Oxygen vibrations in the series Bi2Sr2Can-1CunO4+2n+y

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Oxygen vibrations in the series Bi2Sr2Can-1CunO4+2n+y

Eric Faulques, P. Dupouy, S. Lefrant

To cite this version:

Eric Faulques, P. Dupouy, S. Lefrant. Oxygen vibrations in the series Bi2Sr2Can-1CunO4+2n+y.

Journal de Physique I, EDP Sciences, 1991, 1 (6), pp.901-916. �10.1051/jp1:1991175�. �jpa-00246376�

J. Phys. I1

(1991)

901-916 JUIN 1991, PAGE 901

Classification

Physics

Abstracts

74.70 78.30 61.50E

Oxygen vibrations in the series Bi~sr~ca~_iCu~O~~~~~~

E.

Faulques,

P.

Dupouy

and S. Lefrant

Laboratoire de

Physique Cristalline,

Institut des Matbriaux de Nantes

(*),2

_rue de la

Houssinidre,

F-44072 Nantes Cedex

03,

France

(Received

30 May 1990, revbed 28November 1990, accepted 21February 1991)

Rksumk. Nous

prbsentons

_une discussion _sur les vibrations des atomes

d'oxygdne

dans la sbrie des supraconducteurs

Bi~sr~ca~_jCu~04+2n+y

dans le but

d'interprbter

les spectres ^Raman.

L'analyse des modes norrnaux de vibration de la structure Amaa pour les phases _n

=

I _ou 3

montre que les atomes

d'oxygdne

du plan

Cu02

contenant les centres d'inversion donnent lieu I

une activitb Raman. En

consbquence,

nous proposons une nouvelle attribution _pour les raies de faible intensitb I 297, 316 et 333 cm-I. _{Nous montrons que} le dbdoublement de la bande I 460 cm-I pourrait dire dil I la structure Amaa. Les spectres

enregistrbs

_en

polarisation

croisbe

montrent de faibles bandes

qui

peuvent ^{dire attribubes} aux modes Bj~ ^attendus pour les trois

phases.

Abstract. We present a discussion of the oxygen vibrations in the B12Sr2Ca~ jCu~O~

~~~~~

high

l~ superconductors

with the aim of

interpreting

Raman spectra ^{in the} case of the

non-symmorphic

Amaa structure. Group

theory

shows that the _oxygen atoms

belonging

to the central Cu02

Plane

generate a Raman

activity

for the _n

= 1, ³ phases.

Consequently,

_we propose a novel

assignment

for the lines of weak

intensity

at 297, 316 and 333 cm-I. It is shown that the two components ^of the 460 cm-~ band may be consistent with the Amaa structure.

Spectra

recorded in crossed

polarization

exhibit weak lines which could be

assigned

to Bj~ ^modes

expected

for the three

phases.

1. InUoducfion.

The

crystalline

structures of the bismuth cuprate

superconductors

have been the

subject

of extensive

experimental

work

[1-7].

It has been shown that the unit cells of these materials _are

likely pseudotetragonal

with values of the parameter « a

slightly

different from those of the

parameter

b. The Bi

superconductors

_are characterized

by

the

stacking

_sequences BiO-SrO-

CuO~-SrO-BiO in =1, 2201-phase), BiO-SrO-CUO~-Ca-CUO~-SrO-BiO (n =2,

^2212-

phase), BiO-SrO-CUO~-Ca-CUO~-Ca-Cu02-SrO-BiO in

=

3, 2223-phase).

The BiO

layers

can be described either with _a

Nacl-type

structure

(Sunshine

et al.

[5])

or with _a defective

CUO~-type

structure in which _case half of the oxygen sites in the centers of the Bi squares are

occupied (von Schnering

et al.

[6]).

The

Nacl-type

material

belongs

either to

14/mmm

_or

(*)

UMR l10 CNRS, Universitb de Nantes.

Fmmrn

symmorphic

space groups whereas the defective

CUO~-type

material has the _non-

symmorphic

_{space group} Arnaa. An intermediate

type

^{of BiO}

plane

derived from the Arnaa structure was described

by

Bordet et al.

[7].

^In that structure, the oxygen ^atoms are

moving

off the center of the Bi square and lead to the A2aa arrangement. ^In the first two structures, the oxygen atoms are in the

planes

of the

Bi~O~

sheets for the Nacl-like

compound

whereas

they

_are

slightly

out of this

plane

in the defect

CUO~-like

structure. Furthermore in the Fmmrn structure, the copper and oxygen atoms of the

CUO~

sheets _are not

coplanar.

In this

work _we will _assume that _we have

planar CUO~

and BiO

layers.

It should be added that the

n=I structure is _more controversial. Gao eta?.

[8]

^{have found that Bi-rich}

Bi~(Sro_~~cao_~~Bio,j~)~CUO~

^is

slightly

monoclinic with space group

A2la.

On the other

hand,

the refinement of Onoda and Sato

[9]

attests _a

pronounced

^monoclinic C2 structure

(y

=

I13°55

)

^for

pristine

2201

samples.

A

slight

monoclinic _structure

[10]

^for the

Pb-doped

2223

compound (y

=

90°51 _was also

reported

which contradicts the _recent data of

Sequeira

et al.

[I Ii. However,

most of the Raman work

produced

_so far _on

Bi-cuprates

series has taken the

tetragonal

and orthorhombic structures into account and excluded the monoclinic cells.

Here _we present a vibrational

analysis

of _oxygen motions in these structures. This

study

is

supported by

_{a group}

theory analysis

at the _zone center and

by

lattice calculations from other groups. Our purpose is to show that _a

comparison

of the

phonon

symmetry and atomic

displacements

between

symrnorphic

and

non-symmorphic

structures may be used to

assign

Raman bands and

distinguish

the _n

=

I,

_n

= 2 and _n

=

3

specific features,

_even in the _«

high- frequency

_{» range,}

corresponding

to oxygen motions. A discussion of

low-frequency

_spectra

and cation motions will _not be considered here. Several papers on this

topic

_are available

[12- l4].

Section two of the _paper describes the factor _group

analysis

of normal mode vibrations for each structure

in =1,

2 _or

3).

Section three deals with _some

experimental polarized.

Roman spectra ^taken on

microcrystals

in bulk ceramics in the range

corresponding

to the oxygen motions

(200-700 cm~~).

An

interpretation

of _our results

concerning

all the

vibrational features

occurring

in this

spectral region

is

proposed

in the last section.

2. Normal mode

analysis.

A very careful vibrational

analysis

of

Bi-cuprates

_was

given

earlier

by

Cardona _et al.

[12]

_; this section

completes

it for the _n

=

3 _case and adds _some remarks about the

non-syrnmorphic

structures.

Consider for the

general

case an orthorhombic unit cell constructed with the lattice _vectors a,

b,

_c where _a and b _are the sides of the

rectangle

drawn

by joining

the strontium atoms

separated by

_{an oxygen} atom and let

c/2

be the distance between two Ca

layers in

=

2)

_or two

CUO~ layers in

=

I and

3).

If _we examine the _case of the

symrnorphic

_{space groups} Fmmrn and

14/mrnm

when

a#b (Fmmm),

_we find that the

primitive

translations vectors are

a'=a/2+b/2,

b'

=

a/2

₊

b/2

and c'

=

a/2

₊

c/2

which generate a triclinic

primitive

^{cell with} diamond-like basal

planes (Fig. la).

If _a

=

b,

I-e- for the

tetragonal crystal fimrn),

^the

^primitive

^{cell is}

monoclinic,

the distances a' and c' _are

equal respectively

to

( ^a~

+

b~)/2

and

(fi)/2.

The cells contain

II,

15 and 19 _atoms

respectively.

The volume of these cells is

given by la'x b').

c'

=

abc/4

or

a~c/4 _la

_quarter

_of

_{the unit cell}

_volume).

However,

the

primitive

cells of the

non-symmorphic crystals (Amaa)

which _are constructed with the

primitive

translations _a, b and c' _are monoclinic

(Fig. lb).

In this _case, the volumes of the

respective primitive

^cells are twice those of the

symmorphic crystals

_{as a} consequence of the

particular

oxygen arrangement ⁱⁿ the BiO

planes.

We have indeed

la

_x b

).

c'

= 2

la'

_x

b').

c'

=

abc/2

which is

hay

the unit cell volume. Thus for _n

=

1,

2 and

3,

the number of _atoms per

primitive

cell is

22,

30 and 38

respectively.

N 6 OXYGEN VIBRATIONS IN THE SERIES B12Sr2Ca~_

jCu~04+2n+v

⁹⁰³

a

o

@

°

Bi ~ ~

o

Cu'

2201 2201

b ~

~

n

°

c/2

@

o

o

_-

o ~- w

m

o

o

@

o

o .

-

9

-

2223

a~ b)

Fig.

I. Primitive cells

(heavy lines)

of the _n

= 1, 2 and 3

Bi-cuprates superconductors

for

a)

the 14/mmm (a ₌ b

)

and Fmmm

(a

_{# b}

)

_{space groups ;} b) the Amaa space group. The bold atoms belong

to the cells, the _atoms labeled

prime

_are those located in the central

plane containing

the inversion center.

Table I. Site symmetry

of

the

Bi, Sr, Ca,

Cu and O _atoms.

Bi

O(4,5)

Sr

O(3)

Cu

O(I,

Cu' Ca Ca'

~4v ~4v ~4v

C4v C4v

~2v

_1~4h

D2h

C4v 1~4h

C2v C2v

~2v

C2v C2v

C2

1~2h

C2h

C2v

D2h

C~

C2 Cs

C~ C~

C2

C2h

C2

C~

C2h

One finds that

depending

_on the space group, the atoms _are distributed _{on seven} distinct sites of symmetry C~,

C~, C~~, C~~, C~~, D~~

and

D~~ (Tab. I).

In

particular,

in the

orthorhombic Amaa

cell,

the

positions

of the 2 oxygen ^atoms of the

Bi~O~ (4

^and

5)

and the

CUO~

sheets

(I

and

2)

are not

equivalent.

Thus for _n

= 1, ^{2 and}

3,

there _are

8,

12 and 16 oxygen ^atoms which remain invariant with the

C~~ operation.

The other invariant atoms are

located _on the

C~~

axis and _on the inversion center

(2

atoms, ^Ca or

Cu)

and in the

~yz)

mirror

plane (14,

18 and 22

atoms).

The

glide plane (xz) exchanges

the oxygen

positions

I with 2 and 4 with 5. The

glide plane (xy)

and the

C~

~

axis do not contain _{any atom.}

Thus,

no atom remains invariant under these symmetry ^elements.

Hence,

_{one can} write the normal mode

representations of

the _{oxygen atoms} in each

primitive

cell _as

follows,

where

rj

and

r~

refer to Fmmrn and Amaa group

analyses respectively

_:

N =

ri =2A~+28~~+28~~+A~+3Bj~+48~~+48~~

r~ =4A~+3Bi~+58~~+68~~+3A~+4Bi~+68~~+58~~

n = 2

rj =3A~+Bj~+48~~+48~~+A~+3Bi~+48~~+48~~

r~ =5A~+4Bi~+78~~+88~~+4A~+5Bj~+88~~+78~~

n =

3

ri =3A~+Bi~+48~~+48~~+2A~+4Bi~+68~~+68~~

r~ =6A~+5Bi~+98~~+ ioB~~+5A~+6Bi~+ioB~~+98~~

The

decomposition

for the space group

14/mmm

is obtained

by considering

the

compatibility

relations with Fmmm _:

A~

_~ ^A_{j ~,}

Bj

~ ~

A~

~,

A~

_~

B~

~, B~

~ +

B~

~ ^~

E~, ^B~

~ +

B~

~ ~

E~.

In the group

analysis

of these structures, we see that

B~~ (for D~~)

and

A~ (for

D~ ~

vibrational modes _are silent in the IR. In

addition, doubling

the volume of the

primitive

cell in Amaa induces many more Raman modes

(but

not necessary twice _as

many)

than in the other

symmorphic

structures. For

example,

when _n

=

3 there _are 30 oxygen modes for Arnaa and 12

for14/mmm

and Fmmm.

An

interesting

result of this

analysis

_concerns the Raman

activity

of the central

CUO~ plane

for _n

= I and 3. This

plane yields

_no Raman modes in

symmorphic crystals

because the Cu' and O' atoms have

respectively D~~

and

C~~

^site symmetry ^{for Fmmrn. For}

14/mmm they

have

D~~

^and

D~~

^site symmetry

[15].

However the O' atoms have C~ ^site symmetry ^and are no

longer

at inversion centers in the Arnaa arrangement ^{while the}

Cu' atoms have

C~~

^site symmetry. ^{This results is the} occurence for _n

= I and 3 of _an

additional Raman

activity represented by A~+Bi~+ 28~~+28~~.

Thus the central

CUO~ plane

is Raman active in the _case of

non-symmorphic

structures. One of these modes is

A~

^{and should be detected in Raman} spectra. The Raman

activity

of the central

plane

can be

represented by

the

symmetrized displacements

of the

O'(1, 2)

atoms drawn in

figure

2. The

N 6 OXYGEN VIBRATIONS IN THE SERIES

Bi~sr~ca~_jCu~04+2n+y

905

t-t- j/

~ IIl -~i~

Big Ag

~/fit

-o

d p

~ /~f

+-o

p ^d

B2g B2g

~ j~/

$/~ Ill

~~g ~~g

O'l,2

>iiiiaa

~y

£ '

Fig.

2.

Symmetrized displacements

of the _oxygen atoms of the central CUO~

plane

in the unit cell for

the Amaa structure. Note that _two consecutive central

planes

are

represented.

A~

^{mode is} an

antisymrnetric

vibration which is

analog

to _a modulated

breathing

_» of the

oxygen ^atoms within the

CUO~ planes,

the

O'(I)

and

O'(2)

atoms _move in the _same

direction. The

Bj~

^{mode is} an

analogous

motion but the

O'(I)

and

O'(2)

atoms move in

opposite

directions.

3.

Experimental

results.

We have

prepared

the Bi-materials in _our

laboratory employing

the well-known solid _state reaction

procedure

^of

sintering

^{the mixed} oxides at 860°C. The

synthesis

of the

high

T~

(2223) superconductor

_was achieved

by

_a 15 ifi lead

doping

of the mix _so that the nominal

composition

of this

sample

_was

Bij,~Pbo_~Sr~Ca~CU~O~.

^The

annealing

_{process was very} short for _n =1

(3h),

but much

longer

for _n =3

(120h).

The _n

=

I

sample presented

_a

semiconductor-like behavior but the XRD spectra ^showed

unambiguously

that the

phase

of the material _was

mainly (2201).

In

addition,

the

resistivity dropped

at about 20 K whereas the

susceptibility

increased

significantly

between 5-7 K. The lack of _true

superconductivity

_may

be

explained by

the

difficulty

of

achieving

_oxygen

non-stoichipmetry

in the

synthesis _[4].

The critical temperatures ^of our ceramics and cell parameters ^{fitted from XRD data} are

summarized in table II. The _n

=

I cell parameters

correspond effectively

to a

(2201) phase.

The relative intensities of the XRD spectra ^{showed that about} 50 ifi of the

(2223)

ceramic _was

Table II. Cell parameters

(in I) _of

_the

_{(2201), (2212)}

_and

₍₂₂₂₃₎ superconductors manufactured for

the present work.

Compound

_a b _c T~

(K)

2 201 5.392 _± 0.007 5.400 _± 0.021 24.673 _± 0.026 SC

2 212 5.391 _± 0.013 5.398 _± 0.004 30.756 _± 0.027 85

2 223 5.414 _± 0.006 5,417 _± 0.004 37,137 _± 0.025 107

composed

of pure n = 3

phase

whereas in the

(2212) compound,

weaker

(2223)

features _were observed.

Despite

of the

slight

difference between _a and

b,

the data indicate that _an

orthorhombic structure is

appropriate

for these

superconductors.

This _concurs with the

numerous papers

published

elsewhere

[1-7].

Recent XRD

experiments performed

in the Bi cuprates

family emphasize

that in the

preparation

of the _n

=

3

phase,

it is difficult _to avoid contamination with

n =

I and 2

phases

and with

plumbates [16,17].

The _use of _a Raman

microprobe

rather than conventional

equipement

which examines _a

large

area of the

sample

should be _an

advantage

in the

investigation

of the

(2223) phase.

456

~

^~~~

&)

m 299

$

465

" 454

b

~

632

(

2

r

r ?97

b)

~« _46?

«

C~

633

655

f

C)

300 500 700

0l

(cm'~)

Fig.

3. Polarized

(Id)

Raman spectra ^of

Bi~sr~ca~_jCu~O~~~~~~

recorded at room temperature with the 488nrn laser line. The A- and B-bands _are located

respectively

around 460 and 630 cm~ ^' _n

= I _{curve a ; n}

= 2 _curve b _n

=

3 _{curve c.}

N 6 OXYGEN VIBRATIONS IN THE SERIES

Bi~sr~ca~_ jCu~04+2n+y

⁹⁰⁷

306

$kT )*

~

~~~

~

R)

282

~

~

416 494

~

,~93

* ~ ~

1~

~

Ii)

~

~

5

H

- 281 307

E

f

I

412

~

494

~

~ ~

₅₈₇

cK

C)

300 500 700

0l

(cm'~)

Fig. 4. Polarized

(fl

_I Raman spectra ^of

Bi~Sr2Ca~_ iCu~04+

_2n+y. n = I _{curve a n} 2 _curve b _n

=

3 _{curve c.} The stars indicate the

A~ depolarized

^lines.

Micro-Raman spectra in

backscattering

_geometry have thus been recorded for

sharp edged planar microcrystals

of about 5 _x 5

~m~. Taking

into account

previous

work _on similar

ceramics,

_we have considered that the _c axis _was

aligned along

the

backscattering

direction

z. It _was somewhat difficult to find square

crystals

and therefore in _some

experiments,

their orientation _may have not been _very well defined. Low

frequency _spectra

_were not

attempted

for technical _reasons and therefore _we have limited _our contribution to the vibrational

study

of the oxygen vibrations which should be active in the 200-700 cm~

spectral

range.

The 488 _nm line of _an argon laser _was used to record Raman

spectra

at _room

temperature

with the

polarizations z(yy)

_z,

z(xx)

_z

ill,

_{I I}

)

and

z(yx)

_z

if

_I

).

It should be

kept

ⁱⁿ mind that with these

configurations,

the

B~~(xz)

^and

B~ ~(yz)

^{modes cannot be observed for}

the Fmmrn structure _as well _as the

E~(xz, ^yz)

^{modes of the}

^{14/mrnm crystals.}

^{It should also be}

pointed

out that it _was not

possible

to record the

(zz) polarizations

because _we did _not have free

single crystals

at _our

disposal.

The results _are

presented

in

figures

3 and 4. We have called the bands _near 460 cm~ and 630 cm~ A and B

respectively.

Figure

5 shows spectra obtained

by rotating

the

samples by

^90° in order to _measure the

z(xx)

z

signals.

For _n

odd,

the B-band remains _very intense whereas the A-band

disappears

almost

completely.

For _n

=

2,

the A-band appears alone to the detriment of the B-band which

297 462

l~ l~

333

x8

632

300 50(1 700

j7

/b 443

q 314

j

JT

456

~

2

f

₂₉₉

)

₃₂₉

I ~

454 H 465

°~

l~

632

633

300 500 700

0l

(cm

~)

Fig.

5. Polarized

(fill)

Raman spectra ^of B12Sr2Ca~

jCu~04

+ 2n ₊y

microcrystals

rotated

by

90° with respect to

figure

3. The inset evidences the strong x,y

anisotropy

of the

(2223) compound.

n = I _{curve a ; n}

=

2 _curve b_{; n}

= 3 curve c.

is almost indiscernable. For _n

= 3 _we have

expanded

the

intensity

scale to discern the other

phonons

_more

accurately.

The considerable enhancement of the B-line

provides

evidence for strong

anisotropy

in the

scattering intensity

related to the nature ofthe structures in the

[010]

direction.

4. Discussion.

Contradictory

data _were

reported conceming

the structure of the _n

= I

phase.

It is

supposed

to be

strongly

monoclinic in _{one case} [9] ^rather than orthorhombic

[1, 3, 4, 6].

For the sake of

consistency,

_we will _assume that the three

Bi-cuprate phases belong

to the Arnaa _{space group.}

At least for the _n

= 2 and 3

phases,

_some

experimental

evidence sustains this

assumption.

First,

it has been established that _a structural modulation of about 5 b of the BiO

planes

occurs

along

the b-axis in the three materials

[18]. Second,

recent neutron diffraction studies

N 6 OXYGEN VIBRATIONS IN THE SERIES

Bi~Sr2Ca~_ jCu~04+2n+y

909

confirm this space group for Pb-stabilised 2223

samples [I Ii. Third,

the Arnaa

crystal

should

give

_{more oxygen}

_A~

modes than the Fmmm _one. The group

analysis yields

two and three Raman

A~

^{modes for Fmmrn which is less than observed}

experimentally

in

zlyy)

_z

(4,

5 and sometimes 6 lines

appear). Therefore,

_we have chosen to

study

the oxygen motions in _an Amaa structure. The classification of the

(2201) phase

in Amaa is _more

ambiguous.

If the

structure is monoclinic _our results _{are open} to

interpretation.

The

interpretation

of the Raman spectra

requires

_us to consider _group

theory

classifications

as well _as lattice

dynamics.

Shell models

performed

_on

Bi, Tl-cuprates [19, 20]

with

approximately 14/mmrn

structure have

provided

_{a very}

good insight

into the

physical

nature of

the Raman

phonons.

The recent Tl model is _more accurate than the earlier Bi model

regarding

the

discrepancy

between calculated and

experimental frequencies

and is taken into consideration in the discussion of _our results. The atomic

displacements

obtained with the

dynamical

matrix must be in

principle

mixed

tojether

and

correspond

to combinations of individual

symmetrized displacements

of each _atom.

4,I RAMAN _SPECTRA. The

spectra

are assumed to

originate

from

relatively

_pure

n ₌

1,

2 and 3

phases

_even if the latter

phase

should contain Pb inserted in the structure

[21].

In the

ill) configuration,

_we have obtained _two main bands

(A

and

B)

around

460cm~~

_and

630cm~~

_{associated with weaker modes around}

_297,

_{316 and}

330cm~~

Sidebands at

443,

454 and

450cm~~ in =1,2,

3 and at

653, 655cm~~ in

=

2, 3)

_are

observed. The

spectrum

of the

(2201)

material shows Raman bands and Raman

frequencies

in the _same

positions

as those of Bums et al.

[22],

the B band

being

located at 632 _cm~ and not

shifted towards 650 cm~ like in the spectrum ^{of Denisov} et al.

[23].

The

strong

resemblance between the Raman

spectra

of the three

phases

does _not

permit

_us

to discriminate between them at first

sight

except

by slight frequency

shifts in the bands.

Yet,

group

theory

allows such _a discrimination. The contribution of the

O(3)

and

O(4, 5)

atoms to the

A~

^and

Big

modes is the _same for the three

compounds

of the series but the Raman

activity

of the central

CUO~ plane

for the _n

= I and 3 _cases could contribute to _a

possible

experimental

distinction between the Raman spectra of

(2201), (2212)

and

(2223) phases

at the

microprobe

scale. It is indeed reasonable to consider that for each

species, A~

or

Big,

^the

^{O'(1, 2)}

^and

O(1, 2)

atoms vibrate in the _same

frequency region.

These atoms contribute for 1, 2 and 3

A~ (or Bi

_g~ ^when n

=1,

2 and 3 and it should be

possible

to discriminate between these

phases by counting

the number of modes associated with

O(1, 2)

and

O'(1,

2 vibrations in the spectra.

Nevertheless, identifying

_a Raman spectrum

specific

to the

Bi-(2223) phase

_appears to be

quite

a difficult task at the _moment due to the

lack of pure

(2223) samples.

Raman spectra of the 85 K and 110 K Pb-Sb

doped Bi-cuprates

have been described in _a

previous

_paper

[24].

^A doublet _was observed at 442-460 _cm~ for the A band

roughly

at the _same

positions

_as for

(2201)

and

(2223) crystallites

in the present work.

This band

splitting

could be

explained by

the selection rules inferred

by

_an Arnaa structure _as we will _see below.

In the

(fll ₎

_spectra

_{(Fig. 4),}

_the feature around

282cm~~

can be

unambiguously

classified in

Bj~ ^species.

^{The Raman}

spectrum presented by

Cardona et al.

[12]

for _a

(fl

_I

₎ polarization

exhibits also this line at 282 cm~ ~. In

fact,

for _n

=

2,

this

Bi

~

mode _was also found at lower

frequencies

260 _cm~

[25]

^and 275 cm~

[26].

Note the broadness of this band _: in the _case of

(2212)

and

(2223) phases (Amaa)

at least 2

Bi~

^{modes could} appear

between 260-300

cm~~

_in

(fl

I

) polarization.

The _same remark holds for

A~

^{modes in}

(II ₎

_spectra. In the

(fl

_I

_spectra

the A and B bands appear

weakly

and the

depolarization

can be estimated around 10-15 ifi _as

previously reported.

For instance _a close examination of the

(II)

_spectrum of Cardona shows that the 280-300 _cm~ band is

relatively

broad and

contains _a small shoulder _at 280 cm~ which is

certainly

due to the

Bj

~

component.

^Cardona

et al. also

specified

that

they

did not detect _a

Bj

~

mode for _n

=

I _at this

position.

However,

if the true structure of the

(2201)

material is

Arnaa,

_one should obtain _a

Bj

~

mode _near 280 _cm~ in the

id

_{I spectrum as observed}

_by

_{us at 306 cm~}

_Despite

_{of the}

depolarization

and the weakness of the

signal,

we have detected other lines which could be

Bj

~

modes. We have

peaked

them at

493,

591cm~ for _n

=

I,

at

416, 494,

593

cm~~

_for

n ₌ 2 and at

307, 412, 494, 587cm~~

_for

n =

3. The number of these modes in the

(fl

_I

₎

_spectra

_(3,

4 and

5) corresponds

to the number of

Bi

~

modes

expected

for the three

phases.

Finally, concerning

the

shapes

of the Raman bands _we notice that the

high

number of Raman modes and the

slight orthorhombicity

in Arnaa would

certainly

favor not

only

additional modes in the

low-frequency

_range but also _a

broadening

of the main Raman bands

assigned

to oxygen motions. This conclusion is based _on the _group

analysis performed

above.

For the _n

=1,

2 Amaa

phases

^{12 additional} Raman modes should be activated in the 200-700 cm~ range

(2 A~

+ 3 B

j~ + 3

B~

~ + 4

B~ ).

For the _n

=

3 Amaa

phase,

18 additional modes _are activated with

respect

to the Fmmrn _case

(3 A~

+ 4 B

j ~ + 5

B~

~ + 6

B~ _~).

The

Bj

~,

B~~

^and B~

~

modes must be very weak in

unpolarized

_or

(yz, xz)

_spectra. In the present

ill)

_and

ill experiments, only

the

A~

^and

Bj~

^{modes could contribute} to _a line

broadening.

4.2 OXYGEN VIBRATIONS FOR AMAA _MATERIALS. The Raman spectra ^of n =

I and n=2

Bi-cuprates

have been discussed elsewhere and the main

«high-frequency»

(200-700

cm~ ~) lines have been

assigned

to oxygen motions of

the14/mmm

and Fnlmm

[14, 23, 27],

and Amaa structures

[12, 28]. However,

in _some of these

studies,

_no shoulders _or

sidebands _were found

[14, 22, 27],

whereas

Sugai

and Sato

[28]

and Thomsen and Cardona

[29]

described them.

Tentative

assignment of

the weak lines in

(II )

_spectra. From the oxygen

displacements

of the

CUO~ planes

_{one can} deduce _a

correspondence

between

A~

^and

Bi

~

modes

(Figs. 3,

6 and

7)

I)

^The

antisymmetric O'(1,2)

vibration

(A~

^and

Bj~ species)

and the

antisymrnetric O(1, 2)

vibration _are the _same modes.

ii)

The

Bj

~

and

A~

^motions are similar modes,

Therefore the three weak lines around

297,

316 and 333 _{cm~ can} be

assigned

as follows. In

YBa~CU~O~

~

the modes at 340 _cm~ and 440 cm~

originate

from vibrations of the _oxygens of the

CUO~ planes. They

have been calculated

by

Cohen eta?. at

312cm~~

_and 360 cm~

[30],

the latter

phonon corresponding

to _an

in-phase A~

^O

(2,

3

motion,

the former

being

_an

antisyrnmetric _A~

mode. In the

Bi-cuprates series,

_one should

expect

the

corresponding O'(1,

2

)

and O

(1,

2 _{atoms to} vibrate in the _same

frequency

_range for both

Ag

and

Bj

~

modes.

The line at 314 and 316 cm~ in the

(flfl)

_spectra of the

(2201)

and

(2223) compounds probably

arises from the

A~O'(1,2) antisyrnmetric

vibration

corresponding

to the

340cm~~ antisymmetric phonon

of

YBa~CU~O~_~.

In the

(2212) material,

the

Oil, 2)

motions

give

two

A~

^modes : the

antisymrnetric

and the

breathing

modes

(Fig. 7).

The latter mode should have _a

higher frequency according

_to Cohen _et al.

[30]. Experimentally,

_one finds the first mode at 299 cm~ and the second _one at 329 _cm~ In the

(2223) material,

these two modes _are located

respectively

at

297cm~~

_{and 333}

cm~~

and in

addition,

the

O'(1, 2)

mode of the central

plane

_occurs at 316 cm~

N 6 OXYGEN VIBRATIONS IN THE SERIES

B12Sr~Ca~_jCu~04+2n+y

⁹¹¹

~(~~

~~ ~-~~

Big Big

Ol,2

Aiiaa

~~ _~/ ~ $i ~

~~j _$I

~ ~ _~~

z

fllg

~(O

~

~

l'

O~,~

~ill~d

03 Aiiaa

,

/~k~~ ~

Big O'l,2

Amaa

Fig.

6.

Symmetrized Bj~ displacements

of the oxygen ^atoms for the Amaa structure.

O(3)

_: SrO

plane

_;

O(1, 2)

CUO~

plane O(4, 5)

BiO

plane.

Two consecutive

planes

of the same

species

are

represented.

Origin of

the A band. The

origin

of the A Raman band may be best understood

by considering

both vibrational band

analogies

and lattice

dynamical

calculations in copper oxide

superconductors.

It is

interesting

for instance to look at Raman results obtained for the Tl-

cuprate

^series

(T~

=

110 K and 125

K) [15],

and for the _new

system Pb~sr~Yo ~~cao_~~Cu~Os

~ ~

[31].

Raman bands similar to the

A-phonon

of

Bi-cuprates

_appears

respectively

at

507,

430 and

480cm~~ respectively

in the spectra ^of

YBa~CU~O~_~, Tl-cuprates

and

Pb~sr~Yo_~~cao,~~Cu~Os

~~.

A number of

experiments

have shown in addition that these bands

are

strongly polarized

and

belong

to the

A~ species.

In

YBa~CU~O~_~

the

bridging O(3)

atom between the

Cull)

and

Cu(2)

atoms vibrates at 507 cm~

[32].

The

Cu(I)-Cu(2)

distance is

4,151 _[33]

_{whereas the}

corresponding

distance Bi-Cu in the

Bi-cuprates

is

4.551 [34].

Therefore the

bridging

_oxygen in

Bi-cuprates

should vibrate at _a lower

frequency

and thus the

A-phonon certainly originates

from

bridging

_oxygen motions. The calculation of

Prade _et al.

[19] points

out more

precisely

that this

band,

calculated at 493

cm~~,

_should

involve motions of

O(3)

in SrO

planes

and

O(4)

in BiO

planes.

In their recent results _on Tl- cuprates

[20],

these authors have calculated the A-band

analog

of the

(2223) phase

at

420cm~~ (located experimentally

at

430cm~').

It

corresponds

to a pure

Aj~ breathing

motion of the

bridged

_oxygen atom of BaO

planes

without

mixing

other modes.

PHYSIQUE 6

~~ ^~

~

~n ~a

03 Amaa

~ j~§

~ ~j

Ag Ag

O1

,2

A _mad

~ II

l i~

/ iii ~~g~~

04,5

Amaa

O'l,2

Amia

Fig.

7.

Symmetrized A~ displacements

^{of the} oxygen atoms for the Amaa structure. Two consecutive planes of the _same species are represented.

We should note,

however,

that the Arnaa structure induces _two

A~

^{modes for the}

O

(3)

atom : an axial

breathing

out of the Sr-O

planes along [lo0]

and _a transverse

breathing

out of the

(0 lo) planes along

the

y-axis (Fig. 7). Experimentally

the A Raman band exhibits _a

low-frequency

shoulder for all the

compounds.

After

Sugai

_et al.

[28]

the Bi and Sr _atoms, which have the site symmetry

of

the

O(3)

_atom

(Cs), give

rise to

pairs

of

phonons

at 53-63 cm~ for Bi and 121-132 cm~ for Sr.

Therefore,

_{one can assume} that in this structure the

O(3)

atom should be

responsible

^for the

two-phonon splitting

of the A-band and that the

low-frequency

sideband should

correspond

to a transverse

O(3)

motion. Another fact which

supports

^this

assumption

is

that,

since the

Bi-O(3)

and

Cu-O(3)

bonds _{are more} covalent than the

Sr-O(3) bond,

the axial

A~

^{mode should have} a

greater frequency

than the transverse

A~

^mode.

Furthermore,

the calculations of Kulkami et al, show that _transverse

E~

^modes may have lower

frequencies

^than the

corresponding Aj

~

modes in

14/mmm symmetry.

^{For instance} the

O(I)-Ca

axial mode is calculated at

456cm~~

_{whereas its}

_E~ analog

_occurs at

375cm~~. Therefore,

the

low-frequency

shoulders at

440,

457 and

452cm~~

_{in our}

compounds

_may stem from _a transverse

A~

^mode.

Origin of

the B band. In this

work,

_we have considered that all the observed Raman

phonons originate

from

A~

^{modes of the Arnaa structure. In that} case for _n

=

2, only

bt 6 OXYGEN VIBRATIONS IN THE SERIES B12Sr2Ca~_

jCu~04+2n+y

913

5

A~

^modes occur, of which 4 have been attributed

(299, 329,

454 and 465

cm~~).

For

n =

3,

the 297 and 316 cm~ bands

originate

from

O(1, 2)

and

O'(1, 2) respectively

and 6 oxygen

A~

^modes occur. Then there remains

only

_one

A~ phonon

: the

O(4, 5) vibration,

which should be observable _{as a} strong

intensity

in the

spectra

^because it is _a

breathing

mode.

This

phonon

must be the 630 _cm~

phonon

_~I~

band).

In

fact,

the calculation indicates that this band could be _a mix of

opposite O(3)

and

O(4)

vibrations

despite

the low calculated value

(513

crn~ ~). In the

Tl,(2223) model,

the calculated

frequency

is _very close to the

experimental

measurement

(597

cm~ for 608 cm~ ~) and involves

only

the

displacement

of the

O(4)

atom of the TIO

plane.

This

assignment

is

supported by

the

(I

I spectra ^of

figure

5 which show _an

anisotropic

effect.

By selecting (Id)

_or

_{(it )} configurations

for the Raman

scattering,

the

A/B intensity

ratio

changes drastically.

A similar

anisotropy,

but less

pronounced,

_was also found for 85 K

single crystals [12, 23].

In _our

experiment

the strong

anisotropic

behavior of the B-

band

(shown by

the inset of

Fig. 5)

could be related with the oxygen vibration

responsible

for that line. The modulation of the BiO

planes

with extra oxygen ^atoms should lead to this

anisotropy [18].

Tentative

assignment of

the weak lines in

(fl

_I

₎

_{spectra. For}

n ₌

I,

the 306 cm~ line

should be the

O'(1, 2) Bi~ antisyrnmetric

mode

predicted by

_group

theory.

Its

position corresponds

to that of the

A~

^line

(314

crn~

).

From table III _we

expect

^{that the}

remaining

bands at

493,

591cm~ ^' arise from

O(3)

and

O(4, 5) Bj

~

vibrations

respectively.

Indeed the

frequencies

of these two lines _are very near from those of the

corresponding A~

^lines.

Therefore the 282 and

412/416

cm~ lines should be ascribed to the

O(1,

2

) Bj

~

vibrations of the

(2212)

and

(2223) phases.

The 282

cm~~

line is located very near from the

A~

^{line at}

297cm~~

_{and should be}

assigned

to the _same

type

^{of motion} : an

antisymrnetric

axial vibration.

Table III.

Representations ofthe

vibrations

ofeach

_atom

for

the three

possible

structures

(n

=

1,

2 and

3).

Atom

14/mmm

Fmmrn Arnaa

Cu'

A2u, E~ Biu,

_{B2u, B~~}

A~,

2

Bi~,

2 B~~, B~~

Ca'

Cu, Sr, Bi, O(3) Aj~, _E~ A~,

B~~,B~~ ²

A~, Bj~,

B~~, 2 B~~

Ca

A2u, E~ Biu,

B2u, _B~~

A~,

2

Bj~,

² B~~, B~~

O'(1, 2) A~~,

B~~, ²

E~ A~, Bj~,

2 B2u, 2 B~~

A~, Bj~,

² B~~, 2 B~~

Au, Biu,

2 B2u, ² B3u

O(1, 2) _{Aj~, Bj~,}

2

E~ A~, Bj~,

² B~~, ² B~~ 2

A~,

²

Bj~,

⁴ B~~, ⁴ B~~

A~~,

B2u, ²

E~ A~, Bj~,

² B2u, ² B3u ²

A~,

2

Bj~,

4 B~~, ⁴ B3u

~~~'~~ ~18' ~g ~8' _{~28' ~3g}

_2~g,

~lg,

2 ~2g> 2

~3g

2~2u,

Eu ~lu, ~2u, ~3u

2~u,

Bju,

2

~2u,

2

~3u

S. Conclusion.

We have examined additional Raman modes

by considering

the site

symmetry

^{of the} oxygen atoms of the central

CUO~ plane

for _n odd in the

non-symmorphic

Amaa structures. A _new

assignment

has been

proposed partly

based _on the

dynamical

calculations of

Prade,

Kulkarni et al. and of Cohen et al. and is summarized in table IV.

Group theory

_{arguments on} the site

symmetry ^of the

O(3) bridging

atom lead _us to suppose that the low

frequency

sideband at about

443/454/450

_cm~ in the A bands

originate

from the O

(3

transverse motion. The

high frequency

component at

456/465/462

cm~ may be attributable to the

O(3)

axial

breathing

mode and may be mixed with the O

(4)

axial motion _as evidenced

by

the Bi

cuprate

model. A

comparison

with the theoretical results of Cohen's _{group on}

YBa~CU~O~

indicates that the

297cm~~

_{band could be the}

O(1,2) antisymmetric _A~

mode in

opposition

to the O

(1,

2

breathing

at 329-333 cm~ We confirm _a

Bi

~

line for the

(2212)

and

(2223)

structures

peaked

around 282 _cm~ This line should be the

antisymrnetric

O

(1,

2

)

B

j~ vibration. Other

Bj

~

modes _are

likely

to appear around

306, 415,

494 and 590 _{cm~ ~.} Discrimination of the

three

phases

_may be achieved

by considering only

the

O(1,2)-O'(1,2)

lines. For

n =

I, only

_one

O'(1, 2) A~ phonon

^should occur, I.e. the

antisymmetric

axial

motion,

_as observed

experimentally

at

314cm~~ However,

_we want to

emphasize

that _a monoclinic

structure is

likely

to exist in this

compound

and _so the

reliability

of _our

assignement concerning

the _n

= I

phase

must be taken

cautiously.

In

spite

of this

uncertainty

and _as

predicted by

_group

theory, clearly

_more

A~

^modes are

displayed

in _our

experimental

results in the _n

= 3 material than in the _n

= 2

superconductor.

We

assign

the

remaining phonons

at 630 _cm~ to O

(4,

5 pure motions. This

study

has

permitted

_us to

complete the14/mmm

and Fmrnm Raman

analyses proposed

earlier in these materials but the Amaa and A2aa _structures

cannot

definitely

be discriminated.

Table IV. Raman

frequencies found

in the

Bi~sr~ca~ iCu~O~

~ ~~ _~~ series. The

assignments

are deduced

from

_group

theory

and calculations. Note that the

O(3)

motion is _no

longer

mixed with the

O(4)

motion

for Tl-cuprates.

^The

frequencies

below

340cm~~

_{should also involve}

cation motions mixed with _oxygen

displacements.

Frequency (cm-~) Symmetry

Atom

297

A~ antisymm. O(1, 2) CUO~ plane

314-316

A~ antisymm. O'(1, 2) CUO~ plane

329-333

A~ breathing O(1, 2) CUO~ plane

440-454-450

A~

^transverse

O(3) bridge

SrO

plane-O(4)

456-465-462

A~

^axial

O(3) bridge-O(4 )

632

A~

^axial

O(4, 5)

BiO

plane

282

Bj~

^axial

shearing O(1, 2) _CUO~ plane

306

Bj~

^axial

shearing O'(1, 2) CUO~ plane

412-416

Big diagonal shearing O(1, 2) CUO~ plane

494

Big

^transverse

shearing O(3)

^SrO

plane

587-591-593

Big

^axial

shearing O(4, 5)

^BiO

plane

bt 6 OXYGEN VIBRATIONS IN THE SERIES

B12Sr2Ca~_jCu~04+2n+y

⁹¹⁵

Acknowledgements.

We

acknowledge

Prof. J. D. Comins for _a

reading

of the

manuscript.

We thank Dr. J. P.

Buisson for

stimulating

discussions

concerning

the structures, Dr. T. P.

Nguyen,

Dr. M.

Matus and Dr. G.

Leising

for

conductivity

and

susceptibility

measurements.

References

Ill

MICHEL C., HERVIEU M., BOREL M. M., GRANDIN A., DESLANDES F., PROVOST J., RAVEAU B., Z.

Phys.

B. Cond. Malt. 68

(1987)

421.

[2) HAZEN R. M., PREWITT C. T., ANGEL R. S., ROSS N. L., FINGER L. W., HADIDIACOS C. G., VEBLEN D. R., HEANEY P. S., HOR P. H., MENG R. L., SUN Y. Y., WANG Y.

Q.,

XUE Y. Y., HUONG Z. S., GAO L., BECHOLDS S., CHU C. W.,

Phys.

Rev. Lett, 6o

(1988)

l174.

(3) TARASCON J. M., MACKINNON W. R., BARBOUX P., HWANG D. M., BAGLEY B. G., GREENE L.

H., HULL G. W., LEPAGE Y., STOFFEL N., GIROUD M., Phys. Rev. B 38

(1988)

8885.

[4) ^{TORARDI C.} C., SUBRAMANIAN M. A., CALABRESE J. C., GOPALAKRISHNAN J., MAC CARRON E.

M., MORRISSEY K. S., ASKEW T. R., ELIPPEN R. B., CHOWDUY U., SLEIGHT A. W., Phys.

Rev. B 38

(1988)

225.

[5) SUNSHINE S. A., SIEGRIST T., SCHNEEMEYER L. F., MURPHY D. W., CAVA R. J., BATTLOG B.,

VAN DOVER R. B., FLEMING R. M., GLARUM S. H., NAKAHARA S., FARROW R.,

KRAJEWSKI J. J., ZAHURAK S. M., WASZCZAK J. V., MARSHALL J. H., MARSH P., RUPP L.

W. Jr., PECK W. F.,

Phys.

Rev. B 38

(1989)

893.

[6) ^NON SCHNERING H. G., WALZ L., SCHWARTZ M., BECKER W., HARTWEG M., POPP T., HETLICH B., MULLER P., KAMPF G., Angew. Chem. Int. Ed. Engl. 27

(1988)

574.

[7) BORDET P., CAPPONI J. J., CHAILLOUT C., CHENAVAS J., HEWAT A. W., HEWAT E. A., HODEAU J. L., MAREzIO M., THOLENCE J. L., TRANQUI D.,

Physica

C156

(1988)

189.

[8] ^GAO Y., LEE P., YE J., BusH P., PETRICEK V. and COPPENS P.,

Physica

C160

(1989)

431.

[9] ONODA M. and SATO M., Solid State Commun. 67

(1988)

799.

(10) SHI F., RONG T. S., ZHOU S. Z., WU X. F., DU J., SHI Z. H., CUI L. G., JIN R. Y., ZHANG J. L., RAN Q. ^Z. and SHI N. C.,

Phys.

Rev. B 41

(1990)

6541.

(ll)

SEQUEIRA A., YAKHMI J. V., IYER R. M., RAJAGOPAL H., SASTRY P. V. P. S.,

Physica

C167 (1990) 291.

[12] ^CARDONA M., THOMSEN C., LIU R., VON SCHNERING H. G., HARTWEG M., YAN Y, F. and ZHAO Z. X., Solid State Commun. 66

(1988)

1225.

[13) FARROW L. A., GREENE L. H., TARASCON J. M., MORRIS P. A., BONNER W. A., HULL G. W., Phys. Rev. B 38

(1988)

752.

[14) SAPRIEL J., PIERRE L., MORIN D., TOLEDANO J. C., SCHNECK J., SAVARY H., CHAVIGNON J., PRIMOT J., DAGUET C., ETRILLARD J., BOYER H., Phys. Rev. B 39

(1989)

339.

[15)

KRANTZ M., ROSEN H. J., MACFARLANE R. M., LEE V. Y.,

Phys.

Rev. B 38

(1989)

11962.

[16]

SHILOH M., WooD I., BROWN M., BEECH F., BOYD I. W., J.

Appl. Phys.

68

(1990)

2304.

[17] DuPouY P., NGUYEN T. P., FAULQUES E., J. Less-Common- Met, 164-165

(1990)

1216.

[18) ZANDBERGEN H. W., GROEN W. A., MILJHOFF F. C., VAN TANDELOO G., AMELINCKX S.,

Physica

C156

(1988)

325.

[19] PRADE J., KULKARNI A. D., DE WETTE F. W., SCHROEDER U. and KRESS W., Phys. Rev. B 39

(1989)

2771.

[20] KULKARNI A. D., DE WETTE F. W., PRADE J., SCHROEDER U, and KRESS W.,

Phys.

Rev. B 41

(1990)

6409.

[21]

NGUYEN T. P., DuPouY P. and FAULQUES E., Eur. J. Solid State

Inorg.

Chem. 27

(1990)

689.

[22] BURNS G., STROBEL P., CHANDRASHEKAR G. V., DACOL F. H., HOLTzBERG F. and SCHAFFER M. W.,

Phys.

Rev. B 39

(1989)

2245.

[23] DENisov V. N., MAVRIN B. N., PODOBEDOV V. B., ALEXANDROV I. V., BYKOV A. B.,

GONCHAROV O. K., MELNIKOV O. K., ROMANOVA N. I., Solid State Commun. 70

(1989)

885.

JOURNAL DE PHYSIQUE I T I, bt 6, JUIN [WI 36

[24] FAULQUES E. and DuPouY P., Proc. Int. Conf. _on Modem Aspects of

Superconductivity,

Paris, R.

Suryanarayanan and A. Niku-Lari Eds. (1989) _p. 241.

[25]

KIRILLOV D., BozovIc I., GEBALLE T. H., KAPITULNIK A., MIT» D. B., Phys. Rev. B 38

(1988)

11955.

[26]

SLAKEY F., KLEIN M. V., BuKowsKI E. D., GINSBERG D. M.,

Phys.

Rev. B 41

(1990)

2109.

[27] STAVOLA M., KROL D. M., SCHNEEMEYER L. F., SUNSHINE S. A., FLEMING R. M., WAszczAK J.

V., KOSINSKI S. G.,

Phys.

Rev. B 38

(1989)

5110.

[28] SUGAI S. and SATO M.,

Phys.

Rev. B 40

(1989)

9292.

[29] ^THOMSEN C. and CARDONA M., In Physical

Properties

of

High-Temperature Superconductors,

D. M.

Ginsberg

Ed.

QVorld

Scientific,

Singapore)

1989.

[30] COHEN R. E., PICKETT W. E. and KRAKAUER H., Phys. Rev. Lett. 64 (1990) 2575.

[31] LIU R., CARDONA M., GEGENHEIMER B., HEYEN E. T., THOMSEN C., Phys. Rev. B 40

(1989)

2654.

[32] KUzMANY H., FAULQUES E., MATUS M, and PEKKER S., In Studies of

High Temperature

Superconductors, Nova Science Publishers, A. V. Narlikar Ed.

(New-York)

1989.

[33] CAPPONI J. J., CHAILLOUT C., HEWAT A. W., LEJAY P., MAREzIO M., NGUYEN N., RAVEAU B., SOUBEYROUX J. L., THOLENCE J. H., TOURNIER R.,

Europhys.

Lett. 3 (1987) 1301.

[34] BORDET P., CAPPONI J. J., CHAILLOUT C., CHENAVAS J., HEWAT A. W., HEWAT E. A., HODEAU J. L., MAREzIO M., THOLENCE J. L., TRANQUI D., Physica C153-155

(1988)

623.