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Contributions to the high-temperature behaviour of YBa2Cu3O7−y
Materials Letters 16 ( 1993 f 6 l-67 Noah-HoUand
Contributions
to the hip-temperature
Axe1 Pecina and Karl-Heinz Institutfu’r Technologie
b~haviour of YBa2Cu30,_y
HBrdtl
der Elektrotechnik,
Universitdt Karlsruhe (TH), Hertzstrasse
16, W- 7500 Karlsruhe 21, Germany
Received 2 October 1992
The HTSC material YBazCu307_, is examined in a temperature range between 600 and 900°C under variable oxygen partial pressures between 1 and 10T4 bar. The oxygen deficit y is determined as a function of temperature andpo, by a solid-state titration technique. The results are compared with literature data obtained from TGA measurements. Based on these data a defect chemical model is proposed, which describes the electronic defects as a function of temperature and poz. On thermopower measurements the influence of the preparation history of our samples is shown.
1. Introduction The density of the electronic charge carriers is a very impo~ant quantity of hip-temperature superconductors for it controls the superconducting transition temperature. In recent years, therefore, there appeared a wide variety of papers, dealing with the dependence of T, on the carrier density, see e.g. refs. [ 1-3 1. This carrier density is usually determined by chemical titration of the average copper valence in quenched samples. The variation of the carrier density, however, takes place in the high-temperature regime controlled by the oxygen partial pressure (po, ) of the ambient atmosphere. Thus the properties of a sample at temperatures below room temperature are a result of the high-temperature equilibrium, which is established during the preparation process. The aim of this work is to receive a defect chemical model describing the exchange of oxygen between sample and atmosphere and its influence on the carrier density. The model is based on stoichiometry data of Lindemer et al. [4] and on our own measurements of the amount of the oxygen exchange. While Lindemer et al. used a thermogravimetric method, in this work a new procedure based on coulometric titration was applied [ 51. This new procedure allows one to determine in one single setup the oxygen exchange and the correlated change in conductance. The model applies well to the data of Lindemer et
al. and our own results received from samples prepared from high-purity starting materials. Using, however, starting materials of lower purity (p.a. grade) and/or extensive milling procedures, deviations occur from the ideal behaviour. It will be shown that these deviations can be explained within the model by introducing an additional term in the lattice neutrality condition, which takes into account a formal charge generated by impurities. Fu~hermore, it will be shown that different preparation conditions lead to significant differences of the samples’ conductance and thermopower in the lower poz range where the concentrations of electrons and holes are almost equal, while the extrinsic p range (i.e. the range of high po,) is hardly influenced. Thus, it becomes understandable that it is easy to produce an YBa2Cu307_-ysuperconductor with 92 K transition temperature, but that there is no agreement between the different research groups [ 6- 173 about the appropriate defect chemical description over the whole stability range of the material.
2. Experimental procedure The samples were prepared by a mixed oxide technique using two kinds of starting materials with different degree of purity. While for the high-purity samples a purity better than 99.999Ohwas used, the low-purity samples were prepared from chemicals of
0167-577x/93/$ 06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.
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MATERIALS LETTERS
p.a. grade (better than 99%). Well defined milling and mixing allow a low calcination temperature of 850°C resulting in a line-grained YBa$&O,_, powder with good sintering properties. Pressing to pellets and sintering for 16 h at 950°C in air leads to tine-grained, single-phase ceramics without texture, from which bars of about 15~3x3 mm were cut. Electrical four-probe contacts were attached by wrapping a gold wire around the sample and fixing it by a gold conduction paste. The oxygen exchange is measured in a ZrOz titration cell [ 5 1. For that purpose the sample is placed in a small gas volume separated by a platinum-coated ZrOz membrane from a reference atmosphere with defined po2. This setup is heated to temperatures between 700 and 900°C. Impressing a current through the Zr02 membrane, oxygen is transported between the measuring volume and the reference atmosphere. Integrating the current over the time, the amount of transported oxygen can be determined if one assumes that each oxygen ion carries two elementary charges. Finally, doing this first with a sample in the cell and later without sample, evaluating twice the transported oxygen and subtracting the results, one can obtain the oxygen exchanged by the sample. For receiving absolute values of oxygen stoichiometry it is necessary to know the composition at one definite po2. This knowledge is obtained either by using one data point from Lindemer et al. [ 41 or by applying a nuclear measuring technique working with the transformation of I60 to 16N by fast neutrons and detecting the y-radiation of the following decay [ 181. In situ with the oxygen exchange, the conductance of the sample was recorded by a four-probe measurement. In another experimental setup the thermopower was determined as a function of temperature and oxygen partial pressure. To avoid offset errors, a slow ac technique with a periodically changing temperature gradient was applied. Details of the experimental procedure and setups are described elsewhere [ 191.
3. Theory of the oxygen exchange Starting from the point of view that the copper ions may exist in the valences 1 +, 2 + or 3 + and the va62
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lences of yttrium and barium are fixed, one may write
.. -(vo):i?,(vo)y~*~o:zy,
(1)
using the following assignment [V,] =y(‘) , [Oo]=7-y,
[V;;] =yQ) )
[I&]+
[Cu”]=e,
[V;;] =y
)
[Cu3+]=A,
[cu’+]+[Cu2+]+[Cu3+]=3.
(2)
So the reference composition is YBa2Cu30, and the Cu3+ ions are considered as the p-type carriers. This assumption, however, is arbitrary. Nevertheless, it does not affect the general validity of these considerations, for one can make a transformation to any other reference composition. The term A’ formally represents the influence of charged impurities. The value of 6/Zi corresponds to their concentration per unit cell, while zi means the state of charge, and the sign is due to whether the impurity acts as an acceptor ( + ) or as a donator (-). The electroneutrality condition then reads h-e=
1-2y+6+y(‘).
(3)
By leaving the crystal lattice an oxygen atom creates an oxygen vacancy. The two binding electrons, remaining first in the surrounding of the vacancy, can be donated, thus creating ionized oxygen vacancies. It is assumed, that the oxygen vacancies in the material are at least in the first degree of ionization, cu*++102 *g+v’ osoo+cu3+
10011cu3+ 1 *
[v,l
[cu2+
]
=K1
PA/:
9
(4)
and an equilibrium between singly and doubly ionized vacancies will be established, cu3+ + v’o*v;;
a
+cu*+
[V;;] [cl?+] [Vb] [cLP+]
=K2.
(5)
Furthermore one has to consider the disproportionation of the copper ions
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MATERXALSLETTERS
icu*+ I icu3+ [cu2+]2
2cu~+~cu’++cu’+*
I =K, I’
(6) The aim is to express the concentration of all defect species in the equations above as a function of the oxygen partial pressure. This is possible if the mass action constants KI, K2 and Ki are known. In general, however, this will be not the case. On the other hand, the constants can be determined by a numerica fit, if at least one of the concentrations involved is known as a function of the oxygen partial pressure. This is the case for the amount of the oxygen deficiency y= [ Vh] + [VG], the poz dependence of which is known from the titration measurements and from literature TGA data f41.
4. Results and discussion Solving the defect chemical equations for the oxygen deficiency y and fitting the mass action constants, it is possible to model the quantity y as a function of the oxygen partial pressure. A comparison between those evaluated data and experimental ones is done in fig. 1. The good agreement between evaluation and both, TGA and titration, data is obvious. However, one has to keep in mind, that the modelling is done by choosing three appropriate parameters. Using free and independent parameters it
March 1993
will be possible to get nearly any curve within the model. Therefore it is necessary to check the constants, which one receives from the fitting procedure, on their physical plausibility. Since they are a kind of mass action constants, one expects them to exhibit a temperature activated behaviour. An Arrhenius plot (fig. 2 ) confirms this and allows one to draw further conclusions. So, it is seen that K, decreases with increasing temperature. This means a shift of the equilibrium described in (4) towards the left side, synonymous with an increased occurrence of oxygen vacancies with increasing temperature. This is well established in several investigations. K2 increases with increasing temperature, synonymous with an increased amount of doubly ionized oxygen vacancies in (5 ). This feature seems to be plausible, too. Finally the constant Ki, which describes the disproportionation of the copper (6), increases with temperature, which also seems reasonable.‘In the picture of a semiconducting material the activation energy of Ki is equivalent to the band gap. If these mass action constants are valid, it is now possible to evaluate the po2 dependences of all defect species involved. In figs. 3 and 4 this is done for 500 and 900” C. For better comparability the same scale is chosen, the hatched area in fig. 4 marks the range of chemical instability, where no reproducible results can be obtained. The asterisks denote the experimental data for the oxygen deficit y of Lindemer et al. [ 4 1, while the curves are calculated on the base of the proposed model.
0.8
0
0.0, -6
oara from ilndemer
et
ai
-500
,
/
,
I
j
-5
-4
-3
-2
-3
*c
-141
I
0
1
~g(pO,/bor)
Fig. 1. Oxygen deficit y as a function of pal determined by Lindemer et al. [4] in comparison with experimental and evaluated data (lines) from this work.
0.8
/ 0.9
, 1.0
/ 1.1 1000/T
, 1.2 in
/ 1.3
/ 1.4
1 /I(
Fig. 2. Mass action constants determined from a numerical tit of the proposed model to the stoichiometry data from Lindemer et al. [ 41 and from this work.
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Volume 16, number 2,3
Fig. 3. Evaluated defect ~oncentmtions 500°C.
in YBazCupO,_, for
1
0
8
-1
c
5 2
2
5
5 9
-2 -3 -4 -5
-5
-4
-3
-2
Fig. 4. Evaluated defect concentrations 900°C.
-I
0
in YBa2Cu~07_, for
It is easily seen that at 500°C the holes dominate the charge carriers. Throughout the whole range of investigation their concentration is at least two orders of magnitude higher than that of the electrons. This p-type behaviour is confirmed by conductance and the~opower measurements. At 900°C however, there exists a range, where electrons and holes are present in almost equal concentrations. This mixed p- and n-type behaviour is also seen in the corresponding conductance and thermopower measurements, e.g. refs. [8-lo,19 1. A very interesting feature of this result is the flat po2 dependence of the hole concentration at low temperature (SOO’C). It explains the fact, that it was possible in the recent years for nearly everyone to prepare the 90 K superconductor, without using a well-defined annealing procedure. Keeping in mind, that it is crucial for receiving the maximum transi64
March 1993
MATERIALS LETTERS
tion temperature to adjust the hole concentration near one per unit cell, it is seen, that it is peripheral whether the annealing is done in pure oxygen or in air. As well a change of temperature by several i 10” only slightly affects the hole concentration. The proposed model deals with dilute point defects in spite of the high defect concentrations. This becomes possible with the fo~ulation of a po2-dependent and therefore concentration-dependent degree of ionization of the oxygen vacancies. The interaction between the oxygen vacancies results in the failure to reach the full, double state of ionization. At 500°C and high po2 there exist only few oxygen vacancies, the concentration of singly and doubly ionized vacancies is still comparable. At 900°C already at 1 bar poZ the singly ionized vacancies are clearly in the majority. So the reducing of the state of ionization caused by the increased vacancy concentration is predominant over the influence of the higher temperature, which favours an increased degree of ionization (see mass action constant &)_ If only doubly ionized vacancies are assumed, it is also possible to fit the stoichiometry data rather well. The mass action constants, however, then are lacking their physical plausibility. A further test of the model can be made with the results obtained from titration measurements, which provide combined stoichiometry and conductance data. The poZ in the measuring cell is varied from a starting level (index S) to an end level (index E) and the corresponding conductances are recorded. The ratio of these conductance values then can be expressed as (7) where K(g@ means the geometric factor, q the elementary charge, p the hole concentration and p the mobility of the holes. The exchanged oxygen is written as APol=
Wol,- [Vols.
(8)
With the introduction of an averaged degree of ionization for the oxygen vacancies
A&]
+2A[V;]
z= [V,x] + [V,] + [Vi] = A&l
+2A[V;;l [Vol
(9)
’
and under the conditions p B n and np = const. for the extrinsic p range, one may write
(10)
PE=PS-ZA[VOI. Eq. (7 ) then reads e
= A[V,]
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MATERIALS LETTERS
Volume 16, number 2,3
GS GS - (&,&GE
’
(11)
If it is assumed that between starting and end levels of the po2 the degree of ionization and the hole mobility do not change, it is possible to determine the ratio p/z (or h/z if the concentration is given in holes per unit cell). Fig. 5 shows measured values in accordance with ( 11) and the evaluated curve resulting from the proposed model. The very good agreement between experiment and model may be regarded as a confirmation of the validity of the latter. Only at high po2 there occurs a deviation (circled values), which may be explained with a mobility change (see ( 11) ). For temperatures above 700°C the agreement becomes somewhat worse, in a way that the evaluated curve is below the experimental points. Probably this is the result of the restriction that all oxygen vacancies are regarded as at least singly ionized. If also non-
ionized vacancies are allowed, the averaged degree of ionization z becomes smaller, the ratio h/z therefore larger and a better Iit should be received. Introducing the non-ionized vacancies, however, would require a further mass action constant and make an appropriate lit more uncertain. The proposed model applies well to the data of Lindemer et al. [4] and our own results of high-purity samples. The parameter 6 is zero for these data. However, if one investigates samples prepared from starting materials of lower purity (p.a. grade), there occur deviations from the ideal behaviour. Only just choosing 6= -0.08 allows an appropriate lit (fig. 6 ). The negative value of S indicates the donator character of the disturbing effect resulting from the different preparation method. The absolute value for the oxygen deficit of the p.a. grade sample was determined from Fijrster [ 181 at a quenched sample equilibrated in air at 700°C. Apparently the oxygen deficit is over the whole poz range lower compared with the ideal material. It is also seen, that the deviation is small in the range of high po2 and becomes larger with decreasing Po2.
This result is similar to the investigations of Hong et al. [ 201 with La-doped samples. There is observed a compensation of the n-doping by a reduced oxygen vacancy concentration. Another quite interesting effect of the preparation conditions can be easily shown by observing the thermopower at high temperatures. The change of sign of the thermopower is sensitively influenced by
0 Y
0.4
Lindemer et .I. pa. same
0.3 -5
fg bO,/bar) Fig. 5. The quantity of holes per unit cell divided by the degree of ionization (h/z) in dependence of the oxygen partial pressure - comparison between the result from titration experiment and evaluated data based on the model.
-4
-3
-2
-1
0
1
b(pO,/bor)
Fig. 6. Oxygen deficit y of ideal and non-ideal sample - for the non-ideal sample the impurity parameter 6= -0.08 is introduced to tit the experimental points.
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MATERIALS LETTERS
March 1993
300,
I
,
,
733 ‘t 200-
.vV
VW
,
,
,
8,
V,.p& & 3
*%a
loo*;*“”
>
O_
-
VA
0. -lOO-
-5.01
. 0.85
.
.
. . 0.90
.
.
.
. . 0.95
..I......... 1.00
1.05
( 1.10
A
.A
. . A V
TV
-200 -5
-4
-3
1 OOO/(T/K)
Fig. 7. Oxygen partial pressure at which thermopower changes sign as a function of reciprocal temperature for several samples from this work and literature data [6,7,10,11] with different preparation history.
the ratio of p- to n-type carriers. So the position of the thermopower-zero-point over a log&,)-scale depends not only on intrinsic material properties, but also on possibly existing ionized impurities. In fig. 7 the influence of the milling procedure is shown. Over a 1/T scale the po2 corresponding to the thermopower-zero-point is plotted for several samples denoted by their laboratory notation. The open symbols denote samples treated in an attritor mill with ZrOz balls. This preparation leads to a very homogeneous precursor, but also causes increased abraded particles. The tilled symbols stand for samples prepared in an agate ball mill with less abrasion. It is obvious that the latter ones are closer to the ideal behaviour predicted by the model. This indicates a noticeable amount of charged impurities caused by the ZtQ abrasion. Also the results taken from the literature scatter remarkably, indicating a different preparation history of the samples used. However, the influence is only detectable in the mixed p-/n-type range. Regarding the whole thermopower curve (fig. 8) this is easy to see. There is no or only a small difference between the data in the extrinsic p-branch of the curves. This result is confirmed by the low temperature behaviour. After annealing at 42O”C/ 1 bar po2, two samples with remarkable differences in their mixed range show a pretty good superconducting transition at 92 K (fig. 9). So it becomes understandable, that there is no agreement in the scientific community about the appropriate description of the high-temperature be66
*q.
----..‘--“---_,--____-_-___-_,_.____.__
-2
HI ma El B9o
-1
0
bbO,/bad
Fig. 8. Thermopower as a function of the oxygen partial pressure for several different samples.
0
300
200
100
T/K Fig. 9. Superconducting transition for two samples from fig. 8. 250
I 825 ‘C
50-
0
1, measuremen
._-___-.-_--
-150
-4
1 -3
-2
-1
0
kdpO,/bad
Fig. 10. Shift of the thermopower curve caused by “denaturating” the sample as result of partial decomposing due to annealing for 2 h at low poz .
haviour of this material. It originates from the fact that apparently “different”, not well-defined samples are investigated. A further point, which may lead to confusion,
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MATERIALS LETTERS
should be mentioned. Like the choice of starting materials and milling/mixing procedure also the temperature/p,, treatment may alter the samples irreversibly. Fig. 10 shows a set of measurements performed with the same sample. After the first measurement the sample was annealed for 2 h in the instable range at low oxygen partial pressure, resulting in a partial decomposition. This shifts the mixed range towards lower po2. However, the new state is also a stable one, as the reproducibility shows.
5. Summary
A model was proposed, which considers all defects influencing the conductivity of YBa,C&O,_,. The main feature of this model is the consideration of interactions between the oxygen vacancies by introducing an averaged degree of ionization. By using an impurity parameter 6 the model can be applied also to non-ideal samples. Remarkable is the fact that preparation conditions have a considerable impact on the defect chemistry. Obviously, this was not sufficiently taken into account in the recent literature considering this topic. However, also with those not well-defined samples superconductors with sharp transition at 92 K are obtainable.
References [ 1 ] R.J. Cava, A.W. Hewat, E.A. Hewat, B. Batlogg, M. Marezio, K.M. Rabe, J.J. Krajewski, W.F. Peck Jr. and L.W. Rupp Jr., PhysicaC 165 (1990) 419.
March 1993
[2] J.B. Goodenough and A. Manthiram, J. Solid State Chem. 88 (1990) 115. [ 3 ] P. Steiner, S. Hiifner, V. Kinsinger, I. Sander, B. Siegwart, H. Schmitt, R. Schulz, S. Junk, G. Schwitzgebel, A. Gold, C. Politis, H.P. Mtlller, R. Hoppe, S. Kemmler-Sack and C. Kunz, Z. Physik B 69 (1988) 449. [4] T.B. Lindemer, J.F. Hunley, J.E. Gates, A.L. Sutton Jr., J. Brynestad, C.R. Hubbard and P.K. Gallagher, J. Am. Ceram. Sot. 72 (1989) 1775. [ 5] K. Beetz and K.H. Hardtl, VDI-Berichte 939 ( 1992) 5 19. [ 61 LA. Leonidov, Y.N. Blinovskov, E.E. Flyatau, P.Y. Novak and V.L. Kozhevnikov, Physica C 158 ( 1989) 287. [7] G.M. Choi, H.L. Tuller and M.-J. Tsai, in: Nonstoichiometric compounds, NATO AS1 Series, eds. J. Nowotny and W. Weppner (Kluwer, Dordrecht, 1989) p. 451. [ 81 J. Nowotny, M. Rekas and W. Weppner, J. Am. Ceram. Sot. 73 (1990) 1040. [9] J. Nowotny and M. Rekas, J. Am. Ceram. Sot. 73 (1990) 1048. [lo] J. Nowotny and M. Rekas, J. Am. Ceram. Sot. 73 (1990) 1054. [ 111 M.-Y. Su, S.E. Dorris and T.O. Mason, J. Solid State Chem. 75 (1988) 381. [ 121 J. Maier, P. Murugaraj and G. Pfundtner, Solid State Ionics 40/41 (1990)802. [ 131 J. Maier, P. Murugaraj, G. Pfundtner and W. Sitte, Ber. Bunsenges. Physik. Chem. 93 ( 1989) 1350. [ 141 G.P. Sykora, M.Y. Su and T.O. Mason, in: Nonstoichiometric compounds, NATO AS1 Series, eds. J. Nowotny and W. Weppner (Kluwer, Dordrecht, 1989). [ l$] A. Metha and D.M. Smyth, in: Non-stoichiometric compounds, NATO AS1 Series, eds. J. Nowotny and W. Weppner (Kluwer, Dordrecht, 1989). [ 161 D.J.L. H0ngandD.M. Smyth, J. Am. Ceram. Sot. 74 (1991) 1751. [ 17) J. Nowotny and M. Rekas, J. Am. Ceram. Sot. 74 ( 199 1) 1753. [ 181 H. Forster, Freiberger NE-Metal1 GmbH, Lessingstrasse 41, O-9200 Freiberg/Sachsen, Auftragsanalyse ( 1992). [ 191 A. Pecina, Ph.D. Thesis, University of Karlsruhe (TH), Germany (1992). [20] D.J.L. Hong, A. Metha, D.M. Smyth, E.K. Chang and M.J. Kirschner, J. Mater. Res. 5 (1990) 1185.
67
Contributions
to the hip-temperature
Axe1 Pecina and Karl-Heinz Institutfu’r Technologie
b~haviour of YBa2Cu30,_y
HBrdtl
der Elektrotechnik,
Universitdt Karlsruhe (TH), Hertzstrasse
16, W- 7500 Karlsruhe 21, Germany
Received 2 October 1992
The HTSC material YBazCu307_, is examined in a temperature range between 600 and 900°C under variable oxygen partial pressures between 1 and 10T4 bar. The oxygen deficit y is determined as a function of temperature andpo, by a solid-state titration technique. The results are compared with literature data obtained from TGA measurements. Based on these data a defect chemical model is proposed, which describes the electronic defects as a function of temperature and poz. On thermopower measurements the influence of the preparation history of our samples is shown.
1. Introduction The density of the electronic charge carriers is a very impo~ant quantity of hip-temperature superconductors for it controls the superconducting transition temperature. In recent years, therefore, there appeared a wide variety of papers, dealing with the dependence of T, on the carrier density, see e.g. refs. [ 1-3 1. This carrier density is usually determined by chemical titration of the average copper valence in quenched samples. The variation of the carrier density, however, takes place in the high-temperature regime controlled by the oxygen partial pressure (po, ) of the ambient atmosphere. Thus the properties of a sample at temperatures below room temperature are a result of the high-temperature equilibrium, which is established during the preparation process. The aim of this work is to receive a defect chemical model describing the exchange of oxygen between sample and atmosphere and its influence on the carrier density. The model is based on stoichiometry data of Lindemer et al. [4] and on our own measurements of the amount of the oxygen exchange. While Lindemer et al. used a thermogravimetric method, in this work a new procedure based on coulometric titration was applied [ 51. This new procedure allows one to determine in one single setup the oxygen exchange and the correlated change in conductance. The model applies well to the data of Lindemer et
al. and our own results received from samples prepared from high-purity starting materials. Using, however, starting materials of lower purity (p.a. grade) and/or extensive milling procedures, deviations occur from the ideal behaviour. It will be shown that these deviations can be explained within the model by introducing an additional term in the lattice neutrality condition, which takes into account a formal charge generated by impurities. Fu~hermore, it will be shown that different preparation conditions lead to significant differences of the samples’ conductance and thermopower in the lower poz range where the concentrations of electrons and holes are almost equal, while the extrinsic p range (i.e. the range of high po,) is hardly influenced. Thus, it becomes understandable that it is easy to produce an YBa2Cu307_-ysuperconductor with 92 K transition temperature, but that there is no agreement between the different research groups [ 6- 173 about the appropriate defect chemical description over the whole stability range of the material.
2. Experimental procedure The samples were prepared by a mixed oxide technique using two kinds of starting materials with different degree of purity. While for the high-purity samples a purity better than 99.999Ohwas used, the low-purity samples were prepared from chemicals of
0167-577x/93/$ 06.00 0 1993 Elsevier Science Publishers B.V. All rights reserved.
61
Volume 16, number 2,3
MATERIALS LETTERS
p.a. grade (better than 99%). Well defined milling and mixing allow a low calcination temperature of 850°C resulting in a line-grained YBa$&O,_, powder with good sintering properties. Pressing to pellets and sintering for 16 h at 950°C in air leads to tine-grained, single-phase ceramics without texture, from which bars of about 15~3x3 mm were cut. Electrical four-probe contacts were attached by wrapping a gold wire around the sample and fixing it by a gold conduction paste. The oxygen exchange is measured in a ZrOz titration cell [ 5 1. For that purpose the sample is placed in a small gas volume separated by a platinum-coated ZrOz membrane from a reference atmosphere with defined po2. This setup is heated to temperatures between 700 and 900°C. Impressing a current through the Zr02 membrane, oxygen is transported between the measuring volume and the reference atmosphere. Integrating the current over the time, the amount of transported oxygen can be determined if one assumes that each oxygen ion carries two elementary charges. Finally, doing this first with a sample in the cell and later without sample, evaluating twice the transported oxygen and subtracting the results, one can obtain the oxygen exchanged by the sample. For receiving absolute values of oxygen stoichiometry it is necessary to know the composition at one definite po2. This knowledge is obtained either by using one data point from Lindemer et al. [ 41 or by applying a nuclear measuring technique working with the transformation of I60 to 16N by fast neutrons and detecting the y-radiation of the following decay [ 181. In situ with the oxygen exchange, the conductance of the sample was recorded by a four-probe measurement. In another experimental setup the thermopower was determined as a function of temperature and oxygen partial pressure. To avoid offset errors, a slow ac technique with a periodically changing temperature gradient was applied. Details of the experimental procedure and setups are described elsewhere [ 191.
3. Theory of the oxygen exchange Starting from the point of view that the copper ions may exist in the valences 1 +, 2 + or 3 + and the va62
March 1993
lences of yttrium and barium are fixed, one may write
.. -(vo):i?,(vo)y~*~o:zy,
(1)
using the following assignment [V,] =y(‘) , [Oo]=7-y,
[V;;] =yQ) )
[I&]+
[Cu”]=e,
[V;;] =y
)
[Cu3+]=A,
[cu’+]+[Cu2+]+[Cu3+]=3.
(2)
So the reference composition is YBa2Cu30, and the Cu3+ ions are considered as the p-type carriers. This assumption, however, is arbitrary. Nevertheless, it does not affect the general validity of these considerations, for one can make a transformation to any other reference composition. The term A’ formally represents the influence of charged impurities. The value of 6/Zi corresponds to their concentration per unit cell, while zi means the state of charge, and the sign is due to whether the impurity acts as an acceptor ( + ) or as a donator (-). The electroneutrality condition then reads h-e=
1-2y+6+y(‘).
(3)
By leaving the crystal lattice an oxygen atom creates an oxygen vacancy. The two binding electrons, remaining first in the surrounding of the vacancy, can be donated, thus creating ionized oxygen vacancies. It is assumed, that the oxygen vacancies in the material are at least in the first degree of ionization, cu*++102 *g+v’ osoo+cu3+
10011cu3+ 1 *
[v,l
[cu2+
]
=K1
PA/:
9
(4)
and an equilibrium between singly and doubly ionized vacancies will be established, cu3+ + v’o*v;;
a
+cu*+
[V;;] [cl?+] [Vb] [cLP+]
=K2.
(5)
Furthermore one has to consider the disproportionation of the copper ions
Volume 16, number 2,3
MATERXALSLETTERS
icu*+ I icu3+ [cu2+]2
2cu~+~cu’++cu’+*
I =K, I’
(6) The aim is to express the concentration of all defect species in the equations above as a function of the oxygen partial pressure. This is possible if the mass action constants KI, K2 and Ki are known. In general, however, this will be not the case. On the other hand, the constants can be determined by a numerica fit, if at least one of the concentrations involved is known as a function of the oxygen partial pressure. This is the case for the amount of the oxygen deficiency y= [ Vh] + [VG], the poz dependence of which is known from the titration measurements and from literature TGA data f41.
4. Results and discussion Solving the defect chemical equations for the oxygen deficiency y and fitting the mass action constants, it is possible to model the quantity y as a function of the oxygen partial pressure. A comparison between those evaluated data and experimental ones is done in fig. 1. The good agreement between evaluation and both, TGA and titration, data is obvious. However, one has to keep in mind, that the modelling is done by choosing three appropriate parameters. Using free and independent parameters it
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will be possible to get nearly any curve within the model. Therefore it is necessary to check the constants, which one receives from the fitting procedure, on their physical plausibility. Since they are a kind of mass action constants, one expects them to exhibit a temperature activated behaviour. An Arrhenius plot (fig. 2 ) confirms this and allows one to draw further conclusions. So, it is seen that K, decreases with increasing temperature. This means a shift of the equilibrium described in (4) towards the left side, synonymous with an increased occurrence of oxygen vacancies with increasing temperature. This is well established in several investigations. K2 increases with increasing temperature, synonymous with an increased amount of doubly ionized oxygen vacancies in (5 ). This feature seems to be plausible, too. Finally the constant Ki, which describes the disproportionation of the copper (6), increases with temperature, which also seems reasonable.‘In the picture of a semiconducting material the activation energy of Ki is equivalent to the band gap. If these mass action constants are valid, it is now possible to evaluate the po2 dependences of all defect species involved. In figs. 3 and 4 this is done for 500 and 900” C. For better comparability the same scale is chosen, the hatched area in fig. 4 marks the range of chemical instability, where no reproducible results can be obtained. The asterisks denote the experimental data for the oxygen deficit y of Lindemer et al. [ 4 1, while the curves are calculated on the base of the proposed model.
0.8
0
0.0, -6
oara from ilndemer
et
ai
-500
,
/
,
I
j
-5
-4
-3
-2
-3
*c
-141
I
0
1
~g(pO,/bor)
Fig. 1. Oxygen deficit y as a function of pal determined by Lindemer et al. [4] in comparison with experimental and evaluated data (lines) from this work.
0.8
/ 0.9
, 1.0
/ 1.1 1000/T
, 1.2 in
/ 1.3
/ 1.4
1 /I(
Fig. 2. Mass action constants determined from a numerical tit of the proposed model to the stoichiometry data from Lindemer et al. [ 41 and from this work.
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Fig. 3. Evaluated defect ~oncentmtions 500°C.
in YBazCupO,_, for
1
0
8
-1
c
5 2
2
5
5 9
-2 -3 -4 -5
-5
-4
-3
-2
Fig. 4. Evaluated defect concentrations 900°C.
-I
0
in YBa2Cu~07_, for
It is easily seen that at 500°C the holes dominate the charge carriers. Throughout the whole range of investigation their concentration is at least two orders of magnitude higher than that of the electrons. This p-type behaviour is confirmed by conductance and the~opower measurements. At 900°C however, there exists a range, where electrons and holes are present in almost equal concentrations. This mixed p- and n-type behaviour is also seen in the corresponding conductance and thermopower measurements, e.g. refs. [8-lo,19 1. A very interesting feature of this result is the flat po2 dependence of the hole concentration at low temperature (SOO’C). It explains the fact, that it was possible in the recent years for nearly everyone to prepare the 90 K superconductor, without using a well-defined annealing procedure. Keeping in mind, that it is crucial for receiving the maximum transi64
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MATERIALS LETTERS
tion temperature to adjust the hole concentration near one per unit cell, it is seen, that it is peripheral whether the annealing is done in pure oxygen or in air. As well a change of temperature by several i 10” only slightly affects the hole concentration. The proposed model deals with dilute point defects in spite of the high defect concentrations. This becomes possible with the fo~ulation of a po2-dependent and therefore concentration-dependent degree of ionization of the oxygen vacancies. The interaction between the oxygen vacancies results in the failure to reach the full, double state of ionization. At 500°C and high po2 there exist only few oxygen vacancies, the concentration of singly and doubly ionized vacancies is still comparable. At 900°C already at 1 bar poZ the singly ionized vacancies are clearly in the majority. So the reducing of the state of ionization caused by the increased vacancy concentration is predominant over the influence of the higher temperature, which favours an increased degree of ionization (see mass action constant &)_ If only doubly ionized vacancies are assumed, it is also possible to fit the stoichiometry data rather well. The mass action constants, however, then are lacking their physical plausibility. A further test of the model can be made with the results obtained from titration measurements, which provide combined stoichiometry and conductance data. The poZ in the measuring cell is varied from a starting level (index S) to an end level (index E) and the corresponding conductances are recorded. The ratio of these conductance values then can be expressed as (7) where K(g@ means the geometric factor, q the elementary charge, p the hole concentration and p the mobility of the holes. The exchanged oxygen is written as APol=
Wol,- [Vols.
(8)
With the introduction of an averaged degree of ionization for the oxygen vacancies
A&]
+2A[V;]
z= [V,x] + [V,] + [Vi] = A&l
+2A[V;;l [Vol
(9)
’
and under the conditions p B n and np = const. for the extrinsic p range, one may write
(10)
PE=PS-ZA[VOI. Eq. (7 ) then reads e
= A[V,]
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Volume 16, number 2,3
GS GS - (&,&GE
’
(11)
If it is assumed that between starting and end levels of the po2 the degree of ionization and the hole mobility do not change, it is possible to determine the ratio p/z (or h/z if the concentration is given in holes per unit cell). Fig. 5 shows measured values in accordance with ( 11) and the evaluated curve resulting from the proposed model. The very good agreement between experiment and model may be regarded as a confirmation of the validity of the latter. Only at high po2 there occurs a deviation (circled values), which may be explained with a mobility change (see ( 11) ). For temperatures above 700°C the agreement becomes somewhat worse, in a way that the evaluated curve is below the experimental points. Probably this is the result of the restriction that all oxygen vacancies are regarded as at least singly ionized. If also non-
ionized vacancies are allowed, the averaged degree of ionization z becomes smaller, the ratio h/z therefore larger and a better Iit should be received. Introducing the non-ionized vacancies, however, would require a further mass action constant and make an appropriate lit more uncertain. The proposed model applies well to the data of Lindemer et al. [4] and our own results of high-purity samples. The parameter 6 is zero for these data. However, if one investigates samples prepared from starting materials of lower purity (p.a. grade), there occur deviations from the ideal behaviour. Only just choosing 6= -0.08 allows an appropriate lit (fig. 6 ). The negative value of S indicates the donator character of the disturbing effect resulting from the different preparation method. The absolute value for the oxygen deficit of the p.a. grade sample was determined from Fijrster [ 181 at a quenched sample equilibrated in air at 700°C. Apparently the oxygen deficit is over the whole poz range lower compared with the ideal material. It is also seen, that the deviation is small in the range of high po2 and becomes larger with decreasing Po2.
This result is similar to the investigations of Hong et al. [ 201 with La-doped samples. There is observed a compensation of the n-doping by a reduced oxygen vacancy concentration. Another quite interesting effect of the preparation conditions can be easily shown by observing the thermopower at high temperatures. The change of sign of the thermopower is sensitively influenced by
0 Y
0.4
Lindemer et .I. pa. same
0.3 -5
fg bO,/bar) Fig. 5. The quantity of holes per unit cell divided by the degree of ionization (h/z) in dependence of the oxygen partial pressure - comparison between the result from titration experiment and evaluated data based on the model.
-4
-3
-2
-1
0
1
b(pO,/bor)
Fig. 6. Oxygen deficit y of ideal and non-ideal sample - for the non-ideal sample the impurity parameter 6= -0.08 is introduced to tit the experimental points.
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MATERIALS LETTERS
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300,
I
,
,
733 ‘t 200-
.vV
VW
,
,
,
8,
V,.p& & 3
*%a
loo*;*“”
>
O_
-
VA
0. -lOO-
-5.01
. 0.85
.
.
. . 0.90
.
.
.
. . 0.95
..I......... 1.00
1.05
( 1.10
A
.A
. . A V
TV
-200 -5
-4
-3
1 OOO/(T/K)
Fig. 7. Oxygen partial pressure at which thermopower changes sign as a function of reciprocal temperature for several samples from this work and literature data [6,7,10,11] with different preparation history.
the ratio of p- to n-type carriers. So the position of the thermopower-zero-point over a log&,)-scale depends not only on intrinsic material properties, but also on possibly existing ionized impurities. In fig. 7 the influence of the milling procedure is shown. Over a 1/T scale the po2 corresponding to the thermopower-zero-point is plotted for several samples denoted by their laboratory notation. The open symbols denote samples treated in an attritor mill with ZrOz balls. This preparation leads to a very homogeneous precursor, but also causes increased abraded particles. The tilled symbols stand for samples prepared in an agate ball mill with less abrasion. It is obvious that the latter ones are closer to the ideal behaviour predicted by the model. This indicates a noticeable amount of charged impurities caused by the ZtQ abrasion. Also the results taken from the literature scatter remarkably, indicating a different preparation history of the samples used. However, the influence is only detectable in the mixed p-/n-type range. Regarding the whole thermopower curve (fig. 8) this is easy to see. There is no or only a small difference between the data in the extrinsic p-branch of the curves. This result is confirmed by the low temperature behaviour. After annealing at 42O”C/ 1 bar po2, two samples with remarkable differences in their mixed range show a pretty good superconducting transition at 92 K (fig. 9). So it becomes understandable, that there is no agreement in the scientific community about the appropriate description of the high-temperature be66
*q.
----..‘--“---_,--____-_-___-_,_.____.__
-2
HI ma El B9o
-1
0
bbO,/bad
Fig. 8. Thermopower as a function of the oxygen partial pressure for several different samples.
0
300
200
100
T/K Fig. 9. Superconducting transition for two samples from fig. 8. 250
I 825 ‘C
50-
0
1, measuremen
._-___-.-_--
-150
-4
1 -3
-2
-1
0
kdpO,/bad
Fig. 10. Shift of the thermopower curve caused by “denaturating” the sample as result of partial decomposing due to annealing for 2 h at low poz .
haviour of this material. It originates from the fact that apparently “different”, not well-defined samples are investigated. A further point, which may lead to confusion,
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should be mentioned. Like the choice of starting materials and milling/mixing procedure also the temperature/p,, treatment may alter the samples irreversibly. Fig. 10 shows a set of measurements performed with the same sample. After the first measurement the sample was annealed for 2 h in the instable range at low oxygen partial pressure, resulting in a partial decomposition. This shifts the mixed range towards lower po2. However, the new state is also a stable one, as the reproducibility shows.
5. Summary
A model was proposed, which considers all defects influencing the conductivity of YBa,C&O,_,. The main feature of this model is the consideration of interactions between the oxygen vacancies by introducing an averaged degree of ionization. By using an impurity parameter 6 the model can be applied also to non-ideal samples. Remarkable is the fact that preparation conditions have a considerable impact on the defect chemistry. Obviously, this was not sufficiently taken into account in the recent literature considering this topic. However, also with those not well-defined samples superconductors with sharp transition at 92 K are obtainable.
References [ 1 ] R.J. Cava, A.W. Hewat, E.A. Hewat, B. Batlogg, M. Marezio, K.M. Rabe, J.J. Krajewski, W.F. Peck Jr. and L.W. Rupp Jr., PhysicaC 165 (1990) 419.
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[2] J.B. Goodenough and A. Manthiram, J. Solid State Chem. 88 (1990) 115. [ 3 ] P. Steiner, S. Hiifner, V. Kinsinger, I. Sander, B. Siegwart, H. Schmitt, R. Schulz, S. Junk, G. Schwitzgebel, A. Gold, C. Politis, H.P. Mtlller, R. Hoppe, S. Kemmler-Sack and C. Kunz, Z. Physik B 69 (1988) 449. [4] T.B. Lindemer, J.F. Hunley, J.E. Gates, A.L. Sutton Jr., J. Brynestad, C.R. Hubbard and P.K. Gallagher, J. Am. Ceram. Sot. 72 (1989) 1775. [ 5] K. Beetz and K.H. Hardtl, VDI-Berichte 939 ( 1992) 5 19. [ 61 LA. Leonidov, Y.N. Blinovskov, E.E. Flyatau, P.Y. Novak and V.L. Kozhevnikov, Physica C 158 ( 1989) 287. [7] G.M. Choi, H.L. Tuller and M.-J. Tsai, in: Nonstoichiometric compounds, NATO AS1 Series, eds. J. Nowotny and W. Weppner (Kluwer, Dordrecht, 1989) p. 451. [ 81 J. Nowotny, M. Rekas and W. Weppner, J. Am. Ceram. Sot. 73 (1990) 1040. [9] J. Nowotny and M. Rekas, J. Am. Ceram. Sot. 73 (1990) 1048. [lo] J. Nowotny and M. Rekas, J. Am. Ceram. Sot. 73 (1990) 1054. [ 111 M.-Y. Su, S.E. Dorris and T.O. Mason, J. Solid State Chem. 75 (1988) 381. [ 121 J. Maier, P. Murugaraj and G. Pfundtner, Solid State Ionics 40/41 (1990)802. [ 131 J. Maier, P. Murugaraj, G. Pfundtner and W. Sitte, Ber. Bunsenges. Physik. Chem. 93 ( 1989) 1350. [ 141 G.P. Sykora, M.Y. Su and T.O. Mason, in: Nonstoichiometric compounds, NATO AS1 Series, eds. J. Nowotny and W. Weppner (Kluwer, Dordrecht, 1989). [ l$] A. Metha and D.M. Smyth, in: Non-stoichiometric compounds, NATO AS1 Series, eds. J. Nowotny and W. Weppner (Kluwer, Dordrecht, 1989). [ 161 D.J.L. H0ngandD.M. Smyth, J. Am. Ceram. Sot. 74 (1991) 1751. [ 17) J. Nowotny and M. Rekas, J. Am. Ceram. Sot. 74 ( 199 1) 1753. [ 181 H. Forster, Freiberger NE-Metal1 GmbH, Lessingstrasse 41, O-9200 Freiberg/Sachsen, Auftragsanalyse ( 1992). [ 191 A. Pecina, Ph.D. Thesis, University of Karlsruhe (TH), Germany (1992). [20] D.J.L. Hong, A. Metha, D.M. Smyth, E.K. Chang and M.J. Kirschner, J. Mater. Res. 5 (1990) 1185.
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