High-temperature oxidation of iridium
by Thomas Leigh George
A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE
in Mechanical Engineering
Montana State University
© Copyright by Thomas Leigh George (1975)
Abstract:
An investigation of the oxidation of iridium wires was conducted in the temperature range of 1965 to
2260 C (2238 to 2533 K). The wires were oxidized in naturally convected CO2 at pressures ranging
from 1.32 x 10-3 to 1.32 atm (1 to 1000 torr). The experimental results were compared to values
calculated from a model based on the assumptions that the oxidation rate was controlled by the rate of
CO2 dissociation, the rate of vaporization of IrO2(g), IrO3(g) and Ir(g) and the rate of the subsequent
diffusion of these species through the boundary layer. STATEMENT OF PERMISSION TO COPY
In p re s e n tin g t h is th e s is in p a r t i a l f u l f i l l m e n t o f th e r e q u ir e ­
ments f o r th e degree o f M aster o f S cience in Mechanical E n g in eerin g
a t Montana S ta te U n iv e r s it y ,
a v a ila b le f o r in s p e c tio n .
I agree t h a t th e L ib r a r y s h a ll make i t
I f u r t h e r agree t h a t perm ission f o r
e x te n s iv e copying o f t h is th e s is f o r s c h o la r ly purposes may be gran ted
by my m ajo r p ro fe s s o r, o r , in h is absence, by th e D ir e c t o r o f L ib r a r ie s .
It
is understood t h a t any copying o f p u b lic a tio n o f t h i s th e s is f o r
f in a n c ia l
g a in s h a ll n o t be a llo w e d w ith o u t my w r it t e n p e rm is s io n .
Date
HIGH-TEMPERATURE OXIDATION OF IRIDIUM
by
THOMAS LEIGH GEORGE
A th e s is subm itted in p a r t i a l f u l f i l l m e n t
o f th e req u irem en ts f o r th e degree
o f
'
MASTER OF SCIENCE
in
Mechanical E n g in ee rin g
Approved:
L i
C h airm an ,/E xam ining Committee
Head, M a jo r Departm ent
f j ur - . Gradliate^Dean
MONTANA STATE UNIVERSITY
Bozeman, Montana
August,. 1975
/
ACKNOWLEDGEMENTS
S p e c ia l thanks and a p p r e c ia tio n is due D r. A .J . Kumnick f o r h is
g e n e ro s ity in tim e and e f f o r t th ro u g h o u t th e couse o f t h is rese a rch
p r o je c t and f o r s e rv in g as head o f th e a s s o c ia te d exam ining com m ittee.
A lso to be thanked is D r. R .T . Wimber f o r h is h e lp fu l notes and ad­
v ic e .
Thanks a re a ls o expressed to D r. H.W. Townes and D r. R .L .
Mussulman f o r s e rv in g on th e g ra d u a te com m ittee; .
iv
TABLE OF CONTENTS
Page
V I T A ........................................................................................................................ ....
ACKNOWLEDGMENTS.........................................................................
Ti
iii
LIST OF TA B LES .....................................................................................
LIST OF FIGURES
v
...................................................................................................... . .
Vi
ABSTRACT .............................................................................................................................
v ii
CHAPTER I .
INTRODUCTION
C h a r a c te r is tic s and Uses o f Ir id iu m . . . . . . . . . . . .
Review o f P revious Work . . . . . . . . . . .
................... . .
Purpose o f P re s e n t Study . . . . . . . . . . . . . . . . .
CHAPTER I I .
EXPERIMENTAL PROCEDURE
E xp erim en tal M a te r ia ls
Apparatus and Procedure
CHAPTER I I I .
..................
5
5
. . . . . . . . . . . . . .
^
THEORETICAL MODEL
M odeling O x id a tio n Rates
................................................................. .... .
T h e o r e tic a l Model f o r th e Rate O x id a tio n o f Ir id iu m . . . .
CHAPTER IV .
I
2
3
.10
11
RESULTS ANQ OXYGEN PRESSURE CALCULATIONS
E xp erim en tal R e s u lts . . . . . . .
.........................................................
C a lc u la tio n o f Oxygen P a r t ia l P ressure
. ..............................................
CHAPTER V.
DISCUSSION
E rro rs in T h e o r e tic a l P re d ic tio n s . . . . . . . .......................
Comment on Free E nergies o f IrO g and IrO g ............................ ...
CHAPTER V I.
20
20
31
32
SUMMARY..................................................................... ...........................
36
A P P E N D IX .................................................................................
REFERENCES ...................................................................... ......................................... ....
.
46
V
LIST OF TABLES
Page
TABLE I - Values f o r Unknowns in Rate Equation fo r
COg D is s o c ia tio n s . . . . . . . . . .
.....................................
30
TABLE 2 - Average d e v ia tio n o f T h e o r e tic a l Equations from
E xperim en tal Data . . . . . .
............................ . . . . . .
31
TABLE 3 - Comparison o f R esu lts Using L in e a r Free Energy
Equations ..................................... ................................................................
35
TABLE 4 - E xperim en tal D a t a .......................
38
. .......................................... ....
.
vi
LIST OF FIGURES
Page
FIGURE I
- Schem atic R e p re s e n ta tio n o f O x id a tio n Apparatus
. . . .
6
FIGURE 2
- T y p ic a l Rate P lo t f o r an O x id a tio n E xperim ent
.................
9
FIGURE 3
- Free E nergies o f F o r m a t io n .................................................................. 19
FIGURE 4
- E xperim en tal and T h e o re tic a l R e s u lts Assuming Local
E q u ilib riu m f o r COg D i s s o c i a t i o n ....................... ........................... 21
FIGURE 5 - E xperim en tal and T h e o r e tic a l R e s u lts Assuming Rate
C o n tro l f o r COg D is s o c ia tio n - Best F i t f o r A ll
P r e s s u r e s ......................................................................................................... 22
FIGURE 6
FIGURE 7
- E xperim en tal and T h e o re tic a l R e s u lts Assuming Rate
C o n tro l f o r COg D is s o c ia tio n - Best F i t E xcluding
H ig h e s t P ressure ........................................................................................
23
- R eactio n a t G as-M etal
24
In t e r f a c e
.................................................
v ii
ABSTRACT
An in v e s tig a tio n o f th e o x id a tio n o f ir id iu m w ire s was conducted
in th e te m p e ratu re range o f 1965 to 2260 C (2238 to 2533 K ).
The
w ire s were o x id iz e d in n a t u r a ll y convected CO2 a t pressures ranging
from 1 .3 2 x 1 0 -3 to 1 . 32 atm ( I to 1000 t o r r ) .
The e x p e rim e n ta l r e s u lts
were compared to values c a lc u la te d from a model based on th e assumptions
t h a t th e o x id a tio n r a t e was c o n tr o lle d by th e r a te o f COg d is s o c ia t io n ,
th e r a t e o f v a p o r iz a tio n o f IrO g C g ). Ir O 2 Cg) and I r ( g ) and th e r a te o f
th e . subsequent d if f u s io n o f these sp ecies through th e boundary la y e r .
CHAPTER I
INTRODUCTION
C h a r a c te r is tic s and Uses o f Ir id iu m
Ir id iu m is con sid ered to be th e most c o rro s io n r e s i s t a n t metal
known when i t
is compared w ith a l l
o th e r m etals o ver a broad range o f
te m p e ra tu re and in a g re a t v a r ie t y o f c o rro s iv e environm ents [ I ] .
These c o rro s iv e environm ents in c lu d e numerous a cid s and s a l t s o lu tio n s ,
m olten o x id e s , fused s a lt s and m olten m e ta ls .
When ir id iu m is heated in oxygen to about 600 C (873 K) a th in
o x id e f i l m
is produced.
A t tem peratures g r e a te r than 1000 C (1273 K)
th e o x id a tio n products a re v o l a t i l e r e s u lt in g in an o x id a tio n r a te
which is c o n s ta n t w ith tim e .
a llo w th e use o f ir id iu m
However, t h is r a te is low enough to
in c o n ta c t w ith oxygen a t te m p e ratu re s above.
2000 C (2273 K ).
A lthough ir id iu m has re as o n a b ly good h ig h -te m e p ra tu re s tre n g th
p r o p e r t ie s , i t s
high c o s t l i m i t s
its
use as a s tr u c tu r a l m a t e r ia l.
Ir id iu m w ire s a re used as h e a tin g elem ents in h ig h -te m p e ra tu re f u r ­
naces and as h ig h -te m p e ra tu re therm ocouples.
tio n s f o r ir id iu m
O ther p o s s ib le a p p lic a ­
in c lu d e c o a tin g s f o r components in ro c k e t engines
and le a d in g edges on r e - e n t r y s p a c e c r a ft.
Ir id iu m has a ls o been con­
s id e re d as a p r o te c tiv e c o a tin g f o r components in high te m p e ratu re
gas cooled n u c le a r re a c to rs where GOg is used as a c o o la n t.
p re s e n t study is p a r t i c u l a r l y r e le v a n t to t h is c o n s id e ra tio n .
The
2
Review o f P revious Work
An e x te n s iv e re v e iw o f th e l i t e r a t u r e a v a ila b le on th e o x id a tio n
o f ir id iu m has been p resen ted by Wimber [ 2 ]
and a b r i e f summary o f t h a t
re v ie w is presen ted h e re .
O x id a tio n s tu d ie s o f ir id iu m c a r r ie d o u t by Cordfunke and Meyer
[3 ]
in d ic a te d IrO g as th e m ajor o x id e s p e c ie formed and a t tem peratu res
above 1110 C (1383 K) th e oxides formed were v o l a t i l e .
were o b ta in e d by S c h a fe r and H e itla n d [ 4 ]
S im ila r r e s u lts
and by Alcock and Hooper [ 5 ] .
Cordfunke and Meyer a ls o a r r iv e d a t e q u ilib r iu m co n stan ts f o r th e
o x id a tio n r e a c tio n which were s l i g h t l y h ig h e r than those re p o rte d by th e
o th e r in v e s t ig a t o r s .
A mass s p e c tro m e tric study by Norman, e t a l [ 6 ]
in d ic a te d th e p re ­
sence o f I r + , IrO + , IrO g+ , and IrO g + ions d u rin g th e o x id a tio n o f
ir id iu m a t tem p eratu res between 1557 and 1760 C (1830 and 2033 K ).
IrO g and IrO g were found to be th e m ajo r oxid e s p e c ie s .
o f Ir O (g ) could n o t be ru le d o u t, b u t i f
The presence
i t d id e x i s t , i t s
p a r tia l
p ressu re would be le s s than 1 /5 0 o f th e p a r t i a l p ressu re o f the IrOg
a t th e h ig h e s t te m p e ratu re and oxygen p re ss u re (10~^ atm) in v o lv e d in
th e s tu d y .
The work o f B a r t l e t t [ 7 ] on th e o x id a tio n o f p la tin u m a t tem pera­
tu re s g r e a te r than 800 C (1073 K) is r e le v a n t to th e p re s e n t study
because o f th e chem ical s i m i l a r i t i e s between p la tin u m and ir id iu m
(Ir
is a member o f th e p la tin u m group) such as th e fo rm a tio n o f v o l a t i l e
3
o x id e s .
B a r t l e t t p re d ic te d o x id a tio n r a te s from c a lc u la t io n s in v o lv ­
ing th e r e v e r s ib le r e a c t io n , O2 + P t S PtO2 , which ta k es p la c e a t th e
s o lid -g a s in t e r f a c e and th e subsequent d if f u s io n o f th e o x id e through
:
th e gaseous boundary la y e r which forms as a r e s u l t o f th e n a tu ra l con­
v e c tio n o f th e o x id iz in g gas.
Wahl [ 8 ] d e sc rib e s two models to p r e d ic t o x id a tio n ra te s o f ir id iu m
w ire s in a i r and pure oxygen f o r both fo rc e d and n a tu ra l
c o n v e c tio n .
One model based on th e assumption o f d if f u s io n c o n tro l proved r e l i a b l e
f o r p ressures above 10™^ atm.
The o th e r model p re d ic te d o x id a tio n
r a te s a t low er pressures assuming v a p o r iz a tio n o f th e o x id e species
from th e m etal s u rfa c e as th e r a t e l i m i t i n g process.
More r e c e n tly
an e q u a tio n , s im ila r to t h a t used by B a r t l e t t , was fo rm u la te d to
acconmodate both models and produced a c c u ra te r e s u lts f o r th e e n t i r e
p re ss u re range [ 9 ] .
The m ajor steps in th e d e r iv a tio n o f t h is model
a re p resen ted in C hapter I I I .
Purpose o f P re s e n t.S tu d y
The p re s e n t study a tte m p ts to show t h a t th e d if f u s io n /v a p o r iz a t io n
model d e s c rib e d above [ 9 ]
a p p lie s to th e r a t e o f o x id a tio n o f ir id iu m
in CO2 , g iv en th e amount o f oxygen produced by th e d is s o c ia tio n o f th e
CO2 S ev e ra l approaches were fo rm u la te d to p r e d ic t th e a v a ila b le oxygen
a t th e g a s -s o lid i n t e r f a c e , none o f which proved c o m p le te ly s a t is f a c t o r y
4
These in c lu d e d an approach based on th e assumption o f lo c a l e q u ilib r iu m
a t th e g a s-m etal i n t e r f a c e , an approach assuming k in e t i c c o n tro l f o r
th e e n t i r e d is s o c ia tio n o x id a tio n p ro c es s , and a model based on
k in e t i c c o n tro l f o r th e COg d is s o c ia tio n w ith th e m ajor p o rtio n o f
th e r e a c tio n products being removed by d if f u s io n through th e boundary
la y e r .
CHAPTER I I
EXPERIMENTAL PROCEDURE
E xp erim en tal M a te r ia ls
The 0 .5 0 8 mm d ia m e te r ir id iu m w ire used in t h is study was com­
m e r c ia lly pure and from a s in g le l o t .
Mass s p ec tro m e te r a n a ly s is
in d ic a te d t h a t th e w ire was b e t t e r than 99.8% pure w ith th e m ajor
im p u r itie s being W (800 ppm), Fe (6 0 ppm) and Cu (35 ppm).
The CO2 used was t y p i c a l l y 99.99% pure w ith N2 th e m ajor im p u rity
(2 0 ppm).
P r io r to e n te rin g th e o x id a tio n c e l l ,
anhydrous calc iu m s u lf a t e
i t was d r ie d f i r s t in
( CaSO^) and then in magnesium p e rc h lo ra te
(Mg(ClO4 ) 2 ) .
Apparatus and Procedure
A d e t a ile d d e s c r ip tio n o f th e app aratu s and e x p e rim e n ta l procedure
has been g iv en by Wahl [ 8 ] .
e x p la n a tio n w i l l
C onsequently a more g en eral and b r i e f
be p resented h e re .
A schem atic re p r e s e n ta tio n o f th e e xp e rim e n ta l system is shown in
F ig . I .
The ir id iu m w ire was mounted between two e le c tro d e s in the
w a te r-c o o le d o x id iz in g c e l l .
The c e l l was p rovided w ith two s ig h t
p o rts covered w ith r o t a t a b le pyrex windows.
Through one p o rt an o p t i ­
c al pyrom eter was focused on th e w ire and through th e o p p o s ite window
a m o to r -d riv e n , tim e r -a c tu a te d camera f i t t e d w ith a te le m ic ro s c o p e was
focused on th e same p o in t o f th e w ir e .
Rotam eter
Dryers
Supply Tanks
Autom atic
Pressure
C o n tr o lle r
Servo
V alv e
Timer
B a tte r y
Pressure
M eter
Capacitance
Manometer
M o to rize d Camera ~2.
& Telem icroscope ___
O p tic a l Pyrom eter
DC
Power
Supply
V o ltm e te r
F ig u re I :
Ammeter
Schem atic R e p re s e n ta tio n o f O x id a tio n A p p aratu s.
7
The pyrom eter was c a lib r a t e d to compensate f o r re a d in g s taken
through th e pyrex window as d e s c rib e d by Wahl [ 8 ] .
T h is c a lib r a t io n
was checked p e r io d ic a ll y thro u g h o u t th e course o f th e e xp e rim en ts.
The w ire was m a in ta in e d a t th e d e s ire d te m p e ratu re by s e lf - r e s is t a n c e
h e a tin g .
P ressure was held c o n s ta n t a t a s e le c te d v a lu e by use o f a
s e r v o -c o n tr o lle d v a lv e , coupled w ith a c a p a c ita n c e monometer.
To
in s u re an atmosphere o f COg e s s e n t ia lly f r e e from o x id a tio n p ro d u c ts ,
a s m a ll, c o n s ta n t flo w o f COg was m a in ta in e d by c o n tin u o u s ly o p e ra tin g
a vacuum pump connected to th e system.
.
A t th e begin n in g o f an e xp e rim e n ta l run a le n g th o f ir id iu m w ire
was c lean ed in acetone and mounted between th e e le c tro d e s in th e o x id a ­
t io n c e l l .
The w ire was then annealed in an argon atmosphere a t 1 .0 5
atm (800 t o r r ) and 2200 C (2437 K) f o r 30 m inutes to p re v e n t excessive
r e c y s ta lliz a tio n
measurements.
and g ra in growth from o c c u rrin g d u rin g o x id a tio n
The argon was then pumped o u t; th e c e l l was then le a k -
te s te d and f i l l e d
w ith COg to th e d e s ire d p re s s u re .
The servo mech­
anism was a c t iv a te d and a llo w e d to e s t a b lis h a s tead y flo w .
The w ire
was b rought to te m p e ra tu re by a d ju s tin g th e c u r r e n t from th e power
s u p p ly .
The c a m e ra -tim e r system was s ta r te d and a s e r ie s o f te n expo­
sures was ta k en o f th e w ir e .
The tim e in t e r v a l
between exposures was s e t so t h a t a p p ro x im a te ly
0 .0 2 5 mm would be removed from th e w ire d ia m e te r d u rin g th e course o f
th e ru n .
The w ire te m p e ra tu re was m onitored w ith th e o p tic a l pyrom eter
8
and k ep t c o n s ta n t by c u r r e n t a d ju s tm e n ts .
On lo n g e r runs (up to 48
hours) th e system was shut o f f f o r p e rio d s o f tim e .
T h is procedure
was n o t b e lie v e d to in flu e n c e th e e x p e rim e n ta l r e s u lt s because th e
tim e r e q u ire d to b rin g th e w ire back to te m p e ratu re was n e g lig ib le
compared to th e t o t a l
elapsed tim e .
Upon com pletion o f th e run an
exposure was made o f
a d r ill
le n g th as th e w ir e .
T h is served as a standard f o r d e te rm in in g the
w ire d ia m e te rs .
rod o f known d ia m e te r a t th e
same fo c a l
The w ire images were measured using a m o d ifie d c a th e to -
m eter in which a f o i l w ith a 0 .0 5 mm s l i t was in c o rp o ra te d in th e t e l e ­
m icroscope.
Using a h ig h - in t e n s it y back l i g h t on th e f i l m
and a l i g h t
m eter a tta c h e d to th e eye p ie ce o f th e te le m ic ro s c o p e , th e image w id th
could be o b ta in e d , and c o n verted to a w ire d ia m e te r using
th e r e l a ­
tio n s h ip between th e
known d r i l l
rod d ia m e te r.
+ 0 .0 5 to 0 .1
image w id th o f th e d r i l l
rod and th e
The r e p e a t a b i l i t y o f a s in g le measurement was t y p i c a l l y
p e rc e n t.
H ills
[1 0 ] re p o rte d t h a t in using t h i s procedure
a c o r r e c tio n in th e d ia m e te r measurements must be made due to the
appearance o f a fr in g e zone a t th e edges o f th e w ire im age.
The th ic k --
ness o f t h i s f r in g e zone was determ ined to be a fu n c tio n o f th e w ire
te m p e ratu re and is in c lu d e d in th e f i n a l
c a lc u la tio n s f o r t h i s s tu d y .
T y p ic a l r e s u lt s o f f i l m measurements f o r a s in g le run a re p lo tte d
in F ig . 2 where th e slo p e o f th e l i n e d iv id e d by n e g a tiv e two g iv es th e
re c e s s io n r a t e in cm /sec.
Run No. 27
2110 C
10 T o rr
Slope = -2 .0 3 5 3 x 10
D ia m e te r, cm
Recession Rate = 1 .0
0 .0 4 9
0 .0 4 8
10760
Tim e, Sec
F ig u re 2:
T y p ic a l Rate P lo t f o r an O x id a tio n E xperim en t.
CHAPTER I I I
THEORETICAL MODEL
M odeling O x id a tio n Rates
The term o x id a tio n is used to d e fin e th e r e a c tio n between a metal
and oxygen in th e absence o f w a te r o r aqueous phase.
The o x id a tio n o f
most m e ta ls is c h a r a c te r iz e d by th e b u ild -u p o f an o x id e f i l m
s u rfa c e ; in many cases ( e . g . , Al and Cr o x id a tio n ) th e f i l m
on th e
a c ts as a
p r o te c tiv e c o a tin g , w h ile in o th e rs ( e . g . , Fe o x id a tio n ) th e f i l m
n o n p r o te c tiv e .
is
Over a c e r t a in te m p e ra tu re range some m e ta ls in c lu d in g
tu n g s te n , molybdenum, and ir id iu m form o x id e species which a re v o l a t i l e
The o x id a tio n o f these m e ta ls is c h a r a c te r iz e d by a l i n e a r r a t e law .
From an e n g in e e rin g v ie w p o in t, a f a c t o r o f m ajo r i n t e r e s t in th e
o x id a tio n process is th e r a te a t which i t o ccu rs.
In fo rm u la tin g a
model d e s c rib in g th e o x id a tio n p ro c es s , each s te p must be considered
as p o t e n t i a l l y r a t e l i m i t i n g .
Once th e l i m it in g
step o r steps a re
determ ined and d e s c rib e d q u a n t i t a t i v e l y th e r a t e can be p re d ic te d .
For th e s p e c if ic case o f ir id iu m o x id a tio n in n a t u r a ll y convected COg,
a re as o n a b le sequence o f events based on e a r l i e r work is as fo llo w s [ 2 ]
1)
Oxygen p ro d u c tio n from COg.
2)
A d s o rb tip n o f th e f r e e oxygen onto th e m etal s u rfa c e .
3)
R eactio n o f th e oxygen w ith th e s o lid m a te ria l on th e s u rfa c e .
4)
D e s o rb tio n o f th e o x id e s p ec ie o r species from th e m etal
s u rfa c e .
11
5)
D iff u s io n o f th e oxides through th e boundary la y e r away from
th e m etal s u rfa c e .
T h e o r e tic a l Model f o r th e Rate o f O x id a tio n o f Ir id iu m
Wimber, e t a I
[ 9 ] fo rm u la te d a model f o r th e r a t e o f ir id iu m o x i­
d a tio n assuming th e v a p o r iz a tio n o f IrO 2 ( Q ) 5 IrO g (g ) and I r ( g ) and t h e i r
subsequent d if f u s io n through th e gaseous boundary la y e r surrounding th e
m a te r ia l as th e c o n t r o llin g s te p .
The model c o r r e la te d w e ll w ith
e x p e r im e n ta lly measured re ce s s io n r a te s o f ir id iu m w ire s in n a t u r a lI y
convected a i r and oxygen and in fo rc e d c o n ve c tio n a i r and oxygen.
As m entioned p r e v io u s ly , th e model is a s y n th e s is o f two s e p a ra te
m odels, one which held f o r th e h ig h e r pressures assuming d if f u s io n o f
th e oxides through th e boundary la y e r as th e c o n t r o llin g s te p , and th e
o th e r , f o r th e lo w er p re s s u re s , assuming v a p o r iz a tio n o f th e oxid e
sp ecies as th e c o n t r o llin g s te p .
The b a sis f o r each model and th e man­
n e r in which th e y a re combined in to a s in g le e q u atio n a re summarized
below .
Both models assume each, o f th e o x id a tio n re a c tio n s is a t e q u i l i ­
briu m .
Over th e te m p e ra tu re and pressure, range c o n sid e re d th e dominant
re a c tio n s can be w r i t t e n :
12
I r + O2g ^
Ir O 2 ( g ) s
(I)
K3
I r + 3 /2 O2s x
Ir 0 3 (g )s
(2 )
Ir $ Ir (g )s
(3 )
where th e s u b s c rip t S denotes c o n d itio n s a t th e s o lid boundary, and K2
a n d . Kg a re e q u ilib r iu m c o n stan ts f o r each r e a c tio n .
The o x id a tio n r a t e is expressed in terms o f th e re c e s s io n r a t e o f
th e s u rfa c e o f th e ir id iu m w ir e .
To a v o id d u p lic a t io n , th e re ce s sio n
r a t e due to th e fo rm a tio n o f o n ly one o f th e oxid e s p e c ie s , Ir O 2 ,
w ill
be d e riv e d .
The d e r iv a tio n s f o r th e re c e s s io n r a te s due to th e
fo rm a tio n o f IrO g and I r ( g ) a re e s s e n t i a l l y th e same.
E quation ( I )
re p re s e n ts th e o v e r a ll r e a c tio n and can be broken
down in to th e process whereby oxygen is adsorbed onto th e s u rfa c e ,
c r e a tin g a p o t e n t ia l
s i t e f o r th e o x id a tio n r e a c t io n , and th e v a p o r i­
z a tio n o f th e Ir O 2 m o le c u le .
Assuming e q u ilib r iu m between th e oxygen
and th e m etal s u r fa c e , th e fo llo w in g re a c tio n e q u a tio n can be w r it t e n :
k2b
|S2 X
Ir 0 2(g )s
(4 )
k2 f
where JS2 re p re s e n ts th e e n t i t y a t th e s it e s where th e vapor s p ec ie may
fo rm .
The n e t re c e s s io n r a t e due to th e fo rm a tio n and v a p o r iz a tio n o f
Ir O 2 may be expressed as:
X52 = M k 2 f c s 2 “ k2b P2$)
(5 ).
13
where X52 is th e s u rfa c e re c e s s io n r a t e w ith u n its o f le n g th per tim e ,
P2S is th e p a r t i a l
p ressu re o f I r 0 2 (g ) a t th e i n t e r f a c e , Cg2 is th e
c o n c e n tra tio n o f th e
|S2 e n t i t y , A is an e q u iv a le n t w e ig h t (h avin g th e
u n its o f mass o f ir id iu m consumed per mole o f o x id e sp ec ie s formed)
d iv id e d by th e d e n s ity o f ir id iu m , and k2 f and k2b a re th e fo rw ard and
re v e rs e r e a c tio n r a t e co n stan ts f o r th e r e a c tio n g iven by Eq. ( 4 ) .
Assuming th e fo rw a rd and re v e rs e re a c tio n s as g iv en by Eq. (4 )
a re e le m e n ta ry , a llo w s f i r s t o rd e r r a t e e q u atio n s to be w r it t e n f o r
each r e a c tio n .
S o lv in g f o r k ^
in terms o f k2^ and s u b s t it u t in g back
in t o Eq. (5 ) g ives
X$2 = Ak2 f Cg2 [ I - P g s / f K g
where
(6)
is th e oxygen p a r t i a l p re s s u re .
The q u a n tity k2 f Cg2 is th e v a p o r iz a tio n f l u x and from th e Knudsen
m o d ific a tio n o f th e H e rtz-L a n g m u ir e q u a tio n [ 1 1 ] , th e fo llo w in g r e s u l t
is o b ta in e d :
k2f .C g 2 = K2 pO2 (27rM2 RT)" 1 /2
(7 )
where M2 is th e m o le c u la r w e ig h t o f IrO 2 , R is th e id e a l gas c o n s ta n t,
and T is th e a b s o lu te te m p e ra tu re o f th e m e ta l.
Equation (7 ) gives
th e f l u x in moles o f vapor m olecules per u n it a rea p e r tim e and s u b s t i­
t u t io n in t o Eq. ( 6 ) y ie ld s :
Xg2 , - AK2 Pq 2 ( Z ttM2 R T ) " 172 [ I - p2 g / ( K 2 Pq 2 ) ]
(8)
14
For th e d if f u s io n c o n tro l m odel, th e r a t e o f m o le c u la r d if f u s io n
through th e boundary la y e r is p ro p o rtio n a l to th e o x id e p ressu re g ra ­
d ie n t across th e boundary l a y e r .
S in ce th e e x p e rim e n ta l apparatus
p ro v id es a continuous flo w o f th e o x id iz in g gas through th e c e l l ,
is assumed th e p a r t i a l
it
p re ss u re o f th e o x id e species o u ts id e o f the
boundary la y e r is n e g lig ib le compared to th e p a r t i a l
p re ss u re a t th e
i n t e r f a c e ; th e d if f u s io n f l u x is then equal to th e p ro d u ct o f th e mass
t r a n s f e r c o e f f i c i e n t and th e p a r t i a l
th e boundary la y e r .
p re ss u re a t th e in n e r s u rfa c e o f
Thus th e re c e s s io n r a t e due to th e d if f u s io n f l u x
can be expressed by
XD2 = Akfi2 P25
(9 )
where kG2 is th e mass t r a n s f e r c o e f f i c i e n t f o r IrO 2 .
Assuming n e g lig ib le ra te s o f r e a c tio n between th e o xid es and th e
m a tr ix gas a llo w s e q u a tin g Xq2 to Xg2 .
S o lv in g f o r P2s and s u b s t itu tin g
th e r e s u lt s back in t o Eq. (9 ) y ie ld s th e fo llo w in g :
Akg2 K2Pq 2 (Z ttM2R T ) '172
X
2
(1 0 )
'
kQ2 + (Z ttM2R T )"172
where X2 is th e re c e s s io n r a t e due to th e fo rm a tio n o f Ir O 2 .
(1 0 ) should be v a lid f o r a l l
p re s s u re s .
Equation
S im ila r exp re s sio n s a re ob-
.
ta in e d f o r Xg and Xm, th e re c e s s io n r a te s due to th e fo rm a tio n o f
IrO g and th e v a p o r iz a tio n o f th e ir id iu m m etal r e s p e c t iv e ly .
Assuming
15
each o f th ese mass t r a n s f e r processes o p e ra te s in d e p e n d e n tly , th e t o t a l
re c e s s io n r a t e becomes
+ x3 + XM
(H )
"K g2 K2 Pq 2 (Z-M 2 R T)- 1 /2
kG2 + (2TrM2 R T )"1 /2
,
kG3K3P0 2 3 / 2 <2 ’TM3 RT>"1 /2
kG3 + (2 ttM3R T ) '1 /2
kGMpMi 2* MMRT) " V 2
(1 2 )
kGM + <2- mmRT>"1 /2
where th e s u b s c rip t 3 r e fe r s to th e irO g (g ) and th e s u b s c rip t M r e fe r s
to th e I r ( g ) .
Equation (1 2 ) was, used by H i l l s
[1 0 ] to p r e d ic t re c e s s io n
ra te s
in a i r and oxygen as a fu n c tio n o f te m p e ra tu re and oxygen p re s s u re ,
and w ith a p p ro p ria te m o d ific a tio n was a p p lie d in th e p re s e n t study to
p r e d ic t re c e s s io n r a te s in COg.
The mass t r a n s f e r c o e f f ic ie n t s f o r each o f th e d if f u s in g species
in Eq. (1 2 ) were c a lc u la te d using th e C h ilto n -C o lb u rn eq u atio n s [ 1 2 ] :
c PpDv i
Gl
(1 3 )
^ f cPppBM
where th e s u b s c rip t i r e fe r s to th e i t h
s p e c ie , h is th e f i l m
c o e ffi­
c ie n t f o r c o n v e c tiv e h e at t r a n s f e r , P is th e t o t a l system p re s s u re , c
is th e s p e c if ic h e at o f th e CO2 » Tf i f th e a b s o lu te f i l m
te m p e ratu re
(ta k e n as th e average o f th e w ire te m p e ra tu re and th e am bient temp­
F
16
e r a t u r e ) , PgM is the lo g a r ith m ic mean o f th e pressures o f th e COg
a t the in n e r and o u te r edges o f th e boundary l a y e r , p is th e d e n s ity
o f COg9 k is th e CO2 therm al c o n d u c tiv ity and Dv i is th e gaseous
d i f f u s i v i t y f o r th e i t h
a t th e f i l m
te m p e ra tu re .
s p e c ie .
The COg p ro p e rtie s used were v a lid
The C h ilto n -C o lb u rn e q u atio n s used in ob­
t a in in g Eq. (1 3 ) a re v a l i d f o r P ra n d tl numbers (C p P /k , where y is th e
CO2 v is c o s it y ) in th e range o f 0 .6 to 100 and Schmidt numbers ( IV p Dv1- )
in th e range o f 0 .6 to 2500 [ 1 3 ] .
In th e p re s e n t s tu d y , th e P ran d tl
numbers ranged from 0 .7 5 0 to 0 .7 8 5 and th e Schmidt numbers from 0 .5 4
to 1 .7 0 .
The lo w e s t Schm idt n u m bers;fa11ing s l i g h t l y o u ts id e the
recommended range should n o t cause serious e r r o r in th e d i f f u s i v i t i e s .
The f i l m
c o e f f i c i e n t , h , was c a lc u la te d from th e M a d d e n -P iret
[1 4 ] e q u a tio n f o r h e at t r a n s f e r from h o riz o n ta l w ire s :
2
k
C ](8k Y X )/X y C p [Y + l ] D )
- Cg&n(l + 2X /D ) + C2^
(1 4 )
where
(1 5 ),
(.16)
Y is th e COg s p e c if ic h e at r a t i o , x is th e CO2 mean f r e e p a th , D is th e
w ire d ia m e te r and a is th e therm al accommodation c o e f f i c i e n t f o r energy
exchange between th e ir id iu m s u rfa c e and th e CO2 . . In Eqs.
(1 5 ) and (1 6 )
k , a is th e COo therm al c o n d u c tiv ity e v a lu a te d a t th e mean o f th e tem pWed
£
17
e r a tu r e s o f th e w ire (s u b s c r ip t w) and th e am bient (s u b s c r ip t a ) .
t
S im ila r d e f i n i t i o n s a p p ly to k
and k,
where th e X s u b s c rip t r e f e r s
WjA
A jQ
to one mean f r e e path away from th e w ir e .
The f i r s t two terms in th e
denom inator o f Eq. (1 4 ) dom inate a t low pressure w hereas, C2* is th e
dom inant term a t h ig h e r p re s s u re s .
Wimber [ 9 ] e x p e rim e n ta lly d e te r ­
mined * to fo llo w th e r e la t io n s h ip
* = £ n [8 .8 7 Ra"0 - 3 5 4 ( T / T a ) ' 0 - 4 6 4 ]
(1 7 )
where Ra is th e R a y le ig h number given by
Ra = gp2D3Bcp[ A T ] / ( uk)
(1 8 )
where g is th e g r a v it a t io n a l a c c e le r a t io n , 3 is th e c o e f f i c i e n t o f
expansion f o r CO2 (3 equals th e r e c ip r o c a l o f th e a b s o lu te te m p e ratu re
f o r an id e a l gas) and AT is th e te m p e ra tu re d iffe r e n c e across th e
boundary la y e r .
The gaseous d i f f u s i v i t i e s , D
were c a lc u a lte d acc o rd in g to th e
W ilk e -L e e m o d ific a tio n o f th e H ir s c h fe ld e r -B ir d -S p o tz e q u a tio n [1 5 ]
using a v a lu e o f 33 c c /g -a to m [1 6 ] f o r th e atom ic volume o f ir id iu m
and a v a lu e o f 1 .9 2 tim es th e a b s o lu te m e ltin g te m p e ratu re o f th e oxid e
species f o r th e in t e r a c t io n energy [ 1 5 ] .
The p a r t i a l p re ss u re o f ir id iu m m etal was c a lc u la te d from the
e m p iric a l vapor pressure e q u atio n o f Honig and Kramer [ 1 7 ] :
Log(Pw) = 8 4 6 4 .6 7 /T + 6 5 .5 8 1 2 Log(T)
-
. 0100272T + 5 .4 4 9 8 1 T2
(1 9 )
18
where Pm is th e vapor p re ss u re in t o r r .
CO2 p r o p e r tie s w ere o b ta in e d
from th e NBS Tables [1 8 ] and from Kays [ 1 9 ] .
The ream inging 6 unknowns needed to ap p ly Eq. (1 2 )
(i.e .,
C1 , C2 ,
K1 , K2 , and th e o x id e m e ltin g te m p e ra tu re s ) were assumed o r f i t t e d
th e e x p e rim e n ta l re c e s s io n ra te s using Eq. (1 2 ) by Wimber, e t a l
to
[9 ].
C-] and C2 were expressed as fu n c tio n s o f te m p e ra tu re as fo llo w s :
C1 = 1 8 0 .0 3 - 0 .2 3 6 9 1 T + 1 .0 0 0 5 X IO - 4 T2
- 1 .2 2 1 7 X IO - 8 T3 + 5 .4 4 9 0 X IO -1 3 T4
C2 = 1 .5 3 8 - 5 .3 9 7 X IO - 4 T + 1 .3 6 6 X IO - 7 T2
(2 0 )
(2 1 )
The o x id e m e ltin g te m p e ratu re s were assigned a common v a lu e o f
1627 C (1 9 00 K) when i t was observed t h a t th e o v e r a ll r e s u lt s were
r e la tiv e ly
in s e n s it iv e to th e p a r t i c u l a r tem p eratu res s e le c te d .
K1 and K2 were e v a lu a te d from th e f r e e e n e rg ie s o f each oxid e
s p e c ie , Eqs. ( 2 2 ) ,
(2 3 ).
A F £ [Ir 0 2 ( g ) ] = 1 12 9 5.1 6 - 20.5 07 3 7T + 1 .3 97062 X IO - 2 T2
-4 .2 2 0 8 0 6 X IO - 6 T3 + 4 .7 7 0 0 3 6 X IO -1 0 T4
(2 2 )
A F £ [Ir 0 3 ( g ) ] = -1 9 2 6 5 .5 9 + 35.5 01 2 4T - 2 .4 4 5 6 7 7 X IO - 2 T2
+ 7 .4 7 2 2 2 4 X IO - 6 T3 - 8 .5 3 9 7 8 6 X IO -1 0 T4
(2 3 )
Equations (2 2 ) and (2 3 ) a re p lo tte d in F ig : 3 along w ith r e s u lt s from
o th e r w orkers [ 6 , 2 0 ] .
The unexpected shape O f th e s e curves w i l l be
discussed l a t e r (see C hapter V ).
19
X ,0
2000
F ig u re 3:
2200
T e m p era tu re , K
E xperim ental
Values
2400
Free E nergies o f F o rm ation.
CHAPTER IV
RESULTS AND OXYGEN PRESSURE CALCULATIONS
E xp erim en tal R e s u lts
E x p e rim e n ta lly d eterm ined re c e s s io n r a te s a re p resen ted in F ig s . 4 ,
5 and 6 using d i f f e r e n t symbols to re p re s e n t data taken a t th e v ario u s
te m p e ra tu re le v e l s .
The s p e c ific , te m p e ra tu re and p re s s u re f o r each
d a ta p o in t a re given in T a b le 4 in Appendix A.
The s o lid lin e s in
F ig s . 4 , 5 and 6 a re th e r e s u lts o f re c e s s io n r a t e c a lc u la t io n s using
th e
t h e o r e t i c a l m odel, Eq. ( 1 2 ) , and th e methods d e sc rib e d in the
fo llo w in g s e c tio n to d e te rm in e th e oxygen c o n c e n tra tio n a t th e gass o lid in t e r f a c e .
C a lc u la tio n o f Oxygen P a r t ia l
P ressure
The c a lc u la t io n o f re c e s s io n ra te s using Eq. (1 2 ) re q u ire s know­
led g e o f th e oxygen p a r t i a l p re ss u re a t th e gas-m etal
in te r fa c e .
In
p re vio u s work t h is d id n o t p re s e n t a problem because th e s tu d ie s were
done in oxygen o r a i r where th e oxygen p a r t i a l p re ss u re was im m ed iately
g iven as e i t h e r th e t o t a l o r a c o n s ta n t f r a c t io n o f th e system p re s s u re .
O x id a tio n in CO2 can o n ly occur i f CO2 decomposes and forms oxygen
as one o f th e r e a c tio n p ro d u c ts .
Based on th e f r e e e n e rg ie s a s s o c ia te d
w ith p o s s ib le CO2 re a c tio n s v i r t u a l l y a l l a v a ila b le oxygen was assumed
to be produced acc o rd in g to th e re a c tio n g iven by Eq. ( 2 4 ) .
21
2260 C
2110 C
1965 C
Log (T o ta l P re s s u re , Atms)
F ig u re 4:
E xperim en tal and T h e o re tic a l R e s u lts
Assuming Local E q u ilib riu m f o r CO2 D is s o c ia tio n .
22
2260 C
2110 C
1965 C
Log (T o ta l P re s s u re , Atms)
F ig u re 5:
E xperim en tal and T h e o re tic a l R e s u lts
Assuming Rate C o n tro l f o r CO2 D is s o c ia tio n .
B est F i t f o r Al I P re s s u re s .
23
2260 C
1965 C ^ 6
Log (T o ta l P re s s u re , Atms)
F ig u re 6:
E xperim en tal and T h e o re tic a l R e s u lts
Assuming Rate C o n tro l f o r COg D is s o c ia tio n .
Best F i t E xcluding H ig h e s t P re s s u re .
24
2C02 I
2C0 + O2
Oxygen p a r t i a l
(2 4 )
pressures were c a lc u la te d f o r Eq. (2 4 ) assuming
lo c a l e q u ilib r iu m a t th e w ire s u rfa c e and using th e w ire tem p eratu re
to d e term in e an e q u ilib r iu m c o n s ta n t.
S ince th e r e a c tio n is assumed
to ta k e p la c e o n ly in the im m ediate v i c i n i t y o f th e w ir e , oxygen may
d if f u s e away from th e w ire w ith o u t r e a c tin g w ith th e m e ta l.
Under
stead y s ta te c o n d itio n s th e process may be re p re s e n te d as in F ig . 7.
CO2
)
m
VU
+
*
NC0
Oo
«*» T v fn)
I/ n )X
n02
‘
""3
1 1 Vy y
NM
, Boundary
Layer
F ig u re 7:
R eactions a t G as-M etal
In t e r f a c e .
where Nq q , Nq ^ , N2 , Ng, and N^ re p re s e n t th e mole f l u x o f each o f th e
sp ecies through th e boundary la y e r and each has u n its o f moles per u n it
a re a p er tim e .
A m o le c u la r balance f o r th e oxygen r e s u lts
in the
25
fo llo w in g r e la t io n s h ip :
Ncq = 2N0
+ 2N2 + SN3
(2 5 )
As discussed in C hapter I I I ,
th e p a r t i a l
Eq. (2 5 ) can be w r it t e n
p re ss u re o f each s p ec ie a t th e i n t e r f a c e .
in terms o f
That is :
kGCOpCO = 2kG02P02 + 2kG2P2 + 3kG3P3
^2 6 ^
C o n s id e rin g th e t o t a l system p re ss u re as th e sum o f th e p a r t i a l
p ressu res r e s u lt s
in
P = PC0. + pO2 + PC02 + P2 + P3 + PM
where a g a in
( 2?)
is th e known p a r t i a l p re ss u re o f th e v a p o riz e d ir id iu m
and P is th e t o t a l system p re s s u re .
A t e q u ilib r iu m th e d is s o c ia tio n
r e a c tio n g iv e s th e fo llo w in g r e la t io n s h ip :
2
CO
(2 8 )
Y
where
is th e e q u ilib r iu m c o n s ta n t and each o f th e pressures is th e
p a r tia l
p re ss u re a t th e in t e r f a c e .
Assuming t h a t each o f th e o x id a tio n
r e a c tio n s is a t e q u ilib r iu m y ie ld s :
( 2 9 ) , (3 0 )
K
2
The f i v e e q u a tio n s , ( 2 6 ) ,
(2 7 ),
(2 8 ),
(2 9 ) and ( 3 0 ) ,
in f i v e
unknowns, Pq ^ , Pq0 , Pqq2 * p2 and P3 > were solved n u m e ric a lly using a
26
Newton-Raphson i t e r a t i v e scheme.
The c a lc u la te d oxygen p a r t i a l
sures were s u b s titu te d in Eq. (1 2 ) to g iv e th e o r e t ic a l
which were compared w ith e x p e rim e n ta l r e s u l t s .
p re s ­
re c e s s io n ra te s
The agreem ent was n o t
s a t is f a c t o r y ; th e p re d ic te d re c e s s io n r a te s e x h ib ite d s l i g h t CO2 p re s ­
sure dependence w h ile e xp e rim e n ta l re c e s s io n ra te s in c re a s e d s i g n i f i ­
c a n t ly w ith in c re a s in g CO2 p ressu re as evidenced in F ig . 4 .
i n s e n s i t i v i t y to CO2 p ressu re is in accord w ith L e C h a te li e r ' s
The m odel's
p r in c ip le
which im p lie s t h a t f o r Eq. (2 4 ) a t f ix e d te m p e ra tu re , in c re a s e s in th e
CO2 p ressu re do no t r e s u l t in p ro p o rtio n a l
p re s s u re .
in c re a s e s in th e oxygen
S ince sim ultaneous d if f u s io n o f s e v e ra l gases through a
s ta g n a n t gas can a l t e r th e d i f f u s i v i t i e s
o f each, c a lc u la t io n s using
m ulticom ponent d if f u s io n th e o ry [ 2 1 ] were made to t e s t th e m agnitude
o f th e e f f e c t on th e p re v io u s r e s u l t .
A change o f le s s than 5% was
observed in d ic a t in g independent d if f u s io n o f each gas through th e
boundary la y e r was a re as o n a b le assum ption f o r th e e x is t in g e x p e r im ental c o n d itio n s .
The above r e s u lt s suggest th e assum ption of. lo c a l e q u iI i b i rum f o r
th e CO2 d is s o c ia tio n is n o t v a l i d .
C o n s id e ra tio n was n e x t d ir e c te d
toward CO2 d is s o c ia tio n as th e r a t e c o n t r o llin g process.
A standard
r a t e c o n tro l model was n o t c o n s is te n t w ith th e o b s e rv a tio n t h a t a t th e
h ig h e s t p re s s u re , 1 .3 atm (1000 t o r r ) , th e e q u ilib r iu m model ( F ig . 4 )
p re d ic te d a lo w er o x id a tio n r a t e than was observed e x p e rim e n ta lly ;
27
S ince th e e q u ilib r iu m assumption should g iv e an upper bound f o r th e
amount o f a v a ila b le oxygen-, a r a t e l i m i t i n g model should p r e d ic t an
even lo w er o x id a tio n r a t e and hence n o t agree w ith th e e xp e rim en tal
r e s u lts .
However, th e p h y s ic a l aspects o f th e study ( i . e . ,
th e d is ­
s o c ia tio n o f COg o n ly n e ar an ir id iu m w ir e ) suggest t h a t th e w ire may
a s s is t (o th e r than as a h e a t source) in th e COg d is s o c ia t io n .
One way to ta k e in t o account th e w ir e 's p h y s ic a l presence was to
assume t h a t COg m olecules d is s o c ia te d upon h i t t i n g
th e w ire w ith a
c e r t a in minimum amount o f energy which was governed by th e m o le c u le s '
v e lo c it y and in c id e n t a n g le o f c o l l i s i o n .
The minimum v e lo c it y and
a llo w a b le in c id e n t a n g le were t r e a te d as unknowns to be f i t t e d
to th e
d a ta , using th e k in e t ic gas th e o ry [2 2 ] and th e M a x w e ll-B oltzm an v e l ­
o c it y d i s t r i b u t i o n .
An e q u a tio n f o r th e number o f COg m olecules
s t r i k i n g a u n it a re a o f th e w ire p e r tim e w ith a v e lo c it y above th e
unknown minimum and w ith in th e a llo w a b le in c id e n t a n g le was d e riv e d
.
but comparison w ith e x p e rim e n ta l r e s u lt s produced an u n s a tis fa c to r y f i t
and th e approach was d is c a rd e d .
Ir id iu m 's chem ical s i m i l a r i t y to p la tin u m suggested a second
manner in which th e w ire may in flu e n c e th e COg d is s o c ia t io n .
Since
p la tin u m group elem ents have been known to a c t as c a t a ly s t s in s e v e ra l
r e a c tio n s [ 2 3 ] , an a tte m p t was made to c o n s id e r a c a t a l y t i c type
process f o r th e d is s o c ia t io n o f COg coupled w ith d if f u s io n o f th e
r e a c tio n products through th e boundary l a y e r .
The g e n era l th e o ry o f
28
c a t a ly s is
is lim it e d from a q u a n t it a t iv e s ta n d p o in t and fu rth e rm o re ,
no s p e c if ic in fo rm a tio n f o r CO2 on ir id iu m could be found in th e
lite r a tu r e .
In o rd e r to s im p lif y th e m a th em atics, th e GO2 d is s o c ia tio n
was assumed to be governed by a s im p le r a t e e q u atio n as shown:
R = k (T )[C 0 2 ] °
(3 1 )
where R is th e r a t e o f th e r e a c tio n in m o le s /s e c , t h a t i s , th e number
o f moles o f CO2 which undergo d is s o c ia tio n per second, k (T ) is th e
r e a c tio n r a t e c o n s ta n t, a fu n c tio n o f te m p e ra tu re , [COg] re p re s e n ts th e
CO2 c o n c e n tra tio n and a g iv es th e o rd e r o f th e r a t e law and was assumed
c o n s ta n t.
Again th e s it u a t io n is as d e p ic te d in F ig . 7 w ith th e d is s o ­
c ia t i o n r e a c tio n going o n ly in th e fo rw a rd d ir e c t io n .
It
is assumed
t h a t th e products o f t h i s r e a c tio n a re removed by d i f f u s io n through
th e boundary la y e r a t a r a t e which is f a s t enough to a llo w th e d is s o ­
c ia t i o n to proceed a t a c o n s ta n t r a t e f o r a g iven te m p e ra tu re and
p re s s u re .
Thus, th e mole f l u x o f th e CO must be p ro p o rtio n a l to th e
r a t e a t w hich th e d is s o c ia t io n r e a c tio n proceeds.
T h is can be e xp re s ­
sed as
Nco = IEWPco20
where F (T )
( 32)
is th e m o d ifie d r a t e c o n s ta n t which ta k es th e u n its necessary
to g iv e m oles/cm -sec on th e l e f t o f Eq. ( 3 2 ) ; th e c o n c e n tra tio n from
Eq. (3 1 )
is given in terms o f th e p a r t i a l
ta k en to be th e t o t a l
system p re s s u re .
pressure o f CO2 , which is
29
Once Nqq is found Eq. (2 5 ) becomes
NC0 = kGO2 pO2 + kG2P2 + kG3P3
Eq. (3 3 ) to g e th e r w ith Eqs. (2 9 ) and (3 0 ) g iv e s 3 e q u a tio n s w ith 3
unknowns to be solved n u m e ric a lly .
S ince no in fo rm a tio n could be found re g a rd in g
were t r e a te d as unknowns to be f i t t e d
to th e d a ta .
a
and Y ( T ) , these
A sim ple l i n e a r
re g re s s io n was a p p lie d to th e d a ta from each o f th e th re e tem peratu res
i n d i v i d u a l l y to f in d an optimum v a lu e f o r F (T ) and a a t th e tem pera­
tu re .
T h is gave optimum values o f
a
ra n g in g from 0 .4 4 to 0 .4 8 .
A ll
th e d a ta was then run w ith a being stepped through th e p re s c rib e d range
Optimum k (T ) v alu e s were found f o r each te m p e ratu re a t each v a lu e o f a
and th e s tan d ard d e v ia tio n s c a lc u la t e d .
By m in im izin g th e standard
d e v ia t io n , an optimum v a lu e o f a was found as w e ll as optimum values
fo r k (T ).
The r e s u lts which agree re a s o n a b ly w e ll w ith th e e x p e r i­
m ental d a ta a re presen ted in T a b le I and F ig . 5.
Although th e procedure d e sc rib e d above p re d ic te d re c e s s io n ra te s
which were a l l w ith in a f a c t o r o f two o f th e e x p e rim e n ta l r e s u l t s , th e
model d id not fo llo w th e d a ta tre n d a t th e h ig h e s t p re s s u re .
The
p o s s i b i l i t y . t h a t Eq. (3 2 ) does no t hold f o r th e h ig h e s t p re ss u re (see
C hapter V) suggested re p e a tin g th e search f o r a and F (T ) w ith o u t i n ­
c lu d in g th e h ig h e s t p re ss u re d a ta .
T h is r e s u lte d in a m inor change
in a and more s i g n i f i c a n t changes in th e r a t e co n stan ts which had th e
30
e f f e c t o f s h i f t i n g th e curves upward to g iv e good agreem ent a t le a s t
f o r th e th re e lo w er p re s s u re s .
These r e s u lt s a re p resen ted in Tab le I
and F ig . 6 .
TABLE I
Values f o r Unknowns in Rate
Equation f o r GO2 D is s o c ia tio n
For T h e o re tic a l.
R e s u lts in F ig . 5
,
For T h e o re tic a l
R esu lts in F ig . 6
a = 0 .4 8
a = 0 .4 6
k (2 2 6 0 C)
1 .4 1 7 x IO "4
T .6 9 8 x IO "4
¥ (2 1 1 0 C)
6 .0 3 7 x I O ' 5
7 .6 2 9 x 1 0 "5
¥ (1 9 6 5 C)
4 .0 3 5 X l O " 5
6.061
x IO " 5
CHAPTER V
DISCUSSION
E rro rs in T h e o re tic a l
P re d ic tio n s
Average p e rc e n t e r r o r s a re g iv en f o r th e two models re p re s e n te d by
F ig s . 5 and 6 in th e ta b le below.
TABLE 2
Average D e v ia tio n o f T h e o re tic a l Equations
From E xperim en tal Data
W ire Temp.
( 0C)
Average P erc e n t D e v ia tio n
F ig . 5
F ig . 6
(w /o h ig h e s t p re s s .)
2260
3 1 .5
4 .7
2110
2 7 .6 .
7 .9
1965
4 0 .5
2 7 .0
The d i s p a r i t y between th e model and th e data a t th e h ig h e s t p re s ­
sure is no t e a s i l y e x p la in e d because o f th e many unknown v a r ia b le s
in v o lv e d b u t two suggestions may be o f f e r e d .
Eq. (3 1 )
is v a l i d o n ly
a t c o n d itio n s f a r from e q u ilib r iu m , and th e d is s o c ia t io n re a c tio n may
have moved near an e q u ilib r iu m s it u a t io n a t th e h ig h e s t p re s s u re .
th e system p ressu re is
in c re a s e d , th e d i f f u s i v i t i e s , and hence, th e
As
32
mass t r a n s f e r c o e f f ic ie n t s f o r a l l
sp ec ie s decrease causing more CO and
oxygen to rem ain a t th e i n t e r f a c e .
As th e d is s o c ia tio n products b u ild
up th e re v e rs e r e a c tio n r a t e in c re a s e s and e q u ilib r iu m is reached.
It
is a ls o p o s s ib le t h a t a is not p ressu re independent as was assumed [ 2 4 ] .
F ig s . 4 , 5 and 6 were p lo tte d using an average v a lu e f o r th e w ire
d ia m e te r o f 0 .4 9 mm.
No " s ta n d a rd iz a tio n " o f th e w ire d iam eters f o r
th e e xp e rim e n ta l d a ta , as had been done p re v io u s ly [ 2 5 ] , was attem p ted
because no s tro n g c o r r e la t io n e x is te d between re c e s s io n r a t e and w ire
d ia m e te r.
Comment on Free E nergies o f IrO g and Ir O 3
The h ig h -te m p e ra tu re minimum and maximum observed in th e p lo ts o f
th e f r e e e n e rg ie s o f IrO g and IrO g i F ig . 3 , a re commented upon by
Wimber [ 9 ] in th e fo llo w in g fa s h io n :
" I f th e minimum and maximum
a re r e a l , changes in th e ASf0 v alu e s would be a s s o c ia te d w ith re v e rs a ls
in th e slo pes o f th e curves and would be d i f f i c u l t to e x p la in " .
It
is
suggested by th e p re s e n t a u th o r t h a t th e re may be a n o th e r s e t o f p o in ts
(one f o r each f r e e energy c u rv e ) t h a t would be more in keeping w ith th e
slo pes e s ta b lis h e d by th e f i r s t fo u r p o in ts on each curve b u t s t i l l
g iv e s a t is f a c t o r y c o r r e la tio n s between th e model and th e d a ta .
th e curves a re f i t t e d
Since
to d a ta which re p re s e n ts th e sum o f th e two
o x id a tio n r e a c tio n s , i t
is c o n c e iv a b le t h a t a t th e h ig h e s t te m p e ratu re
t h i s same sum could a ls o be a r r iv e d a t by using a la r g e r v a lu e f o r
33
AFf 0C lrO 3 ]
(which would r e s u l t in le s s Ir O 3 produced) and a correspond
in g ly s m a lle r v a lu e f o r AFf ° [ I r 0 2 ] ( r e s u lt in g in more Ir O 2 produced).
S ince th e computer program used to o p tim iz e th e K2 and K3 v alu e s was
n o t a v a i l a b l e , a sim p le t e s t was devised to d eterm ine th e v a l i d i t y o f
th e above h y p o th e s is .
A s t r a ig h t l i n e was f i t t e d
through th e f i r s t
fo u r p o in ts on each curve and th e r e s u lt in g e q u atio n s were used to
e x t r a p o la te f r e e e n e rg ie s a t th e h ig h e s t te m p e ra tu re ,
The new fr e e
energy e q u a tio n s a r e :
AFf 0C IrO 2 ] = 4 4 .9 7 9 - 0.0 0 80 1 19 T
(3 4 )
AFf 0 C IrO 3 ] = -5 .7 8 4 + 0 .0 1 45 3 7T
(3 5 )
The d a ta to which th e f r e e e n e r g ie s , Eqs. (2 2 ) and ( 2 3 ) , had
o r i g i n a l l y been f i t t e d was s t i l l
a v a ila b le as was a program which
compared t h i s data to re c e s s io n r a te s g iv en by Eq. ( 1 2 ) .
The f r e e
energy e q u atio n s in t h is program were re p la c e d by Eqs. (3 4 ) and (3 5 )
and th e program run using th e o ld d a ta .
The r e s u lt s f o r some o f th e
h ig h e s t te m p e ra tu re runs (th o s e f o r th e o th e r te m p e ratu re s being
e s s e n t i a l l y unchanged) a re compared in T a b le 3 .
The new eq u atio n s
were not expected to improve th e c o r r e l a t i o n , s in ce in a l l
Eqs. (2 2 ) and (2 3 ) do re p re s e n t a "b e s t f i t " ,
th e c o r r e la t io n would s t i l l
c as e .
p r o b a b ilit y
but i t was hoped th a t
be re as o n a b le which appears to be the
The r e s u lt s a re even more re as o n a b le when i t
is con sid ered
how s e n s it iv e th e model is to changes in th e f r e e e n e rg ie s .
A 10%
34
change in th e f r e e energy f o r IrO 3 a t th e h ig h e s t te m p e ra tu re r e s u lts
in a change g r e a te r than 60% in th e re c e s s io n r a t e due to th e fo rm a tio n
o f Ir O 3 .
For th e p re s e n t study Eqs. (2 2 ) and (2 3 ) were used to c a lc u la t e
th e f r e e e n e rg ie s .
Again., s in c e i t
is o n ly th e sum o f th e o x id a tio n
r a te s r e f l e c t e d in th e d a ta , these e q u atio n s should work reaso n ab ly
w e ll to g iv e t h e .c o r r e c t sum as th e y seem to have done in th e previo u s
s tu d ie s .
35
TABLE 3
Comparison o f R e s u lts Using L in e a r Free Energy Equations
Run
No.
32# .
34#
37#
38#
39#
41#
44#
46#
48#
92*
96*
100*
103*
106*
no*
116*
1 20 *
125*
Exp.
Rate (c m /s )
T h e o re tic a l Rate
Using Eqs. (2 2 ) & (2 3 )
T h e o re tic a l Rate
Using Eqs. (3 4 ) & (3 5 )
5 .2 5 E -0 7
8 .1 1 E -0 7
7 .1 7 E -0 7
8 .3 9 E -0 7
6 .7 3 E -0 7
9 .3 4 E -0 7
I .60 E -0 6
2 .2 4 E -0 6
2 .8 2 E -0 6 .
7 .3 6 E -0 7
6 .4 7 E -0 7
8 .4 0 E -0 7
7 .4 3 E -0 7
8 .3 8 E -0 7
T .4 2 E -0 6
5 .5 5 E -0 6
1 .26 E -0 5
3 .4 3 E -0 5
5 .0 2 E -0 7
5 .0 2 E -0 7
5 .0 4 E -0 7
5 .1 7 E -0 7
5 .8 2 E -0 7
7 .5 8 E -0 7
I .34E -06
2 .2 0 E -0 6
2 .7 7 E -0 6
4 .8 7 E -0 7
4 .8 7 E -0 7
5 .0 7 E -0 7
5 .8 7 E -0 7
6 .8 7 E -0 7
1 .7 9 E -0 6
4 .1 7 E -0 6
9 .3 5 E -0 6
2 .7 8 E -0 5
5 .0 2 E -0 7
5 .0 2 E -0 7
5 .0 7 E -0 7
5 .3 6 E -0 7
6 .8 1 E -0 7
I .06 E -0 6
.1.83E -06
2 .5 T E -0 6
3 .1 7 E -0 6
4 .1 0 E -0 7
4 .1 1 E -0 7
4 .3 8 E -0 7
5 .4 7 E -0 7
6 .7 7 E -0 7
2 .3 8 E -0 6
6 .4 3 E -0 6
1 .2 6 E -0 5
2 .5 8 E -0 5
2 1 .0
2 7 .0
Average P e rc e n t E rro r
(Using A ll D ata)..
# In d ic a te s d a ta from n a tu ra l c o n v e c tio n in a i r , .
* In d ic a te s data from n a tu ra l c o n v e c tio n in oxygen.
'
CHAPTER V I
SUMMARY
The o x id a tio n r a t e o f th e ir id iu m w ire s in n a t u r a ll y convected.
COg was assumed to be c o n tr o lle d by th re e s te p s :
1)
The k i n e t i c l y c o n tr o lle d p ro d u c tio n o f oxygen from COg.
2)
The r a t e o f v a p o r iz a tio n o f th e o x id e s p e c ie s , IrO g (g ) and
Ir O g ( g ) , and I r ( g )
3)
from th e ir id iu m s u rfa c e .
The r a t e o f d if f u s io n o f th e o xides and I r ( g )
through th e
boundary l a y e r .
A model was developed to p r e d ic t th e amount o f oxygen a v a ila b le
f o r th e o x id a tio n re a c tio n s a t th e g a s -s o lid i n t e r f a c e .
T h is model
was used in c o n ju n c tio n w ith a p re v io u s ly d e riv e d model f o r th e
y a p o r iz a t i o n / d i f f usi on c o n tro l o f ir id iu m o x id a tio n .
E xp erim en tal d a ta was c o lle c te d f o r ir id iu m w ire tem peratu res
o f 1 9 6 5 ,.2 1 1 0 and 2260 C (2 2 3 8 , 2383,and 2533 K) in COg atmospheres
o f 1 .3 2 x 1 0 "3 , 1 .3 2 x 1 0 "2 , 1 .3 2 x 1 0"1 and 1 .3 2 atm ( I ,
and 1000 t o r r j .
1 0 , 100
The t h e o r e t ic a l p r e d ic tio n agreed w e ll w ith th e
e x p e rim e n ta l r e s u lt s f o r th e th re e lo w e r p re s s u re s .
APPENDIX A-.
38
TABLE 4
E xperim en tal Data
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
36
W ire Temp.
(C)
2260
P res s .
(to rr)
1000
100
-
. 10
I
2110
1000
.
100
10
.
I
1965
..
1000
W ire Diam.
(cm)
0 .0 4 4 5
0 .0 4 8 8
0 .0 4 6 7
0 .0 5 0 8
0 .0 4 4 3
0 .0 4 9 4
0 .0 4 6 5
. 0 .0 4 4 5
0 .0 4 9 8
0 .0 4 8 0
0 .0 4 6 3
0 .0 4 4 7
0 .0 4 4 4
0 .0 4 8 6
0 .0 4 3 8
0 .0 4 8 3
0 .0 4 8 4
0 .0 4 6 0
0 .0 4 6 6
0 .0 4 8 7
0 .0 4 9 2
0 .0 4 7 9
0 .0 4 5 9
0 .0 4 2 7
0 .0 4 9 0
0 .0 4 6 9
0 .0 4 8 7
0 .0 4 6 7
0 .0 4 6 4
0 .0 4 4 4
0 .0 4 8 6
0 .0 4 6 2
0 .0 4 7 0
0 .0 4 8 2
0 .0 4 5 3
. 0 .0 4 2 4
C a lc u la te d
Rate (cm /sec)
E xperim ental
Rate (cm /sec)
.
1 .5 4 E -0 6
I .32 E -0 6
1 .35 E -0 6
I .6 1 E-06
8 .5 6 E -0 7
8 .0 2 E -0 7
7 .5 6 E -0 7
7 .4 1 E -0 7
2 .8 8 E -0 7
2 .8 6 E -0 7
3 .0 9 E -0 7
3 .0 5 E -0 7
2 .8 3 E -0 7
3 .2 0 E -0 7
3 .2 4 E -0 7
3 .4 3 E -0 7
4 .8 1 E -0 7
5 .0 8 E -0 7
4 .8 9 E -0 7
4 .7 1 E -0 7
3 .3 6 E -0 7
3 .0 1 E -0 7
2 .8 5 E -0 7
2 .7 8 E -0 7
9 .5 0 E -0 8
9 .7 5 E -0 8
9 .3 8 E -0 8
9 .7 9 E -0 8
4 .6 3 E -0 8
6 .3 4 E -0 8
4 .7 9 E -0 8
5 .1 6 E -0 8
1 .46E -07
1 .70E -07
1 .8 7 E -0 7
1 .7 5 E -0 7
.
.
3 .1 3 E -0 6
3 .1 4 E -0 6
3 .1 3 E -0 6
3 .1 4 E -0 6
7 .9 8 E -0 7
7 .9 8 E -0 7
7 .9 8 E -0 7 '
7 .9 8 E -0 7
2 .9 3 E -0 7
2 .9 3 E -0 7
2 .9 4 E -0 7
2 .9 6 E -0 7
3 .2 5 E -0 7
3 .1 6 E -0 7
3 .2 6 E -0 7
3 .1 7 E -0 7
9 .2 0 E -0 7
9 .1 9 E -0 7
9 .2 0 E -0 7
9 .2 0 E -0 7
2 .8 8 E -0 7
2 .8 8 E -0 7
2 .8 8 E -0 7
2 .8 9 E -0 7
9 .9 7 E -0 8
9 .9 7 E -0 8
9 .9 7 E -0 8 .
9 .9 7 E -0 8
6 .0 6 E -0 8
6 . T IE -0 8
6 . OOE-0 8
6 .0 6 E -0 8
4 .2 7 E -0 7
4 .2 8 E -0 7
4 .2 7 E -0 7 •
4 .2 6 E -0 7
39
TABLE 4 (C o n t.)
Run
No.
37
38
39
40
41
42
43
44
45
46
47
48
W ire Temp.
(0
1965
P res s .
(to rr)
100
10
I
W ire D iam.
(cm)
0.0491
0 .0 4 7 3
0 .0 4 5 9
0 .0 4 2 7
0 .0 4 4 5
0 .0 4 8 5
0 .0 4 4 6
0 .0 4 8 7
0 .0 4 9 3
0 .0 4 6 5
0 .0 4 9 0
0 .0 4 7 6
. C a lc u la te d
E xperim en tal
R ate (cm /sec) : Rate (cm /sec
I .09E -07
I .03E -07
I .23E -07
1 .1 1 E -0 7
3 .7 5 E -0 8
4 . IlE -O S
4 .1 1 E -0 8
3 .8 2 E -0 8
6 .9 5 E -0 9
7 .6 4 E -0 9
8 .5 1 E -0 9
8 .1 2 E -0 9
1 .18E -07
1 .17 E -0 7
1 .1 7 E -0 7
I .1 7E-07
3 .6 5 E -0 8
3 .6 6 E -0 8
3 .6 6 E -0 8
3 .6 7 E -0 8
I .30 E -0 8
I .3 0 E -0 8
I .3 0 E -0 8
I .3 0 E -0 8
40
C
C
C
C
C
-
C
C
C '
C
C
C
C
C
C
C
C '
C
C :
C
C
C
C
C
C
C
C
C
C
C
C
C .
C
C
C
C ’
C '
C
C
C
C
C ‘
C
C i
C
T H I S PROGRAM CALCULATES RE CE SSI ON RATES US I NG THE
COMBINED K I N E T I C , D I F F U S I O N CONTROL MODEL AND
COMPARES THE RESULTS WITH THE EXPERI MENTAL VALUES
: z :: j z:: s: : : : : : : z
j
;
V A RI ABL E L I S T
NCO - CO FLUX THROUGH BOUNDARY LAYER
I D 2 , I D 3 , I D S , IDM - C O L L I S I O N I NT E GR AL S USED I N CALCULATI NG GASEOUS D I F F U S I V I T I ES
K G2 , KG3, KGS, KGM - MASS TRANSFER C O E F I C I E N T S
K - THERMAL C O N D U C T I V I T Y OF C 0 2
MU - V I S C O S I T Y OF C02
LAMF - MEAN FREE PATH FOR CO2 MOLECULES
M I , M 2 , M 3 , M 5 , MM - MOLECULAR WEIGHTS
NUF - NUS SE LT NO.
G - ACCELERATI ON DUE TO G RAV I TY
R - I D E A L GAS CONSTANT
TM - M E L T I N G P O I N T TEMPERATURE FOR O X I D E S P E C I E S
R I 2 , R I 3 , R l M, R I 5 , E I 2 K , E I 3 K, E I M K , E I SK - TERMS I N
GASEOUS D I F F U S I V I TY COEFS ( C F PERRY 4 TH ED)
J D - WIRE TEMPERATURE I N D I C A T O R
P T - SYSTEM PRESSURE I N TORR
D I A M - MEASURED WI RE DI AMETER
XEXP - EXP ERI ME NTAL RECESSI ON RATE
RATE - K I N E T I C R EACTI ON RATE CONSTANT CTEMP DEPENDENT)
C P - S P E C I F I C HEAT OF CO2
GAM - S P E C I F I C HEAT R AT I O FOR C02
T - WIRE TEMPERATURE (DE G K)
P - SYSTEM PRESSURE I N ATM
TC - WIRE TEMPERATURE (DEG O
CF - CORRECTION FACTOR FOR W IR E DI AMETER
D - CO RRECTED. WI RE DI AMETER
TFK - F I L M TEMPERATURE ( DEG K)
Z 2 , Z 3 , ZM - TERMS I N V A P O R I Z A T I O N FLUX
RHO - D E N S I T Y OF C02
V 2 , V 3 , VS, VM - TERMS I N GASEOUS D I F F U S I V I T I ES
BETF - C O M P R E S S I B I L I T Y FACTOR FOR CO2
RAF - R AY LE IG H N O .
C N , CW - TERMS USED I N CALCULATI ON OF NUS SE LT NO.
H C - F I L M COEFI Cl ENT
D L F 2 , DLF3 - FREE E N E R G IE S FOR O X I D ES
41
C
C
C
C
C
C
C
K 2» K 3 - E Q U I L I B R I U M CONSTANTS
PM - P A R T I A L PRESSURE OF I R ( G )
A - U N I T S COEF.
ALPHA - EXP I N RATE EQUATION
PO2 - P A R T I A L PRESSURE OF 0 2
XDOT - CALCULATED RECESSI ON RATE
PERD - PERCENT D E V I A T I O N
DIMENSION RAT(G)
REAL
REAL
REAL
REAL
F(U )=
& 3 *K G
NCO
I D 2 j> I D 3 » I DM
ID S ,M 5,K G 5
K , M U f L A M F , M l , M 2 , M G , M M , K N , K 2 f K 3 f N U F f K G 2 , K G 3 , KGM
N C O -2 * K G 5 * P * A L 0 G ( P / ( P - U ) ) - 2 * K G 2 * K 2 * U3 *K 3 *U **I .5
Fl (U )=
R A T (I )
RAT(2)
RAT( 3)
- 2 * K G 5 * P / ( P - U ) - 2 * K G 2 * K 2 - 3 * K G 3 * K 3 * I . 5 *S Q R T ( U)
= E X P (-8 .6 8 1 )
= E X P ( - 9 . 481 )
= EXP ( - 9 • 7 I I )
G =980.22
R =82.056
M 1=44® 01
M2 = 2 2 4 . 2
M3 = 2 4 0 . 2
MM= 1 9 2 . 2
M 5= 3 2
TM=I 9 0 0
R I 2= 4 . 2 8 9 5
R l 3= 4« 4 4 5 5
R1M=3«8905
R l 5=3® 71 4 5
E 1 2 K = S Q R T ( 1 9 0 * I . 9 2 * TM)
E13K=SQRT(1 9 0 * 1 . 92*TM )
E1M K=SQ RT(1 9 0 * I . 9 2 * 2 7 2 7 )
E l S K = I 4 4 . 66
K=T.9 6 4 5 E -4
DO 1 00 JK= I , 48
IN P U T
JDf PTf DIAM f XEXP
RATE=RAT(JD)
1
2
3
GO T O ( I f 2
T = 2 5 3 3 ) M U=
T=2383)M U=
T= 2 2 3 8 JMU=
4 P = P T / 760
TC=T - 273
*
, 3
4.
4«
4»
)f JD
9 0 7 6 E - 4J C P = . 3 1 4 1 3 ) GAM= I • I 6 7 9 , GO TO
7 2 8 2 E - 4 ) C P = • 3 1 1 4 7 , GAM= I . I 7 , GO TO 4
5 5 2 8 E - 41 C P = * 3 0 8 6 2 ) GAM= 1 . 1 7 0 7
4
42
CF=2 7 . 2 8 3 2 - o 0 5 1 3 3 8 5 7 2 2 * T C + 3 . 7 3 4 1 2 6 I S E -5 * T C * * 2
& - I o 2 0 0 5 2 19 4 E - 8 * T C * * 3 + I . 4 3 9 29 0 5 9 E - I 2 * T C * * 4
D= C F* DI AM
XEXP=XE X P * C F * I = E - 7
TFK=CT+28 I ) / 2
Z2=44=3*SQRT( 1 /M 2 /T )
Z 3= 4 4 . 3 * SQRTC 1 / M 3 / T )
ZM=4 4 . 3*SQ RTC 1/M M /T)
RHO= . 5 3 6 3 * P / TFK
LAMF= I . 7 0 3 9 E - 3 * M U * SQRTCTFK) / P
V2=TFK/E12K
V 3= T F K / E 1 3K
VM=TFKZE I MK
V 5 = T F K / E 1 5K
I D 2 = EXPC- . 3 0 9 5 8 2 4 - . 5 6 7 7 0 2 1 0 8 * ALOGC V2> + . 1 9 8 7 3 5 8 2 4 *
* CALOGCV 2 ) ) * * 2 - • 4 3 2 9 2 5 6 7 7 E - I * CALOGC V 2 ) ) * * 3 +
& . 3 5 7 7 4 3 6 2 7 E - 2 * C ALOGCV 2 ) ) * * 4 )
I D3= EXPC - . 3 0 9 5 8 2 4 - o 5 6 7 7 0 2 1 0 8 * ALOGC V3> + • 1 9 8 7 3 5 8 2 4 *
AC ALOGC V 3 ) ) * * 2 - . 4 3 2 9 2 5 6 7 7 E - I * CALOGCV 3 ) ) * * 3 +
A = 3 5 7 7 4 3 6 2 7 E - 2 * C ALOGC V3> > * * 4 )
I DM = EXPC- . 3 0 9 5 8 2 4 - . 5 6 7 7 0 2 1 0 8 * ALOGC VM) + . 1 9 8 7 3 5 8 2 4 *
AC ALOGC V M > ) * * 2 - • 4 3 2 9 2 5 6 7 7 E - I * CALOGCVM) ) * * 3 +
& . 3 5 7 7 4 3 6 2 7 E - 2 * C ALOGC V M ) ) * * 4 )
I D S = E X P C - . 3 0 9 5 8 2 4 - . 5 6 7 7 0 2 1 0 8 * A L O G CVS) + . 1 9 8 7 3 5 8 2 4 *
ACALOGC V 5 ) ) * * 2 - . 4 3 2 9 2 5 6 7 7 E - I * C ALOGCV 5 ) ) * * 3 +
A . 3 5 7 7 4 3 6 2 7 E - 2 * C ALOGCV 5 > ) * * 4 )
D V 2 = C 1 0 . 7 - 2 . 4 6 * SQRTC I . ZM I + I . Z M 2 ) >* I . E - 4 * TFK
A * * I • 5 * SQRTC I * ZM I + I . Z M 2 ) Z P Z R 1 2 * * 2 Z I D 2
D V 3 = C I 0 . 7 - 2 . 4 6 * SQRTC I . Z M1 + I . Z M 3 ) ) * I . E - 4 * TFK
& * * 1 . 5 * SQRTC I . Z M 1 + 1 « Z M 3 > Z P Z R 1 3 * * 2 Z I D 3
DVM=C 1 0 . 7 - 2 = 4 6 * SQRTC I . Z M H l . Z MM) ) * I . E- 4 * TFK
A * * I . 5 * SQRTC I . ZM I 4-1 . ZMM >Z P Z R I M * * 2 Z I DM
DVS=C I 0 . 7 - 2 . 46* SQRTC I . ZM H l . ZM5 ) ) * 1 . E - 4 * TFK
& * * 1 . 5 * SQRTC I . ZM I -M . Z M 5 ) Z P Z R I 5 * * 2 Z I D 5
BETF=IZTFK
R A F = G * BET F * R H 0 * * 2 * CT - 2 8 I ) * D * * 3 * CPZMUZK
C N = 1 8 0 . 0 2 7 3 - 2 . 3 6 9 1 3 E - I * T-M . 0 0 0 4 5 8 E - 4 * T * * 2 - I . 2 2 1 7 4 4 E - 8
4*T**3.
5. 449E - I 3 * T * * 4
CW= I . 5 3 8 - 5 . 3 9 7 E - 4 * T + I » 3 6 6 E - 7 * T * T
KN= LAMFZ d
N U F = 2 Z CC N * 8 * K * GAM*KNZMUZCPZ CGAM+I ) + CW* ALOGC8 . 8 7 *
A R A F * * C - . 3 5 4 ) * C T Z 2 8 I ) * * C - . 4 6 4 ) / C 1 + 2 * K N ) )>
HC=NUF * K Z D
I
43
-R-OO
K G 2 = H C * (C P * R H 0 * D V 2 /K )* * (2 ./3 o ) /R /TFK /C P /R H O
K G 3 = H C * ( C P * R H 0 * D V 3 / K ) * * C 2 . / 3 « >/ R / T F K / C P / R H O
K G M = H C * ( C P * R H 0 * D V M / K ) * * ( 2 o/ 3 . ) / R / T F K / C P / R H O
K G5 = H G * CC P * R H O * DV5 / K ) * * ( 2 » / 3 « ) / R / T F K / C P / R H O
DLF 2 = I 129 5 . I 5 5 - 2 0 . 5 0 7 3 7 * T + . 0 1 3 9 7 0 6 2 I * T * T - 4 . 2 2 0 8 0 6 4 E - 6 *
& T **3 + 4.7 7 00 3 6E -1 0 *T **4
DL F 3 = - 1 9 2 6 5 . 59 4 + 3 5 . 5 0 1 2 3 6 * T - 6 0 2 4 4 5 6 7 7 3 * T . * T + 7 . 4 7 2 2 2 4 2 E & 6 *T **3-8.5 39 7 8 8E -1 0 *T **4
K 2 = EXPC- D L F 2 * I 0 0 0 / I . 9 8 7 2 / 1 )
K 3= EXPC - DLF 3 * I 0 0 0 / I . 9 8 7 2 / T )
PM=C I 0 * * < - 8 4 6 4 . 6 7 / 1 + 6 5 . 5 8 I 2 * ALOGI 0 C I ) - . 0 1 0 0 2 7 2 * 7 +
&5. 4498 I E - 7 * 7 * * 2 - 2 0 0 . 9 9 7 ) ) / 7 6 0
A= I 9 2 . 2 / C2 2 . 5 7 / C I . + . 6 6 4 6 3 18 0 5 E - 5 * 7 C - * 2 6 8 7 3 3 8 18 E - 9 * 7 C * *
6 2 + I . 5 3 3 3 1 7 5 3 E - 1 2 * 7 0 * * 3 - » 3 5 0 5 9 2 0 3 6 E- I 5 * 7 C * * 4 ) * * 3 )
A L P H A = . 4 601
NCO= RA 7 E * P * * ALPHA
NL= 0
NN= 0
P O 2=.05*P
31 SAV E= P0 2
I F CNL « G7» 2 0 1 ) 0 U 7 P U 7 * CAN 7 F I N D S 7 A R 7 I N G P 0 I N 7 % J K l
&S70P
I FC PO2 « L 7 . 0 ) NL = N L + I ) P 0 2 = N L * . 0 0 5 * P » NN= 0 J GO 7 0 31
P 0 2 = P 0 2 - FC P 0 2 >/ F I CP 0 2 )
I F CNN . G 7 . 2 0 ) 0 U 7 P U 7 'SLOW CONVERGENCE *» J K ; GO 70 3 2
I F C A B S C C S A V E - P 0 2 ) / S A V E ) . 6 7 . . 0 0 0 1 ) N N = N N + I } GO 7 0 31
3 2 X DO7 = A * CKG 2 * K2 * PO2 * Z 2 / C K G 2 + Z 2 ) + K G 3 * K 3 * P 0 2 * * I . 5 * 2 3 /
&CKG3+Z3)+KGM*ZM*PM/CKGM+ZM))
PERD= CX D 0 7 - X E X P ) * I 0 0 / XEXP
WRI 7E C I 08» 5 0 ) JK» 7 C * P 7 » D» XEXP» X D07» PERD
5 0 FORMA7 C2X» I 4» 3X» I 5» 3X» 1 P E 8 . 1» 3 X » 0 P F 7 . 4» 3C3X» 1 P E 1 0 . 3 ) )
100 C0N7INUE
END
:
44
DATA
( UNCORRECTED)
* * a S * * * o * * * * « * * S « *
TEMP
C
PRESS
TORR
2260
2260
2260
2260
2260
2260
2260
2260
2260
2260
2260
2260
2260
2260
2260
2260
21 I 0
2110
2110
2110
21 I 0
2110
21 I 0
21 I 0
21 I 0
2110
21 I 0
2110
2110
2110
2110
2110
I
I
I
I
000
000
000
000
I 00
I 00
I 00
I 00
I0
. 10
10
I0
I
I
I
I
I 000
I 000
I 000
.1000
I 00
I 00
I 00
I 00
. . 10
10
10
10
I
I
I
I
DIAM
CM
. 0468
• 0513
. 049 I
. 0534
. 0465
.0519
. 0 489
. 0468
. 0518
. 0504
• 0487
• 0470
. 0 466
. 051 I
. 0461
. 0507
. 0505
. 0 48 0
. 0486
• 0509
.05 1 4
• 0499
• 0479
«0446
.0512
. 0489
. 0 509
. 0487
.0484
.0463
.0507
0482
XDOT
CM/ S
'
'
I . 6 2 2 E - 06
1 • 3 8 3 E - 06
1 . 4 1 7 E- 06'
1 . 6 9 3 E- 0 6
8 . 9 9 1 E- 07
8 . 4 2 9 E- 07
7 . 9 4 2 E - 07
7 . 7 9 2 E - 07
3 . 0 2 6 E - 07
3». 0 0 8 E- 07
3 . 2 5 0 E - 07
3 . 2 0 8 E- 07
2 . 9 7 3 E - 07
3 • 3 6 0 E- 07
3« 4 0 4 E - 07
3 . 6 0 3 E - 07
5 . 0 1 9 E - 07
5 • 3 0 4 E - 07
5 . I 0 4 E - 07
4 . 9 1 2 E - 07
3 . 5 0 6 E- 07
3 . 2 0 2 E - 07
2 . 9 7 4 E - 07
2 . 8 9 6 E - 07
9 . 9 1 4 E - 08
1 . 0 1 8 E - 07
9 . 7 9 1 E- 08
1 . 0 2 2 E - 07
4 . 8 3 6 E - 08
6 • 6 1 3 E- 08
4 . 9 9 7 E - 08
5 . 3 8 I E- 08
45
1965
1965
1965
1965
1965
1965
1965
1965
1965
1965
1965
1965
1965
1965
19 65
1965
.
I 000
1000
I 000
I 000
I 00
I 00
I 00
I 00
I0
I0
I0
I0
I
. I
I
I
.
.
O
O
.
■
»
O
e
■
.
e
e
»
O
•
•
,
0 49 1
0504
0 47 3
0 443
0513
0494
0479
0446
0465
0507
0465
0509
0515
0485
0512
0 4 98
I «527E-07
I . 774E-07
I . 9 4 9 E - 07
I • 8 2 S E - 07
I . I 38E-07
I .07 2 E -07
I . 2 9 0 E - 07
I . I 6 1 E - 07
, 3 . 9 2 1 E- 08
3 • 8 8 8 E - 08
4« 2 9 8 E - 08
3 « 9 8 9 E - 08
7 . 2 6 3 E - 09
7 .9 8 4E -0 9
8 . 8 9 I E - 09
8 . 4 8 I E - 09
46
REFERENCES
1.
A n o n ., I r i d iu m 9 The M e ta l, I t s A llo y s , Chemical Compounds and
C a t a ly t ic P r o p e r t ie s , The In t e r n a t io n a l N ic k e l C o ., New Y o rk,
N .Y ., 1965.
2.
R .T . Wimber, H igh -T em p eratu re O x id a tio n o f Ir id iu m , F i r s t Annual
Progress R e p o rt, R L 0 -2 2 2 8 -T 1 -1 , F e b ru a ry , 1971.
3.
E .H .P . Cordfunke and 6 . M eyer, "The System Irid iu m -O x y g e n , I .
Measurements o f th e V o l a t i l e Oxide o f Ir id iu m " , Rec. T r a v . C him .,
8 1 , -pp. 4 9 5 -5 0 4 , 1962.
4.
V .H . S c h a fe r and H .J . H e i t l and, "Gleichgewichtsm essungen im
System Ir id iu m - S a u e r s t o ff G asform iges I r i d i um troxyd", Z . Anorg.
Al I gem. Chem., 3 0 4 , pp. 2 4 9 -6 5 , 1960.
5.
C .B . A lcock and G.W. Hooper, "Thermodynamics o f th e Gaseous
Oxides o f th e P latinum -G roup M e ta ls " , Royal S o c ie ty o f London,
Proceeding S e rie s A, 2 5 4 , pp. 5 5 1 -6 1 , 1960.
6.
J .H . Norman, e t a l , "Mass S p e c tro m e tric Study o f Gaseous Oxides
o f Ir id iu m " , Jou rn al o f P h ys ic al C h e m is try , 4 2 , pp. 1 1 2 3 -4 , 1965.
7.
R.W. B a r t l e t t , "P latin u m O x id a tio n K in e tic s w ith C o nvective
D iff u s io n and S u rfa c e R e a c tio n " , J . E lectrochem . S o c ., 1 1 4 ( 6 ) ,
5 4 7 -5 5 0 , 1967
8.
N.K W ahl, N a tu ra l-C o n v e c tio n H igh-Tem perature O x id a tio n o f
I r i d iu m , M a s te r's T h e s is , Montana S ta te U n iv e r s it y , June, 1974.
9.
R .T . Wimber, e t a l , " K in e tic s o f E v a p o ra tio n /O x id a tio n o f Ir id iu m " ,
To be p u b lish e d in M e t. T ra n s .
1 0 . S.W. H i l l s , H ig h -T em p eratu re O x id a tio n o f I r i d iu m , M a s te r's
T h e s is , Montana S ta te U n iv e r s it y , December, 1974.
1 1 . A.W. S ea rc y, D .V . Ragone, and U. Colombo, Chemical and M echanical
B eh avio r o f In o rg a n ic M a t e r ia ls , pp. 1 0 8 -1 1 0 , W ile y - In t e r s c ie n c e ,
New Y o rk , 1970.
1 2 . T .K . Sherwood and R .L . P ig fo r d , A b s o rp tio n and E x t r a c t io n , 2nd
e d . , pp. 5 2 -9 2 , M c G ra w -H ill, N .Y ., 1952.
47
1 3 . J .R . W e lty , C .E . W icks, and R .E . W ils o n , Fundamentals o f Momentum,
H e a t, and Mass T r a n s f e r , p. 5 5 1 , J . W ile y and Sons, New Y o rk , 1969
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cussion on H eat T r a n s f e r , pp. 3 2 8 -3 3 , IME and ASME, New Y o rk , 1951
1 5. R .E . Emmert and R .L . P ig fo r d , Chemical Engineers Handbook, 4 th
e d . , S e c t. 1 4 , pp. 2 0 -2 1 , M c g r a w -H ill, New Y o rk , 1963.
1 6. R .T . Wimber and H .G . K raus, "O x id a tio n o f Ir id iu m " , M e t. T r a n s ., 5
pp. 1 5 6 5 -7 2 , 1974.
“
1 7. R. Honig and D .A . Kram er, Techniques o f M e ta ls R esearch, Vol I V ,
P a r t I , pp. 5 1 5 -1 6 , John W ile y and Sons, New Y o rk , 1970.
1 8. J . H ils e n r a t h , e t a l , T a b les o f Thermal P ro p e rtie s o f Gases,
NBS C i r c . 5 6 4 , 1 95 5 .
1 9 . W.M. Kays, C o n v e ctiv e H eat and Mass T r a n s f e r , p. 3 5 9 , M c G ra w -H ill,
New Y o rk , 1966.
2 0. A. O l i v e i , "Methods f o r S tudying O xygen-P latinum M e ta ls I n t e r ­
a c t io n " , Journal o f th e Less Common M e ta ls , 2 9 , pp. 1 1 -2 3 , 1972.
2 1 . J .O . H ir s c h fe ld e r , R .B . B ir d , and E .L . S p o tz , " V is c o s ity and O th er
P h y s ic a l P ro p e rtie s o f Gases and Gas M ix tu r e s " , T ra n s , o f ASME,
p . 9 3 4 , November, 1949.
2 2 . R .D . P re s e n t, K in e tic Theory o f Gases, pp. 1 2 -8 0 , M c G ra w -H ill,
New Y o rk , 1958.
2 3 . P .H . Emmet, C a t a ly s is , V o l. I ,
C o rp ., 1954.
pp. 1 1 9 -9 5 , R einhold P u b lis h in g
2 4. G.B. S k in n e r, In tr o d u c tio n to C h e m ic a l. K in e t ic s , p. 9 , Academic
P re s s , New Y o rk , 1974.
2 5 . H.G . Kraus, N a tu ra l C o n v e c tio n , High Tem perature O x id a tio n o f
i r i d iu m , M a s te r's T h e s is , Montana: S ta te U n iv e r s it y , June, 1973.
MONTANA STATE UNIVERSITY LIBRARIES
Ill
762 100 3808 8
N378
G29A
c o p . 2
G e o rg e ,
T h o m as
L
H ig h -te m p e r a tu r e
o x id a t io n
o f
ir id iu m
a * ,*