Corrosion Chemistry - American Chemical Society

3 High-Temperature Corrosion J. B R U C E W A G N E R , JR.

Downloaded by STONY BROOK UNIV SUNY on December 12, 2016 | http://pubs.acs.org Publication Date: January 31, 1979 | doi: 10.1021/bk-1979-0089.ch003

Center for Solid State Science, Arizona State University, Tempe, A Z 85281

T h e p u r p o s e of t h i s review p a p e r is to s u r v e y the princi ples of h i g h t e m p e r a t u r e o x i d a t i o n o r h i g h t e m p e r a t u r e corro s i o n . A typical s i t u a t i o n is that of a m e t a l e x p o s e d to a hot gas w h i c h c a n act a s a n o x i d a n t . In m a n y c a s e s the o x i d a t i o n pro duct f o r m s a layer w h i c h s e p a r a t e s the r e a c t a n t s , the m e t a l and the gas a t m o s p h e r e . U n d e r special c o n d i t i o n s , the k i n e t i c s a r e d i f f u s i o n c o n t r o l l e d , i.e., the r a t e of the reaction (the r a t e of o x i d e t h i c k n e s s g r o w t h ) depends on the d i f f u s i o n of s p e c i e s , i o n s and e l e c t r o n s , t h r o u g h the layer ( s o m e t i m e s c a l l e d a tar nish layer). Actually when a m e t a l o r alloy is e x p o s e d to a cor rosive g a s , the r e a c t i o n k i n e t i c s m a y be c o n t r o l l e d by one o r m o r e of the f o l l o w i n g steps: 1. T r a n s p o r t of r e a c t a n t g a s e s to the s u r f a c e . 2. T r a n s p o r t of r e a c t a n t s ( o r p r o d u c t s ) t h r o u g h a b o u n d a r y layer adjacent to the s u r f a c e . 3. A s u r f a c e c o n t r o l l e d reaction ( p h a s e b o u n d a r y r e a c t i o n ) at the g a s - m e t a l i n t e r f a c e . 4. T r a n s p o r t of r e a c t a n t s t h r o u g h a corrosion p r o d u c t l a y e r e i t h e r b y b u l k d i f f u s i o n o r by migration t h r o u g h cracks and pores. In the p r e s e n t p a p e r , a t t e n t i o n will be f o c u s e d on the f o u r t h s t e p i n v o l v i n g b u l k d i f f u s i o n . T h i s is a classical electrochemical s i t u a t i o n i n v o l v i n g a n anode (the m e t a l ) w h e r e o x i d a t i o n o c c u r s and a cathode (the o x i d e at the o x i d e - g a s i n t e r f a c e ) w h e r e r e d u c t i o n of o x y g e n occurs. T h e o x i d e layer a c t s as the s o l v e n t f o r point defects w h i c h diffuse t h r o u g h i t as will be d i s c u s s e d b e l o w . C o n s i d e r the d i a g r a m s h o w n in Figure 1. T h e o x i d e layer t h i c k e n s w i t h t i m e and s o the r a t e of o x i d a t i o n ( g o v e r n e d by d i f f u s i o n t h r o u g h the o x i d e l a y e r ) d e c r e a s e s w i t h t i m e , t . T h i s s p e c c i a l s i t u a t i o n y i e l d s the p a r a b o l i c r a t e l a w f i r s t r e p o r t e d by T a m m a n (j_) and by P i l l i n g and B e d w o r t h (2). T a m m a n ' s rate e q u a t i o n was s t a t e d in t e r m s of t a r n i s h l a y e r t h i c k n e s s , ΔΧ, 0-8412-0471-3/79/47-089-076$05.00/0 © 1979 American Chemical Society

Brubaker and Phipps; Corrosion Chemistry ACS Symposium Series; American Chemical Society: Washington, DC, 1979.

3.

WAGNER

High-Temperature

Corrosion

77

and is

whence (ΔΧ)

2

= 2k.pt

(2)


where k^ is the Tamman rate constant with dimensions of c m sec. The Pilling-Bedworth rate equation was expressed in terms of weight change per unit area, Am/A. It is i ^ )

2

= V

2

/

(3)

where k is the Pilling-Bedworth rate constant with dimensions of gm /cm sec. These equations describe a parabolic law as is shown schematically in F i g u r e 2. O r i g i n a l l y it was thought that oxidation proceeded by the m i g r a t i o n of oxygen molecules through the product layer to the metal. A c l a s s i c experiment known as m a r k e r movement was performed by P f e i l (3^) in 1929 which in principle can d i s t i n guish whether the migrating species occurs f r o m the gas atmos phere inward or f r o m the metal outward through the oxide. ( F i g . 3 ) P f e i l placed some inert oxide particles ( m a r k e r s ) on the metal surface ( i r o n ) p r i o r to oxidation. A f t e r oxidation had proceeded for some time, he examined the c r o s s sections of the samples and determined the location of the inert oxide p a r t i c l e s , the m a r k e r s . It was found on i r o n that the particles remained at the metal-oxide interface indicating that the migrating species were the i r o n atoms diffusing f r o m the metal-oxide interface to the oxide-gas interface. If the m a r k e r s remained at the oxide-gas interface,then the inference would be that oxygen would have migrated inward towards the metal. These l i m i t i n g cases can be visualized by imagining the moving atomic species as impart ing momentum to the m a r k e r as they move past them. It p

2

4

* T h e two rate constants are related by

Ο

where Z Q denotes the valence of the oxidant (oxygen in the example), ν the equivalent volume of the oxide, and A Q the atomic weight of the oxidant.



CORROSION C H E M I S T R Y

film thickness, Δ χ or weight go in per unit area, Am/A

time

>

Figure 1. Schematic of film thickness or gaininweight per unit area vs. time for oxidation of a pure metal where diffusion is rate controlling. The kinetics are denoted as parabolic oxidation kinetics.

time Figure 2.

>

Schematic of parabolic oxidation kinetics replotted from data of Fig ure 1


3.

WAGNER

High-Temperature

79

Corrosion

remained for C a r l Wagner (4) to p e r f o r m the c l a s s i c e x p e r i ment to distinguish the mobile species in a c o r r o s i o n e x p e r i ment. H i s experimental set-up is shown in Figure 4. The overa l l reaction he studied was 2Ag(s) + S ( 1 ) = A g S ( s ) .


2

His set-up provided an a r t i f i c i a l reaction product l a y e r of two preweighed s i l v e r sulfide pellets separating the reactants, liquid sulfur and the s i l v e r pellet which was also preweighed. A f t e r one hour a l l the pellets were reweighed. The pellet adjacent to the liquid sulfur had gained 124 mg while the pellet adjacent to the s i l v e r had not changed weight but the s i l v e r pellet had lost exactly one milliequivalent of weight ( 108 mg). Thus for this system, s i l v e r migrates f r o m the s i l v e r pellet through both s i l v e r sulfide pellets and the reaction occurs p r i m a r i l y at the s i l v e r sulfide-sulfur interface. The mechanism of diffusion through the c o r r o s i o n product was s t i l l to be decided. C. Wagner proposed (4) that the m i grating particles involved ions and electrons, the ions migrating v i a defects. These lattice defects may be m i s s i n g cations or anions (vacancies ) or cations or anions located in i n t e r s t i t i a l positions. The state of stoichiometry, i.e. , s t r i c t adherence to Dalton's law is not usual in most inorganic compounds and the attainment of this state occurs only at well-defined temperatures and chemical potentials of the constituents. Krftger and Vink (5_) developed a notation for point defects whereby a l l the ions of usual charge on usual lattice sites are denoted without charges while the defects, vacancies or i n t e r s t i t i a l s , exhibit a charge relative to these ions on usual sites. Superior p r i m e s denote negative charges and superior heavy dots denote positive charges. Consider an oxide, MO, wherein both ions are normally divalent. The disorder in stoichiometric c r y s t a l s may be classified in the following l i m i t i n g cases and an equilibrium constant (a function of temperature only) relates the concentrations of each as follows: 1. Schottky Disorder: Equal concentrations of cation vacancies and anion vacancies K

2.

=

V

(4)

V

^ M^ 0^

F r e n k e l Disorder: Equal concentrations of cation vacan cies and interstitial cations K

3.

s

F

=

^

(5)

^

Anti-Schottky Disorder:

Equal concentrations of cation




METAL OXIDE

inert

BEFORE OXIDATION

M A

«

AFTER

inert markers

OXIDATION

Figure 3. Schematic location of inert markers before oxidation (on the surface of the pure metal) and after oxidation (at the metal-metal oxide interface). From this limiting case one may infer that the mobile species diffuses from the metalmetal oxide interface outward through the scale or tarnish layer. If the marker were found at the oxide-gas interface, the inference would be that the mobile species diffused from the oxide-gas interface to the metal-oxide interface.

S (liquid) + 2Ag -2e-=Ag S •===• S R

+

2

2Ag+ 2e~ ] Ag -108 mg Figure 4. Schematic of the experimental setup used by C. Wagner (4) to determine the location of the reaction 2kg + S = Ag S and the migrating species (silver) through the artificially prepared tarnish layer of Ag S separating the reactants, silver and liquid sulfur 2

2


3.

WAGNER

High-Temperature

81

Corrosion

and anion interstitials A-S

K

4.


M

i ^

(*>

A n t i - F r e n k e l D i s o r d e r : E q u a l c o n c e n t r a t i o n s of a n i o n vacancies and anion interstitials K

5.

= t ° i ^

_

A

F

= [O';][O:']

(7)

Anti-Structural Disorder: and anions on cation sites K

Anti-Str.

^

=

M

Cations located on anion sites

0 ^ ° M ^

(

8

)

The above considerations apply to stoichiometry. Fornons t o i c h i o m e t r i c c o m p o u n d s , the e x c e s s o r d e f i c i t of a component m a y a l s o be e x p r e s s e d b y e q u i l i b r i u m constants a n d c h e m i c a l equations. In v i e w of the l i m i t a t i o n s of s p a c e , c o n s i d e r a f e w s e l e c t e d examples. T h e o x i d a t i o n o f c o b a l t is o n e o f t h e b e t t e r s t u d i e d systems. C o b a l t o u s o x i d e is a m e t a l d e f i c i t c o m p o u n d . The r a t i o o f C o t o Ο is l e s s t h a n o n e . A t a g i v e n t e m p e r a t u r e t h e e q u a t i o n f o r t h i s s i t u a t i o n m a y be w r i t t e n a s o (g)

i

2

= o

0

+ v ^

o

+h*

(9)

w h e r e t h e n o t a t i o n o f K r 8 g e r a n d V i n k is a g a i n u s e d . S u p e r i o r p r i m e s and heavy dots denote effective negative and positive c h a r g e s , r e s p e c t i v e l y . Ions o n n o r m a l l a t t i c e s i t e s are designated with no effective charge while defects a r e d e s i g nated w i t h e f f e c t i v e c h a r g e s r e l a t i v e to the n o r m a l i o n s . Thus a n i c k e l o u s i o n o n a n o r m a l s i t e in n i c k e l o x i d e is d e n o t e d a s N i - ^ a n d a n i c k e l i c i o n in N i O w o u l d b e d e n o t e d a s N i j ^ . T h e " e x t r a " o x y g e n is a c c o m o d a t e d o n a n o r m a l l a t t i c e s i t e a n d a cobalt i o n vacancy (with a single effective negative charge) plus o n e c o m p e n s a t i n g e l e c t r o n h o l e is f o r m e d . A n a l t e r n a t i v e d e s c r i p t i o n o f t h e e l e c t r o n h o l e is a c o b a l t i c i o n ( C o or Co ) s i t u a t e d in a s u b l a t t i c e o f n o r m a l l y c o b a l t o u s i o n s . T h e e q u i l i b r i u m c o n s t a n t f o r E q . ( 9 ) is w r i t t e n a s + + +

Κio

= [v£ ][h*]/

K

= exp(-AG^Q /RT)

1

0

p*

o

2

(10)

2

= e x p C f - Δ Ϊ ^ +TAS^)/RT]


(11)


82

w h e r e A G | O > Δ Η | Ο a n d A s | o denote the p a r t i a l m o l a r f r e e e n e r g y , e n t h a l p y a n d e n t r o p y of d i s s o l u t i o n of o n e - h a l f m o l e oxygen into cobaltous oxide. In v i e w of the r e q u i r e m e n t of e l e c t r i c a l n e u t r a l i t y in t h e o x i d e [ ν £ ] Ρ "]· Consequently, 2

2

2

=

0

κ

1 0

= C v ^

2

/ P

0

2

l

=

C

h

'

1

]

2

/

4

(

T h u s i f one s o l v e s e x p l i c i t l y f o r the c a t i o n v a c a n c y Downloaded by STONY BROOK UNIV SUNY on December 12, 2016 | http://pubs.acs.org Publication Date: January 31, 1979 | doi: 10.1021/bk-1979-0089.ch003

o r the e l e c t r o n hole

1

2

)

concentration

concentration,

- ^ « • " - - S ^ *

- 2 ^ - » ·

(

1

3

)

Because D ç ce [ V < ^ ] t h e n i f o n e m e a s u r e d t h e r a d i o t r a c e r d i f f u s i o n o f c o b a l t in C o O , t h e i s o t h e r m a l o x y g e n p r e s s u r e d e p e n dence should exhibit a one-quarter dependence. T h i s is e x a c t l y w h a t C a r t e r a n d R i c h a r d s o n (6_) d i d . T h e i r r e s u l t s a r e s h o w n in F i g u r e 5. T h e e l e c t r o n i c c o n d u c t i v i t y , σ , is Q

0

a=[h]u q

(14)

h

w h e r e the s y m b o l u, d e n o t e s the m o b i l i t y of a n e l e c t r o n h o l e a n d is h e r e a s s u m e d n o t t o b e d e p e n d e n t o n c o m p o s i t i o n . Be c a u s e [ h ] cc p o f t h e n t h e i s o t h e r m a l e l e c t r o n i c c o n d u c t i v i t y s h o u l d a l s o be d e p e n d e n t u p o n the o n e - q u a r t e r p o w e r of the oxygen pressure. T h i s behavior was r e p o r t e d by E r o r and W a g n e r (7_) ( s e e F i g u r e 6 ) . T h e d i f f u s i v i t y o f o x y g e n is n e g l i g i b l e c o m p a r e d to c o b a l t a c c o r d i n g to m a r k e r s t u d i e s and t o s t a b l e o x y g e n i s o t o p e d i f f u s i o n s t u d i e s ( J^O » JJL) · Thus w h e n c o b a l t is o x i d i z e d , t h e m i g r a t i n g s p e c i e s s h o u l d b e cobalt v i a cation vacancies and electrons (as electron holes). F o r an oxide g r o w i n g on a m e t a l by a bulk diffusion c o n trolled process,

C. Wagner ( 4 ) derived an expression for

the

flux as

η A

eq c m sec z

_

RT ΔΧ F

f ° P

2

2

2

(t

1 +

t )t q 2

|£ | 2

u p

o

3

ffOj P Q

2

2


1 ) . T h e e q u a t i o n m a y be written as =

1

4

2

ZnO = Zn* + e'

+ 1/2 0 .

The corresponding e q u i l i b r i u m constant K

2

2

= [Zn!][e'] ι

(21)

2

· p i u

and electroneutrality condition

is (22)

2

is

[Zn:]=[e']


(.23)

86


so that [Ζη']

=/K

1

2 2

p

u

(24) 2


H e n c e , i n c r e a s i n g the o x y g e n p r e s s u r e o v e r z i n c o x i d e g r o w i n g o n z i n c m e t a l a f f e c t s the o x i d a t i o n r a t e v e r y l i t t l e b e c a u s e d i s f u s i o n t h r o u g h z i n c o x i d e is v i a i n t e r s t i t i a l z i n c i o n s . These l i m i t i n g c a s e s a r e s h o w n s c h e m a t i c a l l y in F i g u r e 8 ( 1 3 ) , T h e t e m p e r a t u r e d e p e n d e n c e o f t h e k i n e t i c s at c o n s t a n t o x y g e n p r e s s u r e is o f t e n p l o t t e d a s l o g k p o r l o g krp v e r s u s 1/T. In a d d i t i o n to the m i g r a t i o n e n t h a l p y of the m o b i l e s p e c i e s , the s l o p e of s u c h a n A r r h e n i u s p l o t m a y r e f l e c t a n e n t h a l p y f o r the c h a n g e in c o m p o s i t i o n o f t h e o x i d e w i t h t e m p e r a t u r e . T h e o x i d a t i o n r a t e of a p u r e m e t a l m a y be c a l c u l a t e d f r o m s e l f d i f f u s i o n d a t a . C o n v e r s e l y , o x i d a t i o n k i n e t i c s m a y be u s e d to c a l c u l a t e s e l f d i f f u s i o n d a t a . E q . ( 18) m a y be r e a r r a n g e d a n d the r a t e c o n s t a n t d i f f e r e n t i a t e d w i t h r e s p e c t to l o g o x y g e n p r e s s u r e to y i e l d CrfhD? ' I

D

+

2

} =

f ^ eq

(25)

C

d l n

P

Corrosion Chemistry - American Chemical Society

Recommend Documents