KINETICS OF MANGANESE OXIDE REDUCTION FROM BASIC SLAGS BY SILICON AND CARBON DISSOLVED IN LIQUID IRON Weldon Lee Drines A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan 1966 Doctoral Committee: Associate Professor Robert D. Pehlke, Chairman Associate Professor Adon A. Gordus Professor Lawrence H. VanVlack Professor J. Louis York

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ACKNOWLEDGMENT I would like to extend my thanks to all those who have helped me in carrying out this research program and preparing this thesis. I am especially indebted to the following: To Professor R. D. Pehlke, chairman of the doctoral committee, whose optimism and encouragement kept me going when things looked hopeless, for his suggestions and tutelage, and for giving me the opportunity to do this research. To Professors A. A. Gordus, R. H. Kadlec, L. H. VanVlack and J. L. York for service on the committee and for advice and assistance rendered. To John, Doug, Pete, Fanny, and Al, the shop crew, whose assistance in designing, building and repairing the experimental equipment was invaluable. To the inmates of Room 1048 for their friendship, encouragement, assistance, and cooperation. To Charles Ballard, Robert Bratzler, Robert Moore, and Paul Zenian for endless hours spent doing chemical analyses. To the American Iron and Steel Institute for financial support of this research project. To Barbara for patience and love throughout the long years of graduate study. ii

TABLE OF CONTENTS Page ACKNOWLEDGMENTS............................................. ii LIST OF TABLES..................................................iv LI ST OF FIGURES...............V..... v NOMENCLATURE........................................... vi ABSTRACT........................................................viii INTRODUCTION............................................... 1 REVIEW OF THE LITERATURE........................3................ A. Kinetic Studies of Slag-Metal Systems............. 3 B. Thermodynamic and Transport Data Sources............... 6 EXPERIMENTAL PROGRAM....................................... 8 A. Theoretical Models................................. 8 B. Experimental Procedures............................... 23 EXPERIMENTAL RESULTS..............................39........... 59 A. Manganese Oxide Reduction by Silicon................... 40 B. Manganese Oxide Reduction by Carbon...................58 DISCUSSION...........................................0....... 78 A. Evaluation of the Equilibrium Constant, K'............ 78 B, Effect of 5 on the Calculation of the Energy of Activation, E.......................................... 80 C. Problems of Mixed Control........................... 82 D. Possible Side Reactions............................. 84 E. Accuracy of Results.................................. 85 SUGGESTED FURTHER RESEARCH...*.............................. 86 SUMMARY AND CONCLUSIONS.................................. 88 APPENDIX A - Experimental Parameters...........................90 APPENDIX B - Experimental Time-Concentration Data............... 93 BIBLIOGRAPHY..................................................... 98 iii

LIST OF TABLES Table Page I- Experimental Materials................................... 30 II. The Effect of Stirring Rate on the Reduction of Manganese Oxide by Silicon. a............................. 44 III. The Effect of Temperature on the Reduction of Manganese Oxide by Silicon................................. 46 IV. Comparison of Experimental Energies of Activation with Those Reported in the Literature for the Reduction of Manganese Oxide by Silicon................................ 48 V. The Effect of Melt Geometry on the Reduction of Manganese Oxide by Silicon....... c..n..................... 50 VI. The Effect of the Concentration of Silicon on the Reduction of Manganese Oxide by Silicon................ 52 VII. Comparison of Experimental Diffusion Constants with Those Reported in the Literature for the Reduction of Manganese Oxide by Silicon at 1550~C................................ 56 VIII. Applicability of Possible Models for the Reduction of Manganese Oxide by Silicon............................ 57 IX. The Effect of Stirring Rate on the Reduction of Manganese Oxide by Carbon............................... 63 X. The Effect of Temperature on the Reduction of Manganese Oxide by Carbon..................................... 66 XI. The Effect of Melt Geometry on the Reduction of Manganese Oxide by Carbon.......................................... 67 XII. The Effect of Manganese Oxide Concentration on the Reduction of Manganese Oxide by Carbon.................. 69 XIII. The Effect of Carbon Concentration on the Reduction of Manganese Oxide by Carbon.......................... 71 XIV. The Effect of Slag Composition on the Reduction of Manganese Oxide by Carbon............................72 XV. Comparison of Experimental Diffusion Constants with Those Reported in the Literature for the Reduction of Manganese Oxide by Carbon at 1550~C................................. 75 XVI. Applicability of Possible Models for the Reduction of Manganese Oxide by Carbon.............................. 76 iv

LIST OF FIGURES Figure Page 1. Illustration of Diffusion and Chemical Reaction Control for Reaction M'O + M = MO + M'......................... 11 2. Illustration of Reaction Furnace.........,...,........ 24 3. Illustration of Gas Train.................................. 26 4. Crucible and Support................................ 31 5. Concentration-Time Curves for the Reaction 2(MnO) + Si = (SiO2) + 2 Mn................................. 41 6. Determination of D/5 for Various Theoretical Models for the Reaction 2(MnO) + Si = (SiO2) + 2 Mn........... 42 7. The Effect of Stirring Rate on the Reaction 2(MnO) + Si (SiO) + 2 Mn............................. 43 8. The Effect of Temperature on the Reaction 2(MnO) + Si = (SiO2) + 2 Mn............................... 47 9. The Effect of Silicon Concentration on the Reaction 2(MnO) + Si = (SiO2) + 2 Mn.............................. 53 10. The Effect of Silicon Concentration on the Reaction 2(MnO) + Si = (Si2) + 2 Mn................................ 54 11. Comparison of Concentration-,Time Curves for Reduction by Silicon and Reduction by Carbon...................... 59 12. Determination of D/6 for Various Theoretical Models for the Reaction (MnO) + C = Mn + CO (g).................... 60 13. Determination of k for Various Theoretical Models for the Reaction (MnO)l+ C = Mn + CO(g)......................... 61 14. The Effect of Stirring Rate on the Reaction (MnO) + C = Mn + CO(,................................... 62 15. The Effect of Temperature on the Reaction (MnO) + C = Mn + CO( )..............................00 65 16. The Effect of Simultaneous Reduction by Silicon and Carbon.. 73 17. Illustration of Mixed Control for Reaction M'O + M = MO + M' O...o..0............................. 83 18. Illustration of Mixed Control for Reaction 2(MnO) + Si = (SiO ) + 2 Mn,................... 87 -P =-I * * ** * * ** *** *** **2* * v

NOMENCLATURE A B C. D E AF O J. 1 K K', Klt Ki'Ki i M,M' M,M' _ _ M (MO) MW P Q R S T V W a. f. 1 h. I1 kl k2'k' in 2 Interfacial area, cm Constant Concentration of component i, moles/cm3 Diffusion coefficient, cm /sec Energy of activation Standard free energy of reaction Molar flux of component i, moles/cm /sec Equilibrium constants for equation i Metallic element Element in solution in iron As subscript, metal phase Oxide in solution in slag Molecular weight Pressure, atmospheres W MW M MnO Slag-metal ratio defined by MW WS Mn Gas constant, 1.987 cal/mole/~K As subscript, slag phase Temperature, ~K Volume, cm3 Weight, grams Thermodynamic activity of component i a. Activity coefficient of component i (%i) As subscript, indicates component is a gas Height of phase i, cm Reaction rate constants, mole/cm2 min Natural logarithm vi

n. Moles of component i 1 t Time in seconds unless stated otherwise x. Mole fraction of component i 1 y Rectangular coordinate a. 7i Activity coefficient of component i 1 6 Effective thickness of the concentration boundary layer, cm v Kinematic viscosity, cm /sec p Fluid density, gm/cm3 o As a superscript, concentration of reactant at zero time 0%/ Concentration in weight percent vii

ABSTRACT The reduction of manganese oxide from a basic slag by silicon and carbon dissolved in liquid iron at steelmaking temperatures was studied to determine the rate-controlling step for each process. The two reactions studied were: 2 (MnO) + Si = 2 Mn+ (SiO2) (1) (MnO) + C = Mn + CO(g) (2) The experiments were carried out under an argon atmosphere in a resistance-heated vertical-tube furnace. Crucibles made of zirconia or of graphite held the two liquid phases during the experiment. Sampling and analyzing the slag phase gave time-concentration curves for the system. This da4^dwas applied to theoretical models derived for possible diffusion and chemical reaction rate-limiting steps. Results obtained by varying parameters such as temperature, stirring rate, concentration, and melt geometry indicated which of these theoretical models described the limiting reaction mechanism for the system. The reduction of manganese oxide by silicon is a fast reaction and reaches equilibrium within ninety minutes. The rate of stirring has a marked effect on the rate of this reaction, while on the other hand, the effect of temperature is very small. This identifies the rate-controlling step as diffusion rather than interfacial chemical reaction. The effect of other variables revealed that (a) diffusion of manganese in the iron phase is the slow step, (b) the value of - for manganese in iron at 1550~C -4 is 7 x 10 cm/sec, (c) the energy of activation for the apparent rate constant is 7 Kcal per mole, and (d) increasing the amount of silicon in the iron decreases the diffusion coefficient of manganese. viii

The reduction of manganese oxide by carbon is slower by an order of magnitude than reduction by silicon. Since its rate is quite sensitive to temperature but unaffected by stirring, the rate-controlling step is an interfacial chemical reaction. Of several plausible interfacial reactions, only the reaction (0) = 0 provides a model that is consistent with all the observed data. Therefore, it is postulated that this is the ratelimiting step for manganese oxide reduction by carbon. ix

INTRODUCTION In steelmaking, as in any money-making venture, it is essential to produce the desired product as cheaply as possible. From a technical standpoint, the economics of steelmaking depend to a great extent upon the thermodynamics and kinetics of the two-phase system producing the steel, The thermodynamics of the system determine whether or not the desirable components are largely in a reduced state and the undesirable components are in an oxidized state, as desired at the end of the process; kinetics determines how fast the desired conditions can be obtained. In making stainless steel, an oxidizing slag is first used to remove undesirable components from the iron, such as carbon and phosphorus. At the same time, however, valuable components, such as manganese, will also be oxidized. The economics of the process can be greatly improved by a high recovery of these alloying elements by reducing them again to the metallic state. Of course, the rate of reduction, or time required for the process, is very important. The equilibrium relations pertinent to the reduction of manganese oxide from the slag by silicon and carbon have been studied to some degree, but little is known about the mechanisms that control the rate of the processes. The purpose of this investigation is to study the rate of reduction by silicon and by carbon and to determine the rate-limiting steps for each process. The effects of stirring rate, temperature, composition, and melt geometry are investigated as a means of identifying the slow step. The experimental technique used was to hold slags containing manganese oxide in contact with liquid iron containing silicon or carbon at steelmaking temperatures. The rate of transfer of components in the system -1 -

- - was determined by sampling the slag phase at regular intervals and sampling the metal phase when necessary. The two-phase system was held in a graphite crucible, thus maintaining carbon saturated iron as the metal phase for the reduction of manganese oxide by carbon. A zirconia crucible was used for the reaction when silicon dissolved in liquid iron was the reducing agent. Once the rate-limiting mechanism for these two reactions has been determined, steps could be taken to speed up the commercial process. For instance, if diffusion is found to be the controlling step in the process, then the rate of the reaction can be increased by increased stirring of the system. On the other hand, any temperature change made would be relatively ineffective in changing the rate of the reaction. If an interfacial chemical reaction is the rate-controlling step, just the opposite would be true. It is hoped that the results of this basic study on slag-metal kinetics will contribute to process development in the area of steelmaking kinetics.

REVIEW OF LITERATURE A review of the literature was made in two general areas. Kinetic studies that have been carried out on slag-metal reactions in iron and steelmaking are summarized, and thermodynamic studies that give information pertinent to this investigation are also reviewed. A. Kinetic Studies of Slag-Metal Systems Relatively little work has been done in the area of slag-metal kinetics on a laboratory scale. Two reasons for this are the complexities of the systems and the difficult materials problem confronted in trying to hold liquid metals and oxides in a laboratory crucible at steelmaking temperatures long enough for reactions to occur. Graphite crucibles are stable for these two-phase systems, however, and several investigations have been made on two fundamental reactions. One of these is the study of desulphurization of iron. Chang and Goldman made one of the earliest investigations and determined that the rate of this reaction is increased by increasing the basicity of the slag. Derge, Philbrook, and Goldman investigated the rate of diffusion of sulphur in the slag and came to the conclusion that the concentration gradient of sulphur in the slag was removed by convection rather than by 3 4 diffusion. Grant, Kalling, and Chipman; Grant, Troili, and Chipman; and also Derge, Philbrook, and Goldman5 studied the effect of various alloying elements in iron on the rate of desulphurization. Some alloys, such as silicon and manganese, greatly improved the rate of reaction and it was felt that these metals act as carriers for sulphur across the slagmetal interface. The same elements found in excess in the slag hindered the desulphurization process. The theory that the rate is controlled by two opposing first-order chemical reactions was proposed by the latter -3 -

-4 - investigators. Ramachandran, King, and Grant 678 made studies and presented the possibility that the reaction is electrochemical in nature. Chipman and Fulton9 made a further investigation that showed some effect of stirring on the reaction rate, thereby claiming that diffusion controlled the reaction under constant chemical conditions; however, they concluded that chemical factors had an overriding importance in determining the rate of transfer. Kirkbride and Derge studied the sulphurization of iron and found this reaction much slower than desulphurization, They concluded that the rate-limiting step for this reaction is the transport of silicon or other reducible electro-positive ions to and from the interface so that electrical neutrality was preserved in the slag. Schulz determined the rate-controlling step to be a first-order chemical reaction in both the forward and reverse direction. The second slag-metal reaction that has been studied is the reduction of silica from slag by carbon in graphite-saturated iron. Chip12 man and Fulton did the original work in this area. As for most of these studies, Chipman's and Fulton's work was done in an induction furnace under an atmosphere of carbon monoxide. The research showed that metal composition and stirring rate had very little effect on the rate of reaction. Due to the slow rate and the high energy of activation for the system, the authors concluded that the rate-controlling step was the breaking of the silicon-oxygen bond. Yoshii and Tanimura13 concluded that the rate of reaction was controlled by a chemical reaction with the driving force for the reaction being the concentration 14 of silica in the slag. Rawling and Elliott, in their study of the same reaction, found that transport of oxygen in the metal boundary layer at

-5 - the slag-metal interface was rate-limiting. They also concluded that another step involving either silicate complexes in the slag or interfacial reactions at the slag-metal interface was only an order of magnitude faster than the slow step. Turkdogen, Grieveson, and Beisler15 used a somewhat different experimental approach. Instead of having approximately equal amounts of slag and metal in a graphite crucible, as did the above investigators, they used a slag to metal ratio of 33:1. The purpose of this was to minimize changes in slag composition during the experiment. The system was devised to allow the release of carbon monoxide bubbles at the slagmetal interface. This approach was successful in some runs, but apparently went awry in others. They concluded that when gas bubbles are present at the slag-metal interface, the interfacial chemical reaction is the ratecontrolling process in the transfer of silicon from slag to metal. They also postulated that the slower reaction occurring when gas bubbles were not present at the interface was limited by the transport of oxygen from the slag-metal interface to the walls of the graphite metal container. The reduction of chromium oxide by carbon in graphite-saturated 16 iron was studied by McCoy and Philbrook. A rotating crucible, which maintained the slag in a whirlpool of iron so it would not contact the walls of the graphite crucible, was used. These investigators concluded that the system was reaction-rate controlled and that the reaction was a first-order reaction with respect to chromium concentration in the slag. They found that the rate was independent of temperature and slag basicity. Their rate constant had values ranging over an order of magnitude with an average value of 103 in units of gm min cm (%Cr)

-6 - Sano, Shiomi, and Matsushita17 made an investigation of the manganese transfer rate between molten iron and basic slags, using a resistance furnace. They produced crucibles made of calcium oxide and titanium oxide to hold the two-phase system during the experiment, but, because of the difficulty of making the crucibles, only a handful of runs were made. Four or five of these involved the reduction of iron oxide in the slag by manganese in the metal, and then two runs were made of the reduction of manganese oxide in the slag by silicon in the iron. Because of the small number of runs made, only qualitative statements could be made about the reaction. They concluded that the diffusion of silicon in iron was very important and could be the rate-limiting step for the process. Initial conditions for the two runs made using silicon as the reducing agent were silicon 0.2 and 0.5% and manganese oxide 9 and 12% respectively. With these low silicon concentrations their conclusion is logical. Theoretical considerations for reaction kinetics in the two-phase slag-metal system are presented by Wagner and Ward9. B. Thermodynamic and Transport Data Sources A great deal of material is available in the literature concerning the thermodynamics of the systems involved in this research. Data on viscosities, densities, activities and activity-coefficients, free energies of formation, equilibrium data, diffusion constants, and energies of activation have helped immensely in the experimental design and calculations involved in this project. The primary source for this information has been Volume II, Thermochemistry for Steelmaking by Elliott, Gleiser, and Ramakrishna 20 which is a compilation of thermodynamic and transport properties. Additional sources of data are summarized below.

-7 - Viscosity and liquidus data for the quaternary slag system used in 21 this investigation are found in Osborn, DeVries, Gee, and Kraner; Turkdogan and Bills; Kato and Minowa3; and Kekelidze, Mikiashvili, 24 and Odilavadze Standard free energy of formation revisions for the silicon-silicon oxide system are given by Taylor25. More free energy data is found in 37 Sawamura and Sano. Activities of slag components are given for silica by Rein and Chipman 6, for manganese oxide by Abraham, Davies, and Richardson27, and also by Turkdogan and Pearson, and for oxygen ions by Toop and 29 Samis 29 The activity of silicon in iron alloys is given by Chipman, Fulton, Gokcen, and Caskey and also by Chipman and Baschwitz. Studies concerning equilibrium of manganese between slag and metal phases have been made by Rassbach and Saunders and by Philbrook and Tarb35. 34 Schwerdtfeger has recently determined the diffusion constant of oxygen in liquid iron to be 1.2 x 104 cm /sec. Riddiford35 has developed a relationship between energy of activation found as a function of the diffusion coefficient and the energy of activation found as a function of the diffusion coefficient divided by the boundary-layer thickness. He found that the boundary-layer thickness varied exponentially with temperature. Based on his study, one would expect the energy of activation to be nearly the same, whether it is calculated from D or from. b

EXPERIMENTAL PROGRAM In order to determine the rate-limiting step for the two reactions under consideration, it was necessary to vary certain parameters in the system such as stirring rate, temperature, and melt geometry. Also, it was necessary to find a crucible material other than graphite for melting down the two-phase system in order to study the reduction of manganese oxide by silicon without simultaneous side effects of graphite reduction. The design of the experimental system chosen takes these factors into account. In this section, theoretical models are derived for many of the possible rate-limiting steps. Then the experimental apparatus and procedures are described and discussed in detail. A. Theoretical Models The derivation of the theoretical models is dependent upon the experimental conditions under which the reactions take place. Typical conditions are presented here as a basis for understanding the assumptions and approximations made in the derivations which follow. The reduction of manganese oxide by silicon was a fast reaction. Samples were taken to follow the reaction for twenty-four minutes and to indicate equilibrium conditions at the end of two hours. A typical change in concentration of the various components from the first sample taken at three minutes to the final one at the end of twenty-four minutes is given below in weight percent. Mn 0.5 - 1.5% Si 1.2 - 0.95% MnO 3.8 - 2.0% SiO2 33.7 - 34.51o -8 -

-9 - Initially, there was no manganese in the metal phase. The reduction of manganese oxide by carbon was a slow reaction and samples were taken for two hours to follow the reaction. Typical concentrations of the various components from the first sample taken fifteen minutes after the start of the reaction to the final one at the end of two hours are given below. Mn 0.7 - 1.5% MnO 3.4 - 2.0%o Initially, there was no manganese in the metal phase. The iron remained saturated with graphite throughout the run. The carbon monoxide produced by the reaction maintained one atmosphere CO pressure at the interface between the slag and the metal, although the system was swept out with a very low flow of argon gas at one atmosphere pressure. If a two-phase slag-metal reaction occurs, such as M - (M'O) = M' + (MO) (3) the kinetics of the reaction can be broken down into the following principal steps. 1. Transport of the reactants from the bulk phases to the slagmetal interface. 2. The phase boundary reaction, which may involve several steps. 3. Transport of the reaction products from the slag-metal interface into the bulk phases. Under most conditions, significant concentration differences are found only in the vicinity of an interface. Therefore, according to 18 Wagner, considerations may be confined to the concentration distribution in the boundary layer, and concentration differences in the bulk liquid may be disregarded.

-10 - The possible rate-controlling step for the process can be broken down into one of two main categories, diffusion control or chemical reaction control. If the chemical reaction step is much faster than one or more of the diffusion steps, equilibrium is reached at the interface, and the rate of the process is determined by the diffusion of one or more of the reacting species to or from the interface. If, on the other hand, the chemical reaction step is the slow step in the process, then the concentration of any component is essentially the same at the slagmetal interface as it is in the bulk of the phase, and the rate of the process is determined by the rate of the phase-boundary reaction. This is chemical reaction control. A schematic illustration for these two limiting steps is shown in Figure 1. When the rate of the process is being controlled by a slow diffusion step, the rate can be defined mathematically by applying Fick's First Law, which states that the flux of component i is proportional to the concentration gradient of component i in the direction of diffusion. Stating this mathematically gives*. ac. J. = D — (4) ay By describing the driving force in terms of concentration and distances as shown in Figure la and rewriting the flux in terms of moles, time, and interfacial area, then dn DA dt = C- i(interface) Ci(bulk) *Mathematical terms are defined in the nomenclature at the beginning of the thesis.

-11 - z 0 cr Iz iU 0 ~ Phose I CM'O Phase Boundary Phase 2 CM CMO K' CM'(lnterface) CMO CM CMDo CM' 0 DISTANCE FROM INTERFACE (a) Diffusion of M' in Phase 2 Controls Reoction 0 Iz z 0 Phase I CMO Phase Boundary Phase 2 CM CM' CMO CM CM'O CM' 0 FROM DISTANCE INTERFACE (b) Chemical Reaction at Phase Boundary Controls Reaction Figure 1. Illustration of Diffusion and Chemical Reaction ContrOl for Reaction M'O + M = MO + M'.

-12 - The concentration of component i at the interface is that concentration which is in equilibrium with the other components at their instantaneous compositions in the bulk phase. The law of mass action states that in any system, the rate at which a reaction proceeds is proportional to the activities of the reactants. This law can be applied here in the case of chemical reaction control of the process. In the case of Equation (3), then, the rate in the forward direction is dm pq (6) dt = klaa (M'O) (6) Also, the rate in the reverse direction is dnM r s dM k2M a (MO) (7) dt The powers p, q, r, and s are defined by the stoichiometry of the system, When the system reaches equilibrium, the forward rate will be equal to, but opposite in direction of, the reverse rate. Therefore, the ratio of the two rate constants, kl and k2, is equal to the equilibrium constant for Equation (3) as follows: kI k = K (8) 2 3 At any time during the reaction, the net rate of reaction is the sum of the forward and reverse rate. t- k = a*Ma (M'O) k2a'Ia (MO)9) dt Combining Equations (8) and (9) and eliminating k2 gives

-13 - dnM q 1 r s1 dt I 1 M(M 'O) M- 3a (MO) dt J (10) Using these concepts as a basis, theoretical models are derived on the following pages for cases where one particular step in the overall reaction is rate-limiting. This is done for all possible diffusion ratelimiting steps for both reactions studied and for several postulated chemical reaction rate-limiting steps. The question of whether the reaction can be defined as limited by only one step will be discussed later. 1. Reduction by Silicon - Diffusion Control There are four possible diffusion models for the reaction presented in Equation (1). They are for the diffusion of manganese in the metal and in the slag phase and for diffusion of silicon in the metal and in the slag phase. All four models are derived below. a. Diffusion of Manganese in the Metal Adapting Equation (5) to the reaction shown in Equation (1), when the diffusion of manganese in the metal is the rate-limiting step: dn-[ M4n DA r Mdt A [CMn(interface) CMnbulk) dt 0 j -- -- I (11) Changing concentrations to weight percent, dt- = Mh [%Minterface) - %(bulk)] (12) At equilibrium, for Equation (1): (an)2 (aSi ) K1 = ( 2i (aMnO ) ( asi ) (13)

-14 - Over the small change in composition involved in an experiment, it can be assumed that the activity coefficients for the different components remain constant and that the change in concentration of silicon dioxide is negligible. Combining these constant values with K1 gives ( oMn 2 K' = / 2 (i (14) 1 (UMnO )2 (%Si) This constant can be obtained by allowing the two-phase system to reach equilibrium and then analyzing for manganese, silicon and manganese oxide. Since the manganese in the metal phase at the interface is in equilibrium with the manganese oxide and silicon in the system, Equation (14) can be rewritten interface) = %M nOi 15 ) Substituting this in Equation (12), separating variables, and integrating: /d(OMn) Dt ( (16) =I^t=O [~9MnO KI %S - o M At any time during the run, the concentration of manganese oxide in the slag can be related to that of manganese in the metal by the relationship wMW, ~MnO AMnO O - M[W MW]Mn (17) S Mn Similarly, the concentration of silicon in the metal is %Si = oSiO -Mn (18) Substituting these two terms into Equation (16):

-15-,' int=t 5-n - d()d =-lDth (19) MnJ [(%MnO~ - QOMn)jVK'Si0 - 0.258 K{lMn - oMn] ~ t^, - i - - "WM MWMnO where Q = -W Be.. Mn Now the only variable under the integral sign is the concentration of manganese in the metal and the integral can be evaluated. For convenience in data analysis, all theoretical models will be derived in terms of changing manganese concentration in the metal. b. Diffusion of Manganese in the Slag If the diffusion of manganese in the slag is the rate-limiting step, then the basic equation will be ~ dn(MnO) DA [ (20) dt = - (MnO bulk) - MnO interface)] (20) Going through the same steps as for the diffusion of manganese in the metal, and using the same basic relationships, yields the final rate equation: Q d()n_) Dt (21) j *= --- —--— ) h v21:.t=0 %oMn0O - QMn - KlOSi -0.258KMMn c. Diffusion of Silicon in the Metal Following the same procedure as for the last two systems, there is, first of all, the basic equation dn s i C - i[cDA dt Si(bulk) - SiCinterface) (22)

-16 - which yields the final rate equation rOMn=t 0.258 d(%Mn) Dt -t[=0 OS~ - 0.258 %Mn - %Mn) 2h (23) KloMnO - KqOMn d. Diffusion of Silicon in the Slag The basic equation for this system is dtA C C (24) dn(t [ (SiO2 interface) (SiO2 bulk) (24) The final form in terms of manganese in the metal is r Mt=t J ]d(Mn) Dt (25) "tt= (K'l si0- 0.258 K;%Mn)(%'MnO0 - QlMn)2 %Si0 hS 0.79 (%Mn)2 0.79 A new equilibrium constant is used to define the equilibrium condition for this reaction as follows: 1 (%SiO2) (oMn) 1 1- (%si( nO) Jequilibrium 2. Reduction by Silicon - Chemical Reaction Control No work was done in this area since the energy of activation for the reaction was low and stirring had a marked effect on the reaction rate, both atypical of chemical reaction control. However, one possible model can be set forth as follows:

-17 - dnMn a b c d - - Aka(MnO)b. Ak 2aMn(Si02) (27) dt ~ — -- - Changing concentrations to percent, letting K = k and integrating: r i =t f ad(a)........... d *,to [(0.oo86yMnOMno)a(Si) - K1(%Mn)C (Ol7sSio %S02)d] 100MWMn (28) IPMhM * = Mn 1 ( 28 ) 3. Reduction b Carbon - Diffusion Control These models were derived in a manner identical to that used for the models for reduction by silicon. Simpler equations resulted for this system, however, and so it was possible to go one step further and analytically evaluate the integral to arrive at the final model. a. Diffusion of Manganese in the Metal Equations (11) and (12) apply to the diffusion of manganese in the metal for the reduction by carbon also. However, at equilibrium, for Equation (2): K a C (29) aMnOaC The pressure of carbon monoxide at the interface remains constant at one atmosphere at the interface during the experiment. The liquid iron is maintained at carbon saturation; hence, the activity of carbon is constant. For the few experiments carried out in zirconia crucibles at less than graphite saturation, the concentration of the carbon changed very

-18 - little, such that an average value can be used. It can be assumed that the activity coefficients for the other components remain constant over the small change in composition involved in an experiment. Then a new equilibrium constant is defined as oMn (3 K' = (30) 2 nO This constant is available from the literature for the carbon-saturated system33 and can also be calculated from the relationship K2ac7MnO K' =- -_ _ (31) 124 PC fMn where the factor for changing the concentration of MnO from mole fraction to weight percent is 124. Since the manganese in the metal phase at the interface is in equilibrium with the manganese oxide in the slag, Equation (3) can be combined with Equation (12) and Equation (17), and the variables separated to give d(oMn) dt r --- —----— ^ STT1 [K2 ~oMnO - (QK2+1)Mn Integrating, the final rate equation is K -1 In [KoMnO - (K Q+ 1) %Mn] D t (35) K'Q+1 2 2 5"hM b. Diffusion of Manganese in the Slag If the diffusion of manganese in the slag is the rate-limiting step, then the basic rate equation is given by Equation (20). Going through the same steps as for the diffusion of manganese in the metal, and using the same basic relationships, the final rate equation is

-19 - -KIQ f~ Q+l 1 T1 KQ+ [ Q KQ = h 2r1- - - hid ^ - ^ c. Diffusion of Carbon in the Metal If diffusion of carbon in the metal phase is the rate-limiting step, then the basic rate equation is -dn [. _ DA C C (35) dt C(bulk) C(interface)] From the stoichiometry of Equation (2) it can be seen that -dnC = dnMn. Substituting this relationship into Equation (35), changing concentrations to percent and rearranging, MW d(%oMn) MW -- — = -— n dt (36) WMn [l2(bulk)- 42(interface)] At equilibrium, the equilibrium constant can be written as K = 10MnO %C (37) This constant can readily be evaluated using the same methods used to calculate K2 in Equation (31). Then rewriting Equation (37), oMn o( interface) = no Kn (38) Combining Equations (17), (36) and (38) and integrating gives the final rate equation for the diffusion of carbon in the metal phase as follows: O.218K"QMn o0. 218KCo QoCMnO 0.218K"oMnO~ K Cl+0.28+ 2 - C+.2. X K I(oC+0.218 KtQloC+0.218 K"toC+0.218 2 2 -2 K o _ 1nO (39)K ln [2 - -(02 + 1) %Mn = Eh (39) 0.218 0.218

-20 - d. Diffusion of Oxygen in the Metal The basic equation for diffusion of oxygen in the metal is: dn O DA C - C ~~ ~~ ~~1 (40) dt = ~L O(interface) - CO(bulk ( The concentration of oxygen at the interface can be calculated from the standard free energy of reaction for the reaction (MnO) = Mn + 0 (41) For this reaction, at equilibrium, the equilibrium constant is K41 = (42) 4 (MnO) The activity coefficients of these components are essentially constant for the small composition change occurring during an experiment. Therefore, an equilibrium constant can be defined in terms of percent composition at equilibrium as follows: K1 %MnO (45) 41 -MnO oMnO This constant can be readily evaluated using the same procedure as described previously. From the known thermodynamic data for the graphite-saturated system under consideration, it is estimated that the value of Cinterface) is greater than that of C (bulk) by about two orders of magnitude for the conditions present during an experimental reaction. Therefore, CO(bulk) can be omitted from Equation (40). It can be seen from Equation (41) that the same number of moles of oxygen and manganese is transferred across the interface. Using these facts, changing concentrations in Equation (40)

-21 - to percent, combining Equations (17), (40) and (43), separating the variables, and integrating, the final rate equation for oxygen diffusion in the metal is as follows: -0.29%Mn 0.29%oMnO0 (44) --— l - - In K, I JMn0~ - K I QM.& Dt -(44) K41Q K41Q2 lK~OMn0~ 41 41 n h Dt 4. Reduction by Carbon - Chemical Reaction Control Three reactions are presented here which could represent the ratelimiting step for the overall process. Rate equations are developed for each of the chemical reactions. a. Reaction 1 The first considered is the overall reaction shown in Equation (2). Assuming that the rate of the reaction agrees with the stoichiometry of Equation (2), then the rate can be written as dnM M-=n la aC0 -Ak (45) dt Aklano C 2aMnPCO The pressure of carbon monoxide can be assumed to be one atmosphere at the interface. The activity of graphite in the iron will remain constant throughout the experiment since the iron is saturated with carbon. Then, k2 letting K2 = k changing concentrations to percent, and integrating: -2 k - -l - In 0.0086 aC MnO MnO - (K +0.0086a C7Mn ) JsMnr - 1 K2+O.OO86a CMnOQJ2 a M hn (46) b. Reaction 2 The chemical reaction given by Equation (41) is assumed to be the slow step in the overall reaction here. Again the basic equation can be written as

-22 - dn^ dt =Akl an - Ak2o (47) The activity of oxygen in the metal, a0, is very small and can be assumed k'2 constant. Therefore, setting k2 = kaO and K" = - and again changing 2 2 k ka concentrations to percent and integrating: Tcl~-l-o rOOO86.\MOO Ko8 nsQ 900k t K'0 00567 lnO. [o.0086QMnO - (K+O0.0086yMnOQ)ol n = 2+ 0 MnO hM (48) c. Reaction 3 Assuming that the slow step in the reaction is the chemical change of oxygen going from the slag to the metal phase, the reaction can be represented by (0) = o (49) The rate equation for this chemical step can be written as dn d = Akla(o) - Ak2 (50) For the overall reaction, the number of moles of oxygen and of manganese that cross the interface are equal, or nO = nMn. Also, for a slag of given composition, it can be assumed that the activity of oxygen will remain constant. The activity of oxygen in the metal phase will also be constant and will be very small compared with that in the slag so that the second term of the equation can be ignored. These last two conditions hold only when the system is not close to equilibrium. For the reaction under study, the rate is studied for two hours and equilibrium is not attained in twenty hours, so these two conditions are valid. Then, letting k' = kla(O), changing concentration to percent, and integrating:

oMn = 900k't (51) hM B. Experimental Procedures 1. Apparatus The slag-metal reactions in this program were carried out in a vertical-tube resistance-heated furnace although most previous slag metal studies have been made in induction furnaces. The advantages of a resistance furnace over the induction furnace are better temperature control and better stirring rate control. The equipment was designed and built specifically for this research program. The apparatus consisted of the furnace, the atmosphere system, the temperature measuring and controlling circuits, and the crucibles and stirrers. a. Furnace The design of the furnace used for this experimental study is illustrated in Figure 2. It was a cubic furnace, 24 inches high by 24 inches wide by 24 inches deep. It was insulated with low density alumina and silica Harbison-Walker brick, with an 8-inch cube hot zone in the center of the furnace. Eight vertical silicon-carbide heating elements surrounded the furnace tube. Power was supplied to the heating elements through a 240 volt, 25 amp Variac. The power requirement for heating the furnace to the desired temperature was from three to four kilowatts. The heating elements had a nominal resistance when new of 1.5 ohm each, but the resistance increased as the elements aged. When the elements were new, the heat requirements were met by having the eight elements connected in series. However, a point was reached, as the resistance of the elements increased, at which the desired temperatures could no longer be reached with the elements in series. Then, by rewiring the

-24 - Stirring Rod Speed Motor Brass Head Mullite Tubt SiC Heating Gas Outlet lybdenum Insulating Brick Hot Zone Slag Metal Crucibles Insulating Brick Iross Head; Inlet Support Stand Figure 2. Illustration of Reaction Furnace.

-25 - elements in parallel, the power requirement of the system was achieved for the remainder of the life of the heating elements. The vertical reaction chamber was a mullite tube 36 inches long and 3 inches in inside diameter, sealed at both ends by a combination brass head o-ring arrangement. The crucibles were held in the hot zone as illustrated in Figure 2. The crucible was covered with a graphite lid. The reaction tube was insulated above the crucible by an alumina brick cylinder that was attached to the top head and was therefore removed from the furnace when the head was taken off. A stirring rod was centered in the system and was driven by a variable speed motor capable of speeds from 10 to 100 revolutions per minute. There was a sample hole through the top head, insulation, and crucible lid alongside the stirrer. All access holes into the reaction tube were sealed by vacuum seal fittings. b. Atmosphere System The apparatus was designed to maintain an argon atmosphere in the reaction tube during an experimental run. A diagram of the gas system is shown in Figure 3. High purity argon was passed through a drying-deoxidizing train before entering the reaction tube. The train consisted of a tube containing anhydrous calcium sulphate, a tube filled with copper gauze that was maintained at 500~C in a small auxiliary resistance furnace, and a second calcium sulphate drying tube. Indicating anhydrous sulphate was employed. Bubblers were used both before and after the reaction tube in order to maintain a slight positive pressure of argon in the system during an experimental run. c. Temperature Measuring and Controlling Equipment The temperature was controlled in the reaction chamber by a "high-low" circuit arrangement. Power was provided to the furnace through

Exhaust Outlet Bubbler Argon Inlet CaSO4 Drying Towers Reaction Chamber Vacuum Seal Vacuum Seal I I\ I Relief Bubbler Tygon and Pyrex Linkage Copper Gauze Furnace Figure 3. Illustration of Gas Train.

-27 - a 240 volt Variac auto-transformer wired so two unequal voltages could be tapped. Regardless of the voltage setting of the Variac, the tapped voltages were 40 volts apart. Either a high or a low voltage was fed to the furnace by a relay controlled by a Leeds and Northrup Speedomax H Circular Chart Indicating Recording Controller, Model R. A Leeds and Northrup Rayotube No. 8890 temperature detector, having a full-scale response time of 8 seconds, was used for temperature measurement. As shown in Figure 2, the detector was attached to the side of the furnace and was focused on the outside of the mullite reaction tube, in the middle of the hot zone. The temperature measuring and controlling equipment was calibrated periodically by placing a platinum-6% rhodium vs platinum-30%Y rhodium thermocouple in an alumina protection tube in a liquid metal melt in the reaction zone. Simultaneous readings were taken on the Leeds and Northrup Recorder and the thermocouple setup over a wide temperature range and calibration curves made. Periodic checks of this calibration curve showed that an accuracy to within two degrees centigrade was maintained. The controller was also checked by this same thermocouple system, and it was found that the controller maintained the temperature in the slag-metal system to within one degree centigrade. The thermocouple was checked for calibration against the melting points of pure copper and nickel. d. Crucibles and Stirrers High-purity graphite rods, one foot long and 3/8 inch in diameter, were used to make stirring rods. One end of these rods was flattened to a thickness of 1/8 inch to provide a stirring surface. For one experimental run, to study the effect of higher stirring rate, a 3/4 inch graphite rod was flattened in the same manner for use as a stirrer. The stirrers were

-28 - connected to a 1/4 inch steel rod which extended up through the top head of the furnace tube. Graphite crucibles were machined from 2-3/4 inch diameter commercialgrade graphite rod. The crucibles were made 4-3/4 inches high with a bore 4-1/2 inches deep and 2-1/4 inches in diameter. For the reduction by silicon studies, slip-cast, fine-grain, lowporosity, lime-stabilized cubic zirconia crucibles were used. They were 4-1/2 inches high and 2-1/8 inches in outside diameter with a two inch diameter bore. These crucibles were only slightly attacked by the slag during the process of a run. The amount of zirconia dissolved in the slag during an experiment was less than three percent of the total slag mass and did not vary significantly from run to run. The crucibles were supplied by Zirconium Corporation of America. Several other crucibles were tried but proved unsuccessful in holding the two-phase system. Among these were zirconia, magnesia, and alumina crucibles. The zirconia crucibles had no strength at the high temperatures at which they were used and had to be held inside a graphite crucible, as described above, during the run. This worked very well and there was no apparent reaction between the two crucibles. A sampler was made using Vycor tubing with a copper gauze chill inside the tubing to quench the sample and limit the size of the sample. A suction bulb was used on the other end of the tube to draw the desired sample into the Vycor tubing. Both metal and slag samples were taken in this manner. They were both easily removed from the Vycor tubing. 2. Materials High-purity materials were used as components for the slag and metal phases. The source of these materials and the quoted purity of each are

-29 - summarized in Table I. These materials came in a form ready for immediate use with two exceptions: the silicon oxide had to be crushed and the manganese dioxide had to be reduced to manganese monoxide. The manganese dioxide was reduced by placing it in a quartz combustion boat in a horizontal tube furnace at 10000C and passing hydrogen gas over it. This deoxidation process is rapid, reaching completion in about fifteen minutes. Mass balances were made to determine the oxidation state of the product. The loss in weight showed that the reaction occurring was MnO2(s) + H2(g) = MnO(s) + H20(g) (52) and that the reaction reached completion. Also, Moore36, using the same system, analyzed the resulting manganese oxide using x-ray diffraction techniques and verified that it was manganese monoxide. The slag components were periodically checked to make sure that they were not hydrated. Calcium oxide was found to hydrate rapidly, so it was purchased in one-pound containers and used before hydration could occur to any extent. 3. Procedures for Using Equipment and Making Experimental Runs The description which follows is in terms of runs made to study the reduction of manganese oxide by graphite. Changes in the procedures for the reduction by silicon are noted. First, it was necessary to prepare the crucible-support stand assembly shown in Figure 4. For the reduction by silicon study, a zirconia crucible was placed inside the graphite crucible to hold the two-phase system. The desired components were then weighed out and placed in the crucible. First the iron and the reducing agent, either graphite or silicon, were placed in the crucible. Then the four slag components (aluminum oxide, magnesium oxide, silicon oxide, and calcium oxide) were weighed out. These

-30 - TABLE I EXPERIMENTAL MATERIALS Quoted Form, Material Source Grade Purity - % as Received Fe Glidden A-104 99.8 Fragments Si Var-Lac-Oid Purified 99.999 50 Mesh C Ultra-Carbon Ultra-Pure 99.999 200 Mesh Mn Union Carbide Electrolytic 99.9 Pieces CaO Baker and Reagent 98.0 Powder Adamson MgO Norton Magnorite 98.2+ 14/24 Mesh Grain Al203 Morganite High Purity 99.7 100 Mesh Grain SiO2 General Electric CFQ Scrap 99.9 Pieces MnO2 Fisher Scientific Reagent 99.9 Fine Grain I ~ ~~~ L.l. IlmI. _ i.,,L. i. ll

Stirrer Hole Grapple Holes Figure 4. Crucible and Support.

-32 - components were thoroughly mixed before being placed inside the crucible on top of the metal. For a standard run, 400 grams of iron and 10 grams of graphite were used. By adding some graphite, the dissolution of the crucible was minimized. The slag phase was composed of 90 grams of calcium oxide, 70 grams of silicon oxide, and 20 grams each of magnesium oxide and aluminum oxide for a total of 200 grams. For the reduction by silicon system, 300 grams of iron and 4 grams of silicon were used. Most of these materials were weighed on a triple-beam balance that had a sensitivity of 0.01 gram and weight divisions down to 0.01 gram. Silicon and manganese oxide, which were used in smaller quantities, were weighed on an Ainsworth Type LC Analytical Balance using Class S weights. Therefore, the difference between the reported composition and the actual composition for components of the system should not be more than 0.1% of the reported composition. When the crucible assemblies had been prepared and the ingredients weighed into them, three assemblies were placed in the furnace tube, as shown in Figure 2. The purpose for using this arrangement will be discussed later. The bottom and top heads were secured tightly in place preparatory to starting the run. The alignment of the stirring hole and sampling hole in the crucible lid with the corresponding holes in the top head was checked. The argon gas supply was turned on and an argon atmosphere was maintained in the furnace tube throughout the run. The power was turned on and increased gradually so that the furnace tube would not be broken by thermal shock. After the reaction zone had attained approximately 1000~C, full power required to reach the desired temperature could be applied to the system. After this initial start-up,

-33 - the furnace was kept at approximately 10000C, hence the procedure normally would start from this point. It took approximately 6 to 8 hours for the furnace to reach the desired operating temperature from this level. By the time the system had reached temperature, usually 1550~C, the iron-graphite phase would have been above its melting point for about two hours. Therefore, it can be assumed that it had reached graphite saturation.38 The stirrer was lowered into position, just off the bottom of the crucible, and started at the desired rate. The revolutions of the stirrer were counted manually and the rate was checked periodically throughout the run. The rate of stirring as reported was accurate to within + 2 revolutions per minute. For the reduction by silicon system, the stirrer was lowered to the bottom of the crucible and then raised one inch so that the stirrer was only in the slag phase. Otherwise the iron would dissolve the graphite stirrer in contact with it, thus becoming contaminated with graphite. The temperature was controlled by the Leeds and Northrup Controller, which was set at the desired temperature at the beginning of the heat-up. The manganese oxide was now added to the system through a Vycor tubefunnel arrangement. The moment that the manganese oxide was added to the system was considered zero time for the actual reaction. In a normal run, 10 grams of manganese oxide was used. The Vycor tube-funnel arrangement was long enough to extend inside the crucible lid to insure that all of the manganese oxide was added to the system. Occasionally some of the manganese oxide fused to the wall of the Vycor tube as it flowed through; this did not happen often and when it did, the amount of manganese oxide lost was approximated. Samples were then taken of the

-34 - slag and metal phase as desired to monitor the progress of the run. In this investigation, samples of the slag were taken every 15 minutes for two hours for reduction by graphite, with a metal sample being taken at the end of the two hours to check the mass balance of the system. For reduction by silicon, slag samples were taken every three minutes for 24 minutes and then a slag and a metal sample were taken at the end of two hours when the system had reached equilibrium. Samples of the slag and metal were taken in some instances before the start of the run to check on any side reaction which might have occurred during heat-up. Thirty-six inch lengths of 6 mm OD Vycor tubing were used to take the samples. Copper gauze was placed in one end of the Vycor tubing to chill the sample and limit the size of the sample taken; a suction bulb was used on the other end to draw the sample into the sample tube. For taking metal samples, the Vycor tubing was lowered to the bottom of the crucible and the metal sample drawn from there. It was quenched in water immediately. The sample tube was lowered into the system a predetermined distance so that slag would be drawn into it when a slag sample was desired. The Vycor tubing was reused until the lengths became too short to reach the slag-metal system. The slag samples taken during the run were usually 2 grams or less in size, while the metal samples were approximately 5 grams. The amount of time required for the reduction by silicon reaction to reach equilibrium was determined by taking samples over a wide range of time intervals. The reduction by graphite reaction was allowed to run for 20 hours in one instance and still had not reached equilibrium. Therefore, it was decided to use equilibrium values from the literature instead of trying to reach equilibrium for each run made in the carbon study.

-35 - At the end of the experimental run,, the graphite stirrer was pulled out of the reaction zone and the power input into the system was reduced to allow the temperature to fall back to 1000~C. When the temperature had reached this level, the top head of the furnace tube was removed and the crucible with its supporting brick was pulled out of the furnace. This was accomplished using two small-.. steel rods with hooks on one end to grab the crucibles by the grapple holes shown in Figure 4. The graphite stirrer was then replaced if necessary and the top head arrangement was again secured on the furnace tube. Meanwhile, another crucible with supporting brick was prepared, and metal and slag ingredients weighed into it. Then it was preheated to about a00C, using a heating mantle. It was now ready to be placed in the furnace. The adaptor in the bottom head of the furnace tube was screwed out and the new crucible was pushed up into the furnace through the bottom head, thus pushing the other crucibles farther up into the furnace. The adaptor was then replaced, sealing the system. The top crucible was now in position to begin another run. Again, the alignment of the stirring hole and sampling hole in the crucible cover was checked. The system was now ready to heat up to the desired temperature for another experimental run. The assembly line approach, i.e., placing the crucibles into the furnace in series, was a necessary procedure. At first an attempt was made to use a permanent insulation-support stand in the furnace. Then the crucibles would be lowered into position from the top of the tube. Two problems arose in trying to use this method. First of all, excessive oxidation of the equipment occurred while trying to lower the crucible slowly into the hot zone. Secondly, the effect of placing a relatively cold crucible into the hot mullite furnace tube was to cause serious

-536 - thermal shock in the mullite tube; in fact, after two or three times, it would usually break the furnace tube. Therefore, the present method was devised. In this method the bottom head was removed for only a few moments while the crucible was being pushed into position. Because the other two crucibles had been in the system for some time, they were preheated to the extent that when they were pushed into a hotter zone of the furnace, the temperature differential was not great enough to cause failure in the furnace tube. The only difficulty with this method was that it was necessary to know three runs in advance what conditions would be desired for the run currently being prepared. The crucibles could only be used one time in this experimentation. The stirring rod was not attacked by the slag phase and was only slightly attacked by the metal phase and could be used for two and often three runs before being replaced. The supporting brick was used repeatedly. 4. Chemical Analysis of Samples Wet chemistry methods were used for the analysis of both the slag and the metal samples. Analytical procedures were supplied by McLouth Steel Company of Detroit, Michigan, who also demonstrated the use of the procedures in their laboratories. A volumetric quantitative analysis was used for the determination of manganese in the metal and in the slag. This method involved dissolving the sample, oxidizing the manganese into the form of a permanganate ion and then titrating with a standard sodium arsenite solution to determine the concentration of manganese. A gravimetric quantitative analysis was used for the determination of silicon in the iron. The sample was first brought into solution and then the silicon was oxidized into the insoluble form, SiO2o The solution was

-37 - then filtered and the filter paper containing the SiO2 was ignited and weighed to determine the SiO2 in the original sample. The amount of iron in the slag was determined using a volumetric quantitative analysis method. In this procedure, the slag was dissolved and the ferric iron was reduced to the ferrous state by treatment with hydrochloric acid and stannous chloride. The excess stannous chloride was oxidized with mercuric chloride and the ferrous iron was titrated with a standard potassium dichromate solution. All of these methods gave results that could be reproduced to within one percent. Samples from the National Bureau of Standards were analyzed to check the accuracy of the method. Their analysis was reproduced to within one percent also. 5. Treatment of Data The theoretical models for the reactions under study had been derived in terms of manganese concentrations in the metal. Therefore, manganese concentrations in the metal as a function of time were calculated from the slag manganese oxide concentrations which had been determined by chemical analysis. These calculations were made manually and were based on the material balance in the slag-metal system. Further computations were made on an IBM 7090 computer using programs written in the MAD language for each theoretical model. The computer program determined the value for the left-hand side of these derived models as a function of time. It then made a least-squares fit of the calculated D points. The slope of this line was equal to - for the diffusion models 900k1 and -h for the chemical reaction model. The desired rate constant,, or kl, could readily be evaluated from this slope.

-38 - For those integrals that were too complicated to be integrated mathematically, a Gauss-Legendre numerical analysis procedure was incorporated into the program to evaluate the left side of such equations. Another program was written to evaluate the energy of activation for the two reactions under consideration. The data were submitted to the program as temperature vs reaction constant. The program then made a least-squares fit of the data in terms of natural logarithm of the reaction constant vs reciprocal absolute temperature. The slope of this line is -E -E from which the energy of activation can be readily calculated. R

EXPERIMENTAL RESULTS The results will be presented in two parts. The first section will deal with manganese oxide reduction by silicon; the second section will present the results of manganese oxide reduction by carbon. In order to determine the rate-limiting step for each reaction, the effect of several variables on the systems was studied. These variables were stirring rate, temperature, melt geometry, and concentrationso What might be expected to happen as a result of varying these parameters can be explained in terms of the following equation: Rate = B x Force (53) This is the basic rate equation under consideration. It says that the rate at which the reaction will occur is proportional to the driving force which moves the reaction. For a diffusion controlled reaction, B is equal to the diffusion constant divided by the length of the diffusion path. If an interfacial chemical reaction controls the rate of the process, B is the reaction rate-constant designated by k. These two D constants, D and k, have certain limitations on them. The rate of stirring has no effect on D or k but has a marked effect on 5. A change in temperature has a small effect on D and 5, but a greater effect on k. Changes in melt geometry, specifically phase depth, should not affect any of the constants. The purpose of including this variable is to indicate which phase whascontrols the overall reaction. The effect of concentration on these constants should again be negligible, except possibly for secondary influences on the diffusion coefficient, If the concentration change is large, the character of the medium through which diffusion occurs could be altered enough to cause a change in D, Generally, moderate changes in concentration alter the driving force for the reaction, thereby modifying the rate, whereas D remains constant. -39 -

-40 - In this section, the results obtained by applying the experimental results to the theoretical models derived earlier will be explored in terms of a model meeting the conditions listed above. The model that successfully meets these conditions will define the rate-limiting step for the process. A. Manganese Oxide Reduction by Silicon This was a rapid reaction reaching equilibrium in less than ninety minutes. The change in concentration of the various components as a function of time is shown in Figure 5 for a typical experimental run. Figure 6 is a plot of F(Mn), the left side of Equations (19), (21), (23), and (25) versus time, t, which shows the results obtained upon application of the theoretical diffusion models to the data shown in Figure 5. A good fit is obtained for each model. A compilation of all the experimental data taken during this study is found in Appendices A and B. 1. The Effect of Stirring Rate The rate of stirring had a marked effect on the rate of this reaction, as shown in Figure 7. Here shown are the results of runs using no stirring, stirring with a 3/8 inch stirring rod at 100 rpm, and stirring with a 3/4 inch stirring rod at 100 rpm. The slope is doubled and tripled respectively for the latter two cases, relative to the first case with no stirring. The results shown are those derived using the theoretical model for the diffusion of manganese in the metal, Equation (19), A tabulation of results obtained for each theoretical model using stirring rate as the variable is given in Table II. Since the chemical reaction constant, k, would not be influenced by stirring rate, it can be immediately deduced that this reaction is not controlled by a chemical reaction, but rather is controlled by diffusion.

-41 - 4 -C 0 ". 0 0. en 0 a2 0 I() z 0 U) 0 20 40 60 80 100 120 TIME, MINUTES Figure 5. Concentration-Time Curves for the Reaction 2 (MnO) + Si = (SiO2) + 2 Mn.

-42 - F(Mn) 0.8 0.6 ~~04; ~0 0.4 (23) 0 4 8 12 16 20 24 TIME, MINUTES Figure 6. Determination of D/8 for Various Theoretical Models for the Reaction 2(MnO) + (Si02) + 2 Mn.

F(Mn) 0 4 8 12 16 20 24 TIME, MINUTES Figure 7. The Effect of 2(MnO) + Si = Stirring Rate on the Reaction (SiO2) + 2 Mn.

TABLE II THE EFFECT OF STIRRING RATE ON THE REDUCTION OF MANGANESE OXIDE BY SILICON Stir _ (D/5) X 104, cm/sec Rate, Metal Phase Slag Phase Run RPM Mn Si Mn Si 140 0 3.23 1.65 129 0.069 133 0 3.26 1.59 9.8 o0.46 131 0 2.49 1.30 8.0 0.031 129 0 2.75 1.21 8.1 0.011 166 40 7.06 3.87 27.5 0.112 155 100 7.39 4.28 2.3.9 0.078 154 100 7.30 3.45 22.5 0o105 163 100 7.35 3.89 22.2 O.080 146 100 7.43 4.51 23.7 0.061 143 100 6.94 3.07 21.2 0.109 164 100* 11.31 5.67 36.0 0.157 * A paddle 3/4" wide paddle was used. was used for this run. Ordinarily a 3/8" wide

-45 - 2, The Effect of Temperature Temperature had very little effect on the rate of this reaction, The results obtained by varying temperature are presented in Table III. The effect of temperature can be examined quantitatively by calculating the energy of activation for the process. The diffusion constant, D, is influenced by the temperature exponentially. This relationship can be presented in an Arrhenius-type equation: E D = D e- RT (54) 0 If 5 is either not affected by temperature or is affected exponentially by temperature, then s = ( )oe RT (55) Taking the logarithm of both sides of this equation: D E In - = in () RT (56) D 1 -E Then, by plotting In - vs -, the resulting slope will have the value -R giving the energy of activation for the reaction under consideration. This is done in Figure 8. A regression analysis of this data gives a value of 7 Kcal/mole Mn for the energy of activation, E. This result, along with the energy of activation reported in the literature for the relevant diffusion steps, is presented in Table IV. No value is available in the literature for the diffusion of manganese in slag. However, values for other components in slag are comparable to those for the diffusion of silicon in 20 slag 20. Therefore it is assumed that the value for the energy of activation for manganese in slag will also be a relatively high number with the same order of magnitude as that for silicon in slag. The energy of activation obtained is much lower than would be expected for diffusion of a component in the slag.

-46 - TABLE III THE EFFECT OF TEMPERATURE ON THE REDUCTION OF MANGANESE OXIDE BY SILICON (D/s) X 10, cm/sec Metal Phase Slag Phase Run T, ~C Mn Si Mn.Si 16o 1540 7.21 3.71 22.6 0.103 155 1550 7.39 4.28 23.9 0.078 154 1550 7.30 3.45 22.5 0.105 163 1550 7.35 3.89 22.2 0.080 146 1550 7.45 4.51 23.7 o.o06 143 1550 6.94 3.07 21.2 0.109 159 1560 7.43 4.49 23.5 0.069 148 1570 7.51 4.68 24.5 o.o69 199 1580 7.61 3.08 25.6 0.112 149 1590 7.61 4.07 24.1 0.092

-47 - -7.15 I -7.2 do 0 I c -7.25 0 R E - R x Slope = 7 Kcal /Mole Based on Mn Diffusion in Metal I 0 sO 0 0 I 5.3 54 I/T,~K x 104 5.5 Figure 8. The Effect of 2(MnO) + Si = Temperature on the Reaction (Si02) + 2Mn.

TABLE IV COMPARISON OF EXPERIMENTAL ENERGIES OF ACTIVATION WITH THOSE REPORTED IN THE LITERATURE FOR THE REDUCTION OF MANGANESE OXIDE BY SILICON Diffusion Step E, Experimental E, Literature (Ref. 40, 42) Manganese in Iron 7 Kcal/mole Mn 5.8 Kcal/mole Mn Silicon in Iron 14 Kcal/mole Si 8.6 Kcal/mole Si Manganese in Slag 7 Kcal/mole Mn --- Silicon in Slag 14 Kcal/mole Si 70 Kcal/mole Si.~ ~ ~ ~ ~ ~ ~ ~~7 K.lml.S.i

The results of the study on the effect of temperature shows that the controlling mechanism for this reaction is the diffusion of manganese or silicon in the metal phase. 3. The Effect of Melt Geometry Runs varying the slag-to-metal ratio were made to determine in which phase the controlling step occurred. In calculating the diffusion constant, a function of the manganese concentration (applicable to the diffusion step under consideration) is plotted versus time. The resulting slope has a value Dh where h is the height of the phase in which the diffusion is taking place for the derived model. When the slag-tometal volume ratio is varied, then the relative value of h between a model derived for the slag phase and one derived for the metal phase is also varied. For example, let us assume that one phase depth is increased and the other is decreased. It because of this change in melt geometry, the slope of the curve for the theoretical model increases, then for D - to remain constant, h would have to decrease. In one phase, this would occur. In the other phase, just the opposite would occur and the resulting D calculated values for - would not remain consistent. This, indeed, happened as can be seen in Table V. Experiment 223 had a slag depth half that of the standard run and a metal depth twice the standard. The slope of the curves for the theoretical models was only half that of a typical run. Since = Slope X h for the diffusion of manganese and silicon in the metal Slope X hi, T for the diffusion of manganese and silicon in the metal phase remained constant, but was only one-fourth the normal value for diffusion in the slag phase. Run 172 had a slag depth greater than normal and a metal depth only one-third of normal. Under these conditions the slope of the curves for

-50 - TABLE V THE EFFECT OF MELT GEOMETRY ON THE REDUCTION OF MANGANESE OXIDE BY SILICON Slag Metal(D/5) X 10 cm/sec Depth, Depth, Metal Phase Slag Phase Run cm cm Mn Si Mn Si 225 1.5 4.4 7.26 1.74 5.3 0.029 122 3.0 2.92 6.98 7.12 15.2 0.058 155 3.0 2.2 7.39 4.28 23.9 0.078 154 3.0 2.2 7.30 3.45 22.5 0.105 163 3.0 2.2 7.35 3.89 22.2 o.080 146 3.0 2.2 7.43 4.51 23.7 0.061 143 3.0 2.2 6.94 3.07 21.2 0.109 121 3.0 1.47 7.57 3.85 30.3 0.157 172 4.5 0.75 7.75 2.09 75.6 2.666

-51 - the theoretical model was much greater than normal. Again this was corrected for by the depth of the metal phase, giving consistent results D D of - for the components in the metal phase, and again - for the components in the slag phase were inconsistent, being much greater than usual. The result of the melt geometry study is that the process is controlled by the rate of diffusion of manganese or silicon in the metal phase. This agrees with the results of the temperature study above. 4. The Effect of Concentration By this process of elimination, the controlling step had now been limited to diffusion, and also it had been limited to diffusion of one of the components in the metal phase. It was now necessary to devise a method of determining which diffusion step in the metal phase was the slow one. To do this, runs were made increasing the initial silicon concentration in the metal. A summary of the results obtained is given in Table VI. As can be seen, as the initial silicon concentration is inD creased, the value for - decreases for both manganese in the metal and silicon in the metal. However, the decrease in for silicon diffusion is much greater, as is shown in Figures 9 and 10. D The small decrease in values of - for manganese in the metal as the silicon concentration is increased, is not unrealistic. In the col20 lection of diffusion data by Elliott, et al., the same phenomenon is noted. The diffusion coefficient of carbon in iron is reduced by increasing the concentration of carbon in the iron. Likewise, the diffusion coefficient of silicon in iron is reduced by increasing the concentration of silicon in the iron. However, the changes of the diffusion coefficients are small as is the implied change of the diffusion coefficient for manganese in iron evaluated in this study as the silicon concentration is increased,

-52 - TABLE VI THE EFFECT OF THE CONCENTRATION OF SILICON ON OF MANGANESE OXIDE BY SILICON THE REDUCTION Initial Si.. (D/5) X 10 cm/sec Concentra- Metal Phase Slag Phase Run tion, % Mn Si Mn Si 155 1.32 7.39 4.28 23.9 0.078 154 1.32 7.30 3.45 22.5 0.105 163 1.32 7.35 3.89 22.2 0.080 146 1.32 7.43 4.51 23.7 0.061 143 1.32 6.94 3.07 21.2 0.109 162 1.96 6.14 2.61 25.2 0.070 167 3.85 4.27 0.66 22.7 0.074

G41 0.3 F(Mn) 0.2 0.1 0 TIME, MINUTES Figure 9. The Effect of Silicon Concentration on the Reaction 2(MnO) + Si = (SiO2) + 2Mn.

-54 - F(Mn) 0 4 8 12 16 20 24 TIME, MINUTES Figure 10. The Effect of Silicon Concentration on the Reaction 2(MnO) + Si = (Si02) + 2 Mn.

-55 - D The change of for silicon in the iron evaluated in this experimental study as the concentration of silicon in the iron is increased, is not small. It varies by almost an order of magnitude as the silicon concentration is increased. Considering Equation (44), the inconsistency becomes more apparent. The driving force is increased by approximately a factor of three with increased silicon concentration. The rate of the reaction should also increase by a factor of three. This did not happen. In fact, the rate of the reaction was even slower than before. These results show that the theoretical model describing the ratecontrolling step as the diffusion of silicon in the metal is not valid for this chemical reaction, so only the model for diffusion of manganese in the metal has consistently described the experimental results. 5. Other Considerations One more piece of information available for consideration is the D value of - calculated for each of these diffusion models. By comparing the experimental values with the values of D for these same diffusion steps as reported in the literature, the possible diffusion steps are defined. These comparisons, along with the values of b calculated from the comparisons, are presented in Table VII. The 6's obtained are all reasonable for D a diffusion process. Therefore, in view of the values obtained for, any of these diffusion models could define the rate-limiting step for the reaction. 6. Summry The results obtained above are summarized in Table VIII, which reviews the results obtained from a study of each of the variables. From this summary it can be seen that only the model for the diffusion of manganese in the metal phase gives consistent results throughout. The diffusion of manganese in the metal is therefore postulated to be the rate-limiting step for the reduction of manganese oxide by silicon.

-56 - TABLE VII COMPARISON OF EXPERIMENTAL DIFFUSION CONSTANTS WITH THOSE REPORTED IN THE LITERATURE FOR THE REDUCTION OF MANGANESE OXIDE BY SILICON AT 1550~C D/b, cm/sec, D, cm /sec, 5, cm, Diffusion Step Experimental Literature* Calculated Manganese in Iron 7 x 10-4 4 x 10-5 0o06 Silicon in Iron 4 x 10-4 4 x 10-5 0,1 Manganese in Slag 2 x 10 -- -- Silicon in Slag 1 x 105 10 0,1.........10-5 1 0 - 6.0o * Ref. 39, 40, 41, 42

-57 - TABLE VIII APPLICABILITY OF POSSIBLE MODELS FOR THE REDUCTION OF MANGANESE OXIDE BY SILICON Is Model Applicable?_ Diffusion Metal Slag Phase Phase Chemical Variable Results Mn Si Mn Si Reaction Stirring Pronounced effect on the Yes Yes Yes Yes No rate reaction rate Tempera- Energy of Activation very Yes Yes No No No ture low; E = 7 K-cal/mole Mh Melt Geo- Only models for diffusion Yes? No No metry in the metal phase maintained a consistent reaction constant Concentra- The silicon diffusion in Yes No Yes Yes tion (Si' metal model did not in Metal) give consistent results for varied silicon concentrations Diffusivities Yes Yes Yes Yes

-58. B. Manganese Oxide Reduction by Carbon This reaction was much slower than the reduction by silicon. A comparison of the two is presented in Figure 11. If this reaction is controlled by a diffusion step, results similar to those obtained for the reduction by silicon would be expected; the slow rate of reaction, however, indicates the reaction is controlled by a slower chemical reaction step. The data obtained on this system is compiled in Appendices A and Bo This data has been analyzed in terms of the theoretical models derived for this particular reaction. Figure 12 shows the results obtained for a typical run when the diffusion models, Equations (33), (34), (39), and (44), are applied to it. Figure 13 shows the results obtained when the chemical reaction models, Equations (46), (48), and (51), are applied to this same data. As can be seen, a good data fit is obtained for all of these models, so any of them could define the rate-limiting step. The effect of stirring rate, temperature, melt geometry and concentrations, as well as the magnitude of the rate constant, is considered in determining the rate-limiting step for the reduction of manganese oxide by carbono 1. The Effect of Stirring Rate The model for diffusion of manganese in the metal is used in Figure 14 to demonstrate the effect of stirring rate on this reaction. No apparent effect of stirring is visible. A compilation of all the results obtained when varying the stirring rate is given in Table IX. Since the rate of stirring has no effect on the reaction, it has to be classified as one controlled by a chemical reaction rather than by diffusion. This result is exactly the opposite of the result obtained for reduction by silicon,

-59 - 5 0 Zo OD z Z 4 z U 0 0 0 C 4 3 2 I 0 TIME, MINUTES Figure 11. Comparison of Concentration-Time Curves for Reduction by Silicon and Reduction by Carbon.

-60 - r 11 /(I) 1.8 0/ 1.6 o C 1.2 Ca | / )(2) 20.8 '3 04 c (4) c 0.6 0.03 c Xe 1.00' 1 ~E 0.4 Q02 0 o 0 Run 96 2c | o0 Slope D/8hj | 2 c ( -0.2 (1) Diffusionin Metol (Eq.44) 0.01 c X | (2)C Diffusion in Metol (Eq.39) s _ | (3) Mn Diffusion in Slog (Eq. 34) | (4) Mn Diffusipn in Metvl (Eq. 43), 0 20 40 60 80 100 TIME, MINUTES Figure 12. Determination of D/6 for Various Theoretical Models for the Reaction (MnO) + C = Mn + CO.(g)

l.I I.E 1.4 C 0 C.2 c 0 O._ to 0 c - I 0 U. 1.2 1.0 3 ii 0 ii Ii ii 1 _ IllIll m I) I I 60 08 m 0.6 iii 50 SO 40 5 C em0 0 t C I0 | 20 10 0 0.4 Run 96 Slope = 900 k( /hM (I) (MnO)+C Mn+CO (Eq.46) (2) (MnO)= Mn+ 0 (Eq. 43) 0.2 - (3) (0)- O (Eq. 51) I I I I I. -- I I L..... 0 20 40 60 80 100 TIME, MINUTES Figure 13. Determination of k for Various Theoretical Models for the Reaction (MnO) + C = Mn + CO - - (g)'

-62 - 0.05 0.041 - U. IL 0.0Q3 - (I) (2) 0/ w (3) (I ) Run 93 - 40 RPM (2) Run 95 - 100 RPM (3) Run 96- ORPM I I I I I 0.02 - 0.01 F 0 20 40 60 80 100 TIME, MINUTES Figure 14. The Effect of Stirring Rate on the Reaction (MnO) + C = Mn + CO(g).

TABLE IX THE EFFECT OF STIRRING RATE ON THE REDUCTION OF MANGANESE OXIDE BY CARBON Stir.(D/) x 10, cm/sec kx 10, mole/cm min Rate, Metal Phase Slag Phase Run RPM Mn C 0 Mn ((2)*(2) ()* 96 00.075 0.090 6.1 1.90 0.238 8.5 00125 124 0 0.074 0.078 7.2 1.89 0.238 8.5 0o104 126 0 0.139 0.126 16.2 3.55 0.456 16.3 0,141 58 20 0.063 0.077 5.1 1.60 0.206 7.3 0.109 93 40 0.113 0.113 12.1 2.89 0.372 13.3 0.113 21 40 0.096 0.112 7.7 2.45 0.315 11.3 0.127 45 40 0.089 0.099 8.5 2.27 0.297 10.6 0.133 108 40 0.130 0.135 13.4 3532 0.431 15.4 0.139 20 100 0.067 0o086 5.0 1.70 0.218 7.8 o.o86 22 100 0.071 0.083 6.4 1.81 0.235 8.4 0,113 95 100 0.100 0.107 9.6 2.54 0.321 11.4 0.142 (1) (2) (MnO) (Mno) + C = Mn + CO -- (g) = Mh + O (3) (o) = O

-64 - 2, The Effect of Temperature A change in temperature had a greater effect on this reaction than it did on the first reaction studiedo This is shown in Figure 15, where the natural logarithm of the rate constant is plotted against reciprocal absolute temperature to give the energy of activation for the system, The energy of activation determined by a regression analysis of the data, 25 Kcal/mole Mn, is difficult to rationalize in terms of the possible rate-limiting mechanisms for the reaction. It is too high for the diffusion of the components in the metal; but, on the other hand, it is lower than one would expect for the diffusion of manganese in the slag or for the chemical reactions under consideration. However, there has been no work done in this area, so'the energy of activation is undefined for these processes. The value determined in this study could be valid for the diffusion of manganese in the slag or for the chemical reactions postulated here as the possible slow steps in the overall reaction. The results obtained when varying the temperature are given in Table X. In summary, then, the energy of activation for this system indicates that the rate-limiting step for the reaction is either the diffusion of manganese in the slag or a chemical reaction. 35 The Effect of Melt Geometry The slag-to-metal ratio was varied from.lo4 to 4:1 in this study to see what effect this would have on the calculated rate constants. The results are presented in Table XI. Melt geometry should have no effect D on either or on k therefore, consistent results should be obtained regardless of the slag-to-metal ratio. As can be seen, there is a great deal of scatter in the results for every model. However, the models for diffusion of carbon in the metal phase, Equation (39), and for the chemical

-65 - -II c 4J -11.5 -12. I/T~K x 104 Figure 15. The Effect of Temperature on the Reaction (MnO) + C = Mn + CO(. _ _ (g)'

- S 6 - TABLE X THE EFFECT OF TEMPERATURE ON THE REDUCTION OF MANGANESE OXIDE BY CARBON kI x 10, mole/cm mi (D/b) x 10, cm/sec k x 10, mole/cm min T, Metal Phase Slag Phase Run ~C Mn C 0 Mn ( )* (2)* (3)* 44 1500 0.117 0.092 8.2 1.88 0.251 8.6 0.104 92 1519 0.102 0.092 8.2 1.98 0.253 8.8 0.101 90 1544 o. 089 o, 89 7.7 2.06 0.260 9.2 0.123 93 1550 0.115 0.113 12.1 2.89 0.572 13.5 0.113 21 1550 0.096 0.112 7.7 2.45 0.318 11.3 0.127 45 1550 0.089 0.099 8.5 2.27 0.297 10o6 0.133 108 1550 1.30 0.135 15.4 3.32 0.451 15.4 0.139 91 1567 0.079 0.098 8.1 2.33 0.290 10.5 0.122 47 1600 0.081 0.174 10 6 319 0.418 15:5 0.148 (1) (2) (MnO) (MnO) + C = Mn + CO(g) = Mn + g) =Mn+ 0 (3) (o) = o

-67 - TABLE XI THE EFFECT OF MELT GEOMETRY ON THE REDUCTION OF MANGANESE OXIDE BY CARBON Slag Metal (D/b) x 10, cm/sec k1 x 10 mole/cm min Depth, Depth, Metal Phase Slag Phase-2 Run cm cm Mn C O Mn (1)* (2)* (3)* 224 1.25 5.0 0.306 0.162 9.9 7.65 1.045 57.2 0.188 48 1.88 2.5 0.076 0.097 8.4 1.90 0.259 9.2 0.129 98 1.88 2.5 0.059 0.087 5.2 1.48 0.189 6.7 0.124 93 2.5 2.5 0.113 0.113 12.1 2.89 0.372 13.3 0.113 21 2.5 2.5 o.096 0.112 7.7 2.45 0.518 11.3 0.127 45 2.5 2.5 0.089 0.099 8.5 2.27 0.297 10.6 0.133 108 2.5 2.5 0.150 0.155 15.4 3.32 0.431 15.4 0.159 49 3.12 2,5 0.141 0.126 14.3 3.62 0.472 16.8 0.112 99 3.12 2.5 0.101 0.105 7.8 2.59 0.325 11.6 0.144 100 3.12 2.2 0.077 0.122 19.8 1.90 0.240 8.6 0o099 101 3.12 1.88 0.129 0.128 19.6 3.30 0.413 14.8 0.082 59 3512 1.56 0.085 0.099 9.4 2.21 0.276 9.9 0.128 225 5.0 1,25 0.072 0.095 22.4 1.83 0.199 7.2 o.083 (1) (MnO) + C = Mn + CO(g (2) (MnO) = Mn + O (3) (0) = 0

-68 - reaction of oxygen in the slag going to oxygen in the metal, Equation (51), give much better results than the other models. The scatter for these two models is small and random, and is reasonable in view of the overall accuracy of the data. For the other models, the scatter is three or four times greater than for these two models. 4. The Effect of Concentration Two variables were studied with respect to the effect of concentration on the reaction rate. First of all, the amount of manganese oxide added to start the runs was varied. Secondly, the concentration of graphite in the iron was varied. Zirconia crucibles were used which allowed the use of carbon contents below graphite saturation, The rate constant should not vary as a result of changes in concentration; only the rate itself should be affected. In other words, a higher driving force should give a higher reaction rate, the rate constant remaining the same. The one exception to this is for the reaction of oxygen in the slag being reduced to oxygen in the metal. In the derivation of this model, Equation (51), the activity of the oxygen in the slag was assumed constant and is included in the rate constant. From the work by Toop and Samis 9, it can be assumed that the activity of oxygen in the slag increases very slightly as the concentration of manganese oxide in the slag increases. Therefore, we would expect the rate constant as evaluated with this model also to increase slightly when a higher percentage of manganese oxide is used for the run. This, in fact, turned out to be the case. The effect of manganese oxide concentratio n the rate e of reduction of manganese oxide by carbon is presented in Table XII. As can be seen, the only models which give consistent results as the concentration of

-69 - TABLE XII THE EFFECT OF MANGANESE OXIDE CONCENTRATION ON THE REDUCTION OF MANGANESE OXIDE BY CARBON i L. _ I! I I I I1 _ =, I (D/) x 104, cm/sec__ k x 10, mole/cm min Metal Phase Slag Phase (1)* (2)* (3)* Run oMnO Mn C 0 Mn 138 0.49 0.207 0.022 2.2 5.52 0.667 23.8 0,041 153 0.99 0.300 0,080 6.9 5.58 0.967 34.5 0o093 156 0.99 0.297 0.074 5.0 7.89 0.965 34.4 0.111 135 1.48 0.254 0.077 10.0 6.72 0.985 35.2 0.136 109 2.44 0.190 0.084 12.1 4.98 0.651 23.3 0.099 93 4.75 0.113 0.113 12.1 2.89 0.372 13.3 0.113 21 4.75 0.096 0.112 7.7 2.45 0.318 11.3 0.127 45 4.75 0.089 0.099 8.5 2.27 0.297 10.6 0.133 108 4.75 0.130 0.135 13.4 3.32 0.431 15.4 0.139 (1) (MnO) + C =Mn + CO(g (2) (MnO) = Mn + O (3) (0) = 0

-70 - manganese oxide at the start of the run was varied were for the chemical reaction (O) = 0 and for the diffusion of carbon in the metal. The effect of carbon concentration on the reduction of manganese oxide by carbon is shown in Table XIII. Again the majority of the models do not give consistent results as the graphite concentration is varied. Only chemical reaction models (2) and (3) give consistent results here. In summary, only the model for the activation of oxygen going from the slag to the metal phase gives consistent results as concentrations in the slag-metal system are varied. 5. The Effect of Slag Variation Changes in composition of the slag phase were made to see what effect this would have on the reaction. The results are tabulated in Table XIV. With each change in slag composition it is necessary to estimate a new activity coefficient for manganese oxide in the slag. This involves extrapolations and approximations, and yields results of limited accuracy, This is evident from the general scatter of the results. No influence can be detected on the rate constants as a result of varying the slag composition. 6. The Effect of Silicon Additions to the Melt A run was made adding silicon to the graphite-saturated melt to see what effect this would have on the overall reaction. In effect, this situation involves a simultaneous occurrence of both of the reactions under study in this research program. Figure 16 gives a comparison of the raw data obtained on this run as compared with that for reduction by silicon alone and by graphite alone. The diffusion coefficient of D -4 manganese in the metal for this run is - = 3 x 10 cm/sec. This value is lower than the value for the diffusion coefficient of manganese in metal

TABLE XIII THE EFFECT OF CARBON CONCENTRATION ON THE REDUCTION OF MANGANESE OXIDE BY CARBON (D/6) x 10, cm/sec k1 x 104 mole/cm min _Metal Phase Slag Phase Run loC_ Mn C 0 Mn (1)* (2)* (3)* 196 1.32 3.07 0.789 7.7 4.42 9.40 12,9 0.201 218 2.60 2.04 0.404 25.4 8.70 6.46 20.7 0.141 228 4.75 0.231 0.254 15.4 4.41 0.742 19,8 0.157 93 5.28 0.113 0.113 12.1 2.89 0.372 13.3 0,113 21 5.28 0.096 0.112 7.7 2045 0.318 1103 0,127 45 5.28 o.o89 0.099 8.5 2.27 0,297 10o6 0.153 108 5.28 0.130 0.135 13.4 3,32 0.431 15.4 0.139 (1) (MnO) + C = Mn + CO( - (g) (2) (3) (MnO) = Mn + 0 (o) =o

-72 - TABLE XIV THE EFFECT OF SLAG COMPOSITION ON THE REDUCTION OF MANGANESE OXIDE BY CARBON Slag Composition (D/b) x 10, cm/sec k x 10 mole/cm min % Metal Phase Slag Phase Run CaO-MgO-SiO2-A1203 Mn C 0 Mn (1)* (2)* (3)* 17 49-6-0-45 0.225 0.113 14.9 3.52 0.859 31.0 0.110 18 40-15-35-10 0.075 0.088 6.8 1,92 0.253 9.1 0.097 50 45-10-45-0.116 0.065 7.0 1.81 0.79 1.6 0062 51 45-10-25-20 0.056 0.132 8.7 2.48 0.189 6.7 0,127 52 55-0-45-0 0.125 0.091 5.9 1.95 0.409 14.6 0106 53 35-20-45-0 0.116 0.080 5.8 1.82 0.375 13.4 0.096 54 55-5-10-30 0.045 0.323 20.3 4.42 0.157 5.6 0.185 55 45-5-20-30 0.049 0.153 9.7 2.64 o.160 5.7 0.136 56 50-5-15-50 0.047 0.507 13.6 3.60 0.161 5.8 0.180 57 40-5-25-50 0.062 0.109 6.8 2.13 0.203 7.2 0.120 (1) (MnO) + C = Mn + CO _ - - (g) (2) (3) (MnO) = Mn + 0 (0) = o

5 4 3 0 c 0 *a 0 -C U 0 C a 0 20 40 60 E TIME, MINUTES Figure 16. The Effect of Simultaneous Reduction by Silicon and Carbon.

-74 - evaluated for the first reaction studied, indicating that graphite in iron slows down the diffusion of manganese. However, this value is much higher than the corresponding coefficient for the reduction by carbon. This shows that diffusion of manganese in slag or metal cannot be the rate-limiting step for the reduction of manganese oxide by carbon. 7. Other Considerations The values of D obtained in this study can be compared with those given in the literature. This is done in Table XV. As can be seen, the rate of this reaction is much too slow for the controlling step to be diffusion of manganese or carbon in the metal. Also, since the first reaction studied is much faster than this one, and both reactions involve the diffusion of manganese in the slag, th that step can be eliminated as a possible rate-limiting step for this reaction. Of the diffusion steps studied, only the diffusion of oxygen in the metal can qualify as a possible rate-limiting step for this reaction. A further study was made to check on the possibility that diffusion of oxygen in the metal was the slow step of the reaction. Argon was bubbled through the slag-metal interface, offering sites for carbon monoxide nucleation. This would decrease the diffusion path for oxygen and speed up the rate of the reaction if diffusion of oxygen was the rate-limiting step. However, the rate of the reaction was not affected by this experimental procedure, indicating that diffusion of oxygen in the metal is not the rate-limiting step for the reduction of manganese oxide by carbon. 8. Summary A summary of the applicability of possible models to the reduction of manganese oxide by carbon as influenced by the variables under consideration is presented in Table XVI. The effect of stirring rate, temperature,

-75 - TABLE XV COMPARISON OF EXPERIMENTAL DIFFUSION. CONSTANTS WITH THOSE REPORTED IN THE LITERATURE FOR THE REDUCTION OF MANGANESE OXIDE BY CARBON AT 1550~C D/6, cm/sec, D, cm2/sec,, cm, Diffusion Step Experimental Literature* Calculated Manganese in Iron 1 x 10 4 x 10 4 Manganese in Slag 5 x 10 Carbon in Iron 1 x 10-5 7 x 105 7 Oxygen in Iron 1 x 10 3 1:2 x 10 0.1 * Ref. 34, 39, 40, 41, 45

-76 - TABLE XVI APPLICABILITY OF POSSIBLE MODELS FOR THE REDUCTION OF MANGANESE OXIDE BY CARBON Is Model Applicable? Diffusion Chemical Metal Phase Slag Phase Reaction Variable Results Mn C 0 Mn (1)* (2)* (3)* Stirring Negligible effect No No No No Yes Yes Yes rate Tempera- Energy of activa- No No No Yes Yes Yes Yes ture tion; E = 25,. Kcal/mole Melt Geo- Most models gave No Yes No No No No Yes metry quite scattered data MnO Concen- Only models not No Yes Yes No No No Yes tration directly involving MnO gave good results C Concentra- Only models not No No No No No Yes Yes tion involving C gave good results Diffusivities No No Yes No (1) (MnO) + C = Mn + CO(g) (2) (MnO) = Mn + 0 (3) (o) = O

-77 -and the values of the diffusivities effectively eliminate the possibility of diffusion as being the rate-limiting step. Of the chemical reaction models, only the model for the activation of oxygen going from the slag phase to the metal phase gives consistent results throughout this study, Therefore, it is postulated that the rate-limiting step for the reduction of manganese oxide by carbon is the chemical reaction involved in the process of oxygen going from the slag into the metal.

DISCUSSION There are certain areas of this study which demand further explanation, and it is the purpose of this section of the thesis to explore these areas. First, the equilibrium constants, K', which were used in calibrations, will be discussed. Next, the effect of b on the calculation of the energy of activation, E, will be considered. The derivation of theoretical models and the application of these models to the experimental data involved the premise that one particular step controlled the rate of the overall reaction. The matter of possible mixed control for the reactions will be discussed here also. Then the accuracy of the results obtained by this study will be reviewed. A. Evaluation of the Equilibrium Constant, K' For the reduction of manganese oxide by silicon, each run was allowed to proceed to equilibrium and the equilibrium conditions existing at the end of the run were used to determine K' in the rate equation. As a check, equilibrium conditions were calculated from data available in the literature. The sources of this data were reviewed in the literature survey and will not be repeated here. The equilibrium constant was calculated from values of free energy of reaction from the literature according to AF~ = -RT in K (57) For the reduction of manganese oxide by silicon, the values of the free energy of reaction from the literature for the reactions involved are as follows: MnO (I in FeO) = Mn (%) + O (%) (58) AF~ = -58,400 - 25.98 T (Ref. 20, 43) (59) -78 -

-79 - Si (%) + 2 0 (%) = SiO2(s) (60) AF~ = -142,000 + 55.0 T (Ref. 20) (61) SiO2(s) = SiO2() (62) AF0 = 3,100 + 1.56 T (Ref. 44) (63) 2 MnO(2 in FeO) + Si(%) = 2 Mn(%) + SiO2(L) (64) AF~ = -22,100 + 4.6 T (65) Equations (58) through (63) are taken from the literature. Equations (64) and (65) are the summation of the preceding equations. Using the equilibrium constant evaluated from these data, the calculated quotient for manganese in the two phases at 1550~C is nO E ql ii % IMnOJ Equilibrium - 0,54 (66) The value for the same equilibrium as determined experimentally in this study ranged from 1.1 to 1.2, a factor of two higher than the calculated value. There are factors which could contribute to this. The activity coefficient for manganese oxide in the slag is an approximation taken 27 from the work of Abraham, et al. Their data had to be extrapolated in respect to both temperature and composition of the slag to obtain an activity coefficient for the experimental conditions. In view of this, the difference between the calculated and experimental equilibrium value is reasonable. A secondary effect could be attributed to experimental error. For the reduction of manganese oxide by carbon, Equations (58) and (59) and the following equations apply:

-80 - C (%) + () = cog) (67) (g) AF~ = -5,350 - 9.48 T (Ref. 20) (68) MnO (I in FeO) + C () = Mn (%) + CO(g) (69) AF~ = 53,050 - 35.46 T (70) Equations (69) and (70) are the summation of Equations (58), (59), (67), and (68). For this reaction, the ratio of manganese in the metal to manganese oxide in the slag at equilibrium at 15500C was calculated to be 4.95. Since this reaction was so slow, equilibrium conditions were not determined in this experimental program. However, Philbrook and Tarby 3 did make an investigation of this system and found that the ratio of manganese in the metal to manganese oxide in the slag at equilibrium at 1550~C would be approximately ten. Again the discrepancy between the calculated and experimental equilibriums is approximately a factor of two. The same explanation that was made in the preceding paragraph applies to this reaction. The calculation of the equilibrium constant using the approximation of the activity coefficient of manganese oxide in the slag is common to both reactions. For the reduction by carbon study, a value of ten for the equilibrium ratio between percent manganese in the metal and percent manganese oxide in the slag was used in all the calculations. B. Effect of 5 on the Calculation of the Energy of Activation, E In this section a comparison of Equations (54) and (55) will be made. They are repeated below for convenience. E D = D e RT (54) D () - 8 ()O e- T (55) Equation (54) is generally accepted as showing the relationship between the

diffusion coefficient and temperature. In this experimental study, the relationship shown in Equation (55), which involves the added term 5, is being used. This relationship requires that 5 must also vary exponentially with temperature as does D or otherwise be temperature invariant. In the past, the latter has sometimes been assumed to be the case. Riddiford35 shows that, in fact, b varies exponentially with temperature. He derived the following equations showing,-the relationship between the energy of activation defined in Equation (55) with that in Equation (54). (4 E + E ) E = D (for laminar flow) (71) (T) 6 (D) = 2/3 (ED + E ) (for turbulent flow) (72) In these equations, E. is the energy of activation associated with the shear stress of flow. This term is usually of the same order of magnitude as ED. Therefore, the energy of activation as determined from will be very close to the energy of activation found as a function of D. They should be at least within twenty percent of one another. For this study on the reduction of manganese oxide by silicon, a qualitative comparison is sufficient. The reason for finding the energy of activation in this study was primarily to determine which of many steps could be the rate-controlling step for the process. If the two energies are within twenty percent of one another, then ED would have a value from 5.5 to 8.5 Kcal per mole. This would indicate that the rate-controlling step for the process is the diffusion of manganese or silicon in the metal. This is the same result that was obtained before.

-82 - C. Problems of Mixed Control As illustrated in Figure 1, all the calculations made in this study were based on the assumption that one step in the reaction was slower than the rest and controlled the overall rate of the reaction. The results obtained seem to justify this basic assumption. However, it is possible that another step in the reaction, although faster than the rate-controlling step, could be slow enough to cause secondary effects; this possibility is illustrated in Figure 17. The following equations demonstrate the effect of this second slow step on the apparent diffusion constant. dn DA- 1 (73) dt M'(interface) M'(bulk) () KCCM MO(bulk) ( CM' (interface) CMO(bulk) Equation (73) is the basic rate equation showing that the rate is a function of the concentration difference across the phase boundary. Equation (74), a rearranged equilibrium relationship, defines the concentration of the diffusing component at the interface. The value of the concentration of C is different when taken as the bulk concentration than when taken as M the interfacial concentration. When assuming that one step controls the overall reaction, the bulk concentration of CM is used. If, in fact, there is mixed control, as is shown by Figure 17, the interfacial value of CM should be used. This is a smaller number, and when placed in Equation (74) gives a smaller number for CM,(intefae) This error carries on into Equation (73). The calculated value for the driving force is greater than the actual value. Then for Equation (73) to balance, the calculated value of - has to be proportionally smaller than the actual value. The same effect would result if CMO or CM,0 were involved due to slow diffusion of MO or M'O.

Phase I CM'O Phase 2 CM z 0 i: Z z U 0 C) 0L CM/ (interface) CM K = CM (interfoce) CM'O. CMO CM' 0 FROM DI STANCE INTERFACE Figure 17. Illustration of Mixed Control for Reaction M'O + M = MO + M'.

This consideration can be applied to the reduction of manganese oxide by silicon. A value of D was obtained for the rate-limiting step, the diffusion of manganese in the metal. This value was calculated on the assumption that all other diffusion steps were fast enough to maintain their interfacial concentrations equal to their bulk concentrations. If, in fact, one of the other diffusion steps was slow enough so that this condition was not maintained, then the value of D obtained for the diffusion of manganese in the metal is actually too small. Because of the complexity of this two-phase system, it is impossible to determine if a second diffusion step is contributing to the rate of the overall reaction. All that can be said is that it is a possibility. D. Possible Side Reactions A possible source of error in the calculations of this study is that another reaction is occurring simultaneously with the one under consideration. For the study of the reduction of manganese oxide by silicon, a possible side reaction would be the reduction of manganese oxide by iron. Analyses of the slag were made before the run was started and at the completion of the run to check for this possibility. In all cases investigated, the amount of iron oxide in the slag was always very low and never exceeded 0.3 percent. Therefore, if this side reaction did occur, it was slow enough that it should not affect the accuracy of the calculations for the main reaction under consideration. A possible side reaction that could occur during the reduction of manganese oxide by graphite would be the reduction of silicon oxide by graphite. The study documented in the literature survey on this reaction indicates that it proceeds very slowly. The metal phase was sampled before the start and at the conclusion of several runs and analyzed for silicon.

-85 - These tests indicated that the silicon level in the metal at the beginning of the run was never more than about 0.1 percent and no trace of silicon was present in the metal at the end of these runs. At the end of each run the metal phase was sampled to give a mass balance check on the system. Agreement was obtained for the manganese in the system: the manganese reduced from the slag phase was found to be in the metal phase. Also, for reduction by silicon, a proportionate amount of silicon had been oxidized from the metal phase. This balance verifies that the reaction postulated is the one actually occurring. Therefore, it is submitted that the effect of any side reaction on the two reactions under study is minimal. E. Accuracy of Results An analysis of replicate runs was made to determine the accuracy of the results obtained in this study. For the reduction of manganese oxide by silicon, Runs 143, 146, 154, 155, and 163 were made under identical conditions. The mean value for D obtained for the diffusion of manganese in the metal was 7.28 x 104 cm/sec with a standard deviation of 0.197 x 10 cm/sec. Runs 21, 45, 93, and 108 were replicate runs for the reduction of manganese oxide by carbon. The mean value of k obtained for the chemical reaction involved in the transfer of oxygen from the slag to the metal phase was 1.28 x 10-5 moles/cm2 min with a standard deviation of 0.115 x 10-5 moles/cm min. These replicate runes were made at 1550~C. The energy of activation for the two reactions being studied was calculated by making a regression analysis of the data presented in Figures 8 and 15. For the reduction of mnanganese oxide by silicon the energy of activation was calculated to be E = 6.9 Kcal/mole with a standard error of 1.0 Kcal/mole. For the reduction of manganese oxide by carbon the result was E = 24.9 Kcal/mole with a standard error of 6.5 Kcal/mole.

SUGGESTED FUJRTHER RESEARCH Immediately after the manganese oxide is added to the experimental system to start a run, a very rapid reaction is evident. This undoubtedly is partially due to the fact that the manganese oxide does not become completely fused in the slag for a few moments and is present at the interface at greater than average slag concentration. The effect of this can be seen in Figures 7, 12, and 13. The curves do not go through the origin. It is possible that during the initial moments while the reaction is far from equilibrium, that some other step than the one determined as the rate-limiting step for the bulk of the run is controlling the reaction. This possibility is illustrated further by Figure 18. For this particular run, a slag-to-metal ratio of 1:6 was used in comparison with the normal slag-to-metal ratio of 2:3. For several minutes, the run proceeded at a greater rate than was normally observed for runs studying the reduction of manganese oxide by silicon. Since a large amount of metal was used for this run, the concentration of manganese in the metal was at a very low level. Wagner predicted that the diffusion of a component into a phase in which it is at low concentration will not be the rate-limiting step because there is an infinite driving force into that phase. This principle would apply here. Research in this area could be very profitable. By determining the rate-limiting step under these conditions, it would be possible to determine if this step was slow enough during the remainder of the run to be affecting the calculated values of - for the diffusion of manganese in the metal. This same initial condition is noted for the reduction of manganese oxide by carbon. Studies of this system during the early moments of reaction would be informative. -86 -

-87 - F(Mn) TIME, MINUTES Figure 18. Illustration of Mixed Control for Reaction 2(MnO) + Si = (SiO2) + 2 Mn.

SUMMARY AND CONCLUSION The reduction of manganese oxide by silicon is a fast reaction reaching equilibrium in less than ninety minutes. The rate of stirring in the system has a marked effect on the rate of this reaction. The effect of temperature is very small, with a calculated energy of activation for the system of 7 Kcal per mole. The effect of changing the slag-to-metal ratio over a wide range of values was to indicate that the rate-controlling step was in the metal phase and not in the slag phase. By varying the silicon concentration in the metal at the beginning of the run, it was possible to show that the diffusion of silicon in metal was not the rate-controlling step. The reduction of manganese oxide by carbon, on the other hand, was a very slow reaction. I; failed to reach equilibrium in twenty hours. There was no apparent effect on the rate of this reaction as the stirring rate was varied. The effect of temperature changes was moderate, giving a calculated energy of activation for the reaction of 25 Kcal per mole. Only the model for the reaction (0) = 0 at the interface gave consistent results as the melt geometry and concentration of manganese oxide and graphite were varied. It is interesting to find such different results for these two reactions when the only difference in the two is the reducing agent. However, upon examination of the reaction, one important difference is noticed. When silicon is the reducing agent, only metal species cross the slag-metal phase boundary. When graphite is the reducing agent, it is necessary to remove oxygen from the slag phase into the metal phase. The chemical reaction necessary to do this was found to be the slow step for the reaction. -88 -

-89 - In conclusion, the reduction of manganese oxide by silicon is a diffusion-controlled process. The slow step that controls the rate of the reaction is the diffusion of manganese in the metal phase. The value for the diffusion of manganese in the metal was found to be - = 7 x 10 cm/sec. If mixed control is a factor in the reaction, this value could be somewhat higher. The reduction of manganese oxide by carbon was a very slow reaction and was controlled by a chemical reaction at the interface. This chemical reaction involves the activation of oxygen going from the slag to the metal phase and is represented by the equation (O) = 0. The reaction constant was found to be k' = 1.3 x 10-5 mole/cm min.

APPENDIX A EXPERIMENTAL PARAMETERS Stir... Weight, Grams Rate, Type Run T, ~C RPM Crucible Fe Si C CaO MgO SiO Al 0 MnO 2 25 17 1550 18 1550 20 1550 21 1550 22 1550 35 1550 44 1500 45 1550 47 1600 48 1550 49 1550 50 1550 51 1550 52 1550 53 1550 54 1550 55 1550 56 1550 57 1550 58 1550 59 1550 90 1544 40 40 100 40 100 40 40 40 40 40 40 40 40 40 40 40 40 40 40 20 40 40 C 400 0 10 98 12 0 90 10 C 400 0 10 80 30 70 20 10 C 400 0 10 90 20 70 20 10 C 400 0 10 90 20 70 20 10 C 400 0 10 90 20 70 20 10 C 400 4 10 90 20 70 20 10 C 400 0 10 90 20 70 20 10 C 400 0 10 90 20 70 20 10 C 400 0 10 90 20 70 20 10 C 400 0 10 67.5 15 52.5 15 10 C 400 0 10 112.5 25 87.5 25 10 C 400 0 10 90 20 90 0 10 C 400 0 10 90 20 50 40 10 C 400 0 10 110 0 90 0 10 C 400 0 10 70 40 90 0 10 C 400 0 10 110 10 20 60 10 C 400 0 10 90 10 40 60 10 C 400 0 10 100 10 30 60 10 C 400 0 10 80 10 50 60 10 C 400 0 10 90 20 70 20 10 C 250 0 5 112.5 25 87.5 25 10 C 400 0 10 90 20 70 20 10 -90 -

-91 - APPENDIX A - Continued Stir Weight Grams Rate, Type Run T, ~C RPM Crucible Fe Si C CaO MgO SiO Al20 MnO 2 23 91 1567 92 1519 93 1550 95 1550 96 1550 98 1550 99 1550 100 1550 101 1550 108 1550 109 1550 121 1550 122 1550 124 1550 126 1550 129 1550 131 1550 133 1550 135 1550 138 1550 140 1550 143 1550 146 1550 40 40 40 100 0 40 40 40 40 40 40 100 10 0 0.-.0 0 40o 40 0 100 100 C C C C C C C C C ZrO2 ZrO2 ZrO2 ZrO2 C ZrO2 ZrO2 ZrO2 ZrO2 400 400 400 400 400 400 400 350 300 400 400 200 400 400 400 400 300 300 400 400 200 300 300 0 10)J 90 20 0 10 90 20 0 1D) 90 20 0 10i 90 20 0 100, 90 20 0 10) 67.5 15 0 10' 112.5 25 0 10- 112.5 25 0 10i 112.5 25 0 1O. 0 1o0 4 0 4 0 0 10 0 10 4 0 4 0 4 0 0 10 0 10 4 0 4 0 4 0 90 20 90 20 90 20 90 20 90 20 90 20 90 20 90 20 67.5 15 90 20 90 20 90 20 90 20 90 20 70 20 70 20 70 20 70 20 70 20 52.5 15 87.5 25 87.5 25 87.5 25 70 20 70 20 70 20 70 20 70 20 70 20 70 20 70 20 52.5 15 70 20 70 20 70 20 70 20 70 20 10 10 10 10 10 10 10 20 10 10 5 10 15 10 10 7 10 10 3 1 10 10 10

APPENDIX A - Continued Stir Weight, Grams Rate Type Run T, ~C RPM Crucible Fe Si C CaO MgO SiO Al203 MnO 148 1570 100 ZrO2 300 4 0 90 20 70 20 10 149 1590 100 ZrO2 300 4 0 90 20 70 20 10 153 1550 40 C 400 0 10 90 20 70 20 2 154 1550 100 ZrO2 300 4 0 90 20 70 20 10 155 1550 100 ZrO2 300 4 0 90 20 70 20 10 156 1550 40 C 400 0 10 90 20 70 20 2 159 1560 100 ZrO2 300 4 0 90 20 70 20 10 160 1540 100 Zr02 300 4 0 90 20 70 20 10 162 1550 100 ZrO2 300 6 0 90 20 70 20 10 163 1550 100 Zro2 300 4 0 90 20 70 20 10 164 1550 100* ZrO2 300 4 0 90 20 70 20 10 166 1550 40 ZrO2 300 4 0 90 20 70 20 10 167 1550 100 ZrO 300 12 0 90 20 70 20 10 172 1550 100 ZrO2 100 4 0 135 30 105 30 10 196 1550 100 ZrO2 300 0 4 90 20 70 20 10 199 1580 100 ZrO2 300 4 0 90 20 70 20 10 218 1550 100 ZrO2 300 0 8 90 20 70 20 10 223 1550 100 ZrO2 600 6 0 45 10 35 10 10 224 1550 100 C 800 0 30 45 10 35 10 5 225 1550 100 C 200 0 5 180 40 140 40 20 228 1550 100 ZrO 300 0 15.3 90 20 70 20 10 * A paddle 3/4" wide was used for this run. Ordinarily a 3/8" wide paddle was used.

APPENDIX B EXPERIMENTAL TIME-CONCENTRATION DATA Run 17 t* 0**.......* Run 22 t d/! Run 47 t.. - Run 51 t o 5 15 30 60 120 180 4.02 3.04 2.53 1.91 1.24 0.83 5 15 30 90 122 3.24 3.o6 2.61 2.24 1.90 10 20 31 6o 95 120 2.23 1.84 1.68 1.26 1.08 1.06 15 30 60 90 120 3.53 2.94 2.41 2.03 1.88 Run 18 1.. Run 35 t % Run 48 t %~_ Run 52 t _ _ 5 15 30 61 120 180 3.93 3.20 2.99 2.58 2.12 1.68 5 15 30 60 90 120 1.91 1.15 0.80 0.54 0.50 0.43 5 15 31 6o 90 120 3.84 3.30 3.12 2.93 2.23 1.83 5 15 30 60 90 120 3.75 3.17 2.99 2.49 2.34 2.15 Run 44 t ~ -2 —~ Run 20 t ~I Run 49 t % Run 553 t % 5 15 30 61 90 120 3.66 3.05 2.85 2.44 2.24 2.18 5 15 30 60 90 120 3.77 3.51 3.17 2.76 2.50 2.30 5 15 30 60 90 120 2.59 2.28 1.95 1.59 1.38 1.17 5 15 30 6o 90 120 3.43 3.07 2.68 2.44 2.16 2.10 Run 21 t Run 45 t %_ o Run 54 t lo Run 50 t 5 15 30 60 90 120 3.65 3.06 2.70 2.36 2.12 1.74 5 15 30 35 60 90 120 3.20 3.02 2.52 2.58 2.19 2.01 1.71 6 15 30 60 90 120 2.85 2.36 2.05 1.78 1.75 1.68 5 15 30 60 90 120 3.73 2.92 2,35 1.72 1.32 1.06 * Time, t, in minutes ** Concentration of manganese oxide in slag, weight percent -93 -

APPENDIX B - Continued Run 55 t L Run 90 t, Run 96 t ~ Run 108 t % 12 20 30 60 93 120 3.47 3.19 2.88 2.41 2.00 1.73 25 '.40 55 70 85 100 3.15 2.81 2.58 2.48 2.30 2.11 15 3.35 30 3.07 45 2.81 60 2.58 75 2.42 90 2.24 Run 98 t 0 15 30 45 60 90 600 660 720 780 840 1020 1140 2.86 2.42 2,09 1.86 1.62 0.57 0.48 0.46 0.46 0.43 0.39 0.37 Run 56 t.o 5 15 30 60 90 120 4.16 3.26 2.75 2.14 1.82 1.42 Run 57 t % -2____o 5 15 30 60 90 120 3.74 3.20 2.95 2.41 2.21 2.04 Run 91 t 15 2.79 30 2.45 45 2.04 60 1.94 75 1.88 90 1.63 Run 92 t 15 3.59 30 3.16 45 2.94 60 2.81 75 2.66 90 2.53 Run 93 t % 15 2.58 30 2.19 45 1.86 60 1.81 75 1.68 90 1.50 Run 99 t % 15 2.71 30 2.45 45 2.32 60 2.07 75 2.06 90 1.86 Run 100 t L 20 2.45 35 2.35 50 2.21 66 2.11 80 2.01 95 1.92 15 30 45 60 75 90 4.23 3.80 3.53 3.20 3.10 2.89 Run 109 t, %o 15 1.11 30 0.82 45 0.65 60 0.59 75 0.52 90 0.45 Run 121 t j Run 58 t. 2 4 6 8 60 90 120 3.13 2.90 2.65 2.53 1.86 1.73 1.69 15 30 60 90 120 35.32 2.98 2.85 2.45 2.21 Run 122 t % Run 59 t -_ Run 95 t % Run 101 t % 4 6 10 15 120 150 4.71 4.46 4.13 3.81 2.56 2.55 5 15 30 60 90 120 3.01 2.90 2.64 2.41 2.15 1.90 15 30 45 60 75 90 2.84 2.53 2.37 2.17 1.96 1.82 15 30 45 60 75 90 1.42 1.32 1.20 1.10 1.05 0.97

-95 - APPENDIX B - Continued Run 124 t.. Run 133 t % 15 30 45 60 78 90 105 120 2.72 2.65 2.30 2,2 5 2.09 1.96 1.78 1.70 5 10 15 21 28 35 45 150 3.05 2.95 2.71 2.36 2.46 2.14 2.05 1.63 Run 126 t i% 15 30 45 60 75 90 105 120 2.52 2.18 1.91 1,72 1.59 1.44 1.22 1.06 Run 135 t - 10 o.86 20 0.63 30 0.49 40 0.33 50 0.35 61 0.35 70 0.33 Run 138 __ ____ i.~~an Run 143 3 2.82 6 2.60 9 2.30 12 2.19 15 2.11 18 2.02 21 1.87 25 1.89 60 1.74 90 1.55 120 1.53 Run 146 t,.. 3 4.13 6 3.29 9 2.84 12 2.69 15 2.49 18 2.26 21 2.17 24 2.07 90 1.46 120 1.48 Run 148 -t 3 3.74 6 3.25 9 2.92 12 2.64 15 2.39 18 2.26 21 2.11 75 1.52 90 1.47 3 6 9 12 15 18 21 24 90 120 Run 153 t -, Run 149 t L 3.46 2.99 2.69 2.41 2.28 2.15 2.02 1.96 1.56 1.50 5 10. 15 20 25 30 35 40 0.68 0.59 0.54 0.49 0.45 0.41 0.38 0.35 Run 129 t % 2 2.20 4 2.15 6 2.07 8 1.97 15 1.69 30 1.49 45 1.46 150 1.10 Run 131 t t 5 2.77 10 2.73 15 2.49 20 2.38 25 2.19 30 2.19 35 2.15 40 2.09 140 1.49 5 10 15 20 25 30 35 45 60 0.30 0.27 0.25 0.23 0.21 0.20 0.19 0.17 0.15 Run 140 t Run 154. t. 3 3.03 6 2.71 9 2.43 12 2.26 15 2.15 18 2.06 21 1.96 24 1.89 120 1.51 150 1.49 Run 155 t f 3 3.80 6 3.31 9 2.97 12 2.64 15 2.49 18.5 2.17 22.5 2.09 26 2.00 90 1.47 120 1.48 3 6 9 12 15 18 21 24 240 3.30 3.14 2.94 2.86 2.66 2.56 2.47 2.39 1.69

-96 - APPENDIX B - Continued Run 156 t ffo Run 163 t _i Run 167 t o - Run 218 t _ % 5 0.66 10 0.64 15 0.58 20 0.51 25 0.47 30 0.43 35 0.42 40 0.42 Run 159 ^ __~ w 3 6 9 12 15 18 21 24 120 3.46 3.27 2.88 2.58 2.62 2.30 2.19 2.06 1.55 3 6 9 12 15 18 21 24 120 130 14o 2.04 1.86 1.75 1.58 1.48 1.40 1.37 1.31 0.95 0.93 0.93 Run 164 t % 3 6 9 12 15 18 21 24 120. 3.98 3.35 2.95 2.71 2.49 2.38 2.19 2.09 1.51 3 6 9 12 15 18 21 24 110 120 130 3.74 5.10 2.73 2.54 2.13 1.96 1.87 1.77 1.48 1.45 1.47 Run 172 t % 3.6 9 12 15 135 1.69 1.49 1.40 1.34 1.52 1.24 5 2.74 10 2.58 15 2.54 20 2.50 25 2.i4 30 2.01 45 1.75 60 L.61 75 1.53 90 1.37 Run 223 t... 3 7.03 6 5.64 9 4.66 15 4.08 18 3.97 21 3.88 24 3.81 128 2.95 148 2.96 Run 224 t % 5 3.25 10 2.57 15 1.89 20 1.58 25 1.28 30 1.16 35 0.99 40 0.87 Run 160 t % 3 6 9 12 15 18 21 24 120 3.10 2.82 2.49 2.26 2.15 2.08 1.95 1.85 1.46 Run 166 t % 3 2.88 6 2.43 9 2.23 12 2.06 15 1.89 18 1.76 21 1.70 124 1.61 120 1.28 132 1.30 140 1.27 Run 196 t % 9 3.91 12 3.76 15 3.64 20 3.52 25 3.40 30 3.30 45 3.18 Run 199 t ~ Run 162 t % 3 6 9 12: 15: 18 21 24 120 3.46 2.90 2.58 2.62 2.19 2.00 1.89 1.78 1.22 3 3.20 6 2.81 12 2.54 15 2.19 19 2.11 22 2.04 25 1.98 30 1.96 90 1.64

-97 - Run 225 t % 5 3.99 10 3.77 15 3.77 20 3.51 25 3.46 30 3.46 35 3.27 40 3.12 60 3.06 120 2.76 180 2.49 240 2.22 500 2.01 360 1.82 420 1.67 480 1.55 540 1.43 600 1.31 Run 228 t % 3 4.57 6 4.01 9 5.81 12 3.64 15 3.42 25 3.20 35 2.63 45 2.58 60 2.38 75 2.21 90 1.94

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