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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 M e t a l l u r g y at the U n i v e r s i t y of B r i t i s h Columbia  We accept t h i s t h e s i s as conforming t o the standard r e q u i r e d from candidates f o r the degree of -"Master of A p p l i e d S c i e n c e in 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  8  ABSTRACT  The manganese  thermodynamic p r o p e r t i e s of the  system  were d e t e r m i n e d  the v a p o u r p r e s s u r e using  o f manganese  b y t h e measurement o f tagged  with  over the e n t i r e  composition  showing a s t r o n g p o s i t i v e  y  content,  d e v i a t i o n from  range.  Copper,  low c o p p e r  in  copper-rich compositions.  shows a s l i g h t  negative  The n e g a t i v e  w h i c h c a n be a s s o c i a t e d w i t h an a f f i n i t y manganese,, i s g r e a t e s t a t c o m p o s i t i o n s ese.  The b e h a v i o u r " o f b o t h c o p p e r ideal  a t l o w e r manganese  The alloys  i d e a l behaviour  o f low manganese  departure  departure,  of copper f o r 35$  o f about  and manganese  o f t h e manganese  mangan-  I s much  i n the  and t h e a f f i n i t y  3 5 $ manganese  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 copper  although  compositions.  content  c o p p e r f o r manganese a t a b o u t  figurations  Raoult's  d e p a r t u r e f r o m R a o u l t ' s law  at  more  Mrr^ .  t h e K n u d s e n e f f u s i o n method. Manganese shows a p o s i t i v e  law  copper-  of  appear to  of the e l e c t r o n i c  and manganese i n t h i s  system.  con-  In the  presenting  requirements  of  B r i t i s h  it  freely  agree for  that  available  I  agree  degree  that  purposes  gain  shall  not  of  be a l l o w e d  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada.  by t h e Head It  i s  thesis  Columbia,  make  further  of t h i s  thesis  o f my  understood f o r f i n a n c i a l  my w r i t t e n  MINING AND METALLURGY  JANUARY 1958.  copying  of  University  I  t h i s  without  the  and study.  may b e g r a n t e d  of  at  shall  for extensive  or publication  fulfilment  the Library  o r by h i s representative.  copying  Date  i n p a r t i a l  f o r reference  permission  that  Department  thesis  f o r an advanced  Columbia,  scholarly  Department  this  permission.  11 TABLE .OF CONTENTS Page I.  INTRODUCTION . . . . . . . . . . . . . . . . . Object  of the I n v e s t i g a t i o n  The Measurement II.  EXPERIMENTAL Design  DISCUSSION OF RESULTS  Manganese  V.  8 8 If?  . . . . . . .  20  . . . . . . . . . . .  23  of R e s u l t s U s i n g  Pure  . . . . . . . . . . . . . . . .  23  o f C o p p e r and Manganese  APPENDIXES  1  . . . i|.  . . . . . . . . . . . .  Measurements  Reproducibility  IV.  Pressures  and T h e i r P r e p a r a t i o n  Radioactivity  Alloys  . . . . . . .  . . . . . . . . . . . . . . . . .  of Apparatus  Materials  III.  of Vapour  1  30  . . . . . . . . . . . . . . . . . .  A.  Thermodynamics  B.  D e r i v a t i o n o f the Kriudsen F o r m u l a  C.  Sample  c a l c u l a t i o n o f V a p o u r P r e s s u r e . f?4  D.  Vapour  Pressure  E.  Calculation  BIBLIOGRAPHY  . . . . . . . . . . . .  kk-  and Thermodynamic  I4.4  . . f?0  D a t a f?6  U s i n g Wagner's E q u a t i o n .  . 62  . . . . . . . . . . . . . . . .  6$  iii L I S T -.Off ILLUSTRATIONS Figure  No.  Page  1.  The Copper-Manganese  2.  D i a g r a m o f F u r n a c e and C e l l A r r a n g e m e n t  3-  Furnace Assembly  . . . . . . . . . . . . . .  11  k.  Complete Knudsen  C e l l Assembly  . . . . . . .  11  f?.  Disc  . . . . . . .  Ik  6.  G e n e r a l View  7.  Schematic Diagram of M e l t i n g Apparatus . . .  18  8.  Graph R e l a t i n g Weight A c t i v i t y of Disc  21  9. 10. 11. 12.  13.  Changer  i n Two P o s i t i o n s  l5-  . . . . . . .  of Apparatus  k 9  16  o f Manganese and  Graph R e l a t i n g A c t i v i t y of Disc o f Time o f E f f u s i o n a t 8l8QC  and L e n g t h 2k  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 S p o t o f I n a c t i v e Manganese B a s e  Manganese 2£  G r a p h R e l a t i n g L o g V a p o u r P r e s s u r e o f Pure Manganese and R e c i p r o c a l T e m p e r a t u r e . . .  28  Graph R e l a t i n g Log Vapour Pressure o f Manganese o v e r Copper-Manganese A l l o y s , and R e c i p r o c a l T e m p e r a t u r e . . .  31  The A c t i v i t i e s  o f C o p p e r and Manganese i n . . . . . . . . . .  33  o f C o p p e r and Manganese i n a t 8kfj.°C . . . . . . . . . .  3k  The F r e e E n e r g y o f M i x i n g o f Cu-Mn A l l o y s a t 820°C . . . . . . . . . . . . . . . . .  36  Cu-Mn A l l o y s li|..  Phase D i a g r a m  The A c t i v i t i e s Cu-Mn A l l o y s  at  820°C  16.  The F r e e E n e r g y o f M i x i n g o f Cu-Mn A l l o y s  17.  The E x c e s s F r e e E n e r g y Change and  f o r Copper  Manganese i n Cu-Mn A l l o y s  a t 820°C  18.  Enthalpy  of Mixing  o f Copper-Manganese  19.  Geometry  of Target  and O r i f i c e  . „  . .  38  Alloys  k l 5l  L I S T OF TABLES,.  Table I. II.  No.  Page  C.olllmating Table  Geometry o f C e l l s  13  o f V a p o u r P r e s s u r e D a t a f o r Pure  Manganese  26  V  ACKNOWLEDGMENT The  author Is g r a t e f u l  C o u n c i l and D e f e n s e aid  i n the form  t o the N a t i o n a l  R e s e a r c h Board  Research  o f Canada f o r f i n a n c i a l  of a Research A s s i s t a n t s h i p granted  during  the p a s t y e a r . The provided  funds f o r the m a t e r i a l s  by the N a t i o n a l Research Special  the d i r e c t o r and  thanks  of this  Mr. R. R i c h t e r f o r t h e i r  tance  i n constructing  suggestions  Council.  a r e extended  research,  and a p p a r a t u s were  t o D r . D..R. W i l e s ,  and t o Mr. R.G. B u t t e r s  t e c h n i c a l a d v i c e and a s s i s -  the apparatus.  The many  o f D r . C.S. Samis a r e g r a t e f u l l y  helpful  acknowledged.  I.  Object  of the  The alloys the in  Introduction  Investigation  paramagnetic  were s t u d i e d  properties  r e c e n t l y by M y e r s .  a l l o y s I n t h e gamma p h a s e terms  o f c o p p e r manganese  and  He  1  investigated  interpreted  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  his results  of the a l l o y i n g  constituents. The most was  striking  feature  t h e change o f i t s m a g n e t i c  manganese c o n c e n t r a t i o n s tration  properties 2$%.  around  t h e i n t e r p r e t a t i o n was  be  considered  containing  monovalent  more t h a n 2$%  that  region.  suggested  that  band.  o c c u r s a t a b o u t 2$%  electrons  exist.  manganese c o n t e n t may  f o r the atoms o f t h e  be  manganese which  associated  s t a t e s f o r t h e 3d  electron  a  Myers  Thus t h e change I n p r o p e r t i e s  o f manganese atoms t o c o l l e c t i v e  The  could  However, f o r a l l o y s  f o r c o p p e r and  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  electrons  similar  manganese,, i t became c l e a r t h a 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  f o r m a common 3d  concen-  B o t h c o p p e r and manganese in this  at  t h e manganese  o f l{.s e l e c t r o n s  different  t h e 3d  system  occurring  Below t h i s  given  atoms m a i n t a i n e d a c o n c e n t r a t i o n to t h a t f o r pure c o p p e r .  o f the a l l o y  electrons  treatment of these  alloy.  e l e c t r o n i c changes  be r e f l e c t e d i n t h e thermodynamic  s u g g e s t e d by M y e r s properties  o f the  should alloy  system,, and  a study  of these  i n f o r m a t i o n w h i c h c o u l d be obtained  by M y e r s .  r e a d i l y be  calculated  change w i t h o f the  These  Equations  needed  correlated  most d i r e c t  knowledge  thermodynamic  outline  f o r such  results  thermodynamic p r o p e r t i e s  of the  (An  furnish  with the  f r o m an a c c u r a t e  temperature  components.  p r o p e r t i e s would  of the  calculations  d i x A.)  The  method  activity  o f a c o n s t i t u e n t i n an a l l o y  can  of  the  activities  thermodynamic i s given  of d e t e r m i n i n g  i n Appenthe  i s measurement  of  the  2 vapour p r e s s u r e  of  that constituent.  According  to Lumsden  and  3  o f a component  i s d e f i n e d by  to E q u a t i o n  i f the v a p o u r of the  sidered  1,  a perfect  =  A  and  P  i s the A  same  these measurements  activity according  component c a n be  con-  gas Cu  where  Wagner,^" the  PA  (i)  D ° ^A  vapour pressure  i s the vapour p r e s s u r e  o f component A. i n t h e of pure  component A  alloy  at  the  temperature. The  o b j e c t of  the p r e s e n t  investigation,  was  to determine the  and  manganese by m e a s u r i n g v a p o u r p r e s s u r e s  b e t w e e n 800°C and  thermodynamic p r o p e r t i e s o f  B$0°C.  The  shows t h a t t h e f a c e - c e n t r e d most o f the  composition  was  t o measure  decided  rather  than  phase d i a g r a m  cubic  range a t  $  phase  these  copper temperatures  (Figure l) is stable  temperatures.  the v a p o u r p r e s s u r e  copper because the  at  then,  over It  of manganese  vapour pressure  o f manganese  Figure  !• The Copper-Manganese  Phase; Diagram,  f r o m M e t a l s Handbook  (1948)  is  g r e a t e r by a f a c t o r The  Measurement In  Evaporation He a r r i v e d there  o f 10 .  of Vapour  1882, H e r z p u b l i s h e d h i s c l a s s i c of L i q u i d s , E s p e c i a l l y Mercury,  f o r every  substance  e v a p o r a t i o n w h i c h depends  I n Vacuo".  and t h e s p e c i f i c  a maximum r a t e o f  o n l y on t h e t e m p e r a t u r e of t h e p r o p e r t i e s of the substance.  Numerous methods  6>7  have b e e n  to determine r a t e s o f e v a p o r a t i o n A s u r v e y was made o f t h e s e the  p a p e r "On t h e  a t the f o l l o w i n g fundamental c o n c l u s i o n :  exists  surface  Pressures  system.  and v a p o u r  methods i n o r d e r  one most s u i t a b l e f o r m a k i n g  copper-manganese  devised  pressures. t o choose  determinations  O n l y t h e K n u d s e n and  methods c o u l d be c o n s i d e r e d  i n order  because  t h e method  i n the Langmuir  chosen  -7 had  t o be c a p a b l e  of measuring pressures  a s low a s 10  atmospheres. 8 I n 1 9 0 9 , Knudsen pressure  effusing  i n t o vacuum f r o m a r e l a t i v e l y  i n a closed vessel.  Equation  that the vapour  o f a m a t e r i a l was p r o p o r t i o n a l t o t h e amount  of vapour hole  showed  His formula  i s g i v e n by  2, b e l o w  P where P  small  i s the vapour pressure  the w e i g h t  (2) i n dynes  p e r cm , n r i s  i n grams o f m a t e r i a l o f m o l e c u l a r  w e i g h t , M,  w h i c h e f f u s e s p e r second  from  each  E q u i l i b r i u m must e x i s t b e t w e e n the c e l l .  Also,  molecules (greater Kinetic  the r a t i o  to the diameter  of o r i f i c e  the s o l i d  area.  and v a p o u r  o f t h e mean f r e e of the o r i f i c e  t h a n 1 0 ) ^ . The d e r i v a t i o n Theory  cm  within  p a t h o f the gas  must be  large  of E q u a t i o n 2 from the  o f G a s e s i s g i v e n i n A p p e n d i x B. 1 0  , In 1 9 1 3 , determined  Langmuir  sure of tungsten by weighing dimensions sured  a tungsten filament  p  =  m » /2TTRT « ~i M  i s the weight  ( 3 )  i n grams o f s u b s t a n c e from  second  and (X i s t h e c o n d e n s a t i o n  sation  coefficient  one c m  2  of molecular  of surface per  coefficient.  i s d e f i n e d as t h e r a t i o  The c o n d e n -  of the observed  o f e v a p o r a t i o n i n t o vacuum t o t h e maximum r a t e d e s -  cribed  by Herz.  significance cules  o f known  Langmuir*s e q u a t i o n i s g i v e n below  weight, M > which evaporates  rate  pres-  b e f o r e and a f t e r h e a t i n g I t i n vacuum f o r mea-  l e n g t h s o f time.  where  the vapour  The c o e f f i c i e n t  since  i t shows t h a t  which s t r i k e  has d i r e c t  of a l l the vapour  the s u r f a c e of the condensate,  f r a c t i o n , CX > a c t u a l l y  c o n d e n s e . The r a t e  is  the vapour  therefore less  which have  than  condensation  The condensation  kinetic  most  coefficients  consists  only a  of evaporation  pressure f o r substances  s e n s i t i v e method  coefficient  mole-  less  than one.  o f determining the  of comparing  the rate  6 at which  saturated metal vapour e f f u s e s through  w i t h the r a t e a t which the m e t a l  an o r i f i c e  surface evaporates  into  t h e L a n g m u i r and K n u d s e n methods h a v e  been  9 vacuum,  a s shown b y E q u a t i o n i^..  vn' Both used  / 2.TFRT V M  b y 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 b o t h  liquids  g and  solids.  A c c o r d i n g t o S p e i s e r and J o h n s o n ,  m u i r method  c a n be used  t o measure v a p o u r p r e s s u r e s  are a factor- of 1 0 ^ t o 1(A lower by  t h e Knudsen method.  the Lang-  than those  that  measurable  However, b o t h Hersh"''^,  in his  12  study  of copper,  of z i n c ,  stated  preference they  and M c K i n l e y  and Vance  t h a t they chose  , i n their  t h e Knudsen method i n  t o t h e L a n g m u i r method b e c a u s e i n t h i s way  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  coefficient. No m e n t i o n i s made i n t h e l i t e r a t u r e condensation this  coefficient  o f the  o f manganese, a n d , s h o u l d  v a l u e be known, one would h a v e t o make t h e v e r y  tenuous assumption addition  this  chosen  t h a t i t d i d n o t change w i t h t h e  o f a second  t h e L a n g m u i r method For  study  reason,  component-,, i f one c o n s i d e r e d u s i n g t o s t u d y t h e copper-manganese  system.  then,- t h e Knudsen e f f u s i o n method was  i n p r e f e r e n c e t o t h e L a n g m u i r method.  The of  rate  of e f f u s i o n c a n  s e v e r a l m e t h o d s , some b a s e d  d i r e c t l y , - and  others  amount  of m a t e r i a l  period  of  based  measured by  on m e a s u r i n g  the  on m e a s u r i n g the  w h i c h has  t i m e . The  be  simpler  effused of  one  rate  total  during  a  given  t h e s e methods  include Iii  weighing the and,  effusion c e l l  collecting  the  before  effused  and  v a p o u r on  a f t e r a run a cooled  ,  target.  15" The  v a p o u r on  the t a r g e t 16  radiochemically. m e a s u r i n g the in  an  alloy  The  can  be  latter  vapour pressure  s y s t e m and  was  weighed technique  of  only  o r measured is ideal  one  for  constituent  chosen f o r t h i s  investi-  gation. A K n u d s e n e f f u s i o n a p p a r a t u s was and  built  such that  which effused collector  the  f r o m the  disc.  The  designed  amount o f r a d i o a c t i v e manganese cell  was  c o l l e c t e d on  r a d i o a c t i v i t y of  measured w i t h a p r o p o r t i o n a l  counter.  the  a  disc  cooled was  8 II.  Experimental  Design of Apparatus Knudsen e f f u s i o n 1.00  inches.in  rod.  cells,  1.12$  d i a m e t e r were m a c h i n e d  T h i s m a t e r i a l was  inches high  and  f r o m molybdenum i I t has a  chosen because  low  17 ' and b e c a u s e no r e a c t i o n was  observed  b e t w e e n i t and m o l t e n manganese b y a p r e v i o u s  investi-  vapour pressure  ng  gator. cell  Two  to house 2.  Figure cell  the measuring  making  a stand  negligible  because  t e n t l y r o u n d , and was  p r e p a r e d by  rested  B.  inch  the convex  extrusion  T h i s method  and  was  consisThe  c l a m p i n g t h e molybdenum  not produced  reproducible  plate  t h e r e f o r e were n o t r e p r o d u c i b l e .  edged  was  .003  t h e h o l e s p r o d u c e d were n o t  aluminum p l a t e s  plates  plate.  i n Appendix  produced.  s h e e t b e t w e e n two  was  the t o p of t h e  dimpling  then p o l i s h i n g  f i n a l l y made by  orifice  into  f o r the c o l l i m a t o r  a k n i f e - e d g e d h o l e was  orifice  of the  t h e r m o c o u p l e s as shown i n  t h i c k n e s s , as d i s c u s s e d  molybdenum s h e e t and  discarded  the b o t t o m  Knudsen f o r m u l a assumes an o r i f i c e  O r i f i c e s were f i r s t  until  into  T h r e e r o d s were screwed  The of  h o l e s were d r i l l e d  of l i t t l e  and  drilling.  i n t h i s way consequence.  on t h e t o p o f t h e c e l l  A  knife  but the  error  The  orifice  i n a shallow  9  Kanthai strip  ^.Collimator plate  rad i a t i o n . shields  Orifice plate  Knudsen cell  0  furnace  Scale:  Figure  2X  2. D i a g r a m  ti  ^-thermocouple thermocouple  of, F u r n a c e and  Cell  #1 #2  Arrangement  1 0  d e p r e s s i o n as orifice  p l a t e was The  two  measured  cell  thermocouples.  against  the m e l t i n g  and were f o u n d  2  shown i n F i g u r e  3  +  1°C.  was  stationed  The  t h e r m o c o u p l e s had  point  of f o u r - n i n e s  thermocouples  S i n c e thermocouple and  the c e l l .  pure  was  3 3 8 7 B )  # 1 was  Thermocouple  the  surface  t o r e a d low b e c a u s e  thermocouple  itself.  # 2 ,  best  aluminum  0 . 1 ° C .  used. During  close  f u r n a c e was  wound w i t h K a n t h a l s t r i p  surface, temperature  on t h e o t h e r h a n d ,  ( t h e b o t t o m ) and  would  A temperature  o f one  # 1 was  machined  o f 2 f ? ohm  the  resistance. is easily  before  i t i s baked.  1 2 0 0 ° C ,  A f t e r baking at has  shown mounted  usually  on a s t e e l p l a t f o r m  took about  temperature  to  two h o u r s  85>0°C.  chosen  as  cell.  and  Lava machined  i t is  a low v a p o u r p r e s s u r e m a k i n g 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 is  degree  from l a v a b l o c k  a h y d r a t e d aluminum s i l i c a t e ,  and  be  o f c o n d u c t i o n o f h e a t away  block,  hard,, b r i t t l e ,  of  to the  e s t i m a t e of the temperature w i t h i n  The  the  checked  showed a d i f f e r e n c e  lower than t h a t measured.by thermocouple the  been  f a r f r o m any r a d i a t i n g  near a r a d i a t i n g  expected by  i n t h e f u r n a c e on  r e a d , i f a n y t h i n g , h i g h e r than the a c t u a l  within was  d i a m e t e r of the  t o be a c c u r a t e t o w i t h i n +  furnace windings it  The  microscopically.  A T i n s l e y p o t e n t i o m e t e r (Type a r u n , t h e two  .  to r a i s e  A slow i n i t i a l  furnace  i n Figure  assembly 3 - It  the f u r n a c e rate  of  increase  F i g u r e I ) . . Complete  Knudsen  Assembly  12 of  t e m p e r a t u r e was  n e c e s s a r y t o e n a b l e ' t h e vacuum  to  outgas the a p p a r a t u s . The f u r n a c e t e m p e r a t u r e was  chrome1-alumel t h e r m o c o u p l e Minneapolis Honeywell trolling  c y c l e was  w i t h i n the  controlled  by  a  i n conjunction with a  c o n t r o l l e r . The  on, 3/k-on  n o t d e t e c t a b l e by t h e  con-  thermocouples  cell. Heat  l o s s e s by r a d i a t i o n f r o m  were k e p t t o a minimum by u s i n g d r i c a l molybdenum r a d i a t i o n were trimmed to  system  two  concentric  shields.  near the top to a l l o w  the f u r n a c e  These  cylin-  shields  the e f f u s e d  manganese  escape. 2 and  T h r e e r o d s , as seen I n F i g u r e s were screwed  i n t o t h e t o p o f the K n u d s e n c e l l ,  a stand f o r the c o l l i m a t o r p l a t e . e f f u s e d m a t e r i a l ^ , w h i c h was from the geometry dimensions  o f the c e l l s The  furnace  water  to h o u s e  F i g u r e k.  The  d i a m e t e r and  0.125  c o l l e c t e d , was  arrangement.  The  cooled  platform built discs  o f the  actual 1.  above t h e  i s shown i n  were aluminum, 1.5  Inches  making  computed  used a r e g i v e n i n T a b l e  the c o l l e c t i o n  discs  A disc so t h a t  of t h i s  The f r a c t i o n  3,  inches i n  thick.  c h a n g e r was  built  s e v e r a l measurements c o u l d  into  the a p p a r a t u s  be made w i t h o u t  1.  Table Collimating  G e o m e t r y of. C e l l s Cell  Collimator  having  Plate  Diameter  0.251  #1  Cell  in.  0.251  0.765 i n . 0.769 i n .  io V a p o u r  9.72$  Collected  to stop  connected  the experiment.  t o the d i s c h a r g e r .  eject  9.38$  A b r a s s r o d was f i t t e d  Knudsen c e l l  inch brass plate  pyrex b e l l The  the rod,  and a f r e s h  above t h e c e l l  of the d i s c  s e a l , and one  one would  and  collimator.  c h a n g e r a r e shown I n  $. The  3/k  directly  two p o s i t i o n s  Figure  By r o t a t i n g  the c o l l e c t i n g d i s c  drop i n t o place The  in.  Orifice to Collimator Distance  through the brass base-plate w i t h a Wilson  could  #2.  bell  a s s e m b l y was b u i l t  w h i c h made a s u i t a b l e  j a r 8^- I n c h e s  base f o r a  i n d i a m e t e r and 15  j a r was p o s i t i o n e d  on a O - r i n g  on a  inches  located  high.  ina  groove i n the p l a t e . A  1.5  inch hole  i n the centre t o the l i q u i d  of the plate  was  connected, by O-ring,  was  i n s e r i e s w i t h t h e o i l d i f f u s i o n pump  and  t h e Duo S e a l  vacuum f o r e  pump. A  a i r trap (type  which  VMF-10)  thermocouple  vacuum gauge and a n i o n i z a t i o n  gauge were a l s o  t o t h e b o t t o m o f t h e p l a t e . A second was f i t t e d pumps. and,  into  thermocouple  the l i n e between the d i f f u s i o n  Pressures  o f 2 x 10"^ mm  during experimental  runs,  attached gauge  and  Hg were r e a d i l y  fore  obtained,  p r e s s u r e s a s low as  -6 2 x 10  mm  Hg were o f t e n a t t a i n e d w i t h o u t  using  liquid  air. The couples  furnace  entered  bus b a r s  and t h e f o u r t h e r m o -  the system by g l a s s - t o - m e t a l s e a l s .  T h e s e s e a l s were s o l d e r e d t o a 3 / l 6 I n c h b r a s s w h i c h was  sealed t o the main b r a s s  p l a t e by an 0 - r i n g .  A g e n e r a l view o f the complete shown i n F i g u r e  plate  apparatus i s  6.  M a t e r i a l s and T h e i r P r e p a r a t i o n The Reagent M e t a l impurities and  copper  available  o f 99.7$ p u r i t y .  f o r this The m a j o r  g i v e n by the F i s h e r a n a l y s i s  t i n (.01$ t o t a l ) , The  lead  metallic are antimony  (.002^$),- and i r o n  n o n - r a d i o a c t i v e manganese was  pure,, e l e c t r o l y t i c  manganese d o n a t e d  manganese C o r p o r a t i o n o f A m e r i c a . form  work was F i s h e r  of e l e c t r o l y t i c  (.002$). 99-9$  by the E l e c t r o -  T h i s m e t a l was  i n the  chips.  $k One m i l l i c u r i e in  5 > m l o f HC1  (pHf?) was  of c a r r i e r obtained  f r e e Mn ^ as  from  the Nuclear  MnC^  16  Figure  Science life  6. G e n e r a l  and E n g i n e e r i n g  View of Apparatus  Corporation.  Mn  o f 300 days and d e c a y s by K c a p t u r e  gamma r a d i a t i o n .  The l o n g h a l f  isotope  o f manganese  project  as opposed  w h i c h has a h a l f The experimental  and  makes  i d e a l f o r a long-term  ,8k  this  Mev. radio-  research  t o t h e r a d i o i s o t o p e o f c o p p e r , Cu^",  life  of o n l y  preparation  12.8  hours.  o f t a g g e d manganese f o r  p u r p o s e s was a t t e m p t e d  electrodeposition, evaporation.  life  has a h a l f  i n t h r e e ways: by  b y i s o t o p i c e x c h a n g e and b y  O n l y t h e l a s t method was r e a l l y  successful.  This the  involved surface  simply  of the pure The  RA81j. t y p e  evaporating  prepared  crucible,  ment.  T h i s apparatus  Figure  7.  Melting  s o l u t i o n on  H  i n a c t i v e manganese chips  chips.  were b r o k e n i n t o a N o r t o n  w h i c h was,  l|r i n c h d i a m e t e r v y c o r  t h e Mn  i n turn, placed  i n s i d e the  tube i n d u c t i o n f u r n a c e i s shown  took p l a c e  arrange-  schematically i n In a purified-^argon  a t m o s p h e r e . The manganese was v i g o r o u s l y mixed h a l f minute by the i n d u c t i o n c u r r e n t s . course,  be assumed t h a t no s e g r e g a t i o n  for a  I t can, of o f the r a d i o a c t i v e  manganese i n t h e i n a c t i v e manganese t o o k p l a c e  during  solidification.  About  12 grams o f manganese  containing  0.3  $k millicurie  Mn  were p r e p a r e d  f o r experimental  use. I f  more i n a c t i v e manganese had b e e n u s e d , t h e s p e c i f i c activity  of the r e s u l t i n g  t a g g e d manganese would  b e e n t o o l o w ^ and e f f u s i o n r u n s t a k i n g would h a v e b e e n n e c e s s a r y . subsequently was  used  Since  t o make a l l o y s ,  longer  times  t h i s manganese at least  have  was  12 grams  necessary. Because, d u r i n g m e l t i n g ,  the manganese was  lost  a l a r g e amount o f  to the c r u c i b l e ,  first  thought  large  amounts o f S i 0 2 f r o m t h e c r u c i b l e .  analysis Silica  t h a t t h e manganese c o u l d  i t was a t  on n o n - a c t i v e  was f o u n d  melts  i n manganese  showed  also dissolve Chemical  that only  0.$%  t h a t had r e m a i n e d  molten  18  purified argon  vacuum pump  manometer  aluminum mirror.  vycor  alundum crucible  Figure  7. Schematic :  tube  induction  Diagram  of Melting  coil  Apparatus  for be  a period expected  o f s e v e r a l minutes. i n the a c t u a l melt  was h e l d m o l t e n  Much l e s s  S i O ^ would  containing Mn^  f o r only a half  minute.  S i n c e o n l y t w e l v e grams o f tagged was p r e p a r e d , much more used, The  a l l t h e manganese would be a b s o r b e d  showed  that  examination  the a l l o y s  c r u c i b l e s were homogenous. the e x p e r i m e n t a l a l l o y s during  Possible  would  t h e 2l|-hour p e r i o d  temperatures  to  Inhomogeneiti'es i n  The e x p e r i m e n t a l b e l o w the m e l t i n g  a t 35$ Mn c o m p o s i t i o n . a t e s t f o r the c o n t i n u e d homogeneity o f  samples,  evaporate  a n o n - r a d i o a c t i v e $0-$0 a l l o y was a l l o w e d  i n the Knudsen c e l l u n t i l  10$ o f t h e  The r e m a i n i n g  shown t o be homogeneous b y m i c r o s c o p i c The  by  molybdenum  g i v e n f o r the Knudsen c e l l to  manganese was l o s t b y e f f u s i o n . was  I n these  d i s a p p e a r due t o d i f f u s i o n  were o n l y a f e w d e g r e e s  As alloy  molybdenum-  of the Inactive  prepared  reach e q u i l i b r i u m a t temperature.  point  by the c r u c i b l e .  crucibles. Microscopic  alloys  of not  t h e RA81| c r u c i b l e s be  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  sheet  manganese  i t was n e c e s s a r y t o make a l l o y s  t h a n two g r a m s . S h o u l d  which  compositions  standard e l e c t r o l y t i c  of the alloys  alloy  examination. were  a n a l y s i s f o r copper.  checked The  values from  obtained agreed  the weights  w i t h the compositions  of the m a t e r i a l s used.  Radioactivity  Measurements  A p r o p o r t i o n a l c o u n t e r was used r a d i o a c t i v i t y measurements. found  t o be i n t h e m i d d l e  vs v o l t s ) count  plateau.  was  sensitivity  series  ( T l ^ ^ + ) was  n o t known, no  correlation  existed  dissolved  to a large  Small pipetted  after  drops,  The  many s m a l l s p o t s on i t ,  is  t h e amount o f determined  HC1  and  tagged  the  solution  volume w i t h warm d i s t i l l e d s o l u t i o n were identical  s o l u t i o n was  so t h a t when d r i e d ,  t h a t produced  e m i t t e d by M n ^  sample o f t h e  in a little  volumes o f t h i s  shown i n F i g u r e 10.  of the p r o p o r t i o n a l  between t h e r a d i o -  on t h e s u r f a c e s o f a l u m i n u m d i s c s ,  little  minute,-  T h i s r e l a t i o n was  A c a r e f u l l y weighed  was  diluted  set to  Back-  measured b e f o r e and  b y t h e c o u n t e r and  i n the sample.  as f o l l o w s : manganese  + 1 counts p e r  the r a d i a t i o n s  c o u n t measured  manganese  as  c o n t r o l was  the exact e f f i c i e n c y  counter f o r measuring  active  was  o f measurements.  Since  was  potential  of the (counts p e r minute  a t 13  consistent  a standard  each  The  A 2200 v o l t  for a l l  a l l p u l s e s g r e a t e r t h a n one m i l l i v o l t .  ground and  calculated  a l l within  by the c o l l l m a t e d  water.  evaporated t o t h e one  evaporated i n  t h e aluminum had an a r e a t h e same beam f r o m  size  the Knudsen  21  600-  0  .1 Weight  Figure  Manganese  .2 ( i n grams)  8. Graph, R e l a t i n g Weight, o f Manganese,; a n d A c t i v i t y of, of D i s c . ( J u l y 26, 1957)  cell.  The r a d l p a c t l y l t e s  b y t h e c o u n t e r and related figure  the r e s u l t i n g  to the weight was  s u b s e q u e n t l y used to c o r r e l a t e  the w e i g h t  of vapour Errors  collected  due  a 50-f?0 chance  1^,000 that  1^,000 + ^ 15,000  decrease  discs  the  This  of the d i s c s  small.  counts i n  and  disc.  to the s t a t i s t i c a l nature of  radio-  I f , f o r example,* a  30  in  30  minutes  i s i|87  or  minutes,, t h e r e i s  i f more t h a n one  £00 +k  o f 13  +•• i f .  Considerations i s j v l $ .  The  used.  counts  + 1,  the  e r r o r due  This  d i s c were u s e d  d u r i n g a r u n , s u c h t h a t an a v e r a g e c o u l d be  8.  t h e t r u e mean c o u n t i s  c o u n t o f the s p e c i m e n  vapour  by  C o n s i d e r i n g a background  statistical  was  f o r a l l e x p e r i m e n t a l mea-  the a c t i v i t i e s  a c t i v i t y measurements a r e sample m e a s u r e s  number o f c o u n t s  o f manganese as i n F i g u r e  surements,  minute.  o f t h e s e d i s c s were measured  error to of  per  actual to would  collect several  23 III.  Discussion  Reproducibility The for  of Results  paper.  reproducible observed  o f manganese, v a p o u r .  with time, that  i n the f i r s t  quarter  c o l l e c t e d I n t h e second  from copper, s i l v e r , results.  v a p o u r was g r e a t e r  Is,, t h e manganese  h o u r was o n l y a b o u t  quarter  hour. Discs  made  that the  o f manganese f o r manganese,  than that  of the other  even the s m a l l e s t  g a n e s e was a t l e a s t a h u n d r e d v a p o u r was c o l l e c t i n g  metals f o r  collection  on a manganese  with d i s t i l l e d  experimental run.  surface  prepared by  9 shows t h a t  spots  discs  o f manganese a l r e a d y  of effused  each  the rate of  o f manganese b y t h e s e p r e p a r e d  collimated  f o r most  i n a c t i v e manganese b e f o r e  Figure  d e p e n d e n t on t h e amount  o f man-  atoms t h i c k , manganese  o f e a c h r u n . The d i s c s were t h e r e f o r e  The  half  vapour.  Since  collection  I t was  and molybdenum g a v e no b e t t e r  accommodation c o e f f i c i e n t  coating  metal-  collected per unit  Prom t h e s e r e s u l t s I t a p p e a r e d  manganese  prepared  p o l i s h i n g w i t h #2  t h e amount o f manganese  t i m e was n o t l i n e a r Collected  Pure Manganese  T h e s e d i s c s , , however,, d i d n o t g i v e  collection  that  using  a l u m i n u m d i s c s were i n i t i a l l y  e x p e r i m e n t a l u s e b y .simply  lographic  that  of Results  i s not  Collected.  manganese were  sharp  2k  500  lj.00 Cqunts per Minute  300  200  100  0  1  2 Time  Figure  3  (hours)  9., G r a p h R e l a t i n g ' A c t i v i t y o f D i s c o f E f f u s i o n a t 8l86(5~  and  L e n g t h o f Time  "—  25  Figure  and  clear  collection  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 Manganese S p o t on I n a c t i v e Manganese Base"*  and  disc If  of  manganese  negligible samples. X rays hundred  often is  showed  shown i n F i g u r e  Figure is  interference  9 shows  constant,  it  self-absorbtlon No a p p r e c i a b l e  would be atoms  of  expected  of  A  10.  that  the  also  shows  rate  of  by  of  a layer  of  that  r a d i a t i o n by  absorbtlon  manganese.  patterns.  collection there  the  $ rays only a  is  thicker and few  26 One librium  sizes  effect  of the  on  was  effect  twelve  due  times  to the  t o t h e +••$% e r r o r  of t h i s  size  used  II.  The  i n the  largest  cell. runs  area  smallest.  Any  of the  orifice  size  is negligible this  the  orifice  size  from  orifice  experimental  the  expected  equi-  o f the  the e q u i l i b r i u m w i t h i n  orifices  are t a b u l a t e d i n Table used  requirements  t y p e measurement i s t h a t t h e  s h a l l h a v e no The  o f the b a s i c  type  compared  o f me a s u r e -  9  ment.  Table I I . Table  Temp  o f V a p o u r P r e s s u r e D a t a f o r Pure  (°C)  Orifice (cm ) 2  Area  Manganese  Vapour Pressure (at)  Log V a p o u r Pressure  818  .0668  3.15  x  io"  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  -  6.31  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  io"  - 6.05  7  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  manganese.  were c a l c u l a t e d  average  These r e s u l t s  a c t i v i t y of a s e r i e s  as shown i n F i g u r e 9. Collected  was  determined  A sample c a l c u l a t i o n vapour  p r e s s u r e has  temperature  according from  heat  from  the  of from  weight  two  the  to f i v e  discs  o f t h e manganese  b y m a k i n g use  been p l o t t e d  pure  from  8.  of F i g u r e  i s made i n A p p e n d i x C. against  The  log  reciprocal  11.  i n Figure  The determined  The  pressures of  o f s u b l i m a t i o n o f manganese I s 11  s l o p e o f the c u r v e I n F i g u r e  t o E q u a t i o n A-2.  t h e above r e s u l t s  was  AH  The  T  values obtained  much h i g h e r t h a n  the  values  18 reported  by K e l l y  and  McCabe,  c a l o r i e s p e r mole compared per mole.  The  The  i n experiments  range  and  present results  the  low,  factor  investigators  extending over a  are based  large  on measurements made  range.  I t was  Impossible  t h e p r e s e n t measurements t o l o w e r  because too  these  calories  are considered quite r e l i a b l e .  a v e r y s m a l l temperature extend  i s , 89,000  t o t h e i r 67,000  v a l u e s r e p o r t e d by  were d e t e r m i n e d temperature  that  c o u l d be  I n c r e a s e d b y no more  of f i v e w i t h a v a i l a b l e In  than  much  a  Mn^+.  o r d e r t o r a t i o n a l i z e the e x i s t i n g  crepancy, a thorough  to  temperatures  s p e c i f i c a c t i v i t y o f t h e manganese was  and  over  examination  dis-  o f our t e c h n i q u e  was  28  -5.8:  1  .895  1  1  .900  .905 1  Figure  11.  •  x  .910  —*  .915  10 3  Graph R e l a t i n g the Log Vapour Pure Manganese, and R e c i p r o c a l  Pressure of Temperature  -920  29  made. was  The p o s s i b i l i t y  eliminated  geometry of  temperature  measurement  b y c h e c k i n g t h e p o t e n t i o m e t e r and a d d i n g  a new t h e r m o c o u p l e . corroborated  of f a u l t y  I n b o t h c a s e s , new m e a s u r e m e n t s  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  change a p p r e c i a b l y w i t h t e m p e r a t u r e ,  the c o l l i m a t e d  s p o t would  also  change.  the size  This did not  occur.  The investigation  e x p l a n a t i o n f o r the r e s u l t s  c a n p r o b a b l y be f o u n d a s s o c i a t e d  change w i t h t e m p e r a t u r e of  the c o l l e c t i n g  temperatures  ation coefficient  of  collected  the vapour  and,  during  consists  It. a p p e a r s  Condenses than  that  from  could  the weight o f  u s i n g E q u a t i o n B-$ w i t h t h e w e i g h t  lost.  long  o f c h e c k i n g t h e accommod-  o f comparing  The Knudsen c e l l  weighed  125"  e f f u s i o n runs,, a maximum o f 5  grams o f manganese was l o s t . weight  coefficient  temperatures. A p o s s i b l e method  vapour  with a  o f t h e manganese s t r i k i n g t h e  lower c e l l  higher c e l l  o f the accommodation  p l a t e f o r the vapour.  a smaller percentage d i s c s from  of this  Small variations  n o t be d e t e c t e d b y w e i g h i n g  grams,  millii n this  the c e l l  b e f o r e and a f t e r a r u n . In  o r d e r t o measure t h e v a p o u r  manganese above t h e a l l o y s ,  the a s s u m p t i o n  made t h a t  coefficient  t h e accommodation  pressure of h a s t o be  changes  only  v  w i t h the temperature o f the c e l l . erature,  the vapour  a factor  at  that  f r o m one,  Alloys  (t) Pt  o f Copper Seven  prepared  Is g i v e n  into  and  alloys  f o r this  by  o f t h e a l l o y measured  by  (5)  Manganese  o f c o p p e r and manganese were  investigation.  the c e l l  when the m e t a l was  i s i n error  B,  F  =  temp-  the accommodation c o e f f i c i e n t i s then the a c t i v i t y  temperature  a  placed  p r e s s u r e o f the c e l l  because  different  I f , at a given  The  alloys  as t u r n i n g s w h i c h were  drilled  were produced  o u t o f t h e molybdenum  crucibles. E x p e r i m e n t a l r e s u l t s f o r the v a p o u r p r e s s u r e o f manganese above t h e a l l o y s , are  given  i n A p p e n d i x .D.  were p e r f o r m e d life The  as  before,  S i n c e t h e s e measurements  over a p e r i o d  o f s e v e r a l months  c o r r e c t i o n s were n e c e s s a r y and h a v e b e e n  half made.  l o g vapour p r e s s u r e v a l u e s f o r each a l l o y are  plotted The  calculated  against reciprocal  straight  points  temperature  i n Figure  12.  l i n e s drawn t h r o u g h t h e e x p e r i m e n t a l  are used  f o r a l l subsequent  Little  significance  o b t a i n e d f r o m t h e 11$  calculations.  i s placed  manganese a l l o y .  on v a l u e s The; c o l l e c t i o n  31  Figure  12. : Graph, R e l a t i n g l o g V a p c u r P r e s s u r e o f Manganese o v e r 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  spotty suggesting  manganese v a p o u r was The were d e t e r m i n e d plotted and  that only a f r a c t i o n  collected.  activities  o f manganese  according  to Equation  i n the a l l o y s 1 and a r e shown  i n F i g u r e s 13 and l k f o r t e m p e r a t u r e s  8kk C r e s p e c t i v e l y .  Pure  state.  been c a l c u l a t e d  u s i n g t h e G-ibbs-Duhem  The a c t i v i t i e s  ( E q u a t i o n A-9) and a r e a l s o p l o t t e d Manganese  law. o v e r  shows a p o s i t i v e  the e n t i r e  composition  o t h e r h a n d , shows a s l i g h t Raoult's  s t r o n g l y i n the p o s i t i v e  chosen  of copper  have  Equation  i n F i g u r e s 13 and  d e v i a t i o n from range;  Raoult's  C o p p e r , on t h e  negative departure  law a t h i g h copper  o f 820°C  (3-manganese was  as t h e s t a n d a r d  lk.  of t h e  from  content but deviates  direction  a t low c o p p e r  com-  position.  The rich  behaviour  s o l u t i o n s Is s i m i l a r  rounding  copper  manganese  rich  o f manganese atoms i n c o p p e r to the behaviour  atoms w h i l e  the behaviour  of the suro f Copper i n  solutions i s quite different.  There i s  a s t r o n g r e p u l s i v e f o r c e b e t w e e n t h e two c o n s t i t u e n t s at  these  latter  compositions.  there i s a g r e a t e r tendency W i t h manganese atoms a l s o  At intermediate  f o r manganese  atoms t h a n w i t h c o p p e r  compositions,  atoms t o g r o u p  atoms. The  showa g r e a t e r a f f i n i t y f o r manganese  than f o r copper  atoms.  copper atoms  33  3k  20  kO Mole %  Figure  60  80  100  Mn  l k . , The. A c t i v i t i e s . . o f C o p p e r and. Manganese, i n . Cu-Mn A l l o y s a t 8 k k C u  The  free  energy  and  manganese h a v e b e e n c a l c u l a t e d  and  the a c t i v i t i e s  values  a r e g i v e n i n A p p e n d i x D.  15"  and  p o i n t s based  directly  At  The  are p l o t t e d  a t 820°C and  1 6  using Equation  shown i n F i g u r e s 1 3 and  m i x i n g f o r the a l l o y s Figures  changes f o r b o t h  free  0  energy  energies of  8kk°C  respectively.  The  below the m e l t i n g p o i n t , energy  the ,  curve  o f t h e m e l t i n g p o i n t minimum o f  copper-manganese s y s t e m free  The  on e x p e r i m e n t a l d a t a a r e m a r k e d .  8kk°C, 2 k  to that  A-10  against composition i n  c o m p o s i t i o n , o f t h e minimum o f t h e f r e e corresponds  lk.  of mixing  copper  (Figure  1 ) , as  expected.  i s l e s s n e g a t i v e a t the  the  The  lower  temperature,. 8 2 0 ° C , f o r c o n c e n t r a t i o n s o f manganese g r e a t e r t h a n 20$.  B e l o w 20$,. b o t h f r e e  curves f o l l o w quite on  i d e a l mixing.  configurations this  both  copper  and  Myers  and  lk.  A p p e n d i x D,  that  energy the  of  mixing  curve  based  electronic  manganese were  similar in  range.  excess  free  energy  changes f o r  manganese a t 820°C have b e e n  u s i n g E q u a t i o n A - l l and 13  the f r e e  suggested  o f C o p p e r and  composition  The  closely,  energy  the a c t i v i t i e s  calculated  shown i n F i g u r e s  T h e s e e x c e s s v a l u e s have b e e n t a b u l a t e d I n and  in Figure 1 7 •  are The  shown p l o t t e d , a g a i n s t c o m p o s i t i o n excess f r e e  shows a minimum a t a b o u t  35$  energy  curve f o r  manganese. Here  the  copper copper  36  -200  -kOO  ra © •H o I-l  erf o  -6oo  <D b0  erf ,3 o l>»  -800  bO <D  a  (D CD  -1000  -1200  -IkOO  40 Mole % Figure  60  80  Mn  15>. The, F r e e E n e r g y , o f M i x i n g o f Cu-Mn A l l o y s , a t,  37  -lkOO  20  kO Mole $  F i g u r e , 16.  60  80  10.0*  Mn  The F r e e E n e r g y o f M i x i n g  o f Cu^Mn A l l o y s  at ,  38  Jo  20  ~3o to Mole %  $5  So  70  ~#o  $0 100  Mn  F j g u r e 17..The E x c e s s , F r e e Energy,Change• f o r , 0 o p p e r Manganese i n Cu-Kn A l l o y s a t 820°C :  and  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 Myers  suggested  range a t which  t h a t t h e 3d e l e c t r o n s o f c o p p e r  g a n e s e had f o r m e d greatest  the composition  a common b a n d . The manganese  departure  from  i d e a l behaviour  and manshows i t s  at this  composi-  tion. 19 Wagner can  calculated  has d e r i v e d formulae  p a r t i a l m o l a l excess  the Cu-Mn p h a s e d i a g r a m . (Appendix results excess  energy  937°C was f o u n d  from  i s based  accuracy  than t h i s  could have a v e r y  r  culated  from  concerned.  and f r e e  Should  energy  pressure  the curve  be i n e r r o r b y  However, a s i m i l a r  large effect  e n t h a l p y and e n t r o p y ,  of the c a l -  of the vapour  t h e a c t i v i t y would amount.  The  equation.  on t h e a c c u r a c y  i n e r r o r by $%  on  p e r mole was  results.  of the a c t i v i t y  a t t h e temperature  no more  o f 890 c a l o r i e s experimental  o n Wagner's  molal  p e r mole b a s e d  i s good, c o n s i d e r i n g the n a t u r e  The  be  from  I n a 6 5 £ Mn a l l o y a t  t o be 1200 c a l o r i e s  the present  c u l a t i o n based  curve  s o u r c e . The p a r t i a l  o f manganese  Wagner's E q u a t i o n . A v a l u e  values  free energies  E) i n o r d e r t o compare t h e e x p e r i m e n t a l  free  agreement  w h i c h one  A c a l c u l a t i o n was made  w i t h an independent  obtained  from  error  on t h e v a l u e s o f  s i n c e these q u a n t i t i e s  the slope o f the vapour p r e s s u r e  are c a l curve.  In Equation A-12,  f o r example,  t h e change  i n log  p r e s s u r e b e i n g i n e r r o r b y + 5>$ a t 8kk°C and  the vapour  -$% a t 820°C would be . Oijlj., and t h e r e s u l t i n g the p a r t i a l m o l a l heat would be 10,^00  calories  tion  curve i s found  using Equations  f r e e energy  a t about  composi-  35$ manganese and h a s a v a l u e  p e r mole.  of mixing  enthalpy of mixing, to Figure  against  A-12  The maximum o f t h e e n t h a l p y o f m i x i n g  o f 13>000 c a l o r i e s  similar  on o u r e x p e r i m e n t a l  T h e s e v a l u e s have b e e n p l o t t e d  I n F i g u r e 18,  alloy  p e r mole.  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 A-16.  error i n  o f manganese i n t h e g i v e n  E n t h a l p i e s of mixing based  and  due t o  S i n c e the values of the  a r e S m a l l compared  t o those  the entropy of mixing  of the  c u r v e would be  18.  20 21 Recent dynamics o f s o l i d interested  t h e o r e t i c a l papers metallic  size  the p o s i t i v e  i n many s y s t e m s .  energy, which i s u s u a l l y of  s o l u t i o n s have been  i n rationalizing  mixing found  on t h e t h e r m o -  enthalpies of  The c o n c e p t  associated  primarily  of strain  with the d i s p a r i t y  o f t h e two a t o m s , has b e e n i n t r o d u c e d t o e x p l a i n  the l a r g e  e n t h a l p y o f m i x i n g . However,- i n t h i s  there i s l i t t l e  difference  between the s i z e s  system,  of the  22 copper  and manganese a t o m s .  copper  and manganese a r e I . 2 7 6 A and I . 3 6 A  The  large positive  heat  term  Goldschmidt  radii f o r respectively.  i n the copper-manganese  15000 1  Mole % F i g u r e . 18. E n t h a l p y  of Mixing  Mn o f Cu-Mn A l l o y s  a t 820 C  s y s t e m c a n n o t be i n atomic  size  accounted  f o r by  this  small  difference  alone. 23  Mitsua  and  Mlwa  have e x p l a i n e d  the  bond  e n e r g i e s b e t w e e n u n l i k e atoms i n t e r m s o f t h e i r  electro-  n e g a t i v i t i e s . The  values  were n o t copper  appropriate electronegativity  available  and  f o r the  electronic  manganese i n t h e s e  c o r r e l a t i o n was the e l e c t r o n  possible.  composition,  a l l o y s and  and  any  themselves  a l l o y s are  considered of  the  of  alloy  correct,  be  a f u n c t i o n of  argument b a s e d  on  available  view of these  in this  on the the  misleading.  difficulties,  unwise to attempt  data obtained  views  1  will  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 In  t h e r e f o r e , no  Moreover, I f Myers  s t r u c t u r e of these  electronegativities  Configurations of  too d e t a i l e d  then,, i t was a  comparison  work w i t h e x i s t i n g  theories  structure.. In  summary, t h e f o l l o w i n g p o i n t s a r e  con-  sidered p e r t i n e n t . a) Manganese d o e s n o t i d e a l mixing  at  d e v i a t e s t r o n g l y from  low manganese c o n t e n t . Myers h a s  gested  t h a t t h e manganese atoms would behave  to  C o p p e r atoms a t t h e s e  the  b)  similar  compositions.  C o p p e r shows i t s maximum a f f i n i t y  manganese a t a c o m p o s i t i o n  sug-  o f a b o u t 3$%  for  manganese. A t  k3 the  same c o m p o s i t i o n , manganese  positive suggested form  d e v i a t i o n from that  i d e a l behaviour.  t h e 3d e l e c t r o n s o f c o p p e r  a common band  at this  These r e s u l t s interpretation  shows i t s g r e a t e s t  composition  and manganese  range.  appear t o c o r r o b o r a t e Myers'  of the e l e c t r o n i c  copper-manganese  Myers  c o n f i g u r a t i o n s i n the  system.  i  APPENDIX A  Thermodynamic s  Thermodynamics  Q  of V a p o u r - S o l i d  Equilibria  The e q u i l i b r i u m between a m e t a l , and  7  liquid  or s o l i d ,  i t s vapour  M ^—M^ ^  can be e x p r e s s e d  V l  \  v  (A-i)  (vapour)  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 A-2) i f t h e v a p o u r i s a p e r f e c t specific volume  volume  gas and t h e  o f t h e gas i s l a r g e compared  o f the condensed  d  InP  AM  (A-2)  T  RT2  I n E q u a t i o n A-2,. P i s t h e v a p o u r p r e s s u r e a t m o s p h e r e s and  AH  i s the l a t e n t heat  T  T  o  Kelvin.  The l a t e n t  w r i t t e n as a f u n c t i o n o f t h e temperature A-3, i f no t r a n s i t i o n s  to the  phase.  dT-  T'and T  Equation  occur  of the m e t a l i n  of evaporation heat  c a n be  as i n E q u a t i o n  i n the temperature  interval  . AH  T  =  &H '-J ( C p T  T  ( v a p >  - Cf(  t o n J  )) J T  (A-3)  A H j * i s the heat and  C p (vap) and  vapour  Cp(cond)  and c o n d e n s a t e  assumption in  of vaporization  at constant pressure.  interval  and A-3 c a n be combined equations  InP  more  B  -Cp(cond')  T ' and T  to give  I fthe i s constant  , E q u a t i o n s A-2  and i n t e g r a t e d  commonly employed  as a f u n c t i o n  Since the  a r e the s p e c i f i c heats of the  i s made t h a t C p ( v a p )  the temperature  a t t e m p e r a t u r e T' ,  to give the  the vapour pressure  of temperature.  •=-^--BUT-v-C  &loT  U-k)  term i s small,, the e m p i r i c a l f o r m i s  common.  and C a r e c o 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 determined  activity  by E q u a t i o n  o f a component  i n an a l l o y  c a n be  A-6, when t h e v a p o u r o f t h a t  p o n e n t c a n be c o n s i d e r e d  com-  a p e r f e c t gas.3*^-  p; is  the vapour pressure  and  i s the vapour p r e s s u r e  activity  coefficient,  activity  t o mole f r a c t i o n  The  o f component  ^  G i b b s Duhem E q u a t i o n  o f p u r e component A'  , i s defined  allows  of the f i r s t .  The  as t h e r a t i o o f  as i n E q u a t i o n  A~7.  us t o c a l c u l a t e t h e  t h e r m o d y n a m i c p r o p e r t i e s o f t h e second those  /\ i n t h e a l l o y  The f u n d a m e n t a l  component  from  thermodynamic  relation i s  N  A  dG  A  -P N B d & B  where G" r e p r e s e n t s such  as f r e e  any e x t e n s i v e  energy or entropy.  E q u a t i o n A-8 and i n t e g r a t i n g , relating tuents  0  =  the a c t i v i t y  i n the binary  property  o f the s y s t e m  By s u b s t i t u t i n g  we g e t a u s e f u l  coefficients alloy.^  (A-8)  o f t h e two  into  equation consti-  (t - N A )  I n an i d e a l component activity  i s equal  solution  the a c t i v i t y  t o i t s mole f r a c t i o n  coefficients  (A-9)  2 C!MB  ;  are equal  of each  and t h e r e f o r e  t o one. M e t a l l i c  solu-  t i o n s , - however,, g e n e r a l l y d e v i a t e f r o m R a o u l t ' s l a w w h i c h d e f i n e s an i d e a l coefficient activity from  departure absorbed for  i s g r e a t e r than u n i t y , i t i s s a i d  o f t h a t component  Raoult's  activity  s o l u t i o n . When t h e a c t i v i t y  law.  i s usually upon m i x i n g y  each type  shows a p o s i t i v e d e v i a t i o n  A negative  coefficient  i s less found  departure  than  and i s a s s o c i a t e d w i t h a  o f atom t o g r o u p w i t h  When t h e p u r e state,- the f r e e  change f r o m  the pure  when t h e  one. The p o s i t i v e  similar  metal energy state  tendency  atoms'.  show a t e n d e n c y  atom t o g r o u p w i t h an atom o f t h e o t h e r  the  exists  i n systems i n w h i c h h e a t i s  S i m i l a r l y negative departures  standard  that the  f o r an  component  selected  as the  change a s s o c i a t e d w i t h t o the alloyed  state i s  g i v e n by E q u a t i o n A-10.  (A-10)  ^8 where  i s the p a r t i a l m o l a l f r e e  solution  and  The  excess  F^  free  energy  E  in  o f pure  (\ .  change i s d e f i n e d b y E q u a t i o n A•-11.  -  A  (A-ii)  change i n e n t h a l p y ,  and e n t r o p y ,  p o n e n t /\ c a n be d e t e r m i n e d w i t h temperature  of ^  i s the m o l a l f r e e energy  AF =  The  energy  from  the change  according t o Equations  hS* ? 0  of  com-  /\FA  A-12 and A—13.  (A-12)  (A-13)  The  t h r e e thermodynamic p r o p e r t i e s ,  and  entropy are related  The  A  s u b s c r i p t A has denoted  that  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 enthalpy of mixing below f o r a l l o y s  and e n t r o p y  of A  energy,  according to Equation  AF =AH -T&S A  free  and  &  enthalpy,-  A-lij..  < A - * > -  A  the p r o p e r t y i s a energy  of mixing  of mixing, are defined  k9  (A-15) (A-16)  b&m  =  MAASA  -r-M /\S B  B  (A-17)  5o APPENDIX B  9  Derivation  o f Knudsen F o r m u l a  According  to the K i n e t i c  the mass o f v a p o u r , yy^ of  t h e s u r f a c e p e r second  = where  p  =  r  and  T  (B-l)  -  ^  and V  i s the  The i d e a l g a s l a w s t a t e s  (B-2)  L  RT  weight  i s the a b s o l u t e  the g a s c o n s t a n t .  area  pv  i s the m o l e c u l a r  the p r e s s u r e , . T  a unit  i s g i v e n by Equation B - l .  o f t h e atoms.  p  where M  strikes  Is the d e n s i t y of the vapour  mean v e l o c i t y  M  , which  Theory o f Gases,  of the vapour, temperature  The mean v e l o c i t y  V  P is  and  i s related  R  is to  by  TTM  ,  ^  (B-3)  Combining  Equations  B - l , B-2, and B-3 we g e t  51 w h i c h i s the If ered  a point  Knudsen F o r m u l a . the  source,  e f f u s i n g f r o m the the  orifice the  of a K n u d s e n ' c e l l fraction  of  the  c a n be  total  consid-  vapour  Knudsen c e l l w h i c h i s i n t e r c e p t e d  by  target i s :  I T l  (B-5)  TT  0 o X) the  i s the  radius  of the  t a r g e t and C  c o l l i m a t i n g p l a t e f r o m the  iables  are  shown i n F i g u r e  i s the  orifice.  The  distance other  var-  19.  /  I  col\imatbir  \  \ \  \  r \ \  / /  e' /  i^  omice -cell  Figure  19.  Geometry of T a r g e t  and  Orifice  of  In  the  above d i s c u s s i o n we  orifice  plate  orifice  p l a t e has  short  canal.  of n e g l i g i b l e  canal  to e f f u s e  predicted  E q u a t i o n B-k.  B-k  i s used.  that  If  then i t i s i n r e a l i t y  causes a r e l a t i v e l y  of molecules by  thickness  thickness,  The  h a v e assumed  i n the  foreward  For  short  larger  direction canals  an  the a number  than i s  Equation  becomes  (B-6) where  Jt i s the the  t h i c k n e ss o f  the  p l a t e , and  Q.  i s the  radius  of  orifice. The  v a p o u r and The  orifice  appreciably  Knudsen f o r m u l a  condensate w i t h i n must be affect  small the  so  is valid the  cell  that  the  only are  when  in  the  equilibrium.  vapour l o s t  e q u i l i b r i u m . The  effect  is  does  estim-  9  ated  as  follows.  Consider a closed  cell  OC = c o n d e n s a t i o n p vV=  =  true  where:  coefficient  e q u i l i b r i u m vapour  number of m o l e c u l e s surface' per and  unit  pressure  striking  time  a u n i t area  i n a gas  at  of  Pressure  temperature  S = effective  area  of  sample w i t h i n  the  Knudsen  not  cell  VVD( 5  =• number o f m o l e c u l e s w h i c h would unit  will  evaporate  per  open a h o l e o f a r e a , V\ , i n the c e l l , e q u i l i b r i u m be d i s t u r b e d  hole. P  would  time f r o m S  unit we  per  on S  time  !flC<S = number o f m o l e c u l e s w h i c h  If  condense  A  by  the escape  steady state  such that  will  be  of molecules from  established  the  at pressure  t h e number o f m o l e c u l e s e s c a p i n g w i l l  balanced  by  t h e n e t number e v a p o r a t i n g f r o m  The  rate  of e f f u s i o n  but  at pressure  ^  where ti. i s a n a l a g o u s  h'o< 5 -  k. m u l t i p l y both  surface t o lV  ,  P,  nh  Therefore  i a hh  be  s i d e s by  mass o f t h e m o l e c u l e  ^  HO<S  4- oc  \y\  (B-8)  / 2TTRT  where  Vr/  i s the  then: (B-9)  and  p  =  p  when  Experimentally change i n t h e appreciably.  P Jd.  s  i s assumed  t o be  v a l u e does n o t  e q u a l to  change  P  when a  the p r e s s u r e  APPENDIX C  Sample C a l c u l a t i o n  of Vapour  I n t h e Knudsen f o r m u l a defined of  is  ( E q u a t i o n B-k)  as t h e mass o f v a p o u r w h i c h s t r i k e s  surface i n the c e l l  metal  p e r second.  \rf\  a unit  The w e i g h t  v a p o u r i n t e r s e c t e d by a c o l l e c t i o n  related  disc,  is  area  of the (jj  »  t o YT\ b y  (j) = ynntA-f where "t i s t h e e f f u s i o n area  Pressure  i n cm  2  intersected  and  -f  (c-i)  time  i n s e c o n d s , /\ i s t h e o r i f i c e  i s the f r a c t i o n  by the c o l l e c t i n g  o f the e f f u s e d  plate.  The K n u d s e n  vapour Equation  becomes  n  The measured 1957  with  -  ^  / 2TTR.T  n e t r a d i o a c t i v i t i e s " of t h r e e the p r o p o r t i o n a l counter  collection  on S e p t e m b e r  a r e g i v e n b e l o w f o r a r u n a t 828°C u s i n g an  w i t h an a r e a #1  #2  #3  o f .Olkk  (2  cm  hrs)  (1|hrs) ( H i hrs)  7k + 3  cpm  5 5 + 3 cpm  k99 ± 5  cpm  discs, 27,  orifice  55 The  i s k 2 cpm/hr  average value  made 6 3 d a y s a f t e r  T h i s measurement was measured. =  A correction  k 8 . 6  cpm  effusion. the s t a n d a r d  was  of 1 . 1 6 i s necessary.  factor  i s equivalent (Figure  8 )  to  . 0 2 k 8  Fig Mn  1 . 1 6  •f f o r K n u d s e n  cell  is  # 1  CO  (Table  . 0 9 7 2  1)  2TTRT  M 2  . 0 2 k 8  IT  ( 1 . 9 8 7 )  ( k . l 8 6 ) ( 1 0  55  ( 3 6 0 0 ) ( . O l k k ) ( . 0 9 7 2 )  •50k  dynes/cm  2  . 5ok  or 1 3 - 6  log  x  9 8 1  x  Pressure  7 6  (at.)  =  _7 J4..87  -  x  1 0  6 . 3 0  atmospheres  7  )  ( 1 1 1 3 )  I. -p  <  ©  <D  -P  m  bO o O  k  ©  o a ft ra  >  (D  O M © g  i-H^ rH  O  ft .3 • ©  cd  r)  < ©OJ  o •H B <^ o •rl — » r)  o o  Oft © EH  •  •  1  OJ "LO 0  o H  01  vO CO • Ol  o  CO -do  CO !>-=t O •  o  O OJ CO  o  ro • vO  H  IS^o xo «  iH H 7* « • vO  l>-  O Ol  1 O o H rH  X  o  T-O O • vO  o rH  o1  |  OO -=J• vO  r—  o iH  •  C\J ro  O H  «  i  rH  o  i>-  vO  o  Alloys  "LO vO I  1  rH o  X  O  vO  O  CO O O^ vO ro 1A  X  K  -=±  . x O^ vO CO P— "LO H• • "LO CO  I 1  Manganese and  APPEND IX D  OJ • vO  1  o  H  o 1A ro• ro  O  •  o• CO  o• 0•  ro• 1A  vO CO  O  vO  •  o Ol o  vO  •  o OJ o  3 CO  »  ro CO  o OJ o  ro CO  •  CO rH CO  O Ol o  vO  OJ  OJ  o H rH <!  ON T-O  vO ro ro  rH  O  -dT-O "LO  O O  CO CO  O  1A CO  OJ  o  ro CO  CO o OJ  o  OJ o l>- "LO "LO ro  rH  o  OJ  ro CO  o o o  •o  O  1  Pressure Data f o r  o •  vO  O H  o  O•^ OJ  o o  o  rH  o  •  O  vO H O  •  O  CO CO vO  o o CO  ro  ro  X  o PH  |  vO  Vapour  ©  CO CO rH rH CO CO  CO OJ CO  OJ  (3) 1+0.2$  Alloy  10'-7 10'-7  -6.66 -6.39  X  10'-7 10'-7  5.22  X  10'-7  818  .0206  .01^5  2.20  X  82l|.  .0206  .0202  2.81  X  836  .0206  .0288  4.10  X  840  .0206  .0396  4.26  8I4J+  .0206  .0364  (4) 29.7$  -6.56 -6.37 -6.28  Alloy  820  .0206  .0138  1.94  X  827  .0206  .0166  2.33  X  -7 10 10-7  844  -0206  .0309  4.30  X  10-7  -6.37  1.39  X  10-7  -6.86  1.97  X  -6.705  2.98  X  10-7 10-7  1.30  X  (5) 25.9$  Alloy  822  .0206  .0098  831  .0206  .0140  842  .0206  .0213  6) 23.4$  Alloy  818  .0206  .0092  829  .0206  .0105  1.49  X  835  .0206  .0121  1.69  X  841  .0206  .0147  2.09  X  -6.71 -6.63  -6.525  10-7 10-7  -6.91  10-7 10-7  -6.77  -6.83 -6.68  (7)  20.0$  Alloy  82k  .0206  .0080  1.11  x  10~  828  .0206  ,0090  1.26 x  10~  833  .0206  ,0111  1.53  x  10"  8kl  .0206  .0121  1.70  x  -6*77  8k6  .0206  ,0161  2.27  x  10" 10 -7  837  -0206  ,003k  5-2 x 10  -8  •7.30  8k5  .0206  .0037  6.0 x 10  -8  •7.25  -6.95  7  7  •6.90  7  •6.82  7  -6.65  (8) l k $ A l l o y * ™  The  compositions  and  final  to  o f the a l l o y s  a r e average  c o m p o s i t i o n s . The s l i g h t  the loss  o f manganese f r o m  These r e s u l t s  were n o t p l o t t e d  values  o f the  initial  change i n c o m p o s i t i o n was due  the a l l o y s  during  on t h e a c t i v i t y  effusion. curve  >  o o a rt-  H» CD Cb  as a l r e a d y  discussed.  CO  APPENDIX D Thermodynamic A c t i v i t y  H  O  (\| vO  _=f CO O r-i  TA  O I  1A  ro vO vO I  CM O  -=t-  (Continued) o f Mn  from Vapour Pressure  4 lA  Q3 rO  C*S  O rO  TA CO  GO TA  CO  TA rO  C—  CM  C~-  rO  C—  -d" CM  -d- -d-  CM  rO  sO  CM  O  C M r-i  O CM  co  TA  I  I  I  I  o  CM O  CM Ot— CO vO vO I  I  • \& CM  TA CM  TA  CM CO O O vO vO I  \&  CO CM  TA O  vO I  I  o o  \&.  O  CM  vO  CO 7=f  TA  \&  CM  CM  I—I  CO O  CM CO  CM  CM  vO vO  r-i  r—  vO  o IA CM  I  ^  ro  CM  I  I  ^  o o  CM  APPENDIX D ( C o n t i n u e d ) III-. Thermodynamic V a l u e s f r o m 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. p o o ^ i A w . d v \ o o > -a  •>J  So cn O  V . fcv .v 0\ *  *\ *v »v *  ^  CO O ON P-XO _H-sO ON H ON rO-drOJ <—i rH H  CO^-HlAO 1SO\OC\J -d>o cvi ro-sOMD CM _d-_d-_dHrHrHOOOOOOO I II I Io  1  to S o o x o o o o o o o o o /if- O _d-CM H vO O O CO ON P—ro P-CO O N O J CVI rH OCOvO-d-CVI O H rH rH H I + + + + + + + + ++  00000X00X0000 rHCOvOCVl CAHvOCOn ro O Oco OCO vO -d"OJ H + ++ ++ ++ ++  OOOOOOOOOOO T-00 OCOO f-OOAO OJ P-rH ro O CO XO CM H _d-CVI Ol H rH I I1 III I1 I I I  OOOOOOOT-OO o o o_d-xoco p-cvixoo o H XO C—XA ro CVl XO ro H XOrOCVI H H rH I IIII II I I  c V ?  o  •z W O  cOXOrOroH V O C O X O N O _d"^0 CO -d"XO CVl O P~-roON_drHrHrHOlOJOJOJrHrHOO  rH cvi co cvi -r±o o -d-vo H C O N O O V O rOON_d" OOJrHrHrHHrHOO  ^O  o 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  _d-H p-_d-co oco cvi O P-XO ro OJ CVI O vO r-i O . .„. ..HOO O rH . . . . 1 1 I I I I I I I IO  p . *  I I I I I I I I I IO  XO ro ^d-XO vO XOXO-d" rH O O HvO XA^XA^roOJ H Hi—IrHHrHHrHrHHrHrH  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 O O S xo o _ 2 . -H/Oco roro P—ON CVl Q i—I CVI rOXO^O vO OsO C—CO OO N N ON J  © ra  a^ bd^. R cd g  H o oxooxoo O O O O O H OJ CM rorO-H^XO^O P—CO O  O _dr _ , . _ _ _d"C O O O OOPP-OO —NO O rH OOJOCN M_d _dc "OXOCX ON ON O  -P cd  rH O oxooxoo O O O O O H CVI OJ roro_d"XOvO P—CO QN  61 APPENDIX D  (Continued)  IV. Thermodynamic V a l u e s f r o m G i b b s - D u h e n E q u a t i o n  o  X  O  O  O I  "LA O O O  o o o  o o o o o o  oo oo oo  H_d" H H  (MA H CM  C O s £ ) O C ~ - O v O I _ d " I - d " v O r-i O O O O O O O H I  I  l i l t o  <3  O W I A O O O  O O O O O O I A  TAOCO  I  I  r-i C M H  I  C O  I H I A I H  I I I + + +  oooooooooo  <l  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  vO T A  bo o  6  C5  O  CM CM > - O T A O O O -d'CO  O O  -  I I I  I I I  I  I  I  -  O  H  I I I  I  I  I I  r o O - d - < H CO CO C O 0 I H  H  I I I  s  H  C O T A H O r H _d" H  CO r-i _ d - C M c O - d - r — ^ - H v O T A O O O O O O r-i  T A T A C^-CM CMv 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 H C M I  I  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 CM  O CMT A C M S - C O CM O v £ > f - f - v DT A T A - d ^ } - C O c o  0 0 1  + + +  I  I I + + +  o o o -dco  o o o CM  CO  o  r - r o \Ooovo N r—_ T A O r o - s O r—. - O r O T A O O CM CM O O . h A T A T A  r—  H  O  s  CT^vO CM H I A O - T A f - O O O O O O O O C M C O  6  w  O O O O O O O O O CO O OvO c O ^ OO _ d " H C M T A C M C O 0 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  r O - d r H I^-OJ;r-i r-i r-i C M C M CO C O ^ t - d I  O T A O H E—CVJ v O 0_=J"CM o~\CM I I I ! • + • + +  O  CM C — C O i H H O r H CM C M  O O T A O T A O O O O O  oco c--r— v o vOTA-drcoCM  O O O O O O O T A O O c O £--vOTA -d'CO CM CM  APPENDIX E C a l c u l a t i o n U s i n g Wagner's Wagner has calculate  derived formulae  p a r t i a l m o l a l excess  phase diagram. E q u a t i o n  from  the  s l o p e of the  which  one  can  the  19 f r o m h i s p a p e r i s g i v e n below  (I-NJA. +N.A,  SNf is  Equation  f r e e e n e r g i e s from  "Thermodynamics o f B i n a r y A l l o y s "  ,  19  solidus  £Nf line  1 ) l  at  composition  under c o n s i d e r a t i o n N^-N^ 0  i s the w i d t h i s the  -A-^A^are  of the  solidus-liquidus  temperature  the h e a t s  of f u s i o n  o f the  and  l-Na. Consider  the  loop  Cu-MoSystem  at 65%  ^  Mn  pure  components  (from phase  '^z.  Viz  =0.1  ( f r o m phase  ©  = 1210°  •^-Cu  = 3,120 =  Substituting  5oo =  diagram)  3,600  i n t o Wagner's  (.1)  (1210)  1  ^F  Equation  C^Fn  3360  ^ F „" SN  diagram)  N>  ^  = 13,900  E  SNJ  ^F  RT  m  ^ N*  N»(i-N,)  = 13,900 - 10,450 = 34So •  \ This value  ^MJ  = .35 (3450)  o f 1200 c a l / m o l e  = 1200  cal/mole  i s o n l y as r e l i a b l e  as i s the  phase d i a g r a m and t h e r e f o r e c o u l d be i n e r r o r b y $0% o r more. The v a l u e the  obtained  activity  from  o u r work was  o f manganese d e t e r m i n e d  calculated o at  8J4J4. C  by u s i n g  6k  = (k.575)  \  (1210)  (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  2.  Chipman, J . , D i s c , F a r a d a y  (1956).  S o c , ij., 2 3 ,  3. Lumsden, J . , 'Thermodynamics o f A l l o y s ' ,  (  )  •  I n s t , of  M e t a l s , , (1952) . 4« Wagner, C ,  Wesley, 5.  'Thermodynamics o f A l l o y s ' ,  (1952).  Addison  Knacke,- 0 . , and S t r a u s k i , I.N., ' P r o g r e s s P h y s i c s ' 6, l 8 l , (1956).  6. Chipman, J . , and E l l i o t t ,  J.F./  'Thermodynamics i n (1950).  P h y s i c a l M e t a l l u r g y ' . A.S.M. 7. D i t c h b u r n , R.W.,  H ,  and G i l m o u r ,  i n Metal  J . C . , Rev. Modern  Phys.,  310,. ( 1 9 4 D .  8. Knudsen,,  M., Ann. d e r Physik,- 2 £ ,  179,. (1909).  9. S p e i s e r , . R.,, and J o h n s o n , H.L.,. T r a n s . A.S.M. l\.2,  283, (1950). 10. L a n g m u i r ,  11.  I.,. Phys. Rev., 3 2 9 ,  (1913).  H e r s h , H.N., J . Am. Chem. S o c , £ £ , 1529,  12. M c K i n l e y ,  1120,  (1953).  J.D., and V a n c e , J.E.,, J . Chem. P h y s . 22,  (1954)•  13. T a y l o r , J.B.,- and L a n g m u i r , I . , P h y s . R e v . y 5,1»  753,  (1937).  3J4.. E g e r t o n , A.C., P r o c 15.  Roy. S o c , 10.3, 4^9  0 ' D o n n e l l , . T.A.,, A u s t r a l i a n  r  (1923).  J . Chem. ><8, 4 8 5 ,  16. G o n s e r , U., Z e i t . F . P h y s . Chem.>  1,  (1955).  (1954)-  17. Edwards,. J.W.,. J o h n s o n , H.L., and B l a c k b u r n , P.E.,  J . Am. Chem. S o c . Jjj., 1539, 18.  (1952).  McCabe, C L . , and Hudson, R.G., J . M e t a l s , %  19. Wagner, C , A c t a Met.,  2,. 2 4 2 ,  20. O r i a n i , R.A., A c t a Met.,  ij., 1 5 ,  (1954). (1956).  17,  (1957).  66 21.  Varley,  22.  Ephraim,< F . , ' I n o r g a n i c  J.H.O.,  Publishers 23.  Shimoji,  Phil.  Inc.  Mag., ^  887, (1954).  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