LTHE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING DETERMINATION OF NITRIDE SOLUBILITY PRODUCTS IN THE SOLVENT LI-QUID IRONX: ~,:.. Donald B. Evans A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the University of Michigan Department of Chemical and Metallurgical Engineering 1963 February, 1963 IP-606

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ACKNOWLEDGMENTS The author takes this opportunity to express his appreciation of the assistance rendered him from numerous sources during the preparation of this dissertation. The greatest debt is owed to Professor Robert D. Pehlke who chaired the doctoral committee. Professor Pehlke, whose own doctoral thesis formed the point of departure for this research, was always available for consultation and made many important and valuable suggestions in shaping the course of the investigation. The guidance of the remainder of the doctoral committee, Professor Richard E. Balzhiser, Professor Lee 0. Case, Professor Clarence A. Siebert, and Professor Lawrence H. Van Vlack is also appreciated. Professor $iebert was particularly helpful in the experimental phase of the investigation. Mr. Robert N. Katz who is presently associated with the Watertown Arsenal, Watertown, Massachusetts made the x-ray analyses of the extracted nitrides. Dr. David L. Sponseller who is presently Assistant Professor o Metallurgy at the University of Notre Dame, South Bend, Indiana develope the method of fabrication of the TiN crucibles used in the quenching method of this study. Both his equipment and his knowledge of fabrication techniques were generously made available to the author. Professor J. H. Burkhalter of the College of Pharmacy, University of Michigan provided assistance in the developement of the also made laboratory facilities available for the initial stages of this work. ii

The Carborundum Company donated the AlN crucibles which were used in the quenching experiments. Financial assistance to the author during the course of the investigation was provided by a research contract sponsored by the Atomic Energy Commission. The reproduction of the dissertation was performed by the Industry Program of the College of Engineering, of the University of Michigan. Mr. David F. Evans aided in the preparation of the manuscript. iii

-TABLE OF CONTENTS Page ACKNOWLEDGMENTS ii ~~~~~~~~~~~~IS~~~~~~~~~T OF TABES,,,. 0 IXST OF %%G Re e ~ F eteS ~ ~,. ~ ~ ~ ~ ~ o e ~ 9 e ~ e e 0 9 ~ ~ e 9 9 ~ ~ oe ~ e e * e e X LIST OF TABLES.,,N..............,................, ii LIST OF FIGURES t t * 0 0 * 0 * II SURVEY OF PREVIOUS WORK.,*............ 4 o 2 A. Solubility of Nitrogen in Pure Liquid Iron and Adherence of Dilute Alloys to Sieverts'-Law.......... 2 B. Nitride Solubility Products in Liquid and Solid Iron. * **** **Oe*. * * * *ee* * ** e.ee ee e~ oe 4 C. Nitride Phase Compositions............. 7 A-~ GenOF T...........,,.........................,.. 10 ]III. OUTLINE OF THE PROBLEM.....99t.**....9. 10 A. General.95. 9.. 0 0, 9 *9, 10 B. Systems Chosen for Experimentation........... 10 C. Experimental Methods.......................... 11 D. Possible Methods of Correlating the Experimental Results... e 9 e e O o e e 11 IV. EXPERIMENTAL METHODS AND PROCEDURES..................o 22 A. Comparison of Sieverts MethOd and Quenching Method.. 22 B. Experimental Procedure for the Sieverts Method......- 26 C. Experimental Procedure for the Quenching Method..... 34 D. Determination of the Nitride Phase Composition..... 38 V. RESULTS AND DISCUSSION................4........ 40 A. Calculation of Results From the Sieverts Measurement s.......... e o * e * e e e * * * * e * Q e e e 40 B. Summary of the Nitrogen Absorption Curves Determined by the $ieverts Method. o,.... o..,........ 41 iv

'T BLE OF' CONTEN-S CONT'D Page C. Calculation and Summar of the Interaction Parameters e and e.......43 N 4 D. Calculation and Summary of the Interaction Parameters e...........................,..... 59 E. Calculation of the Nitride Solubility Product by the Method of Interaction Parameters............ 62 F. Calculation of the Nitride SQlubility Product Using the Nitrogen Activity Determined by the Gas Phase.. 62 G. Calculation of- the Nitride Solubility Product Using the j Activity Estimate.d From Fe-j Binary Data. 68 H. Calculation and Summary of Enthalpy and Entropy of Decomposition of Nitrides in Liquid Iron........... 71 I. Discussion of Results of the Various Methods Used to Calculate the Nitride Solubility Products....... 80 J. Summary of the Nitride Solubility Products Measured by the Quenching Method....................87 K. Summary of Methods Used to Determine the Nitride Phase Compositions................ 96 VI. DISCUSSION OF ERRORS............................ 103 A. Sieverts Method............................ 103 B. Quenching Method..........10......................7 VII. CONCLUSIONS...................... 109 VIII. APPENDICES.......................................................111 A. Charge Material Analyses............................111 B. Temperature Calibration.........1.....1...... 15 C. Flowmeter Calibration......................... 117 D. Methods of Chemical Analysis............... 120 E. Methods of Fabrication of Nitride Crucibles....... 122 F. Nitrogen Absorption Curves..................,125

TTABLE OF CONTENTS CONT'D Page G. Calculation of Nitride Compositions by Phase Rule Analysis,...,............ 156 H. X-ray Data......................... 161 I, Calculation of Activity Coefficients in Liquid. Iron.. 167 J. Fre e oeeeee.e.ee.~eee..e... En AeN- fee J. Free Energy of Formation of AiN from the Pure Comnponents..................e... 9......... 170 IX. BIBLIOGRAPHY....,.............,........... 172 vi

LIST OF TABLES Table Page I Summary of Denitrifying Constants Estimated by Chipman7........,,.......... 4 II. Advantages and Disadvantages of the Sieverts Method.... 23 III. Summary qf Measured Values of the Interaction Parameters eN and e 58'3 IV. Summary of Values of the Interaction Parameter e.... 61 V. Summary of the Solubilityy Produ:ts- K't and K Calculated by the Interaction Parameter Method.................... 63 VI. Summary of the Solubility Products Kt and K Calculated Using the Nitrogen Activity Determined from the Gas Phase for the Systems Boron, Vanadium, Columbium, and Tantalum.. 66 VII. Comparison of K Values for the Vanadium System Calculated for Different Values of the Interaction ParamV eter eV,.... 67 VIII. Activity of Silicon in Fe- i oluutions at 14200C. From the Data of Chipman et al 34.. 70 IX*, Calculated Activity of Silicon in Fe-Si.Solutions of 34.0% and 36.7% Silicon at Temperatures from 1420~C to 1700. C..72 X. Summary::of K.Values for the Silicon System Calculated Using the Activity of Silicon Estimated from Fe-Si Binary Data. 7.. * *..... e,o 1 a 5....... 73 XI. Summary of Values of Enthalpy and Entropy of Decomposition of Nitrides in Liquid Iron......... 81 XII. Summary of Results Obtained by the Quenching Method.... 90 XIII. Results of Wet Chemical Analysis of Extracted AlN Residue.9 9 e - 0 O'Oa o 0 a- e O e 0...,*0q 99 vii

LIST OF TABLES CONTI'D Appendices Table Page A-I. Supplier's Analysis of Iron Melting Stock....,,,......, 111 A-II. Supplier's Analysis of Aluminum Melting Stock.,,,,,,, 112 A-III. Supplier's Analysis of Boron Melting Stock,....... 112 A-IV. Supplier's Analysis of Columbium Melting Stock...... 112 A-V. Supplier's Analysis of Silicon Melting Stock.......... 113 A-VI. Supplier's Analysis of Tantalum Melting Stock.......... 113 A-VII. Supplier's Analysis of Titanium Melting Stock.......... 113 A-VIII. Supplier's Analysis of Vanadium Melting Stock.......... 114 A-IX. Supplier's Analysis of Zirconium Melting Stock......... 114 B-I. Comparison Between True and Observed Temperature Scales for the Sieverts Apparatus................... 116 B-II. Comparison Between True and Observed Temperature Scales for the Quenching Apparatus................... 116 C-I. Flowmeter Calibration Data for the Quenching Apparatus............................................. ll8 C-II. Calculated Nitrogen Pressure for Various Combinations of Flowmeter Settings.......................... 119 G-I. Nitride Compositions Calculated from the Phase Rule Analysis....................................... 156 H-I. X-ray Data for Titanium Nitride Samples from the Sieverts Apparatus............................. 161 H-II. X-ray Data for Aluminum Nitride Samples from the Sieverts Apparatus........................ 162 H-III, X-ray Data for Boron Nitride Samples from the Sieverts Apparatus....................................... 163 H-IV. X-ray Data for Columbium Nitride Samples from the Sieverts Apparatus............................. 165 viii

LIST OF TABLES CONT'D Appendi ce.s' Table Page H-V, X-ray Data for Vanadium Nitride Samples from the Sieverts Apparatus..........,.............. 164 H-VI, X-ray Data on Raw Materials Used to Fabricate Nitride Crucibles for the Quenching Method................ 165 I-I. Calculated Values of A. for the Titanium, Zirconium, Aluminum, and Boron Sysems....................... 169 J-I. Free Energy of Formation of AiN from the Pure COmponents..................................... 171 ix

LIST'OF FIGURES Figure Page 1 Absorption of Nitrogen by an Fe-j Melt.............. 14 2 Schematic Diagram of the Sieverts Apparatus..,........ 27 3 Sieverts Apparatus Reaction Chamber.............. 28 4 Relation Between Apparent Hot Volume of Reaction Bulb and Pressure at 1600~C.......... 32 5 Schematic Diagram of the-Quenching Apparatus........ 36 6 Effect of Titanium on the Solubility of Nitrogen,.... 45 7 Effect of Zirconium on the Solubility of Nitrogen..... 46 Effect of Aluminum on the Solubility of Nitrogen...... 47 9 Effect of Boron on the Solubility of Nitrogen......... 48 10 Effect of Vanadium on the Solubility of Nitrogen...... 49 11 Effect of Columbiuxm on the Solubility of Nitrogen.... 50 12 Effect of Tantalum on the Solubility of Nitrogen... 51 13 Effect of Silicon on the Solubility of Nitrogen....... 52 14 Variation of eTi and eN with Reciprocal TemperatureN N54 ature...... O...... O,,........... D. 9 ~~ ~ ~.*.. 54 15 Variation of eAl eb e and e with RecipeN, eN N eN, rocal Temperature..~..............*0............. 55 B 16 Variation of eB with Reciprocal Temperature..... 56 17 Variation of eSi with Reciprocal Temperature....... 57 18 Activity of Silicon in Binary Fe-Si Solutions-at 1420OC...~' 69 19 Variation of Equilibrium Constant With Temperature for the Reaction TiN(s) =Ti + N.............. 74 20 Variation of Equilibrium Constant With Temperature for the Reaction ZrN(s) = Zr + N................... 74 21 Variation of Equilibrium Constant With Temperature for the Reaction AlN(s) - A1 + N............... 75 x

LIST OF FIGURES CONT'D Figure Page 22 Variation of Equilibrium Constant With Temperature for the Reaction BN(s) = B + N............ 76 23 Variation of Equilibrium Constant With Temperature for the Reaction VN(s) = V +.N...,.............. 77 24 Variation of Equilibrium Constant With Temperature for the Reaction CbN(s) = Cb + N0................ 78 25 Variation of Equilibrium Constant With Temperature for the Reaction Si3/4 N(s) = 3/4Si + N....... 79 26 Extrapolation of log K' to Zero Percent j in the Aluminum and Boron Systems.......................... 88 27 Extrapolation of log K' to Zero Percent j in the Vanadium and Col umbium Systems.................... 89 28 Solubility of Nitrogen in Pure Liquid Iron at 1600~C... 92 29 Variation of Equilibrium Constant With Temperature for the Reactions TiN = Ti + N, Til.7N( ) 1.7Ti + N, and Ti2.4N(s) = 2A.4{ + N......... 98 30 Variation of Equilibrium Constant With Temperature for the Reaction V2.5N(s) = 2.5V + N...................... 100 31 Variation of Equilibrium Constant With Temperature for the Reaction Cb2N() = 2Cb N............... 100 xi

LIST OF FIGURES. CONT'D Appendices Figure Page F-1 - F-6 Nitrogen Absorption Curves for the Titanium System..e *. *.. 126 - 128 F-7 - F-15 Nitrogen Absorption Curves for the Zirconium System............................. 129 _ 134 F-16 F-24 Nitrogen Absorption Curves for the Aluminum System.... *.................................. 134- 140 F-25 - F-30 Nitrogen Absorption Curves for the Boron System..... 141 - 146 F-31 - F-35 Nitrogen Absorption Curves for the Vanadium System.. 147 - 151 F-36 - F-39 Nitrogen Absorption Curves for the Columbium System. 151 - 153 F-40 Nitrogen Absorption Curve for the Tantalum System... F-41 - F-42 Nitrogen Absorption Curves for the Silicon System... 155 G-1 Phase Rule Analysis of the O.2128A Titanium Nitrogen Absorption Curve.................. 157 G-2 Phase Rule Analysis of the 0.318% Titanium Nitrogen Absorption Curve.....e,.........., 158 G-3 Phase Rule Analysis of the 1.34% Aluminum Nitrogen" Absorption Curve....,.,...o..o......,..* o.,....,,.. 159 G-4 Phase Rule Analysis of the 1.57% Aluminum Nitrogen Absorption Curve......... 160 xii

ABSTRACT The object of this investigation was to determine the solubility- products of several alloy nitrides in the solvent liquid iron at temperatures in the vicinity of 16000~C the temperature range of steel-making processes. The alloying elements chosen for study were titanium, zirconium, aluminum, boron, vanadium, columbium, tantalum, and silicon. The variables studied were the concentrations of alloying element and nitrogen in the solution from which the nitride was precipitated and the temperature of the solution. Two experimental approaches were employed, a Sieverts method and a quenching method. In the Sieverts method a liquid iron melt containing a known concentration of alloying element at a known temperature was equilibrated with nitrogen gas at various pressures between zero and one atmosphere. The nitrogen solubility at which a departure from Sieverts' Law appeared was measured. From this nitrogen concentration and the known alloy concentration, the alloy nitride solubility product was calculated. In the quenching method a melt of pure iron was equilibrated at a known temperature under a known partial pressure of nitrogen gas with a crucible. made of the alloy nitride whose solubility product was to be measured. The melt was then quenched and analyzed by wet chemical methods for dissolved nitrogen and the alloying element. From these analyses the alloy nitride solubility product was calculated. The composition of the alloy nitride phase was determined primarily by xiii

x-ray analysis. Good agreement of results between the two experimental methods was achieved. The stability of the nitrides studied in contact with liquid iron at 16000C was found to decrease in the order TiN, ZrN, AiN, BN, VN, CbN, TaN, and Si3N4. Only TiN, ZrN, and AiN were found sufficiently stable to contain a liquid iron melt without seriously contaminating it under conditions approaching thermodynamic equilibrium. The solubilities of all nitrides were found to increase with increasing temperature. A thorough investigation of the variables composition and temperature permitted the calculation of the free energy, enthalpy, and entropy of precipitation of the nitrides from liquid iron solution. The interaction parameter approach proposed by Wagner was found to give a reasonably accurate representation of the activities of the alloying element and nitrogen in liquid iron solution at concentrations up to the nitride solubility limits for all of the.alloying elements except silicon. xiv

I. INTRODUCTION The solubility of nitrogen in liquid iron alloys and the interaction of nitrogen with dissolved alloying elements in liquid iron has been the subject of a number of research investigations. Most of this work however has been reported for concentrations well below those necessary for the formation of the alloy nitride phase. Data in the concentration region near the solubility limit of the alloy nitride, particularly for systems exhibiting stable nitrides, are important for at least two purposes not served by data taken in the dilute concentration region. First they are necessary in evaluating the denitrifying power of various alloying elements in a metal bath. Second they are necessary in determining the stability of a given nitride if it is used as a refractory to contain liquid iron alloys. This latter application of nitrides in particular has recently been receiving considerable attention.

II. SURVEY OF PREVIOUS WORK A. Solubility of Nitrogen in Pure Liquid Iron and Adherence of Dilute Alloys to Sieverts' Law The published work of the past twenty-five years on the solubility of nitrogen in pure liquid iron at one atmosphere nitrogen pressure and 16000C has been well summarized by Pehlke and Elliott.(l) They present solubility values in weight per cent nitrogen dissolved from nineteen different researches. The solubility values range from 0.030% up to 0,055% with the majority lying between 0.040% and 0.050%. Values have been measured by both the Sieverts method and the sampling method and no trend depending on the experimental method is apparent. The same researches show the temperature coefficient of nitrogen solubility to be small and positive ranging generally between zero and 3 x 10-5 weight per cent nitrogen per degree centigrade. A number of investigations have also been carried out to determine the effect of nitrogen pressure on solubility both in pure liquid iron and in various liquid alloys. It is universally agreed that for pure iron and sufficiently dilute alloys this can be expressed by the well known Sieverts' Law relation: wt. %N = C \P'N2 (1) Pehlke and Elliott(l) have tested this relationship at nitrogen pressures from 0.5 to 1.0 atmospheres for pure liquid iron at 16000C and for alloys of about 10% chromium, tantalum, tungsten and cobalt and find that it holds quite accurately. Humbert and Elliott(2) have found -2

that it holds over the same pressure range in Fe-Cr alloys up to 57% Cr. However they find deviations for alloys of 61% Cr and above in which wt. %N ceases to be proportional to JPN2. Kashyap and Parlee(3) made repeated measurements on pure iron at 16000C between nitrogen pressures of 50 and 750 mm and found adherence to Sieverts' Law with reasonably good reproducibility in the value of the constant C. Their results substantiate the work of Kootz(4) who also verified Sieverts' Law in pure iron at 1600C at nitrogen pressures between 0.2 and 1.0 atmospheres. Brick and Creevy(5) made measurements on liquid Fe-Cr alloys and on pure liquid chromium at 1 atmosphere and 2 atmospheres nitrogen pressure, They state that both these alloys follow Sieverts' Law with values for C of 0.85 for an Fe-34% Cr alloy and 0.9 for pure chromium:where the units of C~ are weight per cent N/(atm.)l/ However the fact that nitrogen solubilities were determined for only two nitrogen pressures and the fact that the equilibration temperatures were not well known makes these conclusions questionable, particularly in-view of the fact that they conflict with the apparently more accurate measurements of Humbert and Elliott.(2) Finally Schenk, Frohberg, and Graf(6) have verified Sieverts' Law in pure iron at 1600~C between nitrogen pressures of 0.3 and 1.0 atmospheres. They have also determined the effect of additions of carbon, molybdenum, sulfur, and silicon on the value of C. They show a nearly linear decrease in C up to 3% S, 5% C, and 12% Si, and a nearly linear increase in C up to 13% Mo. This indicates that no nitrides were formed at these compositions since formation of a nitride presumably would have caused a discontinuous change intthe value of C at the composition at which the nitride formed,

-4B. Nitride Solubility Products in Liquid and Solid Iron Although several authors have calculated solubility products of nitrides in iron using thermodynamic data derived from various sources, the number of reported experimental attempts to measure them is small. Chipman(7) presents calculated values of the denitrifying constant K' = % x %N for six nitrides which are reproduced in the following table. TABLE I SUMMARY OF DENITRIFYING CONSTANTS ESTIMATED BY CHIPMAN(7) Element j Compound Constant K' Value at 16000C Al AlN %Al x %N 0.55 si Si3N4 (si) /4 x H 14. Ti TiN %Ti x %N 0.00014 v VN %V x %N 1.5 B BN %Bx N like Al Zr ZrN _Zr x %N like Ti Chipman admits these are "rough estimates" made from data on the free energies of formation of the compounds from the pure elements and the free energies of solution of the pure components in liquid iron. Pearson and Ende(8) present calculated plots of standard free energies of formation of various nitrides from their pare components at temperatures of 18000C and below derived from thermodynamic data calculated by Kelley(9) and others. Pearson and Ende's results are significant in

-5that the nitrides follow about the same order of increasing stability and their assumed compositions are the same as in Table Io Several experimentors who have investigated the effect of various alloying elements on the solubility of nitrogen in liquid iron have reported the appearance of solid phases, possibly nitrides, at sufficiently high alloy concentrations. Maekawa, Nakagawa, and Yanagawa(lO) who have made solubility measurements of nitrogen in Fe-A1 and Fe-Ti alloys report the appearance of a solid phase on top of the melt at alloy contents of 0.3% Ti.and 8.0% Al at 1700~C under one atmosphere of nitrogen. They state that at 16000C sufficient solid phase formed to make solubility measurements in the liquid Fe-Ti and Fe-Al alloys impossible. They suggest that these phases were presumably TiN and AiN but made no attempt to measure their solubility products. Their statements are contrasted with the statements of Pehlke and Elliott(l) who at 16000C noted a solid phase appearing on top of Fe-Al melts containing greater than 0-5% Al under one atmosphere nitrogen pressure and who were unable to measure any solubility of nitrogen in Fe-Ti melts at one atmosphere nitrogen pressure because of the formation of a solid phase at very low Ti contents. Pehlke( reports values for solubility products of titanium and zirconium nitrides at 16000C as follows: for TiN K' = %Ti x %N = 0.000112 for ZrN K' = %Zr x %N = 0.00726 These values were calculated from chemical analyses made on ingots which had been equilibrated with one atmosphere of nitrogen gas in a Sieverts' Apparatus. The original aim of these equilibrations was to determine

-6the interaction parameters of titanium and zirconium with nitrogen in liquid iron but a solid phase appeared on the melt and interfered, The most comprehensive experimental determination of nitride solubility products in liquid iron has been reported by Rao and Parlee. (12) They used a Sieverts' method to measure the weight per cent nitrogen absorbed by melts of Fe-V and Fe-Ti as the nitrogen pressure varied between zero and one atmosphere. They report adherence to Sieverts' Law in alloys of 10% —-and 20% vanadium up to one atmosphere nitrogen pressure at 17600C but state that this high equilibration temperature was necessary because the melt tended to solidify at lower temperatures. The "solidification" they observed may well have been the formation of vanadium nitride. With Fe-Ti alloys of 0.5% to 0.8% Ti they determined the solubility product of titanium nitride by measuring the nitrogen concentration at which the nitrogen absorption curve departs from Sieverts' Law. They attempted to calculate the composition of the nitride formed by fitting a Sieverts' Law line for pure iron to the high pressure end of their absorption curves and extrapolating the pure iron line down to zero pressure to determine the weight of nitrogen in the precipitated nitride, They report the following results at 1600~C: Til 7N(N) = 1.7Ti + N K' = (frTioTi)1-7 x (fNON) = 0.0020 The method appears very ingenious and useful but the quantity and accuracy of their data leave something to be desired. Specifically there

-7are not sufficient data points to determine precisely enough the shape of the nitrogen absorption curves. Fountain and Chipman(13) have used the. same method to determine the solubility product of vanadium nitride in solid iron. They indicate that different. points -of. deviation from Sieverts' Law can be determined depending on whether the nitrogen pressure is being increased or reduced. They offer several possible explanations for this, among them the existence of vanadium nitride of more than-one composition and the possibility of non-equilibrium existing above the solubility limit. C. Nitride Phase Compositions A number of nitrides are known or suspected to exist over a range of compositions. For several evidence of a systematic variation of composition with lattice parameter is known. Ehrlich(l4) has studied the variation of lattice parameter with composition in titanium nitride produced by heating pure titanium powder in a nitrogen gas atmosphere. He finds that TiN, which has the NaCl structure, can exist over the range TiNo 42 to TiNl.1.It exhibits a maximum lattice parameter of 4.23A corresponding to a composition of TiN. As the Ti/N ratio varies from 1.0 in either direction the lattice parameter decreases. He also states that titanium nitride has a defect structure with about 4% of the lattice points unoccupied for the composition TiN. Chiotti(l5) reports results of x-ray measurements and chemical analyses on nitrides of titanium, tantalum, and zirconium. He gives a lattice constant of 4.23A for a nitride which analyzed chemically 77.4% Ti

-8and 20.1% N. This corresponds to TiNo.89. He reports that tantalum nitride is hexagonal with a = 3.04A and c/a = 1.62 and suggests that its composition may vary between TaN and Ta2N. He reports a zirconium nitride phase of 10.45% nitrogen calculated from a weight gain of zirconium metal heated to 15000C in a nitrogen atmosphere which has a lattice para0 meter of 4.57A. This corresponds to a co;noszitionl of Zrl3\T. He suggests that this nitride phase is composed of the nitride ZrN with the NaC1 structure and a hexagonal metal phase of zirconium containing nitrogen in solid solution. This contention is also supported by Domagala, McPherson, and Hanson(16) who find practically no variation in lattice parameter (4.567A to 4.569A) for zirconium nitride phases ranging from 10.5% to 13.5% nitrogen but find a zirconium lines of increasing intensity in the nitride x-ray pattern as the nitrogen content drops. They suggest also that the ZrN phase may vary in composition on the metal-rich side as far as ZrN0o46 and make no effort to predict the nitrogen-rich boundary. Hahn(l7) has studied the vanadium-nitrogen system and found two nitrides, VN with the NaCl structure and VN0O37_0Q43 with a hexagonal structure, both of which exist over a composition range. He gives the following data on the composition limits: Upper Boundary Lower Boundary l.00 a = 4.126A VN.7 a = 4.064A 0 0 VNo.43 (10.5%N) a = 2.835A VNo37 (9.3%N) a = 2.831A c = 4.541A c = 46533A

This agrees with Fountain and Chipman(l3) who found two vanadium nitrides existing in solid iron and gave their nominal compositions as VN and V2N. Schonberg has studied the systems niobium-nitrogen(l8) and tantalum-nitrogen(19). In the niobium-nitrogen system he finds four different nitride phases in addition to a metal phase containing dissolved nitrogen. He gives x-ray lattice parameter and crystal structure data on the nitrides and assigns them the following compositions: NbN1.00 (hexagonal), NbNo0 95 (hexagonal-close packed), NbN g. 80 -a 0.90 (WC type), NbNo.40 - 0.0 or Nb2N (metal atoms hexagonally close packed with N interstitially dissolved). In the tantalum-nitrogen system he again finds four nitride phases in addition to a practically pure metal phase. He assigns the nitride phases the compositions TaN...0.0o5, TaN,.~0.40 _-.0.45' TaN 0.80 -..0.90, and TaN. Finally Taylor and Lenie(20) have investigated the properties of aluminum nitride. They state that the Al/N ratio in pure nitride has the stoichiometric composition AlN but that the material often contains some A1203 or A120C. They state that AlN is hexagonal with a _ 3.111 A and c = 4.980 A. This agrees with the data of Paretzkin(21) who gives the values a = 3.114 A and c = 4.986 A.

I II. OUTLINE OF THE PROBLEM A. General The problem may be simply stated in thermodynamic terms as the determination of the solubility product of various alloy nitrides in liquid iron. The two important variables to be dealt with are the composition of alloying element and nitrogen at which the nitride is formed and the temperature. A thorough investigation of these should permit the derivation of all the thermodynamic functions of the nitride systems. B. Systems Chosen For Experimentation In selecting suitable systems for experimental investigation a natural starting point is those systems which previous investigators have noted as forming a solid phase, possibly nitride, in the presence of nitrogen while in solution in liquid iron. In this category are aluminum, titarconium, columbium, and vanadium. Two other elements silicon and boron were known to form stable nitrides in the pure state, although there was no experimental evidence as to whether or not these nitrides were stable in the presence of liquid iron. On examining this list it is seen to contain a majority of elements which markedly increase the solubility of nitrogen in liquid iron. Two others known to have this property are tantalum and chromium. However published data on the solubility of nitrogen in pure liquid chromium indicate no formation of a chromium-nitride phase. The nitride would then certainly be unstable in liquid iron-chromium alloys so this system was disregarded. These eight systems aluminum, silicon, titanium, zirconium, -10

boron, columbium, vanadium and tantalum form the experimental basis of the research. C. Experimental Methods The relative merits and demerits of the two basic methods of investigating the thermodynamic equilibrium between a gas phase and a liquid metal phase, the Sieverts method and the quenching or sampling method, have been the subject of considerable discussion. The choice between the two is normally determined by the system to be studied. Some of the factors to be considered in this choice are discussed in a later sectiono In this research both methods were employed in order to give a comparison of results in several systemso Primary emphasis was placed on the Sieverts method since by this method more variables could be tested in a single determination. However the fact that the equilibrium measurements were to be made in the presence of a solid nitride phase permitted the quenching method to be used employing a nitride crucible to contain the melt. This. eliminated one of the main drawbacks to the Sieverts method, the necessity of holding the melt in an oxide crucible with the resultant possibility of oxygen contamination. D. Possible Methods of Correlating the Experimental Results 1. Determination of the nitride solubility limit by measuring the point of departure of the gas solubility from Sieverts' Law The method of determining the solubility limit of an alloy nitride phase by equilibrating the system with various partial pressures of nitrogen and locating the dissolved nitrogen concentration at which

-12the solution departs from the Sieverts Law relation has been applied by Fountain and Chipman(l3)to solid iron alloys and by Rao and Parlee(l2)to liquid iron alloys. The method however necessarily contains assumptions, and failure to carefully note these assumptions when the method is applied to an experimental system can lead to errors. An analysis of the method according to the phase rule is helpful in pointing out these assumptions. Let the following definitions be adopted. U = the total number of independent variables necessary to specify a system in equilibrium under a given set of conditions with constant temperature and pressure throughout the system. N = the number of chemical individuals in the system. G = the number of independent distribution relations between concentrations of the same chemical indi-. vidual distributed between different phases. E = the number of additional independent relations among chemical individuals. P = the number of phases in the system. A phase is defined as any homogenous portion of matter bounded by a physical surface, not necessarily continuous. C = the number of components in the system, defined by C = N - E. V = the degrees of variance of the system, the difference between the number of variables U and the total number of independent conditions relating them. The phase rule may then be expressed in either of the following two forms: V= U - G E (2) V=C+2 -P (3) Let this formulation of the phase rule be applied to the system of a melt of liquid iron at temperature T containing a dissolved alloying element

-13j in equilibrium with nitrogen gas at pressure PN2o The notation j and N will be used to signify alloying element j and nitrogen in solution in liquid iron. The respective concentrations by weight of j and N will be signified by %j and %N_. The solid nitride phase precipitated from solution by j and N, of unknown composition, will be designated j N. x Three different cases must be considered, Case i - at %j and %N below the solubility limit of jxN. System: gas phase containing N2; liquid phase containing Fe, j, and N; N = 4, G = O, P = 2, U = 4, E = 1 - the Sieverts Law relation between P in the gas phase and %N in the liquid phase which may be written = C PN From Equation (2) or (3): V = 4 - 0 - 1 = 3 or V = (4-1) + 2 - 2 = 3 If T and the total %j in the system are fixed by experimentally imposed conditions, in terms of the above defined quantities adding two more relations E, then V = 1. This means that for each value of there is a discreet %N in accordance with the experimentally observed fact that %N = C PN2 which is called Sieverts' Law. This case is shown by line segment a in Figure 1 where the slope of the line segment is characteristic of the element j and the %j. Case 2 - at %j and %N slightly above the solubility limit of j xN but close enough to the solubility limit that the following assumptions hold: a. jxN has a fixed composition, i.e. x does not change during the course of the precipitation.

-14Fe - j ALLOY _ _ Fe o F Figure 1. Absorption of Nitrogen by an Fe Figure 1. Absorption of Nitrogen by ea Fe-J Melt.

— 15 — b. The weight of j in j N is negligible compared to the weight of j in the liquid phase. System: gas phase containing N2; solid phase containing jxN; liquid phas e containing Fe, j, and N. N - 5, G = 0, P = 3, U = 4 E = 2 -.N= C 4PN2 and K = j x %N -V 2 If T and total %j are fixed, V O. This means that only one aN and PN2 are permitted. In terms of Figure 1 where the ordinate is the total %N in the solid and liquid phases, not just the %N in the liquid phase, the curve must follow a vertical or constant pressure line as in region b. However before the precipitation of jxN has proceeded very far either or both of the assumptions made in case 2 may break down resulting in an increase in V. If x varies as the precipitation of jxN proceeds then one of the conditions E becomes invalid resulting in V = 1. Or if sufficient j N precipitates so that the weight of j used up bex comes appreciable then the fixing of the total %j does not fix %j. Since total %j is not one of the variables U, a condition E is again lost and V = 1. Thus for either or both of these:reasons the absorption curve in Figure 1 may begin to deviate from vertical as the precititation of jxN proceeds. This is shown in region c. Case 3 - at %N far enough above the solubility limit of j xN and with jxN sufficiently insoluble that the concentration of j in the liquid x

-16System: gas phase containing N2; solid phase containing jxN; liquid phase containing Fe and N; N = 4, G= O, P = 3, U 3 E - 1 - %N = C P N V= 2 If T and total %j are fixed V = 1. Again there is a disk creet %N for each PN and these are related by the Sieverts Law relation %N =C CP as shown by the line segment d in Figure 1 where pN2 now the slope of d approaches the slope of the Sieverts Law line of nitrogen in pure liquid iron. By extrapolating the line segment d back to PN 0 and finding its intercept C on the ordinate the weight of nitrogen contained in the phase jxN can be found. From this and the initially fixed total %j in the system the composition of jxN (i.e. the value of x) can be found. This however is only an average composition. It should be noted that it is quite possible for the value of x to change between point A and point B. It is also possible that the nitride might be a complex containing iron of the type (Fe,j)xN in which case this method obviously cannot be used to calculate even its average composition. The %N at A, the %j in the system, and the calculated composition of jxN if it is the same as the composition at A, permit calculation of the weight percent solubility product K' where: K' = (%j)xo (%N) (4) for the reaction: jxN - j + N (5) The value of K' will vary systematically with %j and %N. In order

-17to calculate the solubility product K which is a true constant at constant temperature it is necessary to take into account the Fe-j-N interactions in liquid solution-. 2. Wagner's method of interaction parameters Wagner(22) has suggested representing the activity coefficient of a solute 1 in a solvent also containing solutes 2,3,4,... by the following equation: 6in yl 61nyl, lnyl 6,n-y ln1yl= lnyo + x( X1 ) X1 + ( ) X2 + )X4 (6) where yi is the activity coefficient of component i based on Raoult's Law with the standard state pure i, the infinitely dilute solution, y~ is the activity coefficient at infinite dilution, and Xi is the mole fraction of i in solution. He then defines the interaction parameter eJ by: j a lnyi (): (7) 1 axj The corresponding equation for the activity coefficient based on Henry's Law with the activity equal to the weight per cent at infinite dilution is: gf log fl.l og fl +log fl log fl =" ~% +... (8) a6%l a%2 613 and for the interaction parameter: ej log fi ( The solubility product of jxN in liquid iron may be written: K (a) f) ) ( (10) ajyN _

-18where aj and aN are the activities of j and N in liquid solution, ajxN is taken as one since JxN is assumed pure, and the other quantities are as previously defined. Now using the representation of Equations (8) and (9) for fj and fN in Equation (10) and taking x 1 gives: log K = log K' + e3(%) eN(%N) + eN(%N) + e(%j) (11) -. j _ where K' is given in Equation (4). If the reference state is taken as the infinitely dilute solution of nitrogen in pure liquid iron then fN is defined by: lim(aN/%N) fN = 1 (12) %N -,0 As a result of this reference state and the fact that nitrogen obeys Sieverts' Law in Fe-N solutions the activity coefficient of nitrogen in Fe-j-N solutions is given by: fN =[(%N)pure Fe] (13) (%N)alloy PN2, T In Figure 1 fN is represented by the ratio EF/DF which is obviously independent of what PN2 is chosen. As a result of the fact that nitrogen obeys Sieverts' Law in Fe-J-N solutions below the solubility limit of jxN the interaction parameter e in Equation (11) is zero. The interaction parameter e.- may be found from the slopes of the Sieverts Law lines of a series of plots like Figure 1 for various %j. The fN calculated by Equation (13) at some PN is plotted on a log scale against %j and the slope of this curve is ei. eN may then be found from the Wagner reciprocity relation derived from the Gibbs

-19-. Duhem Equation which says that in dilute solution: iEj~ ~EJ~ ~(14) i j and: ei =ej Mi (15) Mj where Ei and M. are the molecular weights of i and j. The interaction parameter eJ can not be found directly from the nitrogen absorption curves in the Fe-j-N system. It is a property of the binary system Fe-j and is a measure of how fast the activity of j departs from Henry's Law as the %j increases in the Fe-j binary. 3. Approximation of ej from data on the Fe-j-N ternary With sufficient data on the variation of K' with %j it is possible to find an approximate value of eq by a trial and error method. From Equation (11) it can be seen that the variation of K' with %j N and %N depends on the signs and relative magnitudes of e eN, and e. N j Since e and eJ are available from the nitrogen absorption curves it is possible to assume a value for ej and use this along with several experimental values of %j and %N to calculate a series of K values from Equation (11). If these values of K still show a systematic variation with %j or %N then this must be due to error in the assumed value of e j The assumed value is corrected, the direction of the correction being determined by the direction of the variation in K with %j and the sign of e and eN, and the K values are recalculated. This is repeated until there is no longer an observable systematic variation of repeated until there~ is no longer an observable systematic variation of

-20K with %j. The variation in K then remaining is assumed to be experimental and the value assumed for ej the true one. Obviously a fair number of values of %j and %N are necessary to insure reasonable accuracy in ej. 4. Estimation of j activity from the Fe-j binary If the nitride jxN is quite soluble it may require quite high %j to precipitate it. Thus the solution may become so concentrated in j that eJ can no longer be considered even approximately constant. The same condition applies to a system in which the activity of j in the Fej binary departs greatly from Henry's Law at low j concentrations. In such a case it may be more accurate to approximate the activity of j in the Fe-j-N ternary solution by the activity of j in the Fe-j binary at the same j concentration. Of course care must be taken to express all the activities relative to the same standard state. The binary j activity may then be corrected for the effect of N on it by means of the term eN(%N) This effect is often negligible since in systems in which the j concentration in equilibrium with jxN is high the N concentration is likely to be correspondingly low making the term eNI(%N) small. 5. Determination of the N activity from the gas phase It is also possible in the case of a very soluble nitride phase that the j concentration in equilibrium with it may be high enough that eN may not be approximated as constant. This can introduce considerable error since e3 must be multiplied by %j which is large. In this case a more exact method of estimating the N activity in the solution may be

employed since this is fixed by the P in the gas phase. According to Equation (13): N TN [N x fN] T [(%N)pure Fe] (16) [ 2 NP' ia ~PN2, T So the activity of N in equilibrium with a solid nitride phase is equal to the equilibrium %N in pure liquid iron at the same equilibrium PN2. This method of course requires accurate determination of the equilibrium Sieverts Law line for nitrogen in pure liquid iron at temperature T. 6. Determination of K by the extrapolation of K' to zero %j An alternative method to Equation (11) of finding K from K' is to plot values of log K' versus %j and extrapolate with a straight line to zero %j. As %j approaches zero the terms e~(%j) and. e_(%) also approach zero. Therefore again in this method of analysis the term eN(%N) must be neglected, after which Equation (11) yields: lim log K = log K' (17) 0 In order to insure that the term e(%N_) is negligible the values of K' must be at large %j. This requires a graphical extrapolation over a fairly wide range of fj.

IV. EXPERIMENTAL METHODS AND PROCEDURES A. Comparison of Sieverts Method and Quenching Method There are basically only two experimental methods available for the study of gas-liquid metal phase equilibria because of the high equilibration temperatures normally required. In the Sieverts method the equilibration is made in a closed system with the measurement of the volume of gas absorbed by the liquid metal being made directly at the equilibration temperature. In the quenching or sampling method the equilibration is usually made in an open system and the liquid metal phase is then sampled or quenched in such a way that the gas solubility representative of the equilibration temperature is preserved during solidification and cooling of the metal to room temperature for subsequent analysis. Both methods contain inherent and unavoidable sources of error. The choice between them is normally determined by the particular gas and liquid alloy to be studied. In this research both the Sieverts method and the quenching method were employed in order to gain a comparison of the effectivness of the two different methods in the systems under consideration. The advantages and disadvantages of each method may be briefly summarized in tabular form. -22

TABLE II ADVANTAGES AND DISADVANTAGES OF THE SIEVERTS METHOD Advantages: 1. There is a positive measure of the approach of the system to equilibrium. 2. The gas solubility measurement is made directly under the equilib, ration conditions. 3. Several of the variables temperature, nitrogen pressure, and composition may be varied over fairly wide ranges during a single determination. 4. There is no necessity to place primary dependence for determination of liquid phase composition on chemical analyses. Disadvantages: 1. The system must be held for an extended period at pressures below one atmosphere. This can cause vaporization of volatile components out of the melt. 2. The melt is held in an oxide crucible. This presents the possibility of melt-crucible reaction contaminating the melt, particularly with oxygen. Quenching Method Advantages: 1. The system remains always at a total pressure of one atmosphere, minimizing vaporization from the melt and permitting measurements to be made on a liquid alloy containing one or more volatile components. 2. The melt is held in a nitride crucible which reduces the possibility of oxygen contamination. Disadvantages: 1. Since the gas solubility in the liquid phase usually changes with temperature the amount of gas dissolved may change during the quenching.

-24TABLE II (CONT'D) 2. There is the possibility of contaminating the melt by reaction with the quenching medium. 3. The partial pressure of the active gas can be controlled only by diluting it with an inert gas. This means that the accuracy of the nitrogen partial pressure depends on the accuracy of the metering system and introduces the possibility of error through thermal diffusion in the gas phase. 4. When the entire melt is quenched only a single set of values of the temperature, nitrogen'pressure, and composition may be studied in a single determination. The most important source of error in the Sieverts method is the possibility of metal vaporizing out of the melt while the system is being equilibrated at pressures below one atmosphere, causing metal powder to deposit on the cooler walls of the reaction bulb. This introduces three important errors. First it changes the hot volume of the reaction bulb during the course of the experiment. Second the experimental gas may react chemically with or become adsorbed on the fine metal powder causing an apparent increase in the measured solubility. Third and most important, vaporization changes the composition of the melt. A small change in melt composition can have a large effect on the solubility of the experimental gas, particularly if the volatile component being lost is present as a dilute solute. These effects are more pronounced in using the Sieverts method to measure the solubility limit of a nitride phase than in simply making a nitrogen determination under atmospheric pressure of nitrogen. This is due to the necessity of varying the nitrogen pressure over a wide range below atmospheric pressure and to the much longer equilibration times required by the presence of the nitride phase.

-25Another error which may be encountered with the Sieverts method is a reaction between melt and crucible. Since the crucible material is an oxide, in this study A1203 or Zr02O this can introduce into the melt oxygen as well as Al, Zr, or some other element present in the crucible. These elements may all effect the apparent nitrogen solubility. The effect of oxygen is particularly serious since Pehlke and Elliott(l'23) have shown that small amounts of oxygen have a strong retarding effect on the kinetics of nitrogen solution as well as a decreasing effect on the solubility. If the oxygen content of the melt is too high it is possible for the approach to equilibrium to be so slow that the equilibrium nitrogen solubility is not reached in an experimentally reasonable time. The absorption of oxygen by the melt from the crucible can occur even if there is no chemical reaction since the crucible surface generally contains adsorbed oxygen which is impossible to remove even by long outgassing at a high temperature. The most important source of error in the quenching method is the possibility that the gas content of the metal may change appreciably during quenching due to the change in equilibrium gas solubility with temperature. In particular the phase change from liquid to solid may have a large effect on the gas solubility. The avoidance of this error simply requires a rapid enough quench to maintain in metastable equilibrium the gas solubility representative of the equilibration temperature. The loss of gas by solid state diffusion after quenching is negligible in the case of nitrogen although it might become appreciable in the case of a more rapidly diffusing gas such as hydrogen.

-26Since the composition of the metal phase cannot be determined directly with the quenching method as it can with the Sieverts method, reliable methods of chemical analysis are a necessity. B. Experimental, Procedure for the S-ie.ver.ts Method-; In the Sieverts method the equilibration is carried out in a closed system with a measured volume of purified nitrogen gas geing admitted to the reaction chamber and the equilibrium pressure it produces being measured by a mercury manometer. A schematic diagram of the apparatus is shown in Figure 2. The reaction. bulb is Vycor and is designed so as to minimize the free volume of the closed system in which the equilibration takes place. The heating is done by means of an induction coil driven by a high frequency generator which provides stirring of the liquid melt to aid the approach to equilibrium. To make a determination weighed charges of vacuum melted iron (Ferrovac E) and alloying element of highest possible purity were placed in a crucible 1 1/4" in diameter and 1 1/2" deep which was surrounded by a larger crucible to act as a radiation shield. A summary of the analyses of the charge materials used is given in Appendix A. Inner and outer crucibles of recrystallized alumina were used for all systems except zirconium-. The Fe-Zr alloys were found to react with alumina crucibles removing the zirconium from the melt and forming ZrO2. Hence zirconia crucibles were found more suitable for this system. The inner crucible was covered with an alumina or zirconia lid and Alundum insulating discs were placed on the top and bottom as shown in Figure 3.

b C_ 9 C 0~~ F 0 A A L 11 I i I II E ii TO MECHANICAL VACUUM PUMP.A A Ua d ARGON NITROGEN TO ATM-OSPHERE A ANHYDRONE DRYING COLUMNS 3 WAY STOPCOCKS od B COPPER GAUZE FURNACES 450 C 2 WAY STOPCOCKS b,c,efghi C MERCURY RESERVQ1R D GAS BURET E MERCURY MANOMETER F REACTION BULB G WATER COOLING CHAMBER H MERCURY DIFFUSION PUMP Figure 2. Schematic Diagram of Sieverts Apparatus.

TO GAS SYSTEM ALUMINA LID ALUMINA CRUCIBLES COOLIUNG WATER OUT METAL CHARGE - _ALUNDUM INSULATORS -INDUCTION COIL PLEXIGLASS COOLING CHAMBER VYCOR REACTION BULB deKHOTINSKY CEMENT GROUND TAPERED JOINT COOLING WATER IN Figure 3. Sieverts Apparatus Reaction Chamber.

-29After the reaction bulb had been sealed, evacuated, and checked for leaks purified argon was admitted to a pressure of about half an atmosphere. Power was then turned on and the charge raised gradually to its melting point. If the alloy addition was in powder or sponge form the reaction bulb was held under hard vacuum until the charge reached about 10000 C at which temperature the charge was held for 15 to 30 minutes to remove adsorbed gases. Then the bulb was isolated from the vacuum system and pressurized to half an atmosphere with argon to prevent vaporization of metal when the charge was melted. The time for complete outgassing of the charge could be determined by periodically isolating the reaction bulb and checking for a spontaneous pressure rise in the system The melt temperature was measured with a Leeds and Northrop disappearing filament type optical pyrometer sighted vertically downwardly on the center of the melt surface. The temperature scale was calibrated against the observed melting point of pure iron taken as 15360C. The emissivity of all melts was assumed to be that of pure iron, taken as 24 0.43, and was assumed not to change with temperature or composition. A detailed calculation of the relation between the true and observed temperature scales is given in Appendix B. With several of the systems studied pure alloying element could not be added to the melt. Master alloys of 10 to 15 percent alloying element in iron were prepared by melting in the same apparatus under atmospheric pressure of argon. With aluminum this was necessary because the comparatively low melting point of aluminum causes it to be molten for some time before the iron melts. In a melt of 1 to 2 percent aluminum this could cause a sufficient loss of aluminum to make a significant change

-30in the melt composition. With titanium and zirconium the percentages required for nitride precipitation were so small that again a small loss would be significant even though these elements melt at higher temperatures than iron. With all other alloying elements the composition required was generally greater than 5% so these were added as the pure element. All master alloy compositions were aimed either at a binary eutectic composition or within the solid. solubility range in order'to minimize any segregation which might occur on solidification. Vertical cross section pieces of the ingot were used as additions since any segregation which did take place should be on a micro-scale and not a macro-scale. After the charge had melted the reaction bulb was evacuated as rapidly as possible and then stopcock g was closed and a measured volume of purified argon was admitted to bring the bulb pressure up to one atmosphere. The volume was measured by drawing the argon into the closed leg of the gas buret and then balancing the two mercury legs with stopcocks b and c closed and reading the mercury height on the buret scale. Stopcock c was then opened, the argon was drawn into the reaction bulb, the mercury legs rebalanced, and the height again read on the buret scale. The difference between the two buret readings was the volume of gas drawn into the reaction chamber at atmospheric pressure and ambient temperature. The perfect gas law could then be used to calculate the volume at STP. Since argon is insoluble in liquid iron this gives the free volume of-the reaction chamber at the equilibration temperature which is hereafter referred to as the hot volume.

The perfect gas law predicts that the apparent hot volume or the volume of gas measured atmospheric pressure and ambient temperature which is required to fill the hot volume at some pressure less than atmospheric varies linearly with the pressure at which it is measured. Actually there is a slight variation from linearity since the volume of the closed leg of the mercury manometer which is included in the hot volume varies with pressure. However this variation is small and the calibration curve shown in Figure 4 is substantially linear. The deviation at the high end of the pressure scale is caused by friction in the mercury legs of the manometer and solubility measurements very close to but slightly below atmospheric pressure were avoided through out the research because of this inaccuracy in the pressure reading. The variation of hot volume with equilibration temperature is also essentially linear. However the hot volume was determined individually at each equilibration temperature for each run before the start of the solubility measurements. After su.itable determinationsof the hot volume the argon was pumped out of the reaction chamber as rapidly as possible to minimize the length of time that the melt would be exposed to a hard vacuum. Measured volumes of purified nitrogen were then admitted to the reaction chamber and the equilibrium pressure reached.in the chamber was measured by the manometer. The difference between the apparent hot volume at that pressure and the volume of nitrogen admitted was the volume of nitrogen absorbed by the melt. In order to accurately determine the nitrogen absorption curve it was necessary to admit nitrogen in small increments and take a large number of data points.

70 60 650 z + w 40, I+ 30 -- I-J z 20' - + +'+ I 0 I0 - - I I I I I I i I 0 10 20 30 40 50 60 70 80 PRESSURE IN CM. OF MERCURY Figure 4. Relation Between Apparent Hot Volume of Reaction Bulb and Pressure at 16000C.

-33The admission of nitrogen was continued until several equilib- - rations produced the same or nearly the same equilibrium pressure indicating that the vertical segment of the absorption curve (segment b in Figure I) had been reached. Then the admission of nitrogen was stopped and the melt temperature raised 500C. Since in all of the systems studied the solubility of the nitride increased with temperature, this temperature rise caused the nitride formed to redissolve..This was possible only if the nitrogen admission had been stopped-in'-time to prevent too much nitride from precipitating. Then by admitting more nitrogen in sufficiently small increments several data points could be obtained below the new nitr.ide solubility limit to establish the Sieverts Law line at the higher temperature. Nitrogen was then admitted in additional increments until another "pressure halt" was observed. This procedure was repeated until the limit of one atmosphere pressure imposed by the design of the reaction bulb was reached. For some systems the nitride solubility limit could be measured at as many as five different temperatures in a single-"determination. In the more insoluble systems determinations were made to establish the absorption curve at nitrogen concentrations well past the break point to attempt to determine the composition of the, nitride phase. In order to check the approach to equilibrium, measurements were made by both adding nitrogen to and withdrawing it from the same melt. It was found that below the nitride phase solubility limit both methods gave substantially the same Sieverts Law line. However above the solubility limit the two curves were different and the position of the break point depended greatly upon whether it was approached from the low nitrogen or high nitrogen side. The reversability of the equilibrium

with temperature however proved to be much more favorable. Melts in equilibrium with nitrogen pressures below the nitride solubility limit were cooled 50 or 100~C precipitating the nitride and sharply reducing the nitrogen pressure. On heating the melt up to its original temperature the nitrogen pressure returned to its original value. C. Experimental Procedure for the Quenching Method In the quenching method the equilibration is carried out in anopen system with a stream of gas passing over the molten metal. A schematic diagram of the quenching apparatus is shown in Figure 5. The system consists of a gas-tight vertical tube furnace with a pedestal of adjustable height to support the crucible and charge which is heated by an induction coil. A sliding seal in the bottom furnace closure permits the crucible to be lowered out of the heating coil and quenched by a blast of helium while maintaining the furnace atmosphere. The nitrogen pressure over the melt was controlled by mixing metered streams of purified nitrogen and argon gases. The method used to calibrate the flowmeters and compute the value of PN is described in Appendix C. In this method as 2 well as the Sieverts method the temperature was measured with an optical pyrometer and the calculation of the true and observed temperature scales is shown in Appendix B'. A charge of about 40 grams of pure iron was placed in a crucible made of the nitride whose solubility product was being determined, and this was surrounded by an alumina crucible as a radiation shield. In cases where the size of the nitride crucible left an annular space between the two crucibles this space was filled with alumina grain. No crucible lid

-35was used, the top of the melt being left uncovered to increase the quenching rate. After the system had been sealed and purged for 30 minutes and the nitrogen partial pressure set at the desired value the power was turned on and the iron charge melted and brought up to the equilibration temperature. It was desirable to do this as: rapidly as possible since the temperature readings tended to become less accurate as time elapsed because fumes from the crucible and melt, which were carried on the moving gas stream, tended to cloud the optical port. After a suitable equilibration period the power was turned off and the melt was lowered into the bottom of the furnace tube and quenched by a blast of helium. The helium flow was controlled by valve a. in Figure 5. Tank helium was used without further purification and the Small amount of oxygen it contained occasionally caused a slight tarnishing of the top surface of the ingot. This did not appear to affect the results however, the oxidation probably taking place after the ingot had solidified. On quenching from 1600~C solidification took place too rapidly to follow visually, probably in less than a second. On quenching from 17000~C however the solidification took up to five seconds and could easily be followed visually. The ingot was then removed from the crucible and a vertical cross section cut from it and analyzed by wet chemical methods for both nitrogen and the alloying element. A summary of the analytical procedures used is given in Appendix D. This method obviously was limited to the more insoluble nitrides from which crucibles could be fabricated sufficiently dense to contain liquid iron for a reasonable equilibration time. Three nitrides were

-36CLEAR QUARTZ DISC OIL SEAL ON GAS OUTLET / > FUSED SILICA FURNACE TUBE O-RING SEALS IRON CHARGE \ NITRIDE, / ALUMINA CRUCIBLE CURICUBLE -\PEOESTA,NDUCTION COIL BRASS FURNACE QUARTZ TUBING TUBE CLOSURES O- RING/ lU_ -BRASS LOCK SCREW SEAL TAINLESS STEEL TUBING COPPER TUBING PURIFIED A AND N2 IN -CONTROL VALVE a 5HELIUM QIN Figure 5. Schematic Diagram of Quenching Apparatus.

-37studied in this way, aluminum nitride, boron nitride, and titanium nitride. Three AiN crucibles fabricated by hot pressing were donated by the Carborundum Company of Latrobe, Pennsylvania Details of the -hot pressing method are given in Appendix E. The crucibles contained some material, apparently a binder or lubricant, which burned out at about 800~C causing considerable smoke in the furnace chamber. However this smoke was soon removed by the gas stream and no difficulty in temperature measurement was encountered for the remainder of the run. BN crucibles were machined from commercially available bar stock. This stock contained about 2.5% B203 which began to vaporize as soon as liquid iron formed in the crucible. This vapor quickly coated the optical pyrometer port making accurate temperature measurement impossible. However by rapidly raising the melt temperature to 1600~C the temperature could be stabilized with the pyrometer before the coating on the port got too heavy. The temperature could then be controlled reasonably accurately for the rest of the equilibration period by controlling the power input to the induction coil. Because of this temperature control problem however measurements could not be made with BN crucibles at temperatures above 1600~C. An attempt to burn out the B203 by prolonged heating in air at 2500~F caused complete deterioration of the BN compact. TiN crucibles were produced from commercially available TiN powder by a cold pressing and a sintering method developed by SponsellerI25) and described in detail in Appendix E. These crucibles contained no volatile material but proved slightly porous to liquid iron. It was neceisary to cut the equilibration time somewhat to keep enough melt in the

-38crucible to give a sample at the end of the equilibration. Before making any runs with nitride crucibles the effectiveness of the quenching method and the apparatus design were first evaluated by making a series of equilibrations of pure iron in alumina crucibles at various temperatures and partial pressures of nitrogen and comparing the results with data obtained by the Sieverts method. Do Determination of the Nitridee Phase CompOsition Two direct experimental methods were tried to determine the compositions of the various nitride phases precipitated, x-ray lattice parameter measurements and wet chemical analyses. A method described by (26) Beeghly was found very effective in extracting the nitrides from the solidified ingots from the Sieverts method determinations. The alumina crucibles were broken away from the ingots. Then the top 1/8" was cut off with a metal lathe and the chips collected. These were placed in a 250 ml. round bottom flask which was fitted with an 18" long indented West Type reflux condenser. A solution of 3 ml. bromine and 13 ml. methyl acetate for each gram of chips was added to the flask, and the solution was heated with an electric hot plate until it boiled vigorously. The solution was allowed to reflux for four hours during which the iron matrix was completely dissolved. The residue of pure nitride was then filtered off, washed with methyl acetate to remove the bromine, and dried for six hours at 2200F. Care was taken to prevent the nitride from coming in contact with water since this could easily cause oxidation. Both x-ray diffraction techniques and wet chemical analyses were used to attempt to identify the compositions of the nitride residues.

-59Debye - Scherrer powder patterns were made of the nitrides and the d spacings compared with ASTM standard patterns taken of synthetically prepared nitrides. In addition lattice parameter measurements were made on the residues and compared with available' date on the systematic variation of lattice parameter with chemical composition in some of the systems. Wet chemical analyses of the residue for metal and nitrogen were made in one system but these were hampered by the small quantity of residue which could be extracted, even from an entire ingot. However x-ray patterns of extracted residues showed a complete absence of iron lines indicating that the extraction procedure when properly carried out was very effective in producing the pure nitride phase. A complete summary and discussion of the results of these analyses is given in a later section.

V. RESULTS AND DISCUSSION A. Calculation of Results From the Sieverts Measurements The weight percent of nitrogen absorbed by the melt at any nitrogen pressure was calculated from the difference between the volume of nitrogen introduced into the reaction chamber and the apparent hot volume at that pressure. This is expressed by the equation: N h) 73 P 76.0 28 100 - T 76.o P 22,400 W (v-h) 3 (18) TW 76.0 In Equation (18) V is the volume of nitrogen introduced into the reaction bulb in cubic centimeters which produces an equilibrium pressure po P and T are atmospheric pressure and ambient temperature in centimeters of mercury and degrees Kelvin, the conditions which apply to the gas buret and hence to the measurement of the volume V. W is the weight of the metal charge in grams. The apparent hot volume h is the volume of gas measured under conditions P and T which is required to fill the free volume of the reaction chamber at the equilibration pressure p. It is calculated from the linear relation predicted by the perfect gas law: h (19) P where H is the hot volume at atmospheric pressure (i.e. with p = P). The factor X 76.- enters Equation (18) in order to correct the %N measured at pressure P to that which would be measured at a pressure of one standard atmosphere or 76.0 cm. of mercury. This correction -40

-41assumes that the absorption of nitrogen by the melt follows Sieverts' Law. Even where this is not true such as above the solubility limit of-a nitride phase the error is small since the difference between P and one standard atmosphere is small. It is also apparent that since W the weight of the metal charge is used in calculating %N, the weight of dissolved nitrogen has been neglected with respect to W. W lies generally between 100 and 140 grams while the weight of nitrogen dissolved is at most 0.5 grams and usually much less. Thus the error involved in this assumption is negligible. B. Summary of the Nitrogen Absorption Curves Determined by the Sieverts Method The nitrogen absorption curves for all compositions of the eight alloy systems studied are presented in Appendix F with all experimental points plotted to scale. As outlined in the experimental procedure each determination in the Sieverts Apparatus, which is represented by a single graph in Appendix F, was made at a constant alloy composition with absorption curves for this composition determined at from one to five different temperatures. All measured nitrogen absorption values were corrected for the residual nitrogen contained in the charge materials by adding to them the weight percent nitrogen contained in the iron melting stock as given by the supplier's lot analysis. These values were 0.0018%, 0.0001%, and 0.0002% for the three lots of Ferrovac E used in this study. The amount of nitrogen added to the melts by the residual nitrogen in the alloying elements was negligibly small, It should be noted that not all absorption curves of the same determination can be considered equally accurate. Since the nitride was

-42precipitated and redissolved several times in most determinations there is the possibility that in some cases part of the nitride was slow to redissolve or did not redissolve at all. This could be due to adherence to the crucible walls or to the more sluggish kinetics attending the presence of a solid phase. It would effectively remove some nitrogen from the equilibrium and is reflected in a number of the absorption curves by the fact that the first point or two in the Sieverts Law region of a curve for a higher temperature lies above the Sieverts Law line. This means that most of the nitride eventually did redissolve at the higher temperature. However in a few of the curves such as those of the zirconium system the Sieverts Law lines at the higher temperatures do not pass through the origin but have a fairly large positive intercept on the ordinate at zero nitrogen pressure. This indicates that the nitride formed at the lowest temperature never completely redissolved and that only the absorption curve for the lowest temperature in each determination can be depended upon for any degree of accuracy. This condition was particularly bad for the zirconium system because the zirconia crucibles which had to be used to prevent crucible reaction with the Fe-Zr alloys had much more porous surfaces than the alumina crucibles used for the other systems. This caused the nitride to adhere much more readily to the zirconia crucible walls. In the case of the silicon system also, the higher temperature absorption curves are not considered as accurate because of the possibility of reaction between silicon and the A1203 crucible. This effect presumably would become worse the longer the liquid metal charge was held in the crucible.

In most.of the systems one absorption curve was run both in the direction of increasing nitrogen pressure and in the direction of decreasing nitrogen pressure. Decreasing nitrogen pressure was found to shift the part of the curve above the break point to lower pressures giving a lower nitride solubility limit than is found with increasing nitrogen pressures. This "hysteresis" effect is thought to be due to nonequilibrium conditions caused again by the sluggishness of the nitride in redissolving. The true nitride solubility limit is taken as the break point in the absorption curve determined with increasing nitrogen pressure. The opposite effect, supersaturation with increasing nitrogen pressure, can also be observed in a number of the absorption curves. This causes several points on the Sieverts Law line to be measured at nitrogen pressures higher than the equilibrium pressure which exists after the first nitride formation. This effect is not apt to cause error in the determination of the nitride solubility limit however, since the vertical or corn stant pressure portion of the absorption curve can simply be extended downward until it intersects the Sieverts Law portion. The point of intersection then denotes the nitride solubility limit. j N C. Calculation and Summary of the Interaction Parameters eN and e. The interaction parameter eN was defined in Equation (9). Equation (13) gives the activity coefficient fN from which eN is calculated. In order to apply Equation (13) to the experimental nitrogen solubility data it was necessary to select a reference pressure. A value of PN = 20.25 cm. (0.267 atm.) or JPN2, = 4)i5 (Ocm/ was selected since it

was low enough to be below the nitrogen pressure required for nitride precipitation in most of the experiments and high enough so that the differences in nitrogen solubility in the various alloys could be read accurately from the absorption curves. In the few cases where the pressure at which the nitride formed was below 20.25 cm. the Sieverts Law line was extrapolated up to this reference pressure. As was previously noted the choice of reference pressure theoretically makes no difference in fN as long as all alloys obey Sieverts' Law below the nitride solubility limit. However at very low nitrogen pressures the pressure measurement becomes more difficult causing the low pressure end of the absorption curve to be less accurate and resulting in less accuracy in fN if the reference pressure is chosen too low. Similarly if the reference pressure is chosen too high then in a large number of cases the Sieverts Law portion of the absorption curve must be extrapolated graphically far beyond the break point and again less accuracy in fN may result. Using Equation (13) and the reference pressure PN2 = 20.25 cm., fN was calculated for each absorption curve. For each temperature log fN was then plotted against %j and the average slope of this curve was taken as the value of eJ. These plots are shown in Figure 6 through Figure 13. From these values of eA, eA was then calculated by Equation (15). The N N numerical values of eJ and ej are summarized in Table III and compared with the values of other experimenters.( 1,3,12,27,28,29,) The value of eJ is actually given by the limiting slope of the curve of log fN versus _j as %j approaches zero. However in this study the %j had to be high enough to cause nitride precipitation at less than one atmosphere nitrogen pressure so no data points could be

-45-.08 + 600oC o 165o~ c A 1700~ C Ig 1750~ C 0.06 75ec -16500 I.._ 31: 0-04 J~~~~~~~'~~~~~~ _~~~~0.6~~~~~~~"1 I 0 0.10.2 -- 0. _0.2 Figure 6. Effect of Titanium on the Solubility of Nitrogen.

-460. I, + 1600" C o 1650~ C 0.08 A 1700" C o 1750 C 1600" 0.06 ZI 0.04 + 0.02 0 O p-6000CI -0.4 Zi I + I (3 0 0 - _0.6 A 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 WT % Zr Figure 7. Effect of Zirconium on the Solubility of Nitrogen.

+ 1600oo c o 1650 C 0.04 -- A 17000 C 0 El 1750 C 1750C I c _0+ 1 ~~~6~00 C 1700 C 21_0.0 L 16500 C 0.02 0.01 1600 c 0,. o0. I 1650 C ZI 0 4 17O0d C 0 0 -J 0.2 -75c _0.3 0 1.0 2.0 3.0 WT % A_ Figure 8. Effect of Aluminum on the Solubility of Nitrogen.

08 16 1 550 C 0.02 ~ X\\\\ Q 16 0000C 0.9 0.8 _ 1550 0.7 16W % B 0.5Figre 9. Effect of Boron on the Sob0 o Nitrogen o 4 0.2 A.I Figure 9. Effect of Boron on the Solubi!Ity of Nitrogen

-490.5 1600 C 1650 OC X 1600 * C 0.4 1 G 1650'C A 1700C 1 C a 1750O C 1750'C 0.3 zi 0.2 0.1O -0.4 2I -0.8 1 600 ~C -1.6 5 10Q 15 Figure 10. Effect of Vanadium on the Solubility of Nitrogen

1650 C 0.21 1700 C 1550X C 1750'C zi X 1550'C: a s o 1600"C 1650C C 0 1700"C * 1750"C -0.2 -0. -0.6 -0.8,0 1700'C 4 8 12 16 20 24 Wt % Cb Figure 11. Effect of Columbium on the Solubility of Nitrogen

510- 0.20 0.16 X 1550'C O 1600'C A 1650'C 0 1700'C 0.1 2 zl,, t50 -Rc o0' 1600 C 1650 C 0.08 0.04 0.6 s 1650IC 1600"C 0.8 4 8. 10. io 16 20 24 Wt % Tga Figure 12. Effect of Tantalum on the Solubility of Nitrogen

0.04 1650 0C 0.0 ZI0.o2.1600 OC O... ii.. i., i.. 141450 C x 1450 "C 1.6 o 150500 C A 1550 C El 1600 C 0 1650~ C V 1700~ C I.2,,Z~I... ~ I~~~1500 C 00.8 5 1550IC 0.4/ As a 1600'IC l.0 _C 1650 oC,,.. ~ i.. I..,I I. /A I - to 20 30 40, 0 60 Wt % Si Figure 13. Effect of Silicon on the Solubility of Nitrogen

-53obtained for very low %j except in the systems titanium and zirconium where the nitrides are very insoluble. This necessity for using an average slope causes the values of eO to be slightly lower than those of other experimenters which were determined at very low %j as evidenced by Table III. However with the exception of the silicon system in which the nitride is extremely soluble the agreement is quite good. This indicates that the values of eN and ej can be considered reasonably constant in some cases up to surprisingly high %j. Dealy and Pehlke(30) have suggested in view of the relation: ( / ) v;i~~~ 1 H(~~~~~~ a (20) d(i/T) IR 6x 6x* xi xi 0 o which can be derived from the Van't Hoff equation, that E. should be proportional to l/T over short temperature ranges in which the derivative of molar enthalpy with respect to mole fractions of the two dilute solutes can be considered independent of temperature. The same conclusion certainly applies to ej since it is related to E. by a constant: 1 j M solvent (21) (2~303) (100) Mj or in the case of this research in which the solvent is iron: ej _ 0.2425 (22) i M i1 Therefore to test the consistancy of the values of ej given in Table III, the eJ for each system were plotted against l/To These plots are shown in Figure 14 through Figure 17, It can be seen that for the systems aluminum vanadium, columbium, and tantalum the values of ej fit very well a N

-540.1 0.2 - X TITANIUM SYSTEM O ZIRCONIUM SYSTEM 0.3 0.4 0.5 x"x. ~~~\ o.X 0.6 \\ 0.7 o_ O 8 mmON N 0.' Fiue 4 Vraio f ~ ader ih eipoa Tmertr

-55-0.01 I x Al SYSTEM o Cb, a V "........ - 0.0 2 |-O.O XTao -0.03 -0.04 -0.06 -0.07 -0.08 -0.09 -0.10 4.9 5.0 5.1 5.1 52 53 5.4 5.5 I/ TK x 04 Al Cb V Ta Figure 15. Variation of eN, eN, eN, and eN, with Reciprocal Temperature

-560.12. x 0.11 0.10 x 0.09 0.08 0.07 O.06 x- B SYSTEM.ol7 0.05 4.9 50 5.1 5 2 5.3 5.4 5 5. 6 I/T OK x104 Figure 16. Variation of e, with Reciprocal Temperature

-570.06 X Si SYSTEM 0.05 0.04 0.03 0.02 0.01 x 0' -0.01 -0.02 I I 5.9 5.2 5.3 5.4 5.5 5.6 5.7 5,8 I/T ~K x104 figure 17. Variation of eSi with Reciprocal Temperature

58TABLE III SUMMARY OF MEASURED VALUES OF THE INTERACTION PARATERS e AND e Element J Temp ~C e3 e = eJ: Values of other experimenters for e N 3 NMN N Pehlke Maekawa Others Elliott(l) Nakagawa(27'28) 16oo00 -0. 53 -1.82 -0.64 -0.93 Ti 1650 -o.64 -2.20 Rao and (6 runs) 1700 -0.42 -1.44 -0.63 Parlee( 2) 1750 -0.27 -0.93 1600 -o.63 -4.09 Zr 1650 -0.74 -4.81 (6 runs) 1700 -0.73 -4.75 1750 -0.71 -4.62 1600 -0.028 -0.054 0o0025 -0.04 -0.0103 Al 1650 -0.044 -0.0o85 Eklund (29) (9 runs) 1700 -0.051 -o.og8 1750 -0.062 -0.120 1550 O.114 o.o88 1600 o;094 0o.073 B 1650. o80 0 062 (6 runs) 1700 0.o069 0.053 1750 0.059 0.o46 1600 -0. 093 -0.338 -0. l0 -0.11 -0.105 V 1650 -o.o88 -0.320 Kashyap nd (5 runs) 1700 -0.083 -0.302 ParleeM3) 1750 -0.079 -0.288 1550 -0.063 -o. 419 1600o -0. o61 -. 404 -0.067 Cb 1650 -0.057 -0.387 -(4 runs) 1700 -0.053 -0.351 1750 -0.050 -0.331 1550 -0.034 -0.437 Ta 1600 -0.032 -0.413 -0.034 (1 run) 1650 -0.030 -0.390 1700 -0.028 -0.367 1450 0.052 0.104 1500 0.026 0.051 Si 1550 0.021 0.043 (2 runs) 1600 0.0084 0.017 0.047 o.o48 1650 -0.0032 -0.0064 1700 0.0038 0.0076

-59a 1/T dependence. For the boron system the fit is fairly good, while the>t itanium and zirconium systems show some scatter. For the zirconium system this can be explained by the difficulty experienced in redissolving the nitride as previously mentioned. The e~ values for the silicon system show a reasonably good N Si fit to the l/T dependence, but for the line as drawn in Figure 17 eN becomes negative for temperatures of 16500C and above. This would indicate that at these temperatures and silicon concentrations silicon increases the solubility of nitrogen in liquid iron. This conflicts with all other known data on the iron-nitrogen-silicon system which indicate that silicon decreases the nitrogen solubility in liquid iron, This discrepancy is probably caused by reaction between silicon and the A1203 crucible and as a result the entire line of Figure 17 is somewhat questionable. 3 D. Calculation and Summary of the Interaction Parameters e The interaction parameter ej can be determined from information on the variation of the activity of j with composition in binary Fe-j solutions. Wilder and Elliott(31) have used the electrolytic cell method to study the liquid A1-Ag system. From their data in combination with that of Chipman and Floridis(32) on the distribution of aluminum between Al liquid iron and silver layers a value of eA can be calculated for the solvent liquid iron at 16000C. The data show this value to be valid up toabout 13~~~~ ~1. (33) to about 13% Al. Elle and Chipman have studied oxygen activities in liquid Fe-Cb alloys using gas mixtures of H2 and H20. From their data and previously determined values of the free energy of formation of Cb CbO2 a value of eCb can be calculated. which however is expected to be

strictly valid only in very dilute solutions. Chipman et al(34) from measurements on the distribution of Si between liquid iron and liquid silver found a value for eSi in liquid iron which is valid to about 30% Si but becomes invalid with small amounts of additional silicon. Chip:mn(35) gvsr Ti man(35) gives a value for eTi calculated from data on the equilibrium of titanium, oxygen, and TiO in liquid iron. It was previously noted that the ej interaction parameter could also be estimated from data on the Fe-j-N ternary system provided sufficient data were available to show a systematic variation of K' for OV B jN with %j. This method was used to estimate values of eV and e Finally for the zirconium and tantalum systems no known data on the liquid binaries are available and the ternary data were not of sufficient quantity or quality to show the necessary systematic variation of K' with %j. In view of correlations between interaction parameter and atomic number such as the one found by Turkdogan and coworkers e( was estimated by comparing EJ for the unknown element with cj for a j j known element in the same group in the periodic table. A summary of the ej and Ej values used and the sources from which they are derived is given in Table IV. These values are valid only at 1600~C. However because of complete lack of data on the variation of ej with temperature it was necessary to apply the values in Table IV at all experimental temperatures which ranged from 1450~C to 17500C. In all of the systems studied ej was positive and in four of the systems the effect of the j-j interactions was small or negligible compared to the j-N interactions. In the titanium and zirconium systems ej is small while ej is large and negative and %j is also small. j N

-61TABLE IV SUMMARY OF VALUES OF THE INTERACTION PARAMET e Element j e Source cJ S J Ti o.046 Chipman(35) 9.0 Zr 0.025 Estimated from Zr eTi 9.0 ~Zr ~Ti Al 0.048 Wilder and Elliott(31) 5.3 B 0.038 Estimated from experimental data 1.7 V 0.043 Estimated from experimenta data 9.0 Cb 0.0081 Elle and Chipman(33) 3.2 Ta 0.0014 Estim ated from c~, 1/3 Cbb since CCb 1/3 ev 1.0 Cb v Si 0.029 Chipman et al (34) 3.4 Therefore the term ej (%j) in Equation (11) makes a negligible contribution to K. In the columbium and tantalum systems ej is very small while eN is very large and negative so although %j is large the term ej (%j) again makes a negligible contribution to K. In the aluminum system eN and ej are both small and negative while ej is slightly N N j larger and positive. This makes ej important and causes the terms ej (%j), eN (%N), and eJ (%j) to nearly cancel each other making K nearly equal to K'. In the boron, vanadium, and silicon systems the term ej is appreciable with respect to e while %j is large, particularly in the case of vanadium and silicon. In the boron, columbium, vanadium, tantalum, and silicon systems the %j to precipitate nitride must be high, hence the assumption of a -constant ej is questionable. This is particularly true of silicon

since it was noted that Chipman et al found rapid d(eviations from Henry's Law over a short composition range beginning at about 30% silicon, while the silicon content required to precipitate Si3N4 from liquid iron solution under less than one atmosphere nitrogen pressure is about 35%. However since for the majority of these systems no activity data on the Fe-j binary is available it is necessary to assume that ej can be approximated as constant out to the %j required to precipitate the nitride. E. Calculation of the Nitride Solubility Productbyh the Method of Interaction Parameters Using Equation (11) and the interaction parameters listed in Tables III and IV a value of the nitride solubility product K was calculated for each of the absorption curves in Appendix F which shows a point of deviation from Sieverts' Law. The %j and %N associated with the break point of each absorption curve are summarized in Table V together with the values of K' and K calculated. from them. F. Calculation of the Nitride Solubility Product Using the Nitrogen Activity Determined by the Gas Phase It was noted that in the systems boron, vanadium, columbium, and tantalum which have rather soluble nitrides eN may not remain constant up to the %j required to preciptiate the nitride. Although the eJ measured in this study generally agree well with the values of other experimenters obtained in more dilute solutions, any error involved in assuming ej constant can be at least partially eliminated by calculating the nitrogen activity in solution directly from the nitrogen activity in the gas phase which is fixed by the equilibrium nitrogen pressure. This

TABLE V SUMMARY OF THE SOIUBILITY PRODUCTS K' AND K CAWLOUATED BY THE INTERACTION PARAMETER METHOD Element j Temp ~C 0%j 0N K' = %Ti x %N K Ti 1600 0.195 0.0193 0.00376 0.00289 0.228 0.0178 0.00408 0.00294 0.254 0.0145 0.00368 0.00262 0.277 0.0138 0.00382 0.00266 0.318 o.0100 0.00318 0.00214 1650 0.195 0.0390 O. 00760.o00479 0.228 0O.0343 0.00782 o.oo0481 0.277 0.0348 o.oo00964 0.00565 0.304 0.0172 0.00523 0. 00320 1700 0.228 o, 0457 0.0104.2 o.00739 0.254 o.0403 0.01023 0.00722 0.277 0.0517 0.01432 o.00955 0.304 0,.0287 0.00872 O 0.00613 0.318 0.0292 0.00929. o.oo644 1750 0o.304 0.0501 0.01522 0.01172 K' = %Zr x %N Zr 1600 0.253 0.0425 0.01076 0.00506 0.322 0.0432 0.01391 0.00591 0.409 0.0225 0.00921 0.00419 0.558 0.0185 0.01032 o.00396 1650 0,462 0.0765 0.0353 0,.00723 0.558 0.0453 0.0253 0.00607 1700 0.612 0.0787 0.0482 0.00744 1750 O.612 0.1120 o.o686 0.00790 K' = %Al x %N Al 1600 1.07 o.o458 0.0o0 - 0.0512 1.17 0.0381 o.o0445 0.0477 1.34 0.0318 o.o426 o0.0o450 1.57 o.0298 0,0468 0.0500 1.81 0.0211 0.0382 0.0414 1650 1.81 0.0394 o.0693 0.0697 2.26 0.0307 0.0694 0.0702 1700 2.26 0.0495 0.112 0 109 3.14 0.0312 o. 09og8 o.o095 3.85 0.0310 0.119 0.115 1750 3.14 o0.o0541 0.170 0.151

- 64TABLE V (CONT'D) Element j Temp ~C K' = %B x %N K B 1550 3.82 0.0104 0.0397 0.151 5.83 0.0028 0.0163 0.125 7.06 0.0018 0.127 0.150 1600 5.83 0.0045 o.0262 0.154 7.06 0.0033 0.0233 o.g199 1650 5.83 0.0123 0.0717 0.349 7.o6 0.,0050 0.0353 0.236 1700 7.06 0.0079 0.0557 0.324 1750 7.06 0.0163 0.11:5.0.557 K' = V x 9N V 1600 8.05 0.238 1.92 0.634 9.93 0.243 2.41 0.637 15.04 0.280 4.21 0.593 1650 9.93 0.303 3.01 0.858 15.04 0.369 5.55 o.89go 1700 15.04 0.478 7.19 1.282 1750 15.04 0.545 8.2q 1.64o K' = Cb x _N Cb 1550 14.17 0.1625 2.3- 0.327 1600 11.41 0.209 2.38 o.486 14.17 0.218 3.08 o.446 1650 14.17 0.257 3.64 0.589 17.71 0.232 4.38 o.484 1700 17.71 0.205 5.79 0.780 K' = %Ta x %N Ta 1550 20.2 0.141 2.85- 0.547 K' = (%Si)3/4x %N si 1450 34.0 o.oo6 o.00oo78 2.47 1500 34. o. 0054 0o.0702 2.85 1550 36..7 0.0021 0.0313 1.19 1600 34.0 0.0218 0.284 3.04 36.7 0.0117 0.174 2.14 1650 36.7 0.0360 0.536 2.58 1700 36.7 0.0252 0.376 3.27

-65will not completely eliminate any error in K since the j activity required for the calculation of K depends upon eN which in turn is calculated from the experimentally determined value of ej by means of Equation (15). However ej appears in Equation (11) multiplied by %N which is small, while el appears multiplied by %j which is large. Therefore the use of the nitrogen activity determined from the gas phase should definitely lessen any error in K which might be introduced by variation of eJ at higher %j. The recalculation of K by this method for the systems N boron, vanadium, columbium, and tantalum is shown in Table VI. By comparing the K values in Table V and Table VI it can be seen that the use of the nitrogen activity determined by the gas phase causes the K values for the boron system to become much more nearly constant at a given temperature. This indicates that the experimentally B determined values of eN given in Table III may not be constant up to 7% B. For the boron system the values of K in Table VI are probably more accurate than those in Table V. For the columbium and tantalum systems the K values in Table VI are very near the K values in Table V and the differences are considered to be within the limit of accuracy of the experimental method. This is Cb Ta further evidence that eCb and eTa can be considered constant up to the columbium and tantalum contents at which the experiments were run. For the vanadium system the values of K in Table VI show much more scatter at a given temperature than the values of K in Table V. Moreover they show a systematic increase with increasing 1V. This is an indication that the value of eV given in Table III which was estimated from the ternary Fe-V-N data is too high. In Table VII the K values

-66TABE: VI SUMMARY OF THE SOLUBILITY PRODUCTS K' AND K CALCULATED USING THE NITROGEN ACTIVITY DETERMIIND FROM THE GAS PHASE FOR THE SYSTEMS BORON, VANADIUM, COLUMBIUM, AND TANTALUM Element j Temp 0C %j %N K' = %B x %N K B 1550 3.82 0.0104 0.0397 o.145 5.83 0.0028 0.0163 0.143 7.06 0.0018 0.0127 0.143 1600 5.83 0.0045 0.0262 0.175 7.06 0.0033 0.0233 0.197 1650 5.83 0.0123 0.0717 0.292 7.06 0.0050 0.0353 0.260 1700 7.06 0.0079 0.0557 0.346 1750 7.06 0.0163 0.115 O..498 K' = %V x _N V 1600 8.05 0.238 1.92 0.581 9.93 0.243 2.41 0.617 15.04 0.280 4.21 0.736 1650 9.93 0.303 3.01 0.821 15.04 0.369 5.55 0.974 1700 15.04 0.478 7.19 1.570 1750 15.04 o.545 8.20 1.969 K' = %Cb x _N Cb 1550 14.17 0.1625 2.30 0.329 1600oo 11.41 0.209 2.38 o.486 14.17 0.218 3.08 o.464 1650 14.17 0.257 3.64 0.618 17.71 0.232 4.38 0.498 1700 17.71 0.205 5.79 0.716 K' = %Ta x %N Ta 1550 20.2 o.141 2.85 0.550

for the vanadium system from Table V have been reproduced in the column labeled K1 and the K values from Table VI reproduced in the column labeled K2. The K were then recalculated using the activity of nitrogen determined from the gas phase and lower value of eV = 0.028 V (Ev = 6.0). These values are shown in Table VII in the column labeled K3. It can be seen that they are much more nearly constant for a given temperature, and the value of eV = 0.028 is therefore expected to be nearer V to the correct value. TABLE VII COMPARISON OF K VALUES FOR THE VANADIUM SYSTEM CALCULATED FOR DIFFERENT VALUES OF THE INTERACTION PARAMETER eV Temp ~C %V N K' = %V x N K1 K2 K 1600 8.05 0.238 1.92 o.634 0.581. o.455 9.93 0.243 2.41 0.637 0.617 0.454 15.04 0.280 4.21 0.593 0.736 o.457 1650 9.93 0.35053 3.01 o.858 0.821 0.590 15.04 0.369 5.55 o.890 0.974 0.624 1700 15.04 o.478 7.19 1.282 1.570 0.954 1750 15.04 0.545 8.20 1.640 1.969 1.193 The fact that the K1 values are not as constant as the K3 values and in particular that the K1 value for 15.04% V is lower than the other two values for lower vanadium contents indicate that there is probably some change in the value of eV with increasing vanadium conN tents. This is borne out by the work of Pehlke and Elliott(l) who found a value of eV =-0.10 to be good only out to about 5% V. Beyond that N composition they found a slight change in slope of the curve of log Nf

-68versus %V. However the change in slope was small so the error produced in K by assuming eV constant should be correspondingly small. N G. Calculation of the Nitride SolubilitY Product Using the.j Activity Estimated From Fe-j Binary Data Because of the high solubility of Si3N4 in liquid iron the silicon content required to precipitate Si3N4 below one atmosphere of nitrogen pressure is in excess of 30%. It was previously noted that Si this is beyond the silicon concentration for which e may be approxiSi mated as constant. Consequently the use of the interaction parameter method to approximate the silicon activity in Fe-Si-N solutions may lead to serious error producing a low value for the silicon activity and therefore also a low value for the solubility product of Si 3N4 In order to avoid this error the K values for the silicon system were recalculated with the silicon activity estimated from the activity data of Chipman et al(34) which cover the entire composition range of the Fe-Si system. The nitrogen activity in solution was determined from the nitrogen activity in the gas phase. The activity data of Chipman et al(34)for 14200C are shown graphically in Figure 18 and numerical values are given in Table VIII. Fromthese data silicon activities are calculated for the various experimental temperatures used in this study from the relation: alny = Si (23) a (l/T) R where LSi represents the relative partial molal enthalpy of silicon in binary Fe-Si solutions relative to pure silicon and defined by the

I.2 I.0 0.8 XI. E I 0.26 IiS3. I I, x 0.4 Oloop ~ ~ ~ x 02S3 0.2 ~~~~~~~~~~~~~Xsi 0. 535 % /Si 36.77.01.0.1 ~~~~~~~Si =-0.50i _____d HENRY'S LAW LINE — L 0 0. I 0.02 0.3 0.4 0.5 0.6 0.7 Q8 0.9 tO I I I I XSi 5.31 11.70 17.70 25.1 33.6 43.0 54.0 66.9 82.0 100 %/oSi Figure 18. Activity of Silicon in Binary Fe-Si Solutions at 14200C From Data by Chipman, Fulton, Gokcen, and Caskey(34)

-70equation: rSi i S ~S i (24) TABLE VIII ACTIVITY OF SILICON IN Fe-Si SOLUTIONS AT 1420~C. FROM THE DATA OF CHIPMAN ET AL (34) Si -EL aSi mole fr. K cal. -log 7Si'Si (mf) = XSi 7Si 1.0 0.0 0.00 1.00 1.000.g9 0.1 0.01 o.98 o.882 o.8 o.4 0.03 0.93 0.744 0.7 1.7 0.07 0.85 0.595 o.6 4.4 0.12 0.76 o.456 0.535 (36.7%) 7.2 0.19 o.64 0.343 0.507 (34.0%) 8.1 0.24 0.57 0.290 0.5 8.4 0.26 0.55 0.275 0.4 13.4 0.72 0.19 0.076 0.3 19.3 1.45 o.o06 0.0108 0.2 24.1 2.09 0.0081 0.00162 0.1 27.8 2.34 o.oo0046 o.00oo46 0.0 28.5 2.50 0.0032 0.00000 L is known from the work of Korber and Oelsen(37). For lack of other Si information it is necessary to assume that LSi is constant with temperature and treat it as a function of composition only. The silicon activities given by Chipman et al(34) are expressed relative to Raoult's Law with the activity of silicon related to mole fraction and the standard state taken as pure liquid silicon. To use these silicon activities in conjunction with the experimental data they must be expressed relative to Henry's Law with the activity of silicon related to weight percent and the standard state taken as the infinitely dilute solution of silicon in pure liquid iron. This conversion is made by means of the equation: Si (m.f. - Raoult's Law),0.5585y70 (25) aSi (% - Henry's Law) MSi

-71where y~ is the slope of the asi versus mole fraction Si plot at infinite dilution. Implicit in Equation (25) are the assumptions that the mole fraction of silicon isproportional to the weight percent silicon up to the experimental silicon contents and that the weight of silicon is negligible with respect to the total weight of the solution. An exact calculation shows that these assumptions produce an error of 5% to 10% in the calculated silicon activity with respect to Henry's Law. This is a negligible correction compared to the uncertainty in the experimental data. The silicon activities calculated for all experimental temperatures and compositions are shown in Table IX. The effect of the siliconnitrogen interaction on the activity of silicon can be shown to be negligible because of the very small %N in a solution containing over 30% Si. The values of K for Si3N4 calculated by this method from the break points of the nitrogen absorption curves are given in Table X. By comparing these K values with the K values given for the silicon system in Table V it can be seen that the values in Table X are larger as would be expected. However they still do not show the expected systematic variation with temperature. This is probably due to error in the experimental data rather than error in the methods of estimating the silicon and nitrogen activities, H. Calculation and Summary of Enthalpy and Entropy of Decomposition of Nitrides in Liquid Iron The variation of the nitride solubility product with temperature is given by the Van't Hoff Equation:

TABLE IX CALC=lTED ACTIVITY OF SILICON IN Fe-Si SOLUTIONS OF 34.0%.SILICON AT TEMPERATURES FROM 142o.0 to 1700Co ASi at Y.Si 0.1 jw )si ASi (rf -Raoult'.s Law) A51 atAS, 0.-HenryIs Temp OC Xi =0.1 O. 507 xSi 0.535 Xsi 0.1 = 0.507 X51 =0.535 XS =0.50735 1420 o.0o46 0o. 57 o.64 0.000o46 0.290 0.343 o.oo46 3180 5760 1450 0.0054 0.60 0.68 o.ooos4 0.304 0.364 0.0054 2840 3400 1500 omoo66 o.65 0.73 o.ooo66 0.3 0.380 o.0066 2500 2880 3550 o.oo83 o.69 0. 76 0.00083 _0.350 0.407 0.0083 2120 2470 60oo 0.0102 0.72 0.80 0.00102 0.365 0.428 0.0102 1802 23.5 165o 0.0123 0.78 0.83 0.00123 0.396 0.444 0.0323 1621 3820 3.700 0.0148 0.81 0.87 o.mo1348 o.411 0.465 o.ol.48 13398 3.583

-75d(ln K) -.- H~ (26) d(l/T) R TABLE X CALCULATED ACTIVITY OF SILICON IN Fe-Si SOLUTIONS OF 34.0% and 36.7% SILICON AT TEMPERATURES FROM 14200C to 1700~C 3/4 Temp 0C %Si N K' = (Si)x %N K 1450o 34.0 o.ooo6 0.0078 13.10 1500 34.0 0.0054 0.0702 14.02 1550 36.7 0.0021 0.0313 9.45 1600oo 34.0 0.0218 -0.284 10.99 36.7 0.0117 0.174 7.91 1650 36.7 0.0360 o.536 7.66 1700 36.7 0.0252 0.376 8.74 If log K is plotted versus l/T the slope of the curve gives, H~ the standard enthalpy of decomposition of the nitride and the intercept at l/T = 0 gives A S the standard entropy of decomposition of the nitride in liquid iron, i.e. for the reaction as given by Equation (5). The usual procedure is to assume that L H~ and A S are constant over short temperature ranges and therefore to fit a straight line to the points on the Van't Hoff plot. These plots for the seven experimental systems in which the temperature variation of K has been studied are shown in Figure 19 through Figure 25. To obtain these plots the values 0f K from Tables V, VI, VII, and X for a given system were averaged at each temperature and plotted against the reciprocal temperature. The values of L H~ and L So were calculated from these plots by the integrated form of Equation (26): in K _- H~ (1/T) + & S~ - (27) R R

0.02 Ti N(s) = i +N o~oot \01 - 0.02 0.0l 0.009 o.ooe Z r N(s)= Zr +_N 0.007 x 0.006 0.005 0.009 0.004 0.008 0.0074.9 00 3.3 5 4 55 49 5.0 0, 52 6.3 5.4 s.5 30.005 0.002 0.004 0.00304.9 5; 0 5.1 5.2 5.3 5. 4 5a5 49 5.0 5.1 5.2 5.3 5.4 I /TOKxIO4 I /T ~K x 104 Figure 19. Variation of Equilibrium Constant with temperature Figure 20., Variation of Equilibrium Constant with Temperature for the Reaction TiN(s) * Ti + N for the Reaction ZrN(s). Zr + N

-75-v 0.3 0.2 At N.(s) Att A+ _+N 0.1 0.09 0.08.07 ~060 05 )04 )03.02 4.9 5.0 5.l 5.2 5.3 5.4 I/T ~K x 104 Figure 21. Variation of Equilibrium Constant with Temperature for the Reaction AlN(s) n Al + N

1.0 Activity of B determined from interaction parameters. 0.8 Activi-ty of N determined from gas phase. o.7 B N(s = B + N 0.6 0.45 0.32 (A) ~1.0' 0o.9 Activities of B and N determined from interaction parameters. 0.8 0.7 0.6 0.5 0.4 0.S 0.2 (B) 0.1' I I! 4.9 5.0 5.1 5.2 5.3 5.4 5.5 5.6 I/T K x lO4 Figure 22. Variation of Equilibrium Constant with Temperature for the Reaction BN(s) = B + N

1772.0.. Activity of V determined from interaction parameters. Activity of N determined from gas phase. V N(s)- V + N 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 (A) 0.2 Activity of V and N determined from interaction parameters. 1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 (B) 0.2 4.9 5.0 5.! 5.2 5.3 5.4 5.5 5.6 I/r O K xIO4 Figure 23. Variation of &janlibrium Constant with Temperature for the Reaction VN(e) = V + N

_781.0 0.9 Activity of Cb determined from interaction parameters. 0o.8e~ ~Activ'ty of N determined from gas phase ~0.8 ~~~Cb Ns) Cb+N 0.7 0.6 0.5 0.4 X 0.3 0.2 (A) 0.9 Activity of Cb and N determined from interaction parameters. 0.8 0.7 0.6 0.5 0.4 0.3 0.2 (B) 0.1 4.9 5.0 5.1 5.2 5.3 5.4A 55 56 I/ T ~K x IO4 Figure 24. Variation of Equilibrium Constant with Temperature for the Reaction CbN(s) = O + N

-79Si 3/4N s) a3/4Si+N 20 Activity of Si determined from interaction parameters. Activity of N determined from gas phase. 10 x 9-" X 81- X 6 - Activities of Si and N determined from interaction parameters. 4 x _ 2' — 5,1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 I/T ~K x 104 Figure 25.- Variation of Equilibrium Constant with Temperature for the Reaction Si3/4 N(s) 3 3/4 Si + N

-80They are given in Table XI along with the assumed nitride compositions which were used to calculate K. Also given in Table XI are the values of L F~ for the decomposition of the nitrides in liquid iron at 1600~C as calculated from the given values of A H~ and A S~ according to the relation: L F = A H - T A S~ (28) I, Discussion of Results of the Various Methods Used to Calculate the Nitride Solubility Products Because of the possibility of variation in e and eN at N j high solute concentrations it is felt that the values of A Ho, SQ, and A F~600 for the more soluble nitride systems given in the second and third sections of Table XI are more accurate than the values for the same systems given in the first section. For the three more insoluble nitride systems titanium, zirconium, and aluminum the values of H~, A S~ and A F~1600 were calculated by the interaction parameter method only, since in these systems the solute concentrations are low enough that the interaction parameters should definitely remain constant over the required composition range. By comparing Figure22a with Figure 22b it can be seen that the use of the nitrogen activity determined by the gas phase for the boron system considerably reduced the data scatter in the Van't Hoff plot. The lower values of A H~ and A S~ they yield are consequently considered more accurate. With the vanadium system the K values calculated from the nitrogen activity determined by the gas phase (values in column K3 of Table VII) show about the same scatter in the Van't Hoff plot as the K values calculated by the method of interaction parameters. This is seen

TABLE XI SUMMARY OF K VALUES FOR THE SILICON SYSTEM CALCULATED USING THE ACTIVITY OF SILICON ESTIMATED FROM Fe-Si BINARY DATA Element j Temp Cal Cal LL Ho A S A Range OC 0.L Mol Cale LK F0G~ Cal asmd i-Cmet,Range O Mol~e Mole OK l6oooc Mole ride composition Ti 1600-1750 75,200 28.54 22,100 TiN Activities of j and N determined Zr 1600-1750 52,600 6.69 20,100 ZrN 9 ~~~~~~~~~~from interacto parameters Al 1600-1750 65,700 27.91 11,4oo AiN B 1550-1750 50, 200 25.47 6,200 BN V 1600-1750 50,700 26.15 1,800 VN Cb 1550-1700 42, 200 20.93 3,000 CbN Si 1450-1700 3600 5.89 -5300 SiN B 1550-1750 45,900 21,25 6,100 BN Activity of j determined from V 1600-1750 49,000 24.58 3,000 VN interaction parameters. Activity Cb 1550-1700 35,000 17.08 5,000 CbN of N determined from gas phase Si 1450-1700 -10,500 -0.75 -11,900 Si514N Activity of j estimated from Fe-j binary data. Activity of N determined from gas phase

-82from Figure 23a and Figure 23b. However as was previously noted the K values calculated from the nitrogen activity determined by the gas phase are much more constant at a given temperature and therefore the slightly lower A H~ and A S~ they yield are also considered more accurate. Figure 24a and Figure 24b which show K values calculated from the two different methods for the columbium system also show about the same scatter and as previously noted the comparison of the K values in Table V and Table VI show small differences within the limits of experimental error. Nevertheless the values of A H~ determined from the two different sets of K values show an appreciable difference of about 7,000 calories/mole. This emphasizes the difficulty involved in trying to make an accurate determination of A H~ from a Van't Hoff plot over a comparatively small temperature range. Although there is no experimental Cb N evidence of error introduced by variation in eN and eCb, the lower values of A H~ and A S~ determined using the nitrogen activity determined by the gas phase are considered more accurate in the columbium system as well as in the boron and vanadium systems. The A H~ and A S~ values in Table XI show that the results for two systems, zirconium and silicon, are inconsistant with the results of the other five systems. The problem with zirconium is that it is a very strong oxide former. Calculations made from data after Elliott and Gleiser(38) and Chipman(7) show that at 16000C the A F~ of decomposition of ZrO2 in liquid iron exceeds the A F~ of ZrN by more than 60,000 cal./mole of Zr and exceeds the A F~ of A1203 by about 5,000 cal./mole of 0. This indicates that ZrO2 is more stable than either A120l or ZrN in contact with liquid iron at this temperature. This

-83explains the previously noted reaction between Fe-Zr alloys and A1203 crucibles which resulted in the formation of ZrO2 floating on top of the melt with an attendant drop in the zirconium content of the solution. Appendix F contains three nitrogen absorption curves for melts of iron plus up to 0.422% Zr made in A1203 crucibles. These curves all show a Sieverts Law line almost identical with that for pure iron all the way to one atmosphere nitrogen pressure. This indicates that nearly all the zirconium was removed from solution by reaction with the A1203 crucible because if even small amounts of zirconium had remained in solution the nitrogen solubility would have been appreciably increased. It is also quite possible that the reduction of the A1205 crucible by zirconium caused appreciable quantities of aluminum to be dissolved into the melt. However the effect of aluminum on nitrogen solubility is small (i.e. eAlO0) and its presence therefore would not be reflected in the slope of N the Sieverts Law line. The data on the zirconium system consequently were obtained using ZrO2 crucibles to contain the melt. However even these caused the formation of small amounts of floating solid on top of the melt under a hard vacuum. This solid is thought to be ZrO2 formed from oxygen adsorbed on the crucible walls and zirconium from the melt. Another possible source of oxygen is Y203 which is contained in the ZrO2 crucible. The zirconium recovery in the melt therefore may have been somewhat lower than the calculated charge compositions causing the calculated values of K' and K to be slightly high and the values of eZr and eN to'be N Zr slightly low. It is noteworthy however that although the quantity of floating solid formed appeared to vary considerably from run to run the

-84values obtained for the nitrogen solubility and the nitride''solubility limit are reasonably self consistant. The initial data for the zirconium system were obtained with ZrO2 crucibles of 3/4" inside diameter and 2" deep. However with these deep narrow crucibles very little stirring of the molten metal could be observed visually. Moreover on examination of the solidified ingots it appeared in several cases that the charge had never'become a completely homogenous melt. Therefore several melts were made with ZrO2 crucibles of 1 13/16" inside diameter 1 7/16" deep. In these melts the amount of stirring observed was much greater and the solidified ingots all appeared definitely homogenous. However the results obtained were identical to those obtained on the smaller diameter ZrO2 crucibles. It can be seen from Appendix F that in some of the nitrogen absorption curves for the zirconium system the deviation from the Sieverts Law line is in a horizontal instead of a vertical direction. The reason for this is that when sufficient ZrN precipitates to form a continuous film on top of the melt the gas phase is effectively insulated from the liquid phase. Equilibrium'between the gas and liquid phases at higher nitrogen pressures can'be achieved then only'by diffusion of nitrogen through the solid film into the liquid phase where it can react with the zirconium in solution to precipitate more ZrN. This process is so slow that equilibrium is not achieved in an experimentally reasonable time. Consequently once the nitride film has formed the melt will atbsorb almost no more nitrogen and the only volume of gas required to further increase

the nitrogen pressure is that necessary to fill up the hot volume. Of course these absorption curves with a horizontal deviation cannot be considered to define the nitride solubility limit as accurately as the absorption curves with the normal vertical deviation, since the conteracting effects of horizontal deviation due to nitride film formation and vertical deviation due to nitride precipitation may cause the experimental points to appear to follow a straight Sieverts Law line beyond the true nitride solubility limit. However the nitride solubility limits measured from these horizontal deviation absorption curves agree reasonably well with those absorption curves for the zirconium system which show the normal vertical deviations. The effect of nitride film formation was evident for the other alloy systems as well as zirconium. It was reflected in the much longer times required to reach pressure equilibrium at nitrogen pressures above the nitride solubility limit. Below the nitride solubility limit the equilibrium pressure was reached in 5 to 10 minutes while above the nitride solubility limit 30 minutes was minimum and equilibration times of 60 to 90 minutes were not uncommon. However with all systems except zirconium the nitride films were apparently porous enough that the absorption curves showed normal vertical breaks if sufficiently long equilibration times were used. The apparent inconsistency in A H~ and A S~ for the silicon system is attributed to the extreme solubility of Si3N4 which makes estimation of the activities of Si and N less accurate and to the possible reaction of silicon with the A1203 crucibles which may have — produced erroneous values of K at the higher temperatures in each

determination. The experimental values of K' and K are felt to be correct within an order of magnitude, but little faith can be placed in the values of A H~ and S~0 calculated from them. These are thought to be considerably low. A calculation using the data of Pehlke and Elliott (139)and Chipman(7) indicates that the values should be A H~ 21,500 cal./mole, A S~ = 20.21 cal./mole ~K, and. F016o0 = -16,300 cal./mole. The fact that this value of F~O1600 corresponds reasonably to the value in the third section of Table XI is further evidence of an order of magnitude accuracy in the K values, at least for temperatures of 16000C and below. The values of A F~1600 given in Table XI are a measure of the relative stabilities of the various nitrides in contact with liquid iron at 1600~C. They show that the resistance of the nitrides listed in Table XI to liquid iron at 16000C decreases from top to bottom of the table. Only TiN, ZrN, and possibly AlN can be considered as refractory materials which will be reasonably resistant to attack by liquid iron at this temperature. Table XI shows that BN, although it is used in contact with solid iron base alloys at elevated temperatures in a number of applications particularly in nuclear reactor components and is advertised as being resistant to attack from liquid metals such as silicon, aluminum, copper, zinc, and iron, is soluble to a fair degree in liquid iron. Table V suggests that if BN is equilibrated with liquid iron at 1600C under atmospheric pressure of nitrogen gas the melt should dissolve 4 to 5 percent boron. If the partial pressure of nitrogen over the melt is less than one atmosphere the amount of boron dissolved by the melt will be

-87correspondingly higher. The solubility of BN in liquid iron is certainly great enough that if BN is used as a refractory to contain liquid iron the melt will become seriously contaminated with boron. Also if the mass of the melt is sufficiently large with respect to the mass of the refractory the melt may easily dissolve enough BN to corrode through the refractory and run out. Determination of nitride solubility products from the experi.mental data by the method of extrapolation of log K' to zero %j proved to be generally less accurate than the other methods of calculation. For the titanium and zirconium systems the interaction parameters eN are large and negative. This means that the assumption that the term eN( ) is negligible over any appreciable range of -%j is not valid. The plot of K' versus j for the aluminum and boron systems is shown in Figure 26 and for the columbium and vanadium systems in Figure 27. The values of K given in Figure 26 show reasonable agreement with the K values for the aluminum and boron systems given in Table V. The K values given in Figure 27 are slightly higher than the values given in Table V for columbium and in the last column of Table VII for vanadium. This is probably due to the fact that the interaction parameters [eN and eN V Cb are also large and negative. J. Summary of the Nitride Solubility Products Measured by the Quenching Method The experimental results obtained by the quenching method are summarized in Table XII. The first section of the table gives the results of the calibration runs made with pure iron using A12 0 crucibles and compares them with results for the solubility of nitrogen in pure liquid

-880.?3 ELEMENT J TEMPERATURE KK' ATINTERP x Al 1600 c 0.058 0.2~ - -e Al 1650~ c 0.069 Al 1700- C 0.106 a B 150- C 0.134 0' B 1600 c 0.150 0.09 0.01 0o 0.05 0.04, 0.02 0.. 1 0 1.0.0 3.0 4.0 5.0 6.0 ZO Figure 26. Extrapolation of K' to Zero % in'the Aluminum and Boron Systems

-897 6 5'"" 4 - / zi 2 0.9 A Cb 1600 C 0.81 0.5 Cb 1650 0 1. 31!0 4 0.83 X0 4.0 8.0 12.0 16.0 2.0 Figure 27. Extrapolation of i' to Zero %j in the Vanadium and Columbium Systems

-90iron measured by the Sieverts method. The first three runs were made at 1600~C for various equilibration times under atmospheric pressure of nitrogen gas. The nitrogen solubilities determined by Kjeldahl analysis were corrected to one standard atmosphere of nitrogen pressure by multiplying them by [76.0 P P is the atmospheric pressure existing during the equilibration which was read from a mercury barometer. In order to determine if the liquid seal at the gas stream outlet caused the build-up of a pressure/ appreciably above atmospheric in the furnace chamber one outlet line was connected to a manometer and the maximum gas flow to be used was passed through the system. The manometer showed no measurable pressure build-up indicating TABLE XII SUMMARY OF RESULTS OBTAINED BY TYE QUENCHING METHOD Sieverts'() Element j Temp ~C Time (min) PN (atm) %N %N K' PN~~~~~~K 2 Method NONE 1600 15 1.000 0.0452 0.0451 1600 30 1.000 0.0456 1600oo 60 1.000 0.0456 1600 50 0.762 0.0399 0.0395 16o0 50 0.332 0.0288 0.0262 1700 30 1.000 0.0442 o.046o0 Ti 160oo 0 0.332 0.5 0.149 0.00536 1700 15 0.331 0..38 o.0056 0.00213 1700 15 0.977 1.20 0.04 0.o01128 1700*+ 5 0.979 0.11 0.0391 0.00450 Al 1600 30 0.331 1.44 0.0381 0.0549 1600* 30 0.972 1.15 0.0547 0.0629 1650*+ 2-5 0.971 0.50 0.0329 0.0164 B 1600 50 0.978 3.49 o.oo6o 0.0210 16oo 30 0.764 2.51 0.0055 0.0133 *quench not completely satisfactory,+equilibration ended prematurely by equipment failure

-91that it was less than one millimeter of mercury and therefore could be considered negligible. The excellent agreement among the first three runs at 16000C and one standard atmosphere nitrogen pressure and the Sieverts method value for the same conditions indicated that equilibrium between liquid and gas phases in the quenching apparatus was reached within 15 minutes. This however is in the' absence of a solid nitride phase. Because the presence of the nitride phase slowed the attainment of equilibrium in the Sieverts measurements an aim equilibration time of 30 minutes was selected for the equilibrations using nitride crucibles. The next two pure iron runs were made to test the effectiveness of the gas metering system in controlling the nitrogen partial pressure in the quenching apparatus. The results obtained are plotted and compared with the Sieverts method data in Figure 28. While the agreement at one atmosphere and 0,76 atmosphere nitrogen pressure is excellent, the quenching method solubility value at 0.55 atmosphere is slightly higher than the Sieverts method solubility value at the same pressure. This might be t.h e effect of themal diffusion which would tend to cause enrichment of the lighter of two gases in a mixture at the hotter portions of the furnace chamber. This would have the effect of enriching the atmosphere immediately above the melt surface in nitrogen and depleting it in argon, which would account for the higher nitrogen solubility value. However the difference between the quenching method solubility and the Sieverts method solubility is small and may only reflect a small error in the nitrogen analysis. The final run on pure iron was made at 1700~C to test the effectiveness of the quenching system with this extra 1000C of superheat.

-92SIEVERT MEASUREMENTS PATA OF PEHLKE AND ELLIOT(I) 0.05 + QUENCHING MEASUREMENTS 0.04 x 0.03 0.02 0.01 0. I 0.2 4 6 10 I 2 12 14 (P N (Cm) Figure 28. Solubility of Nitrogen in Pure Liquid Iron at 1600~C

-93The nitrogen solubility value obtained was lower than the solubility measured at 16000~C while the Sieverts method data indicates that the nitrogen solubility should increase slightly with increasing temperature. This indicates that on quenching from 1700~C a small but finite amount of nitrogen is lost from solution. In order to determine if an appreciable temperature gradient existed across the diameter of the melt, optical pyrometer readings were taken both at the center and at the outer edge of the melt. These readings showed the melt edge to be approximately 10~C cooler than the melt center. This difference is nearly within the limits of the pyrometer accuracy and in any case is very small. This indicates that the temperature of the melt is substantially uniform and that most of the temperature drop between melt and surroundings is therefore through the crucible walls. These readings would appear to indicate that there is also little or no temperature gradient across a melt in the Sieverts apparatus where direct pyrometer readings cannot be taken since all except the center of the melt surface is covered by a crucible lid. From the results of the pure iron calibration runs it was concluded that the design and operation of the quenching apparatus were basically sound. Equilibrium between melt and gas phase was reached within 15 minutes. The control over the nitrogen partial pressure and melt temperature were sufficiently precise. The quench was sufficiently fast to permit negligible amounts of nitrogen to escape from solution on quenching from 1600~C and very small amounts of nitrogen to escape from solution on quenching from 17000C.

Four runs were made using titanium nitride crucibles and the results of these are summarized in the second section Table XII. It was previously noted that the TiN crucibles proved slightly porous to liquid iron and for this reason the aim equilibration time for all runs at 17000C was cut to 15 minutes instead of the usual 30 minutes. The fourth run was terminated after 5 minutes by burning out of the induction coil, but the analyses are not very different from those obtained in the other three runs so equilibrium must have been approached even in this short time. Over heating of the induction coil had to be carefully guarded against with this system because the electrical and thermal properties of TiN caused the crucibles themselves to heat up to a temperature very near to that of the melt. The agreement between the K' values for TiN in Table XII and those in Table V is only fair. Moreover the nitrogen and titanium analyses and the values of K' are not completely consistant among themselves. For example the second and fourth runs show a lower K' at 17000C than the first run shows at 16000C although it is certain from the Sieverts data that the solubility of TiN in liquid iron increases with increasing temperature. Although the third run shows a K' value which compares well with the K' values for TiN at 1700~C in Table V it is difficult to understand the high titanium analysis. In addition the nitrogen analyses are generally lower than the corresponding nitrogen values in Table Vo This may be accounted for by the fact that difficulty was experienced with this system only in completely dissolving the samples for the Kjeldahl analyses. A small amount of black appearing residue invariably remained undissolved after the sample had been digested. This may

-95have been all or partly a nitrogen bearing compound and thus led to low nitrogen analyses. The results of the three runs made with AIN crucibles are summarized in the third section of Table XII. The values of K' for 1600~C show good agreement with the values of K' at 1600oC for the aluminum system given in Table V. The Table XII values are slightly higher than the Table V values, This may be explained by the fact that with the quenching method the equilibrium is being approached with an excess of nitride present while in the Sieverts method the equilibrium is being approached with the nitride initially absent. The initial presence of the nitride in the quenching method may have the effect of increasing the tendency toward supersaturation in the solution. The aluminum and nitrogen analyses show self consistency, the %N decreasing as the %Al increases. The value of K' increases with decreasing %Al which is the same trend shown by Table V and Figure 26. The run at 1650~C which was cut short by a burned out induction coil obviously did not stay at temperature long enough to reach equilibrium, This accounts for the low values of %Al, %N, and K'. Even in this case however it is significant that the value of K' agrees within an order of magnitude with the K' values for the aluminum system at 16500C given in Table V. The fourth section of Table XII summarized the results of two runs made with BN crucibles. The values of %B, %_N, and K' agree quite well with the values for the boron system at 16000C given in Table V. The %B for the second run apprears to be slightly low and this is thought to be an inaccuracy in the analysis.

-96K. Summary of Methods Used to Determine the Nitride Phase Compositions Attempts were made to determine the compositions of the nitride phases formed both directly by x-ray and wet chemical analyses and indirectly by means of the previously described phase rule analysis and from the variation of the solubility product with temperature. Only three of the alloy systems, titanium, zirconium, and aluminum, have nitrides sufficiently insoluble that the assumption of negligible %j in solution which is inherent in Case 3 of the phase rule analysis might be expected to hold. Of these three, zirconium must be eliminated because of the extreme non-equilibrium conditions which were shown to exist at nitrogen pressures well above the nitride solubility limit. For the titanium and aluminum systems the majority of the nitrogen absorption curves are not suitable for calculation of the nitride phase composition since they were terminated slightly above the break points in order to redetermine the nitride solubility limit at a higher temperature. However two absorption curves in each of the two systems extended to sufficiently high nitrogen pressures to make a calculation of the nitride phase composition possible by the phase rule method. The graphical analysis of these absorption curves and the details of calculation of the nitride phase compositions are shown in Appendix G. The results give nitride compositions of Ti2 2N and Ti2 4N for the titanium system and A13 9N and A145N for the aluminum system. Only for one absorption curve, the 0.228% Ti curve, can a line with the slope of the Sieverts Law line for pure iron be drawn through the data points at high nitrogen pressures with reasonable accuracy. The nitride

-97compositions calculated in Appendix G are all thought to be too high in metal. This is due to the difficulty in completely saturating the liquid and solid phases with nitrogen at a given nitrogen pressure once an initial nitride film has formed on the melt. Apparently even after times of 60 to 90 minutes complete equilibrium does not exist at nitrogen pressures well above the nitride solubility limit. Since the variation of the nitride solubility products with temperature was known it was thought possible to at least infer limits on the nitride compositions by calculating values of K for various nitride compositions, i.e. various values of x in Equations (5) and (10), and determining which compositions gave the best fit to a linear relation between log K and l/T. For at least three of the systems previous work had shown the possibility of the nitride existing with a metal rich stoichiometry. These systems are titanium,(l2)'(14) vanadium, (3),'(7) and columbium.(18) Figure 29 shows the Van't Hoff plot of the Sieverts method data for the titanium system for assumed nitride compositions of TiN, Til 7N the composition calculated by Rao and Parlee(l2), and Ti2 N given as the upper composition limit by Ehrlich(l4) It can be seen that the composition for which the data points show the best fit to a straight line is TiN. The fit for Til 7N is only slightly worse but the fit for Ti24N is definitely worse. With both of the latter two nitride compositions the data points show some positive curvature. This indicates that the composition of the titanium nitride precipitated from liquid iron is no higher in metal than Til7N and probably not that rich in metal. It is definitely not as metal rich as the compositions Ti2 2N and Ti2 4N calculated from the phase rule analysis.

-98Ti N(s)= Tij+N Ti.t7 N(s ) 1.7 Ti+N Ti2.4 N(s)=2,4Ti+N 3' 3t' \X\` ~ x, Ti N(s)= T+Ni 8p X \ \Til7 N(s)=I.7Ti+N 64 3 ~TiQ2.4 N(s)=2.4Ti+N 2.2.3.4 5.6 I/T 0K x104 Figure 29. Variation of Equilibrium Constant with Temperature for the Reactions TiN( t T. +, Ti1.7 N() 1.7 NTi + +N ~"iani(s) =2. Ti N+N

-99Figures 30 and 31 show Van't Hoff plots for the nitrides V2.5N the composition given by Hahn(l7), and Cb2N the most-metal rich columbium nitride found by Schonberg(18) Figure 29 shows greater data scatter than either Figure 23aor Figure 23b and evidence of possible negative curvature. Figure 30 shows slightly greater scatter than Figure 24aand Figure 24b and possible positive curvature. The indications are that the compositions of vanadium nitride and columbium nitride precipitated from liquid iron are not as metal rich as V2.N and Cb2N, although compositions in the ranges Vl.0-2.0N and Cb N are quite possible. 1.0-1.5 Both wet chemical and x-ray analyses were attempted on samples of nitrides extracted from the solidified ingots of the Sieverts method determinations. Wet chemical analyses of the extracted nitrides were successfully used only with the aluminum system. They were hampered by the small quantities of nitride which-could be extracted from an ingot and by the fact that the nitride residue was invariably slightly contaminated with Al 05 from the crucibles. In addition the inaccuracy inherent in wet chemical analyses is reflected by a comparatively large variation in the metal/nitrogen ratio of the nitride. The results obtained with the aluminum system are shown in Table XIII. Details of the analytical procedures used and their estimated accuracies are covered in Appendix D. TABLE XIII RESULTS OF WET CHEMICAL ANALYSIS OF EXTRACTED AlN RESIDUE Total Al (wt. %) Nitrogen (wt. %) Calculated Nitride Composition 59.80 24.80 All. 25N 59.45 26.00 M1i18N

200 Va. N(S) 2.5V+N x Cb2N(s) =2Qb+N 20 tOO~~~~~~~~~~~~~~~~~~~ 900 Y. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 80 -I S. raha 7~~~~~~~~~~~~~~~~~~~~~ 6.9 0A 5.3 H4 5.5 I/T OK 40 104 I7TOK x 104 Figure 30. Variation Of Equilibrium Constant with.Temperature Figure 31. Variation Of.-EQuilibrium Constant with Temuperature for the Reaction V2.5 N(s) = 2.5 V + N for the Reaction C~b2 N4(s-) n 2Cb + N

-101The most generally successful method of identifying the nitride formed and determining its stoichiometry was by x-ray analysis of the extracted nitrides. Powder patterns were made using the Debye-Scherrer technique and the lattice parameters were determined by calculating ao 2 for small values of sin G and extrapolating to 00. Since the amount of material required for this technique isvery small (100 mg. or less) sufficient nitride could be extracted in all systems except zirconium. The details of the x-ray procedure and a summary of the results of the patterns run on each system are given in Appendix H. Lattice parameter measurements on extracted titanium nitride gave a lattice constant of 4.242 4. This is in excellent agreement with Ehrlich's(l4) value of 4.23 A which he claims corresponds to a composition of TiN. Lattice parameter measurements on two samples of extracted vanadium nitride gave lattice constants of 4.062 A and 4.o68 A. According to Hahn(l7) this lattice parameter corresponds to a composition of VN0.71 (or V1o4N) which is about the composition limit on the low nitrogen side for the nitride of nominal, composition VN. These results are quite consistant with the composition limits indicated for these systems by the temperature variation of the solubility products. The results of the efforts made to determine the nitride compositions precipitated from liquid iron solution cannot be considered conclusive. However they indicate that although there may be some composition variation on the metal rich side from the compositions assumed in Table XI it is small. The value of x in Equations (5) and (10) is thought to be less than 1.5 for all of the nitride systems. There is no composition for any system which is sufficiently indicated to justify

-102basing calculation of the thermodynamic quantities K, a HO~ L S~, and F~ on any nitride compositions other than those in Table XI. There is also the possiblity that some of the nitrides may be complexes with iron. Powder patterns run on unextracted samples show intense alpha iron lines and weaker jN lines with no evidence of any FeN lines. This indicates that no complex of the type jN.FeN is formed but does not rule out a complex of the type (Fe, j)N in which Fe atoms replace some of the j atoms in the jN structure. If this occurs it would show up in the powder pattern as a shift in the 4 values which could not be distinguished from the same shift produced by a varying j/N ratio. Its effect on the x-ray measurements would be to cause an error in the calculated lattice constant values. Its effect on the thermodynamic quantities would be to cause the values of K to be slightly low since the activity of j N in Equation (10) would not be unity as assumed but would be less than unity.

VI,, DISCUSSION OF ERRORS A. Sieverts Method Humbert and Elliott(2) have discussed the major sources of error in a Sieverts apparatus substantially identical to the one used in this study and have attempted to estimate the error produced by each source on nitrogen solubility measurements in liquid Fe-Cr-Ni alloys. For some sources the error estimation can be made only in a qualitative way. (11) Pehlke in his analysis of the same apparatus being used to make nitrogen solubility measurements on a number of different binary liquid iron alloys has considered several additional factors. Some of the factors these investigations considered which are likewise important in this study are enumerated below. a. Uncertainty in temperature Humbert and Elliott(2) estimate an uncertainty in temperature measurement of +100C. Pehlke(l) calculates an error of about 70C in the calibration of the temperature scale and estimates an additional error of 5~C in temperature control throughout the run for a total uncertainty of ~120C. He also estimates that the error introduced by assuming constant emissivity of all melts over the necessary ranges of temperature and composition is less than the total uncertainty of +120~C Both investigators agree that a temperature error of this magnitude leads to a maximum error in nitrogen solubility measurement of 1 to 1.5% for alloys of 10% solute or less. The temperature uncertainty in this study is probably of this same order of magnitude. For the very soluble nitride systems such as silicon, tantalum, columbium, and vanadium the uncertainty may be -103

slightly greater because of the high (15%-35%) alloy contents required to precipitate the nitride. b. Uncertainty in gas volume Errors in the measurement of gas volumes resulted from uncertainty in the gas buret reading and variation in the temperature of the gas buret. The uncertainty in the reading was ~0.1 cubic centimeters. The variation in buret temperature was 10~K throughout the course of a six to ten hour run. The buret temperature variation was rather large because the gas buret was not surrounded with a water cooling jacket but varied with the room temperature. The maximum error in volume measurement occurs when a full buret of gas is used and is given by 100 x 1/273 + O.lx2 = 0.57 cc because two buret readings are required for one volume measurement, The hot volume was essentially constant at about 50 cc so the error in its measurement was 50 x 1/273 + O.lx2 = 0.38 cc. The total maximum error possible in the measurement of a volume of nitrogen absorbed is then 0.57 + 0.38 = 0.95 cc. A melt of pure iron at 1600~C weighing about 115 grams requires about 100 cc of nitrogen gas to saturate the melt and fill the hot volume. This represents a maximum error in volume measurement of 1%. Thus for all measurements made at pressures and compositions for which at least 100 cc of nitrogen was admitted to the reaction bulb the volume measurement error was probably less than 1%. However because the majority of the measurements in this study had to be made at reduced pressure and therefore with small volumes of nitrogen admitted to the reaction bulb, the relative error was in some cases greater than this. In the systems titanium, zirconium, aluminum, vanadium, columbium, tantalum, and silicon all break points in the nitrogen

-105absorption curves occurred after nitrogen volumes of at least 20 cc had been admitted to the reaction bulb. This gives a maximum error of 0.65 cc and a maximum relative error of 3.2% at the nitride solubility limit. In the boron system several of the nitride solubility limits occur with nitrogen volumes as low as 5 cc in the reaction bulb. For this system the maximum error is 0.47 cc and the maximurn relative error o10 at the nitride solubility. c. Uncertainty in pressure The solubility of nitrogen in an alloy may be expressed as a function of pressure through Sieverts' Law. N_= C f PN (29) Differentiating this gives: C d PN2 2 2 PN2 The relative error in percent is then: = d x 100 (31) (%N) 2 PN2 (%N) where C has a value of 0,045%/(atm)l/2 or 0.00872%/(cm)l/2 This obviously is most serious at low nitrogen pressures for alloys with low solubilities. For this error also the least favorable case is the boron system. The pressure could be measured to 0.2 cm of mercury for all systems. However for the boron system ~PN2 goes as low as 2.0 (cm)l/2 with %N equal to 0.002. This is a maximum relative error of about 45% at

the nitride solubility limit. For the silicon system the most unfavorable case is PN = 5.0 (cm)/2, %N = 0.002, for a relative error of 8.7%. 2 With the aluminum system the most unfavorable case is PN2 = 4.6 (cm)l/2, %N = 0.03, for a relative error of 0.6%. Thus it can be seen that for alloy systems with fairly soluble nitrides in which the element J does not decrease the solubility of nitrogen in the melt, the relative pressure measurement error at the nitride solubility limit rapidly becomes negligible. This applies to the systems aluminum, vanadium, columbium and tantalum. For the titanium and zirconium systems in which the nitride is quite insoluble but the element j has a strong increasing effect on the nitrogen solubility the most unfavorable case is PN2 = 1.5, %N = 0.01, for a maximum relative error of 5.8%. It can be seen that in making gas solubility measurements at reduced pressures the pressure and volume measurement errors become much more important than they are with measurements at atmospheric pressure where the melt absorbs generally larger volumes of nitrogen. The total error in the measured nitrogen solubility at the nitride solubility limit varies widely from system to system, and within a given system depends on the alloy content at which the nitride forms. d. Possible systematic errors In addition there is the problem of vaporization of metal from the melt. This is an error which is inherent in the Sieverts method and for which no quantitative estimate can be made. None of the alloying elements used in this study has an extremely high vapor pressure in comparison to iron, such as manganese and chromium for which previous researchers have Shown the vaporization error to be appreciable. On the other hand the

-107method used to measure the nitride solubility product required that the melt remain under pressures less than one atmosphere for the entire duration of the run, usually between six and ten hours. Although effort was made to adjust the j composition of the melt so that the nitride would be precipitated at as high a nitrogen pressure as possible, the requirement of reprecipitating the nitride at several higher temperatures made it necessary to make a number of runs at high j contents and therefore forced pressures of 0.1 to 0.5 atmospheres for times in excess of one hour. The appearance of a deposit in the reaction bulb particularly near the end of a run was seldom entirely avoided but the deposit was usually small. In this connection it should be mentioned that a run was made on a melt of 0.741% aluminum without a cover being used on the crucible. This resulted in an extremely heavy deposit in the reaction bulb, Nevertheless the measured solubility for this run was quite consistant with the other data for the aluminum system. B. Quenching Method Two important systematic errors which may enter the quenching method are the changing of the solute contents on quenching of the melt and uncertainty in the equilibrium nitrogen pressure adjacent to the melt due to thermal diffusion in the gas phase. The calibration runs made on pure iron in the quenching apparatus indicate that these errors were avoided by proper design of the apparatus. The method of measuring the melt temperature was substantially the same as in the Sieverts appartus, and the uncertainty in the measured values is therefore expected to be the same.

Concerning the error involved in the wet chemical analyses, -the error in the metal analyses is estimated at ~0.02 weight percent by Cochrane Laboratories Inc. which performed the analyses. The error in the nitrogen analyses is estimated at ~0.0005 weight percent for the pure iron and iron-aluminum systems, and ~0,001 weight percent for the ironboron alloys. The error increases as the nitrogen content decreases because the volume of ammonia given off in the Kjeldahl distillation becomes smaller, and the relative importance of residual nitrogen in the reagent solutions increases. The nitrogen analyses for the iron-titanium system apparently contain some systematic error due to interference of titanium so no error can be estimated for them.

VII. CONCLUSIONS 1. The solubility products of the nitrides of eight strong nitride formers in liquid iron have been measured at temperatures in the vicinity of 1600~C using both the Sieverts method and the quenching method. The results may best be summarized by the following equations giving the standard free energy of precipitation of the nitride from liquid iron solution: for TiN A F~ = 75,200 - 28.34T for ZrN A F~ = 32,600 - 6.69T for AlN A F = 63,700 - 27.91T for BN AF~ = 45,900 - 21.25T for VN AF~ = 49,000 - 24.58T for CbN A F~ 35,000 - 17.08T for TaN A F1550~C = 2,240 for 1/4 Si3N4 (Si3/4N) A F0 = -10,500 + 0.75T 2. Only three of these eight systems form nitrides sufficiently stable to merit consideration for possible use as refractories in contact with liquid iron. These three in order of their stability are TiN, ZrN, and AlN. All the other nitrides listed in (1) above would allow serious contamination of a. liquid iron melt if used as a refractory in contact with it under conditions approaching thermodynamic equilibrium. 3. The compositions of the nitrides precipitated from liquid iron solution approximate those given under (1). For the nitrides TiN, ZrN,, CbN, and VN there is evidence that the composition may vary slightly toward the metal rich side. However in no case does the metal/nitrogen atom ratio appear to be larger than 1.5. -109

-llO4. The nitrogen-metal interaction parameter in liquid iron was determined for boron and zirconium, two elements not previously studied. These results may be expressed by the following equations at 1600~C: log fN = -o.63(%Zr) log fN = O.ll(B) Zirconium increases the solubility of nitrogen in liquid iron while boron decreases it. 5. The nitrogen-metal interaction parameters for any one system showed a linear relation with reciprocal temperature as predicted from basic thermodynamic relations, 6. The Wagner method of interaction parameters gives a satisfactory representation of the activities of metal and nitrogen in solution in iron at concentrations up to the nitride solubility limit for all of the metal-nitride systems listed in (1) with the exception of the. Si3N4 system.

VIII. APPENDICES APPENDIX 1A CHARGE MATERIAL ANALYSES Nine different metals, iron plus the eight alloying elements aluminum, boron, columbium, silicon, tantalum, titanium, vanadium, and zirconium were used in this study. These materials were of the highest purity obtainable. The suppliers of these metals and the suppliers' analyses are summarized in the following tables. TABLE A-I SUPPLIER'S ANALYSIS OF IRON MELTING STOCK Trade name Ferrovac E, supplied by Crucible Steel Company of America of Syracuse, New York in bar form. Element Weight Percent Lot No. 1 Lot No. 2 Lot No. 3 c o.oo4 o.oo4 o.oo8 Mn 0.001 0.001 0.001 P 0.002 0.005 0.004 S 0..009 0 007 0.007 Si. 006 o. oo006 <0.006 Ni 0.033 0.035 0.015 Cr 0.01 0.01 <0.002 V Oo004 0o004 <O.004 Mo 0.01 0.01 0.001 Cu 0.01 0.005 <0.001 Co 0.01 0.007 0.005 N O0.0018 0.0001 0.0002 0 0.0075 oo0.0065 0.0022 H 0.00007 0.00003 0.00002 -111

-112TABLE A-II SUPPLIER'S ANALYSIS OF ALUMINUM MELTING STOCK Supplied by Aluminum Company of America Research Laboratories in ingot form. Element Weight Percent Al, 99.99+ Cu 0.001 Mn, 0.002 Si 0.003 Fe 0.001 TABLE A-III SUPPLIER'S ANALYSIS OF BORON MELTING STOCK Supplied by Cooper Metallurgical Associates of Cleveland, Ohio in the form of -325 mesh powder. Element Weight Percent C 0.10 Fe 0.15 0 0.02 TABLE A-IV SUPPLIER'S ANALYSIS OF COLUMBIUM MELTING STOCK Supplied by Fansteel Metallurgical Corporation of Chicago, Illinois in the form of 0.157" diameter rod. Element Weight Percent 0 0.o018 c 0.015 N 0.015 Ta 0.09 Zr 0.020 Fe 0.015 Ti 0.010 Si <0.01 W <0.01 Ni <0.007

-115TABLE A-V SUPPLIER'S ANALYSIS OF SILICON MELTING STOCK Supplied by Union Carbide Metals Company of Niagara Falls, New York in the form of 60 to 150 mesh powder. Element Weight Percent Si ~ 99.85 Fe 0.018 TABLE A-VI SUPPLIER'S ANALYSIS OF TANTALUM MELTING STOCK Supplied by Fansteel Metallurgical Corporation of Chicago, Illinois in the form of 0.157" diameter rod. Element Weight Percent O 0.0o7 C 0.005 N 0.002 Cb 0.055 W 0.010 Fe 0.010 Mo 0.005 Si <0.01 TABLE A-VII SUPPLIER'S ANALYSIS OF TITANIUM MELTING STOCK Supplied by E. I. duPont in sponge form. Element Weight Percent N 0.020 C 0.025 Mg 0o.o8o Cl 0.120 H 0.005 H20 0.020 EMn~~~~ ~0.050 Fe o.o60 si 0.040

-114TABLE A-VIII SUPPLIER'S ANALYSIS OF VANADIUM MELTING STOCK Supplied by Union Carbide Metals Company of Niagara Falls, New York in the form of -1/4" diameter shot. Element Weight Percent C 0.024 0 0.055 H 0o.ooi0018 N 0.039 TABLE A-IX SUPPLIER'S ANALYSIS OF ZIRCONIUM MELTING STOCK Supplied by Mallory Sharon Metals Company in sponge form. Element Weight Percent Fe 0.0309 C 0.0247 Si 0.006 Mn <0.002 0 0.1162

APPENDIX B TEMPERATURE CALIBRATION The method used to determine the relation between the true melt temperature and the observed optical pyrometer readings for both the Sieverts apparatus and the quenching apparatus was the one proposed by Dastur and Gokcen(24) applied to the Sieverts apparatus by Pehlke and Elliott(1) and Humbert and Elliott(2). The relation between true and observed temperatures is given by the Wien-Planck Equation: ln(Ea) = 2 (1/Tt - /Ta)(B) whereE melt emissivity O = melt transmissivity C2 = Planck constant; 14,330 micron-degrees = wave length of light used; 0.65 microns Tt = true temperature in ~K Ta = observed temperature in ~K Assumining that E and a change negligibly over the ranges of melt temperature and composition in this study Equation (B-l) may be rewritten: 1 1 = K (B-2) Tt Ta The value of the constant K in Equation (B-2) may then be evaluated by measuring Ta for pure liquid iron in the apparatus and taking Tt as 15360C. This value of K is then used to calculate the desired Ta for any other experimental Tt. The temperature scale set up by this method -115

for the Sieverts apparatus is shown in Table B-I and the temperature scale set up for the quenching apparatus is shown in Table B-II. TABLE B-I COMPARISON BETWEEN TRUE AND OBSERVED TEMPERATURE SCALES FOR THE SIEVERTS APPARATUS Tt~C Ta~C 1450 1i67 1500 1307 1536 1335 K - 0o.69 0-4 1550 1347 1600oo 1387 1650 1427 1700 1467 1750 1507 TABLE B-Il COMPARISON BETWEEN TRUE AND OBSERVED TEMPERATURE SCALES FOR THE QUENCHING APPARATUS Tt~C Ta~C -4 1536 1350 K - o.63 lo 1600 1405 1650 1445 1700 1486 Assuming Dastur and Gokcen's (24) value of 0.43 for the emissivity of pure liquid iron at 15360C, Equation (B-l) gives a value of 0.51 for the transmissivity of the Sieverts apparatus and a value of 0.58 for the transmissivity of the quenching apparatus.

APPENDIX C FLOWMETER CALIBRATION The flowmeters used to measure the flow rates of argon and nitrogen gases into the quenching apparatus in order to control the partial pressure of nitrogen in the atmosphere were Fischer and Porter Flowrators with a maximum rated capacity of 0.23ftQ./min. of air measured at 14.7 p.s.i. and 700F. Darken and Gurry(40) found that for CO-C02 mixtures the error in the gas composition due to thermal diffusion could be held to less than 0.25% by maintaining a linear flow rate in the furnace tube of at least 0.6 cm/sec. For a 2 l/4' i.d. furnace tube this is a minimum volume flow rate of 1.96 ft./hr. The flowmeters were calibrated by inserting a 50 ml buret into the line between the flowmeter and the gas inlet to the furnace. A small amount of soap solution was then injected into the gas stream forming bubbles in the buret and the time necessary for a bubble to travel the length of the 50 ml scale on the buret was measured. Thus a direct measurement of the volume flow rate of the gas could be obtained for any given reading of the flowmeter. A series of 10 time measurements was made at each calibration point and these were averaged to determine the volume flow rate. The meters were calibrated for readings of 10%, 15%, 20%, and 25%. It was impossible to obtain accurate calibration readings at higher flow rates since the rate of travel of the bubbles in the buret was too fast to allow accurate time measurements. However these four calibration points permitted a variation of nitrogen partial pressure from about 1/3 atmosphere to one atmosphere which was quite sufficient for this

study. In order to determine if this method of calibration would give a sufficiently precise control over the nitrogen partial pressure the calibration of the nitrogen flowmeter was repeated on a second occasion. The correspondence of the two sets of calibration data is excellent as shown by Table C-I below. TABLE C-I FLOWMETER CALIBRATION DATA FOR THE QUENCHING APPARATUS N2 Flowmeter Time for 50cc Travel (sec.) Vol. Flow Rate (ft. 3/hr.) Setting 1st Cal. 2nd Cal. 1st. Cal. 2nd Cal. 10% 3.44 3.43 1.84 1.85 15% 2.30 2.28 2.76 2.78 20% 1.69 1.69 3.74 3.74 25% 1,32 1.35 4.81 4.80 A Flowmeter Time for 50 cc Travel (sec.) Vol. Flow Rate (ft3/hr) Setting 10% 4.8o 1.32 15% 3.o6 2.08 20% 2.23 2.84 25% 1.76 3.60 Table C-II shows the ratio of nitrogen pressure to total pressure for all possible combinations of flowmeter settings as calculated from the calibration data in Table C-I. To determine the nitrogen partial pressure corrected to one atmosphere total pressure for an equilibration in the quenching apparatus, the PN2/Ptotal value corresponding to the flowmeter settings used was multiplied by P/76.0 where P was the atmospheric pressure existing at the time of the equilibration as measured by a barometer, In all equilibrations a combination of flowmeter settings was chosen such that the volume flow rate of gas was at least 3.74 ft3/hr.

TABLE C-Il CALCULATED NITROGEN PRESSURE FOR VARIOUS COMBINATIONS OF FLOWMNETER SETTINGS Flowmeter Settings VN2/Vtotal = PNPtotal N2 A 10 25 0.339 10 20 0.393 10 15 0.471 10 10 0.582 15 10 0.676 20 10 0.737 2.5 10 0.783 20 -- 1.000

APPENDIX D METHODS OF CHEMICAL ANALYSIS The wet chemical analyses of the extracted residue and the analyses of the quenched ingots for the experiments involving titanium, aluminum, and boron were performed by Cochrane Laboratories, Inc. of Milwaukee, Wisconsin. The following short outlines of procedures were supplied by Cochrane Laboratories. The titanium contents of the quenched ingots were determined colorimetrically after a cupferon separation to eliminate possible interferring elements. The aluminum contents were determined gravimetrically as the phosphate after a bicarbonate separation. The results were rechecked and verified by a hydroxyquinoline separation. The boron contents were determined by distillation as methyl borate and titration as standard alkali. These analyses are presented in Table XII on page 90. In the analysis of the extracted. AlN powder samples the aluminum was determined by quinolate precipitation after fusing the sample with carbonate to render all of it acid soluble. This procedure may have caused a slightly high A1/N ratio since it would also cause to be included in the analyzed aluminum content any aluminum present as A1203. X-ray analysis of the extracted AlN powder showed traces of A1203 present as an impurity. The nitrogen content was determined by a modification of the Allen method. The accuracy of the analyses was hampered by the fact that only about 0.15 grams of nitride could be extracted, providing a rather small sample for these analytical procedures. The accuracy of the nitrogen analyses is estimated as *0.5 weight percent and the accuracy of the aluminum analyses as *1 weight percent. These analytical results are presented in Table XIII on page 99: -120

-121The analyses of the quenched ingots for dissolved nitrogen were performed by the author using the Kjeldahl method(4l'42) This method was chosen in preference to the vacuum fusion method for two reasons. First, the vacuum fusion method is inherently less accurate for nitrogen analysis because nitrogen is determined by the difference between the total volume of gas drawn out of the fused sample and the measured volumes of hydrogen and oxygen in it. Second, the vacuum fusion method tends to give low results if stable nitrides are present since it is difficult to decompose them, The following is an outline of the Kjeldahl procedure used, The analytical sample was in the form of chips, This was found necessary to insure complete digestion The digestion was accomplished in a solution of H P0O and H SO. NaOH solution was then added and the dissolved 34 2 4 nitrogen distilled off as NH3. The NH3 was collected in a solution of H BO~ and then titrated against a standard solution of OolN HC1 using. a mixture of methyl red and methyline blue indicators. The HC1 solution had previously been standardized against Na2CO3 using methyl orange indicator,3) Double distilled water was used in all reagent solutions to minimize errors due to residual nitrogen. The analytical results are presented in Table XII on page

APPENDIX E METHODS OF FABRICATION OF NITRIDE CRUCIBLES 1. Preparation of A1N Crucibles The method used by the Carborundum Company to prepare the AiN crucibles which were used in this study is outlined by Taylor and Lenie(20) Fine aluminum powder obtained from Alcoa was mixed with 1% by weight of sodium fluoride and heated in purified nitrogen, The crucible material used to contain the powder is not specified. The sodium fluoride is added because it catalyzes the nitriding at low temperatures. The temperature of the powder was raised rapidly to 650~C and then increased slowly over a period of 40 hours to a maximum of 18000C. The product obtained was a porous sintered agglomerate. This was ball milled dry in a stainless steel ball mill with stainless steel balls. The product was a light gray powder with an average particle size of about five microns. Chemical analysis of the powder showed 96.0% AlN, 2o.1% A1203, and 1.9% other elements including 0.2% C, p.4% Si, and 0.1% Feo The crucibles which were of about 1/2" inside diameter, 1/4" wall thick.ness, and 1 3/4" deep were formed by hot pressing the milled AlN powder in graphite dies. A pressing temperature of 20000C and a pressing pressure of about 5000 p.soi. were used. Compacts with a bulk density of 3.20 grams/cc or about 98% of the theoretical density for AlN were produced. The crucibles proved completely impervious to liquid iron after equilibration times of 30 minutes. 2. Preparation of TiN Crucibles The method used to prepare the TiN crucibles which were used in this study was developed by Sponseller(25). The starting material was -122

-123-100 mesh TiN powder to which was added 24% by weight of TiH powder. Both materials were supplied by Metal Hydrides Inc. of Beverly, Mass, The powders were blended by ball milling for one hour using stainless steel balls and a glass jar as a container. A weight of paraffin equal to 2 1/2% of the dry powder weight was dissolved in xylene and added to the powder. A sufficient excess of xylene'was added to make the powder about the consistancy of thick cream. The slurry was then dried to 105% of the dry powder weight. It was found necessary to maintain close control over the weight of xylene and paraffin in the powder in order to produce sound crucibles of sufficient green strength. The powder must be stored in an air tight container and loaded into the pressing die as rapidly as possible in order to prevent excessive evaporation of xylene. The pressing of the powder was done at room temperature in a hardened tool steel die (Rc 50-55). The inner surfaces of the crucible were formed by a steel mandrel. A removable sleeve permitted this mandrel and the ram which formed the crucible walls to be loaded independently in two separate steps in the pressing operation. The die, rams, and mandrel were lubricated with a solution of stearic acid dissolved in methyl ether before the powder was loaded into the die. Pressures of 11,000 p.s.i. on the mandrel and 16,000 p.s.i. on the sleeve were used. The green compact was removed from the die by pressing it out the top of the die cavity. The green crucibles were dewaxed by heating in air to 350~F for 1 hour, 4250F for 2 hours, and 500~F for 2 hours. They were then sintered in vacuum using an induction furnace with a molybedenum susceptor. The temperature was raised slowly to about 15000F and held until the TiH had been completely decomposed. When a hard vacuum could be held on the

-124system indicating that all the hydrogen had been removed, the temperature was raised to 29500F and held for one hour, then raised to 3350~F and held for one hour. After cooling the sintered crucibles were reheated in a gas fired kiln to 23000F and held under purified nitrogen gas for 48 hours. This step was necessary to tie up as TiN the excess titanium which had been formed in the compacts by the decomposition of the TiH. The sintered crucibles were about 5/8" inside diameter, 3/16" wall thickness, and 1 1/2" deep. They proved satisfactory although slightly porous to liquid iron. During a 30 minute equilibration at 17000C about one half of a 40 gram melt of liquid iron would be lost by seepage through the crucible walls,

APPENDIX F NITROGEN ABSORPTION CURVES Figures F-1 through F-42 summarize the nitrogen absorption curves obtained by the Sieverts method. Each figure represents a single run in the Sieverts apparatus. -125

0.228% Ti 0.07 x x/x O.OE- 0.195% Ti 0.06 x 1700 OC 0.05 /I0 0.05x' x I7000c 0.04 *65 0 0.04 x zl~~~~~~~~ 16500C 0D03 0.3 X x I~~~~~~~~~ OJD.3 -0.03 t a 0.02 0.02 1600 OC 0~~02~~ ~~I 0 Oc 0.02 0.01 0.01 0 2 4 6 8 10 VrPM21 (CM) 112; (Cm.)" Figure F-1. Nitrogen Absorption Curves for Figure F-2. Nitrogen Absorption Curves for the Titanium System. the Aluminum System.

0.2??1 TTi x/ 0,254p~~~~~~~~~~0.70 7%T 0.06 " 0.06 X x INCREASING P / X X 0 DECREASING P.NX 1I 0.0 0.045 1700 0.04 ~ QX/ ZI IIs X /17,00 OC -~~~~~~~~~~ 0.04 - 1700 o C 00 zI 1650 OC zl - - H 0~ ~ ~ ~ ~ ~~~~~ i-: 0.03 - 0.03 x'.C - X~~ ~~~~~~~~~~/ 0.02 X 0 I X I 1600 OC 1600 ~C 0.01j 0.01 l0 l2 4 6 8 10 0 2 4: 6 8 10 P (Cm.) VP7 (Cm.)'M. Figure F-3. Nitrogen Absorption Curves for Figure F-4. Nitrogen Absorption Curves for the Titanium System. the Titanium System.

0.318% Ti 0.06 0. 304* Ti 0.00 0.07 x 0.06 X INCREASING P2K 0 oDCREASING PNM 0.06 0.05 / 0.05 K loti 21~~~~~~~~~~~ 21f~ 0.04 0.-01 ~ ~ ~ ~ ~~~~x00 1750 OC ~ ~ 081~ ~looO OL03 - I- H I OC 50 ~0.04 I\ I X~~~7()()@(~~~~ 0.03 2/1700 C60 O 0.02 4 6 8 IC 1650 C ~~~~~~~~~~~~0.02 a1 Ji~~~~~~;~~~~, (Cm)'" ~~~~~~~~~~~~(Cm.)" Figure F-5. N~itrogen Absorption Curves for Figure F-6. Nitrogen Absorption Curves for the Titanium System. the Titanium System.

0.06253% Zr Large ZrO2 Crucible 0.05 0.322% Zr X 0.05 Small ZrO2 Crucible 0.04 1600 / 600C. 0.04 - x X.ZI /X':0.03 /.3 X /.-:' 0 [\0 / 1x 2 o6 8 10 PN2 (Cm.) /2 O H0.02 m) 0.01 Figure F-7. Nitrogen Absorption Curves for Figure F-8. Nitrogen Absorption Curves-for the Zirconium System.. -he Zirconium System.

-1300.J409 Zr -0o.08 Bmall ZrO2 Crucible 17500 C 17000C 0.07 0.06 0.05 0.04 0.03 X X 16O0~C 0.02 -- 17S0 C 0O 2 4 6 8 (;;,Cm)1/"2 Figure F-9. Nitrogen Absorption Curves for the Zirconium System.

-131O. 46a Zr 0.10....... Large ZrO2 Crucible 0.09 x 0.08 / 1600~O. 0.06 _! - X 0.0= a 0.08 / I-ix 0.04 X 0.03 -X / 0.02 x 0.01 E2 4 6 8 10 12 JPN2 cCm.)'/a Figure F-10. Nitrogen Absorption Curves for the Zirconium System

0.612% Zr Large ZrO2 Crucible 0.558% Zr 0.12 0.12 Small ZrO2 Crucible 1750 C 17500C 0.10 00.to 17000C 0.08 A 0.08 17001T, A Il 0~~~~~ x~~ 0-04 — 0El 0;061- O O O 00 066 C K 0~~~~~~~~~~~00 0.04 0 0.04 X A -1700OC 4' J7~00C o 16500C I 0.0o2 16000C 4.IC 160 0.0o2 0 1 0 2 4 6 10 C2 -4 6- 8 10 ~ pw2 (Cmt12 (C(m)11 Figure F-il. Ntrogen Absorpton Curves f'orFigure F-12. Nitrogen Absor~ption Curves for th~e Zir~conium Syst~em. the Zirconium System.

0.0810o% Zr 0.1086% Zr 0O 0.05 | -I A1203 Crucible A1203 Cricuble 0 ~~~~~.04t- / 0.04 X/ X/ zI.0 ZI 0.03 OR - te x/ Z4- 0.02O/X0.02 _ 0 2 /X I I X 2 4 6 8 10 0 2 4 6 8 aO IPN (Cm) 112 2 Figure F-13. Nitrogen Absorption Curves for Figure F-ik. Nitrh gen Absorption Curves for the Zirconium System. the Zirconium System.

o. 442 zr o. 741 Al 0.o050.05. xib/ X1600' C A1203 Crucible A1203 x'uee 1600~C 0 0.04 0N / l 0.02 0.020.~01~ 1 0.0- 1 x 0 0 0 2 4 6 8 10 2 4 6 8 10 PN; (Cm)t 1/2 PN2 (Cm)112 Figure F-15. Nitrogen Absorption Curves for Figure F-16. Nitrogen Absorption Curves for the Zirconium System. the Aluminum System

1.07% Al 0.06 0.892% Al 0.05 O 05 e 00 r ~~1 0S 1~~~~0C 0.04 0.0 i 0.03. 0.03 0.02 7 0.02 x / X INCREASING Pr2 o 0 | 0.01 0 DECREAING o I I,,,, I I I I I I, I I I I, 0 2 4 6 8 10 0 2 4 6 8 10 12 F (Cm)1/"2 Figure F-17. Nitrogen Absorption Curves for the Aluminum System Figure F-18. Nitrogen Absorption Curves for the Aluminum System.

1.17% Al 0.08 0.07 0.06.O OC 1650~C 0.05 0.04 - G. 1600' C 0.03 / 0.02 - El 1750 C A 17000 C 0 16500 C 0.01..- X 16000 C 0 2 4 6 8 10 12 iPfz (ATM)I/ Figure F-19. Nitrogen Absorption Curvres for the.I"uiniin m System

-1371.34% Al 0.08 0.07 0.06 0.05 0.04 /'600" C 0.03 0.012 001 / I 0 2 4 6 10.0 J/P"- (Cm) I/2 Figure F-20. Nitrogen Absorption Curves afor the Aluminum System.

L5jA Al 81% Al.0.07 O-Or 0.06 0106 1700~C 0.05 0.01 ZI~~~~~~~ 0.03 OOC * j -0.02 00 I K' A 1700IC 0.01 0 1600 K 1600*C 0 0 a2 4 6 __ _ _ __ _ _ _ _4 _ _ __ _ _ _ __ _ _ _ JPua (~)UI( (P)a (CM)1/2 Frigure 1-21. Nlitrogpen Absorption Cure~s for PFigure -22. Nitrogen Absorption Curves for the Aluminim System. the Admmintm System,

-1392.26% Al 0.08 0.06 1750 ~C 0.05 1700C 0.04 0.0 1650 C 0.02 / a 1750'C 1700~ C ~ ~0.0 I |-X 16500 C I.0 _ Oo 2 4 6 8 10'PNa2 (Cm) l/2 Figure F-23. Nitrogen Absorption Curves for the Aluminum System.

-1403.14% Al 0.09 0.08 0.07 0.06 1750'C 0.05 0.04 1700~ C 0.03 - 0.02 1750 C X 1700 *C O 2 4'6 8 10 IP.. (Cm )1/2 Figure F-24. Nitrogen Absorption Curves for the Aluminum System.

-1410.520% B 0.05 1750 C * 1700~C 1650 C 0,04 - ) 1600~ C 15X I50 ~C 0.03 - zi x 0.02 0 1750~C INCREASING PN2 w 17000C DECREASING PN2 1650~C INCREASING PN2 0 1600~C DECREASING PN2 0.01 - + 1550~C INCREASING PN 1 x o 0t_ ~ ~ ~~ I....., 0 2 4 6 8 10 12 PN2 (Cm )I/2 Figure F-25. Nitrogen Absorption Curves for the Boron System.

-1421.4 B 0.05...... 1750 /17000C 0.04 16500C 1600 9C 0.03_ 0.0 2 1750 C INCREASING + / 17000 C DECREASING ////+ G 1650~C INCREASING PN 0 1600~C DECREASING PN X 1550~ C INCREASING F 0.01 I 0 I I I. 0 2 4 8 o10 12 PN2 (Cm)1/2 Figure F-26. Nitrogen Absorption Curves for the Boron System

-1432.06% B 0.04 1750 eC / /1700 ~ c.03 E1650 e C //ft600 7 C.0 I -0// ) 1750 0 C INCREASING PN2 o 1700 ~ C DECREASING PN2 a 1650 ~C INCREASING PN2 0 1600' C DECREASING Pe2 0.02 Ix AOX 550~ C INCREASING PN2 0 2 4 6 8 10 12 ) (cm1 /2 Figure F-27. Nitrogen Absorption Curves for the Boron System.

-1443.E82% B 0.05 0.04 0.03 zi of 1651750 C oi~~O I i,X,~~~~~~ I oo C +01650,1600 OC 0.02 0.01 5- 50 C o 1750 ~C DECREASING PN2 A 1700'C INCREASING PN2 0 1650 C DECREASING PN2 X 16000 C INCREASING PN2 0 4 6 8 I 0 12 *PN2 (Cm)1/2 Figure F-28. Nitrogen Absorption Curves for the Boron System.

-1455.83% 0.0: 0.02 - 02 1 700 C, 1750'C - 650o C ] / C,\ | 750.01 1750 C INCREASING PN2 I / 1 550~C Ad 1700~ C DECREASING PN2 [ Xx 1700~C INCREASING pN2 0 2 4 6 8 10 /PN2 (Cm"l/2 Figure F-29. Nitrogen Absorption Curves for the Boron System.

maUsgs uoio1 a q 0oJ soAanO uoTcdaosqqv uotolT4N'0-a nr1T 021 1 8 9 ~j 0 0091 200.DoOS/ ~ D 009IZ I'P~~~0 X X II,................... I I IO I ~0 0 -9tT

-1470.09 X INCREASING PNl 0 DECREASING PN2 0,08 0.07 0.06 16000C Z1 W8650 ~C o0' I /I|7 —f1700'C 3 C0.05 t S1750 ~C 0.04 0.03 0.02 0.01 0 2 4 6 8 10'/, (Cm.)"2 Figure F-51. Nitrogen Absorption Curves for the Vanadium System.

-1486.36% v 0.2 X 1600~C,X1650 ~C x INCREASING PN2 X IX 1700'C 0 DECREASING P,.1750'-oC zi -x mm AX 0 2 4 6 8 10 /JPp (Cm.)"2 Figure F-32. Nitrogen Absorption Curves for the Vanadium System.

-1490.4...5oy X INCREASING PN2 0 DECREASING PN2 0.3 16000C IO F;X1650 C (/ 1700'C,0 717 50CI 0.2 / 4 X I / X o.1 00; 2 4 6 8 I0 12 ~PN2 (Cm)1/2 Figure F-33. Nitrogen Absorption Curves for the Vanadium System.

-1509.93% v 1650 ~C 0.4 O X INCREASING PN2 x 17 0XC O DECREASING P- N2 1750C0 0.3 / 0.2 x 0.1 I I I I I,,I I I 0 2 4 6 8 10 1/P, (Cm.)"' Figure F-34. Nitrogen Absorption Curves for the Vanadium System.

15.o4% v 0.6 5X I xL X INCREASING P750 N 4 1750 DC 0 DECREASING P2 -0.5 1700 OC 0zx.4~ l_ 7.1. cb, 0.4 20.2 b ZI 20 p 0.3 f: 16000 I0.2 0.1 IX INCREASING P, 0O DECREASING PN2 4VP~-, (Cm.) 12 4 {cm.) 2 Figure F-36. Nitrogen Absorption Curves for the Columbium System. Figure F-35. Nitrogen Absorption Curves for the Vanadium System.

0.3 ii. 41% Gb, 0.3 14~.17% cb 16501,C t70 16000C 1600" C 0 ~~~16 5 0C 0.2 017 00 *C 0.2 1550"C ZI ZI 0.1 X INCREASING PlN2 0.1 X INCREASING PM, 0 DECREASING- Pf42 0 DECREASING P12l 0 2 4 6 8 10 02 4 6 81'A/PN2 (Cm)1 Figure F-37. Nitrogen Absorption Curves f'or Figure F-38. Nitrogen Absorption Curves for the Columbium System,.h ounix ytm

17. 71% Cb.. X INCREASING PN 1700 ~C 17500o o DECREASING PN2 0.3 1650 OC 0.1 0 2 4 6 8 10 ~/P, (Cm.)"2 Figure F-39. Nitrogen Absorption Curves for the Columbiumn System

-154202% Ta 0, 20 1600 * C 0 1650 ~ C 0.18 / / x1700eC X 1 0,14 155S00 0.12 X 0.10 xZI 0.0 8 0.06 X INCREASING PN2 0 DECREASING PN2 0.04 - 0.02 0 2 4 6 8 10 12 14 Figure F-40. Nitrogen Absorption Curve for the Tantalum System.

0.07 X 1450 C INCREASING N, 0 1450 C DECREASING PM2 0.06 e o 1500 eC A I550C INCREASING PN El 1600 CD 36.7% Si 0.05.- 0.05)5 x 1550 OC 0 16000C 0.04 0.04 zi 0 170D0DC OR 1650 DC 1f-* 0.03 0.03 ZI A~ CI T 1700 DC 1600 DC 7 0.02- 0.02 0.0 ~ ~ 00 1600 DC 0.01 0.01 MOO'0 A*~*-I450 15 I 0 2 4 6 8 10 0 2 4 6 m (cm.) i2a (fN 2 Fiue24.Ntoe bopinCre o Figure F-41. Nitrogen Absorption Curves for Figure F-t2. Nitrogen Absorption Curves for the Silicon System. the Silicon System.

APPENDIX G CALCULATION OF NITRIDE COMPOSITIONS BY PHASE RULE ANALYSIS A graphical phase rule analysis of the 0.228% Ti, 0.318% Ti, 1.34% Al, and 1.57% Al nitrogen absorption curves is shown in Figures G-1, G-2, G-3, and G-4. The calculation of the nitride phase composition for each curve is summarized in Table G-I below. TABIE G-I NITRIDE COMPOSITIONS CALCULATED FROM THE PHASE RULE ANALYSIS Temp. ~C Wt. %j wt. %N Calculated Nitride Composition 165Q 0.228% Ti 0.0277 Ti2.4N 1700 0.318% Ti 0.0425 Ti2.2N 1600 1.34% Al 0.153 A14.5N 1600 1.57% Al 0.212 A13.l As previously noted the compositions given in Table G-I are considered incorrect, being too rich in metal. This error is due to the difficulty in reaching the equilibrium nitrogen pressure at pressures well above the break point in the absorption curve. In view of this difficulty, the validity of any method of calculating the nitride composition which employs the region of the absorption curve above the break point is considered extremely doubtful. -156

0.08 0.07 / / X 0.06 7 00,/ x..//'/ | / /X /PURE IRON X/ X/ 0.0 - 0.01' 2 4 6 8 I0 12 //2 PN (Cm) Figure G-0. Phase Rule Analysis of the 0.2289 Titanium Nitrogen Absorption Curve.

-1580.09 0.08 - / X / / 0.07 / I.00 / x 0.05 /x zi I / 0 / PURE IRON 0,0425 0.04 0.03 0.02 t 0.01,,D... 2..... I _ - O 2 4 6 8 10 12 -f; (Cm)'/2 Figure G-2. phase Rule Analysis of the 0.318% Titanium Nitrogen Absorption Curve.

~aAmD3 uoq.djosqv uaoxq.'l umnuTlunTV %'1T7 aqw Jo 9TsXTlut alTnE ageta:'(-O aniT?, 09 (W3) ZNdj0 01 8 9., Z 0'0 NOIIl 3und X XI` -90 0 80'0 010 0 Iz ~l' O /,' -91'0 j9, - I8 O.6-lh O

0.28 0. 20 0.24 - -- 0.212 0.20 X x 0 o.12 O. 08 0.04 (, PURE IRON 0 2 4 6 8 10 12 PN2 ( m)/2 Figure G-4. Phase Rule Analysis of the 1.57% Aluminum Nitrogen Absorption Curve.

APPENDIX H X-RAY DATA The following tables give the results of Debye-Scherrer powder patterns run on samples chipped from solidified ingots removed from the Sieverts apparatus for which the nitrogen absorption curves indicated that a nitride had precipitated. The notation "extracted" indicates that the iron matrix was dissolved by the method of Beeghly(26) prior to running the powder pattern. TABLE H-I X-RAY DATA FOR TITANIUM NITRIDE SAMPLES FROM THE SIEVERTS APPARATUS 0.318% Ti, extracted 0.195% Ti, extracted Fe radiation, Mn filter Fe radiation, Mn filter d observed substance d observed substance 2.563 A1203 2.442 TiN 2.439 TiN 2.128 TiN 2.372 A1203 1.505 TiN 2.120 TiN 2.o83 A120, 1.599 A1203 1.499 TiN 1.405 A1203 1.376 Al 0 1.278 TiiN 1.239 TiN 1.215 A1203 1.190 A1203 1.147 A1203 1.061 TiN 1.035 A1203 1.001 A1203 -161

-162TABLE H-II X-RAY DATA FOR ALUMINUM NITRIDE SAMPLES FROM THE SIEVERTS APPARATUS 3.85% Al, extracted 1.07% Al, extracted Fe radiation, Mn filter Fe radiation, Mn filter d observed substance d observed substance 3.44 A1203 2.704 AlN 2.679 AiN 2.476 A1N 2,532 A1203 2.347 A1N 2.468 AiN 2.082 A1203 2.353 AiN 1.819 A1N 2.109 A1203 1.594 A1203 1.822 A1N 1.547 AiN 1.729 A1203 1.408 A1N 1.412 AiN 1.369 A1203 1.401 A1203 1.044 A1N 1.371 A1203 1.018 AiN 1.344 AiN 0.996 ALN 1.317 A1N 1.298 ALN 1.17% Al, unextracted 1.245 Al203 Co radiation, Ni filter 1.182 A1N 1,078 A1203 d observed substance 1.046 A1N 1.044 A1203 2.680 A1N 1.019 AiN 2.445 A1203 1.016 AlN 2.026 Fe 0.999 AiN 1.872 A1203 0.996 AlN 1.567 AlN 1.434 Fe 1.321 AiN 1.173 A1N 1.112 A1203 1.082 A1203 1.o48 A1N 1.015 Fe 0.907 Fe TABLE H-III X-RAY DATA FOR BORON NITRIDE SAMPLES FROM THE SIEVERTS APPARATUS 7.o6% B. extracted 3.82% B, unextracted Fe radiation, Mn filter Fe radiation, Mn filter d observed substance d observed substance 3.66? 3.32 BN 3.33 BN 2.16 BN 2.68? 2.112 B2053 2.49? 2.021 Fe 2.19 BN 1.812 BN 2.112 B203 1.662 BN

TABLE H-III (CONT'D) 7.06% B, extracted 3.82% B, unextracted Fe radiation, Mn filter Fe radiation, Mn filter d observed substance d observed substance 2.112 B203 1.662 BN 1.999? 1.428 Fe 1.678 BN 1.252 BN 1.228 BN 1.171 BN 1.146 BN The unidentified lines in the pattern of the 7.06% B sample in Table H-III were of an intensity approximately equal to the intensities of the BN lines. This sample apparently contains some impurity which cannot be identified. TABLE H-IV X-RAY DATA FOR COLUMBIUM NITRIDE SAMPLES FROM THE SIEVERTS APPARATUS 17.71% Cb, extracted 14.17% Cb, extracted Cu radiation, Ni filter Fe radiation, Mn filter d observed substance d observed substance 2.523 CbN0,75 2.785 CbN (hexagonal) 2.193 CbN075 2.531 CbN (cubic) 2.152 CbNo.075 2.500 CbNo 75 1.542 CbN 075 2.313 CbN (cubic) 1.321 CbN0.75 2.201 CbN (cubic) 1.302 CbN075 2.174 CbNo75 1.256 CbNo 75 1.538 CbNo 1.094 CbN CbN cubic) 0.997 CbN0 75 1.314 CbNo 75 CbN 1.261 CbN (hexagonal) O.894 CbN0.75 1.006 CbN (cubic) o.845 CbNo.75 0.999 CbNo. 75 0.979 CbNo.75

-164TABLE H-IV (CONT'D) 11.41% Cb, extracted Co radiation, Fe filter d observed substance 2.513 CbN 75 2.177 CbN0 75 1.546 CbNo 75 1.322 CbN0.75 1.308 CbNo 75 1.259 CbN 1.007 cb",.?7 1.007 CbN0O75 0.999 CbN 5 o.981 CbN. 75 O. 971 CbN0.75 CbN6. 75 Some of the observed d values for the three samples given in Table H-IV differ slightly from the d values given by Brauer and (44) Jander( for the composition CbNo75. This is an indication that all three samples do not have the exact composition CbNo75. However because of the excellent correspondence of the pattern of the d values in all three samples their compositions must be very close to CbNo.75. TABLE H-V X-RAY DATA FOR VANADIUM NITRIDE SAMPLES FROM THE SIEVERTS APPARATUS 15.04% V, extracted 9.93% V, extracted Cu radiation, Ni filter Cu radiation, Ni filter d observed substance d observed substance 2.345 VN0 2.354 VN0 2.302 VN 2.032 VN0~ 7 1.43-7 VN 7 1.437 VNo.7 1,223 0VN.7 1.232 VN07 1.173 VN 7 0.936 VN.7 1.15 VN 07 0.911 VN07 0.7 0.7 o.go8 VN0 0o. 831 v 07

The d values in Table H-V show a considerable shift from the d values recorded by Becker and Ebert(45) for which they give the composition VN, although the patterns both indexed to give a face centered cubic structure. The small 9 lines were used to calculate lattice parameter values. The 15.04% V sample gave a value of ao = 4.062 A while the 9.93% V sample gave a value of ao = 4.o68 A. The work of Hahn(l1) indicates that these lattice parameters corre spond to a composition of about VNo.71. This is the composition limit on the low nitrogen side of the nitride VN which has the NaCl structure. Table H-VI summarizes the results of powder patterns run on the materials from which the nitride crucibles used in the quenching runs were fabricated. The AiN from the hot pressed crucibles supplied by Carborundum Company and the BN bar stock obtained from the same source show excellent agreement with the A.S.T.M. standard patterns for AlN and BN. However the pattern of the TiN powder used to fabricate TiN crucibles shows several extra lines of weak intensity indicating the possible presence of some unidentifiable impurity. TABLE H-VI X-RAY DATA ON RAW MATERIALS USED TO FABRICATE NITRIDE CRUCIBLES FOR THE QUENCHING METHOD TiN powder AMN hot pressed crucible Fe radiation, Mn filter Fe radiation, Mn filter d observed substance d observed substance 2.698? 2.70 ALN 2.449 TiN 2.493 AlN 2.343? 2.369 AlN 2,123 TiN 1.831 AlN 1.652? 1.559 AMN 1.499 TiN 1.417 AlN 1.279 TiN 1.322 AMN 1.224 TiN 1.046 AiN 1.061 TiN O.999 AIN

-166TABIE H-VI (CONT'T) BN bar stock Cr radiation d observed substance 3.341 BN 2.171 BN 2.058 BN 1.661 BN 1.322 BN 1.252 BN 1.173 BN

APPRENDIX I CALCULATION OF ACTIVITY COEFFICIENTS IN LIQUID IRON As an additional check on the consistency of the nitrogen absorption curves values of y2j, the slope of aj vs Xj, were calculated for the systems titanium, zirconium, aluminum, and boron. also represents the activity coefficient of j relative to pure j. It can be calculated at various dilute j concentrations from free energy data on the reaction: (1 or s) + 1/2 N = jN) ( and the nitrogen pressure at which the nitride forms.in equilibrium. withb a melt of known j content. Free energy data on reaction (I-1) are given by Elliott and Gleiser(38) and values of nitrogen pressure corresponding to a given j content can be read from the break points of the nitrogen absorption curves in Appendix F. The equilibrium constant for Equation (I-i) can be written according to the following equation: AF~ = -RTlnK=-RTln jN 1 aj x (PN2) 1/ (7jNj ) x (PN2)l/2 (I-2) From Equation (1-2) a value of yj corresponding to each finite Nj was calculated at 1600~C. These are shown in Table I-I. In order to calculate the value of yj at infinite dilution, designated y', free energy data on the reactions (I-1) and: 1/2N2 =N (I-4) -167

-168jN (s) = + N (I-5) were combined to give the free energy of the reaction: J(l or s) = (1-6) Free energy data of Pehlke and Elliott(l) for-Equation (I-4) were used and free energy data for Equation (I-5) came from Table XI of this study. The equilibrium constant for Equation (I-6) can now be written: Mj AF~ = -RT ln. (I-7) O.55857 and yZ can be calculated from (I-7). These values are also presented in Table I-I. The values of YA1 in Table I-I are lower than those of Wilder and Elliott(31) or Chipman and Floridis(32) The values of 7Zr are considerably lower than the estimate of Chipman(7) and the values of YTi are higher than Chipman's(35) estimate for this system The differences in y values are too large to be explained by the estimated uncertainty in the A F' values for reaction (I-1). The y values in Table I-I for the titanium and zirconium systems show some scatter in that they do not progressively increase with increasing j content. The large difference between yB and the other two y values for the boron system indicates that these solutions are sufficiently concentrated in boron to show large departures.from Henry's Law. In addition the y values in Table I-I are not strictly for the binary systems Fe-j but for the ternary Fe-j-N. However the effect of nitrogen can be shown to be negligible by writing the equation:

-169~ N lnyj = lnyj x + E j (I-8) N and noting that the term E jXN is small for the titanium, zirconium, aluminum, and boron systems.. TABIE I-I CALCUAITED VALUES OF 7j FOR THE TITANIUM, ZIRCONIUM, ALUMINUM, AND BORON SYSTEMS element j % (PN2)1/2 (cm)1/2 71 Ti 0 0.047 0.195 3.22 0.o38 0.228 2.65 0.042 0.254 2.03 0.049 0.277 2.10 0.043 0.318 1.40 0.056 Zr 0 0.0076 0.253 6.10 o.o0043 0.322 5.10 0.0041 0.409 2.40 o,oo68 0.558 1.25 0.0095 Al 0. 019 1.07 8.10 0.021 1.17 6.95 0.022 1.34 5.60 0.024 1.57 4.65 0.025 1,81 3.58 0.028 B 0 0.021 5.83 3.38 0.399 7.06 2.80 0.398

APPENDIX J FREE ENERGY OF FORMATION OF A1N FROM THE PURE COMPONENTS Of the four most stable nitride systems considered in Appendix I there is only one, aluminum, for which the nitride composition and the activity of the metal in iron solution are sufficiently well known to permit accurate calculation of the standard free energy of formation of the nitride from its pure components. For the reaction: A1N(s) Al + N (J-1) the free energy from Table XI of this study may be written: AF~ = 63,700 - 27.91T (J-2) For the reaction: 1/2N2 = N (J-3) Pehlke and Elliott(l) give the free energy as: F~ = 860 + 5.71T (J-4) The free energy for the reaction: Al(1) = Al (J-5) is given by the equation: F~ = 4.575T log 0.5585 y~ (J-6) MAl where y~ is the slope of the curve of aluminum activity versus aluminum mole fraction in liquid iron. However since y~ is known only at 16000C, it is necessary to know the heat of solution of aluminum in liquid iron, i.e. the A H~ for Equation (J-5). If the dilute solution of aluminum in liquid iron is assumed to be regular, then the L H~ for Equation (J-5) is given by: -170

-171a H~ = 4.575T log yO (J-7) By combining Equations (J-6) and (J-7) the A S~ for reaction (J-5) may be found: A FQ A-Ho 0.558H A s~ = -..... - 4.575 log (J-8) T MAl The results of Wilder and Elliott(31) give a value of y~" = 0.063 at 1600"C. Using this value and Equations (J-7) and (J-8) the free energy of reaction (J-5) may be written:' F~ =-10,280 - 7.70T (J-9) By combining reactions (J-1), (J-3), and (J-5) the reaction: Al(l) + 1/2N2 A() (J-10) results. The free energy of this reaction which is the standard free energy of formation of AlN from its pure components can be calculated from Equations (J-2), (J_4), and (J-9) as: i F~ - -75,100 + 25.29T (J-ll) The free energy values given by Equation (J-ll) in the temperature range over which the experimental values for reaction (J-1) were measured are summarized in Table J-I. TABLE J-I FREE ENERGY OF FORMATION OF ALN FROM THE PURE COMPONENTS Temperature ~C A F 1600 -24,600 1650 -23,300 1700 -22,000 1750 -20,700

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