the slag additions decrease T’ and increase A’ but these effects are counterbalanced by the promotion of the glass phase by FeO (i.e. decreases R’ via reductions in f_cryst).^10,11) Thus the magnitude of the radiation conductivity (k_R) is determined by the optical properties of the slag film (Eq. (5)).

6.4.1. Refractive Index (n)

Several investigators have reported refractive indices of mould slags^{9,44,86,110,111)} and values of n fall within the range=1.58 ±0.02.

6.4.2. Absorption Coefficient (α*)

Absorption coefficient data are needed to determine (i) whether a glassy slag film is optically- thick or optically-thin and (ii) the magnitude of k_R for optically- thick slag films (Eq. (5)). Absorption coefficient data are given in Table 2.^{9,43,44,84,86,89,90,112,113)} Calculations based on the assumptions that (i) the mean film temperature is ca. 1000 K (leading to peak absorption at 3000 nm) (ii) d_s=2 mm and (iii) α*=500–1000 m^{−1 84)} at 3000 nm indicate that an initially- glassy slag film is optically –thin (k_R <k_R^{Eq. (5)} i.e. that the actual k_R is lower than that calculated using Eq. (5)). Additions of transition metal oxides increase the absorption coefficient (α*=1100 (% FeO) m^–1) but also tend to promote the formation of glassy phases.

6.4.3. Extinction Coefficient (E)

Values of k_R have been calculated by replacing the absorption coefficient (α*) in Eq. (5) with the extinction coefficient (E) where E=α*+ s* where s*=scattering coefficient. However, absorption and reflection of IR radiation are different processes and values of the albedo (or reflection coefficient) are needed. There are few data available for the albedo. Values of E tend to be much larger than α*^9,44,84,86) and reflection of IR radiation is more efficient when large crystals are formed.^10,11,122)

6.4.4. Emissivity (ε)

The only measurements of the emissivity gave values of 0.91 and 0.89 for the solid and liquid phases, respectively, near the melting temperature.⁴³⁾

6.5. Absorption of Inclusions

The removal of inclusions is key to the production of clean steels. The driving force for dissolution is the concentration difference between the saturated and actual concentration (C_sat-C) of the oxide inclusions. The values of C_sat show considerable variation, ranging from ca. 40% and 50% Al₂O₃, respectively, at 1400 and 1500°C^24,132,133) to ca. 10% TiO₂¹³⁴⁾ ca. 2% ZrO₂ and ca. 0.5% TiN.⁴²⁾ There is a tendency for undissolved particles to accumulate and to agglomerate where (C_sat-C) is low; this can result in (i) shutting down the available space for slag infiltration and loss of lubrication and (ii) sticker breakouts when slag infiltration is completely blocked off by agglomerates in the meniscus region. Solubilities tend to increase (i) with increasing basicity or basicity index⁷⁰⁾ (ii) increasing Na₂O, Li₂O^73,135) etc. (iii) decreasing Al₂O₃^130,136) (iv) B₂O₃ was found to have little effect on Al₂O₃ solubility⁶⁹⁾ and (v) increasing temperature. The kinetics of Al₂O₃ dissolution have been studied by several workers.^137,138,139) The process is diffusion- controlled in the slag boundary layer¹³⁷⁾ but it has been reported that Marangoni flows enhance the effective diffusion coefficients.¹³⁹⁾ Dissolution times of 200 s were reported for 150 μm particles of MgO and Al₂O₃ dissolving in mould slags.¹³⁸⁾

7. Conclusions

(1) The performance of the mould powder is key to the success of the continuous casting process and this, in turn, relies on the optimum selection of mould slag properties.

(2) The optimum properties for lubrication (viscosity, T_br, density) are determined by the mould dimensions and casting conditions and for heat transfer (T_br, f_cryst, optical properties) are determined by the nature of the steel being cast but other properties are also important in minimising defects.

(3) For conventional mould slags there is still a need for the following in order to aid the modelling of properties (i) some property measurements e.g. C_p and density at T>1000 K (ii) improved accuracy in viscosity and surface tension values and (iii) the reporting of post-measurement, chemical compositions.

(4) There is an urgent need for a standardised method of determining f_cryst and to characterise the level of porosity in slag films.

(5) However, the most urgent need is for the resolution of the large discrepancies between k_THW and k_LP at T>1000 K and for the provision of recommended values.

(6) Gaseous convection is a major contributor to the vertical heat flux in the powder bed.

(7) The initial slag film formed in the mould is probably optically- thin.

Nomenclature

A=Area (m²)

a=Thermal diffusivity (10⁻⁶m²s⁻¹)

C_p=Heat capacity (JK⁻¹kg⁻¹)

d=thickness (m)

f=frequency (Hz or cpm) or fraction

f_cryst=fraction of film forming crystals

f*=fraction of powder forming slag

H_T-H₂₉₈=Enthalpy relative to 298 K (Jkg⁻¹)

k=Thermal conductivity (Wm⁻¹K⁻¹)

Q=Measure of polymerisation

Q_s=Powder consumption (kgm⁻²)

q=Heat flux density (J m⁻²)

T=temperature (K)

V=molar volume (m³mol⁻¹)

α=Linear thermal expansion coefficient (K⁻¹)

α*=Absorption coefficient (m⁻¹)

ε_TN=Total normal emissivity

γ_sl=Surface tension of slag (mNm⁻¹)

γ_msl=Interfacial tension (mNm⁻¹)

η=Viscosity (dPas)

ρ=Density (kg m⁻³)

BO=bonding oxygen

FO=Free Oxygen

LP=Laser pulse method

NBO=Non Bridging Oxygen

(NBO/T)=NBO per tetragonal element

scl=supercooled liquid

SEN=Submerged Entry Nozzle

THW=Transient hot wire method

Ceramics shorthand for chemical formulae adopted; A=Al₂O₃; B=B₂O₃; C=CaO; Fl=CaF₂ etc.

References

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