Natural-convective high-temperature oxidation of iridium
by Neil Kelly Wahl
A thesis submitted to the Graduate Faculty in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE in Mechanical Engineering
Montana State University
© Copyright by Neil Kelly Wahl (1974)
Abstract:
An investigation of oxidation of iridium wire in naturally-convected oxygen and air was performed in
the temperature range of 1675 to 2260°C (1948 to 2533°K) and the pressure range of 9.8 x 10^-8 to
1.32 atmospheres (7.5 x 10^-5 to 1000 torr). Two theoretical models were developed, each extending
over specific pressure ranges. One model described the surface recession rate at low pressures where
metal vaporization predominated the rate. The second model described the surface recession rate at
high pressures where it was assumed that diffusion of Ir(g), IrO2(g), and IrO3(g) through a gaseous
boundary layer controlled the rate. A close correlation between the experimental results and theoretical
calculations was achieved for oxidation in both oxygen and air.
Empirical equations that describe the temperature dependence of the free energies of formation of
IrO2(g) and Ir03(g) were developed. Results from these equations agree fairly well with results of
previous investigators. S ta te m e n t
o f P e r m is s io n
t o C opy
In p r e s e n tin 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 l m e n t o f th e re q u ire m e n ts
f o r an a d v a n c e d d e g r e e i n M e c h a n ic a l E n g i n e e r in g a t M ontana S t a t e U n i v e r s i t y ,
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 make i t f r e e l y a v a i l a b l e f o r i n s p e c t i o n .
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 in 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 may b e g r a n t e d by my m a jo r p r o f e s s o r ,
th e D ire c to r o f L ib r a r ie s .
o r , i n h i s a b s e n c e , by \
I t i s u n d e r s t o o d t h a t an y c o p y in 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 llo w e d w i t h o u t my w r i t t e n
. .
p e rm is s io n .
'
D at e
^
L
I r
'
/ 4%
NATURAL-CONVECTIVE HIGH -TEMPERATURE OXIDATION OF IRIDIUM
by
NEIL KELLY WAHL
A t h e s i s s u b m i t te d t o t h e G r a d u a te F a c u l t y i n p a r t i a l
f u l f i l l m e n t o f th e re q u ire m e n ts f o r th e d e g re e
of
MASTER OF SCIENCE
in
M e c h a n ic a l E n g i n e e r in g
A p p ro v ed :
X2
H ead, M a jo r D e p a rtm e n t
C h a irm a n , E x a m in in g C om m ittee
G r a d u a te Dean
MONTANA STATE UNIVERSITY
Bozem an, M ontana
J u n e , 1974
iii
acknowledgments '
.
y
S p e c i a l t h a n k s a n d a p p r e c i a t i o n a r e e x te n d e d t o D r. R. T. Wimber f o r
h i s g u i d a n c e ,an d a s s i s t a n c e i n t h e r e s e a r c h a n d f o r s e r v i n g a s h e a d o f t h e
a s s o c i a t e d e x a m in in g c o m m itte e .
T h an k s a r e a l s o g iv e n t o D r. E . H. B is h o p
a n d D r. R. E . Powe f o r s e r v i n g a s m em bers o f t h e e x a m in in g c o m m itte e .
D r.
Powe i s t h e a u t h o r o f t h e e x t e n s i v e l y u s e d l e a s t —s q u a r e s c u r v e f i t t i n g
c o m p u te r p ro g ra m u s e d i n t h i s r e s e a r c h .
The A tom ic E n e rg y C om m ission i s i
a ls o th a n k e d f o r th e f i n a n c i a l s u p p o rt o f t h i s r e s e a r c h .
iv
TABLE OP CONTENTS
Page
VITA
................................................................................................................. .....................
ACKNOWLEDGMENTS
LIST OF TABLES
ABSTRACT
........................... ............................................................................................ . .
iii
............................................ ............................ .......................... ..............
LIST OF FIGURES
NOMENCLATURE
ii
vi
....................................................................................................................... ..
v ii
................................................ ........................................................................... .
v iii
........................... ........................................ ' ......................................... ..
xi
CHAPTER
I.
INTRODUCTION
C h a r a c t e r i s t i c s a n d U ses - o f I r i d i u m
R eview o f P r i o r Work
II. "experimental
...............................................................
equipment and procedures
E x p e r im e n ta l M a t e r i a l s
IV .
V.
TRUE WIRE TEMPERATURE DETERMINATIONS
EXPERIMENTAL RESULTS
I
^^
2
.
............... ....................... ..................... ...........
E x p e r im e n ta l A p p a r a tu s a n d P r o c e d u r e
III.
, ............... ..
4
...................... ..
4
.................. ..........................
......................... ..
, Il
'
13
THEORETICAL RATE CALCULATIONS
T h e o r e t i c a l R a t e s 'a t H igh P r e s s u r e s
■ T h e o r e t i c a l R a te s a t Low P r e s s u r e s
.................... ....................
17
. . . . . . .. . . . . . . . . . . . .
28
T h e o r e t i c a l R a te C a l c u l a t i o n s a t I n t e r m e d i a t e P r e s s u r e s
30
V
■
CHAPTER
VI.
VII.
VIII.
REFERENCES
APPENDIX
page
DISCUSSION OF RESULTS
SUMMARY
-...........................
............................. ...... ..... ...... .
SUGGESTIONS FOR FUTURE WORK ■....... .................... .
33
' 34
35
..............
36
...................
38
vi
LIST OF TABLES
T a b le
\
Page
5
1.
A n a l y s i s o f I r i d i u m W ire
........................................... ..
2.
R e s u l t s o f T ru e W ire T e m p e r a tu r e D e t e r m in a t io n s
3.
P r o p e r t i e s o f A ir
4.
P r o p e r t i e s o f Oxygen
5.
E f f e c t i v e n e s s o f t h e F i n a l C o r r e l a t i o n f o r R a t e s i n Oxygen
a t P r e s s u r e s G r e a t e r Than 4 x 10 ^ a tm ................. *..............
................. ... ..
„ ............... .........................................................................
............................................................................... . . . .
6.
E x p o n e n t o f D ia m e te r U sed i n D e te r m in in g t h e D ia m e te r
D ep en d en cy •................................................................................
7.
E f f e c t i v e n e s s o f t h e F i n a l C o r r e l a t i o n f o r R a t e s i n Oxygen
a t P r e s s u r e s L e s s Than 3 x 10 ^ a tm .
....................
8.
9.
E f f e c t i v e n e s s o f t h e F i n a l C o r r e l a t i o n f o r R a te s i n Oxygen
a t P r e s s u r e s i n t h e I n t e r m e d i a t e R ange (3 x 10 ^ ^ P / 4 x 1 0 -4 a tm ) ......................................................................................... ..
12
20
21
26
30
. 31
E f f e c t i v e n e s s o f t h e F i n a l C o r r e l a t i o n f o r O x id a tio n i n
Oxygen .......................................................................................
10.
E x p e r im e n ta l C o n d i t io n s a n d E x p e r im e n ta l and C a l c u l a t e d
R e c e s s io n R a t e s f o r Oxygen ..................... ..............................
A p p en d ix A
11.
E x p e r im e n ta l C o n d i t io n s a n d E x p e r im e n t a l- a n d C a l c u l a t e d
R e c e s s io n R a te s f o r A ir
A p p e n d ix B
L IST OF FIGURES
F ig u re
1.
S c h e m a tic o f E x p e r im e n ta l A p p a r a tu s
....................................... ..
2.
E xam ple o f a R a te G raph
3.
E x p e r im e n ta l R e s u l t s a n d T h e o r e t i c a l C o r r e l a t i o n f o r Oxi­
d a t i o n i n Oxygen ................................................................. ..
4-
E x p e r im e n ta l R e s u l t s a n d T h e o r e t i c a l C o r r e l a t i o n f o r O xi­
d a t i o n i n A ir
............... • ................. .................................................... ..
............................................ ................ ..
v iii
NOMENCLATURE
Sym bols
A
E q u i v a l e n t w e ig h t e q u a l t o 1 9 2 .2 gms o f i r i d i u m consum ed p e r gm
m ole o f o x id e fo rm e d d i v i d e d by t h e d e n s i t y o f t h e i r i d i u m .
OC
A ccom m odation c o e f f i c i e n t
Pow er u s e d i n d e s c r i b i n g d i a m e te r d e p e n d e n c ie s
CK
V
V a p o riz a tio n c o e f f i c i e n t
(3
C o e f f i c i e n t o f t h e r m a l e x p a n s io n
-
( 0K )- ^
C
P
S p e c if ic h e a t a t c o n s ta n t p r e s s u r e o f th e o x id iz in g g as
(gm°K)
S p e c i f i c h e a t a t c o n s t a n t volum e o f t h e o x id iz in g g a s
D ia m e te r o f w i r e
-
M o le c u la r d i f f u s i v i t y
-
c a l/
- c a l / (gm°K)
cm
2I
r- cm / s e c
S t a n d a r d - s t a t e . f r e e e n e rg y o f f o r m a t i o n
-
k c a l/m o le
P e r c e n t th e r m a l e x p a n s io n o f t h e i r i d i u m w ir e
I
AT
■
D i f f e r e n c e b e tw e e n w i r e t e m p e r a t u r e a n d a m b ie n t t e m p e r a t u r e
E n e rg y o f m o le c u la r i n t e r a c t i o n
-
e rg s
C1A
F o rc e c o n s ta n t f o r o x id iz in g g a s
e /s
F o r c e c o n s t a n t f o r. o x id e s p e c i e
s
G ra v ita tio n a l a c c e le r a tio n
x
S p e c if ic h e a t r a t i o f o r th e o x id iz in g gas
Gr
G r a s h o f num ber
h
C o n v e c tiv e h e a t - t r a n s f e r c o e f f i c i e n t
-
-
°K
0K
c m /s e c ^
-
c a l / (cm ^ sec °K )
-
°K
'I
i:c
Symbols
C o llis io n in te g r a l fo r d iffu s io n
J
F lu x e q u a l t o m o le s o f v a p o r m o le c u le s t h a t l e a v e a s u r f a c e p e r .
u n i t a r e a a n d tim e
. .
k '
T herm al c o n d u c t i v i t y o f t h e o x i d i z i n g g a s . -
k
B o ltz m a n n c o n s t a n t
K
E q u ilib r iu m - c o n s t a n t .
kG
G a s - f i lm m ass t r a n s f e r c o e f f i c i e n t f o r d i f f u s i o n o f o x id e s p e c i e
t h r o u g h t h e b o u n d a ry l a y e r gm m o l e / ( s e c cm- a tm )
-
I . 38 x 10 ^ e r g s / ° K
Mean f r e e p a t h o f g a s m o le c u le s
-
c a l/(c m
cm
■
M o le c u la r w e ig h t o f t h e o x i d i z i n g g a s
M.
M o le c u la r w e ig h t o f t h e d i f f u s i n g o x id e s p e c i e
V is c o s ity o f th e o x id iz in g g a s
-
.g m /(cm s e c )
Nu
N u s s e l t num ber
P
T o ta l p r e s s u r e
p
L o g a r ith m ic mean p r e s s u r e o f n o n d i f f u s i n g oxygen
-
E q u ilib riu m p r e s s u r e o f th e v a p o r iz in g s p e c ie
atm •
P
BM
eq
P.i
-
atm
;
P a r t i a l p re s s u re o f th e i
th
P a r t i a l p r e s s u r e o f oxygen
s p e c ie
-
-
P r a n d t l num ber
R
I d e a l g a s c o n s ta n t
m ole 0K)
( r O1I
-
-
atm
atm
atm
P a r t i a l p r e s s u r e o f th e ir id iu m m e ta l
Pr
.
■
M
/*
s e c °K)
- ' atm
I . '987 c a l / ( g m m ole °K) o r 8 2 ,06 cm^ atm /(g m
C o l l i s i o n d i a m e te r f o r c o l l i s i o n b e tw e e n o x i d i z i n g g a s m o le c u le s
a n g s tr o m s
-
X
Sym bols
(r O) ) 2
C o l l i s i o n d i a m e te r f o r c o l l i s i o n b e tw e e n m o le c u le s o f i r i d i u m co n
t a i n i n g s p e c i e s -r a n g s tr o m s
r^ ^
C o l l i s i o n d i a m e te r f o r c o l l i s i o n b e tw e e n oxygen m o le c u le an d m ole
c u le o f irid iu m c o n ta in in g s p e c ie s a n g s tr o m s "
Ra
R a y le ig h num ber
p
D e n s i ty o f t h e o x i d i z i n g g a s
("Ir,
D e n s i ty o f i r i d i u m a t
T^1
F ilm t e m p e r a t u r e
■
W ire t e m p e r a t u r e
-
-
-
gm/cm^
gm/cm^
0K
-
0K
-
T
M
M e lt in g t e m p e r a t u r e f o r o x id e s
(V q )^
M o la l vo lu m e o f o x i d i z i n g g a s
- K
-
M o la l vo lu m e o f t h e o x id e s p e c i e
x
S u rfa c e r e c e s s io n r a t e
x_
s
S ta n d a rd iz e d r e c e s s io n r a t e
o
cm^(gm m o le )
-
cm^(gm m o le )
- c m /s e c
-
c m /s e c
ABSTRACT
An i n v e s t i g a t i o n o f o x i d a t i o n o f i r i d i u m w ir e i n n a t u r a l l y - c o n v e c t 'e d
oxygen a n d a i r was p e rf o r m e d i n t h e t e m p e r a t u r e r a n g e o f 1675 t o 2260°C
(1 9 4 8 t o 2533°K ) a n d t h e p r e s s u r e r a n g e o f 9*8 x 10
t o 1 .3 2 a tm o s p h e re s
( 7 .5 x 10 ^ t o 1000 t o r r ) .
Two t h e o r e t i c a l m o d els w e re d e v e lo p e d , e a c h
e x te n d i n g o v e r s p e c i f i c p r e s s u r e r a n g e s .
One m odel d e s c r i b e d th e . s u r f a c e
r e c e s s i o n r a t e a t low p r e s s u r e s w h e re m e ta l v a p o r i z a t i o n p r e d o m in a te d
th e r a t e .
The s e c o n d m odel d e s c r i b e d t h e s u r f a c e r e c e s s i o n r a t e a t h ig h
p r e s s u r e s w h ere i t was assu m e d t h a t d i f f u s i o n o f I r ( g ) , I r O ^ ( g ) , and
IrC L ( g ) t h r o u g h a g a s e o u s b o u n d a ry l a y e r c o n t r o l l e d t h e r a t e .
A c lo s e
c o r r e l a t i o n b e tw e e n t h e e x p e r i m e n t a l r e s u l t s a n d t h e o r e t i c a l c a l c u l a t i o n s
was a c h ie v e d f o r o x i d a t i o n i n b o t h oxygen a n d a i r .
E m p ir ic a l e q u a t i o n s t h a t d e s c r i b e t h e t e m p e r a t u r e d e p e n d e n c e o f t h e
f r e e e n e r g i e s o f f o r m a ti o n o f I r C ^ ( g ) a n d I r 0 ^ ( g ) w ere d e v e lo p e d . R e s u lts ,
fro m t h e s e e q u a t i o n s a g r e e f a i r l y w e ll w i t h r e s u l t s o f p r e v i o u s i n v e s t i - •
g a to rs .
CHAPTER I
INTRODUCTION
C h a r a c t e r i s t i c s a n d U se s o f I r i d iu m
I r i d i u m , t h e 77
th
e le m e n t , i s a p l a t in u m g ro u p m e t a l .
I t i s t h e o n ly
e le m e n t a l m e ta l known t o man t h a t p o s s e s s e s a low e n o u g h o x i d a t i o n r a t e
a n d a h i g h eno u g h m e l t i n g p o i n t , 2454 °G ( 2 7 2 7 ° K ) , t h a t i t c a n b e u s e d un­
p r o t e c t e d i n an oxygen c o n t a i n i n g g a s f o r e x te n d e d p e r i o d s o f tim e a t tem ­
p e r a t u r e s g r e a t e r t h a n 2 0 0 0 0C.
ium fo rm s v o l a t i l e
At t e m p e r a t u r e s g r e a t e r t h a n IOOO0C , i r i d ­
o x id e s a n d a b a r e s u r f a c e i s l e f t b e h i n d .
T h is r e s u l t s
in o x id a tio n r a t e s t h a t a re l i n e a r w ith tim e .
When c o m p a red t o o t h e r m e t a l s , i r i d i u m
i s one o f t h e m o st c o r r o s i o n
r e s i s t a n t o v e r a w id e r a n g e o f t e m p e r a t u r e s a n d c o r r o s i v e e n v ir o n m e n ts .
The c o r r o s i v e e n v ir o n m e n ts i n c l u d e d v a r i o u s a c i d s , s a l t s o l u t i o n s , f u s e d
s a l t s , m o lte n m e t a l s , a n d m o lte n m e ta l o x i d e s .
I r i d i u m h a s b e e n u s e d a s h e a t i n g e le m e n ts i n h i g h t e m p e r a t u r e f u r ­
n a c e s , s t a n d a r d i z e d h i g h - t e m p e r a t u r e th e r m o c o u p le s , a n d f o r p r o t e c t i v e
c o a t i n g s o f l e s s e x p e n s iv e m a t e r i a l s s u c h a s t u n g s t e n a n d t a n t a lu m b a s e
a llo y s .
P o t e n ti a l a p p lic a tio n s f o r irid iu m
a re le a d in g edges o f r e e n tr y
s p a c e v e h i c l e s , r e a c t o r c o m p o n e n ts , a n d p a r t s i n r o c k e t s a n d t u r b i n e
e n g in e s .
Irid iu m a ls o h a s l i m i t a t i o n s .
B e in g ’ a p la tin u m g r o u p m e t a l , t h e
c o s t o f i r i d i u m c o u ld b e a f a c t o r r e s t r i c t i n g e x t e n s i v e u s e .
c o u ld b e a n o t h e r c o n s t r a i n t .
gm /cm ^) e le m e n ts known t o m an.
I r i d iu m
is
W eight
one o f t h e m o st d e n s e ( 2 2 .5 7
The v e r y low e m i tt a n c e o f i r i d i u m c o u ld
2
r e s t r i c t i t s u se as. l e a d in g edges f o r r e e n t r y v e h ic l e s .
The p r im a r y
m eans o f h e a t d i s s i p a t i o n fro m t h e l e a d i n g ed g e i s r a d i a t i o n . ■ The low
e m i tt a n c e w ould t h e n r e s t r i c t t h e h e a t d i s s i p a t i o n .
irid iu m
The e m i tt a n c e o f '
c a n b e e n h a n c e d by o x id e o v e r c o a t s a n d w ould n o t p r e s e n t s e r i o u s
p ro b le m s t o t h e u s e a s a l e a d i n g ed g e m a t e r i a l .
R eview o f P r i o r Work
The b r i e f r e v ie w o f p a s t w ork d o n e on t h e o x i d a t i o n o f i r i d i u m
c o n ta in e d in th e f o llo w in g r e s u l t e d in c o n c lu s io n s u se d a s a s t a r t i n g p o in t
f o r th e p re s e n t s tu d ie s .
S e v e ra l s e p a r a te i n v e s t i g a t o r s have s tu d ie d th e p ro d u c ts o f th e o x i­
d a t i o n o f i r i d i u m an d t h e th e rm o d y n a m ic s i n v o lv e d i n t h e f o r m a ti o n ^ o f t h e s e
p ro d u c ts .
C o rd e fu n k e an d M eyer ( l )
s tu d ie d th e o x id a tio n o f irid iu m in
t h e t e m p e r a t u r e r a n g e o f 1169 t o 1462°C (1 4 4 2 t o 1 7 3 5 ° ^ ) .
t h a t IrO ( g ) was t h e m a jo r s p e c i e f o rm e d .
5
They c o n c lu d e d
T h e ir r e s u l t s w ere c o n fir m e d by
o t h e r w o r k e rs ( 2 , 3 ) .
M ass s p e c t r o m e t r i c s t u d i e s by Norman e t a l ( 4 ) r e s u l t e d i n t h e i r c o n ­
c l u s i o n t h a t I r 0 o ( g ) a n d IrO ( g ) w e re t h e m a jo r s p e c i e s o f o x i d a t i o n .
p r e s e n c e o f I r O ( g ) c o u ld n o t b e r u l e d o u t c o m p l e te l y .
s e n t, i t s
The
I f I r O ( g ) was p r e ­
p a r t i a l p r e s s u r e was e s t i m a t e d t o b e l e s s t h a n 2 p e r c e n t o f t h e
p a r t i a l p r e s s u r e o f IrO p (g ) a t th e h ig h e s t te m p e ra tu re i n v e s t ig a t e d .
w ork o f Norman e t a l i n v o lv e d f e e d i n g oxygen a t 10
-4
K nudsen c e l l h e a t e d t o 1557 - I 7 6 0 0C ( I 83 O - 2 0 3 3 °K ).
The
a tm i n t o an i r i d i u m
S ta n d a rd -s ta te
e n t h a l p i e s a n d e n t r o p i e s o f f o r m a ti o n f o r I r O ^ ( g ) w ere r e p o r t e d a s 4 8 .5
3
+ 0 .8 k c a l / m o l e a n d 3 • 9 ■+ 2 .0 e u r e s p e c t i v e l y .
The s t a n d a r d - s t a t e e n t h a l p i e s
,,and e n t r o p i e s o f f o r m a t i o n f o r I r O . ( g ) w e re r e p o r t e d a s 5 .5 ± 1 . 3 k c a l/ m o l e
a n d - 13*1 + 2 .5 eu r e s p e c t i v e l y .
S tu d ie s p e rfo rm e d by O liv e i ( 5 ) r e s u l t e d in th e c o n c lu s io n s t h a t IrO ^ (g )
a,nd I r O ^ ( g ) w e re t h e m a jo r s p e c i e s f o rm e d .
p r e s s u r e r a n g e o f 10
t o 10 ^
t o 1780°C (1 1 5 3 - 2 0 5 3 ° k ) .
T h is w ork w as d o n e o v e r t h e
atm a n d o v e r t h e t e m p e r a t u r e r a n g e o f 880
M ass s p e c t r o m e t r i c s t u d i e s i n
th e te m p e ra tu re
r a n g e o f 627 t o 2227 °C (900 - 2500 °IC) y i e l d e d s t a n d a r d - .- s ta te e n th a l p y a n d
e n tro p y o f fo rm a tio n f o r I r 0 ^ ( g ) o f 6 .0 k c a l/m o le and - 9 .5
-u r e s p e c tiv e ly .
Wimber a n d K ra u s ( 6 ) c o n c lu d e d t h a t I r ( g ) was a n im p o r ta n t ' s p e c i e a t
h ig h te m p e ra tu re s and t h a t I r 0 ( g ) c o n tr i b u te d v e ry l i t t l e
to th e o v e ra ll
re c e s s io n r a t e .
B a se d upon t h e c o n c l u s i o n s o f t h e s e i n v e s t i g a t o r s , t h e i r i d i u m c o n ­
t a i n i n g s p e c i e s t h a t s i g n i f i c a n t l y c o n t r i b u t e d t o t h e o x i d a t i o n r a t e w ere
th o u g h t t o b e I r ( 'g ) , J rO 5 ( g ) , a n d I r O ^ ( g ) .
- '
CHAPTER I I
EXPERIMENTAL EQUIPMENT AND PROCEDURES
E x p e r im e n ta l M a t e r i a l s
C o m m e rc ia lly p u r e i r i d i u m w ir e was p u r c h a s e d i n t h r e e l o t s .
R e s u lts
o f m ass s p e c t r o m e t r i c a n d e m is s io n S p e c tr o g r a p h iC a n a l y s e s a lo n g w i t h an
i n d i c a t i o n o f t h e s o u r c e s a n d w ir e d i a m e t e r s a r e g iv e n i n T a b le I .
The
m a jo r i m p u r i t y i n L o ts I a n d 2 was t u n g s t e n a t 0 .6 p e r c e n t a n d 0 .0 7 1 p e r ­
cen t re s p e c tiv e ly .
a n d b a riu m ( 0 . 0 2 ^ ) .
The m a jo r i m p u r i t i e s i n L o t 3 w e re t u n g s t e n ( 0 ,0 2 $ )
The a n a l y s e s d i d n o t i n c l u d e a l l known e le m e n t s , b u t
t h e i r i d i u m c o n t e n t w as e s t i m a t e d t o b e 9 9 * 3 , 99»9> a n d '99*9 p e r c e n t i n
L o ts I , 2 , a n d 3 r e s p e c t i v e l y .
.
The o x y g en u s e d i n t h e p r e s e n t s t u d i e s was USP g r a d e .
N i t r o g e n and
a r g o n w e re t h e m a jo r i m p u r i t i e s a n d w e re a ssu m e d t o b e i n e r t t o i r i d i u m .
The oxygen c o n t e n t w as t y p i c a l l y 99*7 p e r c e n t .
The a i r u s e d i n t h e p r e s e n t s t u d i e s was a tm o s p h e r ic a n d was assu m ed
t o h a v e a n oxy g en c o n t e n t o f 21 p e r c e n t ( b a s e d u p o n a v o l u m e .p e r c e n t ) .
E x p e r im e n ta l A p p a r a tu s a n d P r o c e d u r e
The e q u ip m e n t u s e d i n t h e p r e s e n t s t u d y i s shown s c h e m a t i c a l l y i n
F ig u re I .
An i r i d i u m w i r e s p e c im e n . 5 .6 cm lo n g was m o u n te d h o r i z o n t a l l y
b e tw e e n tw o e l e c t r o d e s i n a c e l l .
The c e l l , w h ich h a d w a t e r - c o o l e d
■
c o p p e r w a l l s , h a d t h e i n t e r n a l d im e n s io n s o f 2 .5 x J . 6 x 8 .9 cm.
was p r o v id e d w i t h tw o s i g h t p o r t s c o n t a i n i n g r o t a t a b l e
p y r e x w in d o w s.
The c e l l
o p tic a l-q u a lity
T h ro u g h one w indow , a t i m e r - a c t u a t e d c a m e ra f i t t e d w i t h a
• S,
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I m p u r i t y . c o n t e n t s e x p r e s s e d i n p a r t s p e r m il ­
+■ 25 m il d i a m e te r w i r e draw n by E n g le h a r d I n d ­
u s t r i e s , C a r t e r e t , New J e r s e y .
t
20 m il d i a m e te r w i r e d raw n b y J o h n s o n , M a tth e y
& C b '., L o n d o n , E n g la n d .
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DIFFUSION
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8
t e l e m i c r o s c o p e , was u s e d t o r e c o r d t h e w i r e d ia m e te r , a t 20x m a g n i f i c a t i o n .
T h ro u g h t h e o t h e r w indow , a L e e d s a n d N o r th r u p 8636 -C o p t i c a l p y r o m e te r
e q u ip p e d w i t h a 38 -mm f o c a l l e n g t h l e n s was u s e d t o d e te r m i n e t h e b r i g h t ­
n e s s te m p e ra tu re o f th e w ire .
E r r o r s i n t e m p e r a t u r e m e a su re m e n t w ould
h a v e b e e n c a u s e d b y c o n d e n s a t i o n o f o x id e s on t h e w indow s, b u t w e re e lim ­
i n a t e d b y r o t a t i n g t h e window t o a c l e a n s e c t i o n o n ly when a t e m p e r a t u r e
.
m e a su re m e n t was b e i n g m ade.
The window on t h e c a m e ra s i d e was r o t a t e d t o
a c l e a n s e c t i o n im m e d ia te ly b e f o r e a p i c t u r e was t a k e n a n d im m e d ia te ly
a f t e r t h e p i c t u r e , r e t u r n e d t o . t h e o r i g i n a l p o s i t i o n . , The w indow s w e re
c l e a n e d a n d p o l i s h e d b e tw e e n r u n s .
The o x i d a t i o n c e l l w as m o u n ted on t o p o f a v e r t i c a l c y l i n d e r 10 cm
i n d i a m e te r a n d 20 cm l o n g .
O x i d i z i n g g a s was i n t r o d u c e d . i n t o t h e c y l i n d e r
a t a p o i n t 10 cm b e lo w t h e c e l l .
a b o v e a n d r o t a t e d $0
lo w p r e s s u r e s .
O
T h ro u g h one p r e s s u r e t a p , l o c a t e d 5 cm
fro m t h e g a s i n l e t , a n i o n t u b e was u s e d t o m e a s u re
T h ro u g h a s e c o n d p r e s s u r e t a p , l o c a t e d 5 cm b e lo w an d
r o t a t e d $ 0 ° fro m t h e g a s i n l e t ,
a c a p a c i t i v e m anom eter was u s e d t o m e a s u re
h ig h p r e s s u r e s .
I m m e d ia te ly b e lo w t h e c y l i n d e r was m o u n te d a w a t e r - c o o l e d o p t i c a l l y dense b a f f l e .
A V arian/N R C M odel M-4 (8 0 0 l i t e r / s e c ) d i f f u s i o n pump was
m o u n te d b e lo w t h e b a f f l e ;
The b a f f l e p r e v e n t e d a d i r e c t l i n e o f s i g h t o f
t h e pump o i l fro m t h e pump i n t o t h e o x i d a t i o n c e l l .
By. m eans o f a h o s e
'- V .
a n d t u b i n g , t h e o u t l e t o f t h e d i f f u s i o n pump was c o n n e c te d t o t h e i n l e t o f
a m e c h a n ic a l p u m p .■
9
P r e s s u r e s i n t h e s y s te m t h a t w e re l e s s t h a n 1 .3 2 x IO- ^ atm ( 0 .1 0 t o r r )
w e re m e a s u re d w i t h a W e s tin g h o u s e io n t u b e ( p a r t num ber WL 7 9 0 3 ) and G ra h v i I I e - P h i l l i p s I o n i z a t i o n Gauge C o n t r o l l e r ( s e r i e s 2 2 4 ) s y s te m .
P ressu res .
i n t h e s y s te m t h a t w e re g r e a t e r t h a n o r e q u a l t o 1 .3 2 x IO- ^ atm ( 0 .1 0 t o r r )
w e re m e a s u re d w ith a MKS C a p a c it a n c e M anom eter 77H-1COO a n d a MKS B a r a tr o n
TM Type 77 P r e s s u r e M e te r .
A s i g n a l fro m t h e m e a s u r in g i n s t r u m e n t was u s e d
a s an i n p u t s i g n a l f o r a G r a n v i l l e - P h i l l i p s A u to m a tic P r e s s u r e C o n t r o l l e r
(APC) Mo. 0 - 0 0 -2 1 6 0 0 6 .
The APC o p e r a t e d a s e r v o - d r i v e n v a l v e a n d ' t h u s
r e g u l a t e d t h e f lo w o f t h e o x i d i z i n g g a s i n t o t h e s y s te m .
t h e s y s te m , t h e o x i d i z i n g g a s p a s s e d t h r o u g h tw o d r i e r s
B e fo re e n te r in g
( th e f i r s t con­
t a i n e d c a lc iu m s u l f a t e h e m ih y d r a te a n d t h e s e c o n d c o n t a i n e d a n h y d ro u s
m agnesium p e r c h l o r a t e ) a n d t h e n t h r o u g h a M a th e so n No. 74 r o t a m e t e r .
C u r r e n t fro m a H e w le tt P a c k a r d D .C . Pow er S u p p ly 6260B was u s e d t o
.
s e l f - r e s i s t a n c e h e a t t h e i r i d i u m w ir e s p e c im e n .
The v o l t a g e a c r o s s t h e
c e l l was m e a s u re d w i t h a H o n ey w ell D i g i t e s t M u ltim e te r M odel 333R.
C u rren t
t h r o u g h t h e w i r e was m e a s u re d w i t h a G e n e r a l E l e c t r i c D .C . Altimeter w ith , a
c a p a c i t y o f $0 a m p e r e s .
The th e r m a l e x p a n s io n o f t h e w ir e was accom m odated
b y a c a n t i l e v e r s p r i n g a rr a n g e m e n t on one o f t h e e l e c t r o d e s .
The w ir e was
p r e s t r e s s e d t o a n am ount s u c h t h a t when t h e w ir e was a t t h e o x i d a t i o n tem ­
p e r a t u r e i t was a t n e a r z e r o s t r e s s .
P r i o r t o m ak in g a r u n , t h e w ir e w as c l e a n s e d . i n a c e t o n e , m ounted b e -
■-Mv -^
'.O
tw e e n t h e e l e c t r o d e s , a n d g i v e n a n a n n e a l f o r t h i r t y m in u te s a t 2260 C
(2 5 3 3 °K ) i n a n a rg o n a tm o s p h e r e .
The p u r p o s e o f t h e a n n e a l ,w a s t o e l i m - '
10
i n a t e r e c r y s t a l l i z a t i o n a n d g r a i n g ro w th d u r i n g o x i d a t i o n a n d t o a t t a i n a h
e l e c t r i c a l r e s i s t i v i t y n e a r l y c o n s t a n t w i t h t im e .
o n ly t o e a c h new s e c t i o n o f w i r e .
T h is a n n e a l was g iv e n
A f t e r t h e a n n e a l , t h e s y s te m was e v a c ­
u a te d and th e n b a c k f i l l e d w ith th e d e s ir e d o x id iz in g g a s .
The s y s te m was
a g a i n e v a c u a t e d , le a k :,c h e c k e d , and r e f i l l e d w i t h t h e o x i d i z i n g g a s t o t h e
d e s ire d p re s s u re le v e l .
Once t h e p r e s s u r e s t a b i l i z e d ,
t h e i r i d i u m w ir e
s p e c im e n w as b r o u g h t up t o t h e o x i d a t i o n t e m p e r a t u r e b y s lo w ly i n c r e a s i n g
th e c u r r e n t th ro u g h th e w ir e .
s e r i e s o f te n film
Once t h e t e m p e r a t u r e h a d s t a b i l i z e d , a
e x p o s u r e s w e re made a t a p r e d e t e r m in e d tim e i n t e r v a l .
The tim e i n t e r v a l w as s e l e c t e d s u c h t h a t a p p r o x i m a t e ly 0 .0 2 5 4 mm ( l m i l )
was rem o v ed fro m t h e d i a m e te r o f t h e w i r e d u r i n g t h e t o t a l tim e o f t h e
ru n .
The f i l m was t h e n re m o v e d , d e v e lo p e d , a n d a llo w e d t o d r y f o r a m in­
imum o f 2 h o u r s b e f o r e t h e im a g e s o f t h e w i r e w e re m e a s u r e d .
The im a g e s ■
w e re m e a s u re d b y a n i n s t r u m e n t t h a t c o n s i s t e d o f a m o d if ie d c a t h e t o m e t e r ,
h i g h i n t e n s i t y l i g h t s o u r c e , a n d a G o sse n L u n a -P ro E x p o s u re M e te r .
The
t e l e m i c r o s c o p e o f t h e c a t h e t o m e t e r was m o d if ie d t o i n c l u d e a 0 .0 5 mm (2 m i l )
s l i t a t th e r e t i c l e p la n e .
E a c h f ra m e w as m e a s u re d a t t h r e e l o c a t i o n s
( t h e tw o e n d s a n d t h e c e n t e r o f t h e im a g e ) .
The a v e r a g e d i a m e te r was c o n ­
v e r t e d t o an a c t u a l d i a m e te r b y u s i n g a c o n v e r s i o n f a c t o r .
The c o n v e r s i o n
f a c t o r was o b t a i n e d fro m t h e m e a su re m e n t o f an im age o f a r e f e r e n c e r o d
o f 0 .0 6 5 5 cm ( 2 5 .8 m i l ) i n d i a m e t e r .
m e a su re m e n t was + 0 .0 5 t o 0 .1 p e r c e n t .
The r e p e a t a b i l i t y o f a s i n g l e d i a m e te r
A sym m etry o f t h e w ir e was d e te r m in e d
b y Wimber a n d K ra u s ( 6 ) t o a lw a y s b e l e s s t h a n 1 .2 p e r c e n t .
'
CHAPTER I I I
TRUE WIRE: TEMPERATURE DETERMINATIONS
A th e r m o c o u p le t e c h n i q u e u s e d b y H a lv o rs o n a n d Wimber ( ? ) t o d e te r m in e
t h e r e l a t i o n s h i p b e tw e e n m e a s u re d p y r o m e te r t e m p e r a t u r e a n d t r u e w ir e tem ­
p e r a t u r e was m o d if ie d b a s e d u p o n t h e w ork o f M cLaren e t a l ( 8 ) .
The t e c h ­
n i q u e u s e d i n t h e p r e s e n t s t u d i e s c o n s i s t e d o f f u s i o n w e ld in g e a c h o f t h e
l e a d s o f a n I r - l r 4 0 R h th e r m o c o u p le t o an i r i d i u m w ir e s p e c im e n w h ic h was
m o u n te d b e tw e e n t h e e l e c t r o d e s o f t h e c e l l .
t a n c e h e a t e d b y a n AC pow er s u p p ly .
1The s p e c im e n was. s e l f - r e s i s ­
An R-C f i l t e r i n g c i r c u i t was u s e d t o
b l o c k t h e AC v o l t a g e ' fro m t h e d i g i t a l m i l l i v o l t m e t e r w h ic h was u s e d t o mea­
s u r e t h e th e r m o c o u p le e m f.
The th e r m o c o u p le o u t p u t was t a k e n a s an i n d i c a ­
t i o n o f t h e t r u e w ir e t e m p e r a t u r e a t t h e p o i n t w h ere t h e Ir4 0 R h l e a d o f t h e
th e r m o c o u p le was a t t a c h e d t o t h e s p e c im e n .
T h is p o i n t i s a l s o t h e l o c a t i o n
w h e re t h e s p e c im e n t e m p e r a t u r e was m e a s u re d w ith a n o p t i c a l p y r o m e te r .
T a b le 2 c o n t a i n s a summ ary o f t h e p y r o m e te r t e m p e r a t u r e s m e a su re d
t h r o u g h a window a n d t h e c o r r e s p o n d i n g t r u e w ir e t e m p e r a t u r e f o r w ir e h e a t ­
e d i n oxygen o r a i r .
T a b le 2 . R e s u l t s o f T ru e W ire
T e m p e ra tu re D e t e r m in a t io n s
P y r o m e te r
T e m p e r a tu r e * , °C ( k ).
T ru e W ire
T e m p e r a tu r e , pC (K)
1500
( 1773)
1675
(1 9 4 8 )
1615
(1 8 8 8 )
1820
(2 0 9 3 )
1730
(1 9 0 3 )
1965
(2 2 3 8 )
I 85 O
(2 1 2 3 )
2110
(2 3 8 3 )
1965
( 2238)
2260
(2 5 3 3 )
* M e asu re d t h r o u g h a 3 / l 6 i n c h t h i c k shadow ­
g r a p h - g r a d e , o p t i c a l - q u a l i t y p y r e x w indow.
CHAPTER IV
EXPERIMENTAL RESULTS
F i g u r e 2 c o n s i s t s o f a p l o t o f t h e . d i a m e te r m e a s u re m e n ts v e r s u s tim e
fo r a ty p ic a l ru n .
The s u r f a c e r e c e s s i o n r a t e i s c a l c u l a t e d by d i v i d i n g
t h e s l o p e o f t h e s t r a i g h t l i n e b y m in u s tw o .
F i g u r e 3. c o n t a i n s t h e mea­
s u r e d s u r f a c e r e c e s s i o n r a t e s a t t e m p e r a t u r e s i n t h e r a n g e o f 1675 t o 2260
0C (1948 t o 2533 °K) a n d o v e r t h e p r e s s u r e r a n g e o f 9*8. x 10 0 t o 1 .3 2 a t ­
m o s p h e re s ( 7 .5 x 10 ^ t o 1000 t o r r ) f o r o x i d a t i o n i n o x y g e n .
c l a r i t y n o t a l l t h e r e s u l t s a r e show n.
For sake o f
F i g u r e 4 c o n t a i n s t h e m e a s u re d
s u r f a c e r e c e s s i o n r a t e s i n t h e t e m p e r a t u r e r a n g e o f 1675 t o 2260°C (1 9 4 8
t o 2.533°K) a n d o v e r t h e p r e s s u r e r a n g e o f 9*8 x 10 ^ t o 0 ,6 6 a tm o s p h e re s
( 7 . 5 x. 10 ^ t o 500 t o r r ) f o r o x i d a t i o n i n a i r .
T a b le 10 i n t h e a p p e n d ix c o n t a i n s a summary o f e x p e r i m e n t a l c o n d i t i o n s
a n d r e c e s s i o n r a t e s f o r w ork do n e i n oxygen b y K ra u s ( 9 ) a n d t h e p r e s e n t
in v e s tig a to r.
T a b le 11 i n t h e a p p e n d ix c o n t a i n s a summary o f t h e s e sam e ■
p a r a m e t e r s f o r w ork d o n e i n a i r by t h i s i n v e s t i g a t o r .
A n a l y s is o f e i t h e r t h e F i g u r e s 3 a n d 4 o r t h e T a b le s .10 a n d 11 i n t h e
a p p e n d ix r e v e a l e d n o a p p a r e n t d i f f e r e n c e i n t h e o x i d a t i o n b e h a v io r o f t h e
v a r io u s l o t s o f w ire .
DIAMETER (C M )X IO
5.0 x IO-2TORR
-AD = Q3070 x IO"2 CM
DAVG = 0.4894 X IO"1CM
^ _ 0.3070 IO"2
" 2.0 X9.0 X660.0
^ ^ = 0.2580 x IO"6 CM/SEC
0.500-
5940
T IM E (SEC)
F ig u re 2 .
Exam ple o f a R a te G raph
1675° C (1948 K)
1965° C (2238K)
2110° C (2383K)
2260? C (2533 K)
OPEN SYMBOL=LOT
CLOSED SYMBOL= LOT 2
FLAGGED SYMBOL= LOT 3
-8
-7
-6
EQ 2
EQ14
EQ 13
-5
-4
-3
-2
-I
LOG (TO TA L PRESSURE, ATMS)
F ig u re 3 .
E x p e r im e n ta l R e s u l t s a n d T h e o r e t i c a l C o r r e l a t i o n
f o r O x id a tio n i n Oxygen
O
Vi
O - 1675° C (1948 K)
o pen sy m b o l =l o t i
CLOSED SYMBOL=LOT 2
FLAGGED SYMBOL= LOT 3
EQ 2
-6
-5
-4
-3
_2
LOG (TOTAL PRESSURE, ATMS)
F i g u r e 4»
E x p e r im e n ta l R e s u l t s and T h e o r e t i c a l C o r r e l a t i o n
f o r O x id a tio n i n A ir
CHAPTER V
THEORETICAL RATE CALCULATIONS
The t h e o r e t i c a l s u r f a c e r e c e s s i o n r a t e s w ere c a l c u l a t e d from t h r e e
d i f f e r e n t e q u a tio n s .
ran g e.
E ach e q u a t i o n was v a l i d o v e r a s p e c i f i c p r e s s u r e
The t h r e e p r e s s u r e r a n g e s w e re h i g h p r e s s u r e s (P 2. 4 x IO- ^ a t m ) ,
low p r e s s u r e s (P < 3 x ' 10 ^ a t m ) , a n d i n t e r m e d i a t e p r e s s u r e s (3 x IO- ^
< P < 4 x 10 ^ a tm ) .
T h e o r e t i c a l R a te s a t H ig h P r e s s u r e s
At h i g h p r e s s u r e s (P > 4 x 10 ^ a t m ) , w h ere a b o u n d a ry l a y e r i s
p r e s e n t , t h e o x i d a t i o n r a t e was f o u n d t o b e b e s t d e s c r i b e d a s b e in g c o n ­
t r o l l e d by d i f f u s i o n o f th e ir id iu m - c o n ta in in g s p e c ie s th ro u g h th e bound­
a ry la y e r ( 6 ).
The c o n s u m p tio n o f t h e i r i d i u m m e t a l i s e q u a l t o t h e t o t a l
f lu x o f ir id iu m - c o n ta in in g s p e c ie s and th u s th e o x id a tio n r a t e , e x p re s s e d
a s a s u rfa c e re c e s s io n r a t e ,
i s r e p r e s e n t e d b y t h e f o l l o w i n g e q u a ti o n :
I A k
i
Gi
[ 1]
i
w h e re A i s an e q u i v a l e n t w e ig h t (m a ss o f i r i d i u m consum ed p e r m ole o f d i f ­
f u s i n g s p e c i e fo rm e d ) d i v i d e d b y t h e d e n s i t y , o f i r i d i u m ,
t r a n s f e r c o e f f ic ie n t f o r th e i
i s t h e m ass
s p e c i e , P^ i s t h e p a r t i a l p r e s s u r e o f t h e
i**1 s p e c i e a t t h e i n n e r s u r f a c e o f t h e b o u n d a ry l a y e r ,
and x i s th e s u r f a c e
re c e s s io n r a t e .
The p a r t i a l p r e s s u r e s o f t h e d i f f e r e n t s p e c i e s a t t h e i n n e r s u r f a c e
o f t h e b o u n d a ry l a y e r c a n b e c a l c u l a t e d fro m t h e r e s p e c t i v e e q u i l i b r i u m
c o n s t a n t s ( t r e a t e d a s unknow ns) and t h e ox y g en p a r t i a l p r e s s u r e .
E q u a tio n
i
I , t h e n , "becomes:
x
w h e re K
A (kG2 K2 P
[2 ]
+ k G3 K3 P q} / 2. +. - GM - M
i s t h e e q u i l i b r i u m c o n s t a n t f o r t h e f o r m a ti o n o f IrC L ( g ) , K
th e e q u ilib r iu m c o n s ta n t f o r th e fo rm a tio n o f IrO 3 ( g ) ,
is
i s th e vapor
p r e s s u r e o f t h e i r i d i u m m e ta l a t t h e i n n e r s u r f a c e o f t h e b o u n d a ry l a y e r ,
and P
O2
i s th e p a r t i a l p r e s s u r e o f oxygen.
The p a r t i a l p r e s s u r e o f i r i d i u m m e ta l c a n b e c a l c u l a t e d fro m t h e em­
p i r i c a l v a p o r p r e s s u r e e q u a t i o n o f H o n ig a n d K ram er ( l O ) ;
l o g ( 7 6 0 PM) = - 8 4 6 4 .6 7 /T k + 6 5 .5 8 1 2 I o g (T fc)
- O.OIOO 272 Tfc + 5 .4 4 9 8 1 x IO - 7 Tfc2
[3.1
w h e re P ^ ' i s t h e v a p o r p r e s s u r e o f t h e m e ta l i n a tm o s p h e r e s a n d Tfc. i s t h e
t e m p e r a t u r e o f t h e w i r e i n 0K.
The m ass t r a n s f e r c o e f f i c i e n t s c a n b e c a l c u l a t e d fro m an e x p r e s s i o n
w h ic h w as o b t a i n e d fro m t h e C h i l to n - C o l b u r n e q u a t i o n s ( l l )
h P
fG, ? 9vi
2 /3
[4 ]
B Tf Gp f Pm
w h e re h i s t h e c o n v e c t i v e h e a t - t r a n s f e r c o e f f i c i e n t , P i s t h e t o t a l p r e s ­
s u r e , R i s t h e i d e a l g a s c o n s t a n t , T^ i s t h e f i l m t e m p e r a t u r e ( t h e a r i t h ­
m e tic m ean o f t h e w ir e t e m p e r a t u r e a n d t h e a m b ie n t t e m p e r a t u r e ) , C i s t h e
?
s p e c i f i c h e a t o f t h e o x i d i z i n g g a s a t c o n s t a n t p r e s s u r e , ,0 i s t h e d e n s i t y
o f th e o x id iz in g g a s ,
i s t h e l o g a r i t h m i c mean p r e s s u r e o f t h e n o n d i f ­
f u s i n g o x i d iz in g g a s ( t h u s , P^m
o x i d i z i n g .g a s , and D
P ) , k i s th e th e rm o c o n d u c tiv ity o f th e
i s t h e g a s e o u s d i f f u s i v i t y f o r t h e i ^ r s p e c i e . ...
The p r o p e r t i e s f o r t h e t w o . o x i d i z i n g g a s e s w ere l e a s t - s q u a r e s c u r v e fit
o v e r a f i l m - t e m p e r a t u r e r a n g e o f IOOO0K t o 140C°K f o r o r i g i n a l d a t a
( 1 2 ,1 3 ).
T a b le s 3 and 4 c o n t a i n t h e r e s u l t i n g e q u a t i o n s an d an i n d i c a t i o n
o f th e e f f e c tiv e n e s s o f th e f i t .
The mean f r e e p a t h e q u a t i o n s f o r e a c h
g a s w e re d e v e lo p e d fro m t h e Dushman e q u a t i o n ( 1 4 )»
The c o n v e c t i v e h e a t - t r a n s f e r c o e f f i c i e n t was e v a l u a t e d fro m -tw o d i f - .
f e r e n t e q u a t i o n s f o r t h e N u s s e l t n u m b e r, t h e M a d d o n -P ir e t ( 1 $ ) e q u a ti o n
a n d t h e D ra k e e t a l ( l 6 ) e q u a t i o n .
I n s u b s e q u e n t c o m p u te r c a l c u l a t i o n s ,
i t was fo u n d t h a t t h e M a d d e n - P ire t e q u a t i o n y i e l d e d a s l i g h t l y b e t t e r
c o r r e l a t i o n b e tw e e n c a l c u l a t e d a n d e x p e r i m e n t a l r e c e s s i o n r a t e s .
The M a d d e n - P ir e t e q u a t i o n f o r . t h e . N u s s e l t num ber i s ;
Nu = ________ .
_________
2
_____________ ,
l n ( 6 . 82 / R a V 3 ) + 8k X /* (Y + l) y u C v D - l n ( l + 2 ^ /D )
= h D
k
w h e re \ i s t h e m ean f r e e p a t h i n t h e g a s , D i s t h e d i a m e t e r o f t h e w i r e ,
.«*. i s t h e th e r m a l a c co m m o d a tio n c o e f f i c i e n t ( t r e a t e d a s an u n k n o w n ),
is
t h e s p e c i f i c h e a t a t c o n s t a n t volum e f o r t h e o x i d i z i n g g a s , a n d Ra i s t h e
d i m e n s i o n l e s s R a y le ig h n u m b e r.
G r a s h o f a n d P r a n d t l n u m b e rs ;
The R a y l e ig h num ber i s t h e p r o d u c t o f t h e
20
T a b le 3 .
P r o p e r t i e s o f A ir
IOOO0K < Tf < 1 4 0 0 cK
P ro p e rty
D e n s ity
(gm /cm 5 )
S p e c if ic H eat
( c a l/g m /° K )
V is c o sity
(g m /s e c /e m )
T herm al C o n d u c t i v i t y
( c a l / c m / s e c / K)
S p e c if ic H eat R a tio
(d im e n s io n le s s )
Mean T r e e P a t h
(cm )
1
I
-- —
Ma.x. 'js L e v i a t i o r
R e la tio n
p = 0 .3 5 3 0 P /T f
0 .0 1 1
C = 0 .0 7 7 3 T,.0 *1825
P
0 .0 8 2
/t=
7 .3 1 3 x IO " 6 Tf 0 ,5 8 4 9
k = 1 .2 3 9 x IO " 6 Tf 0 *7023
X = 2 .0 0 1 Tf " 0 ' ° 5 85
0 .0 8 1
0 .3 1
.0 .0 1 8
O m I .O 849
A = 1 .5 3 4 7 x 10 ° 1T
-
P
NOTE:
P i s t h e t o t a l p r e s s u r e i n a tm o s p h e r e s .
Tf i s t h e f i l m
t e m p e r a t u r e i n °K.
.v ;
21
T a b le 4»
P r o p e r t i e s o f Oxygen
IOOO0K <[ Tf < 1 4 0 0 0K
P r o p e rty -
R e la tio n
D e n s ity
S p e c if ic H eat
V is c o s ity
( g m /s e c /c m )
T h erm al C o n d u c t i v i t y
. x 10
S p e c if ic H eat R a tio
( d im e n s io n le s s )
Mean F r e e P a t h
NOTE:
P i s t h e t o t a l p r e s s u r e i n a tm o s p h e r e s .
Tf i s . t h e f i l m
t e m p e r a t u r e i n 0K.
y
22
Ra = Gr P r
= ( g /
D i(3A T ^ 2)(C pyk )
[6]
w h e re g i s t h e a c c e l e r a t i o n o f g r a v i t y , p, i s t h e c o e f f i c i e n t o f th e r m a l
e x p a n s io n f o r t h e o x i d i z i n g g a s , a n d A T i s t h e d i f f e r e n c e b e tw e e n t h e
w i r e t e m p e r a t u r e a n d t h e a m b ie n t t e m p e r a t u r e .
t h e g a s e o u s d i f f u s i v i t y , was c a l c u l a t e d fro m t h e W ilk e -L e e
m o d if ie d H i r s c h f e l d e r - B i r d - S p o t z e q u a t i o n ( I 7 ) :
[ 1 0 .7 - 2 .4 6 ( l/ M . + l /M ) 1/ 2 ] IO - 4 T 3/ 2 ( l/M . + l/M ) 1/ 2
' [7 ]
vi
P r 12 1D
w h ere
i s t h e m o le c u la r w e ig h t o f t h e i
th
•
■
d i f f u s i n g s p e c ie ^
M
i s t h e m o le c u la r w e ig h t o f t h e o x i d i z i n g g a s ,
r, p
(r ) + (r )
= ' o I ______ o 2 , t h e c o l l i s i o n d i a m e te r f o r c o l l i s i o n b e tw e e n
2
t h e o x i d i z i n g g a s m o le c u le a n d t h e m o le c u le o f a n i r i d i u m c o n ­
ta in in g s p e c ie ,
( r Q)^
= ! . I S ( V q ) 1/ 3 , c o l l i s i o n d i a m e te r f o r c o l l i s i o n b e tw e e n o x i d i z ­
i n g g a s m o le c u le s ,
( r Q)g
= ! . I S ( V q ) 1/ 3 , c o l l i s i o n d i a m e te r f o r c o l l i s i o n b e tw e e n m o le ­
c u l e s o f an i r i d i u m c o n t a i n i n g s p e c i e ,
(Vq)^
i s t h e m o la l volum e o f t h e o x i d i z i n g g a s ,
(VQ)g
i s t h e m o la l volum e o f t h e i r i d i u m c o n t a i n i n g s p e c i e ,
I
23
= 0 , 6 7 3 (k Tf / 6 1 9 )
1D
c o llis io n - in te g r a l f o r d iffu s io n
(re ­
s u lt o f a le a s t- s q u a r e s c u r v e f it o f o r ig in a l d a ta ( $ ) ) ,
i s t h e e n e r g y o f m o le c u la r i n t e r a c t i o n ,
k
i s t h e B o ltz m a n n c o n s t a n t ( 1 .3 8 x 10~
The v a l u e o f
was' c a l c u l a t e d fro m t h e e q u a t i o n ;
e 12/ k -
e rg s /° % ).
. . . .
(.(E1A K e 2Z E ) ) 1/ 2
w h e re € ^ / k i s known f o r t h e o x i d i z i n g g a s ( f o r Og = 1 1 3 .2 0K;. f o r a i r = 9 7 .:0
°K) a n d E g / k was d e te r m in e d f o r t h e d i f f e r e n t d i f f u s i n g s p e c i e s fro m t h e
re la tio n ;
.
€ 2/ k
=
1 . 9 2 Tm
Tm i s t h e m e l t i n g t e m p e r a t u r e o f t h e o x i d e s , t r e a t e d a s an unknown i n t h i s
a n a l y s i s ( b u t known t o b e g r e a t e r t h a n 1383°K f o r IrO 9 ( 1 8 , 1 9 ) ) .
The c o e f f i c i e n t , A, o f E q u a tio n 2 was. c a l c u l a t e d fro m t h e e q u a t i o n ;
A = 192»2 gm I r c o n su m e d /m o le d i f f u s i n g s p e c i e fo rm e d
pIr 1 V
w h ere
P
=
I r ’ Tk
^ I r f 298 °K
(I + ^ L
/1 0 0 )3
[83
k
A L , t h e p e r c e n t l i n e a r t h e r m a l e x p a n s io n , w as c a l c u l a t e d fro m t h e e q u a t i o n ;
24
A l
,
=
6 .1 4 4
X
k
10 6 T, 1 *632
-
'
w h ic h was th e - r e s u l t o f c u r v e f i t t i n g t h e t h e r m a l - e x p a n s i v i t y r e s u l t s of. H al
v o r s o n a n d Wimber ( 7 ) .
A s u c c e s s i v e - s u b s t i t u t i o n c o m p u te r m eth o d was u s e d t o d e te r m in e t h e
optim um v a l u e s o f e a c h o f t h e unkn o w n s, <x, K ^, K ^f a n d T ^, f o r t h e e x p e r i ­
m e n ta l r e s u l t s o f o x i d a t i o n .
a t h ig h p r e s s u r e s .
T h is was d o n e o n ly f o r t h e r e s u l t s i n oxygen
From t h i s m e th o d , i t w as fo u n d t h a t ' o x i d e - m e l t i n g tem ­
p e r a t u r e s i n t h e r a n g e o f 1 4 0 0 t o I 8 0 0 °K h a d v e r y l i t t l e
s u lts .
re s u lts ,
e f f e c t on t h e r e ­
As a m e l t i n g t e m p e r a t u r e o f 1400°K ' d i d y i e l d v e r y s l i g h t l y b e t t e r
i t was c h o s e n a s t h e o x id e m e l t i n g t e m p e r a t u r e s .
The a c c o m m o d a tio n c o e f f i c i e n t a n d t h e e q u i l i b r i u m " c o n s t a n t s w ere f u n c ­
t i o n s ' o f w ire te m p e ra tu re .
The optim um v a l u e s o f t h e a c co m m o d a tio n c o e f ­
f i c i e n t w e re l e a s t - s q u a r e s c u r v e f i t o v e r t h e t e m p e r a t u r e r a n g e o f. 1948 t o
o
2533 K.
The r e s u l t i n g e q u a t i o n f o r « w as:
cx = 3 3 5 .6 3 1 - 0 .4 8 8 5 6 4 Tk + 2 .5 5 8 3 7 x 10“4 Tk2
- 5 .5 7 0 9 8 x IO "6 Tk3 + 4 .0 3 3 2 2 x IO "12 Tk4
[ 9]
(maximum d e v ia t io n o f th e eq u a tio n from optimum v a lu e s was 0.000249/&)"
The
f r e e e n e r g ie s o f fo rm a tio n were c a lc u la t e d from th e e q u ilib r iu m c o n s ta n ts
b y u s in g th e e q u a tio n :.
A F , ° = (-R T, I n K ) / l 00.0
I
. . K
«
w h e r e A F ^0 i s t h e f r e e e n e r g y o f f o r m a t i o n , R i s t h e i d e a l g a s c o n s t a n t ,
25
.
Tjc i s t h e a b s o l u t e w i r e t e m p e r a t u r e , a n d . K i s t h e e q u i l i b r i u m c o n s t a n t .
V a lu e s o f t h e f r e e e n e r g i e s o f f o r m a t i o n o b t a i n e d fro m t h e e q u i l i b r i u m c o n ­
s t a n t s w e re a l s o l e a s t - s q u a r e s c u r v e f i t o v e r t h e t e m p e r a t u r e r a n g e o f I 948
t o 2 5 3 3 °K.
The r e s u l t i n g e q u a t i o n s w e re :
A F f 0 L IrO 2 C g )] = 5 4 1 .4 5 8 - 0 .6 6 8 7 3 6 Tjc + '2 .9 1 6 1 0 .
x IO"4 Tk2 - 4 .2 7 2 9 7 x IO"8 Tjc3 , k c a l/m o le
(maximum d e v i a t i o n was 0 , 26 ^ ) , a n d
■
A F - 0L lr d 1Cg)] = 2 1 4 .1 8 0 - 0 .2 9 8 8 1 0 T
X
J
[lO ]
K
+ 1 .4 9 8 3 2
x IO"4 Tjc2 - 2 .4 1 8 9 5 X IO"8 Tjc3 , k c a l/m o le .
[H ]
(maximum d e v ia t io n was 0 . 27 '^).
These e m p ir ic a l e q u a tio n s were u sed in th e c a l c u la t io n o f s u r fa c e r e ­
c e s s io n r a t e s f o r o x id a tio n in oxygen.
N um erical v a lu e s f o r th e c a lc u la t e d
r a t e s a t th e ex p erim en ta l c o n d it io n s a re p r e s e n te d in T able 10 in th e ap­
p e n d ix .
R e c e s s io n r a t e s c a lc u la t e d from E quation 2 f o r a w ire 0 .0 5 5 9 cm
in d iam eter a re r e p r e s e n te d by cu rv es shown in F ig u re 3«
The d e g r e e o f c o r r e l a t i o n b e tw e e n t h e e x p e r i m e n t a l a n d c a l c u l a t e d r a t e s
i s shown i n T a b le 5*
To p e rf o r m t h i s a n a l y s i s , t h e n e c e s s i t y t o d e v e lo p a
m eth o d t h a t w o u ld " s t a n d a r d i z e " t h e r a t e s t o a common d i a m e t e r a r o s e .
T h is
was n e c e s s a r y a s t h e e x p e r i m e n t a l a n d c a l c u l a t e d r a t e s a r e d e p e n d e n t u p o n
t h e w ir e d i a m e t e r .
The d i a m e te r d e p e n d e n c y was fo u n d t o b e d e s c r i b e d , b y
■'
r a i s i n g t h e d i a m e te r o f t h e w i r e t o a p o w er ( r e s u l t o f l e a s t - s q u a r e s c u r v e -
.iV
26
Table 5« E f f e c t iv e n e s s o f th e F in a l C o r r e la tio n f o r R ates
in Oxygen a t P r e ss u r e s G reater Than 4 x IO- ^ atm.
Temp °C
.
Approximate
E xperim ental S c a t t e r , %
C o r r e la tio n
D is p a r it y , *)
6v&
1675
5 .3
1820
4 .4
■ 4 .3
1965
. 5 -1
7 -7
2110
9.3,
. 8 .0
1 2 .4
1 3 .2
7 -4
8 .4
2260
O vera ll
.
f i t o f d a ta by Kraus ( 9 ) ) •
Table- 6 c o n ta in s a sujnmary o f th e powers and
9
th e r e s p e c t i v e tem p era tu res. .
Table 6 . Exponent o f Diam eter Used in
D eterm in ing th e D iam eter Dependency
Wire Temp °G
*
. Exponent o f Diam eter pd
1675
- 0 .7 0
1820
- 1 .1 1 *
1965
- 1 .2 6
2110
- 1 .1 1 *
2260
- 1 .1 7
:
■
E s t i m a t e d .v a lu e s
The w ire d ia m eter ch osen t o r e p r e se n t th e sta n d a r d iz e d v a lu e was 0 .0 5 5 9 'tn
(an avera g e w ire d ia m e te r ).
To c l a r i f y th e c a l c u la t io n s made in d eterm in in g
a sta n d a r d ise d r a t e , th e f o llo w in g -eq u ation may be r e f e r r e d to :
Xg = x ( D /0 .0559
where x
i s th e sta n d a r d iz e d r a t e , x i s th e a c tu a l f a t e f o r a w ire d iam eter
D, and ot1 i s th e a p p r o p r ia te power from T able 6.
The "approxim ate ex p erim en ta l s c a t t e r " i s th e a v era g e a b s o lu te d e v ia ­
t io n o f th e s ta n d a r d iz e d r a t e s from th e mean a t a g iv e n tem p eratu re and
p ressu re.
The " c o r r e la t io n d is p a r ity " i s th e average a b s o lu te d if f e r e n c e
betw een a c tu a l ex p erim en ta l r a t e s and r a t e s c a lc u la t e d from E quation 2
( u s in g ex p erim en ta l tem p era tu res, p r e s s u r e s and d ia m e te r s ).
28
R e c e s s i o n ' r a t e s i n a i r w e re c a l c u l a t e d u s i n g t h e sam e e q u a t i o n s ( w i th
th e a p p r o p r i a t e e q u a tio n s r e p r e s e n t i n g t h e - p r o p e r t i e s o f a i r and th e p a r ­
t i a l p re s s u re o f oxygen) .
N u m e ric a l r e s u l t s f o r t h e s e c a l c u l a t i o n s a r e
p r e s e n t e d i n T a b le 11 i n t h e a p p e n d ix .
F i g u r e 4 show s a c u r v e r e p r e s e n t ­
i n g t h e r e c e s s i o n r a t e s o f a w i r e O.O 559 cm i n d i a m e te r c a l c u l a t e d fro m
E q u a t io n 2 .
L i m i t a t i o n s on t h e r a n g e s o f v a l i d i t y f o r t h e s e e q u a t i o n s a r e d e p e n ­
d e n t u p o n t h e r a n g e , o f v a l i d i t y f o r t h e C h i l to n - G o l b u r n e q u a t i o n ( E q u a tio n
4 ) an d t h e M a d d e n - P ir e t e q u a t i o n ( E q u a ti o n $ ) .
E q u a tio n 4 i s v a l i d f o r
P r a n d t l n u m b e rs i n t h e r a n g e o f 0 .6 t o 100 a n d f o r S c h m id t n u m b ers (w/jpN^^ )
i n t h e r a n g e o f 0 .6 t o 2 5 0 0 .
t h e r a n g e o f 10
8
t o 10
—1
.
E q u a t io n 5 i s v a l i d f o r R a y l e ig h n u m b ers i n
The P r a n d t l , S c h m id t, and. R a y l e ig h n u m b ers i n
t h e p r e s e n t s t u d y w e re i n t h e r a n g e s o f 0 .7 3 1 t o 0 . 7 3 2 , I . 51 t o I . 9 0 , a n d
O
4 .9 8 x 10
•»
t o 1 .9 x 10
'
re s p e c tiv e ly .
T h e o r e t i c a l R a te s a t Low P r e s s u r e s
At lo w p r e s s u r e s
(P C 3 x 10 ^ a tm ) , t h e r a t e w as a ssu m e d t o b e c o n ­
t r o l l e d by th e v a p o r iz a tio n o f th e ir id iu m - c o n ta in in g s p e c ie s .
The f l u x
(m o le s o f v a p o r m o le c u le s t h a t l e a v e a s u r f a c e p e r u n i t a r e a a n d t im e ) c a n
b e c a l c u l a t e d fro m t h e H e r tz - L a n g m u ir e q u a t i o n a s m o d if ie d b y K nudsen (.2 0 ):
J
i'0.(Prr v S p. r ' /2
w h e re d i s t h e f l u x , o<v i s t h e v a p o r i z a t i o n c o e f f i c i e n t ( i n t h e p r e s e n t
s t u d i e s a ssu m e d e q u a l t o o n e ) , P^
i s th e e q u ilib riu m p r e s s u r e o f th e s p e c ie ,
•
29
M i s t h e m o l e c u l a r w e ig h t o f t h e s p e c i e , R i s t h e i d e a l g a s c o n s t a n t , and
Tjc i s t h e a b s o l u t e t e m p e r a t u r e o f t h e w i r e .
P
f o r t h e o x id e s IrO 2 ( g ) a n d
I r O ^ ( g ) c a n b e c a l c u l a t e d fro m t h e r e s p e c t i v e e q u i l i b r i u m c o n s t a n t a n d t h e
p a r t i a l p r e s s u r e o f oxygen.
The e q u i l i b r i u m c o n s t a n t s i n t u r n c a n b e c a l ­
c u l a t e d fro m t h e f r e e e n e r g i e s o f f o r m a t i o n ( E q u a ti o n s 10 a n d 1 1 ) .
The
v a p o r p r e s s u r e o f . t h e i r i d i u m c a n b e c a l c u l a t e d fro m E q u a t i o n 3 .
A s u rfa c e r e c e s s io n r a t e i s e x p re sse d by:
Tk
w h e re J . i s t h e f l u x o f t h e i ^*1 s p e c i e a n d ^
m
i s th e d e n s ity o f irid iu m
1
’ 'k
a t t h e t e m p e r a t u r e T^ ( c a l c u l a t e d fro m E q u a t i o n 8 ) .
t o t h e fo rm :
.
E q u a t io n 12 was r e d u c e d
J
x = 4 4 .3 [ P m( l 9 2 . 2 / T k ) 1//2 + 0 .8 5 7 3 K2 Pq ( 2 2 4 . 2 / t ^ 1/ 2
+ 0 .8 0 0 2 K3 P 0 ^ 5 ( 2 4 0 . 2 /T k ) V 2] / ^
[1 3 ]
W here x i s t h e s u r f a c e r e c e s s i o n r a t e , P ^ i s t h e v a p o r p r e s s u r e o f t h e i r i d ­
ium m e t a l , Tk i s t h e a b s o l u t e w ir e t e m p e r a t u r e , K2 I a t h e e q u i l i b r i u m c o n ­
s t a n t f o r I r O - ( g ) , K, i s t h e e q u i l i b r i u m c o n s t a n t f o r I r O . ( g ) , an d P
is
^
j
f
U2
th e p a r t i a l p r e s s u r e o f oxygen.
A s im p l e c o m p u te r p ro g ra m was u s e d t o c a l c u l a t e r e c e s s i o n r a t e s a t t h e
e x p e r i m e n t a l c o n d i t i o n s , b o t h i n ox y g en a n d . i n a i r .
The r e s u l t s a r e p r e ­
s e n t e d i n T a b l e s 10 a n d 11 i n t h e a p p e n d ix r e s p e c t i v e l y .
The r e s u l t s f o r
b o t h oxygen, a n d a i r a r e shown g r a p h i c a l l y i n F i g u r e s 3 a n d 4 r e s p e c t i v e l y .
30
■
The d e g r e e o f c o r r e l a t i o n b e tw e e n t h e :e x p e r i m e n t a l a n d . c a l c u l a t e d r a t e s i n
o x y g en i s i n d i c a t e d i n T a b le 7*
T a b le 7« E f f e c t i v e n e s s o f t h e F i n a l C o r r e l a t i o n f o r R a te s
i n Oxygen a t P r e s s u r e s L e s s Than 3 x IO-"-3 a tm . "
--------- -— ----------------- --------------------Temp 0C
E x p e r im e n ta l S c a t t e r , fo
C o rre la tio n
D i s p a r i t y , jo
1965
1 0 .0
1 2 .0
2110
1 6 .9
17.-3.
2260
1 8 .9
2 1 .6
O v e r a ll
1 5 .5
1 7 .3
The " e x p e r i m e n t a l s c a t t e r " i s t h e a v e r a g e a b s o l u t e d e v i a t i o n o f t h e e x p e r ­
i m e n t a l r e c e s s i o n r a t e fro m t h e mean a t a g i v e n t e m p e r a t u r e an d p r e s s u r e .
L i m i t a t i o n s on t h e r a n g e o f v a l i d i t y f o r t h e s e c a l c u l a t i o n s d e p e n d s
u p o n t h e r a n g e o f v a l i d i t y f o r E q u a tio n 1 3 .
E q u a tio n 13 i s v a l i d f o r p r e s ­
s u r e s l e s s t h a n 3 x 10 ^ atm ( b a s e d u p o n a K nudsen num ber o f . 5 ( 2 l ) ) .
T h e o r e t i c a l R a te C a l c u l a t i o n s a t I n t e r m e d i a t e P r e s s u r e s
The o x i d a t i o n r a t e s i n t h e i n t e r m e d i a t e p r e s s u r e r a n g e • (3 x 10
P
< 4 x 10 4 a tm ) w e re a ssu m e d t o b e c o n t r o l l e d b y a c o m b in a tio n o f v a p o r i z a ­
t i o n and d i f f u s io n o f th e v a rio u s s p e c ie s .
S e v e r a l c o m b in a tio n s o f t h e r e ­
c e s s i o n r a t e s a s c a l c u l a t e d b y E q u a t io n s 2 a n d 1 3 , w e re t r i e d i n an a tt e m p t
■
'
v
•
t o d e s c r i b e , th e . r a t e s i n t h e i n t e r m e d i a t e p r e s s u r e r a n g e .
...
.
Of t h e e q u a t i o n s 1
■t r i e d , t h e f o l l o w i n g y i e l d e d t h e b e s t c o r r e l a t i o n b e tw e e n e x p e r im e n ta l a n d
31
c a lc u la te d r a t e s ;
l o g ( x ) = 2 4 .0 3 0 Io g (X lj) + 3 . 7 8 l ( l o g ( x D) ) 2 + O.1 9 3 (Io g (X jj) ) 3
- 1 5 . 1 5 5 . l o g ( i v j - 2 . 5 4 8 ( l o g ( x v ) ) 2 - O .1 3 l( lo g ( ic v ) ) 3 + 1 5 .7 6 2
[> < |j
w here- Xjj i s t h e r a t e a s c a l c u l a t e d b y E q u a t i o n 2 an d Xy i s t h e r a t e a s c a l ­
c u l a t e d b y E q u a t io n 13«
T h e se e q u a t i o n s u s e d t o d e s c r i b e t h e r e c e s s i o n r a t e s
a t t h e i n t e r m e d i a t e p r e s s u r e s w e re o b t a i n e d b y l e a s t - s q u a r e s c u r v e f i t t i n g
w ith r e s p e c t t o th e e x p e rim e n ta l r e c e s s io n r a t e s in th e in te r m e d ia te p r e s s u r e
ran g e.
A s im p l e c o m p u te r p ro g ra m was u s e d t o c a l c u l a t e r e c e s s i o n r a t e s a t t h e
e x p e r i m e n t a l c o n d i t i o n s , i n b o t h ox y g en and a i r .
i n T a b le s 10 a n d 11 i n t h e a p p e n d ix r e s p e c t i v e l y .
The r e s u l t s a r e p r e s e n t e d
C u rv e s r e p r e s e n t i n g t h e
s u r f a c e r e c e s s i o n r a t e i n oxygen a n d a i r f o r a w ir e 0 .0 5 5 9 cm i n d i a m e te r a r e
shown i n F i g u r e s 3 a n d 4 r e s p e c t i v e l y .
The d e g r e e o f c o r r e l a t i o n b e tw e e n
e x p e r i m e n t a l r a t e s a n d r a t e s c a l c u l a t e d b y E q u a t io n 14 i s i n d i c a t e d i n T a b le
8.
T a b le 8 . E f f e c t i v e n e s s o f t h e F i n a l C o r r e l a t i o n f o r R a t e s i n Oxygen
a t . P r e s s u r e s i n t h e I n t e r m e d i a t e R ange (3 x 10 ^ <( P
4 x 10
a tm )
C o rre la tio n
D i s p a r i t y , jo
OD
A p p ro x im a te
E x p e r im e n ta l S c a t t e r , 1
J0
VO
Temp 0C
1965
1 4 .2
2110
2 5 .1
2260
2 0 .0
■ 2 1 .8
O v e r a ll
1 9 .8
' 2 1 ,2
.
3 2 .0
32
An i n d i c a t i o n o f t h e c o r r e l a t i o n
10
—8
( o v e r t h e p r e s s u r e r a n g e o f 9 .8 x
t o 1 .3 2 a tm ) o f t h e e x p e r im e n ta l a n d c a l c u l a t e d r a t e s i n oxygen i s
p r e s e n t e d i n T a b le 9 .
T a b le 9« E f f e c t i v e n e s s o f t h e F i n a l
C o r r e l a t i o n f o r O x id a tio n i n Oxygen
Temp 0C
1965
A p p ro x im a te
E x p e r im e n ta l S c a t t e r , $
,
T .8
C o rre la tio n
D is p a rity , %
'
9 .1
2110
1 5 .6
1 6 .7
2260
1 5 .8
1 7 .3
O v e r a ll
1 2 .8
I4 .2
CHAPTER V I
DISCUSSION OF RESULTS
E x a m in a tio n o f F i g u r e s 3 a n d 4 r e v e a l e d no v i s i b l e d i f f e r e n c e s i n t h e
o x i d a t i o n b e h a v i o r o f t h e i r i d i u m w ir e fro m L o ts I ,
2 , and 3.
T h is i s s u b ­
s t a n t i a t e d n u m e r i c a l l y b y T a b le s 10 a n d 11 i n t h e a p p e n d ix .
E x a m in a tio n o f F i g u r e 3 , a l o n g w i t h T a b le s 6 , 7 , 8 , a n d 9 , r e v e a l e d
t h a t an e f f e c t i v e c o r r e l a t i o n b e tw e e n t h e e x p e r i m e n t a l a n d t h e o r e t i c a l
r e c e s s i o n r a t e s f o r o x i d a t i o n i n oxygen was a c h ie v e d .
few d a t a p o i n t s f o r o x i d a t i o n i n a i r ,
s c a t t e r c o u ld n o t b e p e r f o r m e d .
As t h e r e w ere t o o
an a n a l y s i s f o r t h e e x p e r im e n ta l
An e x a m in a tio n o f F i g u r e 4 i n d i c a t e s t h a t
t h e c o r r e l a t i o n b e tw e e n t h e e x p e r i m e n t a l a n d t h e o r e t i c a l r e c e s s i o n r a t e s
w as e f f e c t i v e .
When c o n s i d e r i n g t h e u n c e r t a i n t y o f + 6 .0 t o 6 .5 k c a l / m o l e f o r w ork
d o n e b y Norman e t a l , + 0 .9 k c a l / m o l e f o r w ork done b y O l i v e i , a n d + 0 .3
t o 0 .7 k c a l / m o l e f o r t h e p r e s e n t s t u d i e s , t h e f r e e e n e r g i e s o f f o r m a tio n
f o r IrO ^ (g ) a g re e f a i r l y w e ll.
When c o n s i d e r i n g t h e f r e e e n e r g i e s o f f o r ­
m a tio n f o r I r O g ( g ) , t h e d i s p a r i t y b e tw e e n t h e r e s u l t s o f t h e p r e s e n t
s t u d i e s a n d t h e r e s u l t s o f Norman e t a l i s g r e a t e r .
f r e e e n e r g ie s o f fo rm a tio n f o r IrO g (g ).
O l i v e i r e p o r t e d no
The r e s u l t s o f O l i v e i and t h e
p r e s e n t s t u d y , w h ic h h a v e t h e l e s s e r u n c e r t a i n t i e s , a r e i n c l o s e s t a g re e m e n t
CHAPTER V I I
SUMMARY
T h e re i s q u i t e good a g re e m e n t "between e x p e r im e n ta l a n d t h e o r e t i c a l
s u r f a c e r e c e s s i o n r a t e s f o r o x i d a t i o n i n b o t h oxygen a n d a i r .
The
t h e o r e t i c a l r a t e s w e re b a s e d upon e m p i r i c a l e q u a t i o n s f o r t h e f r e e .e n e r ­
g i e s o f f o r m a t i o n o f t h e s p e c i e s i n v o lv e d i n t h e o x i d a t i o n p r o c e s s .
The
r e s u l t s o f t h e s e e m p i r i c a l e q u a t i o n s a r e a l s o i n q u i t e g o o d a g re e m e n t
w ith th e r e s u l t s o f p r e v io u s i n v e s t i g a t o r s .
Ir(g ),
I r 0 2 ( g ) , a n d I r O ^ ( g ) w e re th o u g h t t o b e t h e m a jo r s p e c i e s
i n v o lv e d i n t h e s u r f a c e r e c e s s i o n o f t h e w i r e .
At low p r e s s u r e s (P ^ 3
x .10 ^ a tm ) , t h e r a t e was assu m e d t o b e p r e d o m in a te d b y t h e v a p o r i z a t i o n
of th e v a rio u s s p e c ie s .
F o r h ig h p r e s s u r e s (P ^ 4 x IQ- ^ a tm ) , t h e r a t e
was th o u g h t t o b e c o n t r o l l e d b y g a s e o u s d i f f u s i o n , o f t h e v a r i o u s s p e c i e s
t h r o u g h a b o u n d a ry l a y e r .
At t h e i n t e r m e d i a t e p r e s s u r e ( 3 x 10~^ ^ P <( 4
x 10 ^ a t m ) , t h e r a t e was assum ed t o b e c o n t r o l l e d b y a c o m b in a tio n o f
v a p o r iz a tio n and d if f u s io n o f th e s p e c ie s .
CHAPTER. V I I I
SUGGESTIONS' FOR FUTURE WORK
A s e a r c h f o r a b e t t e r e q u a tio n d e s c r ib in g th e s u r f a c e r e c e s s io n r a t e
in th e in te rm e d ia te p r e s s u re ran g e i s in o rd e r.
The e q u a t i o n a t p r e s e n t
( E q u a ti o n 1 4 ) d o e s n o t a ll o w f o r a sm o o th t r a n s i t i o n o v e r t h e e n t i r e p r e s ­
su re ran g e.
One p o s s i b l e e q u a t i o n t h a t s h o u ld b e i n v e s t i g a t e d i s
x =
X
V
w h e re P , i s t h e p r e s s u r e a t t h e u p p e r l i m i t o f v a l i d i t y f o r. E q u a t i o n 1 3 ,
Pg i s t h e lo w e r l i m i t o f v a l i d i t y f o r E q u a t i o n 2 , x ^ i s t h e r e c e s s i o n r a t e
a s c a l c u l a t e d fro m E q u a tio n 2 , a n d Xy i s t h e r e c e s s i o n r a t e a s c a l c u l a t e d
b y E q u a t io n 1 3 .
T h is t y p e o f e q u a t i o n f o r c e s a sm o o th t r a n s i t i o n
e n tir e p re s s u re ran g e b u t th e q u a lity o f th e f i t
over th e
o f t h i s e q u a tio n w ith r e ­
s p e c t t o t h e e x p e r i m e n t a l d a t a i s unknow n a t p r e s e n t .
I t s h o u ld b e k e p t i n m ind t h a t t h i s t y p e o f e q u a t i o n i s t h e r e s u l t o f
a s s u m in g t h a t . t h e r e c e s s i o n r a t e i n t h e i n t e r m e d i a t e p r e s s u r e r a iig e i s c o n ­
t r o l l e d by a c o m b in a tio n o f v a p o r i z a t i o n , an d g a s e o u s d i f f u s i o n .
REFERENCES
I.
■ 2.
3«
'4 .
C o r d e ftm k e , E . H. P« a n d M ey er, G ., "T he Systehi irid iu m -O x y g e n , I .
M e a su re m e n ts o f t h e V o l a t i l e O xide o f I r i d i u m " , R e c . f r a v . Chim . ,
8 1 , p p . 4 9 5 -5 0 4 , 1962.
~
A lc c c k , C. B. a n d H o o p e r, G. W ., "T h erm o d y n am ics o f t h e G aseo u s O x id e s
o f t h e P la tin u m G roup M e t a l s " , R o y al S o c i e t y o f L o n d o n , P r o c e e d in g
S e r i e s A, V o l» 2 5 4 , P P • '5 5 1 - 6 1 , i 9 6 0 .
.
. ■ . ■
S c h a f e r , V. H. a n d H e i t l a n d , H. J . , " G le ic h g e w ic h ts m e s s u n g e h im
S y stem I r i d i u m - S a u e r s t o f f G a s f o rm ig e s I r i d i u m t r i c x y d " , Z. A n o r g .A llgem ,. Chem. , 3 0 4 , p p . 2 4 9 - 6 5 , I 9 6 0 .
■N orm an, J . H ., e t a l , "M ass .S p e c tr o m e t r i c S tu d y o f G a se o u s ,O x id es o f
I r i d i u m " , J o u r n a l o f P h y s i c a l C h e m is t r y , V o l. 4 2 , P P . 1 1 2 3 - 4 , 1965•
5»
O l i v e i , A ., "M eth o d s f o r S tu d y in g O x y g e n -P la tin u m M e ta ls I n t e r a c t i o n " ,
J o u r n a l o f t h e L e s s Common M e t a l s , V o l. 2 9 , P P . 1 1 - 2 3 , 1 9 7 2 . ...
6.
W im ber, R. Q1. a n d K r a u s , H. G ., " O x i d a t i o n o f I r i d i u m " , M e t a l l u r g i c a l
T r a n s a c t i o n s , J u l y 1974•
7.
H a l v e r s o n , J . a n d W im ber, R. T . , "T h e rm a l E x p a n s io n o f I r i d i u m a t
H ig h T e m p e r a tu r e s " , J o u r n a l o f A p p lie d P h y s i c s ,. V o l. 4 3 , p p . 2 5 1 9 2 2, Ju n e 1972.
8.
M cL aren, g . H . , M urdock,- E . G ., a n d K ir b y , C. G. M .,
t h e C o n t r o l . a n d M easu rem en t o f W ire T e m p e ra tu re i n
A n n e a ls on S t a n d a r d P t /P t- lO R h T h e rm o c o u p le s " , The
S c i e n t i f i c I n s t r u m e n t s , V o l. 4 3 , No. 5 , P P • 8 2 7 - 8 ,
9.
K r a u s , H. G ., N a t u r a l C o n v e c tio n H ig h T e m p e ra tu re O x id a tio n o f I r i d i u m
M a s t e r 's T h e s i s , M o n tan a S t a t e U n i v e r s i t y , J u n e 1 9 7 3 .
10.
"A M ethod f o r
P re p a ra to ry
R eview o f
May 1 9 7 2 .
H o n ig , R. a n d K ra m e r, D. A ,, T e c h n iq u e s o f M e ta ls R e s e a r c h , V o l. TV,
P a r t I , I n t e r s c i e n c e P u b l i s h e r s ( J o h n W iley & S o n s ) , New Y o rk , p p .
515 - I 6 , 1 9 7 0 .
.
11.
12.
. S h erw o o d , T. K. a n d P i g f o r d , R. L . , A b s o r p tio n a n d E x t r a c t i o n , McGrawH i l l , New Y o rk , p p . 9 1 - 2 , 1 9 5 2 .
'
H i l s e n r a t h , . J . , e t a l , T a b le s o f T h erm al P r o p e r t i e s o f G a s e s , NBS
G iro . 564, 1955.
37
13.
R ohsenow , W. M. a n d " H a r n e t t , J . P . , H andbook o f H e a t T r a n s f e r , McGrawH i l l , New Y o rk , S e c t i o n 2 , p p . 8 4-5» 19737"
14.
Dushm an, S . , S c i e n t i f i c F o u n d a tio n s o f Vacuum T e c h n iq u e , Jo h n W iley &
S o n s , New Y o rk ,, p p . ' 3 0 , 1 9 6 2 .
-
15.
M addeti, A. J„ a n d P i r e t , E . L . , P r o c e e d i n g s of- t h e G e n e ra l D is c u s s i o n
on H e a t T r a n s f e r , I n s t i t u t i o n o f M ech. E n g rs . a n d Am. S o c . o f Mech;.
.E n g rs . , New Y o rk , p p . 328-33» 1 9 5 1 .
16.
D ra k e , R. M ., e t a l , " F r e e C o n v e c tio n H e a t T r a n s f e r fro m H o r iz o n ta l.
C y l i n d e r s t o G a se s a t T r a n s i t i o n K nudsen N u m b e rs", H e a t-M a ss T r a n s ­
f e r a n d T h e rm o d y n a m ic s,' p p . 1 1 9 -1 3 2 .-
17.
Emmert, R. E. . and P ig f o r d , R. L ., "Gas A bsb^gtion and S o lv en t Ex- ■
t r a c t i o n " , C h e m ic a l E n g i n e e r s H an d b o o k , 4 " E d . , R. H. P e r r y , e t a l ,
E d t r s . , M c G ra w -H ill, New Y o rk , p p . 2 0 - 1 , 1 9 6 8 .
18.
B e l l , W.. E . , T a g a m i, M, , a n d I n y a r d , R. E . , ." D i s s o c i a t i o n o f I r i d iu m
O x id e " , J o u r n a l o f P h y s i c a l C h e m is t r y , V o l. JO1 p p . 2 O48 - 5 O, 1 9 6 6 ..
19.
C o r d e fu n k e , E. H. P . a n d M e y er, G ., R e c . T r a v . Chim ♦ , V o l. 8 l , p p .
6 7 0 -8 , 1962.
20.
S e a r c y , A. Vi., e t a l , C h e m ic a l a n d M e c h a n ic a l B e h a v io r o f Irio rfc a n ic
M a t e r i a l s , W ix e y -I n t e r s c i e n c e , New Yo r k , . p p . 1 0 8 - 1 1 , 1 9 7 0 .
: ■
21.
■ J
McAdams, W .-H ., H e a t T r a n s m i s s i o n , M c G ra w -H ill, New Y o rk , p p . 3 2 0 ,
1954.
$
'
APPENDIX
APPENDIX A
T a b le 1 0 . E x p e r im e n ta l C o n d i t io n s a n d E x p e r im e n ta l
a n d C a l c u l a t e d R e c e s s io n R a t e s f o r Oxygen
I*
2*
3*
4*
5*
6*
7*
8*
9*
10*
11*
12*
13*
14*
15*
16*
17*
18*
1.9*
20*
21*
22*
23*
24*
25*
26*
27*
28*
29*
30*
31
32
33
-P
•
OO
Run
N o.
Temp.
(°c )
P re ss.
(T o rr)
A vg. D iam.
(cm )
E x p e r im e n ta l
R a te ( c m / s e c )
C a lc u la te d
R a te ( c m /s e c )
I
I
2
2
I
I
2
2
I
I
2
2
I
I
I
I
I
I
I
2
2
2
2
2
2
2
2
2
2
I
2
I
2
1675
I . OE 00
0 .0 4 0 9
0 .0 6 1 0
0 .0 4 9 2
. 0 .0 5 2 3
0 .0 6 1 6
■O.O 64 O
3 . 5 2E -0?
2 .4 4 E -0 7
2.50E -Q 7
2 .6 8 E -0 7
5 .7 0 E -0 7
5 .3 5 3 - 0 7
6 .2 9 E -0 7
6 . 58 E-O 7
I . 46 E-O 6
I . 50E -06
I . 58 E-O 6
I • 60E—06
6 .3 4 3 - 0 6
5 . 89 E-O 6
6 .5 1 3 - 0 6
7 .2 8 E -0 6
8 . 15 E-O 6
3 .1 0 E -0 7
I . OE 01
0 .0 4 6 5
0 .0 4 9 8
I . OE 02
I . OE 03
1820
I . OE 00
5 . OE 01
I . OE 03
'
1965
7 .5 3 - 0 5
.
5 .OE-O 4
0 .0 5 8 2
O.O 614 '
0 .0 5 0 9
0 .0 4 7 4
0 .0 5 2 2
0 .0 6 1 5
0 . 056,7
O.O 5 I 6
0 .0 4 6 3
0 .0 4 0 1
9 .3 8 3 -0 6
7 .8 4 3 - 0 6
0 .0 5 7 4
0 .0 5 0 6
7 ..07 E-O 6
4 .5 3 3 - 0 7
0 .0 4 9 7
0 .0 5 2 1
4 . 25E-07
4 .9 6 3 -0 7
0 .0 4 6 3
0 .0 6 0 9
1 .7 9 3 - 0 6
O.O 656
I . 583-06
2*263-06
0 .0 4 5 7
9 . 56 E-O 6
0 .0 4 2 8
9 .3 2 3 -0 6
0 .0 4 6 4
0 .0 4 9 4 ' ■ . l.O lE r-0 5
9 . 4 7 3-09 .
0 .0 6 0 9
1 .2 1 3 - 0 8
0 .0 4 9 9
1 .1 3 3 - 0 8
0 .0 5 6 3
' 1 .6 0 3 -0 8
0 .0 4 5 9
2 .4 2 3 -0 7
2 .7 7 3 - 0 7
2 .6 7 3 - 0 7
5 .4 6 3 -0 7
5 .2 9 3 - 0 7
6 .8 2 E -0 7
6 . 46 E-O 7
1 . 58 E -0 6
1 . 51 E-0 6
1 . 74 E-0 6
1 . 843-06
6 .9 0 3 -0 6
6 . 25 E-0 6
6 . 56 E-0 6
6 .9 5 3 - 0 6
7 .4 4 3 - 0 6
8 .1 7 3 - 0 6
6 . 5 IE -O 6
7 .0 4 E -0 6
4 .5 6 3 -0 7
4 .4 7 3 - 0 7
4 . 68 E-0 7
1 .8 3 3 - 0 6
1 .7 3 3 - 0 6
2 .2 8 3 -0 6
9 . 9 OE-O6
9 .4 0 3 -0 6
9 . 033-06
1 .2 7 3 - 0 8
1 .2 7 3 -0 8
1 .2 7 3 - 0 8
1 .3 5 3 - 0 8
40
T a b le 10 ( c o n t i n u e d )
Run
No.
34*
35*
36
37
38
39
40*
.41*
42
43*
44*
45*
46*
47*
48 *
49*
50 *
51*
52*
53*
54*
55*
56 *
57*
58 *
59*
60 *
61 *
62 *
63*
64 *
65 *
66
67
68
69
70
Lot
No.
I
I
2
2
3
2
I
I
2
I
I
I
I
I
2
2
I
I
I
I
I
I
I
2
I
I
2
2
I
I
2
2
2
I
3
2
I
Temp.
(°c )
P re ss.
(T o rr)
1965
5 . 0E -04
1 .0 E - 0 2
5 .0 E - 0 2
I . OE-Ol
I . OE 00
I . OE 01
I . OE 02
I . OE 03
2110
7 .5 E - 0 5
5 .OE-O 4
Avg. : Diam.
(cm )
0 .0 6 1 6
O.O 569
O.O 495
0 ,0 4 7 6 .
0 ,0 4 9 6
0 .0 4 7 7
0 .0 6 1 8
O.O 652
0 .0 5 0 0
0 .0 5 3 8
0 .0 5 0 2
O.O 479
0 .0 5 1 7
0 .0 5 4 7
O.O 505
O.O 4 8 O
0 .0 4 5 5
O.O 552
O.O638
0 .0 6 0 0
0 .0 5 8 3
0 .0 5 1 9
0 .0 4 8 9
O.O 518
■ 0 .0 4 0 6
0 .0 5 3 2
O.O 516
0 .0 4 8 9
0 .0 6 0 4
0 .0 6 3 4
0 .0 5 0 4
0 .0 4 6 3
0 .0 4 4 6
O.0517
0 .0 4 3 6
O.0483
0 .0 3 1 8
E x p e r im e n ta l
R a te ( c m /s e c )
1 .1 2 E -0 8
1 .1 1 E -0 8
3 .1 2 E -0 8
3 .0 9 B -0 8
■3 .4 1 E -0 8
6 .5 1 E -0 8
9 .8 0 E -0 8
7 .7 3 E -0 8
1.55.E -07
1 .5 3 E -0 7
1 .5 7 E -0 7
8 .0 5 E -0 7
5 .4 6 E -0 7
6.80E -07
7 .4 5 E -0 7
7 .7 6 E -0 7
2 .6 1 E -0 6
2 .1 5 E -0 6
1 .6 2 E -0 6
1 .7 6 E -0 6
I . 97 E-O 6
2 .1 3 E -0 6
2 .5 7 E -0 6
2.3O E -06
5 .1 1 E -0 6
3 .6 8 E -0 6
3 .5 7 E -0 6
3 .9 7 E -0 6
1 .0 7 E -0 5
' 9 . 48 E-O 6
1 .1 9 E -0 5
I . 27E -05
4 .7 9 E -0 8
1 .0 6 E -0 7
1 .4 4 E -0 7
7 .7 0 E -0 8
9 .8 0 E -0 8
C a lc u la te d
R a te ( c m /s e c )
I . 3 5 8 -0 8
1 .3 5 E -0 8
3 .2 1 E -0 8
3 .2 1 E -0 8
3 .2 1 E -0 8
8 . 718-08
8 , 738-08
8 . 748-08
I .5 0 8 -0 7
1 .5 0 8 - 0 7
I . 5 OB-0 7
7 . 62 E-0 7
7 .4 3 8 - 0 7
7 .2 8 E -0 7
7 .4 9 8 -0 7
7 .6 2 8 - 0 7
2 .2 9 E -0 6
2 .0 0 E -0 6
I . 808-06
1 . 888-06
2 . 008-06
2 .0 9 E -0 6
2 . 188-06
2 .0 9 E -0 6
5 .O 5 E-O 6
4 .1 2 E -0 6
4 .2 1 E -0 6
4 .3 9 8 - 0 6
1 ,0 4 8 - 0 5
l .O l E -0 5
1 .1 7 8 - 0 5
I . 238-05
I . 048-07
I . 04 E-0 7
I . 04 E-0 7
I .O 6E-0 7
I . 0 6 8 -0 7
41
T a b le 10 ( c o n t i n u e d )
Run
No.
71
72
73
74
75+
76
77
78
79
80
81
82
83*
84*
85 *
86*
87*
"SB*
89*
90*
91 *
92
93
94*
95*
■96
97
98*
99*
100
101
102
103*
104*
105*
106*
107*
108*
109*
Lot
No.
Temp.
( 0C)
P re ss.
(T o rr)
Avg. B iam .
(cm )
2
3
3
I
2
2
I
2
2
I
3
3
2
2
2
2
2
2
2
2
2
3
2
I
I
2
I
I
I
3
3
I
I
■I
I
I
I
I
I
2110
5 .OE-O 4
1 .0 E - 0 2
0 .0 4 2 0
0 .0 4 9 6
O.O 5 O3
0 .0 5 7 3
O.O489
0 .0 4 8 0
0 .0 6 0 4
0 .0 4 8 2
0 .0 4 9 9
0 .0 6 3 0
0 .0 4 8 3
0 .0 4 9 5
0 .0 5 8 1
0 .0 5 5 0
0 .0 4 9 1
O.O 625
0 .0 5 6 9
0 .0 5 1 3
0 .0 6 2 6
O.0583
■ 0.0540
0 .0 4 7 1
0 .0 4 8 8
O.O 564
O.O 65 O
0 ,0 4 6 8
0 .0 6 2 1
0 .0 6 0 5
O.0586
0 .0 4 5 2
• O.0465
0 .0 6 0 3
0 ,0 5 2 1
O.0529
O.O 651
O.0572
0 ,0 5 2 2
0 .0 6 1 3
O.0517
5 .0 E - 0 2
I . OE-Ol
I . OE 00
5 . OE 01
I . OE 03
2260
7 . 5E-0 5
5 .OE-O 4
1 .0 E - 0 2
5 .0 E - 0 2
I . OE-Ol
E x p e r im e n ta l
R a te (c m /S e c )
1 .2 2 E -0 7
1 .3 2 E -0 7
1 .3 2 E -0 7
I . 30E -07
2 .5 8 E -0 7
1 .2 2 E -0 7
1 .9 0 E -0 7
4 .2 6 E -0 7
2 .32E -07
2 .1 7 E -0 7
1 .2 2 E -0 6
1 .0 6 E -0 6
< 1 .3 5 0 -0 6
1 . 4 90-06
1 .2 1 E -0 6
4 . 8 IE -O 6
5 . 09 E-O 6
6 . 05 E-O 6
I . 29 E-0 5
I . 5OE-0 5
I . 58 E-0 5
7 . 490-07
■ 6 .2 4 E -0 7
3 .4 7 0 - 0 7 ■
6« 66 E—07
6 . 590-07
3 . 870-07
5 . 150-07
2 . 66 E-0 7
8 . 560-07
8 .1 2 E -0 7
. 7 .7 5 0 - 0 7
7 .8 1 E -0 7
4 .5 4 0 - 0 7
7 .7 4 0 - 0 7
8 .8 1 E -0 7
7 .2 8 E -0 7
5 .3 0 E -0 7
• 6 .3 5 0 -0 7
C a lc u la te d
R a te ( c m /s e c )
. 1 .0 6 E -0 7
1 .3 7 0 - 0 7
I . 37 O-O 7
1 .3 7 0 - 0 7
I . 62E-07
1 .6 2 0 - 0 7
1 .6 3 0 - 0 7
. 2 . 320-07
2 .3 3 0 -0 7
2 .3 5 0 - 0 7
1 .4 5 0 - 0 6
1 . 430-06
1 .3 5 0 -0 6
I . 38 E-O 6
1 .4 4 0 - 0 6
4 .7 7 0 - 0 6
5 .1 2 E -0 6 ,
5 .54E -06
I . 44 E-O 5
1 .5 1 E -0 5
I . 58 E-O 5
7 .1 5 0 - 0 7
7 .1 5 0 - 0 7
7 .1 5 0 - 0 7
7 .1 5 0 - 0 7
7 .1 7 0 - 0 7
7 . I 7O-O7
7 . 170 - 0 7 .
7 . I 7O-O7
7 .7 3 0 - 0 7
7 .7 3 0 - 0 7
7 .7 3 0 - 0 7
5 .8 5 0 - 0 7
5 . 85 O-O7 ■
5.86E -07
. 6 .9 1 0 - 0 7
6 .9 0 0 - 0 7
6 .9 2 E -0 7
6 .9 0 E -0 7
42
T a b le 10 ( c o n t i n u e d )
Run
No.
HO*
111*
112*
113*
114*
115*
116*
117*'
118*
119*
120*
121*
122*
123*
124*
125 *
126*
127*
128*
Lot
No.
Temp.
( 0C)
I
I
I
I
2
2
2260
I
I
2
2
I
I
I
2 ■
2
I
I
2
2
P re ss.
(T o rr)
I . OE 00
I . OE 01
I . OE 02
I . OE 03
Avg. Diam .
(cm )
E x p e r im e n ta l
R a te ( c m /s e c )
O..O544
O.O 56 I
0 .0 6 4 4
O.O 584
0 .0 4 8 1
0 .0 4 8 1
O.O 564
1 .4 9 E -0 6
1 .6 7 E -0 6
1 .9 3 E -0 6
1 .8 3 E -0 6
I . 96 E-O 6
2 .4 0 E - 0 6 .
5.83E -Q 6
0 ,0 5 6 7
0 .0 5 0 1
0 .0 4 6 3
0 .0 4 8 8
0 .0 4 9 4
0 .0 5 9 7
0 .0 5 1 6
0 .0 5 1 3
0 .0 4 7 5
0 .0 6 3 9
0 .0 4 7 8
0 .0 4 1 6
.
5 .3 3 9 -0 6 .
5 . 6 IE -O 6
6 .3 0 E -0 6
1 .3 2 E -0 5
6.849-O 6
6 .5 2 E -0 6
8 .7 3 E -0 6
I .O 8E-0 5
3 .5 9 9 -0 5
2 .2 0 E -0 5
2.82E -05
3 .2 9 9 - 0 5
*
d e n o te s r u n s p e r f o r m e d b y K ra u s ( 9 )
+
d e n o te s th e ru n r e p r e s e n te d i n F ig u re 2
NOTE:
C a lc u la te d
R a te ( c m / s e c )
1.& 7E -06
. I . 85 E-O 6
1 .7 9 9 -0 6
I.84E-O 6
1 .9 2 E -0 6
v 1 .9 2 E -0 6
5 ,7 4 9 - 0 6
■ 5 .7 2 E -0 6
6 .1 9 9 -0 6
6 . 5OE-O6
I . 24 E-0 5
1 .2 3 9 - 0 5 ..
I . 07 E-0 5
I . 19 E-O 5
1 .1 9 E -0 5
2 .8 7 9 - 0 5 .
2 ,3 8 9 - 0 5
2 . 78 E-0 5
3 .1 4 9 - 0 5
C o m p u ter n o t a t i o n o f 7 » 50E -05 c o r r e s p o n d s t o e i t h e r 1 7*50 x
1 0 To r r o r 7*50 x 10 ^ c m /s e c .
APPENDIX B
T a b le 1 1 .
E x p e r im e n ta l C o n d i t io n s a n d E x p e r im e n ta l
a n d C a l c u l a t e d R e c e s s io n R a te s f o r A ir
Run
No.
I
2
3
.4
5
6
7
8
9. 10
11
12
13
14
15
16
17
18
19
20
.21
22
23
24
25
26
27
28
29
30
31:
32
33
34
35
Lot
No.
Temp.
3
3
3
3
3
3
1675
2
2
2
2
2
3
2
2
2
2
2
2
2
2
2
2
3
3
2
2
2
2
I
2
2
2
I
2
I
( 0C)
P re ss.
(T d rr)
5 . 0E-01
5 . GE 00
5 . OE 01
5 . OE 02
Avg. Diam .
(cm )
E x p e r im e n ta l
R a te ( c m /s e c )
0 .0 4 6 2
O.O 5 OO
0 .0 4 9 8
0 .0 4 9 6
3 .1 2 E -0 8
9 .6 3 E -0 8
7 .9 0 E -0 8
0 .0 4 8 1
0 .0 4 9 3
7
.5
E
0
5
0 .0 4 6 9
1965
5 .OE -0 4
0 .0 4 9 5
0 .0 5 0 8
1 .0 E - 0 2
0 .0 4 9 3
7 .5 E -0 2 ■ 0 .0 4 9 9
0 .0 4 7 8
O.O 509
5 . OE-Ol
O.O 5 O5
5 . Oe oo
0 .0 5 0 2
5 . OE 01
0 .0 4 7 3
O.O 458
. 5 . OE 02
O.O 502
0 .0 5 0 2
2260 7 .5 3 -0 5
0 .0 4 7 4
O.O 4 6 I
O.O 475
5 .0 E - 0 4
O.O 4 8 I
O.O 48 O
0 .0 5 0 2
1 .0 E - 0 2
7 .5 3 -0 2
0 .0 4 9 1
5 . OE-Ol
O.O 485
0 .0 4 4 9
5 . OE 00
O.O 566
O.O 489
0 .0 4 6 3
5 . OE 01
0 .0 4 9 1
' 0 .0 6 0 2
5 . OE 02
0 .0 4 9 9
0 .0 6 1 8
1 .7 3 8 -0 7
6 i0 5 E -0 7
5.28E -07
1 .7 1 E -0 8
9 .6 7 E -0 9
1 .3 5 8 -0 8
1 .0 2 E -0 8
6 . 8 OE-O8
3 .3 2 E -0 8
1 .0 7 E -0 ?
3 .3 8 2 -0 7
3 .3 2 8 -0 7
5 .5 1 8 - 0 7
6 .6 5 2 -0 7
1 .2 2 2 -0 6
1 .1 2 2 -0 6
5 .3 5 8 -0 7
8.6 2 2 -0 7 8 .2 6 2 -0 7
6 .6 1 E -0 7
7 .8 8 2 -0 7 ■
7 .3 0 2 -0 7
8 .5 5 2 -0 7 .
6.85E -07
6 .9 4 2 -0 7
9 .5 2 2 -0 7
9 ,6 6 8 - 0 7
1 .0 3 2 -0 6
1 .6 3 8 -0 6
1 .2 9 2 -0 6
2 .8 7 2 -0 6
2.572-O 6
C a lc u la te d
R a te ( c m /s e c )
4 .0 5 2 -0 8
8 .6 1 2 - 0 8
8 .6 4 2 -0 8
I . 75 E-0 7
5 . 28 E-0 7
5 . 19 E-0 7
1 .2 6 2 -0 8
1 .2 8 E -0 8
1 . 678-08
1 .6 7 2 -0 8
3.50E -08
3 .'5 0 2 -0 8
1 .O 6E-0 7
3 .4 4 8 -0 7
3 . 46 E-07
6 .5 5 2 -0 7
6 . 722-07
1 .2 4 E -0 6
1 .2 4 2 -0 6
7 .1 4 8 -0 7
7 .1 4 8 -0 7
7 . 15 E-0 7
7 .1 5 8 -0 7
7 . I 5 8 -0 7
7 . 27 E-0 7
4 .7 7 8 - 0 7
4 .7 3 8 -0 7
4 .7 8 E -0 7
1 .0 1 E -0 6
•1 .1 0 E -0 6
1 .1 3 2 -0 6
1 .9 8 2 -0 6
1 .7 0 2 -0 6
3 . 50 E-0 6
3 . 032-06
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