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The influence of the semiconductor properties on the Mössbauer emission spectra of 57Co cobalt oxide
1. Phys. Chem. Solti Vol. 45. No. 2, pp. I.91 190. 1984 Pnntcd in Great Britain.
0022-3697!84 f3.00 + .X3 Pergamon Press Ltd.
THE INFLUENCE OF THE SEMICONDUCTOR PROPERTIES ON THE Mt)SSBAUER EMISSION SPECTRA OF 57Co COBALT OXIDE? T. H~AMI, J. LOOCK and E. HUENGES Physik Department E 15 der Technischcn, UniversitPt Miinchen, James-Franck-Str., Federal Republic of Germany
8046 Garching,
J. FONTCUBERTA,X. OBRAWRS and J. TEIADA Fat. Fisica, Univcrsitat de Barcelona, Diagonal 645, Barcelona 28, Spain and
F. PARAK+ lnstitut fiir Physikalische Chemic dcr Universitet Miinster, Schlossplatz 4, 4400 Munster, Federal Republic of Germany
(Received 7 March 1983; accepted 23 June 1983)
Ah&ad--“Co, _XO Mossbauer sources were prepared at 1000°C and different oxygen pressures. The number x of Co vacancies, which depend on the oxygen pressure during the preparation, determine the Fe’+ fraction in the emission spectrum of the source at room-temperature. A theoretical model allows a correlation between these quantities. Measurements on Wo,_,O sources between room-temperature and IOOO”Cproved that at temperatures above 500°C electron relaxations between the “Fe” impurity, introduced in the lattice as a consequence of the “Co decay, and the valence band take place. A theoretical model was developed which describes these relaxation phenomena reasonably well. lNTRODUClTON
Nuclear transformations in solids allow one to study the microscopic properties of the material[l]. It is obvious that phenomena which occur after nuclear decay depend on the local environment of the radioactive impurities [2]. As we show in this paper they are also very sensitive to the nature and concentration of the defects existing in the solid matrix far away from the decaying nucleus. “Co is transformed into “Fe’” by electron capture (EC). Due to the EC process an electron is removed from an inner shell giving rise to the appearance of vacancy cascades which generate the Auger electron cascade. Pollak[3] has calculated that as a consequence of the decay of “Co*+ all ionized states from 2 to 7 are present with different probabilities in Fe. When s7Co is located in a crystal lattice the gamma ray emitted during the final step of the decay process, can be used to study the environment of the decay atom. Usually, the 14.4 keV radiation of “Fe” is analyzed by a “Fe Mossbauer absorber. The Mossbauer spectrum then reveals the environment of the “Co about IO-‘s after its decay. “Co0 is a compound which could be used to produce strong single line sources. However, since 1961[4] it is well known that two cation charge states
*Author to whom correspondence Wedicated
should be addressed. to Prof. U. Gonser on his 60Lbbirthday.
s7Fe2+ and 57Fe3+ are observed
in the Mossbauer emission spectra of “COO. Several interpretations have been tried in order to explain the appearance of “Fe)+ in the Miissbauer spectra[C14]. Wertheim[4] suggested that Fe*+ is the stable valence state. The Fe’+ is only an intermediate state before the capture of the last electron. Since the Miissbauer spectrum reveals the state about 10 ’ s after the “Co decay Fe’+ can still be present. Trifthiuser and Craig[S] performed delayed coincidence measurements on “Co0 in order to follow the Fe’ + to Fe -+* transition. However, no time dependence of the Fe’+ fraction of the Miissbauer spectrum was seen in the time range between 10 .’ and 10m9s. They, therefore, assumed that the “Fe’+ is permanently stabilized by a coupling of electron capture effects and some sort of preexisting lattice defects. Mullen and Ok[6-81 proposed the existence of two different Co0 species labelled Co0 (I) and Co0 (II), respectively. “Co0 (I) and “Co0 (II) compounds only produce “Fe* + and “Fe3 + , respectively. Normally, a mixture of Co0 (I) and Co0 (II) is formed depending on the conditions of the preparation giving rise to the two charge states in the Mossbauer spectra. Okada et al.[9] concluded from low temperature Mossbauer emission studies on “Co0 that the “Fe3+ is a metastable charge state. Schroer et al. [lo] and Trousdale er al.[l I] suggested that the presence of the ferric line in the Mossbauer spectra is related to the size of the particles and of the defects. Helms and Mullen’s[lZ] studies of Li, Ga, Cr 181
182
T.
HARAMI et al.
doped 57Co0 verified the dependence of the anomalous 57Fe3f line intensity on doping. Bhide and Shenoy [ 131 studied 57Co0 at different temperatures and observed that increasing the temperature increases the ferric line intensity. This was attributed to a monotonic increase of the relaxation time of the ferric ion with temperature. The temperature dependence of the relative area of the ferric line was also studied by Song and Mullen[l4]. In spite of the large number of investigations of Co0 no satisfying explanation for the existence of the Fe’+ line in the Mossbauer spectrum was given. Although the correlation of the 3 + valence state with the existence of Co defects was often suggested the following important problem was not solved: According to the phase diagram of Fisher and Tannhauser[lS] Co0 is not stoichiometric and should be written Co,-,O. In the compounds, investigated by Mossbauer spectroscopy, x was typically 10e4. Nevertheless, the Mossbauer spectrum showed that about one third of the iron was in the 3 + state. How can a small number of defects give rise to this amount of Fe’ +? Tejeda and Parak [161gave a physical model for the correlation of the number of Co vacancies and the formation of Fe’+ in 57Co,_,O. The aim of this paper is to explain the appearance of the ferric line in the Mossbauer spectra of 57Co,_,O in a more quantitative way taking into account the semiconductor properties of this compound. At the same time the temperature dependence of the 2+ and the 3 + valency state of the iron is investigated.
SEMICONDUCTOR PROPERTIES OF Co, _.O
Cobalt oxide, Co, _,O, is an oxygen excess p-type semiconductor which has the NaCl structure with a lattice parameter of 4.26 A[l7]. The Co vacancies act as acceptors and can be un-ionized, single or double ionized. Fisher and Tannhauser[ 151 have performed thermogravimetric and electrical conductivity measurements on Co, mXOin the temperature range between 900°C and 1450°C. They determined the temperature and oxygen pressure dependence of the vacancy concentration, the ionization energies of the vacancies, the free hole concentration in the valence band and the non-stoichiometry parameter x. Dieckmann[l7] has also analyzed the data of the non-stoichiometry, electrical conductivity and cation tracer diffusion on the basis of the defect model of Fisher and Tannhauser[lS]. The band structure of Co, -.O has also been clarified by electrical and optical measurements[l8]. The cobalt d band which characterizes the pertinent properties of Co, _,O is located between the cobalt 4s band and the oxygen 2p band. The energy gap between the cobalt d band and the cobalt 4s band is 2.8eV[l8]. According to the work of Fisher and Tannhauser [ 151and Dieckmann [ 171the defect structure of cobalt oxide involving x Co vacancies randomlv distributed without interactions between them
may be described by the equations ;o,=ot
(l-3):
[V*l=K p0 2l/Z
+ v*;
X
(1)
(2)
~v”l[Pl~ K w*1 *
V’Z$ v”+p;
-
(3) where [V*], [V’] and [I”‘] are the molar concentrations of neutral, single charged and double charged cationic vacancies respectively. [p] is the molar concentration of free holes and AH, is the change in the enthalpy when a cationic vacancy is created in the lattice. To each cationic vacancy belongs one O,* atom in the Co, _XO lattice which has to be created from an O2 molecule of the atmosphere containing 0, with the partial pressure PO*. E, and E2 are the energies which an electron belonging to the valence band needs in order to jump into the level V* or V‘, respectively. Adding one valence band electron to the neutral vacancy V* yields a free hole and a single charged vacancy V’ which in turn can accept one electron from the valence band yielding a double charged vacancy V” and another free hole. K,, K,, and Km are equilibrium constants taking into account the entropic terms. The electrical neutrality of the crystal is written [p] = [V’] + 2[ V”]. The total vacancy concentration gen excess is written as:
(4)
[x] giving the oxy-
[xl = [P] + [v’] + [VI.
(5)
From eqns (1) to (5) the total vacancy concentration [x] can be calculated for two different temperature regions:
[xl = [XIV,4, [xl = fxl(T,, 4,
E2r
E2,
Ho,
H,,
PO2)
PO,)
T
T’
>
Tct,
(6)
<
Tee,.
(7)
Tq is a characteristic equilibrium temperature which has to be determined by experiment. In the temperature regions below and above Tcq, [x] is determined by different parameters. Above T, the total vacancy concentration, [xl, depends on temperature. Well below T,, practically no defects can be incorporated into the lattice. The relative concentrations of the different vacancies change but the x-value re-
Influence of semiconductor properties of Miissbauer emission spectra of “Co cobalt oxide mains constant. The value of the energies AH,, E, and E, and the equilibrium constants have been determined by several authors[l7-191. In Table 1 we list the values of the above parameters used in this paper, taken from Ref. [17]. In the temperature range corresponding to T > T,, the molar concentrations of vacancies of all types can be calculated from eqns. (1) to (5). For the total free hole concentration, [PI, one obtains from these equations [PI3 - K,K, P02”*[p] - 2K,K,K, PO,“’ = 0.
(8)
For temperatures T’ < Teq the parameter x describing the difference to the stoichiometric compound remains to be x = x(T,,). The concentrations of the different types of vacancies have to be calculated in two steps. First of all eqns (lt(5) are used to calculate [x(T,)] at T = Tes. Then, this value is used together with eqns (2k(5) in order to get [V*], [V’] and IV”]. The temperature T enters eqns (2) and (3). Equation (1) is no longer used. As solution for the single charged vacancy concentration [V’] one obtains:
183
absolute PO2 values in our figures and tables may show a large error bar. At PO* = 1.2 x lo-’ bar the oxygen valve was closed and the sample was evacuated. At other oxygen pressures the oxygen gas was streamed through the tube. After oxidation the sample was cooled to room temperature in about 3 minutes. High temperature Miissbauer emission meaout in the range surements were carried 22°C < T < 1000°C at several pressures of O2 and at a number of different temperatures. The emission line of “Co, _ .O was analyzed with a conventional Mossbauer spectrometer using I(4 57Fe(CN), as absorber. Figure 1 shows room temperature Mlissbauer spectra of 57Co,_,O sources synthesized at different PO2 values at 1000°C. At the lowest value of PO* = 1.2 x lo-* bar only a ferrous single line spectrum is present, at higher POZ values two lines corresponding to ferrous and ferric ions aj)pear. Least square fits to the experimentally obtained Miissbauer spectra were performed with one or two Lorentzians, respectively. Table 2 summarizes the Mossbauer parameters of these spectra and the relative area of the ferrous line as a function of P02.
[v’]’ + (K, - 2[x( T,,)] - 4K,)[ I”]’
- (3K,]x(T,,)I + K,KJ]v'l
+ 2K,]x(T,,)12 = 0. (9)
EXPERIMENTAL DETAILS AND RESULTS
“CoCl, doped CoCl, was dropped onto an A&O3 disk and reduced to Co-metal in a HZ-atmosphere for 3 hours. The oxidation was performed in a quartz tube of 50 cm length at 1000°C at different pressures of O2 (to be denoted PO,). The tube was first evacuated and then filled with pure 02, the pressure of which was measured by a conventional vacuum pressure control device from Leybold-Heraeus. In the first series of experiments the pressure control was performed between the end of the quartz tube and the turbo vacuum pump. From the experimental results it became obvious that the PO* at the sample in the middle of the quartz tube differed drastically from the pressure measured at the control point. Therefore, a second pressure control was installed between the oxygen valve and the quartz tube. The pressures measured on both instruments differed up to two orders of magnitude. In the following we give the average value between the two measurements assuming a linear pressure gradient within the quartz tube. It should be mentioned, however, that the
-20 -10 a0 1.0 VELOCITY [mm Is1
Fig. 1. Miissbauer emission spectra of “Co, _ XOsources at room temperature. The sources were prepared at 1OOOC with the following oxygen pressures: (a) 1.2 x 10-s bar; (b) 7.9 x lo-‘bar; (c) 1.6 x 10m7bar; (d) 7.3 x 10-‘bar. The solid line gives a least squares fit with two Lorentxians. The parameters of the fit are listed in Tab. 2.
Table 1. Parameters of eqns (I x5) E, = 0.53 eV E2 = 0.74 eV
AH,, = 0.27 eV Kti=
1.6 x 10-2s
20
used in this paper. K,, = 2.4 [mol - ‘1 K,=O.l7[mol-‘1
184
T. HARAMIet
al.
Table 2. Parameters obtained from a least squares fit of two Lorentzians to the Mossbauer spectra in Fig. 1. The sources were prepared at 1000°C and the partial pressure, PO,, of oxygen and investigated at room temperature. 6.9 and r,, gives the isomer shift and the experimental line width. respectively, as measured with a K,Fe (CN), absorber. The errors in 6s and Fur, are about +0.005 nun/s.
A,(R)/(A,(R) + A,(R)) gives the relative contribution of the Fe2+ line to the total area of the Miissbauer spectrum at room temperature. The error is about 3%
6S
1.2 x 7-9 x 1.6 x 7.3 x
[mm/s1
[mm/s1
A,(R) A,(R) + A,(R)
1.094 1.090 1.101 1.082
0.395 0.382 0.383 0.414
100 85 83 78
10-s 10-n lo-’ 10-7
l- -P
Figure 2 gives the value A,(R)/&(R) + A,(R)) as a function of PO* at the preparation. (R) refers to room temperature Mossbauer spectra. Miissbauer spectra of 57Co,_,O sources in the temperature range between 22 and 1000°C keeping PO, constant are shown in Fig. 3 and Fig. 4. The Mijssbauer parameters of these spectra together with the results of two other series of measurements at different PO, values are listed in Table 3. Figure 5 gives the isomer shifts for the different sources as a function of the source temperature. Below 500°C for PO2 > 1.2 . lo-* bar, the spectra consist of two lines corresponding to ferrous and ferric ions, respectively. The line intensities can be deduced from the area under the two lines in the Mossbauer spectra. Above 500°C the ferrous and ferric lines collapse into a single line. One may assume that in this temperature region the experimentally obtained isomer shift, SS is still an average of contributions from Fe* + and Fe3 + . It can empirically be described by: 6s = ~StFe2+)+W’W2(T)
l.O/
%
6S
l- CXP
[mm/s1 [mm/s1
0.437 0.443 0.425
0.624 0.455 0.561
The isomer shifts 6S(Fe*+), and 6S(Fe3+), of the Fe*+ and the Fe3+ contributions at the temperature T are obtained from a linear extrapolation of the values measured between room temperature and 400°C according to the solid lines in Fig. 5. It is then possible to adjust the areas A,(T) and A,(T) of the Fe2+ and the Fe3+ component according to eqn (10) in order to get the experimentally obtained 6S value.
+ A3V))
+ GS(Fe3+)rA3(T)I(A2(T) + A,(T))
E 0.8.
Fe3+ fraction
Fe2+ fraction
PWarl
(10)
__--__--_
z .'
E 2 -T+ + 0.6. a= -74 a 0.L.
-log(l%,
(bar))
Fig. 2. Area fraction A,(R)/(A,(R) + A,(R)) of the Fe*+ line in the Miissbauer spectrum at room temperature as a function of the oxygen pressure during the preparation at 1000°C. The dashed line corresponds to a fit of eqn (13).
Fig. 3. Miissbauer emission spectra of 57Co,_,O source prepared at 1000°C and PO, = 1.2 x 10-s bar. The PO, was kept constant at this value during the measurements where the sources were at the different temperatures. The solid line gives a least squares fit with two Lorentzians. The parameters of the fit are listed in Table 3.
Influence of semiconductor properties of Miissbauer emission spectra of 57Cocobalt oxide
1
Fig. 4. The same as Fig. 3. The oxygen pressure was, however, PO, = 7.9 bar. Note that at 400°C the contributions of Fe2+ and Fe’+ start to give resolved Lorentzians.
The relative area of the Fez+ contribution to the Miissbauer spectra, A*(T), is plotted as a function of the temperature in Fig. 6 for different “CO, _,O sources. Carrying out the oxidation at O2 pressures higher than lo-’ bar and temperatures above 600°C a mixture of Co,O, and Co0 revealed itself in the MGssbauer spectrum. No comparisons with our calculations were performed for such samples. DISCUSSION
In this chapter we want to show that the semiconductor properties of Co, _,O as outlined in chapter 2 can explain the presence of Fe’+ in a Miissbauer emission spectrum of s7Co, _XO sources quantitatively. During the decay 57Cois transformed into 57Femby K or L electron capture (EC). Due to the EC process, an electron is removed from one inner shell giving rise to the appearance of vacancy cascades and the emission of Auger electrons. The emitted Auger electrons having energies between 1 keV and 7 keV are then absorbed in the Co0 material. Due to the large Coulomb potential created by the iron daughter, practically all Auger electrons come back to the iron in a time less than IO-’ s yielding “Fern3 + . In pure Co, _,O the only defects existing are cationic vacancies which give rise to the appearance of acceptor levels in the energy gap. Very shortly after the EC
185
process in 57Co takes place a new level appears in the energy gap corresponding to the “Fem3+ daughter which corresponds to a singly ionized iron level (compare Fig. 7). There remains the discussion of the mechanisms involved in the process of electron recombination for the last Auger electron appearing after each nuclear decay. A rough estimate tells us that the Auger electron is absorbed in a sphere with a radius of about 1000 A around the decaying 57Co. It reaches the conduction band and can freely move till it reaches the Fe’+ yielding Fe ’ + after recombination. Since the distance of maximal 1000 A is rather small the recombination occurs normally in times much shorter than lo-‘s . Fem3+ recombines to Fe&+ before the emission of the 14.4 keV radiation thus giving rise to a Fez+ line in the Miissbauer spectrum. During the motion in the conduction band the last Auger electron can reach, however, an unionized or a single ionized vacancy which acts as a recombination center. The electron is trapped and is no longer available for the recombination with Fern3+ . Therefore, Fern3+ decays yielding in the Miissbauer spectrum the Fe3+ line. The trapping of the last Auger electron occurs in a time which is short compared to lo-‘s. It is, therefore, obvious that Triftshauser and Craig[S] could not resolve any time dependence of the formation of the Fern3+ . The probability that the last Auger electron is trapped before reaching the Fe’“3+ is clearly correlated with the number of vacancies. There exists, however, a second possibility to reduce the Fem3+ to Fe”‘+. An electron from the valence band of the Co, _,O may jump to the Fem3+. We shall use this second process for the discussion of the temperature dependence of the Co, _*O emission spectra between 200 and 1000°C. The analysis of our spectra justifies the assumption that this process occurs only at higher temperatures and has a characteristic time of the order of lo-’ s. Therefore, relaxation phenomena between Fe3+ and Fe*+ are obtained in the Mijssbauer spectra at higher temperatures in accordance with Song and Mullen [14]. Since the time scales of the two reduction mechanisms of Fem3+ are rather different one can treat the processes separately. We consider first the fast process which dominates the room-temperature spectra. The maximal energy of an Auger electron following the EC in “Co is the energy of the Km transition in iron (6.5 keV). The maximal range of this electron in the Co0 material can be estimated by [20]: R[g/cm*]=O.ll(,/(l
+22.4E2(MeV))-
1). (11)
Taking into account a density of Co0 of 6.43 g/cm3 the electron is absorbed in a distance not longer than 1000 A from the decaying 57Co. For our estimations we assume that, in the average, such an electron can be trapped by vacancies in a sphere with a radius of about 1000 A. Even in a source with a very high specific activity it is very improbable that two Fem2+
0.796 0.725 0.649 0.513 0.492 0.382
500 600 700 800 900 1000
rev
[mm/s1
0.365 0.389
0.504 0.465 0.481 0.569 0.475 0.465
6S
[mm/s1
1.005 0.870
0.214 0.176 0.124 0.067 0.022 0.029
0.731 0.459 0.385 0.424 0.518 0.546
0.372 0.404
[mm/s1
78 90
%
73 11
0.469 0.579 0.393 0.429 0.434 0.438 0.454 0.477
0.963 0.785 0.135 0.081 0.034 0.003 - 0.035 0.029
M'-)+4(T)
A,(T)
0.437 0.480
rev
0.362 0.239
Fez+
0.304 0.192
[mm/s1
6S
unresolved unresolved unresolved unresolved unresolved unresolved
Fe3 +
0.574 0.438
[mm/s1
r ev
unresolved unresolved unresolved unresolved unresolved unresolved
0.339 0.213
[mm/s1
84 12
6S
AZ(T)
Fe3’
A,(T) + A,(T) %
PO, = 7.9 x 10m8bar
IO-‘bar
%
l&S
0.700 0.538 0.524 0.492 0.495 0.542
0.463 0.369 0.206 0.085 0.056 0.092 PO,=7.3x
0.359 0.441
[mm/s1
r“P
0.966 0.793
[mm/s1
6s
[mm/s1
rw
-
[mm/s1
I- -P
Fe2 +
[mm/s1 I [mm/s1
Fe’ +
unresolved unresolved unresolved unresolved unresolved unresolved
bm/sl
6S
Fe’+
[mm/s1
6S
unresolved unresolved unresolved unresolved unresolved unresolved
A,(T) A,V)+A,(T)
100 100
%
A,(T) + A,(T)
A,(T)
PO, = 1.2 x 10m8bar
PO, = 1.6 x IO-‘bar
Fez+
1.002 0.870
200 400
[mm/s1
I- ew
[“Cl
6S
Fe2+
temo.
Source
0.653 0.523
[mm/s1
rcw
Table 3. Parameters obtained from Miissbauer spectra with K,Fe(CN), absorber and 57Co,_r0 sources, prepared at 1000°C at four different oxygen pressures. 6S and Fexp give the isomer shift and the experimental line width, respectively. The errors in SS and Fe_, are about +O.O05mm/s. A,(T)/(A,(T) + A,(T)) gives the relative contributions of the Fe ‘+ line to the total area of the Miissbauer spectrum at the temperature T. The error is about 3%. Each source was investigated at eight different temperatures
Influence of semiconductor
properties of Miissbauer emission spectra of 57Co cobalt oxide
.
oc
200 Gco 600 800 loo TEMPERATURE (“Cl
TEMPERATURE
(“C)
1
0
1
,
200 400 600 800 1000 TEMPERATURE
I
0
200 600 TEMPERATURE
I°C )
200 400 600 800 1000 TEMPERATURE (‘C)
1oC t’-
Fig. 5. Isomer shift 6.9 [mm/s] as a function of the source temperature; upper line: GS(Fe’+), lower line: SS(Fe”+), petted line: 6s as a sum of contributions3f+rom Fe*+ and resolved Fe*+ and Fe lines. (a) PO2 1 1.; 10m8bar; (b) PO, = 7.9 x lo-* bar; (c) PO2 = 1.6 x lo-‘bar; (d) PO, = 7.3. lo-‘bar; at 1000°C during preparation. centers are available within IO-’ s in the volume of this sphere. Therefore, [V*] neutral vacancies [v’] single charged vacancies and one Fe”“+ per 4 x lo-” cm’ yielding [Fe”‘+] = 2.8 x lOI mol-’ are in competition for this Auger electron. The probability of the capture of electrons he-
. 0
.
.
200 LOO 600 800 1ooc TEMPERATURE (“C)
Fig. 6. Fraction A,(T)/(A,(T)+A,(T)) of the Fe*+ contribution to the Miisbauer spectrum at different temperatures. The sources were prepared at (a) PO, = 1.2 x 10e8 bar; (b) PO1 = 7.9 x IO-* bar; (c) PO,= 1.6 x lo-‘bar; (d) PO,= 7.3 x IO-‘bar. The circles give experimental values, the solid line is the least squares fit of a theoretical model. In Fig. 6(a) PO, values were used in the fitting procedure which differ from the measured values. For details compare the text.
T. HARAMIer al.
188
longing to the conduction 1211:
band by a trap is given by
A” = ?&(F) .
c a,,N,
(12)
where N, is the molar concentration of trap center i at the temperature T, G,,,(F)is the thermal velocity of electrons in the conduction band and u,, is the electron capture cross section for the trap center i. The relevant cross sections are: u,,., cry and urc which refer to the electron capture by a neutral, a single charged and a Fe’“‘+ trap, respectively. The ratio of Auger electrons trapped in the vacancies and in the ionized iron levels can be written:
A,(R) -= A,(R)
ur[V*l+ u,[U = a[V’] + b[V’]. (13)
spectra dealing now with electron transfer between the Fe” acceptor and the valence band, Now the concentration [Fe”)+ lo _ , s. The ionized ,,1,fm3y longer constant during level may be occupied by an electron coming from the valence band and a hole of the valence band can recombine with an electron belonging to the “Fem2+ level. Since our experiments are performed as emission Miissbauer spectroscopy, we have: [Fe”] = [Fem2+(t)] + [Fem3+(r)] = 2.8 x IO” mol- I. (14) The change of [Fem2+(t)] with time can be written: d[Fem2+(r)J = - L2[Ff12+(r)] dt
crrc[Fem3+]
If no electron transfer between the Fe” level and the valence band occurs the ratio A,(R)/A,(R) gives the ratio of the ferric and ferrous Mossbauer line intensities at room temperature. We are now in the position to compare our room temperature experiments with the theoretical model described above. The ratio A,(R)/&(R) is taken from the Mosbauer spectrum. In order to explain our room temperature experiments one has to adjust the two parameters a = uy/(uFe. [Fem3+]) and b = u,J(ur,[Fem3+]). For a calculation of the vacancy concentrations [I’*] and [V’] one has to estimate the equilibrium temperature Tq. Using T, = 1000°C and assuming this way that the total vacancy concentration, [xl, is at room temperature the same as at 1000°C proved to be a bad assumption. No values for a and h could be obtained to explain all relevant experiments. This was, however, possible, when T, was taken to be 400°C in agreement with [23] and v41. The dashed line in Fig. 2 was obtained with a = 1.3 x lO-‘9 [mol] and b = I.1 x 10mi9 [mol]. Note that here not A,(R)/A,(R) is plotted but A,(R)/(A,(R) + A,(R)). It is important to mention that only one set of parameters a and b can explain Mossbauer spectra from samples prepared at different PO,-values. We proceed to the discussion of the temperature dependence of the “Co, _,O emission Miissbauer
+ d,([Fe”] - [Fem2+(r)])
(15)
where i, characterizes the recombination probability of an iron electron with a hole in the valence band while i, gives the probability that an electron of the valence band jumps to Fe’ + . Equation (I 5) can easily be solved giving: --
a3 12 +
x
,-ca+wr+
13
13 (16) 1.2 +
I3
where
[Fem2’W/~Feml = A2WI(A2W + A3VW (17) A,(R) and A,(R) are the ferrous and the ferric absorption areas of the Miissbauer spectrum at room temperature where the electron relaxation between the valence band and the Fe” impurity can be neglected. The Mossbauer emission spectroscopy follows the jumping of electrons between the iron and the valence band over about 7M = lo-‘s. The spectrum at higher temperatures measures, therefore, an average concentration ([Fem2+]): 3j
[Fem2+W1 e-,,fu 0
dt
(18)
P’“l
yielding:
I> _ 4 Fe’“1 1, + I.3 A,(R) +
([Fe”‘+
A,(R) + A,(R)
=
(I’*) and Fig. 7. Band structure of Co, _ xO with un-ionized __,.. smgle ionized (V’) vacancies and a ke”” impurity.
(n264
,>.
--
a3
I
1.2+ 1, > r&l, + A,) + 1 (19)
Calculated (n,(A)) values according to eqn. (19) using A2and A3as adjustable parameters can now be compared with the experimental values obtained
Influence of semiconductor properties of Mossbauer emission spectra of “Co cobalt oxide from A,(T)/@,(T) + A,(T)) at higher temperatures, using eqn (IO). Instead of using & and & as free parameters in a fit procedure we tried to correlate the transition probabilities with physical quantities of the Co, ..O compound. We assume:
Ip) is again the molar inundation of free holes while (p’] = N, exp (~~~~(~~~)~. N, represents the density of states in the valence band and is given by N, = 2(2nm,,k,T/h*)‘/* where m, is the effective mass of a small polaron and has been taken to be mp = 4m, in accordance with [22]. kB is the Boltzmann constant and h is the Planck number. & is the energy which is necessary to promote an electron of the valence band to Fe3 + . Equation (20) assumes that the transition probabilities depend only on the concentrations b] and Ip’]. The proportionality constant, /I, is assumed to be equal for both processes and can be written in the form of a cross section, uw: cf%= s /r3,ho,)
(21)
where rYJh(p)is the thermal velocity of a free hole in the valence band. In Fig. 6 the solid lines give the results of a least squares Iit of eqn (19) using also eqn (20) and eqn (21) with T- =4OO”C. Our model reproduces well the strong variation of the ferrous line intensity at T s 500°C which in fact is related to the increasing defect concentration at T > T_,, For T > 700°C the increase of the ferrous component of the observed single line is connected with the temperature at which relaxation phenomena appear. The quantitative agreement between calculations and experimental data is, however, of different quality for the different PQ-values. While it is reasonably good at PO2 = 7.9 x 10’“*bar, the quantitative discrepancy becomes quite for large PG2= 1.6 x 10 .‘bar and PG2=7.3* IO-‘bar at higher tcm~ratur~. This is not surprising since our theoretical model is based on a number of assumptions which are only approximately valid. We used the values of the free hole concentration b] and the vacancy concentrations, [I’&] and [V&J, from the above discussion of the defect structure. However, there has been no useful data for physical quantities of the defect structure on Co, _XO in the whole temperature range 22-1000°C. The electrical properties of Co, _ .O have been studied mostly by doping, for example with Li[25], Co, _,O without dopants has only been measured at high temperatures above 900°C. The presence of other phase Co,O,[24] in Co, _,O and the different kinds of more complex defects(271 and grain boundariesj251 make it complicate to get a better model at present. Good agreement between the experimental data and the calculation was obtained from the preparation at extremely low oxygen pressure. It was necessary, however, to use PQ = 1.2 x IO-‘*bar in the calculation instead of the observed
189
PQ = 1.2 x IO-* bar. The solid lines give calculated Fe”’ fractions for different oxygen pressures. It is obvious that our pressure control was not sensitive enough to give a realistic value at these conditions. In practice we used the best vacuum which we could obtain by our turbo pump during the measurements of this sample. From the fits shown in Fig. 6 we obtained cr,+= 1 x lo-i9 cm2 and & = 0.62 eV as optimal parameters. The distance of 0.62 eV of a Fe3 ’ impurity from the valence band formed by the 3d6 electrons of the Co in COO seems reasonable. Together with the parameters u and b obtained according to eqn (13) from the room temperature experiment using (Fe”] = 2.8 x IO” mol-” ’ one gets the following cross sections for electron captures: ur = 3.8 x 10-23cm2 and ey = 3 x 10-23cm2. The comparison with ure = 1 x 10 - I9cm* shows that the acceptor character of an Fe’+ impurity is much higher than those of cationic vacancies. CONCLUSIONS
The Miissbauer emission spectra of “Co, _ ,O are very sensitive to the nature, charge and concentration of the point defects existing in the solid matrix. The cationic vacancies act as trapping centers for the emitted Auger electrons. The iron daughter impurities also act as trapping centers with higher cross section. The charge state “Fe3+ in the Miissbauer spectra is related to the existence of cationic vacancies in the lattice. Increasing the concentration of vacancies, increases the probability of Auger electron capture. In the case of stoichiometric cobalt oxide, no Auger electrons are lost due to the non-existent of point defects in the lattice. Therefore, in order to produce single iron divalent sources, stoichiometric “Co0 must be obtained. Unfortunately, electron traps can be introduced not only by vacancies but also by rather low impurities. The preparation of single line s7CoG source often fails if the “‘Co is not purified enough. We have also carried out Miissbauer emission experiments introducing ‘Co in p.p.m in a Co0 single crystal. The results are similar to those obtained in the case of powder samples. Hence it can be concluded that the particle size has no influence on the Miisshauer emission spectra. At temperatures below 500°C the Fe*’ as well as the Fe3” state is stable. Taking into account the charge exchange between acceptor level and the valence band one can explain the variation of the ferric line intensity at higher temperatures. ~c~ffwIe~e~~r~-~is work was supported by the Bund~i~i~~urn f”ur Forschung und Technologie der Bundesrepubiik Deutscbland. We gratefully acknowledge the continuous support of R. L. Mbssbauer and H. Morinaga. We thank U. Gonser and R. L. Miissbauer for many helpful discussions. REFERENCES
I. ~TP-In~e~ational
Review of Science Radj~~emis~r,~.
VoL 8. Consultant Editor H. J. Emeleus. FRS volume Editor A. G. Maddock (1972).
T. HARAMIet al.
190
2. Newton G. W. A. (Rd.), Specialist Report of the Chemical Society, Radiochemistry I, l-37. Chemical Society,
London (1972). 3. Pollak H.. Phvs. Stat. Solidi 2, 720 (1962). 4. Wertheim G. K., Phys. Reu. 124, 764 (1961). 5. Triftshiiuser W. and Craie._.P. P.. Phvs. Rev. 162. 274 (1967). 6. Mullen J. G. and Ok H. N., Phys. Rev. Lett. 17, 287 (1966). 7. Ok H. N. and Mullen J. G., Phys. Rev. 168, 550 (1968). 8. Ok H. N. and Mullen J. G., Phys. Rev. 168,563 (1968). 9. Okada K. and Shinjo T., J. Phys. Sot. Japan 36, 1017 (1974). 10. Schroer D. and Triftshluser W., Phys. Rev. L.ett. 20, 1242 (1968). 11. Trousdale W. and Craig P. P., Phys. Z.&t. 2717, 552 (1968). 12. Helms W. R. and Mullen J. G., Phys. Rev. B4, 750 (1971). 13. Bhide V. G. and Shenoy G. K., Phys. Rev. 147, 306 I<
(1966). 14. Song C. and Mullen J. G., Phys. Rev. 14B, 2761 (1976).
15. Fischer B. and Tannhauser D. S., J. Chem. Phys. 44, 1663 (1966). 16. Tejada J. and Parak F., Hyp. Int. 10, 1227 (1981). 17. Dieckmann R., Z. Phys. Chem., Neue Forge Bd. 1075, 189 (1977). 18. Goodenough J. B., Les Oxides des Metaux de Transition. Gautiers-Villars, Paris (1973). 19. Kruger F. D. and Vink H. S., Solid St. Phys. 3, 310 (1965). 20. Siegbahn K., Alpha- Beta- and Gamma-ray Spectroscopy, p. 23. North Holland, Amsterdam (1968). 21. Milnes A. G., Deep Impurities in Semiconductors. Wiley, New York (1973). 22. Adler D. and Heinlieb J., Phys. Rev. B2, 3112 (1970). 23. Osbum C. M. and Vest, R. W., J. Phys. Chem. Solids 32, 1343 (1971). 24. Choi J. S. and Yo C. H., Znorg. Chem. 13, 1720 (1974). 25. Bosman A. J. and van Daal H. J., Aduan. Phys. 19, 1 (1970). 26. Spencer C. D. and Schroer D., Phys. Rev. B9, 3658 (1974). 27. Hed A. Z., .I. Chem. Phys. 50, 2935 (1969).
0022-3697!84 f3.00 + .X3 Pergamon Press Ltd.
THE INFLUENCE OF THE SEMICONDUCTOR PROPERTIES ON THE Mt)SSBAUER EMISSION SPECTRA OF 57Co COBALT OXIDE? T. H~AMI, J. LOOCK and E. HUENGES Physik Department E 15 der Technischcn, UniversitPt Miinchen, James-Franck-Str., Federal Republic of Germany
8046 Garching,
J. FONTCUBERTA,X. OBRAWRS and J. TEIADA Fat. Fisica, Univcrsitat de Barcelona, Diagonal 645, Barcelona 28, Spain and
F. PARAK+ lnstitut fiir Physikalische Chemic dcr Universitet Miinster, Schlossplatz 4, 4400 Munster, Federal Republic of Germany
(Received 7 March 1983; accepted 23 June 1983)
Ah&ad--“Co, _XO Mossbauer sources were prepared at 1000°C and different oxygen pressures. The number x of Co vacancies, which depend on the oxygen pressure during the preparation, determine the Fe’+ fraction in the emission spectrum of the source at room-temperature. A theoretical model allows a correlation between these quantities. Measurements on Wo,_,O sources between room-temperature and IOOO”Cproved that at temperatures above 500°C electron relaxations between the “Fe” impurity, introduced in the lattice as a consequence of the “Co decay, and the valence band take place. A theoretical model was developed which describes these relaxation phenomena reasonably well. lNTRODUClTON
Nuclear transformations in solids allow one to study the microscopic properties of the material[l]. It is obvious that phenomena which occur after nuclear decay depend on the local environment of the radioactive impurities [2]. As we show in this paper they are also very sensitive to the nature and concentration of the defects existing in the solid matrix far away from the decaying nucleus. “Co is transformed into “Fe’” by electron capture (EC). Due to the EC process an electron is removed from an inner shell giving rise to the appearance of vacancy cascades which generate the Auger electron cascade. Pollak[3] has calculated that as a consequence of the decay of “Co*+ all ionized states from 2 to 7 are present with different probabilities in Fe. When s7Co is located in a crystal lattice the gamma ray emitted during the final step of the decay process, can be used to study the environment of the decay atom. Usually, the 14.4 keV radiation of “Fe” is analyzed by a “Fe Mossbauer absorber. The Mossbauer spectrum then reveals the environment of the “Co about IO-‘s after its decay. “Co0 is a compound which could be used to produce strong single line sources. However, since 1961[4] it is well known that two cation charge states
*Author to whom correspondence Wedicated
should be addressed. to Prof. U. Gonser on his 60Lbbirthday.
s7Fe2+ and 57Fe3+ are observed
in the Mossbauer emission spectra of “COO. Several interpretations have been tried in order to explain the appearance of “Fe)+ in the Miissbauer spectra[C14]. Wertheim[4] suggested that Fe*+ is the stable valence state. The Fe’+ is only an intermediate state before the capture of the last electron. Since the Miissbauer spectrum reveals the state about 10 ’ s after the “Co decay Fe’+ can still be present. Trifthiuser and Craig[S] performed delayed coincidence measurements on “Co0 in order to follow the Fe’ + to Fe -+* transition. However, no time dependence of the Fe’+ fraction of the Miissbauer spectrum was seen in the time range between 10 .’ and 10m9s. They, therefore, assumed that the “Fe’+ is permanently stabilized by a coupling of electron capture effects and some sort of preexisting lattice defects. Mullen and Ok[6-81 proposed the existence of two different Co0 species labelled Co0 (I) and Co0 (II), respectively. “Co0 (I) and “Co0 (II) compounds only produce “Fe* + and “Fe3 + , respectively. Normally, a mixture of Co0 (I) and Co0 (II) is formed depending on the conditions of the preparation giving rise to the two charge states in the Mossbauer spectra. Okada et al.[9] concluded from low temperature Mossbauer emission studies on “Co0 that the “Fe3+ is a metastable charge state. Schroer et al. [lo] and Trousdale er al.[l I] suggested that the presence of the ferric line in the Mossbauer spectra is related to the size of the particles and of the defects. Helms and Mullen’s[lZ] studies of Li, Ga, Cr 181
182
T.
HARAMI et al.
doped 57Co0 verified the dependence of the anomalous 57Fe3f line intensity on doping. Bhide and Shenoy [ 131 studied 57Co0 at different temperatures and observed that increasing the temperature increases the ferric line intensity. This was attributed to a monotonic increase of the relaxation time of the ferric ion with temperature. The temperature dependence of the relative area of the ferric line was also studied by Song and Mullen[l4]. In spite of the large number of investigations of Co0 no satisfying explanation for the existence of the Fe’+ line in the Mossbauer spectrum was given. Although the correlation of the 3 + valence state with the existence of Co defects was often suggested the following important problem was not solved: According to the phase diagram of Fisher and Tannhauser[lS] Co0 is not stoichiometric and should be written Co,-,O. In the compounds, investigated by Mossbauer spectroscopy, x was typically 10e4. Nevertheless, the Mossbauer spectrum showed that about one third of the iron was in the 3 + state. How can a small number of defects give rise to this amount of Fe’ +? Tejeda and Parak [161gave a physical model for the correlation of the number of Co vacancies and the formation of Fe’+ in 57Co,_,O. The aim of this paper is to explain the appearance of the ferric line in the Mossbauer spectra of 57Co,_,O in a more quantitative way taking into account the semiconductor properties of this compound. At the same time the temperature dependence of the 2+ and the 3 + valency state of the iron is investigated.
SEMICONDUCTOR PROPERTIES OF Co, _.O
Cobalt oxide, Co, _,O, is an oxygen excess p-type semiconductor which has the NaCl structure with a lattice parameter of 4.26 A[l7]. The Co vacancies act as acceptors and can be un-ionized, single or double ionized. Fisher and Tannhauser[ 151 have performed thermogravimetric and electrical conductivity measurements on Co, mXOin the temperature range between 900°C and 1450°C. They determined the temperature and oxygen pressure dependence of the vacancy concentration, the ionization energies of the vacancies, the free hole concentration in the valence band and the non-stoichiometry parameter x. Dieckmann[l7] has also analyzed the data of the non-stoichiometry, electrical conductivity and cation tracer diffusion on the basis of the defect model of Fisher and Tannhauser[lS]. The band structure of Co, -.O has also been clarified by electrical and optical measurements[l8]. The cobalt d band which characterizes the pertinent properties of Co, _,O is located between the cobalt 4s band and the oxygen 2p band. The energy gap between the cobalt d band and the cobalt 4s band is 2.8eV[l8]. According to the work of Fisher and Tannhauser [ 151and Dieckmann [ 171the defect structure of cobalt oxide involving x Co vacancies randomlv distributed without interactions between them
may be described by the equations ;o,=ot
(l-3):
[V*l=K p0 2l/Z
+ v*;
X
(1)
(2)
~v”l[Pl~ K w*1 *
V’Z$ v”+p;
-
(3) where [V*], [V’] and [I”‘] are the molar concentrations of neutral, single charged and double charged cationic vacancies respectively. [p] is the molar concentration of free holes and AH, is the change in the enthalpy when a cationic vacancy is created in the lattice. To each cationic vacancy belongs one O,* atom in the Co, _XO lattice which has to be created from an O2 molecule of the atmosphere containing 0, with the partial pressure PO*. E, and E2 are the energies which an electron belonging to the valence band needs in order to jump into the level V* or V‘, respectively. Adding one valence band electron to the neutral vacancy V* yields a free hole and a single charged vacancy V’ which in turn can accept one electron from the valence band yielding a double charged vacancy V” and another free hole. K,, K,, and Km are equilibrium constants taking into account the entropic terms. The electrical neutrality of the crystal is written [p] = [V’] + 2[ V”]. The total vacancy concentration gen excess is written as:
(4)
[x] giving the oxy-
[xl = [P] + [v’] + [VI.
(5)
From eqns (1) to (5) the total vacancy concentration [x] can be calculated for two different temperature regions:
[xl = [XIV,4, [xl = fxl(T,, 4,
E2r
E2,
Ho,
H,,
PO2)
PO,)
T
T’
>
Tct,
(6)
<
Tee,.
(7)
Tq is a characteristic equilibrium temperature which has to be determined by experiment. In the temperature regions below and above Tcq, [x] is determined by different parameters. Above T, the total vacancy concentration, [xl, depends on temperature. Well below T,, practically no defects can be incorporated into the lattice. The relative concentrations of the different vacancies change but the x-value re-
Influence of semiconductor properties of Miissbauer emission spectra of “Co cobalt oxide mains constant. The value of the energies AH,, E, and E, and the equilibrium constants have been determined by several authors[l7-191. In Table 1 we list the values of the above parameters used in this paper, taken from Ref. [17]. In the temperature range corresponding to T > T,, the molar concentrations of vacancies of all types can be calculated from eqns. (1) to (5). For the total free hole concentration, [PI, one obtains from these equations [PI3 - K,K, P02”*[p] - 2K,K,K, PO,“’ = 0.
(8)
For temperatures T’ < Teq the parameter x describing the difference to the stoichiometric compound remains to be x = x(T,,). The concentrations of the different types of vacancies have to be calculated in two steps. First of all eqns (lt(5) are used to calculate [x(T,)] at T = Tes. Then, this value is used together with eqns (2k(5) in order to get [V*], [V’] and IV”]. The temperature T enters eqns (2) and (3). Equation (1) is no longer used. As solution for the single charged vacancy concentration [V’] one obtains:
183
absolute PO2 values in our figures and tables may show a large error bar. At PO* = 1.2 x lo-’ bar the oxygen valve was closed and the sample was evacuated. At other oxygen pressures the oxygen gas was streamed through the tube. After oxidation the sample was cooled to room temperature in about 3 minutes. High temperature Miissbauer emission meaout in the range surements were carried 22°C < T < 1000°C at several pressures of O2 and at a number of different temperatures. The emission line of “Co, _ .O was analyzed with a conventional Mossbauer spectrometer using I(4 57Fe(CN), as absorber. Figure 1 shows room temperature Mlissbauer spectra of 57Co,_,O sources synthesized at different PO2 values at 1000°C. At the lowest value of PO* = 1.2 x lo-* bar only a ferrous single line spectrum is present, at higher POZ values two lines corresponding to ferrous and ferric ions aj)pear. Least square fits to the experimentally obtained Miissbauer spectra were performed with one or two Lorentzians, respectively. Table 2 summarizes the Mossbauer parameters of these spectra and the relative area of the ferrous line as a function of P02.
[v’]’ + (K, - 2[x( T,,)] - 4K,)[ I”]’
- (3K,]x(T,,)I + K,KJ]v'l
+ 2K,]x(T,,)12 = 0. (9)
EXPERIMENTAL DETAILS AND RESULTS
“CoCl, doped CoCl, was dropped onto an A&O3 disk and reduced to Co-metal in a HZ-atmosphere for 3 hours. The oxidation was performed in a quartz tube of 50 cm length at 1000°C at different pressures of O2 (to be denoted PO,). The tube was first evacuated and then filled with pure 02, the pressure of which was measured by a conventional vacuum pressure control device from Leybold-Heraeus. In the first series of experiments the pressure control was performed between the end of the quartz tube and the turbo vacuum pump. From the experimental results it became obvious that the PO* at the sample in the middle of the quartz tube differed drastically from the pressure measured at the control point. Therefore, a second pressure control was installed between the oxygen valve and the quartz tube. The pressures measured on both instruments differed up to two orders of magnitude. In the following we give the average value between the two measurements assuming a linear pressure gradient within the quartz tube. It should be mentioned, however, that the
-20 -10 a0 1.0 VELOCITY [mm Is1
Fig. 1. Miissbauer emission spectra of “Co, _ XOsources at room temperature. The sources were prepared at 1OOOC with the following oxygen pressures: (a) 1.2 x 10-s bar; (b) 7.9 x lo-‘bar; (c) 1.6 x 10m7bar; (d) 7.3 x 10-‘bar. The solid line gives a least squares fit with two Lorentxians. The parameters of the fit are listed in Tab. 2.
Table 1. Parameters of eqns (I x5) E, = 0.53 eV E2 = 0.74 eV
AH,, = 0.27 eV Kti=
1.6 x 10-2s
20
used in this paper. K,, = 2.4 [mol - ‘1 K,=O.l7[mol-‘1
184
T. HARAMIet
al.
Table 2. Parameters obtained from a least squares fit of two Lorentzians to the Mossbauer spectra in Fig. 1. The sources were prepared at 1000°C and the partial pressure, PO,, of oxygen and investigated at room temperature. 6.9 and r,, gives the isomer shift and the experimental line width. respectively, as measured with a K,Fe (CN), absorber. The errors in 6s and Fur, are about +0.005 nun/s.
A,(R)/(A,(R) + A,(R)) gives the relative contribution of the Fe2+ line to the total area of the Miissbauer spectrum at room temperature. The error is about 3%
6S
1.2 x 7-9 x 1.6 x 7.3 x
[mm/s1
[mm/s1
A,(R) A,(R) + A,(R)
1.094 1.090 1.101 1.082
0.395 0.382 0.383 0.414
100 85 83 78
10-s 10-n lo-’ 10-7
l- -P
Figure 2 gives the value A,(R)/&(R) + A,(R)) as a function of PO* at the preparation. (R) refers to room temperature Mossbauer spectra. Miissbauer spectra of 57Co,_,O sources in the temperature range between 22 and 1000°C keeping PO, constant are shown in Fig. 3 and Fig. 4. The Mijssbauer parameters of these spectra together with the results of two other series of measurements at different PO, values are listed in Table 3. Figure 5 gives the isomer shifts for the different sources as a function of the source temperature. Below 500°C for PO2 > 1.2 . lo-* bar, the spectra consist of two lines corresponding to ferrous and ferric ions, respectively. The line intensities can be deduced from the area under the two lines in the Mossbauer spectra. Above 500°C the ferrous and ferric lines collapse into a single line. One may assume that in this temperature region the experimentally obtained isomer shift, SS is still an average of contributions from Fe* + and Fe3 + . It can empirically be described by: 6s = ~StFe2+)+W’W2(T)
l.O/
%
6S
l- CXP
[mm/s1 [mm/s1
0.437 0.443 0.425
0.624 0.455 0.561
The isomer shifts 6S(Fe*+), and 6S(Fe3+), of the Fe*+ and the Fe3+ contributions at the temperature T are obtained from a linear extrapolation of the values measured between room temperature and 400°C according to the solid lines in Fig. 5. It is then possible to adjust the areas A,(T) and A,(T) of the Fe2+ and the Fe3+ component according to eqn (10) in order to get the experimentally obtained 6S value.
+ A3V))
+ GS(Fe3+)rA3(T)I(A2(T) + A,(T))
E 0.8.
Fe3+ fraction
Fe2+ fraction
PWarl
(10)
__--__--_
z .'
E 2 -T+ + 0.6. a= -74 a 0.L.
-log(l%,
(bar))
Fig. 2. Area fraction A,(R)/(A,(R) + A,(R)) of the Fe*+ line in the Miissbauer spectrum at room temperature as a function of the oxygen pressure during the preparation at 1000°C. The dashed line corresponds to a fit of eqn (13).
Fig. 3. Miissbauer emission spectra of 57Co,_,O source prepared at 1000°C and PO, = 1.2 x 10-s bar. The PO, was kept constant at this value during the measurements where the sources were at the different temperatures. The solid line gives a least squares fit with two Lorentzians. The parameters of the fit are listed in Table 3.
Influence of semiconductor properties of Miissbauer emission spectra of 57Cocobalt oxide
1
Fig. 4. The same as Fig. 3. The oxygen pressure was, however, PO, = 7.9 bar. Note that at 400°C the contributions of Fe2+ and Fe’+ start to give resolved Lorentzians.
The relative area of the Fez+ contribution to the Miissbauer spectra, A*(T), is plotted as a function of the temperature in Fig. 6 for different “CO, _,O sources. Carrying out the oxidation at O2 pressures higher than lo-’ bar and temperatures above 600°C a mixture of Co,O, and Co0 revealed itself in the MGssbauer spectrum. No comparisons with our calculations were performed for such samples. DISCUSSION
In this chapter we want to show that the semiconductor properties of Co, _,O as outlined in chapter 2 can explain the presence of Fe’+ in a Miissbauer emission spectrum of s7Co, _XO sources quantitatively. During the decay 57Cois transformed into 57Femby K or L electron capture (EC). Due to the EC process, an electron is removed from one inner shell giving rise to the appearance of vacancy cascades and the emission of Auger electrons. The emitted Auger electrons having energies between 1 keV and 7 keV are then absorbed in the Co0 material. Due to the large Coulomb potential created by the iron daughter, practically all Auger electrons come back to the iron in a time less than IO-’ s yielding “Fern3 + . In pure Co, _,O the only defects existing are cationic vacancies which give rise to the appearance of acceptor levels in the energy gap. Very shortly after the EC
185
process in 57Co takes place a new level appears in the energy gap corresponding to the “Fem3+ daughter which corresponds to a singly ionized iron level (compare Fig. 7). There remains the discussion of the mechanisms involved in the process of electron recombination for the last Auger electron appearing after each nuclear decay. A rough estimate tells us that the Auger electron is absorbed in a sphere with a radius of about 1000 A around the decaying 57Co. It reaches the conduction band and can freely move till it reaches the Fe’+ yielding Fe ’ + after recombination. Since the distance of maximal 1000 A is rather small the recombination occurs normally in times much shorter than lo-‘s . Fem3+ recombines to Fe&+ before the emission of the 14.4 keV radiation thus giving rise to a Fez+ line in the Miissbauer spectrum. During the motion in the conduction band the last Auger electron can reach, however, an unionized or a single ionized vacancy which acts as a recombination center. The electron is trapped and is no longer available for the recombination with Fern3+ . Therefore, Fern3+ decays yielding in the Miissbauer spectrum the Fe3+ line. The trapping of the last Auger electron occurs in a time which is short compared to lo-‘s. It is, therefore, obvious that Triftshauser and Craig[S] could not resolve any time dependence of the formation of the Fern3+ . The probability that the last Auger electron is trapped before reaching the Fe’“3+ is clearly correlated with the number of vacancies. There exists, however, a second possibility to reduce the Fem3+ to Fe”‘+. An electron from the valence band of the Co, _,O may jump to the Fem3+. We shall use this second process for the discussion of the temperature dependence of the Co, _*O emission spectra between 200 and 1000°C. The analysis of our spectra justifies the assumption that this process occurs only at higher temperatures and has a characteristic time of the order of lo-’ s. Therefore, relaxation phenomena between Fe3+ and Fe*+ are obtained in the Mijssbauer spectra at higher temperatures in accordance with Song and Mullen [14]. Since the time scales of the two reduction mechanisms of Fem3+ are rather different one can treat the processes separately. We consider first the fast process which dominates the room-temperature spectra. The maximal energy of an Auger electron following the EC in “Co is the energy of the Km transition in iron (6.5 keV). The maximal range of this electron in the Co0 material can be estimated by [20]: R[g/cm*]=O.ll(,/(l
+22.4E2(MeV))-
1). (11)
Taking into account a density of Co0 of 6.43 g/cm3 the electron is absorbed in a distance not longer than 1000 A from the decaying 57Co. For our estimations we assume that, in the average, such an electron can be trapped by vacancies in a sphere with a radius of about 1000 A. Even in a source with a very high specific activity it is very improbable that two Fem2+
0.796 0.725 0.649 0.513 0.492 0.382
500 600 700 800 900 1000
rev
[mm/s1
0.365 0.389
0.504 0.465 0.481 0.569 0.475 0.465
6S
[mm/s1
1.005 0.870
0.214 0.176 0.124 0.067 0.022 0.029
0.731 0.459 0.385 0.424 0.518 0.546
0.372 0.404
[mm/s1
78 90
%
73 11
0.469 0.579 0.393 0.429 0.434 0.438 0.454 0.477
0.963 0.785 0.135 0.081 0.034 0.003 - 0.035 0.029
M'-)+4(T)
A,(T)
0.437 0.480
rev
0.362 0.239
Fez+
0.304 0.192
[mm/s1
6S
unresolved unresolved unresolved unresolved unresolved unresolved
Fe3 +
0.574 0.438
[mm/s1
r ev
unresolved unresolved unresolved unresolved unresolved unresolved
0.339 0.213
[mm/s1
84 12
6S
AZ(T)
Fe3’
A,(T) + A,(T) %
PO, = 7.9 x 10m8bar
IO-‘bar
%
l&S
0.700 0.538 0.524 0.492 0.495 0.542
0.463 0.369 0.206 0.085 0.056 0.092 PO,=7.3x
0.359 0.441
[mm/s1
r“P
0.966 0.793
[mm/s1
6s
[mm/s1
rw
-
[mm/s1
I- -P
Fe2 +
[mm/s1 I [mm/s1
Fe’ +
unresolved unresolved unresolved unresolved unresolved unresolved
bm/sl
6S
Fe’+
[mm/s1
6S
unresolved unresolved unresolved unresolved unresolved unresolved
A,(T) A,V)+A,(T)
100 100
%
A,(T) + A,(T)
A,(T)
PO, = 1.2 x 10m8bar
PO, = 1.6 x IO-‘bar
Fez+
1.002 0.870
200 400
[mm/s1
I- ew
[“Cl
6S
Fe2+
temo.
Source
0.653 0.523
[mm/s1
rcw
Table 3. Parameters obtained from Miissbauer spectra with K,Fe(CN), absorber and 57Co,_r0 sources, prepared at 1000°C at four different oxygen pressures. 6S and Fexp give the isomer shift and the experimental line width, respectively. The errors in SS and Fe_, are about +O.O05mm/s. A,(T)/(A,(T) + A,(T)) gives the relative contributions of the Fe ‘+ line to the total area of the Miissbauer spectrum at the temperature T. The error is about 3%. Each source was investigated at eight different temperatures
Influence of semiconductor
properties of Miissbauer emission spectra of 57Co cobalt oxide
.
oc
200 Gco 600 800 loo TEMPERATURE (“Cl
TEMPERATURE
(“C)
1
0
1
,
200 400 600 800 1000 TEMPERATURE
I
0
200 600 TEMPERATURE
I°C )
200 400 600 800 1000 TEMPERATURE (‘C)
1oC t’-
Fig. 5. Isomer shift 6.9 [mm/s] as a function of the source temperature; upper line: GS(Fe’+), lower line: SS(Fe”+), petted line: 6s as a sum of contributions3f+rom Fe*+ and resolved Fe*+ and Fe lines. (a) PO2 1 1.; 10m8bar; (b) PO, = 7.9 x lo-* bar; (c) PO2 = 1.6 x lo-‘bar; (d) PO, = 7.3. lo-‘bar; at 1000°C during preparation. centers are available within IO-’ s in the volume of this sphere. Therefore, [V*] neutral vacancies [v’] single charged vacancies and one Fe”“+ per 4 x lo-” cm’ yielding [Fe”‘+] = 2.8 x lOI mol-’ are in competition for this Auger electron. The probability of the capture of electrons he-
. 0
.
.
200 LOO 600 800 1ooc TEMPERATURE (“C)
Fig. 6. Fraction A,(T)/(A,(T)+A,(T)) of the Fe*+ contribution to the Miisbauer spectrum at different temperatures. The sources were prepared at (a) PO, = 1.2 x 10e8 bar; (b) PO1 = 7.9 x IO-* bar; (c) PO,= 1.6 x lo-‘bar; (d) PO,= 7.3 x IO-‘bar. The circles give experimental values, the solid line is the least squares fit of a theoretical model. In Fig. 6(a) PO, values were used in the fitting procedure which differ from the measured values. For details compare the text.
T. HARAMIer al.
188
longing to the conduction 1211:
band by a trap is given by
A” = ?&(F) .
c a,,N,
(12)
where N, is the molar concentration of trap center i at the temperature T, G,,,(F)is the thermal velocity of electrons in the conduction band and u,, is the electron capture cross section for the trap center i. The relevant cross sections are: u,,., cry and urc which refer to the electron capture by a neutral, a single charged and a Fe’“‘+ trap, respectively. The ratio of Auger electrons trapped in the vacancies and in the ionized iron levels can be written:
A,(R) -= A,(R)
ur[V*l+ u,[U = a[V’] + b[V’]. (13)
spectra dealing now with electron transfer between the Fe” acceptor and the valence band, Now the concentration [Fe”)+ lo _ , s. The ionized ,,1,fm3y longer constant during level may be occupied by an electron coming from the valence band and a hole of the valence band can recombine with an electron belonging to the “Fem2+ level. Since our experiments are performed as emission Miissbauer spectroscopy, we have: [Fe”] = [Fem2+(t)] + [Fem3+(r)] = 2.8 x IO” mol- I. (14) The change of [Fem2+(t)] with time can be written: d[Fem2+(r)J = - L2[Ff12+(r)] dt
crrc[Fem3+]
If no electron transfer between the Fe” level and the valence band occurs the ratio A,(R)/A,(R) gives the ratio of the ferric and ferrous Mossbauer line intensities at room temperature. We are now in the position to compare our room temperature experiments with the theoretical model described above. The ratio A,(R)/&(R) is taken from the Mosbauer spectrum. In order to explain our room temperature experiments one has to adjust the two parameters a = uy/(uFe. [Fem3+]) and b = u,J(ur,[Fem3+]). For a calculation of the vacancy concentrations [I’*] and [V’] one has to estimate the equilibrium temperature Tq. Using T, = 1000°C and assuming this way that the total vacancy concentration, [xl, is at room temperature the same as at 1000°C proved to be a bad assumption. No values for a and h could be obtained to explain all relevant experiments. This was, however, possible, when T, was taken to be 400°C in agreement with [23] and v41. The dashed line in Fig. 2 was obtained with a = 1.3 x lO-‘9 [mol] and b = I.1 x 10mi9 [mol]. Note that here not A,(R)/A,(R) is plotted but A,(R)/(A,(R) + A,(R)). It is important to mention that only one set of parameters a and b can explain Mossbauer spectra from samples prepared at different PO,-values. We proceed to the discussion of the temperature dependence of the “Co, _,O emission Miissbauer
+ d,([Fe”] - [Fem2+(r)])
(15)
where i, characterizes the recombination probability of an iron electron with a hole in the valence band while i, gives the probability that an electron of the valence band jumps to Fe’ + . Equation (I 5) can easily be solved giving: --
a3 12 +
x
,-ca+wr+
13
13 (16) 1.2 +
I3
where
[Fem2’W/~Feml = A2WI(A2W + A3VW (17) A,(R) and A,(R) are the ferrous and the ferric absorption areas of the Miissbauer spectrum at room temperature where the electron relaxation between the valence band and the Fe” impurity can be neglected. The Mossbauer emission spectroscopy follows the jumping of electrons between the iron and the valence band over about 7M = lo-‘s. The spectrum at higher temperatures measures, therefore, an average concentration ([Fem2+]): 3j
[Fem2+W1 e-,,fu 0
dt
(18)
P’“l
yielding:
I> _ 4 Fe’“1 1, + I.3 A,(R) +
([Fe”‘+
A,(R) + A,(R)
=
(I’*) and Fig. 7. Band structure of Co, _ xO with un-ionized __,.. smgle ionized (V’) vacancies and a ke”” impurity.
(n264
,>.
--
a3
I
1.2+ 1, > r&l, + A,) + 1 (19)
Calculated (n,(A)) values according to eqn. (19) using A2and A3as adjustable parameters can now be compared with the experimental values obtained
Influence of semiconductor properties of Mossbauer emission spectra of “Co cobalt oxide from A,(T)/@,(T) + A,(T)) at higher temperatures, using eqn (IO). Instead of using & and & as free parameters in a fit procedure we tried to correlate the transition probabilities with physical quantities of the Co, ..O compound. We assume:
Ip) is again the molar inundation of free holes while (p’] = N, exp (~~~~(~~~)~. N, represents the density of states in the valence band and is given by N, = 2(2nm,,k,T/h*)‘/* where m, is the effective mass of a small polaron and has been taken to be mp = 4m, in accordance with [22]. kB is the Boltzmann constant and h is the Planck number. & is the energy which is necessary to promote an electron of the valence band to Fe3 + . Equation (20) assumes that the transition probabilities depend only on the concentrations b] and Ip’]. The proportionality constant, /I, is assumed to be equal for both processes and can be written in the form of a cross section, uw: cf%= s /r3,ho,)
(21)
where rYJh(p)is the thermal velocity of a free hole in the valence band. In Fig. 6 the solid lines give the results of a least squares Iit of eqn (19) using also eqn (20) and eqn (21) with T- =4OO”C. Our model reproduces well the strong variation of the ferrous line intensity at T s 500°C which in fact is related to the increasing defect concentration at T > T_,, For T > 700°C the increase of the ferrous component of the observed single line is connected with the temperature at which relaxation phenomena appear. The quantitative agreement between calculations and experimental data is, however, of different quality for the different PQ-values. While it is reasonably good at PO2 = 7.9 x 10’“*bar, the quantitative discrepancy becomes quite for large PG2= 1.6 x 10 .‘bar and PG2=7.3* IO-‘bar at higher tcm~ratur~. This is not surprising since our theoretical model is based on a number of assumptions which are only approximately valid. We used the values of the free hole concentration b] and the vacancy concentrations, [I’&] and [V&J, from the above discussion of the defect structure. However, there has been no useful data for physical quantities of the defect structure on Co, _XO in the whole temperature range 22-1000°C. The electrical properties of Co, _ .O have been studied mostly by doping, for example with Li[25], Co, _,O without dopants has only been measured at high temperatures above 900°C. The presence of other phase Co,O,[24] in Co, _,O and the different kinds of more complex defects(271 and grain boundariesj251 make it complicate to get a better model at present. Good agreement between the experimental data and the calculation was obtained from the preparation at extremely low oxygen pressure. It was necessary, however, to use PQ = 1.2 x IO-‘*bar in the calculation instead of the observed
189
PQ = 1.2 x IO-* bar. The solid lines give calculated Fe”’ fractions for different oxygen pressures. It is obvious that our pressure control was not sensitive enough to give a realistic value at these conditions. In practice we used the best vacuum which we could obtain by our turbo pump during the measurements of this sample. From the fits shown in Fig. 6 we obtained cr,+= 1 x lo-i9 cm2 and & = 0.62 eV as optimal parameters. The distance of 0.62 eV of a Fe3 ’ impurity from the valence band formed by the 3d6 electrons of the Co in COO seems reasonable. Together with the parameters u and b obtained according to eqn (13) from the room temperature experiment using (Fe”] = 2.8 x IO” mol-” ’ one gets the following cross sections for electron captures: ur = 3.8 x 10-23cm2 and ey = 3 x 10-23cm2. The comparison with ure = 1 x 10 - I9cm* shows that the acceptor character of an Fe’+ impurity is much higher than those of cationic vacancies. CONCLUSIONS
The Miissbauer emission spectra of “Co, _ ,O are very sensitive to the nature, charge and concentration of the point defects existing in the solid matrix. The cationic vacancies act as trapping centers for the emitted Auger electrons. The iron daughter impurities also act as trapping centers with higher cross section. The charge state “Fe3+ in the Miissbauer spectra is related to the existence of cationic vacancies in the lattice. Increasing the concentration of vacancies, increases the probability of Auger electron capture. In the case of stoichiometric cobalt oxide, no Auger electrons are lost due to the non-existent of point defects in the lattice. Therefore, in order to produce single iron divalent sources, stoichiometric “Co0 must be obtained. Unfortunately, electron traps can be introduced not only by vacancies but also by rather low impurities. The preparation of single line s7CoG source often fails if the “‘Co is not purified enough. We have also carried out Miissbauer emission experiments introducing ‘Co in p.p.m in a Co0 single crystal. The results are similar to those obtained in the case of powder samples. Hence it can be concluded that the particle size has no influence on the Miisshauer emission spectra. At temperatures below 500°C the Fe*’ as well as the Fe3” state is stable. Taking into account the charge exchange between acceptor level and the valence band one can explain the variation of the ferric line intensity at higher temperatures. ~c~ffwIe~e~~r~-~is work was supported by the Bund~i~i~~urn f”ur Forschung und Technologie der Bundesrepubiik Deutscbland. We gratefully acknowledge the continuous support of R. L. Mbssbauer and H. Morinaga. We thank U. Gonser and R. L. Miissbauer for many helpful discussions. REFERENCES
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