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Thermodynamics of magnesium in liquid nickel solutions Samuelsson, Eva 1987

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THERMODYNAMICS OF MAGNESIUM IN LIQUID NICKEL SOLUTIONS by EVA SAMUELSSON M.Sc. Royal Institute of Technology, Stockholm, Sweden, 1981 M.A.Sc. University of Br i t i sh Columbia, Vancouver, B . C . , Canada, 1983 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES Metals and Materials Engineering Department We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December 1987 © Eva Samuelsson, 1987 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Metals and M a t e r i a l s Engineering The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date Dec 28, 1987 DE-6 (3 /81 ) Abstract A novel experimental method to determine the act iv i ty of alloy components in very dilute l iquid metal solutions has been developed. The method is applied to the measurement of magnesium vapour pressure over nickel alloys to find the thermodynamic properties of magnesium in dilute l iquid solutions at 1470°C. The experimental method employs a commercial Atomic Absorption Spectrophotometer to determine direct ly the vapour pressure of magnesium over the al loys . A radiatively heated Knudsen c e l l inside a vacuum system contains the metal. Equilibrium constants are given for the reactions, Mg(g) + 2 Al(%) + 4 0(%) * MgO'Al 20 3(s) and Mg(g) * Mg(%), where A l , 0 and Mg are dissolved in l iquid nickel . Further, values for Me Al the metal-oxygen i n t e r a c t i o n coe f f i c i en t s e^  and e^  are determined. F ina l ly , a value for the Raoultian act iv i ty coefficient at inf ini te di lut ion is suggested. A significant change in the act iv i ty of magnesium upon the addition of 20% chromium or iron to the dilute l iquid nickel - i i i -alloys was not detected. This is believed due to overpowering magnesium-oxygen interaction at these levels of chromium and iron. - iv -TABLE OF CONTENTS Page Abstract i i Table of Contents iv List of Tables v i i i List of Figures x Nomenclature^. . - xiv Acknowledgements xvi 1. Introduction 1 2. Literature Review 4 2.1 Magnesium In Superalloys 4 2.1.1 Melting Practice , 6 2.1.1.1 Vacuum Induction Melting 6 2.1.1.2 Vacuum Arc Remelting 8 2.1.1.3 Electro Slag Remelting 10 2.1.1.4 Electron Beam Melting 11 2.1.2 Alloy Properties 15 2.1.2.1 Hot Working 15 2.1.2.2 Weldability 20 2.1.2.3 Mechanical Properties 20 2.2 Atomic Absorption Studies of Vapour over Condensed Phases . 23 2.2.1 Herbenar et al 23 2.2.2 Scatchard et al 26 2.2.3 Vidale 27 - v -Page 2.2.4 Brebrick and Strauss 30 2.2.5 Raperport and Pemsler . 32 2.2.6 Masson et al 32 2.2.7 E l i u t i n and Timofeev 33 2.3 High Temperature Experimental Methods 34 2.3.1 Knudsen Cell Methods 34 2.3.1.1 Heating and Temperature Measurement 36 2.3.1.2 Detection Methods 40 2.3.2 Pseudoisopiestic Method 45 2.4 Thermodynamic Data 50 2.4.1 Background 50 2.4.2 The Pure Elements Ni , Mg, Ca and Al 53 2.4.3 Magnesium and Calciuim in Nickel and Iron Alloys . . . 55 2.4.4 Deoxidation Equilibrium 63 2.4.4.1 Magnesium and Calcium 72 2.4.4.2 Aluminum 73 3. Experimental Work 76 3.1 Equipment 76 3.1.1 Atomic Absorption Spectrophotometer 76 3.1.2 Vacuum System 79 3.1.3 Furnace 81 3.1.4 Knudsen Cells 82 3.1.5 Temperature Determination 86 3.2 Materials 89 3.2.1 Basic Alloys 89 - v i -Page 3.2.2 Tin Alloys 89 3.2.3 Nickel Alloys 92 3.3 Experimental Procedure 93 3.4 Calibration 94 3.5 Test of the Method 95 3.6 Nickel Alloy Experiments 96 3.7 Chemical Analysis 96 4. Results and Discussion 98 4.1 Calibration 98 4.1.1 Cause of Discrepancies 103 4.2 Test of Method on Tin Alloys 107 4.3 Nickel Alloys 112 4.3.1 Preliminary Results 112 4.3.2 Applicable Equilibriums 112 4.3.3 Stat i s t i ca l Model 116 4.3.3.1 Equilibrium Constant 120 4.3.3.2 Interaction Coefficients 125 4.3.4 Energy of Solution 126 4.3.5 Raoultian Activi ty Coefficient 127 4.4 Alloys Containing Chromium and Iron 129 5. Conclusions 132 6. Suggestions for Further Work 134 - v i i -Page References 135 Appendicies 141 A - Equations in the Literature Review 142 B - Procedures for Chemical Analysis 151 C - Doppler Shift 154 D - EDX Analysis of Oxide Phase 159 E - Regression Analysis 164 F - Equations for Figure 4.7 168 - v i i i -LIST OF TABLES Chapter 2 Table Page 2.1 Examples of Nickel Base Superalloys and Their Applications 5 2.2 Summary of Atomic Absorption Studies of Vapour Pressure over Condensed Phases . . 24 2.3 Data for the Pure Elements 54 2.4 Behaviour of Deoxidizers and Oxygen at Infinite Dilution in Liquid Iron . . . . . 69 2.5 Behaviour of Deoxidizers and Oxygen at Infinite Dilution in Liquid Nickel 69 2.6 F irs t Order Interaction Coefficients, e ,^ in Liquid Iron at 1600°C 70 2.7 Firs t Order Interaction Coefficients, e^  in Liquid Nickel at 1600°C 70 2.8 Deoxidation Equi l ibr ia in Iron Alloys 71 2.9 Deoxidation Equi l ibr ia in Nickel Alloys 71 Chapter 3 3.1 Summary of Thermocouple Types used 88 3.2 Basic Alloys used in This Project 91 Chapter 4 4.1 Results of Calibration Measurements with Pure Mg, using a Standard Knudsen Cel l 99 4.2 Results of Calibration Measurements with Pure Mg, using an Isopiestic C e l l . Orif ice Temperature = 900°C 100 - ix -Chapter 4 (Cont'd) Table Page 4.3 Results of Calibration Measurements with Pure Mg, using and Isopiestic Cel l Orif ice Temperature = 1470°C 101 4.4 Summary of Sn-Mg Experiments 109 4.5 Data from Nickel-Magnesium Experiments 117 4.6 Y° from Experimental Data 130 - x -LIST OF FIGURES  Chapter 1 Figure Page 1.1 Secondary Ion Mass Spectrometry (SIMS) dot maps of a polished nickel alloy (superalloy 718) surface showing the relative concentrations of the following ions: a) 2 4 M g + , b) 3 2 S ~ , c) 1 6 0 ~ and d) 2 7 A 1 + 2 Chapter 2 2.1 Variation of oxygen act iv i ty &Q and total oxygen content Orj, during vacuum induction melting of alloy 718 using virgin and revert charges; md, melt-down; r , end of refining period; other symbols on hor i -zontal axis represent element additions to melt 7 2.2 Reduction in melt sulphur content [ s] over vacuum induction melting period 9 2.3 Effect of MgO content in the ESR slag on Mg content in produced ESR ingots 12 2.4 The hot duct i l i ty of Waspaloy b i l l e t s with and without magnesium additions. RA% = Percent area reduction 14 2.5 Effect of Ca and Mg additions and S content on hot duct i l i ty of Inconel 600 1 4 18 2.6 Effect of Mg (a) or Ca (b) on hot tensile duct i l i ty of Ni-based a l l o y s 1 6 18 2.7 Variation of S/Ni intensity ratio as function of distance from intergranular fracture surface for various Inconel 600 alloys 19 2.8 Inconel 718 microjjjissuring susceptibi l i ty versus magnesium content 21 2.9 (a) Transparent quartz absorption vessel and (b) heating furnace 25 - xi -Chapter 2 (Cont'd) Figure Page 2.10 Optical path diagram 2 6 28 2.11 Cross sectional diagram of ce l l and furnace 29 2.12 Diagram showing the correlation between three sets of experiments, A, B and C presented by Vidale , according to equation 2.1 31 2.13 Typical Knudsen ce l l s , (a) Tungsten c e l l , (b) Cel l used with vacuum balance, (c) Cel l with thermo-couple and near-ideal or i f i c e , (d) Knudsen's original apparatus for determining the vapour pressure of mercury 37 2.14 An apparatus for effusion studies by the col lection technique 42 2.15 Some torsion-effusion ce l l s . (a) Two-temperture ce l l made of fused alumina. The lower reservoir is made of Corning No. 7280 glass, fused directly to the alumina upper part, (b) Opposed-orifice ce l l for comparing vapour pressures, of two systems. (c) Four-orif ice ce l l machined: from graphite. (d) Welded tantalum c e l l , showing removable yoke for suspending i t from the torsion wire. (e) Demountable two-section c e l l , with 0.5 in . over-lap to be suspended similarly to (d) 43 2.16 Twin crucible effusion source 46 2.17 Schematic of an "isopiestic balance"^ 6 '^ 48 A Q 2.18 Isopiestic equilibration tube y 49 2.19 The magnesium-iron binary phase diagram^ 56 58 2.20 The magnesium-nickel binary phase diagram 57 59 2.21 Schematic calcium-irori binary phase diagram 58 2.22 The calciuim-nickel binary phase diagram6"'" 59 Chapter 2 (Cont'd) - x i i -Figure Page 2.23 Act iv i ty of calcium in some Ni-Ca and Ni-Fe-Ca alloys as a function of the molar fraction of calcium 61 2.24 Act iv i ty of magnesium in nickel-magnesium binary a l l o y s 6 3 62 2.25 Estimated liquidus surface in Fe-Ni-Mg system and range of magnesium-rich phases observed after so l id i f i ca t ion of Fe-Ni a l l o y s 6 3 64 2.26 Estimated activity of magnesium in the Fe-Ni-Mg system 65 2.27 Estimated theoretical and effective so lubi l i ty of magnesium in nickel alloys based on Figure 2.26 and experiments 66 2.28 Solubi l i ty of oxygen vs (a) aluminum, (b) titanium, and (c) vanadium contents. The curves are calculated on the basis of a f i r s t order interaction formalism with (a) e^1 = -360, (b) e j 1 = -87, (r) ejj = -27.7. The points are from experimental work 68 2.29 (a) Calculated equilibrium contents of oxygen and magnesium in iron. (b) Actual oxygen and magnesium contents in iron. 1- Mg introducted. in a methane stream and 2- in an air stream 75 Chapter 3 3.1 The•experimental furnace and vacuum system in position in the Atomic Absorption Spectro-photometer 77 3.2 Block diagram of an Atomic Absorption Spectro-photometer. Emission from the line source is sp l i t into sample and reference beams, then recombined and passed through monochromator. Signal from photo-detector Is amplified and fed into c ircui try which produces a manual electronic nul l . The sampling burner is replaced by the vacuum be l l - jar in this study 78 3.3 Schematic drawing of the vacuum be l l - jar containing the molybdenum resistance furnace 80 Chapter 3 (Cont'd) - x i i i -Figure Page 3.4 Molybdenum Knudsen ce l l 83 3.5 Alumina Knudsen ce l l 84 3.6 Isopiestic Knudsen c e l l 85 3.7 Arrangement of thermocouples in the magnesium slug used for cal ibrat ion. Measurements in mm 90 Chapter 4 4.1 Summary of calibration experiments 102 4.2 The relationship between oxygen part ial pressures and compositions for the Ti-0 and Zr-0 systems at 1 0 0 0 ° C 8 * 105 4.3 Results of the test experiments .on- t in alloys 108 4.4 Calculated vapour pressures using equation 4.14 versus experimental results. . 119 4.5 Surface plot from results calculated using equation 4.14, for Mg contents up to 100 ppm and Al contents up to 500 ppm. (Minor variations evident in the lower part of the plot are a r t i f i c i a l and due to that a f inite number of points were used to produce the plot) 121 4.6 Contour map showing the content of oxygen as a function of magnesium and aluminum content. Experimental points: x 17-19 ppm 0, o 20-25 ppm 0, * 26-30 ppm 0. Experiment numbers, see Table 4.5 122 4.7 Area predominance diagram. Equations 1-5 are given in Appendix F, p 168. pMg= 10 , — PMg= data from l i terature . • PMg= suggested data 124 4.8 Comparison between data for alloys containing no major additions and alloys containing 20% Fe or 20% Cr 131 - xiv -N O M E N C L A T U R E A Area AAS Atomic Absorption Spectrophotometry a^ Raoultian activity. A l , CJ, Mg Elements in l iquid metal solution B Q , B p B£ Constants c Average molecular speed C^, C^ Constants d Thickness of absorbing space, orif ice diameter dco Solid angle EB Electron Beam EBCHR Electron Beam Cold Hearth Refining EDX Energy Dispersive X-ray analysis J ' i e~* Firs t order free energy interaction coefficient of j on i (Henrian) ESR Electro Slag Remelting f^ Henrian act ivi ty coefficient h^ Henrian act iv i ty I q , I Intensity of AAS light beam before and after entering absorbing vapour K Absorption coefficient K Equilibrium constant nn - X V ' -MA MgO»Al 2 0 3 M^, Mj Molecular weight of i , j N/V Number of molecules per unit volume of the gas N(9)/Z Probability o p, p^ Vapour pressure, atm p° Vapour pressure of pure element %i , %k Weight % of i , k R Gas constant i k r^' Second order interaction coefficient (Henrian) T Temperature, K,°C t time VAR • Vacuum Arc Remelting VIM Vacuum Induction Melting w Weight loss Molar fraction of component i a Evaporation or condensation coefficient Y , Raoultian act ivi ty coefficient Firs t order free energy interaction coefficient of j on i , (Raoultian) 9 Angle to normal \ Mean free path i k p^' Second order interaction coefficient (Raoultian) a Col l i s ion diameter of molecules -- xvi -Acknowledgement 8 In completing this project I am indebted to many people: - My supervisor Professor A. Mitchell and co-supervisor Professor E . Peters for their Interest and guidance. - Personnel of the Metals and Materials Engineering Department for their assistance with many different tasks. - Fellow graduate students for their friendship. - My husband Fred for his love and encouragement. I thank them a l l . Financial assistance, provided by Teledyne Allvac Inc. and the Natural Science and Engineering Research Counci l i s g r a t e f u l l y acknowledged. - 1 -1. I n t r o d u c t i o n Magnesium is an important alloying element in nickel base alloys for two major reasons. It is added to these alloys to improve the mechanical properties in the finished product. In addition, i t enhances the hot duc t i l i ty of the al loys , which Is sometimes necessary for the fabrication process. Nickel alloys with controlled additions of magnesium were patented in the early 1970's. One of these alloys exhibited an increased high temperature rupture l i f e , and in the production of another alloy an expensive heat treatment cycle could be eliminated as a result of the magnesium content. Other benefits of magnesium additions, such as improved low cycle fatigue l i f e , have since been suggested In the l i t e r a -ture. Generally, the improvement of properties is achieved at a very low content of magnesium, less than 100 ppm and typical ly around 50 ppm. The exact function of magnesium in the nickel alloys has not been 3 e s t a b l i s h e d . It has been suggested that "the magnesium addi t ion finishes any additional deoxidation of the superalloy, and then combines with residual sulphur to render the sulphur innocuous. Further, any remaining magnesium migrates to energy-lowering s i tes , such as grain boundaries and twin inferfaces where i t acts to prevent dislocation pileup and b r i t t l e behaviour by promoting dislocation tangling." The association of magnesium with oxygen and sulphur is clearly shown in Figure 1.1. - 2 -Figure 1.1 Secondary Ion Mass Spectrometry (SIMS) dot maps of a polished nickel alloy (superalloy 718) surface showing the relative concentrations of the following ions: a) ^ M g + , b) I L S ~ , c) 1 6 0 " and d) 2 7 A 1 + . - 3 -Magnesium is added during primary melting, usually vacuum induction melting. The alloys are then subjected to secondary melting, most commonly Electro Slag (ESR) or Vacuum Arc (VAR) Remelting. Theoretical assessment of the magnesium content during melting has not \ been possible as thermodynamic data for magnesium in l iquid nickel solutions have not been available. For instance, the distribution of magnesium between slag and metal during ESR melting has been d i f f i cu l t to calculate. With the introduction of Electron Beam Cold Hearth remelting of superalloys, the need to calculate evaporation rates of magnesium has become more urgent due to the large bath surface coupled with the low pressure ut i l ized in the process. Such calculations require a knowledge of thermodynamic properties. The objectives of this work are to develop an experimental method suitable for act iv i ty determinations for very dilute alloy components, such as magnesium in l iquid nickel solutions, and to determine the basic thermodynamic properties of magnesium in l iquid nickel al loys. In this thesis, the pertinent l iterature is discussed in Chapter 2, a description of the experimental equipment and methods is given in Chapter 3, and the experimental- results and mathematical treatment of the data are discussed in Chapter 4. F ina l ly , the conclusions are presented in Chapter 5. - 4 -2. Literature Review 2.1 Magnesium In Superalloys A superal loy has been defined by Sims and Hazel^ as "an alloy developed for elevated temperature service, usually based on group VIIIA elements, where relat ively severe mechanical stressing is encountered and where high surface s tab i l i ty is frequently required". Hence, superalloys are mainly used in gas turbines, but also in space vehicles, nuclear reactors, petrochemical equipment and in other high temperature applications. Nickel-based superalloys are used, for instance, in many parts of aircraft gas turbines in both wrought and cast form. Some examples of nickel based superalloys and their applications are given in Table 2.1. Magnesium is added to nickel-based superalloys to improve high temperature duc t i l i t y . This property is important both from the manufacturing point of view, particularly in terms of open-die forge-a b i l i t y , and also from the in-service standpoint where rupture duct i l i ty is of primary importance. Further, i t has been suggested that 2 magnesium improves the low cycle fatigue strength . TABLE 2.1. Examples of Nickel Base Superalloys  and Their Applications Alloy Designation Ni Cr Co Mo W Nb Al Ti Fe Mn Si c B Zr Applications Hastelloy Alloy X 47.3 22.0 1.5 9.0 0.6 18.5 0.50 0.50 0.10 Wrought sheet alloy, used in combustion cans. Inconel Alloy 718 53.0 18.6 3.1 5.0 0.4 0.9 18.5 0.20 0.30 0.04 — — Forged turbine discs Waspalloy 58.3 19.5 13.5 4.3 - - 1.3 3.0 - - - 0.08 0.006 0.06 Forged turbine discs Udimet 500 52 18.0 19.0 4.2 3.0 3.0 0.07 0.007 0.05 Cast alloy used in turbine blades. Rene 80 60 14.0 9.5 4.0 4.0 3.0 5.0 0.17 0.015 0.03 Cast alloy used in turbine blades• - 6 -1.1.1 Melting Practice Melting of aerospace grade superalloys generally takes place in 3 two or three steps. Cremisio has described the melting of superalloys in de ta i l . The alloy is i n i t i a l l y melted from scrap and/or virgin materials using Vacuum Induction Melting (VIM). The second step consists of either Vacuum Arc Remelting (VAR), Electro Slag Remelting (ESR) or Electron Beam (EB) Remelting. For some applications the metal is melted a third time, again u t i l i z i n g either of the three remelting methods. 2.1 .1 .1 Vacuum Induction Melting A typical VIM cycle starts with the charging of either virgin raw materials or scrap. Following the pumping down, the furnace contents are melted. When the metal is entirely molten and the bath stable, desulphurizing or deoxidizing additions are made. F ina l ly , reactive elements are added, and when the bath composition is correct the melt is 3 cast . The change of oxygen and oxide content during a VIM melting 4 sequence is i l l u s t r a t e d by Figure 2.1 . As can be seen, additions of aluminum and alkaline earth (AE) or rare earth (RE) metals decrease the act iv i ty and content of oxygen during the melting of a virgin heat. The - 7 -Figure 2.1 Variation of oxygen act iv i ty aQ and total oxygen content 0^ , during vacuum induction melting of alloy 718 using virgin and revert charges; md, melt-down; r, end of refining period; other symbols on h o r i -zontal axis represent element additions to melt . - 8 -increase of oxygen in the revert heat is probably due to pick-up from the refractories . In both cases however, the AE or RE additions help with the removal of oxygen-containing Inclusions by the suggested 4 mechanism of globurizing the alumina clusters . Calcium, magnesium, and rare earth metals are also strong 4 desulphuriz ing agents. Figure 2.2 shows that the sulphur content can readily be reduced from ~ 150 ppm to ~ 10 ppm. The sulphide products deposit on the crucible walls. Hence, i t is c r i t i c a l that the correct 4 amount of desulphurizing agent can be predicted for each charge . 4 Alexander suggests that the removal of magnesium from VIM melts i s contro l l ed by l i q u i d mass transfer while Fu et al"' suggest that the controll ing steps are l iquid mass transfer and the evaporation reaction. However, the latter were forced, for lack of better data, to assume that the act iv i ty of magnesium in nickel alloys is equal to the content. Clearly, additional data are required for more accurate analysis of the evaporation process during Vacuum Induction Melting. 2.1.1.2 Vacuum Arc Remelting Aerospace grade superalloys are frequently produced via VIM and Vacuum Arc Remelting (VAR). VAR is basically consumable electrode melting under vacuum. Chemical interference from refractories is - 9 -T 1 1 1 1 1 r ir o n m e l t - d o w n • a t mctt e n d H E A T No. Figure 2.2 Reduction in melt sulphur content [s ] over vacuum induction melting period • - 10 -avoided as the so l id i f i cat ion takes place in a water-cooled copper crucible . The sequence VIM-VAR combines the chemical control of the VIM process and the so l id i f i cat ion control with low macro and micro-3 segregation of the VAR process . Fu et a l ^ inves t iga ted the evaporation of magnesium from a nickel-base superalloy during VAR. They found that magnesium evaporates mainly from the electrode t ip . It was suggested that the evaporation rate is limited by the transport of magnesium through the melt to the surface. However, the analysis of the problem is limited by lack of fundamental data. 2.1.1.3 Electro Slag Remelting The Electro Slag remelting process is similar to the VAR process in that both include consumable electrode melting into a water-cooled 3 copper mould . In the ESR process the melting takes place through a resistance-heated slag. Thus, i t is possible to control the Ingot inclusion content and chemistry. The process is also an efficient desulphurizer. However, problems have been encountered in remelting titanium and aluminum-containing alloys as these elements tend to be 3 lost in the slag during remelting . Ichihashi et a l investigated the abi l i ty of the ESR process to - 11 -retain titanium, aluminum, and magnesium in the metal using different slag compositions. They show that increasing the contents of CaO and MgO wi l l increase the content of magnesium in the ingot, as seen in Figure 2.3. They also suggest that titanium or aluminum can be lost to the slag through following reactions: 3MgO + 2A1 t A1 2 0 3 + 3 Mg 2Mg0 + T i t T i 0 2 + 2 Mg_ Simultaneously, these reactions would increase the magnesium content in the al loy. It may be noted that proper control of the reactive element content is dependent on a delicate balance between slag and metal chemistry. Ich ihas i^ also found that magnesium can not be retained in the metal unless the slag is protected from air oxidation by an inert atmosphere, for instance argon. Generally, the conclusions of Chen 7 6 et al agree with those of Ichihashi . 2.1.1.4 Electron Beam Melting The Electron Beam melting process has recently emerged as another g a l t e r n a t i v e for superalloy refining . The process, usually applied in the form of a Cold-Hearth Refining (EBCHR) furnace, offers more - 12 -150 cn 50 h O: _ _ __mol% CaO > 25 O : 9 : 15 * CaO s 25 5< CaO^ 15 -• : CaO <, 5 #(CaF2-MgO) 0 o f 0 / „ , mol* ' Ca0=10 Ca0=30/ t nolX A , ® / / ® mo IX • Ca0=0 20 M0 MgO (molZ) 60 Figure 2.3 Effect of MgO content in the ESR slag on Mg content in produced ESR ingots. - I n -f l e x i b i l i t y as to melting speed and ingot shape than the VAR process, since the heat source is independent of the charge material. However, the large area to volume ratio in the EBCHR process makes evaporation of alloying elements unavoidable. Hence, knowledge of the evaporation parameters of a l l o y i n g elements is important i f desired a l l o y compositions are to be produced. 9 10 M i t c h e l l and Herbertson have discussed the evaporation of 9 magnesium from superal loys during EBCHR refining. Mitchel l suggests that the evaporation rate is controlled by the evaporation step and gives an evaporation rate constant of 2.5 x 10 7m s ^ at 1700°C. On the other hand, Herbertson^ claims that the evaporation rate is controlled by bulk mass transfer and gives a Langmuir evaporation rate constant of 1.5 x 10 m^ s 1 at 1427"C. It appears that Herbertson^ has arrived at this value assuming an act ivi ty coefficient for magnesium in the l iquid superalloy of unity. Using the suggested act ivi ty coefficient by 9 -3 M i t c h e l l of 10 for magnesium in l i q u i d n i c k e l , one arrives at an -4 -1 e v a p o r a t i o n r a t e c o n s t a n t of 1.2 x 10 m s at 1 4 2 7 ° C and - 4 - 1 11 3.6 x 10 m s at 1 7 0 0 ° C . T h i s would mean that magnesium evaporation is controlled by a combination of l iquid mass transfer and evaporat ion. Hence, the a c t i v i t y coe f f i c i ent is important in determining the rate-controll ing step for evaporation during EBCHR ref ining. - 14 -100 -90 -80 -^ . _ N i M f l Q<jd*d 1900 2000 2100 2200 Figure 2.4 The hot duct i l i ty of Waspaloy b i l l e t s with and without magnesium additi ons• RA% — Percent area reduction . 2.1.2 Alloy Properties In particular, small carefully controlled additions of magnesiuim greatly affect the hot workability of superalloys, as demonstrated for 3 Waspalloy in Figure 2.4. It is suggested that "the magnesium addition finishes any additional deoxidation of the superalloy that can be achieved. In addition, magnesium combines with residual sulphur to render the sulphur innocuous. F ina l ly , any remaining magnesium migrates to energy-lowering sites , such as grain boundaries and twin interfaces where i t helps to prevent dislocation pileup and br i t t l e behaviour by 12 13 promoting d i s l o c a t i o n tangl ing ." Holt and Wallace ' have reviewed the influence of impurities and beneficial trace elements on the properties of nickel-base superalloys. 2.1.2.1 Hot Working The ab i l i ty of magnesium and calcium to counteract a relatively 14 high content of sulphur is shown in Figure 2.5 . It also shows that excess alkaline earth metal indeed causes embrittlement of the al loy. This topic has been further investigated by deBarbadil lo^. He shows that excess magnesium or calcium leads to the formation of intermetallic compounds, such as Ni^ Mg or Ni^Ca. Particularly in the case of calcium these compounds occur as continuous intergranular films, causing severe hot and cold shortness. While equilibrium solubi l i ty is higher, - 16 -< LU cr < o z o o Q UJ cr 100 80 60 40 20 — r-2 3 V / ; / s Ca Mg // /1 15 2 2 V / 2 49 22 66 4 " \ / ' 3 67 - -106 125 900 1000 1100 1200 1 300 TEMPERATURE. °C Figure 2.5 Effect of Ca and Mg additions and S content on hot duct i l i ty of Inconel 600 . S, Ca, and Mg contents in ppm. - 17 -deBarbadi l lo found that due to severe segregation upon freezing the intergranular compounds occur already at solute concentrations of 0.05 weight percent. T u r n e r ^ points out that the malleability of nickel alloys is much more sensitive to excess Ca than excess Mg as seen in Figure 2.6. This is probably due to the ease of dissolution of Ni-Mg phases during heat treatment. A marked increase in high temperature rupture l i f e and duct i l i ty 17 18 has been o b s e r v e d i n magnesium t r e a t e d n i c k e l a l l o y s ' Schramm et al^ achieved increases in rupture l i f e from 185 h to 1015 h and increases in area reduction from 32% to 70% for an addition of 350 ppm magnesium compared to an untreated al loy. The tests were done at 650°C (1200°F) and 4.8 x 108 N/m2 (70,000 ps i ) . Muzyka and Whitney 1 8 were able to eliminate an expensive heat treatment cycle to produce grains in the range of ASTM 6-8 by treating alloy 718 with magnesium. They found that alloys carefully treated with magnesium, calcium or neodymium attain roughly the same duct i l i ty for grain sizes coarser than ASTM 6 as untreated alloys for ASTM 6-8. 19 Yamaguchi et a l suggest that optimum duct i l i ty can be achieved by keeping 0.003 > tS > -0.004, where AS = %S - 0.8 x %Ca - 0.3 x % Mg - 0.5 x % Y - 0.1 % Zr (% = weight %). They found that at /S > 0.003 and a temperature of 950-1150°C fracture occurs intergranularly, and significant amounts of sulphur were segregated to the grain boundaries. Figure 2.7 also shows that no detectable segregation of sulphur occurs - 18 -501 o-»» 0 001 O02 003 004 O05 Mg,wt-% 50| 1 r 0 . 0 0 0 5 0-01 0015 0 0 2 0 0 2 5 Ca ,wt- 7o Figure 2.6 Effect of Mg (a) or Ca (b) on hot tensile duct i l i ty of Ni-based a l l o y s 1 6 . - 19 -I I I I I I I I 0 2 4 6 8 10 12 14 ARGON-ION SPUTTERING TIME, min Figure 2.7 Variation of S/Ni intensity ratio as function of distance from intergranular fracture surface for various Inconel 600 alloys . - 20 -in alloys treated with Mg or Ca. This is due to the formation of MgS and CaS which are present as inclusions in the nickel matrix. 2.1.2.2 V o i d a b i l i t y 20 Morrison et al found that the tendency to microfissuring during welding of alloy 718 decreased with increasing magnesium content as shown in Figure 2.8. The decrease is suggested due to the formation of MgS, eliminating harmful effects of free sulphur. However, Gittos and 21 Scott claim in a review paper that the effects of Mg on weld cracking are variable. This, they suggest, could be due to the existence of c r i t i c a l ranges within which an element is harmful. 2.1.2.3 Mechanical Properties 2 Moyer has shown that decreasing the carbon content of both laboratory and production line heats of alloy 718 to 0.01% does not lead to deteriorating tensile properties provided that the metal has been treated with magnesium. On the contrary, tensile properties appear to improve with lower carbon content. This finding, Moyer claims, offers the poss ibi l i ty to produce alloys with improved low cycle fatigue (LCF) properties, as LCF fracture may be init iated at carbides. 22 Chen et a l found that magnesium addit ions to superal loys improve the creep properties. Further, they suggest that magnesium Figure 2.8 Inconel 718 microfissuring susceptibi l i ty versus magnesium content - 22 -defines the grain boundary carbides (mainly M^C). As opposed to 18 Yamaguchi et a l , Chen observed segregation of Mg to the grain boundaries. This segregation increased with treatment at 850°C for 1200 h suggesting that the segregated magnesium is in the metallic unbound state. Hence, i f a l l magnesium in the Yamaguchi study is bound as sulphide or oxide the findings need not be contradictory. - 23 -2.2 Atomic Absorption Studies of Vapour over Condensed Phases The technique of measuring vapour pressure over a condensed phase using atomic absorption spectrophotometry has been used in a number of 23-35 inves t iga t ions . A l l of these studies have been carried out at a temperature of less than 1100°C, as can be seen in the summary given in Table 2.2. Since these papers are important to this work, they w i l l be given a re lat ive ly detailed discussion in chronological order. 23 2.2.1 Herbenar et a l 23 Herbenar et a l measured the vapour pressure of zinc over solid a-brasses at temperatures up to 970°C. Their l ight source consisted of a spark produced by a high tension discharge between two electrodes of pure zinc. Further, a double prism type spectrograph was used in conjunction with photographic plates to measure the intensity. The absorption vessel was contructed from transparent quartz to f i t inside a heating furnace as shown in Figure 2.9. The c e l l was calibrated using pure zinc of known vapour pressure. The intensity was measured at the 3076 A resonance l ine of the zinc spectrum and at 3035 A where no tendency for absorption was detected. The absorption could then be represented by TABLE 2.2 Summary of Atomic Absorption Studies of Vapour Pressure over Condensed Phases Investigators Discussion in Section Cel l Alloy System Temperature Standard Ref. Herbenar et a l 2.2.1 Quartz-Vacuum w. side-arm Zn in Cu-Zn 642-970°C Pure Zn(Jl) 22 Scatchard et al 2.2.2 As above Zn In Ag-Zn Cd in Ag-Cd 527-927°C 350-600°C Pure Zn(Jl) Pure Cd 23 24 VIdale 2.2.3 Open ce l l In Ar-atm. Na in glass 900-1020°C None 25 Brebrick & Strauss 2.2.4 Quartz-Vacuum w.side-arm PbTe 725-924°C Pure Te & PbTe 26 Rapperport & Pensler 2.2.5 Quartz-Vacuum cylinder Ag & Cd In Ag-Cd Zn in Cu-Zn < 800°C 400-600°C Pure Ag & Cd Pure Zn 27 28 Masson et a l 2.2.6 Quartz-Vacuum w. side-arm Zn In Au-Zn In in Cu-In In in Ag-In Zn in Ni-Zn 478-738°C 694-822°C 758-863°C 340-652°C Pure Zn Pure In Pure In Pure Zn 29 30 31, 32 33 El int in & Timofeev 2.2.7 Essentially open Cr ,Al ,Fe ,SI and Zr in binary melts ? None 34 - 25 -Figure 2.9 (a) Transparent quartz absorption vessel and (b) heating furnace - 26 -_ l o g h m . . K E D ( 2 A ) 3035 where K = absorption coefficient p = pressure T = absolute temperature d = thickness of absorbing space If Beer's absorption law is va l id , as appears to be the case in the study of Herbenar, a plot of log ^3076^3075 v e r s u s results in a straight l ine relationship. Experiments for solid Cu-Zn alloys were conducted in a similar fashion to the cal ibrat ion. 24 25 2.2.2 Scatchard et a l ' 24 Scatchard and Westlund applied the experimental technique of 23 Herbenar et a l to s o l i d s i l v e r - z i n c al loys . Later, Scatchard and 25 Boyd replaced the spark source with a hollow cathode lamp and the photographic plates with an electronic system. This system was used to measure the vapour pressure of cadmium over solid silver-cadmium al loys. 25 Scatchard and Boyd found a large deviation from l ineari ty in Equation 2.1. They speculated that i t may be due to the distribution in the emitting vapour not being Maxwellian. - 27 -26 2.2.3 Vldale 2 6 Vidale chose to employ an experimental system consisting of a tube furnace as shown in Figures 2.10 and 2.11. The c e l l is a cylinder with openings in both ends as a light path. By f i l l i n g the tube furnace with argon the diffusion of measured atoms out of the c e l l is restr icted. Thus, a ce l l length equal to that of the physical c e l l is assumed. The system was tested by measurement of the pure sodium vapour pressure at temperatures from 120°C (393 K) to 135°C (408 K). The experimental procedure consisted of measuring the beam intensity (I) at the elevated temperatures, and then-amaximum intensity (I Q ) at a lower temperature when the furnace had been turned off. The theoretical assumptions of Vidale differ signif icantly from apply Beer's law to the absorption of unresolved l ines . Instead, a relationship taking Doppler and pressure broadening as well as the effect of hyperfine structure of the line into account is developed. The relationship takes the form the e a r l i e r papers 23-25 He states that i t is never permissible to ln I/I = C\ + C P (2.2) o 2 T3/2 CHOPPER QUARTZ WINDOW F R O N T SURFACE MIRROR PHOTOMULTIPLIER T U B E OO GRATING MONOCHROMATOR SLITS QUARTZ CELL HOLLOW CATHODE DISCHARGE TUBE FURNACE Figure 2.10 Optical path diagram 2 6 . Figure 2.11 Cross sectional diagram of ce l l and furnace . - 30 -where and are constants. In fact, the three sets of experiments A, B and C each can be well represented by equation 2.1 as shown in Figure 2.12. Linear regression analysis gives a correlation coefficient of at least 0.99 for each experiment. The dashed l ine in Figure 2.12 occurs i f ln I/I is o c a l c u l a t e d us ing equation 2.2 and l i t e r a t u r e values for p„ as a Na function of T. Hence, either of the relationships 2.1 or 2.2 describe well the data for sodium given by Vidale. One explanation for this may be that the temperature interval is very small, only 15°C. It is not clear why the relat ively large discrepancy between experiments A and B/C 2 6 o c c u r r e d . V i d a l e also used the system to determine the vapour pressure of sodium over glasses. In these experiments he used a platinum c e l l to contain the vapours. 27 2.2.4 Brebrick and Strauss Brebrick and Strauss used a closed s i l i c a c e l l , similar to 22-24 e a r l i e r invest igat ions , to measure the vapour pressure of Te 2 and PbTe over sol id PbTe at temperatures of 725 to 924°C. They calibrated a system consisting of interference f i l t ers and electronic detectors using pure Te and PbTe. By switching f i l t ers they were able to measure the absorption of the two vapour species almost simultaneously. - 31 -1 I I I I L 2 3 U 5 6 7 P/T * 1012 (atm/ K) Figure 2.12 Diagram showing the correlation between three sets of experiments, A, B and C presented by Vidale , according to equation 2.1. - 32 -28 29 2.2.5 Rapperport and Pemsler ' Rapperport and Pemsler used closed cy l indr ica l s i l i c a vacuum cel ls to measure the vapour pressure of s i lver or cadmium over solid 28 29 silver-cadmium alloys and zinc over solid copper-zinc alloys . They used hollow cathode lamps as light sources and electronic equipment to 23-25 record the absorpt ion. As in earl ier investigations , they assume and are able to use a linear relationship according to Beer's law. The authors or ig inal ly intended to measure both the vapour pressure of zinc 29 and copper over brasses using the same quartz cel ls . However, they found that different length cel ls were required due to the relationship of the absorption coefficients and vapour pressure variation with 29 temperature 30 3 A 2.2.6 Masson et a l Masson et al employed a system similar to that of earl ier 23-25 31 work as described by Lee . It consisted of a sealed quartz ce l l with a side arm containing the specimens. The ce l l was placed in a tube furnace which in turn was placed in the beam path of a commercial atomic absorption spectrophotometer. The following alloy systems were 30 31 3? 33 investigated: Au-Zn at 478-738°C, Cu-In at 694-822°C, Ag-In » at 34 758-863°C, and Ni-Zn at 340-652°C. The vapour pressures measured were those of Indium or z i n c Also in these investigations i t was found that - 33 -Lambert-Beers law was obeyed, except occasionally at high absorption (> 0.7). 35 2.2.7 E l i u t i n and Timofeev E l i u t i n and Timofeev attached atomic absorption equipment to an Electron Beam button melting furnace. They claim that the evaporation rate during melting can be continuously followed, although the electron beam had to be switched off during a measurement. The paper is rather sketchy and the notation poorly explained. However, a method of 26 calculation similar to Vidale appears to be applied. Further, the c e l l consists of only part of the atomic beam over the melt as the light beam from the spectrophotometer has been "boxed in", with only a short segment open to the vapour. - 34 -2.3 High Temperature Experimental Methods Excellent reviews of the l i terature covering most aspects of high temperature thermodynamic experimental methods have been published by 36 37 Rapp and Kubaschewski and Alcock . This survey has been limited to Knudsen c e l l methods and isopiestic methods as they are of major importance to this investigation. 2.3.1 Knudsen C e l l Methods 36 37 In a d d i t i o n to a l r e a d y mentioned reviews ' , a general l i terature survey and discussion of the Knudsen Cel l or Effusion method 38 39 i s given by Cater ' , and the mass transfer aspect is discussed by Geiger and P o i r i e r 1 1 . The following paragraph discusses the fundamental assumptions applying to the Effusion method. If a condensed phase is contained In a closed container i t w i l l develop a vapour pressure that is in equilibrium with the condensed phase. If the pressure is low enough to give molecular diffusion conditions the gas molecules w i l l follow a Maxwellian distribution. This assumes molecular chaos, meaning that molecules strike the walls in random directions. The cosine law then gives the probability that a molecule strikes the wall at an angle 9 to the normal, - 35 -c cos 9 dw 4u (2.3) o where dw = 2u sin 0 dQ, N/V = number of molecules per unit volume of the gas and c = average molecular speed. This is the cosine law. Assuming that an area, A, small enough not to disturb the equilibrium, is removed from the container wall , the emerging molecules then w i l l follow the distribution of the cosine law. Two additional restrictions apply to this concept, that the edge of the orif ice is so thin that the chance of a molecular co l l i s ion with the edge is negligible and that the pressure is low enough so that intra-molecular col l is ions are absent within the o r i f i c e . Under these conditions the Hertz-Knudsen equation applies, where p = pressure of gas, w = weight loss, t = time, R = gas constant, T = temperature and M = molecular weight. In real i ty an in f in i te ly thin orif ice opening is d i f f i cu l t to construct, but so called Clausing factors are available to correct for effusion through an ideal orif ice has been set at roughly K/d = 10, where \ is the mean free path and d is the or i f ice diameter. The mean free path is given by P = w_ 2-nRT V 2 At ^ M ' (2.4) cy l indr ica l and conical openings. The upper l imit for molecular . rN , , 2 r l (2.5) where a is the co l l i s ion diameter of the molecules. Some typical Knudsen cel ls are depicted in Figure 2.13. 2.3.1.1 Heating and Temperature Measurements For the cosine equation to be va l id , uniform temperature distribution in the c e l l is important. a. Thermocouples Thermocouples const i tute one a l t e r n a t i v e for temperature measurements. They can be either attached or situated adjacent to the c e l l i f radiation heating is applied. It is generally recommended that / either several thermocouples are attached to the c e l l , e.g. to the top and bottom, or that the temperature distribution be determined in dummy experiments. The major disadvantage with thermocouples is that e lec tr ica l leads have to be fed through the vacuum wal l . - 37 -Three tungsten legs Ceramic kinematic table Fused silica table Threaded black body hole Fused silica support tube Thin orifice plate welded to lid • — ^ - T h e r m o c o u p l e Support rod Tungsten wires to vacuum balance arm Thermostatted, evacuated bulb Mercury Cold, graduated condensation tube (c) (d) Figure 2.13 Typical Knudsen ce l l s , (a) Tungsten c e l l , (b) Cel l used with vacuum balance, (c) Cel l with thermo-couple and near-ideal or i f i ce , (d) Knudsen's original apparatus for determining the vapour pressure of mercury . - 38 -b. Optical Pyrometry The other alternative for temperature measurements is optical pyrometry. The pyrometer is sighted through a window or prism either into the c e l l or i f ice or into a blackbody hole dr i l l ed elsewhere on the c e l l . The sighting window must be shuttered to prevent deposition of vapour which would change the transmissivity. c. Radiation Shielding Several alternatives for c e l l heating are available. Regardless of heating method, the c e l l is generally surrounded by several layers of radiation shielding. The shielding should f i t as closely as possible to minimize heat loss by radiation. Annular shields are frequently la id on top of the effusion c e l l to maintain the temperature of the or i f i ce . Shields around inductively heated containers have to be slotted or spl i t to minimize direct heating in the high frequency f i e l d . d. Resistance Heating The c e l l is heated by passing an e lec tr ica l current directly through i t or through a band or filament wrapped around i t . Thus, i t - 39 -must be made from an e lec tr ica l ly conducting material. Another disadvantage is that severe temperature gradients may occur where the e l ec tr i ca l leads are attached. e. Induction Heating Induction heating of an e lec tr ica l ly conducting c e l l has the advantage that no part of the heating system is inside the vacuum system. However, i t has the serious disadvantage that the f ie ld may interfere with adjacent electronic equipment or thermocouple c i rcu i t ry . f. Electron Bombardment Heating Effusion cel ls can be heated by electron bombardment by setting up a potential of 200-1000 V between the ce l l and a surrounding hot filament. This is an eff ic ient , direct way of heating the container. However, for stable e lectron bombardment, a good vacuum (p < 5 x 10 ^ torr) is required. This may be d i f f i cu l t to maintain during outgassing of the c e l l . Further, as with resistance heating, the c e l l must be made of an e l ec tr i ca l ly conducting material. - 40 -g. Radiation Heating Using radiation heating, the c e l l may be surrounded by a res is t ive ly or inductively heated sleeve. Among the advantages are that the c e l l can be made of any suitable material and that temperature measurements can be made by thermocouples which need not be attached to the c e l l . However, the hot sleeve or filament may result in a deteriorated vacuum due to outgassing. 2.3.1.2 Detection Methods 40 Knudsen in his landmark measurements of mercury vapour pressure simply condensed the effusate and measured the volume. Subsequently, a number of detection methods have been developed. However, only mass spectrometry has provided direct intensity measurements of specific vapour species. a. Weight Loss Methods The simplest approach to Knudsen experiments is to weigh the c e l l before and after heating to the experimental temperature. This of course assumes that significant evaporation of only one species occurs. The technique suffers from two major disadvantages. F i r s t , the vacuum has to be broken for each measurement. Secondly, weight loss during the heating and cooling cycle must be accounted for. Both of these problems - 41 -are resolved by suspending the c e l l from a vacuum balance b. Collection Techniques If the effusate is condensible, i t may be collected on targets coaxial with the or i f i c e . An example of such a system is shown in Figure 2.14. This technique has two major advantages. F i r s t , Clausing correction factors are not needed. Secondly, as the target is exposed direct ly to the evaporating surface the collected effusate Is more l ike ly to be representative of the equilibrium pressure than i f the molecules had f i r s t collided with the ce l l wall . However, sensitive analytical methods are needed to analyse the frequently small amounts of effusate. c Torsion Measurements By measuring the deflection of a Knudsen c e l l , frequently with two or more orif ices (see Figure 2.15) and suspended by a torsion wire, the vapour pressure of the contained substance can be determined. This technique can be applied for instance to alloys by placing one pure alloy component in one chamber and the alloy in the other. Further, a combination of vacuum balance and torsion techniques can be used to determine the molecular weight of the effusing species as the torsion technique is independent of the molecular weight. - 42 -Liquid Nitrogen Contoiner Receiver for Exposed Torgets Beryllio and Fused S i l ica Tables Fused S i l i c a Support Tube Ouortz to Pyrex Graded Seal •Fused S i l ica Shutter Optical Pyrometer Copper Foil Rodiotor Housekeeper Sea l , Copper to Pyrex Stock of Platinum Torgets, Each Held in Aluminum Ring Stainless Steel Collimator Tungsten Ejector Rod Iron Slug Fused Si l ica Shutter Normol to Page Fused Sil ico Condenser Effusion Cell Induction Coil To Pumps Philips Gouge Tube Optical Window Prism 0 I 2 3 4 3 Inchtt A p p r o x i m a t t S c a n i I I I i I ure 2.14 An apparatus for effusion studies by the col lect ion technique . - 43 -Suspension rod Feeder tube Higher temperature effusion cell Lower temperature /"* sample reservoir Tapered Recessed area to provide shorter orifice lengths (c) Suspension Figure 2.15 Some torsion-effusion ce l l s . (a) Two-temperture c e l l made of fused alumina. The lower reservoir is made of Corning No. 7280 glass, fused directly to the alumina upper part. (b) Opposed-orifice c e l l for comparing vapour pressures of two systems. (c) Four-orifice c e l l machined from graphite. (d) Welded tantalum c e l l , showing removable yoke for suspending i t from the torsion wire. (e) Demountable two-section c e l l , with 0.5 in . over-lap to be suspended similarly to (d) - 44 -d. Mass Spectrometry Mass spectrometry applied to high temperature experiments has been 41 42 discussed by Drowart and Buchler . The method has the unique ab i l i ty -3 to analyse the composition of a complex vapour in the range of 10 to _g 10 t o r r . A mass spectrometer system consists of a vapour source, a region where ions are produced, a mass analyser and a detector. Two major types of mass spectrometers are used, magnetic deflection and time of f l ight (TOF) instruments. Typically the metal vapour is ionized by bombardment with an electron beam. In the magnetic deflection instruments the ion beam is then accelerated by an electric f ie ld before entering the mass analyser. Mass analysis is performed by varying a magnetic f i e l d . In the time of f l ight instruments the ions are accelerated into a field-free space. Analysis is achieved by monitoring the time i t takes for ions of different mass to pass through the f ield-free space. Generally, magnetic deflection instruments are more sensitive than TOF instruments. Pressures are deduced from the detected mass to charge ratios. A pract ical problem in this respect arises as one Ion species may be produced directly or through dissociation of more complex molecular species. Hence, the fundamental problems in data analysis consist in i d e n t i f i c a t i o n of species effusing from the Knudsen c e l l and establishment of the part ia l pressures of each species. Absolute - 45 -pressures can be determined by incorporating a substance of known vapour pressure in the c e l l . Direct determination of alloy vapour pressures can also be achieved by using a twin crucible arrangement as shown in Figure 2.16. Another obvious alternative to overcome problems caused by changes in the absolute sensit ivity of the spectrometer is to measure the ratio of ion currents of the solution components. 2 . 3 . 2 P8eudoi8opie8tlc Method Literature surveys dealing with the isopiestic method have been 43 44 presented by Norman and Lange . The isopiestic equil ibration of two or several condensed phases is accomplished at isothermal conditions. This technique is not particularly applicable to high temperature systems as i t requires very different v o l a t i l i t i e s of solute and solvent. Instead the nonisothermal equilibration in a closed system is more useful and has been given the name "pseudoisopiestic method". One interesting application of this method is that of Milstead and 45 co-workers . They determined the sorpt ion of cesium on carbon by equilibrating cesium at the lowest temperature and carbon at a higher temperature in a glass-stainless steel system. By doping the cesium with radioactive tracer they were able to analyse the sorption directly at several consecutive temperatures. 46 47 E l l i o t t et a l ' c o n s t r u c t e d a quartz system, shown in - 46 -Figure 2.16 Twin crucible effusion source - 47 -Figure 2.17, attached to an analytical balance for direct measurements of cadmium vapour pressure over cerium and gallium al loys . By loading known amounts of the alloy components in the alloy leg, the alloy composition is known by the weight gain in the cadmium leg, and the vapour pressure is determined by the temperature of the cadmium leg. 48 49 Eldridge et al ' developed a system where several specimens are located in a temperature gradient in a closed reaction tube. This system is depicted for the determination of magnesium act ivity in l iquid t in alloys in Figure 2.18. Tin contained in covered graphite crucibles was equilibrated with pure magnesium. The resulting alloy compositions were simply determined by weighing the crucibles before and after the equil ibration experiments. - 48 -WEIGHT OF SYSTEM ROD WEIGHT CONDENSATE HERE Figure 2.17 Schematic of an "isopiestic balance" » - 49 -Figure 2.18 Isopiestic equil ibration tube . - 50 -2.4 Thermodynamic Data 2.4.1 Background The thermodynamic act iv i ty of a component, i , in solution can be defined a s ^ a i " p l ^ p i » ( 2 , 6 ) where p^ , = pressure of component i and p° = vapour pressure of the pure metal i at the same temperature. The act iv i ty coefficient, which is based on Raoultian behaviour with the pure substance as standard and reference state, is defined as y± = a i / X i (2.7) where X^ = molar fraction of component i . For dilute metal solutions i t is customary to apply a reference state of in f in i t e ly dilute solution with a hypothetical 1 weight % solution as standard state. Thus, the composition coordinate is also changed from mole fraction to weight %. This standard state yields another definition of the act iv i ty coefficient, h i / (%i). (2.8) As this standard state is frequently called Henrian, the act iv i ty is written h^. To describe mathematically the variation of act iv i ty coefficient with composit ion, Wagner"*^ " suggested a Taylor series expansion for the logarithm of the act iv i ty coefficient, written here in the notation of The f i r s t term on the right refers to the act iv i ty coefficient of i at i n f i n i t e d i l u t i o n , as the expansion i s made for the l imiting case of X,-*-!. The f i r s t order terms are defined as E l l i o t et a l 50,52-53 (2.9) 1 o In Y. (2.10) and called the f i r s t order free energy interaction coefficients. S imilarly , the higher order coefficients are defined as - 52 -. , , d^ln y p ? , k - —f^-r [ ]. (2 . i i ) " l n ! n , ! L r i . n , J ' J fc (ax.) J (dx^) k where n. and n, are integers from 0 to 2, and the sum of n and n, is 3 fc J fc equal to 2. For the weight percent coordinate equation 2.9 becomes log f - I ej(%j) + I rj(%j) 2 + I I r j'k(%j)(%k) + 0(%)3 (2.12) j-2 j=2 j=2 k=2 where the f i r s t order coefficients are defined < a log f t ! i = t of] J %i * 100 (2-13) and the higher order terms defined J . f c _ a log f. n.!n. ! J k (a%j) i . n. J(a%k) (2.14) similarly to expression 2.11. In equation 2.12 the zeroeth-order term disappears since the act ivi ty coefficient f ° , is assigned the value of one at inf ini te d i lut ion . - 53 -The most commonly used relationships between the different parameters are given by the following equations. z{ = (2.15) M . M - M M,~ M. 2 pJ = 130_ [100M2 r j + M (M -M ) e J l + i (-i 1) H i ( M 2^ L - L u u n j r i n j a y e i J 2 ^ M 1 ; (2.17) Firs t order interaction coefficients have been determined for a large number of solutes in iron. However, only in a few cases are the experimental data accurate enough to suggest second order interaction parameters of the type r^ . In no case has the experimental accuracy . ,53-55 permitted ca l cu la t ions of r j ' . Unfortunately the amount of data for nickel solutions is more limited than for iron solutions^ 6 . 2.4.2 The Pure Elements N i , Mg, Ca and Al Basic data for the pure elements are well established. Pertinent equations are summarized in Table 2.3. TABLE 2.3 Data f o r the Pure Elements Element Melting Point [•c] Boiling Point [ ° c ] Vapour Pressure for Solid Element [torr] Vapour Pressure for Liquid Element [torr] Ref. Ni 1455 2920 log p = ~ 2 2 ^ Q ° - .96 log T + 13.6 log p = " 2 2 ^ ° ° - 3.02 log T + 16.95 37 Mg 650 1105 log p = ~ 7 ^ 8 ° - .855 log T + 11.41 log p = ~ 7 ^ 5 ° - 1.41 log T + 12.79 37 Ca 843 1483 -9350 log p = - 1.39 log T + 12.82 log p - * - 1.39 log T + 12.45 37 Al 659 2450 log p = " 1 6 3 8 ° - 1.0 log T + 12.32 37 - 55 -2.4.3 Magnesium and Calcium In Nickel and Iron Alloys As pointed out in Section 2.4.1 the thermodynamic data of dilute 55 56 i r o n so lut ions are better known than those for nickel solutions ' Because of that, when data for nickel alloys are lacking, many Investigators apply those for iron as a best approximation. While this may be a val id approach for many systems, In the case of magnesium and calcium i t is probably far from correct. While the Mg-Fe phase diagram is incomplete, as can be seen in Figures 2.19 and 2.20 the binary systems Mg-Fe and Mg-Ni are essentially 57 58 opposites ' . Nickel-magnesium-exhibits complete so lubi l i ty in the l iquid phase and two intermetallic compounds in the sol id phase, whereas iron-magnesium has an extensive misc ib i l i ty gap in the l iquid phase and no sol id intermetallic phases. The situation is similar for the calcium-nickel and calcium-iron systems. The Ca-Fe phase diagram is 59 even more tentat ive than the Mg-Fe diagram , Figure 2.21, but i t is well known that the so lubi l i ty of calcium in l iquid iron is only 0.032 60 weight percent • As in the nickel-magnesium system, nickel-calcium exhibits several solid intermetallic compounds and complete so lubi l i ty in the liquid** 1 , as can be seen in Figure 2.22. In terms of act iv i ty data one can then expect that the Raoultian ac t iv i ty coefficients of Ca and Mg w i l l be larger than one in iron, as in these systems the l ike atom attractions are stronger than the unlike - 56 -1600 1400 1300 0° >200 3 a looo i> °r goo E £ 800 700 Weight Percent Iron 9 1 ? ? * L L + (dFe) ^r.'I . - . t tBBS / L + ( 7 F e ) 812* / L + (aTt) — ( M g ) - • •! i ( M l ) + ( aFe ) . 0 02 0.4 0.6 0.8 1 12 1.4 1.6 Mg Atomic Percent Iron 1600 1500 1400 1300 1200-1100 1000 900 800 700 600-500 400 992 Weight Percent Iron 99.4 99* 99.8 T1 '!•"> ' ' L + ( W e ) \ ( «» ) . . . I M f l t t . L + ( 7 F e ) L t- ( o F e ) 04j£E ( M f ) + ( a F e ) 98.2 98.4 98* 98.8 99 99.2 99.4 99* 99.8 100 Atomic Percent Iron Fe Figure 2.19 The magnesium-iron binary phase diagram 5 7 . Figure 2.20 The magnesium-nickel binary phase diagram . - 58 -1600 O o uf a tr. ui tt 2 bl r-I-Z0O • f ^ LIQOGcO » (6-Ffel I 1 ATM. B.RofCo aoo 4 0 0 -VAR <Ca> f UQ.(Fe) " iiaT <c£> "V "uaTcFeY 8*tO, Mf». »f Ca (t-Ca.) + (oc-fe.) A64, C a a * « * («-Ca'> v «*-Fe} 1636. M.R«f Fe 1392. F« »V 8 911, F« * * J * Ca ATOM % PB Fe Figure 2.21 Schematic calcium-iron binary phase diagram . Figure 2.22 The calcium-nickel binary phase diagram . - 60 -atom attractions. In contrast, in nickel solutions the act iv i ty coefficients of Ca and Mg ought to be smaller than one as the intermetall ic compounds indicate unlike atom attraction. This is also 6 2 confirmed by Meysson and Rist for n i c k e l and i r o n - r i c h solutions containing calcium as shown in Figure 2.23. This l i terature survey w i l l therefore concentrate on magnesium/calcium in nickel solutions. 6 3 deBarbadi l lo thoroughly surveyed published data for Mg and Ca in nickel-base al loys . Much of this review w i l l be based on his paper. The act iv i ty of calcium in nickel and iron alloys has been 62 measured using a pseudo isopiestic technique at 1480°C . The results are shown in Figure 2.23. As can be seen, the resulting act iv i ty c o e f f i c i e n t at inf ini te d i lut ion , y° , is equal to 0.4. While act iv i ty \^ a data for sol id nickel-magnesium alloys of a l l compositions are 64 available l i t t l e experimental work has been done on the l iquid al loys . 6 5 Schmahl and Sieben measured the vapour pressure of magnesium over eight nickel-magnesium al loys . Two of these al loys, at molar fractions of 0.95 and 0.89 of magnesium were in the l iquid state at temperatures 63 of 580 to 700°C. deBarbadillo extrapolated the data given by Schmahl and S i e b e n 6 5 a t 750°C to 100% n i c k e l as shown in Figure 2.24. This treatment yields an estimate of y° =0 .1 . Mg 6 3 deBarbadi l lo also discusses the influence of other alloying - 61 -Figure 2.23 Activi ty of calcium In some Ni-Ca and Ni-Fe-Ca alloys as a function of the molar fraction of calcium • - 62 -w /o MAGNESIUM 0 10 20 30 40 50 60 70 80 90 100 <Vb MAGNESIUM Figure 2.24 Act iv i ty of magnesium in nickel-magnesium binary a l l o y s b J . - 63 -elements on the so lubi l i ty of magnesium in nickel a l loys . For instance, iron and chromium decreases the magnesium so lubi l i ty . While insufficient data are available deBarbadillo also proposes a tentative ternary l i q u i d phase diagram for the Fe-Ni-Mg system. This diagram is reproduced in Figure 2.25. Figure 2.26 reproduces estimated act iv i ty data based on the limited data for the binary Ni-Mg system^ and data for the system Si-Fe-66 63 Mg . deBarbadi l lo added magnesium to binary n i c k e l a l loys in a furnace open to atmosphere. Essentially he found that high nickel (>50%) alloys retained a l l of the 3% additions seen in Figure 2.27. This indicates a very low act iv i ty coefficient in these al loys . 2.4.4 Deoxldation Equi l ibr ia A deoxldation reaction in a l iquid metal may be written^ 7 x M (%) + y 0 (%) <- M 0 where M Is the deoxidizing element added to the solution. Then a M 0 M 0 x 7 K = * y _ (2-18) [ % M ] x f* OF fyQ - 64 -Figure 2.25 Estimated liquidus surface in Fe-Ni-Mg system and range of magnesium-rich phases observed after so l id i f icat ion of Fe-Ni a l l o y s 6 3 . - 65 -- 66 -i 1 1 1 1 1 1 1 r • MOLYBDENUM J I I I I I I I I 90 80 70 60 50 40 30 20 10 0 (N£M)< ' *» Figure 2.27 Estimated theoretical and effective solubi l i ty of magnesium in nickel alloys based on Figure 2.26 and experiments . - 67 -or log K = log a M Q - x(log %M + log f^) -y (log %0 + log f Q ) (2.19) x y where K is the equilibrium constant. Deoxidizing elements have great M a f f i n i t y to oxygen. Hence, the oxygen metal interaction parameter, e ,^ i s negative and large, in absolute terms generally much larger than the M self- interaction parameter e „ . M Contents of the deoxidizers A l , T i , and V in iron solution are plotted versus oxygen content in Figure 2.28. As can be seen, the deoxidizing equi l ibria exhibit minima, which in terms of f i r s t order 67 interaction coefficients can be expressed (%M) = " ° M 4 3 4 X M (2.20) min yeQ + x eM Deoxidation equi l ibria for the elements Mg, Ca and Al w i l l be discussed. Published data for these elements in iron or nickel solution are summarized in Tables 2.4 to 2.9. - 68 -oi 1000 800 500 400 300 200 -100 I 1 1 1 I I I 0.2 0.S 1.0 2.0 5.0 10 20 wt.% Figure 2.28 Solubi l i ty of oxygen vs (a) aluminum, (b) titanium, and (c) vanadium contents in iron at 1600°C. The curves are calculated on the basis of a f i rs t order interaction formalism with (a) £ Q = -360, (b) £Q = -87, ( O ^ o = ~ 2 7 * 7 * T h e points are from experimental work - 69 -TABLE 2.4 Behaviour of Deoxidlsers and Oxygen at Infinite Dilution ln Liquid Iron Element Y ° (1873 K) M (pure) t M (X, !) CG° (X), cal/mole M (pure) t M(%, !) &'(%), cal/mole Al (!) Ca (JO 1/2 0 2(g) 0.029 2240 -1500 + 1.03 T -9430 + 20.3T -15100 - 6.67 T -9430 + 11.8T -28000 - 0.69 T TABLE 2.5 Behaviour of Deoxidizers and Oxygen at Infinite Dilution i n Liquid N i c k e l 5 6 Element Y° (1873 K) M (pure) ? M (X,I) M (pure) t M (%, !) CG° (X), cal/mole tG0 (%), cal/mole Al (!) 0.0002 -37000 + 2.98 T -37000 - 4.61 T Ca (!) 0.6 (?) -1920 -1920 - 8.37 T Ca (g) 1.27 -44520 + 24.25 T -44520 + 15.88 T Mg (!) 0.32 (?) -4200 (?) -4200 - 7.38 T (?) Mg (g) 2.2 -38910 + 22.34 T(?) -38910 + 14.96 T (?) 1/2 0 2 (g) — — -16970 + 0.336 T - 70 -TABLE 2.6 F i r s t Order In te rac t ion C o e f f i c i e n t s , e^ i n L i q u i d I ron at 1600 oC (References in Brackets) i j * Al Ca 0 Al -0.0045(55) -0.047 (55) - 6.6 (55) Ca -0.072 (55) -0.002 (55) 0 -3.9 (55) -3.9 (73) -4.6 (72) -5.2 (68) -1 (74) -62 (68) -0.20 (55) TABLE 2.7 F i r s t Order In te rac t ion C o e f f i c i e n t s , e^ i n L i q u i d N i c k e l at 1600°C (References in Brackets) i j * Al Ca 0 Al 0.08 (56) Ca 0.004 (56) 0 -1 (74) 0 (56) - 71 -TABLE 2.8 Deoxldat ion E q u i l i b r i a i n Iron A l l o y s Deoxldation Reaction* K T (°C) Ref. 2 Al + 3 0 t A1 2 0 3 (s) 13 1.8 x 10 1 J 13 7.9 x 1(T 13 1.7 x 10 J 1600 1600 1600 73 72 68 Ca + £ + CaO(s) 6.2 x 105 1.1 x 106 1600 1600 68 69,70 Mg + 0 t MgO(s) 5 x 105 1600 69,70 TABLE 2.9 Deoxldat ion E q u i l i b r i a i n N i c k e l A l l o y s Deoxldation Reaction* log K K T (°C) Ref. 2 Al + 3 0 t A1 2 0 3 (s) 6 0 7 9 5 - 18.81 T . 4.48 x 101 3 1600 56 Ca + 0 t CaO (s) 27959 L l „ - 6.59 T 2.16 x 108 1600 56 Mg_ + 0 t MgO (s) 26009 _ 7 > 3 g T 3.2 x 106 1600 56 * Henrian standard state on a weight % basis for the dissolved elements. - 72 -2.4*4.1 Magnesium and Calcium No experimental study of the deoxidation equi l ibria of Mg and Ca in nickel-base alloys has been found in the l i terature . Some work has 68—71 been done on these elements in various iron-based solutions . While these data may be useful in establishing deoxidation equi l ibria in nickel-base alloys the different so lubi l i ty of Mg/Ca in the two solvents cannot be forgotten. 68 Gustafsson f i tted solubi l i ty data for the calcium-oxygen system from several investigations using regression analysis. An interaction Ca c o e f f i c i e n t , e^  of -62 is suggested in conjunction with an equilibrium constant K„ n of 1.6 x 10 6 . This equilibrium constant is inconsistent OaU with one deduced from the work of Sponseller^^ of roughly 10 but f i t the data better. G a t e l l i e r et a l ^ ' 7 ^ measured the a c t i v i t y of oxygen using an oxygen probe in iron solutions. The melts were pre-deoxidized with carbon and aluminum and then treated with either magnesium or calcium. Unfortunately the raw data, for Instance, the contents of oxygen and alkaline earth metals, are not presented. Equilibrium constants —6 —7 K^gQ = 2 x 10 and K r j a g = 9 x 10 are given, but without oxygen interaction parameters. - 73 -Voronova discusses the treatment of hot metal with magnesium. A solubi l i ty product of 5 x 10 7 at 1600°C can be deduced from equations given. Voronova presents a calculated graph along with plant data, both presumably at 1650 K as seen in Figure 2.29a and b. Clearly, the plant data do not f i t the calculated graph. 2*4.4.2 Aluminum Investigations of the deoxidation equilibrium with aluminum in l iquid iron solutions are abundant and only a few examples are considered 68 7 2 — 7 3 here ' . In c o n t r a s t , l i t t l e is published on the aluminum deoxidation equilibrium in nickel . Hence, most of the data have been taken from a compilation^^. 72 McLean e q u i l i b r a t e d iron melts with H2/H2O gas mixtures to determine the act iv i ty of aluminum-oxygen. The same equilibrium was 73 72 invest igated using an oxygen probe by Fruehan . Both McLean and 73 Fruehan suggest values of the deoxidation equilibrium constant and Al 6 interaction coefficient e^  that are not vastly different (see Tables 2. 68 and 2 .8 ) . On the other hand, Gustafsson suggests that the older data are better represented by a second-order regression-fitted expression than by the tradit ional interaction coefficients. As a compromise he also gives values for the tradit ional equilibrium constant and interaction coefficient. - 74 -Vachet et a l compared a c t i v i t y coe f f i c i ent s of oxygen and aluminum in iron, nickel and cobalt solutions. They suggest that the same interact ion parameter can be applied for a l l three solvents as differences in y°/.-,/yX tend to compensate. - 75 -(a) 0 0,005 0,010 0,0/5 [r\q],% 0 ,/<7_jr% o o 02 < o Q K > C ) o ° X X X X 1 (b) 6 ra m 18 Figure 2.29 (a) Calculated equilibrium contents of oxygen and magnesium in iron. (b) Actual oxygen and magnesium, contents in iron. 1- Mg introducted in a methane stream and 2- in an air stream - 76 -3. Experimental Work 3.1 Equipment The major equipment used in this work consists of a vacuum system containing a molybdenum resistance furnace. The furnace and vacuum system were bui l t to f i t in the beam path of a commercial Atomic Absorption Spectrophotometer. Figure 3.1 shows an overview of the system in position in the Atomic Absorption Spectrophotometer. 3.1.1 Atomic Absorption Spectrophotometer To generate the monochromatic l ight and measure the absorption, a Perkin Elmer model 306 Atomic Absorption Spectrophotometer was used. An e a r l i e r model of th is instrument has been described by Kahn 7 5 . The spectrophotometer is schematically shown in Figure 3.2, with the "sampling burner" replaced by the vacuum bel l jar in this study. Br ie f ly , features of this type of Instrument include high s tab i l i t y and the a b i l i t y to discriminate between emission from the vapour source and the hollow cathode lamp. This is accomplished by using a double beam system and by chopping the l ight from the lamp. For - 77 -Figure 3.1 The experimental furnace and vacuum system in position in the Atomic Absorption Spectro-photometer. - 78 -J R E F E R E N C E B E A M j W A V E L E N G T H ( C O U N T E R I S P E C T R A L ROTATING S A M P L I N G B E A M S O U R C E C H O P P E R B U R N E R N E C O M B I N E R MONOCHROMATOR PHOTOMULTIPLIER OE T E C T O R 4 Figure 3.2 Block diagram of an Atomic Absorption Spectro-photometer. Emission from the line source is sp l i t into sample and reference beams, then recombined and passed through monochromator. Signal from photo-detector is amplified and fed into c ircui try which produces a manual electronic nul l . The sampling burner is replaced by the vacuum be l l - jar in this study. - 79 -the experiments in this work either the spectrophotometer d ig i ta l meter or a separately connected Honeywell Electronic 196 recorder was used to read the output. 3.1.2 Vacuum System A Pyrex bel l jar (Figure 3.3) with commercial-grade ground and polished quartz windows was made to f i t in the beam path of the Atomic Absorption Spectrophotometer. The windows were attached to a short length of Pyrex tubing with epoxy glue. The window-pieces could in turn be attached to the bel l jar with a glass-O-ring-glass seal . The removable design was chosen to fac i l i ta te cleaning, and to make replacement of the windows possible. In the wavelength range of the strongest magnesium absorption line (285 nm) quartz windows transmit a 76 minimum of 90% of the l i g h t . Thus, the absorption measurements are distributed minimally. In this case a design where a complete ce l l is heated to the experimental temperature, as has been done before (see Chapter 2.2), can not be used. This simpler design can only be used for temperatures up to about 8 7 0 ° C , which is the tr idymite t r a n s i t i o n temperature for q u a r t z 7 7 . The b e l l jar is sealed to a water-cooled brass bottom plate with a ground glass-0-ring type of seal. The brass plate is part of a conventional metal vacuum system (Figure 3.1) consisting of a CEC VMF-10 - 80 -Figure 3.3 Schematic drawing of the vacuum be l l - jar containing the molybdenum resistance furnace. - 81 -o i l diffusion pump backed by an Edwards E2M8 double stage rotary pump. The pressure is monitored by an NRC thermocouple gage and ionization -5 gage with corresponding meters. Vacuums of 10 torr were achieved. 3.1.3 Furnace The furnace part of the system can be seen in detai l in Figure 3.3. As the furnace was to be used close to electronic equipment, a resistance heated furnace was chosen instead of an induction furnace. This caused some problems as the molybdenum heating c o i l is prone to break. The heating c o i l was made from 0.9 mm thick molybdenum wire and supported by three notched pure recrystal l ised alumina rods to prevent sagging. The rods were in turn held In place by two 0.25 mm thick molybdenum end plates. Two 6 mm diameter copper rods connect the furnace winding through the bottom plate using Kovar vacuum power feed- throughs. Power was supplied by a Metals Research Variac high current transformer. Two to three layers of either molybdenum or zirconium radiation shields surrounded the furnace. The zirconium radiation shields served the additional purpose of oxygen (and nitrogen) getters. The zirconium radiation shields work as getters at temperatures of roughly 700°C to 1000°C. Thus, at the lower temperatures two Zr radiation shields would be used, while at the higher temperatures two inside molybdenum shields - 82 -and an outside Zr radiation shield is more suitable. The furnace was designed to make replacement of the radiation shields, as they broke or became oxidized, convenient. The complete assembly is supported by a threaded copper rod attached to the bottom plate. To protect the quartz windows during experiments, a strip of zirconium f o i l served as a window shutter. When an absorption reading was to be made, the shutter could be manipulated using magnets. 3.1.4 Knudsen Cells A Knudsen ce l l used in the t in alloy experiments and some nickel alloy experiments is shown in Figure 3.4. These cel ls were machined from molybdenum. The top of each ce l l can hold an ori f ice plate securely by f i t t ing a spring-loaded circular segment of 0.9 mm thick molybdenum wire into the top notch. The alloys were contained inside the c e l l in pure Al jO^ c r u c i b l e s . However, in a l loy experiments at 1470°C these cells deteriorated rapidly, probably because of the direct contact with metal vapours. They were therefore replaced by an arrangement of an alumina tube, f i t t ing the inside crucibles snugly, as shown in Figure 3.5. An isopiestic type of Knudsen ce l l was used to calibrate the system. A schematic drawing of the ce l l can be seen in Figure 3.6. The c e l l was fabricated from a thin-walled tantalum tube with a molybdenum - 83 -s c a l e Figure 3.4 Molybdenum Knudsen c e l l . - 84 -ORIFICE PLATE ALLOY Scale 2:1 Figure 3.5 Alumina Knudsen c e l l . - 85 -33 Orifice plate, Mo -Thinwalled Ta tube •Bottom of resistance furnace winding Baffle radiation shield .Mg Tight- fitting plug -Thermocouples scale V-1 Figure 3.6 Isopiestic Knudsen c e l l . - 86 -machined top. The dimensions of the tops of the two metal types of cel ls are ident ica l . Thus, i f desired, the same orif ice plates could be used for both calibration and alloy experiments. The isopiestic c e l l was f i tted with four baffle-type radiation shields designed not to Impair the molecular flow of magnesium from the bottom part of the tube. The source of magnesium vapour for the calibration experiments was a piece of solid magnesium roughly f i t t ing the cross-section of the tube and approximately 12 mm thick. F ina l ly , to minimize back-streaming of vapour, the tube was f i tted with a t ight - f i t t ing plug of either Inconel or copper below the magnesium slug. The orif ice plates were made of 0.04 mm thick molybdenum f o i l . To produce consistent orifices the plates were pierced with a machinist scribe on a surface of four layers of paper on top of a steel plate. The orif ices obtained were not round, but the area was reproducible. The ori f ice areas were measured on a Leitz surface image analyser. 3.1.5 Temperature Determination The furnace temperature was continuously measured with a thermocouple installed between the furnace co i l and the inside radiation shield. The temperatures of the orif ice plates were calibrated with a dummy plate with a separated thermocouple junction. Similarly, the temperature inside the crucible was calibrated to the stationary - 87 -thermocouple using a beaded thermocouple. A l l thermocouples were fed through the bottom plate using compressed rubber seals. The types of thermocouples used are summarised in Table 3.1. At 1470°C platinum-based thermocouples were used where good mechanical duct i l i ty was needed. However, for the stationary thermocouple tungsten 32% rhenium versus tungsten 25% rhenium was more suitable as i t gets poisoned at a slower rate. The hot junctions of a l l thermocouples were periodically renewed to ascertain that false temperature readings were not obtained by a poisoned thermocouple. In addition, the thermocouples were occasionally calibrated using the melting points of pure gold and 78 nickel as reference points The furnace temperature was continuously monitored with a Honeywell Electronik 196 recorder, and the power input manually adjusted to obtain a steady temperature. For accurate measurements of the temperature during calibration or immediately before an absorption reading the thermocouples were switched to a PYE portable potentiometer. Correct measurement of the temperature attained by the top of magnesium slug used in the calibration experiments is v i t a l as i t direct ly gives the vapour pressure. Measurement of the surface temperature by a thermocouple attached to the surface was rejected as - 88 -TABLE 3.1 SUMMARY OF THERMOCOUPLE TYPES USED Position in System Test Experiments at 900°C Experiments at 1470°C Stationary Chromel-Alumel W 3% Re - W 25% Re Dummy Orifice Plate Chromel-Alumel on Stainless Steel. Plate Pt 30%Rh - Pt 6%Rh on Pt plate Beaded - inside Chromel-Alumel Pt 30%Rh - Pt 6%Rh - 89 -attaching a thermocouple to magnesium proved impossible. Furthermore, i t was suspected that the presence of the thermocouple could alter the temperature reading. The arrangement f inal ly arrived at can be seen in Figure 3.7. It consists of two butt-welded thermocouples running perpendicular to each other at different distances from the top surface. The holes containing the thermocouple junctions were dr i l l ed as narrow as pract ical ly possible (0.9 mm diameter) and thin (0.33 mm diameter) wires were used to prevent cooling of the junction by conduction along the wires. The temperature measurements were taken to represent the average temperature at the specific height in the magnesium slug. 3.2 M a t e r i a l s 3.2.1 Bas ic A l l o y s The basic alloys used in this project are identified In Table 3.2. Impurity content in the magnesium containing alloys has not been analysed as these alloys are extremely dilute in the experimental a l loys . 3.2.2 T i n A l l o y s Master alloys containing up to 1000 ppm of magnesium were prepared by melting in the experimental vacuum furnace. For this purpose a 25 mm outside diameter alumina crucible covered by an alumina - 90 -s c a l e U: 1 Figure 3.7 Arrangement of thermocouples in the magnesium slug used for cal ibrat ion. Measurements in mm. - 91 -TABLE 3.2 BASIC ALLOYS USED IN THIS PROJECT Alloy Composition Comments Pure Mg Mg >99% Solid cast alloy used for Mg slug and Mg-Sn al loys . Ni-Mg Ni Mg C 83.7% 14.8% 1.8% Granular alloy used for Ni-Mg master alloy Inco Nickel 270 Ni C Fe Mn,S,Si , Cu, Cr Ti and Co a l l 99.98% 0.01% 0.003% 0.001% Solid bar - major Ni source. Glidden Electro lyt ic Iron Fe C Co Pb Mo Ni 0 Others, 99.91% 0.0025X 0.005% 0.010% 0.005% 0.060% 0.015% <0.005% ea Fisher Chromium Metal Cr > 99% - 92 -disc was used. The appropriate amounts of Mg and Sn were placed in the crucible and the system sealed. The vacuum system was pumped overnight to ensure a good vacuum and the contents of the crucible melted. The furnace was then held at temperature for a minimum of half an hour to ensure homogeneity of the a l loy . The master alloy together with pure t in in different proportions was then melted in each vapour pressure experiment. Starting contents of magnesium varied from 500 to 1000 ppm. 3.2.3 Nickel Alloys Master alloys containing about 2000 ppm magnesium were prepared by melting the granular nickel-magnesium alloy with appropriate amounts of nickel 270. The alloys were melted in alumina crucibles in a controlled atmosphere induction melting furnace. To ensure a clean, low oxygen atmosphere the furnace was evacuated and re f i l l ed with dried, hot 79 titanium-treated argon several times before melting. The melt was held at approximately 1500°C for 15 minutes to ensure a homogenous a l loy . The nickel master alloy was combined with suitable amounts of nickel , iron, chromium and aluminum to produce each experimental sample. Starting contents of magnesium varied from 1000 to 2000 ppm. 3.3 Experimental Procedure The following procedure, with minor modifications, was used for both calibration and alloy experiments. The details pertaining to the specific type of experiments w i l l be described in sections 3.4 to 3.6. 1. Clean the bel l jar and windows thoroughly and dry in drying oven. 2. If necessary, clean any radiation shields that w i l l be reused, and the window shutter. 3. Position the Knudsen ce l l in the furnace. 4. Replace a l l radiation shields. Make sure that oxidized zirconium shields are replaced by new shields. 5. Assemble the bel l jar parts and put the shutter in position. Seal the system. 6. Pump the system for a minimum of an hour or unt i l a vacuum of -4 10 torr or better is achieved. 7. While the vacuum system is pumping down, start the atomic absorption 80 spectrophotometer . The standard procedure for s t a r t i n g the spectrophotometer can be used except no burner is installed and no flame l i t . It is also important that the lamp current is kept constant (in these experiments it was kept at 6 mA) to make the cal ibration graph va l id . The strongest magnesium line at 285 nm was used together with a s l i t width of 0.7 nm. - 94 -8. Put the bel l jar into the beam path, and adjust the position unt i l the minimum absorption is observed. Zero the spectrophotometer. 9. When the spectrophotometer is stable, the window shutter is closed and the power turned on. The furnace is rapidly heated to the desired temperature. 10a.For cal ibrat ion, the furnace is then left to run for 2-4 hours. Readings of temperature and absorption are then taken every half to f u l l hour unt i l the measurements s tabi l ize . 10b.For an alloy experiment, the f i r s t measurement is taken after half an hour at temperature and additional readings taken every 15 minutes up to 1 hour. 11. Immediately after the last absorption reading the furnace is turned off. When the furnace has cooled down to 200-500°C a stable f inal absorption reading is made. The f inal low temperature reading plus a blank reading is deducted from the last absorption reading. This number then constitutes the result of a particular experiment. 3.4 Calibration The isopiestic Knudsen ce l l used in the calibration experiments has been described in section 3.1.4. The calibration graph was produced by heating the ori f ice plate to the same temperature as the corresponding alloy experiments. Thus, a beam of magnesium atoms of the same shape and velocity was produced in both cases. - 95 -The slug of magnesium was heated only by radiation from the radiation shields and the tantalum tube. By varying the height of the magnesium piece In the tube, the temperature could also be varied. In this manner a calibration graph could be produced. 3.5 Test of the Method To prove that the system employing both a novel atomic absorption application and a novel isopiestic Knudsen c e l l does indeed work, measurements were made on tin-magnesium alloys. This alloy system was 49 selected as i t is well documented . The experiments were conducted using the Knudsen c e l l previously described i n . 3.1.4. To prevent oxidation of magnesium in the c e l l , both the wall and the orif ice plate were lined with zirconium f o i l . The experiments were conducted as described in 3.3 at an orif ice plate temperature of 9 0 0 ° C At the conclusion of each experiment the 3 g samples were collected and later chemically analysed. Given the chemical composition 49 and the a c t i v i t y coe f f i c i en t , the a c t i v i t y and hence the vapour pressure of magnesium over the t in alloy can be calculated. - 96 -3.6 Nickel Alloy Experiments Similar to the t in experiments, the nickel alloy experiments were conducted using the basic Knudsen c e l l , and the alumina "tube ce l l" . The melts were also, as before, contained in pure alumina crucibles. For each experiment, desired amounts of the master nickel-magnesium al loy, pure nickel , and for the ternary alloy experiments some Fe or Cr, were weighed into the alumina crucible. The compositions of these alloys with regard to the major elements were taken to be determined by the weights. The experiments were conducted at 1470°C. Generally, the time at temperature was shorter than for the test experiments. The f i r s t absorption reading was taken after 20 minutes and the second and usually f ina l reading at no more than 40 minutes. The resulting samples, weighing roughly 5-12 grams, were collected for later chemical analysis. 3.7 Chemical Analysis Analysis for magnesium and aluminum in a l l alloys followed the same basic procedure. The samples were digested in acid. The resulting concentrated solutions were treated in the standard manner to obtain dilute solutions suitable for flame atomic absorption chemical analysis. The accuracy in resulting metal alloy magnesium and aluminum content was ±3 and ±25 ppm. Oxygen analysis was performed using the inert carr ier-- 97 --gas method. The uncertainty of the this analysis was ±5 ppm. The procedures for chemical analysis are described in detai l in Appendix B. - 98 -4. Results and Discussion 4.1 Calibration Two methods of cal ibration were attempted. The f i r s t method entails heating pure magnesium to different temperatures in a standard Knudsen c e l l lined with an iron crucible resulting in varying magnesium vapour pressures. In this method the temperature of the orif ice varies with the magnesium temperature. Results from these cal ibration experiments are given in Table 4.1. The second method entails using the isopiestic Knudsen c e l l . Hence, the temperature of the magnesium slug is varied by moving the slug up and down while the or i f ice plate is kept at a constant temperature. Calibration experiments using this method were performed at or i f ice temperatures of 900 to 1470°C corresponding to the series of test experiments on t in alloys and the nickel experiments. The results of these experiments are summarized in Table 4.2 and 4.3. The results of the three sets of calibration experiments are summarized in Figure 4.1. As can be seen, the results of experiments - 99 -TABLE 4.1 Results of Calibration Measurements with Pure Mg,  Using a Standard Knudsen Cell Experiment Absorbance (measured) T[ ° C ] (measured) (Eq.Table 2.3) 1 0 8 PMg A 0.295 439 1.46 x 10~5 -4.84 0.315 446 1.84 x 10"5 -4.74 0.450 474 4.54 x 10"5 -4.34 0.476 478 5.14 x 10~5 -4.29 0.560 498 9.33 x 10"5 -4.03 B 0.075 369 0.10 x 10~5 -6.00 -5 0.115 382 0.18 x 10 -5.74 -5 C 0.140 388 0.22 x 10 -5.66 -5 0.285 432 1.14 x 10 -4.94 D 0.320 450 2.10 x 10~5 -4.68 0.500 478 5.14 x 10~5 -4.29 0.500 485 6.36 x 10~5 -4.20 - 100 -TABLE 4.2 Results of Calibration Measurements with Pure Mg, using  an Isopiestic C e l l . Orifice Temperature = 900°C Absorbance T[ °C] PMg[atm.] log p (measured) (measured) (Eq.Table 2.3) 0 354 5.4 X lO" 7 -6.27 0.671 420 7.6 X lO" 6 -5.12 0.499 395 2.9 X l O ' 6 -5.53 0.251 375 1.3 X lO" 6 -5.88 0.541 390 .2. ,4 X- lO" 6 -5.62 0.683 400 3.5 X l O ' 6 -5.45 0.992 430 10.7 X l O ' 6 -4.97 0.542 388 2.2 X l O ' 6 -5.63 0.133 382 1.7 X io' 6 -5.76 0.019 362 7.6 X lO" 7 -6.12 0.85 423 8.3 X IO"6 -5.08 - 101 -TABLE 4.3 Results of Ca l i b r a t i o n Measurements with Pure Mg, using  an Isopiestic C e l l . O r i f i c e Temperature = 1470°C Absorbance (measured) T [ ° C ] (measured) PM g[atm.] (Eq.Table 2.3) log p 0.94 431 11.05 x 10"6 -4.96 0.67 406 4.46 x 10~6 -5.35 -7 0.20 368 9.82 x 10 -6.01 0.69 409. 5.00 x 10~6 -5.30 0.23 371 1.11 x 10~6 -5.95 1.0 0.8 LXJ O ^0.6 CD cr CO < 0.2 - ' DATA FR6M 1 • Standard cell A — Isopiestic cell, 900 °C - O —Isopiestic cell,U70°C 0 -6.5 o -60 -5.5 -5.0 -45 tog PMg(atm) -4\0 Figure 4.1 Summary of calibration experiments. - 103 -using the isopiestic c e l l yield almost identical graphs, which can be represented by the regression f i t ted equations, at 1470°C. Equations 4.1 and 4.2 are subsequently used for cal ibration of the t in test experiments and the nickel experiments. Further, as can be seen in. Figure 4.1 the cal ibration using a standard c e l l yields an entirely different relationship. The reasons for the discrepancies w i l l be discussed in the following section. 4.1.1 Cause of Discrepancies Possible explanations of the variation in calibration results may be found in the following areas: - Doppler shift - formation of dimers or oxides, and physical reasons Absorbance = 4.82 + 0.778 log p [atm] (4.1) Absorbance = 4.46 + 0.710 log p [atm] (4.2) - 104 -The Doppler sh i f t ' occurs as the atoms are emitted from the Knudsen ce l l or i f ice in directions other than perpendicular to the light beam. As the speed of the atoms varies with the temperature, there is a poss ib i l i ty that different fractions of the atoms absorb at the different temperatures. Calculations (see Appendix C, p 152) show however, that the Doppler shift is very small in the range of interest. Thus i t is unlikely that a Doppler shift causes the discrepancies between standard ce l l and isopiestic c e l l calibrations. The likelihood of formation of dimers should also be considered. Dimers may form according to the equilibrium 2 Mg(g) t Mg2(g) (4.3) —3 83 which has an equi l ibrium constant of 10 or less for the considered temperatures. Hence, dimer formation is not l ike ly to affect the absorption measurements. Oxide formation in the gas phase can be assumed insignificant for the isopiestic experiments as zirconium at temperatures of roughly 600 to 800°C was present as an oxygen getter in the system. As demonstrated by Figure 4.2, solutions of oxygen in zirconium w i l l form 84 p r e f e r e n t i a l l y to MgO at 1000°C . Further, as the pressure of Mg is only ~ 10 6 atm in the present system, the Mg - MgO line in Figure 4.2 - 105 -Figure 4.2 The relationship between oxygen partial pressures and compositions for the Ti-0 and Zr-0 systems at 84 1000°C . - 106 -would move approximately 270 kj up In the diagram, making MgO formation even more unlikely. The same situation applies to the isopiestic system although the temperature is s l ight ly lower. However, the standard ce l l cal ibration was carried out at temperatures below 500°C. At this temperature the zirconium does not function well as an oxygen getter for kinetic reasons. There exists therefore a poss ibi l i ty that a portion of the magnesium vapour was oxidized in these experiments with the result that the absorption readings were decreased. Another possible cause of the lower absorption when the standard c e l l was used is physical. After standard c e l l experiments, deposits of magnesium were observed on the radiation shields. Such deposits were not observed after the ' isopiestic c e l l ' experiments. This should not affect the fraction of the atomic beam that Intercepts the l ight path as no shields were placed direct ly in front, of the o r i f i c e . It does however indicate that at these lower temperatures, sticking of atoms may occur also ins ide the Knudsen c e l l . Such sticking-, which i s part icularly l ike ly i f the or i f ice plate is colder than the rest of the c e l l , would invalidate the Knudsen equation and cause fewer atoms to effuse. On the other hand, using the Isopiestic c e l l , the magnesium slug is always the coldest surface, and subsequent sticking is much less l i k e l y . The absorbance measures do not follow Lambert-Beer's law. The reasons for this are not well understood. - 107 -4.2 Test of Method on Tin Alloys The results of the test experiments on t in alloys are presented in Table 4.4 and Figure 4.3. The sol id line in Figure 4.3 represents the regression f i t ted graph from the isopiestic cal ibration at 900°C. The numbered points are the results of the t in experiments. As can be seen in Figure 4.3 the points show a fa ir bit of experimental scatter. This is to be expected as the work was carried out at very low pressures of magnesium. It can also be seen in the figure that, on average, the t in results show a good f i t with the cal ibration graph. This is taken as an indication that this novel method can be applied to determine the act iv i ty of magnesium in other al loys . Figure 4.3 and Table 4.4 also show that the results are independent of the ori f ice area within the given l imits . This is 37 reasonable considering the equation - p R (1 + A / a A g ) (4.4) where p eq = equilibrium vapour pressure, P K = determined vapour pressure, A = or i f ice area, - 108 -Figure 4.3 Results of the test experiments on t in al loys. - 109 -TABLE 4.4 Summary of Sn-Mg Experiments No Absorbance XMg (Chemical analysis) PM g[atm.] (Chemical Analysis & Literature Data) log PMg ORII 'ICE SIZE Area [mm^  ] Equivalent Diameter [mm] 1 0.951 0.0057 1.97 x 10"5 -4.70 0.063 0.28 2 0.955 0.0032 1.10 x 10~5 -4.96 0.063 0.28 3 0.624 0.0014 5.00 x 10"6 -5.30 0.063 0.28 4 0.954 0.0038 1.32 x 10~5 -4.88 0.063 0.28 5 0.992 0.0021 7.37 x 10~6 -5.13 0.52 0.82 6 0.807 0.0017 5.79 x 10~6 -5.24 0.52 0.82 7 0.941 0.0024 8.16 x 10~6 -5.09 0.022 0.18 8 0.720 0.0014 4.74 x 10"6 -5.32 0.022 0.18 - 110 -A = area of evaporating surface, and, s a = condensation coefficient In this case A / A g <0.003 and any influence would be smaller than the experimental scatter. The condensation coefficient is equal to one for most metals, hence p = p.,. req r K The pierced orifices are clearly not ideal . However, i t has been found that when collection techniques (see 2.3.1.2,b) are used Clausing correction factors are not needed. As this technique measures the absorption in a similar area directly over the ce l l i t is assumed that the effects of non-ideality may be neglected. It is possible that the irregular shape produced when piercing the orif ice may account for some of the experimental scatter. The l imit for molecular effusion, \/d>10, is not approached at either 900°C or 1470°C for magnesium. It is estimated to be larger than 3 10 in a l l cases. Both t i n and nickel have lower vapour pressures at the applied temperatures than the magnesium, and should not influence the mean free path. It should be noted that some of the restrictions of other Knudsen methods may not be applicable here. The calibration and experiments were run under conditions that were as similar as possible. For - I l l -instance, a l l orif ices for both calibrations and experiments, with the exception of the t in experiments, were punched in a consistent manner to produce an or i f ice diameter of roughly 0.20 mm. - 112 -4.3 N i c k e l A l l o y s 4 .3 .1 Pre l iminary Resul ts Original ly , chemical analysis of only magnesium in the alloys was performed. However, preliminary results indicated a strongly negative self interaction coefficient for magnesium. This is not reasonable as a negative coefficient would indicate attraction between l ike atoms. On the contrary, a positive coefficient is expected as several intermetallic Ni-Mg compounds form in the solid state. The results indicated that some other solute influenced the results . Oxygen is a prime candidate given that magnesium-oxygen should have a strongly negative interaction coefficient. Consequently, experiments were conducted where both magnesium, aluminum and oxygen were analysed. 4.3.2 A p p l i c a b l e Equ i l ib r iums Given that the samples were contained in aluminum oxide crucibles, an equilibrium including some oxide phase was suggested. The oxide layers on the inside of several crucibles were therefore analysed using Energy Dispersive X-ray analysis. In addition, the outside layer of a nickel button was analysed. While the results from the crucibles occas iona l ly showed higher than 50 molecular percent of Al^O^, the sample surfaces show almost exactly the composition of MgO^A^O^, a spinel . It is expected that the crucibles would show a higher than 50 - 113 -percent kl^O^ because the e lec tron beam penetrates the thin surface layer of spinel to the underlaying pure alumina. However, i t may be concluded that the oxide phase in dynamic equilibrium with the elements i n l i q u i d n i c k e l so lu t ion i s most probably the s p i n e l , MgO'A^O-j. (Original results of the EDX analysis are presented in Appendix D, page 157). It should be noted that no evidence of sulphur was detected during the analysis. Sulphur, given i ts high af f in i ty to magnesium, could otherwise also take part in a magnesium containing equilibrium. In view of the above discussion, the following reaction w i l l be considered Mg(g) + 2A1(%) + 40(%) «• MgO'Al 2 0 3 (s) . (4.5) Further, the reaction subject to experimental investigation was Mg(g) *• Mg (%). (4.6) It should be emphasised that these are dynamic equi l ibr ia and the chemical composition w i l l change with time. However, by analysing for the content of magnesium at the time the pressure was measured the e q u i l i b r i u m 4.6 i s "pinned down", as was also proven in the tin-magnesium alloy experiments. - 114 -The equilibrium equation for reaction 4.5 is v - M.A P Mg h Al h 0 where = equilibrium constant for reaction 4.5, ^ A = act iv i ty of M g O ' A l ^ , = vapour pressure of magnesium, atm, h ^ = Henrian act iv i ty of aluminum, and tig = Henrian act iv i ty of oxygen. The Henrian act iv i t ies can be expressed h Q = (%0) f Q , and h A 1 = (%A1) f M where f = the respective Henrian act iv i ty coefficients The act iv i ty coefficients can in turn be expressed log fQ = e ° (%0) + e A 1 (%A1) + ejj8 (%Mg) log f = e A J (%A1) + e^f (%Mg) + e ° (%0) - 115 -M As discussed in section 2.4.4, the oxygen interaction coefficient e^  is M g e n e r a l l y in absolute terms much larger than the metal-metal , e^, interaction parameters. For instance, for iron solutions, (see Table A l Ca 2 .6) , the parameters e ^ and e ^ are at least two orders of magnitude smaller than e^ in absolute numbers. Similarly, the e^  is an order of magnitude smaller than the e^ coefficient. This reasoning applies as Ca wel l for calcium-oxygen interaction as has been given as -62, Ca three order of magnitude larger than Although these are values for iron solutions, a similar relationship can be expected for nickel M 0 solutions. Hence, i t w i l l be assued that e^  and e^  can be neglected. Equation 4.7 can then be rewritten in logarithmic form, incorporating relationships 4.8-4.11, to give log K = log (a^) - log (p M g ) - 2 log ( h M ) - 4 log (hQ) = = log (a M a ) - log (p M g ) - 2 log (%A1) - 4 log (%0) - 2 e°kl - 4 [e A 1 (%A1) + e M g (%Mg) ] (4.12) Further, as M 0 ^Al Al 6A1 = M Q e 0 (4.13) - 116 -and a^=l , equation 4.12 can be reduced to log K = -log (p ) - 2 log (%A1) - 4 log (%0) Mg r _ _ 7 , i / • 5 ' A I \ 1 Al -4 (%Mg) e*g- [3.37 (%0) + 4 (%A1)] e^  (4.14) Given the experimental data in Table 4.5 and l iterature values Me Al for K, equation 4.14 has two unknowns, e^  and . However, the value for K in available l i terature is probably erroneous and wi l l also be treated as an unknown. The discrepancies between the l i terature value and the calculated value for K wi l l be discussed in section 4.3.3.1. 4.3.3 S t a t i s t i c a l Model Mg A l To ca lcu late , and e^  multiple regression analysis with two predictors was applied. A program in the commercially available computer package "Minitab" was used to perform the s ta t i s t i ca l 85 86 calculations ' . The program regresses to a graph of the form y = B Q + B l X l + B 2 x 2 (4.15) on given data. In this case y = log (p ) + 2 log (%A1) + 4 log (%0), - 117 -TABLE 4.5 Data from Nickel-Magnesium Experiments Experiment PMg [ atm ] Weight % Mg Weight % Al Weight % 0 No. 1 1.8 x 10"6 0.0035 0.0332 0.0026 2 0.8 x i o " 6 0.0006 0.0257 0.0018 3 0.6 x l O " 6 0.0002 0.0132 0.0020 4 0.5 x i o " 6 0.0001 0.0130 0.0017 5 1.0 x i o " 6 0.0001 0.0260 0.0019 6 2.1 x i o " 6 0.0012 0.0513 0.0030 7 2.0 x i o " 6 0.0083 0.0107 0.0021 8 0.7 x IO" 6 0.0003 0.0255 0.0017 9 1.8 x i o ' 6 0.0022 0.0298 0.0019 - 118 -B Q = l o g ^ , Al B l = e o • c = - [3.37 (%0) + 4 (%A1)], Mg '0 ' x 2 = -4 (%Mg) Sample computer output is given in Appendix E, page 162 together with explanations of the output. The calculations yield the following results: log K 1 = 22.0 ± 0.17 e A 1 = -16.7 ± 1.3 e^8 = -27.7 ± 6.2 Mg While the standard deviation of e^  is large, the calculated parameters are a l l s ta t i s t i ca l l y s ignif icant . Figure 4.4 shows the experimentally determined vapour pressures of magnesium plotted versus pressures calculated for each data point using equation 4.14 and the above parameters. The solid line is the idea l case, p . , = p , , , . The graph gives a visual experimental ca lcu lated - 119 -Figure 4.4 Calculated vapour pressures using equation 4.14 versus experimental results. - 120 -picture of the spread of experimental data in this work. Equation 4.14 is plotted in three dimensions in Figure 4.5. The graph is reduced to two dimensions in Figure 4.6, where the data-points are also included. As can be seen, the experimental points do not always conform to the calculated oxygen content contours. However, i t should be noted that oxygen analysis is only accurate to approximately ± 5 ppm. 4.3.3.1 Equilibrium Constant The equilibrium constant as given by equation 4.7 can be calculated from the constants for the following reactions: Mg(g) + 2A1(A) + 202(g) t Mg0'Al 2 0 3 (s) (4.16) log K = 46.367 (at 1743 K, ref. 83) Al ( ! ) + Al (%, Ni) (4.17) log K 17 - 5.647 (at 1743 K, ref. 56) \ 0 2(g) t 0 (%, Ni) (4.18) log K 18 = 2.054 (at 1743 K, ref. 56) - 121 -Figure 4.5 Surface plot from results calculated using equation 4.14, for Mg contents up to 100 ppm and Al contents up to 500 ppm. (Minor variations evident in the lower part of the plot are a r t i f i c i a l and due to that a f ini te number of points were used to produce the plot ) . 0.001 0.009 0.018 0.026 0.034 0.042 0.051 0.059 0.067 0.075 0.084 0.092 0.100 0.060 0.052 0.043 0.035 % A l 0.026 0.018 0.009 0.001 U I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I M I I I I U 0.002 0.002 T r r n - r i i I i i i i i i i i I i I i i i i i i i i i i i r T T T - n - T T T T i i i i i i i i H-H=1 0.060 0.052 0.043 0.035 0.026 0.018 0.009 0.001 0.001 0.009 0.018 0.026 0.034 0.042 0.051 0.059 0.067 0.075 0.084 0.092 0.100 % Mg x 10 Figure 4.6 Contour map showing the content of oxygen as a function of magnesium and aluminum content. Experimental points: x 17-19 ppm 0, o 20-25 ppm 0, * 26-30 ppm 0. Experiment numbers, see Table 4.5. - 123 -The value of log for reaction 4.5 is then given by: log K x = log K 1 6 - 2 log K 1 ? - 4 log K l g = 26.86 (4.19) This value should be compared to the value of 22.0 determined in this work. The discrepancy between the l i terature and the calculated equilibrium constant may have several explanations. It is quite unlikely that the free energy of solution of oxygen in l iquid nickel is erroneous as this reaction has been well investigated"^' 8 7 The free energy of solution of aluminum in l iquid nickel is not nearly as well d o c u m e n t e d ^ ' ^ . Hence, i t i s qu i t e poss ib le that part of the discrepancy may be explained by an error in the free energy of dissolution of aluminum. In addition, the discrepancy between the l i terature and calculated value could be explained partly by an erroneous free energy of formation of MgO'A^O-j. While the l i terature I the fref 68,91-92 83 value is taken from a credib le source , errors in the free energy of formation value for oxides have been discussed before The results are further i l lustrated by the area predominance diagram in Figure 4.7. The diagram provides a confirmation that MgO^A^O^ i s the stable oxide phase in these experiments. The solid lines and dashed lines in the diagram are calculated from the l i terature - 124 --7 -6 -5 -L -3 -2 -1 0 log h 0 Figure 4.7 Area predominance diagram. Equations 1-5 are given in Appendix F, p 168 . p Mg = 1 0 ~ • ~g p Mg = 1 0 ~ d a t a f r o m l i terature . • p Mg = ^ suggested data. - 125 -data for p__ = 10 atm and 10 , respectively. The dash-dotted line is Mg calculated from equation 4.14 using the equilibrium constant suggested by this work. It is uncertain how this change in equilibrium constant would affect the other lines in this diagram. 4.3.3.2 Interaction Coefficients Al Values of -17 and -28 for the interaction coefficients and M B e^  were found. They should be compared to values given in Tables 2.6 Al and 2.7. As can be seen, e^  has been suggested equal to -1 in previous work. This value was however not based on experimental data but rather 74 on l i t e r a t u r e data for iron solutions . For iron solutions, values of A l ep between -1 and -5.2 have been published with -3 .9 as the most Mg probable value. The magnesium-oxygen coefficient, e^6 could be compared Ca to eg in iron which has been suggested to be -62. For the case of the magnesium and aluminum i n t e r a c t i o n coefficients in nickel solution, the following facts should be considered. The free energies of formation of the oxides are almost identical at 1470°C for both aluminum and magnesium (Figure 4.2). The atoms of both elements are quite s imilar, and It may be expected that their behaviour in solution w i l l not be widely different. It may - 126 -therefore be suggested that the metal-oxygen interaction coefficients for both magnesium and aluminum in nickel solution should be quite s i m i l a r . In th is l i g h t , the values of -17 for e A 1 and -28 for e^ calculated in this work seem reasonable. These values also f a l l within the l i terature values for similar parameters in iron solution. 4.3.4 Energy of Solution The equilibrium constant for reaction 4.6 Mg(g) + Mg (%) may be calculated by substracting Mg (%) + 2A1 (%) + 40 (%) + MgO'Al 2 0 3 from reaction 4.5. Doing this for the experiments given in Table 4.5 using calculated Interaction coefficients yields an average log = 19.3 and consequently log ^ = 2.7. This compares favourably with a l i t e r a t u r e " ^ value of 1.6 which was calculated"' 6 assuming a 6 5 r e g u l a r so lu t ion using data for s o l i d n i c k e l at 6 5 0 - 8 5 0 ° C . The equilibrium constant for reaction 4.6 corresponds to a free energy of solution of -21.5 kcal at 1470°C. - 127 -4.3.5 Raoultian Act iv i ty Coefficient The Raoultian act ivi ty coefficient for magnesium, YMg> In nickel solution is given by Yv„ = r * ^ f — (4.20) when the act ivi ty of magnesium is defined by Further, ln Y„ - In Yw + e ° X n (4.22) Mg Mg Mg 0 Hence, the act ivi ty coefficient at in f in i te ly dilute solution is given by The values of Y° for experiments 1-9 (see Table 4.5) are given in - 128 -Table 4.6, using e = -2667 calculated from e * = -28. The act iv i ty Mg u coefficient Is also calculated for an additional four experiments, #10-13 for which oxygen was not analysed but calculated using equation 4.14. As can be seen the values for log Y° varies between -2.9 and -1.3. The average value is -2.1 (± 0.4). This value fa l l s between the 63 9 l i t e r a t u r e values suggested by deBarbadillo of -1 and by Mitchell of -3 . - 129 -TABLE 4.6 y° from Experimental Data * ( Calculated using Equation 4.14) Experiment PMg [ atm. ] *Mg x o 1 0 8 YMg No. 1 1.8 X lO" 6 8.5 X 10~5 9.5 X io" 5 - 2.6 2 0.8 X lO" 6 1.4 X IO"5 6.6 X io" 5 - 2.2 3 0.6 X lO" 6 0.5 X io" 5 7.3 X io" 5 - 1.8 4 0.5 X 10"6 0.2 X 10"5 6.2 X io" 5 - 1.6 5 1.0 X i o ' 6 0.2 X io" 5 7.0 X io" 5 - 1.3 6 2.1 X lO" 6 2.9 X 10"5 1.1 X io" 4 - 2.0 7 2.0 X 10"6 2.0 X io" 4 7.7 X io" 5 - 2.9 8 0.7 X 10"6 0.7 X 10"5 6.2 X IO" 5 - 1.9 9 1.8 X 10"6 5.3 X IO"5 7.0 X i o ' 5 - 2.4 10 0.4 X 10"6 1.9 X I O ' 5 * 3.2 X i o ' 4 - 2.3 11 4.4 X IO"6 3.2 X IO" 4 * 2.3 X io" 4 - 2.6 12 11.7 X IO" 6 2.8 X IO"4 * 1.3 X io"4 - 2.2 13 13.3 X IO" 6 1.0 X io" 4 * 5.1 X io"4 - 1.8 - 130 -4.4 Alloys Containing Chromium and Iron Raw data from experiments without any major alloy addition are compared to data from experiments with alloys containing 20% iron or chromium in Figure 4.8. As discussed ear l ier , Interaction between metals in solution can be generally expected to be much smaller than the interaction between strong oxidizers, such as magnesium and aluminum, and oxygen. It is therefore not surprising, that no major differences 63 are detectable between the a l l oys in Figure 4.8. deBarbadillo was also unable to detect a major change in magnesium so lubi l i ty in nickel at less than 50% of the alloying element (see Figure 2.27). - 131 --1.5 -2.0 -2.5 log(%Mg) -3.0 -3.5 h -4.0 1 1 — i i i • o — • ' A A • A • • • A O A o°°o A A " A O A AO A no addition A O O • 20% Fe 20% Cr — 1—A A i • • -6.5 -6.0 -5.5 -5.0 - 45 log (pM g) Figure 4.8 Comparison between data for alloys containing no major additions and alloys containing 20% Fe or 20% Cr. - 132 -5. C o n c l u s i o n s The following conclusions are presented in this investigation: - A novel high temperature experimental method has been developed that employs Knudsen effusion in conjunction with Atomic Absorption Spectrophotometry. - The experimental method was verif ied on l iquid t in al loys , which have well known magnesium ac t iv i t i e s , for a calibration method employing a pseudoisopiestic Knudsen c e l l . - The method was successfully applied to magnesium vapour pressure determinations for l iquid nickel alloys at 1470°C. Using the novel experimental method, the following thermodynamic data for dilute l iquid nickel solutions at 1470°C were determined. - The equilibrium constant, log K = 22.0 ± 0.2 for the reaction Mg(g) + 2 Al(%) + 4 0(%) * MgO'Al 20 3(s) - 133 -- The magnesium-oxygen interaction coefficient, e^5 = -27.7 ± 6.2, for magnesium and oxygen contents up to 100 ppm each. A l - The aluminum-oxygen i n t e r a c t i o n c o e f f i c i e n t , e^  = -16.7 ± 1.3 for aluminum contents up to 500 ppm and oxygen contents up to 100 ppm. - The equilibrium constant, log K = 2.7 ± 0.2 for the reaction Mg(g) +• Mg(%) - The Raoultian act iv i ty coefficient for an in f in i te ly dilute solution, log Y° = -2.1 ± 0.4. - A significant change in magnesium act iv i ty for 20 weight percent iron or chromium additions to the dilute nickel alloys could not be detected. - 134 -6. Suggestions for Further Work This work suggests further development or refinement in the following areas: 1. The Atomic Absorption-Knudsen method may be extended to measure the vapour pressure of several elements simultaneously. Thus, the act iv i ty of several elements in a l iquid metal solution could be determined. 2. Determination of the magnesium act ivity in MgO crucibles may yield Me va lues of g r e a t e r c e r t a i n t y as i n t e r f e r e n c e from Al is eliminated. 3. It is suggested that any further work using the developed experimental method employs an AAS dedicated to this task. This would eliminate experimental scatter due to equipment changes. - 135 -R E F E R E N C E S 1. C T . Sims, W.C. Hagel, eds.: "The Superalloys", John Wiley & Sons Inc. , 1972. 2. J .M. Moyer: Superalloys 1984, Prof. Fifth Int. Symposium on Super-al loys, eds.: M. Gell et a l . , 1984, pp. 443-454. 3. R.S. Cremiso: "Melting" in "The Superalloys", eds.: Sims et a l , John Wiley & Sons Inc., 1972, pp. 373-401. 4. J . Alexander: Material Science and Technology, Feb. 1985, V . l , pp. 167-170. 5. J . Fu, H. Wang, D. Wang, E.P. Chen: Proc. 7th ICVM, 1982, Tokyo, Japan. 6. H. Ichihashi, R. Baba, T. Ikeda: Proc. Vacuum Metallurgy Conf. 1984, pp. 75-82, Published by the Iron and Steel s o c , Eds: G.K. Bhat, L.W. Lherbiev. 7. C X . Chen, R.F. Gao, W.X. Zhao: 8th In t l . Conf. on Vacuum Met l . , Linz, Austria, Sept.30 - Oct.4, 1985, V.2, pp. 1046-1052. 8. C. d'A. Hunt, J . 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Timofeev: Proc. 7th Int. Conf. Vacuum M e t l . , Iron and Steel Inst . , Jpn. , 1982, Tokyo, Japan, pp. 1012-1019. 36. R.A. Rapp, editor: "Physiochemical Measurements in Metals Research" Parts I and 2, Interscience Publishers, 1970 (Volume IV of the series "Techniques of Metals Research", editor: R .F . Bunshah). 37. 0. Kubaschewski, C B . Alcock: "Metallurgical Thermochemistry", F i f th ed. , Pergamon Press, 1979. 38. E.D. Cater: P r o c of the 10th Materials Research Symp. on Characterization of High Temperature Vapors and Gases, Guthersburg, MD, 1978, pp. 3-38, Published as National Bureau of Standards Special Publication 561, 1979. 39. E.D. Cater: ref . 36, pp. 21-94. 40. Knudsen, M. : Ann. Physik, V. 28, 1909, pp. 75-130. 41. J . Drowart, P. Goldfinger: Angew. Chem. Internat. E d i t . , V. 6, 1967, No. 7, pp. 581-596. 42. A. Buchler, J . B . Burkowitz-Mattuck: ref. 36, pp. 161-195. 43. J . H . Norman, P. Winchell: ref . 36, pp. 143-145. 44. K.W. Lange, H. 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E l l i o t t : i b i d , Sept. 1966, pp. 1019-1032. 55. G.K. Sigworth, J . F . E l l i o t t : Metal. S c i . , V. 8, 1974, pp. 298-310. 56. G.K. Sigworth, J . F . E l l i o t t , G. Vaughn, G.H. Geiger: Metallurgical Society of CIM, Annual volume featuring molybdenum, 1977, pp. 104-110. 57. A.A. Nayeb-Hashemi, J . B . Clark, L . J . Swartzendruber: Binary Alloy Phase Diagrams, ed. T .B. Massalski, Am. Soc. Met l . , 1986, p. 1076. 58. A.A. Nayeb-Hashemi, J . B . Clark: i b i d , p. 1529. 59. W.G. Moffatt: "Handbook of Binary Phase Diagrams", Genium Publ. Corp. , 1984. 60. D .L. Sponseller, R.A. Fl inn: Trans. Met. Soc. AIME, V. 230, 1964, pp. 876-888. 61. W.G. Moffatt: ib id ref . 57, p. 628. 62. N. Meysson, A. Rist: Revue de Metallurgie, V. 62, 1965, pp. 1127-31. 63. J . J . deBarbadillo: "Magnesium and Calcium Treatment of Nickel-Base Alloys", Presented at American Vacuum Society Conf. 1975 (Available from the author at Inco Alloys Int . , Huntington, W. VA). 64. J . F . Smith, J . L . Christian: Acta Metallurgica, V. 8, 1960, pp. 249-255. - 139 -65. N.G. Schmahl, P. Sieben: "The Physical Chemistry of Metallic Solutions and Intermetallic Compounds", Chemical Publishing Co. , Inc. , New York, 1960, pp. 268-290. 66. P.K. Troi an, R.A. Fl inn: Trans. Am. Soc. Met., V. 54, 1961, pp. 549- 566. 67. C.H.P. Lupis: "Chemical Thermodynamics of Materials", Elsevier Science Publishing Co. , 1983. 68. S. Gustafsson, P-0. Mellberg: Scand. J . of Met., V. 9, 1980, pp. 111-116. 69. M. Joyant, C. Gatel l ier: "Influence d'une addition de calcium ou de magnesium sur la solubi l i te de l'oxygene et du soufre dans l 'ac ier l iquid", IRSID PCM-RE 1108, May 1984. 70. M. Nadif, C. Gatel l ier: i b i d , PCM-RE 1108 Bis , June 1985. 71. N.A. Voronova: "Desulphurization of Hot Metal by Magnesium", Int. Magnesium Ass. and AIME, 1983, pp. 67-102. 72. A. McLean, H.B. Be l l : J . Iron Steel Inst. , Feb. 1965, pp. 123-130. 73. R . J . Fruehan: Met. Trans., V. 1, Dec. 1970, pp. 3403-3410. 74. F. Vachet, P. Desre, E . Bonnier: Comptes Rendu Acad. Sc i . Paris, V. 260, pp. 1943-1946. 75. H .L . Kahn, W. Slavin: Appl. Optics, V. 12, No. 9, 1963. 76. Quartz Scientif ic Inc.: Catalogue of Fused Quartz Laboratory Ware. 77. G.W. Morey: "The Properties of Glass" 2nd ed., Am. Chemical Soc. Monograph Series, 1954. 78. ASTM Special Technical Publication 470B: "Manual on the Use of Thermocouples in Temperature Measurement", 1981, p. 125. 79. P .A .F . White, S .E. Smith: "Inert Atmospheres", Butterworths, London, 1962, p. 58. 80. Perkin-Elmer: "Analytical Methods for Atomic Absorption Spectro-photometry" - 140 -81. T .P . G i l l : "The Doppler Effect", Logos Press L t d . , London, 1965. 82. B.V. L'Vov: "Atomic Absorption Spectrochemical Analysis", Adam Hilger L t d . , London, 1970. 83. D.R. S t u l l , H. Prophet et a l : JANAF Thermochemical Tables, 2nd ed. and supplement in J . Phys. Chem. Ref. Data. 84. 0. Kubaschewski, W.A. Dench: J . Inst. Met l . , 1955-56, v 84, pp 440 - 444. 85. B.F. Ryan, B . L . Joiner, T.A. Ryan: "Minitab Handbook", Duxburg Press, 1985. 86. "Minitab" Stat i s t i ca l package: available from Minitab Inc., 3081 Enterprise D r . , State College, PA 16801, U .S .A. 87. E . S . Tankins: Met. Trans., v. 1, May 1970, pp. 1465-1467. 88. E .S . Tankins: i b i d , July 1970, pp. 1897-1904. 89. E .S . Tankins, N.A. Gokcen: Met. Trans., v. 2, June 1971, pp. 1605-1611. 90. W.A. Fischer, D. Janke: Z. Metallkunde, v. 62, 1971, pp. 747-751. 91. A. Mitchel l : Private Communication. 92. R. J . Fruehan: Met. Trans. , v 1, Apr 1970, pp 865 - 870. 93. "The determination of gases in metals," Special report No 68, The Iron and Steel Institute, 1960, pp 75 - 92. 94. "Instructions and Operation, # 589-600 Rapid Oxygen and Low Carbon Analyser," LECO Corporation manual # 176B. - 141 -APPENDICTES - 142 -APPENDIX A Equations In the Literature Review This appendix w i l l describe the deduction of equation 2.2 as 26 presented by Vidale and the deduction of the cosine law (Eq. 2.3) and the Hertz-Knudsen equation (2.4). V i d a l e 2 6 a. Absorption equation When a paral le l beam of l ight of intensity I having a frequency v is passed through a homogeneous gas of thickness, ! , the absorption of this beam is given by: -k A 1 = 1 e v v o v (Nomenclature for Appendix A is given on page 147). If no broadening effect were present, k would be Infinite at v = v and would be zero v o elsewhere. -143 -b. Doppler broadening If Doppler broadening is the only form of broadening present, k. = k exp v o v-v - r — ° c J _ i M, 2 1 • 2RT-(A.2) and = /* M o 2RT mv Nf (A.3) 26 For sodium, which was considered by Vidale , -1 v = 16 973 cm , M. = 23, f = 0.65. o i ' This yie lds , 12 P k = 1.563 x 10 -4TT o T,3/2 (A.4) and hence = exp - 1.563 x 10 12 PA n3/2 (A.5) and A v = 0.0505 at 400 K. o - 144 -c. Natural broadening Natural broadening can generally be neglected in comparison with Doppler broadening. d. Pressure broadening According to the simple pressure broadening theory of Lorenz, the half width due to pressure broadening alone Av is given by: l_i 2 p A V l = = 0.359 a* * / g ^ + g i - (A.6) For sodium, a = 9.0 A, and M = 23 Li JL For argon M 2 = 40, and the experimental conditions of Vidale were set at a temperature of 397 K and an argon presure P^ = 9.1 cm Hg. This yields Av = 0.0457 c m - 1 . When both Doppler and pressure broadening are present, the value of is given by - 145 -. 2 k +°° -y k~~ = n f 2 . , .2 ( A , 7 ) o - 0 > a + (u—y) where a - / In 2 = 0.7534 (A.8) 2(v-v ) oo = - ^ - j - ^ / In 2 = 1.926 for V = V q + 0.0584 ( A > 9 ) 0 for v=v o 26 A numerical method was used by Vidale to determine the integral . The following results were obtained: k(v=v ) k(v=v + 0.0584) k ° — = 0.5057 2 : = 0.1363. (A.10) o o e. Hyperfine structure effect If the radiating atoms consist of a mixture of isotopes, or i f they have a non-zero nuclear spin, the atomic line w i l l contain more than one component both in the emission spectrum from the source and in 26 the absorption spectrum in the furnace . The sodium line is a doublet and only the separation of the two components were considered by 2 6 V ida le for the vapour pressure calculations. The intensity ratio of - 146 -the two components is 5:3 and the separation 0.0584 cm ^. Equation A . l can then be written I' 3 5 In — = - — VS.-— SV n I' 8 o 8 K(v=v + 0.584) o o (A.11) I" 5 3 ln — = - — k £ - - Ik o o The second term in each equation is present as there is an overlap 26 between the two components. The monochromator of Vidale could not resolve the two components and therefore the measured intensities are I' +1" and I* + I". Also I 1 = ~ (I' +1") and I" = | - (I' + I") so that o o o 8 o o o 8 o o ' i ^ e x p - F T T 7 • I e x P ["* {f k o + I k ( v - v + 0.0584)}^ ( A - 1 2 ) o c o o o The results presented in equation A.10 substituted into A.12 yields ( f ) = | exp (- 0.2748 k A ) + | exp (-0.3672 k A), (A. 13) o p and i f the result in equation A.4 is ut i l ized and S. set at the ce l l length (10.16 cm) ( r°exp = I 6XP ( _ 4'3 4 7 x 1()12 -T72") + | e x P ("5.809 x 10 1 2 -Lj-) (A.14) This equation in simplified form is presented in the thesis as (2.2). - 147 -X. LIST OF SYMBOLS FOR THE WORK OF VIDALE c = velocity of light e = charge of the electron f = oscillator strength of the line in question ^ F° = standard molar free energy of vaporization A H = molar enthalpy of vaporization A H ° = standard molar enthalpy of vaporization lyl = intensity of the light beam of frequency V after passing through absorbing path I Q 1 1 j = original intensity of the light beam of frequency V from the source / n 1 I -rf - experimentally measured value of —, when monochromator slit is much >^ ^  wider than the line under study o ky = absorption coefficient of the gas for light of frequency l) k = absorption coefficient of the gas at the center of the line when only ° Doppler broadening effects are present jl = length of the absorbing path m = mass of the electron M = molecular weight of the gaseous species = atomic weight of absorbing species M 2 = molecular weight of gas responsible for Lorentz broadening N = density of the species under consideration P = partial pressure of gas being analyzed P = pressure of gas responsible for Lorentz broadening A R = gas constant - 148 -standard molar entropy of vaporization temperature number of collisions that the absorbing species makes with other molecules per second frequency of the light Doppler breadth of the line Lorentz half breadth of the line frequency shift of the center of the line due to pressure effects frequency of the center of the absorption line, when no shift is present effective cross section for collisions between absorbing atoms and species responsible for the Lorentz broadening lifetime of the atom in the resonance state - 149 -37 The Cosine law The distribution of molecular velocities in a gas at low pressure obeys the Maxwell-Boltzmann distribution law which, expressed in terms of molecular speeds independent of direction is dN(c) . , M ,3/2 2 ,Mc 2 N . . ~~N = 4 1 1 ( 2^RT } C 6 X P <RT"> ( A - 1 5 ) o (Symbols are explained in "Nomenclature", p. xv). The average molecular speed i s , 1/2 c = (8RT/WM) ' (A.16) The rate of co l l i s ion of molecules on unit area of the wall in unit time i s , Z q = (N/V) (c/4) (A.17) The assumption of molecular chaos leads to the probability that a molecule approaches the wall of an angle 9 to the normal within the element of sol id angle dw: N(9) N - ft du) fk ia\ = - c cos 9 ^ _ (A.18) o - 150 -This is the cosine law, also presented as equation 2.3. The Hertz-Koudsen equation The molecular density N/V is related to the pressure for an ideal gas by p - (N/V) kT = (N'/V)RT (A.19) Combining equations A.16 - A.19 2 p - -7- (2ukTm) 1 / 2 (A.20) or in terms of the weight loss accompanying the effusion process P = AT ( 2 7 t R T / M ) 1 / 2 (A.21) Equations A. 20 and A.21 (2.4) are different forms of the Hertz-Knudsen equation. - 151 -APPENDIX B Procedures for Chemical Analysis Each metal sample was either cut in half and analysed for magnesium/aluminum and oxygen or the entire sample was analysed for magnesium/aluminum only. a. Magnesium Analysis Mechanically cleaned solid metal samples (nickel-base or tin-base) were weighed. Generally, 3-6 g of metal was analysed. Each sample was d iges t ed in a 50% so lut ion of e i ther HNO^ or HCI or a combination of the two acids and deionised H2O. The proportions of acids varied, depending on al loy, e.g. i t was found that the dilute nickel alloys dissolved well in n i tr i c acid after ~ 10% hydrochloric acid was added. Care was taken to ensure that the alloy used as a standard was treated in the same manner as the sample solutions for each set of analysis. The solutions were heated in covered beakers unti l no metal remained. The solutions were then quantitatively transferred to either 100 ml or 200 ml volumetric flasks (depending on original amount of metal), cooled and diluted to volume with de-ionised water. - 152 -Portions (usually 5 ml) of concentrated solution were pipetted off into 50 ml volumetric flasks. 5 ml of a lanthanum chloride solution (29 g L a 2 0 3 + 200 ml HC1 di luted to 1000 ml) was added to each flask, and the solutions diluted to volume with de-ionised water. One sample of each set, which had a low magnesium content, was prepared for analysis according to the standard addition method. Thus, 0, 5, 10 and 20 ml of a 5 ppm magnesium stock solution was added to four solutions of the same concentrated solution prepared as above. This standard addition set of solutions was also used as standards for samples prepared in the same manner. A l l glassware used was thoroughly washed in laboratory detergent, rinsed in hot tap water, then soaked overnight in 5% n i t r i c acid and f ina l ly rinsed repeatedly in de-ionised water. Atomic Absorption Analysis was performed in the standard manner using an air-acetylene flame. Repeated analysis of the same metals showed a variation of ± 3 ppm. b. Aluminum A n a l y s i s Aluminum analysis solutions were prepared from the concentrated solutions described in section a, in the same manner as the magnesium solutions with the following exceptions. Generally, solutions of double - 153 -concentration were analysed. The AAS analysis was performed using a nitrous oxide - acetylene flame. The uncertainty is ± 25 ppm. c. Oxygen Analysis The i n e r t c a r r i e r - g a s method was a p p l i e d for the oxygen 93 analys i s . The equipment employed consisted of a LECO Corporation oxygen analyser (#589-600) and induction furnace (#537-100). The 94 procedure described in the LECO manual for sample preparation and analysis was followed throughout. Oxygen calibration samples containing 89 ppm oxygen were u t i l i s e d . Three 1 g so l id , clean samples of each nickel alloy were analysed. Generally, the difference between the highest and lowest results were less than 10 ppm. The average value from the three samples is taken as the oxygen content, except where one value differed widely from the other two, in which case the average of the closer two was taken as the oxygen content. The uncertainty is estimated to be ± 5 ppm. - 154 -A P P E N D I X C Doppler Shift The light emitted from a hollow cathode lamp is produced by a gas of Maxwellian dis tr ibut ion. Its peak wavelength, and hence peak absorption wavelength in these experiments is equal to 2852.13A = \ . However, the atoms are emitted from the Knudsen ce l l in a directional manner, as schematically i l lustrated in Figure B . l . Thus, the peak absorption wavelength of the atoms emitted from the Knudsen ce l l may be shifted out of the "absorption window". The following is a simple calculation to gain an understanding of how the Doppler effect may influence the absorption measurements in this investigation. The distribution of atoms emitted from the ori f ice is determined by Lamberts cosine law, which in two dimensions is given by I f l = I cos 9 (B. l ) 9 o where I is the intensity of the beam perpendicular to the orif ice plate and I Q i s the beam intensity at angle 9. This equation is independent of the temperature and is not significant for these calculations. - 155 -Figure B . l - 156 -The Doppler shift for electro-magnetic radiation is given by 81 f - f v 1 + c 1 - V c 1/2 (B.2) where f f' v c frequency of shifted l ine; frequency of original line speed of atoms speed of light in vacuum The frequency is given by f'= r - (B.3) and the speed of atoms by 1 2 3 E = j mv = j kT m (B.4) Data: \ = 2852.13A; T = 900°C c = 2.997925 x 10 1 0cm/s - 157 -k = 1.38054 x 10~ 2 3 J/K = 1.38054 x 1 0 - 2 0 £ m -s K -23 = 24.312 g/mole = 4.036848 x 10 g/at om and f' = j- = 1.051118 x 1 0 1 5 S - 1 = / " I l = 1, m 097016 x 10 cm/s f = f v 1 + c 1 - V c J 1/2 = 1.051122 x 1 0 1 5 s - 1 X = j = 2852.12A AX = O.OlA Similarly for 1470°C: X = 2852.12A AX = O.OlA Hence, there is no difference in Doppler shift for 900°C and 1470°C. lower temperatures the shift would be even smaller. The half width of a hollow cathode lamp has been measured 82 L'Vov for the following conditions: - 158 -p. =1.6 torr and r A r I = 5 mA. The width given is Av = 0.17 cm AX = 0.01AA - 159 -A P P E N D I X D EDX A n a l y s i s of Oxide Phase Raw output of EDX analysis of the oxide phase is presented for the surface of a nickel sample in Figures D . l and D.2 and for the inside of a crucible in Figures D.3 and D.4. The analysis was in both cases done at low magnification and covers areas large enough to be representative of the specimens. Both cases also show elemental nickel . In the case of the sample surface, the nickel content was picked up by the beam from the substrate. In the case of the crucible, the nickel was present as droplets on the surface. The sample surface show a ratio of 1.03 molar percent MgO/A^O^, and the crucible a ratio of 0.93 molar percent Mg0/Al_0„. 9 - M a r - 1 9 3 7 1 0 : U U : 43 SURFACE OF SAMPLE - l a r g e a r e . V e r t = 5 0 2 7 c o u n t s D i s p = 1 4<::::::::::::::::::::::':::::::::::-P r e s e t = E l a p s e d 2U0 s e c 200 s e c 0 . 000 Range = • • -_ • 9 1 0 . 2 3 0 kev I n t e 9 r a 1 0 1 0 . 1 1 0 13943b Figure D . l - 161 -Mar. 9. 1987 SURFACE OF SAMPLE -Accelerating voltage Beam - s a n i D i e incidence angle Xray emergence angle Xray - window incidence angle Window thickness £8. 8 Kev1 90. 8 degrees £5.8 degrees £5.8 degrees £0. 8 microns STANDARDLES EDS ANALYSI  (ZOF CORRECTIONS VIA MAGIC V) ELEMENT WEIGHT PRECISION OXIDE OXIDE fc LINE K-RATIO*  PERCENT £ SIGMA FORMULA PERCENT 0 * Mn KA Al KA Ni KA TOTAL 41.21 0.194£ 0.5873 0.£185 16. 85 34. 46 8. £8 8. 17 8. 16 8. 09 MgO A1 £03 N i £6. 6£ 65. Ii 8. £8 180. 00 * DETERMINED BY STOICHIOMETRY *NOTE: K-RATIO = K-RATIO x R where R = reference (standard )/reference (sarnDie) NORMALIZATION FACTOR: 8.571 Figure D.2 y - H a r - 1 9 8 ? 0 9 : 1 7 : 3 d 0 3 0 3 : 1 C R U C I B L E V e r t = 4 8 1 0 c ou n t s D i s p = 1 P r e s e t = E l a p s e d 2tiW s e e s 2 0 0 s e e s •hi-fi . WWW Ran g e = 1 U . 2 3 0 k e V IN I I n t e g r a l 0 1 0 . 1 1 0 1 9 0 3 S 2 Figure D.3 - 163 -n a r . 9 . 1 9 8 7 0 J 0 , 3 : i CRUCIBLE Hcceieratinn voitaae Beam - s a r n D i e incidence angle Xrav ernernence angle Xray - window incidence angle Window thicknes  £ 0 . 0 KeV 9 ® . 0 degrees £ 5 . 3 deorees £ 5 . 8 degrees £ 0 . IZI microns STANDARDLES  EDS ANALYSI  <ZAF CORRECTIONS VIA MAGIC V) ELEMENT LINE • * ,1a KA Ai KA Mi KA TOTAL. WEIGHT K-RATIO* PERCENT 0 . 0 9 5 £ 0 . 3 5 4 3 0 . 5 5 0 5 3 6 . 5 4 1 3 . 0 5 3 1 . 4 3 1 8 . 9 8 PRECISON £ SIGMA 0 . 1 6 0 . 1 5 0 . 1 0 OXIDE FORMULA M a G A I £ 0 ; Ni OXIDE NO. OF CATIONS PERCENT IN FORMULA £ 1 . 6 4 5 9 . 3 6 1 8 . 9 8 NUMBfcR Uh LAli 'UlMb uALCULAThU ON BASIS Ur-1 0 0 . 0 0 3 OXYGEN ATOMS. 0 . 7 0 5 1 1 . 5 3 0 0 0 . 0 0 0 0 £ . £ 3 5 0 * DETERMINED BY STOICHIOMETRY *NOTE: K-RATIO = K-RATIO x R w h e r e R = r e f e r e n c e ( s t a n d a r d ) / r e f e r e n c e ( s a n i D i e ) N O R M A L 1 i AT I UN F H C I ' O K : 0 . 5 ^ 1 Figure D.4 - 164 -A P P E N D I X E Regression Analysis The following are comments on the attached computer run of linear 85 86 multiple regression analysis using "Minitab" ' (p. 166). 1) "VLP" (=y) is regressed on "CALO" (=X^ and "CMG" (=X 2). Residuals for each experiment are saved in column C9. 2) The computer regressed equation. 3) Stdev = estimated standard deviation t -rat io = test of significance, t = B- (hypothesized value) estimated stdev of B ' where hypothesized value = 0. Should be > 2. 4) s = standard deviation of y (=VLP) about the regression line R-sq = square of the correlation coefficient, in this case, R = 98.3%. ( Idea l ly should be 100%), R-sq = R e g r e s s i o n s s x 1 0 0 s e e  J / » M Total ss ' also below. - 165 -5) Analysis of Variance table: Regression SS = regression sum of squared deviations, part of Total SS explained by the regression l ine . Total SS = total sum of squared deviations. The column of major interest is the "Residual" column. It shows the difference between the calculated y using the regressed equation and the given y (VLP). F ina l ly , page 167 gives the total table of experimental data as printed from the computer. - 166 -iiTB > REGRESS * VLP' on 2 p r e d i c t o r s 'CALO', 'CMG'; SLJBO RESIDUALS i n t o C 9 . The r e g r e s s i o n e q u a t i o n i s vIp = - 2 2 . 0 - 1 6 . 7 c a l o - 2 7 . 7 cmg P r e d i c t o r Coef Stdev t - r a t i o C o n s t ant •22. 0290 0 . 1 6 7 6 - 1 3 1 . 42 (3) c a l o - 1 6 . 7 3 9 1 .294 - 1 2 . 94 cmg - 2 7 . 7 2 3 6 . 201 - 4 . 47 s = 0 . 1346 R-sq = 9 6 . 67. R - s q ( a d j ) = • 95 . 57. (4) A n a l y s i s of V a r i a n c e SOURCE DF SS MS (5) Regres s i on 5 . 8 3 5 7 2 . 9 1 7 8 E r r o r 6 0 . 2 0 4 5 0 . 0 3 4 1 T o t a l 8 6 . 0 4 0 2 SOURCE DF SEQ SS c a l o 1 5 . 1 5 4 4 cmg 0 . 6 3 1 3 • bs. c a l o v l p F i t S tde v . F i t. Res i d u a l S t . Re s i d 1 - 0 . 1 4 2 - 1 9 . 0 4 2 6 - 1 9 . 27' 12 0 . 0 8 9 6 0 . 2237 1. 42 - 0 . 1 0 9 ' - 2 0 . 2 5 6 0 —2 O 1401 0 . 0 6 3 7 —0 . 1 159 —0. 63 - 0 . 0 6 0 - 2 0 . 7 7 6 6 —21 0101 0 . 1 0 2 3 0 . 2336 1. 52 4 - 0 . 0 5 3 - 2 1 . 1 5 1 3 -21 . 0515 0 . 1 0 5 2 —0 . 0993 - 0 . 66 5 - 0 . 1 10 - 2 0 . 0 5 5 0 - 2 0 . 1693 0 . 0 7 4 3 o . 1148 0 . 68 6 - 0 . 2 1 5 - 1 3 . 3 4 9 1 - 1 3 . 2913 0 . 1 4 9 2 —0 . 0573 - 0 . 53 / - 0 . 0 5 0 - 2 0 . 3 5 1 3 • - 2 0 . 2 ~j "•' ~> 0 . 1 7 4 4 - 0 . 0777 X • 23 S - 0 . 1 0 3 -20, . 4200 - 2 0 . 1924 0 . 0 7 2 5 —0 . 2276 _ -l .L it 34 o - 0 . 1 2 6 -19, . 6313 - 1 9 . 6325 0... 0666 0 . 0012 0 „ 0 1 - 167 -•o r-j -JJ o cr- ro o 0- to rt ••0 -0 t a ui r- o -r-i r- r-i in 03 rO 03 u rt 03 i> h- ul a- in =T in ui 1—'. <t r-i o o r-< • ~ : t—t ! I i ! ! i i ! i a -0 •0 ro 1^1 rt ro ro Ci •0 i—i r> rt =J N 10 til i l l IN ca Ci h- 1-1 o ro ro t -o i> r'. 1—". CO o o s> 1—f r-i CL Ci r-i r-i i i ! ! I CL CO CO -0 U l O O CO O rt f--J O rt 99 9 x 'w' ' _ ' 5 9 9 9 x 'x 'x x' 9 9 y y =w> ' : Q -43 CO O N Ch O rt f N Ch Ci rt C-J rt rt f.-j C-j rt y y y y y y y y y ' _ ' W : ~ : ' - , 'w' rt a N. IN o o ro ui CO <n ro in ro ro o rt o in cr-'o r i -< ^ c-i ui rt ci a '-• •-' •-• cr ui C-i rt rt r-i ro ro r-i s ro y o o rt 03 '~' Ci o y y o • u ! rt u Q. rt f-.j Ci rt rt rt +J x r OJ «j <r m N a* in r--- 0 s rt o o o o o o o o o L ro ro ro ro ro ro ro ro ro C L 3 rt r-j M « t UT - Q is . m f> 0 a h- ce O'- rt o 0s -0 03 rt r> O U iii Lil Ul O CO N N rt Ki -o co ui co r-- r-i <s -O ri 03 in ro o- q- r-. N N rt r-i rt ro o- rt ui N a o a rt r-i o rt o o r-j o o o o o o o o o o ! ! ! ! I CP o ** co --3- co r-r c-j co s r-i o o o t ro rt co u P 9 9 9 9 9 t ? 9 9 : — : :w: 'w" ' ~ ' 'w' •„= : - ' : - : w O i ! ! i I ! I I ! 3 rt r-i ro « t ui -o 'N co r> a cc - 168 -A P P E N D I X F Equations for the area predominance diagram given in Figure 4.7. 1. Mg(g) + 2 Al(%) + 4£(%) t MgOAl 20 3(s) log K x = - log p M g - 2 log h M - 4 log h Q 2. MgO(s) + 2A1(%) + 30(%) *• MgOAl 20 3(s) log K 2 = - 2 log h A 1 - 3 log h Q 3. A l 2 0 3 ( s ) + Mg(g) + 0(%) t MgO'Al203(s) log K 3 - - log p M g - log h Q 4. Mg(g) + 0(%) t MgO(s) log K 4 = - log p M g - log h Q 5. 2A1(%) + 30(%) t A l 2 0 3 ( s ) log K 5 = - 2 log hA]_ - 3 log h Q 

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