Carbon Solution in Liquid Iron and Iron Alloys

Haiping Sun1, Katsumi Mori1, Veena Sahajwalla2 and Robert D. Pehlke3

1 Department of Materials Science and Engineering, Kyushu University, Fukuoka 812, Japan 2School of Materials Science and Engineering, The University of New South Wales, Sydney, NSW, Australia 3Department of Materials Science and Engineering, The University of Michigan, Ann Arbor, MI 48109 USA

(Received October 23, 1997)

ABSTRACT chemical reactions in a cupola /1-3/, it was clear that the iron-based charge material, during its descent The dissolution of carbon into liquid iron and iron through the cupola, undergoes several different carbon alloys was investigated using four independent transfer reactions. They are carbon dissolution (from experimental approaches, i.e., immersion of a graphite coke), and carbon loss (due to oxidation by gas and slag cylinder in a melt bath using an electric resistance phases). These phenomena dictate the carbon content furnace, immersion of a coke particle in a melt bath of the tapped metal stream, and hence, understanding using an induction furnace, a molten droplet on a these reactions is critical for the accurate prediction of graphite plate using an induction furnace and sliding a final carbon content and for describing the melting metal droplet down a graphite spiral in a resistance process in the cupola. The dissolution of carbon into furnace. The dissolution rate was analysed by assuming liquid iron alloys has been studied by many that this reaction is governed by the diffusion of carbon investigators /4-8/, and it is generally agreed that this from the carbon-metal interface to the bulk liquid metal reaction is governed by the diffusion of carbon from the through a boundary layer. The experimental results for carbon-metal interface to the bulk liquid metal through each case were well interpreted by both concentration a boundary layer. However, a considerable lack of and activity driven models. The variation in the carbon agreement exists on the carbon transport rate among dissolution rate with the experimental method was these studies. The primary objective of this study was explained by the Olsson relation or the penetration to determine consistent values of the carbon pickup rate theory. for various experimental conditions. An increase in carbon dissolution rate with temperature was observed. The carbon dissolution rate into liquid Fe-C alloy was not changed by addition of EXPERIMENTAL RESULTS 1.9 wt% silicon to the melt, while a decrease in the Carbon pickup rates were investigated using four dissolution rate of carbon was observed by adding 1 independent experimental approaches, i.e., an wt% sulfur to the melt. immersion method using an electric resistance furnace, an immersion method using an induction furnace, a plate method using an induction furnace and a spiral INTRODUCTION method using an electric resistance furnace. These experimental methods are described in more detail as In a recent series of researches on the modeling of follows.

257 Vol. 17, No. 4, 1998 Carbon Solution in Liquid Iron and Iron Alloys

1. Carbon pickup from immersed graphite particles then immersed into the liquid Fe-C alloy to start the in an electric resistance furnace ~ carbon dissolution process. Before being immersed, the graphite particle, in the shape of a cylinder, 20 mm in An electric resistance furnace, as shown in Figure 1, height and 13 mm in diameter, was heated to the was employed for heating and melting iron-caibon experimental temperature near the melt surface for alloys in an alumina crucible. Both ends of the reaction several minutes. After a certain reaction time, the tube were closed with water-cooled brass caps, sealed incandescent graphite sample immersed for a pre- with an O-ring, and flooded with purified argon gas to determined time period was withdrawn from the melt. prevent the oxidation of liquid iron by air. The Some metal samples (1-3 grams) for carbon analyses temperature was measured with a thermocouple placed were withdrawn before and after the graphite immer- just below the alumina crucible in the homogeneous sion using a quartz tube. The reaction areas were temperature zone (15 cm long) and was controlled to calculated from the average dimensions of the graphite within ±0.5°C. cylinder before and after its immersion. About 100 grams of iron-carbon alloy was first To prevent the reduction in the graphite sample melted in an alumina crucible under an argon size, which could affect the reaction area, the above atmosphere. After the experimental temperature was experimental procedure was repeated using a new attained, the graphite particle fixed to a quartz rod was graphite sample to create a carbon content versus time relationship. The carbon saturation levels for each run -> Gas outlet condition were determined by the carbon content of the metal bath into which a graphite rod was immersed for Water-cooled brass cap up to 2 horns until a variation of carbon content with time could not be observed. Alumina tube

Quartz rod 2. Carbon pickup from immersed coke particles in an induction furnace SiC heating element As shown in Figure 2, an induction furnace was

Alumina Pyrometer crucible Prism Metal Graphite Gas Outlet

Quartz rod

Refractory brick Coil Protection crucible Alumina supporter Graphite foil Alumina crucible Coke Thermocouple lump Metal protection tube Quartz support JL Water-cooled Quartz tube I brass cap Gas inlet Thermocouple Argon gas inlet

Fig. 1: Schematic diagram of immersion of graphite cylinder in liquid iron using electric resistance Fig. 2: Schematic diagram of immersion of coke lump furnace. in liquid iron using induction furnace.

258 Haipung Sun et al. High Temperature Materials and Processes used for heating and melting iron-caibon alloys in an The steel sample was placed on a graphite plate, alumina crucible under an argon atmosphere. The which was set in the melting unit. As expected, some bottom of the reaction tube, made of quartz, was closed, carbon pickup occurred during melting. To account for while the upper portion was closed by a quartz cap this, immediately after the completion of melting, the sealed with vacuum grease. The temperature was power was turned off and a metal sample was quenched measured with an optical pyrometer viewing the surface to prevent any further carbon pickup. This sample was of the metal and was adjusted to 1873 ±20 K. The taken as the reference initial sample for the carbon carbon particles used in the measurement were made of pickup investigation. The experimental procedure was coke in the shape of a foreshortened cube, 10 mm in as follows. The steel sample, after the completion of height, 15 mm in length and 15 mm in width. melting, was allowed to pick up carbon for fixed The experimental procedure was essentially lengths of time. The droplets were immediately identical to those used with the electric resistance quenched by shutting off the power and analyzed for furnace. their carbon contents. The reference initial sample was analyzed, and was found to have a carbon content of 2.79 wt%C and the Si content remained the same as the 3. Carbon pickup from graphite plate in induction original, i.e. 0.58 wt% Si. furnace

An experimental investigation of carbon pickup 4. Carbon pickup from graphite spiral in an from a graphite plate was conducted at 1773 Κ under electric resistance furnace an argon atmosphere, in an induction melting unit, using plain carbon steel of composition 0.31 wt%C, as A carbon pickup investigation was conducted by shown in Figure 3. running molten steel droplets down a graphite spiral, located in a resistance furnace at a temperature of 1773 Pyrometer Κ under an argon atmosphere as shown in Figure 4. Prism The spiral was machined from a graphite rod with the dimensions given below:

-Inlet Length = 28.4 cm

Quartz Diameter = 2.05 tube Total spiral length = 46 cm Groove height = 2.8 cm Droplet -^-Induction Groove depth = 1.9 cm Ο „ coil Ο Distance between bottom ο of a groove and top of a

ο Graphite consecutive one = 3.2 cm ο base Pitch = 2.8 + 3.2 = 6.0 cm ο Ο Slope of groove = 37° To estimate the residence of a liquid droplet in the Quartz spiral, simulation experiments were conducted at room support temperature using various size steel balls, and water and mercury droplets. Based on these experiments, the Outlet average residence time (for ~0.5 gm) was found to be ~1 sec, which is equivalent to a velocity of about 46 Fig. 3: Schematic diagram of melting of a metal cm/sec. The iron particle was melted at the top of the droplet on graphite plate in an induction spiral and then allowed to roll down the spiral. The furnace. time period until the particle was allowed to roll down

259 Vol. 17, No. 4, 1998 Carbon Solution in Liquid Iron and Iron Alloys

GRAPHITE the spiral after melting was about one second. The car- SPIRAL bon pickup during metal droplet travel in the graphite spiral was determined by the carbon analysis in metal noitofqir samples before and after their travel down the graphite spiral. The measured results are given in Table 2. The experimental conditions and results for these METAL four methods are summarized in Table 1 and Table 2. DROPLET The reaction areas for carbon pickup from the graphite plate and the graphite spiral were determined GRAPHITE by the shape of the iron droplet on a graphite base. Iron SLEEVE droplet shape was observed using an electric resistance furnace as shown in Figure 1 equipped with an X-ray source. An iron sample of about 0.5 gram shaped as a cylinder was placed on a graphite base in the furnace under an argon atmosphere, and then the temperature of the sample was raised. The starting carbon contents of the iron samples used for this segment of the investigation were 0 and 4.8 wt%. The contact angle between the iron droplet and the graphite base was measured on the X-ray photographs taken at several temperatures. The measured contact angles between iron droplets and graphite are summarized in Table 3. As seen in Figure 5 and Table 3, it was found that the contact angle of a sample of initial carbon = 0 wt% was SPIRAL LENGTH=46 CM 59° at 1773 K, while that of a sample with 4.8 wt% TRAVEL TIME=~1 sec carbon was 118°. It was considered that the contact Fig. 4: Schematic diagram of graphite spiral used in angle for a low caibon sample is very small, as seen in an electric resistance furnace. Figure 5a, because a lower interfacial tension exists

Table 1 Initial Conditions

Metal compositions Run method furnace Temp 3 3 3 [Si] [S] [Mn] IC]M, kcXl0 Rc kaXl0 R„ kdX10 Rd Κ weight % cm/s cin/s CITI/S

T1 immersion resistance 1573 0 0 4.589 1.82 .963 1.44 .985 3.14 .912 T2 immersion resistance 1673 0 0 4.824 1.99 .979 1.59 .993 2.72 .845 T3 immersion resistance 1773 0 0 5.101 2.54 .890 2.04 .958 4.58 .729 SI immersion resistance 1773 1.88 0 4.579 2.80 .989 2.17 .984 3.97 .921 S2 immersion resistance 1773 0 1.00 4.729 1.71 .978 0.87 .991 9.51 .430 11 immersion induction 1873 0 0 5.300 10.7 .986 7.41 .998 39.4 .930 VI plate induction 1773 0.58 .025 4.859 19.3 1.00 12.4 1.00 33.8 .997 V2 spiral resistance 1773 0.58 0 0.58 5.033 58.6 .681 17.3 .580 235 .715 Carbon saturation levels forTl, T2, T3, SI and S2 were measured and others were calculated.

260 Haipung Sun et al. High Temperature Materials and Processes

Table 2 Experimental Results

t A Wm [C] [C] ac ac Dc Da Dd A-t/V sec cm2 g initial final initial final s/cm wt% wt%

T1 60 8.172 108.9 2.995 3.084 0.334 0.356 0.057 0.034 0.136 31.292 120 7.819 103.3 3.084 3.285 0.356 0.411 0.143 0.090 0.325 63.127 300 8.803 99.3 3.285 3.748 0.411 0.566 0.439 0.304 0.903 184.836 600 7.671 94.8 3.748 4.132 0.566 0.729 0.610 0.470 1.093 337.427

T2 60 7.770 113.3 2.396 2.538 0.184 0.206 0.060 0.027 0.176 28.597 120 7.843 109.7 2.532 2.844 0.205 0.260 0.146 0.072 0.406 59.627 300 7.905 102.7 3.322 3.833 0.366 0.517 0.416 0.271 0.912 160.486 600 7.562 90.2 4.340 4.585 0.715 0.833 0.706 0.533 1.904 349.596

T3 30 7.848 101.9 1.527 1.691 0.076 0.089 0.047 0.014 0.179 16.058 60 7.448 92.5 1.657 2.109 0.086 0.129 0.141 0.048 0.506 33.576 60 7.524 88.3 2.072 2.435 0.125 0.168 0.128 0.051 0.424 35.532 120 7.466 74.0 3.037 3.658 0.263 0.402 0.358 0.208 0.925 84.144 60 7.852 122.4 2.582 2.832 0.189 0.227 0.105 0.049 0.315 26.751 120 7.510 115.4 2.832 3.157 0.227 0.287 0.155 0.080 0.436 54.275 120 7.679 111.1 3.135 3.430 0.282 0.345 0.163 0.092 0.428 57.644 300 8.359 99.4 3.953 4.370 0.486 0.630 0.451 0.329 0.941 175.337

51 60 7.800 135.0 1.821 1.902 0.139 0.149 0.030 0.012 0.095 24.093 120 7.903 130.1 1.879 2.245 0.146 0.199 0.146 0.063 0.442 50.662 300 7.583 111.9 3.973 4.120 0.655 0.717 0.278 0.197 0.471 141.292 600 7.657 107.5 4.120 4.395 0.717 0.845 0.914 0.606 1.297 297.020

52 60 8.899 138.0 1.745 2.002 0.098 0.123 0.087 0.029 0.289 26.890 180 8.953 128.2 2.223 2.803 0.149 0.232 0.251 0.103 0.713 87.365 420 8.323 114.0 4.125 4.352 0.561 0.645 0.383 0.212 0.568 213.113 600 8.916 107.5 4.352 4.588 0.645 0.740 0.665 0.310 0.733 345.858

II 15 8.985 99.3 1.571 2.041 0.071 0.109 0.135 0.042 0.522 9.433 15 9.330 98.5 2.041 2.446 0.109 0.151 0.133 0.048 0.473 9.875 30 9.700 97.6 3.000 3.430 0.227 0.303 0.207 0.104 0.613 20.722 30 9.110 97.0 3.430 3.780 0.303 0.380 0.207 0.117 0.571 19.582 60 8.840 95.7 4.240 4.580 0.504 0.618 0.387 0.260 0.967 38.519 60 9.170 94.9 4.580 4.810 0.618 0.706 0.385 0.263 0.994 40.294 120 9.130 94.3 4.810 5.100 0.706 0.834 0.896 1.568 3.382 80.747

VI 5 0.896 1.04 2.790 3.600 0.242 0.422 0.272 0.284 1.206 29.902 10 0.790 0.86 2.790 4.200 0.242 0.617 0.684 0.724 2.458 63.715 15 0.802 0.88 2.790 4.500 0.242 0.741 1.074 1.153 3.399 94.843

V2 1 0.505 0.44 0.310 1.320 0.011 0.066 0.241 0.058 1.048 7.966 1 0.621 0.60 0.310 2.190 0.011 0.151 0.508 0.152 2.021 7.184 1 0.873 1.00 0.310 2.500 0.011 0.193 0.623 0.203 2.395 6.059

261 Vol. 17, No. 4, 1998 Carbon Solution in Liquid Iron and Iron Alloys

Table 3 Contact angle between liquid iron and graphite

Initial carbon content Temperature in droplet, mass % 1573 Κ 1673 Κ 1773 Κ

0 66° 60° 59° 4.8 110° 120° 118°

θ =59° θ =118°

a) Initial carbon=0 wt% b) Initial carbon=4.8 wt%

Fig. 5: Contact angle between graphite and iron droplet at 1773 K.

during the rapid initial carbon pickup reaction content and the carbon saturation level for the occurring at the metal-graphite interface. This initial particular experimental condition. The carbon pickup rapid carbon pickup is considered to occur during can be described by the following equation: melting and immediately after melting. Once the vd[%ci , . interfacial area extends during the initial carbon pickup = kcA([%C] [%C]sat) (1) dt reaction, it cannot recover to the shape shown in Figure 5b where a higher carbon content sample was used, Where: even though the carbon content reaches the saturation level. V is the volume of the metal, cm3 The reaction area, as shown in Table 2, for iron [%C] is the carbon level at any time t, wt%. droplets mounted on the graphite base and in the [%CU is the saturation carbon level, wt%, which is graphite spiral was estimated by assuming that the a function of composition of metal and shape of the droplet was hemispherical and that the temperature. contact angle is 59° at 1773 K. is the transport coefficient in the metal phase where the difference in concentrations is the driving force, cm/s.

KINETIC ANALYSIS kc = D δ (2) 1) Model 1 D is the difiusivity of carbon in liquid metal, The solution of carbon is governed by the diffusion cm2/sec. of carbon from the graphite/metal interface to the bulk is the boundary layer thickness in liquid through a boundary layer, while molten metal is in metal, cm. direct contact with a graphite surface. The driving force is the area of contact over which carbon for diflusion is the difference between the carbon pickup occurs, cm2.

262 Haipung Sun et al. High Temperature Materials and Processes

Integrating the carbon pickup equation between the ln ac= In Xc+ In fc+ e^Xc+p^Xc+e^Xsi+e^Xsi limits of the initial and final carbon levels in a time (8) +ε£ΙηΧΜη period, t, leads to:

ln [%CU - [%C]ini = k^A t ln ύΡ. =-2.013 + 2Z12 (9) (3) Τ [%c- [%C]fin V Where: ec=.3.55 + 7m (10) Τ [O/oCU is the initial carbon level at time t = 0, wt%. t%C]fin is the final carbon level at time t, wt%. 2 pC =.47.36 + 194500.!.6 (1θ!) t is the time period over which carbon pickup Τ Τ (11) occurs, s. ε?·' =-0.4294 + I&2&Q (12) As presented in Table 1, carbon saturation levels for Τ the experimental conditions of run ΤΙ, T2, T3, SI and ,4 2 S2 were experimentally determined and their values for Pc =-151.8 + 51S63£) -5.24 (l£) (13) Τ Τ II, VI and V2 were calculated by the following equation /9/: and/10,11/

[%C] =1.3+0.0025TCC)-0.31[%Si]-0.45[%S] sat (4) Ec=3.474 (14) +0.28[%Mn] £cn=-1.338 (15) 2) Model 2

When the carbon dissolution rate is expressed in where terms of the change of carbon activity in the melt, the γ0 is the activity coefficient of carbon in melt, driving force for diffusion is the difference in carbon νr °c is the activity coefficient of carbon in melt, activity in the metal and the carbon activity at the satu- Χ. is the mole fraction of i in melt, ration level, i.e., unity. The differential and integrated ε^ is the first order interaction coefficient between rate equations are then: carbon and i in melt. Pc is the second order interaction coefficient V^=kaA(l-ac) (5) dt between carbon and i in melt Τ is in Kelvin. and

1-acini k A The temperature dependence of ε® and ε^1" were ln = a t (6) l-ac,rin V calculated assuming that the melt follows the regular respectively. solution model. Where: a« is the carbon activity at any time t. 3) Model 3 kg is the transport coefficient in the metal phase where the difference in concentration is the driving force, There is an alternative consideration, i.e., that the cm/s. caibon pickup rate is expressed by the change of carbon content in melt but the driving force for diffusion is the The carbon content was represented in terms of difference in carbon activity in the metal and the carbon activity using /10/, carbon activity at saturation. The rate equation is given by: ac=ycXc (7) w d %C , A/1 λ V—4—- = kaA(l-ac) (16) dt 263 Vol. 17, No. 4, 1998 Carbon Solution in Liquid Iron and Iron Alloys

or

W=kdAt (17) 1-ac V

Where: kd is the transport coefficient in the metal phase where the difference in activity is the driving force, cm/s.

The computed results based on the experimental data using equations (3), (6) and (17) are presented in

Figures 6-8 (equation (3)), Figures 9-11 (equation (6)) 100 200 300 400 and Figures 12-14 (equation (17)). As shown in the A-t/V (sec/cm) figures, linear relations were observed using equations

(3) and (6) for most runs except for the run by spiral Fig. 6: Relation between At/V and In (([C]Mt method. The variation in the measured values of run [C]i)/([CW-[C],)) at various temperatures. V2, as given in Table 2, could result from the observa- tion that mercury droplets during their descent down the spiral demonstrated a tendency to break up into • Fe smaller size droplets which could subsequently re- ο 1.9 wt%Si-Fe • 1.0 wt%S-Fe combine, resulting in a variation in the residence times or the contact areas. The carbon pickup dining the iron b particles melting at the top of the spiral could also cause the variation in the measured values. The carbon ο pickup during this period were estimated at less than οί 0.1 wt% from the rate coefficient ko, obtained for run T3 using a resistance furnace at 1773 Κ and the dura- tion of the particles melting of about one second. The rate coefficients for run V2 were obtained by assuming 400 600 800 the lines go through the origin. A't/V (sec/cm) The transport coefficients for the various conditions, Fig. 7: Relation between At/V and In (([C]^- kc based on equation (3), k. based on equation (6) and [C]i)/([C]„r[C]f)) for various metal kd based on equation (17) were obtained from the slopes compositions. of each line in Figures 6-8, Figures 9-11 and Figures 12-14, respectively, and are presented in Table 1. The lines in these figures were calculated based on the least squares method. The correlation coefficient for each rlMfinU[c]find[%CI ] (for Rd calculation), respectively; χ is case (Ro, R. and Rj) calculated from the following J[C]üi 1 equation are also given in the table. the average of Xi, y is the average of yi.

R _ Σ(Χ| -x)(yj -y) (18) V Σ(χί -x)2I(yi -y)2 DISCUSSION where: 1) Mechanism x, is At/V; y, are In 1%C]m ~[%Clmi (for Rc [%C]Mt-t%C]fm As seen in Figures 6-8 and Figures 9-11, and in Table 1, it was found that thefitted line s go through the calculation), In -—(for R. calculation) and 1-a c.fin origins of the semi-log plots, the experimental results

264 Haipung Sun et al. High Temperature Materials and Processes

• Immersion (resistance) ο Immersion (induction) - · 1573 Κ α Plate (induction) ο 1673 Κ • Spiral (resistance) • 1773 Κ

0.0 0 50 100 150 200 250 300 0 100 200 300 400 A't/V (sec/cm) A't/V (sec/cm) Fig. 9: Relation between At/V and In ((l-aoO/il-a^) Fig. 8: Relation between At/V and In (([C]«*- at various temperatures. [C]i)/([C]Mt-tC]£)) for various experimental

methods. 0.7

• Fe ο 1.9 wt%Si-Fe for each case were better interpreted by the activity α 1.0 wt%S-Fe driven model than by the concentration driven model. The regression parameters for the concentration driven model are slightly smaller than those for the activity driven model. These results suggest that the diffusion of carbon is driven by the difference in the carbon activity from the saturation level. Linear relations were not observed in Figures 12-14 where equation (17) was used, and the regression para- 0 100 200 meters were smaller than for the other two models. A-t/V (sec/cm) This suggests that the carbon pickup rate should not be Fig. 10: Relation between At/V and In ((l-acj)/(l-acf)) expressed by the change of carbon content in the melt, for various metal compositions. whereas diffusion of carbon is driven by the difference in the carbon activity from the saturation level. 1.4 • Immersion (resistance) ο Immersion (induction) α Plate (induction) • Spiral (resistance) 9 2) Effect of temperature

An increase in the carbon dissolution rates with temperature is shown in Figures 6 and 9. kc and k, obtained from these experiments were also found to increase with temperature as reported in Table 1. Figure 15 shows an Arrhenius plot of the transport coefficients. The activation energies for diffusion of caibon were found to be 38.2 kJ for kc and 40.0 kJ for A't/V (sec/cm) k,. These small energy values correspond well with a Fig. 11: Relation between At/V and in ((Ι-^/Οβ^) diffusion limiting mechanism. for various experimental methods.

265 Vol. 17, No. 4, 1998 Carbon Solution in Liquid Iron and Iron Alloys

1.2 • Ο 1.0 • Immersion (resistance) • • ο Immersion (induction) ° Plate (induction) —ι ο 0-8 • Spiral (resistance) Ora c Ό lr~ - E i o 0.6 • ° • • 1573 Κ • . α "ζ 0.4 • · ο 1673 Κ • 1773 Κ • * ο . • 0.2 " oo• • 0.0 I ι 1 0 100 200 300 400 0 100 200 300 400

A-t/V (sec/cm) At/Vm (sec/cm)

Fig. 12: Relation between At/V and at Fig. 14: Relation between At/V and i[C,]fin-®-for J[c]ini l-ac various temperatures. various experimental methods.

1.5 -5.0 • Fe ο 1.9 wt%Si-Fe Ο Ο In kc, aciivaiion cncrgy=38.2 kj α 1.0 wt%S-Fe • In ka. aciivaiion encrgy=40.0 kj -5.5 - 1.0 Ol to • · c Ό ._ • 1 — s • υ a. ο • -6.0 0.5 - · ο Β • -6.5 - 0 1 1 0.0 , 100 200 300 400 A-t/V (sec/cm) -7.0. 5.0 5.5 6.0 6.5 7.0 Fig. 13: Relation between At/V and f[c)fin-^L for JlcJira l-ac 104/Γ, κ

various metal compositions. Fig. 15: Effect of temperature on transport coefficients.

3) Effect of metal compositions

As seen in Figure 7, a decrease in the carbon disso- elements, such as sulfur, were present in the bath. A lution rate was observed by adding 1 wt% sulfur into decrease in the carbon dissolution rate with increasing the melt. This trend is in accord with the estimation in sulfur content in the melt is considered to occur because other work /13/ that the addition of 0.2 wt% sulfur can a portion of the boundary reaction sites is occupied by decrease the mass transport coefficient for the dissolu- the sulfur atoms. A change in carbon dissolution rate tion of graphite by approximately 20%. Further in- was not observed for the melt containing 1.9 wt% creases in sulfur content have progressively less effect. silicon. An increase in silicon content in the melt Recent research on the sulfur effect /8/ showed that the decreases δ because the viscosity of the melt decreases dissolution rate was controlled by both mass transport with increasing silicon content /18/. On the other hand, and phase boundary reactions when surface active since silicon has a negative effect on the activity

266 Haipung Sun et al. High Temperature Materials and Processes coefficient of carbon, D is estimated to be decreased by 5) Transport coefficient the addition of silicon in the melt /4/. According to a) Olsson et al. relation equation (2), These two contrary effects lead to a weak effect of silicon on the carbon transport coefficient k„. Taking the rate coefficient obtained in Run T3, where the resistance furnace result was used as the base

rate coefficient at velocity = 0, i.e., k°a and k°0, the rate 4 Effect of dissolution method coefficients for Run II, VI where the induction furnace Figures 8 and 11 present the carbon dissolution was used, and Run V2 where the spiral was used, rates for four independent experimental methods, i.e., assuming that the iron droplet slides down the spiral as immersion by a resistance furnace, immersion by an shown in Figure 16a, could be estimated by the induction furnace, plate in an induction furnace and following relation proposed by Olsson et al. 151: spiral in a resistance furnace. The rate coefficients measured for these runs are presented in Table 1. It was k=k0.Ve0.7 (19) found that the transport coefficients obtained for the induction experiment are about 4~5 times higher than where: that for the resistance furnace. This is because of the k rate coefficient, cm/s stirring of the melt by induced currents. Measurement k° rate coefficient at velocity = 0, cm/s by Knüppel and Oeters /14/ showed that the velocity of Ve Velocity, cm/s flow in the melt bath was about 20 cm/sec, which is dependent on the strength and frequency of the power Calculated values of kg and k« for each run, as supply and the physical properties, volume and shape of shown in Figure 17, approximately follow equation the melt. For example, in an induction furnace, as (19). shown in Figures 8 and 11, the carbon transport rate observed for a small metal droplet on a graphite plate b) Penetration theory was larger than that for a melt in which a coke particle was immersed. The transport coefficient for the spiral test can also be estimated using penetration theory /15/, i.e., after a The velocity of metal droplet travel is about 46 cm/ lifetime period of the interface of the iron droplet that sec for the spiral method, and hence a greater disso- contacts graphite, the interface is replaced with the next lution rate was observed in this experiment. one as shown in Figure 16b. If this time period is short,

iron droplet

0.7 ,1/2 a) k=koVe b) kc=2(D/jrc) Olsson relation penetration theory

Fig. 16: Carbon pickup models for spiral test.

267 Vol. 17, No. 4, 1998 Carbon Solution in Liquid Iron and Iron Alloys

0.20 7 Ο kc=kc0Ve°· RunT3.Il, VI, V2 x ds 1 7 A ο • ka=ka0Ve°' Run T3, II, VI, W2y 1/2 ^average _ · _ 4r m kc=2(D/7H) Run V2 (23) 0.15 Ve · π ds rd(|> ο8 C a 0.10 where: •οo xa the contact time of liquid iron with graphite at 0.05 point As .ο Ο length that the droplet moved during which point A contacts the graphite, cm 0.00 0.00 0.05 0.10 0.15 0.20 radius of interfacial area between droplet and

Calculated transport coefficient, cm/s graphite, cm angle between the radius at point A and the Fig. 17: Comparison between calculated and observed direction that the droplet moves, rad transport coefficients at 1773 K. ^average the average lifetime period of the interface between the droplet and graphite, s ds length element of circumference, cm the diffusion behavior at the interface can be considered as non-steady state diffusion into a static liquid of semi- kc can be given by assuming: infinite length. The average carbon flux across the ^—^average interface is expressed by: (24)

Jc=2(-ß-)1/2([%C]sai-[%C]) (20) The diameter of the contact area of a droplet with π·τ graphite was calculated by assuming that the shape of The transport coefficient is the droplet was hemispherical and the contact angle was 59°. The velocity of the droplet traveling in the 1/2 spiral was calculated by spiral length/residence time = kc=2(-k-) (21) π·τ 46 cm/s. The experimental value of D = 0.00007 cm2/s 116/ was used in this calculation. The transport where: coefficients, kc, calculated by penetration theory for the D : diflusivity, cm2/s three experiments of run V2, are 0.090, 0.085 and τ : lifetime period of an interface between droplet 0.078 for 0.44, 0.60 and 1.00 gram droplets, and graphite, s respectively. The observed rate coefficients k<. for each experiment of run V2 shown in Figure 17 were calcu- Figure 16b shows the calculation of the lifetime [%C]Mt -[%C]„ period of an interface between the droplet and graphite. lated using Dc (= In ), Da (= In The contact time of liquid iron with graphite at a [%C]Mt -[%C]fin 1-a, certain point starts at point A when the time is t and _ f[c]and[%C] _ •) or Dd (= Γ ) = 0 at t = 0 and finishes at point Β when the time is t + τΑ. During this 1-a c,fin leu l-a„ time period, xa, the droplet moves a distance of L their values at each time t. (=2r-cos φ), ta is given by The results of these calculations are compared with the observed values in Figure 17. The Olsson et al. _ 2 r» cos φ xa= (22) relation is in general agreement with the values Ve Ve observed from either resistance furnace, induction fur- The average lifetime period is then given by nace, or spiral experiments. The transport coefficients

268 Haipung Sun et al. High Temperature Materials and Processes calculated by the penetration theory for the three used to determine the rate of carbon solution in liquid experiments of run V2 using the spiral were larger than iron from solid carbon. The graphite-liquid iron contact those determined experimentally. This difference could angle was also measured. The following conclusions result from an underestimation of the contact area for a can be derived from experimental results and kinetic moving droplet on the graphite base because the shape analyses. shown in Figure 5a was used for the area calculation. The experimental results for each case were well interpreted by both concentration and activity driven models. An increase in carbon dissolution rates with 6) Contact angle temperature in the range from 1573 to 1773 Κ was The lowering of interfacial tension between two observed. The carbon dissolution rate into liquid Fe-C phases due to the mass transport across the interface alloys was not changed by addition of 1.9 wt% silicon has been observed by a number of investigators in the to the melt, while a decrease in dissolution rate of past /19-22/. The reason for this phenomenon is not yet carbon was observed on adding 1 wt% sulfur to the clearly understood. In the present study, the lowering of melt. The carbon pickup rate increased in the following the interfacial tension at the carbon-iron interface is order of method of experiment: immersion of a graphite considered to occur due to the intensive carbon cylinder in a melt bath using an electric resistance transport across the interface while a lower carbon furnace, immersion of a coke particle in a melt bath sample was used, and subsequently results in the using an induction furnace, placing a molten droplet on lowering of the contact angle between carbon and a graphite plate using an induction furnace, and sliding molten iron. This low value of the contact angle was a metal droplet down a graphite spiral in a resistance maintained even when the carbon transport rate was furnace. This trend is described by the Olsson relation slowed down at higher carbon content in the liquid or by the penetration theory. droplet during the later period of carbon solution The contact angle for a lower carbon content iron reaction. Thus for the sessile droplet run (Run VI) the droplet on graphite is about twice as large as that for a reaction area was reasonably estimated by this lower carbon content near the saturation level. This behavior value of the contact angle (59°). For the moving droplet results in a greater contact area for carbon pickup than run using spiral (Run V2), however, an overestimation would be predicted from the measured contact angle for of the reaction area, which is an unsolved problem in a carbon saturated iron melt with graphite. the present study, could be caused by using these lower angle values for the entire period of the traveling of the droplet in the spiral since the contact angle could be REFERENCES raised due to the decrease of the carbon transport rate as the carbon content in the liquid increases. This same 1. V. Sahajwalle, R.D. Pehlke, C.F. Landefeld and S. phenomenon was considered to occur in the cupola Katz, AFS Transactions, 99, 269-276 (1996). melting furnace when plain steel scraps are charged. 2. Haiping Sun and Robert D. Pehlke, AFS An extensive study on the relation between molten Transactions, 100, 305-312 (1992). iron-carbon contact angle and carbon transport rate 3. Haiping Sun and Robert D. Pehlke, AFS across the molten iron-carbon interface or initial carbon Transactions (accepted for publication, 1995). content of the metal phase is considered necessary for 4. Yasuji Kawai and Katsumi Mori, Technology the future modeling of carbon transport in a cupola Report of Kyushu University, 1968, 993-997. furnace. 5. R.G. Olsson, V. Koump and T.F. Perzak, Trans- actions of the Metallurgical Society of AIME, 236, 426-429 (1966). CONCLUSIONS 6. L. Kalvelage, J. Markert and J. Potschke, Archiv. Eisenhuttenwes., 50, 107-110 (1979). Four independent experimental approaches were 7. O. Angeles, G.H. Geiger and C.R. Loper, AFS

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