Journal of the Chinese Chemical Society, 2006, 53, 1109-1111
1109
The Plausible Motion’s Confinement of Electrons by the Structure in
YBa2Cu3O7-x
Yng-Long Lee (
)
Mekkem Industrial, Inc., No. 80, Lane 524, Ho-Mu Road, Shen Gang County, Taichung, Taiwan, R.O.C.
A hypothesis is proposed that tryies to correlate the observed structure transitions of YBa2Cu3O7-x for
x from 0 to 1 with measured super-conductivity and electric properties.
Keywords: YBa2Cu3O7-x; Superconductivity; Cooper pair; Color centers.
INTRODUCTION
In 1911, Heike Kamerlingh Onnes discovered the
phenomenon of superconductivity in mercury as he measured the resistivities of metals around the temperature of
liquid helium. In 1933, Walter Meissner and R. Ochsenfeld
discovered that all the magnetic flux was expelled out from
the superconductor as the superconductor was cooled
through its critical temperature in a magnetic field. The
mechanism of the superconductivity was not evident until
the isotope effect was observed by C. A. Reynolds et al. and
E. Maxwell, respectively. The isotope effect showed that
the superconducting state was aroused from the interaction
of electrons with lattice vibration rather than from electrostatic interaction between electrons. The earlier history
about the superconductivity has already been reviewed and
discussed in many books and papers.1,2 For two electrons of
opposite spins, Cooper proposed a formula which indicated
the pairing of two electrons due to that the phonon mediation had lower energy.3 The binding energy was a very sensitive function of the total momentum K of the electron
pair, being a maximum where K = 0.3 The proposed formula showed
having opposite waver
rthat two
r electrons
r r
vectors, k1 = -k 2 or K = k1 + k 2 = 0, was a critical condition
for the Cooper pair.
In 1986, Bednorz and Müller prepared a sintered multiphase mixture with nominal composition: La5-xBaxCu5O5(3-y)
exhibiting possible superconductivity at 35K.4 In the following year, Wu et al. reported superconductivity being observed above 90K in a multiphase sample with nominal
composition Y1.2Ba0.8CuO4-x prepared through solid state
reaction of appropriate amounts of Y2O3, BaCO 3, and
* Corresponding author. E-mail: [email protected]
CuO.5 Soon after this discovery, the single-phase compound responsible for the high TC superconductivity as
YBa2Cu3O7-x was identified by several groups.6-8 From the
x-ray powder diffraction data, Cava et al.6 determined an
orthorhombic structure that could be described as an oxygen deficient perovskite with tripling of the c-axis caused
by the ordering of the Ba and Y atoms. The neutron diffraction experiments confirmed the space group Pmmm and the
main structure features of YBa2Cu3Ox for 6.8 £ x £ 7.0.9-12
The structure of YBa2Cu3O7 and the assignments of the atoms are schematically shown in Fig. 1(a). The most impressive characteristic feature for the YBa2Cu3O7 structure
was the complete vacancy of the O(5) positions.
All investigations revealed that no phase transitions
take place in going from room temperature down to 5K.10-12
But it was observed that the total oxygen stoichiometry decreased smoothly with increasing sintering temperature.13
The oxygen atoms removed from the structure were exclusively those located at the O(4) sites at (0, 1/2, 0). The in
situ neutron powder diffraction measurements13 showed
that the assigned positions of O(5) at (1/2, 0, 0) were gradually filled with oxygen atoms as the temperature increased, and when the occupancies of the two sites became equal, the symmetry of the structures changed from
orthorhombic to tetragonal as shown in Fig. 1(b). The oxygen stoichiometry at the transition was always at x = 0.5 for
YBa2Cu3O7-x, so that the orthorhombic phase existed between 0 £ x and x £ 0.5. Over the transition, continuing
heating at higher temperatures resulted in further loss of the
oxygen atoms from the sites of O(4) and O(5) until the
stoichiometry reached YBa2Cu3O6 as shown in Fig. 1(c).
The investigations of superconductivity as a func-
1110
J. Chin. Chem. Soc., Vol. 53, No. 5, 2006
tion of the oxygen content showed that in the orthorhombic phase, the values of TC decreased as the total oxygen
stoichiometry decreased, and it became zero as the crystallographic transition was approached. 14 Superconductivity has been found in the tetragonal phase for any
stoichiometry, and the electric property in this phase was
semi-conducting.15
DISCUSSION
In this paper the author proposes a hypothesis that
tryies to correlate the observed structure transitions of
YBa2Cu3O7-x for x from 0 to 1 with the measured superconductivity and electric property accompanying the structure transitions.
For YBa2Cu3O7, the space group was assigned to
Pmmm. This assignment indicates the positions of O(4) and
O(5) are not equivalent. The coordinate number for Cu(1)
in YBa2Cu3O7 is 4, not 6 as in the parent perovskite struc-
Lee
ture. Generally the Cu(1) atom is viewed to coordinate with
two neighboring O(4) oxygen atoms and two O(1) oxygen
atoms and is surrounded by a nearly square or distorted
square planar configuration with the plane parallel to the
b-c plane. All these nearly square or distorted square planar
units are connected into a chain structure through the sharing of the O(4) oxygen atoms along the b-axis. The Cu(2)
atom coordinates with O(2) and O(3) oxygen atoms as a
square pyramidal base and coordinates with the O(1) oxygen atom as the apex of the pyramid. A very impressive
characteristic feature for the structure of YBa2Cu3O7 is the
long one-dimensional channel surrounded by two one-dimensional long chain fencelike walls. These walls are built
by the nearly square or distorted square planar CuO4 units
which are capped by the pyramidal CuO5 units on the top
and bottom sides of the CuO4 units along the channel as
shown in Fig. 1(a). Along the channel there are two barium
atoms located near the caps on both sides in each unit cage.
The two barium atoms in each cage create a periodic variation or sine wave form potential environment along the
Fig. 1. The comparison of the structures of (a) YBa2Cu3O7, (b) YBa2Cu3O6.5, (c) YBa2Cu3O6.1
The Motion’s Confinement of Electrons in YBa2Cu3O7-x
channel. As the O(4) oxygen atoms are gradually removed
and parts of the vacancies of O(5) are gradually filled, the
stoichiometry will reach YBa2Cu3O6.5 with the structure
being transited into the tetragonal phase. Then the corresponding positions of O(4) at (0, 1/2, 0) and O(5) at (1/2, 0,
0) become symmetry equivalent and equally occupied or
unoccupied.13 The configuration of Cu(1) in YBa2Cu3O6.5
can be viewed as a octahedron consisting of partially occupied O(4) and O(5) oxygen atoms and two fully occupied
O(1) oxygen atoms. In this situation all previously described channels are blocked and the channel structure is
destroyed.
It is well known that electrons can be trapped in the
negative ion vacancies which are originally the locations of
anions in ionic crystal.16 The most famous example is the
color centers or electron centers in sodium vapor doped
rock salt. As compared with the parent perovskite structure,
all periodic vacant O(5) positions along the channels in
YBa2Cu3O7 can be viewed as the trapping sites for electrons. In other words, the channels can be viewed as the
passing routes for electrons. Then if electrons are forced to
move in these channels, these
can only have one
r electrons
r
of the two wave
k or
r vectors,
r
r -rk. This
r fulfills the critical
condition as k1 = -k 2 or K = k1 + k 2 = 0 of the
r Cooper
r
theory.
That
means
the
critical
condition
of
k
k
=
1
2 or
r r r
K = k1 + k 2 = 0 for the Cooper pair is natural in YBa2Cu3O7.
Another impressive characteristic feature in YBa2Cu3O7
is the anomalously large thermal parameters for O(4) oxygen atoms.12 In this paper the author proposes that the anomalously large thermal parameters reflect the possibility
of strong vibration or phonon effect on the electrons which
are moving in the channels. This strong phonon effect
causes the pairing of electrons which are moving in the
channels.
Except for this anomalously large thermal vibration
effect, maybe in YBa2Cu3O7 there is another mechanism to
J. Chin. Chem. Soc., Vol. 53, No. 5, 2006
1111
enlarge the energy gap between the superconducting state
and the normal state. In 1930, Philip M. Morse showed that
the periodic variation of potential inside the crystal created
bands of forbidden energies inside the crystal.17 If the electron pair moved in these periodic changed potential channels, the energy gap between the superconducting state
and the normal state due to the interaction between two
electrons of opposite wave vectors mediated by phonons
could be enhanced. Then the electron pair could condense
in even lower energy levels. This may result in a higher TC
or higher temperature to destroy the electron pair.
Received January 16, 2006.
REFERENCES
1. Kresin, V. Z.; Wolf, S. A. Fundamentals of Superconductivity; Plenum Press: New York, 1992.
2. Bardeen, J. Phys. Rev. 1950, 80, 567.
3. Cooper, L. N. Phys. Rev. 1956, 104, 1189.
4. Bednorz, J. G.; Müller, K. A. Z. Phys. 1986, B64, 189.
5. Wu, M. K.; et al. Phys. Rev. Lett. 1987, 58, 908.
6. Cava, R. J.; et al. Phys. Rev. Lett. 1987, 58, 1676.
7. Grant, P. M.; et al. Phys. Rev. 1987, B35, 7242.
8. Hinks, D. G.; et al. Appl. Phys. Lett. 1987, 50, 1688.
9. Beno, M. A.; et al. Appl. Phys. Lett. 1987, 51, 57.
10. Greedan, J. E.; et al. Phys. Rev. 1987, B35, 8770.
11. Beech, F.; et al. Phys. Rev. 1987, B35, 8778.
12. David, W. I. F.; et al. Nature 1987, 327, 310.
13. Jorgensen, J. D.; et al. Phys. Rev. 1987, B36, 3608.
14. Cava, R. J.; et al. Phys. Rev. 1987, B36, 5719.
15. Jorgensen, J. D.; et al. Phys. Rev. 1987, B36, 5731.
16. Kittel, C. Introduction to Solid State Physics; 5th Edition;
John Wiley & Sons: New York, 1976; p 546.
17. Morse, P. M. Phys. Rev. 1930, 35, 1310.