SOLUBILITY OF NITROGEN IN LIQUID IRON ALLOYS SOLUBILITY OF NITROGEN IN LIQUID IRON ALLOYS By DAVID WILLIAM GOMERSALL, M.Sc. A Thesis Submitted to the Faculty of Graduate Studies in Partial Fulfi l met1"b ; of "'the Requirements for the Degree Doctor of Philosophy McMaster University September 1967 DOCTOR OF PHILOSOPHY (1967) McMASTER UNIVERSITY ( lVJ e ta l lurgy) Hamilton, Ontario. TITLE: Solubility of Nitrogen in Liquid Iron Alloys AUTHOR: David William Gomersall, B.Sc. (Liverpool University) M.Sc. (University of Alberta) SUPERVISOR: Professor AG McLean NUMBER OF PAGES: x, 105 ABSTRACT: An investigation has been made concerning the solu­ bility of nitrogen in pure liquid iron, iron-carbon and iron­ aluminium alloys. A technique involving levitation melting and a r~pid 1 quench d~vice has been used. The experimental data obtained have been expressed in terms of the interaction coefficients proposed by Wagner and Lupis and Elliott. The data have also been used to test the formalisms developed recently by Darken and Chipman. A simple model for liquid metal solutions in which the solutes may be · considered "inter­ stitial" has been -developed and"tested using the results of the present study and published data for a number of ternary solutions~ ii ACKNOWLEDGMENTS The author wishes to express his gratitude to Dr. R. G. Ward, under whose supervision this work was initiated, and to Dr. A. McLean for many helpful discussions during the course of this investigation. Acknowledgments are made to Mr~ Van Oosten for assistance with the carbon analyses. The author also wishes to express his gratitude to the National Research Council of Canada and the Ontario Provincial Government for financial assistance. TABLE OF CONTENTS CHAPTER PAGE 1. Introduction . 1 2. Thermodynamics of Metallic Solutions . . 9 2.1 Lupis and Elliott Formalism .. 9 2.1.1 Introduction 9 2 .1. 2 Free energy, enthalpy and entropy i nteraction parameters 12 2.1.3 Interaction parameter relationships. 15 2.2 Darken Formalism....... . 17 2.3 Thermodynamic interactions and physical models of solutions .. 22 2.3.1 Regular solution ... 22 2.3.2 Sub-regular solutions. 24 2.3.3 The quasi-chemical model 25 The quasi-regular solution model . 31 3. Literature Review. 33 3.1 Solubility of nitrogen in pure iron . 33 3.2 Solubility of nitrogen in liquid iron- carbon alloys . ,, . . . .. . . . • . . . 38 3.3 Solubility of nitrogen in liquid iron­ aluminium alloys ...•••...• 41 4. Experimental Techniques Used in Previous Investigations . . . . . . . • . . • . . . . . 44 4.1 The Sieverts' technique 44 4.2 Disadvantages 46 ' 'iv 4.2.1 Hot volume calibration 46 4.2.2 Crucible attack. 47 4.2.3 Initial nitrogen content of the melt 47 4.2.4 Gas adsorption on metal films. 48 4.3 The sampled bath technique .. 48 4.4 Disadvantages . ~ .. 49 5. Experimental Procedure . 50 5.1 The levitation technique .. 50 5.2 Advantages of 1evitation melting.. 51 5.2.1 NGncontamination of the melt . 51 5.2 .. 2 Efficient stirring of the melt 51 5.2.3 Temperature range of investigation may be increased . . . . . . 52 5.3 Disadvantages of levitation melting . 52 5.4 Quenching procedure . . . 53 5.5 Attainment of equilibrium . 55 5.6 Temperature measurement and control . 55 5.7 Gas train . 56 5.8 Materials used .. 57 5.9 Experimental procedure. 58 5.9.1 Pure iron.... 58 5 .. 9 .2 Iron-carbon alloys 58 5.9.3 Iron-aluminium alloys. 58 5.10 Nitrogen analysis . 59 5.11 Carbon analysis .. 60 5.12 Aluminium analysis. 60 v 6. Presentation of Results ...• 6.1 The solubility of nitrogen 6.2 The solubility of nitrogen carbon alloys. . . . . . . 6.3 The solubility of nitrogen aluminium alloys . . . . Discussion. Summary and Conclusions .. Suggestions for Further Work .. References. . . Appendix A .. . . Appendix B. App·endix C . . Figures Tables . . ,. . . in liquid in liquid . . . . . in liquid . . . . 61 iron. . . 61 iron­ . . . 62 iron­ . . . 69 73 85 88 89 94 99 104 vi LIST OF FIGURES FIGURE 1. Change of metal composition with time in the basic Bessemer Converter process. 2. Variation of Log K with temperature for the solubility of nitrogen in pure iron (after Pehlke and Elliott (47) ). 3. Some recent investigations of the solubility of nitrogen in pure iron~ 40 Solubility of nitrogen in iron-carbon alloys found by previous investigators. 5. Solubility of nitrogen in liquid Fe-Al a l loys at 1700°c (after Maekawa and Nakagawa (44) ). 6. Solubility of nitrogen in liquid Fe-Al alloys at 16o6°c (after Pehlke and Elliott (47) ). 7. Solubility of nitrogen in liquid Fe-Al alloys (after Evans and Pehlke (53) ). 8. Reaction Chamber of Sieverts 1 apparatus. 9. Schematic diagram showing the configuration of the levitat i on coil usedo 10. Nitrogen content of samples quenched into a copper moulo. 11. Schematic diagram of quench apparatus. 12. The quench apparatus. 13. Close-up of quench apparatus. 14. Circuit diagram for quench apparatus. vi i 15. Typical que~ched sample. 16. The steam distillation apparatus. 17. Solubility of nitrogen in pure iron. 18. Comparison of present results with previous investigations. 19. Solubility of nitrogen in Fe-C alloys at 1450°c. 20. Solubility of nitrogen in Fe-C alloys at 155o 0 c. 21. Solubility of nitrogen in Fe-C alloys at 166o0 c. 22. Solubility of nitrogen in Fe-C alloys e. t 1750°c. 23. Solubility of nitrogen in Fe-C at 175o0 c, 166o0 c, 1550°C, and 145o0 c .. 24. Comparison of present results for Fe-C alloys with those of previous investigationso 25" Log fN versus pct .. Carbon. 26. l/T°K versus Log wt. pct. N. dH~lloy ., andliS~lloy versus Wt .. pct .. C ..27" 28. Schem~tic diagram demonstrating first and second order free energy interaction parameters. 29. ec and re versus l/T°K. N N 030. Solubility of nitrogen in Fe-C alloys at 155o c (in terms of atom fractions) .. yC ­ 31. Logo versus X for Fe-C alloys at 1550°c. N C 320 Solubility of nitrogen in Fe-Al alloys. 33. Log rt1 versus pct .. Al. Al 34. The effect of temperature on eN .. 35. The effect of Al content on entropy and enthalpy of solution. viii j36. hj versus e N.N 2 37. Lo (X~~/x' ) + 2.38 x versus x ( 1 - x ) . g N N G c N 38. Log't versus at 145o0 c.zcN c 39. LogfN versus zc at 155o0 c. 40. Log~ versus at 166o0 c.zc 41. Log~ versus zc at 1750°c. 42. Log ZN versus z0 • _ix LIST OF TABLES TABLE 1. Solubility of nitrogen in liquid iron (previous investigations). 20 Aluminium-nitrogen interaction parameters in liquid iron (previous investigations). 3. Rate of approach to equilibrium. 4. Solubility of nitrogen in pure iron. 5. Solubi lity of nitrogen in iron-carbon alloys. 6. Previous values obtained for eN c at 160o0 c. 7. Experimental values for the various first and second order carbon-nitrogen interaction parameters. 8. Variation of solubility of nitrogen with temperature for fixed levels of carbon in iron. 9. Heat of solution of nitrogen as a function of carbon content. 10. Entropy of solution as a function of carbon content. 11. Solubility of nitrogen in iron-carbon- alloys on the mole fraction scale. 120 The activity of nitrogen in Fe-C alloys at 15_5o 0 c on the Raoultian Scale. Solubility of nitrogen in liquid iron-aluminium alloys. ei1 as a function of temperature. j Comparison of predicted and experimental values of e i for "interstitial" solutions. x CHAY.rER l INTRODUCTION From the first iron d~oplets formed in the bosb of the blast furnace, to the final casting of the finished steel product, liquid iron, throughout many of its various stages of refinement, is in contact with nitrogen from the atmosphereo The droplets in the bosh of the blast furnace are e xposed under reducing conditions to essentially one atmosphere partial pressur~ of nitrogen, and it seems likely that the liquid metal is saturated with nitrogen at this stage. As the droplets fall into the well of the fur­ nace their carbon content increases and the temperature decreasBs. Both effects result in a decreasing solubility of nitrogeno The iron tapped from the blast furnace gener­ ally contains about 00006 wto pctu nitrogen, however it has fallen to 00004 wt 0 pcto by the time the metal reaches the mixer, which suggests that the metal in the furnace is supersaturated with respect to nitrogen. The iron tapped from the furnace contains consider­ able quantities of carbon, phosphorus, sulphur, silicon and manganese all of which, with the exception of manganese, decrease the solubility of nitrogen in liquid iron. During the conversion to steel, the bulk of these impurities are removed and this allows the solubility of nitrogen in the 1 2 melt to increase. The extent of this increase will depend on the type of process used. In a traditional air-blown converter, the gas entering the molten metal through the tuyeres contains 79 pct. by volume of nitrogen. The oxygen in the gas reacts to form oxides and hence the gas passing through the metal is essentially pure nitrogen, exc~pt during the carbon reaction when carbon monoxide is also present. The variation in the nitrogen content of the metal in the course of the basic process is shown in Fig. 1, (1). While the silicon and manganese are being oxidised, the g~s pas­ sing through the metal is almost pure nitrogen but the low temperature and high carbon content keep the nitrogen solu­ bility at a low level. Towards the end of this period the temperature rises and continues to rise during the oxidation of carbon. The nitrogen content however remains at a low level and may actually decrease slightly since the nitrogen passing through the metal now has a much lower partial pres­ sure d~e to the presence . of carbon monoxide. The boil becomes less vigorous when the carbon content of the melt reaches about 1 wt. pct. At this stage the carbon monoxide content of the gas decreases rapidly, the partial pressure _of hitrogen increases and since the carbon content of the ~etal is greatly reduced, the concentration of nitrogen in the melt increases rapidly during the final minutes of t he ('carbon blow". 3 In the basic Bessemer process an "after ·blow" is required to remove the phosphorus. During this period the nitrogen content of the metal continues to rise due to the increased temperature, the low carbon content of the melt, and the fact that the partial pressure of nitrogen is almost unity. At the end of the "after blow", the nitrogen content of the metal is in the region of 0.015 to 0.025 wt pct. In the acid Bessemer process where there is no phosphorus removal, the converter is turned down immediately after the carbon flame drops and the final nitrogen content of acid Bessemer steels remains fairly low (around 0.01 wt. pob.). It is im~ortant that the _converter is turned down as1 quickly as possible since the nitrogen content of toe melt rises rapidly after the carbon has been oxidized; a delay of a few seconds will significantly alter the nitrogen content of the steel. It has been estimated that the rate of nitro­ gen dissolution is of the order of 0.005 wt. pct. for each · minute of blowing time after carbon oxidation has ceased. (1). The lowest nitrogen contents in converter steels (0.003 t o 0.006 wt. pct.) are obtained by either eliminating or min­ imising the nitrogen in the blowing gas. This can be accom­ plished by bottom blowing with oxygen-steam or oxygen-carbon dioxide gas mixtures or by enriching the air with oxygen up to a practical limit of 40 pct. by volume. These procedures reduce both the time required for a given blow and also the partial pressure of nitrogen in the gase~ passing through . I • 1 4 the metal, thereby reducing the final nitrogen content of the melt. In side blown air converters, nitrogen dissolution is reduced by blowing air tangentially over the slag surface through tuyeres in the side of the vessel. The nitrogen con~ tent of the metal is kept at a low level, since nitrogen from the gas phase cannot easily penetrate the slag layer above the metalo However, the overall refining rates are greatly de­ creased and this process has never been widely accepted. On the other hand, top blown converter processes such as the L.D. (Linz-Donawitz), · have become popular during the past ten years. In these processes commercially pure oxygen i~ blown into the melt through water cooled copper lances. In this manner .high rates of production are achieved and the nitrogen content of the steel generally does not exceed O.OOS wt. pct. In the conventional open-hearth process, the oxygen required for refining is obtained mainly from slag-metal reactions rather tha~ gas-metal reactions and the metal is therefore protected from the nitrogen in the atmosphere by a slag layer in a similar manner to the side blown converter. A considerable quantity of nitrogen may enter the metal with the scrap charged but this is effectively flushed out by the carbon monoxide bubbles during the carbon oxidation and nitro­ gen contents as low as 0.002 wt. pct. are obtained at tap. Nitrogen may be absorbed during the tapping operation and also from additions made to the ladle in finishing the steel. 5 As a consequence, open-hearth steels generally have a n itrogen content in the range 0.004 to 0.007 wt. pct. Steels prepared in the electric arc furnace usually h ave hi gher nitrogen contents than those obtained from the op e n- hearth process since some of the nit ~ ogen in the atmos­ phe re above the mel t is ionized by the arc. Nitrogen in t h i s form i s in a more active state and will dissolve much more readily in the liquid metal. In addition, the carbo n boi l is less i ntense than in the open-hearth and thus the f l ush i ng action of carbon monoxide bubbles on dissolve d ni t rogen i s less effective in this process. Many of th e ad d i ti ons used in maki ng high alloy steels in the electric arc furnace often contain considerable quantities of nitro­ g e n . Frequently these additions raise the solubility of ni t r ogen _in liquid iron and the nitrogen contents of stee ls p re p are d i n this manner are generally in the region of 0.005 t o 0 .010 wt . pct. Oxy gen d i ssolved in liquid iron inhibits t he dis s o­ lu t i on of ni t r oge n i n the metal due to the presence of a surfa ce a cti ve layer of oxygen which poisons the sites availa b l e f or the e nt r y of n itrogen. (2). I n general, a fte r the r efi ni ng process steels have a high oxygen content, a nd ni t r oge n absorption during tapping, when the l i qui d metal is e xposed to the atmosphere, is not great. However, wh e n a steel has been thoroughly deoxidized the me tal does not have th i s protection. Usually when the steel is poured 6 from the ladle into the mould the nitrogen absorbed may be considerable. This absorption of nitrogen is not encountered when deoxidized additions are made to the mould rather than t he ladle, but the advantage of this procedure is frequently offset by the high incidence of inclusions in the solidified ingot. In the production of rimming steels, the metal is only partially deoxidized so the rate of nitrogen absorption during pouring is reduced. In addition, some of this nitrogen will be flushed out by the evolution of carbon monoxide during the freezing process. Although the solubility of nitrogen in iron base alloys is i n general small, the effects of nitrogen on the properties of steel may be quite profound. For most purposes nitrogen in finished steels is undesirable particularly in the low carbon grades, since on cooling to room temperature the solubility limit of nitrogen in the steel may be exceeded and this can lead to embrit t lement and loss of ductility of the steel on ageingo On the other hand, nitrogen improves the work harden­ i ng properties and machinability of steels. In combination with aluminium, as AlN, it can cause intergranular fracture i n c ast steels. However, if the AlN is precipitated in a fi nely divided form, it can lead to improvements in mechan­ i cal properties. In some stainless steels nitrogen is actually necessary as an alloying element in order to stabilize the austenite phase and hence nitrogen pick up in the electric arc furnace is not always a disadvantage. (3). 7 In the light of the above discussion, it is clearly desirable that one should be able to predict the solubility of nitrogen in liquid iron alloys under a variety of steel­ making conditions. To do this, information is required con­ cerning the interaction between nitrogen and the various alloying elements which may be present in liquid iron. There have been a number of investigations of these effects in recent years and the interactions between nitrogen aria many elements dissolved in liquid iron are now known to a high degree of precision at steelmaking temperatures. Unfortun­ ately, several elements which are of importance in steelmaking have proved difficult to deal with using the standard experi­ mental techniques for this type of investigation. Two of these elements are carbon and aluminium. Carbon is always present to some extent in the metal and aluminium is . the element most commonly used for deoxidation purposes. In this investigation a new technique has been de­ vised to study nitrogen solubilities which incorporates levitation melting together with a rapid-quenching device . . Using this technique, the solubility of nitrogen has been de t ermined in the following systems: a) Pure liquid iron over the tempera t ure range 1530° - 1780°c . ~) .Iron-carbon alloys for t he composi t i on range 0 - 5 wt. pct. C and the t emperature range l l 1-50 ° - 175 0 °c . 8 c) Iron-aluminium alloys up to the solubility limit of aluminium nitride and for the tem­ perature range 1550° - 1750°c. The experimental data obtained from this investigation have been expressed in terms of the interaction coefficients proposed by Wagner (5) and Lupis and Elliott (6). The data have also been used to test the formalisms developed recently by Darken (9,10) and Chipman (67). A model for liquid metal solutions in which the solutes may be considered nintersti­ tialn has been developed. The prediction powers of this model have been examined using the results of the present study together with published data for a number of ternary solutions. CHAPTER '2 THERMODYNAMICS OF METALLIC SOLUTIONS 2 .1 Lupis and Elliott formalism. 2.1~1 Introduction. Chipman (4) has shown that for a solvent 1 containing solutes 2, 3, the activity coef­ ficient a" 2 of solute 2 is a function of the other solutes present and may be expressed approximately by the ~elati on y - y2 3 4 0 2 - 0 2 x '4 2 x a2x - - - ( 2. 1) Where "/{ ~ is the· activity coefficient of solute 2 in the binary solution 1 - 2 cont~ining a mole fraction x2 ~ '{~, ~ ~ 1 - --- represent the effects of solutes 3, 4, on the activity coefficient of 2. In this case, the reference sta~e for the activity coefficient is based on Henry's law, so that t he coefficient becomes equal to unity for an infinitely dilute solution. Wagner (5) has shown that the partial moiar free e ne rgy of a solute, or alternatively the logarithm of the activity coefficien t of the solute, can be expressed in terms of ~ a Ta y lor series .. If the series for ln ~ i is expanded abol;lt, the point Xi ~ O, the following expression is obtained: 9 Ln ¥.i = Ln '( ~ + x (d l~ (f i) +X . (' 0 ( 2. 53 )Log a ;; ~ 2 where the asterisk denotes the quantity which is maintaine d 22 at a fixed activity. For ternary solutions ., ::: o( o( x2Log 't ;; 0~ x f (-2 + x ) + 12 2 2 13 3 ( 2 . 54) + ( o<. 23 - o(l2 - o(l3) x ( l-X ' )3 2 Where the prime denotes the quantity which is at fixed activity in the ternary solution. ~ ~(- ~:-S ince under these conditions -:~ = i s a 2 2 X2 constant then ( 2 .55 ) combining Eq. (2.45), (2.53) and (2.54) it follows that: x2Log(X2~~-/x 1Y) + o( [ Xv ( 2-X i) -X ~:-( 2-X -~'°~- CX - 12 2 2 2 . 2 1 13 3 :::: ( o( 23- o{l2- 0('13) X3 ( l-X;) ( 2.56) thus o<.. 23 may be eva lua tea from solubili t y data when o{ 12 and cX.. 13 , which are characteristic of the binary solutions, are known. '' 2 . 3 Thermodynamic interactions and physical models of solutions. A number of attempts have been made to predict solu­ tion behaviour using physical models of solutions. Expres­ s i ons for the excess free-energy derived from these models may be used to calculate interaction effects. 2.3.1 Regular solution. In 1927 Hildebrand (12 ) · introduced the concept of the regular solution in · which. t he l. 23 entropy of mixing is ideal while the enthalpy of mixing is finite. It may be shown that for such solutions the activ­ ity coefficients are directly related to the partial molal heats of mixing. e.g. RT ln 0 . == L\ H~ (2.57) l l Many solutions behave approximately in this manner but solutions which are strictly regular appear to be almost as rare as : those which are ideal (15). Hildebrand and Scott (13) later showed that the activ­ ity coefficient of component i in a regular ternary solution could be represented by: A HMl. v ~ = i ( sLn ((. == l RT hr i +f1. b +;1. ~ (2.58) l i J j ¢ is the volume fraction v is the molar volume 8 is the solubility parameter which is defined as the square root of the energy of vapourization per cubic cen­ timetre and represents the !!cohesive energy density 11 of an element. Interaction parameters may be obtained by differen­ tiating with respect t o mole fraction of i or j. i.e. E i j = ( 5;)1~ ."6 i) = -_2_ (v~:j) cSk-8ii2 x = x = 0 RT iJ j (2.59) 24 and c i i = ( d ln xi) ()Xi xi ::: xj = = 0 -2 RT v? l- vk (a 1-cfc 2 ) ( 2 . 60 ) These expressions predict a linear relation with tho rec i procal of the absolute temperature. It is found however (14) that even for ternary sys-_ terns for which corresponding binaries are regular the above relations only predict the sign of the interaction parameter correctly in 50% of the cases examined. Thus the regular solution does not appear to be very useful for predicting interaction effects in metallic systems. According to Richardson (15) the main source of error in this model is I probably the assumption that interaction energies between atom pairs are independent of the composition of the solution. 2~3.2 Sub-regular solutions. Hardy (16) proposed that the excess free energy be taken as a function of con­ centration; he termed this the,flsub regular" model and de­ rived the following expression for the excess free energy: F = X • X [ Ao . j + (X . - X . ) A ~ i . ] == X . X . [A '? .+ ( l -2X j ) A! .l 1 j 1 l J J 1 J lJ 1J J (2.61) A plot of pE/RT versus X. should thus be linear with a finite l slope. This treatment was extended to ternary systems hy Yokokawae t al . (17) who derived the following expression for the excess free energyG 25 x .-x. pE 0 0 0 J lt X.X.A .. - XiXkAik + xkx jAkj + x.x. A.. ' J l lJ J l lJx .+x-.J :1 Xi '""Xk xk-xi A'+xx +XX Ajk ' i k ik k i ( 2" 62)Xi +Xk Xk +Xi where the A's are constants characteristic of the appropriate binary system and defined from the assumption that the heat of solution of a binary solid solution is given by .LlH t (A? . x + A ~ . y) xylJ lJ A relation may also be derived for the excess chem­ ical potential of constituent i which may then be differen­ tiated with respect to the mole fraction of component j to obtain an expression for the interaction parameter£ { in terms of the constants of the sub-regular model (14): (2.63) It is assumed here that the interactions A0 and A I are not affected by additional solutes and/or solvents. While this model appears to predict the sign of the interaction parameter rather better than that of regular solution, the actual magnitude of the parameter is only in very approximate agreement with experimental values (14). The model is limited in that the binary behaviour must be known experimentally and the solution must conform to the expression for a sub-regular solution. 2.3.3 The quasi-chemical model. This model was developed by Guggenheim (18) and allows for the fact that 26 the distribution of atoms or molecules cannot be perfectly random if there is a heat of mixing. The basic assumptions of this model are: i) The motion of an atom is confined to its oscil­ lation about an equilibrium position. ii) Only the configurational partition function is considered to contribute to the thermodynamic excess proper­ ties. Effects due to changes in vibrational frequency of solute atoms due to changes in environment of- the atom are n~glected. So the main source of excess entropy is config­ urational and hence its sign is always negative. Another source of excess entropy which is neglected is the change in bond energy with temperature. This effect - is generally con­ sidered negligible for the temperature ranges encountered in practice. iii) Only pairwise interactions occur i.e. only the influence of nearest neighbours is considered. iv) Solutions are considered to be dilute hence the number of nearest neighbours to any atom is assumed to be equal to the coordination number of Z of the pure solvent. Using this model Alcock and Richardson (19) derived the following expression: (2.64) At low concentrations of j it was assumed that Ll Si( jk)=~Si(k) 27 so that.. L!l H ­ AHi(k)- /1 Hj(k ) .i ( "j) (2.6~) Alcock and Richardson then made the ·following assumptions: a) ~si(j) = L\Si(k) at Xi--+ 0 b) ¥ and 't are taken relative to the same . i ( j) i(k) standard state for i. c) A Sj(k) is Raoultian. Under these conditions equation (2.65) becomes = ln )' i ( j) - ln '( i ( k) - ln ~ j ( k) (2.66) Later Alcock and Richardson (20) using a more rigor­ ous quasi-chemical approach took into account the possible effect due to clustering and obtained the expression: v O' i( j) Ln oi{ jk) = ln 'g ( j+k""J where l/Z K =[ '6 i ( k ) '{ H j +kl] ( 2. 67) '8' i < j > rk < j +k and Z is the coordination number of pure solvent. This expression was differentiated to obtain an expression for the interaction paramter: /din '{i)l aln xj ( 2. 68) ~---------------------__,- 28 which reduces to c j c:. i = - Z(K - 1) (2.69) when the solutes are present at infinite dilution. Wada and Saito (21) used the zeroth approximation of Guggenheim's quasi-chemical method for regular solutions and assumed the coordination number in a liquid metal solution to be between 10 and 12. Dilute solutes were then assumed to be placed substitutionally in this very nearly close-packed lat- t ice, statistical thermodynamics applied, and the following e xpression for the interaction par~meter derived: = _l_ (W .. - W.k ·:- W. k) (2.70 ) RT l J J l where the W's are interchange energies between the compon­ e nt s indicated by the subscripts. This expression is identical in form to that obtained by Alcock and Richardson based on a random solution model. However Wada and Saito determined their interchange energies independently by using an expression proposed by Mo t t (22) for the excess free energy of mixing in binary s olut ions and an expression for the excess free energy of mi xi n g in dilute solution. ~ ::: w.. I. I. (2.71)i l J l J The expression for the interchange energy then becomes 2w :::::: 8 J.) - 23, 060 n ex. - x.) ( 2 .72)ij -i -J 29 Mwhere V =molar volume; X = electronegativity; n = number of ij bonds; S= solubility parameters. Except for n, these parameters are known for most elements. Wada and Saito (21) suggested that the smaller value of the valency of the two components may be employed as the value of n and vM should be taken as the arithmetic average of the atomic volumes of the two components in the solid state. Lupis and Elliott (23) have recently used the quasi- chemical model in order to predict first and second or der free energy interaction coefficients in multi-compon~nt solutions. \ They derive the following series expression tor the excess free energy of the dilute (1-i-j) solution. ~ == g xi in( 1- \ li) + ~ x .1n( 1 + A1 . ) RT 2 2 J J -£i A1i· x? - t? A1 . x~ - ~ f""' · · x. x . 2 l 2 J J / lJ l J ~r. .)x~J. . I i J i (2.73) Where .A ij = exp (2 w lJ.. ) -1 u·. + u .. w.. U· • - ll ,],]=lJ lJ 2 u is the bond energy of the appropriate pair. ~ = l/KT 30 = exp [15 (w . + w - w.. )] -1 1 . 1-- l J l J = [ (1 + Ali) ( 1 + ,A i ,j )J ~ -1 (1 + .Aij) The terms in the expansion correspond to equivalent terms in the Taylor expansion for GE/RT. Thus expressions for the various interaction coefficients may be obtained by direct comparison. Lupis and Elliott (23) also express these coefficients in terms of lower order interaction coefficients. e.g.[ r g ~. in terms of quasi-chemical co-I i J efficients ~/Z)(l- 5/g) ] } or C~ l (1- r/~)i-j binary the thermodynamic equivalent of the quasi-chemical express~on. Similar exp r essions were also derived for the second order interaction para~eters. i.e. l l ~ = g /--· . A1. + 2zH/:· .) 2 +~A ijlJ l lJ 2 or l ~ = [Et ] 2 + E ~ (£j E) l 2~ ~ i 2 The agreeme n t between the observed and calculated values for the various coefficients appears to be reasonably good in the systems compared by Lupis and Elliott (23). The agreement was poorest for · solute elements having small radii, which one would expect since the model assumes that the··atoms of the solute are placed 11 subs ti tu tiona lly" on the pseu_d_o lattice rather than "interstitially". 31 The two assumptions of the quasi-chemical model which are most open to criticism are firstly the assump­ tion of pair wise interactions or of the non-dependence of the bonding energies on the concentration of the solutes and secondly the neglect of the vibrational contribution ~ to the excess properties. The first difficulty can be largely avoided by adopting the reference stat~ of infinite dilution of the corresponding solute in the solvent. One c onsequence of the second assumption is that the only excess entropies taken into account are configurational and henc~are negative contrary to the experimental evi­ dence that positive excess entropies are frequently observed. 2.3.4 The quasi-regular solution model. In a subsequent paper Lupis and Elliott (24) attempted to elim­ inate some of the weaknesses of the quasi-chemical model and at the same time develop a solution model that would predict enthalpy and entropy interaction coefficients for liquid metal solutions. This model was based to a large extent on the cell model of the liquid state (25). In the liquid state far below the critical temperature, some short range order would be expected to exist. The field acting on each atom will fluctuate rapidly but this fluctuating field can be replaced by an average field - of spherical symmetry. In this model the partition function is described in terms of probabilities associated with different configurations in the nearest neighbour well about a central atom. The 32 c onfiguration depends mostly on the number of atoms present of any particular kind. The regular solution assumes complete randomness of the different atoms and that the only source of entropy of mixing is configurational. Lupis and Elliott call the sim­ plest form of this model the quasi-regular solution model. This retains the assumption of complete randomness and hence E S conf. = O. However other contributions to the total excess entropy are not neglected and they obtain the following expression for the excess free energy: == ZXAXBWAB( 1 - 1) ?:: where Z is the average coordination number. XA, XB are mole fractions of components A and B respectively WAB == UAB - UAA + UBB 2 uAB is bond energy of atoms A and B L is a "characteristic temperature" of the solut ion . CHAPTER 3 LITERATURE REVIEW 3elo Solubility of nitrogen in liquid iron. Metallurgists became interested in a thermodynamic approach to metallic solutions following the development of Gibbs's phase theory in 1887 and the discovery of Raoult's Law in 1888. Investigation into the solubilities of gases in metals and alloys was stimulated by the extensive work of Sieverts a nd Krumbhaar (26) around 1910,who discovered the relationship between solubility and gas pressure, now known as Sieverts' Law. No accurate determinations of the solubility of nitrogen in liquid iron or liquid iron alloys were recorded until Chipman and Murphy (30) measured its solubility in liquid iron in 19350 Prior to this date, a number of ap­ proximate results had been obtained. In 1911, , And rew (27) melted iron under nitrogen at 200 atmospheres pressure and suc ceeded in diss olving 0.3 wt. pct. nitrogen. Strauss (28), in 1914, introduc e d between 0003 and Oe04 wt. pct. nitrogen i n to steel by the ac t ion of ammonia and nitrogen on the liquid metalo Sawyer (29), in 1923, using nitrogen pressures up to three a t mospheres, found that his results and Andrew's could be expressed by the equation: Wt. Pct. Nitrogen~ 0.02 W 33 34 where P was the pressure in atmospheres. However, pre­ vious to Chipman and Murphy's determination, investiga­ tors had ne ver established that equilibrium had in fact been a ttained betwee n the gas phase and the liquid metal. The method used by Chipman and Murphy (30) con­ sisted in heating a charge of iron in a closed induction furnace a nd equilibrating the melt with a nitrogen atmos­ phere at temperatures between 1540°c and 1760°c. The melt was then cooled in the furnace and the resulting ingot was analy sed using the vacuum fusion method. The absorption of nitrogen by the melt was followed by adding small amounts of ni trogen through gas burettes to maintain the pressure over the mel t at one atmosphere. Absorption was judged to be complete when it was no longer necessary to add more gas to maintain the pressurev The cooling process was also fol­ lowed using the gas burettes and by this means any gas evolved on s o lidification could be monitored and ad ded as a correct ion factor to the percentage of nitrogen in the ingot. Using this method, the solubility of nitrogen in liquid iron was found to be 0.040 wto pct. at 160o0 c and a value was calculated for the temperature coefficient of solubility . of 1.5 x 10-5 wt. pct. per 0 c 0 Independently, Sieverts a n d Zapf (31) in Germany determined the solubility of nitrogen in liquid iron using what has become known as t he Sieverts' method. With this method (whic h is described in more detail in Chapter 4) , http:solubility.of 35 the absorption of nitrogen was measured directly at con­ stant temperature and pressure with gas burettes. The value of 00031 wt. pcto obtained by Sieverts and Zapf for the solubility of . nitrogen in liquid iron at 1540°C was markedly lower than that obtained by Chipman and Murphy. , Following these investigations there was an increased demand for further information concerning the effect of gas­ eous elements dissolved in steel, particularly as the irreg­ ular behaviour of well-known steels was frequently attributed to the presence of dissolved gases. Hence, in the ensuing years a large number of investigations into the solubility of nitrogen and other gases in liquid iron and its alloys were performed. Two methods were widely used; the sampled bath technique and an improved Sieverts' technique. Paradox­ ically, the Europeans appeared to prefer the sampling tech­ nique while the Americans preferred the Sieverts' technique. In 1941, Kootz (35) established the important fact that the dissolution of nitrogen in pure liquid iron obeyed Sieverts' Lawo Thus, the dissolution of nitrogen in liquid iron could ' be represented by the reaction ~N2 -----?" B where the B denotes nitrogen dissolved in liquid iron. Interest in these types of investigation received a n added stimulus when Wagner (5) and Chipman (4) around 1950 advan ced solution thermodynamics to the stage where the effects of alloying elements on the solubility of other 36 solutes could be predicted through atomic interaction effects (Chapter 2). In order to make effective use of the se concepts more accurate data were required. In 1957, Kashyap and Parlee (41) repeated the work of Koo tz and confirmed that Sieverts' Law is obeyed by ni­ trogen dissolving in liquid iron, up to one atmosphere pre ssure. These workers also determined the solubility of nitrogen in Fe - Ni, Fe - Mo, Fe - V and Fe - Mo - V alloys and were able to test the validity of Wagner and Chipman's approximation formulae for the prediction of nitrogen sol­ ubilities in these alloys. Good agreement was found between experimentally determined nitrogen solubilities in the t ernary alloys, and calculated values obtained from the relevant binary data. By 1960, Elliott and co-workers (46, 47) had made an extensive study of the solubility of nitrogen in a wide var­ iety of liquid iron alloys. In the course of this work, two separate investigations were conducted concerning the solu­ bility of nitrogen in pure iron. Humbert and Elliott (46) determined the solubility of nitrogen at one atmosphere pressure in pure liquid iron at 1600°c, to be 0.0438 wt. pc t . They also determined the solubility over the t emperature range 1540°C to 1700°c and found the temperature coefficient 0 -6 0of solubility at 1600 C to be 7.7 x 10 wt • pc t . per c , which was approximately half the value previously reported for this coefficient. Their results yielded the following 37 values for the heat and free energy of solution of nitrogen in liquid iron : Cl H0 = 1200± 400 ca la / g . a t om AF 0 - 1200 + 5.56 T- + 200 cals/g. a tom Pehlke and Elliott (47) in their investigations, a g a in using the Sieverts' method, found that the dissolu­ tion of nitrogen in pure liquid iron obeyed Siever ts ' Law to a very high degree of precision up to one atmosphere p ressure of n i trogen. This confirmed the results of all p revious in­ vest i gations, except those of Kasamatu and Matoba (40), who f ound a departure from SievertsY Law at all concentrations . Pehlke and Elliott found the solubility of nitrogen in pure liquid iron ·to be 0.0451t 0.0,006 wt. pct. at 1600°C. The -6 te mperature coefficient of solubility was found to be 8 x 10 wt. pct. per 0 c at 1600°c. The heat and free energy of solution were reported as: AH 0 ~ 860± 400 cal/g. atom 0 + +AF :::: 860 5.71 T- 100 cal/g. atom These data are in good agreement with those of Humbert and Elliott (46), but it is worth noting, tha t wh ile highly consistent data were obtained from any one expe riment, the consistency of the data from one experimebt to anoth er is, by comparison, rather poor. This inconsistency results in a relatively large error in the average value for the heat of solution, in spite of the fact that the root mean square error 38 on all experiments performed at 16oo0 c was only 0.0006 wt. pct. N. (Fig. 2). A more recent investigation of nitrogen solubility in pure liquid iron is that by Turnock and Pehlke (51) in 1966. Using the Sieverts' technique, they obtained results which agre ed well with those of Elliott and co-workers (46, 47). The solubility of nitrogen in pure liquid iron at 16oo 0 c has also been measured by a number of other investi­ ga t ors who were primarily interested in determining its solubi l i ty in liquid i ron alloys. A summary of the results available in the literature for the dissolution of nitrogen in pure liquid iron is shown in Table 1 and some of the more recent values for solubili­ ties determined as a function of temperature are plotted in Fig. 3. It will be noted that, while there are discrepan­ cies between the results of the various workers, the data from the last three investigations mentione~ (46, 47, 51), are in good agreement. 3. 2 Solubility of ni trogen in liquid iron-carbon alloys. If prediction formulae are to be useful for steel­ making purposes , a precise knowledge of the interaction effects between nitrogen a nd carbon in liquid iron is required. Unfortunately, this system has proved difficult to deal wi th using t h e Sieverts' method, probably because of the diffi cul- ~ ties associated with the gaseous reaction product which c a n form when iron carbon alloys are held in a refractory cruc ible. 39 Since t his technique requires the melt to be held in a closed reaction vessel, and the nitrogen absorption to be measure d direct ly using gas burettes, any gaseous products formed during®experiment will give low values for the solubility of nitrogen. For t his reason, it is considered that the most reliable data to be found in the literature for this p ar ticular system are those obtained by the sampled bath techni que. The first reported study of the solubility of nitro­ gen in liquid iron carbon alloys was made by Eklund (32) i n 1939. Using the sampled bath method, he found that carbon markedly decre ased t he solubility of nitrogen in liqui d iron . Solubi lities were measured at 155o0 c in the range 0 to 4 wt. pct. C. From his various data, Eklund selected only the highest values for nitrogen solubility as a basis for drawing his solubility curve. (Fig. 4). More recently, Chipman (52) has shown that whe n all of Eklund's results are taken i nt o c onsideration a value of +0.13 is obtained for the c f i rst order free energy interaction parameter, eN· Kootz (35) obtained data for the solubility of nitrogen in liquid iron c arbon alloys at 16oo0 c. Again the sampled bath technique was used. From the results of thi s work, Pehlke a nd Elliott (47) have c alculated a value of 0.13 for e~. Saito (37, 38) has used both the Sieverts' and s am­ pled bath techni ques for determining nitrogen solubilit ies - - --- --·~.._ ~-·- ~ -~~ ---­ 40 in this system. The two solubility curves obtained at 16oo0 c had approxi mately the same slope, but the Sieverts ' method gave considerably lower solubility values, probably for the reason mentioned previously. The value for the interaction parameter e~ obtained from this . work was 0.135. Using the sampled bath technique, Maekawa and Nakagawa (44) found that the logarithm of the ac tivity co­ efficient, f~, could be represented as a linear func ti on of the carbon content, in the range 0 - 4 wt. pct. o.j and in the temperature range 1550° to 1700°0, by the equation: Log f~ = 0.135 <%c) i.e. e~ = 0.135 Again, using the sampled bath technique, Schenc.:ket al. ( 42 ) have determined nitrogen solubilities in liquid iron carbon alloys in the temperature range 1550° to 165o0 o, at one at­ mosphere pressure and in the range 0 to 5 wt. pct. C. They found that their results could be represented by a first order free energy interaction parameter, e~ = 0.125. Solu­ bilities were measured at various partial pressures of nitro­ gen (1, 0.52, 0.32, 0.16 atmospheres) at 1600°0 and it was found that on a plot of (%.N) alloy/PN2 versus carbon content, all the data could be represented satisfactorily by the same line. This indicated that nitrogen obeys Sieverts' Law in all liquid iron carbon alloys up to 5 wt. pct. carbon a t 16oo0 c. A recent investigation of the solubility of nitroge n in liquid iron carbon alloys was reported by Peblke and 41 Elliott (47). These workers found that the Sieverts' technique was unsuitable for this system, and their data were obtained using the sampled bath method. For a given concentration of carbon, their results for the solubility of nitrogen were lower, and thus the value for e~ (0.25) was higher than those obtained in previous investigations. Again it was found that Sieverts' Law was obeyed throughout the carbon concentration range investigated (0 - 5 wt. pct.). The solubility relationships obtained in the above investigations are shown in Fig. 4, and it is evident that a lack of agreement exists between the various data. It h a s been noted already that of the two techniques employed for nitrogen solubility studies, the most reliable data for iron carbon alloys has been obtained using the sampled bath method. However, evidence obtained during the present in­ vestigation (Chapter 5) indicates that the quench rates achieved in the sampled bath technique may not always be adequate to retain all the nitrogen in the metal during solidification. 3.3 Solubility of nitrogen in liquid iron-aluminium alloys. Eklund (32) has studied the solubility of nitrogen in liquid iron-aluminium alloys (0 to 3 wt. pct. aluminium) at 1550°C using the sampled bath technique. The few data col­ le c ted were somewhat scattered, but did indicate that alum­ inium tends to increase the solubility of nitrogen in liquid iron . From this work, Pehlke and Elliott (47) have calculate d Al a value for eN of -0.0103. Maekawa and Nakagawa (44) investigated this system i n the range 0.5 to 8.5 wt. pct. Al, at 1700°c, using the sampled bath t echnique. At lower temperatures difficulties were experienced due to the formation of aluminium nitride, a n d satisfactory results were not obtained. However, at 17 00°C it was found that the nitrogen content of the melt de crease d sharply with increasing aluminium content (Fig. 5 ) . Using t he results from this investigation and their data f or nitrogen solubility in pure iron, they obtained a Al re la t ionship for log fN in terms of aluminium concentrati on, wh i ch could be rep r esented by the equation: 2~ 0.009 (%All + 0.008 (Al)(Log rt1 J17000c valid for alloys with aluminium contents less th~n 8 wt. pct . Pehlke and Elliott (47), using the Sieverts' method, determined the solubility of nitrogen in liquid iron-alumin­ ium al loys a t 160o 0 c and one atmosphere pressure in the range 0 to 0.5 wt . pct. Al; above this concentration they note d tha t a film of "what appeared to be aluminium nitrid e " forme d on the surface. It was found that aluminium slightly decre ased the solubility of nitrogen, and a value of 0.0025 was p rop osed for eNAl at 16006C. (Fig. 6) , The only other work reported in the literature f or thi s s y stem is that of Evans and Pehlke (53) using the Sieverts' method. These workers measured the equilibrium nit rogen sol ubility in liquid Fe - Al alloys as a function 43 of nitrogen gas pressure. Measurements were made for alloys containing up to 3.85 wt. pct. Al in the temperature range 1600° to 1750°C and 0.01 to 0.85 atmospheres of nitrogen. They determined the solubility product by admitting nitrogen in small increments until a deviation from Sieverts 1 Law in the form of a "pressure halt" was observed. X-ray powder patterns and wet chemical analyses were used to iden­ tify the nitride phase precipitated. These values were sub­ sequently checked by equilibrating liquid iron in an aluminium nitride crucible under a known partial pressure of nitrogen. When equilibrium had been attained, the crucible was quenched and the resulting ingot was analysed for aluminium and nitrogen. Fig. 7 shows the results plotted by Evans and Pehlke (53). A pressure of 20.25 cm Hg (0.267 atm.) was selected by them for tabulation of the solubility data, since it represents a pressure below that required for the precipi­ tation of AlN in most of their experiments. Aluminium-nitro­ gen interaction parameters obtained by these investigators and others mentioned previously are presented in Table 2. It will be noted that the data of Evans and Pehlke (53), like those of Eklund (32), indicate that aluminium increases the s olubility of nitrogen in liquid iron; whereas, the data of Elliott and Pehlke (47) and Maekawa and Nakagawa (44) indi­ cate that aluminium decreases the solubility of nitrogen in liquid iron. CHAPTER 4 EXPERIMENTAL TECHNIQUES USED IN PREVIOUS INVESTIGATIONS In th e past, two methods have been widely used to determi ne ni t roge n solubilities. The Sieverts' technique, in whic h the amount of nitrogen required to saturate a gi ven mass of liquid metal at a particular temperature or p res s u re is measured volumetrically, and the sampled bath techni qu e , i n which the melt is equilibrated with a nitro­ gen a tmosphere, and samples drawn from the melt are · que nched a nd analysed . 4.1 Th e Sieverts' technique. A diagram of a typical appar­ atus is shown in Fig. 8. The apparatus consists of a reac­ tion vessel, a gas burette, a manometer and gas train. The des i gn of th e reaction vessel is critical, as the volume of gas a b ove th e mel t must be kept to a minimum to obtain ac cu r­ ate r esults. A crucible, usually alumina, containing the melt i s l oc a t ed insi de a second crucible, which acts as a radi a t ion s h i eld . These crucibles rest on insulators, which are in turn supported b y a water-cooled pedestal. The react i on vesse l is completely surrounded by a water-jacket, except for a n arrow nec k jus t above the melt through whi ch the gas en t ers. Temperatures are generally measured by view­ ing the surf ace of the melt with an optical pyrometer . 44 45 The pressure within the reaction vessel is measured with a mercury manometer. If the capillary of this mano­ meter is too large, unnecessary error may be introduced dur­ ing the hot volume calibration of the apparatus. If it is too small, the pressure measurements may contain errors due to surface tension effects. A suitable capillary diameter has been found to be approximately 1 mm. The gas burettes generally have a capacity of 100 ml. and may be read to an accuracy of ±0.05 ml. They are enclosed in isothe rmal water-jackets and mercury is generally employed as the pumping and measuring fluid. The melt is heated by means of an induction coil sur­ rounding the reaction vessel. At the start of each experi­ ment, the charge is heated to about 150o0 c for approximately thirty minutes under a reduced pressure of about 10 microns Hg in order to degas the apparatus. An inert gas with phys­ ical characteristics very similar to those of the experimenta l gas is then introduced into the reaction vessel, and the charge is brought t o the desired temperature. The bulb is evacuated, a nd the hot volume is measured at different pres ­ sures with the inert gas. The reaction vessel is again evacuated to approximately 10 microns. At this stage metal may evaporate from the melt and deposit on the cooler por­ tions of the reaction chamber and this may cause significant error in determining nitrogen solubilities; the melt should therefore be held under vacuum for as short a time as 46 possible, commensurate with proper evacuation; this time is usually on the order of ten minutes. Following this prelim­ inary procedure, the volume of nitrogen required to saturate the melt at a given temperature and pressure is measured. The melt is judged to be saturated when the pressure remains c onstant with temperature without further addition of gas. Th e time required to reach equilibrium is generally about 2 to 3 hours. After an experiment a further check is made of the hot volume calibration. 4.2 Di sadvantages. 4.2.1 Hot volume calibration. The term 11 hot volume" refers to the volume of gas in the space between the surface of the melt and the gas burette, when the melt is held at the temperature at which the solubility is to be measured. The determination of this volume is carried out under identical c ondit ion s to those prevailing during an experiment except that an inert gas is used. This gas should have similar thermal properties to those of the gas under investigat ion. For example, in the determination of nitrogen solubi li ties argon is used to measure the bot volume. The temperature profile through argon will not, however, be identical to that through nitrogen, hence for a given melt temperature, the hot volumes for the two gases will not be exactly the same. Another factor which tends to make this calibration imprecise i s that the bot volume is continually changing with time during a particular run, due to evaporation from t h e 47 melt . These errors are in addition to the error involved in me a surin g the actual volume of gas flowing from the bure tte. + Ga s volumes c an usually be read to an accuracy of - 0.05 ml. but the fluctuation of the water temperature in the jacke t + of the burette is ge nerally about -0.5C 0 and this will i n- cre ase the total error in the measurement of gas volumes to app r oxima t ely ±0.25 ml. (46). As the experimental technique involves the subtraction of two volume readings (i.e. the n itrogen volume - the inert hot volume) this error is i n­ c reased to about -+0.5 ml. For a melt containing 50 gm. of pur e iron the volume of nitrogen actually dissolved in t he melt would be about 20 ml. at 160o0 c and one atmosphere p res­ sure o He nc e the uncertainty in the actual measurement of t he +nitrogen solubility is about -2.5 pct. In the presence of alloying elements which decrease the solubility of n i trogen in l i quid iron these errors could be much greater. 4.2. 2 Crucible attack. Uncertainty in the de te r min­ ation of ga s solubilities may be introduced by reaction b e­ twee n the mel t a n d the c rucible material . The solubi l ity of n i t roge n in the mel t will be influenced by the presenc e of other e lements t ake n into solution from the walls of the c ruc i b l e s . Furthermore, if the melt reacts with the crucible material t o form a gaseous reaction product, the measure d solub i l ity wi ll be less than the true value. 4. 2 . 3 Ini tial nitrogen content of the melt. The charged ma t er i al wil l in general contain a small amount of 48 n i trogen. This must be determined by a separate analys is a nd taken into account in the final result. This effec t will in general be small and will probably amount to no more t h&n ~o.0002%N in the final result. 4.2.4 Gas adsorption on metal films. During a pro­ longed experiment evaporation of the melt will gi ve r i s e t o the formation of metallic films on the cooler porti ons of t he reaction chamber. These freshly deposited highly active films will adsorb nitrogen from the gas phase. This effect will produce anomalously high values for the nitrogen solubility in the melt. 4.3 The Sampled-Bath technique. In this method the melt is held in a refractory cru­ cible, usually alumina, and heated in an atmosphere of nitro­ gen. Sometimes the gas is bubbled through the melt in order to obtain a more rapid approach to equilibrium. The temper­ ature may be measured by an optical pyrometer or a thermo­ couple, however the former is preferable since there · is less r i sk of contamination. At frequent intervals during a n experiment, samples are drawn from the melt with ei t her s i lica or copper tubes approximately 2 to 5 m.m. I~D~ and immediately quenched in watero The nitrogen content of these samples is then determined using either the Kjeldahl technique or the vacuum-fusion method. A comparison of these two analytical techniques is given in section 5.10. 49 4.4 Disadvantages. The main disadvantage ~ of the sampled bath method is the possibility that some nitrogen may be lost or gained during the quenching operation (45). Again, a possible source of error is contamination of the melt by the crucible material, but in general this effect will be small. Large errors due to crucible-melt reactions which produce gaseous products are eliminated in this technique as these products are continuously swept away in the gas stream. CHAPTER 5 EXPERIMENTAL PROCEDURE 5.1 The Levitation technique (54). Conducting material when placed in a coil of proper geometry through which a high frequency alternating current is flowing, may be made to levitate. This effect is due to the interaction of electro-magnetic fields due to the current in the coil and the induced currents in the specimen. The eddy currents will also heat the specimen to temperatures which will depend on: a) Geometry of the coil. b) Power · into the coil, and the ratio of voltage to current in the coil. c) The nature of the specimen. i.e. density, ther­ mal and electrical conductivity. d) Size of specimen. e) The atmosphere in which the specimen is located. A conductor placed in an electromagnetic field will move to the weakest part of the field~ Hence, for levitation the field strength must decrease vertically to provide a lifting force and radially towards the field axis to provide a restoring force towards the centre of the coil. The levitation coil assembly used in the present work was of the form shown in Fig. 9. The coil was wound from 1/8 50 51 inch copper tubing enclosed in fibre-glass sleeving. This sleeve material prevented shorting between the various turns of the coil during operation. The bottom coil, consisting of four turns, was wound on a conical former having a half angle of 30°. The two reverse turns placed co-axially above the main levitating coil gave the specimen greater stability. Cooling water was passed through the windings to prevent over-heating of the coil. The induction unit used in the present work was a 450 kc/s, 10 kw Toccotron generator and the high frequency current was delivered to the levitation coil through a 7.5: 1 ste p - down transformer. By using the transformer it was much easier to obtain temperatures in the range 1400° to 160o 0 c. 5.2 Advantages of levitation melting. 5.2.1 Noncontamination of the melt. In the past there have been a number of physico-chemical studies in which t he reaction between the melt and the crucible material has presented problems. Difficulties of this nature are avoided with levitation melting since there is no physical contact be t ween the melt and any supporting material. 5.2.2 Efficient stirring of the melt. The high f requency current induced in the specimen produces very ef­ fi c ie n t stirring. This results in a rapid attainment of equilibrium, particularly since a relatively large metalli c surface is exposed to the gas phase. It also ensures good mixing of alloying elements throughout the bulk of the spe cimen . 52 5.2.3 Temperature range of the investigation may be inc reased. The temperature range in which a gas/liquid metal system can be studied is often extended to much higher temper­ atures than those which most crucible materials are able to withstand. Also, in many cases lower temperatures may be attained using this technique since the absence of a cruc i­ ble decreases the chance of heterogeneous nucleation in a supercooled melt. The degree of undercooling will however depend upon the conductivity of the gaseous atmosphere and the chemical nature of the reaction. A further advantage of this technique is that hot volume calibrations and complex glassware involving gas burettes are not required. 5~3 Disadvantages of levitation melting. The main disadvantages of the technique are due to difficulties i n temperature control (section 5.6) and the rela tively severe vaporization of volatile elements from the mel t due to the large surface to volume ratio of the droplet, and th e rapid stirring_ induced by the high frequency current. It is frequently found that when sufficient power is provided for levitation, the energy transferred to the drop ­ let produces excessively high temperatures. The coil design used in the present work was selected because of all the types inves tigated it gave the greatest degree of lif t with the minimum degree of heating (55, 56). .53 5o4 Quenching procedure. When this project was initiated, the levitated metal was dropped into a copper mould held in the reaction tube approximately one inch below the coil. The results of these preliminary experiments on the solubility of nitrogen in pure iron are shown in Fig. 10. It was clear from the random nature of the results and tbe spread in the data, (approx. ~0.00 2 wt. pct. B compared with an expected uncertainty of ±0.0003 wt. pct. due mainly to error in the chemical analy­ sis) that nitrogen was being lost from the specimen duri ng quenching. The quenching method finally adopted was a mod ifi­ cati on of a technique developed by Pietrokowsky (57). The quenching effect is obtained by allowing the levitated drop­ let to fall between two copper blocks which then come togeth­ er rapidly, squeezing the droplet between them. A diagram and photographs of the apparatus are shown in Fig s~ 11, 12, 13 and 14. The reaction tube (a) is held by a n 0- ri ng and clamp (b) in the mild steel cylinder (c). When the specimen is to be quenched the pendulum (d) is re­ leased. At a point along the path of the pendulum, contact betwee n a slide (g) (fixed to the pendulum) and the brass slide rod (h) is broken. This breaks a relay circuit, (Fig. 14) which in turn trips a relay in the generator, cutting the power to the levitation coil. The liquid metal drople t th e n falls freely down the Vycor tube and between the two 54 c opp er blocks (i). At the same instant, the base of the p e ndulum hits the piston (m) and the droplet is squeezed between the two copper blocks (i) to give a thin disc ap­ proximately 0.005 inches thick and two inches in diameter. To reduce the effect of gas exhausting up the reac­ tion tube as the copper blocks come together, two solenoid va l ve s are plac ed in the system. When contact is b r oken be twe e n (g) and (h), the solenoid valve (j) is closed a nd a t the same time, the solenoid valve (k) is opened. The ga s tra ppe d be twee n the two blocks and the normal gas flow now esc a pe t hrough the valve (k) and thus hindrance to the free fall of the droplet by an upward flowing gas stream i s elimi nated. Assuming the quenched disc of metal (Fig. 15) wa s liqui d with this shape just before solidification, it is estimated that the quench rate at the solidification temp e r ­ 6ature was approximately 10 c 0 /sec. (Appendix C). I n orde r to ch e ck t hat t his quench rate was suff i cient to r etai n t he equi l i b rium me l t concent ration of n itrogen in t h e iron a t room temp e rature s e c on dary experiments wer e made i n which the copper b locks were fa c ed with iron, wh i ch has a the r ma l con­ ducti v i ty a pproximately one order of magn itude less t h a n that of c opp er. Th i s arrangement gave a quench rate app r oxima tely l /lOth that obtained with the copper blocks. Usi n g b oth the copp er a n d iron que nching systems, the values obtai ned for nit rogen s olubili t y were in agreement within the limi ts of 55 experimental error. It was concluded therefore that the quench obtained with the copper blocks was sufficiently rapid to retain all the nitrogen in solution during solidifi­ c ation. The reproducibility of the data obtained using the copper blocks also confirms this conclusion. 5~5 Attainment of Equilibrium. A series of preliminary experiments were performed in order to determine the optimum time required, at temperature, fo r the specimen to reach equilibrium with the nitrogen at­ mosphere. Specimens were held under identical conditions for 2, 4, 8 and 16 mins. but no significant difference in the ni trogen content of the specimens could be detected. (Table 3). During an actual experiment, melts were equilibrated with the gas phase for four minutes and then quenched. 5.6 Temperature measurement and control. The temperature of a specimen was measured by means of a Milletron two colour pyrometer. The specimen was viewed through an optical flat arrangement as shown in Fig. 11. The pyrome ter was calibrated by viewing the surface of pure liquid iron contained in an alumina crucible and held under a nitro­ gen atmosphere. The pyrometer readings were compared with those obtained from a standard Pt/Pt-13% Rh thermocouple im­ mersed i n the melt. The optical arrangement used during calibration was the same as that shown in Fig. 11. Several calibration experiments were performed using a carbon saturated iron melt contained in a graphite c r ucible. 56 These experiments established that carbon dissolved in the melt had no effect on the temperature, as indicated by the pyrometer. Calibration experiments were made over the temperature range 1350 0 C to 1700 0 C. The suitability of the calibration data for the solubility experiments was confirmed by observ­ ing the melting point of pure iron droplets under levitation conditions. This latter procedure was used to check the pyrometer calibration each time it was used. The temperature of the droplet was coarsely controlled by adjusting the flow rate of nitrogen over the specimen and finely controlled by adjusting the level of power in the coil. The latter adjustment had the effect of varying the height of the specimen in the coil and hence, the transfer of energy to the specimen. By these means, a specimen could be held to within ±5c0 of the desired value. Allowing for an error of ±cco/ in the calibration of the pyrometer, it is considered that the reported temperatures are accurate to within ±100°. 5o7 The Gas-train. The gases were passed over magnesium perchlorate and a proprietry material (Indicarb) to absorb any moisture or carbon dioxide respectively which might be present. The gas was then passed through the quench unit, over the spe cime n in the Vycor tube, through solenoid valve (j), thence through a bubbler to exhaust. The exhaust tube just touched the surface of the oil in the bubbler, in order to minimize the 57 back pressure in the system. For the same reason all tubing had an internal diameter equal to that of the reaction cham­ ber (15 mm). All specimens were equilibrated in a nitrogen atmosphere at atmospheric pressure. 5 ~8 Materials used. The specimens for the various experiments were pre­ p are d from the following materials; (the analytical data are reported in ppm.): Armco Iron having an analysis: .Q..Q _§ .. \.i 120 170 250 750 were levitated and deoxidized in a hydrogen atmosphere at 16oo 0 c for four minutes before use. By this treatment, the oxygen content was reduced to less than 10 ppm. AUC graphite with the following ·analysis was obtained from Union Carbide : 50 160 Total ash as oxide ~ 300 ppm Alumi nium was obtained from a high purity aluminium ingot which had the following composition: l1g Others 150 10 10 A prepurified grade of nitrogen with the following analys is was obtained from Matheson of Canada Ltd.: 0 H2 o co2 Argon 5 11 5 20 58 5.9 Experimental Procedure. 5.9.1 Pure Iron. Pieces of Armco iron approximately 1 gm in weight were cut from 1/4" rod. The rubber stopper "o" (Fig.11) was removed and a pyrex glass rod placed in the reaction tube. The Armco iron was dropped onto the rod from "p", the current into the coil was increased to the maximum value, the rod removed, and the specimen levitated in the coil. The system was flushed with nitrogen and the specimen then deoxidized in hydrogen at I6oo0 c for four minutes. After deoxidation, pure nitrogen was passed over the melt, which was then held at the required temperature for a fur­ ther four minutes to ensure attainment of equilibrium. The I specimen was quenched between the copper blocks and analysed for nitrogen using the standard Kjeldahl steam distillation technique ( 5. 10). 5.9.2 Iron-carbon alloys. Each alloy was prepared in situ as follows. A hole was drilled in a one gram sample of Armco iron and graphite placed in the hole which was then closed by squeezing in a vice. The specimens were equilib­ rated in nitrogen, quenched and cut into two halves. One half was analysed for nitrogen and the other half for carbon using the Leco combustion techniqueo 5.9.3 Iron-aluminium alloys. Nitrides may form in these alloys at 160o0 c and one atmosphere pressure of nitre­ gen 9 when the aluminium concentration exceeds about 1 wtg pct. Alloys having the following compositions 0.9, 0.8, 0.63, 0.52~ 59 oy47, 0.43, and 0.2 wt. pct. Al, were prepared by melting a weighed amount of Armco iron in an alumina crucible and passing hydrogen over the melt for about 30 minutes in order to deoxidize the iron. The melt was then held under argon and a weighed quantity of aluminium added. After about 10 minutes a suction sample was withdrawn from the melt by means of a quartz tube, quenched in water, and weighed. More alum­ inium was added to the melt and the same proc edure followed until the required number of alloys was obtained. The alloys were ground in order to remove any surface oxide which might be present and samples approximately one gm in weight cut from each rod. After equilibration in ni­ trogen, the samples were quenched, cut in half and one piece retained for nitrogen analysis, the other for aluminium. 5.10 Nitrogen analysis. Specimens were analysed for nit rogen using the Kjeldahl steam-distillation technique (58). The full proc edure is presented in Appendix A. The only other technique generally available for the determination of nitrogen in metals is the vacuum-fusion method. An exhaustive study (58) has been made of the meth­ ods for determining nitrogen in steel in which the chemi cal method a nd the vacuum-fusion method were compared. The results obtained from a number of laboratories indicated t hat the confide nc e limits for the chemical method were in general closer than those for the vacuum-fusion method. This was true both for the agreement between different laboratories 60 and within a single laboratory. In the present study preliminary checks on the ac­ curacy of the chemical method were made by determining the nitrogen content of various quantities of standard aluminium ammonium sulphate solutions. From these results it was found that the analyses were accurate to ±3 ppm at a nitro­ gen level equivalent to 450 ppm in an iron sample. A further check was made to determine whether there was any segregation or variation of the quantity of nitroge n i n tbe metal at the thinner periphery region of the quenched disc. All checks showed that there was no such radial varia­ tion in nitrogen content. 5.11 Carbon analysis. Samples were analysed for carbon using the standard Leco combustion method. This method has been described in detail elsewhere (59). The accuracy of the analytical procedure was checked using standard samples from the National Bureau of Standards, and it is considered that the reported carbon analyses are + ac curate to at least -0.05 wt. pct. C. 5.12 Aluminium analysis. The samples were analysed for aluminium by a colori ­ metric method using 11 Chromazurol S 11 as the colouring agent. This method was obtained through the courtesy of The Steel Company of Canada and is described in Appendix A. It is estimated that the aluminium contents measured using this +proce dure .are accurate to -0.02 wt. pct. Al . solution of nitrogen in liquid CHAPTER 6 PRESENTATION OF RESULTS 601 The solubility of nitrogen in liquid iron. Data for the solubility of nitrogen in liquid iron a t temperatures in the range 1530° to 1780°C are shown in Table 4 and Fig. 17. The error bars on this plot represent the effect of errors of ±0.0003% in the nitrogen analysis. A _least s quares fit to the data y i elds the following equa­ tion for the effect of temperature on the solubility of nitrogen in liquid iron, when the nitrogen pressure in the gas phase is one atmosphere: + Log [ Wt %N] == 1.21 (-0.01) (6.1) When the iron is described by the reaction !N2 (gas) =E (in liquid iron) ( 6. 2) the equilibrium constant K is giv~n by: K = [ aN] I l ( PN )2 2 _ = (Wt%N) • - f N I l ( PN ) 2 2 ( 6. 3) where the reference state for the activity coefficient fN is taken as the infinitely dilute solution of nitrogen in liquid iron. It has been establi shed by previous investigators (35, 41, 47) that ni trogen dissolved in liquid iron obeys Henry's law, a nd thus th e a ctivity coefficient of nitrogen in binary iron nitrogen solutions can be taken as unity. 61 62 Thus: Log K == log (wt.%N) - t log PN 2 ( 6 . 4.) Since the solubility dhta in this study are all referre d to one atmosphere pressure of nitrogen, the effect of tempe ra­ ture on the equilibrium constant is given by: Log K = -285 (±110) - 1.21 (2°0.01) · ( 6.5 ) T The standard free energy change for the reaction is: 6F0 == 1300 ( ±500) + 5 .5 ) (~0.03) T ( 6. () ) and the heat of solution is: 6Ho == 1300 (±500) cals /gm atom ( 6. 7) The results of the present study are compare d with those of previous investigators in Fig. 18 and Table 1 and it is evident that the data for the solubility and heat of solution of nitrogen in' liquid iron, as determine d by the levitation technique, are in good agreement with the data obtained by Elliott and co-workers (46, 47), and Turnoc k and Pehlke (51) using the Sieverts' method. 6.2 The solubility of nitrogen in liquid iron-carbon alloys. The effect of carbon on the solubility of nitrogen in liquid iron at 1450°, 1550°, 1660° and 1750°C is shown in Table 5 and Figs. 19, 20 9 21 9 22 and 23. At 145o0 c solubil­ ity data were obtained for carbon concentrations between 1.5 and 5 wt. pct. The intercept value for the solubility of nitrogen in pure liquid iron at this temperature wa s obtained by extrapolation of the data shown in Fig. 17. Conseque ntly, the hypothetical carbon-nitrogen solubility r elationsh ip at 1450°c for carbon concentrations below about 1.5 wt. pct. is --·· · . -· ----~---------------------- 63 represented in Fig. 19 by a broken line. At the o t her tem­ peratures, data were obtained for carbon concentrations be ­ tween pure iron and the solubility limit of carbon in l i qu i d iron. The results of the present study have been use d to compute solubilities at 16oo0 c, and these are compared wi th those of previous investigators in Fig. 24. While there is marked disagreement between the various published data, the results of the present investigation are in good agreement with the work of Schenck et al. (42). At one atmosphere pressure of nitrogen, and a cons t ant temperature, the activity of nitrogen in the melt is the same for both pure iron and iron-carbon alloys and thus: [ Wt%N] Fe := Fe-C j f N[wt%N] (6.8) Activity coefficients of nitrogen in the ternary al­ loys were calculated from equation (6.8) and the logarithm of the activity coefficient is plotted against carbon con­ centration in Fig. 25. (See Table 5). Fig. 26 shows the effect of temperature on the solu­ bility of nitrogen in liquid iron-carbon alloys for different carbon levels. The equations for these lines yield values for the heat of solution (AHNalloy) and the entropy of solu­ tions (ASNalloy) of nitrogen in th~ various alloys. In Fig. 27 these heats and entropies of solution are plotted against carbon concentration and it is found that the 64 relationships obtained can be represented by parabolic equa­ tions of the form: 2y = a + bx + cx ( 6 .. 9) 11 11The coefficient a represents the enthalpy or entro­ py of solution of nitrogen in pure liquid iron, as given in equation (6.6). The coefficients band c were determined by least squares analysis.. This treatment yields the followi ng equations: L\ Halloy N ::::: 1300 + 1646 (foe) + 504 (%c) 2 (6.10) .A s alloy N -5.53 + 0.409 (%C) + 0.233 (%c) 2 (6 .11) Combining equations (6.10) and (6.11), an expressi on i s obtained for the effect of temperature and carbon conc e n­ tration on the free energy of solution of nitrogen in liquid iron: Ll palloy ::::: 1300 + 1646 (%c) + 504 (%c) 2N - [-5.53 + 0.409 (%c) + 0.233 (%c) 2 J T ( 6" 12) From equation (606), the free energy of solution of ni trogen in pure liquid iron is given by ( 6 .. 6) The exc ess free energy of solution YE is de fined a s N L\ Falloy - A F 0 == RT l n f ( 6. 13)N n Combini n g equations (6.6) and (6.13): 'f E 2 N "' 1646 (%G) + 504 ( %c) - [ o.409 ( %G) + 0 .233(%c) 2 ] T (6.14) 65 and thus: Log f N ::::: ~T [1646 <%c> + 504 <%c) 2 J 1 [0 . 4 0 9 ( %C ) + 0. 233 (%c) 2} 4.575 - ---(6. 15 ) Since Log [ Wt. %N] Fe-C :::: Log [ Wt%NJ - Log f NFe ----(6.16) combining equation (6.1), (6.15), and (6.16) yields an e x ­ press ion for the solubility of nitrogen in liquid _i ron-· carbon alloys which is valid for 1 atm. pressure of nitrogen and for temperatures between i450°c and l 750°C: i.e. Log [wt.%N)= - [ 285 + 1. 21 + ( %c) [1646-0 .409J T 4.575 T 2 + ( %c) [ 5..QJJ_ o. 233 J] . 4.575 T ----(6.17) . Equation (6.17) yields nitrogen solubility values which agree with the experimental values to within ±0.001 wt. pct. N. For carbon levels below 1 wt. pct. the term i nvol­ ving (%c) 2 may be neglected without introducing appreciable error. As stated previously in Chapter 2, Wagner (5) ·has shown that the activity coefficient of a solute in a multi­ component alloy may be expressed in the form of a Taylo r series. In this case, where the third and higher order t erms are neglected the activity coefficient of nitrogen in liquid iron-carbon solutions is given by: d Log fN %N + C) Log f N [%c]'~(%N) C) (%c J 66 1 ~2Log fN 2 + [ %c)2 + 1. O Log fN 2 2 . [%N] 2 d [%c ] 2 d [%~ + d 2log fN [%c] . [%N] 'J{%(fj[ %NJ ----- ( 6 . 18 ) Since nitrogen dissolved in liquid iron obeys Henry's law, the first and fourth terms in the above expression are zero. In the present study, measurements were made at one atmosphere pressure of nitrogen and the cross interaction contribution of the fifth term cannot be determined. Devia­ tions from linearity of the curves shown in Fig. 25 are therefore ascribed soleiy to the second order carbon effect •. Equation (6.18) can now be written Log f N ::::: °C> Log . fN o [%c] . [ %c] + 1 2 d 2 1 ag fN 0 [%c] 2 [%c] 2 ----(6.19) Using the convention of Lupis and Elliott ( 6) d Log f N/d [ %c] is defined as the first order interaction para- C 1~2 . · me~er eN~ and 2 a log f N/ &[%cf is defined as the second order. interaction parameter r~. Equation (6.19) t hen becomes: G d G 2Log fN = eN (;oC) + rN (%c) ( 6. 20) A diagramatic representation of this equation is shown in Fig. 28. 67 The excess enthalpy of solution,'}{ ~ is defined as alloy o = AHN - ll H ( 6 . 21 ) E As · stated previously,J!N may be expresse d i n th e f orm of a E Taylor series i n a similar manner tor NI RT. i.e. /(, E N (%0 ) 2 (6.·-22) Enthalpy interaction parameters defined in terms of the above first and second order derivatives are and (6.23) Using equations ( 6.21) and ( 6.22), equat-ion ( 6.23) can now be written in the form: (6.24) Similarly, the entropy of solution of nitrogen in these alloys may be expressed in the form .4 sa11oy == 6 s o + s c (%c ) + c (%c ) 2 N N PN ( 6. 25) c c where sN and pN are first and second order entropy paramet e rs r espectively and are defined in t erms of the excess ent ropy of solution.~~: i.e .. c s = ()~ ~ and c==i~~~N p 2J[%c] N iG d(%cJ ( 6. 26) 68 Comparison of equations (6.10) and (6.11) with equations (6.24) and (6.25) yields the following values for the first and second order enthalpy and entropy paramenters h c le= 1646 = 504 N N c s :::: 0 .. 409 p c = 0.233 N N The excess properties are related by the equation: rE :::: RT ln f N N ( 6. 27) Using this relation it was shown in Ch~pter 2 that the va~ious first and second order interaction parameters are related in the following way: e :::: 1 N c [ h~ S N c ]4.575 T (6.28) c c :::: 1rN [ iP ­ PN..::JI4.575 -T J ( 6. 29) Substi tuting the values for the parameters in the bracketed terms: c c ( 6. 30) c c e and r are plotted against the reciprocal of the absolute N N temperature in Figw 29. At 160o 0 c, e~ = 0.103 and r~ = 0.007. Values obtained in previous investigations for e~ at 1600°c are listed in Table 6. Values for the various interaction parameters ob­ tained in the present sutdy are listed in Table 7. 69 Turkdogen (60) has suggested that if the logari t hm of the activity coefficient O' C (where the reference state N i s the infinitely dilu t e solution of nitrogen in liquid iron) were plotted against mole fraction of carbon, a linear rela­ tionship might be obtained and if so the data could then be expressed in terms of first order parameters alone. The data obtained at l))o0 c are plotted on a mole fraction scale in Fig. 30. In Fig. 31, Log ~ ~ is plotted as a funct i on of Xe but the curve through the points was drawn using t he para- C C meters eN and rN determined on the wt. pct. scale and conver­ ted to the mole fraction scale using the relationship deriven by Lupis and Elliott. It will be seen that the data in Fig. I 31 follow a non-linear relationship and that the derive d curve is in good agreement with the experimental points even up to 0.20 mole fraction carbon where the second order effects become more significant. In Table?, values are given for the various parameters on the; mole fraction scale. These have all been calculated from the corresponding parameter on the wt. pct. scale using the conversion relationships of Lupis and Elliott (6) which were presented in Chapter 2. 6.3 The solubility of nitrogen in liquid iron-alum:inium alloys. Experimental results .for the effect of alumi nium cin the solubility of nitrogen in liquid iron at 1550°, 1650° and 1750°c up to approximately the concentration of aluminium for which AlN becomes stable are presented in Table 13 and Figs. 70 32, 33. From these data it can be seen t hat aluminium de­ creases the solubility of nitrogen in liquid iron and that t he effect of aluminium decreases with increasing tempe ra­ t ure . These results do not a gree with those of Pe h lke and Evans (53) (Fig. 7) or with those of Eklund· ( 3 2), but a re i n fair a gr~ement with those of Pehlke and Elliott (47 ) ( Fi g . 6). When the AlN phase becomes stable the tot al nitro gen content of the sample (i.e. nitrogen dissolved in t h e metal together with nitrogen combined with aluminium in t he f orm of AlN) increases ~apidly and hence the alumini um content corresponding to the critical concentrations for alum i nium nitride formation can ~e estimated from the breaks in t he nitrogen solubili t y curveo These breaks occur between 0. 6 and 0.7 wt. pct. at 155o0 c and between 0.75 and 0.85 wt . p c t ~ at 1650° and 1750°c. _ Figure 33 shows the effect of aluminium on the l ogar­ ithm of the activity coefficient of nitrogen dissolved in liqtlid iron. It will be ·seen that there is a spread in the data for each of the temperatures investigated. This is largely attributable to the fac t that el c Pure Fe -!!!~-C.-~~-"--~-- N a l loy i s close to unity and hence a small error in t he denomi na t or gives rise to a large error in ~l which is magni fi ed whe n the logarithm of the coefficient is taken. The l i n e s as d rawn are based on a least squares analysis of t he da ta . The logarithm of the activity coefficient of ni t rogen i n iron aluminium alloys may be represented in terms of free 71 energy interaction parameters. However, in this caoe the accuracy of the data does not warrant the use of second or higher order parameters and thus the relationohip between Log ~l and aluminium content are adequately represented by first order equations. The slope of these lines yield val­ ues for the first order free energy interaction parameter Al eN The values of this parameter for the various temper-Q atures at which solubilities were determined are given in Table ··14Q These va ues o eN are p o e agains . e recipro­·1 f Al 1 tt d . t th . cal of the absolute temperature in Fig. 34. The equation of the line is given by: e Al ::: ill 0.28 (6.31) N T Comparing the above equation with the relation: Al Al h e t::: l N N ( ( 6. 32)4.575 'fl the following values foi the enthalpy and entropy interaction parameters are obtained: h Al N :::: 2700 ( 6 ~ 33) Al s N = 1.28 ( 6. 34) Combining these data with equation (6Q6) for the free energy of solution of nitrogen in liquid iron expressions are ob­ tained for the effect of aluminium on the enthalpy and entropy of solution of nitrogen in liquid iron: 72 alloy AH ::: 1300 + 2700 (faA.l) (6.J5) N .6Sa11oy = -5.53 + 1.28 (%Al) (6.36) N These quantities are plotted as a function 9f alum i nium c on­ centration in Fig. 35. From equations (6.35) and (6.36) the effect of aluminium on the free energy of solution of nitro­ gen in liquid iron is given by: 4Falloy = 1300 + 2700 (%/1.1) - T f-.5 •.53 + l.28(%All] N ( 6 •·37) Since: ::: [ %Al] (6.38) equation (6.38) may be rewritten in the form: Log f ~ -~ 1. 281 (6. 39) N 4.5() Combining equations (6.1) and (6.39) and using the relation­ ship: Log [wt.%N) Fe-Al= Log [wt.%N]Fe - Log fN ( 6. 40) an expression is obtained for the solubility of nitrogen in iron-aluminium alloys in terms of temperature and aluminium c