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Study of the reaction of pyrrhotite with sulphur dioxide Ogle, Iain Colquhoun Gibson 1971

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A STUDY OF THE REACTION OF PYRRHOTITE WITH SULPHUR DIOXIDE BY IAIN COLQUHOUN GIBSON OGLE B.A.Sc., University of B r i t i s h Columbia, 1965 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of METALLURGY We accept t h i s thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1971 In presenting th i s thes i s in pa r t i a l f u l f i lmen t of the requirements fo r an advanced degree at the Uh ivers i ty of B r i t i s h Co 1umbia, I agree that the L ib ra ry sha l l make i t f r ee l y ava i l ab le for reference and study. I fu r ther agree that permission for extens ive copying of th i s thes i s for scho la r l y purposes may be granted by the Head of my Department or by h i s representat ives . It is understood that copying or/publ ication-of th i s thes is f o r f i nanc i a l gain sha l l not be allowed without my wr i t ten permiss ion. Department of -• M e t a l l u r g y The Un ivers i ty of B r i t i s h Columbia Vancouver 8, Canada Date Sept. 15, 1971 - i i -ABSTRACT The oxidation of thin rectangular plates of pyrrhotite by sulphur dioxide between 700 and 900°C has been studied at sulphur dioxide p a r t i a l pressures ranging from 0.25 to 1.0 atm. As reaction proceeded, an outer layer of magnetite thickened at the expense of pyrrhotite, sample dimensions remaining constant. Observations of p a r t i a l l y oxidized samples have indicated a line a r reaction front and the lack of retained pyrrhotite. Weight loss curves have indicated two types of behaviour: constant rate with increasing porosity at high sample densities, and increasing rate with increasing porosity at lower sample densities. Analysis by a transport control model has shown that chemical processes have no effect on the reaction rate and that the rate i s controlled by gaseous di f f u s i o n through a laminar gas f i l m at onset of reaction of low density samples. As the magnetite layer thickens, control s h i f t s to that of gaseous d i f f u s i o n through the porous magnetite. By correlation of observations and effective d i f f u s i o n c o e f f i c i e n t s , i t i s demonstrated that the structure of magnetite varies as a function of i t s thickness and i s dependent on reaction temperature and pressure. The primary mode of d i f f u s i o n i n the porous magnetite layer i s determined to be t r a n s i t i o n a l for the range of pyrrhotite densities investigated. High density samples are subject to rupturing. This causes approxi-mately l i n e a r reaction rates which are independent of sample density. It i s proposed that reaction i s c y c l i c i n that i t proceeds by the transport of oxide ions to the reaction front, subsequent rupturing, and gaseous dif f u s i o n u n t i l pore di s t r i b u t i o n s prohibit Knudsen d i f f u s i o n . - i i i -TABLE OF CONTENTS Page I. INTRODUCTION 1 A. General 1 B. Past Research 3 1. K i n e t i c s of P y r r h o t i t e Reaction with Sulphur Dioxide . 3 2. Cry s t a l l o g r a p h i c Nature of the S o l i d Species .. 7 3. Thermodynamics of the Reaction of P y r r h o t i t e with Sulphur Dioxide 11 4. Gas-Solid Reactions 23 CD General 23 ( i i ) Analysis of Iron Oxide Reduction by Hydrogen 28 5. P h y s i c a l C h a r a c t e r i s t i c s of Product Layers .... 32 6. D i f f u s i o n i n Porous Solids 33 C. Objective and Scope of the Present Work 36 I I . EXPERIMENTAL 38 A. Apparatus 38 1. Measurement of Weight Change 38 2. Furnace and Reaction Chamber 42 3. Gas P u r i f i c a t i o n Systems 44 B. Materials 46 1. Iron Sulphide 46 2. Sample Preparation 50 3. Preliminary Tests 56 C. Procedure 60 1. K i n e t i c Experiments 60 - i v -Page 2. Marker Experiments 61 3. Chemical Analysis 62 4. Metallographic Examination 62 I I I . RESULTS 63 A. K i n e t i c s 63 1. Time Dependence 63 2. Temperature Dependence 67 3. Pressure Dependence 67 B. Marker Experiments 102 C. Metallographic Examination 102 1. External Oxidized Surfaces 102 2. Internal Structures 105 IV. DISCUSSION OF RESULTS 1 2 2 A. Features of Recorded Weight Change Curves I 2 2 1. Weight Loss on Heating ^ 2 2 2. Weight Gain 1 2 2 3. Major Weight Loss l 2 ^ B. Mixed Control Model I 2 6 1. General 1 2 6 2. Heat Transfer Analysis ^ 2 ^ 3. D i f f u s i o n Through a Laminar Boundary Layer at Onset of Reaction 131 4. Transport Process Control 139 5. Relative Contributions to Control 158 - v -Page C. St r u c t u r a l C h a r a c t e r i s t i c s of the Product Layer ... 173 1. V a r i a t i o n i n E f f e c t i v e D i f f u s i o n C o e f f i c i e n t .. 173 2. Cor r e l a t i o n of D^^ Variations with Metallo-graphy 173 D. Oxidation Mechanisms 182 1. Transport Processes 182 2. E f f e c t of Temperature 185 3. E f f e c t of Pressure 188 4. Chemical Processes 190 V. CONCLUSIONS 191 RECOMMENDATIONS FOR FURTHER WORK 194 APPENDICES 196 1A Development of a General Model 196 1. Laminar Gas Film 196 2. Porous Product Layer 197 3. Chemical Reaction 199 4. General Model f or Reaction of FeS. with S0 o.. 200 1+y 2 IB Solutions to Transport Control Model 202 2A Gas Film Control at Onset of Reaction 225 2B Polynomial Curve F i t t i n g ..' 226 3A Counterdiffusion Through a Porous Magnetite Layer Assuming the E f f e c t of Net Bulk Flow to be N e g l i g i b l e 228 3B Counterdiffusion with Net Bulk Flow Through a Porous Layer 229 3C Counterdiffusion Through a Gas Film and a Magnetite Layer Assuming the E f f e c t of Net Bulk Flow to be Ne g l i g i b l e 2 3 0 BIBLIOGRAPHY 2 3 1 - v i -LIST OF FIGURES Figure Page 1 Iron Sulphur Phase Diagram 8 2 S t a b i l i t y Diagram for Sulphides and Oxides of Iron at 800°K" 14 3 S t a b i l i t y Diagram for Sulphides and Oxides of Iron at 1000°K 15 4 S t a b i l i t y Diagram for Sulphides and Oxides of Iron at 1200°K 16 5 Stoichiometry Dependence of P y r r h o t i t e on H /H_S Ratio .... 20 6 Arrhenius Diagrams as a Function of Extent Reaction 25 7 (a) Apparatus for K i n e t i c Experiments 39 (b) Hot-Pressing Apparatus 53 8 Fractured Surfaces of a 96 Percent Dense Hot-Pressed Compact 57 9 C r i t i c a l Flow Rate 59 10 Schematic Weight Loss Curve 64 11 k.^  Versus Pyrrhotite Density at 900°C and 1.0 atm SO ..' 68 12 k 2 Versus P y r r h o t i t e Density at 900°C and 1.0 atm S0 2 69 13 k 3 Versus P y r r h o t i t e Density at 900°C and 1.0 atm S0 2 70 14 Versus Pyrrhotite Density at 850°C and 1.0 atm S0 2 72 15 k Versus P y r r h o t i t e Density at 850°C and 1.0 atm 16 k Versus P y r r h o t i t e Density at 850°C and 1.0 atm 17 k Versus P y r r h o t i t e Density at 800°C and 1.0 atm so 2  - v i i -F i g u r e Page 18 k 2 V e r s u s P y r r h o t i t e D e n s i t y a t 800°C and 1.0 atm S 0 2 77 19 k 3 V e r s u s P y r r h o t i t e D e n s i t y a t 800°C and 1.0 atm S 0 2 78 20 k 1 V e r s u s P y r r h o t i t e D e n s i t y a t 700°C and 1.0 atm S 0 2 80 21 k 2 V e r s u s P y r r h o t i t e D e n s i t y a t 700°C and 1.0 atm S 0 2 81 22 1<3 V e r s u s P y r r h o t i t e D e n s i t y a t 700°C and 1.0 atm S 0 2 82 23 A r r h e n i u s Diagram f o r k^, k 2 , and k^ a t P y r r h o t i t e D e n s i t y of 4.05 g c m - 3 84 24 A r r h e n i u s Diagrams f o r k^, k 2 > and k^ a t P y r r h o t i t e D e n s i t y o f 4.15 g c m - 3 85 25 k x V e r s u s P y r r h o t i t e D e n s i t y a t 900°C and 0.85 atm S 0 2 87 26 k 2 V e r s u s P y r r h o t i t e D e n s i t y a t 900°C and 0.85 atm S 0 2 88 27 k 3 V e r s u s P y r r h o t i t e D e n s i t y a t 900°C and 0.85 atm S 0 2 89 28 ^ V e r s u s P y r r h o t i t e D e n s i t y a t 900°C and 0.50 atm S 0 2 91 29 k 2 V e r s u s P y r r h o t i t e D e n s i t y a t 900°C and 0.50 atm S 0 2 92 30 k 3 V e r s u s P y r r h o t i t e D e n s i t y a t 900°C and 0.50 atm S 0 2 93 31 ^ V e r s u s P y r r h o t i t e D e n s i t y a t 900°C and 0.25 atm S 0 2 95 32 k 2 V e r s u s P y r r h o t i t e D e n s i t y a t 900°C and 0.25 atm S 0 2 96 33 k 3 V e r s u s P y r r h o t i t e D e n s i t y a t 900°C and 0.25 atm S 0 2 97 34 P r e s s u r e Dependence o f Rates k^, k^, and k 3 f o r Samples o f D e n s i t y 4.05 g c m - 3 . • 99 35 P r e s s u r e Dependence o f r a t e s k 1 , k , and k_ f o r samples o f D e n s i t y 4.15 g c m - 3 7. ..7 100 36 S u r f a c e s o f H i g h D e n s i t y Samples O x i d i z e d a t 900°C ... 104 37 S u r f a c e R e p l i c a s o f Sample 3-1, O x i d i z e d a t 900°C 106 38 F r a c t u r e d S e c t i o n A c r o s s a B l i s t e r i n Sample 15-1, x 250 108 39 F r a c t u r e d S e c t i o n A c r o s s a B l i s t e r i n Sample 16-1, x 300 . 109 40 F r a c t u r e d S e c t i o n s o f Samples O x i d i z e d a t 900°C H O - y i i i -Eigura Page 41 Internal Structures of Samples Oxidized at 900°C .. 113, 42 Magnetite Structures of Samples Oxidized at 900°C. 114 43 General Sections of Samples Oxidized at 800°C 115 44 Internal Structures of Samples Oxidized at 800°C .. 117 45 General Sections of Samples Oxidized at 700°C 118 46 Sections Adjacent to Surfaces of Samples Oxidized at 700°C I V . . 119 47 Magnetite Grain Structures 120 48 Schematic Cross-Section of a P a r t i a l l y Oxidized Pyrrhotite Sample I l l u s t r a t i n g P a r t i a l Pressure Gradients 128 49 Predicted and Experimental Weight Loss Curves 142-153 50 Sulphur P a r t i a l Pressures at Sample Surface and Reaction Front During T r i a l 43-1 155 51 Predicted Weight Loss Curves 161-172 52 Variations i n D 174-178 eff . 53 Arrhenius Diagram for Rates of Reaction at 1 atm SO- as Predicted by Laminar Film Control 187 - i x -LIST OF TABLES 1 Calculated Diffusion Coefficients as a Function of Temperature and Pore Volume 5 2 Enthalpies and Free Energies of Reaction for Equations (1) , (2) and (4) i n Kcal/mole FeS 11 3 Equilibrium Sulphur P a r t i a l Pressure over Pyrrhotite. 12 4 Equilibrium Sulphur P a r t i a l Pressure over Pyrrhotite at 1 Atmosphere Sulphur Dioxide 12 5 Stoichiometry Factor u of FeS^ at Various Temperatures and Sulphur Dioxide P a r t i a l Pressures 21 6 Sulphur P a r t i a l Pressures (mm Hg) at Various Tempera-tures and Sulphur Dioxide P a r t i a l Pressures 21 7 K e Values (c.g.s. units) at Various Temperatures and Sulphur Dioxide P a r t i a l Pressures 22 8 Enthalpy of Formation of F e S 1 + y at 298°K (Kcal/mole) 22 9 Enthalpy and Free Energy of Reaction for Equation (5) (Kcal/mole FeS, , ) 2 3 1+u 10 Operational Specifications of a Stratham UC2 Transducer ^1 11 Spectrographic Analysis of Pyrrhotite i n Weight Percent Impurity 47 12 Debye-Scherrer Results Using Co K^:Radiation ^9 13 Hot-Pressing Temperatures and Resultant Densities ... 55 14 Features of Portions A and B of Weight Loss Curves for Low Density Samples 65 15 Experiments at 900°C and 1 Atmosphere S0 2 71 16 Experiments at 850°C and 1 Atmosphere SO^ 75 17 Experiments at 800°C and 1 Atmosphere S0 2 79 18 Experiments at 700°C and 1 Atmosphere S0 2 8 3 19 Arrhenius Plot Data at Densities of 4.05 and 4.15 gcm-3.. 86 - X -Table Page 20 Experimental Data at 0.85 Atmosphere S0 2 and 900°C .. 90 21 Experimental Data at 0.50 Atmosphere S0 2 and 900°C .. 94 22 Experimental Data at 0.25 Atmosphere S0 2 and 900°C .. 98 23 S p e c i f i c Reaction Rate Versus Pressure Data at Densities of 4.05 and 4.15 g cm - 3 101 24 Data from Marker Experiments 103 25 Heat Transfer Data at 900°C and 1 Atmosphere S0 2 132 26 Symbol D e f i n i t i o n s and Nomenclature 134 27 (a) Binary D i f f u s i o n C o e f f i c i e n t s ( i E S 2 , j i S 0 2 ) at 1 Atmosphere S0 2 135 (b) Ternary D i f f u s i o n C o e f f i c i e n t s at 900°C (i=S 2, j=S0 2, k=A) 135 28 (a) Comparison of Experimental Flux at a Reaction Time of 1 Second and Flux Dictated by Boundary Layer Control 137 (b) Experimental Conditions 137 29 E f f e c t i v e D i f f u s i o n C o e f f i c i e n t s i n the Porous Layer at Various Experimental Conditions 140 1- 1 D e f i n i t i o n of Symbols (c.g.s. units) 203 2- 1 Polynomial C o e f f i c i e n t s f o r F i t t e d Curves 227 - x i -ACKNOWLEDGEMENT The author wishes to express h i s gratitude to Dr. I.H. Warren for h i s advice and encouragement as d i r e c t o r of t h i s research. Gratitude i s also extended to Dr. J.K. Brimacombe f o r h i s assistance i n the l a t t e r stages of t h i s study. Thanks are also expressed to other members of the Faculty of Metallurgy f o r t h e i r advice. The f i n a n c i a l assistance of the Aluminium Company Limited and the National Research Council of Canada by way, of Assistantships i s greatly appreciated. To my wife, my thanks f o r her patience and understanding. i - 1 -I. INTRODUCTION A. General Commercial interest i n iron sulphides i s based on inherent sulphur values and, as such, the economics of processing such ores must be examined i n terms of relevance to the sulphur industry. Of a t o t a l of over 9 m i l l i o n long tons of sulphur produced i n the United States i n 1967, only about 9 percent originated from the processing of metal sulphide ores; less than half of t h i s , i n turn, resulting from the treatment of iron sulphides."^" Frasch-produced sulphur accounted for roughly 77 percent of the t o t a l sulphur production, while sulphur recovered from sour refinery gases constituted the balance.^ Whereas sulphur resulting from these l a t t e r two processes i s i n an elemental form, the f i n a l product from the majority of iron sulphide processing plants i s sulphuric acid. This type of process also yields iron oxide with or without contained precious metals. The sale of these by-products aids i n s t a b i l i z i n g this p a r t i c u l a r process sector of the sulphur industry i n conditions of widely fluctuating sulphur price. Even so, at low sulphur prices, sulphur burning becomes a cheaper source of sulphuric acid. Methods of processing iron sulphides are varied and involve both hydrometallurgical and pyrometallurgical techniques. An example of the former i s the thermal decomposition of iron pyrites and subsequent aqueous - 2 -2 oxidation of the decomposition product, pyrrhotite. Recovery of sulphur i n i t s elemental form was reported to be 90 percent. Pyrometallurgical treatments commonly employed are those involving a i r , chlorinating, sulphating, or fla s h roasting. In the present economic climate surrounding the sulphur industry, i t i s now thought to be advantageous to convert inherent sulphur i n iron sulphides to the elemental form rather than to sulphuric acid. There are two reactions of interest involving high temperature gaseous oxidation which indicate the p o s s i b i l i t y of pyrometallurgical processing to form ele-mental sulphur d i r e c t l y . One of these i s represented by equation (1), which when considered i n conjunction with a i r oxidation (see equation (2)) and the gaseous conversion reaction of hydrogen sulphide and sulphur dioxide (see equation (3)), yields elemental sulphur. In order that a l l 3FeS + AH„0 — T Fe„0. + 3H.S + H„ (1) 3FeS + 50 2 • Fe 30 4 + 3S0 2 (2) 2H2S + S0 2 : --^r_ 3/2 S 2 + 2H20 (3) sulphide sulphur be converted to elemental sulphur, two-thirds of the pyrrhotite must be reacted v i a equation (1). . This reduces the effectiveness of the inherent heat effi c i e n c y introduced by the exothermicity of equation (2). In addition, the production of large volumes of hydrogen further decrease e f f i c i e n c y of the ov e r a l l process. - 3 -A second p o s s i b i l i t y of iron sulphide processing presents i t s e l f on examination of equation (4) which describes the oxidation of pyrrhotite by sulphur dioxide to form elemental sulphur i n a more direct manner than that outlined i n the preceding paragraph. This reaction i s c h a r a c t e r i s t i c 3FeS + 2S0 o —»- Fe.O. + 6/2 S„ (4) I 3 4 2 of many gas-solid reactions i n which a less dense product layer superposes a more dense unreacted portion, thus necessitating d i f f u s i o n of reacting arid product gases through the product layer. I t i s the study of t his reaction which constitutes the body of this thesis. B. Past Research 1. Kinetics of Pyrrhotite Reaction with Sulphur Dioxide 3 The f i r s t researchers to study the k i n e t i c s of iron sulphides from a commercial standpoint investigated methods of desulphurization at elevated temperatures. They concerned themselves primarily with the quantification of amounts of sulphur loss obtained by reacting pyrites. with common gases such as a i r , steam, hydrogen, carbon monoxide and dioxide, and coal gas. In addition to t h i s , they also determined the p a r t i a l pressures of sulphurous product gases. Although iron sulphide (the decomposition product of iro n pyrites) has been described to this stage i n the thesis as a stoichiometric compound, FeS, i t i s now generally accepted to exist over a range of stoichiometry. This range varies from a S/Fe r a t i o of 1.0 to a value greater than t h i s . The stoichiometric compound i s referred to i n the l i t e r a t u r e as t r o i l i t e , while the non-stoichiometric, iron-deficient compound i s ca l l e d pyrrhotite. - 4 -E q u a t i o n (4) d e s c r i b i n g t h e r e a c t i o n o f p y r r h o t i t e w i t h s u l p h u r d i o x i d e i s t h u s more c o r r e c t l y d e s c r i b e d by e q u a t i o n ( 5 ) , i n w h i c h t h e S/Fe r a t i o i s d enoted by t h e term (1 + u ) . Because o f t h e c o m p l e x i t y i n t r o d u c e d by 3 F e S 1 + y + 2 S 0 2 ^ F e ^ + S 2 (5) d e a l i n g w i t h t h e s u l p h i d e as a n o n - s t o i c h i o m e t r i c compound, the m a j o r i t y of s t u d i e s o f t h i s r e a c t i o n have been r e s t r i c t e d t o e q u i l i b r i u m thermo-dynamic i n v e s t i g a t i o n s . I n a d d i t i o n t o t h e few k i n e t i c s t u d i e s , t h e r e has a l s o been some work o f r e l e v a n c e t o t h e p r e s e n t s t u d y c o n d u c t e d on the c o r r e s p o n d i n g r o a s t i n g ^ r e a c t i o n . 4 5 6 Of t h e k i n e t i c s t u d i e s , I r i a r t e e t a l . ' and S u s u k i have examined some a s p e c t s o f o x i d a t i o n o f f i n e l y d i v i d e d p y r r h o t i t e by s u l p h u r d i o x i d e . The o n l y r e s e a r c h c o n c e r n i n g t h i s r e a c t i o n p l a n n e d from a m e c h a n i s t i c s t a n d p o i n t i s t h e work by M o r a w i e t z . ^ As w e l l as s t u d y i n g t h e e q u i l i b r i u m thermodynamics o f e q u a t i o n (5) as a f u n c t i o n o f t e m p e r a t u r e and p a r t i a l p r e s s u r e o f s u l p h u r d i o x i d e , he d e v e l o p e d a c o u n t e r d i f f u s i o n a l a n a l y s i s to e x p l a i n e x p e r i m e n t a l o x i d a t i o n b e h a v i o u r a t 1 atmosphere p r e s s u r e o f s u l p h u r d i o x i d e and t e m p e r a t u r e s f r o m 700°C t o 900°C. I n t h i s work, M o r a w i e t z p r e p a r e d s p h e r i c a l p e l l e t s f rom e l e m e n t a l s u l p h u r and i r o n powder by s i n t e r i n g a t 900°C. The p e l l e t s were o x i d i z e d i n d i v i d u a l l y i n a f l o w o f s u l p h u r d i o x i d e w i t h t h e sample w e i g h t b e i n g c o n t i n u o u s l y r e c o r d e d . He o b s e r v e d an o u t e r s h e l l o f m a g n e t i t e w h i c h t h i c k e n e d a t the expense o f t h e u n r e a c t e d c o r e ad t h e r e a c t i o n p r o g r e s s e d . At c o m p l e t i o n , a m a g n e t i t e s p h e r e o f h i g h e r p o r o s i t y t h a n t h e u n r e a c t e d s p h e r e and o f i d e n t i c a l d i m e n s i o n s t o t h e o r i g i n a l r e m a i ned. A t any t i m e - 5 -during r e a c t i o n , s e c t i o n i n g of a p e l l e t revealed what was noted to be a sharp boundary or i n t e r f a c e between the sulphide core and outer oxide s h e l l . The k i n e t i c experiments were c a r r i e d out using p y r r h o t i t e samples which when o x i d i z e d r e s u l t e d i n p o r o s i t i e s i n the magnetite v a r y i n g from 35.0 to 58.5 percent. Because the r e a c t i o n i n t e r f a c e was observed to be a sharp boundary, the r a t e determining process was assumed to be d i f f u s i o n of reactant and product gases through the product l a y e r . A counter-d i f f u s i o n a l a n a l y s i s was then derived i n order to c a l c u l a t e e f f e c t i v e d i f f u s i o n c o e f f i c i e n t s from the experimentally obtained weight change data. The d i f f u s i o n c o e f f i c i e n t s determined by these means are reproduced i n Table 1 together w i t h the corresponding experimental c o n d i t i o n s of temperature and r e s u l t a n t magnetite p o r o s i t i e s . Table 1. C a l c u l a t e d D i f f u s i o n C o e f f i c i e n t s as a Function of Temperature and Pore Volume T(°C) Pore Volume (%) D p e Q (cm sec ) 3 4  700 58.6 0.095 800 58.5 0.127 900 58.7 0.163 900 49.0 0.074 900 35.5 0.0059 900 58.6 0.160 900 58.6 0.167 - 6 -Although the derivation of the mathematical model and necessary assumptions was not provided i n Morawietz' paper, a j u s t i f i c a t i o n of the g counterdiffusional analysis was l a t e r presented by Jost. On examination of the stoichiometry of equation (5) i t can be seen that there must be a net bulk flow of gas: a greater volume of sulphur leaving the reaction interface than sulphur dioxide a r r i v i n g . Jost explained that Morawietz recognized the existence of t h i s net bulk flow by introducing unique diff u s i o n c o e f f i c i e n t s for sulphur dioxide and sulphur into the derivation. This made i t possible to treat the counterdiffusional analysis as i f i t were equimolar. Morawietz presented the d i f f u s i o n c o e f f i c i e n t s , which were calculated from one p a r t i c u l a r oxidation t r i a l , as a function of percent reaction. On increasing extent of reaction, the coefficients exhibited a general increasing trend with an o v e r a l l v a r i a t i o n of + 15 percent from the average. Using t h i s average value for d i f f u s i o n c o e f f i c i e n t , a theoretical oxidation curve was predicted and compared with the corresponding experimental curve. Agreement was r e l a t i v e l y good between the two curves, with predicted rates of reaction being greater than the experimental rates during the i n i t i a l stages of reaction and less than the experimental rates for the l a t t e r part of reaction. On a basis of observation of a sharp reaction interface, Morawietz assumed that the oxidation of pyrrhotite by. sulphur dioxide was controlled by transport through the magnetite layer for the range of pyrrhotite density investigated. By applying a counterdiffusional analysis to experimental reaction rates he was able to calculate e f f e c t i v e d i f f u s i o n coefficients as a function of reaction extent. Since these values were r e l a t i v e l y constant, he concluded that the assumption of rate c o n t r o l was v e r i f i e d . By a l l u s i o n to a pore model, the magnitude of e f f e c t i v e d i f f u s i o n c o e f f i c i e n t s r e l a t i v e to bulk molecular d i f f u s i o n c o e f f i c i e n t s was q u a l i t a t i v e l y explained such that the d i f f u s i o n mechanism was postulated to be that of molecular d i f f u s i o n . 2. Crystallographic Nature of the S o l i d Species Natural pyrrhotites have been shown to consist of t r o i l i t e , low temperature hexagonal p y r r h o t i t e , monoclinic p y r r h o t i t e , or mixtures of 9 either the f i r s t or l a s t two forms. This becomes apparent on examination of the iron-sulphur phase diagram as constructed by K u l l e r u d 1 ^ (see Figure 1). The composition range of relevance to t h i s study f a l l s within the room temperature two phase region i n which t r o i l i t e and low temperature hexagonal p y r r h o t i t e e x i s t ; while at temperatures at which pyr r h o t i t e oxidation w i l l be studied, the composition range i s e n t i r e l y within the one phase region where only the high temperature hexagonal form of p y r r h o t i t e i s found. Both hexagonal forms and the t r o i l i t e v a r i e t y of p y r r h o t i t e are based on a simple n i c k e l arsenide hexagonal structure referred to i n the l i t e r a t u r e as the.B-8 structure. This basic structure, as reported by 11 o o Haraldsen, has an a axis of about 3.43 A and a c axis of about 5.75 A. 2-It i s best considered a hexagonal close packed S l a t t i c e containing 2+ Fe ions i n octahedral i n t e r s t i t i a l p o s i t i o n s . At temperatures below 320°C, that of the 3 t r a n s i t i o n , pyrrhotites i n the two-phase region under discussion have been described by several unique c r y s t a l l o g r a p h i c super-structures, a l l of which are r e l a t e d to the B-8 structure. At room - 8 -6 0 0 5 5 0 5 0 0 4 5 0 4 0 0 O 3 5 0 o cJ 3 2 0 o v_ QJ CL E ^ 2 5 0 3 0 0 -2 0 0 -J L. Hexagonal high temp, pyrrhotite Hexagonal low temp, pyrrhotite Hexagonal high temperature pyrrhotite + pyrite Hexagonal low temperature pyrrhotite + pyrite 3i0 Monoclinic pyrrhotite + pyrite • • Monoclinic pyrrhotite Pyrite + monoclinic sulfur -Monoclinic pyrrhotite + F e 3 S 4 Fe,S 3°4 F e 3 S 4 + pyrite Pyrite + liquid sulfur 114 5 JQ2_ Pyrite + orthorhombic sulfur F e 7 S 8 4 5 F e 3 S 4 4 0 Atomic per cent Fe 35 FeS, 30 Figure 1. Iron-Sulphur Phase Diagram. - 9 -temperature, both synthetic and natural pyrrhotites have been described 9 11 12 13 as consisting of two structures ' ' ' : The B-8, char a c t e r i s t i c of low temperature hexagonal pyrrhotite; and a superstructure with an a o o axis of about 5.96 A and a c axis of about 11.75 A, which i s attributed to t r o i l i t e . Within the range of sulphur concentration 50.0 to 53.5 atomic 11 14 percent sulphur, Haraldsen and Hagg and Sucksdorff have shown that on increasing sulphur concentration, the superstructure which was most strongly detected at 50.0 atomic percent sulphur had disappeared from 51.0 to 51.4 atomic percent sulphur. As the iron deficiency further increased (from 51.4 to 53.5 atomic percent sulphur), l a t t i c e calculations of the B-8 structure indicated l i n e a r l y decreasing l a t t i c e parameters. Any pyrrhotite i n the two phase region at room temperature, when heated to temperatures between 700°C and 900°C, converts to the high temperature hexagonal form at the g t r a n s i t i o n temperature (shown i n Figure 1 as 320°C). Although superstructures have been reported to exist i n pyrrhotite quenched from about the 0 t r a n s i t i o n temperature, "*""* 16 d i f f r a c t i o n experiments undertaken at 320°C found only B-8 ref l e c t i o n s . Another char a c t e r i s t i c of the high temperature hexagonal form i s the random 2+ ordering of Fe vacancies as opposed to the various degrees of ordering present i n low temperature hexagonal forms. The s o l i d product species of equation (5), magnetite, unlike the forms of pyrrhotite discussed above, i s of the cubic family of structures: 34. 2+ 3+ an inverse spinel described by the formula Fe (Fe Fe )0^. Of the 24 iron ions i n a unit c e l l , one half or 8 of the f e r r i c ions are situated i n tetrahedral s i t e s , the remainder plus 8 ferrous ions f i l l i n g - 10 -the octahedral s i t e s . The 32 oxygen Ions can be described as lying i n a close packed cubic array. A comparison of t h i s structure with those of FeO and Fe^O^ shows the s i m i l a r i t i e s of three l a t t i c e s . The oxides FeO, Fe^O^, and y-Fe^O^ can be regarded as having i d e n t i c a l structures with only the number of i n t e r s t i t i a l iron ions changing,"*"^ On the basis of a cube consisting of 32 oxygen ions, cube edges at 1000°C for the three oxides would be o o from 8.60 A to 8.56 A for FeO (double the unit c e l l l a t t i c e parameter), o o 8.37 A for Fe o0. and 8.30 A for Y-Fe„0„. Thus there i s a close 3 4 2 3 relationship between the structures of these oxides of iron. The more stable form of hematite at high temperature, a-Ye^O^, has a corundum structure of rhombohedral symmetry and can be described as a s l i g h t l y distorted, hexagonal close packed oxygen ion l a t t i c e with i n t e r s t i t i a l metal ions. E p i t a x i a l relationships between the various iron oxides have been 18 determined. Mehl and McCandless observed a common (001) plane of iron atoms having directions <010> i n wustite p a r a l l e l to <110> i n iron. They also found wustite and magnetite to have a common (001) plane of oxygen ions. In oxidation of magnetite to a~~Fe^0^, the d i s t o r t i o n 19 i s considerably greater but Gruner has shown that a common oxide plane exists for this oxide plane as w e l l . o In the case of iron oxidation, values of density of Iron i n the . j . , 7.85 gm Fe 4.43 gm Fe 3.74 gm Fe successively formed layers are: — — B , — ^ — ° , j-a  „ cm Fe cm FeO cm Fe o0. 3 67 gm Fe 3 H and — ' -—2 _ f i . I f the r a t i o of the value of a product layer to that of cm F e2^3 a reactant i s less than one, then conditions are s a t i s f i e d for formation - 11 -20 of a homogeneous oxide layer as set f o r t h by P i l l i n g and Bedworth. I f , however, the r a t i o of these values i s greater than unity as i n the case of hematite reduction, . each successive oxide layer w i l l form i n a manner which i s p h y s i c a l l y discontinuous i n r e l a t i o n to the underlying layer. The corresponding value of density of i r o n i n stoichiometric , ^. ^  . 3.06 gm Fe n . ,^ ,. , , pyr r h o t i t e i s ^— s . Since the corresponding value for magnetite cm FeS i s greater, the oxidation of p y r r h o t i t e should r e s u l t i n the formation of a p h y s i c a l l y discontinuous magnetite layer. 3. Thermodynamics of the Reaction of P y r r h o t i t e with Sulphur Dioxide The reactions representing the oxidation of p y r r h o t i t e by steam (see equation (1)) and by sulphur dioxide (equation (4)) have been b r i e f l y discussed previously. The enthalpy and free energy of each reaction i n addition to those of a i r oxidation (see equation (2)) have been calculated for stoichiometric p y r r h o t i t e and are shown i n Table 2. Table 2. Enthalpies and Free Energies of Reaction f o r Equations (1), (2) and (4) i n Kcal/mole FeS Equation (1) Equation (4) Equation (2) T°K • AH AF AH AF AH AF 1300 6.716 13.845 6.428 6.620 -137.7 -99.8 1200 6.643 13.284 6.517 6.601 -137.6 -102.7 1100 6.518 12.713 6.549 6.584 -137.7 -105.6 1000 6.318 12.145 6.505 6.581 -137.8 -108.5 900 6.092 : 11.551 6.428 6.571 -137.9 -111.5 - 12 -It can be noted that both the oxidation by steam and by sulphur dioxide are s l i g h t l y endothermic and almost i d e n t i c a l . A more d e t a i l e d analysis of the endothermicity of the sulphur dioxide oxidation reaction w i l l be presented i n the discussion of heat transfer. F i r s t , a thermodynamic base must be developed f o r the sulphur dioxide oxidation reaction i n terms of the iron-sulphur-oxygen system. Iron p y r i t e s , FeS2, loses sulphur on heating i n an i n e r t atmosphere, such that by 690°C i t can be completely converted to FeS^ + ) J (the p a r t i a l pressure of sulphur over p y r i t e s i s 1 atmosphere at t h i s temperature).^ The sulphur p a r t i a l pressure over p y r r h o t i t e also increases with tempera-ture but i s much lower i n magnitude as shown i n Table 3. Table 4 gives Table 3. Equilibrium Sulphur P a r t i a l Pressure over P y r r h o t i t e T°K 1300 1200 1100 1000 900 P Q (atm) b2 2.11xl0~ 7 2.10xl0~ 8 1.382xl0" 9 5 . 3 6 x l 0 - 1 1 1.023xl0~ 1 2 Table 4. Equilibrium Sulphur P a r t i a l Pressure over P y r r h o t i t e at 1 Atmosphere Sulphur Dioxide T°K P c (atm x 10 2) S 0 (%) 2  1300 ' 4.63 4.4 1200 3.60 3.5 1100 2.70 2.6 1000 1.88 1.86 .900 1.22 1.20 the calculated values of sulphur p a r t i a l pressure and percent sulphur i n the equilibrium gas mixture r e s u l t i n g from oxidation of stoichiometric p y r r h o t i t e by sulphur dioxide at 1 atmosphere sulphur dioxide pressure. 21 22 Using standard thermodynamic data, ' s t a b i l i t y diagrams have been 23 constructed, a f t e r the fashion of Ingraham's predominance area diagrams, for the iron-sulphur-oxygen system as a function of p a r t i a l pressures of sulphur and sulphur dioxide at temperatures of 800°K, 1000°K, and 1200°K. These appear i n Figures 2, 3, and 4, r e s p e c t i v e l y , and have been calculated by consideration of equations (6) to (19) i n c l u s i v e . 2Fe + S 2 ^—*; 2FeS (6) 2FeS + S 2 2FeS 2 (7) 4FeO + S 2 ^2 4Fe + 2S0 2 (8) 4Fe 30 4 + S 2 12FeO + 2S0 2 (9). 12Fe„0 o + S„ y 8Fe o0. + 2S0„ (10) 2 3 2 -< 3 4 2 Fe o0. + S 0 »- 3Fe + 2S0 o (11) 3 4 2 -* 2 4FeS + 2S0 2 4Fe0 + 3S 2 (12) 6FeS + 4S0„ »- 2Fe n0. + 5S„ (13) 2 -< 3 4 2 3FeS 0 + 2S0„ y Fe.O. + 4S„ (14) 2 2 •* 3 4 2 8FeS 2 + 6S0 2 ^ 4Fe 20 3 + l i s (15) FeS + 2Fe0 3Fe + S0 2 (16) Figure 2. S t a b i l i t y diagram for sulphides and oxides of iron at 800°K. Figure 3. S t a b i l i t y diagram for sulphides and oxides of iron at 1000°K. Figure 4. S t a b i l i t y diagram for sulphides and oxides of iron at 1200°K. FeS + 3Fe.O. »- lOFeO + SO. (17) 3 4 •* 2 5FeS„ + Fe o0. »- 8FeS + 2SO. (18) 2 3 4 •* 2 FeS. + 16Fe„0o —-»- llF e , 0 . + 2SO„ (19) 2 2 3 < 3 4 2 Values of the enthalpies and free energies of formation of the sulphides used i n these calculations were those reported by E l l i o t and 22 Gleiser. I t should be noted that the thermodynamic data for pyrrhotite which they have tabulated are based on formation of stoichiometric pyrrhotite form i t s elements. On the other hand, the data for pyrites are i n reference to formation from pyrrhotite and sulphur vapour. In this case, pyrrhotite i s not stoichiometric but has a S/Fe r a t i o of about 1:15, even though the thermodynamic data for pyrites has been determined by using the enthalpies and free energies of formation of stoichiometric pyrrhotite. However the errors incurred by this assumption are l i k e l y to be small since the maximum difference between enthalpies of formation 24 of stoichiometric and non-stoichiometric pyrrhotite are only s l i g h t l y greater than the uncertainty i n the values as quoted by E l l i o t and 22 Gleiser. Choosing the 1200°K s t a b i l i t y diagram, i t can be seen that by imposing a pressure of 1 atmosphere sulphur dioxide on pyrrhotite, only magnetite i s obtained as a reaction product. I f , as i n the experimental procedure of the present study, a flow of impure sulphur dioxide at 1 atmosphere pressure i s passed over pyrrhotite, the effect of oxygen contamination should be considered. At 1200°K, the calculated value -9 for p a r t i a l pressure of sulphur from equation (2) i s approximately 7x10 - 18 -1/2 S 2 + 0 2 ^ S0 2 (20) atmospheres, which i s w e l l within the boundaries of s t a b i l i t y of magnetite at 1 atmosphere pressure of sulphur dioxide. If oxygen contamination i s present to an extent where magnetite i s no longer stable, there are two possible routes by which hematite can be formed: eit h e r d i r e c t l y by equation (21) or i n two stages as shown by equations C22) and C23). Thermodynamic c a l c u l a t i o n s suggest that the l a t t e r route 4FeS + 70 2 ^ 2 F e 20 3 + 4S0 2 (21) 3FeS + 50 2 ^ F e 3 0 4 + 3S0 2 (22) 2 Fe 30 4 + 1/2 0 2 ^ 3Fe 20 3 (23) i s preferred. On t h i s basis, the calculated oxygen p a r t i a l pressure required for t h i s route i s only s l i g h t l y greater than that r e s u l t i n g from the sulphur dioxide d i s s o c i a t i o n equilibrium. Hence, only a small extraneous oxygen contamination can cause formation of hematite as an a d d i t i o n a l product during oxidation of p y r r h o t i t e by sulphur dioxide. Again r e f e r r i n g to the s t a b i l i t y diagrams, no stable range of existence can be found for wustite, FeO, at 800°K. At a temperature of 1000°K, wustite can e x i s t thermodynamically as a stable product over a f i n i t e range of p a r t i a l pressures of sulphur dioxide and sulphur. Although the extent of t h i s range increases with temperature, wustite can only e x i s t i n the system when the imposed sulphur dioxide p a r t i a l - 19 -pressure Is less than 3.5x10 ~* atmospheres. The formation of i r o n sulphates has not been included i n ca l c u l a t i o n s f o r the s t a b i l i t y diagrams 25 because i t has been reported that they are not stable over 650°C. Although there i s a s c a r c i t y of thermodynamic enthalpy and free energy data reported i n the l i t e r a t u r e for non-stoichiometric p y r r h o t i t e , the following arguments provide a b r i e f review of dependency of the S/Fe r a t i o of pyr r h o t i t e on temperature and pressure i n sulphur-sulphur dioxide and hydrogen-hydrogen sulphide gaseous environment. 2 6 Niwa and Wada have experimentally determined the equilibrium-r e l a t i o n s h i p s between stoichiometry of py r r h o t i t e and the hydrogen-hydrogen sulphide r a t i o i n the gas phase. Their reproduced data i s presented i n Figure 5. Reference i s made to other studies: those of 27 28 Rosenquist and Sano and Okajima. 7 29 30 31 Several studies ' ' ' have been conducted to examine the thermodynamics of pyr r h o t i t e i n the sulphur-sulphur dioxide system from a standpoint of v a r i a b l e stoichiometry. Of prime i n t e r e s t i n t h i s regard i s the work of Morawietz.^ The author has used the data of Morawietz and interpolated to d i f f e r e n t temperatures and pressures. The re s u l t i n g dependencies of stoichiometry on temperature and pressure of sulphur dioxide are shown i n Table 5. S i m i l a r l y Table 6 gives interpolated data f o r the dependence of sulphur p a r t i a l pressure on temperature and p a r t i a l pressure of sulphur dioxide. Since stoichiometry of py r r h o t i t e i s an experimental parameter, the reaction of py r r h o t i t e with sulphur dioxide must be considered as written i n equation (5). In th i s case, the equilibrium constant i s given by equation (24). The corresponding values calculated from the data - 20 -0 CM X a \ CO CVi X CL O - 2 — o 1.00 X XX + OD O A SO O © x 6 A A X © Method 1 Method II O • 4 5 0 ° ' A A 5 0 0 ° V V 5 5 0 ° * Authors • m 6 0 0 ° o 7 0 0 ° , 0 4 5 0 ° C Sano and Okajima X 7 0 0 ° ~ 8 0 0 ° C 1 _ + 9 0 0 ° ~ I 2 0 0 ° f R o s e n 9 v l 5 f 1.05 1.10 1 + x in FeS , + •X" X 0 I.I5 Figure 5. Stoichiometry Dependence of Pyrrhotite on H^ /H^ S Ratio. - 21 -Table 5. Stoichiometry Factor u of FeS^ +^ at Various Temperatures and Sulphur Dioxide P a r t i a l Pressures p s o 2 ( a t m ) T(°C) 0.25 0.50 0.85 1.0 900 0.096 0.104 0.106 0.108 800 0.115 0.122 0.123 0.123 700 0.135 0.142 0.143 0.144 Table 6. Sulphur P a r t i a l Pressures (mm Hg) at Various Temperatures and Sulphur Dioxide P a r t i a l Pressures p s o 2 ( a t m ) T(°C) 0.25 0.50 0.85 1.0 900 8.00 17.2 25.8 26.8 800 4.52 9.85 14.7 15.2 700 2.38 5.10 7.60 8.00 i n Tables 5 and 6 i n c.g.s. unit are presented i n Table 7. By using these experimentally derived K g values (converted to appropriate u n i t s ) , new values f o r the free energy of equation (5) were calcu l a t e d . These - 22 -are reported i n Table 9 and can be compared with the corresponding values of free energy for equation (4) which appear i n Table 2. The e f f e c t of S/Fe r a t i o of p y r r h o t i t e on the enthalpy of formation at 0 24 298 K has also been studied, the data being reproduced i n Table 8. On the assumption that the small enthalpy change due to stoichiometry i s constant with temperature, enthalpies of reaction f or equation (5) have been calculated and are presented i n Table 9. I t i s i n t e r e s t i n g to note that the enthalpies of formation (Table 8) increase negatively over the region 50.0 to 51.4 atomic percent sulphur, thus coinciding with Haraldsen's f i e l d of s t a b i l i t y of mixed structures. 1"'' From 51.4 to Table 7. Values (c.g.s. units) at Various Temperatures and Sulphur Dioxide P a r t i a l Pressures p s o 2 ( a t m ) T(°C) 0.25 0.50 0.85 1.0 900 0.696 1.482 1.571 1.271 800 V : 0.198 0.438 0.450 0.355 700 0.0679 0.152 0.159 0.135 Table 8. Enthalpy of Formation of FeS,^, at 298°K (Kcal/mole) x+u U+u) AH (1+u) AH (1+u) AH 1.005 -22.4 1.043 -24.9 1.09 -25.4 1.01 -22.1 1.05 -24.45 1.103 -24.9 1.025 -23.55 1.066 -25.38 1.13 -25.0 Table 9. Enthalpy and Free Energy of Reaction for Equation (5) (Kcal/mole FeS-, ) T(°K) AH AF 1200 9.12 6.811 1100 9.15 7.323 1000 9.11 7.866, 53.5 atomic percent sulphur, the enthalpy of formation remains constant at approximately -25.0 Kcal/mole. 4. Gas-Solid Reactions (i ) General Since the early 1960's much progress has been made i n the analysis of gas-solid reactions of the type: The majority of research i n t h i s f i e l d has been focussed on the reduction of i r o n oxides by hydrogen f o r the obvious reason of i t s s i g n i f i c a n c e to the m e t a l l u r g i c a l industry and the simple stoichiometry involved. 32 In a general review of the progress of 1970 of the a n a l y t i c a l treatment of gas-solid reactions, Bradshaw has l i s t e d the seven well-known p h y s i c a l and chemical processes which should be considered i n any analysis. These are: a S 1 (25) - 24 -( 1 ) d i f f u s i o n of the reactant gas specie from the bulk gas stream to the p a r t i c l e surface; (2) d i f f u s i o n of t h i s reactant gas through a product layer to the reaction interface; (3) adsorption of the reactant gas at the interface; (4) chemical reaction at the interface; (5) desorption of the product gas specie at the inteface; C6) outward d i f f u s i o n of the product gas through the product layer; and (7) d i f f u s i o n of the product gas from the p a r t i c l e surface to the bulk gas stream. In addition, i t must be determined whether isothermal or non-isothermal conditions p r e v a i l during reaction. I f the l a t t e r , heat transfer to or from the reaction interface, depending on whether the reaction i s endothermic or exothermic, must be included i n the analysis of experimental reaction rates. In l i g h t of the steps involved i n a gas-solid reaction, during which a porous product layer i s formed, the overall rate of reaction can be determined by one of three processes: gaseous d i f f u s i o n through a gas f i l m ; gaseous d i f f u s i o n through a product layer; and i n t e r f a c i a l processes. Let the rate at which a reaction proceeds i n the absence of d i f f u s i o n a l effects define the term i n t r i n s i c reaction rate. Hence when the observed rate i s less than the i n t r i n s i c rate, d i f f u s i o n of gases through a product layer or a gas f i l m becomes the rate determining step. The regimes of d i f f u s i o n a l and of chemical control i n gas-solid reactions involving a product layer can best be explained by referring to Arrhenius activation energy diagrams of log rate versus reciprocal temperature. A t y p i c a l plot i s shown i n Figure 6b depicting three Figure 6 ( c ) . Arrhenius diagram near completion of reaction. - 26 -separate slopes i n the three regimes A, B, and C, which represent control by gas f i l m d i f f u s i o n , by pore Body d i f f u s i o n , and by i n t e r f a c i a l processes, respectively. If the rate determining process i s that which consumes the greatest part of the chemical p o t e n t i a l , then the existence and range of the three regimes can be readily understood. Typical activation energies for d i f f u s i o n a l processes are much less than those for chemical or i n t e r f a c i a l processes. In recognition of t h i s , there i s some temperature below which the i n t r i n s i c rate i s low enough that very l i t t l e chemical potential i s consumed by di f f u s i o n through a gas f i l m and a porous layer. However, as the temperature increases, the i n t r i n s i c rate increases i n such a way that progressively more chemical potential i s consumed by di f f u s i o n a l processes. At some temperature (denoted BC i n Figures 6(a), (b), and ( c ) ) , pore body d i f f u s i o n becomes rate l i m i t i n g . S i m i l a r l y , on further increase of temperature, the lowest activation energy process, that of gas f i l m d i f f u s i o n , w i l l become the l i m i t i n g process (at a temperature denoted AB). In a gas-solid reaction with porous product layer formation, the extent of reaction influences the range of each regime because, for a constant pore size d i s t r i b u t i o n , an increase i n length of d i f f u s i o n path causes an increase i n consumption of chemical potential. A comparison of Figures 6(a), (b) and (c) i l l u s t r a t e s the manner i n which the regimes of control are affected by the extent of reaction. Figure 6(a) shows that at onset of reaction, the low consumption of chemical potential by pore body d i f f u s i o n through a thin product layer permits chemical control to extend to a higher temperature than i n the case of figure 6(b). - 27 -In the same way by comparison with Figure 6(b), Figure 6(c) shows the opposite e f f e c t on t r a n s i t i o n temperature BC caused by higher consumption of chemical p o t e n t i a l by pore body d i f f u s i o n through a t h i c k product layer. Generally, the a l t e r a t i o n of phy s i c a l properties of the product layer i n such a way as to increase the observable rate of reaction at constant product layer thickness w i l l r a i s e the segment B (but not increase the slope) and increase the t r a n s i t i o n temperature. By a s i m i l a r argument, i t can be reasoned that as the product layer increases i n thickness, the t r a n s i t i o n from pore body d i f f u s i o n a l control to that of gas f i l m d i f f u s i o n occurs at i n c r e a s i n g l y higher temperatures. Although t r a n s i t i o n temperatures i n going from one regime of control to another are depicted as f i n i t e , t h i s i s so only because of the d e f i n i t i o n of rate c o n t r o l . Mathematically, r e l a t i v e consumptions of chemical p o t e n t i a l by p o t e n t i a l l y rate determining processes are described by expressions of continuity. This then indicates that the t r a n s i t i o n from one regime to another i s not defined by a unique temperature but occurs over a range of temperature. It must also be pointed out that although the two d i s t i n c t slopes i l l u s t r a t e d f o r control by pore body d i f f u s i o n and by gas f i l m d i f f u s i o n i n f e r d i f f e r e n t a c t i v a t i o n energies for each process, such i s not necessa r i l y the case. Where a gas - s o l i d reaction i s t r u l y topochemical, each process has the same a c t i v a t i o n energy. However, i n the extreme opposite case (that of heterogeneous c a t a l y s i s ) where pore body d i f f u s i o n and i n t e r f a c i a l processes simultaneously consume chemical p o t e n t i a l , the corresponding regime of control has a c h a r a c t e r i s t i c observed a c t i v a t i o n energy equal to the average of those for the d i f f u s i o n and - 28 -chemical processes. In a non-catalytic reaction where some unreacted s o l i d i s retained i n the product layer and where pore channels i n the unreacted s o l i d are long r e l a t i v e to sample dimensions, i t might be expected that the activation energy observed for pore body d i f f u s i o n be higher than that exhibited by gas f i l m d i f f u s i o n . ( i i ) Analysis of Iron Oxide Reduction by Hydrogen Although the seven p o t e n t i a l l y rate-determing steps were recognized as being of importance i n the analysis of gas-solid reactions involving the formation of a porous product layer, a n a l y t i c a l treatment of observed reaction rates prior to 1960 involved v e r i f i c a t i o n of an i n i t i a l assumption of single control, either by chemical processes or by transport through a porous product layer. As a result of recent advances i n a n a l y t i c a l procedure, i t i s now possible to examine the p o s s i b i l i t i e s of control by gas f i l m d i f f u s i o n and control i n the t r a n s i t i o n regimes. A br i e f review of some of the recent research i n the f i e l d of hematite reduction by hydrogen w i l l serve to elucidate the development of mathematical models for gas-solid reactions. 34-37 By applying the pr i n c i p l e of conservation of mass, McKewan 1/3 interpreted experimental weight loss data by a r e l a t i o n of (1-m ) with time, where m i s the unreacted mass fr a c t i o n of a spherical sample. On discoverying that this relationship was linea r throughout reaction, he postulated that chemical processes were rate-determining. By using 36 37 an inert diluent gas to vary the hydrogen p a r t i a l pressure ' he again observed a linear relationship. As he l a t e r discovered, at high hydrogen 38 pressures, s p e c i f i c reaction rates approached a maximum value. This - 29 -anomaly was attributed to a decreasing a v a i l a b i l i t y of adsorption s i t e s towards eventual saturation as the hydrogen pressure increased. In a mechanistic study of reduction of magnetite to wustite i n hydrogen-water 39 vapour environments, Quets et a l . l i k e McKewan, interpreted l i n e a r relationships between reaction rate and time to indicate control by i n t e r f a c i a l processes. 40 41 On studying the same reaction as McKewan, Warner ' found that at low hydrogen p a r t i a l pressures (achieved by lowering t o t a l pressure) s p e c i f i c reaction rate versus time plots exhibited a de f i n i t e non-linear nature. He also observed metallographically a sharp reaction front and absence of any retained wustite i n the reduced i r o n , both of which observations indicate transport control. Chemical control during reaction of a porous p e l l e t would cause reaction to occur throughout the p e l l e t simultaneously. In addition to transport control by gaseous d i f f u s i o n , Warner included i n a mathematical analysis the effects of di f f u s i o n of reactant and product gases through an external laminar gas f i l m around the perimeter of the specimen. This l a t t e r process was found to have a f i n i t e influence on the reaction rate under certain experimental conditions. From the results of his analysis, Warner proposed what has been referred to as a mixed control model. This i s often stated i n the l i t e r a t u r e as meaning rate control by transport processes as well as by chemical or i n t e r f a c i a l processes. The significance of mixed control i n r e l a t i o n to the discussion i n the general section on gas-solid reactions i s that mixed control i s similar to control i n the t r a n s i t i o n between the two regimes of control. Although by d e f i n i t i o n of i n t r i n s i c ' reaction rate, mixed control implies a - 30 -dif f u s i o n limited rate, the interactions between the two modes of control necessitates inclusion of mathematical expressions representing both modes of control i n the analysis. The method of analysis involved separation of the t o t a l resistance to reaction into resistances which were encountered by the three processes: transport through a gas f i l m ; transport through a porous product layer; and i n t e r f a c i a l processes. Warner found resistances due to transport processes to be the most s i g n i f i c a n t at high temperatures and pressures. He explained McKewan's results at high hydrogen pressures by showing that i f gaseous d i f f u s i o n through a product layer i s the greatest resistance, then reaction rate would be ess e n t i a l l y independent of pressure since the d i f f u s i o n c o e f f i c i e n t i s inversely proportional 42 to t o t a l pressure. Warner was supported by St. C l a i r who proposed a mathematical model to analyze the rate of simple gas-solid reactions determined by control i n this t r a n s i t i o n region between transport and chemical control. 43 44 Olsson and McKewan ' have since corroborated Warner's work by studying separately the rates of equimolar counterdiffusion of hydrogen and water vapour through porous iron. The resistance attributed to this p a r t i c u l a r rate c o n t r o l l i n g step was found to increase with increasing temperature and pressure. The effect of temperature and pressure on the pore size was also investigated with the conclusions that on increasing reduction temperature, the pore size increased and that at 900°C, normal or molecular gaseous d i f f u s i o n was occurring while at 500°C, di f f u s i o n was c l a s s i f i e d as t r a n s i t i o n a l (between pure molecular and pure Knudsen) i n nature. - 31 -Several papers^"* ^ have been published since Warner's which have supported the concept of mixed control i n the p a r t i c u l a r system of reduction of i r o n oxides by hydrogen. In t h e i r second of two papers, Spitzer et a l . have formulated a general model for hematite reduction i n which were considered transport processes to and from, i n addition to chemical processes at each of the three i n t e r f a c e s : hematite-magnetite; magnetite-wustite; and wustite-iron. Also included was transport through an external gas f i l m . To t h i s point, only dense p e l l e t models have been mentioned i n 48 49 th i s review. Researchers such as Kawasaki et a l . and Bogdandy et a l . ' have shown the importance of transport control i n reference to a porous p e l l e t model. Both groups, however, considered only transport processes i n the determination of a r a t e - c o n t r o l l i n g step. The s i g n i f i c a n c e of heat transfer has been discussed by Lahiri,^"'" who showed that the endothermicity of the reduction of hematite by hydrogen causes a s i g n i f i c a n t variance between sample and ambient temperatures. In f a c t , t h e o r e t i c a l analyses applied to a 0.7 cm diameter p e l l e t yielded temperature differences as high as 40°C and 25°C at ambient temperatures of 900°C and 800°C r e s p e c t i v e l y . 52 A very complete review by H i l l s demonstrates the importance of considering a l l possible processes when attempting to determine rate c o n t r o l l i n g steps. Only when the r e l a t i v e e f f e c t s of each i s evaluated i n terms of the experimental data can i t s s i g n i f i c a n c e i n the o v e r a l l k i n e t i c model be ascertained. - 32 -5. Physical Characteristics of Product Layers A knowledge of the physical nature of the product and reactant layers i s essential i n that k i n e t i c data are often complicated by the v a r i a t i o n i n physical properties during a p a r t i c u l a r k i n e t i c experiment. A review of the factors which can influence a chemically controlled 53 reaction rate has been presented by Prosser. These include c r y s t a l structure, surface orientation, the presence of dislocations, impurites i n s o l i d solutions, and non-stoichiometry. In reactions which are transport controlled, the most important physical properties are density, grain s i z e , and the size shape, and d i s t r i b u t i o n of pores i n the s o l i d reactant. What i s more d i f f i c u l t to assess i s the relationship between these properties of the reactant and t h e i r counterparts i n the resulting s o l i d product. Since observed d i f f u s i o n coefficients are effected by the nature of the product layer, they cannot be derived but can be determined by independent experiments. Some work of interest has been carried out to indicate relationships between experimental reaction conditions and the physical nature of product s o l i d s . By pressing boehmite pe l l e t s to various densities, Cadle and 54 S a t t e r f i e l d determined the v a r i a t i o n i n density of segments of porous pe l l e t s as a function of the location of the s l i c e i n the o r i g i n a l p e l l e t . They found density to increase as distance from the top of the p e l l e t increased, the effect being greater at higher p e l l e t densities. Measure-ments of hydrogen fl u x through a sample enabled them to calculate d i f f u s i o n c o e f f i c i e n t s which reflected the density v a r i a t i o n . 40 Warner investigated the effect of reaction temperature on the pore structure of reduced iron and found that the pore size increased - 33 -with reduction temperature. Measurements of pore s i z e by mercury penetration porosimetry yielded minimum diameters and since 'bottlenecks' were observed i n the pore structure of the reduced i r o n , i t was presumed that they were responsible f o r the measured minimum diameters. In t h i s case, the e f f e c t i v e pore diameters would have been considerably larger than those indicated by the measured values. 6. D i f f u s i o n i n Porous Solids Many papers have been published on the topic of d i f f u s i o n of gases i n porous media, a primary area of i n t e r e s t being the t r a n s i t i o n region i n which both molecular and Knudsen d i f f u s i o n contribute to transport of gases. Because the nature of the d i f f u s i o n mechanism i s dependent on pore s i z e , shape, and d i s t r i b u t i o n , the formulation of a pore model i s an i n t e g r a l part of studies of d i f f u s i o n of t h i s type. Comprehensive review papers on t h i s subject have been written by D u l l i e n and Batra"^ and Younguist."^ AO From the pore measurements reported by Warner, pore diameters of the reduced i r o n s h e l l ranged from 0.1 u at 650°C to a s t a t i s t i c a l maximum of 2.0 u at 950°C. Where X i s the mean free path and r the pore radius, i t has generally been accepted that an r/X r a t i o l e s s than .0.1 indicates that Knudsen d i f f u s i o n i s the predominant mechanism, while molecular d i f f u s i o n occurs only at r/\ values greater than 10. It would be expected, then, that the pore diameters measured by Warner would r e s u l t i n d i f f u s i o n i n the t r a n s i t i o n region as was suggested by Scott and D u l l i e n . ^ However, d i f f u s i o n c o e f f i c i e n t s calculated from mass transfer analyses were i n the range of magnitude of those - 34 -a t t r i b u t a b l e to molecular d i f f u s i o n . This led Warner to his explanation of the existence of 'bottlenecks' being responsible for the measured values of pore diameters. Discrepancies between the calculated d i f f u s i o n c o e f f i c i e n t s and those of molecular d i f f u s i o n were accounted f o r by consideration of a 58 t o r t u o s i t y f a c t o r , as described by Carman as a function of the i n t e r -connection of pores, and the void f r a c t i o n of porosity. Olsson and 43 44 McKewan ' have since supported Warner's theory i n the sense that independent d i f f u s i o n experiments have resulted i n the f i n d i n g of s i m i l a r d i f f u s i o n c o e f f i c i e n t s with t o r t u o s i t y factors of the porous s o l i d varying between 2.3 at 1000°C and 5.2 at 400°C. I t appears, then, that for the reduction of hematite by hydrogen, d i f f u s i o n a l analyses can be based on the assumption that the predominant mechanism i s that of molecular d i f f u s i o n . Pure Knudsen d i f f u s i o n i s described as transport of gaseous molecules where the rate i s dependent only on c o l l i s i o n with pore walls and not on c o l l i s i o n of gaseous molecules. The Knudsen d i f f u s i o n c o e f f i c i e n t of a specie i , D i s defined by equation (26), where r , R, T, l _ 2 ,8RT\l/2 K. = 3 r ( ^ T T ) ( 2 6 ) 1 1 and M^ are r e s p e c t i v e l y : pore radius, gas constant, temperature, and molecular weight of specie i . D v being a function experimentally only K . 1 of pore radius, temperature and molecular weight, i t i s i n t e r e s t i n g to note that the Knudsen d i f f u s i o n c o e f f i c i e n t s of sulphur and sulphur dioxide w i l l be e f f e c t i v e l y equal under s i m i l a r conditions of pore structure and temperature, since t h e i r molecular weights are v i r t u a l l y i d e n t i c a l . The f l u x r e s u l t i n g from Knudsen d i f f u s i o n i s given by equation (27), where (P. - P. ) i s the pressure drop over a d i f f u s i o n 1 L 1 0 length L. DK N i - - s ( \ - v (27) Analysis of d i f f u s i o n through porous s o l i d s i n the Knudsen and t r a n s i t i o n regions i s considerably more complex than that i n the molecular d i f f u s i o n region as a r e s u l t of the dependencies on pore structure. 59 Cunningham and Geankoplis have tested a random pore model for the t r a n s i t i o n region which i s based on a t r i d i s p e r s e d s o l i d consisting of two macropore and one micropore diameter. The s e l e c t i o n of two macropore diameters was thought to be more rigorous since most compressed porous s o l i d s contain macropores i n a broad pore siz e d i s t r i b u t i o n . By analysis of d i f f u s i o n data using t h i s model, l i m i t s of the range over which d i f f u s i o n occurred i n the t r a n s i t i o n region were found to be greater than the accepted values mentioned previously by an approximate factor of 2. The range, of course, i s very l a r g e l y a function of the pore model chosen for analysis. For the general case of d i f f u s i o n i n the t r a n s i t i o n region, the f l u x can be defined as shown i n equation (28), where D.. i s the molecular d i f f u s i o n c o e f f i c i e n t , P the t o t a l pressure, a = 1 + , and i s t n e mole f r a c t i o n of specie i . D. . 1-cry. + D..P V N i = l n D T P ( 2 8 ) l - a Y . + ^ 0 K. - 36 -I t i s apparent that while d i f f u s i o n c o e f f i c i e n t s can be determined from k i n e t i c experiments, i t i s d i f f i c u l t to ascertain the r e l a t i v e contributions of molecular and Knudsen d i f f u s i o n . In order to accomplish t h i s , independent d i f f u s i o n experiments must be conducted using a porous s o l i d which i s physically similar to that formed as reaction product i n the k i n e t i c experiments. The d i f f u s i o n data must then be analyzed by employing a pore model that i s v a l i d for the p a r t i c u l a r system. C. Objective and Scope of the Present Work Since the study on oxidation of pyrrhotite by Morawietz,^ the understanding of controlling processes operant i n gas-solid reactions, during which a porous product layer i s formed, has advanced considerably. This i s primarily the result of research i n the p a r t i c u l a r f i e l d of iron oxide reduction by hydrogen. That analysis by consideration of either transport control or i n t e r f a c i a l control singly i s misleading has been demonstrated by the number of papers published i n this f i e l d . The end r e s u l t , at present, has been the formulation of a mixed control model i n which any or a l l of the possible mass transport processes may contribute s i g n i f i c a n t resistances to gaseous fluxes during reaction. These resistances may, i n turn, vary r e l a t i v e to one another during a part i c u l a r experiment. In this work, much e f f o r t has been focussed on the preparation of pyrrhotite samples with reproducible physical properties. This was thought to be necessary since k i n e t i c data obtained from this type of gas-solid reaction often exhibit a large s e n s i t i v i t y to physical characteristics of the porous product layer. The weight loss of thin - 37 -rectangular pyrrhotite plates, prepared by sintering under pressure, has been measured as they reacted with sulphur dioxide. Reaction conditions consisted of oxidation of plates of a range of density at temperatures between 700°C and 900°C and at sulphur dioxide pressures between 0.25 and 1.0 atmospheres. Analysis of the weight loss data has been accomplished by using a mixed control model as applied to thin rectangular plates. This has enabled the author to attri b u t e r e l a t i v e importance to the po t e n t i a l l y rate-determining processes: transport through a laminar gas f i l m and a porous product layer; and i n t e r f a c i a l processes. The effect of heat transfer on the ki n e t i c s has also bee investigated. By analysis of k i n e t i c data obtained from various sets of experimental conditions, effective d i f f u s i o n c o e f f i c i e n t s have been calculated, from which di f f u s i o n mechanisms have been inferred. Additional marker experiments and metallographic examination of product layers by techniques of electron microscopy have been used to aid i n the determination of rate c o n t r o l l i n g processes and di f f u s i o n mechanism. - 38 -I I . EXPERIMENTAL A. Apparatus 1. Measurement of Weight Change The diagram shown i n Figure 7a schematically i l l u s t r a t e s the experimental apparatus, the major component parts of which are l a b e l l e d . The device employed to measure continuous weight change was a Statham UC2 green c e l l transducer (component C i n Figure 7a). Used i n conjunction with i t was a micro-scale accessory; simply a levered balance arm. By u t i l i z i n g the f u l l length of the balance arm, the transducer i s rated as described i n Table 10. A readout u n i t , also supplied by Statham Industries, was used to obtain s e n s i t i v i t y and balance c o n t r o l , while a Sargent SR recorder monitored the s i g n a l . Because weight changes were small r e l a t i v e to sample weights, i t was necessary to use a suppressed zero i n order to increase the r e s o l u t i o n of a recorded s i g n a l . This was accomplished by i n s e r t i o n into the c i r c u i t of a 'bucking box'. I t consisted of a ten turn potentiometer of 500 Q resistance, a 1.4 V mercury c e l l , and an external resistance of 6800 Q. By use of t h i s c i r c u i t , i t was possible to 'buck out' or suppress the zero s u f f i c i e n t l y so that good r e s o l u t i o n of weight change could be obtained. - 39 -Figure 7(a). Schematic cross-section of experimental apparatus. - 40 -Legend for Figure 7(a) A. Furnace B. Reaction chamber C. Transducer D. Thermocouple w e l l E. Gas s e a l F. P y r r h o t i t e plate G. Argon p u r i f i c a t i o n system H. Sulphur dioxide p u r i f i c a t i o n system - 41 -Table 10. Operational S p e c i f i c a t i o n s of a Statham UC2 Transducer Force range 30 g Force range at f u l l extension of balance arm 3 g Displacement 0.06 mm F u l l scale (F.S.) output 8 mV/V Non - l i n e a r i l y and hysteresis 0.15% F.S. Thermal s e n s i t i v i t y s h i f t <0.01% F.S./°F Thermal zero s h i f t <0.01% F.S./°F Rated e x c i t a t i o n 7.5 V maximum Bridge resistance 350 Q The power source for transducer e x c i t a t i o n was a serie s of f i v e 1.4 V mercury c e l l s . Voltage s t a b i l i t y with respect to time i s rated at about 0.1 percent; and with respect to temperature at 43 uV/°F from 70°F. The maximum error r e l a t i v e to weight recorded i s , however, magnified due to use of the suppressed zero to 0.8 percent or 1.5 mg, while the l i m i t s of measurement of recorded weight from a chart i s + 0.2 mg. The errors due to thermal i n s t a b i l i t y and zero s h i f t are n e g l i g i b l y small i n comparison, since the e x c i t a t i o n source i s maintained within 5°F of room temperature. The transducer ( b a s i c a l l y an unbonded s t r a i n gauge) can also be the source of thermal i n s t a b i l i t y and zero s h i f t s during an experiment. To minimize the extent of these e r r o r s , the transducer was mounted i n a thermally insulated casing, the l e v e l of which was maintained at not less than 10 inches above the top of the gas s e a l . - 42 -2. Furnace and Reaction Chamber The furnace (component A) surrounding the 28 mm I.D. quartz r e a c t i o n chamber (components B and E) was constructed as two hinged hal\res i n order to f a c i l i t a t e i n s e r t i o n and removal of the r e a c t i o n tube. Each half of the furnace consisted of a standard nichrome wound 11/4 i n . diameter mullite h a l f s h e l l of 12 i n . length set i n i n s u l a t i n g b r i c k 1 i n . thick. This, i n turn, was encased i n a hollow s t e e l h a l f s h e l l . Rated power consumption for t h i s unit was 750 watts. I t was found that the maximum temperature gradient across a t y p i c a l sample at the thermal centre of the furnace was 2°C. Experiments showed that the magnitude of the power surge as the relay switched to 'on' cycle affected the recorded weight. To minimize th i s e f f e c t , the ' o f f cycle of the relay switch was s h o r t - c i r c u i t e d i n such a way that the v a r i a b l e voltage was applied through an external f i x e d resistance to the furnace. With t h i s c i r c u i t , i t was then possible to obtain a stable s i g n a l to the recorder while c o n t r o l l i n g temperature to within 2°C at a temperature of 900°C. Extraneous noise was minimized by connecting a 4000 Mf capacitor across the s i g n a l to the recorder. Although t h i s decreased the recorder response time, the experimental rate of weight losses incurred were slow enough i n every case that the slower response time did not a f f e c t accuracy of the resultant curves. The reaction chamber consisted of two sections (B and E) joined by a ground glass j o i n t ; part B having dimensions 28 mm I.D. and 30 mm O.D. This lower section contained a thermocouple w e l l which was fused at the base of part B and extended up the centre of the tube. The inner w a l l of the well was sealed to the outer wall of the tube at the base. The - 43 -end of the well at the centre of the furnace was also sealed. The length of the w e l l was chosen so that while the inner end was located at the thermal centre of the tube (when inserted i n the furnace), the top of the tube (B) projected a pre-determined distance above the furnace. This distance was f i x e d so that very l i t t l e sulphur vapour condensed at the top of the tube, the bulk of i t passing i n t o the gas seal (component E). I t was found to be necessary to provide sheathing for the chromel-alumel thermocouples as a r e s u l t of the corrosive properties of sulphur dioxide at high temperatures. The gas seal (E) was employed f o r reasons of safety; as a deterrent to corrosion of other equipment; and as a means of suspending the sample (F). The exhaust tube, connected to a v e n t i l a t i n g system, was able to cope with maximum flow rates. In order to avoid contamination by a i r entering at the top of E, the flow of exhaust gases was regulated so that a small amount escaped through the top of E. This was c o l l e c t e d by a second exhaust tube. The sample (F) was suspended by a drawn quartz f i b r e , the optimum diameter of which was determined by conditions of r i g i d i t y and b r i t t l e n e s s r e s u l t i n g from extensive periods of exposure to sulphur dioxide at reaction temperatures. I t was found that f i b r e s with diameters between 0.15 mm and 0.20 mm were large enough to withstand corrosion and s u f f i c i e n t l y f l e x i b l e that the reactant gas flow did not a f f e c t the recorded weight. The f i b r e was hung from the balance arm, passed through the top of E, and i n t o the section B. The l e v e l of the transducer casing was adjusted so that the sample did not contact the upper end of the thermocouple w e l l . - 44 -3. Gas P u r i f i c a t i o n Systems As mentioned i n Section I.B.3, i t was necessary to ensure that magnetite was the only iron oxide formed during oxidation of p y r r h o t i t e . Indeed, when Matheson anhydrous sulphur dioxide (99.8 percent pure) was used i n the as-received condition, product layers on reacted p y r r h o t i t e samples consisted of some hematite as w e l l as magnetite. Removal of oxygen and water vapour impurities was c l e a r l y important. Knowing that gaseous equilibrium are f a s t ; that the equilibrium constant for sulphur dioxide d i s s o c i a t i o n i s fixed f o r any temperature; and that the p a r t i a l pressures of sulphur and oxygen i n equilibrium with sulphur dioxide are linked by stoichiometry, a l e v e l f o r p a r t i a l pressure of oxygen can be set by subjecting a flow of sulphur dioxide to l i q u i d sulphur. The value of the oxygen p a r t i a l pressure w i l l then depend on the temperature of the l i q u i d sulphur and the pressure of sulphur dioxide. Advantage was taken of the fact that the v i s c o s i t y of l i q u i d sulphur approaches a minimum low temperature value at 152°C,^ so that a maximum amount of convection i n the l i q u i d can occur. At temperatures higher than t h i s the v i s c o s i t y increases r a p i d l y up to a temperature of 189°C, only to decrease again at temperatures above t h i s . Log K g f o r the formation of sulphur dioxide by equation (19) at 21 150°C i s given, as approximately 37.2. Since K^ i s defined by equation (29) the equilibrium p a r t i a l pressure of oxygen can be calculated K e (29) - 45 -to be about 2x10 atmospheres under the imposed condition of 1 atmosphere pressure of sulphur dioxide. This i s well beloxj the l i m i t of oxygen p a r t i a l pressure corresponding to i n h i b i t i o n of hematite formation, and indeed, experimentally none was detected. Removal of water vapour impurity from the as-received anhydrous sulphur dioxide was achieved by bubbling sulphur dioxide through two flasks of sulphuric acid i n series by means of dispensing tubes. P u r i f i c a t i o n of argon also entailed the removal of oxygen and water vapour to acceptable l i m i t s , although the levels of impurity were not as high as i n sulphur dioxide. Argon composition specifications were given as 99.995 percent argon, 33 p.p.m. nitrogen, 10 p.p.m. water vapour, 5 p.p.m. oxygen, and 2 p.p.m. hydrogen. The technique of removal of oxygen and water vapour involved the flowing of argon through consecutive columns of drying agent, deoxidizing agent, and drying agent. The two columns of drying agent were maintained at room temperature, the deoxidizing agent column regulated at 150°C. The drying agent employed was Linde, type 4A (1/16 i n . c y l i n d r i c a l p e l l e t s ) . This molecular sieve i s more effective than s i l i c a gel as a drying agent but has the disadvantage of i t being more d i f f i c u l t to ascertain the point of saturation. I t was for this reason that a column of drying agent was placed i n series after the deoxidizing column as well as before i t . Regeneration of saturated molecular sieve p e l l e t s was achieved by heating the material to 320°C i n a flow of a i r as 61 described by White and Smith. For the deoxidizing column, a very convenient and effec t i v e getter was found i n B.A.S.F. activated copper. This agent i s actually cuprous oxide which has been ground to a very - 46 -small mesh size and p e l l e t i z e d . It i s most e f f e c t i v e at temperatures near 150°C. The approach to saturation i s r e a d i l y noticeable as the p e l l e t colour changes from black to green ( c h a r a c t e r i s t i c of cupric oxide). Regeneration was accomplished i n s i t u by heating slowly to 200°C i n hydrogen (which was deoxidized by a standard c a t a l y t i c p u r i f i e r ) . Gas l i n e s i n the p u r i f i c a t i o n system were a l l constructed from 7 mm pyrex tubing, non-glass j o i n t s , where necessary, being neoprene. B. Materials (1) Iron Sulphide The p y r r h o t i t e used throughout t h i s study was supplied by Rocky Mountain Research Incorporated and was reported to be 99.9 percent i n pur i t y . Spectrographic analysis of a sample which had been ground i n a vibrat o r y b a l l m i l l y ielded the r e s u l t s quoted i n Table 11. In addition to these impurities, magnetite arid some hematite were noticeable by eye on c e r t a i n external surfaces of the as-received clinker-form sulphide. Oxygen analyses by neutron a c t i v a t i o n gave oxygen contents ranging from 132 p.p.m. to 662 p.p.m. depending on the o r i g i n a l sample. This, when converted to percent magnetite i n d i c a t e s that from 0.05 to as much as 0.24 percent magnetite was present i n the as-received p y r r h o t i t e . As a r e s u l t of t h i s f i n d i n g , i t was considered to be necessary to subject p y r r h o t i t e to a high temperature s u l p h i d i z i n g atmosphere during the preparative procedure i n order to decrease or convert the contained i r o n oxide. The purpose of the s u l p h i d i z a t i o n treatment, i n addition to the above mentioned, was to create samples with approximately the same S/Fe r a t i o s . P y r r h o t i t e , as received, was f i r s t pulverized to -10 mesh, - 47 -Table 11. Spectrographic Analysis of Pyr r h o t i t e i n Weight Percent Impurity. Element % Impurity Element % Impurity A l 0.7 - Mo 0.01 Ca 0.1 Ni 0.01 Cr 0.001 S i 0.1 Co 0.003 Sr 0.001 Cu 0.003 T i 0.01 Pb 0.01 V 0.003 '••r Mg 0.03 Zn 0.01 - 48 -then ground dry i n a vibra t o r y b a l l m i l l using ceramic b a l l s . I t i s th i s l a t t e r procedure which i s assumed to be responsible f o r the high analyses of A l , Ca, and S i . The -325 mesh f r a c t i o n was placed i n a large porcelain boat, 1 i n . deep by 6 i n . i n length, which i n turn was inserted i n a ho r i z o n t a l tube furnace. A f t e r heating to 900°C i n argon, a mixture of hydrogen sulphide and hydrogen of P 0/P,, =0.6 was passed through the H^S H2 furnace. I t was found by neutron a c t i v a t i o n analysis that a f t e r treatment for f i v e hours, maximum oxygen content was 35 p.p.m. oxygen or 0.013 6 2 percent magnetite. By standard BaSO^ analysis f o r sulphur the S/Fe. r a t i o i n py r r h o t i t e a f t e r s u l p h i d i z a t i o n varied, between 1.068 and 1.074. As can be seen from Figure 5, t h i s corresponds with the values obtained by 26 Niwa and Wada. The stoichiometry as a function of gas composition i s r e l a t i v e l y independent of temperature between 450°C and 900°C, hence tempera-ture gradients within the s u l p h i d i z a t i o n furnace were unimportant. In addition to the various analyses f o r impurity and stoichiometry of p y r r h o t i t e , X-ray Debye-Scherrer powder photographs were taken of sulphidized p y r r h o t i t e using cobalt r a d i a t i o n with an i r o n f i l t e r at a voltage of 30 kV and a current of 10 ma. The s u l p h i d i z a t i o n environment was defined by P u C/P„ = 0.05 for the sample to which the data of Table H 2 S H2 12 r e f e r s . The r e s u l t i n g S/Fe r a t i o was determined by BaSO^ analysis to be approximately 1.03 ot 50.8 atomic percent sulphur. Also l i s t e d i n Table 12 are the indices corresponding to each l i n e a f t e r the method of 11 Haraldsen. Although l i n e s c h a r a c t e r i s t i c of the superstructure were present, the i n t e n s i t y of each was very low. This would i n d i c a t e that t h i s p a r t i c u l a r sample had a S/Fe r a t i o close to the upper l i m i t of existence of the superstructure. Debye-Scherrer powder photographs taken of the p y r r h o t i t e sulphidized to a S/Fe r a t i o of 1.07 showed only l i n e s - 49 -Table 12. Debye-Scherrer Results Using Co K Radiation Basic structure Superstructure I/I o 17°30* 100 110 50 19°47* 101 112 70 25°38' 102 114 100 27°36' - 211 3 31°28' 110 300 70 33°50' - 214 5 36°59' 004 008 2 38°31' 201 222 10 42°38' 202 224 30 49°28' - 321 7 54°14' 114 308 30 56°37' - 325 2 58°35' 212 414 20 59°47' - 407 1 64°04.' 300 330 10 0012 67°03' 213 416 15 420 - 50 -char a c t e r i s t i c of the basic structure. 2. Sample Preparation Several exploratory techniques for the preparation of dense samples from sulphidized or as-received pyrrhotite were investigated so that samples of uniform density and reproducible physical properties could be obtained. The methods attempted included s o l i d i f i c a t i o n from the molten state, s i n t e r i n g , and hot-pressing. S o l i d i f i c a t i o n t r i a l s were conducted u t i l i z i n g conditions of controlled cooling so that some measure of re p r o d u c i b i l i t y of grain size could be established. The basic d i f f i c u l t y encountered was the formation of thermal cracks during s o l i d i f i c a t i o n from the melt due to the thermal shock s e n s i t i v i t y of pyrrhotite. In order to achieve grain size s u f f i c i e n t l y small for subsequent k i n e t i c experiments, very high cooling rates were found to be necessary. Forced cooling was controlled by varying the flow of water through a copper mold. Only at cooling rates i n excess of 30°C/min did the resulting grain size measure less than 1 mm. However at these rates, many cracks were present i n the s o l i d i f i e d structure. At lower cooling rates, where no cracks resulted, grain size measured up to several millimeters at which stage, the structure lacked cohesive strength. This approach was then abandoned. The second preparation technique attempted was that of sint e r i n g . By sintering pre-pressed green compacts i n a hydrogen sulphide-hydrogen mixture, a separate sulphidization step was avoided. Attempts were made to s i n t e r compacts to as wide a density range as possible. I t was hoped that by hydrodynamically pre-pressing, densities of sintered compacts would be homogeneous. I t was also assumed that there would be - 51 -l i t t l e or no grain growth during s i n t e r i n g . To cold press, p y r r h o t i t e powder was f i r s t tamped on top of a blank cy l i n d e r i n a 6 i n . section of 1 i n . diameter rubber tubing which had been sealed beneath the blank. The tube was then sealed at the top end a f t e r s u f f i c i e n t powder to make a 2 i n . long c y l i n d r i c a l green compact had been packed into the tube. The tube was then placed i n a c y l i n d r i c a l container of o i l , plungers being sealed by rubber 0-rings, and a pressure of about 25,000 p . s . i . applied through the o i l medium to the compact. Green densities of approximately 65 percent were obtained by t h i s method. The a b i l i t y of these compacts to s i n t e r was found to be dependent on the composition of the gaseous environment. A r a t i o of P„ C/~P = 0.6 H 2S H 2 resulted i n l i t t l e or no s i n t e r i n g a f t e r 20 hours at 1075°C. Sin t e r i n g at a temperature of 1125°C i n t h i s atmosphere only resulted i n rapid grain growth, grain sizes up to 3 mm not being uncommon. By adjusting the gas mixture to P /P = 0.05, some s i n t e r i n g did occur with a r^b n 2 minimum of grain growth. Following t h i s , however, the sintered compacts were treated by the regular sulphdizing atmosphere at 900°C for 6 hours. Using t h i s technique, densities up to 84 percent t h e o r e t i c a l resulted from s i n t e r i n g at 1050°C f o r 20 hours. S i n t e r i n g for the same length of time at 1125 PC yielded d e n s i t i e s up to 90 percent t h e o r e t i c a l , but again, a large increase i n grain s i z e resulted. Any attempt to achieve den s i t i e s higher than 85 percent t h e o r e t i c a l caused extensive grain growth with very l i t t l e increase i n density. Over the range of density 75 to 85 percent t h e o r e t i c a l , measured grain s i z e ranged from 50 u to 80u respectively. At densities 87 percent t h e o r e t i c a l and higher, domains - 52 -were observed i n which grains ranged up to 400 u i n si z e . The i n a b i l i t y to sinter samples to greater than 90 percent t h e o r e t i c a l , and the va r i a t i o n in grain size with sintered density led the author to seek another method of forming dense pyrrhotite samples. Since grain growth appeared to be the prime deterrent i n obtaining homogeneous samples and samples of high density, the technique of hot-pressing or sintering under pressure was attempted. Although u n i - d i r e c t i o n a l pressure i s accepted as causing non-homogeneous density, grain growth should be n e g l i g i b l e due to the use of considerably lower sintering times and temperatures. In f a c t , l i t t l e or no v a r i a t i o n i n grain size with sintered density was detected, the average size being approximately 20 u. A schematic section of the basic apparatus for hot-pressing i s shown i n Figure 7b. Power for the induction c o i l was supplied by a P h i l i p s 12 kwatt unit. Before inserting the die into the c o i l , sulphidized pyrrhotite powder was pre-pressed i n the die by a small hand press to 1500 p . s . i . Then, u t i l i z i n g a controlled heating rate of 20°C/min from room temperature to sintering temperature, pressure was applied slowly so that the f u l l pressure, 17,500 p . s . i . , (previously determined as the optimum pressure) was reached at a temperature 150°C below the intended holding temperature. This pressure was maintained throughout the remaining time required to reach the holding temperature and was held for 2 min at this temperature. I t was then released slowly as the temperature was decreased at a controlled rate of 8°C/minute. This cooling rate was necessitated by cracking of the sintered discs at higher cooling rates. Table 13 l i s t s t y p i c a l temperatures for hot-pressing - 53 -Figure 7(b). Schematic cross-section of hot-pressing apparatus. - 54 -Legend for Figure 7(b) A. Thermocouple w e l l B. Fixed plungers C. Graphite ends D. Quartz sleeve E. Molybdenum die plungers F. Graphite susceptor, sleeves, and spacers G. Water cooled copper induction c o i l H. Cold pressed pyrrhotite compact - 55 -Table 13. Hot-Pressing Temperatures and Resultant Densities _3 T(°C) Density (g cm ) p/ p 340 4.03 0.851 360 4.07 0.860 400 4.11 0.868 425 4.15 0.876 450 4.17 0.882 475 4.20 0.887 500 4.22 0.891 525 4.25 0.897 575 4.38 0.925 600 4.44 0.938 625 4.48 0.946 650 4.50 0.951 700 4.53 0.956 - 56 -and the corresponding sintered densities, a pressure of 17,500 p . s . i . being used throughout a l l preparations. By regulating a 2 l i t r e per minute flow of argon within the outer quartz sleeve, only a small amount of oxidation occurred during hot pressing. Neutron activation analyses reported an oxygen content of 30 p.p.m. i n samples which had been sintered from sulphidized pyrrhotite containing 27 p.p.m. oxygen. Figures 8(a), (b), and (c) are electron photomicrographs taken from chromium shaded carbon replicas of a fracture surface of a disc sintered to 96 percent theoretical density. Samples i n the shape of thin rectangular plates were formed from the hot-pressed discs by using an ultrasonic cutting tool and d r i l l , and a ceramic grinding wheel. Each disc was ground to approximately 1 i n . square, then halved. A small hole, 0.020 i n . diameter, was then d r i l l e d near the edge of the shorter side. Following t h i s , each sample was ground further on the ceramic wheel, then polished by hand to about 0.030 i n . i n thickness on a succession of emergy papers, the l a s t of which was 000 paper. P r i o r to each oxidation t r i a l , samples were measured caref u l l y to obtain values of surface area and average density. 3. Preliminary Tests Although i t has been indicated that no s i g n i f i c a n t amount of oxidation occurred during hot-pressing, there was a p o s s i b i l i t y that some may have taken place during the heating of pyrrhotite plates to reaction temperature. To test this point, three pairs of pyrrhotite plates were heated at rates i d e n t i c a l to those used i n the k i n e t i c experiments to temperatures of 700°C, 800°C, and 900°C, then were cooled i n argon. Each pair of plates was then analyzed for oxygen by the neutron -57-(c) x 5K Figure 8. Fracture Surfaces of a 96 Percent Dense Hot-Pressed Compact. - 58 -activation technique. The corresponding analyses for each pair yielded oxygen contents of 32 p.p.m., 16 p.p.m., and 23 p.p.m. A l l plates were cut and polished from hot-pressed discs originating from sulphidized pyrrhotite analyzing 27 p.p.m. oxygen. Since accepted sampling technique was not adhered to when the powder was weighed for hot-pressing, no conclusions can be drawn as to the increase i n oxygen as a function of t o t a l heating time to temperature. However, i t would seem that the amount of oxidation caused by heating i n argon i s n e g l i g i b l e . As mentioned i n Section I . B . 4 . ( i i ) , a l i m i t i n g flow rate of sulphur dioxide must be attained i n order to prevent starvation of the reactant 40 gas at the sample surface. Preliminary oxidation t r i a l s were under-taken to determine this value at a temperature of 900°C and at 1 atmosphere pressure of sulphur dioxide. Samples oxidized were a l l of -3 density 4.12 g cm . This density was chosen for two reasons: i t was high enough that r e p r o d u c i b i l i t y was r e l a t i v e l y simple; and low enough that substantial rates of oxidation were obtained. Pyrrhotite plates were oxidized i n sulphur dioxide flow rates of 50 ml min ^  to 900 ml min "'"; the results are shown i n Figure 9. The minimum flow of reactant gas to be used i n k i n e t i c experiments was set at 400 ml min ^ . Each rate was measured from i t s corresponding weight loss curve at a weight loss which _3 corresponded to a product layer thickness of 2.45x10 cm. Taking the -2 average half-thickness of a sample as 3.60x10 cm, weight loss to form th i s thickness of product represents, on the average, 6.8 percent t o t a l reaction. Figure 9. C r i t i c a l flow rate. - 60 -C. Procedure 1. Kinetic Experiments Because of the large effect of sample density on the rate of reaction, and the d i f f i c u l t y i n obtaining good re p r o d u c i b i l i t y of density especially at the lower l i m i t of density, oxidation rates were measured as a function of density under varying imposed conditions of either temperature or p a r t i a l pressure of sulphur dioxide. On investigating the effect of temperature, t r i a l s were undertaken at temperatures of 700°C, 800°C, 850°C, and 900°C, the p a r t i a l pressure of sulphur dioxide being held constant at 1 atmosphere. The effect of p a r t i a l pressure of sulphur dioxide was determined by oxidation of pyrrhotite plates at 900°C by four gas mixtures with argon: 1 atmosphere, 0.85 atmosphere, 0.50 atmosphere, and 0.25 atmosphere sulphur dioxide. Experimental procedure was the same i n a l l oxidation t r i a l s , except where demanded by the imposed t r i a l conditions of temperature and pressure. Prio r to each sample oxidation, the microbalance sector of the apparatus was calibrated with standard weights. Both the main reaction tube and the gas seal were flame dried and any condensed sulphur burnt o f f . Before use, the controller was calibrated for use with chromel-alumel thermocouples. A new thermocouple was inserted i n the sheath before each run. Each sample was heated at a constant l i n e a r rate of 8°C min ^  i n an argon flow of 400 ml min When the desired reaction temperature was reached the argon flow was diverted while at the same time, the sulphur dioxide flow was redirected to the reaction tube i n l e t and increased to 400 ml min ^ . Sulphur dioxide had previously been flushed through.its - 61 -own p u r i f i c a t i o n system for a minimum of 15 minutes. I t was permitted to flow at a rate of about 25 ml min u n t i l the time at which i t was diverted to the reaction chamber i n l e t . Every oxidation t r i a l was allowed to continue u n t i l at least 35 percent reaction had been completed. At least one t r i a l from each unique set of experimental conditions of temperature and pressure was continued u n t i l constant weight was reached for purposes of comparison with predicted oxidation behaviour. Following termination of each experiment, the samples were cooled i n a flow of argon. 2. Marker Experiments Three oxidation t r i a l s were carried to or near completion using pyrrhotite plates with 0.001 i n . gold wires pressed i n them. One sample contained two wires, the other two had four each. During the cold-pressing procedure prior to hot-pressing, half the t o t a l weight of pyrrhotite was f i r s t pre-pressed. The wires were placed on the top surface followed by the remainder of the powder. Pressure was again applied cold, and maintained for about 2 minutes. The die and contents were then inserted within the induction c o i l and the normal hot-pressing procedure carried out. Cutting and d r i l l i n g of each disc was si m i l a r to that adopted for regular samples. However, the f i n a l polishing was conducted so that the wires, while approximately p a r a l l e l to the faces of a plate, were situated very close to one face. Proximity to a face, as measured at the edges varied from 50 y to 260 y. Following oxidation to at least 60 percent reaction, the edges of each sample were repolished s u f f i c i e n t l y - 62 -so that the unreacted core was exposed. Distances of each wire from the near face were again measured. 3. Chemical Analysis The chemical analysis of pyrrhotite for contained sulphur was what 62 i s referred to as the BaSO^ analysis. The oxidizing agent employed was a bromine-potassium bromide solution. P r e c i p i t a t i o n of sulphur as barium sulphate was accomplished by the slow addition of barium chloride solution to a large volume of cold sulphur containing solution. 4. Metallographic Examination Electron microscopy was used to examine surfaces of high density compacts before and after oxidation. Carbon replicas were obtained from the desired surfaces and chromium shadowed. Examination and photography of these replicas was conducted on a Hitachi HU 11A electron microscope. For oxidized samples, where i t was necessary to view s p e c i f i c lengths of interface which had been exposed by purposeful fracture, a JEOLCO JXA-3A electron microprobe was used. This technique was p a r t i c u l a r l y useful when the degree of coherence at an interface was investigated. Where general viewing of fractured samples was undertaken, a Cambridge Stereoscan I I stereoscanning electron microscope was used. Because of less cohesion i n pyrrhotite plates of low densities, i t was not possible to obtain replicas for use i n the electron microscope. Also, higher porosities encountered at lower densities reduced the effectiveness of viewing by the electron microprobe. - 63 -I I I . RESULTS A. Kinetics 1. Time Dependence A t y p i c a l weight loss curve exhibited constant weight during heating i n argon to about 580°C, with the exception of a 1 to 2 mg weight loss i n the i n i t i a l 200°C which was probably the result of loss of adsorbed moisture. Weight losses up to 10.2 mg were measured on further heating to reaction temperature. This portion of a t o t a l weight loss curve has been denoted A i n Figure 10. When the argon flow was diverted to exhaust and sulphur dioxide flow to the reaction chamber i n l e t , a small, rapid increase i n weight was observed. This was followed by a period of up to fi v e minutes where the recorded weight remained approximately constant (for samples of density less than 90 percent theo r e t i c a l ) . This part of the t y p i c a l weight loss curve has been denoted B i n Figure 10 and i s followed d i r e c t l y by the portion C which represents the weight loss due to reaction of sulphur dioxide with pyrrhotite. Average values of weight loss during heating i n argon and time over which this i n i t i a l weight loss occurred (part A); and weight gain and time delay (part B) prior to the normal oxidation weight loss (part C) are presented i n Table 14 for temperatures of 700°C, 800°C, and 900°C. In part B, the effect of decreasing pressure CD Q. E o CO Time Figure 10. Schematic weight loss curve. - 65 -T a b l e 14. F e a t u r e s o f P o r t i o n s A and B o f Weight L o s s Curves f o r Low D e n s i t y Samples T(°C) P o r t i o n A P o r t i o n B Weight L o s s Time Weight G a i n D e l a y Time (mg) (min) (mg) (min) 900 10.2 64 6.6 0 800 7.6 44 6.1 2 700 4.6 24 4.6 5 - 66 -was to proportionately decrease the magnitude of weight gain. An increase i n sample density was observed to cause a decrease i n amount of weight gain and an increase i n delay time. For sample densities greater than 90 percent t h e o r e t i c a l , the rate of weight gain i n part B was much slower resulting i n maximum weight being reached only after several hours. The portion C of recorded curves corresponding to conversion of sulphide to oxide were found to be dependent on sample density as wel l as on the reaction parameters of temperature and pressure. These weight losses can be c l a s s i f i e d into two groups: those resulting from oxidation of samples with densities less than and greater than about 90 percent theoretical. A l l curves over the low density range were smooth and exhibited a decreasing rate of weight loss with increasing time u n t i l constant weight was attained. Curves describing oxidation of high density samples, however, were irre g u l a r and showed a character-i s t i c i n t i a l increase i n rate of weight loss followed by approximately linear rates. The s p e c i f i c rates of reaction of FeS^ +^ were measured by taking the slopes of recorded weight loss curves; the accuracy of the slopes were randomly checked by mirror. For each curve, three rates are reported: k^, k 2, and k^. These were measured at weight losses _3 corresponding to fixed calculated product layer thicknesses of 2.45x10 -3 -3 cm, 4.90x10 cm, and 9.80x10 cm, respectively. Units of the reported - 2 - 1 rates are g FeS^ +^ cm sec . Because t o t a l thicknesses of samples varied, the three thicknesses can only be related to average percent t o t a l reaction, then being 6.8 percent, 13.6 percent, and 27.2 percent respectively. - 67 -2. Temperature Dependence The rates k^ ,' k^, and k^ have been plotted as a function of sample density for a density range of 84 to 95 percent t h e o r e t i c a l . Separate plots are presented for temperatures of 700°C, 800°C, 850°C, and 900°C; a l l reactions i n this series were conducted at 1 atmosphere pressure sulphur dioxide. The method of least mean squares has been employed to construct linear relationships over the low density range. The graphs plotted at 900°C for k^, k^, and k^ appear i n Figures 11, 12, and 13; those at 850°C i n Figures 14, 15, and 16; those at 800°C i n Figures 17, 18, and 19; and those at 700°C i n Figures 20, 21, and 22. Tables 15, 16, 17, and 18 contain sample densities, s p e c i f i c reaction rates and the numbering of experiments at the four reaction temperatures. Activation energy plots of log k against reciprocal temperature have also been constructed by the method of least mean squares for the three -3 -3 rates at sample densities of 4.05 g cm and 4.15 g cm (see Figures 23 and 24). The s p e c i f i c reaction rates used for this purpose were the values dictated by the least squares lines for the corresponding rate versus density curves. A summation of the s p e c i f i c reaction rates, temperatures, and resultant activation energies i s given i n Tables 19(a) and (b). 3. Pressure Dependence Three s p e c i f i c reaction rates, also denoted k^, k^, and k^, were measured as described i n Section I I I . A . l . Least squares lines were constructed to f i t l i n e a r relationships between rates and density for three pressures of sulphur dioxide. A l l experiments with varying pressure - 68 -- 69 -- 70 -T 1 1 r o o o 8 ° 0 ° I I I I I l _ 4.0 4.1 4.2 4.3 4.4 Density (g. cm"3) Figure 13. k Versus Pyrrhotite Density at 900°C and 1.0 atm SO - 71 -Table 15. Experiments at 900°C and 1 atmosphere SO Sample no. Density k l k2 , (g cm 3) -2 (g FeS.. , cm sec l+M • ^ x l O 5 42-2 4.03 4.40 3.46 1.82 50-1 4.04 3.44 2.69 1.90 43-2 4.05 3.22 2.64 1.77 49-1 4.05 3.39 2.84 1.75 43-1 4.07 3.28 2.51 1.53 44-1 4.07 2.96 2.59 1.38 51-1 4.07 2.92 2.44 1.59 50-2 4.08 3.43 2.97 1.59 51-2 4.09 2.82 2.28 1.36 52-1 4.09 3.12 2.39 1.44 52-2 4.09 3.24 2.44 1.56 44-2 4.10 3.29 2.42 1.67 45-1 4.14 2.53 1.96 1.31 53-2 4.15 2.11 1.66 1.09 45-2 4.16 1.28 0.995 0.841 46-1 4.18 1.12 0.967 0.816 53-1 4.18 1.73 1.41 0.948 46-2 4.20 1.12 0.923 0.816 47-1 4.20 0.848 0.653 0.463 48-1 4.22 0.405 0.390 0.280 48-2 4.22 0.697 0.582 0.498 47-2 4.23 0.468 0.459 0.230 22-1 4.27 0.205 0.178 0.156 22-2 4.27 0.224 0.155 0.109 7-1 4.29 0.269 0.184 0.148 6-2 4.30 0.155 0.148 0.166 6-1 4.36 0.127 0.116 0.100 5-1 4.38 0.129 0.150 0.160 4-1 4.44 0.137 0.168 0.214 - 75 -Table 16. Experiments at 850°C and 1 atmosphere SO Sample no. Density k l k2 k3 (g cm 3) -2 (g FeS,. cm sec 1+y •w 83-1 4.00 3.39 2.53 1.48 84-2 4.02 3.14 2.51 1.58 84-1 4.04 2.98 1.98 1.29 83-2 4.05 2.46 1.92 1.33 85-2 4.06 2.81 1.92 1.19 86-2 4.11 1.98 1.36 1.03 86-1 4.12 2.54 1.76 1.12 87-2 4.16 1.23 0.858 0.525 87-1 4.17 1.17 0.812 0.567 88-1 4.19 1.24 0.817 0.467 88-2 4.23 0.07 0.507 0.388 82-2 4.23 0.409 0.332 0.211 - 76 -Figure 17. k Versus Pyrrhotite Density at 800°C and 1.0 atm SO - 77 -- 78 -- 79 -Table 17. Experiments at 800°C and 1 atmosphere so 2. Sample no. Density k l k2 k3 (g cm 3) (g FeS -2 i. cm sec 1+y • ^ x l O 5 27-1 4.05 1.90 1.62 1.06 26-2 4.06 1.71 1.32 0.873 49-2 4.06 1.79 1.50 1.08 26-1 4.08 1.44 1.34 0.879 28-1 4.08 1.42 1.21 0.757 27-2 4.10 1.50 0.830 0.628 20-2 4.11 0.768 0.644 0.404 28-2 4.11 1.33 1.09 0.539 29-1 4.12 1.01 0.819 0.442 20-1 4.14 0.756 0.677 0.344 29-2 4.14 0.712 0.458 0.299 30-1 4.14 1.06 0.695 0.488 30-2 4.15 1.04 0.695 0.401 21-1 4.17 0.566 0.419 0.277 21-2 4.21 0.488 0.340 0.165 23-1 4.25 0.120 0.096 0.099 23-2 4.26 0.130 0.107 0.106 31-1 4.33 0.132 0.094 0.150 31-2 4.33 0.077 0.093 0.170 54-2 4.41 0.188 0.284 0.358 - 80 -0.75 L to o o CD to 0.50 h CM I E C P CM 0.25 h 0 4.0 4.2 4.3 Density (g. cm.'3) 4.4 Figure 21. k 2 versus pyrrhotite density at 700°C and 1.0 atm. SO, • •" i — — i : — 1 — •' 1" in o 0.50 -X sec."1 CM 1 . £ o 0.25 -cn ro 0 - Q - ~ Q _ O O °cT§ o ^ o _ 0 _ o o o 0 • 1 « • 4.0 4.1 4.2 4.3 4.4 Density (g. cm."3) Figure 22. k~ versus pyrrhotite density at 700°C and 1.0 atm. S0 o - 83 -Table 18. Experiments at 700°C and 1 atmosphere so 2. Sample no. Density k l k 3 (g cm 3) (g FeS -2 , . cm sec 1+y -w 39-2 4.02 1.153 0.548 0.125 37-1 4.04 1.033 0.503 0.139 32-2 4.05 0.932 0.483 0.166 32-1 4.06 0.872 0.178 0.109 39-1 4.06 0.966 0.262 0.116 40-1 4.07 0.919 0.137 0.103 40-2 4.07 0.987 0.361 0.081 33-1 : 4.09 0.634 0.213 0.092 34-1 4.09 0.628 0.256 0.114 37-2 4.09 0.799 0.295 0.141 33-2 4.10 0.579 0.193 0.142 34-2 4.13 0.433 0.175 0.089 35-2 4.13 0.414 0.228 0.088 35-1 4.15 0.308 0.177 0.075 36-1 . 4.16 0.447 0.234 0.092 36-2 4.19 0.410 0.174 0.081 38-1 4.22 0.145 0.101 0.095 41-1 4.30 0.101 0.089 0.063 54-1 4.43 0.035 0.044 0.062 - 84 -i 1 r • A k2, Ea=23.5 kcal. mole"1 • k3, E a = 30.4 kcal. mole"1 I 1 1— L_ .85 .90 .95, 1.0 l / T ( ° K XIO ) Figure 23. Arrhenius Diagrams for k^, k^, and k^ at Pyrrhotite -3 Density 4.05 g cm - 85 -.90 .95 l/T ( 0 K _ I X|0 3 ) 0 Figure 24. Arrhenius Diagrams for k^, k^, and at Pyrrhotite -3 Density 4.15 g cm - 86 --3 Table 19(a). Arrhenius Plot Data at 4.05 g cm density. TCC) k]_ k 2 k 3 (g FeS, cm 2sec ^ ) x l 0 ^ 1+u 900 3.72 2.89 1.75 850 2.80 2.04 1.30 800 1.82 1.51 1.01 700 0.950 0.366 0.125 E (kcal mole" 1) 15.5 23.5 30.4 3. _3 Table 19(b). Arrhenius Plot Data at 4.15 g cm density T(°C) k± k2 k3 -2 -1 5 (g FeS., . cm sec )xl0 & 1+u 900 2.05 1.54 1.06 850 1.57 1.12 0.734 800 0.779 0.542 0.313 700 0.422 0.177 0.089 E (kcal mole" 1) 18.3 25.1 28.6 a - 87 -Figure 25. k Versus Pyrrhotite Density at 900°C and 0.85 atm SO - 88 --89-- 90 -Table 20. Experimental Data at 0.85 atmosphere SO and 900°C Sample no. Density k^ k^ ( g ° m } (g FeS x cm~ 2sec~ 1)xl0 5 61-1 55-2 58-2 60- 2 61- 2 55- 1 60-1 64-1 56- 1 58- 1 59- 1 59-2 63-1 63-2 4.02 4.03 4.05 4.07 4.07 4.08 4.11 4.12 4.14 4.16 4.18 4.19 4.25 4.30 3.94 3.08 3.13 2.95 2.88 2.44 2.56 2.51 2.34 1.64 1.14 1.56 0.610 0.484 2.96 2.69 2.64 2.07 2.50 1.93 2.27 1.87 2.02 1.25 0.860 1.28 0.535 0.376 1.75 1.51 1.72 1.53 1.66 1.62 1.49 1.15 1.21 0.891 0.548 0.916 0.504 0.324 -91--92-Figure 29. : k Versus Pyrrhotite Density at 900°C and 0.50 atm. -93-- 94 -Table 21. Experiments at 0.50 atmosphere SO and 900°C Sample no. Density k^ k^ (g cm 3) , „ „ -2 -1. , „5 6 (g FeS cm sec )xl0 62-2 3.99 3.41 2.53 1.76 62-1 4.04 2.77 1.99 1.40 66-2 4.04 2.22 1.97 1.51 70-2 4.05 2.74 2.27 1.67 70-1 4.06 2.71 2.28 1.28 65-1 4.07 2.21 1.95 1.33 65-2 4.07 2.21 1.91 1.32 66-1 4.11 1.51 1.14 0.981 67-2 4.11 1.45 1.10 0.749 67-1 4.14 1.12 0.883 0.640 68-1 4.17 0.673 0.573 0.481 68-2 4.20 0.540 0.457 0.374 69-2 4.22 0.479 0.453 0.253 69-1 4.27 0.261 0.325 0.367 -95-Figure 31. k 1 Versus Pyrrhotite Density at 900°C and 0.25 atm. -97-- 98 -Table 22. Experiments at 0.25 atmosphere S0 2 and 900°C Sample no. Density k l k2 k3 (g cm ) (g F e S 1 + y cm' sec )xl0 71-2 4.02 1.04 0.919 0.769 72-1 4.03 1.17 1.09 0.976 77-2 4.04 1.12 0.991 0.763 71-1 4.06 0.956 0.871 0.743 77-1 4.07 1.12 0.965 0.743 73-2 4.08 1.10 0.874 0.650 74-1 4.08 1.04 0.877 0.704 72-2 4.13 1.16 0.982 0.656 73-1 4.13 1.12 0.999 0.690 74-2 4.15 0.993 0.812 0.418 75-1 4.20 0.721 0.579 0.459 75-2 4.21 0.502 0.407 0.357 76-1 4.23 0.645 0.500 0.434 76-2 4.25 0.464 0.353 0.260 - 99 -10 r 4 0 I0"5 CD CO CM 1 . E o CP 10 -6 10 -I T 1 1 1 — M i l l o k, , Slope = 0.831 A k 2 , Slope = 0.751 • k3 , Slope = 0.570 J I I I 1 M I P*„ (atm.) so Figure 34. Pressure dependence of rates k^, k^, and -3 k^ for samples of density 4.05 g. cm - 100 -1 1 1—I—I I I I I o k, , Slope= 0.663 A k 2 , Slope = 0.596 • k 3 , Slope = 0.516 - 101 -Table 23(a). Specific Reaction Rate versus Pressure Data at -3 4.05 g cm density. pso 0 k l k2 k 3 Z (atm) (s F e S i + y cm sec )xl0 1.0 3.72 2.89 1.75 0.85 3.17 2.56 1.64 0.50 2.51 2.01 1.41 0.25 1.13 0.990 0.780 Slope 0.831 0.751 0.570 Table 23(b). Specific Reaction Rate versus Pressure Data at _3 4.15 g cm density. pso 2 k l k2 k 3 (atm) (S F e S l + y "2 i n 5 cm sec )xl0 1.0 2.05 1.54 1.06 0.85 1.90 1.53 1.05 0.50 1.05 0.877 0.656 0.25 0.857 0.721 0.545 Slope 0.663 0.596 0.516 - 102 -were conducted at 900°C. The r e l a t i o n s h i p s at 0.85 atmosphereare shown i n Figures 25, 26, and 27; those at 0.50 atmosphere i n Figures 28, 29, and 30; and those at 0.25 atmosphere i n Figures 31, 32, and 33. Summary Tables 20, 21, and 22 contain the values of the s p e c i f i c reaction rates measured, the various sample d e n s i t i e s , and the numbering of the experiments conducted at the three p a r t i a l pressures. Two graphs of log rate versus log pressure have been constructed for each of the -3 -3 rates at sample densities of 4.05 g cm and 4.15 g cm . These appear i n Figures 34 and 35 r e s p e c t i v e l y with a summation of the relevant data and r e s u l t i n g slopes given i n Tables 23(a) and (b). B. Marker Experiments Observations of fractured and polished cross-sections showed that locations of the gold wire a f t e r oxidation of plates 56-2, 57-1, and 57-2 had not changed s i g n i f i c a n t l y . Distances from wire centre l i n e s to edges of nearest faces were measured before and a f t e r oxidation f o r each plate (see Table 24). Also included i n t h i s table are sample thicknesses at points where distances were measured. Each grouped p a i r of bracketed measurements represents the p o s i t i o n s of opposite exposed ends of one gold wire. C. Metallographic Examination 1. External Oxidized Surfaces Stereoscanner photomicrographs i l l u s t r a t e the surface structure of magnetite and the v a r i a t i o n i n topography of the faces of oxidized plates. Figure 36(a) shows the rather uniform magnetite grain s i z e of sample 15-1 which was oxidized at 900°C i n a 1 atmosphere pressure - 103 -Table 24. Data from Marker Experiments Measurement before oxidation after oxidation no. wire to face thickness wire to face thickness GO GO GO GO Plate 56-2 1 82 954 80 952 2 54 897 71 909 3 231 974 236 976 4 n. d. n.d. n.d. n.d. Plate 57-1 1 105 1554 108 1556 2 n.d. n.d. n.d. n.d. 3 141 1550 171 1576 4 n.d. n.d. n.d. n. d. 5 157 1547 199 1572 6 196 1575 223 1587 7 73 1546 105 1572 8 188 1576 226 1591 Plate 57-2 1 98 1577 108 1588 2 50 1513 66 1543 3 169 1498 161 1498 4 95 1439 110 1456 5 233 1412 231 1423 6 n.d. n.d. n.d. n.d. 7 235 1375 238 1396 8 260 1298 266 1326 - 104 -(a) surface of sample 15-1 oxidized at 900°C, x 1030 (b) b l i s t e r e d surface of sample 15-1, x 210 Figure 36. Surfaces of High Density Samples Oxidized at 900°C. - 105 -sulphur dioxide. The o r i g i n a l density of this pyrrhotite plate was 96 percent theroetical. The average grain size of the surface structure of magnetite i s 6 p compared to a 20 u grain size of pyrrhotite as hot-pressed. Typical surface topography of high density samples (greater than 90 percent theoretical density) after oxidation can be seen i n Figure 36(b) which i s also representative of sample 15-1. The outstanding features or bumps i n figure 36(b) are hereafter referred to as b l i s t e r s . In general, the number of b l i s t e r s per unit area appeared to increase as o r i g i n a l sample density increased from 90 percent theoretical. At densities less than this no surface i r r e g u l a r i t i were detected. Figures 37(a) and (b) are electron photomicrographs of replicas obtained from the oxidized surface of sample 3-1. This plate was oxidized under i d e n t i c a l conditions as was sample 15-1, and had a density of 96.5 percent theoretical. The presence of dislocation networks within magnetite are made apparent by the ordering of thermal etch p i t s . The arrows associated with these two figures indicate the direction of shadowing. 2. Internal Structures Preparation of oxidized samples for examination of i n t e r n a l structures involved the fracturing of samples i n order to expose cross-sections of the thicknesses of plates. Presentation of results of metallographic examination of these cross-sections w i l l appear i n two parts: those of high density and low density samples. Two samples characteristic of the high density group were plates 15-1 and 16-1 of densities 96 percent and 98.5 percent theoretical respectively. Both samples were p a r t i a l l y oxidized and fractured such - 106 -(b) x 4K Figure 37. Surface Replicas of Sample 3-1, Oxidized at 900°C. - 107 -that the cross-sections beneath large surface b l i s t e r s were exposed. The b l i s t e r cross-section of sample 15-1 (see Figure 38), photographed by the stereoscanner, also shows the fine i r r e g u l a r structure of magnetite i n contrast to the larger, smoother grain structure of pyrrhotite. Although the interface i s not wel l defined, i t i s w e l l inside the b l i s t e r . A much larger b l i s t e r was exposed i n sample 16-1 and i s shown as a composite electron microprobe photograph (see Figure 39). Again the interface i s poorly defined with some magnetite noticeable to the inside of the b l i s t e r . The following results refer to the inte r n a l structures of oxidized samples of low density. Several stereoscanner photographs are presented i n this section to determine q u a l i t a t i v e l y the effect between pore structure of magnetite layers and both density of o r i g i n a l samples and temperature of oxidation. Theyare also important for the purpose of establishing the shape of the reaction interface. Figures 40(a), (b), (c), and (d) i l l u s t r a t e the effect of sample density on the pore structure of magnetite layers on plates oxidized at 900°C. The lower density samples (Figures 40(a) and (b)) exhibit smaller macropores than the higher density samples (Figures 40(c) and (d)). The former also appear to be r e l a t i v e l y evenly distributed. However, general trends of increasing macropore size both with increasing distance from the surface and with increasing density are evident. The interfaces between reactant and product are approximately linea r and p a r a l l e l to the faces of each plate. Sample 56-1 (Figure 40(c)) was oxidized to completion hence no interface i s present. The - 108 -Figure 38. Fractured Section Across a B l i s t e r i n Sample 15-1, x 250. - 109 -Figure 39. Fractured Section Across a B l i s t e r i n Sample 16-1, x 300. - 110 -(b) t r i a l 56-1, 4.14 g cm density, x 102 Figure 40. Fractured Sections of Samples Oxidized at 900°C. - I l l -Figure 40. Fractured Sections of Samples Oxidized at 900°C. - 112 -interface i n sample 47-2 (Figure 40(d)) appears to be more ir r e g u l a r than those of the two lower density samples, 49-1 and 59-2. The edges of sample 47-2 also appear to be wavy, reminiscent of b l i s t e r e d surfaces of high density samples. Further magnification of s p e c i f i c areas of magnetite structures permits a better comparison of macropore sizes (see Figures 41(a), (b) and (c)) and i l l u s t r a t e s the existence of much smaller pores, referred to as small macropores. Approximate average diameters of the larger macropores y i e l d values of 6.9 u for sample 49-1 (Figure 41(a)); 8.1 p for sample 59-2 (Figure 41(b)); and 9.8 p for sample 47-2 (Figure 41(c)). Whereas the f i r s t two f i e l d s of view were selected adjacent to interfaces, the l a t t e r extends from the surface to within a few u of the interface, although i t i s not v i s i b l e . The increase i n large macro-pore diameters towards plate centres i s obvious by a comparison of Figures 42(a) and (b) which represent structures at the centre of sample 56-1 and midway between the surface and interface of sample 59-2 respectively. Corresponding averages of diameters of the large macropores are 7.7 u and 3.4 u respectively although sample 59-2 was of higher density than sample 56-1. Another interesting aspect of these two structures i s the r e l a t i v e d i s t r i b u t i o n of large and small macropores. When the diameters of large macropores are low (Figure 42(b)) there exists a high frequency of small macropores. The l a t t e r were measured at less than 0.3 u. Similar stereoscanner photographs of samples oxidized at 800°C seem to corroborate the above trends. General cross-sections i n Figures 43(a) and (b) again indicate the increase i n large macropore diameter with - 113 -(a) t r i a l 49-1, 4.05 g cm density, reaction interface, x 1060 (c) t r i a l 47-2, 4.23 g cm-3 density, x 570 Figure 41. Internal Structures of Samples Oxidized at 900°C. - 114 -(a) centre of sample 49-1, x 1210 (b) midway between surface and centre of sample 59-2, x 1130 Figure 42. Magnetite Structures of Samples Oxidized at 900°C. - 115 -(b) t r i a l 54-2, 4.41 g cm ' density, x 119 Figure 43. General Sections of Samples Oxidized at 800°C. - 116 -increased density. The increase i n large macropore size with increasing distance from the surface i s again apparent i n Figure 43(b) and substantiated by Figures 44(b) and (c) which represent structures at the surface and centre of sample 54-2 respectively. Figure 44(a) indicates the smaller large macropore size c h a r a c t e r i s t i c of lower density samples. The general trends attributed to structures of magnetite i n samples oxidized at 900°C and at 800°C do not appear to apply for those reacted at 700°C. The general cross-sections i n Figures 45(a) and (b) delinate two d i s t i n c t l y d ifferent bands of magnetite structure: an outer one of about 70 y containing no large macropores; and an inner band which extends to the interface and i s composed of a large frequency of large macropores. Figures 46(a), (b) and (c) better i l l u s t r a t e t h i s porosity d i s t r i b u t i o n . The large macropores showed no s i g n i f i c a n t dependency on sample density; average diameter was about 10 u. As a result of the small and irregular grain size of magnetite i n the figures presented, no useful measurements can be obtained. At high magnification, however, the r e l a t i v e magnetite grain sizes of samples 47-2, 54-2, and 54-1 (see Figures 47(a), (b), (c), and (d)) which were reacted at temperatures of 900°C, 800°C, and 700°C, respectively, becomes very apparent. Although the grain size i n Figure 47(a) cannot be d i r e c t l y measured, i t can be estimated to be of the order of 6 u. By comparison, average grain sizes of magnetite resulting from oxidation at 800°C and 700°C are about 4 u and 1.5 u respectively. A l l f i e l d s of view i n this case were selected from regions of maximum macropore size adjacent to interfaces. - 117 -(a) t r i a l 27-1, reaction interface, x 560 (b) t r i a l 54-2, structure adjacent to surface, x 1200 (c) t r i a l 54-2, magnetite structure, x 1280 Figure 44.. Internal Structures of Samples Oxidized at 800°C. - 118 -Figure 45. General Sections of Samples Oxidized at 700°C. - 119 -(c) t r i a l 38-1, 4.22 g cm d e n s i t y , x 645 F i g u r e 46. S e c t i o n s A d j a c e n t t o S u r f a c e s o f Samples O x i d i z e d a t 700°C. - 120 -(b) t r i a l 54-2, oxidized at 800°C, x 12,000 Figure 47. Magnetite Grain Structures. - 121 (c) t r i a l 54-1, oxidized at 700°C, x 12,700 (d) t r i a l 54-1, oxidized at 700°C, x 11,600 Figure 47. Magnetite Grain Structures. - 122 -IV. DISCUSSION OF RESULTS A. Features of Recorded Weight Change Curves 1. Weight Loss on Heating Of the three unique weight changes which comprise the continuously recorded weight versus time curves, the f i r s t i s the one most ea s i l y explained (see Figure 10: portion A). This weight loss was observed during heating i n argon from 580°C to reaction temperatures. Neutron activation analysis of samples heated to temperatures of 700°C, 800°C, and 900°C at the normal heating rate, and subsequently cooled, have shown that no s i g n i f i c a n t increase i n oxygen content resulted during this stage. Thus the entire weight change can be attributed to loss of sulphur. Since the amount of sulphur l o s t per unit time did not appear to be affected by heating to higher temperature, i t would appear that l i t t l e or no s o l i d state d i f f u s i o n of sulphur to the surface could have occurred. Hence, decreased sulphur losses obtained by the heating of samples of increased density are probably a result of lower surface roughness factors of higher density samples. 2. Weight Gain Although Morawietz^ did not report the observation of this portion of the k i n e t i c weight change curve (see Figure 10: portion B), - 123 -he did discuss the equ i l i b r a t i o n of stoichiometry during equilibrium 6 3 studies of f i n e l y divided pyrrhotite. Niwa et a l . observed a similar increase i n weight when roasting -170 + 200 mesh pyrrhotite with a S/Fe r a t i o lower than that of equilibrium. Their interpretation necessitated the d i f f u s i o n of ferrous ions to p a r t i c l e surfaces where they reacted to form magnetite with no evolution of sulphur dioxide. This process continued u n t i l the S/Fe r a t i o had increased to equilibrium, then was followed by normal oxidation which resulted i n formation of magnetite and evolution of sulphur dioxide. Niwa 26 and Wada l a t e r supported t h i s mechanism by an argument based on increasing a c t i v i t y of iron i n pyrrhotite with a decreasing S/Fe r a t i o . 63 Similar to the pyrrhotite used by Niwa et a l . pyrrhotite oxidized i n a l l experiments i n the present study also contained less than the equilibrium amount of sulphur. The highest discrepancy i n sulphur concentration was present i n experiments at 700°C and 1 atmosphere pressure sulphur dioxide (see Table 5). However, the highest weight losses (see Table 14) occurred during heating to 900°C. Thus while i t i s possible that some of the weight gained was caused by the S/Fe ra t i o being less than the equilibrium value, the larger part of the weight was probably caused by depletion of sulphur i n a surface layer during heating. Since the a c t i v i t y of iron i n this sulphur poor layer would have been high, i t i s l i k e l y that iron was oxidized, as shown i n 2 6 equation (30), i n a similar way to that described by Niwa and Wada. [ F e J F e S + 2/3 S0 2 > 1/3 Fe 30 4 + 1/3 S 2 (30) - 124 -In a discussion of the paper by Niwa and Wada, McCabe reported that magnetite formed on p y r r h o t i t e during t h i s weight gain stage was non-porous. An examination of Figures 40(d), 41(c) and 44(b) indicates the presence of a surface layer which appears to d i f f e r s t r u c t u r a l l y from i n t e r n a l magnetite. Densities of the samples which these f i e l d s of view represent are 89.2 percent f o r the f i r s t two figures and 93.0 percent t h e o r e t i c a l f o r the l a s t . No s t r u c t u r a l l y unique surface layers were detected i n samples with d e n s i t i e s less than 89 percent t h e o r e t i c a l . Therefore, the slow times reported for completion of t h i s weight gain for samples of high density i n the present study can be explained by the formation of a very high density magnetite layer. Because no such magnetite layer was observed on low density samples, and because times f o r completion of the weight gain f or these samples was short, i t must be assumed that surface magnetite layers formed on low density samples was porous. 3. Major Weight Loss C h a r a c t e r i s t i c s of the major weight loss portions of curves (see Figure 10: portion C) appeared to f a l l i nto two categories: those r e s u l t i n g from oxidation of samples above and below about 90 percent t h e o r e t i c a l . The former exhibited weight losses which were non-uniform throughout and which tended to increase from i n i t i a t i o n of weight loss u n t i l approximately l i n e a r rates were recorded. Photomicrographs of surfaces and i n t e r n a l magnetite structures of t h i s group has shown the existence of b l i s t e r s . The occurrence of a s i m i l a r phenomenon during reaction of oxygen with p y r r h o t i t e has previously been reported 26 by 'McCabe (discussion with Niwa and Wada ) w h o observed rupturing of - 125 -what has been described as the surface layer of dense magnetite. At temperatures above 1000°K, i t was also suggested that the t o t a l pressure of sulphur and sulphur dioxide was s u f f i c i e n t to cause rupture of a continuous magnetite layer. McCabe postulated the transport of oxide ion to be the mechanism by which the reactant gas was able to reach the interface. In the present study, the reactant gas, sulphur dioxide, i s not l i k e l y to diffuse through the surface layer of magnetite since b l i s t e r i n g indicates that the layer i s very dense. However, i t i s possible that oxide ions may diffuse through t h i s surface layer and react with pyrrhotite to form magnetite and sulphur dioxide. As the sulphur dioxide pressure builds up i n l o c a l i z e d regions, the magnetite could rupture with a subsequent decrease i n pressure. There are two possible sources of oxygen: one source i s the existence of a p a r t i a l pressure of oxygen resulting from the equilibrium dissociation of sulphur dioxide; the other could occur as the result of the chemi-sorption of sulphur dioxide. When a rupture occurs, a path becomes available for gaseous d i f f u s i o n of sulphur dioxide. This establishes a pressure gradient through the magnetite layer which causes a corresponding gradient i n p a r t i a l pressure of oxygen. Although only a small thickness of dense magnetite structure was observed on the surface of pyrrhotite plates, the wavy nature of recorded curves were an indication of c y c l i c rupturing occurring throughout reaction. This i r r e g u l a r i t y i n recorded weight loss was more noticeable for samples of density close to 95 percent theoretical. I t i s quite l i k e l y that the porosity of the internal structure of - 126 -magnetite was not s u f f i c i e n t to permit gaseous d i f f u s i o n of sulphur dioxide. The major contribution to r e a c t i o n would then occur by the transport of oxide ions wLth subsequent b l i s t e r formation. The r e l a t i o n s h i p s between s p e c i f i c reaction rate and density i n the high density range can also be s a t i s f a c t o r i l y explained i n terms of rupturing within product lay e r s . If a reaction i s transport c o n t r o l l e d , an increasing thickness of product la y e r , and thus d i f f u s i o n path, w i l l r e s u l t i n a decreasing reaction rate (provided the e f f e c t i v e d i f f u s i o n c o e f f i c i e n t remains constant). The r e l a t i v e l y s t r a i g h t i n t e r f a c e observed at various thicknesses of magnetite i n t h i s study i s an i n d i c a t i o n that a large degree of transport c o n t r o l e x i s t s . But, b l i s t e r i n g could cause the e f f e c t i v e d i f f u s i o n c o e f f i c i e n t to increase i n such a way that an approximately l i n e a r rate of weight loss would be observed. Weight loss curves of samples i n the low density range were much more consistent with the theory of transport c o n t r o l . Rates of reaction decreased evenly with increasing magnetite thickness and reaction interfaces were observed to be l i n e a r except when the manifi-cation was high enough to d i s t i n g u i s h d i s c r e t e grains. To i n v e s t i g a t e the p o s s i b i l i t y of i n t e r a c t i o n s between chemical and transport processes, analyses of weight loss w i l l be conducted on the basis of a mixed control model for rectangular p l a t e s . B. Mixed Control Model 1. General Observations and r e s u l t s so far presented have indicated that the reaction of p y r r h o t i t e with sulphur dioxide i s of the type which - 127 -forms a magnetite layer of density higher than that of the underlying pyrrhotite. Since external dimensions are constant, the magnetite layer has a higher porosity than the pyrrhotite from which i t i s formed. The results given i n Section III.C.2 are evidence of a reaction interface which i s line a r when observed metallographically at magnifications less than that at which discrete grains are distinguish-able. Too, no retained pyrrhotite was noticeable i n magnetite layers. A l l these are characteristics of a topochemical gas-solid reaction. However, i t has been pointed out i n Section I.B.4.(i) that although a reaction of th i s type i s limited by the processes of gaseous di f f u s i o n through a product layer and sometimes d i f f u s i o n through a laminar gas f i l m , s i g n i f i c a n t consumption of chemical potential by adsorption, desorption, and chemical reaction can occur. This can be stated i n another way. Where a reaction i s chemically controlled, no pressure gradients exist across the product layer and laminar gas f i l m . S i m i l a r l y , where a reaction i s t o t a l l y transport controlled, equilibrium exists at the reaction interface. However, when the gas compositions at the reaction interface are between those of equilibrium and those i n the bulk gas phase, the reaction i s subject to what has been referred to as mixed control. Under these conditions, the rate of reaction i s s t i l l l imited by d i f f u s i o n a l processes and appears to be topochemical. In order that this l a t t e r p o s s i b i l i t y be included i n the analysis, a mixed control model for reaction of rectangular plates has been formulated. A schematic diagram of the model i s i l l u s t r a t e d i n Figure 48 which represents the half-thickness of a p a r t i a l l y oxidized - 128 -Figure 48. Schematic cross-section of a p a r t i a l l y oxidized pyrrhotite sample i l l u s t r a t i n g p a r t i a l pressure gradients. - 129 -sample. The approach undertaken for the analysis of results w i l l be 64 similar i n some aspects to that suggested by H i l l s . Temperature differences between the bulk gas phase and the reaction interface w i l l be calculated for heat transfer through a laminar gas f i l m and a product layer to an interface where an endothermic reaction i s proceeding. This w i l l establish whether or not to* consider the reaction as isothermal. Since there i s no a p r i o r i knowledge of the chemical rate constant for the reaction of pyrrhotite with sulphur dioxide, mathematical equations representing the mixed control model are insoluble for any time after onset of reaction. However, by consider-ing the very onset of reaction, the porous product layer i s i n f i n i t e l y thin and contributes no resistance to d i f f u s i o n . Under these circumstances, the only s i g n i f i c a n t processes are those of chemical reaction and gaseous di f f u s i o n through the laminar gas f i l m . If chemical reaction i s assumed ne g l i g i b l e , theoretical fluxes can be calculated on the basis of control simply by d i f f u s i o n through the laminar gas f i l m . When these calculated fluxes are compared with experimentally obtained fluxes, chemical control can be said to be important only i f the l a t t e r are s i g n i f i c a n t l y less than the former. If this i s not the case, simultaneous solution of equations representing the two types of processes at onset of reaction w i l l y i e l d a chemical rate constant, which w i l l enable the general case of control to be solved. 2. Heat Transfer Analysis The analysis of heat transfer through a laminar gas f i l m over a 65 f l a t plate i s based on the expression developed by Polhausen. Conditions - 130 -selected for the analysis are a reaction temperature of 900°C and a sulphur dioxide pressure of 1 atmosphere. Lahiri^"'" has reported similar calculations for the reduction of a sphere of hematite, conclud-ing that non-isothermal conditions p r e v a i l . He chose a spherical model with a dense unreacted hematite core surrounded by successive layers of magnetite, wustite, and ir o n . Although enthalpies were calculated by considerations of the ov e r a l l reaction, a single thermal conductivity value (that of the porous iron s h e l l ) was assumed. However the values of AT resulting from heat transfer across the product layers were said to be n e g l i g i b l e , thus i t i s u n l i k e l y that a smaller conductivity coeff i c i e n t would have caused a s i g n i f i c a n t difference. The major contribution to AT was a result of gas f i l m resistance to heat transfer. The values of AT calculated by L a h i r i have previously been quoted (see Section I . B . 4 . ( i i ) ) . To determine the rate of heat transfer, through a laminar boundary layer over a f l a t plate, from a bulk gas phase at temperature T^  to a sample surface at temperature T , convective and radiative heat transfer processes are considered. Terminology and relevant values employed i n these heat transfer calculations are given i n Table 25. The relationship on which calculations are based i s given by : equation (31). From i t can be derived an expression for (equation (32)) while h^ i s defined by equation (33), where a i s the Stefan-Boltzmann constant. Nu = 0.664 Re (31) Nu k, SO h 2 (32) c 131 -h = 4erjT, 3 C33) r b 51 52 Whereas L a h i r i and H i l l s predicted maximum temperature drops of 40°C across a laminar f i l m , a temperature drop of less than 1°C has been calculated as corresponding maximum temperature drop for experiments i n this study. The reason for t h i s difference stems from the much lower s p e c i f i c reaction rates encountered during pyrrhotite oxidation. For purposes of comparison a s p e c i f i c rate of reduction _3 of hematite at 900°C and 1 atmosphere hydrogen i s about 2 x 10 -2 -1 34 g cm sec The assumed rate of oxidation quoted i n Table 25 i s a maximum value over the range of temperature, pressure, and sample density from which rates were measured. Since the calculated temperature difference between the bulk gas phase and reaction interface i s less than 1°C, the reaction can be assumed to be isothermal. 3. Diffusion Through a Laminar Boundary Layer at Onset of Reaction Wakao and F u j i s h i r o ^ have derived a r e l a t i o n describing a gas laminar boundary on a f l a t plate. To predict fluxes r e s u l t i n g from the condition of t o t a l control by di f f u s i o n through a laminar gas f i l m , the calculation of several constants was f i r s t necessary. Where equation C34) defines flow through a gas boundary layer, the mass Sh =. 0.664 S c ^ R e 1 / 2 (34) transfer coef f i c i e n t i s given by equation C35). In a binary system the d i f f u s i o n coefficient i s referred to as D. and i n a ternary system - 132 -Table 25. Heat Transfer Data at 900°C and 1 atmosphere SO Re Reynolds Number 13.6 Pr Prandtl Number 0.86 Nu Nusselt Number 2.4 Thermal conductivity of porous Fe^O^ 0.005 c a l cm "'"sec 1 ft 1 — 1 k g 0 Thermal conductivity of S0 2 at 900°C 9.8xl0~ c a l cm" sec °C e Emissivity of F e ^ 0.70 -4 -2 -1 • h Convective heat transfer c o e f f i c i e n t 1.17x10 c a l cm sec °C c -3 -2 -1 h^ Radiative heat transfer c o e f f i c i e n t 6.12x10 c a l cm sec °C I Length of sample 2.0 cm 6 Maximum d i f f u s i o n distance through 0.045 cm F e3°4 n-, „/A Maximum s p e c i f i c reaction rate per 4.5x10 ^ gm cm 2sec 1 i?eS . ° unit area -3 —2 —1 q/A Required heat flux/unit area 4.5x10 c a l cm sec T -T. AT between surface and interface 0.04°C s i T -T AT between bulk and surface 0.72°C b s - 133 -V = e D i / / 3 ( 3 5 ) as D^ , . The constants g, D. . , and D^ , for various conditions of temperature and p a r t i a l pressure of sulphur dioxide are given i n Tables 27(a) and (b) while Table 26 l i s t s the symbols employed i n the following analyses. Diffusion coefficients for the binary system were determined by standard Chapman-Enskog theory. However a (molecular diameters) and e/K values for sulphur, which were necessary for calculation of diffusion c o e f f i c i e n t s , were estimated at 3.5 A and 115°K respectively. The basis for these estimates were corresponding Lennard-Jones 6 7 parameters for other gases as reported by Hirschfelder et a l . Ternary d i f f u s i o n coefficients were calculated after the method proposed by H e l l u n d . ^ By referring to Figure 48 which represents a p a r t i a l l y oxidized sample, i t i s obvious that at the onset of reaction there i s no porous product layer (sample surface and reaction front coincidental). Transport of sulphur dioxide and sulphur through the gas f i l m can therefore be defined by equations (36) and (37) respectively. I t i s k nS0 gS0 — " "RT- <PS02*b - P S 0 2 S i > ( 3 6 ) S2 b2 (P c s, - P c g,) (37) RT v S 2 i ^S^b also reasonable to assume that, since gas flow rates used were greater than the c r i t i c a l value, the p a r t i a l pressure of sulphur i n the bulk gas phase i s zero. I f s t r i c t transport control i s assumed (no interactions - 134 -Table 26. Symbol Definitions and Nomenclature % sample length w sample width A sample area X Q sample half thickness x half thickness of unreacted portion m r R molar gas constant n^ molar rate of reaction of species i u factor y i n FeS,, 1+y equilibrium gas constant for reaction (5) k^ forward rate constant for reaction (5) k, backward rate constant for reaction (5) D p„ „ molar density of FeS,, FeS J 1+y concentration of gas specie i P^ p a r t i a l pressure of specie i i n the bulk gas phase Pj_ ^ p a r t i a l pressure of specie i at the gas-solid interface g P^ ^ p a r t i a l pressure of specie i at the reaction interface k ^ mass transfer c o e f f i c i e n t of gas i through the laminar layer D^ di f f u s i o n coefficient of gases i and j i n a binary system D^ , d i f f u s i o n c o e f f i c i e n t of gas i i n j and k i n a ternary system Sh Sherwood number = k .£/D.. g i I J Sc Schmidt number D Knudsen di f f u s i o n c o e f f i c i e n t of specie i 1 - 135 -Table 27(a). Binary Diffusion Coefficients ( i = S 2, j = S0 2) at 1 atmosphere S0 2 T(°K) 3 °ij = D j i ( G 1 , , 2 s e G ~ 1 ) 1173 1.082 1.097 1073 1.066 0.826 973 1.042 0.605 Table 27(b). Ternary Diffusion Coefficients at 900°C ( i = S 2, j E S0 2, k = A). _ _ _ _ _ _ _ Pressure of S02(atm) g D^ ^ (cm sec ) D ^ (cm sec ) 0.85 1.063 1.691 1.044 0.50 1.007 2.503 1.425 0.25 0.997 1.957 1.124 - 136 -between chemical and d i f f u s i o n a l effects) then equilibrium as defined i n equation (38) exists at the reaction interface because chemical reaction i s very fast. Equation (39) represents the stoichiometric relationships of the fluxes of species i n the reaction of FeS^ +^ with ,5+3yN (P s s <• 2 > . 2 V K ( P S ) 2 OS) ^ S0 0 . ; 2 x • • —6 • nFeS = 3 / 2 n S 0 2 = 5+3p" % (39) SG^. By substituting equations (38) and (39) into equations (36) and (37) an expression results (see equation (40)) from which a solution for n_ _ can be obtained. h eb • g 2 • 4 5+3y nFeS ^2 „ (5+3Ti) nFeS RT x (5+3y ) ~6 W~ Ke ( SO 0 8 u ~ 2 / 3 "T~ IT } 2 b gso 2 (40) The fluxes determined by this method (see Appendix 2) are simply those that would be measured experimentally at the outset of reaction i f chemical reaction were very fas t . Various experimental conditions and the theoretical flux at outset of each reaction under each set of conditions are l i s t e d i n Tables 28(a) and (b). Experimental fluxes under i d e n t i c a l reaction conditions are also given i n Table 28(a). These were calculated by the following technique. Weight loss curves - 137 -Table 28(a). Comparison of Experimental Flux at a Reaction Time of 1 second and Flux Dictated by Boundary Layer Control Run Number Experimental Flux n„ „ (moles sec "S FeS T h e o r e t i c a l Flux n„ „ (moles sec FeS 43-1 58-2 65-2 74-1 27-1 39-2 1.92x10 -6 1.74x10 1.36x10 -6 5.65x10 -7 9.83x10 5.21x10 -7 2.18x10 -6 1.88x10 -6 1.07x10 -6 6.84x10 -7 9.26x10 4.47x10 -7 -7 Table 28(b). Experimental Conditions Run Number Reaction Temperature Sample Density SO P a r t i a l Pressure "C g cm (atm) 43-1 900 4.07 1.0 58-2 900 4.05 0.85 65-2 900 4.07 0.50 74-1 900 4.08 0.25 27-1 800 4.05 1.0 39-2 700 4.02 1.0 - 138 -for each set of reaction conditions were f i t t e d to polynomials of degree 6 (see Appendix 2). Slopes at the beginning of each experiment (1 second reaction time) were then computed and from these, experimental fluxes were calculated. 64 H i l l s raises two objections to the extrapolation of experimental weight change curves to zero time. The f i r s t i s that the estimation of i n i t i a l rates of reaction involve drawing tangents at zero time. In this study, weight loss curves were f i t t e d to a 6th degree polynomial and extrapolated. The i n i t i a l rates of reaction were i n most cases approximately l i n e a r so that errors incurred by extrapolation of f i t t e d polynomials were probably small. Larger errors were l i k e l y to have resulted from the recording of weight loss curves. His second c r i t i c i s m of this technique i s that i t i s during the i n i t i a l stages of reaction that temperature i n s t a b i l i t i e s occur as a result of heat transfer. I t can only be assumed i n this study that since s p e c i f i c reaction rates are low, the temperature of the reaction front remains stable (see Section IV.B.2). From a comparison of the fluxes predicted for laminar boundary layer control and those obtained experimentally, i t i s apparent that corresponding values are closely related. This s i m i l a r i t y indicates that chemical reaction must be very fast compared to the rate of mass transport through the laminar gas f i l m . Furthermore, because the resistance due to mass transfer increases as the reaction proceeds (the product layer thickens with time) while the resistance due to chemical reaction remains r e l a t i v e l y f i x e d , the rate of reaction must be controlled solely by the transport processes for the entire experiment. - 139 -Since a thin layer of magnetite forms during weight gain prior to i n i t i a t i o n of weight loss, i t might have been expected that experimental fluxes would have been consistently s l i g h t l y less than corresponding predicted fluxes. However, there appears to have been a negligible effect.' 4. Transport Process Control. Thus, the o v e r a l l rate of reaction of pyrrhotite with sulphur dioxide can be described by mass transfer equations for d i f f u s i o n of sulphur dioxide and sulphur through a gaseous boundary layer and a porous product layer. Since chemical reaction i s very f a s t , equilibrium may be assumed to exist at the reaction interface. The f i v e expressions which describe these processes are derived and given as equations (1-1), (1-4), (1-13), (1-14), and (1-18) i n Appendix 1A. These equations have been simultaneously solved to y i e l d values of eff e c t i v e d i f f u s i o n coefficients at a product layer thickness i d e n t i c a l to -3 that at which the experimental rate, k^, was measured (2.45x10 cm). Effective binary and ternary d i f f u s i o n coefficients i n the product layer so calculated are shown i n Table 29 together with t r i a l run numbers and conditions of sample density, reaction temperature, and p a r t i a l pressure of sulphur dioxide. The values of eff e c t i v e d i f f u s i o n coefficients were then substituted into the set of equations from which they were o r i g i n a l l y calculated i n order to predict weight change as a function of time for the same set of twelve unique experimental conditions. By this technique, the values of acted e s s e n t i a l l y as 'toes' for prediction of the curves shown i n Figures 49(a) to (1) - 140 -Table 29. E f f e c t i v e D i f f u s i o n C o e f f i c i e n t s i n the Porous Layer at Various Experimental Conditions T r i a l Number Density Temperature (g cm ) (°C) SO2 Pressure (atm) E f f e c t i v e D i f f u s i o n C o e f f i c i e n t (cm sec ) 43-1 48-2 27-1 23-2 39-2 58- 2 59- 1 63-2 65-2 68-1 74-1 76-1 4.07 4.22 4.05 4.26 4.02 4.05 4.18 4.30 4.07 4.17 4.08 4.23 900 900 800 800 700 900 900 900 900 900 900 900 1.0 1.0 1.0 1.0 1.0 0.85 0.85 0.85 0.50 0.50 0.25 0.25 1.04x10 -2 4.91x10 -4 1.61x10 1.36x10 -4 7.62x10 -2 1.07x10 -2 1.08x10 -3 3.60x10 -4 8.52x10 -3 8.82x10 -4 1.76x10 -2 3.05x10 -3 - 141 -Legend for Figures 49(a) to (1) Inclusive. Experimental weight loss curves. Weight loss curves predicted by transport control model involving counterdiffusion with net bulk flow through a laminar gas f i l m and a porous magnetite layer. 0.65 \-LJ & 0.60 I LiJ _J Q. < CO 0.55 7.2 14.4 21.6 TIME (sec. x I0" 3) 4>-N3 28.8 Figure 49(a). Predicted and experimental weight loss curves for t r i a l 43-1. 0.75 0.70 I cn X o UJ LU CO 0.65 I 0.60 14.4 21.6 28.8 TIME (sec. x I0" 3) Figure 49(b). Predicted and experimental weight loss curves for t r i a l 48-2. 36.0 0.65 - 0.60 x LU LU _J Q_ < CO 0.55 h 0.50 3.6 Figure 49(c), 7.2 10.8 14.4 TIME (sec. x I0"3) P r e d i c t e d and experimental weight loss curves for t r i a l 27-1. 18.0 0.70 X LU LU _J a. < co 0.65 \-0.60 28.8 43.2 57.6 TIME (sec. x I0" 3) 72.0 Figure 49(d). Predicted and experimental weight loss curves for t r i a l 23-2. 0 . 6 0 I 1 r 1 1 1 1 ! r h-X CD LLI LU _J CL < CO 0 . 5 5 \ \ - - o n - o - n ^ - t r o 4> 0 . 5 0 J I L J L 0 14.4 2 8 . 8 4 3 . 2 5 7 . 6 T I M E ( s e c . x I0~ 3 ) 7 2 . 0 Figure 49(e). Predicted and experimental weight loss curves for t r i a l 39-2. 7.2 10.8 TIME (sec. x I0 ' 3) Figure 49(f). Predicted and experimental weight loss curves for t r i a l 58-2. 0.65 £ 060 LU LU _l a. < 0.55 h 0 7.2 14.4 21.6 TIME (sec. x I0"3) 28.8 Figure 49(g). Predicted and experimental weight loss curves for t r i a l 59-1. 0.65 h X LU LU C L , <: CO 0.60 h 0.55 0 7.2 14.4 21.6 TIME (sec. x I0" 3) 28.8 36.0 Figure 49(h). Predicted and experimental weight loss curves for t r i a l 63-2. 0.60 3.6 7.2 10.8 TIME (sec. x I0" 3) 14.4 Figure 49(i). Predicted and experimental weight loss curves for t r i a l 65-2. - 1ST -~ 0.55 X o LU LU _ l Q_ < CO 0.50 I 3.6 7.2 TIME (sec. x I0"3) 10.8 Figure 49(k). Predicted and experimental weight loss curves for t r i a l 74-1. 0.60 LU LU _J Q_ < CO 0.55 \-0.50 Figure 49(1) 14.4 28.8 43.2 TIME (sec. x I0~3) Predicted and experimental weight loss curves for t r i a l 76-1 57.6 Ln - 154 -inclusive. Method of solution and solutions can be found i n Appendix IB. I t can be seen (Figure 49(e)) that this p a r t i c u l a r predicted curve was toed by used a D .. value determined towards the end of J ef f reaction i n addition. Values of sulphur dioxide and sulphur at the sample surface and reaction front were also obtained from these solutions. For each set of experimental conditions, only the sulphur p a r t i a l pressure at the sample surface was found to d i f f e r appreciably during any p a r t i c u l a r experiment. For example, solutions for t r i a l 43-1 y i e l d values of s ranging from 0.971 atm at 8.5 percent reaction to 0.967 atm at 2 i 99.2 percent reaction; values of P g from 0.981 atm to 0.995 atm 2 l for the same points of reference; P s from 0.0344 atm to 0.0343 atm; b2 i and P g values as shown i n Figure 50. b2 i It i s interesting to note that the t o t a l pressure at the reaction front i s greater than that i n the bulk gas phase at a l l times. Bradshaw has developed an analysis for a general gas-solid reaction with the formation of a porous product layer on the basis of transport control by gaseous dif f u s i o n through a laminar gas f i l m and a porous product 32 layer. To eliminate pressure variables he has assumed that t o t a l pressures i n the bulk gas phase and at the reaction front are equal; i n the general case. Spitzer et a l . , i n the analysis of hematite 46 reduction by hydrogen, also found a discrepancy between p a r t i a l pressures i n the bulk phase and at the reaction front, a 6 percent excess of t o t a l pressure being calculated at the reaction front. I t can be shown by the following analysis of control by the two transport processes that t o t a l pressures are equal at the reaction front - 155 -I I I L 0 50 100 % Reaction Figure 50. Sulphur p a r t i a l pressures at sample surface and reaction front during t r i a l 43-1. - 156 -and sample surface but not equal at the sample surface and i n the bulk gas phase for the reaction of pyrrhotite with sulphur dioxide. Equations (1-13) and (1-14) i n Appendix 1A can be rewritten and summed (see equation (41)). In order to write this equation (41) i n n S 0 pso- + V - ' + V - ^ 2 x 2 x 2 x 2 x eff P S 0 8 + P S 0 S  2 ± 2 ± )1 - [ ( ^ ) - ( ^ H . ) pso s + p s s + pso 8 + p s g b U 2 i S2 i S°2 i S2 i P q s + P g 2 i 2 i ( — )]} (41) 2 x 2 x 2 x 2 x the form presented,the effective d i f f u s i o n coefficients of sulphur dioxide and sulphur have been assumed equal. This i s a reasonable assumption since the binary molecular d i f f u s i o n c o e f f i c i e n t s are equal and since Knudsen dif f u s i o n coefficients are v i r t u a l l y equal (by reason of similar molecular weights). I t i s obvious that the right hand term (within curly brackets) of equation (41) i s equal to zero thus proving equality of t o t a l pressures at the reaction front and sample surface. Consideration of mass transfer through the laminar gas f i l m yields equation (42) (obtained by addition of equations (1-1) and (1-4) i n Appendix 1A). When no diluent gas i s employed, the mass transfer - 157 -p s c , s . + V i 2 i 2 l P e +. p g + 2 b 2 b g RT nS0 8S —1 K 5 ± 3 J i _ _ f 2 A 4 k J SS0„ C42) coeff i c i e n t s are equal and the difference i n t o t a l pressure should be d i r e c t l y proportionate to reaction temperature and reaction f l u x . In a ternary system (with argon as a diluent) the mass transfer coefficients are not equal. In the present study, differences i n t o t a l pressure between the bulk gas phase and the reaction front were indeed found to increase with increasing temperature and with decreasing sample density and p a r t i a l pressure of sulphur dioxide. From the ternary d i f f u s i o n data i n Table 27 i t can be seen that the t o t a l pressure difference as defined by equation (42) should also increase as the sulphur dioxide pressure decreases. The largest difference - an excess of 2 percent t o t a l pressure at the sample surface and reaction front - occurred i n solutions for t r i a l 74-2 (0.25 atm sulphur dioxide) at i n i t i a t i o n of reaction. On examination of equation (41), i t can be noted that reaction stoichiometry has no effect on the t o t a l pressures across a porous layer. However, i f the effective d i f f u s i o n coefficients of the gaseous reactant and product are not equal ( i . e . H^ and H^ O) then the two values of D rj. must be included i n the right hand term. Under these conditions ef f b i t w i l l not disappear. S i m i l a r l y , examination of equation (42) shows that i f a reaction i s stoichiometric and the mass transfer coefficients are equal, the t o t a l pressure at the sample surface and i n the bulk gas phase are equal. - 158 -In pyrrhotite oxidation, i t i s apparent that the cause of excess pressure at the reaction front i s the existence of an outward net bulk flow and that this excess pressure i s a direct result of net bulk flow through the laminar gas f i l m . 5. Relative Contributions to Control Mixed control models have often been analyzed i n terms of the separate resistances which can be attributed to processes of transport through a laminar f i l m and product layer and to chemical reaction at the reaction front. This i s a simple mathematical procedure for the reduction of hematite by hydrogen but cannot be calculated by the same technique for the oxidation of pyrrhotite. by sulphur dioxide because of the complexity of the reaction stoichiometry. Instead a graphical comparison has been made possible by c a l c u l a t i of predicted weight loss curves for several sets of assumptions. These consist of: (1) counterdiffusion with net bulk flow through a product layer and a laminar f i l m ; (2) counterdiffusion with net bulk flow through a product layer; (3) counterdiffusion through a laminar f i l m and product layer assuming the effect of net bulk flow to be negl i g i b l e ; and (4) counterdiffusion through a product layer assuming the effect of net bulk flow to be negl i g i b l e . The derivations of expressions representing each set of assumptions i s provided i n Appendix 3, while the weight loss curves appear i n Figures 51(a) to (1) inclusive. The r e l a t i v e importance of the resistances to mass transfer throug the laminar boundary layer i s apparent when slopes of curves predicted - 159 -by assumptions (1) and (2) are compared at equal weight loss. Qualita-t i v e l y , resistance of the laminar f i l m i s ne g l i g i b l e for reaction of _3 samples of density higher than 4.17 g cm (see Figures 51(b), (d) , and (h) and refer to Table 29 for experimental conditions) except at low sulphur dioxide pressures (see Figures 51(i) , ( j ) , (k), and (1)). _3 For samples of low density (4.02 to 4.08 g cm ) the effect i s very noticeable, especially at onset of reaction, but decreases to being negligible on nearing completion of reaction (see Figures 51(a), (c), (e), ( f ) , (g), ( i ) , (k), and (1)). It i s also interesting to compare weight loss curves based on assumptions (3) and (1), and (2) and (4). In each pair of assumptions, the effect of net bulk flow i s assumed to be n e g l i g i b l e ; the former including transport through both a laminar f i l m and a product layer, the l a t t e r considering only transport through a product layer. Curves representative pf assumptions (2) and (4) are almost exactly coincidental under a l l experimental conditions. This would indicate that when the mass transfer equations for laminar f i l m transport are not included, the effect of net bulk flow i s accommodated simply by adjustment i n magnitude of P s and P s . However by including these equations, 2 l 2 l the effect of net bulk flow i s s a t i s f i e d by an additional change i n the f l u x ; thereby a l t e r i n g the weight loss curves. (As sample density increases, the differences between curves predicted decreases so that i n Figures 5 l ( b ) , (d), (e), (g), (h), and ( j ) , curve (3) has not been included but can be assumed to be between curves (1) and (2)). - 160 -Legend for Figures 51(a) to (1) Inclusive. Predicted weight loss curve for condition (1) (curve 1) Predicted weight loss curve for condition (3) (curve 3) Predicted weight loss curve for conditions (2) and (4) (curves 2 and 4) Conditions counterdiffusion with net bulk flow through a laminar gas f i l m and a porous magnetite layer. counterdiffusion with net bulk flow through a porous magnetite layer. counterdiffusion through a laminar gas f i l m and a porous magnetite layer assuming the effect of net bulk flow to be neg l i g i b l e . counterdiffusion through a porous magnetite layer assuming the effect of net bulk flow to be n e g l i g i b l e . - T 9 T -0.75 14.4 21.6 28.8 TIME (sec. x I0" 3) 36.0 Figure 51(b). Predicted weight loss curves for t r i a l 48-2. 0.65 cn 0.60 x CD LU LU _J Q. < CO 0.55 7.2 10.8 TIME (sec. x I0" 3) 14.4 Figure 51(c). Predicted weight loss curves for t r i a l 27-1. 0.70 0.65 0 .60 28.8 43.2 TIME (sec. x |Q'3) 57.6 72.0 Figure 51(d). Predicted weight loss curves for t r i a l 23-2. CP O 0. LU L U _ l C L < C O 55 0.50 «8: •Q: 0 14.4 28.8 43.2 TIME (sec. x I0"3) 57.6 Figure 51(e). Predicted weight loss curves for t r i a l 39-2. SAMPLE WEIGHT (g.) - 991 -SAMPLE WEIGHT (g.) P p o cn cr> cr> cn O cn - L9l -070 ON 0 0 14.4 21.6 TIME (sec. x fO" 3) 28.8 3 6.0 Figure 51(h). Predicted weight loss curves for t r i a l 63-2. SAMPLE WEIGHT (g.) O O O cn T I u IU 111 a t>p Ul I u I ll Ul 11 ll I o I o •V7 - 691 -& 0.60<\ x o LU LU _J CL CO 0.55 k o 14.4 28.8 43.2 TIME (sec. x I0"3) 57.6 51(j). Predicted weight loss curves for t r i a l 68-1. T T X L J LU _ J Q_ < C O 0 . 5 5 LN>. 0 . 5 0 • " a \ • "Si ^ 2 : D \ a • 0 . 4 5 i 1 L _ 0 3 . 6 Figure 51(k) J 1 1 1 I I I 7 . 2 1 0 . 8 1 4 . 4 1 8 . 0 T I M E ( s e c . x I 0 ' 3 ) Predicted weight loss curves for t r i a l 74-1. - 172 -C&) 1H9I3M 31dlAIVS - 173 -C. Structural Characteristics of the Product Layer 1. Variation i n Effective Diffusion Coefficient It i s quite evident from examination of Figures 49(a) to (1) that i f the assumed transport control model i s correct, effective d i f f u s i o n coefficients must be changing during the extent of a single t r i a l . In order to determine the degree of va r i a t i o n i n D r n , values were ef f calculated at various magnetite thickness for each set of experimental conditions for which curves were predicted. These values are plotted i n Figures 52 (a) to (e) incl u s i v e . The general trends exhibited by Dg££ as a function of thickness of magnetite can be categorized into two groups: one of low density -3 C4.02 to 4.08 g cm or 84.8 to 86.1 percent theoretical density); _3 and one of high density (4.17 to 4.30 g cm or 88.0 to 90.8 percent theoretical density). For high density samples, values of increase i n a l l cases with increasing magnetite thickness. However, at p a r t i a l pressures of sulphur dioxide of 0.50 atm and 0.25 atm, D decreases on thickening from 30 to 60 percent reaction to completion. Calculations of D e£j i n the case of low density samples result i n a relationship opposite to that above described. Without exception, ^eff ^ e c r e a s e s with increasing magnetite thickness. T r i a l 39-2 (conducted at 700°C) exhibits an extraordinarily rapid decrease i n D£££ during formation of the i n i t i a l 75 u thickness of product layer. 2. Correlation of Variations with Metallography A comparison of calculated values and metallographic observa-tions can best be conducted by again separating samples to be discussed by density. Metallographic examination of both surface and inte r n a l 10 -I - 174 -T — o 43-1 • 4 8 - 2 A 3 9 - 2 10 -2 i CM O CD to E o V -O—O-• CD 10 - 3 • A v • 0 2.0 4.0 Core Half Thickness (cm. x io2) Figure 52(a). Variation i n Deff. for t r i a l s 43-1, 48-2, and 39-2. - 175 -r — 1 r o 27-1 • 2 3 - 2 0 2.0 4.0 Core Half Thickness (cm. X |Q2) Figure 52(b). Variation i n Deff. for t r i a l s 27-1 and 23-2. - 176 -Figure 52(c). Variation i n Deff. for t r i a l s 58-2, 59-1, - 177 -10 -2 O -O O — Q \ I o CD CO CM E o ^ 10 - 3 h • I • / 10 o 6 5 - 2 • 6 8 - 1 J 0 2.0 4.0 Core Half Thickness (cm. X|Q 2 ) Figure 52(d). Variation i n Deff. for t r i a l s 65-2 and 68-1. - 178 -F I 1 1 — , J J 0 2.0 4.0 Core Half Thickness (cm. X |Q2) Figure 52(e). Variation i n Deff. for t r i a l s 74-1 and 76-1. - 179 -structures of high density samples led to the discovery of b l i s t e r formation or rupturing at the interface between product and reactant s o l i d s . Although there was no evidence of b l i s t e r s near the centre of samples, this does not rule out the presence of ruptures. In fa c t , the c y c l i c wavy nature of weight loss curves of high density samples throughout reaction would seem to indicate that some form of rupturing was occurring throughout. This facet of these weight loss curves together with the observation of approximately l i n e a r rates of weight loss are consistent with the type of v a r i a t i o n of D r r calculated ef f for high density samples. One possible mechanism for rupturing at greater thicknesses of magnetite i s linked with the metallographic observation that the diameters of large macropores i n high density samples were greater than those i n low density samples. I t might be expected that as the thickness of magnetite increases, the physical constraint applied by this increasing thickness at the interface also increases. This, i n turn, would imply an increase i n the pressure required to cause rupturing at the interface s i m i l a r to that found at a small magnetite thickness. I f the pressure for b l i s t e r formation i s too high, i t i s possible that this rupturing adopted a less obvious form. I t i s proposed that at greater thicknesses of magnetite rupturing takes the form of enlargement of large macropores. The behaviour of D e££ i n high density samples under conditions of lower p a r t i a l pressures of sulphur dioxide cannot be supported by metallographic evidence since the pressure effect on structure was not investigated. The i n i t i a l increase i n D e£f i s quite l i k e l y explained by the same argument as above. However the calculated decrease i n D eff subsequent to the i n i t i a l increase i s d i f f i c u l t to understand i n l i g h t - 180 -of the proposed s o l i d state transport of oxide ion i n samples with small pore siz e . The only r a t i o n a l explanation would seem to be a gradual change i n pore size and d i s t r i b u t i o n with increasing magnetite thickness to one of more uniform and more evenly distributed pore siz e . Although k i n e t i c results show the lower l i m i t of this high density group to be approximately 90 percent theoretical density, there i s no reason to believe that the process of rupturing ceases to be active below a d e f i n i t e l i m i t . From De^£ calculations, i t appears that this process occurs i n samples of density at least as low as 88.0 percent theoretical density. The v a r i a t i o n of D £_ with distance from the surface of a low ef f density sample appears to be a f a i r l y uniform decrease at temperatures of 800°C and 900°C. Observations of structures of samples reacted at these temperatures also preclude the presence of b l i s t e r s . General characteristics of these structures were increasing size of large macro-pores with increasing distance from the surface, the effect being larger at 800°C than at 900°C. A comparison of areas at a sample centre and midway between the surface and centre of a sample indicated that where the large macropores increased i n s i z e , the frequency of small macropores decreased. While D r r i s a function of the i n t e r -ef f connection of large macropores, t h i s does not necessarily inf e r that only the observable small macropores served t h i s purpose. But i t i s apparent that the pore size and d i s t r i b u t i o n of macropores changes with distance from a sample surface. Consequently i t i s quite possible that the effective pore radius might decrease with distance from the sample surface. - 181 -Correlation of D with structures of samples reacted at 700°C ef f while s l i g h t l y different i s also possible. I t would seem that the rapid decrease of D e^ with distance from the sample surface to a thickness of 75 y corresponds d i r e c t l y with the microstructures. These cle a r l y defined a band, of approximately the same average width, which contains no large macropores. Because ov e r a l l dimensions of samples remain constant during oxidation, by deduction the effec t i v e pore radius should be r e l a t i v e l y large. For reasons which remain unexplained the structure of magnetite exhibits a rapid change at this distance from the surface to one i n which large macropores are present. Metallographic examination also contributed to the knowledge of size of the magnetite grains formed at temperatures of 700°C, 800°C, and 900°C (larger grain size at higher temperature). I t might be expected that smaller grain sizes would increase the frequency of micropores r e l a t i v e to macropores such that the eff e c t i v e pore radius 40 would decrease. In the reduction of hematite by hydrogen, Warner measures pore sizes which increased by about a factor of 10 with a temperature increase from 750°C to 950°C. Disregarding the outer structural band of the sample reacted at 700°C i n this study, values of D ^ decrease quite markedly with temperature for approximately equal sample densities. This decrease i s more than could be expected by temperature dependence of either a molecular or Knudsen dif f u s i o n c o e f f i c i e n t . Thus i t i s quite l i k e l y that the decrease i n grain size of magnetite with temperature causes a similar decrease i n effective pore radius. A pertinent factor related to the va r i a t i o n of D which has ef f yet to be discussed, i s the va r i a t i o n i n density of pressed compacts. - 182 -Cadle and S a t t e r f i e l d found that effective d i f f u s i o n coefficients varied by as much as a factor of 4 as a function of the location of the sample s l i c e i n an o r i g i n a l compact. The value of c o e f f i c i e n t s , though, placed d i f f u s i o n i n a range which was t r a n s i t i o n a l i n type but probably close to molecular d i f f u s i o n adjusted by a tortuosity factor. As density increases and pore size decreases, the r a t i o of the amount of Knudsen d i f f u s i o n occurring to that of molecular d i f f u s i o n increases. Thus at high densities, a -much greater v a r i a t i o n i n effective d i f f u s i o n coefficient w i l l result from a density gradient. In the present study the r e l a t i v e location of plates i n thei r o r i g i n a l discs varied so that some cross sections should have displayed a l i n e a r porosity gradient from one surface to the opposite. Because this was not observed, i t i s believed that the effect of density v a r i a t i o n i s small and i s probably n u l l i f i e d i n any case by the var i a t i o n i n pore size and d i s t r i b u t i o n . D. Oxidation Mechanisms 1. Transport Processes The. mechanisms upon which control of the two transport processes are based are both d i f f u s i o n a l . That of mass transport through the laminar gas f i l m i s simply molecular d i f f u s i o n . In this p a r t i c u l a r study where a diluent gas was used to vary the p a r t i a l pressure of sulphur dioxide, molecular d i f f u s i o n was defined i n both a binary sulphur dioxide-sulphur system and a ternary sulphur- dioxide-sulphur-argon system. The means by which gaseous d i f f u s i o n occurs i n the porous magnetite - 183 -layer i s somewhat more d i f f i c u l t to establish. The range of X/r for which d i f f u s i o n i n the t r a n s i t i o n region i s defined i s dependent on the model chosen to represent the experimental s i z e , shape and d i s t r i b u t i o n of pores i n the porous layer. In addition calculated coefficients are observed or effective d i f f u s i o n c o e f f i c i e n t s . Since independent diff u s i o n experiments were not undertaken i n r e l a t i o n to the present study, some model must be assumed so that t o r t u o s i t i e s can be approximated. The choice of a model can be determined by two factors: the shape and orientation of pore channels and the pore d i s t r i b u t i o n . I t has been pointed out that both large macropores (4 to 10 u diameter) and small macropores (about 0.5 u diameter) were observed. I t can probably be assumed that in. a hot-pressed s o l i d an average micropore diameter 59 i s also warranted. However, no knowledge of the shape and orientation of pore channels has been gained by metallographic observations. As a result of the observations made, a random pore model formulated by 59 Cunningham and Geankoplis for a tridispersed porous s o l i d w i l l be used as a basis on which to approximate t o r t u o s i t i e s for the present study. By varying the pressure at which experiments were conducted, they found that molecular and Knudsen t o r t u o s i t i e s were sim i l a r i n value and that both increased as the porosity decreased. They determined values of V2r for t r a n s i t i o n a l d i f f u s i o n ranging from 0.00026, below which molecular dif f u s i o n occurs, to 1.3, above which Knudsen d i f f u s i o n i s predominant. These values correspond to average pore r a d i i i n 6 ° 6 ° this study of 3.46x10 A and 2.88x10 A for molecular d i f f u s i o n at o o 900°C and 700°C, and 692 A and 575 A for Knudsen dif f u s i o n at 900°C - 184 -and 700°C respectively. Although the pore r a d i i for molecular dif f u s i o n appears to be very large i t must be noted that, for the transport of molecules, the e f f e c t i v e pore radius i s considerably smaller due to tortuosity. To calculate e f f e c t i v e d i f f u s i o n c o e f f i c i e n t s , tortuosity factors of 3 for low density samples and 6 for high density 59 samples were assumed from reported values which ranged with increasing density from 1.8 to 6.5. Use of a tortuosity factor of 6 at a volume pore f r a c t i o n of 0.32 results i n e f f e c t i v e Knudsen d i f f u s i o n coefficients of 2.54 x i c f 3 cm 2sec _ 1 at 900°C and 2.32xl0~ 3 cm 2sec _ 1 at 700°C. Similar approximations of l i m i t i n g e f f e c t i v e molecular d i f f u s i o n coefficients using a tortuosity factor of 3 and a volume pore f r a c t i o n of 0.35 yields values of 4.27xl0~ 2 cm 2sec _ 1 at 900°C and 2.35xl0~ 2cm 2sec - 1 at 700°C. The significance of these values l i e s i n their relationship to experimental effective d i f f u s i o n coefficients as determined by the transport control model. If the experimental values f a l l between corresponding effective molecular and Knudsen coeff i c i e n t s this i s an indication that the d i f f u s i o n mechanism i s t r a n s i t i o n a l . The majority of d i f f u s i o n coefficients determined by the transport control model for low density samples (see Figures 52(a) to (1)) f a l l i n the t r a n s i t i o n region. One exception i s the d i f f u s i o n c o e f f i -cient of the outer structural band, formed during the s t a r t of t r i a l 39-2 (see Figure 52(a)), which indicates that molecular d i f f u s i o n probably., occurs. Other exceptions appear during oxidation of high _3 density samples (p > 4.20 g cm ) where Knudsen di f f u s i o n i s apparently operative. However i t has been shown that b l i s t e r s form i n the magnetite layer during oxidation of these samples thereby causing the - 185 -effect i v e d i f f u s i o n coefficients to increase. In l i g h t of th i s i t i s rather interesting when the effective pore radius i s calculated for the onset of reaction of a high density sample at 900°C (see Figure -4 2 52(a): t r i a l 48-2). An effective d i f f u s i o n c o e f f i c i e n t of 4x10 cm sec o corresponds to an effective pore radius of 1.06 A. Since the molecular o radius of sulphur dioxide i s 2.15 A, i t should not be possible for Knudsen di f f u s i o n to occur, thus implying that a s o l i d state mechanism for transport of reactant i s operative. 2. Effect of Temperature Determination of a reaction mechanism may be aided by construction of an Arrhenius plot i f the kin e t i c s are r e s t r i c t e d to simple cases l i k e a single rate co n t r o l l i n g step. However, to state an activation energy calculated by this means with any confidence, assurance i s necessary that independent variables of the experimental procedure remain constant during the extent of a single t r i a l . Only under these circumstances can an activation energy be u t i l i z e d to determine the ki n e t i c s of a reaction. Reference to activation energies calculated for rates measured at 6.8 percent, 13.6 percent, and 27.2 percent reaction over a temperature range of 700°C to 900°C and at a pressure of 1 atmosphere (see Figure 23 and 24) accomplishes l i t t l e towards the deduction of the nature of the rate controlling process at f i r s t glance. The values of E vary from 15.5 kcal mole to 30.4 kcal mole ^ for the a bases selected. S i m i l a r l y , an Arrhenius plot constructed from rates predicted by the transport control model at the onset of reaction, - 186 -for what was presumably laminar f i l m control, yielded an activation energy of 14.5 kcal mole ^ (see Figure 5 3). Since the activation energy for molecular d i f f u s i o n i s expected to be 1 to 5 kcal mole an explanation of the differences was necessary. Referral to equations (36) and (37) shows that the reaction flux for transport through a laminar f i l m i s proportional to a pressure driving force i n addition to a mass transfer c o e f f i c i e n t . The variation i n K with temperature i s known so that an approximation of the contribution to E resulting from a changing pressure driving force 9. can be determined. This i s possible because equilibrium can be assumed at the reaction front. Table 6 l i s t s equilibrium sulphur p a r t i a l pressures at one atmosphere sulphur dioxide of 26.8 mm Hg at 900°C and 8.0 mm Hg at 700°C. Assuming the sulphur p a r t i a l pressure in the bulk gas phase to be zero, the effect of this change i n driving force with temperature on reaction flux i s equivalent to an activation energy of 13.8 kcal mole The difference, 0.7 kcal mole t h e n r e p r e s e n t s the temperature effect of mass transfer c o e f f i c i e n t on r e a c t i o n f l u x . As r e a c t i o n proceeds, contribution to c o n t r o l s h i f t s from that of t r a n s p o r t t h r o u g h t h e l a m i n a r gas f i l m to t h a t o f transport through t h e porous p r o d u c t l a y e r . Contributions to o b s e r v e d activation energies must t h e n include the temperature effects of (1) mass transfer c o e f f i c i e n t ; (2) pressure driving force across the laminar gas f i l m ; (.3) d i f f u s i o n c o e f f i c i e n t i n the porous layer; (4) pressure driving force across the porous layer; - 1 8 7 -3 . 5 r r— •4.0 4.5 E a = 14.5 kcal. mole - 1 5.0 L 8 0 1.0 1/T (°K~' X I0" 3) Figure 53. Arrhenius diagram for rates of reaction at 1 atm. SO, as predicted by laminar f i l m control. - 188 -and (5) increasing pore size with increasing temperature at constant 40 volume fr a c t i o n porosity. Warner measured a 10 fold increase i n pore size with an increase i n temperature from 750°C to 950°C and the grain size of magnetite i n th i s study was observed to increase 4-fold with a temperature increase from 700°C to 900°C. Thus, i t would seem that one of the largest contributions to observed activation energy when a s i g n i f i c a n t thickness of magnetite had formed would be the temperature effect of increasing pore size with temperature. I f the effective pore radius increases 4-fold as does the grain s i z e , the resultant effect on reaction f l u x i s an activation energy of 15.8 kcal mole There w i l l also be contributions to the activation energy from effects (2) and (4) on the reaction flux . Hence i t would seem that i t i s not unreasonable to expect an observed activation energy of 30.4 kcal mole 1 although the reaction i s transport controlled by gaseous d i f f u s i o n . Although the reaction of pyrrhotite with sulphur dioxide appears to be topochemical, i t i s l i k e l y that on a micro-scale i t i s not s t r i c t l y so. In this case, activation energies can exhibit values higher than expected for transport processes as discussed i n Section IV.B.l. Although this has not been l i s t e d as a source of contribution to observed activation energy i t remains a p o s s i b i l i t y . 3. Effect of Pressure It was hoped that by determining the pressure dependency of reaction rate, some conclusions could be drawn regarding the r e l a t i v e amounts of Knudsen and molecular d i f f u s i o n under the various experimental - 189 -conditions. A Knudsen d i f f u s i o n c o e f f i c i e n t i s independent of pressure hence reaction f l u x i s proportional to pressure. On the other hand, a molecular d i f f u s i o n c o e f f i c i e n t i s inversely proportional to pressure thus reaction f l u x i s pressure independent. Referral to log-log relationships between s p e c i f i c reaction rate and sulphur dioxide _3 p a r t i a l pressure for samples of density 4.05 g cm (see Figure 34) _3 and those of density 4.15 g cm (see Figure 35) shows slopes for these relationships between 0.5 and 0.85. This should indicate t r a n s i t i o n a l d i f f u s i o n . These slopes decrease with increasing magnetite thickness and are generally higher for low density samples. This implies that proportionately more Knudsen than molecular d i f f u s i o n occurs as the volume fr a c t i o n of porosity increases ( D e f f decreases with magnetite thickness). This, of course, i s highly u n l i k e l y . Another implication i s that proportionately more molecular than Knudsen d i f f u s i o n occurs during oxidation of higher density samples. While D did increase with b l i s t e r i n g , values for low density samples were generally higher than those for high density samples. Since no metallographic observations were conducted to investigate the effect of pressure on the structure of magnetite i t i s not possible to show how pore d i s t r i b u t i o n was affected. However, there i s some evidence to this effect i n the behaviour of D '' as a function of ef f magnetite thickness and of sample density at different p a r t i a l pressures of sulphur dioxide (see Figures 52(a) to (1)). The char a c t e r i s t i c decrease i n D c r with magnetite thickness i s smaller as the p a r t i a l ef f pressure decreases. This could explain the decreased pressure dependency - 190 -with increased magnetite thickness. Another effect of pressure on D j,* can be seen i n Figures 5 2(d) and (e) where D .... f i r s t increases eff ° eff then decreases i n case of higher density samples at lower pressures. I t i s thought that this could be the reason for the decreased pressure dependency at higher sample densities. In any case, i t would seem that factors affecting the formation of magnetite n u l l i f y a l l but the most general interpretation that can be made regarding pressure dependency. 4. Chemical Processes L i t t l e can be established from this study concerning the mechanisms of chemical reaction. Analysis of weight loss curves which were obtained experimentally (representative of a l l sets of experimental conditions) demonstrated that only the transport process of d i f f u s i o n through a laminar gas f i l m was controlling the overall rate at onset of reaction. Since resistances to mass transfer increased from onset, at no time during any single experiment was i t possible to obtain a s i g n i f i c a n t amount of control by chemical processes. Hence i t was not possible to determine either an order of reaction or a chemical rate constant, the dependencies of which must be analyzed for the formulation of a reaction mechanism. - 191 -V. CONCLUSIONS Pyrrhotite samples of densities ranging from 80.0 percent to at least 98 percent theoretical density can be prepared by sintering under pressure. I t i s possible, by this method, to produce porous compacts of a small, uniform grain s i z e ; the average grain size i s the same for each sample regardless of sintered density. However small density gradients exist i n each sample. The k i n e t i c s of oxidation of s o l i d rectangular plates of pyrrhotite by sulphur dioxide can be s a t i s f a c t o r i l y defined by a mathematical model. This model involves the mass transfer of reactant and product gases through a laminar gas f i l m and a porous magnetite layer. Expressions which constitute the transport control model account for the existence of a net bulk flow of gas through both the laminar gas f i l m and magnetite layer. The model also recognizes the non-stoichiometric nature of pyrrhotite and i t s relationship with the experimental conditions of temperature and p a r t i a l pressure of sulphur dioxide. The reaction although endothermic, i s s u f f i c i e n t l y isothermal that thermal i n s t a b i l i t y at the reaction interface can be neglected at a l l times. With gas flow rates of 400 ml min \ transport through the laminar gas f i l m controls the ov e r a l l rate at onset of reaction - 192 -under experimental conditions of sample densities from 84.4 percent to 98.6 percent t h e o r e t i c a l , reaction temperatures from 700°C to 900°C, and p a r t i a l pressures from 0.25 atm to 1.0 atm sulphur dioxide (pressure less than 1 atm being achieved by use of argon as a diluent). As the reaction proceeds and the magnetite layer thickens at the expense of pyrrhotite, the balance of transport control s h i f t s from that resulting from resistance to transport through the laminar gas f i l m to that due to resistance to transport through the porous magnetite layer. As the layer thickens, the l a t t e r c o ntrolling process becomes the more s i g n i f i c a n t , especially at high o r i g i n a l sample densities. The phenomenon of rupturing at the reaction interface confuses the k i n e t i c s of oxidation of samples of o r i g i n a l density greater than about 88 percent theoretical density. Where the thickness of magnetite layer i s small, i t takes the form of large b l i s t e r s or longitudinal ruptures. At greater magnetite thickness i t appears to be r e s t r i c t e d to the enlargement of large macropores. Other experimental parameters being held constant, a decrease i n p a r t i a l pressure of sulphur dioxide decreases the amount of rupturing especially during l a t e r stages of reaction. Effective d i f f u s i o n coefficients of the magnetite layer appear to vary throughout any p a r t i c u l a r experiment. Rupturing during reaction of high density samples i s manifest i n an increase i n D r r with b J r e f f increasing magnetite thickness, while reaction of samples of density lower than 86 percent theoretical causes a decrease i n D r r with eff increasing magnetite thickness. This decrease i s apparently the result of a process i n which large macropores increase i n size while - 193 -the frequency of small macropores decreases. The mechanism of transport control through the laminar gas f i l m i s that of molecular d i f f u s i o n as defined by the binary sulphur-sulphur dioxide system or the ternary sulphur-sulphur dioxide-argon system. However, the mechanism of d i f f u s i o n through the porous magnetite layer can be molecular, t r a n s i t i o n a l , or that of Knudsen di f f u s i o n . Molecular d i f f u s i o n occurs only under conditions of small magnetite thicknesses and at a reaction temperature of 700°C. A l l other low density samples show values of D characteristic of t r a n s i t i o n a l d i f f u s i o n as ef f determined by a tridispersed random pore model. Knudsen d i f f u s i o n i s the predominant mechanism for oxidation of high density samples. However, an alternate mechanism i s also operative for this group of samples; i t i s thought to be that of oxide ion transport i n the s o l i d state. - 194 -RECOMMENDATIONS FOR FURTHER WORK This study has indicated that i n the case of py r r h o t i t e oxidation by sulphur dioxide, the pore d i s t r i b u t i o n of the product layer v a r i e s s i g n i f i c a n t l y with thickness as well as with reaction temperature and 40 pressure. Warner also observed a dependence of structure of porous ir o n on temperature. Variations i n D^^ during an experiment can cause considerable disagreement between predicted and observed reaction behaviour and thus mis i n t e r p r e t a t i o n of mixed control models. I t i s thought that independent d i f f u s i o n experiments are warranted using porous s o l i d s i n the forms that they occur as oxidation or reduction products. Gas flow rates used i n t h i s study were not s u f f i c i e n t to permit i n t r i n s i c reaction rates to be reached. One reason for t h i s i s that the d r i v i n g force for d i f f u s i o n i s always low due to reaction equilibrium. It would be i n t e r e s t i n g to investigate the p o s s i b i l i t y of a t t a i n i n g a conditions of chemical control at least during i n i t i a l stages of 64 reaction by increasing the gas flow rate. Although H i l l s objects to t h i s technique of determining reaction rate constants, i t i s believed that errors incurred by t h i s method for the reaction of pyr r h o t i t e with sulphur dioxide w i l l be small. The mechanism of oxidation of dense p y r r h o t i t e by sulphur dioxide was proposed to be that of oxide ion transport. It i s of s c i e n t i f i c i n t e r e s t to evaluate t h i s hypothesis. Weight loss curves for oxidation of high density samples exhibited an i n i t i a l l y increasing reaction rate. During at least the i n i t i a l stages of th i s behaviour, presumably l i t t l e or no rupturing occurs. Too, reaction rates are s u f f i c i e n t l y - 195 -low that gas f i l m resistance w i l l be neg l i g i b l e . Hence, i t should e possible to investigate the transport mechanism more thoroughly. - 196 -APPENDIX 1 A. Development of a General Model 1. Laminar Gas Film The fluxes of sulphur dioxide and sulphur from the bulk of the gas phase to the sample surface are defined by equations (1-1) and (1-2) k n v S0 2 s 0 2 — - 1 1 1 - <PS0 8 " P S0 8 } ( I ' D 2 b 2 l k ~ nS gS ~t = IT ( p s g ' p s 8 } ( 1- 2 ) 2 i 2 b The direction into the sample i s defined as positive. The maximum p a r t i a l pressure of sulphur under the experimental conditions of this study i s 0.04 atm (at 1 atm S0 2 and 900°C). This w i l l be dissipated rapidly by the high flow rate of reactant gas past the sample so that P g can be assumed equal to zero. From stoichiometry of the b2 b reaction of S0 2 with FeS^ +^, and assuming steady state,reaction (1-3) can be derived which when substituted into equation (1-2) yields equation (1-4). The flux of sulphur dioxide and of sulphur through the -n = ( 5 + 3 p) n (1-3) S 2 4 ' S0 2 ^ J ; • k nso 8S 2 4 2 A = (-5+3y) RT P S 2 § i ( 1 _ 4 ) laminar gas f i l m are described i n terms of n by equations (1-1) and (1 - 197 -2. Porous Product Layer The general expression for transport of gases through a porous s o l i d i n the presence of a net bulk flow i s given by equation (1-5). n. (n./A + n./A)C. dC I 2 i n  A C. + C. i j dx i _ -I _± _ „_;• 1 ( 1 _ 5 ) (n./A + n./A) where the mole centre vel o c i t y i s defined by — - — ^ . By i J substituting SO^ for specie i and for specie j and adhering to the sign convection of equation (1-6), equation (1-7) can be derived for the transport of SO^ through porous magnetite of thickness (x -x^). AFeS = 3 / 2 A S 0 2 = ' 5+% A S 2 ( 1 _ 6 ) nso • pso Dso 9,s. pso g " p s o 9 s . A v 4 vP„ n + P_ RT • x -x S0 2 S 2 o m Because the maximum concentration gradients of SO,, and S 2 are small even where equilibrium exists at the interface, they are assumed here to be linea r across the porous layer (see equations (1^8), (1-9), and (1-10). The approximation, equation (1-11), can also be made resulting P S 0 9 = ( PS0 * + P S 0 ? S . ) / 2 ( 1 ^ 8 ) 2 2 I 2 I P g = (P s + P g g )/2 (1-9) 2 2 i 2 i - 198 -psc, . p s o * + p s o , a  2 2 x 2 i ( 1 _ 1 0 ) P s o + % pso g + pso * + ps * + ps g 2 2 2 l 2 i 2 i 2 i i n equation (1-12) after substitution into equation (1-10). Substitution of equation (1-12) into equation (1-7) results i n equation (1-13) which describes the transport of SO2 through the porous product layer. S i m i l a r l y , the transport of from the reaction interface to the sample surface can be described by equation (1-14). PS0 g + ps g = PS0 8 bu 2 . b 2 . bo 2 b (1-11) SO, pso 8 + pso s b u 2 ± b u 2 ± pso 2 + p s 2 pso ? s. + \ s . + p s o 8 I 2. 2 i 2 x 2 b (1-12) SO, pso 8 + pso s bu 2 ± bu 2 ± b u 2 i b 2 ± b u 2 b Dso s pso 8 - pso s su 2,b 2 bo2 . bu2 . ^ RT x -x o m (1-13) 2 r/5+3p. A u 4 ; P q s + P g b2 i b2 i ( 1 + 3 ^ ) ( 4 ^P.n s + P c s + P s o g •)] so. . s 0 . 2 x 2 x 2 b DS SO PS S " PS 8  2 2 ' ( _ 2 J L _ _ _ 2 _ i ) RT x -x o m (1-14) - 199 -3. Chemical Reaction An expression can be written which describes the flu x as governed by chemical reaction. However, prior knowledge of the order of reaction and magnitude of the rate constant must be obtained, preferably from 64 independent experiments. As discussed by H i l l s , the confidence with which a chemical rate constant can be determined at onset of reaction i s dubious for i t i s dependent on the accuracy of extrapolation of experimental curves to zero time and on the extent of thermal i n s t a b i l i t y . In the absence of the above prior data, one of two other approximations can be made i n order to account for the resistance offered by chemical processes i n a general model. When i t i s suspected that the reaction i s far from equilibrium, the Guldberg Waage Law of 69 mass action for a reversible reaction as suggested by Gadsky et a l . can be assumed. The reaction f l u x can then be described by equation (.1-15). However, i n gas-solid systems this law i s seldom v a l i d as Manes et a l . ^ have indicated. ( ^ ) • ( PS s } J T L - k f [ C P s o 9 s . > 2 " 3 ^ ' 1 5 ) 2 i e An alternate assumption can be made i f the reaction i s close to equilibrium. I t can be shown that, i n this case, the reaction i s f i r s t order with respect to any variable describing distance from equilibrium. Reaction flux i s then described by equation (1-16) , where k^ i s the pseudo f i r s t order rate constant and i s defined by equation (1-17). Although equation (1-16) may permit calculation of k£, the pseudo f i r s t order rate constant depends on the true order of - 200 -n SO s - P ) (1-16) 2 i 5+3y ) (1-17) SO K reaction, which was assumed to be stoichiometric for the derivation of equation (1-17). Of the methods above mentioned for the treatment of chemical reaction i n a mixed control model, the f i r s t (independent experiments) i s the most e f f i c i e n t . Dependency of on pressure should establish a reaction order. For the prediction of o v e r a l l reaction rates, the use of equation (1-15) would probably provide s u f f i c i e n t accuracy, but i t s use for determination of magnitude of k^ i s not recommended. 4. General Model for Reaction of FeS,, with S0„ 1+y 2 Two unique sets of conditions apply for the establishment of a general model: control by transport processes of d i f f u s i o n through a laminar gas f i l m and a porous magnetite layer i n addition to or without control by chemical processes. In order that chemical processes be important, gas flow rates i n the bulk gas phase must be higher than those used i n this study. Transport control i s represented by simultaneous consideration of equations (1-1) and (1-4) for the laminar gas f i l m and equations (1-13) and (1-14) for the magnetite layer together with equation (1-18) which i s a consequence of 'negligible effects from chemical control. Where the i n t e r f a c i a l processes are - 201 -( P s s ) H \ =  e very f a s t r e l a t i v e to experimental reacton rates, p a r t i a l pressures at the reaction front w i l l be governed by the equilibrium constant for the chemical reaction. Provided that e f f e c t i v e d i f f u s i o n c o e f f i c i e n t s i n the porous magnetite layer have been evaluated independently, t h e o r e t i c a l experimental rates can r e a d i l y be predicted by s o l u t i o n of these equations. If there i s no a p r i o r i knowledge of D e £ £ values, they can be obtained from the equations by s u b s t i t u t i n g experimental rates and magnetite thicknesses for n S Q and x^x^. However to do t h i s , D i s assumed equal to D regardless 2 2 ^ U2' 2 of d i f f u s i o n mechanism i n the porous layer. In a binary system, these c o e f f i c i e n t s are equal f o r molecular d i f f u s i o n . S i m i l a r l y , i n a binary SO2-S2 system, they are equal for Knudsen d i f f u s i o n since t h e i r molecular weights are e s s e n t i a l l y equal. However i n a ternary system, the c o e f f i c i e n t s f o r molecular d i f f u s i o n are not equal while those for Knudsen d i f f u s i o n can again be assumed equal. In the analysis i n t h i s study, d i f f u s i o n was found to be t r a n s i t i o n a l i n cases x^here argon was used as a diluent and sample densities were low. At high sample d e n s i t i e s , Knudsen d i f f u s i o n was concluded to be operative. In t r a n s i t i o n a l d i f f u s i o n , the Bosanquet approximation (see equation (1-19) defines the e f f e c t i v e d i f f u s i o n c o e f f i c i e n t . Thus errors induced by assuming the respective molecular d i f f u s i o n - 202 -c o e f f i c i e n t s equal i n a ternary system w i l l decrease as the r e l a t i v e proportion of Knudsen d i f f u s i o n increases. If i n t e r f a c i a l processes do a f f e c t the o v e r a l l rate to a s i g n i f i c a n t extent, equilibrium i s not established at the reaction front and equation (1-18) does not apply. The f i f t h equation, instead, i s one described mass transport as di c t a t e d by chemical reaction. For p r e d i c t i o n of o v e r a l l rate by simultaneous s o l u t i o n of t h i s set, e f f e c t i v e d i f f u s i o n c o e f f i c i e n t s i n the porous magnetite, the order of chemical r e a c t i o n , and the magnitude of the rate constant for chemical reaction must be known. B. Solutions to Transport C o n t r o l Model This section contains the computer programs f o r s o l u t i o n of (from experimental data at 6.8 percent reaction) and the p r e d i c t i o n of weight loss as a function of time (using solutions of D ^ ^ ) . It can be noted that there are two sets of r e s u l t s f o r t r i a l run 39-2. The f i r s t involves 'toeing' of the predicted weight loss curve at 6.8 -2 2 - 1 percent reaction (D c r = 7.617x10 cm sec ) while the second r e s u l t s eff _ ^ 2  from 'toeing' at about 50 percent reaction (^^^ = 9.225x10 cm sec ). For the second set of r e s u l t s , the value of D calculated at 6.8 e f f percent reaction i s bypassed so that the alternate could be used. D e f i n i t i o n s of the symbols adopted for the programs are l i s t e d i n Table (1-1). NONLIN i s a Univ e r s i t y of B r i t i s h Columbia subroutine package for the s o l u t i o n of a set of non-linear equations. - 203 -Table (1-1)• D e f i n i t i o n of Symbols (c.g.s. units) RHOM Molar density of FeS, , 1+u RHO Density of FeS, , 1+u XMU Stoichiometry factor TEMPK Reaction Temperature °K PPS02 Pressure of SO^ i n bulk gas phase RPMW Molecular Weight of Magnetite 1/2 XK. 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"-r r c 3 . 1 0 1 4 f 04 0 . 5 76fE C6 0.1C12E C7 0.2922E -06 C.6860E 00 0.2565E 05 * 1 1 = 4 5 NO c . 3 ft ft F c c 0.1CC5F 04 0 . 9 7»fF C6 0.1 0) 2E 07 -0.2896E -06 0 .6856E 00 0.2610E 05 U I T = 4 S NO. 0. 3 4 ' ft F C5 P.nOft?F 07 P.97fi6F C6 O.1012F C7 0.2871F -06 0.6852E CC 0.2655E 05 » 1 T = <•$ NP 0 . n c n . 9 f 7FF C3 C.9786F 06 0 .1012F 0 7 C.2E4ftE -06 0 .6848E 00 0.270PF 05 « I T = ".S \ " . ' c . •"•ft'jf 05 O.P795F 0? C .<;7e6E C6 0.1012E 07 0 .2822E -06 C.684AE 00 0.2745E C5 H I T = 4 S N(. 0 . 1 4 <• ftf C5 0 . 9 714E 03 0.97S6F Cf. 0.1C12E C7 0.2799E -06 0 .6840E 00 0.2790E 05 tt I r = 4 S NO 0 . -•4ft/;F 05 P.9 ft35F 03 P.9786F C6 0.1C12E C7 0.2776E -06 0 .6836E CO 0.2835F 05 * I T = 4 S NO r. 0 = C. 95 59F C ** C.S7P6F Cft 0.1012E C7 0.2754E -06 0 .6832E 00 0.2880F 05 K I 1 = 4 S NG o. ? '• ft ft F r ft P.9AR?F C3 0.97SfcE C6 0.1012E C7 0.273 3E -06 0.6828E 00 0.2925F 05 H I T = 4<> NO c . i t f p. C5 0 . 14 10F 0 3 0 . 9 7 S f : E C6 0.1012E 07 0 . 2 7 U E -06 0 .6824F 00 0 .2970F 05 » I T - 4S NO c . 3 4/ ft F c c 0.9;?HF 03 0.97Rf,E 06 0.1012E C7 0.2691E -06 0.6820F 00 0.3015F 05 * I T = 4 S \r 0. o t 0.9^f .C.F C3 C.9786E C6 0 .1012F 07 0.2671E -06 0 .6817E 00 0.3060E 05 tt I I = 4 S hC. c . 05 200F 0 3 C .<; 7?ftE C6 0.1012F 07 0 .2S51E -06 0 .6813E 00 0. 310?F 05 U I r = 4 S .\o. c . j /. / <• p cs 0.9131F 03 C.9786F C6 C.IC12E C7 0.263 IF -06 0 .6S09E 00 0.3150E 05 tt 1 T = 4 S :^P c . f 5 0.TP67K 03 0.9786F 06 0.1012E C7 0.2613E -06 0.6806E 00 0.3195E 05 * I T = 4S NO n . 3<,AftF 0 5 G.9eC?.F C3 C.9786F 06 0.1012E C7 0.2594E -06 0.680 2E 00 0 .3240F 05 « 1 T = 4 S \'\ C. 0 <. p 05 O.aOAOE 0 3 o.<;7etF C6 0.1012E 07 0 .2576E -06 C.6798E 00 0. 328 5F 05 4 I T - 4 S Nr; r . ": '•' r C5 C. *iP7flF 0 3 0.97P6E C6 0.1C12F 07 0.2558E -06 0 .6796E 00 0.3330E 05 « I T - 4S NO c. C5 O.BSISE 03 0 .9786E 06 0.101ZE C7 0.2541E -06 0.6791E CC 0.337SF 05 tt I 7 = 4S .^o 1 0. 3'.ft<-E 0 c 0 .F759F C3 C.97P6F 06 0.1012F 07 0.2524F -06 0.6787E 00 0.342CE 05 « I 7 = 4S NO 1 c . "•AftF r<= 0 .S701E 03 Cc. 7P6E C6 0.1012E 07 0.2507E -06 .C.678AE 00 0.3465E 05 tt I 7 = 4 S v.; r.. C5 0 . 3 ' , 4 4 F 03 0.9786F C6 C. lC12F 07 0.2491E -06 0 .6780E 00 0.3510E 05 tt I I = 4S Nr-c . - 4 ft ft F C5 0 . » 5 F S.F 03 0 .9786F Cft 0.1012E C7 0.2475E -06 0.6777E CO 0.3555E 05 tt I 7 = 4 S NO p. A^(7';F c ; P.8534F 03 C.S7F.6E C6 0.1012E C7 0.2A59F -06 0.6773E 00 0.360CE 05 tt I T = 4 $ NO n. " • f t 5 F ("5 P.84O0E 0 3 C.S7P.6F C6 0.1C12E C7 0.2443E -06 0.6770E 00 0.3645E 05 H I 7 = 4 S c . 1 4 P ft F Cft P . 0 4 Z 7 F 03 P.9765E C6 0.1012F 07 0.2A28E -06 0 .6766E 00 0.3690F 05 It 1 7 = 4 S tvO 0 . ' '• ( t F C5 P . °3 7 ,^F C3 ' C.97R5E 06 0.1012E C7 0.2413E -06 0.6763E CO 0.3735F 05 tt I 7 = 4S ^ G 0 . " 4ft ft F o c 0 . Q ^ ? 5F C3 C.9785E 06 0.1012E C7 0.2399F -06 0.6760E 00 O.3780E 05 * I 7 = 4 S N". c . " r G F P5 0 . * 27 5F 03 C.9785F C6 0.1012E 07 0.23P4E -06 0.6756E 00 0. 3825E 05 H I 7 = 4 S N j c . C5 0 . fl??6F 0 3 0. 9 78 5F C6 0.1012E 07 0.2370F -06 0 .6753E 00 0.3870E 05 tt I 7 = 4S NO p. ? 4 ft 6 F 05 0.S17RF C3 C.9785E C6 0.1012E C7 0.2356E -06 0.6750E 00 0.3915E 05 tt I 7 = 4 S liC c . 3 46ft F C5 0 .8121F P. 3. C.C765F C6 C.1012E C7 0.2343E -06 0.6746E 00 0.3960E 05 « I 7 = 4 S ti p. c . 1 '.ftftF 05 0 . ^ 0 8 4 p 03 C.^7a5F C6 C.1012E C7 0.2329E -06 0.67A3E 00 0.4005E 05 tt 1 7 = 45 1-0 n. ^4ftftF C5 0. 8039F 03 0 .9785E Cft C.1C12F 07 0.2316E -06 0 .6740F 00 0.4050F 05 tt I 7 = 4S KC, c . '^.(•f F p 5 P.7 n 94E P3 P.9785E 06 0.1012E C7 0.2303E -06 0.6736E 00 0.4C95F 05 tt 1 7 = 4S NT 0. 7 /. 1.1 F C5 0.79,50^ C3 C.9785E C6 0.1012E 07 0.2291E -06 0.6733E 00 0.A140E 05 # I 7 = 4 i i\:', c . i i r- P5 0.79'C6F 03 C6 0.1012E C7 0.2278E -06 0.6730E 00 0.41HSF 05 * .1 7 = u 5 NO r. 3 ft ft F P5 0.7R64F 03 0 . 9 7 E S E Cft 0.1012E 07 0.2266E -06 0 .6727F 00 0.4230F 05 U 1 7 = 4S NO 0 . i /, ^ ^ c C5 P.7S22F 03 0 .9785E 06 0.1012E C7 0.2254F -06 0.6724E CC 0.47 7 5E 05 « I I = 4S Nl^  0 . > i, ft ft, F o c 0 . 77BCE C C.9785E C6 0.1012F 07 C.2242E -06 0.6720E 0 0 0 .432 CE 05 tt I 7 - 4S G p. '.< 4 ft 6 F 05 P.7739E 0 3 C.S7B5E C6 0.1012E 07 0.2230E -Oft C.6717E 0 0 0.436 5E 05 tt I 7 = 4 5 r . 1 4 ft ft F P5 0.7699F 03 0 . 9 7e5F C6 0.1C12F 07 0.2218E -06 0 .6714E CO 0 .4410E 05 ft 1 7 = 4S n. ? 4 6 ' f C5 0.7660F 03 0 .9735E 06 0.1012E C7 0.2207E -06 0.6711F 00 0.4455F 05 * I 7 = '•i NG 0 . T i ' . f F 05 P.7621F C3 C6 G.1012F C7 0.2196E -06 0 .6708E 00 O.i^OPE 05 a 1 7 = ^ c NO p. •; 4 ib F C5 0 .7583E 03 0.9785F C6 0.1012E C7 0.2185E -06 0.6705E 00 0.4545F 05 0 1 7 = 4 1 N"" r . 34ftftE C5 0.7545F 03 0.9785E Cft C. l012E C7 0.217AE -Oft 0 .6702F 00 0 . 4 5 9 0 F 05 •t 1 r = :•. G 0. •"<i ftp C5 0.75CRF 03 0 .9785E 06 0.1012E C7 C.2163E -06 0.6699E c c 0.4ft35E 0 5 n 1 i = ;.r n . 34P6E 05 P.7471E C3 C.9785F 06 0.1012E 07 0.2153E -06 0.6696E 00 0.46PCF 05 tt l 7 = s C. --4ft ft,F 05 0.7435E 03 C.S785E C6 0.1012E 07 0 .2142E -06 0.6693F 00 0.4725F 05 t 1 7 = 4 s C . 34ftft;F c c 0.73 9 9 F 03 0 . 9 7 f 5 E Cft C. lC12F C7 0.2132F -06 0.ftftP°F 0 0 O .4770F 05 ft \ 7 = $ 0 . '4ftft.F C5 0 .73( - 4 F 03 0 .9785F C6 0 .1012F f 7 P.2122E -06 0 . ft ft 8 6 F PC 0 . 4 8! 5F 05 t 1 T = '• 5 ^ G C. 34ft ftE 05 P . 73 ? t r C3 f .9785F 06 0 .1012F 07 0.2112F -C6 0.ft683E 00 0 . 4 8f.r-p "5 * 1 T = '1 '-G 1 c . 34/,ftF Oft 0 . 7 ; 9 6 E 0" P.>;7f.5F Cft 0.1012F 07 0 . ? n 2 f= -C6 0 .6681F 00 49() 5F ) c « 1 T = ••. - f.p 1 c . 3 4 h ft F r c 0. 7 2t>?F 0 3 P.9785F Cft C.1C12F C 7 0 . 2 0 a 2 E - 0 6 0 ,ft67»F 0 0 f),A<jSOF 0 5 ft 1 f = 4'". ! 0. '3 4 ft.6 F c c n . 77 >>ir r 1 0 . 9 7 P. S F Oft . 0 • 1 0 1 ? F r •» r. 2 C 8 3(--P6 0 . ft 6 7 5 F r r 0.4995F 05 * 1 1 = i* ^ 0 . •> ' ft j: rr- P . 7 1 P h P '• 1 rft 0 . 1P1 ?F 0 7 0 . ? C 7 ? F - P ft 0 . ft ft 7 ? F ro P. 504 T 1 I T = ^ 1 R U N M I * R F K = 2 7 - 1 oih^ COEFF PS? si PS? r.r PSC2 SI PSO2 GI O . U U F - C 1 C 200AF OE 0.1760E 05 0.9975E 06 0.9999E C6 * IT = 7SING 1 P P ? ? ! P S 2 GI P S O ; SI " S T ? GI R A T E W E I G H T T I MP C 2 0 0 4 E n c 0 . 1 7 F 3 G C E 0 . 9 < : 7 E E 0 6 0 . 9 9 9 7 F 0 6 0 . A 7 5 6 F - OE 0 . 6 2 0 E F 0 0 0 . A 5 0 0 E 0 3 I T - E S I N 0 1 C . 2 C C 3 E CE 0 . 1 6 2 0 E C E 0 . 9 9 7 1 E C 6 c i r c l e 0 7 0 . A 3 2 1 F - 0 5 0 . 6 1 5 2 F CO 0 . 9 0 0 0 F 0 3 k I T - i S I N O 1 C . ? 0 0 ? E C E r . 1 4 9 A E C E C . 9 9 6 R E 0 6 0 . 1 0 O 2 E C 7 C . 3 9 8 5 E - 0 5 0 . 6 1 0 A E OC 0 . 1 3 5 C E OA 1 I T - SSU.r, 1 C . 2 0 C 2 E C 5 0 . 1 3 9 3 F C E C . 9 9 6 5 F C 6 C . 1 0 0 3 E C 7 0 . 3 7 1 EE - 0 5 0 . 6 0 5 9 E 0 0 o . i e c o F OA It I T = 5 S l r N r , 1 C 2 0 O 2 F C E 0 . 1 3 C 9 E O E C . 9 9 6 3 E C 6 C . 1 C C 3 E C 7 0 . 3 A 9 3 F - 0 5 0 . 6 0 1 6 F 0 0 0 . 2 2 5 0 E OA n I T 5 S I N " , ' C 2 C C 2 E C 5 n . 1 2 3 9 E OS 0 . ° 9 M E C 6 C . 1 C C A F 0 7 O . 3 3 0 6 E - 0 5 0 . E 9 7 6 F 0 0 0 . 2 7 0 0 F O A u IT E S U v G ! 0 . 2 0 C 2 E C 5 0 . 1 1 7 9 F OE 0 . 9 9 6 0 F 0 6 0 . 1 C C A F r . l C 3 1 A 5 E - O E 0 . 5 9 3 7 F c c 0 . ? 1 5 OF OA It I T E S I N H ! C 2 0 0 1 E 0 5 0 . 1 I 2 7 E C E C . 9 S S 9 E 0 6 o . i r o E F 0 7 C . 3 C C 6 E - 0 5 0 . 5 9 0 1 < = 0 0 0 . 3 6 0 C E OA ft I T = 5 S I N C 1 C . 2 0 0 1 F C 5 0 . 1 0 3 1 F 0 5 C . O S 5 7 E C 6 G . 1 0 C 5 E C 7 0 . 2 P 8 A F - 0 5 0 . 5 H 6 6 F 0 0 O . A 0 5 0 F OA H I T E S I K G 1 C ' C - C I F C 5 n . 1 O A O F O E 0 . 9 9 5 6 E C 6 C 1 C C 5 F C 7 0 . 2 7 7 5 E - 0 5 0 . E 8 3 2 E 0 0 O . A 5 0 0 F O A » IT A S I ' . O ! 0 . 2 C 0 1 E C 5 0 . 1 C C 3 F C 5 0 . 9 9 5 5 E C 6 0 . 1 C C 6 F C 7 0 . 2 6 7 7 E - C E 0 . E 7 9 9 E CC 0 . A 9 5 OF OA * I T = A s i IN n 1 0 . 2 . 1 0 I F O E 0 . 9 7 C 5 F CA C . 9 9 E 5 F 0 6 0 . 1 0 0 6 F 0 7 0 . 2 5 8 9 E - 0 5 0 . 5 7 6 8 F 0 0 0 . E A C O F OA * I T A S I NC, 1 C . ? R 0 1 F C E 0 . 9 4 0 5 E OA C . 9 9 E A E C 6 C 1 C C 6 E C 7 0 . 2 E 0 9 F - 0 5 C . 5 7 3 7 E 0 0 0 . 5 8 E C F OA H I T = A S I M " . 1 r . s o c 1 E a 1 ; 0 . 9 ] ? 2 E CA C . ^ S I E C 6 0 . 1 0 C 6 E C 7 0 . 2 A 3 6 E - 0 5 0 . 5 7 0 7 E 0 0 0 . 6 3 C C F OA tt I T A S I ? ; G 1 0 . 2 0 r r E C E 0 . P 3 6 0 E OA 0 . 9 9 E 3 E C 6 0 . 1 0 0 6 F 0 7 0 . 2 3 6 9 F - 0 5 0 . 5 6 7 9 E 0 0 0 . 6 7 E C F OA V I T A S IN"" . I c . ? C O O E C E 0 . CA C 9 S E 2 E C 6 0 . 1 0 0 7 E C 7 0 . 2 3 0 7 F - 0 5 0 . 5 6 5 0 F 0 0 0 . 7 2 0 0 F OA n I T - A S l N G 1 r . 2 0 0 C E C E 0 . 3 A 3 A E 0 4 C . 9 9 E 1 F c e 0 . 1 C C 7 E C 7 0 . 2 2 5 0 E - 0 5 0 . 5 6 2 3 F CO 0 . 7 6 5 C E OA a I T A S I N G 1 C 2 C r . C E C E 0 . B 2 3 4 F 0 4 0 . 9 9 E 1 E C 6 0 . 1 C C 7 F 0 7 0 . 2 1 9 7 E - 0 5 0 . 5 5 9 6 E 0 0 O . P 1 0 0 F O A tt IT A SI NO 1 0 . P O O C F •CE c . 8 0 A 8 E 0 4 0 . 9 9 5 0 F C 6 0 . 1 0 C 7 E C 7 0 . 2 1 A 7 E - 0 ? 0 . 5 E 7 0 E CC 0 . 8 E 5 0 F C A » 1 T A S I NG 1 0 . 2 8 0 0 E C E 0 . 7 E 1 4 E CA C . 9 9 5 0 E 0 6 0 . 1 0 C 7 E 0 7 0 . 2 1 0 1 E - 0 5 0 . E 5 A A E 0 0 0 . 9 0 0 C E OA tt I T A S I N O 1 C 2 0 0 C E C 5 0 . 7 7 1 0 E OA C . 9 « ; 5 0 E C 6 0 . 1 0 C 7 E 0 7 0 . 2 0 5 7 E - 0 5 C . E 5 1 9 F 0 0 0 . 9 A 5 0 E C A tt I T = A S I N G 1 C ? c r c E C 5 0 . 7 5 5 7 E OA 0 . 9 9 A 9 F C 6 C . I C C 7 E 0 7 0 . 2 0 1 6 E - 0 5 0 . 5 A 9 5 E 0 0 0 . 9 9 0 0 E O A H IT A S INC. ! C . 2 0 T C E C 5 0 . 7 4 J . 2 E OA 0 . . 9 9 A 9 E 0 6 0 . 1 0 C 7 F C 7 C . 1 9 7 7 E - 0 5 0 . E A 7 1 F 0 0 0 . 1 0 3 EE O E tt I T = A S I N G 1 0 . ' ' . G O E O E 0 . 7 2 7 E F CA C . 9 9 A 9 E 0 6 0 . 1 0 0 8 E 0 7 0 . 1 9 A 1 F - 0 5 0 . 5 A A 7 E 0 0 0 . 1 C R C E 0 5 tt I T A S I N G I 0 5 0 . 7 1A EE OA C . 9 9 A 8 P 0 6 0 . l c r e E C 7 0 . 1 9 0 6 E - 0 5 0 . 5 A 2 A E 0 0 0 • 1 1 2 EE O E tt I T - A S I N G 1 C . 2 T C F C E 0 . 7 0 2 2 F OA 0 . 9 9 A 8 E C 6 C . 1 C C R F C 7 0 . 1 R 7 3 E - 0 5 0 . 5 4 0 1 F 0 0 . 0 . 1 1 7 0 E 0 5 tt I T = A S I N G ! c . ? r r c E C 5 0 . 6 9 C EE OA 0 . 9 9 A « F 0 6 0 . 1 C C B E C 7 C . 1 8 A 2 E - 0 5 0 . 5 3 7 9 E C C 0 . 1 2 1 5 F O E tt I T A S I N G '. C . ? r C C E C E 0 . E 7 S 4 E OA C . 9 9 A . 7 E C 6 0 . 1 C C R E 0 7 0 . 1 8 1 2 E - 0 5 0 . 5 3 E 7 F 0 0 0 . 1 2 6 0 E 0 5 « I T A S I N G 1 C . ? 0 0 C F C E 0 . 6 6 8 8 E OA 0 . 9 9 A 7 E C 6 0 . 1 C 0 8 E C 7 0 . 1 7 8 A F - 0 5 0 . 5 3 3 5 E CO 0 . 1 3 0 E E 0 5 tt I T A S I N ' : 1 C ? f CCE 0 S 0 . 6 E 8 6 F OA 0 . 9 9 A 7 F C 6 0 . 1 C C 8 F C 7 0 . 1 7 E 7 E - 0 5 0 . 5 3 1 3 E 0 0 0 . 1 3 E 0 F 0 5 tt IT A S I N'-. ! P . ? o r n E CE r . 6 A 9 0 E OA 0 . 9 9 A 7 E 0 6 0 . 1 C C 8 E C 7 0 . 1 7 3 1 F - 0 5 0 . E 2 9 2 F c c 0 . 1 3 9 E F OE tt I T A S I N G 1 C . 1 9 ' 9 F O E 0 . f 3 c . 7 F CA C . 9 9 A 6 E 0 5 0 . 1 0 0 8 E 0 7 C 1 7 C 7 E - O E 0 . 5 2 7 2 F 0 0 0 . 1 A A O F C 5 H I T - 4 S I . ' ; G ! 0 . 1 9 9 9 F C E 0 . 6 3 C 3 P OA C . 9 S 4 6 F C 6 O . K C P E C 7 0 . 1 6 8 3 E - 0 5 C . 5 2 5 1 E 0 0 0 . 1 A R E F OE H I T = A S 1 NG '. n t ' F r r . F F F c P. ? E l P S ? 01 PSO? SI psr>2 G I o . n r 7t - c n . ! O< ,HF t'E 0 . 1 2 0 C F 04 C . 9 9 27F 0 6 0 . 1 0 1 2 F 07 * ! T 5S1 NG 1 P?2 c,i P SO 2 S I PS02 GI R A T E W E I G H T TI WE 0. 1 ',-:•<•: 0 5 r .3 2E9F C4 C . 9 E 7 BF C6 0 . 1C11F C 7 0 . 8 2 6 7 F - 0 6 0.6 3 4 4 F 0 0 0 . 9 0 0 C F 03 4 I T 7S U G 1 c . 0 , ? i n r 04 0 . < l Q 7 t F C6 o.101 i r C 7 0 . 5 3 E 6 E - 0 6 0 . 6 B 3 C E CO 0 . 1 K O C F 0 4 * 1T t S N r, T o . r r- n . 1 (• C 6 1 - C4 C . C S 3 4 E CE 0.1012F 0 7 C . 4 2 C 0 E - 0 6 0 . 6 8 1 9 E n o 0 . 2 7 C 0 F 04 » 1T = 5S MG 1 r . 1 r - o r 0 . l A o o r 04 C . O E 7 4 F C6 0 .1 C1 2 F C7 0 . 3551 E - 0 6 0 . 6 R 1 O E 00 0 . 3 6 0 0 E 04 « IT b S I NO ] C . lfCKf 0 . 1 272F 04 C . 0 < » ? 3F C6 0 . 1 0 1 2 F 07 0. 7 1 2 6 F - 0 6 0 . 6 8 0 2 E 0 0 0 . 4 5 0 0 E 0 4 H IT ES NO 1 o . 1 9 c f F C E r . i n ? F . 04 0 . 1 0 7 3E 0 6 0 . 1 C 1 2 E C 7 0 . 2 B 2 1 E - 0 6 0 . 6 7 9 E F C C 0 . E 4 0 OF 04 tl 1 T = E S \r. \ o . 0 C 0 . i c ? U C4 r.<=933E 06 0 . 1 0 1 2 F 07 0 . 2 5 R 9 E - C 6 0 . 6 7 8 9 F 00 O . t 7 0 C F 04 » I T 4 i NO i o . I < 9 ?r C E 0 . /, F /, r C C . 9 S 3 3 F C6 0 . 1 0 1 2 F C 7 0 . 2 4 0 5 F - 0 6 0 . 6 7 8 2 E 00 0 . 7 2 0 0 E 04 » 1T 4 S INC- 1 c . 1 c c. 7F r c 0 0 ' P . 9 9 3 3E C6 C . l 0 1 ? F C7 0 . 2 2 E 5 E - O 6 0 . 6 7 7 7 E 00 O . P 1 0 0 c 0 4 H IT 4S '•" 1 r>. 1 ' : i 7 f c c r) . p a c n E C O . ^ P S P F 0 6 0 . 1 0 1 2 F C7 0 . 2 1 3 C E - 0 6 0 . 6 7 7 1 F CC C . 9 C 0 0 F 04 I T 4 S I N G 1 C . T - 7 F o c 1 . 79 7 7 F C3 C . 9 9 3 2E 06 0 . 1 0 1 2 F 0 7 0 . 2 C 2 3 E - C 6 0.6 7 6 6 F 0 0 C . 9 9 C CE 04 S I T 4 S N G 1 r . 1 r .: -> F C-E n . 7 6 1 ? E o 2 C . 9 9 3 2 E C6 0.10 1 2 E C 7 0 . 1 9 7 1 E - 0 6 C . 6 7 6 1 F 0 0 0 . 10 ° 0 F OE tt IT 4 S V", 1 c . i c c-,r. r.s . 7 2 9 3 r-0 3 0 . 9 9 7 2 F C6 0 . 1 C 1 2 E 07 0. 1 P E 0 F - 0 6 0 . 6 7 E 6 F CO 0 . 1 1 7 0 F P E » IT = 4 S N i r . I ' i n r - c n . 7r j nF 03 0 . 9 9 3 2F 0 6 0 . 1 C 1 2 E C7 0 . 1 7 7 8 E - 0 6 0 . 6 7 5 2 F CG 0. 1 2 6 0 E 05 tf I T 4S INC ! n . 1 •': K 7 c r c 0 . <• 7 E F F C3 C . 9 9 3 2 E 06 0 . 1 0 1 2 E 07 0 . 1 7 1 4 E - 0 6 0 . 6 7 4 P F 0 0 0 . 1 3 E C F C5 .« I T — 4 S NO 1 r . ! ' ^ 7 i - os n . 6 E 21 F 0 5 C.9 9? ?F C6 0 . 1 0 1 3 F 07 0 . 1 6 5 6 E - 0 6 0 . 6 7 4 3 F 0 0 0.1 4 4 0 F OE * I T ' s NG 1 c . c s 0 . 1 •? 2EK 0 7 0 . 9 9 3 2 F C6 C . 1 C 1 3 C 07 0 . 1 6 0 4 F - 0 6 0 . 6 7 3 9 E 00 0. 1 E 3 0 E O E 4 IT 4S f:G 1 r . l i t " , F c - C . E l :>7F 03 0 . 9 9 3 2E 06 0 . 1 0 1 3 F C7 0 . 1 5 S 6 E - 0 6 0 . 6 7 3 5 F C C C . l 6 2 C C 05 H 1 T 4 S I NO 1 0 . !9~7F r l " . E C f EF C 1 1 C . 9 9 3 2 F 06 0 . 1 0 1 3 E 0 7 0 . 1 5 1 3 E - 0 6 0 . 6 7 3 I E 0 0 0 . 1 7 1 C E 05 '/ I T 4 S N G I C . 1 CC7f e s o . 5 F C 6 F 0 C . 9 9 3 2 F C6 0 . 1 C 1 3 E 07 0 . 1 4 7 3 E - 0 6 0 . 6 T 8 E 00 0 . l f i O O E 05 a IT 4 S iWc 1 C . ! 1 c. IT C E ft . E f c0F 0 . r - 9 7 2 F C6 C . 1 0 1 3 E 07 0. 1 4 3 5 E - 0 6 C . 6 7 2 4 E 0 0 0.1890E " 5 tt IT 4S NG 1 C . c ? 0 . E E 2 ^ F r ^ C . 9 C 3 2 F CA 0 . 1 0 1 3 E C7 0 . 1 4 0 1 E - C 6 0 . 6 7 ? 0 F c c 0 . 1 9 R 0 E OE » 1 T 4 S .'•G 1 C . l ' . ' S U o s o C.3 C . 9 9 3 2 E C6 0. 1 0 1 3 E 07 0. 1 3 6 9 F - 0 6 0 . 6 7 1 7 E 00 0 . 2 C 7 C E 05 « I T - 4 S \ 1 c . 1 7F rc n . ? 2 7f! F C.9 93 2F C6 C . 1 0 1 3 E C7 0 . 1 3 3 9 F - 0 6 0 . 6 7 1 7 E 00 0 . 2 1 6 0 F OE « IT - 4 S \'G 1 c 3 F C 7 F os n . E 1 6 ? r 0 3 0 . 9 9 7 2 E C6 0 . 1 0 1 3 E 07 0. 13 1 0 F - C 6 0 . 671 OE 0 0 0. ? 2 I ; 0 E 0 E I r - 4S N 0 1 0 . 1 C C . 7 F r e 0 . E C 6 2 F 03 0 . 9 9 7 2 F 0 6 0 . 1 C 1 3 E C7 C . 1 2 8 4 E - 0 6 0 . 6 7 0 7E o o 0 . 2 7 4 0 F 05 « 1 T 4S N G V c . 1 c q -7 r C E 0 . <.o6 4F. 03 C . 9 9 3 2 F 06 0 . 1 0 1 3 E 07 0 . 1 2 5 9 E - 0 6 C . 6 7 0 4 F 00 0 . ? 4 3 0 E O E ft I T - 4 S i r . 1 r<;7F C E r- , t> i71F 0 3 0 . 9 9 7 2 F 06 C . 1 0 1 3 F 07 0 . 1 2 3 E E - 0 6 0 . 6 7 O 0 F 00 0 . 2 5 2 0 E OE * 1T 4S ^ o ! c . 1 r c 7 F r s n .47=?3F C3 0 . 9 9 3 2 E 0 6 0 . 1 0 1 3 F C7 0 . 1 2 1 3 E - 0 6 0 . 6 6 9 7 F c c O . 2 6 1 0 F 06 ti I T 4 S ^ C- 1 r,. 1 - 7 7 F 0 . A 7 C C F C3 C . 9°"' 1 F 06 O . 1 0 1 ? 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CJ o o • r . rvj ivj C O L '• c O CJ r-- r -C O CJ CJ o o r- r-. — t_. cj - 216 -0. r~. o c. o c c c Li' LL- LU u . tL C O V/- LH LP. LT a H -r a «j cr fl P", ^ - H c sC J ! ^ O >0 O o o c o c c-c u IT- C ' fl <t J -J-J • O O O C C C- LT C LT C ' o re a. rv r-Q . _ rv rv <j O n" -— r- . rv rv ( (-> c o C O c rv LP i—' f—• cr • LP r- u- •— tv rv (""•• •j- , j u'. u> u-, u-a: T u.' cr cc- of C O O C- C c LP LT Ll". U1 Lp LT. r - V rv r~ , ^ tr fi c t C <V. <-'<-• c f (<-. re r O O C <-J < c L_> G O C <— U J u-i u.' a- L L cc r*- • •—« -L-^ u' >r -r f ff, ^ c f . r r . U Lv c c O O o C O O IP. C LP C LP O >J O J*. O O C. o o c •o w, r- c LP o o o c c a • c- c c <-' <* C C O c_ c c 1L UJ u. U' U. _L LT cc r~ ex. O rv f! C ^  vJ rv tT a, CL r- r- r- • LP LP I P LP IP LP. - o c c c c L. LL li. LU U. vj <vj - >f f-LP -J" r-rv P-J rv vC «L" -V <J C O <_> O c a. X.' c a a a. C c o o c > c c o o c C LP O LT, t_ • f r— f\j »c »—1 > -L' •£ r- r- a" . rv rv in cc- u i ^- o N - LT. C U - *» r rv r\, —< r-i (-rv rv rv* rsi rv rv , LP LP LP, LP LP. • rv rp 07 cr CT' C CT O C ' CL' vf tp sj o c_ o ^ y. s ^ • O C C LT O c u» c r cc 1 o *r cr o e o o o c c c vL> vf vt' Lf u> u LP If. IP If'. LP IP O t_; e c o c- o c- c o * L r- r -C LT C CVj — — o o o o o o MU CT L> r-o vO vO o r- r-LP IP LP LP. LP LP ID (T (T CT LU tr o o o O C c-C O C C C j LT r- LT-vT r-. • <r vi -j-o o o c_ o o o c- o c_ c o c o - 217 -•*", r* • sr sf -J ; C • C C C7 C • L.I LiJ LL LL U. Z> O CJ O O CJ C If C' LP O • Iri cj fn o. <\ r* ^ CJ* »—• «—I P' f\i L> O C C O C c c C J o o c U LL! LU U-i LL' D C CJ O O if. C i n O o H ^ G IT. tT vt -J- >i> - r LO c c o o c c ; Lf co ? m o - rv f\: Ui It' LU * jvj m -CC vO < J ND -CJ. o c c J — LU LL' LL t ". sT 0' p- if. ro O O O O C O < .-. j.' \ r - r~ 1 m LT-r - r - re cc d L J O C J O O O C J O O O C J O I rf. f. <\- f\j • co ou cc c. ksj f -J1 -T -J J CJ C O O C.: CJ O C; O O O C G CJ CJ C J C. LL: U. Lu LL UJ O CJ O O G CJ LP. O If CJ LP. O cc m r- r\i —J x; p- f- co o o c o O o LL UJ LU LU UJ UJ I1, r-i CO ITl 1*0 CT CL O LO J^-— o e c - c -c >c -c -c C C O CJ c - CT- Cf CT- J O C ^ r H O Cf LT1 H H L> a c o o c o o f- CC J O r -• OJ CL CO Cf Cf , LP If If IP> LP. I a: CC CO X L LU U- IU UJ - c o r e m rvj _^  o cr cc : o c tr c vO sD LP- LT a o o a c c 1 LL1 LL LU LL l 1 >r r*1 rv *~< < Lf Cf CT CJ'' ( 1 rv c\j rv f\j ( cc cc- cc < C O O CJ1 CJ c "J -f J ^  "3 <t O O C. C J c c — a o f r - x x <; •— ci' 0 sr p . CM o r * -o "4 ^ sr f . p*1. c C. C. c c O C J L C- O C ^ 2 : i . * :z ^ • 1 |v; v/i 1/. w sT -J sf J -J" '< II II II II It II II II II " II * * * » LU ti: LL LU LL O C CJ' C Lf O '• O LP. O f' cu ' c -f a O O cc Cf Lf C7 »~* o o c o o a — f. rv 1 C Lf. C 1 1 c- -J- or p' 1 sr >j LT. 1 •c r- r*- o" c. Q 0 0 0 0 0 0 o o c o c c- c o o o o c • c c c c cv r . X lu U L_ U_-a p f~ — -c cr c c - . .-1 rv fv iv ( CJ C O C C f vj i f >r - ii r~ i*- «C CT> Sf f ; f\l C C* Cf CT Lf f> if If If Lf\ If LP. CJ O O O CJ o J LL- LL' UJ I - r- i cc i - o cr cc a . • C CO LL I LT: If If LP> C O LJ o C' C L L U «• <• cr <V LT T ( •G LT If sf f«' • a- a : ir 07 cc. 1 1 LC\ If. If If Lf I •-> O O C' G C U". IP LT LP Ip, c o o c o c ":• c c.' c t c ' • cc rv -c c >r < • cc <x r- r— . p- r- r- t~ 1 LP LT Lf • 111 If Vj LP. <T sf Cf I*--ff CL' C f -1 p- sr r\i Cf r -cf oc cc cr. r*" f-o u o c 0 0 1 ^ -o «c u <c : l o o o c 0 0 I 1 1 l I -1 LL LULU LULL' 1 >C st LO I*- O c o cv ir. cr if. rf. >—• cr r~ -o r*- f— <J «0 >o 0 o C J c o o I I I I CJ o o c c (J n m sr *T ; cr t f Lf n tp. LP U 1 D CD CC * O O CJ LJ O c ' LU LU LU LU LL1 i-Ll Lu LL LL' LL LL ^ tP <J -4J \D P" f- ^ CO Cf OJ rt ^ L f t f c f c f c f c f j'rjc^c^Lfcf 1 |lf LO Ul If. If If J* LP IP U" Lf ' CO CO CC Ct) CL. LiJ CT) CT CT3 CU CO CJ O O O O CJ o G o o o c ' If. Cv cc c-O O C J c o o cr Lf cr cr cr tr cr cr cr cr cr Jf LP U1 U. > Lf1 LP x> cu co cc cr cr • O O O C3 U c\j P". ^ iv, O •v if. a -V - - L C' r LP ui LP. LP <r U O C C' u o rf» a;- sj r- tv *c -f < l 1 . ki CV L ST sf ST 1^ -J sT z- c o o o c LU LU UJ LU LU LL-U C O L O O CJ o o c O o •O C •£ -Li co cc co cc or o c a C J c C J J CJ - H ^ O CJ Ci C G C sf, st? sC X' a' aj a , tt j u o O u u k 1 cr r~ cc cc • CM rv C CJ O C- O CJ LL' LU 1^  f-X LO LL U. LL LU f~- O •L' -O a cc a a rv rv rv o» cr U J a ' a' U O U C C J D J-' U- a LU LU LL' <> m m u- IP LP. CC LL CU X CO 04 p; rv pj rv X to iv a cc i c e O o t LL UJ LU LL sr sr <r J <r sr CC CC CC ' rv cv rv cv r\j r\i 1/ a.' a 1 LL uj cc O O C U c c C ' c -< <: *L -c <• •z- o c a. a ; 1 v.' L • t_. l _ ' . r\j c • rv p. . Vj CV CV fV PkJ Pi O U Q C U ( <r sr sr sr sr -o C J o o o c . A CP f- -C sT CJ "~ o sr r* Lf - O f a r -rft f. r^ r^  P1 cv C" o c; C c, r \ H i f »r N ^ ~* <r r~ 10 o s- <] a- ui sr sr v. P , rv cv CVJ rv c r- tv o —1 -J -c PS, a i"\ f: IV P rv rv rv r\i fv . . H C Q rv LJ r~ sr - 1 a. tf. * — t ; c." o tr cr c c c o o c; c c. • o c c o c cr sr c -L" sr rv u' r- LP rv L.' a- rc a - «"- cr.' 0 c C Cj o C C o c V-J CJ C L U ( j U U . Li Lt-~ LL LL L.1 U. CJ C- O L, ^' CJ C C - O C J CJ C: C - O » ; L_. L, C C. CJ C V rv rv cv n • K vc sr c\, c a' •~- P - f- p- c C C C- C: C: C ; : C VJ C' O J L C C O I • C C. LL Li L- U-r, c <•-• L • c r . O (' . 1 5.721' r . " ? f . ? F 06 0 . 0 60 1 F c e C . 4 3 5 C E - 0 6 0 . 5 7 2 5 F 0 0 0 . ?'!•[ C5 * I T = •• ; r, ; -c. •>35rr r s r . J b'-. H F 04 C . R 2 8 2 R 0 6 C - 8 6 0 2 F 0 6 0 . 4 3 1 0 F - 0 6 0 . 5 7 1 9 E 0 0 0 . 2 5 2 0 E 0 5 » IT AS I NO i c - ? 5 C F r c r . 1 5 4 4 F C4 C .P.2P. ? f C 6 0 . 3 6 0 2 E C6 C . 4 2 7 1 F - 0 6 0 . 5 7 1 4 F r o 0 . 2 5 6 5 F . 0 5 * 1 1 4 S I N r i r V T I C F r r. r . ]•!" ?.PF C i C . P 7 P 2 F C6 C . 8 6 C 2 E 0 6 0 . 4 2 7 4 E - 0 6 0 . 5 7 C ° E 0 0 0 . 2 6 1 CE 0 5 * 1T ' S I N G 1 r •a SlIF CE 0 . 1 5 1 7 F 0 4 G . 6 2 R 2 E C6 C . 8 6 0 2 E 0 6 0 . 4 1 9 7 E - 0 6 0 . 5 7 C 3 E 0 0 0 . 2 6 5 5 F 0 5 ft I T A S I NO 1 c •"7SCF. c c - 0 . 1 5 C i t 0 4 0 . 8 ? R ? F C6 C . 8 6 0 2 F 06 0 . 4 1 6 1 F - 0 6 0 . 5 6 9 8 F 0 0 0 . 2 7 0 0 F 0 5 * IT 4S I\ R ' - 1 0 " ? C C F c c f! . 1 4 9 2 E P4 0 . P 2 8 2 E C 6 0 . P f C 2 F 0 6 0 . 4 1 2 6 E - 0 6 0 . 5 6 9 3 F CO 0 . 2 7 4 5F 0 5 d 1 T = 4 S I N 0 1 fi ( I s 0 . 14 79F C4 C . « 2 R ? F 0 6 C . 8 6 0 2 E 0 6 C . 4 C 9 3 E - 0 6 0 . 5 6 8 R E 0 0 0 . 2 7 9 C E 0 5 U 1 T z: A S I N G 1 C c 0 . 1 4 6 7 T 0 4 C . R ' 3 2 E 06 C . 8 6 0 2 E 0 6 0 . A 0 5 9 E - 0 6 0 . 5 6 8 3 E 0 0 0 . 2 P 3 5 E 0 5 # I T A S I N G 1 n 3 3 ECF C E r . 1 4 5 6 F 04 0 . 8 2 8 2 E C6 C . 8 6 0 2 E 0 6 0 . 4 0 2 7 E - 0 6 0 . 5 6 7 8 E 0 0 0 . 2 8 P 0 F 0 5 ft IT A S I N G I I to 0 0 I - 219 -rv tu i/i r-Q. CO J _ U J U . U J U . l X ' O G O O G O O C G O O O o cc r- >c in -f - CM m .j- «• • o o o o o o 1 UJ UJ LL' UJ t r»- in r- I-J . rsj o cr ' Ifl IT. U ' . i rf) rf) rf) vC • --• c o c o o * a « * a a o o o e o o o o o o o x n <\ « c cj' o x f* co cr or •-> o o o o o o CM o co r - sc o ,0 tn m rvi r-. o c *r -J >r »f -J" rf) rf) rf) rf) -C rfj I i i JJ UJ LU r- re, G >T — i CO > I I LU LU U J -4- M oj m a- r -(Nj sQ f> rf) LT. O O O G C O ^ <e « < >c G G G G C i UJ LU LU LU LL1 0 <E ^  if i re re a. r- cr-CO U'I (NJ O CC , «f < «J c-o o o o o o n to m rf- r» cc LT cr LT <r i^ U> IT. U> cc a; cc a ' o o G O G O UJ LU LL LU LU re cr r- LO U" CC CC u.' CO rv rv rv rv rv cc a cr a. u. O G G G O O - r" a. t*> o - — rfj r*' i-< - P p. rv rv c o f-• t j o c G G G G C C II « II II H II LU LU UJ LU LU LL' G G O C G C rf) in vj- re rv rv re vj L T sO o o o o o o u LU LU LL LU -O r- x <J- —. re cr cr. r-- vO vO Ln e re re re re ^ rf) «c •« rf) >c O G O C G (-> O O O G C O G O < i rfj rf) . i a.1 cc ( ' G O ' L  LL LL' »f re re LU rx. x rv rv CC' CO cc LL.' CO rv rv vu cc C G G O C G U LL LL Li. U.. rf; C co -j ,r u~-re cr LL rj- vj ? h -c iT IT c G C C G C- G O C G O G O : % «: at LU L L LL, L U L U L L Q G O O G O •-< o cr a.. r» rf) fv- co co cr o —• o o o o o o L LU LU LU LU LL r— c CM Ln cc re ro rv _ i o r c i re, re rfj rf) rf) rf) vL •e LT G M f- LT. LT ~y Ti m fA vj- a- re re rv ce re rv re m rn Q C O P C C rf5 rf} rf0 rf) vC l£ O O O O o c I < I I I II L U LL' L U L U P . LP. O G rf) LT. rf,' CT rv ^  (jn 6 cr co cc r-rv rv rvt rv eg C G C O G c O G rf) rf) x or O G O G rf rf- vfl rf) aa cc x CC G G G G O L-J rv _ cc cc cc rv rj rv cc OL; <r 1 L L L L L L L L L CO CC CO < r\j rv rv ' cc cc cc < • o o G G c i a; -J <-_' rf. LL- LU LL U.: O O G G G G LP - T re rv —• O rv re -j- LP. rfj r-PO rv (M rv rvi rv O C G G C G O G G G C G \ CC (M LP, ( • cc co r» i „ rv rv rv ( o o o o o G ii u-- r- re, o co re cu vj- o - i 1 LP •«$" «r *r vi <M rv; rvi CM fsi O O O O O O vT *f -vf vT -J- LP G G O O O G rf> rf) rf) rf) rf) rf; CO CO CC CC CO G G O G G O U_ LU LU LU U. LU < CC CC °-: : rv rv rv CC CC <-D or cc -rv rv rv CP X J J ^ "I •J O L J c c c re rv ir» c LP rv re G i - VT rv G — •—•Or*." G G G C' G G G U . Lf' Lf. Lf LT' r p~ fj c r'1 G C G G G c II II II 11 II II C O C C O o CT cc r- rf) LO vj-r- cr o- o —* rv rv rv Pj m fr- re O G G C O C LL. LL- LU L L • — in cr «r 1 IT vT r^  f. , rv rv rv rv : rf:, rf) vc vC G C G C O O rf; rf; rf; rf> vc v O G" C G O f I I I I I JJ LU LU LU LL L c — L~. a rf; v rf) rv cc- ip, r-i t re rO rv rv rv * rv rv rv rv rv r G O C O D C JU UJ LU LU LU U . LP. IP U1 LP. LP O O G G O G rf) rf; rfj rf; rf; no CC CO CO X C. G V o o o ui a- LL LL OJ LT* U • C C LT p- r- p- p- r-rv rj rv r\ rv <J- a; cr cc LL' G C O O G G C C C G c r- G -r • — ™ rv IT. vL I rf) vj- r>j G ' c r o cr ; o c* o cr j- cr-T vr -r vr -T -+ ~ p-. p p- re P*; G O G O A n tr ^ * C O G O G O re rv — i C a a" - T LP vO rfj r*-m P> re r*. P> P - 1 C O G O O G cc n-- > rv rv r-i rv rv cv rf) rf; vr -J rf; L / r- ac pv rv cr rH C rv *"v rv G G G G C G 11 Lf'. LP rfj vL' G G" G G G- L-J rf; M.' rf; -o vc vj x co cc CO CC' OL G G O G G G U_- LL LU U, LU Lu cr cr cr cr c* r- r- p- r~ r-rv rv rv rv rv CP aj u- a- a, <r c G G o G G \ -u rv ,-e P* f: f O -j N l vi' p~ cv G G C O C G U G u. U-u- cr c c LT u-G G 1 ' G G G O O G O O C rf. Li" • vj- p . fx; cr o rv rf. re vj vj- o j rv rfj - C G rv rv: r-: vP rf; rf? C C O C C C-cr O" cc cc- r~ r*-rf) < —• o O G O C G C O G - O G G O G • rf) rf) **-' O G G rf) -C rfJ CC CC CL G G rf; rf; X rf; rf) rf) rf) • cr LT cr • r~ r-Pv rv rv LT a' r~ r-rv rv G G G G G G P- re p • p-. p^  re u- G C G G c: J- Li. u_ LU u. t— cr o LT - i r v* G G L. G C C 1 D rf) rf, rft rfJ c o o c c i LU Li- Li' LU G X rfv u» "> -r rv c cr LT- c a-X- LU UJ LU i - J G G G G V_ rf: rf. cr. a.' L J c . rf rf: —• r\ - P cr i i- rv — w c - r- r- r- r < U > M J t ' B F P = 6 5 - 2 0 II F C O E F F F S ? SI P S 2 G I P S 0 2 SI P S O ? G I C . P 5 2 0 E - 0 2 0 . 2 2 4 1 F C5 0 . 1 6 4 1 E 05 0 . 49 20E 06 0 . 4 9 8 0 E 06 * IT = = 6 S I N & 1 P S ? $1 P S 2 GI P S C 2 SI P S 0 2 GI R A T E W E I G H T T I HE 0 . 2241 E C5 0 . I 643E 05 0 . 4 9 2 0 E 06 0 . 4 5 8 C E 06 0 . 5 4 4 5 E - 0 5 0 . 5 7 1 2 E 00 0 . 4 5 0 0 E 03 * I T 4 S I N G ! 0 . 2 2 3 6 F 05 0 > 1 3 4 6 E 05 0 . 4 9 C 6 E 06 0 . 4 S S 5 E 06 0 . 4 4 5 9 E - 0 5 0 . 5 6 5 9 E 00 0 . 9 0 0 0 E 0 3 * I T 5 S I N 0 1 C . 223 3E C5 0 . 1 1 6 4 E 05 0- ft 89 EE C6 0 . 5 C C 5 E 06 0 . 3 8 5 5 E - 0 5 0 . 5 6 1 3 E 00 0 . 1 3 5 0 F 0 4 D IT 5 S I NO I 0 . 223 1E C5 0 . ! 038E 05 0 . 4 8 9 2 E 0 6 6" . 5 0 1 IE C6" 0 . 3 4 3 9 E - 0 5 " 0 . 5 5 7 1 E CC O . 1 8 O 0 E 04 » I T - 5 S I S 0 1 P . ? 2 2 ° F 0 5 0 . 9 4 5 2 F Cft C . 4 8 8 8 E 06 0 . 5 0 1 6 F 06 0 . 3 1 3 1 F - 0 5 0 . 5 5 3 4 E o o 0 . 2 2 5 0 F 04 « I T = 5 S I N G 1 P.. 2 7 2 S F 05 0 . 8 7 3 0 E 0 ' C . 4 E F 4 F C6 0 . 5 0 2 0 E 06 0 . 2 B 9 2 E - C 5 r . 5 4 9 9 E 00 0 . 2 7 0 0 E 0 4 « IT 5 S I N G 1 C . 222 7F C5 0 . S 1 5 0 F Oft 0 . 4 F 8 1 E C6 C . 5 0 2 3 E 06 0 . 2 7 C 0 E - 0 5 0 . 5 4 6 7 E 0 0 0 . 3 1 5 0 E 04 * IT = 5 S I N G 1 0 . 2 2 2 7 F C5 .0 . 7 6 6 9 E Oft 0 . 4 8 7 9 E 06 0 . 5 0 2 S E CSk 0 . 2 5 4 1 E - 0 5 0 . 5 4 3 7 F o c 0 . 3 6 0 C E 04 * I T 5 S I N G 1 P . 2 2 2 6 F 0 5 0 . 7 26 4E Oft 0 . 4 F 7 7 E C6 0 . 5 0 2 7 E C 6 \ C . 2 4 C 7 E - 0 5 O . 5 4 0 8 E o o 0 . 4 0 5 C F 04 * IT = 5 S I N C 1 P . 2 2 2 5 F 05 0 . 6 9 1 6 F Oft 0 . 4 6 7 6 E C6 0 . 5 C 2 9 E 06 0 . 2 2 9 1 E - 0 5 0 . 5 3 8 1 F 00 0 . 4 5 0 0 F 04 * I T 4 S I M 0 1 C . ? ? 2 C F n . ftft 13E 04 0 . 4 E 74E C6 C . 5 C 3 1 E 06 0 . 2 1 9 1 F - 0 5 0 . 5 3 5 5 E o c 0 . 4 9 5 0 E 04 tt IT = 4 S I N G 1 P . 2 2 ?. 4 F C5 0 . 6 3 4 6 E Pft 0 . 4 8 7 3 E 06 0 . 5 0 3 2 F Cft 0 . 2 1 0 3 E - 0 5 0 . E 3 2 5 F CC 0 . 5 4 O 0 E 04 tt I T 4 S I N G 1 0 . 2 2 24F 05 0 . 61 C9E CA C . 4 6 7 2 F 06 0 . 5 0 3 3 E 0 6 0 . 2 0 2 4 E - 0 5 0 . 5 3 0 5 F 00 0 . 5 8 5 C E 04 tt I T = 4 S I N G 1 c . 2 2 2 4 E 0^ 0 . 5 8 9 6 F Oft 0 . f t f 71E C6 0 . 5 C 3 5 F 06 0 . 1 9 C 3 F - 0 5 C . S 2 8 2 F CO 0 . 6 3 0 0 E 0 4 tt IT 4 SI NG. 1 c . ' 2 2 2 E c e 0 . ft704E Oft 0 . AF 70F Cft C . 5 C 3 5 F 06 0 . 1 8 9 0 E - 0 5 0 . 5 2 5 9 E 00 0 . 6 7 5 OF 04 « IT = 4 S I N 0 1 n . 2 222F C5 0 . ' 529F Oft 0 . 4 3f ,9F 06 C . 5 0 3 6 E C6 0 . 1 8 3 2 F - 0 5 0 . 5 2 3 7f o c C . . 7 2 0 C F 04 * I T 4 S I N G 1 0 . 2 2 2 3 E Cft p . 5 369F 0 ' C . 4 8 6 9 E 06 0 . 5 0 3 7 F 06 0 . 1 7 7 9 6 - 0 5 0 . 5 2 1 6 E 00 0 . 7 6 5 C F 04 * IT 4 S I N G 1 p . 2 2 2 3 F 05 0 . 5 223E n i 0 . f t E 6 8 F C6 0 . 5 C 3 8 E 06 0 . 1 7 3 0 F - 0 5 0 . 5 1 9 5 E 0 0 0 . 8 1 0 0 F 04 U I T 4 S I N G 1 c . 2 ? 2 2 E C5 0 . 5 0 R 7 E Oft 0 . f t 8 6 7F 06 0 . 5 C 3 9 F 06 0 . 1 6 8 5 E - 0 5 0 . 5 1 7 5 E 00 0 . 8 5 5 0 F 0 4 n IT - 4 S I N G 1 0 . 2 ' 2 ? E Cft 0 . 4 9 6 2 F pft o . f t a f , 7 E 0 6 0 . 5 C 3 9 E 06 0 . 1 64 4 E - 0 5 0 . 5 1 5 6 E C O . C . 9 0 0 0 E 0 4 « 1 T 4 S I N G 1 0 . J 2 2 2 F 05 0 . 4 645F Oft P.ft 8 6 6 E 06 0 . 5 0 4 0 E 06 0 . 1 6 0 5 E - P S 0 . 5 1 3 6 E 00 0 . 9 4 5 C F 04 tt 1 T 4 S I N G 1 0 . 2 2 2 2 F C5 0 . 4 7 3 6 E 0 ft o . f t e 6 6 E C6 0 . 5 0 4 1 E 06 0 . 1 5 69E - 0 5 C . 51 1 8 F 0 0 0 . 9 9 O 0 F 04 tt IT 4 SI NG 1 C . 2 2 2 2 F C5 0 . 4 6 3 4 F Oft r>. 4 E 6 5 E C5 C . 5 C 4 1 F C6 0 . 1 5 3 5 E - 0 5 0 . 5 0 9 9 E 00 0 . 1 0 3 5 E 0 5 * IT = 4 S I N G 1 0 . 2 2 2 2 F C5 0 . 4 5 3 OF Oft 0 . A 8 <, 5 F 0 6 0 . 5 C 4 2F C6 0 . 1 5 0 4 E - 0 5 0 . 50 81 F PC 0 . 1 P B C F 05 <* I T = 4 S 1 N G 1 P . 2 7? IE 0 c 0 . ftiftEF Cft C . 4 8 6 4 F 06 0 . 5 0 4 2 F 0 6 0 . 1 4 7 4 E - 0 5 0 . 5 0 6 4 E 0 0 0 . 1 1 2 5E 05 s i ^ = 4 S 1 N G 1 C . 2 22 1 T 0 5 0 . 4 3 6 4 F 04 0 . 4 E 6 4 E C6 C . 5 C 4 2 F 06 0 . 1 4 4 6 E - 0 5 0 . 5 0 4 6 E 00 0 . 1 1 7 C F 05 <t IT = 4 S1NG 1 C . ? ' ? 1 F C5 n . A 2 8 3 E Oft 0 . 4 E 6 3 F Cft 0 . 5 C 4 3 F 06 0 . 1 4 1 9 E - 0 5 0 . 5 0 3 0 E 00 0 . 1 2 1 5 F 0 5 * IT = 4 S I N G 1 p . 2 " 2 1 E C5 0 . 4 2 C 7 E Oft 0 . 4 3ft. 3F 0 6 0 . 5 C 4 3 F Cft 0 . 1 3 9 4 F - 0 5 0 . 5 0 1 ?ft GC 0 . 1 2 6 P F Oft H I T = 4 S I N G 1 0 . 2 ; <-1 F 05 0 . 4 1 35E Cft C . 4 8 * 3 E 06 0 . 5 0 4 4 E - C6 0 . 1 3 7 0 F - 0 5 0 . 4 9 9 6 F 00 0 . ! 3 0 5 F 05 a I T 4 S I N G 1 ' P . ? 2? IE P5 0 . 4 0 6 7 E Oft 0 . 4 C f 2F C6 0 .50 .44 F 06 0 .1247f t - 0 5 C . 4 9 8 0 F 00 0 . 1 350"= 05 « IT 4 S I N G 1 C . 2221 F C 5 0 . 4 AC IF Oft 0 . 4 8ft 2F Cft 0 . 5 C 4 4 E Oft 0 . 1 3 2 6 F - 0 5 0 .4 96 5F OC 0 . 1 ' O f t F 0 5 It IT = 4 S 1 N G 1 0 . 222 1F C5 0 . 3 9 3 9 E Oft 0 . 4 8 6 25 06 0 . 5 P 4 5F f 6 0 . 1 3 0 5 F - 0 6 0 . 4 0 4 9 E GO 0 . 1 440= 05 o I T = 4 S I N G 1 A . 2 2 - P E 05 0 . 3 E F C F Cft P , c 8 6 2F 06 0 . 5 0 4 5 E 0 fc 0 . 1 2 8 5 F - 0 5 0 . 49 3 4 F 00 0 .148.5F. 05 * I T 4 S ! N G 1 r . ? 22 PF 05 p . 38 23E Oft 0 . 4 F 6 1 E Cft C . 5 C 4 5 F 06 0 . 12 67E - 0 5 C . 4 9 1 BE no 0 . 1 570 = 05 * IT = 4 S I N G 1 P . ? ' 2 P E C5 p . 3769F Oft 0 . 4 E ft 1 F C6 0 . 5 0 4 f t F 06 0 . 1249 E - 0 5 P ,4 QOA F 00 0 . 1 5 7 5 r 05 1 IT = 4 b I N G 1 0 2 2 ' P F C5 p . 3 7 1 6 E Oft 0 . 4 3 6 IF 0 6 0 . 5 C 4 6 F r 0 . 1 2 3 IE - 0 5 0 . 4 8 8 c F CC 0 . 1 6 3 pc 05 tt 1 T 4 S l N r 1 0 . 2 J 2 P E p c 0 . 3 ft 6 60 pft 0 . 4 86 1 E 06 0 . 5-"46F Oft 0 . 1 2 1 5 E - 0 5 0 . 4 P 7 4 F " 0 0 . 1 66 5F 05 « I 1 = 4 SI NO 1 C . 2??0F. 05 Q . 36 18E Oft C . 4 E 6 P F Cft 0 . 5 O 4 6 E 06 0 .1 1 C 9 F - 0 5 P . 4 8 6 0 F - or. 0 . 1 7 1 OF 05 i' I T 4 S I N G 1 c . 2 2 / P F P5 p , 3 5 7 2 E Oft 0 . 4 " f OF Cft 0 . 5 C 4 7F 06 0 . 1 18 3 E - 0 5 0 .4 846 - 00 o . 1 7 5 ft c " 5 « IT = 4 S I N G 1 P IJVJ N l l ^ R F P -( F-| F F PS 7 S 1 P S7 01 p s r i 2 s i P S C 2 GI R3 7 1 F - 0 ' r . 7 2 ??F C5 0 . A 9 9 A F OA C . A P 6 7 F 06 0. 5 0 3 9 F 0 6 # I T = • 5 S I N G 1 PS7 S ! P52 r,t PSO7 SI PSD 2 01 R A T F W E I G H T T I VE C . ? 7?4F cr- 0.6 19 7 E OA O . A E 72F C6 0 . 5 O 3 3 E 06 C . 2 0 C A E - O b 0 . 5 9 6 1 E 00 0 . 9 C 0 0 F 0 ? .* IT = 6S \G 1 0 . ? ? 1 1 E 0 5 0 . A16 5F OA C . 4 86 3E 0 6 0 . 5 0 A ?F C6 0 . 1 3 A 7 E - 0 5 0 . 5 9 2 7 F 00 0 . 1 R O O E 04 H IT = 6S N G 1 c . 7 ? ? G F C5 0 . 3 3 0 5 F OA 0 . A E 5 9 E C6 C . 5 C A 8 E C6 0 . 1 0 6 9 F - 0 5 C . 5 9 0 C E 00 0 . 2 7 0 0 E 04 * IT = 5S NG 1 C . 7 2 1 9R C5 C . 2 8 1 2 E OA 0 . A F 5 7 E C6 0 . 5 0 5 C E C6 0 . 9 C 9 2 E - 0 6 0 . 5 R 7 7 F CO 0 . 3 6 0 0 E OA H IT = 5S N-G 1 0 . 2 2 1RE C5 0 . 2 4 8 4 E OA O . A R 5 5 E 06 0 . 5 C 5 2 E C6 C . 8 0 3 2 E - 0 6 0 . 5 R 5 6 E CC 0 . A 5 0 O E 04 n n - 5S NG ! 0 . 2 2 ! ° F 0 r 0 . 2 2 4 7 E CA C . 4 5 5 A E 06 0 . 5 0 5 3F 06 0 . 7 2 6 6 E - 0 6 0. 5 R 3 8 E CO 0 . 5 A 0 0 F OA * I T = 5S NG I 0.>7|It 05 0 . 2 0 6 6 E OA 0 . A E 5 3 E C6 0 . 5 C 5 A E 06 0 . 6 6 8 C E - C 6 C . 5 8 2 I E 00 0 . 6 3 0 0 E 04 * IT = A S MG 1 C . 7 7 1 7 F 0 . 1 9 2 2 E OA 0 . A 8 5 2 F C6 0 . 5 C 5 5 E 06 0 . 6 2 1 A E - 0 6 0 . 5 R 0 5 E 00 0 . 7 2 0 0 E OA it IT = AS NO 1 0 . ' 7 1 7 F C5 C . 1 R C 3 E OA 0 . A 8 5 ?E 06 0 . 5 0 5 6 E 06 0 . 5 8 3 2 E - 0 6 0 . 5 7 9 1 F cc C . 8 1 0 0 E 04 I I T = AS NG 1 0 . - ? 17 F 0 5 0 . 1 7 C A F OA- C . A e 5 1 E C6 0 . 5 0 5 6 E 06 C . 5 5 1 2 E - 0 6 0 . 5 7 7 7 E 00 C . 9 0 0 C E 04 * IT = 4 S U G 1 C . . ? ? l 7F 0 " 0 . 16 JOE OA 0 . A E 5 1 E C6 0 . 5 C 5 7 E 06 0 . ? 2 3 8 E - C 6 C . 5 7 6 3 E 00 0 . 9 9 0 0 F OA * IT = 4 S NG 1 C . -2 ?1 7F C1^ 0 . 1 5 4 7 E OA 0.A 8 5 1 F C6 C . 5 C 5 7 F 06 0 . 5 0 0 1 F - 0 6 0 . 5 7 5 1 E 00 P . 1 0 B 0 F 0 5 * IT = 4S NG i 0 . ? ? 7 E C5 0 . 1 4 8 2 E OA 0 . A 3 5 O E 06 0 . 5 0 5 7 E C6 0 . A 7 9 A E - 0 6 0 . 573 8E c c 0.117 0 F 05 H I T = 4S NG 1 0 . 2 2 17F 0 5 " . 1 426E CA C . 4 e 5 0 E C6 0 . 5 0 5 8 E C6 0 . A 6 1 0 E - 0 6 0. 5 7 2 7 E 00 0 . 1 2 6 0 F 05 * I T = 4 S NG 1 c . ? ? l 6 E C5 0 . 1 3 7 5 E OA 0 . 4 E 5 C E C6 C . 5 C 5 8 F 06 0 . A A A 5 E - 0 6 C . 5 7 1 5 E 00 0 . 1 3 5 0 F 05 H IT = 4 S NG 1 C . 7 2 1 F C R 0 . 1 3 2 9 E OA C . A R 5 0 E C6 C . 5 C 5 8 E C6 0 . A 2 9 7 E - 0 6 0 . 5 7 0 5 E 00 0 . 1 A A 0 E 05 * I T - 4S NG 1 C. 77.1 t E C5 C.1 26 7E OA C . A R 5 0 E 0 6 0 . 5 0 5 6 E C6 0 . A 1 6 2 E - 0 6 0 . 5 6 9 A E OC 0 . 1 5 3 C E 05 H 1 T = AS NG 1 n . 2 7 1 f.-F 0> 0 . 1 749E' CA C . A E A 9 E C6 0 . 5 C 5 9 E C6 0 . A C 3 9 E - 0 6 0 . 5 6 8 A E 00 0. 1 6 2 C E 05 4 I T = AS NG 1 C . 7 2 1 6 F Cb 0 . 1 2 ! 4 E OA 0 . A 8 A 9 E t 6 0 . 5 C 5 9 E 06 0 . 3 9 2 7 F - 0 6 0 . 5 6 7 A E 00 0 . 1 7 1 0 E 05 # 1 1 = AS NG 1 C . 7 2 1 6E C5 0 . 1 1 8 2 E OA 0 . A E A 9 E C6 0 . 5 C 5 9 E 06 0 . 3 8 2 3 E - 0 6 0 . 5 6 6 A E 00 0. 1 8 0 0 E 0 5 # IT = AS NG 1 0 . 7 7 ] t F C5 0 . U 5 3 E OA 0 . A 8 A 9 E 0 6 0 . 5 C 5 9 E C6 0 . 3 7 2 7 E - 0 6 0 . 5 6 5 5 E cc 0 . 1 8 9 OE 05 # I T = AS NG 1 0 . 7 2 16E 05 0 . 1 12RE CA C . A 8 4 9 E 06 0 . 5 O 5 9 E 0 6 0 . 3 6 3 8 E - 0 6 0 . 5 6 4 5 E 00 0 . 1 9 8 C F 05 4 1 T = AS NG 1 C . 7 2 1 t E 05 0 . I 0 9 9 F OA O . A E A S E C6 0 . 5 C 5 9 E 06 0 . 3 5 5 5 E - 0 6 C . 5 6 3 6 E 00 0. 2 0 7 0 E 05 * IT = A S NG 1 C . 2 J U F C5 0.1 0 7 5 E OA 0.A F A 9 E C6 0 . 5 C 5 9 E 06 0 . 3 A 7 7 E - 0 6 0 . 5 6 2 8 E 00 0 . 2 1 6 0 E 0 5 U IT = AS NG ! 0 . 7 7 U E C5 0 . 1 0 5 3 E OA O . A S A R E 0 6 0 . 5 0 6 C E C6 0 . 3 A 0 A E - 0 6 0 . 5 6 1 9 F OC 0 . 2 2 5 O E 05 » I T = AS NG ! 0 . 2 7 16F 0 5 0 . 1 C 3 2 E CA C . A 8 A 8 F 06 0 . 5 0 6 0 E 0 6 0 . 3 3 3 6 E - 0 6 0. 5 6 1 0 E 00 0 . 2 3 A C E 05 » I T = AS NG 1 C . 7 7 14F C5 6 . 1 0 1 2 E OA O . A E A S E C6 0 . 5 0 6 0 E 0 6 0 . 3 2 7 1 E - C 6 C . 5 6 0 2 E 00 0. 7 A 3 0 E 0 5 * 11 - A S N'G 1 C .771 f.F C5 0 . 9 9 2 R E 03 0 . A E A S E C6 C . 5 C 6 0 E b S 0 . 3 2 1 0 E - 0 6 0 . 5 5 9 A E 00 0 . 2 5 2 0 E 0 5 It IT = AS NG 1 0 . 2 2 1 6 E C5 O . 9 7 5 0 E 03 C . A 3 A 8 E 06 0 . 5 0 6 0 E C6 0 . 3 1 5 3 F - 0 6 0 . 5 5 8 6 E CO 0 . 2 6 1 O E 05 It I T = A S NG 1 C . 7 7 1 6 F 05 0 . 9 5 8 IE 03 C . A E A 8 E C6 0 . 5 0 6 0 E 06 0 . 3 0 9 8 E - C 6 0 . 5 5 7 8 F 00 0 . 2 7 0 0 E 05 * IT = AS NG I C . 2 2 1 6: F a 0 . 9 4 2 0 E 03 0 . A E A 8 F C6 0 . 5 t 6 0 £ 06 0 . 3 0 A 6 E - 0 6 0 . 5 5 7 0 E c o 0 . 2 7 9 0 E 05 * I r = A S NG I C . 2 716E C5 0 . 9 2 6 7 E 03 O . A E A R F C6 C . 5 . C 6 C E 06 0 . 2 9 9 7 E - 0 6 0 . 5 5 6 3 E 00 0 . 2 R 8 0 E 0 5 tt IT = AS NG 1 0 . ? 7 1 ft E C5 0 . 9 1 2 2 F 03 C . A 8 A 8 F 06 0 . 5 0 6 0 E 06 0 . 2 9 5 0 E - 0 6 0 . 5 5 5 5 F 00 0 . 2 9 7 0 E 05 tt IT ~ AS NG 1 9 . 7 7 1 4 E C5 0.8 9 8 2 E 03 C•A 64 8E C6 0 . 5 0 6 0 E 0 6 0 . 2 9 0 5 E - 0 6 0 . 5 5 A 8 E 00 0 . 3 C 6 0 E 05 f IT = AS MG 1 0 . 7 216F C5 0 . R 8 4 9 E 03 O . A E A S E C6 0 . 5 C 6 C E C6 0 . 2 8 6 2 E - 0 6 0 . 5 5 A 1 E 0 0 0 . 3 1 5 O E 05 tt IT = A S NG 1 0 . 7 7 1<F C5 0 . 8 7 2 2 E 0 3 0. A E A R E C6 0 . 5 C 6 0 E 06 0 . 2 8 2 0 E - 0 6 0 . 5 5 3 A E 0 0 0 . 3 2 4 0 E 0 5 tt IT = AS NG 1 0 . 7 7 1 6 F C f O . R 6 C 0 E 03 O . A E A S E 06 0 . 5 0 6 1 E 06 C . 2 7 8 1 E - 0 6 0 . 5 5 2 7 E CC 0 . 3 3 3 0 F 05 W I I = AS NO 1 C . 7 2 1 6 F C5 O . R A 8 3 E 03 C . A 8 A 8 E C6 C . 5 C 6 1 E 06 0 . 2 7 A 3 E - 0 6 0 . 5 5 2 0 E 00 0 . 3 A 2 C E 05 * IT = AS NG ! 0 . 2 2 16E C5 0 . S 3 7 1 E 03 0 * 4 F A 7 E C6 0 . 5 C 6 1 E C6 0 . 2 7 0 7 E - 0 6 0 . 5 5 1 3 E 00 0 . 3 5 1 0 E 0 5 A IT = 4 S NG 1 C . 7 7 1 6 F C c 0 . 8 2 6 3 E 03 0 . A E A 7 E C6 0 . 5 C 6 1 E 06 0 . 2 6 7 2 F - 0 6 0 . 5 5 0 6 E 00 0 . 3 6 0 0 E 0 5 « IT = AS NG 1 0 . 2 2 1 6 F C5 0 . S 1 5 9 E 03 0 . A 8 A 7 E 0 6 0 . 5 C 6 1 F C6 0 . 2 6 3 8 E - 0 6 0 . 5 A 9 9 E cc 0 . 3 6 9 0 F 05 * I T = AS NG 1 C . 7 7 ! 6 F 05 0 . 8 C 5 9 E 03 C . A E A 7 F 06 0 . 5 C 6 1 E 0 6 C . 2 6 0 6 E - 0 6 0 . 5 A 9 3 F 0 0 0 . 3 7 8 C E 05 tt I \ ~ A S NG 1 0 . 2 2 1 6 ? 0? 0 . 7 9 6 2F (5 3 0 . A F A 7 E £ 6 (5-506 1 E 06 0 . 2 5 7 5E - C 6 0 . 5 A 8 6 E 00 0. 3 S 7 0 E 05 tt IT = A S NG 1 0.721<-F C c 0.7869E 03 0 . A 8 4 7 E 0 6 0 . 5 C 6 1 E 0 6 0 . 2 5 A 5 E - 0 6 0 . 5 A 8 0 F 00 0 . 3 9 6 0 F 0 5 tt IT = AS N " 1 C. 2 2 1 ;F 05 0 . 7 7 7 ° E 03 C . A 8 A 7 E 06 0 . 5 0 6 IE C6 0 . 2 5 1 6 F - 0 6 0 . 5 A 7 3 E 00 0 . A 0 5 C E 05 # I T = AS NC- 1 0 . 2 2 1 5 E 05 0 . 7 6 5 2 E C3 C . A F A 7 E C6 0 . 5 C 6 1 E 0 6 0 . 2 A 8 7 E - 0 6 0 . 5 A 6 7 F 00 0 . 4 1 A n F 05 * IT = AS NO 1 0 . 2 2 1 5 F C5 0 . 7 6 C e E 03 0 . A E A 7 F C6 0 . 5 C 6 1 F C6 0 . 2 A 6 C E - 0 6 0 . 5 A 6 1 E 00 0 . 4 7 3 0 F 0 5 « 1T = AS NG 1 C . 2 2 I 5 E C5 0 . 7 5 2 7 E 07 0 . A E A 7 E C6 0 . 5 0 6 1 F 06 0 . 2 A 3 A E -0 6 0 . 5 A 5 5 F 00 0 . A 3 2 C F 0 5 ft IT = AS NG 1 0 . 7 7 1 5 F C5 0 . 7 4 A S E 03 O . 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C: C c-o c C: c CJ c C c c c o c, CJ c O o o C c o o c c O o c ° o CJ o O o o c O o C; c c CJ c o C c- o C" ^ : c cv LP in ir m •c -C >c •£> sC <; J : %L' >c -o sU ^ -c •CJ •J2 sO sO *c »o •c •C •JJ o •C -c o o sC -c o sC >c *c sf JT- «f >L < sC •4J o c C c- o CJ c-o O o o o c C o c c c CJ c-o O o o O C o c CJ C J CJ: C CJ CJ c c-C_' c C J CJ o c c o a tv O c c-o o Cj- o CJ, c U. l l u u. LU LU LL' LJ LU UJ LL LL' LL- LL' LL' LU LL LU LU LU LU LL UJ LU g'. LL' LL LU LL LL' LL UJ LU LL Ui LL a ' LL' LU UJ LL- LU Jj L L LL LU LL LL' LL U-. LU LL' LL LU u' -T- cc r^ c" CC r~ CC NC O rv -3 (Vj rv cr rv r~ Lf. (VJ co rv 6 CV o rv tr cr ro o O f a" o CO rv P- ro -r o p' CC Lf' Pi if a < C '7* o ro rv sr (•'• cv J.' •C CT If. <r LO r~ CVJ r~ sr rv o o O rv sf -C cc r~ L(i cr ro r- >C-—i •c rv p- P": tr u- r- sr CJ P- Sf •X If (V 0 s; P. r- c_ r- ii V sr o (*: C CC sT pj tr CP r~ *c LP-. sr p. cv o cr a-CC r- u% sr ro P' rv OJ rv (-• CJ U* ir cr 0" a — — —* 0 u r- r— O s0 If. 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P~ (T-p~ P". P - rt-. r.i -r sf -r SI vr sr S) S| - J sr sr sr <r sr sj sr sr sr V" sr sr sr sr ST sr sr NT si ST vi' sr SJ sr sr SJ Si ST sr sr >J sr sr si •«-T sr •J" •a; sr SI >- PJ. r\.- •"V o. rv rv p. r.: rv rv pj rv (Vi rv c- cv (V o; rv rv (V) r: CM r - p. rv rv r v P> rv rv rv cv rv rv rv rv rv rv rv rv rv r. rv O: P , rv rv .-v Pv O u. c* - L.' CV C C , CJ CJ C C CJ -c C CJ o a o CJ C C C LJ CJ- c c-C C_ e c-O o o C O ^ c~ O C' o C c c: C c C c_ C C sf <r ^ sr sr v. sr s) sf sr sr sr ^. sr sr si St <r sr sr sr •0 <r sr <r si sr SJ' sr ^ sr sr sr St •J sT sr r~ t; C Li c C t_' C. c c - C c-o o c CJ o c- ? o CJ C_- C o c '— CJ C c ' c-o C CJ o CV CJ ° ' o o C c. O o c U. u lu Li u u . M .• JL. LL L_ u- Ll; L_ LU u U- u. a- u. Lu a. u U-' UJ M LL: u. LL- Lu' LU Li.' LL L... LL' Li_ LU LU' LL U-. LU Lu LL Li LU LU U- LL g_ •ST si r- a C' -c CC vT u c r- CC r~ < cc rv a sr CC •C) O •C. If. CV cr r- sr sr P . ro P -' r- sT IP. if rv a-sr U" p a P' r- LO CJ' a sr a. NC rv LJ cr p. rv CJ r-—4 p 1 a* <r O' r- sr r\ CV CJ CJ 0* X a. r~ t- r- J J LP. u". sr si •r P> P • t<~ rv IV (V (VI IV If • T p P'- P <\. p . r^ i Oj c\ p. r: r- — — r-H — 1 — 1 — — J — *-- •— —i - ' — —' .-i — —• — — — — — — — —• —' C C' o <~ ~ c c c c r C-C J CI- V c C r c c* c - c c cr c c c c c C" r- C C" C" e C c C c O o c o c- C ' L' LT u. Ll u u ir. LP u- u- •j L, ir ii • IP u Lf J- u- Li" Ll'. u - LC u- u . O: u . ll' b-L- u w u u • u% IT Lf b-. if a-u if Lf U ' c_ C J CJ CJ - LJ L , c c S J c c-L. C- 1 - c- L, c. c L_ C" c C c- L, C ' 1- c u c L_ c-o c- c t_ o c L_-LL Uj a. LL LL u". u J - L_ L. u. Li LL a. u . u. u L_ _^ LL- LL a. u. LL _^ L (J. LU LL L_, L. . Lu L- L^  LL Lu LL' u. u_ LL r-r~ -c • L •r T t c { - L r c. r - f - '-' T.: f- - c c. C ' c. c C C L C " " c C c CJ l_ C c C J o C. o o c t. o C' c-c o c C c C c: C c CJ Cv c o C - CJ o CJ C J c L - C c c c C' o CJ C c - 224 c- c c o CJ c i f <r c <v — o O O *-" <"*, f >T LP U" U"' 'U"'. U • U LU LU L . . L L P - Cj fO <• CT f . r- ^. if *j p'. c f r - . IP LP LTI LP c c ; O O I I I I I LL L . U. Li.- LL- LU NJ' — f~ O -< 7 C r\j co f- r - p- p-i\ rj (\ r., r\, i\ CJ o c j p.- f*.; pj c\, c; c L ; p_ c o C J L J O O C J LL U.' LL' LL1 IX' -r 'J ' <r rP P* ("*• rr. <*". "J ^ -J *J «» rv r\, r\. r^ ' <\i ( V O CJ C ' C J C -• c. j cr. -j- p P . o «j c C c_ o C C L_' t. C- o - 225 -APPENDIX 2 A. Gas Film Control at Onset of Reaction On the assumption that the rate of oxidation i s controlled only by d i f f u s i o n of SO2 and through a laminar gas f i l m at the onset of reaction, the following conditions can be stated: (1) the magnetite layer has zero thickness; and (2) chemical reaction i s very fas t . This implies that equilibrium exists at the reaction front. Because there i s no magnetite layer, the sample surface and reaction front are coincident at zero time so that equations (1-1), (1-2), and (1-18) i n Appendix 1A can be written as shown i n equations (2-1), (2-2), and (2-3). n s o g S 0 ( P e n g " P e n s.) (2-1) A RT S 0 „ & , SO- . 2 b 2 x k 2 ( 4 ) P_ s = K (5+3u } ( P Q O s ) 5 + 3 ) J (2-3) S 2 . e S 0 2 . By applying the stoichiometric relations of equation (1-6), by equating P g to zero, and by substituting for P„ s and P s , b 2 b b2 i b U 2 i equation (2-4) results. The theoretical fluxes of Table 28(a) are solutions to this equation. - 226 -5+3y nFeS _ S2 v (5+3y ) nFeS RT N (5+3y ) ~6 A" " ~ K T K e C SO * " 2 / 3 ~ T ~ k } 2 b g s o 2 (2-4) B. Polynomial Curve F i t t i n g The experimental fluxes shown i n Table 28(a) are slopes (at a time of 1 sec) of the s i x t h degree polynomials which were computed as best f i t s for corresponding weight loss curves. Equation (2-5) W = P + P,t + P„t2 + P_t 3 + P,t 4 + P c t 5 + P.t o 1 2 3 4 5 6 (2-5) represents a general polynomial, where W i s the instantaneous weight i n g and where the values of the various coefficients are given i n Table 2-1 together with the t r i a l numbers for each set of coefficients Table 2-1. Polynomial Coefficients for Fitted Curves. Run no. 43-1 58-2 65-2 74-1 27-1 39-2 po 6. 626xl05 6.455xl0 5 5.777xl0 5 5.577xl0 5 6. 259xl0 5 5.560xl0 5 P l -3. 461x10 -2.965x10 -1.665x10 -1.036x10 -1. 509x10 -7.580x10 P2 1. 732xl0"2 1.248xl0 - 2 2.127xl0" 3 3.016xl0" 3 2. 096xl0~ 3 1.176xl0 - 3 P3 -5. 568xl0~6 -4.928xl0~ 6 -3.650xl0~ 9 -1.049xl0~ 6 -1. 751xl0~ 7 -8.561xl0~ 8 V 9. 217xl0_1° 1.153xl0~ 9 -4.022xl0 - 4 1.993xl0~ 1 0 5. -12 739x10 2.191xl0" 1 2 P5 -7. -14 439x10 -1.351xl0"1 4 5.205x10"15 -1.846xl0" 1 4 -1. 846xl0~ 1 4 -1.846xl0 - 1 4 2. 322xl0" 1 8 1 8 6.121x10 -1.949xl0~1 9 6.633xl0 - 1 9 6. -19 633x10 6.633xl0"1 9 - 228 -APPENDIX 3 A. Counterdiffusion through a Porous Magnetite Layer Assuming the Effect of Net Bulk Flow to be Negligible. (Curve no. 4 i n Figures 51(a) to (1)). Assuming this set of conditions, the mole centre v e l o c i t y terms of equations (1-13) and (1-14) (which define the f l u x of SC^ and through the porous layer) can be eliminated. Rearranging the resulting expressions yields equations (3-1) and (3-2). Since chemical i s f a s t , • ."so 2 i 2 b eff "so P_ s = P g + (^ ±5E) — - 1 ^— (x -x ) (3-2) S 2 . S 2 b 4 A D e f f o m equation (1-18) describing equilibriumat the interface applies; P_ g b2 b can be assumed zero; while sample geometry provides equation (3-3). By substitution for n and P s (from equation (1-18)) and by 2 2 I n S 0 2 = 2 / 3 n F e S = 2 / 3 p F e S A f (3-3) addition, equation (3-4) i s obtained which can be solved by approximating ,5+3iu ,5+3u. [ C ^ ) P _ . ' F-<*.-«J] * * + [2/3 K 1 / 2 P R T -6 FeS D - £ v o : m J vdt L e FeS D • eff eff / M dx o m dt (3-4) - 229 -dx by a f i n i t e difference r a t i o . The method of solution contains a dx loop which tests successive solutions of (x0~xm)'^£' ^ o r converging values of time u n t i l the difference between solutions i s less than 0.01 percent. These f i n a l values of f i n i t e time difference were also u t i l i z e d for solution of the non-linear equations representing the other three conditions of mass transport. B. Counterdiffusion with Net Bulk Flow through a Porous Layer (Curve no. 2 i n Figures 51(a) to (1)). The assumptions inferred by these conditions are s i m i l a r to those of Appendix 3A with the exception that the mole centre v e l o c i t y terms i n equations (1-13) and (1-14) are included. The equations to be solved then are these two and equation (1-18) which describes gaseous equilibrium at the reaction front. Because the method of solution of simultaneous non-linear systems involves i t e r a t i o n about i n i t i a l guesses (subroutine package NONLIN), the r e l a t i v e nature of curves represented by these equations effects the maximum deviation of initial-guesses from time solutions for which solutions can be obtained. To increase the range of deviation over which i n i t i a l guesses could be successful, the number of equations i n a system was reduced to a minimum by substitution. For the conditions of analysis for this section, the system was reduced to two equations. These were obtained by substitution of n (from equation (3-3)) and of 7 s (from equation (1-18) into equations b U 2 i (1-13) and (1-14). - 230 -C. Counterdiffusion through a Gas Film and a Magnetite Layer Assuming  the Effect of Net Bulk Flow to be Negligible (Curve no. 3 i n Figures 5l(a) to (1)). Under these conditions of analysis, equations (1-1) and (1-4), which define mass transfer through a laminar gas f i l m , are combined with equations (3-5) and (3-6), the l a t t e r two describing transport of SC>2 and through a magnetite layer while neglecting mole centre v e l o c i t y terms. Also to be included i n this system i s equation (1-18) since chemical reaction i s ggain assumed to be fas t . By n S 0 9 D _ PS0„ g. PS0_ S. 2 B ( L i ( 3 _ 5 ) A RT x -x ' K ' o m *S0 D PS S " PS S ,5+3u, b U 2 _ De£f , b 2 i b2 1 (___) _ _ ( _ _ ) ( 3 _ 6 ) o m substitution of n (from equation (3-3)) into equation (1-4) and dx subsequently for - 7 — ; for P - g (from equation (1-1)) and for P s Clt D U - . t>u« 2 1 2 x (from equation (1-18)) into equations (3-5) and (3-6), two equations i n unknowns P g and P s result for which solutions can be obtained. b2 i b2 i - 231 -BIBLIOGRAPHY 1. Hazelton, J.E., "The Economics of the Sulphur Industry", . John Hopkins Press, London, 1970. 2. 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