Creep and oxygen diffusion in magnetite

Acta metall, mater. Vol. 38, No. 12, pp. 2567-2572, 1990

0956-7151/90 $3.00 + 0.00 Copyright © 1990 Pergamon Press pie

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CREEP A N D OXYGEN DIFFUSION IN MAGNETITE A. G. C R O U C H and J. R O B E R T S O N Central Electricity Research Laboratories, Central Electricity Generating Board, Kelvin Avenue, Leatherhead, Surrey KT22 7SE, England (Received 4 May 1990)

Abstract--The creep rate of polycrystalline Fe 304 has been measured as a function of stress and oxygen partial pressure in the temperature range 480-I 100°C. A regime of power law creep is found at high stress, with a stress exponent of -~3.1 and an activation energy of 264 kJ/mol. A regime of diffusional flow is found at lower stresses and is interpreted as Nabarro-Herring creep. The data for the two regimes are combined to deduce an oxygen diffusion coefficient of --10 -s exp(-264 kJ/mol/RT)m 2 s -I, with oxygen vacancies suggested as the mobile species. R~sum~-La vitesse de fluage de Fe304 polycristallin est mesurre en fonction de la contrainte et de la pression partielle d'oxygrne dans la gamme de temprratures 480 l l00°C. Un rrgime de fluage avec une loi de puissance est trouv6 pour de fortes contraintes, avec un exposant de contrainte de ==_3,1 et une 6nergie d'activation de 264kJ/mol. A des contraintes plus basses, on trouve un rrgime d'rcoulement par diffusion qui est interpr~t6 comme du fluage de Nabarro et Herring. Les donnres pour ces deux rrgimes sont combinres pour obtenir un coefficient de diffusion de l'oxygrne de l'ordre de 10-Sexp(-264kJ/mol/RT) m 2 s -~, les lacunes d'oxygrne 6tant suggrrres comme les drfauts mobiles. Zusammenfassung--Die Kriechrate von polykristallinem Fe304 wird in Abh/ingigkeit vonder Spannung und dem Sauerstoff-Partialdruck im Temperaturbereich zwischen 480 und 1100°C gemessen. Bei hoher Spannung finder sich ein Bereich des Potenzgesetzkriechens; der Spannungsexponent betr/igt =3,1, die Aktivierungsenergie ist 264 kJ/Mol. Ein Bereich des diffusionsgesteuerten Fliel3ens findet sich bei niedriger Spannung; dieser wird dem Nabarro-Herring-Kriechen Zugeschrieben. Aus den Ergebnissen zu diesen beiden Bereichen wird ein Sauerstoff-Diffusionskoeffizient von -~ 10-5 exp(-264 kJ/mol/RT) m 2 s -1 abgeleitet, wobei die Sauerstoff-Leerstelle der naheliegende bewegliche Defekt ist.

1. INTRODUCTION The oxide scales which grow on metal components exposed to high temperature environments will protect the metal from rapid degradation provided that they remain continuous and attached to the metal [1-4]. However, stresses arising from either the oxidation process itself or external sources can often cause a cracking or detachment of the scale due to a build-up of elastic strain [1-3]. The magnitude of the elastic strain can be reduced if the scale is able to deform sufficiently by creep in the timescale of the stress application [3, 4]. Therefore, the creep behaviour of protective oxides is of considerable interest in the field of oxidation. However, while the creep behaviour of A1203, Cr203, Fe203, NiO, CoO, M n O and FeO have each been investigated [5-13], that of the most c o m m o n scale forming oxide, magnetite, Fe304, has not. This paper presents data on the deformation rate of polycrystalline Fe304 samples in the temperature range 480-1100°C and stress range 0 . 5 - 2 7 M P a at defined values of oxygen partial pressure. Two creep regimes are observed, a regime of power law creep attributed to dislocation climb, and a regime of diffusional flow attributed to N a b a r r o - H e r r i n g (intra-grain) creep. AM3S/~2--M

In compounds, the rates of mass transport processes such as creep or grain growth are controlled by the self-diffusion coefficient of the slowest moving species. Conversely, the growth rate of an oxide by oxidation is proportional to the self-diffusion coefficient of the fastest species. Fe is generally believed to diffuse faster than oxygen in magnetite, although only the diffusion of Fe has been explicitly measured under the relevant conditions. In this paper, the creep data are used to deduce an oxygen self-diffusion coefficient for magnetite and it is found that Fe is indeed more mobile than oxygen. 2. EXPERIMENTAL The Fe304 specimens were prepared by the reduction of Fe2 03. The Fe 203 specimens were identical to those used in earlier creep measurements [8] on Fe203. They were prepared by isostatic pressing and sintering of Fe203 powder of impurity content - 2 p p m . These specimens were then reduced to Fe304 by annealling in a 1.5% CO/CO2 gas mixture at 1000°C for 60 h, during which the transition from haematite to magnetite was monitored by a 4-probe conductivity technique to a constant resistance level, typically < 0.5 f~, and subsequently by X-ray diffraction.

2567

2568

CROUCH

and ROBERTSON:

CREEP

AND

The creep rates were m e a s u r e d by deforming the specimens at c o n s t a n t load o n a four point bending a p p a r a t u s as described earlier [8], modified to allow a t m o s p h e r e control a n d the remote c h a n g i n g of applied loads. Tests were carried out at c o n s t a n t load to give two ranges of outer fiber stress, 0.53, 0.86,

OXYGEN

DIFFUSION

IN MAGNETITE

Table 1. Fitting of creep rates at each temperature, T, and gas composition, % CO, to ~ = A a " = A'(a/a)'. A' is the prefactor normalised to a mean stress o f a = 10 MPa ( < 798°C) or a = 1 M P a ( > 798'~C)

T(°C) 480 497

%CO 1.5 1.5

tr(MPa) 20 5-27

log]0(A' )

n

--

11.51 -11.44

3 3.03

529

1.5

20

- 10.66

3

5-27

--7.81

1.19, 1.52, 1.86 a n d 2.35 M P a a n d 5.05, 9.43, 13.25, 20.17 a n d 27.41 MPa. The first range of stresses was used for the higher t e m p e r a t u r e tests, which was largely limited by the m i n i m u m weight o f loading assembly t h a t could be achieved. Generally, loads were applied in a n increasing sequence. Measure-

566 602 610 663 679 679 679

1.5 1.5 1.5 1.5 0.1 1.5 10.1

20 %20 9 9-27 13 20 5-20 5-20

m e n t s were repeated at selected stresses to confirm the stability of the creep rates. D e f o r m a t i o n was limited to 5 % total strain. As F e 3 0 4 is only stable in a reducing atmosphere, the tests were carried o u t in a reducing a t m o s p h e r e of C O 2 a n d 0.1, 1.5 or

715 778 778 778 797 798

1.5 0.1 1.5 |0.1 1.5 10.1

10.1 v o l . % CO. The gas mixtures were passed t h r o u g h a molecular sieve a n d over platinized asbestos to m a i n t a i n the effective oxygen partial pressure.

897 900 990

Following any change in temperature, stress or C O level, specimens were allowed to re-equilibrate or to

990 I000

712

897

990

1000

achieve steady-state conditions, as determined by a c o m p a r i s o n of successive strain rate measurements.

-10.09 -9.64 -9.08 - 8.52 -9.00 -7.71 -7.46

3 4.14 3 3.47 4.28 1.84 3.68

5-20 13 5-20 13 5-20 0.67

-7.33 -6.70 -- 6.28 -5.74 -6.19 -9.21

3.10 3 3.68 3 3.10 1

10.1 1.5 0.1

0.67 0.86-2.35 0.67

-9.21 -8.94 -8.32

1 2.45 1

10.1 0.1

0.67 0.592.75

-5.96 -8.22

1 1.97

1.5

1.5

0.67

1.5

3.26

-9.73

0.67

1

-7.32

I

1000 1100

10.1 0.1

1.5

0.53-2.75

-7.19

1.57

1100 1100

1.5 10.1

0.53-2.75 0.53-2.75

-6.77 -6.70

1.20 1.10

0.53-2.75 0.53 2.75

-6.45 -7.19

1.08 1.38

3. RESULTS T h e majority of reliable creep rates were o b t a i n e d o n two specimens, one tested at high stress levels up to 797°C a n d one at lower stresses above 797°C. The creep rate vs stress values for each t e m p e r a t u r e a n d gas c o m p o s i t i o n were fitted to a power law o f the form =Aa"

(1)

a n d the resulting values o f A a n d n are given in Table 1. The d a t a for 1.5% C O for b o t h specimens are s h o w n in Fig. 1. A is given in Table 1 as A ' , a value normalized to a m e a n stress o f 10 M P a for the high stress tests a n d 1 M P a for the low stress tests. The d a t a for temperatures below 798°C are seen to c o n f o r m to power law creep with a stress e x p o n e n t of n = 3. W h e n tests were carried o u t at only one stress, the value o f A ' given in Table 1 assumes n = 3. The creep rates above 798°C were m e a s u r e d at lower stress levels. U n f o r t u n a t e l y , the two sets of d a t a barely overlap. These rates fitted to e q u a t i o n (1) give a lower stress e x p o n e n t which declines with increasing temperature, tending to n = 1 at 1100°C. The oxygen activity, ao2, is defined by the CO2 to C O pressure ratio as

Figure 2 shows the activity dependence at 679°C. The d a t a show considerable scatter, b u t overall a m e a n value o f m ~ 0.59 was f o u n d for this regime. The C O dependence at 1000°C in the low stress regime is s h o w n in Fig. 3. There was m o r e data in this regime. A dependence of m ~- - 0 . 7 is f o u n d at 1000°C a n d m ~ - 0 . 2 at 1100°C. Overall, a value of m ~- - 0 . 5 6 is f o u n d for this regime. The m a g n i t u d e of the rates at 1100°C, 10% C O a n d 990°C, 10% C O a p p e a r to be too low, p e r h a p s because they were the last to be m e a s u r e d o n the specimen a n d it m a y have accumulated too m u c h strain.

10"6 104

10-7

1100o

"~1000°

715o

~

7121 663

L"

778

10"8 10"9

610o+/

X 566°

/

10-10

= Kc (P_c°2") 2

a%

\P--~o/

X 897 °

.~0

+

629°

(2)

with [15] Kc = 1.17' 109 e x p ( - 67.5 k J / m o l / R T ) . The dependence of creep rate o n the oxygen activity was f o u n d by fitting ~ at any t e m p e r a t u r e a n d stress to

10"11

~ o

407°-

T (°C)

10"lz I [1111 0 1

,

~ , I ,,,,I

10

,

I t

o" (MPo)

\Pco /

Fig. 1. C r e e p r a t e v s stress f o r 1.5% C O a t 4 8 0 - 1 1 0 0 ° C .

CROUCH and ROBERTSON:

CREEP AND OXYGEN DIFFUSION IN MAGNETITE

The temperature dependence of creep in the power law regime was found by fitting the creep rate, normalized to 1.5% CO and the mean stress of 10 M P a (A' in Table 1), to an Arrhenius law, giving = 7.9.10-16 0.3.09 e x p ( - 280 k J / R T ) s -l

I

lOne*e

2569

I

(4)

or

104

d=3.36"10

150.3exp(-264kJ/mol/RT)s

i

(5)

if it is contained to obey a n = 3 law. The latter fit is illustrated in Fig. 4. The temperature dependence of the lower stress regime is less well-defined. This is shown in Fig. 5, normlized to a mean stress of 1 M P a and 1.5% CO. The data is reasonably consistent with the expression g

=

2.53" 10-3 a exp(--264 k J / m o l / R T ) s -l

~o.53

(6)

which is also shown in Fig. 5. The two sets of data are consistent with two concommitant creep processes, i.e. a creep rate given by the sum of rates (5) and (6) =

lO-a

10 .9

I 103

102

L 104

PCO 2 / P C O

Fig. 3. Creep rate vs CO content at 1000°C for indicated stresses.

(2.53- 10 -3 0- + 3.36- 10 -15 a 3) × e x p ( - 2 6 4 k J / m o l / R T ) s -l.

(7)

Figure 6 shows this expression compared to a selection of the observed creep rates. The expression is seen to reproduce the observed rates reasonably well, particularly at high stresses, but its main error is that it underestimates the stress level at which creep changes from an n = 1 to an n = 3 regime.

of the difficulties is extracting diffusion coefficients from creep rates for oxides are discussed by Philibert [15] and Chokshi [16]. Creep in the lower stress regime, equation (6), is attributed to diffusional flow of the N a b a r r o - H e r r i n g (intra-grain) type. This mechanism produces a creep rate given by [15-19] al (0.7b 3)D0-

d2kT

-

4. DISCUSSION The oxygen self-diffusion coefficient in magnetite, D Ocan be deduced from the present creep data. Some

where ~ = 0 . 7 b 3 is the atomic volume, b is the Burger's vector, D is the self-diffusion coefficient of the rate determining species, d is grain size, k is the 10"|

1°4 o" (MPa)

I

20.17°

(8)

I

'

I

~

I

~

I

~

I

MPa,1.15%C0

r 10"7

679°C

104 104 T3.2B~ '~ 10"°

10"1¢

m

10"11

lO'~/

I loz

I lO~

I lO4

PCO,:, / PCO

Fig. 2. Creep rate vs CO content at 679°C for indicated stresses.

I~ n

I

9

,

I

10

,

I

11

,

I

12

,

I

13

104"/T(K)

Fig. 4. Temperature dependence of the normalized creep rate for the power law creep regime.

2570

CROUCH and ROBERTSON:

CREEP AND OXYGEN DIFFUSION IN MAGNETITE

Boltzman constant and T is the absolute temperature. This assignment is consistent with the relatively small grain size of the specimens although strictly a dependence on grain size d as d - 2 must be observed to confirm this. Creep in the power law regime is attributed to a dislocation climb mechanism. This gives a creep rate of [15-19] kT

\G,i

d=10/~m

_

"Y/S

lO-S

10-7 -

/ ./..4/7 ;/././.

(9) ,w

where G is the shear modulus. We take b=0.3nm,

10"$

and

10"9

G=94GPa, 10-10

the latter from the single crystal elastic constants [20] using G = [0.5(eli - c1=)c44]°'5. The rate determining diffusion coefficient D, can be found from the two prefactors in (7). al and a 2 are constants. Early treatments of diffusional flow gave a value of a I ~ 14 but more recent work suggests a~ ~- 42 [17, 19]. a 2 Is the D o r n constant which takes a value of a 2 ~ 1 for n = 3 [19]. However, it increases very strongly if n > 3 [21]. The prefactors in (7) actually favour a lower value of a~ and a higher value of a 2 than suggested theoretically. Bearing in mind that our data for the power law creep regime are better, while the theoretical basis for a, is firmer, we take a i -- 14, a 2 = 116 and obtain D o = 1.2. l0 -5 e x p ( - 2 6 4 k J / m o l / R T ) m 2 s -l.

(10)

The consistency of our description of creep was checked by calculating a deformation map for Fe3 04, following the procedures of Frost and Ashby [19]. Figure 7 shows a deformation map for a l0 g m grain size and an oxygen activity of a CO2, 1.5% C O gas

10-8

I

I ~-Ao 1 MPa, 1.S%CC

10-11

10-12 10"1

102

(MPo)

Fig. 6. Comparison of observed creep rates with expression (7). mixture. Three extra regimes are added to complete the map, due to diffusional flow along grain boundaries (Coble creep), to power law creep at low temperatures by the climb of dislocations along their cores and to plastic flow. The parameters used to describe these regimes were taken as follows. A grain boundary diffusion parameter of t~Db = 1.2. l0 -15 e x p ( - 167 k J / m o l / R T ) m 3 s -l, is used for the Coble creep regime, where 6 is the grain boundary thickness. These values were chosen to maintain an n = 3 regime over a sufficiently large stress range at 700°C. The low temperature power law creep has a stress exponent of n = 5 and a dislocation core diffusion parameter chosen to be a c D c = 2.1. l0 -25 e x p ( - 167 k J / m o l / R T ) m 4 s -1,

10-1

~ l

10.7

000 I

,

120o ,

,

1~o0c

IlO"

Fe304, GRAIN SIZE ~ 10 pm I 10":

im

~

103

1o-2-

\\~,~

DISLOCATION

~ "~

\

\

~

\

~

-11o~

~le-l~

i

b 10.4

10-s

10

1o-._DiFFU61ONAL FLOW 10-i

10

1

I

I

8

9

10

IO4/T(K)

Fig. 5. Temperature dependence of the normalized creep rate for 800-1100°C.

0.2

\\

~,

\

BOUNDARY \ I \ BULK\ (COBLE| \ ! ~(N.H.) \ . . . . . . . . . . . . . . 0.4 0.6 0.8

\

-I10-, I

\ ~ ~

I J

2 10" 1.0

T/T M

Fig. 7. Deformation map for Fe304 for a grain size of 10/~m and an oxygen activity of a CO 2, 1.5% CO gas mixture.

CROUCH and ROBERTSON: CREEP AND OXYGEN DIFFUSION IN MAGNETITE where ac is the core cross-sectional area. These values were chosen to maintain a stress exponent of n - 3 down to ~ 500°C, as observed. The plastic regime is described by the standard oxide values [19] of a 0 K flow stress of 0.05 G and a plastic/climb boundary of 0.005 G. The resulting map and parameter values show that a reasonably consistent description of creep in Fe 304 has been found. It has been suggested that the creep of polycrystalline oxides in CO2 can be affected by the intergranular deposition of carbon [22]. This is not expected to affect our results as the deformation map confirms that our data involve only intragranular transport regimes, which are not affected. The value of D,~ in equation (10) can also be compared to that found in similar systems (Fig. 8). O'Bryan and DiMarcello [23] found

in NiCr204 spinel at 1200-1500°C, according to the data in their Fig. 2. A slightly lower value of D o might be expected in NiCr204 spinel than in magnetite because its cation diffusion coefficients are also lower. Figure 8 also shows the value of Do measured in magnetite under hydrothermal conditions by Castle and Surman [25] at 300-550°C and Gilette and Hess [26] at 500-800~C. It is difficult to evaluate the results of Castle and Surman because of their very low activation energy, but it is seen that the magnitude of their Do is not too different from ours. The values of Gilette and Hess [26] are also quite similar to ours, but lie a little lower at higher temperatures because of their lower activation energy. The diffusion of oxygen could be mediated by either oxygen vacancies of interstitials, giving rise to a diffusion coefficient of general form (11)

where [V] and [I] are the concentration of vacancies and interstitials, respectively. Vacancies are formed according to the equilibrium (12)

so their concentration is given by mass action as

[Vo] = Kvoao2m

(13)

with a negative exponent of a%. No charge is assigned to the defects because of the metallic character of magnetite. Conversely, interstitials are formed according to ½02 = Io

10-14

'"'"

O00

I '

400

I i

l

X '%%

I,

~

I

i

300°C I D D°

....

\%%%DF*

F

\\ \, iX \', ", Fo~mNi o~04

'~ 1¢0

FeaO4(CREEP)

lo -~

~,,~4104

I 6

I 8

I 10

I 12

(H)

I I'~ 14 16

lS

20

lO4/T(K)

D O= 2.6- 10 -8 e x p ( - 2 9 5 kJ/mol/RT) m 2 s -z

½0z + Vo = 0

iCr20'

800

i

10=

at 1140-1340°C in single crystals of the closely related Ni ferrite spinel, Fe2.s2Ni0.6804, very similar to D Oin equation (10). Kingery et al. [24] measured

D,[I]

' I

~

D O= 5.10 ~e x p ( - 255 kJ/mol/RT) m 2 s -1

D = Dv[V] +

1200

i0"Iz

2571

(14)

Fig. 8. Diffusion coefficients of Fe and O in magnetite, Ni ferrite, NiCr204 and magnetite under hydrothermal conditions (H). giving [I1 =

K,oa~~

(15)

with a positive exponent of ao2. The creep rate of magnetite was measured at three Pco values and was found to vary with (PcojPco)" and m = -0.56. This is equivalent to a variation as a3~ ']z by equation (3), a negative exponent, and so is consistent with oxygen diffusion mediated by vacancies. However, it is not clear why the magnitude of the exponent exceeds the theoretical values by a factor of two. Other data on the identity of the mobile oxygen species is contradictory. O'Bryan and DiMarcello [23] found that Do of Ni ferrite increased with increasing a%, consistent with transport by oxygen interstitials. The Ni ferrite used is very similar to magnetite but it has a slightly narrower stoichiometry range [23, 27] because the Ni remains divalent. On the other hand, Yan [28] found that grain growth in Fes 04, which is also limited by oxygen diffusion, increased rapidly with decreasing a%, consistent with oxygen vacancy transport, although their measured activation energy was too high. The nature of the defects may change under hydrothermal conditions. Nevertheless, Castle and Surman [25] found that D o under hydrothermal conditions varied as ao °5, as required for oxygen vacancies, while Gilette and Hess [26] found little dependence on a% at all. The source of these various differences is unclear. It is finally of interest to confirm that Fe is indeed more mobile than oxygen in magnetite. The tracer diffusion coefficient of Fe, D%, has been measured

2572

CROUCH and ROBERTSON: CREEP AND OXYGEN DIFFUSION IN MAGNETITE

by Dieckmann and Schmalzried [29] as a function of temperature and oxygen partial pressure. D ~e was found to be mediated by both Fe vacancies and interstitials, denoted life and IFo, respectively. This causes D*~ to be strongly dependent on ao2 O*e -- ~v-o2A ~2/3 + dlao2/3

(16)

because the vacancy and interstitial concentrations depend strongly on ao2. Fe vacancies are created according to equilibrium 202 = 1/3 Fe304 + VF~

(17)

and their concentration is given by mass action as [ V ] = / ¢J". v t~2/3 402.

(18)

The concentration of interstitials is given analogously. The ao2 dependence in (16) causes D?e to have a pronounced m i n i m u m denoted DF~n at a particular value of a o where dv = d~. This m i n i m u m value plotted in Fig. 8 confirms that D o is indeed lower than DF~ in magnetite, on average, but it is also seen that D Obarely exceeds DF"~n at that specific value of ao2. A n advantage of using COs, CO mixtures is that the temperature dependence of K~ in equation (2) is similar to that of the stoichiometry coefficient of magnetite. Hence, while DFm~ n occurs at a a% which varies rapidly with temperature, it occurs at a relatively stable CO content of = 1%, independent of temperature. The oxidation rate of Fe to magnetite is controlled by the Fe diffusion rate, provided that interfacial reaction rates are fast. The relevant Fe diffusion rate is now given by that of D*~ integrated across the appropriate stoichiometry range of magnetite [30]. It • ~-. is denoted here by D*e and ls considerably larger than DF~~ (Fig. 8). It has been shown to be consistent with the observed oxidation rates [30, 31]. Magnetite therefore appears to conform to the structural trend for diffusion coefficients in the series MO, M304and M 2 0 3. In the divalent oxides with the rocksalt structure, MnO, NiO, CoO and FeO, cation diffusion is much faster than oxygen diffusion. NiO has been particularly studied in this respect [31]. In the hexagonal oxides A1203, Cr203 and Fe203, the cation and oxygen diffusion rates are more nearly equal [31-35]. The bulk diffusion rates for cations seem to be the larger in Al 203 and Cr 203 but the rates seem to be similar in Fe203. Magnetite is an intermediate case, its cations diffuse faster than its oxygen ions, but by a smaller ratio than in NiO. Acknowledgements--The authors are grateful to M. R. Taylor and M. I. Manning for help with the numerical analysis. This paper is published with the permission of the Central Electricity Generating Board.

REFERENCES

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