Lattice dynamics of YBa2Cu3O6 and YBa2Cu3O7, a rigid ion model

PhysicaC 162-164 (1989) 1429-1430 No~h-HoUand

LATTICE DYNAMICS OF YBa2Cu306 AND YBa2Cu307,

A RIGID ION MODEL

Raffaele Guido DEI/2~ VALLE Universita' di Venezia, 30123 VENEZIA, Italy

Dipartimento

di Chimica-Fisica,

Dorsoduro,

Calle Larga S. Marta 2137

Rigid ion models are used to investigate the lattice stability of YBa2Cu30 x. The samiconducting compounds, YBa2Cu306, is found to be stable, while superconducting YBa2Cu307 is destabilized by vibrations involving the copper atoms.

Several lattice dynamics treatments new superconducting calculations Born-Karman approach)

of the

ceramics have appeared.

Most

so far have been based either on force fields

("springs and masses"

or on ionic models

in various forms.

y3+, Ba2+ and 02- . The distances around the coppers suggest a partially covalent character for the Cu-O bonds. However,

for simplicity,

a

purely ionic model has been adopted for the coppers as well. Discrete Cu charges Cu + and

The validity of Born-Karman models is difficult

Cu 2+, fixed at Cu I and Cu 2 sites respectively,

to assess at the moment,

are certainly present 1,2 in YBCO 6. These charges

unambiguos

experimental

due to the scarcity of data on phonon energies

and symmetry properties.

Simple ionic models,

where a precise meaning may be assigned to each term of the potential,

appear to be preferable

in the present situation. mation,

The simplest approxi-

namely the rigid ion model, has been

are consistent with the stoichiometry,

with the

non metallic behaviour of YBCO 6, and with the oxygen coordination

and distances around the Cu

ions. On the contrary the Cu charges

in YBCO 7 .

probably have an itinerant character 1,2. The stoichiometry

requires an average Cu charge

adopted in this paper for YBa2Cu30 x (YBCO x for

equal to 2.3333 if the charge is completely

short). The analytical

delocalized,

form of the potential

model and the values of its parameters

have been

while Cu 3+ and Cu 2+ ions fixed on

Cu I and Cu 2 sites respectively

are expected in

chosen mainly through a careful analysis of the

the localized charge limit. The Cu-O distances

crystallographic

suggest that an intermediate

structure of YBCO 7 and YBCO 6.

General consensus has now been reached I on

the delocalized

case, quite near to

limit, probably holds for YBCO 7.

the structure of YBCO 6 and YBCO 7. YBCO 6 forms

Two potential models have been developed.

tetragonal crystals,

computational

space group P4/rmmn-D4h I.

Each unit cell contains two coppers,

labelled

Cu 2, in square pyramidal coordination,

and one

copper, Cul, in linear O-Cu-O coordination.

The

convenience

For

an effective pairwise

additive central potential has been adopted: Vij = qiqjrij -I + exp[(Ai+Aj)-(Bi+Bj)rij ]. The first term is the electrostatic

interaction

structure of YBCO 7 may be obtained from that of

between two ions i and j with charges qi and qj,

YBCO 6 by inserting an extra oxygen along the b

while the other term, a Born-Mayer core overlap

axis between two Cu I. Consequently becomes orthorombic,

the crystal

space group Pn.~t-D2hl , and

Cu I aquires square planar coordination. oxygen-metal

distances

The

around the Y and Ba atoms

repulsion,

prevents the oxygens from falling

onto the cations. potential

The form chosen for the

is compatible with the observed addl-

tlvity of the ionic radii in YBCO x. The nominal

are consistent with a purely ionic environment

ionic charges have been assigned to y3+, B2+ and

where all the atoms have their nominal charge

O 2-, and the sites Cu I and Cu 2 in YBCO 6 are

092 I--4534/89/$03.50 © Elsevier Science Publishers B.V. (North-Holland)

R.G. Della Valle / Lattice dynamics of YBa2Cus06 and YBa2Cus07

1430

occupied by Cu + and Cu 2+ ions respectively.

Two

l~niting cases have been considered for the Cu charges in YBCO7: model fractional

(i) with the average

charge 2.3333, model

(2) with the

discrete charges +3 and +2 on sites Cu I and Cu 2. The potential parameters empirically

Table i. Potential parameters, as determined by minimizing the potential derivatives with respect to cell axis and atomic coordinates. Potential in Kcal/Mol, distances in ~. Atomic species

have been determined

Y Ba Cu O

(table I) by fitting the structure

predicted by the models to the experimental

Model A 4.067 7.383 9.101 11.515

Model (2)

(i) B

A

1.255 1.943 5.966 3.969

3.466 6.775 8.920 11.753

B

1.524 2.188 5.906 3.861

structure of YBCO 6 and YBCO 7. In order to check the stability of the models and the reliability of the potential parameters, then been reversed,

the procedure has

and the equilibrium

structure has been determined

Table 2. Calculated and experimental cell axis (~), symmetry independent atomic z coordinates.

for each parameter

YBa2Cu307

set (table 2). Both models are in fairly satisfactory

agreement with experiment,

The phonon frequencies the equilibrium ximation,

structure

for k=O, computed at in the harmonic appro-

are given in table 3. As expected,

delocalization

the

of the Cu charges for YBCO 7

yields a "softer" potential generally

(i)

(model i), with

reduced frequencies.

The phonon frequencies

conducting compound,

YBCO6,

positive with both models:

for the semi-

are real and the lattice is stable

against small atomic displacements. on the contrary, frequencies

both models predict

For YBCO7, imaginary

for two modes involving motion of Cu

atoms. The observed structure

is thus at the

local maximum of a syrmnetric double well, rather than at a potential minimum.

The resulting

instability may greatly enhance the lattice distortion

that accompanies

under appropriate electron-phonon temperature Eliashberg

3.953 3.812 3.821 3.823 3.976 3.885 11.207 11.144 11.676 .1831 .2041 .1841

Cu 2 O1 02

.3283 .1656 .3676

.3384 .1631 .3718

.3549 .1581 .3779

03

.3683

.3732

.3777

(i) 3.831

YBa2Cu306 (2) Exp 3.887

3.863

12.347 11.277 11.830 .2054 .2093 .1934 .3578 .3390 .3604 .1478 .1652 .1533 .3801 .3740 .3793

Table 3. Phonon frequencies (cm -I) and symmetry correlation for potential models (1) and (2). YBa2Cu306 Sym (i) (2) Alg 1035 1186 A1g

985 1102

Alg Blg Alg

607 201 251

Eg Eg Eg Eg Eg

821 237 321

1172 1448 648 502 491 454 244 96

272 57

an electron and,

circumstances 3, the increased

interaction might lead to high

superconductivity

EXP

The results for

the two models are otherwise qualitatively similar.

a b c Ba

(2)

through a modified

strong coupling mechanism 3.

REFERENCES i. Y. Syono et al., Physica 148B (1987) 218. 2. E.E. Alp et al., Physica 150B (1988) 74. 3. J.R. Hardy and J.W. Flocken, Left., 60 (1988) 2191

Phys. Rev.

A2u ~129 1204 A2u 1056 1022 B2u 488 383 A2u 381 381 A2u 311 331 A2u 144 288 A2u 0 0 E u 1193 1473 Eu 653 515 Eu 540 482 Eu 325 294 Eu 181 198 Eu 93 93 Eu 0 0

Sym

(i)

Ag Ag Ag Ag Ag B2g B2g B2g B2g B2g BIu BIu BIu Blu Blu B1u Blu Blu B2u B2u B2u B2u B2u B2u B2u B2u

1254 1068 695 387 252 1047 838 327 149 -330 1348 1128 1067 581 480 362 316 0 1235 1089 657 474 289 217 0 120

YBa2Cu307 (2) Sym 1414 1185 818 329 245 1436 621 498 290 74 1631 1227 1017 396 389 329 276 0 1529 1440 374 348 217 168 0 -190

(i) (2)

B3g_ B3a B3g B3a B3a

1088 1417 1031 1053 383 303 205 195 111 129

B3u B3u B3u B3u B3u B3u 83u B3u

1072 1460 866 648 536 602 406 339 307 313 198 212 0 0 -328 -310