Oxygen Diffusion in YBa₂Cu₃O_x

Karsten J. Foos, Germany

http://www.fkp.physik.tu-darmstadt.de/Winf pages_e/ybco_e.htm

0. Abstract

YBa₂Cu₃O_x (YBCO) is an oxydic ceramic, that for instance is of technical interest because of its superconducting properties. It is of tetragonal or orthorhombic structure (fig. 1) depending on its oxygen content (usually x between 6 and 7) and temperature [1]. These two structures correspond to different oxygen configurations. The phase transitions between the structures are order-disorder processes due to diffusion jumps of the oxygen atoms in Cu-O planes. This diffusion jumps can be induced by mechanical spectroscopy. Thereby the change of the oxygen dynamics near the phase transitions can be measured.

The tetragonal-to-orthorhombic phase transition is interesting due to several reasons. It is ferroelastic, i.e. small stresses can cause huge strains (comparable to ferromagnetism or ferroelectricity). Therefore YBCO can be used as a model system for ferroelastic phase transitions. In addition one can use the ferroelastic behaviour to prevent twinning during crystal growth or to countermand it subsequently.

1. Cristal Structure

ab

Figure 1: Unit cell of YBCO in tetragonal (a) and orthorhombic (b) phase. The sites of the oxygen atomes in the Cu(1) plane drawn darkgray are occupied with a probability below 1, the sites of the oxygen atomes draw white are occupied with a probability equal 1. The O(5) sites are not represented because they are approximatly not occupied.

YBCO exists in a tetragonal (fig. 1a) and at least two orthorhombic phases (fig. 1b, 2) depending on x (6 < x < 7) and the temperature [1-7]. The phases differ in number and order of O atoms on interstitial sites in the Cu(1) plane. The several orthorhombic phases differ from each other in oxygen configuration superstructures.

The oxygen atoms in the Cu(1) plane occupy two types of interstitial sites (O(1) and O(5)), depending on whether the neighbouring Cu atoms are in a- or b-axis direction. Only a fraction of this sites are populated. The maximum average probability is 0.5 for the case of x = 7. In the tetragonal phase the occupation probabilities of the O sites are equal, whereas the probabilities of the O(1) and O(5) sites in the orthorhombic case differ. The orthorhombic strain is proportional to the difference of these propabilities. The orthorhombic phases differ in the long range order of the O atoms [8, 9]. The transition between the orthorhombic and the tetragonal phase is at least abouve 600K of second order [10].

Figure 2: Phase diagram calculated theoreticaly [8, 9]. T labels the tetragonal phase, OI, OII etc. label the orthorhombic phases. The diagram is calculated by Monte Carlo simulations of an asymmetric next-nearest-neighbour-Ising model. The projection of the 3D crystal lattice to a 2D Ising model is possible because the phase transition takes place in the Cu(1) plane. The influence of the O interaction perpendicular to this plane can be neglected.

A consequence of the large number of O vacancies is that O diffuses in YBCO nearly exclusively via jumps between sites in the Cu(1) planes [11].

2. Ferroelasticity and (Critical) Slowing-down

Ferroelasticity means that already tiny mechanical stresses cause huge strains. This effect can be compared with ferroelectricity or ferromagnetism. Like in the case of these effects the interaction, that causes the order (the orthorhombic structure) below a critical temperature, can be described by a mean-field ansatz as a first aproximation. The result is a Curie-Weiss law [12, 13, 14].

(Critical) slowing-down is a collective effect of all jumping O atoms ("critical" is written in brackets because this phase transition effect already appears in a wide range around the transition). It is not a slowing-down of the specific jumps of the O atoms. It is an increase of the time that is needed to change the ratio of the populations of the O(1) and O(5) sites respectively - although such a change is generated by specific jumps. The reason is an increase of the correlation time of the fluctuations of this ratio, that is the order parameter of the present transition [13]. Thus an occupation probability deviating from the equilibrium value approaches this value the slower the closer the system is to the phase transition. This leads to a diverging anelastic relaxation time.

3. Anelasticity Experiments onto YBCO

YBCO in anelasticity and internal friction experiments exhibits a wide range of effects (survey is given in [15]).

In the internal friction spectra many peaks can be found due to different typs of relaxation (most of them O jumps in the Cu(1) plane). E. g. one can find peaks associated with low activation energies (about 0.1eV) at samples with low oxygen content. Here the O atomes are solitary in the Cu(1) plane and do not interact. Additionaly one can find peaks associated with higher energies (1eV) at oxygen rich samples. At high O content the O atomes form chains and are bounded stronger. For a jump the binding energy of the chains additionaly must be brought up, leading to higher activation energy. In addition the electric charge of the O atoms makes the neighbour vacancy energeticaly unfavorable. At first this peaks have nothing to do with the phase transitions described above.

Further peaks of the internal friction and anomalies of the young's modulus are due to different phase transitions. The best supported transition in this connection is the tetragonal-to-orthorhombic phase transition. Since this structural phase transition requires O jumps, it can be observed in the anelastic relaxation. Here the internal friction exhibits a maximum and the young's modulus exhibits a minimum [16]. Quasi-static experiments support an increase of the relaxation strength (ferroelasticity) [17, 18] and relaxation time (critical slowing-down) [19] in the range of the phase transition.

4. Present Experiments

Nearly all anelasticity experiments executed before were performed in vacuum. The great disadvantage of this technique is the oxygen loss of the sample at temperatures above 600K due to outgasing. So it was not possible to execute the measurements at constant oxygen concentration or to reproduce it properly. In order to avoid this problem our group presently performs internal friction measurements (vibrating-reed technique) in an oxygen chamber under well defined controlable pressure (between 10^-4 und 10²mbar).

We measured spectra at frequencies between 100 and 1700Hz at temperatures between 400 and 1000K at constant pressure or constant concentration x. Our aim is to reproduce these measurements performed under exactly determined conditions in model calculations including ferroelasticity and slowing-down.

5. Literature