Lattice vibrations in Bi2CaSr2Cu2O2

Solid State Communications, Vol. 72, No. 6, pp. 555-557, 1989. Printed in Great Britain.

0038-1098/89 $3.00 + .00 Pergamon Press plc

LATTICE VIBRATIONS IN Bi2CaSr2Cu20 s Chellam Ramakrishnan, R.K. Rajaram and N. Krishnamurthy* School of Physics, Madurai Kamaraj University, Madurai 625 021, India (Received 17 April 1989 by M.F. Collins) The lattice dynamics of Bi2CaSr2Cu2Os is worked out employing the conventional central force model. The nearest neighbour interactions within a radius of 4 A are taken into account. The force constants for these interactions are calculated from the already available crystal data and from the vibrational frequencies of diatomic molecules. The calculated values of zone centre phonon frequencies compare reasonably with the available Raman scattering data. I. INTRODUCTION RECENTLY, there have been reports of superconductivity in the Bi-Ca-Sr-Cu oxide system in the 80 K range [1-3]. The general formula for these oxides is Bi2Ca,_lSr2Cu, O4+2, and there are one, two, three or four square planar Cu-O layers sandwiched between bismuth oxide layers in these oxides. The superconducting transition temperature, T~, is generally found to increase with increasing n, the number of such Cu-O layers [4]. Studies of the high T~ superconducting phases in the series Bi2.1(Ca, Sr),+lCUnO2n+4+tf [5], with starting compositions near 2122 of the Bi-Ca-Sr-Cu oxide (Bi2CaSr2Cu20 ~) system have shown that Tc is maximised by reacting and sintering in the partial melting region at 860-870°C followed by a rapid quench. Resistivity measurements by Tallon et al. [5] have shown that the single phase 2122 sample exhibits zero resistance at 91 K and these Bi based oxides have rather lower resistivities than YBa2Cu307_~. Electron microscopic investigations [6] have reported the Bi2CaSr2Cu208 to be a layered compound that cleaves easily on a preferred plane. It consists of layers of perovskite sandwiched between Bi-O layers. The electron microscopic studies have given the unit cell of Bi2CaSr~Cu2Os to be having dimensions x/r2ap x 5,¢r2ap where ap is the perovskite lattice parameter equal to 3.8A in agreement with X-ray and neutron diffraction results. From X-ray powder diffraction, a pseudo tetragonal sub cell having a = b = 5.4A and c = 30.76 A is reported [6]. The structure is a-centered comprising of CuO2-SrO-BiO-BiO-SrO-CuO2-Ca * To whom all communications should be addressed.

sequences mirrored about Ca. The following additional features (i) in the "a" direction, a cell dimension of 5.4 A (ii) in the "b" direction a cell dimension of 5.4 A and a 19/4x incommensurate structure of 25.7 A and (iii) in the "c" direction a cell dimension of 61.4A or a 2xC axis superstructure have also been reported [61. Raman back scattering measurements in the Bi2CaSr2Cu2Os crystal have been reported by Burns et aL [7]. The room temperature Raman spectra indicate peaks at 164, 292, 464 and 625 cm -1. The aim of our present investigation is to explain the occurrence of these peaks in Raman spectra by studying the lattice dynamics of Bi2CaSrzCu208 using a central force model [8]. Since this crystal has a layered structure, lattice dynamical calculations are carried out without taking the long range interactions into account. 2. GEOMETRY OF THE LATTICE The structure of 2122 Bi oxide is taken to be a Table 1. Atomic positions in Bi2CaSr2Cu20s a = 3.812A, c = 30.66A, Tc .~ 80K Atom

Co-ord. of equivalent positions

+ (~1 ~1 ½) ca Srl, Bil, CUl, 011, 013 , 021 , 031 ,

555

(0 0 0) Sr2 Bi2 Cu2 012 014 022 032

_+(00Z) + (00 Z 1) + (0 0 Z2) + (0 ½ Zs) "1-(½ 0 Z5) -Jr"(0 0 Z3) -[-(0 0 Z4)

Z = 0.098 ZI -- 0.301 z 2 = 0.445

Zs = 0.454 Z3 = 0.199 Z4 = 0.370

556

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L A T T I C E VIBRATIONS IN Bi2CaSr2Cu208

Table 2. Interatomic distances Atom

Nearest neighbour

Dist. in A

Atom

Nearest neighbour

Dist. in A

Ca

Oi1 , O12, Oi3 , Oi4 Srl, Sr2 CUl, Cu2 O12, O14

CUl

Oll , Oi3 O31 Cu2 O12, OI4 O12, O14 032 CUl Oi1, O13 O13 Oi2 O31

022

2.3711 3.0047 3.1795 2.4849 2.8685 3.0006 2.4849 2.8685 3.0006 2.1155 2.6955 3.1273 2.1155 2.6955 3.1273

032 O31

3.4265 3.4265

1.9259 2.2995 3.3726 3.6362 1.9259 2.2995 3.3726 3.6362 2.6955 2.8207 3.204 3.90 ! 6 2.6955 3.204 3.9016 2.8207 3.204 3.204

Srl

032 Cu2 Sr 2

Oil , O13

Bil

O31 Cul O31 022 O21

Bi2

032 O21

Cu2

O11

Oi4

O14

O12

032 Oi3 O14 O31

Ol3 O21 022

body centered tetragonal structure belonging to the space group D~7-I4/mmm [7]. The position of atoms in the unit cell as given by Burns et al. are listed in Table 1. In determining the zone centre phonons, only the atoms in the primitive cell, which contains half the number of atoms in a conventional unit cell, are considered. The interatomic distances up to 4 A from a given atom have been calculated to find the neighbours of each atom employing a computer program. The interatomic interactions for these neighbouring atoms within 4 A are assumed to be dominant and the other interactions are assumed to be negligible. The typical interatomic distances are listed in Table 2. 3. R E S U L T S A N D DISCUSSION The lattice dynamics of this 2122 bismuth compound is studied in the body centered tetragonal phase with 15 atoms in the primitive cell. The normal vibrational modes at the Brillouin zone centre are classified according to the irreducible representations of the point group and are found to be

6Aig

+

Big -~ 7Eg + 7A2u + B2, + 8Eu

of which 6dig + Big + 7Eg are Raman active, 6A2u + 7E~ are IR active and A2u + E~ are acoustic modes. The zone centre phonons in the Bi2CaSrzCu208 can be obtained using a de Launay type central force model which assumes a radial force between neigh-

O14

032

bouring atoms and solving the secular equation

ID~(KK') - o)26~KK'I = 0 where the dynamical matrix with elements D~a(KK') is of order 45 x 45. The force constants for various interactions such as Sr-O, C a - O and O - O are obtained from the diatomic molecular data [8] and Badger's rule connecting interatomic distances and force constant as ke(r e -

dij) 3

=

1.86 x l0 s,

where r e is the equilibrium interatomic distance and dij is a constant for a given diatomic molecule [9]. Weber [10] has reported that the strongest bond in La2_x(Ba, Sr)xfuO4- planar C u - O - has a bond stretching force constant lying between 120 and 176 K dyn cm- 1. For our present work, the average force constant f o r the nearest C u - O interaction is taken to be 140 K dyn cm -I and is scaled to different distances. Small variations in the force constants are

Table 3. Force constants in Kdyncm -l for different interactions Nearest interacting atoms

Force constant in K dyn cm- 1

Ca-O Bi-O Sr-O Cu-O Oll--Ol2

70 70 78 140 20

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LATTICE VIBRATIONS IN Bi2CaSr2Cu208

557

Table 4. Zone centre phonons Experimental Raman frequency in cm- t

Calculated frequencies in cm-

Alg

BIg

E~

A2~

B2u

E~

164 292 464 625

62.6 148.0 197.4 236.0 438.8 488.7

437.8

24.0 100.9 151.2 283.2 328.1 446.8 618.9

88.5 184.0 231.4 296.8 438.8 474.6

416.6

36.1 144.2 238.6 287.7 328.4 497.0 623.2

effected to satisfy the equilibrium conditions of the lattice. The force constants for different interactions are tabulated in Table 3. The 45 x 45 dynamical matrix is block diagonalised using group theory to find the phonon frequencies corresponding to the various normal modes of vibration. The symmetry co-ordinates are constructed and the transformation matrix to block diagonalise the dynamical matrix is obtained. In the block diagonalised form, we have 6 x 6 matrix for Aig, 7 x 7 matrices for Eg, 7 × 7 matrix for A2~, 8 x 8 matrices for Eu, 1 × 1 matrices for B~g and B2u. Computations were carried out to solve the smaller blocks and obtain phonon frequencies. These frequencies are listed in Table 4 along with the experimental Raman frequencies. A comparison of the phonons in Atg with A2u , B~g with B2u, Eg with Eu indicates some kind of Davydov pairing in which one mode is symmetric and the other one is antisymmetric with respect to the centre of symmetry with similar frequencies. The zone centre phonons calculated using de Launay model for La2CuO4 [11], YBa2Cu307 [12] and BiECaSr2CuEOs have shown that the A~g phonon has a maximum frequency around 400-500 cm -~. Eg modes in the point group D4h have correlation with B2g + B3g modes of the point group D2,. The B2g and B3g modes in YBa2Cu307 have the highest frequency around 600cm -~. Eg modes in the 2122 Bi oxide have a maximum of 618.9cm -1. Hence the experimental value of 625cm -~ for 2122 oxide may correspond to the Eg mode. The observed width of spectral lines at 464 and 625cm -1 is around 60 and 100cm -~. Hence the observed difference in the calculated frequency from the experimental value could be accounted for

on the basis of the width of the line. Further experimental work and lattice dynamical computations taking into account a screened coulomb interaction will help to understand some aspects of high frequency modes in these oxides. REFERENCES 1.

C. Michael, M. Herview, M.M. Borel, A. Grandin, F. Deslandes, J. Provost & B. Raveau, Z. Phys. B68, 421 (1987). 2. A. Khurana, Phys. Today 41 (No. 4), 21 (1988). 3. H. Maeda, Y. Tanaka, M. Fukutomi & T. Asano, Jap. J. Appl. Phys. 27, L209 (1988). 4. J.M. Wheatley, T.C. Hsu & P.W. Anderson, Nature 333 (No. 12), 121 (1988). 5. J.L. Tallon, R.G. Buckley, P.W. Gillberd, M.R. Presland, I.W.M. Brown, M.E. Bowden, L.A. Christian & R. Goguel, Nature 333 (No. 12), 153 (May 1988). 6. E.A. Hewat, M. Dupuy, P. Bordet, J.J. Capponi, C. Chaillout, J.L. Hodeau & M. Marezio, Nature 333 (No. 5), 53 (May 1988). 7. G. Burns, G.V. Chandrashekar, F.H. Dacol, M.W. Shafer & P. Strobel, Solid State Commun. 67, 601 (1988). 8. J. de Launay, Solid State Physics, Vol. 2 (Edited by F. Seitz & D. Turnbull), Academic Press, New York (1956). 9. G. Herzberg, Infrared and Raman Spectra, Nostrand, Princeton (1945). 10. R.M. Badger, J. Chem. Phys. 2, 128 (1934). 11. W. Weber, Phys. Rev. Lett. 58, 1371 (1987). 12. T. Brun, M. Grimditch, K.E. Gray, R. Bhadra, V. Maroni & C.K. Loong, Phys. Rev. B (USA) 35, 16, 8837 (1987). 13. N. Krishnamurthy & Chellam Ramakrishnan,

DAE National Symposium on Solid State Physics, Bhopal, Dec. (1988).