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Isotope effect for cation diffusion in CoO
N. Peterson, W. Chen
To cite this version:
JOURNAL DE PHYSlQLt Colloque C 6 , suppli.nzcnf au no 7 , Tome 41, Juillet 1980, puge C6-319
Isotope effect for cation diffusion in COO
(*)
N. L. Petcrson and W. K . Chen
Argonne Nat~onal Laboratory Argonne, 1L 60439, U.S.A
Rbumk. -- La diffusion simultanke de et 6 0 C ~ dans COO a ete mesuree en fonction de la pression d'oxygene dans I'intervalle lo-' < pol < 1 atm. a la temperature de 1 200 "C. La valeur de la pente de la courbe de log D$
en fonction de logpo2 change de 114 aux grandes valeurs de po, a 115 aux basses valeurs de po,, en bon accord avec les nombreux resultats de Dieckmann. L'effet isotopique est independant de PO,, ce qui indique que la dif- fusion par polylacunes, par ions interstitiels de Co, ou par dkfauts introduits par les impuretes, n'est pas impor- tante dans ces experiences. Les rkultats sur la conductibilitC electrique, sur la diffusion, et sur I'effet isotopique s'accordent avec un rnkanisme de la diffusion par monolacunes neutres, chargees, o u doublement chargees. La contribution de chaque esptce d e hcune varie avec po,.
Abstract. - The simultaneous diffusion of "Co and 60Co has been measured in COO a s a function of equilibrium oxygen pressure in the range lo-' < po, < 1 atm. a t 1 200 OC. The slope of the log D& vs. logpo2 plot changes from a value of about 114 at high po2 to about 115 a t low po, in agreement with the extensive measurements of Dieckmann. The isotope effect is independent of p,,, which suggests that diffusion by defect clusters, interstitial C o ions and impurity-induced defects is not important in the present measurements. Conductivity, diffusion, stoichiometry, and isotope-effect results are consistcnt with diffusion by neutral, singly charged, and doubly charged vacancies ; the relative contributions from the various vacancies varies with po,.
1. Introduction. - Cobalt monoxide is an off- stoichiometric, NaC1-structured oxide exhibiting p- type semiconduction at high temperatures with oxy- gen pressures near 1 atm. The extensive measurements
of the deviation from stoichiometry 6, as a function of po2 [I-61 show an excess of oxygen ions relative to
cobalt ions. The rapid cation tracer diffusion [ l , 7-91 relative to the anion tracer diffusion [ l o ]
(D&,/Dd
--
5 x lo4 at 1 200 OC) strongly suggests that the excess oxygen ions are accommodated by the formation of cation vacancies rather than anion interstitials.It is apparent from the above that the principal point defects to be considered in COO are cation vacan- cies and electron holes. Various charges are possible for the cation vacancies. The formation of neutral vacancies can be expressed as follows :
112 O,(g) =
+
0 , . ( 1 )Singly charged vacancies can be formed by the dissocia- tion of neutral vacancies :
V:, = V&,
+
h.
(2)Further dissociation of electron holes yields doubly charged vacancies :
V;-, =
v:,,
+
h.
( 3 )(*) Work supported by the U.S. Department of Energy.
If only one type of cation vacancy is present in COO, and the defect concentration is sufficiently low that
defect-defect interactions can be neglected, then the application of the law of mass action to eqs. (1)-(3) allows one to relate the defect concentration to the oxygen partial pressure :
[V&1 ( ~ 0 , ) " ~ (4)
[V;.,1
x
(pO,)li4 (5)[V;',I ( ~ 0 , ) " ~
.
(6)The bracketed quantities are the fraction of point- defect species per mole of cation lattice sites. If the mobility of the various cation-vacancy types is the same and independent of po,, then a measurement of the cation tracer diffusivity as a function of po,
may be related to the deviation from stoichiometry 6 and provide a determination of the dominant vacancy type from its pol dependence,
Most measurements of 6 [I-3, 5 , 61, electrical
conductivity [3, 11-13] and cation tracer diffusion [ l ,
7 , 81 are concentrated at high pol values and may be
fitted to eq. (5), indicating a dominance of singly charged cation vacancies. Several measurements of
6 [4], electrical conductivity [ 2 , 5 , 141, and cation tracer diffusion [9] cover a large range of PO,. These
measurements show a curved plot vs. log po2, indicat- ing that more than one type ofdefect is present in COO.
Dieckmann [9] has made an extensive analysis of the literature data on the po, dependence of 6
C6-320 N. L . P E T E R S O N A N D W . K. C H E N
and electrical conductivity, and of his own results on cation tracer diffusion. In addition to neutral, singly charged and doubly charged vacancies [eqs. (1)-
(3)], he also included Frenkel point-defect equili- brium and Schottky point-defect equilibrium in his analysis. Dieckmann was able to obtain an acceptable fit of this simple five-defect ideal solution model to the existing data. He concludes that the concentrations of cobalt interstitials and oxygen vacancies are negli- gible; the dominant defects are vacancies on the cation sublattice and electron holes, and the vacan- cies can be formally treated as neutral, singly, or
doubly charged. The curvature in the plots of log
DE,
vs. log po, (and similar plots for 6 and electrical con- ductivity as a function of po2) can be quantitatively interpreted in terms of a change in relative contribu- tions of differently charged vacancies with varying pOZ as shown by Dieckmann [9]. Other possible inter- pretations of the data include (a) impurity-induced (extrinsic) defects at low po, and (b) defect clustering at high PO,.
One measurement that may distinguish between the possible interpretations of the data is the po2 depen- dence of the correlation factor f for cation diffusion :
(a) If the interpretation of Dieckmann is correct,
f for cation diffusion should be independent of po2 (if the vacancies do not interact with each other).
(b) If there is a small concentration of trivalent impu- rity ions in the COO, these ions would introduce extrinsic vacancies that would make a larger relative contribution at low po2 than at high po2. Cobalt diffusion by bound impurity-vacancy pairs will occur with a much smaller f than for cation diffusion by free vacancies. Thus, f for cation diffusion would decrease with decreasing pO2. (c) Defect-clustering effects may be important at high po2 where the total vacancy concentration may reach 1
%.
As an example, calculations by Catlow et al. [15] for MnO show that at 6 = (corresponding to low po2 in COO), allthe defects are isolated vacancies; at 6 =
(corresponding to highp,, in COO), 87
o/,
of the vacan- cies are in clusters of four vacancies or larger. If the calculations for MnO are at all relevant for COO, defect clustering may be expected to play a major role in cobalt monoxide. Measurements on Fe, -60 suggest that f decreases when defect clustering becomes important [16]. Thus one expects f to decrease with i n c r e a ~ i n g p ~ , if defect clustering is important in C o o . In this paper we present results on the p,, depen- dence of f using isotope-effect techniques in order to select the appropriate interpretation of the diffu- sion and conductivity outlined in the above para- graph. Values ofD&
as a function of po2 are a by- product of the isotope-effect experiments and may be used to check the recent values of Dieckmann.For tracer diffusion in solids, information concern- ing the value o f f may be obtained from the relative diffusion rates of two isotopes of the same element [17]. The general expression for the isotopic mass effect
in diffusion is [18]
E
(
1 ) / [ ( ~ ) " ' - I] = f A K , (7) where the subscripts a and pertain to isotopes with masses m, and mp, respectively. The term AK is the fraction of the total translational kinetic energy at the saddle point, associated with motion in the direc- tion of the diffusional jump, that belongs to the j u m p ing atom. The measured value of E and the allowed values of f and AK may permit an unambiguous determination of the diffusion mechanism. Although AK may have different values for different mechanisms, AK is thought to be independent of pol for a given mechanism at constant temperature.2. Experimental results and discussion.
-
The tra- cer-sectioning technique was employed for the measu- rements of 60Co diffusion in COO single crystals. The various values of po2 were established by a C 0 2 - CO or Ar-0, gas mixture or pure O 2 flowing through the furnace. The samples were diffusion annealed at 1 200 OC and at the same po2 as was used for an extensive preanneal. For the isotope-effect measure- ments, "Co and 60Co were diffused simultaneously in the COO crystals. The ratio of the specific activities of the two isotopes, necessary for the determination of (DJDp) - 1, was determined at various positions in the sample to within 0.1%
by a half-life separation of the y activity of 55Co and 6 0 C ~ . Details of the expe- rimental technique may be found in reference [7]. Diffusion and isotope-effect measurements were made at six values of po2 a t 1 200 OC. The values of logD&
are plotted vs. log po2 in figure 1 ; the earlier- I 0
r
[ 0 PRESENT WORK AT I 2 0 0 t I'C0 MECKMANN 119771 AT 1210.~
MECKMANN (1977)AT 1 2 0 0 ' ~ CHEN e l ol (19691
A PRESENT WORK AT 12002 I'C
A CHEN el ol (19691
Z
4
0.60ISOTOPE EFFECT FOR CATION DIFFUSION IN COO* C6-32 1
results of Dieckmann [9] and the present authors [7] are also shown. The solid line is a result of Dieck- mann's empirical fit of the defect model to the non- stoichiometric data, the electrical conductivity data and his diffusion data [9]. The present results are in acceptable agreement with Dieckmann's empirical model. Lines with a slope of 114 and 116, correspond- ing to diffusion by singly ionized and doubly ionized vacancies [eqs. (5) and (6)], respectively, are also shown.
The values of f AK are also plotted vs. log po2 in
figure 1. A value o f f AK = 0.58 (within 3
%),
inde- pendent of temperature and oxygen partial pressure, is probably the best value for COO. This value off AK is consistent with diffusion by noninteracting vacancies and AK = 0.75 as previously discussed [7]. Of the four possible causes of curvature in the log
D;$
vs. log po, plot discussed in the Introduction,only the change in relative contribution of differently charged vacancies with varying po2 is consistent with the present, po2-independent value of f AK.
The other possible causes of curvature are expected to produce a po2-dependent value of .f AK that would
be observable within the present experimental error. As an example, if impurity-induced (extrinsic) defects or interstitials at low pO2 are responsible for the cur- vature in the log
D&
vs. log po2 plot, we can estimate the corresponding po2 dependence of f AK on theassumption that diffusion at po2 = 1 atm. is entirely
due to singly charged unassociated vacancies. We may assume that a 15
%
change in E with po2 is easily detected. The curvature in the logD$
vs. log po, plot then requires that 0.65 > E,,, > 0.45 for the extrinsic o r interstitial defects in order for the requir- ed po2 dependence of E to go undetected. However, E,,, would be expected to be less than Ein,/2(E,,, = 0.55, the value at high p,,) for a dumbbell interstitial [19], an interstitialcy [20], or an impurity- vacancy pair [21] mechanism or near unity for a freely migrating interstitial [22], none of which are within the range of 0.45 to 0.65 that would be consistent with the experimental observations. More qualitative arguments suggest that defect clustering, to the extent suggested by theory for MnO [15], is also inconsistent with the observed po, dependence of E.
DISCUSSION
Question. - J . PHILIBERT. Question. - L. W . BARR.
Are similar experiments being carried out on nickel Could the correlation factor not be deduced from oxide ? the conductivity and diffusion data ?
Rep&.
-
N. L. PETERSON.Similar measurements are possible for NiO but Reply.
-
N. L. PETERSON.they have not been performed. The isotope effect for Since electrical conductivity is by electron holes and nickel diffusion is possible (57Ni/66Ni) but it is not not cations in COO, the correlation factor cannot be an easy measurement. determined from conductivity and diffusion data. Conductivity does provide information about the hole
Question. - A. D. LE CLAIRE. (and vacancy) concentration and hole mobility.
If the mean charge state is varying with oxygen partial pressure, as you propose, might there not be corresponding changes in A K ? You said it was independent of pol.
Reply. - N. L. PETERSON.
A comparison of the electrical conductivity (which is related to the defect concentration) and the cation diffusion (which is related to the defect concentration and mobility) indicate that the defect migration energy must be independent of defect charge state and defect concentration over the investigated composition range in COO (see the analysis of Dieckmann). Thus, one might expect AK to be independent of p,,, which seems to be observed experimentally.
Question. - R. A. MCKEE.
If you could measure the chemical diffusion coef- ficient in this system, would you expect it to change much with dcfect concentration ?
Reply. - N. L. PETERSON.
A small change in chemical diffusion coefficient with varying po, may be expected since vacancy blocking effects on the diffusion of vacancies will change with po2. However, the accuracy in most chemical diffusion measurements would probably not permit the detection of this effect.
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