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Oxygen dependence of the mechanical spectrum of Bi2Sr2CaCu2O8+x in the temperature range 80–600 K
PHYSICA ELSEVIER
Physica C 250 (1995) 75-81
Oxygen dependence of the mechanical spectrum of Bi2Sr2CaCu208+ x in the temperature range 80-600 K L. Donzel *, Y. Mi 1, R. Schaller Institut de G~nie Atoraique, Ecole Polytechnique F~d~rale de Lausanne, CH-IO15 Lausanne, Switzerland
Received 4 April 1995
Abstract The elastic modulus and mechanical loss of ceramic Bi2Sr2CaCu2Os+ x specimens have been measured between 80 K and 600 K in the kHz frequency range. The mechanical-loss spectrum is composed of two relaxation peaks located at ~ 145 K and ~ 450 K. The two peaks are certainly correlated with the oxygen content (x) because the peak heights depend on the thermal treatments, i.e. oxygen content. The 450 K peak can be associated with the diffusion of the additional oxygen atoms in the BiO layers. The 150 K peak may be due to the hopping of holes in the CuO 2 layers. Finally, the elastic modulus shows a strong hysteresis between heating and cooling, which could result from an "order-disorder" transition of oxygen atoms in the BiO layers and from the stress induced in polycrystalline samples by the anisotropy of thermal expansion.
I. Introduction The mechanical spectrum of YBa2Cu306+ x superconducting ceramics is composed of four mechanical-loss peaks in the temperature range 8 0 - 6 0 0 K [1-9]. In particular a high-temperature peak (450 K) has been interpreted as due to the diffusion of the additional oxygen atoms in the CuO planes [5,9]. Two low-temperature peaks (90 and 110 K) could be interpreted as due to the hopping of holes created by oxygen doping [5]. In the present research, we are interested in studying the effect of oxygen on the mechanical spectrum of Bi2Sr2CaCu2Os+x, another copper oxide superconductor. In Bi2Sr2CaCu2Os+x, several mechanical-loss
* Corresponding author. 1 Present address: Max-Plank Institut for Metallforschung, Institut fair Werkstoffwissenschaft,D-70174 Stuttgart, Germany.
peaks have been observed at 35 K [10], 150 K [10-14], 225 K [12] and 285 K [12] (kHz range) and at 373 K and 573 K (Hz range) [15]. The peaks at 35 K, 225 K and 285 K are either unstable or are not always observed. Measurements at different frequencies have shown that the 150 K and the 373 K peaks are relaxation peaks with an activation energy of 0.28 eV [13,14] and 1.1 eV [15], respectively. D u e t al. [14] and Zeng et al. [15] have observed that these two peaks are oxygen dependent. However, these peaks are still unexplained and the influence of the oxygen content on the mechanical spectra has not been studied. In the present work, mechanical-loss spectra of Bi2Sr2CaCu208+ x samples have been measured between 80 K - 6 0 0 K for samples annealed under different conditions, that is different oxygen content [16]. Possible relaxation mechanisms are proposed to explain the origin of the 150 K and 373 K mechanical-loss peaks.
0921-4534/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0921-4534(95)00355-5
L. Donzel et al. /Physica C 250 (1995) 75-81
76
2. Experimental methods The mechanical spectroscopy measurements were carried out in a resonant bar apparatus [17]. This technique allows the measurement to be made of the elastic modulus and the internal friction, i.e. the mechanical loss, as a function of temperature in the kHz frequency range. The internal friction ( Q - l ) is determined by the free decay method, and the Young modulus (E) is deduced from the resonance frequency of the bar. The internal friction is given by A0
where n is the number of the vibration cycles, during which the vibration amplitude decreases from A 0 to A n. The Young modulus (E) is related to the resonance frequency (f,) by
-4.4 -'n Fz
2 0-I
i
I00
i i i i "~ 4.1 200 300 400 SO0 600 Temperature [K]
Fig. 1. The temperature dependence of the internal friction Q-1 and of the square of the resonant frequency fr2 for Bi2Sr2CaCu2Os+x.
The resistance was measured by the standard four-probe method.
flpl 4
E=
a2 fr2,
3. Results where p is the sample density, l is the length, a the thickness and fl a constant determined by the boundary conditions, the mode of vibration and the crosssection of the sample. For free/free-end boundary condition, fundamental mode and rectangular crosssection, fl = 0.94. Different resonant frequencies can be obtained by exciting the sample in harmonic modes. In mechanical spectroscopy, an anelastic relaxation phenomenon gives rise to an internal-friction peak and a modulus defect. The peak's height and the amplitude of the modulus defect are related to the concentration of relaxing entities, and the peak's position is determined by their mobility. For pure Debye relaxation, the height of the peak is half of the modulus defect. For the mechanical-spectroscopy measurement, rectangular bars of 40 × 4 X 1 mm 3 were cut from Bi2Sr2CaCu208+ * rods produced either by Hoechst AG (density 5.1 g / c m 3) or in our laboratory from B i 2 . 1 2 S r l . q o C a l . 0 2 C U l . 9 6 0 8 + x powder prepared by a solid-state reaction method at the University of Geneva [18] (density 2.7 g/cm3). Samples were annealed under vacuum (10 -5 Tort) or under oxygen flux at different temperatures in order to change the oxygen content (x).
The typical temperature dependence of Q-1 and f f of Bi2Sr2CaCu208+ x between 80 K and 600 K is shown in Fig. 1. Two internal-friction peaks appear in this mechanical-loss spectrum: at 150 K the lowtemperature peak (PET), and at 450 K the high-temperature peak (Prrr). The modulus defects associated with the internal friction peaks can be seen in the if(T) curve, which is proportional to the Young modulus. A hysteresis in the modulus is observed during the thermal cycling. The Q-I(T) curves do not present such a hysteresis. These results were qualitatively the same for all of the samples. However, the peak heights and the shape of the modulus loop depend on the oxygen content of the samples. The two peaks are frequency dependent, in other words, they are relaxation peaks. The peaks' positions shift towards higher temperature as the measurement frequency is increased. The activation energy is 0.29 eV for the PET peak and and 0.9 eV for the PHT peak, respectively. The frequency factor is of about 1013 s -1 for both peaks. The two peaks are broader than pure Debye peaks by a factor of about four. The modulus defects are greater than would be expected for Debye peaks, even for broadened peaks
L. Donzel et al. / Physica C 250 (1995) 75-81 10-
77
Under O z
e
8-
8
Under vacuum
o
~
- 100
c
- 90
o
oos
8 o-
d
-80
o
~4-
?04-
a
70
"(~ 20-
PLT 2-
60
OI
100
I 200
I 300
I 400
Temperature
I 500
rn -
-
/i
600
[K]
Fig. 2. Influence of thermal treatments on the internal friction spectra. From (a) to (e) there is a decreasing oxygen content. (a) Low-density sample annealed 4 days under oxygen flux at 673 K. (b) to (e) Hoechst samples: (b) annealed 4 days under oxygen flux at 673 K, (c) as-received, (d) annealed 2 h under vacuum at 773 K, (e) annealed 2 h under vacuum at 973 K. The dashed line is the extrapolated background (see text).
[17]. The influence of annealing conditions on the internal friction spectra can be seen in Fig. 2. Both peak heights are affected by the annealing conditions, i.e. by the oxygen content. To study quantitatively the behavior of the two peak heights, we subtracted from the experimental internal-friction data an extrapolated background. For the high-temperature range, the internal-friction spectrum of the sample annealed under vacuum at 973 K was considered to be the background, because it shows only a slight increase as a function of temperature and presents no peak. For the low-temperature range, a constant value was taken. The results are shown in Fig. 3. It can be seen that the height of the PHT peak decreases monotonically as the oxygen content decreases (as the samples were annealed, under vacuum, at higher temperatures). On the contrary, the height of the PET peak has a dome-shape dependence on the oxygen content, reaching a maximum for the sample annealed under vacuum at 773 K. An interesting result is that the height of the peak PLT varies in the same way as the superconducting transition temperature Tc. The results for one sample annealed under oxygen flux, i.e. with a higher oxygen content, have been added to Fig. 3. The position of this sample on the scale is arbitrary; however, it shows the trend of the superconducting transition temperature and the height of the peaks' dependence on the oxygen content in a larger range.
i
i
i
-i
50
600 700 800 900 1000 Annealing temperature [K] P decreasing
oxygen content
Fig. 3. Dependence of the peaks' heights on annealing conditions: (12) height of the high-temperature peak, (©) height of the low-temperature peak, ( A ) superconducting transition temperature. The results for one sample annealed under oxygen flux, i.e. with a higher oxygen content, have been added.
In Fig. 4, if(T) curve for a sample showing a particularly high hysteresis of the elastic modulus (E = f f ) is presented. Apart from the modulus defects associated with the two relaxation peaks, some interesting features can be noticed: a softening of the elastic modulus observed during cycling at low temperature (Estat e 1 > Estate 2a,b); a hardening of the modulus after cycling at high temperature (Estat e 2b
4.8-
1
~4.7 -
-'--.
,/~
~_
o
"~.
2b
C W
g4.5 tJ_
4.4 I
I
Ir
I
I
I
100
200
300
400
500
600
Temperature [K]
Fig. 4. Thermal hysteresis of the elastic modulus. Dashed line: minor low-temperature cycle, 300-200-300 K, dotted line: minor high-temperature cycle, 300-480-350 K, plain line: major temperature cycle 300-80-600-300 K.
78
L. Donzel et al. /Physica C 250 (1995) 75-81
< Estat e 3a.b); a rapid increase in the elastic modulus
while heating at high temperature ( > 500 K, i.e. higher than the Pax's temperature). Moreover, one can see that the greater the thermal cycle the larger the softening (hardening). The thermal hysteresis of two samples having different densities is presented in Fig. 5. The relative strength of the hysteresis is greater for the denser material (75% of the theoretical density) compared to the lighter material (40% of the theoretical density).
a)
a
1. b)
4. Discussion and interpretation The PHT peak is the same as the 373 K peak observed by Zeng et al. at a frequency of 1 Hz [15]. The activation energy of the PHT peak (0.9 eV) is close to the diffusion energy of oxygen in the ab plane (0.93 eV, determined by tracer diffusion [19]), which suggests that this peak could be associated with the movement of oxygen atoms in the ab plane. The frequency factor is in the range of the Debye frequency, and the intensity of the relaxation seems to be proportional to the number of additional oxygen atoms. These are the characteristics of a pointdefect relaxation. So the Pax peak may be due to the movement of additional oxygen in the ab plane. The additional oxygen atoms (x > 0) are found inside the BiO layers at interstitial positions between two bismuth atoms [20]. In these layers, the atoms are arranged in so-called BiO chains. The additional oxygen can be found either in intra- or in extra-chain
1 •
o
|
o density Z.6 g/cm 3
I
100
200
300
\N.\\ NKNK ~'-~
400
N
S00
Temperature [K] Fig. 5. Thermal hysteresis of the elastic modulus for two samples of different density.
Fig. 6. Anelastic processes in the BiO layers associated with the diffusion of oxygen. (a) Possible positions, OA and OB, for additional oxygen atoms. (b) Hopping of additional atoms and reorientation of the lattice distortion under compressive stress applied along the a-axis (for an intra-chain and an extra-chain additional oxygen); ( © ) bismuth, ( 0 ) oxygen, ( O ) intra-chain additional oxygen and ( O ) extra-chain additional oxygen.
interstitial positions between two bismuth atoms, in both cases creating a local distortion of the structure (Fig. 6). At equilibrium, the interstitial sites along the a- and b-axis are equivalent. But when a compressive stress is applied along the a-axis for example, the interstitial sites along the b-axis (site O B) are energetically more favorable than the sites along a (site OA), SO the interstitial oxygen should be found preferentially in the O B sites. When under stress an extra-chain atom jumps from site OA to site O B, or when an intra-chain atom leaves the site OA and pushes a "central" atom to the O B site, there is a reorientation of the local distortion (Fig. 6), which is an anelastic relaxation mechanism, and gives rise to an internal-friction peak (Snoek type relaxation) [17]. However, the hopping activation energies for the intra- and extra-chain oxygen can be slightly different. This could explain why the experimental Pax peak is four times broader than a pure simple
79
L. Donzel et al. / Physica C 250 (1995) 75-81
Debye peak, and why the modulus defect is too large to be explained by a Debye relaxation. The fact that the motions of the additional oxygen atoms involve the rearrangement of the atoms in the BiO chains may also contribute to the broadening of the peak. The frequency factor of the low-temperature peak is in the range of the Debye frequency. The activation energy (0.29 eV) is very small, suggesting that the peak could not be due to an atomic diffusion process but could be rather interpreted by an electronic-relaxation mechanism. Effectively, hopping of electrons (holes) needs less energy than jumping of ions between two positions (typically 1-2 eV for ions and 0.1-0.5 eV for electronic charges [21]). Moreover Som et al. [22] have observed a dielectric relaxation peak in BSCCO glasses (activation energy 0.35 eV, deduced from Fig. 5 in Ref. [22]). These glasses become superconducting in their glassceramics form. Furthermore, Murawski et al. [23] have observed that the activation energy of the mechanical-loss peak observed in the partially crystallized semiconducting BSCCO glasses (0.3 eV), which is similar to the low-temperature peak observed in superconducting Bi2Sr2CaCu2Os+ x, is the same as that of the activation energy of the DC conductivity. The similarity of the activation energies suggests that the mechanical-loss peak and the DC conductivity might be attributed to the same mechanism. However, the mechanism proposed by Murawski, charge transfer between the crystalline granules, should not be retained, because, as it is not associated with a reorientation of a lattice distortion, it does not explain the mechanical-loss peak. Considering the resuits of Som et al. and Murawski et al., it seems then possible that electronic relaxation takes place in BSCCO superconducting ceramics. Considering also that the variation of the PLT peak's height with the oxygen content is similar to the variation of the superconducting transition temperature Tc (Fig. 3), and that Tc depends upon the number of holes in the CuO 2 layers [24], the origin of the peak could be linked to the holes in the CuO 2 plane. Additional holes in the CuO 2 layers are created when Bi2Sr2CaCu2Os+ x is doped with oxygen (x > 0) by charge transfer from the CuO 2 layers to the BiO layers where the additional oxygens are found. The mechanism leading to the anelastic relaxation could be the hopping of the holes on oxygen ( O - )
C++
Cu++
,O-
O
O1 -b Fig. 7. Anelastic process in the CuO2 layers leading to the PBT peak; hoppingof one hole betweentwo oxygenions and reorientation of the associatedlattice distortion. between two sites. The O - ions are more positive than the 0 2-, so the neighbor Cu 2+ ions will be slightly pushed when there is a hole on the oxygen, which causes a local distortion of the structure (Fig. 7). At equilibrium the hole sites along the a- and b-axes (01 , 0 2 sites of Fig. 7) are equivalent. Applying a compressive stress along a, for example, may favor site O 2 and preferentially induce hopping of holes from site 01 to site O 2. Such a hopping will lead to the reorientation of the lattice distortion, i.e. anelastic relaxation and internal-friction peak. Following this model, the intensity of relaxation (peak height) should be proportional to the oxygen content. However, the experimental data show that this is not the case (Fig. 3). As the number of holes shows a monotonic dependence upon the oxygen doping [25], the explanation of this experimental fact cannot be a diminution of the hole number with overdoping. One possible explanation is that, when a certain concentration of holes is reached, the hopping of one hole is no longer independent of the position of the other holes. Effectively, when a hole is present at the O 1 ( 0 2) site, an internal compressive stress along the a(b-) axis is created (Fig. 7), this changes the energy of the neighboring sites. For example if there is already an 01 hole, it will be less favorable for a neighboring hole to be also in an 01 site along the same CuO line, because there is a compressive internal stress along the a-axis which makes these sites less favorable. At low concentration, as the holes are far apart from each other, this effect does not play any role in the hopping process. On the other hand, at higher concentration, this could prevent the hopping, because hopping under an external stress will be more difficult if the internal stresses act against it.
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L. Donzel et al. / Physica C 250 (1995) 75-81
So even if there are more holes in the CuO 2 layers, fewer holes will hop and then the intensity of relaxation will decrease with increasing hole concentration. In parallel one observes that the superconducting transition temperature Tc decreases also, showing the relation between the elastic waves and the superconductivity. It is interesting to note that the coordinated motion of two holes (one from site 01 to site 02, the other from site 02 to site 01) gives rise to a resulting elastic distortion which is zero. Then in the superconducting state, the motion of hole pairs would create no elastic distortion of the lattice. A thermal hysteresis of the modulus (not associated with hysteresis in the internal friction) has also been observed in YBCO ceramics. In this case, the hysteresis has been interpreted as due to the effect of the internal stresses induced at the grain boundaries during thermal cycling resulting from the anisotropy of thermal expansion along the a, b and c directions [5]. In Bi2Sr2CaCu208+ x there is also such an anisotropy [26] which may contribute to the observed hysteresis loop. In this sense in the low-density materials, internal stresses are less important and so the relative intensity of the hysteresis is not so pronounced (Fig. 5). However, this explanation cannot deal with the experimental fact that the modulus increased drastically in the temperature region higher than 500 K, so the hysteresis does not result from the anisotropy only. In fact, the main contribution to the change of elastic modulus during thermal cycling may be associated with an "order-disorder" transition in the BiO layers. During heating, the oxygen atoms of the BiO layers can jump from one site to another (peak PHx)" The strong increase in the modulus, after Prrr, observed in Fig. 5, could result from the beginning of the long-range diffusion under the concentration gradient (the experiments are conducted in vacuum). Then oxygen atoms leave their equilibrium positions in the BiO layers and jump to non-equilibrium positions, where they locally stiffen the lattice, giving rise to an increase of the sample rigidity. As there is a concentration gradient, the oxygen atoms do not come back to equilibrium positions when the sample is cooled down to room temperature. It is only during cooling at low temperature ( < room temperature), that there should be a progressive reshuffling of these displaced oxygen atoms, under an "ordering force", because if at
" h i g h " temperature the entropy term can make up for the mismatch in the BiO layers, at low temperature a disordered state is no longer acceptable. The rigidity of the sample will then decrease when thermal cycling at low temperature is performed.
5. Conclusions T h e B i 2 S r 2 C a C u 2 0 8 + x superconducting c e r a m i c s present a characteristic mechanical spectrum composed of two mechanical-loss peaks located at 150 K and 450 K. The two peaks are relaxation peaks associated with the additional oxygen atoms. The high-temperature peak can be explained by the short-range diffusion of the additional oxygen atoms in the BiO layers. The low-temperature peak may be due to the motion of holes, created by oxygen doping, in the CuO 2 layers. A thermal hysteresis of the elastic modulus, which is not accompanied by a hysteresis of the internal friction, has been observed. This behavior may due to order-disorder states of oxygen in the BiO layers and to stresses related to the anisotropy of the thermal expansion in polycrystalline Bi2Sr2CaCu208+ x.
Acknowledgements The authors would like to thank R. Flukiger for providing the Hoechst samples, and G. Triscone for providing the BiE.12Srl.90Cal.o2CUl.9608+x powder.
References [1] G. Cannelli, R. Cantelli, F. Cordero, G.A. Costa, M. Ferretti and G.L. Olcese, Europhys. Lett. 6 (1988) 271. [2] G. Cannelli, R. Cantelli, F. Cordero, M. Ferretti and L. Verdini, Phys. Rev B 42 (1990) 7925. [3] B. Kusz, R. Barczynski, M. Gazda, P. Pastuszak, M. Murawski, O. Gzowski, I. Davoli and S. Stizzaet, Solid State Commun. 75 (1990) 789. [4] Y. Mi, R. Schaller, H. Berger, W. Benoit and S. Sathish, Physica C 172 (1191) 407. [5] Y. Mi, PhD. thesis, Ecole Polytechnique F6d6rale de Lausanne, Switzerland (1994). [6] P.P. Pal-Val, LN. Pal-Val, V.V. Demirskii, V.D. Natsik and V.V. Prytkin, Superconductivity 4 (1991) 1450.
L. Donzel et al. / Physica C 250 (1995) 75-81 [7] L. Sun, Y. Wang, H. Shen and X. Cheng, Phys. Rev. B 38 (1988) 5114. [8] M. WeUer, H. Jaeger, G. Kaiser and K. Schulze, Physica C 162-164 (1989) 935. [9] X.M. Xie, T.G. Chen and Z.L. Wu, Phys. Rev. B 40 (1989) 4549. [10] E. Rodriguez, J. Luzuriaga, M.N. Regueiro and C. Fainstein, Solid State Commun. 77 (1991) 777. [11] R.L. Jacobsen, T.M. Tritt, A.C. Ehrlich and D.J. Gillespie, Phys. Rev. B 47 (1993) 8312. [12] O.M. Nes, K. Fossheim, N. Motohira and K. Kitazawa, Physica C 185-189 (1991) 1391. [13] M. Weller, H. Jaeger, N. Riiffer, G. Kaiser and K. Schulze, in: Proc. ICMC 90 Conf. Garmisch- Partenkirchen (1990). [14] J. Du, Y. Sun, J. Jiang, F. Zeng and H. Yin, Phys. Rev. B 41 (1990) 6679. [15] W.G. Zeng, J.X. Zhang, G.M. Lin and C.L. Du, Solid State Commun. 70 (1989) 333. [16] M. Majewski, Adv. Mater. 6 (1994) 460. [17] A.S. Nowick and B.S. Berry, Anelastic relaxation in crystalline solids (Academic Press, New York, 1972).
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[18] T. Tsukamoto, G. Triscone, J.-Y. Genoud, K.-Q. Wang, E. Janod, A. Junod and J. Muller, J. Alloys Comp. 209 (1994) 225. [19] M. Runde, J.L. Routbort, S.J. Rothman, K.C. Goretta, J.N. Mundy, X. Xu and J.E. Baker, Phys. Rev. B 45 (1992) 7375. [20] A.A. Levin, Y.I. Smolin and Y.F. Shepelev, J. Phys. Condens. Mat. 6 (1994) 3539. [21] A.M. Stoneham and L.W. Smith, J. Phys. Condens. Mat. 3 (1991) 225. [22] K.K. Som, S. Mollah, K. Bose and B.K. Chaudhauri, Phys. Rev. B 47 (1993) 534. [23] L.L. Murawski, R.J. Barczynski, K. Trzebiatowski, D. Samatowisz, B. Koscielska, M. Gazda, B. Kusz and O. Gzowski, J. Alloys Coump. 211&212 (1994) 287. [24] Y. Koike, Y. Iwabuchi, S. Hosoya, N. Kobayashi and T. Fukase, Physica C 159 (1989) 105. [25] T. Schweizer, R. Miiller and L.J. Gauckler, Physica C 225 (1994) 143. [26] R.H. Arendt, M.F. Garbauskas and C.A. Meyer, Physica C 182 (1991) 73.
Physica C 250 (1995) 75-81
Oxygen dependence of the mechanical spectrum of Bi2Sr2CaCu208+ x in the temperature range 80-600 K L. Donzel *, Y. Mi 1, R. Schaller Institut de G~nie Atoraique, Ecole Polytechnique F~d~rale de Lausanne, CH-IO15 Lausanne, Switzerland
Received 4 April 1995
Abstract The elastic modulus and mechanical loss of ceramic Bi2Sr2CaCu2Os+ x specimens have been measured between 80 K and 600 K in the kHz frequency range. The mechanical-loss spectrum is composed of two relaxation peaks located at ~ 145 K and ~ 450 K. The two peaks are certainly correlated with the oxygen content (x) because the peak heights depend on the thermal treatments, i.e. oxygen content. The 450 K peak can be associated with the diffusion of the additional oxygen atoms in the BiO layers. The 150 K peak may be due to the hopping of holes in the CuO 2 layers. Finally, the elastic modulus shows a strong hysteresis between heating and cooling, which could result from an "order-disorder" transition of oxygen atoms in the BiO layers and from the stress induced in polycrystalline samples by the anisotropy of thermal expansion.
I. Introduction The mechanical spectrum of YBa2Cu306+ x superconducting ceramics is composed of four mechanical-loss peaks in the temperature range 8 0 - 6 0 0 K [1-9]. In particular a high-temperature peak (450 K) has been interpreted as due to the diffusion of the additional oxygen atoms in the CuO planes [5,9]. Two low-temperature peaks (90 and 110 K) could be interpreted as due to the hopping of holes created by oxygen doping [5]. In the present research, we are interested in studying the effect of oxygen on the mechanical spectrum of Bi2Sr2CaCu2Os+x, another copper oxide superconductor. In Bi2Sr2CaCu2Os+x, several mechanical-loss
* Corresponding author. 1 Present address: Max-Plank Institut for Metallforschung, Institut fair Werkstoffwissenschaft,D-70174 Stuttgart, Germany.
peaks have been observed at 35 K [10], 150 K [10-14], 225 K [12] and 285 K [12] (kHz range) and at 373 K and 573 K (Hz range) [15]. The peaks at 35 K, 225 K and 285 K are either unstable or are not always observed. Measurements at different frequencies have shown that the 150 K and the 373 K peaks are relaxation peaks with an activation energy of 0.28 eV [13,14] and 1.1 eV [15], respectively. D u e t al. [14] and Zeng et al. [15] have observed that these two peaks are oxygen dependent. However, these peaks are still unexplained and the influence of the oxygen content on the mechanical spectra has not been studied. In the present work, mechanical-loss spectra of Bi2Sr2CaCu208+ x samples have been measured between 80 K - 6 0 0 K for samples annealed under different conditions, that is different oxygen content [16]. Possible relaxation mechanisms are proposed to explain the origin of the 150 K and 373 K mechanical-loss peaks.
0921-4534/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0921-4534(95)00355-5
L. Donzel et al. /Physica C 250 (1995) 75-81
76
2. Experimental methods The mechanical spectroscopy measurements were carried out in a resonant bar apparatus [17]. This technique allows the measurement to be made of the elastic modulus and the internal friction, i.e. the mechanical loss, as a function of temperature in the kHz frequency range. The internal friction ( Q - l ) is determined by the free decay method, and the Young modulus (E) is deduced from the resonance frequency of the bar. The internal friction is given by A0
where n is the number of the vibration cycles, during which the vibration amplitude decreases from A 0 to A n. The Young modulus (E) is related to the resonance frequency (f,) by
-4.4 -'n Fz
2 0-I
i
I00
i i i i "~ 4.1 200 300 400 SO0 600 Temperature [K]
Fig. 1. The temperature dependence of the internal friction Q-1 and of the square of the resonant frequency fr2 for Bi2Sr2CaCu2Os+x.
The resistance was measured by the standard four-probe method.
flpl 4
E=
a2 fr2,
3. Results where p is the sample density, l is the length, a the thickness and fl a constant determined by the boundary conditions, the mode of vibration and the crosssection of the sample. For free/free-end boundary condition, fundamental mode and rectangular crosssection, fl = 0.94. Different resonant frequencies can be obtained by exciting the sample in harmonic modes. In mechanical spectroscopy, an anelastic relaxation phenomenon gives rise to an internal-friction peak and a modulus defect. The peak's height and the amplitude of the modulus defect are related to the concentration of relaxing entities, and the peak's position is determined by their mobility. For pure Debye relaxation, the height of the peak is half of the modulus defect. For the mechanical-spectroscopy measurement, rectangular bars of 40 × 4 X 1 mm 3 were cut from Bi2Sr2CaCu208+ * rods produced either by Hoechst AG (density 5.1 g / c m 3) or in our laboratory from B i 2 . 1 2 S r l . q o C a l . 0 2 C U l . 9 6 0 8 + x powder prepared by a solid-state reaction method at the University of Geneva [18] (density 2.7 g/cm3). Samples were annealed under vacuum (10 -5 Tort) or under oxygen flux at different temperatures in order to change the oxygen content (x).
The typical temperature dependence of Q-1 and f f of Bi2Sr2CaCu208+ x between 80 K and 600 K is shown in Fig. 1. Two internal-friction peaks appear in this mechanical-loss spectrum: at 150 K the lowtemperature peak (PET), and at 450 K the high-temperature peak (Prrr). The modulus defects associated with the internal friction peaks can be seen in the if(T) curve, which is proportional to the Young modulus. A hysteresis in the modulus is observed during the thermal cycling. The Q-I(T) curves do not present such a hysteresis. These results were qualitatively the same for all of the samples. However, the peak heights and the shape of the modulus loop depend on the oxygen content of the samples. The two peaks are frequency dependent, in other words, they are relaxation peaks. The peaks' positions shift towards higher temperature as the measurement frequency is increased. The activation energy is 0.29 eV for the PET peak and and 0.9 eV for the PHT peak, respectively. The frequency factor is of about 1013 s -1 for both peaks. The two peaks are broader than pure Debye peaks by a factor of about four. The modulus defects are greater than would be expected for Debye peaks, even for broadened peaks
L. Donzel et al. / Physica C 250 (1995) 75-81 10-
77
Under O z
e
8-
8
Under vacuum
o
~
- 100
c
- 90
o
oos
8 o-
d
-80
o
~4-
?04-
a
70
"(~ 20-
PLT 2-
60
OI
100
I 200
I 300
I 400
Temperature
I 500
rn -
-
/i
600
[K]
Fig. 2. Influence of thermal treatments on the internal friction spectra. From (a) to (e) there is a decreasing oxygen content. (a) Low-density sample annealed 4 days under oxygen flux at 673 K. (b) to (e) Hoechst samples: (b) annealed 4 days under oxygen flux at 673 K, (c) as-received, (d) annealed 2 h under vacuum at 773 K, (e) annealed 2 h under vacuum at 973 K. The dashed line is the extrapolated background (see text).
[17]. The influence of annealing conditions on the internal friction spectra can be seen in Fig. 2. Both peak heights are affected by the annealing conditions, i.e. by the oxygen content. To study quantitatively the behavior of the two peak heights, we subtracted from the experimental internal-friction data an extrapolated background. For the high-temperature range, the internal-friction spectrum of the sample annealed under vacuum at 973 K was considered to be the background, because it shows only a slight increase as a function of temperature and presents no peak. For the low-temperature range, a constant value was taken. The results are shown in Fig. 3. It can be seen that the height of the PHT peak decreases monotonically as the oxygen content decreases (as the samples were annealed, under vacuum, at higher temperatures). On the contrary, the height of the PET peak has a dome-shape dependence on the oxygen content, reaching a maximum for the sample annealed under vacuum at 773 K. An interesting result is that the height of the peak PLT varies in the same way as the superconducting transition temperature Tc. The results for one sample annealed under oxygen flux, i.e. with a higher oxygen content, have been added to Fig. 3. The position of this sample on the scale is arbitrary; however, it shows the trend of the superconducting transition temperature and the height of the peaks' dependence on the oxygen content in a larger range.
i
i
i
-i
50
600 700 800 900 1000 Annealing temperature [K] P decreasing
oxygen content
Fig. 3. Dependence of the peaks' heights on annealing conditions: (12) height of the high-temperature peak, (©) height of the low-temperature peak, ( A ) superconducting transition temperature. The results for one sample annealed under oxygen flux, i.e. with a higher oxygen content, have been added.
In Fig. 4, if(T) curve for a sample showing a particularly high hysteresis of the elastic modulus (E = f f ) is presented. Apart from the modulus defects associated with the two relaxation peaks, some interesting features can be noticed: a softening of the elastic modulus observed during cycling at low temperature (Estat e 1 > Estate 2a,b); a hardening of the modulus after cycling at high temperature (Estat e 2b
4.8-
1
~4.7 -
-'--.
,/~
~_
o
"~.
2b
C W
g4.5 tJ_
4.4 I
I
Ir
I
I
I
100
200
300
400
500
600
Temperature [K]
Fig. 4. Thermal hysteresis of the elastic modulus. Dashed line: minor low-temperature cycle, 300-200-300 K, dotted line: minor high-temperature cycle, 300-480-350 K, plain line: major temperature cycle 300-80-600-300 K.
78
L. Donzel et al. /Physica C 250 (1995) 75-81
< Estat e 3a.b); a rapid increase in the elastic modulus
while heating at high temperature ( > 500 K, i.e. higher than the Pax's temperature). Moreover, one can see that the greater the thermal cycle the larger the softening (hardening). The thermal hysteresis of two samples having different densities is presented in Fig. 5. The relative strength of the hysteresis is greater for the denser material (75% of the theoretical density) compared to the lighter material (40% of the theoretical density).
a)
a
1. b)
4. Discussion and interpretation The PHT peak is the same as the 373 K peak observed by Zeng et al. at a frequency of 1 Hz [15]. The activation energy of the PHT peak (0.9 eV) is close to the diffusion energy of oxygen in the ab plane (0.93 eV, determined by tracer diffusion [19]), which suggests that this peak could be associated with the movement of oxygen atoms in the ab plane. The frequency factor is in the range of the Debye frequency, and the intensity of the relaxation seems to be proportional to the number of additional oxygen atoms. These are the characteristics of a pointdefect relaxation. So the Pax peak may be due to the movement of additional oxygen in the ab plane. The additional oxygen atoms (x > 0) are found inside the BiO layers at interstitial positions between two bismuth atoms [20]. In these layers, the atoms are arranged in so-called BiO chains. The additional oxygen can be found either in intra- or in extra-chain
1 •
o
|
o density Z.6 g/cm 3
I
100
200
300
\N.\\ NKNK ~'-~
400
N
S00
Temperature [K] Fig. 5. Thermal hysteresis of the elastic modulus for two samples of different density.
Fig. 6. Anelastic processes in the BiO layers associated with the diffusion of oxygen. (a) Possible positions, OA and OB, for additional oxygen atoms. (b) Hopping of additional atoms and reorientation of the lattice distortion under compressive stress applied along the a-axis (for an intra-chain and an extra-chain additional oxygen); ( © ) bismuth, ( 0 ) oxygen, ( O ) intra-chain additional oxygen and ( O ) extra-chain additional oxygen.
interstitial positions between two bismuth atoms, in both cases creating a local distortion of the structure (Fig. 6). At equilibrium, the interstitial sites along the a- and b-axis are equivalent. But when a compressive stress is applied along the a-axis for example, the interstitial sites along the b-axis (site O B) are energetically more favorable than the sites along a (site OA), SO the interstitial oxygen should be found preferentially in the O B sites. When under stress an extra-chain atom jumps from site OA to site O B, or when an intra-chain atom leaves the site OA and pushes a "central" atom to the O B site, there is a reorientation of the local distortion (Fig. 6), which is an anelastic relaxation mechanism, and gives rise to an internal-friction peak (Snoek type relaxation) [17]. However, the hopping activation energies for the intra- and extra-chain oxygen can be slightly different. This could explain why the experimental Pax peak is four times broader than a pure simple
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L. Donzel et al. / Physica C 250 (1995) 75-81
Debye peak, and why the modulus defect is too large to be explained by a Debye relaxation. The fact that the motions of the additional oxygen atoms involve the rearrangement of the atoms in the BiO chains may also contribute to the broadening of the peak. The frequency factor of the low-temperature peak is in the range of the Debye frequency. The activation energy (0.29 eV) is very small, suggesting that the peak could not be due to an atomic diffusion process but could be rather interpreted by an electronic-relaxation mechanism. Effectively, hopping of electrons (holes) needs less energy than jumping of ions between two positions (typically 1-2 eV for ions and 0.1-0.5 eV for electronic charges [21]). Moreover Som et al. [22] have observed a dielectric relaxation peak in BSCCO glasses (activation energy 0.35 eV, deduced from Fig. 5 in Ref. [22]). These glasses become superconducting in their glassceramics form. Furthermore, Murawski et al. [23] have observed that the activation energy of the mechanical-loss peak observed in the partially crystallized semiconducting BSCCO glasses (0.3 eV), which is similar to the low-temperature peak observed in superconducting Bi2Sr2CaCu2Os+ x, is the same as that of the activation energy of the DC conductivity. The similarity of the activation energies suggests that the mechanical-loss peak and the DC conductivity might be attributed to the same mechanism. However, the mechanism proposed by Murawski, charge transfer between the crystalline granules, should not be retained, because, as it is not associated with a reorientation of a lattice distortion, it does not explain the mechanical-loss peak. Considering the resuits of Som et al. and Murawski et al., it seems then possible that electronic relaxation takes place in BSCCO superconducting ceramics. Considering also that the variation of the PLT peak's height with the oxygen content is similar to the variation of the superconducting transition temperature Tc (Fig. 3), and that Tc depends upon the number of holes in the CuO 2 layers [24], the origin of the peak could be linked to the holes in the CuO 2 plane. Additional holes in the CuO 2 layers are created when Bi2Sr2CaCu2Os+ x is doped with oxygen (x > 0) by charge transfer from the CuO 2 layers to the BiO layers where the additional oxygens are found. The mechanism leading to the anelastic relaxation could be the hopping of the holes on oxygen ( O - )
C++
Cu++
,O-
O
O1 -b Fig. 7. Anelastic process in the CuO2 layers leading to the PBT peak; hoppingof one hole betweentwo oxygenions and reorientation of the associatedlattice distortion. between two sites. The O - ions are more positive than the 0 2-, so the neighbor Cu 2+ ions will be slightly pushed when there is a hole on the oxygen, which causes a local distortion of the structure (Fig. 7). At equilibrium the hole sites along the a- and b-axes (01 , 0 2 sites of Fig. 7) are equivalent. Applying a compressive stress along a, for example, may favor site O 2 and preferentially induce hopping of holes from site 01 to site O 2. Such a hopping will lead to the reorientation of the lattice distortion, i.e. anelastic relaxation and internal-friction peak. Following this model, the intensity of relaxation (peak height) should be proportional to the oxygen content. However, the experimental data show that this is not the case (Fig. 3). As the number of holes shows a monotonic dependence upon the oxygen doping [25], the explanation of this experimental fact cannot be a diminution of the hole number with overdoping. One possible explanation is that, when a certain concentration of holes is reached, the hopping of one hole is no longer independent of the position of the other holes. Effectively, when a hole is present at the O 1 ( 0 2) site, an internal compressive stress along the a(b-) axis is created (Fig. 7), this changes the energy of the neighboring sites. For example if there is already an 01 hole, it will be less favorable for a neighboring hole to be also in an 01 site along the same CuO line, because there is a compressive internal stress along the a-axis which makes these sites less favorable. At low concentration, as the holes are far apart from each other, this effect does not play any role in the hopping process. On the other hand, at higher concentration, this could prevent the hopping, because hopping under an external stress will be more difficult if the internal stresses act against it.
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So even if there are more holes in the CuO 2 layers, fewer holes will hop and then the intensity of relaxation will decrease with increasing hole concentration. In parallel one observes that the superconducting transition temperature Tc decreases also, showing the relation between the elastic waves and the superconductivity. It is interesting to note that the coordinated motion of two holes (one from site 01 to site 02, the other from site 02 to site 01) gives rise to a resulting elastic distortion which is zero. Then in the superconducting state, the motion of hole pairs would create no elastic distortion of the lattice. A thermal hysteresis of the modulus (not associated with hysteresis in the internal friction) has also been observed in YBCO ceramics. In this case, the hysteresis has been interpreted as due to the effect of the internal stresses induced at the grain boundaries during thermal cycling resulting from the anisotropy of thermal expansion along the a, b and c directions [5]. In Bi2Sr2CaCu208+ x there is also such an anisotropy [26] which may contribute to the observed hysteresis loop. In this sense in the low-density materials, internal stresses are less important and so the relative intensity of the hysteresis is not so pronounced (Fig. 5). However, this explanation cannot deal with the experimental fact that the modulus increased drastically in the temperature region higher than 500 K, so the hysteresis does not result from the anisotropy only. In fact, the main contribution to the change of elastic modulus during thermal cycling may be associated with an "order-disorder" transition in the BiO layers. During heating, the oxygen atoms of the BiO layers can jump from one site to another (peak PHx)" The strong increase in the modulus, after Prrr, observed in Fig. 5, could result from the beginning of the long-range diffusion under the concentration gradient (the experiments are conducted in vacuum). Then oxygen atoms leave their equilibrium positions in the BiO layers and jump to non-equilibrium positions, where they locally stiffen the lattice, giving rise to an increase of the sample rigidity. As there is a concentration gradient, the oxygen atoms do not come back to equilibrium positions when the sample is cooled down to room temperature. It is only during cooling at low temperature ( < room temperature), that there should be a progressive reshuffling of these displaced oxygen atoms, under an "ordering force", because if at
" h i g h " temperature the entropy term can make up for the mismatch in the BiO layers, at low temperature a disordered state is no longer acceptable. The rigidity of the sample will then decrease when thermal cycling at low temperature is performed.
5. Conclusions T h e B i 2 S r 2 C a C u 2 0 8 + x superconducting c e r a m i c s present a characteristic mechanical spectrum composed of two mechanical-loss peaks located at 150 K and 450 K. The two peaks are relaxation peaks associated with the additional oxygen atoms. The high-temperature peak can be explained by the short-range diffusion of the additional oxygen atoms in the BiO layers. The low-temperature peak may be due to the motion of holes, created by oxygen doping, in the CuO 2 layers. A thermal hysteresis of the elastic modulus, which is not accompanied by a hysteresis of the internal friction, has been observed. This behavior may due to order-disorder states of oxygen in the BiO layers and to stresses related to the anisotropy of the thermal expansion in polycrystalline Bi2Sr2CaCu208+ x.
Acknowledgements The authors would like to thank R. Flukiger for providing the Hoechst samples, and G. Triscone for providing the BiE.12Srl.90Cal.o2CUl.9608+x powder.
References [1] G. Cannelli, R. Cantelli, F. Cordero, G.A. Costa, M. Ferretti and G.L. Olcese, Europhys. Lett. 6 (1988) 271. [2] G. Cannelli, R. Cantelli, F. Cordero, M. Ferretti and L. Verdini, Phys. Rev B 42 (1990) 7925. [3] B. Kusz, R. Barczynski, M. Gazda, P. Pastuszak, M. Murawski, O. Gzowski, I. Davoli and S. Stizzaet, Solid State Commun. 75 (1990) 789. [4] Y. Mi, R. Schaller, H. Berger, W. Benoit and S. Sathish, Physica C 172 (1191) 407. [5] Y. Mi, PhD. thesis, Ecole Polytechnique F6d6rale de Lausanne, Switzerland (1994). [6] P.P. Pal-Val, LN. Pal-Val, V.V. Demirskii, V.D. Natsik and V.V. Prytkin, Superconductivity 4 (1991) 1450.
L. Donzel et al. / Physica C 250 (1995) 75-81 [7] L. Sun, Y. Wang, H. Shen and X. Cheng, Phys. Rev. B 38 (1988) 5114. [8] M. WeUer, H. Jaeger, G. Kaiser and K. Schulze, Physica C 162-164 (1989) 935. [9] X.M. Xie, T.G. Chen and Z.L. Wu, Phys. Rev. B 40 (1989) 4549. [10] E. Rodriguez, J. Luzuriaga, M.N. Regueiro and C. Fainstein, Solid State Commun. 77 (1991) 777. [11] R.L. Jacobsen, T.M. Tritt, A.C. Ehrlich and D.J. Gillespie, Phys. Rev. B 47 (1993) 8312. [12] O.M. Nes, K. Fossheim, N. Motohira and K. Kitazawa, Physica C 185-189 (1991) 1391. [13] M. Weller, H. Jaeger, N. Riiffer, G. Kaiser and K. Schulze, in: Proc. ICMC 90 Conf. Garmisch- Partenkirchen (1990). [14] J. Du, Y. Sun, J. Jiang, F. Zeng and H. Yin, Phys. Rev. B 41 (1990) 6679. [15] W.G. Zeng, J.X. Zhang, G.M. Lin and C.L. Du, Solid State Commun. 70 (1989) 333. [16] M. Majewski, Adv. Mater. 6 (1994) 460. [17] A.S. Nowick and B.S. Berry, Anelastic relaxation in crystalline solids (Academic Press, New York, 1972).
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[18] T. Tsukamoto, G. Triscone, J.-Y. Genoud, K.-Q. Wang, E. Janod, A. Junod and J. Muller, J. Alloys Comp. 209 (1994) 225. [19] M. Runde, J.L. Routbort, S.J. Rothman, K.C. Goretta, J.N. Mundy, X. Xu and J.E. Baker, Phys. Rev. B 45 (1992) 7375. [20] A.A. Levin, Y.I. Smolin and Y.F. Shepelev, J. Phys. Condens. Mat. 6 (1994) 3539. [21] A.M. Stoneham and L.W. Smith, J. Phys. Condens. Mat. 3 (1991) 225. [22] K.K. Som, S. Mollah, K. Bose and B.K. Chaudhauri, Phys. Rev. B 47 (1993) 534. [23] L.L. Murawski, R.J. Barczynski, K. Trzebiatowski, D. Samatowisz, B. Koscielska, M. Gazda, B. Kusz and O. Gzowski, J. Alloys Coump. 211&212 (1994) 287. [24] Y. Koike, Y. Iwabuchi, S. Hosoya, N. Kobayashi and T. Fukase, Physica C 159 (1989) 105. [25] T. Schweizer, R. Miiller and L.J. Gauckler, Physica C 225 (1994) 143. [26] R.H. Arendt, M.F. Garbauskas and C.A. Meyer, Physica C 182 (1991) 73.