ISOTOPE EFFECT AND CATION SELF-DIFFUSION IN METAL-DEFICIENT OXIDES

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ISOTOPE EFFECT AND CATION SELF-DIFFUSION IN METAL-DEFICIENT OXIDES

W. Chen, N. Peterson

To cite this version:

W. Chen, N. Peterson. ISOTOPE EFFECT AND CATION SELF-DIFFUSION IN METAL- DEFICIENT OXIDES. Journal de Physique Colloques, 1973, 34 (C9), pp.C9-303-C9-307.

�10.1051/jphyscol:1973954�. �jpa-00215429�

J O U R N A L DE PHYSIQUE C~lloque C9, supplkment au no 11-12, Tome 34, Novembre-DPcembre 1973, page C9-303

ISOTOPE EFFECT

AND CATION SELF-DIFFUSION IN METAL-DEFICIENT OXIDES (*)

W. K. CHEN

A r g o n n e National Laboratory, Argonne, Illinois, U S A a n d

N. L.

P E T E R S O N

Institut fiir theoretische u n d angewandte Physik d e r Universitat Stuttgart,

Stuttgart, G e r m a n y , O n leave f r o m Argonne National Laboratory, Argonne, Illinois,

USA

RBsumB. - I1 est admis genkralement que les defauts principaux dans les oxydes deficients en metal, NiO, COO et

<

FeO

>

sont des lacunes cationiques. Dans la formule generale M I - = 0 , x est environ egal a 0,001-0,01 dans NiO et COO et 0,05-0,13 dans

<

FeO

>.

Des mesures ant&

rieures, la diffusion simultanee des traceurs 57Ni et 66Ni dans NiO et 55Co et 60C0 dans COO ont donne des valeurs de,fAK independantes de la teniperature et egales a 0,61 0,02 et 0,58 & 0,01 respectivement. Ces valeurs experimentales de j' AK imposent que I'autodiffusion du cation dans NiO et COO soit due a un mecanisme par lacunes isolees. La structure du defaut dans

<

FeO

>

est beaucoup plus complexe que dans NiO et COO en raison de son large ecart a la stcechiometrie.

Des mesures recentes montrent que la diffusivite isotherme de 5YFe est peu sensible a la valeur de s dans Fel-,O. L'effet de masse dans la diffusion simultanee de ZlFe et ' T e dans

<

FeO

>

donne des valeurs de YAK comparables, quoiqu'un peu plus faibles, a celles obtenues dans NiO et COO. Des effets eventuels d'agglomeration de lacunes sur la diffusivite du cation dans

<

FeO

>

sont discutes.

Abstract. -The predominant point defect in metal-deficient oxides, NiO, COO and < F e O > , is generally recognized to be a cation vacancy. In a general formula M I-.,0, x is about 0.001, 0.01, and 0.05-0.13 for NiO, COO, and < F e O > , respectively. In previous measurements, the siniultaneous diffusion of the tracers 57Ni and ( ~ ~ ~ N i in NiO and "Co and 6ClCo in C o o give values of f'AK that are independent of temperature and equal to 0.61 k 0.02 and 0.58 3~ 0.01, respectively. These experimental values of,/'AK require that cation self-diffusion in NiO and COO occur by a single-vacancy mechanism. The defect structure in < F e O > is much more complex than that in NiO and COO because of its extended deviation from stoichionietry. Recent rneasu- rements show that the isothermal diffusivity of 5"Fe is rather insensitive to the value of x in Fel-,O. The mass effect for simultaneous diffusion of "Fe and y)Fe in < F e O > gives values o f f AK that are similar to, but somewhat smaller than, those obtained for NiO and COO. POS- sible effects of vacancy clustering on cation self-diffusiviry in < F e O > are discussed.

1. Introduction. - Unlike alkali halides, many metal oxides a r e stable over a range of compositions.

An excess o f cations o r anions in a n oxide creates non-stoichiometric point defects in the crystal latlice.

Thus t h e concentration o f lattice defects in a n oxide, has, i n m a n y cases. been controlled by equilibrating the oxide t o the partial pressure of a constituent.

From t h e dependence of the diffusion coefficient on the ambient partial pressure of o n e of the consti- tuents (usually oxygen), a model can be formulated.

The model, in turn. c a n be used t o deduce the defect structure in the lattice and. in turn, the diffusion mechanism.

Another a p p r o ; ~ c h t o thc study of the diffusion mechanism is the measurement of the isotopic mass effect o n diffusion. T h i s a p p r o a c h has been used successfully f o r diffusion in rnctals a n d s o m e alkali

(*) Work performed under thc ;tuspices of the U S Atoinic Energy Comniission.

halides [ I ] but h a s only recently been attempted in metal oxides [ 2 ] - [ 5 ] . T h e present paper reports a recent study of the isotope effect for cation diffusion in < F e O > . T h e results will be discussed in conjunc- tion with those previously obtained in C O O a n d NiO. T h e oxides, NiO, C O O a n d < F e O > , a r e cation-deficient oxides that exhibit p-type semiconduc- tion a t high temperatures in a proper oxygen partial pressure. I n a general formula M,-,O, t h e value of s I S a b o u t 0.001, 0.01 a n d 0.05-0.13 f o r N i O , C O O and < F e O > , respectively. Previous studies have considered the d o m i n a n t non-stoichiometric defect in these oxides t o be a cation vacancy. T h e crystal structure of these oxides is of the NaCl type.

2. Correlation factors and isotopic mass effect. -

For randorn atomic j u m p s in a cubic crystal, the diffusion coeficient D is givcn by

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1973954

C9-304 W. K. C H E N A N D N . L. PETERSON

where r is the atomic jump frequency, and

r

is the jump distance. If tlie jump direction of

a

given atom

depends on the direction of a previous jump, then

D = -

n2 ^f', (2)

where the correlation factor

.f

takes into account the correlation between the directions of successive atomic jumps. For self-diffusion in a cubic lattice, f is a numerical factor determined only by the crystal lattice and the diffusion mechanism, and it has been calculated for several diffusion mechanisms in

a

number of crystal structures [6], [7]. Thus, direct measurement of f ' m a y enable a unique determination of the mechanism of diffusion.

For tracer diffusion in solids.

J'

can be obtained from a n accurate measurement of tlie relative diffusion rates of two isotopes of the same element. The isotope effect in diffusion has been expressed by Schoen [8], and later by Tharmalingam and Lidiard [9], as

where the subscripts

x

and

/I

pertain to the isotopes with masses

ma

and

nip,

respectively. In those cases in which only one aton1 undergoes an atomic dis- placement during the jump process and its jumping motion is not coupled with the surrounding atoms, the ratio of the jump frequencies may be approximated by the simple relation

However, if the motion of the jumping atom is coupled with the surrounding atoms, the ratio of the jump frequencies, as given by Mullen [lo], is

Here AK is the fraction of tlie total translational kinetic energy at the saddle point, associated witli motion in the direction of the diffusional jump, that belongs to the jumping atom. From eq. (3) and (5), the general expression for the isotopic mass effect in diffusion becomes

F o r diffusion mechanism that involve more than one atom in the jump process, Vineyard [I I] has shown that the quantity

(m,/mO)112

in eq. (6) should be replaced by

where n is the number of atoms participating in the jump process, and

m

is the average mass of the

nontracer atoms.

From the above expressions, one can determine

,f A K by measuring the relative diffusion coefficients

of two isotopes of tlie same element. The measured value of

J' A K and the allowed values of ,f

and AK may permit an unambiguous determination of the diffusion mechanism and thus provide a unique value of A K .

3. Experimental.

^-

All experiments on < F e O >

were performed on liigh-purity single crystals. The crystals were grown by tlie Verneuil process in

a

controlled oxygen partial pressure. The '"Fe isotope was purchased from New England Nuclear- Corpo- ration, Boston, Mass., in the form of FeCl, in 0.5 N HCI. The "Fe isotope was produced by 36 MeV 3He bombardment of "CI- by the nuclear reaction

"Cr(%e, 3 I I ) " F ~ in the Argonne National Labo- ratory cyclotron. The "Fe isotope was cliemically separated from tlie cliromiuni target by ion exchange.

The final product was in the form of FeCI, in 0.5 N HCI.

Tlie diffusion samples of approximately 10 by 10 by 5 mm were cut from crystal boules and were ground parallel and flat. The finished samples were preannealed in

a

given oxygen partial pressure at tlie diffusion temperature. Tlie preannealing time was at least twice as long as tlie difl'usion annealing time to ensure that tlie oxide satiiples were in thernio- dynamic equilibrium a ( a given temperature t~nd oxygen partial pressure. The radioactive tracers were deposited

⁰¹¹

a sample surface by drying a drop of a solution containing either "'Fe o r

a

mixture of

5 2

Fe and "Fe in a sulfate form.

The samples were diffusion annealed in

a

g i ~ e n oxygen partial pressure at

a

given temperature. A partial pressure of oxygen was obtained froni

^;I

C 0 , - C O gas mixture and was monitot-ed with

a

gas partitioner.

After the diffusion anneal, the edges of the sariiples were ground to eliminate edge effects. Tlie penetration of radioactive tracers was determined by

a

serial sectioning technique. Tlie radioactivity in each section was counted using a well-type Nal(T1) crystal scintillation counter. For these experiniental boundary conditions, tlie distribution of specific activity

C

of

a

radioactive tracer may be expressed in the usual exponential form [I 21

where X i s the penetration distance, D is tlie difrusion coefficient, M is the activity per unit area deposited at

t =

0 in the plane X

⁼

0, and

t

is the diffusion annealing time.

For the isotope-effect nieasurenients, the "Fe and "Fe isotopes were diffused simultaneously

ill

the crystal. The ratio of specific activities ( C 5 , / C j g ) as a function of penetration (i. e., C s g ) can be shown from eq. ( 8 ) to be

In (C,,/C,,)

⁼

const.

^- [ I -

(D,,/D,,)] In C,,

^,

(9)

ISOTOPE EFFECT A N D CATION SELF-DIFFUSION IN METAL-DEFICIENT OXIDES C9-305 where the subscripts

52

and 59 pertain to "Fe and

"'Fe. Thus, a plot of In (C,,/C,,) versus In C,, permits a determination of the relative diffusion coefficient

1

- (D59/D52). In this manner, errors arising from the diffusion annealing time, tempera- ture, stoichiometric composition, and sectioning are eliminated. The ratio of the specific activities (C5,/C5,) was determined at various positions in the sample to within 0.1

%

by

a

half-life separation of the y activities of "Fe (half-life = 8.285 f 0.009 h) and 59Fe (half-life = 45 days).

4. Results and discussions. -. Penetration plots for

a

typical run from each temperature in this expe- riment are presented in figure l . Since all penetration

FIG. I . - Log of specific activity of 5sFe vs penetration distance squared for the diffusion of 5sFe in F e 1 - . ~ 0 .

plots are straight lines over two to three decades in activity, the calculated diffusion coefficients represent bulk diffusion.

The temperature dependence of the diffusion coefficient for Fe,,,,,O in the temperature range 700-1 340 O C can be expressed as

Figure 2 illustrates the diffusivity of 59Fe in Fe, -,O as a function of deviation from stoichiometry a t given temperatures.

In

contrast to the previously reported results [2], [13]-[14!, figure

2

shows that the

0 " ~ e . THIS WORK

a 5 5 ~ e , AT Y33'C. HIMMEL. MEHL 8 BIRCHENALL 119531

FIG. 2. - Diffusion coefficient of 59Fe in F e 1 - ~ 0 a s a function of deviation from stoichiometry. Plotted as log D vs X.

diffusivity decreases with an increase in

x

at 802 O C ,

is rather insensitive to any change in x at ! 003

OC,

and increases slightly with an increase in

x

at 1 200 O C .

This general trend was supported by a recent study of the Mossbauer line broadening for 57Fe in Fe,-,O by Anand and Mullen [15].

Figure 3 presents the plots of In (C5,/C5,) versus

-4 ---*_ J--*--"

---._----*--

NULL EFFECT

which is in fair iigreement with that previously F ~ ~ , 3. - pjOtS Of i n ( c ~ ~ , c ~ ~ ) vs I n

css

for the cation self- obtained by Himme1 ul. [I31 for Fe,,,,,O between diffusion in Fe, = o ; In (Cs2/CS9) increases from the bottom

700

and 1 000 "C. to the top, and In C ~ , I decreases from the left to the right.

W. K. CHEN AND N. L. PETERSON

Isotope efect for cation sey-dijiision in non-stoichiometric oxides

Temperature

Oxide x

^O

C f

AK

Isotopes

-

- - - -

Nil -,O < 0.001 1 200-1 680 0.613 + ^{0.021 57Ni/66Ni}

Co, -,O < 0.01 1 080-1 410 0.582 + ^{0.009 55C0/60C0}

0.057 1 000 0.440 + 0.010

Fe, -,O 0.111 1 000 0.360

)

0.016 52Fe/59Fe

0.077 803.7 0.443 f 0.019

In CSg for the simultaneous diffusion of "Fe and

" ~ e in Fel-,O. The values o f f AK obtained from these measurements are listed in table I. In previous studies [3], 141, measurements of the simultaneous diffusion of "Ni and 66Ni in NiO and "Co and 6 0 ~ o in COO gave values of j'AK (Table I) tliat are independent of temperature. The values of

,f

AK for N10 and COO are consistent with cation self-diffusion by a single-vacancy mechanism ( i . e.,

j'= 0.78) with AK =

0.78 and 0.75, respectively, for NiO and COO.

In view of the large defect concentration (i. e., x - ^{0.05 -} 0.13 in Fe, -,O), a simple linear relation- ship between the cation diffusivity D and the deviation from stoichiometry that exists in NiO and COO would not be anticipated at all temperatures in Fel-,O.

Simple calculations show that the random probabilities of a vacancy with none, one, or two other vacancies as nearest neighbors are 0.54, 0.24 and 0.

l

I, respecti- vely, in a face-centred-cubic (fcc) lattice with a vacancy fraction of 0.05. From neutron diffraction studies, Roth [I61 suggests a model of Fe, -,O that contains defect complexes consisting of two cation vacancies in octahedral sites and an interstitial cation in a tetra- hedral site of the fcc oxygen sublattice. Further studies by Koch and Cohen [I 71 of superstructure diffraction peaks from Fe,-,O suggest tlie existence of periodi- cally spaced clusters of vacancies in quenched speci- mens. Thus, a simple defect model that does not include defect clustering would appear to be inappro- priate for this oxide.

Although a quantitative understanding of the diffu-

sion results is not available at this time, a plausible interpretation may be developed in terms of defect clustering. The interpretation of the data in figure 2 may be that iron ions migrate by free mobile vacancies (or divacancies) which coexist with higher order defect clusters. As the deviation from stoichiometry is increased, a larger number of the vacancies are

i n

the form of immobile defect clusters. Thus tlie diffu- sion coefficient will decrease with an increase in non- stoichiometric defects at lower temperatures, but may increase with increasing defect concentration at higher temperatures where the defect binding energy is less important relative to

k T . The smaller value of f AK

in Fe, -,O relative to NiO and COO and the decrease in f'AK with increasing defect concentration at

1000 OC suggest tliat the correlation factor ma) decrease with increasing defect concentration. This suggests that divacancies (and possibly trivacancies) are contributing to diffusion in Fe, -,O. (The term AK may be the same in Fe,-,O as in NiO and COO because the saddle point atoms are oxygen atoms or;

a complete sublattice in all three materials.) The linear Arrhenius plot for Fe, ,,O requires a propel balance between binding energies and migratior energies of the various vacancy groups. If the migra.

tion energy for the divacancies is smaller than thr migration energy for the monovacancies in Fe, -,O a:

in fcc metals, the divacancy contribution will be mort important at low temperatures than at high tempera tures in a material containing a constant number of

defects like Fe,,,,O.

References See, for example, PETERSON, N. L., Solid State Phys.

22 (1968) 409.

DESMARESCAUX, P. and LACOMBE, P., Metn. Scietit. Rev.

Met. 60 (1963) 899 ;

DESMARESCAUX, P., BOCQUET, J. P. and LACOMBE, P., Bull. Soc. Chitn. Frmzce 15 (1965) 1106.

CHEN, W. K., PETERSON, N. L. and REEVES, W. T., P I I ~ s . Rev. 186 (1969) 887.

[4] VOLPE, M. L., PETERSON, N. L. and REDDY, J., P I I ~ s . Rev. B 3 (1971) 1417.

[5] CHEN, W. K. and PETERSON, N. L., J. PIIJ~s. Chen~. Solicls 33 (1972) 881.

[6] COMPAAN, K. and HAVEN, Y., Trans. Farariny Soc. 52 (1956) 786 ; 54 (1958) 1498.

[7] MULLEN, J. G., Phys. Rev. 124 (1961) 1723.

[8] SCHOEN, A. H., Phys. Re,). Lett. 1 (1958) 138.

[9] THARMALINGAM, K. and LIDIARD, A. B., Phil. Mug. 4 (1959) 899.

[lo] MULLEN, J. G., Phys. Rev. 121 (1961) 1469.

[ I l l VINEYARD, G. H., J. PIlys. C h e t ~ . Solids 3 (1957) 121.

[I21 CRANK, J., Mathetnatics qf' Diffirsion (Oxford University Press, New York) 1956, p. 11.

[13] HIMMEL, L., MEHL, R. F. and BIRCHENALL, C. E., Tram.

AIME 197 (1953) 827.

[I41 HEMBREE, P. and WAGNER, J . B., Jr., Trans. Met. Soc.

A I M E 245 (1969) 1547.

[I51 ANAND, H. R. and MULLEN, J. G., private communication (1973).

[16] ROTH, W. L., Acta Cr~jst. 13 (1960) 140.

[17] KOCH, F. and COHEN, J . B., Actn Cryst. B 25 (1969) 275.

/SO TOPE EFFECT AND CA TION SELF-DIFFUSION IN METAL -DEFICIENT OXIDES

DISCUSSION

R. A. SWALIN. - I t has been postulated on the basis of EMF studies that three subfields exist in the Fe, -,O phase. These presumably are not discrete phases (if they exist at all) but represent regions of different types of defect structures. Did you examine your diffusion anomalies in the context of these pre- sumed regions

?

It would seem to me that careful diffusion research of the type you have done could be useful in proving o r disproving whether these regions exist in Fe,-,O.

N.

L. PETERSON. -

The curves of the diffusion coefficients as a function of composition shown in figure 2 traverse more than one of the proposed subfields in the Fe,-,O phase. We see no abrupt change in slope at our curves (Fig. 2).

F. BENIERE.

- HOW are calculated the error bars

shown on the isotope effect plots

?

Are they smaller than the statistical fluctuations

?

N. L. PETERSON.

-

The error bars on the data points in figure

3

are simply one standard deviation of the least squares error in the fitting of the counting data from a given section to the equation

:

C, = C,

exp(-

I., t )

+

^C,,

exp(-

; j p t )

.

In this equation

C,

is the total activity of the section as a function of time r from some arbitrary time zero.

C,

and

C,,

are the concentrations of isotopes

cr

and p at

time zero, and

I., and i p

are the decay constants

of isotopes

r

and 8. The error bars are somewhat

larger than the 0.1 % error resulting from counting

statistics. The possible systematic errors resulting

from slight changes in counting geometry from one

section t o the next are not included in the error bars

for a given section.