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A vapour-pressure study of the [gamma] phase in copper-manganese alloys. Peters, Bruno Frank 1958

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A VAPOUR-PRESSURE STUDY OP THE ^ PHASE IN C0PPER-MANGANESE ALLOYS by BRUNO PRANK PETERS A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of Mining and Metallurgy at the University of B r i t i s h Columbia We accept t h i s thesis as conforming to the standard required from candidates f o r the degree of -"Master of Applied Science 8 i n M e t a l l u r g i c a l Engineering Members of the Department of Mining and Metallurgy THE UNIVERSITY OF BRITISH COLUMBIA JANUARY, 1958 ABSTRACT The thermodynamic p r o p e r t i e s of the copper-manganese system were determined by the measurement of the vapour pressure of manganese tagged w i t h Mrr^ y. u s i n g the Knudsen e f f u s i o n method. Manganese shows a p o s i t i v e d e v i a t i o n from Raoult's law over the e n t i r e composition range. Copper, alt h o u g h showing a st r o n g p o s i t i v e departure from Raoult's law at low copper content, shows a s l i g h t n e g a t i v e departure i n c o p p e r - r i c h compositions. The n e g a t i v e departure, which can be a s s o c i a t e d w i t h an a f f i n i t y of copper f o r manganese,, i s g r e a t e s t at compositions of about 35$ mangan-ese. The behaviour" of both copper and manganese Is much more i d e a l a t lower manganese compositions. The i d e a l behaviour of the manganese i n the a l l o y s of low manganese content and the a f f i n i t y of copper f o r manganese a t about 35$ manganese appear to co r r o b o r a t e Myers I n t e r p r e t a t i o n of the e l e c t r o n i c con-f i g u r a t i o n s of copper and manganese i n t h i s system. I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l m a k e i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s m a y b e g r a n t e d b y t h e H e a d o f m y D e p a r t m e n t o r b y h i s r e p r e s e n t a t i v e . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t b e a l l o w e d w i t h o u t m y w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f MINING AND METALLURGY T h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n c o u v e r 8, C a n a d a . D a t e JANUARY 1958. 11 TABLE .OF CONTENTS Page I . INTRODUCTION . . . . . . . . . . . . . . . . . 1 Object of the I n v e s t i g a t i o n . . . . . . . 1 The Measurement of Vapour Pressures . . . i|. I I . EXPERIMENTAL . . . . . . . . . . . . . . . . . 8 Design of Apparatus . . . . . . . . . . . . 8 M a t e r i a l s and T h e i r P r e p a r a t i o n If? R a d i o a c t i v i t y Measurements . . . . . . . 20 I I I . DISCUSSION OF RESULTS . . . . . . . . . . . 23 R e p r o d u c i b i l i t y of R e s u l t s U s i n g Pure Manganese . . . . . . . . . . . . . . . . 23 A l l o y s of Copper and Manganese 30 IV. APPENDIXES . . . . . . . . . . . . . . . . . . kk-A. Thermodynamics . . . . . . . . . . . . I4.4 B. D e r i v a t i o n of the Kriudsen Formula . . f?0 C. Sample c a l c u l a t i o n of Vapour P r e s s u r e . f?4 D. Vapour Pressure and Thermodynamic Data f?6 E. C a l c u l a t i o n Using Wagner's E q u a t i o n . . 62 V. BIBLIOGRAPHY . . . . . . . . . . . . . . . . 6$ LIST -.Off ILLUSTRATIONS i i i F i g u r e No. Page 1. The Copper-Manganese Phase Diagram . . . . . k 2. Diagram of Furnace and C e l l Arrangement . . 9 3- Furnace Assembly . . . . . . . . . . . . . . 11 k. Complete Knudsen C e l l Assembly . . . . . . . 11 f?. D i s c Changer i n Two P o s i t i o n s . . . . . . . Ik 6. General View of Apparatus 16 7. Schematic Diagram of M e l t i n g Apparatus . . . 18 8. Graph R e l a t i n g Weight of Manganese and A c t i v i t y of D i s c 21 9. Graph R e l a t i n g A c t i v i t y of Disc and Length of Time of E f f u s i o n at 8l8QC 2k 10. C o l l e c t i o n D i s c Showing R a d i o a c t i v e Manganese Spot of I n a c t i v e Manganese Base 2£ 11. Graph R e l a t i n g Log Vapour Pressure of Pure Manganese and R e c i p r o c a l Temperature . . . 28 12. Graph R e l a t i n g Log Vapour Pressure of Manganese over Copper-Manganese A l l o y s , and R e c i p r o c a l Temperature . . . 31 13. The A c t i v i t i e s of Copper and Manganese i n Cu-Mn A l l o y s at 820°C . . . . . . . . . . 33 l i | . . The A c t i v i t i e s of Copper and Manganese i n Cu-Mn A l l o y s at 8kfj.°C . . . . . . . . . . 3k l 5 - The Free Energy of Mixing of Cu-Mn A l l o y s at 820°C . . . . . . . . . . . . . . . . . 36 16. The Free Energy of Mixing of Cu-Mn A l l o y s 17. The Excess F r e e Energy Change f o r Copper and Manganese i n Cu-Mn A l l o y s at 820°C . . 38 18. E n t h a l p y of Mixing of Copper-Manganese A l l o y s k l 19. Geometry of Target and O r i f i c e . „ 5 l LIST OF TABLES,. Table No. Page I. C.olllmating Geometry of C e l l s 13 I I . Table of Vapour Pressure Data f o r Pure Manganese 26 V ACKNOWLEDGMENT The author Is g r a t e f u l to the N a t i o n a l Research C o u n c i l and Defense Research Board of Canada f o r f i n a n c i a l a i d i n the form of a Research A s s i s t a n t s h i p granted d u r i n g the p a s t year. The funds f o r the m a t e r i a l s and apparatus were provided by the N a t i o n a l Research C o u n c i l . S p e c i a l thanks are extended to Dr. D..R. W i l e s , the d i r e c t o r of t h i s r e s e a r c h , and to Mr. R.G. B u t t e r s and Mr. R. R i c h t e r f o r t h e i r t e c h n i c a l a d v i c e and a s s i s -tance i n c o n s t r u c t i n g the apparatus. The many h e l p f u l suggestions of Dr. C.S. Samis are g r a t e f u l l y acknowledged. I . I n t r o d u c t i o n Object of the I n v e s t i g a t i o n The paramagnetic p r o p e r t i e s of copper manganese a l l o y s were studied r e c e n t l y by Myers. 1 He i n v e s t i g a t e d the a l l o y s In the gamma phase and i n t e r p r e t e d h i s r e s u l t s i n terms of the e l e c t r o n i c c o n f i g u r a t i o n s of the a l l o y i n g c o n s t i t u e n t s . The most s t r i k i n g f e a t u r e of the a l l o y system was the change of i t s magnetic p r o p e r t i e s o c c u r r i n g at manganese c o n c e n t r a t i o n s around 2$%. Below t h i s concen-t r a t i o n the i n t e r p r e t a t i o n was g i v e n that the manganese atoms maintained a c o n c e n t r a t i o n of l{.s e l e c t r o n s s i m i l a r to that f o r pure copper. Both copper and manganese could be considered monovalent i n t h i s r e g i o n . However, f o r a l l o y s c o n t a i n i n g more than 2$% manganese,, i t became c l e a r that a d i f f e r e n t e l e c t r o n i c c o n f i g u r a t i o n must e x i s t . Myers suggested that the 3d e l e c t r o n s f o r copper and manganese form a common 3d band. Thus the change In p r o p e r t i e s which occurs at about 2$% manganese content may be a s s o c i a t e d w i t h the t r a n s i t i o n from l o c a l i z e d s t a t e s f o r the 3d e l e c t r o n s of manganese atoms to c o l l e c t i v e e l e c t r o n treatment of these e l e c t r o n s f o r the atoms of the a l l o y . The e l e c t r o n i c changes suggested by Myers should be r e f l e c t e d i n the thermodynamic p r o p e r t i e s of the a l l o y system,, and a study of these p r o p e r t i e s would f u r n i s h i n f o r m a t i o n which could be c o r r e l a t e d w i t h the r e s u l t s obtained by Myers. These thermodynamic p r o p e r t i e s can r e a d i l y be c a l c u l a t e d from an a c c u r a t e knowledge of the change wi t h temperature of the thermodynamic a c t i v i t i e s of the components. (An o u t l i n e of the thermodynamic Equations needed f o r such c a l c u l a t i o n s i s g i v e n i n Appen-d i x A.) The most d i r e c t method of determining the a c t i v i t y of a c o n s t i t u e n t i n an a l l o y i s measurement of the 2 vapour p r e s s u r e of that c o n s t i t u e n t . A c c o r d i n g to Lumsden 3 and Wagner,^" the a c t i v i t y of a component i s defined by these measurements a c c o r d i n g to E q u a t i o n 1, i f the vapour of the component can be con-s i d e r e d a p e r f e c t gas C u = PA ( i ) A D ° ^ A where i s the vapour p r e s s u r e of component A. i n the a l l o y and P A i s the vapour p r e s s u r e of pure component A a t the same temperature. The o b j e c t of the p r e s e n t i n v e s t i g a t i o n , then, was to determine the thermodynamic p r o p e r t i e s of copper and manganese by measuring vapour p r e s s u r e s a t temperatures between 800°C and B$0°C. The phase diagram ( F i g u r e l ) shows t h a t the f a c e - c e n t r e d c u b i c $ phase i s s t a b l e over most of the composition range a t these temperatures. I t was decided to measure the vapour p r e s s u r e of manganese r a t h e r than copper because the vapour p r e s s u r e of manganese F i g u r e !• The Copper-Manganese Phase; Diagram, from Metals Handbook ( 1 9 4 8 ) i s g r e a t e r by a f a c t o r of 10 . The Measurement of Vapour Pressures In 1882, Herz p u b l i s h e d h i s c l a s s i c paper "On the Ev a p o r a t i o n of L i q u i d s , E s p e c i a l l y Mercury, In Vacuo". He a r r i v e d at the f o l l o w i n g fundamental c o n c l u s i o n : there e x i s t s f o r every substance a maximum r a t e of eva p o r a t i o n which depends o n l y on the temperature of the surface and the s p e c i f i c p r o p e r t i e s of the substance. to determine r a t e s of e v a p o r a t i o n and vapour p r e s s u r e s . A survey was made of these methods i n order to choose the one most s u i t a b l e f o r making determinations i n the copper-manganese system. Only the Knudsen and Langmuir methods could be considered because the method chosen -7 had to be capable of measuring p r e s s u r e s as low as 10 atmospheres. pressure of a m a t e r i a l was p r o p o r t i o n a l to the amount of vapour e f f u s i n g i n t o vacuum from a r e l a t i v e l y s m a l l h o l e i n a clos e d v e s s e l . H is formula i s giv e n by Equat i o n 2, below Numerous methods 6>7 have been devised i n order 8 In 1909, Knudsen showed that the vapour P (2) where P i s the vapour pressure i n dynes per cm , nr i s the weight i n grams of m a t e r i a l of m o l e c u l a r weight, M, which e f f u s e s per second from each cm of o r i f i c e a r e a. E q u i l i b r i u m must e x i s t between the s o l i d and vapour w i t h i n the c e l l . A l s o , the r a t i o of the mean f r e e path of the gas molecules to the diameter of the o r i f i c e must be l a r g e ( g r e a t e r than 1 0 ) ^ . The d e r i v a t i o n of E q u a t i o n 2 from the K i n e t i c Theory of Gases i s g i v e n i n Appendix B. 1 0 Langmuir , In 1 9 1 3 , determined the vapour p r e s -sure of tungsten by weighing a tungsten f i l a m e n t of known dimensions before and a f t e r h e a t i n g I t i n vacuum f o r mea-sured l e n g t h s of time. Langmuir*s e q u a t i o n i s g i v e n below p = m» /2TTRT ( 3 ) « ~i M where i s the weight i n grams of substance of m o l e c u l a r weight, M > which evaporates from one cm 2 of s u r f a c e per second and (X i s the condensation c o e f f i c i e n t . The conden-s a t i o n c o e f f i c i e n t i s d e f i n e d as the r a t i o of the observed r a t e of e v a p o r a t i o n i n t o vacuum to the maximum r a t e des-c r i b e d by Herz. The c o e f f i c i e n t has d i r e c t k i n e t i c s i g n i f i c a n c e s i n c e i t shows t h a t of a l l the vapour mole-c u l e s which s t r i k e the s u r f a c e of the condensate, only a f r a c t i o n , CX > a c t u a l l y condense. The r a t e of e v a p o r a t i o n i s t h e r e f o r e l e s s than the vapour p r e s s u r e f o r substances which have condensation c o e f f i c i e n t s l e s s than one. The most s e n s i t i v e method of deter m i n i n g the condensation c o e f f i c i e n t c o n s i s t s of comparing the r a t e 6 at which saturated metal vapour e f f u s e s through an o r i f i c e w i t h the r a t e at which the metal s u r f a c e evaporates i n t o 9 vacuum, as shown by Equ a t i o n i^.. used by many i n v e s t i g a t o r s f o r s t u d i e s on both l i q u i d s g and s o l i d s . A c c o r d i n g t o S p e i s e r and Johnson, the Lang-muir method can be used to measure vapour pressures that are a factor- of 1 0 ^ to 1(A lower than those measurable by the Knudsen method. However, both Hersh"''^, i n h i s 1 2 study of copper, and McKinley and Vance , i n t h e i r study of z i n c , s t a t e d t h at they chose the Knudsen method i n pre f e r e n c e to the Langmuir method because i n t h i s way they could e l i m i n a t e the c o n s i d e r a t i o n of the condensation c o e f f i c i e n t . condensation c o e f f i c i e n t of manganese, and, should t h i s value be known, one would have to make the very tenuous assumption that i t did not change wi t h the a d d i t i o n of a second component-,, i f one considered u s i n g the Langmuir method to study the copper-manganese system. F o r t h i s reason, then,- the Knudsen e f f u s i o n method was chosen i n p r e f e r e n c e to the Langmuir method. vn' / 2 . T F R T V M Both the Langmuir and Knudsen methods have been No mention i s made i n the l i t e r a t u r e of the The r a t e of e f f u s i o n can be measured by one of s e v e r a l methods, some based on measuring the r a t e d i r e c t l y , - and others based on measuring the t o t a l amount of m a t e r i a l which has e f f u s e d d u r i n g a g i v e n p e r i o d of time. The s i m p l e r of these methods i n c l u d e I i i weighing the e f f u s i o n c e l l b efore and a f t e r a run , and, c o l l e c t i n g the e f f u s e d vapour on a cooled t a r g e t . 15" The vapour on the t a r g e t can be weighed or measured 16 r a d i o c h e m i c a l l y . The l a t t e r technique i s i d e a l f o r measuring the vapour pr e s s u r e of o n l y one c o n s t i t u e n t i n an a l l o y system and was chosen f o r t h i s i n v e s t i -g a t i o n . A Knudsen e f f u s i o n apparatus was designed and b u i l t such t h a t the amount of r a d i o a c t i v e manganese which e f f u s e d from the c e l l was c o l l e c t e d on a cooled c o l l e c t o r d i s c . The r a d i o a c t i v i t y of the d i s c was measured wi t h a p r o p o r t i o n a l counter. 8 I I . E x p e rimental Design of Apparatus Knudsen e f f u s i o n c e l l s , 1.12$ inches h i g h and 1 . 0 0 i n c h e s . i n diameter were machined from molybdenum i rod. T h i s m a t e r i a l was chosen because I t has a low 17 vapour pressure ' and because no r e a c t i o n was observed between i t and molten manganese by a p r e v i o u s i n v e s t i -ng g a t o r . Two h o l e s were d r i l l e d i n t o the bottom of the c e l l to house the measuring thermocouples as shown i n F i g u r e 2 . Three rods were screwed i n t o the top of the c e l l making a stand f o r the c o l l i m a t o r p l a t e . The Knudsen formula assumes an o r i f i c e p l a t e of n e g l i g i b l e t h i c k n e s s , as d i s c u s s e d i n Appendix B. O r i f i c e s were f i r s t prepared by dimpling . 0 0 3 i n c h molybdenum sheet and then p o l i s h i n g the convex e x t r u s i o n u n t i l a knife-edged h o l e was produced. T h i s method was dis c a r d e d because the h o l e s produced were not c o n s i s -t e n t l y round, and t h e r e f o r e were not r e p r o d u c i b l e . The o r i f i c e was f i n a l l y made by clamping the molybdenum sheet between two aluminum p l a t e s and d r i l l i n g . A k n i f e edged o r i f i c e was not produced i n t h i s way but the e r r o r was r e p r o d u c i b l e and of l i t t l e consequence. The o r i f i c e p l a t e s r e s t e d on the top of the c e l l i n a shallow 9 K a n t h a i s t r i p ^ . C o l l i m a t o r p l a t e O r i f i c e p l a t e Knudsen c e l l 0 furnace S c a l e : 2X rad i a t i o n . s h i e l d s ti ^-thermocouple #1 thermocouple #2 F i g u r e 2. Diagram of, Furnace and C e l l Arrangement 1 0 d e p r e s s i o n as shown i n F i g u r e 2 . The diameter of the o r i f i c e p l a t e was measured m i c r o s c o p i c a l l y . The c e l l was s t a t i o n e d i n the furnace on the two thermocouples. The thermocouples had been checked a g a i n s t the m e l t i n g p o i n t of f o u r - n i n e s pure aluminum and were found to be a c c u r a t e to w i t h i n + 0 . 1 ° C . A T i n s l e y potentiometer (Type 3 3 8 7 B ) was used. During a run, the two thermocouples showed a d i f f e r e n c e of 3 + 1 ° C . Since thermocouple # 1 was c l o s e to the furnace windings and f a r from any r a d i a t i n g s u r f a c e , i t read, i f a n y t h i n g , h i g h e r than the a c t u a l temperature w i t h i n the c e l l . Thermocouple # 2 , on the o t h e r hand, was near a r a d i a t i n g s u r f a c e (the bottom) and would be expected to read low because of conduction of heat away by the thermocouple i t s e l f . A temperature of one degree lower than that measured.by thermocouple # 1 was chosen as the b e s t estimate of the temperature w i t h i n the c e l l . The f u r n a c e was machined from l a v a b l o c k and wound wi t h K a n t h a l s t r i p of 2 f ? ohm r e s i s t a n c e . Lava b l o c k , a hydrated aluminum s i l i c a t e , i s e a s i l y machined before i t i s baked. A f t e r baking a t 1 2 0 0 ° C , i t i s hard,, b r i t t l e , and has a low vapour p r e s s u r e making i t i d e a l f o r f u r n a c e s i n h i g h vacuums. The furnace assembly i s shown mounted on a s t e e l p l a t f o r m i n F i g u r e 3 - I t u s u a l l y took about two hours to r a i s e the f u r n a c e temperature to 8 5 > 0 ° C . A slow i n i t i a l r a t e of i n c r e a s e F i g u r e I ) . . Complete Knudsen Assembly 12 of temperature was n e c e s s a r y to enable'the vacuum system to outgas the apparatus. The f u r n a c e temperature was c o n t r o l l e d by a chrome1-alumel thermocouple i n c o n j u n c t i o n w i t h a Minneapolis Honeywell c o n t r o l l e r . The on, 3/k-on con-t r o l l i n g c y c l e was not d e t e c t a b l e by the thermocouples w i t h i n the c e l l . Heat l o s s e s by r a d i a t i o n from the f u r n a c e were kept to a minimum by u s i n g two c o n c e n t r i c c y l i n -d r i c a l molybdenum r a d i a t i o n s h i e l d s . These s h i e l d s were trimmed near the top to a l l o w the e f f u s e d manganese to escape. Three rods, as seen In F i g u r e s 2 and 3, were screwed i n t o the top of the Knudsen c e l l , making a stand f o r the c o l l i m a t o r p l a t e . The f r a c t i o n of the e f f u s e d m a t e r i a l ^ , which was c o l l e c t e d , was computed from the geometry of t h i s arrangement. The a c t u a l dimensions of the c e l l s used are g i v e n i n Table 1. The water cooled p l a t f o r m b u i l t above the furnace to house the c o l l e c t i o n d i s c s i s shown i n F i g u r e k. The d i s c s were aluminum, 1.5 inches i n diameter and 0.125 Inches t h i c k . A d i s c changer was b u i l t i n t o the apparatus so t h a t s e v e r a l measurements could be made without Table 1. C o l l i m a t i n g Geometry of. C e l l s C e l l #1 C e l l #2. C o l l i m a t o r P l a t e Diameter O r i f i c e to C o l l i m a t o r D i s t a n c e io Vapour C o l l e c t e d 0.251 i n . 0.765 i n . 9.72$ 0.251 i n . 0.769 i n . 9.38$ having to stop the experiment. A brass rod was f i t t e d through the br a s s b a s e - p l a t e w i t h a Wilson s e a l , and connected to the d i s c h a r g e r . By r o t a t i n g the rod, one could e j e c t the c o l l e c t i n g d i s c and a f r e s h one would drop i n t o p l a c e d i r e c t l y above the c e l l and c o l l i m a t o r . The two p o s i t i o n s of the d i s c changer are shown In F i g u r e $. The Knudsen c e l l assembly was b u i l t on a 3/k i n c h b r a s s p l a t e which made a s u i t a b l e base f o r a pyrex b e l l j a r 8^ - Inches i n diameter and 15 inches h i g h . The b e l l j a r was p o s i t i o n e d on a O-ring l o c a t e d i n a groove i n the p l a t e . A 1.5 i n c h h o l e i n the centre of the p l a t e was connected, by O- r i n g , to the l i q u i d a i r t r a p which was i n s e r i e s w i t h the o i l d i f f u s i o n pump (type VMF-10) and the Duo S e a l vacuum f o r e pump. A thermocouple vacuum gauge and an i o n i z a t i o n gauge were a l s o attached to the bottom of the p l a t e . A second thermocouple gauge was f i t t e d i n t o the l i n e between the d i f f u s i o n and f o r e pumps. Pressures of 2 x 10"^ mm Hg were r e a d i l y obtained, and, d u r i n g experimental runs, p r e s s u r e s as low as -6 2 x 10 mm Hg were o f t e n a t t a i n e d without u s i n g l i q u i d a i r . The furnace bus bars and the f o u r thermo-couples entered the system by g l a s s - t o - m e t a l s e a l s . These s e a l s were so l d e r e d to a 3/l6 Inch brass p l a t e which was sealed to the main brass p l a t e by an 0 - r i n g . A g e n e r a l view of the complete apparatus i s shown i n F i g u r e 6. M a t e r i a l s and T h e i r P r e p a r a t i o n The copper a v a i l a b l e f o r t h i s work was F i s h e r Reagent Metal of 99.7$ p u r i t y . The major m e t a l l i c i m p u r i t i e s g i v e n by the F i s h e r a n a l y s i s are antimony and t i n (.01$ t o t a l ) , lead (.002^$),- and i r o n (.002$). The n o n - r a d i o a c t i v e manganese was 99-9$ pure,, e l e c t r o l y t i c manganese donated by the E l e c t r o -manganese C o r p o r a t i o n of America. T h i s metal was i n the form of e l e c t r o l y t i c c h i p s . $k One m i l l i c u r i e of c a r r i e r f r e e Mn ^ as MnC^ i n 5 > ml of HC1 (pHf?) was obtained from the Nuclear 16 F i g u r e 6. General View of Apparatus Science and E n g i n e e r i n g C o r p o r a t i o n . Mn has a h a l f l i f e of 300 days and decays by K capture and ,8k Mev. gamma r a d i a t i o n . The long h a l f l i f e makes t h i s r a d i o -i s o t o p e of manganese i d e a l f o r a long-term r e s e a r c h p r o j e c t as opposed to the r a d i o i s o t o p e of copper, Cu^", which has a h a l f l i f e of on l y 12.8 hours. The p r e p a r a t i o n of tagged manganese f o r experimental purposes was attempted i n three ways: by e l e c t r o d e p o s i t i o n , by i s o t o p i c exchange and by ev a p o r a t i o n . Only the l a s t method was r e a l l y s u c c e s s f u l . T h i s i n v o l v e d simply e v a p o r a t i n g the Mn H s o l u t i o n on the s u r f a c e of the pure i n a c t i v e manganese c h i p s . The prepared c h i p s were broken i n t o a Norton RA81j. type c r u c i b l e , which was, i n t u r n , placed i n s i d e the l|r i n c h diameter v y c o r tube i n d u c t i o n furnace arrange-ment. T h i s apparatus i s shown s c h e m a t i c a l l y i n F i g u r e 7 . M e l t i n g took p l a c e In a purified-^argon atmosphere. The manganese was v i g o r o u s l y mixed f o r a h a l f minute by the i n d u c t i o n c u r r e n t s . I t can, of course, be assumed that no s e g r e g a t i o n of the r a d i o a c t i v e manganese i n the i n a c t i v e manganese took p l a c e d u r i n g s o l i d i f i c a t i o n . About 12 grams of manganese c o n t a i n i n g 0.3 $k m i l l i c u r i e Mn were prepared f o r experimental use. I f more i n a c t i v e manganese had been used, the s p e c i f i c a c t i v i t y of the r e s u l t i n g tagged manganese would have been too low^ and e f f u s i o n runs t a k i n g l o n g e r times would have been necessa r y . Since t h i s manganese was subsequently used to make a l l o y s , a t l e a s t 12 grams was necessary. Because, d u r i n g m e l t i n g , a l a r g e amount of the manganese was l o s t to the c r u c i b l e , i t was at f i r s t thought t h a t the manganese could a l s o d i s s o l v e l a r g e amounts of Si02 from the c r u c i b l e . Chemical a n a l y s i s on n o n - a c t i v e melts showed t h a t o n l y 0.$% S i l i c a was found i n manganese t h a t had remained molten p u r i f i e d argon 18 vacuum pump manometer alundum c r u c i b l e aluminum m i r r o r . v y c o r tube i n d u c t i o n c o i l F i g u r e 7. :Schematic Diagram of M e l t i n g Apparatus f o r a p e r i o d of s e v e r a l minutes. Much l e s s SiO^ would be expected i n the a c t u a l melt c o n t a i n i n g M n ^ which was h e l d molten f o r on l y a h a l f minute. Since o n l y twelve grams of tagged manganese was prepared, i t was necessary to make a l l o y s of not much more than two grams. Should the RA81| c r u c i b l e s be used, a l l the manganese would be absorbed by the c r u c i b l e . The a l l o y s , were t h e r e f o r e made i n f o l d e d molybdenum-sheet c r u c i b l e s . M i c r o s c o p i c examination of the I n a c t i v e a l l o y s showed that the a l l o y s prepared In these molybdenum c r u c i b l e s were homogenous. P o s s i b l e Inhomogeneiti'es i n the experimental a l l o y s would disappear due to d i f f u s i o n d u r i n g the 2l|-hour p e r i o d g i v e n f o r the Knudsen c e l l to reach e q u i l i b r i u m a t temperature. The ex p e r i m e n t a l temperatures were o n l y a few degrees below the m e l t i n g p o i n t at 35$ Mn composition. As a t e s t f o r the continued homogeneity of a l l o y samples, a n o n - r a d i o a c t i v e $0-$0 a l l o y was allowed to evaporate i n the Knudsen c e l l u n t i l 10$ of the manganese was l o s t by e f f u s i o n . The remaining a l l o y was shown to be homogeneous by m i c r o s c o p i c examination. The compositions of the a l l o y s were checked by standard e l e c t r o l y t i c a n a l y s i s f o r copper. The v a l u e s obtained agreed with the compositions c a l c u l a t e d from the weights of the m a t e r i a l s used. R a d i o a c t i v i t y Measurements A p r o p o r t i o n a l counter was used f o r a l l r a d i o a c t i v i t y measurements. A 2200 v o l t p o t e n t i a l was found to be i n the middle of the (counts per minute vs v o l t s ) p l a t e a u . The s e n s i t i v i t y c o n t r o l was set to count a l l p u l s e s g r e a t e r than one m i l l i v o l t . Back-ground was c o n s i s t e n t at 13 + 1 counts p e r minute,-and a standard (Tl^^+) was measured before and a f t e r each s e r i e s of measurements. Si n c e the exact e f f i c i e n c y of the p r o p o r t i o n a l counter f o r measuring the r a d i a t i o n s emitted by M n ^ i s not known, no c o r r e l a t i o n e x i s t e d between the r a d i o -a c t i v e count measured by the counter and the amount of manganese i n the sample. T h i s r e l a t i o n was determined as f o l l o w s : A c a r e f u l l y weighed sample of the tagged manganese was d i s s o l v e d i n a l i t t l e HC1 and the s o l u t i o n was d i l u t e d to a l a r g e volume wi t h warm d i s t i l l e d water. Small p i p e t t e d volumes of t h i s s o l u t i o n were evaporated on the s u r f a c e s of aluminum d i s c s , i d e n t i c a l to the one shown i n F i g u r e 10. The s o l u t i o n was evaporated i n l i t t l e drops, so that when d r i e d , the aluminum had many smal l spots on i t , a l l w i t h i n an area the same s i z e as t h a t produced by the c o l l l m a t e d beam from the Knudsen 21 600-0 .1 .2 Weight Manganese ( i n grams) F i g u r e 8. Graph, R e l a t i n g Weight, of Manganese,; and A c t i v i t y of,  of D i s c . ( J u l y 26, 1957) c e l l . The r a d l p a c t l y l t e s of these d i s c s were measured by the counter and the r e s u l t i n g number of counts was r e l a t e d to the weight of manganese as i n F i g u r e 8 . T h i s f i g u r e was subsequently used f o r a l l experimental mea-surements, to c o r r e l a t e the a c t i v i t i e s of the d i s c s and the weight of vapour c o l l e c t e d by the d i s c . E r r o r s due to the s t a t i s t i c a l nature of r a d i o -a c t i v i t y measurements are s m a l l . I f , f o r example,* a sample measures 1^,000 counts i n 30 minutes,, there i s a 50-f?0 chance t h a t the t r u e mean count i s 1^,000 + ^ 15,000 i n 30 minutes or £00 +k counts per minute. C o n s i d e r i n g a background of 13 + 1 , the a c t u a l count of the specimen i s i|87 +•• if. The e r r o r due to s t a t i s t i c a l C o n s i d e r a t i o n s i s j v l $ . T h i s e r r o r would decrease i f more than one d i s c were used to c o l l e c t vapour dur i n g a run, such t h a t an average of s e v e r a l d i s c s could be used. 23 I I I . D i s c u s s i o n of R e s u l t s R e p r o d u c i b i l i t y of R e s u l t s u s i n g Pure Manganese The aluminum d i s c s were i n i t i a l l y prepared f o r e x perimental use by .simply p o l i s h i n g w i t h #2 metal-l o g r a p h i c paper. These discs,, however,, d i d not g i v e r e p r o d u c i b l e c o l l e c t i o n of manganese, vapour. I t was observed t h a t the amount of manganese c o l l e c t e d per u n i t time was not l i n e a r with time, t h a t Is,, the manganese C o l l e c t e d i n the f i r s t q u a r t e r hour was only about h a l f that c o l l e c t e d In the second q u a r t e r hour. D i s c s made from copper, s i l v e r , and molybdenum gave no b e t t e r r e s u l t s . Prom these r e s u l t s I t appeared that the accommodation c o e f f i c i e n t of manganese f o r manganese, vapour was g r e a t e r than t h a t of the othe r metals f o r manganese vapour. Since even the s m a l l e s t c o l l e c t i o n of man-ganese was a t l e a s t a hundred atoms t h i c k , manganese vapour was c o l l e c t i n g on a manganese s u r f a c e f o r most of each r u n . The d i s c s were t h e r e f o r e prepared by co a t i n g w i t h d i s t i l l e d i n a c t i v e manganese b e f o r e each experimental run. F i g u r e 9 shows that the r a t e of c o l l e c t i o n of manganese by these prepared d i s c s i s not dependent on the amount of manganese a l r e a d y C o l l e c t e d . The c o l l i m a t e d spots of e f f u s e d manganese were sharp 2k 500 lj.00 Cqunts per Minute 300 200 100 0 1 2 3 Time (hours) F i g u r e 9., Graph R e l a t i n g ' A c t i v i t y of D i s c and Length of Time of E f f u s i o n a t 8l86(5~ "— 2 5 F i g u r e 10. C o l l e c t i o n D i s c S h o w i n g R a d i o -a c t i v e M a n g a n e s e S p o t o n  I n a c t i v e M a n g a n e s e B a s e " * a n d c l e a r a n d o f t e n s h o w e d i n t e r f e r e n c e p a t t e r n s . A c o l l e c t i o n d i s c i s s h o w n i n F i g u r e 10. I f F i g u r e 9 s h o w s t h a t t h e r a t e o f c o l l e c t i o n o f m a n g a n e s e i s c o n s t a n t , i t a l s o s h o w s t h a t t h e r e i s n e g l i g i b l e s e l f - a b s o r b t l o n o f r a d i a t i o n b y t h e t h i c k e r s a m p l e s . No a p p r e c i a b l e a b s o r b t l o n o f $ r a y s a n d X r a y s w o u l d b e e x p e c t e d b y a l a y e r o f o n l y a f e w h u n d r e d a t o m s o f m a n g a n e s e . 26 One of the b a s i c requirements of t h i s e q u i -l i b r i u m type measurement i s t h a t the s i z e of the o r i f i c e s h a l l have no e f f e c t on the e q u i l i b r i u m w i t h i n the c e l l . The s i z e s of the o r i f i c e s used i n the experimental runs are t a b u l a t e d i n Table I I . The l a r g e s t o r i f i c e area used was twelve times the s i z e of the s m a l l e s t . Any e f f e c t due to the o r i f i c e s i z e i s n e g l i g i b l e compared to the +••$% e r r o r expected from t h i s type of me a sure-9 ment. Table I I . Table of Vapour Pressure Data f o r Pure Manganese Temp (°C) O r i f i c e Area (cm 2) Vapour Pressure (at) Log Vapour Pressure 818 .0668 3.15 x i o " 7 - 6.k6 818 .0092 2.90 x 10~'7 - 6 .k9 820 . 00k8 2.86 x 10~7 - 6.52 828 .Olkk k.k^ x 10" 7 - 6 . 3 1 83k .0090 5-30 x 10" 7 - 6.2k 838 .0208 7.00 x 10" 7 - 6.11 8k0 .Olkk 6.70 x 10" 7 - 6.13 8kk .0055 8.20 x i o " 7 - 6.05 27 Table I I . g i v e s the t a b u l a t e d r e s u l t s f o r the e x p e r i m e n t a l l y determined vapour p r e s s u r e s of pure manganese. These r e s u l t s were c a l c u l a t e d from the average a c t i v i t y of a s e r i e s of from two to f i v e d i s c s as shown i n F i g u r e 9. The weight of the manganese C o l l e c t e d was determined by making use of F i g u r e 8 . A sample c a l c u l a t i o n i s made i n Appendix C. The l o g vapour pressure has been p l o t t e d a g a i n s t r e c i p r o c a l temperature i n F i g u r e 11. The heat of s u b l i m a t i o n of manganese Is determined from the slope of the curve In F i g u r e 11 a c c o r d i n g to Equation A-2. The A H T v a l u e s obtained from the above r e s u l t s was much h i g h e r than the v a l u e s 18 r e p o r t e d by K e l l y and McCabe, t h a t i s , 89,000 c a l o r i e s per mole compared to t h e i r 67,000 c a l o r i e s per mole. The values r e p o r t e d by these i n v e s t i g a t o r s were determined i n experiments extending over a l a r g e temperature range and are considered q u i t e r e l i a b l e . The present r e s u l t s are based on measurements made over a v e r y s m a l l temperature range. I t was Impossible to extend the p r e s e n t measurements to lower temperatures because the s p e c i f i c a c t i v i t y of the manganese was much too low, and could be Increased by no more than a f a c t o r of f i v e w i t h a v a i l a b l e Mn^+. In order to r a t i o n a l i z e the e x i s t i n g d i s -crepancy, a thorough examination of our technique was 28 -5.8: 1 1 1 • — * .895 .900 .905 .910 .915 -920 1 x 103 F i g u r e 11. Graph R e l a t i n g the Log Vapour Pressure of Pure Manganese, and R e c i p r o c a l Temperature 2 9 made. The p o s s i b i l i t y of f a u l t y temperature measurement was e l i m i n a t e d by checking the potentiometer and adding a new thermocouple. In both c a s e s , new measurements corroborated the p r e v i o u s v a l u e s . Should the c o l l i m a t l n g geometry change a p p r e c i a b l y w i t h temperature, the s i z e of the c o l l i m a t e d spot would a l s o change. T h i s d i d not occur. The e x p l a n a t i o n f o r the r e s u l t s of t h i s i n v e s t i g a t i o n can p r o b a b l y be found a s s o c i a t e d w i t h a change w i t h temperature of the accommodation c o e f f i c i e n t of the c o l l e c t i n g p l a t e f o r the vapour. It. appears t h a t v a s m a l l e r percentage of the manganese s t r i k i n g the d i s c s from lower c e l l temperatures Condenses than from h i g h e r c e l l temperatures. A p o s s i b l e method of checking the accommod-a t i o n c o e f f i c i e n t c o n s i s t s of comparing the weight of vapour c o l l e c t e d u s i n g E q u a t i o n B-$ w i t h the weight of the vapour l o s t . The Knudsen c e l l weighed 125" grams, and, d u r i n g long e f f u s i o n runs,, a maximum of 5 m i l l i -grams of manganese was l o s t . S m all v a r i a t i o n s i n t h i s weight could not be detected by weighing the c e l l b e f o r e and a f t e r a r u n . In order to measure the vapour pressure of manganese above the a l l o y s , the assumption has to be made that the accommodation c o e f f i c i e n t changes only w i t h the temperature of the c e l l . I f , at a g i v e n temp-e r a t u r e , the vapour pressure of the c e l l i s i n e r r o r by a f a c t o r because the accommodation c o e f f i c i e n t i s d i f f e r e n t from one, then the a c t i v i t y of the a l l o y measured at that temperature Is g i v e n by a = F(t) Pt B, (5) A l l o y s of Copper and Manganese Seven a l l o y s of copper and manganese were prepared f o r t h i s i n v e s t i g a t i o n . The a l l o y s were placed i n t o the c e l l as t u r n i n g s which were produced when the m e t a l was d r i l l e d out of the molybdenum c r u c i b l e s . E x p e r i m e n t a l r e s u l t s f o r the vapour p r e s s u r e of manganese above the a l l o y s , c a l c u l a t e d as b e f o r e , are g i v e n i n Appendix .D. Since these measurements were performed over a p e r i o d of s e v e r a l months h a l f l i f e c o r r e c t i o n s were necessary and have been made. The l o g vapour pressure v a l u e s f o r each a l l o y are p l o t t e d a g a i n s t r e c i p r o c a l temperature i n F i g u r e 12. The s t r a i g h t l i n e s drawn through the experimental p o i n t s are used f o r a l l subsequent c a l c u l a t i o n s . L i t t l e s i g n i f i c a n c e i s placed on v a l u e s obtained from the 11$ manganese a l l o y . The; c o l l e c t i o n 31 F i g u r e 12. : Graph, R e l a t i n g l o g Vapcur Pressure of Manganese over Copper-Manganese A l l o y s , a n d R e c i p r o c a l Temperature 32 d i s c s were spo t t y suggesting that only a f r a c t i o n of the manganese vapour was c o l l e c t e d . The a c t i v i t i e s of manganese i n the a l l o y s were determined a c c o r d i n g to Equation 1 and are shown p l o t t e d i n F i g u r e s 13 and l k f o r temperatures of 820°C and 8kk C r e s p e c t i v e l y . Pure (3-manganese was chosen as the standard s t a t e . The a c t i v i t i e s of copper have been c a l c u l a t e d u s i n g the G-ibbs-Duhem Equation (Equation A-9) and are a l s o p l o t t e d i n F i g u r e s 13 and l k . Manganese shows a p o s i t i v e d e v i a t i o n from R a o u l t ' s law. over the e n t i r e composition range; Copper, on the other hand, shows a s l i g h t n e g a t i v e departure from R a o u l t ' s law a t h i g h copper content but d e v i a t e s s t r o n g l y i n the p o s i t i v e d i r e c t i o n at low copper com-p o s i t i o n . The behaviour of manganese atoms i n copper-r i c h s o l u t i o n s Is s i m i l a r to the behaviour of the s u r -rounding copper atoms while the behaviour of Copper i n manganese r i c h s o l u t i o n s i s q u i t e d i f f e r e n t . There i s a strong r e p u l s i v e f o r c e between the two c o n s t i t u e n t s at these l a t t e r c o m positions. At in t e r m e d i a t e compositions, there i s a g r e a t e r tendency f o r manganese atoms to group With manganese atoms than w i t h copper atoms. The copper atoms a l s o showa g r e a t e r a f f i n i t y f o r manganese atoms than f o r copper atoms. 33 3k 20 kO 60 80 100 Mole % Mn F i g u r e l k . , The. A c t i v i t i e s . . of Copper and. Manganese, i n . Cu-Mn A l l o y s at 8 k k uC The f r e e energy changes f o r b o t h copper and manganese have been c a l c u l a t e d u s i n g E q u a t i o n A-10 and the a c t i v i t i e s shown i n F i g u r e s 1 3 and l k . The values are given i n Appendix D. The f r e e e n e r g i e s of mixing f o r the a l l o y s are p l o t t e d a g a i n s t composition i n F i g u r e s 1 5 " and 1 6 a t 820°C and 8 k k ° C r e s p e c t i v e l y . The p o i n t s based d i r e c t l y on e x p e r i m e n t a l data are marked. At 8kk°C, 2 k 0 below the m e l t i n g p o i n t , the , composition, of the minimum of the f r e e energy curve corresponds to that of the m e l t i n g p o i n t minimum of the copper-manganese system (Figure 1 ) , as expected. The f r e e energy of mixing i s l e s s n e g a t i v e a t the lower temperature,. 820°C, f o r c o n c e n t r a t i o n s of manganese g r e a t e r than 20$. Below 20$,. b o t h f r e e energy of mixing curves f o l l o w q u i t e c l o s e l y , the f r e e energy curve based on i d e a l m i x i n g . Myers suggested that the e l e c t r o n i c c o n f i g u r a t i o n s of Copper and manganese were s i m i l a r i n t h i s composition range. The excess f r e e energy changes f o r both copper and manganese at 820°C have been c a l c u l a t e d u s i n g Equation A - l l and the a c t i v i t i e s shown i n F i g u r e s 1 3 and l k . These excess v a l u e s have been t a b u l a t e d In Appendix D, and are shown pl o t t e d , a g a i n s t composition i n F i g u r e 1 7 • The excess f r e e energy curve f o r copper shows a minimum at about 3 5 $ manganese. Here the copper 36 -200 -kOO ra © •H o I - l erf o <D b0 erf ,3 o l>» bO <D a (D CD -6oo -800 -1000 -1200 -IkOO 40 60 Mole % Mn 80 F i g u r e 15>. The, Free Energy, of Mixing of Cu-Mn A l l o y s , at, 37 -lkOO 20 kO 60 80 10.0* Mole $ Mn Figure, 16. The F r e e Energy of Mixing of Cu^Mn A l l o y s a t , 3 8 Jo 20 ~3o to $5 So 70 ~#o $0 100 Mole % Mn F jgure 17..The Excess, F r e e Energy,Change• for, :0oppe r and Manganese i n Cu-Kn A l l o y s a t 820°C atom shows I t s g r e a t e s t a f f i n i t y f o r manganese. The minimum c o i n c i d e s w i t h the composition range a t which Myers suggested that the 3d e l e c t r o n s of copper and man-ganese had formed a common band. The manganese shows i t s g r e a t e s t departure from i d e a l behaviour a t t h i s composi-t i o n . 19 Wagner has d e r i v e d formulae from which one can c a l c u l a t e d p a r t i a l m o l a l excess f r e e e n e r g i e s from the Cu-Mn phase diagram. A c a l c u l a t i o n was made (Appendix E) i n order to compare the exp e r i m e n t a l r e s u l t s w i t h an independent source. The p a r t i a l m o l a l excess f r e e energy of manganese In a 65£ Mn a l l o y a t 937°C was found to be 1200 c a l o r i e s p e r mole based on Wagner's E q u a t i o n . A value of 890 c a l o r i e s per mole was obtained from the present experimental r e s u l t s . The agreement i s good, c o n s i d e r i n g the nature of the c a l -c u l a t i o n based on Wagner's equation. The accuracy of the a c t i v i t y and f r e e energy values i s based on the accuracy of the vapour pressure curve a t the temperature concerned. Should the curve be i n e r r o r by $% r the a c t i v i t y would be i n e r r o r by no more than t h i s amount. However, a s i m i l a r e r r o r could have a ve r y l a r g e e f f e c t on the va l u e s of enthalpy and entropy, s i n c e these q u a n t i t i e s are c a l -c u l a t e d from the slope of the vapour p r e s s u r e curve. In Equation A - 1 2 , f o r example, the change i n l o g due to the vapour pressure b e i n g i n e r r o r by + 5>$ a t 8kk°C and -$% at 820°C would be . Oijlj., and the r e s u l t i n g e r r o r i n the p a r t i a l m o l a l heat of manganese i n the g i v e n a l l o y would be 10,^00 c a l o r i e s per mole. E n t h a l p i e s of mixing based on our experimental d e t e r m i n a t i o n s have been c a l c u l a t e d u s i n g Equations A-12 and A -16 . These val u e s have been p l o t t e d a g a i n s t composi-t i o n In F i g u r e 18, The maximum of the enthalpy o f mixing curve i s found a t about 35$ manganese and has a value of 13>000 c a l o r i e s per mole. S i n c e the valu e s of the f r e e energy of mixing are Small compared to those of the enthalpy of mixing, the entropy of mixing curve would be s i m i l a r to F i g u r e 18. 20 21 Recent t h e o r e t i c a l papers on the thermo-dynamics of s o l i d m e t a l l i c s o l u t i o n s have been p r i m a r i l y i n t e r e s t e d i n r a t i o n a l i z i n g the p o s i t i v e e n t h a l p i e s of mixing found i n many systems. The concept of s t r a i n energy, which i s u s u a l l y a s s o c i a t e d w i t h the d i s p a r i t y of s i z e of the two atoms, has been in t r o d u c e d to e x p l a i n the l a r g e e n t h a l p y of mixing . However,- i n t h i s system, there i s l i t t l e d i f f e r e n c e between the s i z e s of the 22 copper and manganese atoms. Goldschmidt r a d i i f o r copper and manganese are I .276 A and I . 3 6 A r e s p e c t i v e l y . The l a r g e p o s i t i v e heat term i n the copper-manganese 15000 1 Mole % Mn F i g u r e . 18. E n t h a l p y of Mixing of Cu-Mn A l l o y s at 820 C system can not be accounted f o r by t h i s s m a l l d i f f e r e n c e i n atomic s i z e alone. 23 M i t s u a and Mlwa have ex p l a i n e d the bond energie s between u n l i k e atoms i n terms of t h e i r e l e c t r o -n e g a t i v i t i e s . The a p p r o p r i a t e e l e c t r o n e g a t i v i t y v a l u e s were not a v a i l a b l e f o r the e l e c t r o n i c C o n f i g u r a t i o n s o f copper and manganese i n these a l l o y s and t h e r e f o r e , no c o r r e l a t i o n was p o s s i b l e . Moreover, I f Myers 1 views on the e l e c t r o n s t r u c t u r e of these a l l o y s are c o r r e c t , the e l e c t r o n e g a t i v i t i e s themselves w i l l be a f u n c t i o n of the composition, and any argument based on a v a i l a b l e e l e c t r o n e g a t i v i t y v a l u e s would be m i s l e a d i n g . In view of these d i f f i c u l t i e s , then,, i t was considered unwise to attempt too d e t a i l e d a comparison of the data obtained i n t h i s work w i t h e x i s t i n g t h e o r i e s of a l l o y s t r u c t u r e . . In summary, the f o l l o w i n g p o i n t s are con-s i d e r e d p e r t i n e n t . a) Manganese does not d e v i a t e s t r o n g l y from i d e a l mixing a t low manganese content. Myers has sug-gested that the manganese atoms would behave s i m i l a r to the Copper atoms at these compositions. b) Copper shows i t s maximum a f f i n i t y f o r manganese at a composition of about 3$% manganese. At k3 the same composition, manganese shows i t s g r e a t e s t p o s i t i v e d e v i a t i o n from i d e a l behaviour. Myers suggested that the 3d e l e c t r o n s of copper and manganese form a common band at t h i s composition range. These r e s u l t s appear to c o r r o b o r a t e Myers' i n t e r p r e t a t i o n of the e l e c t r o n i c c o n f i g u r a t i o n s i n the copper-manganese system. i APPENDIX A Thermodynamic s Q Thermodynamics of Vapour-Solid E q u i l i b r i a 7 The e q u i l i b r i u m between a metal, l i q u i d or s o l i d , and i t s vapour M ^ — M ^ v \ (A-i) ^ V l ( v a p o u r ) can be expressed by the C l a u s i u s - C l a p e y r o n E q u a t i o n (Equation A-2) i f the vapour i s a p e r f e c t gas and the s p e c i f i c volume of the gas i s l a r g e compared to the volume of the condensed phase. d I n P A M T (A-2) dT- R T 2 In E q u a t i o n A-2,. P i s the vapour p r e s s u r e of the metal i n atmospheres and A H T i s the l a t e n t heat of e v a p o r a t i o n To K e l v i n . The l a t e n t heat can be w r i t t e n as a f u n c t i o n of the temperature as i n E q u a t i o n A-3, i f no t r a n s i t i o n s occur i n the temperature i n t e r v a l T'and T . A H T = &H T'-J ( C p ( v a p > - C f ( t o n J ) ) J T (A-3) T A H j * i s the heat of v a p o r i z a t i o n a t temperature T' , and Cp (vap) and Cp(cond) are the s p e c i f i c heats of the vapour and condensate at constant p r e s s u r e . I f the assumption i s made that Cp(vap) -Cp(cond') i s constant i n the temperature i n t e r v a l T' and T , Equations A-2 and A-3 can be combined and i n t e g r a t e d to give the equations commonly employed to give the vapour pressure as a f u n c t i o n of temperature. I n P • = - ^ - - B U T - v - C U - k ) Since the & l o T term i s small,, the e m p i r i c a l form i s more common. B and C are co n s t a n t s . Thermodynamic R e l a t i o n s i n A l l o y s The a c t i v i t y of a component i n an a l l o y can be determined by Equation A-6, when the vapour of that com-ponent can be considered a p e r f e c t gas.3*^-p ; i s the vapour pressure of component /\ i n the a l l o y and i s the vapour p r e s s u r e of pure component A' The a c t i v i t y c o e f f i c i e n t , ^ , i s d e f i n e d as the r a t i o of a c t i v i t y to mole f r a c t i o n as i n Equation A~ 7 . The Gibbs Duhem Equation allows us to c a l c u l a t e the thermodynamic p r o p e r t i e s of the second component from those of the f i r s t . The fundamental thermodynamic r e l a t i o n i s N A dGA -P NB d& B = 0 (A-8) where G" r e p r e s e n t s any e x t e n s i v e p r o p e r t y of the system such as f r e e energy or entropy. By s u b s t i t u t i n g i n t o E q u a t i o n A-8 and i n t e g r a t i n g , we get a u s e f u l equation r e l a t i n g the a c t i v i t y c o e f f i c i e n t s of the two c o n s t i -tuents i n the b i n a r y a l l o y . ^ (t - NA) ; 2 C!MB (A-9) In an i d e a l s o l u t i o n the a c t i v i t y of each component i s equal to i t s mole f r a c t i o n and t h e r e f o r e a c t i v i t y c o e f f i c i e n t s are equal to one. M e t a l l i c s o l u -tions,- however,, g e n e r a l l y d e v i a t e from R a o u l t ' s law which d e f i n e s an i d e a l s o l u t i o n . When the a c t i v i t y c o e f f i c i e n t i s g r e a t e r than u n i t y , i t i s s a i d that the a c t i v i t y of t h a t component shows a p o s i t i v e d e v i a t i o n from Raoult's law. A neg a t i v e departure e x i s t s when the a c t i v i t y c o e f f i c i e n t i s l e s s than one. The p o s i t i v e departure i s u s u a l l y found i n systems i n which heat i s absorbed upon mixingy and i s a s s o c i a t e d w i t h a tendency f o r each type of atom to group w i t h s i m i l a r atoms'. S i m i l a r l y n e g a t i v e departures show a tendency f o r an atom to group with an atom of the other component standard state,- the f r e e energy change a s s o c i a t e d w i t h the change from the pure s t a t e t o the a l l o y e d s t a t e i s g i v e n by Eq u a t i o n A-10. When the pure metal s e l e c t e d as the (A-10) ^8 where i s the p a r t i a l m o l a l f r e e energy of ^ i n s o l u t i o n and F^ i s the m o l a l f r e e energy of pure (\ . The excess f r e e energy change i s d e f i n e d by E q u a t i o n A•-11. AF A E= - ( A - i i ) The change i n enthalpy, and entropy, hS*0? com-ponent /\ can be determined from the change of /\FA w i t h temperature a c c o r d i n g t o Equations A-12 and A—13. (A-12) (A-13) The three thermodynamic p r o p e r t i e s , f r e e energy, enthalpy,-and entropy are r e l a t e d a c c o r d i n g t o Equation A-lij.. A F A = A H A - T & S A < A - * > -The s u b s c r i p t A has denoted t h a t the p r o p e r t y i s a p a r t i a l m o l a l p r o p e r t y . The f r e e energy of mixing, enthalpy of mixing and entropy of mixing are d e f i n e d below f o r a l l o y s of A and & k9 b&m = M A A S A - r - M B / \ S B (A-15) (A-16) (A-17) 5o APPENDIX B 9 D e r i v a t i o n of Knudsen Formula A c c o r d i n g to the K i n e t i c Theory of Gases, the mass of vapour, yy^ , which s t r i k e s a u n i t area of the surface per second i s g i v e n by Equ a t i o n B - l . = pv (B-l) where p Is the d e n s i t y of the vapour and V i s the mean v e l o c i t y of the atoms. The i d e a l gas law s t a t e s p = - ^ L (B-2) r RT where M i s the m o l e c u l a r weight of the vapour, P i s the pressure,. T i s the a b s o l u t e temperature and R i s the gas constant. The mean v e l o c i t y V i s r e l a t e d to M and T by TTM , ^ (B-3) Combining Equations B - l , B-2, and B-3 we get 51 which i s the Knudsen Formula. I f the o r i f i c e of a K n u d s e n ' c e l l can be c o n s i d -ered a p o i n t source, the f r a c t i o n of the t o t a l vapour e f f u s i n g from the Knudsen c e l l which i s i n t e r c e p t e d by the t a r g e t i s : I T l TT 0 o ( B - 5 ) X) i s the r a d i u s of the t a r g e t and C i s the d i s t a n c e of the c o l l i m a t i n g p l a t e from the o r i f i c e . The o t h e r v a r -i a b l e s are shown i n F i g u r e 19. \ \ \ \ r \ \ / I col\imatbir / / e' / i^ o m i c e - c e l l F i g u r e 19. Geometry of Target and O r i f i c e In the above d i s c u s s i o n we have assumed that an o r i f i c e p l a t e of n e g l i g i b l e t h i c k n e s s i s used. I f the o r i f i c e p l a t e has t h i c k n e s s , then i t i s i n r e a l i t y a s h o r t c a n a l . The c a n a l causes a r e l a t i v e l y l a r g e r number of molecules to e f f u s e i n the foreward d i r e c t i o n than i s p r e d i c t e d by Equation B-k. F o r short c a n a l s E q u a t i o n B-k becomes the o r i f i c e . The Knudsen formula i s v a l i d only when the vapour and condensate w i t h i n the c e l l are i n e q u i l i b r i u m . The o r i f i c e must be s m a l l so that the vapour l o s t does not a p p r e c i a b l y a f f e c t the e q u i l i b r i u m . The e f f e c t i s e s t i m -9 ated as f o l l o w s . Consider a c l o s e d c e l l where: OC = condensation c o e f f i c i e n t p = true e q u i l i b r i u m vapour pr e s s u r e vV= number of molecules s t r i k i n g a u n i t area of surface' per u n i t time i n a gas at Pressure and temperature S = e f f e c t i v e area of sample w i t h i n the Knudsen c e l l (B-6) where Jt i s the thickne ss of the p l a t e , and Q. i s the r a d i u s of VVD( 5 =• number of molecules which would condense per u n i t time on S !flC<S = number of molecules which would evaporate per u n i t time from S I f we open a h o l e of area, V\ , i n the c e l l , e q u i l i b r i u m w i l l be d i s t u r b e d by the escape of molecules from the h o l e . A steady s t a t e w i l l be e s t a b l i s h e d a t p r e s s u r e P such that the number of molecules escaping w i l l be balanced by the net number e v a p o r a t i n g from s u r f a c e The r a t e of e f f u s i o n i a hh where ti. i s analagous to lV , but at p r e s s u r e P, T h e r e f o r e n h ^ h'o< 5 - HO<S ^ k . 4- oc (B-8) m u l t i p l y both s i d e s by \y\ / 2TTRT where Vr/ i s the mass of the molecule then: and p = p when (B -9) E x p e r i m e n t a l l y P i s assumed to be e q u a l to P when a s change i n the Jd. v a l u e does not change the pressure a p p r e c i a b l y . APPENDIX C Sample C a l c u l a t i o n of Vapour Pressure In the Knudsen formula (Equation B-k) \rf\ i s defi n e d as the mass of vapour which s t r i k e s a u n i t area of s u r f a c e i n the c e l l per second. The weight of the metal vapour i n t e r s e c t e d by a c o l l e c t i o n d i s c , (jj » i s r e l a t e d to YT\ by (j) = ynntA-f (c-i) where "t i s the e f f u s i o n time i n seconds, /\ i s the o r i f i c e area i n cm 2 and -f i s the f r a c t i o n of the e f f u s e d vapour i n t e r s e c t e d by the c o l l e c t i n g p l a t e . The Knudsen Equation becomes n - ^ / 2 T T R . T The net r a d i o a c t i v i t i e s " of three c o l l e c t i o n d i s c s , measured w i t h the p r o p o r t i o n a l counter on September 27, 1957 are g i v e n below f o r a run a t 828°C us i n g an o r i f i c e w i t h an area of .Olkk cm #1 (2 hrs) 7k + 3 cpm #2 ( 1 | h r s ) 5 5 + 3 cpm #3 ( H i hrs) k99 ± 5 cpm 55 The average value i s k 2 cpm/hr e f f u s i o n . T h i s measurement was made 6 3 days a f t e r the standard was measured. A c o r r e c t i o n f a c t o r of 1 . 1 6 i s neces s a r y . 1 . 1 6 = k 8 . 6 cpm i s e q u i v a l e n t ( F i g u r e 8 ) to . 0 2 k 8 Fig Mn •f f o r Knudsen c e l l # 1 i s . 0 9 7 2 (Table 1 ) CO 2 T T R T M . 0 2 k 8 ( 3 6 0 0 ) ( . O l k k ) ( . 0 9 7 2 ) 2 IT ( 1 . 9 8 7 ) ( k . l 8 6 ) ( 1 0 7 ) ( 1 1 1 3 ) 55 or •50k dynes/cm 2 . 5ok 1 3 - 6 x 9 8 1 x 7 6 _7 = J4 . . 8 7 x 1 0 atmospheres l o g Pressure (at.) - 6 . 3 0 -p < APPEND IX D I. Vapour Pressure Data for Manganese and Alloys bO o O m © vO o OJ o iH 7* T-O OO C\J "LO ro OJ H 7* O -=J-ro • • 0 • • • « • • • vO vO vO vO vO vO "LO vO I o vO -P k <D o a ft ra > © | 1 0-1 IS-^ 1 1 l>-1 o-1 r— | I i>-o O o o o O o o o 1 O 1 o i o PH H H H H H rH rH iH H rH rH X X . x K « X X ro o vO xo o o O -=± 1A O^ vO CO O^ CO ro o Ol o ro P— "LO H • • • « • • • • • • • • ro OJ Ol 1A 0-CO ro "LO CO (D O M © g i-H^ rH O ft .3 cd • © o o CO OJ 1A OJ o vO OJ vO CO O o o -d-CO l>-"LO CO ro O^ vO CO rH o OJ rH "LO ro rH OJ ro ro 1A o o o •o o o O O O O O O r) < ©OJ o •H B <^ o •rl —» r) o o O ft © EH © vO CO CO H !>-CO -=t vO O O O • O • o • CO CO rH rH CO CO O OJ CO O CO OJ CO o o o CO o OJ o ro ro CO CO -d-T-O "LO O O CO CO vO vO vO vO O o o o Ol OJ OJ Ol o • o » o • o • o H rH <! ON T-O CO rH CO ro CO ro CO 3 CO OJ (3) 1+0.2$ A l l o y 818 .0206 .01^ 5 82l|. .0206 .0202 836 .0206 .0288 840 .0206 .0396 8I4J+ .0206 .0364 (4) 29.7$ A l l o y 820 .0206 .0138 827 .0206 .0166 844 -0206 .0309 (5) 25.9$ A l l o y 822 .0206 .0098 831 .0206 .0140 842 .0206 .0213 6) 23.4$ A l l o y 818 .0206 .0092 829 .0206 .0105 835 .0206 .0121 841 .0206 .0147 2.20 X 10' -7 2.81 X 10' -7 4.10 X 10' -7 4.26 X 10' -7 5.22 X 10' -7 1.94 X 10 -7 2.33 X 10 -7 4.30 X 10 -7 1.39 X 10 -7 1.97 X 10 -7 2.98 X 10 -7 1.30 X 10 -7 1.49 X 10 -7 1.69 X 10 -7 2.09 X 10 -7 -6.66 -6.56 -6.39 -6.37 -6.28 -6.71 -6.63 -6.37 -6.86 -6.705 -6.525 -6.91 -6.83 -6.77 -6.68 (7) 20.0$ A l l o y 82k .0206 828 .0206 833 .0206 8 k l .0206 8k6 .0206 (8) l k $ Alloy*™ 837 -0206 8k5 .0206 .0080 ,0090 ,0111 .0121 ,0161 ,003k .0037 1.11 x 10~7 1.26 x 10~7 1.53 x 10" 7 1.70 x 10" 7 2.27 x 10 -7 5-2 x 10 6.0 x 10 -8 -8 -6.95 •6.90 •6.82 -6*77 -6.65 •7.30 •7.25 > The compositions of the a l l o y s are average values of the i n i t i a l and f i n a l compositions. The s l i g h t change i n composition was due to the l o s s of manganese from the a l l o y s d u r i n g e f f u s i o n . These r e s u l t s were not p l o t t e d on the a c t i v i t y curve as a l r e a d y d i s c u s s e d . o o a rt-H» CD Cb CO APPENDIX D (Continued) Thermodynamic A c t i v i t y of Mn from Vapour Pressure H (\| 4 Q3 O O vO lA rO C*S rO TA GO CO TA I—I CO CO TA rO CM CM O _=f CO O r-i C— CM C~- rO CM -d- -d- T A C— -d" CM sO CM CO O CM rO vO vO CM T A O ro CM O- CM CO vO t— CO O O vO vO vO vO vO I I I I I I TA CM O r-i O r-i CM co TA r— vO vO vO I I I I I I I I 1A CM O -=t-• \ & \ & \&. CM TA CM CO CM O CM 7=f o o CO o TA CM O \& ^ ^ CM o IA CM ro CM o o CM III-. APPENDIX D (Continued) Thermodynamic Values from A c t i v i t y Curves S o o o o o o o o o o o ^ o o o o o o o o o o X. poo ^ i A w.dv\oo> -a V . fcv .v 0\ * *\ *v »v * ^ •>J CO O ON P-XO _H-sO ON H ON rO-drOJ <—i rH H So CO^-HlAO 1SO\OC\J cn -d>o cvi ro-sOMD CM _d-_d-_d-O H r H r H O O O O O O O 1 I I I I I o to S o o x o o o o o o o o o /if- O _d-CM H vO O O CO O N P—ro P-CO O N O J CVI rH OCOvO-d-CVI O H rH rH H I + + + + + + + + + + 0 0 0 0 0 X 0 0 X 0 0 0 0 rHCOvOCVl CAHvOCOn ro O Oco OCO vO -d"OJ H + + + + + + + + + O O O O O O O O O O O T-00 OCOO f-OOAO OJ P-rH ro O CO XO CM H _d-CVI Ol H rH I I 1 I I I I 1 I I I OOOOOOOT-OO o_d-xoco p-cvixoo o H XO C—XA ro CVl XO ro H XOrOCVI H H rH I I I I I I I I I o o c V ? o cOXOrOroH V O C O X O N O _d"^0 CO -d"XO CVl O P~-roON_d-rHrHrHOlOJOJOJrHrHOO rH cvi co cvi -r±o o -d-vo ^ O H C O N O O V O rOON_d" OOJrHrHrHHrHOO o o •z W O vO -d-cvi HCOH XA^ J-CVl O-O P—OXOH O COXO_d-OJ ( M H H O O O o o e « t> « * o p . * I I I I I I I I I I O _d-H p-_d-co oco cvi O P-XO ro OJ CVI O vO r-i O . . „ . . . H O O O rH . . . . 1 1 I I I I I I I I O 5 XOCVI P- P-CO O P-_d-H S -d"-d"XO P~-cO vO XOXO ro CVI H ^ H rH rH rH H H rH rH rH rH rH XO ro ^d-XO vO XOXO-d" rH O O HvO XA^XA^roOJ H Hi—IrHHrHHrHrHHrHrH O O O O o J _ _ , . _ _ CVl Q i—I CVI rOXO^ O vO C—CO O N O N C O rH OJ CM _d"XOXO P-OO O N ON S xo _dr 2 . -H/Oco roro P—ON OsO _d" O O  ON_d-cO CO P— N O  H -P rH © cd ra a ^  o oxooxoo O O O O O O oxooxoo O O O O O bd^ . H OJ CM rorO-H^ XO^ O P—CO O H CVI OJ roro_d"XOvO P—CO QN R cd g APPENDIX D (Continued) 61 IV. Thermodynamic Values from Gibbs-Duhen Eq u a t i o n o X O O I o o o o o o o o o o o o o o o H _ d " ( M A H H H C M O " L A C O s £ ) O C ~ - O v O O I _ d " I - d " v O r-i O O O O O O O O O H I I l i l t <3 o O W I A O O O TAOCO C M C — C O i H H O r H C M C M I I r-i C M H C O I H I A I H I I I I + + + O O O O O O I A O T A O H E — C V J v O O 0 _ = J " C M o ~ \ C M I I I ! • + • + + <l o o o o o o o o o o C O rl rl ( v y L A C M O C O v d - C M C M T A C " - O r-i C M T A C O O C M H r-i r-i H C M C M I I I I I I I I I I O O O O O O O O O C O O O v O c O ^ O O _ d " H C M T A C M C O 0 s C M v £ ) r ~ - c o r-i r-i r-i C M C M C M C M I I I I I I I I I o bo o v O C M C M > - O T A O O r— T A O - d ' C O r O - d r H I ^ - O J ; -O r-i r-i r-i C M C M CO CO^t-d -I I I I I I I I \Ooovo N r—_ T A O r o - s O r—. O O C M C M O O . r - r o - O r O T A h A T A T A I I I I I I I I I 6 C5 O O C M T A C M S - C O C M O v £ > O f - f - v D T A T A - d - ^ } - C O c o C O _ d " C M v O r-i O C O O c O T A T A ^ J - r o c O C M C M 6 CT^vO C M H I A O - T A f - O O O O O O O O C M C O H H H r o O - d - < H C O T A H C O C O C O 0 s O r H _ d " I H H H w O o o o C M C O o T A T A C ^ - C M C M v O C O T A O O r-i C O ^ d - C M r-i C M O T A O O O O O O O O H C M I I I I I + + + O O T A O T A O O O O O oco c--r— v o vOTA-drcoCM C O r-i _ d - C M c O - d - r — ^ - H v O T A O O O O O O r-i 0 0 1 I I I + + + o o o - d -co O O O O O O O T A O O c O £ - - v O T A - d ' C O C M C M APPENDIX E 19 C a l c u l a t i o n Using Wagner's E q u a t i o n Wagner has derived formulae from which one can c a l c u l a t e p a r t i a l m o l a l excess f r e e e n e r g i e s from the phase diagram. Equation 19 from h i s paper "Thermodynamics of B i n a r y A l l o y s " i s g i v e n below , S N f ( I - N J A . + N . A , £ N f 1 ) l i s the slope of the s o l i d u s l i n e at composition under c o n s i d e r a t i o n N ^ - N ^ i s the width of the s o l i d u s - l i q u i d u s loop 0 i s the temperature -A-^A^are the heats of f u s i o n of the pure components and l - N a . ^ Consider the Cu-MoSystem at 6 5% Mn (from phase diagram) '^z. Viz =0.1 (from phase diagram) © = 1210° •^-Cu = 3,120 = 3,600 S u b s t i t u t i n g i n t o Wagner's Equ a t i o n (.1) (1210) C^Fn 5oo = 3360 N> ^ ^ F „ SN 1 " = 13,900 ^ F E ^ F m RT SNJ ^ N* N»(i-N,) = 13,900 - 10,450 = 34So • = .35 (3450) = 1200 cal/mole \ ^MJ T h i s value of 1200 cal/mole i s o n l y as r e l i a b l e as i s the phase diagram and t h e r e f o r e could be i n e r r o r by $0% or more. The value obtained from our work was c a l c u l a t e d by u s i n g o the a c t i v i t y of manganese determined a t 8J4J4. C 6k = ( k . 5 7 5 ) ( 1 2 1 0 ) ( 1 . 6 ) = 8 9 0 cal/mole \ 65 V. B i b l i o g r a p h y 1. Myers,. H.P. •,. Can. J . Phys., 3]±, $2J (1956). 2. Chipman, J . , D i s c , Faraday S o c , ij., 2 3 , ( ) • 3. Lumsden, J . , 'Thermodynamics of A l l o y s ' , I n s t , of Metals,, (1952) . 4« Wagner, C , 'Thermodynamics of A l l o y s ' , Addison Wesley, (1952). 5 . Knacke,- 0 . , and S t r a u s k i , I.N., 'Progress i n Metal P h y s i c s ' 6, l8l, (1956). 6. Chipman, J . , and E l l i o t t , J . F . / 'Thermodynamics i n P h y s i c a l Metallurgy'. A.S.M. (1950). 7. D i t c h b u r n , R.W., and Gilmour, J.C., Rev. Modern Phys., H , 310,. ( 1 9 4 D . 8. Knudsen,, M., Ann. der Physik,- 2£, 179,. (1909). 9. Speiser,. R.,, and Johnson, H.L.,. Trans. A.S.M. l\.2, 283, (1950). 10. Langmuir, I.,. Phys. Rev., 329, (1913). 11. Hersh, H.N., J . Am. Chem. S o c , ££, 1529, (1953). 12. McKinley, J.D., and Vance, J.E.,, J . Chem. Phys. 22, 1120, (1954)• 13. T a y l o r , J.B.,- and Langmuir, I . , Phys. Rev . y 5,1» 753, (1937). 3J4.. Ege r t o n , A.C., P r o c Roy. S o c , 10.3, 4^9r (1923). 15. 0'Donnell,. T.A.,, A u s t r a l i a n J . Chem. ><8, 4 8 5 , (1955). 16. Gonser, U., Z e i t . F. Phys. Chem.> 1, (1954)-17. Edwards,. J.W.,. Johnson, H.L., and Blackburn, P.E., J . Am. Chem. Soc. Jjj., 1539, (1952). 18. McCabe, C L . , and Hudson, R.G., J . Me t a l s , % 17, (1957). 19. Wagner, C , A c t a Met., 2,. 242, (1954). 20. O r i a n i , R.A., Acta Met., ij., 1 5 , (1956). 66 21. V a r l e y , J.H.O., P h i l . Mag., ^ 887, (1954). 22. Ephraim,< F., 'Inorganic Chemistry' I n t e r s c i e n c e P u b l i s h e r s I nc. (1947). 23. S h i m o j i , M., and Niwa, K., A c t a Met., 5 , 496, (1957). 24. Darken, L.S., and Gurry, R.W., ' P h y s i c a l Chemistry of Metals,»McGraw H i l l , - (1953). 

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