THE UNIVERSITY OF MICHIGAN COLLEGE OF ENGINEERING Cast Metals Laboratory Technical Report EQUILIBRIUM IMMISCIBILITY RELATIONS FOR THE DEVELOPMENT OF MAGNESIUM-FERROSILICON ALLOYS P. J. Guichelaar P. K. Trojan R. A. Flinn ORA Project 08681 under contract with: UNION CARBIDE CORPORATION MINING AND METALS DIVISION NEW YORK, NEW YORK administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR January 1969

SUMMARY Magnesium ferrosilicon alloys have been extensively used for the production of ductile cast iron. However, certain properties of the commercially available alloys have limited their more widespread application. Equilibrium data which would define the characteristic parameters of more efficient alloys have not been available because of experimental difficulties. The purpose of this investigation was therefore to determine the extent of the miscibility gap between iron and magnesium in the iron-magnesium-silicon system and also to determine the magnesium vapor pressure relations within the immiscibility envelope. Desired bulk compositions were equilibrated in a specially developed crucible under argon pressure to prevent the magnesium from boiling. Samples were taken in situ from the liquid metal layers for chemical analysis. Magnesium vapor pressure measurements were made using a liquid boiling technique specifically developed for this investigation. The validity of the method was verified by determining the vapor pressure of pure magnesium over a range from 3 atmospheres to 15 atmospheres. The liquid miscibility gap in the iron-magnesium-silicon system at 2650'F can be categorized into three regions: 1. An initial region where the magnesium solubility in the iron-rich liquid increases from 0.85 percent to 2.5 percent as the silicon content increase from 5.3 percent to 17 percent and where the iron solubility in the magnesium-rich liquid remains almost unchanged at 3.0 ii

percent from zero to 10 percent silicon. 2. A region where the magnesium solubility changes rapidly in the ironrich phase to 15.2 percent at 34 percent silicon and the iron content of the magnesium correspondingly increases to 21.5 percent at 33 percent silicon. 3. The critical composition region at a total silicon content of 35 to 40 percent where the two miscibility curves meet. Fourth element additions of cobalt, manganese, carbon, and zirconium had only a minor effect on solubility and vapor pressure relations. The solubility and vapor pressure relations have important implications for the design of more efficient alloys to produce ductile cast iron. Magnesium-iron-silicon alloys with a low silicon-to-magnesium ratio, a high density, and a reasonable vapor pressure are entirely feasible in view of the results. iii

TABLE OF CONTENTS Page LIST OF TABLES v LIST OF FIGURES vi I. INTRODUCTION 1 II. REVIEW OF THE LITERATURE 3 A. Available Equilibrium Information 3 B. Theoretical Considerations 4 III. EXPERIMENTAL METHOD 6 A. Experimental Design 6 1. Solubility Study 6 2. Vapor Pressure Determination 9 B. Experimental Equipment 13 1. Pressure Vessel 13 2. Crucible Preparation 16 3. Temperature Measurement and Control 20 4. Boiling Determination for Vapor Pressure Measurement 22 5. Bath Sampling Device 25 6. Raw Materials 27 C. Conduct of a Typical Experiment 27 1. Component Assembly 27 2. Heat Procedures 30 3. Time to Attain Equilibrium 31 D. Interpretation of Experimental Data 34 1. Chemical Analysis Techniques 34 2. Magnesium Vapor Pressure Analysis 36 3. Regression Analysis of Data Groups 41 IV. DISCUSSION OF RESULTS 43 A. Experimental Data 43 1. Liquid Miscibility Relations at 2650~F 43 2. Temperature Effects on Magnesium Solubility 48 3. Magnesium Vapor Pressure over the Miscibility Gap 48 4. Fourth Element Effects 52 iv

TABLE OF CONTENTS (Concluded) Page B. Theoretical Considerations 53 1. Implications of the Solubility Data 53 2. Implications of the Vapor Pressure Data 58 C. Commercial Applications 62 V. CONCLUSIONS 73 APPENDIX I: CHEMICAL ANALYSIS TECHNIQUES 75 APPENDIX II: VAPOR PRESSURE ANALYSIS PROGRAM 77 APPENDIX III: SOLUBILITY DATA ANALYSIS PROGRAM 81 BIBLIOGRAPHY 94

LIST OF TABLES Page I. Chemical Analysis of Raw Materials 28 II. Chemical Analysis of Time-to-Equilibrium Heats 32 III. Sample Segregation and Chemical Analysis Reproducibility 35 IV. Chemical Analysis of Experimental Heats 44 V. Vapor Pressure of Magnesium in Ternary and Quaternary Melts 50 VI. Solubility Relations as Affected by Additions of Fourth Elements 59 VII. Solidification Behaviour of Compositions Lying on the Ternary Immiscibility Curve 66 VIII. Calculated Nodularizing Properties of Saturated Mg-Fe-Si Alloys 68 IX. Calculated Manufacturing Parameters of Saturated Mg-Fe-Si Alloys 69 vi

LIST OF FIGURES Figure Page 1. Idealized model for vapor pressure determination under boiling conditions. 11 2. The pressure vessel and auxiliary equipment used in the investigation. 14 3. Sectional view of pressure vessel showing interior details. 15 4. Temperature well die and fabricating tools. 17 5. Induction sintering furnace used in crucible fabrication process. 18 6. Crucible die components and fabricating tools. 19 7. Powder compact, sintered crucible, and finished crucible. 19 8. Thermocouple placements for melt and vapor temperature measurement. 21 9. Temperature-pressure relationships during a typical boiling experiment (Heat 238). 24 10. Sampling device and sampling lines. 26 11. Time at temperature to attain equilibrium in the iron-base and magnesium-base liquids. 33 12. Data from Figure 9, Heat 238, replotted to show method of magnesium vapor pressure determination. 39 13. Vapor pressure of pure magnesium. 40 14. The iron-magnesium-silicon liquid miscibility gap at 26500F. 46 15. Temperature effect on solubility relations. 49 16. Vapor pressure of magnesium at 2650~F for compositions lying on the ternary immiscibility curve. 51 vii

LIST OF FIGURES (Concluded) Figure Page 17. Changes in magnesium solubility with fourth element additions. 52 18. The iron-magnesium-silicon liquid miscibility gap at 2650~F, atomic percent basis. 54 19. Silicon partition between the immiscible liquid phases at 2650~F. 55 20. Activity coefficients of magnesium for compositions lying on the immiscibility curve. 61 21. Density of iron-rich portion of ingots from this investigation. 65 viii

I. INTRODUCTION Ductile cast iron with its highly desirable spheroidal shaped graphite has become a significant engineering material following its introduction less than twenty years ago. The range of physical properties which can be obtained and the ease with which complex configurations can be cast compare favorably with its relatively low cost. However, the manufacturing technology associated with producing ductile cast iron is still evolving at a fairly rapid rate, reflecting the complex and little understood underlying physical phenomena. The literature is replete with descriptions of various manufacturing processes which can be used to produce ductile cast iron.(l 2 3) Of these, the majority involve adding magnesium to a molten cast iron bath, either as part of a, master alloy or in elemental form. Since the vapor pressure of pure magnesium is over 10 atmospheres at the usual treatment temperatures, the addition of magnesium is generally accompanied by considerable pyrotechnics. This behavior is common even for the most widely used master alloy, magnesium ferrosilicon. For example, when using the popular 10 percent magnesium, 45 percent silicon, 45 percent iron alloy, over 75 percent of the available magnesium can be lost through oxidation and vaporization. The problem is compounded by the comparative low density of the alloy which causes it to rise to the iron bath surface where it can oxidize and vaporize rapidly. The intimate contact between the alloy and the iron bath is therefore lessened when compared to an immersed condition which would favor higher alloy recovery. 1

2 This family of nodularizing alloys, the magnesium ferrosilicons, has become commercially dominant chiefly due to its low cost, relative ease of application, and consistent nodularizing quality. Nevertheless, the high silicon contents (40 to 50 percent) and low density (3.5 to 4.0 gm/cc) of the common alloys do not represent the most desirable condition. Present manufacturing practice is limited to these silicon contents since at the temperature range for molten ferrosilicon the magnesium vapor pressure exceeds 1 atmosphere at lower silicon contents. Alloys of higher iron content, lower silicon content, and higher density would be very desirable. However, the magnesium solubility and vapor pressure information necessary to define the manufacturing parameters is not available. This investigation was therefore undertaken to determine the solubility relationships within the iron-magnesium-silicon ternary system at low silicon contents and to also determine the corresponding magnesium vapor pressures. Additional effects of fourth elements were also investigated to determine if the basic ternary relations could be modified.

II. REVIEW OF THE LITERATURE The literature pertinent to the equilibrium investigation can be divided into two categories: A. Available equilibrium information. B. Theoretical considerations. A. AVAILABLE EQUILIBRIUM INFORMATION The major objective of this investigation deals with the equilibrium relationships within the ternary system, magnesium-iron-silicon. However, the boundaries of the ternary are the three distinct binary systems which comprise the limiting conditions for these equilibrium relationships. Of these three binaries, the system iron-silicon has been thoroughly investigated, both with regard to phase relations and thermodynamic data.(5'6) The strong negative deviation from ideal solution behavior, characteristic of compound formation as present in this system, is indicative of Fe-Si atomic clustering in the liquid state. Similarly, the phase diagram for the magnesium-silicon system shows compound formation and thus the liquid solutions would also be expected to show a negative departure from ideality.(5) (8) Eldridge, et al., showed the negative deviation in their isopiestic study of the Mg-Si system. The binary system iron-magnesium has not been fully established. The available data indicate that molten magnesium has a very limited solubility for iron.(5) The data of Trojan(9) show a liquid-liquid miscibility gap between carbon-saturated iron and magnesium, with a limited 3

solubility of magnesium in the iron-rich liquid. Sponseller(10) established immiscibility for a similar system, calcium-iron. Thus, for the iron-magnesium system, it appears that there is a very strong positive departure from the ideal solution behavior. Very little information is available for the iron-magnesium-silicon ternary system. Zwicker(11) shows what is essentially a crystallization diagram for compositions containing at least 50 percent silicon. This 50 percent silicon limit was imposed by the magnesium vapor pressure which exceeded 1 atmosphere at lower silicon contents. Significantly, the diagram makes no reference to any immiscibility between liquid iron and liquid magnesium in direct contrast to the findings of Trojan. The results of Trojan indicate a silicon partition factor of 50:1 in favor of the iron-rich phase. Additionally, the magnesium solubility in the iron-rich phase was enhanced by higher silicon contents, but the solubility of iron in the magnesium-rich phase did not appear to increase with higher silicon contents. The results of Sponseller were similar for the effect of silicon which enhanced calcium solubility in pure iron. Therefore, the silicon partition in the iron-magnesium-silicon ternary system should be in favor of the iron-rich phase. B. THEORETICAL CONSIDERATIONS Although there have been attempts to mathematically represent the condition of liquid immiscibility in metallic systems, the theories have not yet been developed to the degree where they could serve in place of laboratory techniques. In a recent review paper, Klodt() points out that the various pre

diction theories cannot yet uniquely define the state of immiscibility. With regard to the more complex condition of a ternary system, he indicated that the elementary correlations obtainable showed major inconsistencies when several known systems were compared. The justification for experimental work in this field is therefore apparent.

III. EXPERIMENTAL METHOD In the present investigation, the effect of silicon on the shape of the miscibility gap between iron and magnesium was determined. Additionally, the magnesium vapor pressure was determined for compositions lying on the miscibility curve. The effect of additions of certain fourth elements on the solubility relationships and the magnesium vapor pressure was also measured. The experimental method developed to make these determinations is described under the following divisions: A. Experimental design. B. Experimental equipment. C. Conduct of a typical experiment. D. Interpretation of experimental data.. A. EXPERIMENTAL DESIGN 1. Solubility Study The particular technique used to study the liquid immiscibility required equilibration of a two-phase melt at a desired temperature and bulk composition under argon pressure. If two-liquid miscibility prevails for these conditions, samples can be removed from each of the liquid layers for chemical analyses. Gibb's phase rue is particularly useful for analysis of a system of this type. It can be stated in a generalized form as 6

7 V =C - P + 2 where V = variance or degrees of freedom C = the number of components P = the number of phases in equilibrium and 2 refers to the phase-rule variables of temperature and pressure. For the situation where iron, magnesium, and silicon are equilibrated under an argon atmosphere, C = 4 (iron, magnesium, silicon, argon) P = 3 (iron-rich liquid, magnesium-rich liquid and vapor phase). Thus, the variance becomes V = 4 - 3 + 2 = 3. When the temperature is held constant and the pressure is maintained constant at some value above the boiling pressure of magnesium, the variance is reduced by 2. Therefore, the variance becomes, V =1. This implies that for a fixed silicon addition, the one degree of freedom has been utilized and the system becomes unique or completely defined. (All other phase variables such as compositions of the liquid phases and vapor phase are fixed.) Correspondingly, if the composition of one of the equilibrium liquid phases is known, the composition of the other liquid phase must be fixed and related to the first liquid in a unique manner. With the conventional

8 representation for ternary equilibrium systems, the relationship would be a unique two-phase tie-line. Therefore, by appropriate changes in the bulk silicon composition over a series of experiments at constant temperature and pressure, the profile of the miscibility gap is traced out and the corresponding tie lines define the two-phase liquid equilibria. The inclusion of argon gas as a phase-rule component does not imply that it represents a solubility parameter. The argon is necessary to establish a system pressure to prevent the magnesium from boiling away. Argon, being an inert gas, does not have a measurable solubility in liquid metals. The effect of this argon gas pressure on the liquid solubility relationships is negligible. However, the gaseous phase is composed of both argon and magnesium vapor and therefore, the presence of argon gas must be considered in the phase rule analysis. In an experiment where the effect of an additional alloying element is to be determined, (Fe-Si-Mg-A-X), the phase rule analysis yields: V = C - P + 2 =5 - 3 + 2 = 4 As before, at constant temperature and pressure, V = 2. To uniquely define this system, two variables must be determined or fixed. For convenience, the silicon content and the alloying element (X) content of the overall mixture can be specified. However, the convenient graphical representation of the ternary system discussed for the previous system cannot be

9 made without the addition of an extra dimension due to the extra degree of freedom in the system. Correspondingly, any unique change in the magnesium solubility in iron rich phase and the iron solubility in the magnesium rich phase must now be a function of both the silicon concentration and the alloying element concentration in each of the liquid phases. Thus the immiscibility gap for the Fe-Si-Mg-X system can be established by suitable chemical analyses of the liquid phases. 2. Vapor Pressure Determination Vapor pressure data can be reliably determined by many quite different techniques. Nesmeyanov, in an extensive review of the subject, has shown the choice of experimental technique to be very dependent upon the temperature range of interest and the magnitude of the corresponding vapor pressures. For pure magnesium at 26500F, an extrapolation of the available data yields a va(T) por pressure of 10 atmospheres. Under these conditions, a variation on the basic liquid boiling method is recommended. The method is based on the observation that a liquid boils when the pressure of its saturated vapor is equal to the external pressure. In 1929, Hartmann and Schneider(17) published vapor pressure data for magnesium obtained from a series of boiling experiments. These data have been considered to be quite accurate by various reviewers.(l6l8l9) Their technique involved measurement of the temperature of a stagnant bath and the vapor temperature at a point just above the bath. With a decrease in the ambient pressure over the bath, boiling (or ebullition) could be made to occur. At that point, the temperature difference between the bath and the vapor decreased

10 to about 20%F from an initial condition of approximately 90'F difference. Also, the indicated vapor temperature profile remained constant over a small incremental distance above the bath surface and then decreased sharply. The reported experimental values were the indicated vapor temperature and the vessel pressure. Nesmeyanov considers the boiling method to be one of the most reliable methods for the determination of high vapor pressures, providing that the experimental technique can accurately delineate the condition of boiling. Temperature and pressure can be reliably determined by various conventional techniques. However, these data become meaningful only when they are obtained under a defined condition of boiling. In the experiments of Hartman and Schneider, the state of boiling was determined by the decreased temperature difference between the bath and the vapor and also by the presence of the constant temperature zone immediately above the bath surface. The experimental method used in the present investigation is derived from that of Hartman and Schneider. The idealized model will be considered at this point. As shown schematically in Figure la, the melt is contained in a crucible and is heated inductively. Since under these conditions, all the heat is generated within the melt, the net heat flux is outward from the melt to the colder vessel walls. The two thermocouples, as shown, measure the melt temperature and the vapor temperature, respectively. The inert gas pressure over the melt is variable as desired. For a typical experimental run, the power input is adjusted such that the bath temperature is constant at the temperature of interest. The vessel pressure, initially at some pressure

l1 MELT VAPOR THERMOCOUPLE THERMOCOUPLE \ II / INLET GAS'??////]t 1o NON BOILING 0G; O 1 CONDITION 9 D 0.0 VAPOR TEMP 0,o' w s'# It DETERMINATION, O o! c O) t, EQUILIBRIUM VAPOR VESSEL PRESSURE CURVE RECIPROCAL TEMPERATURE — (a)l Idea lized Experimental (c) Melt Teperature - Conditions. Pressure Analysis. Data Transposed from (b). IJU nIMELT TEMPERATURE w TEMPERATURE vn a. o b.I a. to tl t2 t3 TI ME ——' (b)Pressure and Temperature Profiles Over the Course of an Idealized Experiment. Figure 1. Idealized model for vapor pressure determination under boiling conditions.

12 above that of the corresponding equilibrium vapor pressure, is then decreased by bleeding off some of the inert gas. As shown in Figure lb, the thermocouples will not indicate any temperature changes until the ambient pressure reaches the equilibrium vapor pressure. At that point, time tl, boiling ensues and the melt temperature decreases, due to the heat required for vaporization. Simultaneously at time tl, the vapor thermocouple indicates a higher temperature due to increased convective heating from the escaping vapors. The system is now in a state of equilibrium boiling; if the pressure is dropped still further, the temperature will drop correspondingly as more liquid is vaporized. However, when the inert gas pressure is increased to its initial value at time t2, boiling ceases immediately and the melt temperature slowly increases to its initial value at time t3. Simultaneously at time t2, the vapor temperature decreases sharply due to the decreased convective heating. There are two independent sets of vapor pressure relations which can be developed from the data of an experiment of this type. First, at the point where the vapor temperature thermocouple indicates a sharp temperature rise, a condition of boiling is indicated. Therefore, the pressure and melt temperature values at that point define a point on the vapor pressure-temperature curve. The second set of vapor pressure relations is derived from a consideration of the melt temperature as a function of ambient pressure. If the melt temperature is plotted against the ambient pressure on a conventional logarithm pressure versus reciprocal temperature graph, as shown in Figure lc, the state of boiling can be defined. Prior to the onset of boiling, only the pressure

13 is changing, while the temperature remains constant. The data thus plot as a vertical line. However, when boiling occurs, both pressure and temperature decrease. The plotted data then reflect the Clausius-Clapeyron vapor pressure relation, d(~nP) _ yap d(l/T) R' which is a straight sloping line on a log P versus 1/T coordinate system. Again, a condition of boiling can be defined and the meaningful pressure and temperature values can be delineated. An experiment of this type thus satisfies the basic requirements of a boiling experiment in that temperature, pressure, and the condition of boiling are precisely defined. The two sets of vapor pressure data determinations can be compared to provide a check on the validity of the experimental technique. The data derived from the second method of analysis also define the vapor pressure as a function of temperature, which adds to the utility of the data. B. EXPERIMENTAL EQUIPMENT 1. Pressure Vessel (9) The pressure vessel originally built by Trojan and later modified by Sponseller(10) comprises the major piece of equipment used in this study. The basic vessel, shown in Figure 2, was originally designed to be experimentally versatile and therefore only slight modifications were necessary for this investigation.

14 Figure 2. The pressure vessel and auxiliary equipment used in the investigation. The essential vessel components and their relative placement are shown in Figure 3. The rack and pinion mechanism was reconstructed to permit remote indexing of various devices over the melt. The four-station control head, located adjacent to the induction coil, can be moved vertically over a range of 4 inches and rotated through 360~. Vertical location is indicated on a calibrated dial to an accuracy of 0.05 inch. Rotational location is achieved to an accuracy within 20 by moving the lower rotating levers against a hinged stop. Prior to the experimental work, the various pressure vessel components were disassembled, inspected, and reassembled. The pressure gauges were cali

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16 brated using a hydraulic dead weight tester. The unit was then pressure tested to 750 psig. The new 600 psig emergency relief valve was also tested to insure the proper relief pressure and provide an index of the speed of the relief. 2. Crucible Preparation The presence of both magnesium and iron along with third and fourth elements in solution at high temperatures posed a unique container problem. Refractory metals such as molybdenum, tantalum, and tungsten have been shown to (20) be very resistant to attack by molten magnesium. However, they can be readily dissolved in molten iron. Conversely, the results of Trojan( and Sponseller(lO) indicated that commercial crucibles such as magnesia, alumina, zirconia, etc., would probably fail prematurely due to selective attack of the (21) binder materials by the highly reactive magnesium. Chiotti, et al., experienced similar problems with graphite, beryllia, and magnesia crucibles in contact with liquid uranium and magnesium. However, they successfully used a crucible made from high purity magnesium oxide with 10 percent magnesium fluoride added as a binder. This formula was selected for this study since both the binder and the matrix are magnesium compounds; possible melt contamination from the crucible is thus minimized. The crucibles used in the investigation are prepared by a tamping method with a magnesium fluoride content of 15 percent as recommended by Chiotti.(2) The reagent grade magnesium oxide and magnesium fluoride powders are mixed for 6 hours in a ball mill and then vacuum dried at 2T50F for 12 hours. The temperature well is prepared by tamping the powder mixture into the die assembly

shown i Figusre l.r Th.< is done on a vibrating tab].e in or.der to achi.eve the ml.axilmum possibl.e density. After talut:lpng, -the inner mnet:al form J.is removed and t-he g~raphi.te s l0eevre wTrhich contai.ns the powder conmpiact il.s p1)aeced:in a. graphi te'cyl.inder wh.ich w:wi:llt. act as a suseeltor in a.n induction fi.:.elid.i Thi's assemnbtly.s then pl.^aced in'the i-nduct'i. on si.nteri.ng furn ace showan ]i.n Fi.gure 5 A sight tube ^I.s pl.aced over the susceptoSr so thiat the tem-lperature of the comjpac.t can be detefrmined with an opt'i.)ca. pyrometer..The susceptor and the lower porti.on:of the sig.lht- tube are ijnlsunlatet d by 1.00 mesth grsaph i.te ^po-wder wh.ichi.c alhSo mini. mizes ox..-u dati.on of the susceptor. The assemb:l.y is heated to 2650:01 in a period of a)bout 20 mni nutes s. The si-nteri ng rxeacton occurs over a te.n)rature range of aproxi. ma-tel]gy 1.900~0' to 22000F. Tfi.s'i<. determined from the gross shri.nkage observed at these ti-;emperatures. Aflter coo ling to room temlperature, the well. -i.s re-moved and ground sli.ghtl.)y eto remnove^ surface i.p..tperfectit,.ons uoi.gu:.re t, Te'l't:mperaur't.'ce wel.A] di e and f'abr'i.a.ta'tlg too]ls,

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20 Over the course of the investigation, certain disadvantages associated with these crucibles became apparent. The crucibles are prone to mechanical failure by either thermal shock or unrelieved expansion of a compacted metal charge. A disproportionate amount of time and labor is required to produce an acceptable crucible. Additionally, even though the melt thermocouple is encased in an alumina sheath, a few instances were noted of corrosive attack of the sheath and thermocouple by the crucible material. This attack is evidenced by premature thermocouple failure. Significantly, there has been no evidence of chemical attack of the crucible walls by the metal bath. 3. Temperature Measurement and Control Melt temperatures are measured with a platinum-platinum 10 percent rhodium thermocouple located within the temperature well of the crucible. Initial trials indicated the thermocouple to be susceptible to attack by the fluoride ions in the crucible body, which lead to a premature catastrophic failure. This failure was remedied by enclosure of the thermocouple within an alumina sheath. The thermocouple assembly and placement are shown in Figure 8. The thermocouple leads are connected through asbestos wrapped compensating leads to the main control panel. At this point, by means of switching circuits, the output can be directed either to one of two continuous temperature recorders or through a bucking circuit to the other recorder. The bucking circuit is incorporated so that a reference voltage from a small laboratory potentiometer can be added to the thermocouple output voltage, thus extending the range of the recorder. There is also provision for the switching

21 D1; O =0 CONTROL HEAD VAPOR THERMOCOUPLE'//////// =z zRADIATION SHIELD o [1.. O.... iiS — GRAPHITE SUSCEPTOR O,,- ~ --- CRUCIBLE I INCH 0. -'Mg BASE LAYER Fe BASE LAYER O:I -------- ALFRAX INSULATION ~!.: INDUCTION COIL |Io~~~.!, O rw'': l REFRACTORY BASE 0:0,0 oo 0 /,,111 oo~.-r._*.o L" MOUNTING BLOCKS:";";". 0,_1 I,0 0.,,'O, -VA SUPPORT BRIDGE LOWER THERMOCOUPLE SUSPENSION DEVICE MELT THERMOCOUPLE Figure 8. Thermocouple placements for melt and vapor temperature measurement. of a semi-precision potentiometer into the circuit to permit calibration and standardization of the recorders. The accuracy of temperature measurement was determined in two separate heats by comparing the temperature indicated by the melt thermocouple with

22 the temperature indicated by a second thermocouple protected by an alumina sheath suspended in the bath. For both heats, the indicated temperature difference was less than 100F, measured with a precision potentiometer. After the second heat, the two thermocouples were checked against a platinum/platinum10 percent rhodium secondary standard thermocouple which had been previously calibrated by the National Bureau of Standards. No significant drift in calibration was observed and thus it was presumed that there was no appreciable contamination of the respective thermocouples. To insure consistent accuracy in temperature measurement, the thermocouple hot junctions are cut back 1/2 inch after each heat and rewelded. All of the thermocouple wire used in the investigation came from one calibrated lot. Additionally, one of the recorders was factory calibrated at the outset of the investigation. The melt temperature is controlled by manual adjustment of the input power. Since there is no electrical feedback from the melt thermocouple, a certain amount of overshoot can occur. However, the indicated temperature could be maintained within 10'F of the desired temperature after an adjustment period of 2 minutes. Considering all the possible sources of error, it is estimated that the indicated temperature lies within 100F of the true temperature. Therefore, the true temperature is estimated to be within 20~F of the desired temperature for any particular heat. 4. Boiling Determination for Vapor Pressure Measurement In the previous section dealing with the design of the vapor pressure experiments, three simultaneous and continuous measurements were shown to be re

23 quiredo These are the bath temperature, the vapor temperature, and the ambient vessel pressure. The bath temperature is monitored continuously by one of the recorders as described previously. The vapor temperature is monitored on the second recorder by means of a thermocouple suspended from the main control head, as shown in Figure 3. At the time of the vapor pressure experiment, the vapor thermocouple, enclosed in an alumina sheath, is positioned just below the susceptor cover, as shown in Figure 8. At this position, the indicated vapor temperature is 300~F to 400~F lower than the bath temperature. Attempts to determine the vapor temperature immediately above the bath surface were largely unsuccessful as the relative position of the surface changes appreciably with small changes in the inductive power input. The ambient vessel pressure is monitored at discrete incremental values. As the vessel pressure is decreased over the course of an experiment, pressure values are read from the gauges on the control panel. At 10 psig intervals, a null button is manually pressed. This action produces a direct short across both thermocouple outputs with the observable effect being an inflection on both strip chart records. The estimated accuracy of pressure measurement is +1 psig. The temperature records from a typical vapor pressure experiment are shown in Figure 9, transposed to one figure for clarity in presentation. The melt temperature profile decreases toward the end. of the experiment, implying a condition of boiling. Concurrently the vapor temperature profile increases to a sustained peak. As the pressure is subsequently increased, the respective temperatures revert to their original values. The analysis of such a

2700 l l l Melt Temperature 2600 U-:Li I t t t t t it t t t:D Decreasing Pressure, psig -- -Vessel I 2500 170 160 150 140 130 120 140 100 90 80 70 RepresLU I II Isurized 2400.Vapor Temperature 0 20 40 60 80 100 120 TIME, SECONDS Figure 9. Temperature-pressure relationships during a typical boiling experiment (Heat 238).

25 record will be presented later in the report. 5. Bath Sampling Device The sampling operation requires inserting two tubes of different length into the bath so that one enters each liquid layer. A representative sample is drawn into each of the tubes; the tubes are then immediately removed from the melto Extreme care must be taken to insure that representative and sufficient samples are removed for subsequent chemical analysis. The magnesium-base liquid is superheated approximately 1500'F above its liquidus temperature. The (9) results of Trojan show that considerable segregation can occur if the samples are not rapidly frozen. Conversely, the iron-base liquid is superheated only about 2000F to 3000F above its liquidus temperature, thus presenting a fluidity problem. If this liquid sample is frozen prematurely, an insufficient sample will be obtained. The sampling operation is further compounded by the extreme difference in densities of the two-liquids. Thus, for a given pressure differential, the magnesium-base sample will rise higher into a sampling tube than will the iron-base sample. After experimental evaluation of several designs, the sampling device described in Figure 10 was developed. The iron-base liquid sampling tube is an alumina tube cemented inside a molybdenum tube to protect against thermal shock. The magnesium-base liquid sampling tube consists of a molybdenum tube with constricting alumina orifices cemented in at the bottom and top. During the sampling operation, the bottom orifice impedes the flow of the magnesiumbase liquid into the sampler. The upper orifice acts both to reduce the pres

LEGEND ( Rubber Sampling Lines ril l l _ (' ~ Upper Alumina Orifice ~ Sampling Tube Holder cA I Il +i - (G Control Head j ~,Molybdenum Tubes | ~I l~~ 0Crucible 0 I j ~ ~ r X (~ Magnesium Liquid Level! I1 E a, (( I Lower Alumina Orifice _-, I_.., X () Iron Liquid Level ( Alumina Sampling Tube ( Pyrex Tee (i Main Sampling Line ( Pressure Vessel Wall ( Needle Valves Figure 10. Sampling device and sampling, lines.

27 sure differential used to draw the sample up and also prevents further flow once the tube is filled. This combination of a flow restricting sampler for the magnesium-base liquid and an open sampler for the iron-base liquid yields sufficient and representative samples for chemical analysis. The pressure differential necessary to force the respective liquids into the samplers is developed by bleeding argon from the sampling line to the atmosphere. This is done after the samplers are positioned within the melt. Argon gas flow control is maintained by suitable adjustment of the needle valves located on the outside of the vessel. 6. Raw Materials The possible influence that small amounts of impurity elements can have on solubility relationships makes the choice of raw materials important. The materials listed in Table I were used for this investigation. C. CONDUCT OF A TYPICAL EXPERIMENT 1L Component Assembly After the various sub-components described in previous sections have been fabricated, a trial assembly is made outside the pressure vessel. The melt thermocouple is adjusted on the thermocouple bridge so that it extends to within 1/32 inch of the top of the crucible temperature well, as shown in Figure 8. The components are then reassembled within the vessel. The melt thermocouple circuit is checked by placing a heated refractory tube around the exposed thermocouple and observing the recorder response. Next, the crucible is inserted and the sampling device is attached to the control head. The relative

28 TABLE I CHEMICAL ANALYSIS OF RAW MATERIALS Material Supplier Major Impurities Ferrovac'E' Crucible Steel vacuum-melted Company Ni 0. 035 pct iron Si less than 0.03 pct Cu 0.01 pct Cr less than 0.01 pet S 0.005 pet C 0.004 pct Al less than 0.003 pet P 0.002 pet Mn 0.001 pet Mg less than 0.001 pet Ca less than 0.001 pet Primary stick Dow Metal Al less than 0.03 pet magnesium Products Company Ca less than 0.01 pet Cr less than 0.001 pet Fe 0.036 pet Mn less than 0.03 pet Ni less than 0.001 pet Pb less than 0.01 pet Si less than 0.01 pet Sn less than 0.01 pet Zn less than 0.02 pet Be less than 0.0001 pet Electronic grade Texas Instruments, Less than 0.0001 pet silicon Inc. total impurities Zirconium Mallory Sharon Metals Fe 0.051 pet Company C 0.025 pet Si 0.006 pet Mn 0.002 pet 0 0.116 pet Electrolytic Union Carbide Less than 0.1 pct total manganese Company impurities Cobalt strip Sherritt Gordon Mines, Ni 0.10 pet Ltd. Cu 0.005 pet Fe 0.018 pet C 0.014 pet S 0.004 pet Graphite'G' Graphite Specialties, Less than 0.5 pet total carbon Inc. impurities

29 positions of the separate sampling tubes are adjusted so that when the control head is at its lowest position, the iron-liquid sampling tube extends to within 3/16 inch of the crucible bottom and the magnesium-liquid sampling tube is located about 3/8 inch above the temperature well. After the sampling lines are attached, the samplers are rotated to the side and the crucible is removed for volume measurement. The crucible volume is measured by adding alcohol from a burette. Two volumes are measured, the volume of alcohol required to just cover the temperature well and the total volume up to a level 5/8 inch from the top of the crucible. These volumes, which represent the desired volumes of the iron-rich liquid and the total melt, respectively, are used to calculate the charge composition. The computation is based upon the elemental liquid. densities, the measured volumes, and an assumed silicon partition. Although it is not precise, the results represent an adequate estimate. After the crucible is replaced in the vessel, the charge is added. A typical charge, weighed to within 0.1 gram, is placed in the crucible in the following sequence. The crushed silicon chips are placed in the bottom up to the top of the temperature well. Then the magnesium slug, cut from a cylindrical rod, is placed in the crucible. The iron slug is placed on the magnesium and any remaining silicon chips are poured into the space between the slugs and the crucible wall. For those heats in which a fourth element is added, the required amount is placed at the bottom with the silicon chips. After the crucible cover and the radiation shield have been positioned, the susceptor plug is attached to the control head. This plug, which fits

30 loosely within the access hole, prevents undue vaporization losses and heat losses. The vapor thermocouple is then attached to the control head and tested for proper response. Lastly, the vessel cover is lowered into position and bolted down. 2. Heat Procedures Before turning the power on, the vessel is evacuated to 500 microns pressure for 1 hour, flushed with argon gas and then evacuated again for 1/2 hour. The charge is heated at a rate of about 2000F per minute to about 20000F and then at a rate not exceeding 100~F per minute. Argon gas is added when the temperature reaches 600~F to a pressure of 25 psig. Additional argon gas is added in several stages, paralleling the temperature rise, until the working pressure is achieved. As the temperature approaches the desired experimental temperature, the power input is adjusted so that this temperature is maintained. The major portion of the solubility study has been conducted at a working temperature of 2650~F. This temperature exceeds the liquidus temperatures across the magnesium-silicon phase diagram and similarly exceeds the liquidus temperatures across the iron-silicon phase diagram for silicon contents greater than 5 percent.(5) Several heats were also conducted at 2550~F and 2750~F to establish the temperature sensitivity of the immiscibility relations. Since the extrapolated vapor pressure of pure magnesium ranges from 95 psig at 2550~F to 182 psig at 2750~F, the minimum working pressures necessary to prevent boiling are established approximately 60 psi higher than the extrapolated vapor pressure, i.e., from 130 psig to 230 psig.

31 After holding at temperature for 2 minutes while making the final minor power adjustments, the susceptor plug is lifted and the vapor thermocouple is moved into position. The switching circuit is set so that the melt temperature is indicated on one recorder while the vapor temperature is indicated on the second recorder. When the vapor thermocouple is indicating a steady value, the exhaust valve is opened slightly. As the vessel pressure decreases, the null button is pressed at 10 psi intervals. After the vapor thermocouple has indicated a sharp temperature increase and the melt temperature has dropped 300F to 500F, the exhaust valve is closed. The vessel is then repressurized to the initial pressure setting. The vapor thermocouple is lifted and the sampling device is rotated into position. A short delay occurs while the bath temperature increases to the initial temperature. The power is then turned off and the samplers are plunged into the melt. After a delay of 3 seconds, to allow the samplers to be heated slightly, the sampling valve is opened and samples are drawn up into the respective samplers. The sampling device is then lifted and the susceptor plug is moved back into its initial position. This entire procedure requires 5 to 6 minutes to complete, measured from the time at which the working temperature initially is reached until the samples are taken. 3. Time to Attain Equilibrium An important experimental factor is the time at temperature to establish dynamic equilibrium between the phases. This variable was investigated by making a special series of heats within a narrow bulk composition range at

32 2650~F. Samples were taken after the melt had been at temperature for 10 seconds, 2, 5, 6.5, and 15 minutes. The resultant chemical analyses are listed in Table II. The general trend of the data, Figure 11, shows that TABLE II CHEMICAL ANALYSIS OF TIME-TO-EQUILIBRIUM HEATS Heat Holding Iron-Base Liquid Magnesium-Base Liquid No. Time V/Mg %Si %0Si /0Fe 181 10 sec 2.21 17.13 6.10 2.66 210 10 sec 2.45 16.58 4.94 2.44 257 10 sec 1.78 16.81 83 2 min 1.94 17.49 7.01 3.30 282 2 min 2.01 16.99 135 5 min 1.94 16.27 4.38 2.81 143-1*** 5 min 2.18 16.91 ** 3.96 -2 2.20 17.21 * * 3.47 209 5 min * * 16.03 4.65 2.13 146-1*** 6.5 min 2.17 16. 83 * * 2.52 -2 2.18 16.99 * * 2.93 183 15 min 2.32 17.19 5.71 1.69 227 15 min 2.56 17.74 *Sample not obtained. **Analysis not obtained. ***Duplicate samples from same melt. equilibrium is attained within a time period of less than 5 minutes. Those points showing the greatest deviation from the general grouping are from heats equilibrated for 10 seconds and 2 minutes. The scatter of these data around the overall ternary solubility curve (discussed later in the results section), implies that the variance inchemical analysis (particularly in the magnesiumrich samples) and the interdependence of magnesium solubility and silicon content are at least as significant as the equilibration time.

33 MAGNESIUM-RICH SAMPLES z 7 ZO ~' 6 LLEGEND __ Fn c 6 Symbol Time at 26500F \ rl V) 0 I 0 Seconds r 5 L 2 Minutes i O 5 5 Minutes 0 6.5 Minutes V 15 Minutes A -- Ternary Solubility Curves 89 90 91 92 93 94 PERCENT MAGNESIUM IN MAGNESIUM-RICH PHASE 18 IRON-RICH SAMPLES z _ -w O3) OX LIJ 16 / 16 2 3 PERCENT MAGNESIUM IN IRON-RICH PHASE Figure 11. Time at temperature to attain equilibrium in the iron-base and magnesium-base liquids.

This relatively rapid rate of equilibration is consistent with the results (9) (10) of Trojan and Sponseller which were 5 minutes and 3 minutes, respectively, for similar investigations. D. INTERPRETATION OF EXPERIMENTAL DATA A typical heat, as described in the previous section, yields the two samples from the equilibrated liquids and the two temperature records from the respective temperature recorders. The analysis techniques used to convert the samples and the temperature records to functional data are described in the following categories. 1. Chemical analysis techniques. 2. Magnesium vapor pressure analysis. 3. Regression analysis of data groups. 1. Chemical Analysis Techniques The samples are analyzed in the analytical laboratory of an industrial research group. These determinations are not commercially routine and the techniques are quite specialized; however, the staff of the research laboratory routinely analyzes various special magnesium-ferrosilicon alloys and therefore is intimately familiar with the general procedures. The specific analytical procedures are described in Appendix I. The degree of segregation within a drawn sample was checked by analyzing two iron-base samples and one magnesium-base sample, each of which was cut into three portions. As shown in Table III, the magnesium content in an

35 TABLE III SAMPLE SEGREGATION AND CHEMICAL ANALYSIS REPRODUCIBILITY Heat Sample Iron-Base Sample Magnesium-Base Sample No. No. %Mg %si %Si %Fe 119 Top 1/3 2.98 * * Middle 1/3 5.58 16.57 Bottom 1/3 16.45 120 Top 1/3 17.25 5.92 22.10 Middle 1/3 4.60 16.76 0.58 8.32 Bottom 1/3 1.50 4.72 10.66 143 Sample 1 2.18 16.91 ** 3.96 Sample 2 2.20 17.21 ** 3.47 146 Sample 1 2.18 16.99 ** 2.52 Sample 2 2.17 16.83 ** 2.93 100 Sample 1 13. 67 32.57 * Sample 2 14.37 33.44 *Sample not obtained. **Analysis not obtained. ***Sampler mispositioning resulted. in two iron-base samples. iron-base sample can vary by a factor of three between different portions of the sample while the silicon content changes very little. Correspondingly, the iron and silicon contents are typically quite low in the middle portion of a magnesium-base sample compared to either end. These variances reflect rapid solidification at the top of a sample and. settling of the heavier microconstituents from the middle portion to the bottom as solidification progresses. Chemical analysis reproducibility is also shown in Table III. For these heats, the experimental variance was minimized by simultaneously drawing two samples from the melt. As shown, the accuracy of magnesium analysis in iron is approximately +0.5 percent of the amount analyzed at the 2 percent magne

36 sium level (+O.OlMg) and +3 percent at the 14 percent magnesium level (+0.35 %Mg). Silicon in iron can apparently be determined to within +~0.9 percent of the amount analyzed at 17 percent Si (+O.l~oSi) and to within +1.5 percent at the 33 percent silicon level (+0.43%Si). A larger deviation would be expected for analyses of the magnesium base sample due to the more severe segregation possible; however, the solubility data do not indicate a severe scatter of points. (9) Trojan indicated chemical analysis accuracy to be approximately +2 percent of the amount analyzed for magnesium in iron at 1 percent levels. The analyses of the present investigation show a similar accuracy at considerably higher magnesium levels which indicates an equivalent if not higher degree of precision. 20 Magnesium Vapor Pressure Analysis Two temperature records with accompanying pressure measurements are available from each heat. The vapor temperature record characteristically shows three distinct zones, as shown in Figure 9. Throughout the first zone, the vapor temperature remains fairly constant, showing only slight perturbations. The second stage is evidenced by an abrupt temperature rise of 100~F to 200~F. This temperature rise is sustained until the vessel is repressurized, at which time the vapor temperature drops to approximately its initial value. This region is denoted zone three. Likewise, the melt temperature, Figure 9, characteristically remains constant during the initial part of the experiment. Then, shortly after the vapor temperature shows an abrupt

37 temperature rise, the melt temperature decreases. This decrease is similarly sustained until the vessel is repressurized, at which time the melt temperature increases to its initial value. Vapor pressure data are derived from a consideration of both the nature of these two temperature profiles and the pressure and melt temperature values. The initial, relatively constant temperature indicated by the vapor thermocouple reflects radiation from the bath, crucible, and susceptor, plus conduction up the sheath to the brass support arm, Figure 8. When boiling begins, the thermocouple is additionally heated by the effusing magnesium vapor giving rise to an abrupt increase in temperature. Next, as the vessel is repressurized, boiling stops and the vapor temperature decreases. Thus, at the point of the abrupt vapor temperature increase which indicates the initiation of boiling, a pressure value can be determined from the pressure reading at this point on the vapor temperature record. The corresponding melt temperature can be determined from the melt temperature record. In this way, each heat therefore gives a definite value of the vapor pressure of the melt at a chosen temperature. The melt temperature record can be used to provide additional vapor pressure information. The initial portion of this temperature profile is maintained as level as possible by adjusting the power input such that all thermal losses are balanced. Then, during the experiment, when the pressure is lowered to initiate boiling, the heat required to vaporize the effusing magnesium results in a steady decrease of the melt temperature. Thus, the condition of boiling can again be defined, although not as distinctly as is possible when

38 considering the vapor temperature record. However, if the set of vessel pressure-melt temperature values from the chart record are plotted as logarithm pressure versus reciprocal temperature, the curve indicated by these plotted points should approach the relations shown for the idealized case in Figure lo Nonboiling conditions are shown by a vertical line and a negatively sloped line reflects the Clausius-Clapeyron relation between temperature and pressure under boiling conditions. Therefore, if these two line segments can be uniquely identified from the data, a condition of boiling can be defined and a relationship can be derived between vapor pressure and temperature. The data interpretation can be best presented by consideration of an example. The heat data shown in Figure 9 are replotted in Figure 12 in the previously described manner. The melt temperature data indicate a slightly lower vapor pressure value (85 psig) than the vapor temperature data (90 psig). This is attributed to the slight thermal lag imposed on the melt thermocouple by the necessary shielding materials. However, the absolute difference, in general, is less than 5 psig regardless of the vapor pressure level measured. As a means of estimating the relative accuracy of the method of determining vapor pressures, data were obtained for pure magnesium over a temperature range of 2300~F to 2800~F. These data, analyzed as described, are shown in Figure 13 and listed in Appendix II. A regression analysis of all the experimental data yields the relation Log Press. (atm) = 4.928 - 1.220 x 104/Temp (~R), +0.017

39 TEMPERATURE, OF 2650 2640 2630 2620 2610 ~~~I.I~. 00I Inc I I -i -j 170 160 1.050 150 140 1.000 130 I-~~~~~~~~~~~~~~~? 120 03.950 a0. w o w CI1~~~~ ~ ~ 0 u. IIIiI IzJ c- 110 a: cn U)~~~~. U) w I cn I~,~.900 w a. I 1-10 o 0850 C -I00: 0, — Vapor Temperature Rise at 90 psig.850 90 -80.800 70.750 03.210 3.220 3.230 3.240 3.250. 3.260 RECIPROCAL TEMPERATURE x104, R Figure 12. Data from Figure 9, Heat 238, replotted to show method of magnesium vapor pressure determination.

40o 1.20 1.10 1.00 w I (f).90 0 Ij.80 0_ ~ LEGEND leMelt Analysis xVapor Analysis u oa These Data:e.60 Log P= 4.928- 1.220 x 104/T ~+.017 Extrapolated Data from Literature: - -.50 Log P 5.021-1.250 x 104/T _ ~.082 3.00 3.10 3.20 3.30 3.40 3.50 3.60 RECIPROCAL TEMPERATURE, IO,000/TOR Figure 15. Vapor pressure of pure magnesium.

41 Since magnesium vapor pressure data for this pressure range were not available in the literature, the data of this study are compared with extrapolated low temperature data. Included are the results of those investi(17,23,24,25) (16) gators considered most reliable by Nesmeyanov and Hultgren, et al. A regression analysis yields the relation: Log Press. (atm) = 5.021 - 1.250 x 104/Temp(~R) +0.082, as shown in Figure 13. The vapor pressure of pure magnesium at 26500F as predicted by the various analyses illustrates the validity and accuracy of the experimental technique. The absolute pressure values are: Predicted Vapor Source Uncertainty Pressure Extrapolated Literature Data 147.1 psia + 28.3 psia Experimental Vapor Temperature Data 141.9 psia + 3.0 psia Experimental Melt Temperature Data 151.0 psia + 5.5 psia All Experimental Data 148.6 psia + 5.6 psia As indicated by these values, the data of the present study are within the uncertainty of the extrapolated data and the combined data (vapor and melt temperature data) agree almost exactly with the extrapolated values. 35 Regression Analysis of Data Groups The various solubility and vapor pressure data groups were analyzed using a standard regression method on a digital computer. The vapor pressure data

42 were fit to a linear equation. As shown in Appendix II, the format was designed so that pressure and temperature values are used for input and output data directly. For the solubility data, regression equations were calculated up to a fifth-order polynomial. The choice of best representation of the particular solubility data group is made on the basis of the calculated standard deviation and the characteristics of the plotted polynomial curve. The program format was also designed to allow average solubility data to be calculated, as shown in Appendix III.

IV. DISCUSSION OF RESULTS The solubility and vapor pressure data obtained in the investigation are presented in Tables IV and V. These data and their significance will be discussed in the following sequence: A. Experimental data. B. Theoretical considerations. C. Commercial applications. A. EXPERIMENTAL DATA For the sake of simplicity in discussion, the experimental data have been divided into several broad categories as shown below: 1. Liquid miscibility relations at 26500F. 2. Temperature effects on magnesium solubility. 3. Magnesium vapor pressure over the miscibility gap. 4. Effect of fourth elements on magnesium solubility and vapor pressure. 1. Liquid Miscibility Relations at 2650~F The liquid immiscibility data for the iron-magnesium-silicon ternary system, shown in Figure 14, form the basis for the discussion of the other equilibrium data. The liquid-solid equilibria in the iron-rich corner of the diagram were constructed from the data given by Hansen(5) for the binary ironsilicon system. The regression program shown in Appendix III was used to construct the profile of the miscibility gap. These regression calculations show an overall standard deviation of o.48 percent magnesium for a fourth-order

TABLE IV CHEMICAL ANALYSIS OF EXPERIMENTAL HEATS Heat Iron-Base Liquid Magnesium-Base Liquid No. %Mg %Si SX si loFe e X Basic Ternary Data at 2650~F 68 * * 29.58 17.01 82 0.97 6.71 o.54 2.76 100-1 13.67 32.53 *** 100-2 14 37 33.44 135 1.94 16.27 4.38 2.81 143-1 2.18 16.91 ** 3.96 143-2 2.20 17.21 ** 3.47 146-1 2.18 16.99 ** 2.93 146-2 2.17 16.83 ** 2.52 180 lo0. 42 30.o6* * 181 2.21 17.13 6.10o 2.66 183 2.32 17.19 5.71 1.69 207 * 4.11 2.77 208 5.66 24.9go 209 ** 16.o3 4.65 2.13 223 1.73 11.76 1.56 2.64 225 6.17 23.43 226 12.33 31.15 * * 227 2.56 17.74 * 238 6.38 25.42 242 o.90 5.84 * * 258 6.10o 25.19 259 10.75 30.92 * * 263 7.86 27.33 264 11.57 30.00 * * 265 4.9go 20.87 278 lo.43 29.56 30.38 17.94 279 5.64 24.57 20.47 8.26 280 3.87 21.18 14.43 4.47 282 2.01 16.99 * * Ternary Data at 25500F 239 1.47 11.62 2.31 1.97 261 8.11 29.36 23.74 9.355 *Representative sample not obtained. **Chemical analysis not obtained. ***Sampler mispositioning resulted in two iron-base samples.

TABLE IV (Concluded) Heat Iron-Base Liquid Magnesium-Base Liquid No. %Mg %Si %SX %Si FFe Ternary Data at 2750~F 240 2.58 11.67 2.40 2.79 260 6.86 26.o8 22.29 12.57 Quaternary Data at 2650~F (Cobalt Series) 283 1.77 10.65 5.40 co 2.23 3.21 0.50 Co 302 7.17 23.09 5.61 co 19.47 6.84 1.23 Co (Zirconium Series) 84 0.87 6.34 3.84 Zr 0.o6 2.37 0.33 Zr 284 1.09 10.02 6.17 Zr 1.25 2.13 0.84 Zr 300 4.83 23.37 7.44 Zr 21.76 8.02 1.10 Zr (Manganese Series) 85 1.12 6.36 3.64 Mn 0.30 2.08 0.90 Mn (Carbon Series) 87 2.25 6.27 3.33 C o.85 2.91 ---

Si I0 90 2~~ ~~0 80 4 30 70 4 ~ 2 ~ 2650'0 ~ 40 60 7039 0 Figur 14.The ron-mgnesum-slioliquid mi sblt gaI t260F 80 205 Z Q-~~~~~~~~~~~~~~~~~~~~~~-+ 10 2 0 0 5 60 70 0 90 Fiur 4.Te ro-ageiu-slco iquid micblt apa 60F

polynomial representation of the iron-rich solubility data and a standard deviation of 0.35 percent magnesium for a second-order polynomial representation of the magnesium-rich solubility data. On the iron-rich side of the liquid miscibility gap, the terminal magnesium solubility is 0.85 percent magnesium at 5.3 percent silicon. The magnesium solubility changes only slightly (0.85 percent to 2.3 percent) as the silicon content increases from 5.3 percent to 17 percent. However, in the range from 17 percent to 34 percent silicon, the magnesium solubility increases from 2.3 percent to 15.2 percent. On the magnesium-rich side of the miscibility gap, the solubility of iron in liquid magnesium at 2650'F is 3 percent. This terminal solubility of iron does not change significantly up to a. silicon of 10 percent. Then, in a manner similar to the iron-rich side, the solubility of iron increases markedly as the silicon content is increased. The tie-lines which extend across the miscibility gap define the respective compositions of equilibrated liquid phases. In a general equilibrated system the tie lines do not have to be parallel nor does the change in their slopes have to indicate that the critical point lies at the summit of the miscibility curve.(26) The tie lines of Figure 14 do indicate slight slope changes with increasing silicon content; however, these slope changes are not wholly in the same direction. The tie-line slopes appear to increase in the initial range up to 15 percent silicon and then decrease as the miscibility envelope becomes smaller. This anomalous behavior is attributed to the marked effect that a small variance in the solubility data at either end of a tie line has on the slope of that tie line. Nevertheless, the general trend shown by these tie

48 lines indicates that the critical point of the miscibility gap lies near the summit of the curve. The exact determination of the midrange solubility relations cannot be more accurately defined with the present experimental technique. Within this composition range (33-50 %Si), the densities of the two liquid layers become almost identical. Under these conditions representative samples of each liquid phase are difficult to obtain since inductive stirring causes intimate mixing of the two liquids into a suspension. 2. Temperature Effects on Magnesium Solubility The basic solubility relations have been established at the primary experimental temperature, 2650~F. To determine their temperature dependence, a series of heats were made at 25500F and 27500F and two bulk compositions. The results, shown in Figure 15, indicate that changes in temperature have only a minimal effect on the solubility relations. Of the eight compositions shown in Figure 15, four apparently are within the standard deviation of the basic solubility curves. Additionally, all of these compositions have an inherent uncertainty. Therefore, although these solubility data indicate slight changes in the extent of the miscibility gap as the temperature changes, this effect is minor when compared with the absolute accuracy of the solubility data. 3. Magnesium Vapor Pressure Over the Miscibility Gap The vapor pressure data obtained over the ternary melts are listed in Table V and are graphically shown in Figure 16. These data can be expressed by the polynomial regression relation:

49 100 MAGNESIUM-RICH LIQUID LEGEND 0 25500 Data 95 0 27500 Data I "a KI Standard Deviation of LLIW-' 2650~Solubility Curve (~$90 -E ~E <> two Liquid Region One Liquid Region z U70 z 60 0 5 10 15 20 25 30 PERCENT SILICON IN MAGNESIUM-BASE LIQUID ~110 W 1 e (Two Liquid Region) bLr ~'__(~.-~ (One Liquid Region) -. n,' z 0 5 I 0 15 20 25 30 a. PERCENT SILICON IN IRON-RICH LIQUID Figure 15. Temperature effect on solubility relations.

50 TABLE V VAPOR PRESSURE OF MAGNESIUM IN TERNARY AND QUATERNARY MELTS Heat Vapor Pressure, psig Iron-Base Chemistry No. Melt Data Vapor Data VMg %Si 0X Basic Ternary Data at 2650~F 179 128 ** 1.50* 12.00* 180 ** 74 10.42 30.06 181 128 128 2.21 17.13 208 ** 100 5.66 24.o90 223 136 137 1 73 11.76 226 72 76 12.33 31.15 242 139 ** 0.90 5.84 258 101 101 6.10 25.19 259 70 ** 10.75 30.92 265 109 107 4.90 20.87 Ternary Data at 2550~F 239 96 95 1.47 11.62 261 83 73 8.11 29.36 Ternary Data at 2750~F 240 195 200 2.58 11.67 260 137 130 6.86 26.08 Quaternary Data at 2650~F (Cobalt Series) 283 124 13 4 1.77 10.65 5.40Co 302 102 108 7.17 23.09 5.61Co (Zirconium Series) 284 ** 132 1.09 10.02 6.17Zr 300 99 102 4.83 23537 7.44Zr *Calculated from general solubility data. **Data not taken.

51 160 LEGEND ) Vapor Analysis Melt Analysis 140 -~ Standard Deviation Pure w IOATM a::I Magnesium o t C) g 120 a. a. _____a_ ___._____8ATM >100 80 Vap. Press(PSIG)=138+0.69 (Si) -~ 0.091 6ATM 0.091 (% Si)2 Std Dev =4.1 60 0 8 16 24 32 PERCENT SILICON IN IRON-BASE LIQUID Figure 16. Vapor pressure of magnesium at 2650~F for compositions lying on the ternary immiscibility curve. Vap. Press. Mag. (psig) = 138 + 0.69 (%Si) - 0.09 (%Si)2 with a standard deviation of 4 psig. Over the range of silicon contents from 5 percent to 15 percent, significant changes in the vapor pressure are not indicated. For higher silicon contents, however, the magnesium vapor pressure decreases significantly to a value of 68 psig at a silicon content of 32 percent. This behavior directly

52 parallels the solubility results which also indicate a marked inflection at about 17 percent silicon. 4. Fourth Element Effects The effect of additions of several fourth elements on the solubility relations are shown in Figure 17. Although the indicated changes in magnesium solubility are of the same magnitude as the standard deviation, certain trends are evident. At the lower silicon values, additions of carbon and cobalt have the greatest effect on magnesium solubility. Manganese and zirconium additions appear to have only a minor effect; however, the two zirconium compositions investigated both resulted in a slight decrease in the magnesium solubility. At 5 LEGEND i --- Ternary Solubility Curve 5.61%Co'O W 0 Cobalt Addition n 6 [ElO Zirconium Addition m | < > Carbon Addition 0o |A Marganese Addition 744%Zr - 4 Standard Deviation C, 5.40%Co Xi 0 5 10 15 20 25C fourth el3.64%Mement6.17% Zradditions. z o 3.84%Zr fourth element additions.

53 the 23 percent silicon level, the cobalt addition of 5.61 percent increases the magnesium solubility by 2.18 percent over the ternary value. Again, the 7.44 percent zirconium addition resulted in a slightly decreased magnesium solubility. The vapor pressure data obtained for the cobalt and zirconium melts at 10 percent and 23 percent silicon appear to be substantially the same as those data obtained for the ternary melts. B. THEORETICAL CONSIDERATIONS An insight into the solution behavior of the two immiscible liquids can be derived from a consideration of the ternary data and the quaternary data. The various implications will be considered first from the standpoint of the solubility relations and then from the standpoint of the vapor pressure data. 1. Implications of the Solubility Data The two-liquid equilibrium in the Fe-Mg-Si system can be idealized as an iron-rich liquid and a magnesium-rich liquid, both of which are competing for the available silicon. When the system is at equilibrium, the activity of silicon must be the same in both liquid phases. However, if the silicon is attracted more strongly by one of the phases, that phase can show a higher silicon concentration then the other phase. The ternary phase diagram, redrawn in Figure 18 on an atomic percent basis, shows this competition for the silicon as the slope of the tie lines in the two-liquid region. A more direct representation is shown in Figure 19. Here the silicon partition, defined as

Si 30 0 ICC~~C~7 p 3 2~~650OF 4 0 60 A'. )~~~~~~~~~~~~~) 80 0 5 Z 9 0 0 0 40 50 6 0 0 9 o LiquTOMC ERCNT RO Figre18 Te ro-mgneiu-slionliui msciiltyga a 250F. atomc percent basis.V~ ~d~- 2

55 30 25 Cn cn 0 20 0 0 F:I, z 0 H'5 azIO 0: z 10 0 O 10 20 30 40 50 MOLE PERCENT SILICON IN IRON-RICH LIQUID Figure 19. Silicon partition between the immiscible liquid phases at 2650OF.

56 mole fraction Si in iron-base phase Si partition = mole fraction Si in magnesium-base phase is plotted against the silicon content of the iron-base liquid. At low silicon contents, the silicon partition is quite large, reaching a value of 28 at 12 atomic percent silicon. This high partition value implies a strong tendency toward Fe-Si atomic clustering in the liquid and, correspondingly, a much weaker tendency for Mg-Si atomic clustering. At silicon contents greater than 30 atomic percent, the slope of the partition curve is rapidly decreasing, resulting in relatively low partition values. Correspondingly, the ternary phase diagram, Figure 18, indicates appreciably enhanced magnesium solubility in the iron-rich phase for this range of silicon contents. The increased solubility for magnesium at higher silicon contents may be interpreted either as (a) the iron and silicon atoms tend to mutually associate thereby reducing the natural repulsion between iron and magnesium atoms, or (b) the addition of silicon makes the iron-base melt more "silicon-like" thereby reflecting atomic clustering between magnesium and silicon atoms. Additional evidence for the possibility of atom clustering in the liquid phases can be derived from a consideration of the critical point composition. The silicon partition curve, Figure 19, extrapolates to unity, the critical point, at about 45 atomic percent silicon. The corresponding iron content shown on the ternary diagram, Figure 18, is approximately 20 atomic percent. This composition can also be approximately calculated by considering that at the

57 critical composition, the liquid structure reflects the two most stable binary silicon compounds Mg2Si and FeSi. Thus, Compound Composition of Compound FeSi 20%oFe 20%Si Mg2Si 20%Si 40oMg Total 20%oFe 40%Si 40%Mg The solubility data of Figure 18 indicate a somewhat higher silicon content in the critical composition range. This probably reflects a ratio of Mg2Si to FeSi other than unity, as assumed here. The addition of a fourth alloying element to an immiscible system of this type presents an even more complex situation. Since, as Klodt points out, the existing theories cannot accurately describe ternary immiscibility phenomena, there is little basis for the prediction of possible relationships in a quaternary. Nevertheless, the data are of some theoretical interest, although they were obtained primarily to determine their possible effects on magnesium solubility and vapor pressure. The four elements chosen, cobalt, carbon, manganese, and zirconium in conjunction with the ternary elements iron, magnesium, and silicon, exhibit quite different inherent characteristics. However, they can be roughly grouped according to their relative positions in the periodic table, their heats of sublimation, their atomic volumes, and their respective electronegativities. On these bases, cobalt and manganese are elementally similar to iron, carbon is similar to silicon, and zirconium is similar to magnesium.

58 The changes in magnesium solubility in the iron-rich phase with fourth element additions are shown in Table VI. In general, these changes are not significant in comparison with the calculated standard deviation (+0.48%oMg) of the ternary data. However, at each major silicon level, a trend is nevertheless evident. The solubility is enhanced by additions of those elements most similar to silicon (carbon) and less significantly by additions of those elements similar to iron (cobalt and manganese). Additions of zirconium resulted in decreased magnesium solubilities. On the basis of this apparent periodic effect on the solubility changes, various interactions could be hypothesized, such as fourth element substitution for silicon, etc. However, due to the paucity of information available for the six binary systems and four ternary systems which form the basis for any one of these four quaternary systems, any further rationalization would be highly speculative. 2. Implications of the Vapor Pressure Data The vapor pressure data were obtained for both pure magnesium (Figure 13) and for compositions lying on the ternary immiscibility curve (Figure 16). For data of this type, the thermodynamic activity of magnesium over the ternary miscibility gap is defined as: P a g (1) Mg po P Mg where P = vapor pressure of magnesium in the ternary solution P = vapor pressure of pure magnesium (standard state is liquid magnesium at the same temperature)

TABLE VI SOLUBILITY RELATIONS AS AFFECTED BY ADDITION OF FOURTH ELEMENTS Heat No.: 84 85 87 284 283 300 302 6% Silicon Level 10% Silicon Level 230 Silicon Level Fourth Element: Zr Mn C Zr Co Zr CO Iron-Base Liquid %Mg*. 87 1.12 1.70 1.09 1.77 4.83 7.17 %Si 6.34 6.36 6.27 10.02 10.65 23537 23.09 lox 3.84Zr 3.64 Mn 3-33C 7.17Zr 5.40Co 7.44Zr 5.61Co Magnesium-Base Liquid %Si 0.06 0.30 0.85 1.25 2.23 21.76 19.47 oFe 2.37 2.08 2.9 2.13 3.21 8.02 6.84 oX O. 33Zr O.90Mn ---. 84Zr O. 50Co 1.10Zr 1.23Co Vap. Press.** NA NA NA 132.3 134.3 100.9 104.2 Ternary Mg-Fe-Si Reference Data (Comparisons based on Si content) %Mg in Fe 0. 97 0.97 0.97 1.20 1.25 5.18 4.99 Vap. Press.** 139.4 139.4 139.4 136.4 135.8 105.1 106.4 AoMg in Fe - 0.10 + 0.15 + 0.73 - 0.52 - 0.35 + 2.18 AVap. Press --- --- --- - 4.1 - 1.5 - 4.2 - 2.2 *All compositions on weight percent basis. **Psig, at 2650~F.

6o Correspondingly, the activity coefficient of magnesium is defined as a P x _ Mg (2) - =(2) Mg NX NX PO Mg Mg Mg where NM mole fraction magnesium in the x-base ternary liquid. mg The activity coefficients of magnesium at 2650'F in the two immiscible liquids are shown in Figure 20. The slight scatter evident in these values is attributed to the variance in the two sets of vapor pressure data. Additionally, calculated values based on silicon partition are used where the magnesium-base liquid composition data is incomplete. Activity coefficients for the data obtained at 2750'F and 2650'F are not included as there are an insufficient amount of data to permit valid conclusions to be drawn. The magnesium base solutions show ideal solution behavior, as the activity coefficients show only a slight decrease from unity over the range N = 0.98Mg to N = 0.60Mg. This ideal solution behavior over this composition range is required at the higher magnesium contents and is consistent with the high degree of superheat at lower magnesium contents. At lower temperatures the solu(8) tion behavior is slightly less ideal, as shown by Eldridge, et al., for the magnesium-silicon system at 1970~F. In direct contrast, the solution of magnesium in the iron-base liquids shows a very strong positive deviation from ideality at low silicon contents. However as the silicon content approaches 0.45 mole percent, the activity coefficient has a value of approximately 2.0, indicating that at higher silicon contents the solution may approach more ideal behavior.

61 1.20 Magnesium-Base Melt m'1.000.80 0.10.20.30.40.50 Nsi IN MAGNESIUM-BASE PHASE _ s60 Iron-Base Melt w 50,40 -L. 0 w 3X UL w 20 0 0_ I I I 0 0.10.20.30.40.50 Nsi IN IRON-BASE PHASE Figure 20. Activity coefficients of magnesium for compositions lying on the immiscibility curve.

62 These activity coefficient data support the conclusions drawn from the solubility data regarding atomic clustering. The very high activity coefficients of magnesium at low silicon contents in the iron-base liquid are quite consistent with the concept of strong Fe-Si clustering to the almost complete exclusion of magnesium. As the silicon content increases, the activity coefficient decreases, implying increased accommodation for magnesium. The vapor pressure data from the fourth element heats are shown in Table VI to be not significantly different from the corresponding vapor pressure data for the ternary heats. Therefore, any discussion of fourth element effects relative to changes in the activity coefficient of magnesium revert to the effect that the fourth element addition has on the overall composition, a subject already considered. C. COMMERCIAL APPLICATIONS The solubility and vapor pressure data have thus far been discussed as a fundamental addition to the physical chemistry of immiscible liquid metal systems. However, the study was originally suggested by a desire to improve the process for the manufacture of ductile iron through modification of existing magnesium-ferrosilicon alloys. The following discussion, therefore, points out the significance and utilization of these data. Magnesium ferrosilicon alloys have gained a substantial share of the nodularizing alloy market. They are relatively economical, flexible in regard to addition method, and yield consistent results. Alloy production is accomplished rather easily and economically by adding magnesium to the molten ferrosilicon

product of the submerged arc furnace. The two most important compositions are the 10 percent alloy (8-10%Mg, 45%Si, balance Fe) and the 5 percent alloy (5%Mg, 45%Si, balance Fe). Although minor amounts of cerium and calcium may also be present, the major constituents are thus seen to be the same as those of the ductile cast iron product. Nevertheless, these alloys also possess certain characteristics which handicap their more widespread use. The most troublesome handicap is the high silicon to magnesium ratios of these alloys, which range from 4.5 to 9.0. Magnesium additions generally constitute about 0.20 lb of magnesium per 100 lb of molten iron. Associated with this magnesium addition is the addition of 0.9 to 1.8 lb of silicon, or a corresponding increase in the silicon content of the ductile iron product of over 1 percent. A silicon pick-up of this magnitude is considered excessive for many operations. Another handicap is the low density of the solid alloy (3.8-4.5 gm/cc) as compared to that of molten cast iron (6.60 gm/cc). Thus if the alloy addition is not mechanically entrapped as in the plunging process, it will readily rise to the surface where the magnesium will burn and be lost. A superior magnesium ferrosilicon alloy would thus be one which has a higher density, a lower silicon content, and a lower magnesium vapor pressure than the present alloy, but which is still economically comparable. Since silicon is a light element and since silicon pick-up is objectionable, replacement of silicon by iron shows some potential. However, this replacement would result in an increased magnesium vapor pressure, based on the results shown in preceding sections. Correspondingly, the present alloy manufacturing process

is relatively unsophisticated. If a major processing change is dictated, the relative economics could be quite drastically affected. Therefore, an optimization of the above considerations is required. The preceding equilibrium results represent most of the information basic to composition optimization. The ternary miscibility curve, Figure 14, indicates the limiting magnesium contents which can be attained at silicon contents less than 35 percent. Magnesium vapor pressure values for these limiting compositions are shown in Figure 16. The effect of fourth element additions on the solubility and vapor pressure relations is shown in Tables IV and V. To provide a reasonable estimate of the density values which can be obtained at various silicon contents, density measurements were made on the iron base portion of selected ingots from this investigation. The results, shown in Figure 21, indicate that at the lower silicon levels, a density almost twice that of the current commercial alloys can be attained. Additional information for composition optimization is derived from consideration of the solidification characteristics of the various compositions. As mentioned previously, the melt thermocouple, which extends up into the crucible, is sensitive to temperature changes. It is thus possible to record the cooling inflections evidenced by the melt after the sampling operation has been completed. It should be pointed out that the basic experimental design was dictated by the desire to obtain immiscibility relationships. The use of the melt thermocouple to record cooling inflections was not meant to represent an optimum technique for the determination of the crystallization of these alloys. On the other hand, the very existence of several inflections in the

65 LEGEND O Iron-base Ingots this Investigation 7 rCQ I V Commercial 5 %Mg Alloy O Commercial 8.5% Mg Alloy 4. 0 10 ~0 30 40 50 NOMINAL SILICON CONTENT Figure 21. Density of iron-rich portion of ingots from this investigation. cooling curves would suggest crystallization relationships which are dependent upon the alloy chemistry. The following discussion, therefore, attempts to rationalize these changes in crystallization as recorded by a technique considered not to be the most desirable for this application. Cooling inflections evidenced by a series of alloys with varying silicon contents are shown in Table VII together with a description of the phases present in the solidified ingots. These phase determinations were made on

TABLE VII SOLIDIFICATION BEHAVIOR OF COMPOSITIONS LYING ON TIHE TERNARY IMMISCIBILITY CURVE Heat Composition Temperature of Cooling Primary Iron Base Mag. Base Curve Inflections Solid Other Phases ) o. %Mg Si %Si %Fe 1 2 3 4 5 Phase 242.90 5.84.60 1.91 2545 2450 2315 2210 Iron-Fe (1) Iron-Mg Mag. -Mg Mag.-Mg2Si, Fe 223 1.73 11.76 1.56 2.64 2510 2300 2277 2250 2209 Iron-Fe Iron-Mg Mag. -eut. Mag.-Fe, FeSi Mg+Mg2Si 181 2.21 17.13 6.10 2.66 2375 2202 2128 2097 1944 Iron-Fe Iron-Mg, FeSi, Mg2Si Ma.g.-Mg2Si Mag.-Mg, FeSi, Fe 280 3.87 21.18 4.43 4.47 2335 2220 2095 1935 Iron-FeSi Iron-Fe, Mg2Si, Mg Mag.-Mg2Si Mag.-Mg, FeSi, Fe 279 5.64 24.57 20.47 8.26 2350 2290 2225 2095 1935 Iron-FeSi Iron-Fe, Mg2Si, Mg Mag.-Mg2Si Mag.-FeSi, Mg, Fe 278 10.43 29.56 30.38 17.94 2380 2220 2080 1935 Iron-FeSi Iron-Mg2Si, Fe, Mg Mag.-Mg2Si Mag.-FeSi, Mg, Fe (1) Fe-iron saturated with silicon. (2)Listed in approximate order of amount present.

67 polished and etched samples using reflected and polarized light to identify the phases on the basis of color, shape, and etching characteristics. No indications of the presence of the FeSi2 compound were detected, even at the highest silicon content studied. All of this basic information then can be used both to predict the behavior of various compositions when applied as a nodularizing agent to produce ductile cast iron and also to predict some of the manufacturing parameters. The results of some sample calculations are shown in Tables VIII and IX. These results can best be discussed by noting the implications over various ranges of silicon contents and comparing these with comparable results for current alloys. The compositions low in silicon content (5, 10, and 25 percent silicon) are characterized by low saturated magnesium contents, comparatively high vapor pressures, and high densities. For low saturated magnesium contents, the magnesium recovery after addition to a cast iron melt should be quite high, as (4) shown by the results of Clark and McCluhan. Their data show an inverse parabolic relationship between magnesium recovery and the magnesium content of the treatment alloy. Thus, since less magnesium has to be used, the amount of silicon also added is reasonably low, in spite of the comparatively high siliconto-magnesium ratios. A factor which could limit the application of these compositions is the amount of alloy which must be added to ensure an adequate residual magnesium content. As shown in Table VIII, a quantity about twice that for current alloys would have to be added. The resulting thermal losses could conceivably be too high. However, these calculations show that the application of these compositions as nodularizing alloys is feasible.

TABLE VIII CALCULATED NODULARIZING PROPERTIES OF SATURATED Mg-Fe-Si ALLOYS Vapor Assumed Lb Alloy Lb Si Nomi~nal Sattd Net Alloy Mg fr04g Ade Si Mg Density, Press., Si/Mg Lvcpsig Si/ Recovery in 100 lb in 100 lb Level Content gm/cc (1)~B Ratio e((2) (3) (4) 5 0.95 7.22 134 6.3 8o% 5.26.26 10 1.20 7.15 134 8.3 70% 4.76.48 15 1.75 6.8_ 127 8.6 57% 4.01.6o 20 3.4o 6.20 116 5.9 37% 5.18.64 25 6.45 5.45 100 5.9 24% 2.58.65 30 10.60 4.70 77 2.8 18% 2.10.63 Reference Data for Current Alloys(2) 45.o 5.0 4.30 (5) 9.0 29% 2.76 1.24 45.o 9.0 5.90 (5) 5.0 20% 2.22 1.00 (l)At 2650'F equilibrium conditions. (2)Reference 4. (3)b alloy= (100)(0.o4) b recovery)( %Mg in 100 alloy Lb Si = (lb alloy)( %Si in alloy 100 ()Less than one atmosphere at 2600'F (O psig).

TABLE IX CALCULATED MANUFACTURING PARAMETERS OF SATURATED Mg-Fe-Si ALLOYS Nominal Sat'd Liquidus Vapor Press. Net Lb Mg Balanced Charge Composition* Si Mg Temp., at Liquidus, Density, per ft3 for 100 lb of Mg-Fe-Si Alloy Level Content ~F psig lb/ft3 Alloy Lb 50oFeSi Lb Fe Lb Mg 5 0.95 2540 95 450 4.3 o10 89.0.95 10 1.20 2510 85 446 5.4 20 78.8 1.20 15 1.75 2375 60 428 7.5 30 68.25 1.75 20 3.40 2335 32 386 13.1 40 56.6 3.40 25 6.45 2350 25 340 21.9 50 43.55 6.45 30 10.60 2380 25 293 31.1 60 29.40 10.60 45 5.0 2375 ** 268 13.4 90go 5.0 45 9.o 2275 ** 243 21.9 90o 1.0o.o *Assumes 10 recovery of all additions. **Less than 1 atmosphere (O psig).

70 The calculated manufacturing parameters shown in Table IX indicate that the production of such compositions may not be entirely feasible. The liquidus temperatures and the magnesium activities are quite high; thus, the vapor pressure at the melting point varies from 5 to 7.5 atmospheres. This imposes rather severe restrictions on furnace design and operations. Additionally, if the material input of molten 50 percent ferrosilicon, cold steel scrap and magnesium ingot is assumed, the dilutions would be so severe that a melting step would be necessitated. A process incorporating an entirely cold charge and a complete melting procedure might be more practical. In any event, the associated manufacturing costs would probably be excessive in comparison with the present process. The intermediate compositions with silicon contents of from 20 percent to 30 percent show a better balance of properties, as shown in Table VIII. The densities are still considerably better than those of the current alloys, the vapor pressures are more reasonable as the magnesium activity is lower, and the silicon-to-magnesium ratios are quite low. Since the saturated magnesium contents are considerably higher than for the lower silicon alloys, the magnesium recoveries should be consequently lower, as predicted again by the results (4) of Clark and McCluhan. However, the silicon pick-up of a treated bath would be reasonably low, since the silicon-to-magnesium ratios are low. Additionally, the amount of alloy addition required is less than for the lower silicon alloys, so the temperature loss of a melt would be expected to be lower after the treatment process. Thus the application of compositions over this range of silicon contents appears to be entirely feasible.

71 Referring to Table IX, the production of these compositions also appears to be more practicable than for the lower silicon alloy. Since both the liquidus temperatures and the magnesium activities are lower, the vapor pressures at the melting points range from about 2.7 atmospheres to 3.2 atmospheres. Suitable pressure furnace designs for this pressure range would be less sophisticated and consequently less costly. Additionally, the amount of magnesium per cubic foot of alloy is almost an order of magnitude greater than for the lower silicon alloys, thus increasing the possible furnace throughput. However, charge calculations similar to those shown previously indicate that a melting step would be necessitated, thus increasing the complexity of the process. The optimum composition range appears to be 20 percent to 25 percent silicon with associated saturated magnesium contents of from 3.4 percent to 6.5 percent. Such an alloy composition would be capable of achieving proper ductile iron treatment at a reasonable magnesium efficiency with a minimum amount of silicon pick-up. Although the production cost would undoubtedly be higher than the current alloy production cost, the density and the contained magnesium per cubic foot of alloy would be higher than the current alloys. There is one additional factor which might be considered. If the magnesium content is lowered while keeping the iron-to-silicon ratio constant, the vapor pressure would also correspondingly decrease. This enhanced property would have to be weighed against the associated increase in the magnesium-tosilicon ratio which could be significant if the magnesium recovery did not increase proportionally. It is conceivable, however, that practical production

72 limitations might favor compositions which do not approach imminent immiscibility. These considerations should become more evident as further development transpires. The data shown for the influence of fourth element additions indicated only minimal effects on solubility and vapor pressure. Therefore, for the elements investigated (Co, Mn, Zr, C) and conceivably for other similar elements, the possible benefits which could be achieved would seem to be chiefly economic. However, under current conditions, the relative low cost of silicon would negate any such promise. The results of this investigation thus show that new composition ranges for magnesium-ferrosilicon alloys are technically feasible, both for application and production. Future optimization of composition limits will be required in order to develop these alloys for commercial application and to evaluate the economic variables. It is felt the best solution to the alloy and economic development problems can now be most readily accomplished by Union Carbide Corporation.

V. CONCLUSIONS The following conclusions may be drawn from the results of the present investigation: 1. A technique for the determination of vapor pressures in excess of one atmosphere has been developed which can be applied to other systems with one highly volatile component. The validity of the technique has been verified by determining magnesium vapor pressures over a range from 3 atmospheres to 15 atmospheres. 2. A crucible design and a sampling technique have been developed which are suitable for future investigations with corrosive high temperature metallic liquids. 3. The liquid miscibility gap in the iron-magnesium-silicon system at 2650~F can be divided into three regions for the iron-base liquid,; an initial region where the magnesium solubility in the iron phase increases from 1 percent to 2.5 percent as the silicon content increases from 5 percent to 18 percent, a rapidly changing region where the magnesium solubility further increases to 14 percent at a silicon content of 33 percent, and the critical composition region (35 to 40 percent silicon) where the miscibility gap is closed. The corresponding iron solubility regions in the magnesium-rich liquid for these levels are: 3 percent at zero silicon, 3 percent at 10 percent silcon, and 21.5 percent at 33 percent silicon. 4. The vapor pressure of magnesium over the ternary liquid at 26500F is 75

74 approximately 134 psig for silicon contents up to 16 percent. At higher silicon contents the vapor pressure decreases significantly reaching a value of 68 psig at 32 percent silicon. 5. The fourth element additions investigated (cobalt, manganese, carbon zirconium) had only a minor effect on solubility and vapor pressure relations. 6. These data provide the necessary information for further development of iron-magnesium-silicon addition alloys through optimization of magnesium content and density. 7. In the iron-magnesium-silicon system, the solubility phenomena can be rationalized on the basis of interaction between the elemental species. Several subjects deserving future work are suggested by this investigation. These include: 1. Utilization of the vapor pressure technique in the single phase areas to describe the iso-activity curves, 2. a similar investigation of systems such as iron-magnesium (transition element) which might be less interactive to further delineate the theoretical aspects of liquid metal immiscibility at high temperature, and, 3. an intensive investigation at several bulk compositions of the effect of fourth elements on solubility relations.

APPENDIX I CHEMICAL ANALYSIS TECHNIQUES The following general analytical procedures, specially adapted to this investigation, were used. A. IRON BASE SAMPLE ANALYSIS 1. Silicon Determination The crushed sample is fused with Na202, the fusion is dissolved in HC1, and the Si02 is dehydrated with HCIO4. (In the case of high SiO2, a double dehydration is made.) The resultant silica precipitate is then filtered, ignited, and weighed. Finally, the Si02 is volatilized with HF and H2.SO4 and the %SiO2 calculated. 2. Magnesium Determination The crushed sample is first treated with concentrated HN03 on a dry platinum casserole with a dropwise addition of HF. Next, HCIO4 is added and the solution is evaporated to fumes. Lanthanum chloride is added to an aliquot of this solution and the magnesium content is determined by Atomic Absorption Spectroscopy. B. MAGNESIUM BASE SAMPLE ANALYSIS 1. Silicon Determination The crushed sample is first treated with concentrated HNO3 in a dry cas75

76 serole. Then HCIO4 is added and heated until the HCIO4 fumes. After cooling, water is added, and the solution is filtered. The filtrate is reserved. The filtered residue is ignited to oxides in Vycor. These cooled oxides are then brushed into an iron crucible for fusion with Na202. The subsequent cooled fusion is combined with the reserved filtrate. From this point the silicon determination follows that for the iron base material. 2. Iron Determination The crushed sample is first dissolved in a dry, platinum dish with HN03, HF, and HCIO4. This solution is then taken to fumes of HCIO4, cooled and transferred to a Pyrex beaker where it is ammoniated, boiled, and filtered. The Fe(OH)3 is dissolved in HC1 and boiled. The iron is reduced with SnC12 and oxidized with titrated K2Cr207 in the Zirmmermann-Reinhardt reaction.

APPENDIX II VAPOR PRESSURE ANALYSIS PROGRAM The program for analysis of vapor pressure data uses a standard linear regression calculation to yield a best-fit line, the standard error of the data about that line, and the correlation coefficient. The calculated results are then used to determine vapor pressure values at selected temperatures from 2000~F to 30000F. The data illustrated here comprise all of the vapor pressure data obtained in this investigation for pure magnesium. Similar calculations were made for all ternary and quaternary heats that yielded suitable melt temperature data. The correlation of the melt temperature data was then checked against the vapor temperature determination to provide an estimate of the accuracy of the data. 77

78 VAPOR PRESSURE ANALYSIS PROGRAM 23 AUG 68 VERSION., FOLLW ING ARE THE RESULTS OF A REGRESSION ANALYSIS USING SU3ROLTINE LINREG. THE RESULT IS AN EQUATION OF THE FORM Y = A + B*X WHERE Y= LOC- OF PRESSURE IN ATMOSPHERES X= RECIFROCAL TEMPERATURE (10000/DEGREES RANKINE) THE EXPERIMENTAL DATA TO BE ANALYZED FOLLOW TEMPERATURE PRESSURE DEG F DEG R PSIA ATM 2290.0 2749.70 44.7 3*04 2.335. 2764.70 44.7 3.04 2315.0 2774.70 49.7 3.38 233O.0 2789*70 54.7 3.72 2390.C 2849.70 64.7 4.40 2410.0 2869.70 74.7 5.08 2445.0 2904.70 84.7 5. 76 240.0 2939.70 89.7 6*10 25_5.0 2984.70 99*7 6.78 253.*C 3009 70 114.7 7.80 2610.o 3069.70 124.7 8*48 2622.0 3081.70 134.7 9.16 2622.0 3081.70 134.7 9.16 2643.0 3 C99.70 134*7 9.16 2645.0 3104.70 144.7 9.84 2720.C 3179.70 169.7 11.54 2740.0 3199.70 194.7 13*24 2745.C 3204.70 194*7 13* 24 2760*C 3219.70 204.7 13.93 2760*C 3219.70 204.7 13.93 2772.0 3231.70 214.7 14*61 2775. O 3234.70 214.7 14.61 27'92.0 3251 70 224.7 15*29 2792. C 325170 224.7 15*29 RESULTS THE EQUATION OBTAINED IS -- LOGP l 4*92797 ) + ( -1.21995 ) * 10000/T STANEARD ERROR OF ESTIMATE = 0.01320 CORRELATION COEFFICIENT = 0. 99839 THE RESULTS WHICH FOLLOW ARE OBTAINED USING THE INDICATED TEMPERATURES IN THE ABOVE EQUATION.

79 TEMPERATURE PRESSURE DFG F EG R 10000/EQEG R LOG P PSIA 200000.0O 2459.70 4. C655 -0.0318 13.66 20 10.00 2469.70 4.0491 -0.0117 14*31 2020*00 2479.70 4*0327 0.0082 14.98 2030*00 2489. 70 4.0165 0.0280 15.68 2040.00 2499*70 4.0005 0.0476 16.40 2050.00 2509.70 3.9845 0O 0670 17.15 2060.00 251 S70 3 9687 0.0863 1.7.93 2070.00 252?9.70 3. 9530 0* 1055 8 74 2080.00 2539.70 3.9375 0.1244 19.58 2090.00 2549.70 3.9220 0. 1433 20.45 2100.00 2559. 70 3.9067 0*1620 21.34 2110.00 2 5 5. 70 3. 8915 0. 1805 22.28 2120.00 25 7U.70 3.8764 0.1989 23.24 21 30.00 2589.70 3.8615 0* 2172 24.24 2140.00 25'. 70 3. 8466 0.2353 25.27 2150.00 2603.7(0 3.8319 0.2533 26*34 2160.00 2619.70 3.8172 0.2711 27.44 21 70.00 2629.70 3.8027 0.2888 28.59 21 80.00 2639.70 3. 7883 0.3064 29.77 2190.00 2649.70 3. 7740 0.3239 30.99 2200.00 26 59).70 3.7598 0.3412 32.25 2210.oO 269.70 3. 7457 0.3583 33.55 2220. 00 2679.70 3.7318 0.37.54 34.89 2230*00 2689.70 3.7179 0.3923 36. 28 2240.00 269.70 3.7041 0.4091 37.71 2250.CC00 27C9.70 3.6904 0.4258 39.19 2260.00 2719.70 3.6769 0.4424 40.71 22 70.00C 2729.70 3.6634 0.4588 42.28 2280.00 2739.70 3.6500 0.4751 43.90 2290.00 2749.70 3. 6368 0.4913 45.56 23000 C 2759.70 3. 6236 O. 5074 47.28 2310.00 2769.70 3*61 05 0. 5233 49.05 2320.C0 2779.70 3.5975 0.5392 50.87 2330.00 2789.70 3. 5 846 0.5549 52. 75 2340.00 27c9.70 3. 5718 0.5705 54.68 2350.00 28C".70 3.*5591 0.5860 56. 67 2360.00 2819.70 3. 5465 0.6014 58.72 2370.00 2829*70 3.5339 0.6167 60 82 2380.00 2 839.70 3. 5215 0 6319 62. 98 2390.00 2849'.70 3. 5091 0.6470 65.21 2400.00 2859.70 3.4969 0.6620 67*50 2410.00 286.,70 3.4847 0.6768 69,85 2420*00 28 79.70 3.4726 0.69 16 72*26 2430*00 2889.70 3, 4606 0.7062 74.74 2440.00 2899.70 3.4486 0.7208 77.29 2450.0 0 29C9.70 3. 4368 0.7353 79.91 2460.00O 2919.70 3.425-0 0.7496 82. 59 2470.00 2929.70 3. 4133 O. 7639 85.35 2480.00 2939.70 3.4017 O. 7780 88. 18 2490.00 2949.70 3. 3902 O. 7.921 91.08

8o TEMPER ATUR E PRESSURE r FG F DiEG R 10000/DEG R LOG P PSI A 2500.00 2959.70 3.3787 O.8061 94.06 2510.00 2969.70 3. 3673 O 8200 97.12 2520.O0 2979.70 3.3560 0. 8338 100* 25 2530.GO 2989.70 3.3448 0.8475 103.46 2540.C 2999.70 3.3337 0.861'1 106.75 2550. O C 3CC. 70 3. 3226 0. 8746 11013 2560. C 3019.7u 3.3116 O.-8880 113*58 2570.0C C 3029.70 3. 3007 0.9013 117. 12 2580.0C 3039. 70 3 2898 0. 9 146 12 O. 75 2590.0C 3049.70 2790 0. 9277 124. 47 2600.00 3 59. 70 3. 2683 0.940 8 12 8. 27 2610.00 306. 70 3. 2576 0.9538 132. 16 2620. 0 30 7 9.70.24 71 0. 9 667 136. b 15 2630.00 308 9 70 3.2366 0. 9795 14023 2640.0C 3OC~.70 3.2261 0. 9923 144. 40 2650.00 3109,I70 3.21 57 1.0049 148*67 2660*.00 3119.70 3.2054 1.01 75 153.04 2670.00 3129.70 3. 1952 1.0 300 157.51 2680.00 3139.70 3.1850 1.0424 162*08 2690.CO 3149.70 3. 1749 1.0547 166.75 2700.00 3159.70 3. 1649 1.0670 171*52 2710.00 1 9. 70 3. 1549 1.0792 176*40 2720.0C 3179. 70 3.1449 1 0913 181.38 2730.00 3189.70 3. 1351 1.1033 186.48 2740.00 3199.70 3.12 53 1. 1153 191.68 2750.00 32CS.70 3. 1156 1.1271 197. 00 2760.00 321 g.70 3.1059 1.1389 202.42 2770.00 322S. 70 3.0963 1.1507 207.97 2780*00 3239.70 3.0867 1.1623 213.63 2790.0OC 3249.70 3.0772 1. 1739 219*40 2800.00 325 9.70 3. 0678 1. 1854 225.30 2810.00 32569 70 3. 05.84 1.1 969 231.32 2820.00 3279.70 3. 0491 1.2083 237.45 2830.C'3289.70 3. 0398 1. 2196 243*72 2840.00 32c9.70 3. 0306 1.2308 250* 11 2850.00C 33C9.70 3. 0214 1*2420 256*62 2860.00 331C.70 3.0123 1.2531 263. 27 2870.00 3329. 70 3.0033 1 ~ 2641 270 05 2880.0C 33 3. 70 2.9943 1. 2 751 276.95 2890.00 3349.70 2.9853 1. 2860 2 84. 00 2900.00 3359.70 2.9765 1. 2968 291.17 29 10.3 0 33659.70 2. 9676 1.3076 298.49 2920.00 33 79.70 2.9588 1.3 183 305.94 2930.00 3389*70 2* 9501 1*3290 313.54 2940.00 3399.70 2. 9414 1.3396 321.27 29 50.00 0 340i9.70 2.9328 1 3 501 329* 15 2960.00o 3419.70 2. 9242 1.3605 337.1 8 29 70.0 0 3429.70 2.91 57 1.3 709 345. 35 2980.CO 3439.70 2.9072 1.3813 353.68 2990.00 344. 70 2. 89.88 1.3916 362.15 3000.00 3459.70 2. 8904 1.4018 370.77

APPENDIX III SOLUBILITY DATA ANALYSIS PROGRAM The program for analysis of the solubility data used a standard nth order polynominal regression calculation. First through fifth order polynominal curves are fit to the input data and the standard deviation of the points about these curves is calculated. Equilibrium magnesium solubilities are also calculated for each curve at integral silicon contents from 1 to 40 percent. Two sets of solubility data are shown in this appendix. The first set comprises the iron-rich compositions and the second set is the magnesium-rich compositions. A fourth-order regression polynomial was judged to fit the ironrich data most satisfactorily and a second-order regression polynomial was judged to best represent the magnesium-rich data. These judgements were based on the relative values of the standard deviations and the characteristics of the plotted curves. The calculated compositions for the two most representative polynominals were used to plot the ternary curves in Figure 14 and for comparative purposes in the succeeding analyses.

82 SOfLUBILITY DATA ANALYSIS' PROGRAM FOCLLOWING ARE THE INPUT AND RESULTS OF A REGRESSION ANALYSIS PROGRAM WHICH ANALYZES SOLUBI LITY DATA USING 5 PCLYNOMIALS FROM FIRST THROUGH FIFTH ORDER INCLUSIVE THE RESULTS-ARE PRESENTED AS AN EQUATION EXPRESSING THE EQUILIBRIUM, MAGNESIUM CITNTENT AS A POLYNOMIAL FUNCTION OF SILICON CONTENT. THE EXPERIMENTAL DATA TO BE ANALYZED FOLLOW: HEAT PC T MG PCT. SI HEAT PCT. MG PCT SI 82 0*97 6.71 100 13.67 32.57 100 14.37 33.44 135 1.94 16.27 143 2.20 17.21 143 2.18 16.91 146 2.18 16.99 146' 2.17 16.83 180 10,42 30.06 181 2.21 17.13 183 2.32 1 7.19 208 5.66 24.90 223 1.73 11.76 225 6*17 23.43 226 12.33 31.15 227 2.56 17.o74 238 6.38 25.42 242 0.90 5.84 258 6*10 25.19 259 10.75 30.92 263 7.86 27.33 264 11.57 30*00 265 4*90 20. 87 278 10.43 29.56 279 5.64 2-4.57 280.3.87 21.18 282 2.01 16.99

83 ______E_.- Ct C._..O.R_.EAiN E....LAIICNU- I ___.__ _ TH $STI.AR0 _EVl_!._O F_ T _HIS. EAXP ERA _OLThA__AU____ CALCULATED CURVE IS 1.5902 FOR A POLYNOM[AL REGRESSION OF CRDER 1~ THE.C. STA!..TS OF THE CALCULA_'E_ PLYNOMIAL ARE: A= -5.703 B(1)= 0.5228 B(2).= 0.0 B 3)= 0.0 ~B314)= 0.0 B(5)= e.o THE CALCULATED MAGNESIUM CCNTENTS WHICH FOLLOW WERE CALCULA'TED USING THE CCNSTANTS LISTED ABOVE. __I'_PCT.,G....PC, _._.___ PCG S. PCT MG 1.0 -5.18 2.0 -4.66 3.0 -4.13 4.0 -3,61 5.0 -3.09 6.0 -2.57 7.0 -2.04 8.0 - 1.52 9.0 -1.00 10.0 -0.4811.0 0.05 12.0 0.57 13.0 1.09 14.0 1.62 15.0 2.14 16.0 2.66 17.0 3.18 18.0 3.71 19.0 4.23 20.0 4.75 21.0 5.28 22.0 5.80 23.0 6.32 24.0 6.84 25.0 7.37 26.C 7.89 27.0 8.41 28.0 8.93 29.0 9.46 30.0 9.98 31.0 10.50 32.0 1 1.03 33.0 11.55 34.0 12.0C7 35.0 12.59 36.0 13.12 37.0 13.64 38.0 14.16 39.0 14.69 40.0 15.21

84 ___THE.. S. _TANRD _ C EV FI A_ N_ BI. _ S E _ A.._ _ AEI A L 41EAA _k._ _AB_3OT _TE__ _ CALCULATFD CURVE IS 0.4t926 FOR A PLLYNCAIAL REGRESSION OF ORDER 2. THE CONSTANTS [)F THE CALCULATED POLYNUMIAL ARE: A= 3.073 B(1)= -,.451 ~ B ( 2):5 C2350 6(3)= 0.0 B(4)= C.,....................._........ __.........._....._..... __._............,:......._.._......_..._........~......_.... _.. _ _ _. _. __._.._.._.......... THE CALCULATEi) MAGNESIUY CONTENTS viHICH FCLLUW WERE CALCULATED USING'THE CONSTANTS LISTED Ab'UJVE. PCT, S. P CT. G. FCPT. SI PCT._ MG PC. SI PC.T MG 1.0 2.65 2.0 2,26 3,0 1,.93 4,0 1.64 5 1.40 6.0 1.2 7.0 1.07 38.: 7 9.0 0.91 10.0 C.91 i11 0 95 12.0 1.04 13.0 1.18 14.0 1.36 15.0 1.59 16.0 _ 1. 8 7 7.0 2.19 18.0 2.56 19.0 2.98 20.0 -3. 45 21.0 3.96 22.0 4.52 23.0 5.12 24.0, 5.78 25.0 6.48 26.C 7,23 27.0 8.02 28.0 8. R6 29:.0 9.75 30.0 __10.68 31.0 11.67 32.0 12.703 33.0 13.77 34.0 14.90 35.0 16.C7 36.0 17.28 37.0 18.55 3.' 19 86 39. 0 21.22 40.0 22.62

85 DATA CORRELATION NUMBER 3 THE STANDARD DEVIATIGN FOR THIS EXPERIMENTAL DATA ABOUT THE CALCULATED CURVE IS 0*.4746 FOR A POLYNOMIAL REGRESSION OF ORDER 3. THE CONSTANTS OF THE CALCULATED POLYNOMIAL AR E _ A= 1.3 3_67 B( 1)= -O 0 912 B(2)= 0.00248 B( 3)= 0.000361 B(4.= 0.0. B( 5).= 0O0 THE CALCULATED MAGNESIUM CONTENTS WHICH FOLLOW WERE CALCULATED USING THE CONSTANTS LISTED ABOVE. PCT SI PC T MG PCT. SI PC T MG PCT. SI PCT. MG 1*0 1.28 2.0 1.20 3*0 1. 13 4.0 1 07 5.0 1.02 6.0 0o99 7.0 0.91 8.0 0*98 9.0 1. 01 10.0 1.06 11. 0 1. 15 12.0 1.25 13.0 1.4C 14.0 1.57 15.0 -1.78 16.0 2.02 17.0 2 31 18.0 2.64 19.0 3 01 20.0 3.43 21.0 3*89 22.0 4*41 23.0 4*98 24.0 5.60 25.0 6 28 26*0 7.02 27.0 7.83 28.0 8. 69 29.0 9.62 30*0 10.62 31*0 11.69 32.0 12.83 33.0 14.04 34.0 15.34 35*0 16*71 36*0 18*16 37.0 19..69 38*0 21*31 39o0 23*02 40*0.24. E1

86 DATA CORRELATION NUMBER 4 THE STANDARD DEVIATION FOR THIS.EXPERIMENTAL DATA ABOUT THE CALCULATED CURVE IS 0.4833 FOR A POLYNOMIAL REGRESSION OF ORDER 4. THE CONSTANTS OF THE CALCULATED.POLYNOMIAL.ARE__:_ A= -0.047 B('1)=.0.3112 B(2) -0.033360 B(3)= 0300.1651 _( 48(= -0.000160 o 8(51=.00 THE CALCULATED MAGNESIUM CONTENTS WHICH FOLLOW WERE CALCULATED USING THE CONSTANTS LISTED ABOVE. PCT. S'I PCT. MG PCT. SI PCT. MG PCT. SI PCT. MG 1.0 0.23 2.0 0. O45 3.0 0.63 4.0 0.76 5.0 0.87 6.0 0.95 7.0 1.01 8.0 1.07 9.0 1.13 10.0 1.23 11.0 1.27 12.0 1.37 13.0 1.49 14.0 1.64 15.0 1o.82 16.0 2.04 17.0 2.31 18.0 2.62 19,0 2.S7 20.0 3.38 21.0 3.85 22.0 4.37 23.0 4.94 24.0 5.58 25.0 6.2 e 26.0 7.03 -27-0 7.85 28.0 8.73 29.0 9 67 30.0 10.66 31.0 11.72 32.0 12.83 33.0 13.99 34.0 1 5.20 35.0 1 6. 46 36.0 17.77 37.0 19.11 38.0 20. 50 39.0 o 21.91. 40.0 23.~35 _

87 DATA CORRELATION NUMBER 5 THE STANDARD DEVIATION FOR THIS EXPERIMENTAL DATA ABOUT THE CALCULATED CURVE IS 0.4934 FOR A POLYNOMIAL REGRESSION OF ORDER 5. THE CONSTANTS OF THE CALCULATED POLYNOMIAL ARE: A= -2.747 B( 1)= 1.2379 B(2)= -0.14576... (3 0.07875 8(4) = -0.001776 B (5)= o 000000159 THE CALCULATED MAGNESIUM CONTENTS WHICH FOLLOW WERE CALCULATED USING THE CONSTANTS LISTED ABOVE. PCT. SI PCT. MG PCT. SI PCT. MG PCT. SI PCT_. MG 1.0 -1.65 2.0 -0.79 3.0 -0.15 4*0 0.33 5.0 0.68 6.0 0*92 7.o t. 08. 80 1.18 9.0 1.26 10. 0 1.31 11. 0 1.37 12.0 1.44 13*0 1.53 14.0 1.66 15.0 1.82 16.0 2.C3 17.0 2.29 18.0 2.60 19*0 2. o6 20.0 3.38 21.0 3*86 22.0 4.39 23.0 4.97 24. 0 5.61 25*0 6.a 1 26.0 7.06 27.0 7.86 28.0 8.73 29.0 9.65 30.0 10.63 31*0 11*69 32. 12*81'33*0 14.02 34.0 15. 31 35*0 16.71 36.0 18. 23 37.0 19.8e 38.0 2.1.68 39.0 23.65 40.0 O 25.*E2

88 SCIUBILITY DATA ANALYSIS PROGRAM FOLLOWI' NG ARE THE INPUT AND RESULTS OF A REGRESSION ANALYSIS PROGRAM WHICH ANALYZES' SOLUBILITY DATA USING 5 POLYNOMIALS FROM FIRST THROUGH FIFTH ORDER INCLUSIVE THE RESULTS ARE PRESENTED AS AN EQUATION EXPRESSING THE EQUIL IBRIUM MAGNESIUM CONTENT AS A POLYNOMIAL FUNCTION OF SILICON CONTENT. THE EXPERIMENTAL DATA TO BE ANALYZED FOLLOW:' HEAT PCT. T G PCT. SI HEAT PCT. MG PCT. SI 68 53.41 -.29-58 82 96*70 O. 54 135 92.81 4.38 181 91.24 6.10 183 92. 60 5. 71 207 93. 12 4. 11 209 93.22 4.65 223 95*80 1.56 278 51.68 30.38 279 71.27 20.47 280 81.iC 14.43

89 DATA CORRELATION NUMBER 1 THE STANDARD DEVIATION FOR THIS EXPERIMENTAL:DATA ABOUT THE CALCULATED CURVE IS 1*9439 FOR A POLYNOMIAL REGRESSION OF ORDER 1. THE CONSTANTS OF THE CALCULATED POLYNOMIAL ARE: A= 99.829 B(1)= -1.5189 8251= 0.0 B(31 = 0.0 THE CALCULATED MAGNESIUM CONTENTS WHICH FOLLOW WERE CALCULATED USING THE CONSTANTS LISTED ABOVE. PCT. SI PCT. MG PCT. SI PCT. MG PCT. SI PCT. MG 1*0 98*31 2*0 96.79 3.0 95*27 4.0 93.75 5.0 92.23 6.0 90*72 7.0 89.20 8.0 87.68 9.0 86*16'10*0 848.64 11.0 83.12 12.0 81.60 13.0 80.C8 14.0 78*56 15.0 77.05 16.0'75 53 17.0 74.01 18.0 72*49 19.0 70.S7 20*0 69*45 21.0 67.93 22.0 66.41 23.0 64.89 24.0 63*38 25.0 61 E6 26.0 60.34 27. 0 58.82 28.0 57.3C 29.0 55.78 30.0 54.26 31.0 52*74 32*0 51.22 33.0 49*71 34*0 48. *1 35. 0 46.67 36.0 45.15 37.0 43.63 38.0 42.11 39.0 40.59 40.0 39. C7

90 OATA CORRELATION NUMBER 2 THE STANDARD DEVIATION FOR THIS EXPER IMENTAL DATA ABOUT THE CALCULATED CURVE IS 0.3463 FOR A POLYNOMIAL REGRESSID4 JF ORDER 2.. THE CONSTANTS OF THE CALCULATED POLYNOMIAL ARE:.. 97. 023................... B( 1 = -0.- 7587 6( 2)- -0 02419 8(3)= 0.0 B(4}= 0.0 B( 5)= o.THE CALCULATED MAGNES IUM CONTENTS WHICH FOLLOW WERE CALCULATED USING THE CONSTANTS LISTED ABOVE. PCT. SI PCT. IMG PC T SI PC T MG PCT SI PCT. MG 1.0 96.24 2.0 95*41 3.0 94 53 4.0 93.6C 5.0 92. 62 6.0 91.60 7.0 90.53 8.0 89.41 9.0 88*24 10.0 87*02 11.0 85.75 12*0 84.44 13.0 83. C7 14.0 81.66 15*0 80.20 16*0 78*69 17.0 77.13 18.0 75.53 19.0 73.88 20.0 72.17 21.0 70.42 22*0 68. 63 23.0 66* 78 24.0 64*.88 25.0 62.94 26.0 60.95 27*0 58.91 28. o 56.82 29.0 54.68 30.0 52.49 31*0 51*. 2 6 32.0 47.98 33* 0 45.65 34t.0 43.27 35.0 40.84 36.0 38. 36 37.0 3 5.84 38,* 33' 27 39.0 30*65 40*.0 27*98

91 DATA CORRELATION NUMBER 3 THE STANDARD DEVIATION FOR THIS EXPERIMENTAL DATA ABOUT THE CALCULATED CURVE IS 0,3696 FOR A POLYNOMIAL REGRESSION OF ORDER 3. THE CONSTANTS OF THE CALCULATED POLYNOMIAL ARE: A= 96*997 B( 1)= -0 7472 B( 2)= -002518 8( 3)- 0.000022 B{) 41:i 0.0 B 1 5! =.0.0 B(5)= 0*0 THE CALCULATED MAGNESIUM CONTENTS WHICH FOLLOW WERE CALCULATED USING THE CONSTANTS LISTED.ABOVE. PCT. SI PCT. MG PCT. SI PCT. MG PCT. SI PCTo MG 1.0 96.22 2.0 95.40 3.0 94.53 4.0 93.61 5.0 92.63 6.0 91.61. 7.0 90.54 8.0 89.42 9.0 88.25 10 0 87.03 11.0 85.76 12.0 84.44 13*0 83.07 14.0 81.66 15*0 80.20 16.0 78*68 17.b 77, 12 18.0 75.51 19.0 73*86 20.0 72.15 21.0 70.40 22.0 68. 60 23*0.66*75 24.0 64.86 25.0 62.91 26*0 60.93 27.0 58 89 28*0 56.81 29.0 54.68 30.0 52.K50 31*0 50.28 32.0 48*01 33*0 45.69 34*0 43.33 35.0 40.92 36.0 38*47 37* 0 35 97 38.0 33.42 39.0 30.83 40.0 28.2 _

92 OATA CORRELATICN NUMBER 4 THE STANDARD DEVIATION FOR THIS EXPERIMENTAL DATA ABOUT THE CALCULATED CURVE IS 0,3918 FOR A POLYNOMIAL REGRESSION OF ORDER 4 THE CONSTANTS OF THE _CALCULATED POLYNOMIAL. ARE:* _A=. 97.094 B( 1= -0.8336 B(2)= -0.00818 B( 3 ) = -0 000990 B(4- 0.0000179 B 5)-= 0.0 THE CALCULATED MAGNESIUM CONTENTS WHICH FOLLOW WERE CALCULATED USING THE CONSTANTS LISTED ABOVE. PCT. SI PCT, MG PC T, SI PCT, MG PCT* SI PCT. MG 1.0 96.25 2*0 95.39 3.0 94, 49 4.0 93.57 5*0 92* 61 6*0 91,61 7.0 90.56 8.0 89.47 9.0 88*33 10. 0 87, 13 11.0 85. 88 12.0 84*57 13.0 83.21 14.0 81*79 15.0 80.31 16*0 78*78 17,0 77.19 18*0 75.55 19.0 73. 85 20.0 72 10 21*0 70.30 22.0 68.45 23*0 66. 56 24.0 64. 63 25.0 62.617 26.0 60.67 27.0 58*66 28.0 56.62 29.0 54,56 30.0 52.50 31*0 50.44 32*0 48.38 33.0 46.34 34.0 44.3-2 _35.0 42.33 36.0 40. 38 37.0 38.48 38*0 36*63 39*0 34, 86 40. 0 33* 16

93 DATA CORRELATION NUMBER 5 THE STANDARD DEVIATION FOR THIS EXPERIMENTAL OA'TA ABOUT THE CALCULAT'ED CURVE IS 0.4195 FOR A POLYNOMIAL:REGRESSION OF ORDER ~5. THE CONSTANTS OF THE CALCULATED POLYNOMIAL ARE: A= 97,241 B l) - 1,344 8(2)= 3.04892 8(3)= -J 0.06614 B44)' 0.0002420 8( 5 )= - 0.0000 0309 THE CALCULATED MAGNESIUM CONTENTS WHICH FOLLOW WERE CALCULATED US-ING THE CONSTANTS LISTED ABOVE. PCT, SI PCT, MG -PCT. SI PCT. MG PCT. SI PCT. MG 1.0 96.25 2.0 95.32 3,.0' 94.42 4.0 93. 52 5.0 92.61 6.0 91 66 7.o-0.....90.-66 8.0 89,.60 9.0 88.48 10.0 87 29 11. 0O 86.02 12.0 84.69 13. 0 883.929 14 0 81, 83 15.0 80 31 16,0 78,74 17.0 77.12 18.0 75,46 19,0 73. 6 20.0 72.03 21.0 70.27 22.0 68.45 23.0 66.67 24.0 64.82 25.0 62 94 26.0 61.01 i 27.0 59.02 28.0 56. $6 29.0 54.80 30.0 52.52 31.0 50.09 32.0 47.468 33.0 44.64 34. 0 41. 52 35.0 38.09 36.0 34,26 37,.0.2 9'. 8 38.0 2 25.17 39. 0 19o.75 40.0 13.63

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UNIVERSITY OF MICHIGAN 3 9011111111111111111111111111111111111111111111111115 03027 6847 3 9015 03027 6847