Natural convection high temperature oxidation of iridium
by Hal Gene Kraus
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 Hal Gene Kraus (1973)
Abstract:
The experimental study of the natural convection oxidation of iridium was performed at temperatures
of 1600, 1900, and 2200°C and pressures ranging- from 0.00132 to 1.32 atmospheres. A theoretical
model describing the surface, recession rate was derived assuming that the rate was controlled by the
diffusion of Ir, IrO2, and IrO3 through the gaseous boundary layer, adjacent to the iridium specimen.
Average values for the standard state enthalpy and entropy changes for the formation of IrOg and IrCh
were calculated for the 1600 to 2200 °C temperature range. A value for the partial pressure of Ir at
22000C was found. Correlation between experiment and the theoretical model was good with the
overall mean % error of experimental rates from theoretically predicted rates being 13.3% for the 1600
to 22000C range. S ta te m e n t o f P e rm is s io n t o Copy
I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l l m e n t o f th e r e q u ir e m e n ts
f o r t h e M a s te r 's D egree i n M ech an ical E n g in e e r in g a t M ontana S t a t e U n iv e r­
s i t y , I a g re e t h a t th e L ib 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 in s p e c ­
tio n .
I f u r t h e r .a g re e t h a t p e r m is s io n f o r e x te n s iv 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 rp o s e s may be g r a n te d by my m a jo r p r o f e s s o r , o f , i n
h i s a b s e n c e , by th e D ir e c t o r o f L i b r a r i e s .
I t i s u n d e rs to o d t h a t any
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 in s h a l l n o t be
a llo w e d w ith o u t my w r i t t e n p e r m is s io n .
S ig n a t u r e
D ate
j
J 9 y ^
NATURAL CONVECTION HIGH TEMPERATURE OXIDATION OF IRIDIUM
by
HAL GENE KRAUS
A t h e s i s s u b m i t t e d ,t o t h e G ra d u a te F a c u lty ih_ p a r t i a l
f u l f i l l m e n t ' o f t h e r e q u ir e m e n ts f o r th e d e g re e
of ;
.
MASTER -OF SCIENCE
in '
.
'
M ech an ical E n g in e e r in g
V•
A pproved:
■: H ead, M ajor D e p a ^ ^ e n t
~
C hairm an, -Exam ining C om m ittee
G raduate^ Dean
MONTANA STATE UNIVERSITY
Bozeman, M ontana
J u n e , 1973
iii
' ACKNOWLEDGEMENT
S p e c ia l th a n k s a r e g iv e n t o D r. R. T. Wimber f o r h i s g u id a n c e and
a s s i s t a n c e i n th e r e s e a r c h and f o r s e r v in g a s h ead o f th e a s s o c i a t e d
c o m m itte e . The A to m ic E n erg y Comm ission i s a l s o g iv e n s p e c i a l th a n k s
f o r th e f i n a n c i a l s u p p o r t o f t h i s r e s e a r c h .
Thanks a r e a l s o i n o r d e r t o D r. E. H. B ishop and D r. R, E. Powe
f o r t h e i r a c t i v e i n t e r e s t i n th e r e s e a r c h and f o r s e r v in g a s members
o f th e a s s o c i a t e d c o m m itte e . D r. Powe i s th e a u th o r o f th e much u s e d ,
l e a s t s q u a r e s ' c u rv e f i t t i n g s u b r o u tin e , u s e d i n t h i s r e s e a r c h .
iv
TABLE OF CONTENTS
Page
LIST OF TABLES . ................................................................................................................
LIST OF F IG U R E S ....................................................................................................
v
vi
NOMENCLATURE...................................................................... .................................................. v i i
ABSTRACT ......................................................................................................
INTRODUCTION ............................................... . . . . . .
...............................................
xi
I
REVIEW OF PAST W O R K ..............................................................................
2
THEORY ........................ . . . . . . . .
7
.................................................... . . . .
IRIDIUM ANALYSIS ............................................... .... . . .......................................... .
8
EXPERIMENTAL EQUIPMENT AND PROCEDURE. . . . .
...........................................
8
EXPERIMENTAL RESULTS AND THEORETICAL RATECALCULATIONS ..........................
I?
DISCUSSION OF RESULTS'
. ........................‘....................................................................36
' SUMMARY AND CONCLUSIONS.............................................................................................38
BIBLIOGRAPHY ......................................■.......................... ......................................... ....
40
V
LIST OF TABLEST a b le
I.
II.
III.
IV .
V.
V I.
V II.
V III.
IX .
'
Page
DEPENDENCY OF RECESSION RATE ON OXYGEN PARTIAL PRESSURE . . .
6
SPECTROGRAPHIC ANALYSIS OF IRIDIUM
9
EXPERIMENTAL DATA
........................................................
...................................................................... 19
OXYGEN PROPERTIES .......................................................................... ....
SUMMARY OF Ah !! AND A S ° VALUES OF PAST EXPERIMENTERS . . .
I
•
I
INITIALLY PREDICTED EQUILIBRIUM CONSTANTS . . .
22
. 28'
............................. 28
OPTIMIZATION RESULTS - FINAL VALUES FOR EQUILIBRIUM
CONSTANTS AND ACCOMODATION COEFFICIENT . .......................................... 31
1
FINAL CORRELATION DATA . .
............................ ......................................... .34
TYPICAL TRENDS FOR VOLATILE DIOXIDE AND TRIOXIDE SPECIES
AS A FUNCTION OF TEMPERATURE . . ............................................... ....
37
Vl
■ LIST OF FIGURES
F ig u re
1.
EXPERIMENTAL EQUIPMENT SCHEMATIC...........................................................
2.
SAMPLE PLOT FOR DETERMINATION OF EXPERIMENTAL SURFACE
RECESSION R A TE..................................................................................................
3.
PLOT OF EXPERIMENTAL AND THEORETICAL RECESSION RATES VERSUS
OXYGEN PARTIAL P R E S S U R E ................................. .... ......................................... .... .
P age
11
18
33
v ii
’ NOMENCLATURE
S y m b o ls
A, E f f e c t i v e e q u i v a le n t w eig h t e q u a l t o 192.2 gms o f ir i d iu m consumed p e r
gm m ole o f o x id e form ed d iv id e d by th e d e n s it y o f t h e ir id iu m
of, A ccom odation c o e f f i c i e n t
C o e f f i c i e n t o f th e rm a l e x p a n s io n - l/ T ^ , (°K ) **
C, C o n s ta n t i n d i f f u s i v i t y e q u a t i o n ■
CP, C o r r e c t i o n . f a c t o r f o r h e a t t r a n s f e r c o e f f i c i e n t due t o c e l l e n c lo s u r e
Cp, C o n s ta n t p r e s s u r e h e a t c a p a c i t y o f oxygen - c a l/g m
Df D^v , A verage e x p e r im e n ta l w ire d ia m e te r - cm
2,
Dv , M o le c u la r d i f f u s i v i t y - cm / sec
APf , S ta n d a rd s t a t e f r e e e n e rg y ch an g e - k c a l/m o le
AHf , S ta n d a rd s t a t e e n th a lp y o f f o r m a tio n - k c a l / m o l e .
A Sf , S ta n d a rd s t a t e e n tro p y o f f o r m a tio n - eu ( k c a l/m o le ° K)
E n erg y o f ' m o le c u la r i n t e r a c t i o n - e r g s
£ / £ , F o rc e c o n s ta n t f o r oxygen - °K
F o rc e c o n s ta n t f o r o x id e s p e c ie - °K
f , T * rictio n f a c t o r
/
g , G r a v i t a t i o n a l a c c e l e r a t i o n - cm /sec
2
tP y S p e c i f i c h e a t r a t i o o f oxygen
G^ 1 M olal mass v e l o c i t y - gm m o le s /s e c cm^
C r, G ra sh o f number - g ^y # (T g - T ^ D ^ /n f
h , F ilm h e a t t r a n s f e r c o e f f i c i e n t - c a l/c m
se c
K
v iii
S y m b o ls
, C o l l i s i o n i n t e g r a l f o r d i f f u s i o n - f u n c ti o n o f
C h ilto n - C o lb u rn f a c t o r s
k , Therm al c o n d u c t i v i t y o f oxygen - c a l/c m se c
IC
k , B oltzm ann c o n s ta n t - 1.38x10 ^ e r g s / K
kc , Mass t r a n s f e r c o e f f i c i e n t - gm m o le s /( s e c cm^)(gm m ole/cm ^)
k g , G a s -film 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 ie
th ro u g h th e b o u n d ary l a y e r - gm m o le /s e c cm^ atm os
K, E q u ilib r iu m c o n s ta n t
Mean f r e e p a th o f oxygen m o le c u le s - cm
L e, Lew is number - P r/S c o r C ^ D ^ /k
M1 , M o le c u la r w e ig h t' o f oxygen
Mg, M o le c u la r w eig h t o f o x id e s p e c ie
V is c o s ity o f oxygen - cp ( c e n t i p o i s e o r gm/cm s e c )
V is c o s ity o f oxygen - p ( p o is e )
6 '
.
.n
n , E xponent o f P q w here Xg OC (P q )
Nu, N u s s e lt number - hD/k
Nu , F i c t i t i o u s N u s s e lt number
P 1 T o ta l p r e s s u r e - atm os
PBM’P0 * P a r t i a l p r e s s u r e o f oxygen - atm os
P
1 P a r t i a l p r e s s u r e o f ir id iu m - atm os
P ^ , P a r t i a l p r e s s u r e o f oxygen - t o r r
P r , P r a n d tl number - G M / k
ix
S y m b o ls
(r 0 )l»
- c o l l i s i o n d ia m e te r f o r oxygen m o le c u le /o x y g e n
m o le c u le c o l l i s i o n - an g stro m s
(rp jg ,
■' • I
1/3
1 . 18( V0
- c o l l i s i o n d ia m e te r f o r o x id e m o le c u le / o x id e m o le-
c u l e c o l l i s i o n - a n g stro m s
r 1 2 ’ ( ( r o ) i + ( r C-Jj) ) / 2
c o l l i s i o n d ia m e te r f o r oxygen m o le c u le /o x id e
m o le c u le c o l l i s i o n - an g stro m s
p , D e n s ity o f oxygen - gm/cm^
P jj, D e n s ity o f ir id iu m
gm/cm^
R, U n iv e r s a l Gas Law C o n s ta n t - 8 1 .7 cm^ atm os/gm m ole 0K o r 1.987 c a l /
gm mole
0
K
Ra, R a y le ig h number - G rPr
S c, S chm idt number - ,A / p D^
0
Ta , Ambient c e l l te m p e r a tu r e -
C
O
T^, E x p e rim e n ta l f il m te m p e r a tu r e - K
O
E x p e rim e n ta l w ire te m p e r a tu r e - K
M e ltin g te m p e r a tu r e f o r o x id e s T , E x p e rim e n ta l w ire te m p e r a tu r e S
U
av
0
0
K
C
, Mean g a s v e l o c i t y - cm /sec
(V0 ).]» M olal volum e o f oxygen - cm^/gm m ole
(V0 )g , M olal volum e o f o x id e s p e c ie - cm^/gm mole
*
%
Xq , E x p e rim e n ta l s u r f a c e r e c e s s i o n r a t e - cm /sec
*>X
, S ta n d a r iz e d e x p e r im e n ta l s u r f a c e r e c e s s i o n r a t e a t D = O.5 8 8 cm - cm /sec
X
Symbols
.>
x , , S ta n d a r iz e 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 a t D = 0 .5 8 8 cm - cm /sec
st
f
■
,
x ^ , T h e o r e tic a l s u r f a c e r e c e s s i o n r a t e - cm /sec
xi
ABSTRACT
The e x p e rim e n ta l s tu d y o f th e n a t u r a l c o n v e c tio n o x i d a t i o n . o f - i r i d i u m
was p e rfo rm e d a t te m p e r a tu r e s o f 1600, 1900, and 2 2 0 0 o C and p r e s s u r e s :
ra n g in g - from 0 .0 0 1 3 2 t o 1 .3 2 a tm o s p h e re s . A t h e o r e t i c a l model d e s c r i b i n g
th e s u rf a c e , r e c e s s i o n r a t e was d e r iv e d assu m in g t h a t t h e r a t e was c o n t r o l ­
l e d by th e d i f f u s i o n o f I r , IrO g , and IrO ^ th ro u g h t h e g a se o u s b o u n d ary
l a y e r , a d j a c e n t t o th e ir id iu m sp ecim en . ^A verage v a lu e s f o r th e s ta n d a r d
s t a t e e n th a lp y and e n tro p y ch an g e s f o r . th e f o r m a tio n o f IrCL and IrCh w ere
c a l c u l a t e d f o r th e 1600 t o 2200 °C te m p e r a tu r e r a n g e . A v a lu e f o r th e p a r ­
t i a l p r e s s u r e o f I r a t 2 2 0 0 ° C was fo u n d . C o r r e l a t i o n b etw een e x p e rim e n t
and th e t h e o r e t i c a l model was good w ith th e o v e r a l l mean % e r r o r o f e x p e r i ­
m e n ta l r a t e s from t h e o r e t i c a l l y p r e d i c t e d r a t e s b e in g 13 »3$ f o r th e 1600
to 2 2 0 0 0 C ra n g e .
INTRODUCTION
I r id iu m i s one o f th e p la tin u m g ro u p m e ta ls .
I t i s th e o n ly e l e ­
m e n ta l m e ta l known t o man p o s s e s s in g a h ig h enough m e ltin g p o in t and a
low enough o x id a tio n r a t e t o be u s e d u n p r o te c te d in a i r f o r an e x te n d e d
o
p e r io d o f tim e i n th e 2000 t o 2300 C r a n g e . A t h i n o x id e f il m i s form ed
on i t s s u r f a c e when ir id iu m i s s u b je c t e d t o te m p e r a tu r e s from 600 t o 1000
O
C in an oxygen c o n t a in in g g a s .
When t h e te m p e r a tu r e o f th e ir id iu m e x -
c e e d s 1000 C i t fo rm s v o l a t i l e o x id e s , and th e o x id a tio n r a t e becom es l i n ­
e a r w ith tim e , l e a v i n g th e s u r f a c e s h in n y .
Ir id iu m i s c o n s id e r e d t o be th e m ost c o r r o s io n r e s i s t a n t m e ta l when
i t i s com pared w ith a l l 'o th e r m e ta ls o v er a b ro a d ra n g e o f te m p e r a tu r e s
and e n v iro n m e n ts .
Numerous 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 lten
m e ta ls, and m o lte n m e ta l o x id e s a r e among th e c o r r o s i v e e n v iro n m e n ts co n­
s id e re d .
Ir id iu m h a s - b e e n u s e d f o r s ta n d a r d i z e d h ig h te m p e r a tu r e th erm o co u ­
p le s ,, f o r h e a t i n g e le m e n ts i n h ig h te m p e r a tu r e f u r n a c e s , and f o r p r o t e c ­
t i v e c o a t i n g s f o r l e s s e x p e n s iv e h ig h te m p e r a tu r e s t r u c t u r a l m a t e r i a l s
su ch a s tu n g s te n and ta n ta lu m b a s e a l l o y s .
The m ost r e c e n t r e s e a r c h on
ir id iu m o x id a tio n h a s shown th e p o t e n t i a l a p p l i c a t i o n s f o r th e le a d in g
edge o f s p a c e c r a f t , f o r com ponents i n n u c l e a r r e a c t o r s , and f o r p a r t s i n
r o c k e t and t u r b i n e e n g in e s .
B ein g a p la tin u m g ro u p m e ta l, ir i d iu m i s e x p e n s iv e .
T h is l i m i t s
.
.
■ '
- i t s u s e a s a p rim a ry m a t e r i a l in s t r u c t u r a l a p p l i c a t i o n s , even th o u g h i r i ­
dium h a s r e a s o n a b ly good s t r e n g t h p r o p e r t i e s .
■
2
Among o th e r p r o p e r t i e s , ir id iu m h a s v e r y low o m itta n c e and v e ry
h ig h d e n s i t y .
The low e m itta n c e c a u s e s p ro b lem s when ir id iu m i s u se d t o
any e x t e n t on s p a c e c r a f t b e c a u se th e p rim a ry means o f h e a t d i s s i p a t i o n
on th e n o se o f s p a c e c r a f t r e - c e n t e r in g ' t h e e a r t h 's atm o sp h e re i s by r a d ­
ia tio n .
Where w e ig h t i s a c o n s t r a i n t , th e 2 2 .5 7 gm/cm^ d e n s i t y o f i r i ­
dium ( a t room te m p e r a tu r e ) g r e a t l y r e s t r i c t s i t s a p p l i c a t i o n .
In f a c t ,
ir id iu m i s e i t h e r th e m ost o r th e n e x t t o th e most d e n se elem en t known
t o man.
(C o n tro v e rs y e x i s t s on w h e th e r ir id iu m o r .osmium i s th e . m ost
d e n se due t o th e i n c o n s i s t e n c i e s o f d e n s i t y m easu rem en ts b a s e d on th e l a t ­
t i c e s t r u c t u r e and a c t u a l p h y s ic a l m e a su re m e n ts.
A c tu a l m easurem ents r e ­
v e a l ir i d iu m t o b e th e m ost d e n s e .)
REVIEW OF PAST WORK
A s h o r t re v ie w o f th e r e c e n t b u t r e l e v a n t work done on th e o x id a tio n
o f ir id iu m i s in w hat f o ll o w s .
From t h i s re v ie w , c o n c lu s io n s o f a g e n e r­
a l n a t u r e w ere made w hich s e r v e d a s a s t a r t i n g b a s i s f o r th e work o f t h i s
re p o rt.
The c o m p o s itio n o f th e p r o d u c ts o f ir id iu m o x id a tio n and th e th e rm o /
dynam ics in v o lv e d hav e b een i n v e s t i g a t e d by s e v e r a l p e o p le . C ordfunke
and Meyer
1
p a s s e d oxygen, o r o x y g e n -n itro g e n m ix tu r e s , o v er a b o a t sh ap ed
o
specim en c o n t a i n i n g ir id iu m in th e ra n g e o f 1169 t o 1462 C. They c o n c lu d e d
t h a t th e m ain v o l a t i l e o x id e fo rm ed was IrO ^ .
H o lb u rn , H enning, and A u stin ^ s e l f r e s i s t a n c e h e a te d a p ie c e o f t h i n
o
ir id iu m f o i l t o 1670 C o v e r w hich th e y p a s s e d oxygen, a i r , o r n i t r o g e n c o n -
3
t a i n i n g 1 .7 7 ^ o x y g en .'
They a l s o c o n c lu d e d t h a t IrO ^ was th e m ain g a s ­
eo u s o x id e s p e c ie fo rm ed .
Norman a t a l f^ p e rfo rm e d a seq u en ce o f m ass s p e c tr o m e tr i c s t u d i e s
o f o x id i z in g i r i d iu m .
T h is was done by i n t r o d u c i n g oxygen i n t o a Knud-
s e n C e ll i n w hich an ir id iu m sp ecim en was p la c e d and h e a te d in th e ra n g e
o
o f 1557 t o 1760 C.
The e x i t i n g g a se o u s s p e c ie s w ere th e n "bom barded"
w ith a s tre a m o f e l e c t r o n s .
and IrO ^
+
+
4They d e t e c t e d th e p r e s e n c e o f I r , IrO , IrO g
io n s , b u t c o n c lu d e d t h a t IrO g and IrO ^ w ere th e main v o l a t i l e
o x id e s p e c ie s p r e s e n t i n t h e i r work.
V a rio u s r e l a t e d k i n e t i c s t u d i e s h av e a l s o b een p e rfo rm e d .
al
Norman a t
a l s o m easu red v a l u e s o f th e s ta n d a r d s t a t e e n th a lp y and e n tro p y ch an ­
g e s f o r th e f o r m a tio n o f IrO g o f 4 8 .5 -■ 0 .5 k c a l /m o l e ; an d 3*9 - 2 .0 eu ,
and f o r I r O^ 5*5 - 1 .5 k c a l/m o le and - 1 3 .1 - 2 .5 eu i n t h e i r r e s p e c t i v e
o rd ers.
5
O liv e i^ p e rfo rm e d some m ass s p e c tr o m e tr i c s t u d i e s a l s o , i n th e ra n g e
0
o f 1627 t o 2227 C, from w hich i t was fo u n d t h a t th e s ta n d a r d s t a t e e n t h a l )
py and e n tro p y o f f o r m a tio n f o r IrO ^ w ere 6 .0 k c a l/m o le and - 9 . 0 eu r e ­
s p e c tfu lly .
F or th e f r e e e n tro p y o f f o r m a tio n o f o x id e s o f a g e n e r a l m e ta l M,
v a l u e s o f 2 0 . 6 , 3 .5 - 2 . 1, and -1 0 t o - 1 5 e u , a s a v e r a g e s f o r v o l a t i l e
g a s e o u s m onoxide MO, d io x id e MOg, and t r i o x i d e MO^ s p e c ie s r e s p e c t i v e l y ,
6
w ere i n d i c a t e d by S e a rc y .
7
P h i l l i p s p e rfo rm e d some k i n e t i c s t u d i e s o f ir id iu m o x id a tio n in
4
a i r moved o n ly by n a t u r a l c o n v e c tio n .
The specim en was a l / 4 in c h in
d ia m e te r by l / 2 in c h lo n g ir i d iu m r o d .
The ra n g e o f te m p e r a tu r e s i n v e s -
0
t i g a t e d was 65O t o 1300 C f o r w hich P h i l l i p s fo u n d an a c t i v a t i o n e n e rg y
o f 9 .2 k c a l/m o le .
K r ie r and J a f f e e ^ h e a te d an ir i d iu m specim en by means o f a f u r n a c e 0
th ro u g h w hich slow moving a i r r w a s p a s s e d i n th e ra n g e o f 1000 t o 1400 C,
They fo u n d a v a lu e o f 16 k c a l/m o le f o r th e a c t i v a t i o n e n e rg y . .
G r is c io n e 9 p a s s e d oxygen o r an o x y g en -arg o-n m 'ix tu re p a r a l l e l ; t o a
l / 2 in c h d ia m e te r ir id iu m ro d h a v in g a h e m is p h e r ic a lly sh ap ed en d , i n th e
ra n g e o f 1150 to - 1900
0
.
C an d a t a p r e s s u r e o f 0 .9 3 5 a tm o s p h e re s .
He 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 f o r th e h e m is p h e r ic a l end and fo u n d an
a c t i v a t i o n e n e rg y o f 23 k c a l/m o le .
IWorkvby-V.1 K u ria k o s e and M argrave
10
in v o lv e d h e a t i n g an ir id iu m f o i l
0
0 .0 0 2 in c h e s t h i c k .su sp en d ed i n a f u r n a c e f o r te m p e r a tu r e s up t o '1301 C
and r e s i s t a n c e h e a t i n g a 0 .0 1 in c h i n d ia m e te r ir i d iu m w ire i n s i d e a I in c h
d ia m e te r p y re x tu b e f o r h ig h e r te m p e r a t u r e s .
They p a s s e d oxygen o r oxy­
g e n -h e liu m m ix tu r e s th ro u g h th e tu b e p a r a l l e l t o th e tu b e le n g th a t a t o ­
t a l p r e s s u r e o f I a tm o s p h e re .
For th e ir i d iu m f o i l th e y fo u n d a c t i v a t i o n
e n e r g i e s o f 70 and 7»1 k c a l/m o le f o r te m p e r a tu r e s below 1100 C i and f o r
0
te m p e r a tu r e s b etw een 1100 and 1300 C r e s p e c t i v e l y . A c ti v a tio n e n e r g ie s
f o r t h e ir i d iu m w ire w ere fo u tid t o b e 1 2 .5 and 30-33 k c a l/m o le a t 1150 t o
1600
and 1600 t o 2217 °C r e s p e c t i v e l y .
' Among o th e r d e p e n d e n c ie s , i t h a s b e e n fo u n d t h a t th e s u r f a c e r e c e s ­
5
s io n r a t e o f a sp ecim en d ep en d s u p o n ' th e oxygen p a r t i a l p r e s s u r e t o some
pow er.
T a b le I sum m arizes t h i s d ep en d en cy a s fo u n d b y v a r io u s e x p e rim e n .11
t e r s o f w hich Tempero
i s th e o n ly one n o t p r e v io u s l y m e n tio n e d .
E x cep t f o r th e work r e c e n t l y done by Wimber and Tem pero, no work
h a s l e d t o th e c h a r a c t e r i z a t i o n o f th e o x id a tio n p r o c e s s w hich would a llo w
t a k i n g i n t o a c c o u n t th e e f f e c t s o f v a r y in g te m p e r a tu r e , oxygen p a r t i a l
p r e s s u r e , flo w r a t e p a s t a specim en and sp ecim en s i z e .
Wimber and Tempero
r e s i s t a n c e h e a te d an ir id iu m w ire i n th e ra n g e o f 1600 t o 2200
G.
The w ire
was v a r i e d from 0 ,0 6 3 5 t o 0.0381 cm i n d ia m e te r and oxygen was p a s s e d p e rp e n ­
d i c u l a r t o th e w ir e .
Among t h e i r i n v e s t i g a t i o n s o f d e s c r i b i n g th e r e c e s ­
s io n r a t e t h e o r e t i c a l l y , th e y had some s u c c e s s i n a model w hich c o n s id e r e d
t h e e q u ilib r iu m d i f f u s i o n o f g a se o u s IrO g and IrO ^ th ro u g h th e b o u n d ary
l a y e r a d j a c e n t t o th e sp ecim en .
I n v iew o f th e m e n tio n ed p a s t work on ir id iu m o x i d a t i o n , th e f o llo w ­
in g c o n c lu s io n s w ere a r r i v e d a t .
1.
IrO g and IrO ^ a p p e a r t o b e t h e m ain v o l a t i l e o x id e s p e c ie s fo rm ed
above 1600
2.
O
C.
V a lu e s f o r t h e s ta n d a r d s t a t e e n th a lp y and e n tro p y o f th e s e two
m a jo r s p e c ie s a r e known a t c e r t a i n t e m p e r a t u r e .l e v e l s , b u t a r e
e x p e c te d t o v a r y w ith te m p e r a tu r e .
3.
A c ti v a tio n e n e r g i e s a r e e x p e c te d t o v a ry w ith sp ecim en e n v iro n ­
ment o f oxygen, sp ecim en c o n f i g u r a t i o n , and sp ecim en te m p e r a tu r e .
4.
The s u r f a c e r e c e s s i o n r a t e , a t l e a s t , d ep en d s upon th e oxygen p a r -
6
T a b le I
DEPENDENCY OF RECESSION RATE ON P,
^ e ^ o /
H olburn
et al
C r is c io n e
K u ria k o s e &
M argrave
Tempero
Ir id iu m
Specim en
E nviron m en t
F o i l - slow
flo w in g
Rod p a ra lle l
flo w
F o il & w ire
p a ra lle l
f I OW
W ire p e r p e n d ic u ­
l a r flo w
E x p o n e n tia l
D ependency -
n = 1 .5
@ 1670 a C
n = 1.3 4
@ 1900° C
F o il n = 1.1
@ 1181 °G
n = 0 .2 3 4
@ 1600 to
2200 0 C
T em p eratu re
Range
Oxygen
P a rtia l
P re ssu re
Range
W ire n - 1 .2
@ 1717 0 G
Ph
= 0 .0 1 7
2
t o 1 .0 0
atm os
P
= 0 .0 2
2
t o 0 .9 3
atm os .
___ i___________ i_______________ ------------------------
P
= 0 .0 2
2
t o 1 .0 0
- atm os
P
=0 .0 0 4 6
U2
t o 1 .3 0
, atm os
7
t i a l p r e s s u r e , and t h e sp ecim en c o n f i g u r a t i o n and te m p e r a tu r e ,
THEORY
When ir id iu m i s o x id iz e d above 1000
O
C i t fo rm s v o l a t i l e o x id e s p e ­
c i e s , f o r w hich t h e a s s o c i a t e d r a t e i s e x p e c te d t o b e c o n t r o l l e d by one
o r more o f th e f o llo w in g s t e p s i n t h e p r o c e s s ;
1»
B ulk t r a n s p o r t o f th e oxygen b e a r i n g g a s from th e s o u rc e t o th e
g e n e r a l v i c i n i t y o f th e m e ta l b e in g o x id iz e d ,
2,
D if f u s io n o f th e oxygen th r o u g h th e g a s e o u s b o u n d ary la y e r a d j a ­
c e n t t o t h e s u r f a c e o f th e m e ta l.
3«
A d s o rp tio n o f th e oxygen from th e g a s p h a s e o n to th e s u r f a c e o f
t h e m e ta l.
4«
R e a c tio n on th e m e ta l s u r f a c e in c lu d in g p o s s i b l e re a rra n g e m e n t
and m ig r a tio n p r o c e s s e s ,
-■
■
5»
D e s o rp tio n o f th e o x id e ( s ) from th e s u r f a c e o f th e m e ta l.
6.
D if f u s io n o f th e o x id e ( s ) th r o u g h th e g a se o u s b o u n d ary l a y e r w ith
p o s s i b l e f u r t h e r c h e m ic a l r e a c t i o h ( s ) w ith in th e b o u n d ary l a y e r o f
one o f th e o x id e s p e c ie s w ith th e same o r d i f f e r e n t o x id e s p e c ie
a n d /o r oxygen.
A t h e o r e t i c a l model was d e r iv e d by Wimber
12
, w h ich ta k e s i n t o a c c o u n t
th e fo r m a tio n o f I r O l IrO 2 , and IrO ^ a t t h e i r e q u ilib r iu m p a r t i a l p r e s ­
s u r e s on th e in n e r s u r f a c e o f th e b o u n d a ry l a y e r .
The model a l s o a c c o u n ts
-for m e ta l v a p o r i z a t i o n w hich o c c u rs t o an a p p r e c ia b le e x t e n t a t h ig h te m - ,
p e r a t u r e s and low p r e s s u r e s .
T h is m odel assum es t h a t th e s u r f a c e r e c e s s i o n
8
r a t e X^f i s c o n t r o l l e d by th e r a t e o f d i f f u s i o n ' o f th e s e g a se o u s s p e c ie s
th ro u g h th e g a se o u s b o u n d ary l a y e r c o r r e s p o n d in g t o th e f i r s t p a r t o f
s t e p , 6, and was e x p r e s s e d a s ,
(D
w here the: s u b s c r i p t s 1 ,2 ,3 ,a a n d M r e f e r t o IrO , IrCb,-,
t i v e l y , and;
A = E f f e c t i v e e q u iv a le n t w eig h t e q u a l t o 192.2 gms o f ir id iu m con^
sumed p e r gm m ole o f o x id e fo rm ed d iv id e d - b y th e d e n s i t y o f I r ,
kG =
G a s -film mass t r a n s f e r c o e f f i c i e n t - gm m o le /s e c cm^ atm os,
K = E q u ilib r iu m c o n s ta n t ,
P
= P a r t i a l p r e s s u r e o f oxygen - atm o s.
°2
.V a l id it y o f e q u a tio n ( l ) was t e s t e d by co m p ariso n o f e x p e rim e n ta l d a t a
ta k e n i n t h e , n a t u r a l c o n v e c tio n area ., to . r e s u l t s p r e d i c t e d by t h i s m odel.
IRIDIUM ANALYSIS
The o x id a tio n s t u d i e s in n a t u r a l c o n v e c tio n w ere c o n d u c te d u s in g two
d i f f e r e n t l o t s o f c o m m e rc ia lly p u re ir i d i u m , p u rc h a s e d from E n g e lh a rd
I n d u s t r i e s , C a t e r e t , New J e r s e y .
A s p e c tr o g r a p h ic a n a l y s i s o f t h i s i r i ­
dium was r e q u e s te d o f E n g e lh a rd I n d u s t r i e s D iv is io n .
shown in T ab le I I .
T hese a n a ly s e s a r e
The r e s u l t s o f t h e s e two l o t s o f ir id iu m w ere com par­
ed e x p e r im e n ta lly .
EXPERIMENTAL EQUIPMENT AND PROCEDURE
F ig u r e I i s a s c h e m a tic r e p r e s e n t a t i o n o f th e eq u ip m en t u s e d .
An
ir id iu m sp ecim en was p la c e d h o r i z o n t a l l y betw een two e l e c t r o d e s in a c e l l
9
T ab le II."
Im p u rity
Pt
Rh
Pd
Ru
Au
Ag
Pb
Sn
Zn
Fe
Cu
Si
Mg
Ca
Al
Ni
Cr
Mn
Sb
B
Co
As
Bi
Cd
W
N
H
0
■ Ta
In
Zr
Ga
V
Ti
K
Cl
S
SPECTROGRAPHIC ANALYSIS OE IRIDIUM*
L ot #1 d ia m e te r 25 m ils L ot #2 d ia m e te r 20 m ils
99
20
10
166
<1
50
■ <5
5
<10
170
96
43
41
78
14
10
31
10
<10
<50
100
<10
<1
<1
0.6$
■ 50
4
70
—
—
—
-
< 0 .5
3 8 .0
1 1 .0
1 .5
< 0 .5
< 0 .5
< 0 .5
0.41
64
17
6.1
1.1
0.61
35
1.1
O.8 4
0 .6 9
< 0 .5
0 .0 0 3 2
1 .8
0 .0 6 6
710
0 .2 4
8 .3
46
0 .2 6
1.1
0 .2 0
O4O96
0 ,4 9
0 .6 7
' O.5 9
0 .5 7
10
T ab le I I .
P
Na
F
C
Li
—
-
(C o n tin u e d )
• 0.81
2 .2 '
. 0 .2 ?
15 .0
0 .0 0072
I m p u r i t i e s a r e g iv e n in p a r t s p e r m i l l i o n u n le s s o th e rw is e s p e c i f i e d .
ROTAMETER
DRYERS
SUPPLY TANKS
AUTOMATIC
PRESSURE
CONTROLLER
SERVO VALVE
TIMER
MICROSCOPE AND
MOTORIZED CAMERA
BATTERY
INSIDE CELL WALL
CAPACITANCE
manometer
WIRE
OPTICAL
PYROMETER
PRESSURE
METER
CHART
RECC ’ TER
AMMETER-
VOLTMETER
DC POWER SUPPLY,
HO VAC
TRAP
F ig u re I .
MECK VAC. PUMP
EXPERIMENTAL EQUIPMENT SCHEMATIC
12
I in c h w ide by 3 in c h e s lo n g by 3 in c h e s d e e p .
The e l e c t r o d e s w ere
u se d t o d e l i v e r th e c u r r e n t t o r e s i s t a n c e h e a t th e w ir e .
To accom odate
th e th e rm a l e x p a n sio n o f th e w ire and th u s p r e v e n t i t s b e n d in g , a l e a f
s p r i n g ty p e mount was u se d on one en d .
T h is e n a b le d th e w ire t o be lo a d ­
ed t e n s i l e l y t o a p r e - d e te r m in e d l e v e l su ch t h a t when th e w ire was h e a t ­
ed t o th e d e s i r e d l e v e l , th e l e a f s p r i n g w ould no lo n g e r b e d e f l e c t e d
and th u s le a v e th e w ire in a n e a r z e ro s t r e s s I e v e ] .
On th e u n d e r s id e o f th e c e l l was c e n t e r e d a 4 in c h t o I in c h r e d u c ­
t i o n c o p p e r plu m b in g " T " , su ch t h a t th e 4 in c h d ia m e te r m a in " p o r tio n o f
th e VTV was c e n t e r e d ab o u t a v e r t i c a l a x i s th ro u g h th e c e n t e r o f th e c e l l .
A 4 in c h d ia m e te r c i r c u l a r p l a t e was th e n s o ld e r e d on th e b o tto m o f th e
"T" t o c l o s e i t o f f .
To th e r e m a in in g h o r i z o n t a l one in c h o u t l e t , was
a l i n e l e a d i n g to . th e t r a p and e v e n t u a ll y t o th e m e c h a n ic a l pump.
On th e
o p p o s ite s id e and same e l e v a t i o n a s th e 1 in c h o u t l e t , was l o c a te d t h e oxy­
gen g a s i n l e t .
The pow er t o h e a t th e w ire was s u p p lie d by a H e w le tt P a c k a rd DC
Power S u p p ly , LVR S e r i e s , Model 6260B w hich h a s th e c a p a b i l i t y o f m a in /
.
•
t a i n i n g a c o n s ta n t v o lt a g e a c r o s s o r a c o n s ta n t c u r r e n t th ro u g h w h a te v e r
i t i s c o n n e c te d t o .
In t h i s work th e pow er s u p p ly was u s e d so t h a t t h e
v o lt a g e d ro p a c r o s s th e e l e c t r o d e s was c o n s t a n t , w hich m in im ized th e po­
wer ch an g e d u r in g a r u n .
The c u r r e n t was m easured by a DC Ammeter and
th e v o lt a g e was m easu red by a H oneyw ell D i g i t a l M u ltim e te r , D i g i t e s t
Model 333R.
13
E i t h e r oxygen o r a rg o n was in tr o d u c e d i n t o th e c e l l .
The arg o n was
d i r e c t l y c o n n e c te d t o th e c e l l th ro u g h v a l v e s , w h ereas th e oxygen was p a s ­
s e d th ro u g h a D r i e r i t e D ry in g Column ( t o rem ove any m o is tu r e i n th e oxy­
g e n ) , a #74 M atheson Tube F lo w m eter, a m anual v a l v e , th e s e r v o v a lv e and <
e v e n t u a l l y t o th e c e l l . '-A G r a n v i l l e - P h i l l i p s A u to m atic P r e s s u r e C o n t r o l l e r
No. 0 -0 0 -2 1 6 0 0 6 (w h ich in c lu d e d th e s e r v o v a l v e ) , was u s e d i n c o n ju n c tio n
w ith a MKS B a r a tr o n TM Type 77 P r e s s u r e M e te r.
The MKS u n i t s e n s e d p r e s ­
s u r e by means o f a MKS C a p a c ita n c e M anometer 77H -1000.
The l i n e ta p f o r
t h e c a p a c it a n c e m anom eter was l o c a t e d a b o u t 2 in c h e s lo w e r and r o t a t e d JO
d e g re e s from th e i n l e t f o r th e o x y g en , in th e w a ll o f th e p lu m b in g VT",
th u s p r e v e n t in g any p o s s i b l e p r e s s u r e h e a d from th e oxygen flo w w hich m ight
c a u s e an i n c o r r e c t p r e s s u r e r e a d i n g .
Gas e x i t i n g t h e c e l l d u r in g a ru n was p a s s e d th ro u g h a t r a p d e s ig n e d
t o co n d e n se th e , o x id e s p r e s e n t .
L iq u id n i t r o g e n was u se d i n th e t r a p
when t h e ru n p r e s s u r e P - , was l e s s th a n 0 .2 5 a tm o s p h e re s . When P
was
^2
2
g r e a t e r th a n 0 .2 5 a tm o s p h e re s , d ry i c e was u s e d , s i n c e a t t h e te m p e r a tu re
o f l i q u i d n i t r o g e n and h ig h p r e s s u r e s , P f. , th e b o i l i n g p o in t o f oxygen
2
i s g r e a t e r th a n th e te m p e r a tu r e o f th e l i q u i d n i t r o g e n . B ecau se o f t h i s ,
i f l i q u i d n i t r o g e n w ere u s e d , th e oxygen co n d en sed i n t h e t r a p .
Thus,
s in c e th e b o i l i n g p o in t o f th e oxygen a t th e te m p e r a tu r e o f d ry i c e and
p re s s u re P^
g r e a t e r th a n 0 .2 5 a tm o s p h e re s i s l e s s th a n t h e te m p e r a tu r e o f
2
d ry i c e , th e d ry i c e was u se d f o r P
g r e a t e r th a n 0 .2 5 a tm o s p h e re s . From"-'
.2
a tm o s p h e r ic , p r e s s u r e d e c r e a s e in th e c e l l was a c h ie v e d by u s e o f a m e d ia n -
14
i c a l pump.
A ll p a r t s o f th e c e l l w ere c o o le d by c o ld w a te r c i r c u l a t i o n th ro u g h
tu b e s on i t s s u r f a c e .
S ig h t p o r t s w ere lo c a t e d on o p p o s ite s i d e s o f th e c e l l a t th e v e r t i ­
c a l e l e v a t i o n o f a m ounted sp e c im e n .
Shadowgraph q u a l i t y p y re x windows
w ere u s e d t o p r o v id e v i s i b l e a c c e s s t o th e c e l l .
T hese windows w ere c l e a n ­
ed and p o li s h e d p e r i o d i c a l l y due to . a c c u m u la tio n o f o x id e s on t h e i r s u r ­
fa c e s.
Tc m easu re th e te m p e r a tu r e o f th e sp ecim en , a L eeds and N o rth ru p
6836-C O p tic a l P y ro m e te r was u s e d , w hich was a l ig n e d t o e n a b le s i g h t
th ro u g h one o f th e s i g h t p o r t w indow s.
The o p t i c a l p y ro m e te r was c a l i b r a ­
t e d t o ta k e i n t o a c c o u n t th e e f f e c t s o f th e p y re x windows and th u s e n a b le
a t r u e te m p e r a tu r e r e a d i n g .
by H a lv o rso n and Wimber
13
T h is c a l i b r a t i o n was done a s p a r t o f th e work
■
■
on th e th e rm a l e x p a n s io n o f i r i d i u m .
A lig n e d f o r
s i g h t th ro u g h th e o th e r window was a B e s e le r T opcorn S u p er D Camera and
E l e c t r i c M otor D riv e f i t t e d w ith a T opcorn M icro sco p e A tta ch m en t Model I I I ,
w hich i n c o n ju n c tio n w ith a L a f a y e tt e Model 51012T T im er, e n a b le d th e t a k ­
in g o f a se q u en ce o f p i c t u r e s a t a p r e d e te rm in e d i n t e r v a l and 20X m a g n if i­
c a tio n .
used.
F o r many o f t h e r u n s , a L a y f a y e tte Model 58 0 3 3 i 5 - I N - I Tim er was
The l a t t e r tim e r e n a b le d lo n g e r i n t e r v a l s b etw ee n p i c t u r e s .
B ecau se o f th e p o s s i b i l i t y o f pow er o r w a te r l o s s , th e system was
f i t t e d w ith a n e tw o rk o f r e l a y s w hich a c t e d a s p r o t e c t i o n d e v ic e s i f
W ater o r pow er s u p p ly s h o u ld b e l o s t d u r in g a r u n .
• -
To p e rfo rm a r u n , a 2 7 /3 2 in c h s e c t i o n o f ir i d iu m w ire was c u t ,
15
c le a n e d w ith a c e to n e , g ro u n d
in th e c e l l ,
f l a t , on one end f o r r e f e r e n c e and m ounted
( i n th e f i r s t few r u n s , r o t a t i o n a l p i c t u r e s w ere ta k e n o f
th e w ire b e f o r e and a f t e r th e r u n .
From th e s e i t was d e te rm in e d t h a t th e
e c c e n t r i c i t y o f th e w ire was l e s s th a n 1. 2$ and th u s t h i s p ro c e d u re was d i s ­
c o n tin u e d a t t h a t p o i n t . )
A r e f e r e n c e p i c t u r e was th e n ta k e n o f a d r i l l
ro d o f known d ia m e te r ( 0 .0 6 5 5 cm) in o r d e r t o p r o v id e a r e f e r e n c e f o r th e
s i z e o f th e p i c t u r e s . o f th e ir id iu m w ir e .
An arg o n a tm o sp h ere o f O.9 2
a tm o sp h e re s was th e n in tr o d u c e d i n t o th e c e l l in w hich th e w ire w as. a n n e a le d ■
f o r 30 m in u te s a t 2200
C.
(The a n n e a l was p erfo rm e d upon th e u se o f eac h
new s e c t i o n o f w ire f o r th e p u rp o se o f a c h ie v in g a g r a i n s i z e and e l e c t r i ­
c a l r e s i s t i v i t y t h a t w ould be e s s e n t i a l l y i n v a r i a n t w ith tim e f o r th e r u n s . )
The a rg o n was th e n rem oved and th e c e l l f i l l e d w ith oxygen.
Then th e oxygen
was pumped o u t and a p r e s s u r e le a k t e s t ta k e n t o in s u r e a n e a r p u re oxygen
e n v iro n m en t i n th e c e l l . .
The p r e s s u r e and te m p e r a tu r e a t w hich a ru n was
t o be made w ere th e n s e t on th e e q u ip m en t'..
The w ire was th e n o x id iz e d f o r
a s h o r t p e r io d o f tim e t o c h a r a c t e r i s t i c a l l y t e x t u r i z e i t s s u r f a c e .
The
c y c le tim e r was th e n a c t i v a t e d a t i t s p r e - d e te r m in e d c y c l e i n t e r v a l . A ru n
.
c o n s i s t e d o f te n e x p o s u re s o f th e w ir e , w hich i n t o t a l l e n g t h , -c o rre s p o n d ­
ed w ith c h a n g in g th e w ire d ia m e te r by 0 .0 0 1 $ t o 0 .0 0 3 5 cm.
(The " 0 .0 0 1 $
t o 0 . 003$ cm" ra n g e .was a r r i v e d a t b e c a u s e a p p ro x im a te ly a one m il diam e­
t e r chan g e was n e c e s s a r y t o o b ta in r e a s o n a b le d a t a , b u t i f th e d ia m e te r
changed much more th a n one m il, to o much v a r i a t i o n i n th e o x id a tio n r a t e
o c c u re d due t o i t s dep en d en cy on th e d ia m e te r o f th e w i r e . )
16
B ecau se o f th e te n d e n c y o f th e p y re x windows t o s lo w ly r e c i e v e a
c o a t i n g o f o x id e d u r in g a r u n , th e y w ere r o t a t e d p e r i o d i c a l l y ' t o in s u r e
good p i c t u r e s and c o r r e c t r e a d i n g s on t h e o p t i c a l p y ro m e te r.
(A lso a
h a b i t was made o f c h a n g in g th e s e windows b etw een e v e ry r u n . )
The te m p e r a tu r e o f th e w ire and t h e oxygen p r e s s u r e i n t h e c e l l
w ere c o n tin u o u s ly m o n ito re d th ro u g h o u t a r u n .
Flow o f th e oxygen g a s was /
m a in ta in e d th ro u g h th e "T" s e c t i o n b e n e a th th e c e l l w here th e w ire was
m ounted, i n o r d e r t o k eep a c o n t in o u s ly f r e s h s u p p ly o f oxygen t o th e
c e l l , th u s k e e p in g th e oxygen c o n c e n t r a t i o n e s s e n t i a l l y IOO7& and p r e ­
v e n t i n g d e p l e t i o n o f t h e oxygen.
Upon c o m p le tio n o f th e d e s i r e d num ber o f f ilm e x p o s u r e s , th e sy stem
was s h u t down, th e f il m rem oved from t h e cam era and d e v e lo p e d .
T h is f i l m
w a s .a llo w e d t o d ry f o r a t l e a s t a 2 h o u r p e r io d t o m in im ize s h r in k a g e d u r­
in g th e p r o c e s s o f r e a d i n g th e w ire d ia m e te r .
The f il m was th e n p la c e d
b etw een two d i s k s o f o p t i c a l q u a l i t y f u s e d q u a r tz 3 /1 6 in c h t h i c k m ounted
i n a m e ta l fra m e .
The l i g h t o f a lamp was p a s s e d th ro u g h th e d i s k - f i l m
c o m b in a tio n , d i r e c t l y i n t o a G a e rtn e r M icro sco p e A tta c h m e n t-G a th e to m e te r
a rra n g e m e n t..
A G ossen L u n a-P ro E x p o su re M eter was p la c e d on th e v ie w in g
end o f t h e m ic ro s c o p e a tta c h m e n t.
T h is c a th e to m e te r p r o v id e d m easurem ent
o f th e f ilm n e g a t iv e s by l i g h t i n t e n s i t y m easu rem en ts and e v e n tu a l c o n v e r­
s io n t o t h e i r e q u i v a le n t w ire d ia m e te r th r o u g h u s e o f t h e d r i l l ro d r e f e r ­
en ce p i c t u r e on eac h f i l m .
T h is u n i t was c a l i b r a t e d t o r e a d a c c u r a te t o
I 1 m ic ro n , b u t th e a c t u a l r e p e a t a b i l i t y when r e a d i n g th e f il m was n e a r
17
- 10 m ic ro n s .
Each n e g a t iv e was m easu red in th e m id d le and a t each en d ,
and th e s e v a lu e s a v e ra g e d in o r d e r t o a c h ie v e b e t t e r d a t a s t a t i s t i c a l l y .
A p l o t o f d ia m e te r v e r s u s tim e was th e n made and a l i n e a r a v e ra g e r e c e s s io n r a t e d e te r m in e d .
F ig u r e 2 r e p r e s e n t s a t y p i c a l r u n , show ing th e r e l a t i v e
d e v i a t i o n o f th e d a t a p o i n t s from an a p p ro x im a te ly l i n e a r r e l a t i o n s h i p
and th u s i l l u s t r a t e s th e v a l i d i t y o f assu m in g Xq was e s s e n t i a l l y c o n s ta n t
f o r ea c h r u n .
The v a lu e o f D
was a l s o d e te rm in e d from t h i s p l o t .
av
EXPERIMENTAL RESULTS AND THEORETICAL HATE CALCULATIONS
The e x p e r im e n ta l d a t a o b ta in e d f o r th e n a t u r a l c o n v e c tio n o x id a tio n
o f ir id iu m a r e t a b u l a t e d i n T a b le I I I , i n o r d e r o f i n c r e a s i n g te m p era­
t u r e and i n c r e a s i n g oxygen p r e s s u r e .
<o
I t was a l s o fo u n d t h a t th e e x p e r im e n ta l s u r f a c e r e c e s s i o n r a t e Xq ,
was d e p e n d e n t.u p o n t h e w ire .d i a m e t e r .^ As a r e s u l t , t h i s dependency i n
th e R a y le ig h number ra n g e from 8 .6 5 x 1 0
e x p e r im e n ta lly .
—
12
t o 2 .0 6 x 1 0
—1
, was i n v e s t i g a t e d
I t was fo u n d t h a t t h i s dependency c o u ld be d e s c r ib e d by
t h e d ia m e te r o f t h e w ire r a i s e d t o th e - 1 .1 1 pow er.
T h is dep en d en cy r e ­
s u l t e d i n a maximum d e v i a t i o n o f 2 .7 6 $ from e x p e rim e n t.
Then, t o f a c i l i ­
t a t e c o m p ariso n o f e x p e rim e n ta l and. 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 ,
th e y w ere c o n v e r te d t o e q u iv a le n t v a lu e s a t a d ia m e te r o f O.O588 cm.
The
s u b s c r i p t " s " on x , th u s i n d i c a t e s t h i s s t a n d a r d i z a t i o n o f r e c e s s i o n r a t e s
t o a d ia m e te r o f 6 .0 5 8 8 cm.
I t was s e e n , th ro u g h e x a m in a tio n o f th e v a lu e s o f X56 i n T ab le I I I ,
t h a t th e s u r f a c e r e c e s s i o n r a t e s v a r i e d o n ly w ith in e x p e rim e n ta l r e p e a t a -
1900*
C
PoP = .0132 Atmos
6 0 Sec. BETWEEN FILM EXPOSURES
DIAMETER, Cm. X IO
^
_ (.5293 -.5 0 5 0 ) X IO- l Cm.
2 X 5 4 0 s ec .
. 2 3 0 X IO
Cm. / Sec.
CHANGE IN D = . 0 0 2 4 8 Cm.
.05178 Cm.
TIM E, SECS.
F ig u r e 2 .
SAMPLE PLOT FOR DETERMINATION OF EXPERIMENTAL SURFACE RECESSION RATES
19
T a b le I I I .
T
S
- °C
1600
1600*
1600
1600
1600
1600
1600
1600
1600
1600
1600
1600
1600
1600*
1600
1900
1900
1900
1900
1900
1900
1900
1900
1900
1900*,
1900
1900
1900
1900
1900
2200
2200
2200 ■
2200*
2200
2200
2200
Vatm os
0.0 0 1 3 2
0 .0 0 1 3 2 .
0 .0 0 1 3 2 '
0 .0 1 3 2
0 .0 1 3 2
0 .1 3 2
0 .1 3 2
1.32
1.32
1.32
1.32
1.32
1 .3 2
1.32
1.32
0.0 0 1 3 2
0.0 0 1 3 2
0 .0 0 1 3 2
0 .0 1 3 2
0 .0 1 3 2
0 .0 1 3 2
0 .0 1 3 2
0 .0 1 3 2
0 .0 1 3 2
0 .0 1 3 2
0 .0 1 3 2
0 .1 3 2
■
0 .1 3 2
1.32
1.32
0 .0 0 1 3 2
0 .0 0 1 3 2
0 .0 0 1 3 2
0 .0 0 1 3 2
0 .0 0 1 3 2
0 .0 1 3 2
0 .0 1 3 2
EXPERIMENTAL DATA
x
xIO^ ■
e
cm /sec
x
xIO*
se
cm /sec
0 .3 5 2
0 .2 4 4 .
0 .2 5 0
• 0 .5 7 0
0 .5 3 5
1.4 6
1 .5 0
6 .3 4
5 .8 9
■ 6.51
7 .2 8
8 .1 5
9 .3 8
7 .8 4
7 .0 7
0 .8 0 5
0 .5 4 6
0 .6 8 0
2.61
2 .1 5
. 1.6 2
1.7 6
1.97
2 .1 3
. 2 .5 7
2 .3 0
5-11
3 .6 8
TO.7
9 .4 8
1.49
1.67
. 1.93
1.83
1.9 6
5 .8 3
5 .3 3
■
0 .2 4 9
0 .2 6 9
0 .2 1 7
.0 .6 3 5
0 .6 3 2
1 .5 3
■ 1 .6 7
5 .M
6 .5 6
6 .6 2
6 .6 8
6 .6 3
6 .4 9
8 .0 9
6 .3 4
0 .6 7 9
0. 501;
0 .6 6 5
2 .0 8
2 .1 2
1 .8 8
1 .9 0
1 .9 5
1 .9 6
2 .2 2
2 .1 2
3 .5 9
3 .4 9
1 1 .7
to ; 9
1 .4 5
1 .6 8
2 .2 6
1 .9 2
1.66
6 .9 5
5 .4 2
D
- cm
av
0 .0 4 0 7 0 /
0 .0 6 1 0
0 .0 4 9 2
0 .0 6 1 6
O.O64O
0 ,0 5 8 2
0 .0 6 1 4
0 .0 5 2 2
0 .0 6 1 5
0 .0 5 6 7
0 .0 5 1 6
0 .0 4 6 3
0.0401
O.O574
0 .0 5 0 6
0 .0 4 7 9
0 .0 5 1 7 •'
0 .0 5 4 7
0 .0 4 5 5
0 .0 5 5 2
0 .0 6 3 8
0 .0 6 0 0
O.O553
0 .0 5 1 9
0 .0 4 8 9
0 .0 5 1 8 ;
0 .0 4 0 6
0 .0 5 3 2
0 .0 6 0 4
0 .0 6 3 4
O.O544
O.O5 6 I
0 .0 6 4 4
O.O584
0.0481
O.O564
0 .0 5 6 7
R a y le ig h
Number
-8
6.05x10 °
2 .0 1 x 1 0 “ j
1.06x10"*/
2 . 07x 10] /
2 .3 2 s 1 0 ] /
1.7 4 x 1 0 _ r
2 . 05x 10 /
1 .2 6x10“ '
|2 .0 6 x 1 0 “
1.61x10“
1.22x10
8 .8 1 x 1 0 “ ' '
5.6 9 x 1 0 “ ^
1.68x10 ‘
1. 15x 10 0
6.63x10-%
8 .3 3 x 1 0 ];
9 . 90x 10" ;
5 .6 8 x 1 0 _ r
1 .0 2 x 1 0 j?
1.57x10 /
1 .3 0 x 1 0 /
1.02x10 /
8 .42x10 ;
7 .0 8 x 1 0 ] ;
8.3 9 x 1 0 “%
4 . 05x l o J
9. IIx io J j
.
1 .3 3 x 1 0 j
1.54x10 %
6 .8 8 x 1 0 Q
7.55x10 %
1-14x10 '
8 . 52x 1 0 °
4 .7 6 x 1 0 :
1.20x10 /
7 .8 1 x 1 0 “ °
20
Table III.. (Continued)
0 .1 3 2
0.132
0 .1 3 2
1.32
1.32
1.32 .
13.2
6 .8 4
6 .5 2 .
3 5 .9
• 22.0
. 2 8 .2
11.4
5.97._.
7 .0 2
3 0 .0
2 5 .6
2 4 .8
* Designates runs done using lot #2 Ir wire
1 Is the run shown on Figure 2.
)
0 .0 4 8 9
0 .0 4 9 4
0 .0 5 9 7
0 .0 4 7 5
0 .0 6 3 9
0 .0 4 9 8
5.00x10
5 .17x 10'
9 .09 xi0 _
4 .5 8 x 1 6 I
1.12x10“ '
5.28x10“^
^
2200
2200
2200
2200
2200*
2200
21
M l i t y , b etw een t h e two l o t s o f i r i d i u m . In f a c t ', f o r any ru n u s in g
.
O
<f*
th e seco n d l o t o f i r i d i u m , th e % d e v i a t i o n o f x
from t h e mean o f x
se
se
f o r t h e g ro u p h a v in g th e same te m p e r a tu r e and p r e s s u r e ,, was l e s s th a n
13% in a l l c a s e s , a lth o u g h th e mean e x p e rim e n ta l d e v i a t i o n f o r a l l th e
r u n s was 8.5%«-
(S ee T ab le V I I I , th e colum n h ead ed ufo E x p e r. D e v .")
Thus
th e 0.6% tu n g s te n in l o t 1 had no p e r c e p ta b le e f f e c t on t h e o x id a tio n r a t e .
I n c a l c u l a t i n g 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 from e q u a tio n ( l )
i t i s n e c e s s a r y t o hav e v a lu e s o f th e unknowns in v o lv e d . '
i s known
2
from t h e e x p e r im e n ta l c o n d i t i o n s and i n th e p r e s e n t c a s e i s th e t o t a l p r e s ­
s u r e o f th e s y ste m .
S e v e r a l p r o p e r t i e s o f oxygen w ere needed-.and b e c a u s e
th e y v a r i e d w ith p r e s s u r e a n d /o r te m p e r a tu r e , th e y w ere l e a s t s q u a r e s
c u rv e f i t i n th e r a n g e o f 1000 K t o 1400 K from o r i g i n a l d a t a . 1^ ’ . ^
(1083
*
■'
.
■
t o 1 3 8 3 &K was th e ra n g e o f f i l m te m p e r a tu r e s T^ e n c o u n te re d e x p e r i m e n t a l l y .)
The r e s u l t i n g r e l a t i o n s f o r th e s e p r o p e r t i e s a r e shown i n T ab le IV.
In o rd e r, t o o b ta in v a lu e s f o r t h e mass t r a n s f e r c o e f f i c i e n t s k ^ , th e
f o llo w in g C h ilto n - C o lb u r n r e l a t i o n s w ere em ployed.
16
(
= f/2
By e q u a tin g th e e x p r e s s io n s f o r
k GRTf and f o r t h i s c a s e
k
w here;
G
and
2 .)
(3)
and s o lv in g f o r k ^ , w here k^ =
= P,
= (h/C pT fR )(L e)2/3
(4 )
;
22
T a b le IV .
OXYGRN PROPERTIES
1000 °K < Tp ^ 1400 a K
I
R e la tio n
0^ P r o p e r ty
io V a r ia t io n from d ata.
D e n s ity
/) = 0.3899PQ /T ^
0.04
S p e c i f i c H eat
Cp = 0 .1 l6 T f ^ * 117
0 .2 1
V is c o s ity
J L = .5 .3 7 4 x 1 0- 6 Tf 0 *650
0 .4 4
Therm al c o n d u c t i v i t y
k = 9 .4 8 x 1 0 - 7 Tf 0 *758
0.31
S p e c i f i c H eat R a tio
y =
0 .0 8
1 .6 8 2 T f 0 '° 3 5 9 .
.
23
Cp = S p e c i f i c h e a t r a t i o o f oxygen - c a l/g m ° K f
= M o le c u la r d i f f u s i v i t y - c m ^ /se c ,
f = F ric tio n f a c to r ,
2
= M olal m ass v e l o c i t y - gm m o le s /s e c cm ,
h = F ilm h e a t t r a n s f e r c o e f f i c i e n t - c a l/c m
se c
K,
j p , j p = C h ilto n - C o lb u r n f a c t o r s ,
k = Therm al c o n d u c t i v i t y o f oxygen - c a l/c m se c
k
K,
2
3
= Mass t r a n s f e r c o e f f i c i e n t - gm m o le s /( s e c cm ) (gm mole/cm"3),
Le = Lew is number - p r /S c o r C^^D^ k ,
yt(j= V i s c o s i t y o f oxygen - cp ( c e n t i p o i s e o r gm/cm s e c ) ,
P = T o ta l p r e s s u r e .
RgM = P a r t i a l p r e s s u r e - atm o s,
P r - P r a n d tl number - C .4kJk ,
P
O = D en sity - o f oxygen - gm /cm"1,
• R = U n iv e r s a l Gas Law C o n s ta n t - 8 1 .7 cm^ atm os/gm mole °K ,
Sc = S chm idt number -Jb /jo D y
Tp = E x p e rim e n ta l f il m te m p e r a tu r e -
o
K,
U^v = Mean gas, v e l o c i t y - cm /sec^
In e q u a tio n ( 4 ) a l l p a r a m e te r s a r e known a t t h i s p o in t" a t any g iv e n
te m p e r a tu r e and p r e s s u r e e x c e p t h and D
w hich w ere fo u n d a s f o llo w s .
To f i n d th e v a lu e o f h , th e v a lu e o f th e N u s s e lt num ber, Nu, was
f i r s t fo u n d from th e e x p r e s s io n b elow d e v e lo p e d by Madden and P i r e t .
17
T h is i s f o r n a t u r a l c o n v e c tio n from h e a te d h o r i z o n t a l w ir e s o f 0.00701
24
and. 0,0251 cm in d ia m e te r i n a i r o r h e liu m and p r e s s u r e s from 0^00658 t o
1 .0 a tm o s p h e re s .
2
+ 8 / & # b P r ( ^ + l)D - ln (1 + 2% /D )
*
w here th e f i c t i t i o u s N u s s e lt number Nu
is.,
Nu* = 2 / l n ( 6 . 8 2 / R a l / ^ ) ,
and f o r th e work o f t h i s r e p o r t
t i a l l y assum ed e q u a l 1 0 0 .8 .
(5 )
.
(g )
th e acco m o d atio n c o e f f i c ie n t ? w a s i n i ­
The o th e r p a r a m e te r s i n e q u a tio n s ( 5 ) and (6 )
a re ;
P - C o e f f i c i e n t o f th e rm a l e x p a n s io n .~ l/T^. ( 0K) ^ »
D = A verage e x p e r im e n ta l w ire d ia m e te r - cm,
Q '- S p e c i f i c h e a t r a t i o f o r o x y g e n ,
g = G r a v i t a t i o n a l a c c e l e r a t i o n - c m /s e c ^ ,
Gr = G rash o f number - gp2yP(Tg - T ^ )D ^ ^ |2 ,
^ a = Mean f r e e p a th o f oxygen m o le c u le s - cm-,
Ra = R a y le ig h number - P r G r ,
0
-T
= E x p e rim e n ta l w ire te m p e r a tu r e -
C, .
T = Ambient te m p e r a tu r e i n s i d e th e c e l l a
■
0
G.
S in c e th e p r o p e r t i e s o f oxygen a r e v e r y n e a r t h a t o f a i r , t h i s e x p r e s s i o n ■
was assum ed v a l i d f o r p u re oxygen a l s o .
T h is h e a t t r a n s f e r c o r r e l a t i o n i s
v a l i d i n th e ra n g e o f 10"®^
V a lid u s e o f e q u a tio n ( 5 ) i s i n d i
Ra — 10 1.
c a t e d by th e l i s t i n g o f th e c o r r e s p o n d in g R a y le ig h num bers o f each- e x p e r­
im e n ta l runv i n . T a b le I I I .The v a lu e f o r /I m i n e q u a tio n ( 5 ) was c a l c u l a t e d from th e Dushman
25
e q u a tio n
,
= ( .8 .5 8 ^ /P t ) ( T /M .,//2
w here;
= V i s c o s i t y o f oxygen - p ( p o is e )
= M o le c u la r w e ig h t o f oxygen
= P a r t i a l p r e s s u r e o f oxygen - t o r r
By c o n v e r t i n g ^ , end P
u s in g
t o / L and P f s u b s t i t u t i n g f o r X , from T ab le IVj and
f o r oxygen a s 3 2 .0 , th e above e x p r e s s io n becam e, •
= I . 0 7 4 x 1 0 - ^ 1 " 1 5 /p
From e q u a tio n {7),~X
o f " te m p e r a tu r e
(? )
c o u ld th e n b e r e a d i l y c a l c u l a t e d f o r any c o n d i tio n
and p r e s s u r e P c o r r e s p o n d in g t o e x p e r im e n t.
At t h i s
p o in t Nu was c a l c u l a t e d and h was fo u n d from e q u a tio n ( 8 ) .
/
h =• CF(NukyZD)
(8 )
The CF was a-, c o r r e c t i o n f a c t o r f o r th e h e a t t r a n s f e r c o e f f i c i e n t due t o
th e p r e s e n c e o f t h e l i d on to p o f th e c e l l and c o n n e c tin g cham ber o f "T"
below th e c e l l . . The v a lu e o f CF was fo u n d t o b e l l ,0 w ith in th e - Vfo accur.r* •
a c y o f th e e x p e r im e n ta l e q u ip m en t: used'.-- B ecause t h e i n v e s t i g a t i o n s o f
t h e v a lu e o f CF c o u l d n 't ta k e i n t o a c c o u n t th e e f f e c t s o f th e s i d e - w a l l s
on th e h e a t t r a n s f e r ,
( t h e e x p e rim e n ts t o d e te rm in e CF w ere p e rfo rm e d w ith
t h e c e l l open on to p and b o tto m a s o p p o sed t o th e f u l l y a s s e m b le d a p p a r a t u s ) t h i s , was a l s o i n v e s t i g a t e d .
A c c o rd in g t o J o n es and Masson
, if
th e r a t i o o f th e d i s t a n c e from th e w a ll t o th e c e n t e r o f th e c y l i n d e r t o
th e c y l i n d e r d ia m e te r i s g r e a t e r th a n 0.7? th e h e a t t r a n s f e r i s n o t a f f e c t e d .
26
In th e p r e s e n t c a s e t h i s r a t i o was a p p ro x im a te ly 2 0 , so t h a t t h i s p o s s i ­
b i l i t y was r u l e d o u t.
I t was a l s o sh o w n .in th e e x p e r im e n ta l s t u d i e s t h a t t h e r e was no e f f e c t .
on th e h e a t t r a n s f e r , and th u s th e o x id a tio n r a t e , due t o t h e oxygen flo w
J
th ro u g h th e "T" s e c t i o n b e n e a th t h e c e l l .
The v a lu e s f o r D w ere c a l c u l a t e d from th e W ilke and Lee m o d if ic a t i o n o f th e H ir s h f e l d e r , B ir d , and S p o ts
^
=
20
e q u a tio n w hich i s ,
0T_ (1/M. +
-------------—
B ir 12
'
(9 )
D
w here *
C = 1 0 ,7 - 2 ,4 6 ( 1 /® / -s- l / M j l / 2 x10~4 ,
Lp = C o l l i s i o n i n t e g r a l f o r d i f f u s i o n ,
M0 = M o le c u la r W eight o f o x id e s p e c i e ,
2.
*
( r 0 ),| = 1. 18(V0 ) 1
c o l l i s i o n d ia m e te r f o r oxygen m o le c u le /o x y g e n .
m o le c u le .^ c o llis io n - a n g s tr o m s ,
( 1 ^ )2 = 1»18(V0
c o l l i s i o n d ia m e te r f o r '..oxide., m o le c u le /o x id e
m o le c u le c o l l i s i o n - a n g s tr o m s ,
( r p ) -i + ( r o ^2
/
■r 10 = --------—r --------— , c o l l i s i o n d ia m e te r f o r oxygen m o le c u le /o x id e
m o le c u le c o l l i s i o n - a n g s tro m s ,
■ (V0 ) 1 = M olal volum e o f oxygen - cn r/g m m o le ,.
(V0 );? - M o lal volum e o f o x id e s p e c ie --cm ^ /g m :. mole„
As n o te d i n th e NOMENCLATURE, I p i s a f u n c t i o n o f th e p a ra m e te r ( k T p / ^ ^ ) *
From d a t a t a b u l a t e d i n r e f e r e n c e 2 0 , I p was l e a s t s q u a r e s c u rv e f i t a s a
/
27
f u n c t i o n o f ( k T ^ / g ^ ) f o r 1 ,8
e x p e r im e n ta lly .
(kT ^,/^
) ^ - 2 .8 , t h e ra n g e e n c o u n te re d
The maximum -'jo d e v i a t i o n from d a t a was 0 . 30/& f o r th e r e l a ­
tio n ,
w here.
^ 2 ~ E n erg y o f m o le c u la r i n t e r a c t i o n - e rg s
k = B oltam ann c o n s ta n t - 1 .3 8x10 ^ er^gs/^K .
The v a lu e o f
was - d e te rm in e d from th e r e l a t i o n ,
^ 12/ k . ((S1Zk)(^2ZE) ) 1 /2
w here th e f o r c e c o n s ta n t ^ / k
i s known f o r oxygen a s 113®2
K and th e
f o r c e c o n s t a n t ^ g /k was d e te rm in e d f o r th e v a r io u s o x id e s p e c ie s from
th e r e l a t i o n ,
. ^ 2ZE - 1 . 9 2 V
The v a lu e o f T , t h e m e ltin g te m p e r a tu r e s o f th e o x id e s i n th e above
e x p r e s s io n , i s unknown.
F o r IrO , IrO g , and IrO ^ , T^ was assum ed t o be'-I ^OO
O
"
K i n i t i a l l y , w h ereas th e known v a lu e o f th e m e ltin g te m p e r a tu r e , 2727
ciK f o r I r was u s e d .
U sin g e q u a tio n ( 9 ) th e n , w ith th e a p p r o p r ia te conr-
s t a n t s s u b s t i t u t e d in f o r eac h s p e c i e ,
was c a l c u l a t e d f o r each e x p e r i ­
m e n ta l c o n d i tio n o f w ire te m p e r a tu r e and oxygen p r e s s u r e .
The k^ v a lu e s
w ere th e n c a l c u l a t e d u s in g e q u a tio n ( 4 )•
The e q u ilib r iu m c o n s ta n t s f o r IrO , IrO g and IrO ^ w ere i n i t i a l l y
e s tim a te d by u s e o f th e c o r r e s p o n d in g AH^sand 4 S | i o f p r e v io u s e x p e rim e n t e r s . - a s sum m arized i n T ab le V.
The e q u ilib r iu m c o n s t a n t , K^, f o r I r was
28.
T a b le V.
SUMMARY OF A E ° & 4 s " VALUES BY PAST EXPERIMENTERS
E x p e rim e n te r
S p e c ie
*
IrO
MO**,
IrO
MOg
IrO
IrCT
MO ^
M argrave
S e a rc y
Norman et_ a l
. S e a rc y
Norman a t a l
O lie v i
S e a rc y
AH0
k c a l/m o le
AlS eu
[k c a l/m o le TC]
105.
4 8 . 5 - 0 .8
5 . 5 - 1 .5
6 .0
Xi
2 0 .6
3 .9 T 2 .0
3 .5 - 2 .1
- 1 3 .2 * 2 .5
- 9 .0
-1 0 t o -1 5
Temp.
Range 0 C
1010-2217
25
1557-1760
25
1557-1760
1627-2227
25
* These v a lu e s w ere u se d t o i n i t i a l l y e s ti m a t e th e v a lu e s o f th e e q u i l i ­
briu m c o n s t a n t s f o r IrO , IrO g , and I r O y
T a b le V I.
INITIALLY PREDICTED EQUILIBRIUM CONSTANTS
W ire T em p eratu re
&
K1
K2
■ K3
1600 °C
2.19X 10™11
1.78x10*8
1.56x10*5
1. 67x 1O* 3
1900 0 C
6.2 7 x 1 0 * 9
8 .7 3 x 1 0 * 7
9 .4 2 x 1 0 * 5
2 . 09x 1O" 3
2200 ° C
4 .5 6 x 1 0 * 7
1.67x10*5
3 .6 8x10*4
2 .4 7 x 1 0 * 3
29
se e n t o b e e q u a l t o t h e p a r t i a l p r e s s u r e o f th e ir i d iu m o r i t s v a p o r
p re ssu re .
The v a p o r p ressu r e: b f i I r jl P j r $ was i n i t i a l l y e s tim a te d from
th e v a p o r p r e s s u r e e q u a tio n r e s u l t i n g from th e work o f Hampson and W alker
21
T h is r e l a t i o n i s ,
I n ( P ^ ) = 7 .1 3 9 - 3 3 ,3 3 7 /T g =
(1 0 )
The v a l u e s o f a l l th e e q u ilib r iu m c o n s t a n t s a t 1600, 190 0 , and 2200 °C
a s i n i t i a l l y , e s ti m a t e d , a r e shown i n T a b le V I.
I n f i n d i n g t h e v a lu e f o r A, th e o n ly o th e r p a r a m e te r i n e q u a tio n (1 ),.
th e d e n s i t y o f th e ir id iu m had t o b e fo u n d a s a f u n c t i o n o f te m p e r a tu r e .
D ata w ere ta k e n from th e r e s u l t s o f work done by H a lv o rs o n and Wimber 13
on th e th e rm a l e x p a n s io n o f ir i d iu m and l e a s t s q u a r e s c u rv e f i t i n th e
'
K, w hich i s th e - r a n g e o f T^ e n c o u n te re d e x p e r i r
..
.
■
T h is r e s u l t e d i n a maximum jo d e v i a t i o n o f 0.035/^ f o r th e r e l a ­
ra n g e o f 1873 to- 2473
m e n ta lly .
o
t i o n a s shown b elo w .
6 .1 4 4 x 1 0 -6Tk 1e632.
( 11 )
w here DL i s th e % ch an g e i n le n g th o f .ir id iu m from 298
i s th e e x p e r im e n ta l w ire te m p e r a tu r e i n
@ 298 K
&
K.
K t o T, , and T,
U sin g th e e x p r e s s io n ,
(I +(DL @ T ) / l 0 0 ) 3
(
12)
th e d e n s i t y o f th e ir id iu m a t any p a r t i c u l a r e x p e r im e n ta l v a lu e o f w ire
te m p e r a tu r e T ^f was fo u n d .
Then t h e v a l u e o f A was fo u n d f o r each r u n ,
w h ere,
19 2 .2 gm ir id iu m consum ed/m ole o x id e fo rm ed
@ T1
(1 3 )
'
.
30
At t h i s p o in t th e t h e o r e t i c a l r e c e s s i o n r a t e , x ^ , was c a l c u l a t e d
from e q u a tio n ( I ) f o r ea c h o f th e'' e x p e r im e n ta l c o n d i tio n s o f th e ru n s
m ade.
C om parison o f e x p e rim e n t w ith t h e o r y 'r e v e a l e d a d i f f e r e n c e o f ab o u t
one o r d e r o f m a g n itu d e i n . t h e r e c e s s i o n s r a t e s o f th e o r y and e x p e rim e n t.
I t was a l s o n o te d t h a t th e b e s t c o r r e l a t i o n r e s u l t e d when
( l ) was e s s e n t i a l l y z e r o .
o f e q u a tio n
I t was th e n c o n c lu d e d t h a t i f IrO i s p r e s e n t
a t a l l , i t i s so i n r e l a t i v e l y s m a ll q u a n t i t i e s .
Thus th e term c o r r e s p o n ­
d in g t o IrO p a r t i c i p a t i o n was e x c lu d e d from f u r t h e r c o n s i d e r a t i o n , ch an g ­
in g e q u a tio n (1 ) t o ,
Xt = A(k G2K2P02 + k G3K3P 02
B ecau se o f th e f a c t t h a t th e
+ k GMicM?
an d
■ ( 14 )
v a lu e s h av e c o n s id e r a b le
u n c e r t a i n t y a s s o c i a t e d w ith them, a s may s e e n by c l o s e e x a m in a tio n o f
T a b le V, i t was deemed r e a s o n a b le t o th e n t r e a t th e e q u ilib r iu m c o n s ta n t s
'K2 a n d * a s
unknow ns.
The e q u ilib r iu m c o n s t a n t 'K^, th e acco m o d atio n c o e f ­
f i c i e n t ^4, a n d .th e m e ltin g te m p e r a tu r e T^ o f th e IrO g and IrO ^ w ere th e
o n ly o th e r u n c e r t a i n p a r a m e te r s in v o lv e d i n th e c a l c u l a t i o n o f x ^ , and
th u s w ere a l s o t r e a t e d a s unknowns.-
The r e s u l t s o f em p lo y in g an o p tim i­
z a t i o n p r o c e s s t o f i n d t h e b e s t v a lu e s o f th e unknowns Kg, K^,
f o r d i f f e r e n t v a lu e s o f T a r e l i s t e d i n T ab le V II.
m
o<.
The colum n h ead ed
"Mean % E rro r"- i s th e a v e ra g e o f th e d i f f e r e n c e b etw ee n x^ and x
by x^ f o r th e .ru n s : a t t h a t p a r t i c u l a r l e v e l o f Tg .
and
d iv id e d
I t was n o te d t h a t th e
. t o t a l o f th e mean $ e rro r.- o f th e t h r e e Tg l e v e l s , o r th e q u a l i t y o f t h e f i t
o f th e t h e o r e t i c a l model, was b e s t a t th e 1400 and 1500
o
K .v a lu e s f o r T^.
.
. O
AFf° - IrO 2
K3
k c a l/m o le
'
- ^ 03
k c a l/m o le
Mean tJa
2 .6 7 x 1 0 -3
22.1
1500* 1600
8 .8 0
2 6 .2
2 .7 0
2 2 .0
•o '
V
1600
1600
9 .0 5
26.1
2 .7 0 ' "
2 2 .0
1700
1600
9 .3 0
2 6 .0
2 .7 0
2 2 .0
1800
1600
9 .5 4
2 5 .9
2 .7 0
1900
2 .1 7 x 1 0“ 3
2 6 .5
1900
2 .1 9
1600
1900
1700
13.5
0 .3 9 5 -
13.4
< 1 0 " ,d
0 .4 0 0
14.1
<:io~12
0 .4 0 6 '
14.7
2 2 .0
< 1 O"12
O.410
15.3
3 .6 3
24^3
CIO-1 2
■ 0 .6 4 5
11.8
2 6 .5
3 ,6 6
2 4 .2
^ IO " ^ 2
0.6 4 5
"•11.8
2 .2 0
2 6 .4
3 .6 8
2 4 .2
^ i o " ''2
0.643
11.8
1900
2 .2 0
2 6 .4
3.71
2 4 .2
^ io -I2
O.690
12:1
1800 " 1900
2 .2 0
2 6 .4
3 .7 5
24.1
^ io -I2
I
0 .7 5 4
- 12.5
2200
8 .6 3
2 3 .4
4 .6 8
2 6 .4
2 .4 6 x 1 O™8
I
0 .2 1 9
14.9
2200
8 .6 8
2 3 .3
4 .7 3
2 6 .3
2 .4 6
0.221
15.0
1600
2200
8 .7 2
2 3 .3
L 78
2 6 .3
2 .4 6
0 .2 2 3
15.2
1700
2200
8 .7 7
2 3 .3
2 6 .2
2 .4 6
0 .2 2 4 -
15.2
1800
2200
8.81
2 3 .2
|4.86
2 6 .2
2 .4 6
0.2 2 7
15.3
1500
*
1400
1500
*
.
.
* T hese v a lu e s w ere u s e d i n th e f i n a l c o r r e l a t i o n o f Xfc w ith x q .
(
1400
'
OJ
0 .3 8 9 "
OJ
CO
2 6 .2
1600
v
E rro r
8 .8 1 x 1 0 -4
1400
o<
" kM
0 I^
fo
K2
OPTIMIZATION RESULTS - FINAL VALUES FOR EQUILIBRIUM
CONSTANTS AND ACCOMODATION COEFFICIENT
A
T . ra
. I
O0 COie
| I
T a b le V II.
I
32
B ecause th e v a lu e o f
m ust th e n be b etw een 1400 and 1500
K, and th e
q u a l i t y o f th e f i t i s v e r y i n s e n s i t i v e i n t h i s r a n g e , th e v a lu e o f
1500 0 K f o r IrO
and IrO-. was r e t a i n e d .
=
The f i n a l c o r r e l a t i o n was b a s e d
on th e s ta n d a r d i z e d s u r f a c e r e c e s s i o n r a t e s
and Xgg a s a r r i v e d a t
u s in g th e v a lu e s o f K^, K^, .K^f an.d»4 a s in d i c a t e d i n T a b le V II t o c a l c u ­
la te x , .
st
F ig u r e 3' shows th e r e s u l t s g r a p h i c a l l y o f x
S6
w h ile T a b le V I I I i n d i c a t e s th e n u m e ric a l r e s u l t s .
.an d x , v e r s u s Pn ,
Su
Ug
'I n T a b le V I I I , th e
colum n h ead ed "fa E r r o r " i s th e fa d i f f e r e n c e betw een x
Xg^ .
and x g g , b a s e d on
The t h e o r e t i c a l model d e s c r ib e d by e q u a tio n (1 4 ) f i t th e ex p erim en ­
t a l r e s u l t s w ith cai mean
e r r o r p e r r u n , o f 13*4% a t 1600
1900 ° C , and 15.0% a t 2200
th e 1600 t o 2200 r a n g e .
d i f f e r e n c e b etw een x
se
Cf 11.8% a t
C, o r 13«3% f o r an a v e r a l l mean % e r r o r i n
A ls o , th e colum n h ead ed "% E x p e r. D ev." i s th e
and th e mean v a lu e o f x
se
d iv id e d by th e mean x
,
se
f o r a p a r t i c u l a r s e t o f r u n s a t th e same te m p e r a tu r e and p r e s s u r e , i . e .
th e fa e x p e rim e n ta l d e v i a t i o n .
The mean % e x p e rim e n ta l d e v i a t i o n f o r a l l
th e ru n s was 8 . 5% .'
1
To e n a b le a c o m p ariso n o f
and
'
w ith p r e v io u s - e x p e r im e n te r s ,
O '
th e v a l u e s o f AF^ f o r IrO g and IrO ^ in T a b le V II, w ere l e a s t s q u a r e s c u rv e
f i t t o th e l i n e a r r e l a t i o n A F^ =
v a lu e s o f A H° and AS
I
I
T h is c a l c u l a t i o n o f th e
" f i l t e r s " o u t t h e s m a ll d ep en d en ce o f th e s e p a r am e -
t e r s on te m p e r a tu r e i n th e 1600 t o 2200
O
C r a n g e , a s can b e se e n by in s p e c ­
t i o n o f T ab le V I I . '' The r e s u l t s o b ta in e d w ere, f o r IrO g i
= 35*7 k c a l /
SURFACE RECESSION RATES Xse, Xst x IQ0 Cm/Sec
THEORETICAL —
EXPERIMENTAL O
- LOT 2
- 2200° C
P o ,, OXYGEN PARTIAL PRESSURE, ATMOSPHERES
P ig u re 3 .
PLOT OF EXPERIMENTAL AND THEORETICAL RECESSION RATES VERSUS OXYGEN PARTIAL PRESSURE
34
T a b le V I I I .
FINAL CORRELATION DATA
x , &x
@ D = O.O588 cm
st
se
T , ebC
s’
1600
1600*
1600
1600
1600
1600
1600
1600
1600
1600
1600
1600
1600
16001600*
1900
1900
1900
1900
1900
1900
1900
1900
1900
1900*
1900
1900
1900
1900
1900
2200
2200
2200
2200*
2200
2200
‘
6
cm /sec
x ,xIO ^
st
cm /sec
0 .2 4 9
0 .2 6 9
0 .2 1 7
.0 .6 3 5
0 .6 3 2
1.53
1. 6?
5 .8 8
6 ,5 6
6 .6 2
6 .6 8
6 .6 3
6 .4 9
8 .0 9
6 .3 4
L 0 .6 7 9
0 . 50.1
0 .6 6 5
" 2 .0 8
2 .1 2
1 .8 8
1 .9 0
1.9 5
■1.9 6
2 .2 2
2 .1 2
3 .5 9
3 .4 9
11.7
10 .9
1.45
1 .6 8
2 .2 6
1.92
1 .6 6
6 .9 5
0 .3 0 4
0 .3 0 4
0 .3 0 4
0 .8 0 2
0 .8 0 2
1.8 7
. 1 .8 7
6 .4 5
6 .4 5
6 .4 5 '
6 .4 5
6 .4 5
6 .4 5
6 .4 5
6 .4 5
0 .9 2 9
O.9 2 9
0 .9 2 9
1 .9 6
1 .9 6
1 .9 6
1 .9 6
1 .9 6
1 .9 6
1 .9 6
1 .9 6
• 3 .8 0
3 .8 0
1 0 .9
1 0 .9
1 .9 3
1 .9 3
1 .9 3
1 .9 3
1 .9 3
6.3 1
'jo E r r o r
jo E x p e r.
:
- 1 8 .2 •
—1 1 .6
- 2 8 .6
- -2 0 .8
- 2 2 .4
- 1 8 .2
-1 0 .8
-8 .9
1 .7
2 .6
3 .5
2 .7
0 .6
2 5 .4
--u s
-2 6 .9
■1
- 4 6 eI
1
- 2 8 .4
5 .9
8 .1
- 4 .3
—3 »0
;
- 0 .7
:
0 .0
• 1 3 .0
7 .8
- 5 .6
- 8 .2
' 7 .3
0 .3 ■
- 2 4 .9
- 1 3 .0
A T il
- 0 .2
- 1 3 .9
1 0 .3
Dev 0
1 .6
8 8 .9
-1 2 .9
0 .2
—0 • 2
- 4 .6
4 .2
-1 3 .3
- 1 .5
'- 0 .6
0 .3
-0 .5
—2 .6
17.7
-5 .0
9 .0
- 2 2 .8
8.1
2 .4
; 4 .2
-8 .0
-6 .8
—4« 1
- 5 .7
8 .6
4 .2
1 .4
—1 »4
3 .4
- 3 .7
-2 3 .7
—6 .9
2 0 .6
6 .6
-8 .1
1 1 .0
I
I
!
|
I
j
;
I
I
35
T a b le V I I I . .
2200
2200
2200
2200
2200
2200*
2200
(C o n tin u e d )
5 .4 2
11.4
5 .9 7
7 .0 2
3 0 .0
2 5 ,6
2 4 .8
* Has sai.iv m eaning a s i n T ab le I I I .
6.31
1 1 .8
' 11. 8
11. 8
2 5 .3
2 5 .3
2 5 .3
-1 4 .0
—3» 1
—49«1
—4 0 .3
1 8 .4
0 .8
-2 .0
- 1 4 .1
2 8 .7
-3 6 .2
-1 5 .8
—10» 7
—4*7
- 8 .1
mole and J
i = 4« 77' eu and f o r IrO ^ , AH^1 = 8 .6 3 k c a l/m o le and
=
—7 .1 6 eu*
DISCUSSION OF RESULTS
The o v e r a l l mean % e r r o r o f th e s u r f a c e r e c e s s i o n r a t e s p r e d i c t e d
t h e o r e t i c a l l y was 13. 3% a s com pared t o a mean % e x p e r im e n ta l d e v i a tio n
o f 8.5% .
.When c o n s id e r i n g th e ty p e o f work in v o lv e d in th e p r e s e n t s tu d y ,
and th e in h e r e n t e x p e rim e n ta l e r r o r o r e x p e rim e n ta l d a t a s c a t t e r , t h i s v
was s e e n t o be an e x c e l l e n t d e g re e o f c o r r e l a t i o n !
B ecau se
and A S ^ a r e te m p e r a tu r e d ep en d e n t p a r a m e te r s , d i r e c t
c o m p a ris o n ■o f t h e s e v a lu e s f o r IrO ^ and IrO ^ i n th e p r e s e n t r e p o r t , t o
th o s e sum m arized i n T a b le V, i s n o t f u l l y p o s s i b l e .
T a b le IX shows some
o
o
t y p i c a l tr e n d s i n th e AH^ and ASf v a l u e s f o r .o n e v o l a t i l e d io x id e s p e c ie
and tw o v o l a t i l e t r i o x i d e ' s p e c i e s , show ing th e te m p e r a tu r e d ep en d en ce i n v o l ved.
2 2 .2 3
'
o
I t was s e e n t h a t th e AHp f o r MoCL te n d s t o d e c r e a s e w ith te m p e r-
o
a t u r e , and .th u s AHf f o r IrO ^ m ig h t a l s o b e e x p e c te d t o d e c r e a s e w ith tem p­
e ra tu re .
M aking a c o m p a riso n , t h e AHf o f 35*7 k c a l / m o l e . f o r th e 1600 t o
2200 0 C ra n g e o f th e p r e s e n t work i s in d e e d l e s s th a n th e v a lu e o f 4 8 . 5k c a l /
mole r e p o r t e d by Norman e t a l , f o r th e 1557 t o 1760
e x p e c te d .
Q
C r a n g e , a s m ig h t be
6
When ex am in in g th e A Sf o f MoO2 , a s l i g h t d e c r e a s e i s se e n w ith
o
,
o
te m p e r a tu r e , w h ereas th e ASf = 4«77 eu f o r IrO 2 i n t h e 1600 t o 2200
C of
th e p r e s e n t work f a l l s w ith in th e ra n g e o f b o th Norman e t a l ' s v a lu e o f
3 .9 - 2 .0 eu i n t h e 1557 t o 1760
3 .5 . ^ 2 .1 eu f o r MOg a t 25 ^ C.
C ra n g e f o r IrO g and S e a r c y 's v a lu e o f
Erom t h i s , r e s u l t s o f th e p r e s e n t w ork,
T a b le IX.
TYPICAL TRENDS FOR VOLATILE DIOXIDE AND TRIOXIDE SPECIES
AS A FUNCTION OF TEMPERATURE
Oxide S p e c ie
AHf °
^5 ^
k c a l/m o le
MoO223
MoO322
“ 3
eu
-4 .3 3
8 .4 5
1000
- 5 .3 9
7 .5 3 '
1500
-6 .9 9
6 .6 5
2000
- —40« 3 ’
1068
- 2 8 .1
1530
- 1 .2 4
.2 5 0 0
- 120.
-1 0 7 .
00
Temp. ^ K
-8 2 .9
'
.
-I 3 3 .O
-3 7 .9
1743
- 1 1 5 .8
-2 8 .0
2100
- 8 3 .2
- 1 2 .5
2500
.
38
Norman e t a l 1s w ork, and S e a r c y 's work seem t o i n d i c a t e t h a t A S ^ f o r IrOg
i s r e l a t i v e l y te m p e r a tu r e i n s e n s i t i v e i n th e 25 t o 2200
o
C ra n g e .
By u s in g T a b le s V .an d IX a g a in , an i n c r e a s i n g .t r e n d w ith te m p e r a tu re
c
'
■
was s e e n f o r AHf o f MoOy WO^ and I r O y
T h is te n d e d t o b e t r u e f o r th e
c
p r e s e n t work f o r w hich AHf f o r IrO ^ was 8 .6 3 k c a l/m o le i n th e 1600 t o 2200
°C ra n g e when com pared t o th e . 5 .5 - 1 .5 k c a l/m o le i n th e 1557 t o I 76O* C
ra n g e o f Norman e t a l 1s w ork.
But t h e 8 .6 3 k c a l/m o le was a l i t t l e h ig h e r .
th a n th e 6 .0 k c a l/m o le f o r IrO ^ i n th e 1627 t o 2227 ° C ra n g e r e p o r t e d by
0
O l i e v i . TheA
v a l u e s show a s i m i l a r i n c r e a s i n g t r e n d w ith te m p e r a tu re
0
T h is was m o s tly th e c a s e , f o r A S „ f o r IrCL o f
I
3
O
- 7 .1 6 eu o f th e p r e s e n t work i n t h e 1600 t o 2200 -C ra n g e when co m p arin g
, 0
0
t h e A S j, v a lu e s o f -1 0 t o -1 5 eu f o r MO^ a t 25 C r e p o r t e d by S e a rc y , th e
f o r MoO.-» HOj, and I r O j .
3
.
3
-13« 1 - 2 .5 eu f o r IrCL in th e 1557 t o 1760 C ra n g e by Norman e t a l , and •
■ " 0
't h e - 9 .0 eu f o r IrCL i n th e 1627 t o 2227 C ra n g e r e p o r t e d by O lie v i. The
0
\
0
A S^1 f o r IrO ^ o f - 7 .1 6 eu i s m ost d i r e c t l y co m p arab le t o , and was se e n t o
b e somewhat lo w e r ■th a n .-th e - 9 . 0 eu b e c a u s e o f th e s i m i l a r te m p e r a tu r e r a n g e s
o f 1600 t o 2200
C and 1627 t o 2227
C re s p e c tiv e ly .
SUMMARY AND CONCLUSIONS
I t was s e e n t h a t th e m ain s p e c ie s p r e s e n t in th e o x id a tio n o f ir i d iu m
a r e IrO g , I r O y an d I r w ith th e l a t t e r b e in g im p o r ta n t o n ly a t th e 2200
le v e l.
0
.
0
E x cep t f o r th e i n c l u s i o n o f I r a t 2200 C t h e s e r e s u l t s c o in c id e
•w ith th e l i m i t e d t h e o r e t i c a l s u c c e s s o f Tem pero' s work i n th e f o r c e d con­
v e c t i o n o x id a tio n o f ir id iu m a r e a .
The t h e o r e t i c a l l y p r e d i c t e d r e c e s s i o n
C
r a t e s , by u se o f e q u a tio n ( 14) , y e i l d e d a mean -$ e r r o r from ex p e rim e n t
o f 13. 4 > I -U S 1 and 15»0/o a t 1600, 1900, and 2200
o v e r a l l mean '% e r r o r - o f
fo u n d f o r
0'
and
2200 °Q and a r e ;
0
G r e s p e c t i v e l y , o r an
f o r th e 1600 t o 2200 6 G r a n g e . " V alu es w ere
f o r IrOg and IrO ^ f o r th e te m p e r a tu r e ra n g e 1600 t o
35*7 k c a l/m o le and 4*77 eu an d ;
e u , in t h e i r r e s p e c t i v e o r d e r s .
8 .6 3 k c a l/m o le a n d '- 7 .1 6
40
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■ "I
'I
41
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23«
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MONTANA STATF UMTVFDCn-v , T r ,r..* .__
'vv'^V/I y
V f M
w378
K868
cop . 2
K r a u s, H a l Gene
H a tu ra l c o n v e c tio n
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
Anp aopi»«*»
i
- :
(
/r,
A /4 7 ?
-I