Cation self-diffusion and the isotope effect in Fe2O3

J Phys Chem Sdrds Vd

46, No

3, pi

315-382,

1985

0022-3697/85 $3 00 + 00 Rrgamon Rew Ltd

mntedIntheUSA

CATION

SELF-DIFFUSION AND THE ISOTOPE IN Fe203f

EFFECT

K. HOSHINO and N. L. PETERSON Materials Science and Technology Dlvlsion, Argonne Natlonal Laboratory, Argonne, IL 60439 (Recewed 19 July 1984, accepted 13 September 1984) Abstract-Self-diffusion of “‘Fe parallel to the c axis m single crystals of Fe203 has been measured as a function of temperature (I 150-1340°C) and oxygen partial pressure (2 X lo-’ 5 par s I atm) The temperature dependence of the cation ddTus.lvltym air ISBven by the expression flL = (1 9:::) x 109exp _ 14’ 4 * 4iTkcal/mole) Cm2/s ( The unusually large value of Do IS Interpreted m terms of the values of the preexponentlal terms m the reaction constants for the creation of defects m Fe203. The oxygen-partial-pressure dependence of the dlffuslvlty mdlcates that cation selfddfuslon occurs by an mterstmal-type mechanism The stmultaneous

dtffuston of “Fe and “Fe has been measured m Fe*O,. The small value of the isotope effect suggeststhat Iron ions ddfuse by an noncolhnear mterstltlalcy mechamsm, which ISconsistent with the crystal structure of Fe,O, .

I. INTRODUCTION Numerous studies have been made on transport properttes m the non oxtdes Fe0 (wustlte), Fe304 (magnettte) and o-Fe203 (hematite) because of then importance to the understanding of the oxtdatton processes m Fe and Fe-based alloys [I]. Studies of cation and anion self-diffusion, devtatton from stotchtometry, and electrical conducttvtty as functtons of oxygen partial pressure pal and temperature provide a detailed knowledge of the concentrattons, mobthttes and types of defects m oxides which ts necessary for understanding the mechanisms and kinetics of oxrdatton Cation self-diffuston has been measured extensively m Fe0 [2] and m Fe30s [3, 41 and the cation self-dtffuston mechanisms have been clanfied by means of tsotope-effect measurements [2, 41. Like a-A120s and Cr203, Fe203 has the corundum structure, but differs from A1203 and Cr20, m that tt may show measureable devtattons from the stoichtometnc composition [5, 61. Measurements of the thermodynamic properttes of Fez03 solid soluttons mdtcate that Fe203 is slightly oxygen deficient [5, 61, which suggests that the predomment atomic point defects are oxygen vacancies and/or mterstmal Fe ions. Cation selfdtffuston in Fe20, has been measured in both pressed-powder compacts [7] and natural single crystals [8, 91; the latter results are about one order of magnitude smaller than the former. The effect of oxygen partial pressure on canon selfdtffuston in FezOJ has also been measured by Chang and Wagner 191. They observed that the dtffustvtttes decrease wtth mcreasmg po2, mdrcatmg that Fe tons diffuse mtersttttally. However, considerable dtsagreet Work supported by the U S Department of Energy

ment exists among these drffusron studies, and the mechanism of selfdtffuston has not been established m detail. If the Fe tons m the Fe203 lattice dtffuse by an interstitial-type mechanism, it is interesting to know whether they diffuse by the free-interstitial mechamsm or by the mtersttttalcy mechanism. A measurement of the isotope effect for cation selfdtffuston may dtfferentiate between these diffusion mechanisms [4] In the present work, selfdtffuston of “Fe parallel to the c axts m single crystals of Fe203 has been measured as a function of temperature ( 1I 50- I 340°C) and po2 (2 X 10V3i p% 5 1 atm). Furthermore, to identify the mechanism of cation self-dtffusion, the stmultaneous dtffuston of 5zFe and “Fe (isotope mass effect) has been measured at I25 I “C and po2 = 1.9 I X IO-* atm. The character&n of the isotope-effect technique are briefly discussed m the next sectton 2. ISOTOPE EFFECT IN DIFFUSION Informatton concerning the mechanism of dtffusion may be obtained from the relative diffusion rates of two isotopes of the same element. For self-dtffuston mechanisms mvolvmg the Jump of only one atom and fulfilhng certain symmetry conditions, the isotope effect m dtffuston can be expressed by the relatron 110, 111

E-($-1)/[(?)‘“-I]=fAK, (I) where D* and m are the tracer dtffuston coeffictents and masses, respecttvely of two isotopes LYand 8, f is the correlatton factor and AK 1s the fi-actton of the

375

K HOSHINO and N L PETERSON

376

total transiatlonal kmetlc energy at the saddie point, associated with motion m the dlrectlon of the dlffuslonal Jump, that belongs to the Jumpmg atom. The correlation factor takes mto account the correlation between the dIrectIons of successive atomic Jumps For self-dlffunon m a pure crystal, f 1s generally a numerical factor determmed only by the crystal structure and the dlffuslon mechamsm [ 121 For dtffuston mechanrsms that mvolve more than one atom m the Jump process, the quantity (mp/ m,,)‘” m eqn (I) should be replaced by [ 131

1’

(n - 1)m + mp “’ t (n-

i)m+m,,

3.2. Dlfluslon measurements The smgle crystals used m this study were -3 X 3 X 0 3 mm m size, and the dIrectIon of tracer dlffuslon was parallel to the c axis of the hcp oxygen sublattice Smce the samples were very thm, they were mounted on NIO crystals with an adhesive dunng the pohshmg and sectlonmg. The mounted samples were pohshed and exammed for parallehsm and flatness. Each of the finshed samples was removed from the mount and preannealed at the same temperature and oxygen partial pressure (po,) that were later used for the dlffuslon anneal The preannealmg time was generally four times longer than the diffusion anncalmg time to ensure that the samples were m thermodynamic equlhbnum at the given temperature and po2 The po2 was estabhshed by an Ar-02 gas mixture flowmg through the furnace at a hnear rate of - 1 cmlsec The composltlon of the Ar-OZ mtxture was either obtained from a cahbrated mtxture (po, = 2 I X IO-’ atm) or was blended from pure 02 and pure Ar m calibrated gas blenders (Math~on Mass-Flow ControIlers) The outlet gas from the furnace was conttnuously momtored with a Thermox I (Ametek, Thermox Instrument Divlslon) gas analyzer, and the value of po2 was determmed from the observed EMF [ 161 The radloactlve tracers were deposited on the sample surface by drymg a few ~1 drop of a solution of either “Fe or a mixture of “Fe and “Fe in the sulfate form The specific actlvlty of all isotopes was suffictently high so that the thickness of the deposlted layer was estimated to be less than 0.1 pm. The samples were drffusaon annealed at the same temperature and po2 that were used for the preannealmg The temperature of the anneals was monitored wrth a cahbmted Pt-Pt 10% Rh thermocouple After the dlffus:on anneal, the edges of the sample were ground to ehmmate the posslblhty of actlvlty diffused from the sides of the sample. The concentration profile of the radloactlve tracer was determined by a senalsectlonmg techmque through the use of a precision parallel grmder. The radloacttvIty m each sectlon was counted using a well-type NaI(T I J-crystal scmtlllatlon counter. For these expenmental boundary condltlons, the dlstnbutlon of specific actlvlty C of a radloactlve tracer IS expressed m the usual exponential form

m

where n 1s the number of atoms (host + tracer) partlclpatmg in the JUmp process, and m IS the average mass of the nontracer (host) atoms For noncollmear mterstltlalcy Jumps, eqn (1) often has to be replaced by the more general expresston [4, 141

= FTf )AK

by the ~m~rdment of Cr metal by 36-MeV 3He ions and the subsequent chemical separation by ton exchange

(3)

where F(J) IS a function of the correlation factor, the crystal structure, and the particular dlffuslon mechamsm consldered Necessary and sufficient conditlons for the vahdlty of eqn (1) are discussed m some detail by Mehrer et al [ I!$ The values off and F(f) are equal wlthm 3% for all noncolhnear mterstmalcy Jumps constdered m the Irterature (FexO, [4] and AgBr [14]) One can determme the quanti~ [(LZ/&#) - 11 by measunng the relative dl~usion coefficients of two isotopes of the same element The measured value of E and the allowed values off and AK may permxt an unambiguous determmatlon of the dlffuslon mechamsm. In the present case of 5’Fe and “Fe dlffuslon m FeZOs, if one considers the free-interstitial mechamsm (n = 1) for which E - I (taking f = 1 and assuming AK to be near its maxlmum value of umty [ 12]), one might expect [(O;t/@) - I] - 0.06 For an mterstltlalcy mechansm, E may be much less than umty as observed for the isotope-effect measurements m Fe,04 [4f and rn the silver hahdes [14]. Thus, the me~urement of E may be useful m ldentlfymg the m~hanisms of diffuston m FeZ03.

C = [M/(~Dt)‘~*] 3. EXPERIMENTAL

exp(-x2/4LTt),

(4)

PROCEDURES

3.1, Materials Smgle crystals of pure Fe203 were purchased from Cnstal Tee (Grenoble, France) The “Fe Isotope was purchased from New England Nuclear m the form of FeC& in 0.5 M HCl, with a specific activity of -20 Cl/g. The “Fe Isotope was produced __ - m camer__ free form wa the nuclear reaction ‘Q- (‘He, 3n) “Fe

where x ts the penetration distance, M 1s the actlvlty per umt area deposited at t = 0 on the plane x = 0, and t IS the diffusion-annealmg time 3.3. Isotope-efect measurements For the isotopic-mass-effect measurements, the “Fe and “Fe Isotopes were d&used simultaneously in the sample. The ratm of spec#tc activEties (C5$&) as a

377

Catton ~lfdlffuslon and the tsotope effect tn Fez03 functton of ~netmtion (or, eqmvalently, can be shown from eqn (4) to be In KS&~)

= const - 11 -

(DWajldl In C59,

(5)

where the subscripts 52 and 59 pertain to 5’Fe and “Fe, respecttvely. Thus, a plot of In (C52/C59) vs In Gc) permits a determmatron of the relative drffusron coefficient [I - (D$,/&&)] In this way, errors ansmg from the diffusionanneahng time, temperature, stotchtometric composmon and se&toning are ehmmated The ratio of the specrfic acttvrtres (C&&) was determined to wnhm 0.1% at various positions m the sample by a half-life separation of the y actmtres of “Fe (half-life = 8 280 f 0007 h) and “Fe (half-life = 45 d) [2,4]. The decay of the total specific activity C,,,,,, m a section is expressed by (6) where ‘I 1sthe elapsed time from an arbttrary reference time, and X5>and Xsuare the decay constants for “Fe and “Fe 9 respectively, Each of the sections was counted 6 or more times in a well-type NaI(Tlfcrystal ~intillation counter over a penod of about five days. Usually, more than 10”counts were collected

k

each time to ensure statistical errors of less than 0.1% The total counts were corrected for counter dead time, background and finite counting time. The spectfic acttvittes of “Fe and “Fe at the reference time were obtained by a least-squares fit of the data to eqn (6)

of In Css)

DIFFUSION OF -Fe

IV. RESULTS AND DISCUSSION

Figure 1 tllustrates the plots of log (specific actrvrty) versus the square of the ~netmtion dtstance for typical dtffuston runs m the present expenments Since all penetration plots are straight lutes over 2-3 decades m activity, the dtstnbutron of radroacttve tracer accurately follows eqn (4), and the calculated diffusion coefficients should represent bulk diffusion. Although evaporation of the tracer was observed m the penetrafron plots of samples annealed in air and po2 = 1 atm, hneanty in the region of deeper penetration m Fig 1 ts consistent with volume drffusion The values of the drffusron coefficients, as well as diffusion time, temperature and po2 are listed m Table 1. The errors m the drffuslon coefficients, determined from a least-squares fit to eqn (4), are about 5%. The temperature dependence of the cation seif-drffuston

IN Fe& T P-3

pD2htm)

I 91xIO-2 mEI7 81252 021 8 1250 6 l8xiO-2

r\

0

(8

02

04

X2 W5 Ftg.

I

08

06

IO

12

cm21

I. Typreal plots of log (specrficactrvrty) vs the square of the penetration distance for the d&&on of ‘YFem Fe203

378

K

HOSHINO

and N L

PETERSON

Table I Cation self-diffusion in FezO, T (‘0

PO2

Time

(atm)

1151

1.0

248.4

set)

Die

(cm*/*)

1 .96x10-l3

1150

0 21

172.8

3 60~10-~~

1149

1.91x10-2

100.8

8.89~10-~~

1150

2 11x10-13

1200

0.21

27.0

169.2

2 12x10-12

I

.93x10-~~

1250

10

18.0

6.04~10-~~

1252

0.21

54.0

1.01x10-11

1250

6.18x10-2

14.4

1.54x10-11

1249

1.91x10-2

54

2.47~10-~~

1251

1.91x10-2

18 0

2.93xlo-ll*

1252

1.91x10-2

14.4

2 91x10-11

1300

0.21

7.23

5 14x10-11

1340

1 .o

2.41

5.82x10-”

1339

0 21

1.18

1.12x10-10

*Isotope-effect

measurement.

coeffictents DW for Fe20J m au between I 150 and 1340°C IS shown m Fig 2 and can be expressed as D& = (1 9:; :) X 10’ Xexp

(lo3

_ 1414+40kcal/mole RT

cm’/s

(7)

In Fig 2, the data obtamed by previous mvestrgators [7-9, 171 are also shown for comparison The present results are in good agreement with those determmed usmg the macro-sputter secttonmg techmque by Atkmson [ 181, for T r lOOO”C, Atkmson reports Do = 1.6 X IO9cm*/s and Q = 138 kcal/mole for catton self-diffusion parallel to the c axis The activation energy determmed m the present experiment is much htgher than the values obtamed by Chang and Wagner (86 k&/mole m po2 = 1 atm) [9] and by Lmdner (112 kcal/mole m air) [7] The higher values of the diffusion coefficients obtamed by Lmdner [7] and Izvekov et al [ 171 may result from the polycrystalhne nature of the samples. Figure 3 shows the diffusivity of “Fe m Fez03, plotted as a function of po2 at a gtven temperature The po2 dependence of the dtffusivtty determmed by Chang and Wagner [9] IS also mcluded for companson The slopes of log D& vs log po2 at 1150, 1250 and 1340°C are m the range between -0 39 and -0 42, the negative po2 dependence suggests that cation self-diffusion occurs by an mterstrtial-type mechamsm. These results are discussed in the next subsection m terms of the defect structure of Fe20S

4.2. Defect structure of Fe203 If Fez03 is oxygen deficient, two types of atomic point defects may be important, oxygen vacancies and Fe mtersttttal ions The equations for the formation of these two types of defect may be wntten

111

and (9) where O;, Vi;, Fe&, Fe:’ and e’ denote a neutral oxygen ion on an oxygen sublatttce site, a doubly charged oxygen vacancy, a neutral Fe ton on a cation sublattice site, neutral or charged Fe mtersttttals ((u = 0 to 3) m mterstitial sttes, and an electron, respectively Apphcatton of the law of mass action to these equations leads to K, 8 = [ F’;][e’]‘&

(10)

and KFLy= [Fe;*][e’]‘“&z, where the square brackets denote concentrations of defects If V;;, Fe;” and e’ are the only charged defects, the electroneutrahty condition is given by [e’] = 2[ Vi;] + cr[Fe:*]

(12)

Canon ~lf~lffus~on and the notope effect rn Fez03 PC)

10-S

1300

I200

I

I

E

II00

If the Fe tons diffuse as singly charged positive interstitial ions,

loo0 I

379

-i

0 PRESENT WORKMIR) 0 ATKINSON et 01 (AIR)

II& cc [Fe;] cc ~2”~.

(14c)

3

IZVEKOV

at al

7 I/T

8

fl0-4

K-‘1

Fig. 2. Temperature dependence of Z& in FezOr, pre vrously published data of D& in FezOpare also shown for comparison

Iron-ion diffusion by doubly charged mterstmal tons IS not compattble wtth the present expenmental results tf [Fe;*] i3>(2/cr)[ Vi]. Smce both eqns (13~) and ( 14~) are compattble wtth the present expenmental observattons, either Fe; or Fey may be responsible for canon self&IIiuaon, dependmg upon which atomtc defect Vi or Fe:‘ 1s dominant in Fe24 Since the oxygen ~lf~ffislon coeffictents [ 19-2 l] are comparable wnh the canon self-ddbrston coefFrcrents obtained m thus study, which of the atomic defects m Fez03 1s dominant remams unclear Recently, Dieckmann [22] has reported can&l weight-change measurements on Fe20s as a function of po2, His results are consistent with [I’;;] ti [Fe;>, hence, our results would suggest that Fey 1s the dominant atomic defect on the cation sublattice The value of d log DFJa log po2reported by Chang and Wagner f9] IS nearly -3. Since then values of electrical conductivity are inde~ndent ofp, Chang and Wagner have concluded that mtnnsrc electronic behavior IS more Important than deviation from stotchiometry m Fez03, t e.

I

I

I

I

I

1

PRESENT WOAK ---CCnANG8W&NER

a

The slopes of the plots of log D& vs log po2 shown m Rg 3 (-0.39--0.42) are consistent wnh two types of non mterstmal tons. (a) If oxygen vacancies are the predominant atomic defects m Fez4 (1 e [Vi] P (a/2) [Fef]),

to-‘*

1250*c

[e’] = 2fVJ = (2Kr x)“fp&I/h

(13a)

\ \

\

\

\

and

\t3oo’C

\

\

\ IFep‘]

KF& = (2K&/3

_ (i-3, p*

\

\

(13b) 1;

\

’ \

If the Fe tons dtffuse as doubly charged posmve intersttttal tons (1.e if cr = 2),

115O*c

y2oo*c \

l200’Ce

\ \ \

\ -5/12

Iron-ton dlffuslon by singly charged inte~tltlal ions IS not compatible with the present experimental results tf [Vi] ti (ar/2)[Fep’]. (b) If Fe mterstittal ions are the dommant atomic defects (1 e [Fe<] $ (2/(r)[V&, [e’] = ol[Fep*]= (aK~.p)I/W~&/~a+l)

(14a) d3.

and

!,“\ -3/8

-3

-2

-1

0

log s2 (otml [‘;;I

=

GO

(,KFer)2/@+1)

-(cl--2)/2(&I) pm

(14b)

Fig 3 The pa dependence of D& In FezOr The data of Chang and Wagner [9] are also shown for comparison

380

K

HOSHINO

Icy,

and N L

PETERSON

mterstittal mechamsm IS not conststent wtth our general knowledge of the isotope effect [ 121 Thus, the mtersttttal-type mechanism observed for cation where h’ IS an electron hole, and selfdtffuston in Fe203 1s most likely an mtersttttalcy mechanism. Smce two atoms parttctpate dunng a (15b) Jump by the mterstttdcy mechanism, n = 2 m eqns (2) and (3), and E becomes 0 132 + 0.032. Since f [or F(f)] 1s generally greater than 0 5 for dtffuston Although the present dtffuston results are mconsistent by the mtersttttalcy mechanism [4, 141 (an exact with this defect model, the weight-change measurevalue is not known for the corundum structure), a ments of Dteckmann [22] are not inconsistent with value of AK < 0.26 is required m order to be this model. However, tf [e’j is independent of poz consistent with the isotope-effect results Although becauseit 1scontrolled by tmpunttes, a po2dependence values of AK - 1 have been observed for dtffuston of Dk tdenttcal to that described by eqn ( 15b) ~111 by the collinear mtersttttalcy mechannm, very small result [see eqn (1 I)] Although the present results and values of AK (-0. I) have been found for cation those of Chang and Wagner [9] disagree with respect dtffiston by the noncolhnear mterstinalcy mechanism to the pnmary conditions responstble for electroneum AgBr and AgCl [ 141. For the stmultaneous motion trahty, they do agree that the predominant cation of two atoms by the noncolhnear mterstmalcy mechdefect IS an mterstmal iron ton anism, large mteracttons may occur between the atoms m the saddle-pomt configuratton, resultmg m a small value of AK 4 3. Isotope-e#ect and d@iuslon mechanisms Support for the noncolhnear mtersttttalcy mechaThe isotope-effect measurement was made at 1251°C and pe= 1.91 X IO-* atm A plot of nism comes from a constderatton of the possible mterstmalcy Jumps m the corundum structure. The In (&/&J vs In (C,,) is shown m Fig. 4. The error crystal structure of Fe203 can be regarded as a nearly bar at each point represents the standard error obhexagonal close packing of oxygen tons with the tamed from a least-squares fit of the counting data to eqn (6). The experimental results are 1 - (DW tnvalent Fe tons occupymg two-thirds of the octahedD&) = 0.0041 + 0.0010 and E = 0.067 + 0 016 The ral sites The atomtc arrangement looking down on the basal plane of the hcp oxygen sublatttce IS shown null-effect experiments are also shown m Fig 4, these m Fig. S(a). An mtersttttal non ton at site MI can indicate that the measured isotope ratios are not Jump to any one of the nearest-netghbor substttutronal senously affected by the counting rates These points cation sites [such as M(l)] m the corresponding were obtamed by counting and analyzing, as described rumpled cation plane, and the iron ion on the above, ahquots of a “Fe-“Fe mtxture covenng the substttuttonal cation site can Jump to a netghbonng range of acttvmes m the sample sections mtersttttal site (such as I,). Each mtersttttal site M, If the diffusion of Fe tons occurs by a free-interstitial has eight near-netghbor substttuttonal sites, SIXin the mechanism, the correlation factorfmay be assumed cation basal plane and one tmmedtately above and to be unity, and a very small value of AK (0.07) one immediately below the mterstttial site When the would be required to be consistent with the isotopesubstttuttonal non ton at M(1) 1s displaced by the effect results. Such a small value of AK for a free[e’] = [h’l =

I -

I

(154

I

I

I

52Fe AND “Fe

Ill1

I

I

I

I

I

I

II

I

I

I

I

(

I

l

l

I

I

I

I

I

IN Fe203

I

I

I

I

Frg 4 A plot of In (Clrz/&,) vs In (C,,) for cation self-diffusion in Fe203 The value of In (CJ#&) increases from the bottom to the top and that of In (C,,) decreases from the left to the right

Cation self-diffusion and the Isotope effect m Fe203 [tioo] \

:oi’O1

[loio]

I

[ioio]

4

2

I

Io&

;,ooj

Rg 5 Crystal structure of a-Fe203. Arrangement of iron ions (filled circles), oxygen ions (large open circles), and mterstltlal sites (dotted arcles) projected onto (a) the basal plane of the hcp oxygen sublattlce and (b) the (1 I 20) plane of the corundum structure An mterstltlal Iron ton IS located at site M, Although the oxygen Ions m the basal plane he m a flat plane, the Iron Ions associated with the basal plane he m a rumpled plane as seen m (b)

interstitial iron ion from Ml, it can jump to any one of three mterstitial sites, two m the canon basal plane I, and one immediately above M(l) [shown as Z2 m Fig. 5(b)]. The atomic arrangement m the (I I 2 0) plane is shown m Fig. S(b). Diffusion m the c direction can result from three ddferent types of mterstmalcy jumps. (a) The iron ion at the mterstmal site it41 can jump to any one of the SIXnearest-neighbor substituttonal sites [such as M(l)], three of these substitutional iron ions can jump m the plus c directton to mterstttial sites Z,, and three can jump m the mmus c due&ion to mterstmal sites three iron planes below Z3. (b) The iron ion at the mterstmal site il4, can jump to M(2) and the substitutional iron ion at M(2) can jump to three equivalent Zz sites (c) The non ion at the mterstitial site M, can lump to M(2) and the substitutional iron ion at M(2) can jump to three equivalent Z, sites The oxygen ions denoted by O(I) and O(2) are sufficiently out of the plane in Fig. 5(b) so as not to sigmficantly mterfere with the jumps of M, to M(2) or M( I) to Zr. However, the oxygen ton denoted by O(3) IS situated m a manner that would suggest that the jump from site M(2) to Z, will be a highly energetic jump. Note that all mterstmalcy jumps must be noncolhnear as suggested by the isotopeeffect expenment, collmear jumps are always blocked by the presence of a substitutional iron ion The suggested sites for the iron mterstmal ions are based purely on size considerations of open spaces m the corundum lattice. Other mterstitial configurations are conceivable that would lead to only noncollmear interstitialcy jumps. 4.4. Values of Do and Q The values of Do ( IO9 cm’/s) and Q (141.4 kcal/ mole) reported m eqn (7) are somewhat unexpected. Cation selfdiffision studies in the isostructural oxides

ar-A1203 [23] and Cr203 [24] give values of DOof the order of IO cm*/s and Q - 120 kcal/mole. However, cation self-diffusion in Cr203 (and probably m A&O,) takes place by a vacancy mechanism, and it 1s probably inappropriate to compare the diffusion behavior m FerO, with that m A&O, or CrzO,. The motion of iron ions by the mterstmalcy mechanism is well documented for FeI04 [3, 41. The apparent values of Do and Q for D& by the mterstitialcy mechanism m FeJOa are Do = 10’ cm*/s and Q = 146 kcal/mole [25], in general agreement with the values reported m eqn (7). The temperature dependence of the equihbnum constants may be written m the form K Fc~

=

(KFLr)oexp

(l6a)

(16’3 If [I’;] $ (cu/Z)[Fe; ] and (Y= 2, the value of DO is given by the expression

DO

=

{Mi~it?* exM”lR)} X (Kdo/[2(Kl

do1*I’,

(l7a)

where g IS a geometrical constant, YIS an appropnate vibration frequency and s:” is the entropy of migration by the mterstttialcy mechanism. If [Fe:‘] $ (21 a)[ V;] and (Y= I, Do = {gvfi~‘” exp(s~/R)}(KF,;~‘2.

(IW

Since the term m curly brackets m eqns (l7a) and

K HOSHINOand N L PETERSON

382

(17b) 1s of order unity, the entropy term (KFel$” or

tlalcy mechamsm Probable mterstltlalcy the corundum structure are noncollmear

4.5. Addmonal comments The fourteen values of D& reported m Table 1 were obtained from multiple expenments on three different samples. These results represent a self-conslstent set of measurements that may represent cation self-dlffuslon m pure Fe20s. Several addltlonal measurements were made on two other samples that gave values of D& whtch were about 75% larger than those reported m Table 1. Five measurements were made on one other sample, these gave values of D& that were about 20 times larger than those reported m Table 1, however, the values of a log D&/,/alog po2 observed for this sample were slmdar to those reported m Fig. 3 These differences from sample to sample are highly reproducible and are thought to anse from different levels of lmpunty content m the different samples. The maccuracles m the spectrochemlcal analyses of the very small amounts of matenal remammg after numerous dlffuslon runs on each sample were too large to establish a correlation between sample punty and relative values of D& obtamed from different samples

Acknowledgements-The

(KFet)o/[2(KI&]*”must be large (- 108)

5. CONCLUSIONS (1) Tracer self-dlffunon of “Fe has been measured m Fe20, as a function of both temperature and po2 The temperature dependence of the cation dlffuslvlty m air IS given by the expresslon DR = (1

9’::) X lo9 exp -

14 1 4 f. 4 0 kcal/mole

RT

cm2/s

(2) The dlffuslvltles decrease with increasing po2 m the expenmental ranges of temperature (1 1501340°C) and poz (2 X lo-’ < poz 5 1 atm), mdlcatmg that cation self-dlffuslon occurs by an mterstlal-type mechanism The Fe; 1s the most probable defect, but the dominant charged-defect type (electromc or lomc) must be established before the charge state of the iron mterstltlal ion can be confirmed (3) The small value of the isotope effect ISconsistent with dlffuslon of Fe ions by a noncolhnear mterstl-

Jumps m

authors wish to thank S J Rothman, C L Wiley, G Talaber and L J Nowlckl for their able assistancewith the expenmental studies The production and punficatlon of the “Fe isotope by M Oselka and M Wahlgren are gratefully acknowledged REFERENCES Kofstad P , Nonstorchlometry. Drffislon and Electrrcal Conductrvrty m Bmary Metal Oxtdes Wiley-Intersclence, New York ( 1972) 2 Chen W K and Peterson N L , J Phys Chem Solrds 36, 1097 (1975)

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