Structure and superconductivity in Tl2Ba2CaCu2O8

11 July 1994

Physica C 229 (1994) 331-345

ELSEWIER

Structure and superconductivity

in T12BapCaCu208

V.N. Molchanov a, R.A. Tamazyan a, V.I. Simonov a, M.K. Blomberg bT*, M.J. Merisalo b, V.S. Mironov c a Institute of Crystallography, RAS, Moscow, I1 7333, Russia b Department of Physics, P.O. Box 9, University ofHelsinki, FIN-00014 Helsinki, Finland c Institute of Chemical Physics, RAS, Moscow, 117915, Russia Received

14 May 1994; accepted 11 June 1994

Abstract The structure of superconducting T12Ba+IZaCqOs ( Tc = 110 K) was refined from single-crystal X-ray diffraction data measured at temperatures 296, 160, 130, 90 and 60 K. The refinements indicate a positional disorder of the thallium and oxygen atoms in the Tl-0 layers, resulting in locally orthorhombic symmetry. The macroscopic symmetry of the specimen remains tetragonal through the transition to the superconducting state. Some of the structure parameters show anomalous behaviour in the vicinity of G. A possible mechanism of the transition to the superconducting state and its relation to the observed structural changes are discussed.

1. Introduction Superconductivity in the thallium-based cuprates was first discovered in 1988 by Sheng and Hermann [ 11. These compounds exhibit critical temperatures up to 125 K [ 21. There exist two series of these compounds, with the general formulae TlBazCa,_,C~~0z,,+~ and TlzBa2Ca,_IC~n02n+4, n = l-5. The structure and properties of these compounds have been discussed in a number of publications (see e.g. reviews [ 3,4] ). Single-crystal X-ray diffraction studies on the structure of TlzBazCaCuzOs (Tl-2212) have been reported for example in Refs. [5-g] and powder neutron diffraction studies in Refs. [9-121. However, several features in the crystal structure have remained unclear. In particular, more accurate data on the stoichiometry disturbance, on the quantitative changes of isomorphous replace* Corresponding author.

merits, and on the static atomic shifts in the cationic and anionic sublattices, are required. An important question is also the character of the structure modulations. Satellite reflections or diffuse scattering have been observed by electron diffraction techniques [ 4,10,13,14] and by single-crystal X-ray diffraction methods [ 151 for almost all the phases, including Tl-2212. Furthermore, the behaviour of the crystal structure during the superconducting phase transition requires more experimental studies. Since the discovery of high-Tc superconductivity in (La,Ba)zCuOd [ 161, the problem whether the superconducting phase transition is related with changes in crystal structure or whether it occurs solely due to changes in electronic configuration, has remained unresolved. The results - or the interpretations of the results - of different authors are often in contradiction to each other. For example, in several X-ray and neutron powder diffraction studies on YBazCu307_8 (Y-123)

0921-4534/94/$07.00 @ 1994 Elsevier Science B.V. All rights reserved ssDr0921-4534(94)00358-M

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at temperatures above and below Tc,anomalies in the temperature dependence of the Cu-0 distances [ 171, in the thermal lattice contraction [ 17-201, or in the orthorhombic strain [ 18,211, were found in the vicinity of the phase transition temperature. However, most of the observed effects are small and their interpretation is controversial. Besides, in similar studies [22,23 ] no clear evidence was found for an anomalous change in any of the structural parameters, including the orthorhombic strain. Especially the Cu-0 distances and the possible anomalies in their behaviour [ 171 are of considerable interest due to their sensitivity to the amount of charge transfer between the copper-oxygen planes and chains in Y- 123. The choice of Tl-22 12 as an object for our study was accounted for by the live-fold coordination of copper, which is similar to that in Y123. In contrast to Y-123, these crystals are not twins, which ensures a greater accuracy and reliability of the structure parameters obtained from the diffraction data. Further, the temperature dependence of the structural parameters of thallium cuprates has not been studied so extensively as that of the yttriumbased compounds. Cox et al. [9] refined structural parameters for Tl-2223 (T,=125 K) at 150 and at 13 K. They found no significant changes through the superconducting critical temperature. The unit-cell parameters, measured in the temperature range 13150 K, did not show any anomalies either. Gao et al. [7] performed measurements on single crystals of Tl-2212 at room temperature and at 125 K, i.e. slightly above the critical temperature, Tc= 110 K. No structural changes near the phase transition were found, except the natural temperature reduction of the lattice parameters and, accordingly, the reduction of the interatomic distances. The present paper reports a precision X-ray diffraction study of singlecrystalline Tl2Ba2CaCu2Gs at three temperatures before the phase transition and at two temperatures in the superconducting state, thus allowing a more detailed analysis of the temperature dependence of the structure parameters. A brief preliminary communication about the results was published earlier [ 241.

2. Diffraction experiments The technique of growing the Tl2BazCaCuzGs single crystal samples was reported in Ref. [25]. The sample chosen for the experiments was ground to a sphere with a radius of 0.113 mm. It was mounted on a quartz thread using beeswax to minimize possible temperature-influenced stresses on the sample at low temperatures. The measurements were performed in Helsinki on a Huber 5042 four-circle diffractometer equipped with a Displex 202 closed-cycle two-stage helium cryostat. Graphite-monochromatized MO Kor radiation was used, and the measurements were carried out on the sample at temperatures 296, 160, 130, 90 and 60 K. The stability of the measurement temperature was kO.5 K. The unit cell dimensions of the tetragonal lattice were determined by a least-squares refinement of the setting angles of 18-20 well centred Friedel reflection pairs located in the region 42” < 1281 < 56”. The results are shown in Table 1. The analysis of systematic extinctions in the diffraction data did not reveal any deviations from the adopted space group 14/mmm. The crystal symmetry did not depend on temperature. The possible existence of a modulated structure was tested at room temperature by scrupulous scanning with steps of 0.1 in the region of reciprocal space limited by the planes (300), (030) and (004). No satellite reflections were found. A similar test was performed using the Huber six-circle diffractometer of the X7B beamline at the National Synchrotron Light Source, Brookhaven. The sample was cooled to 20 K with a Displex cryostat (similar to the one described above). Measurements were carried out using radiation of wavelength 0.9389 A. Some very weak extra reflections were observed. However, these are probably due to an intergrowth of a small amount of another phase of the structural family, rather than due to structure modulations. The results are in agreement with those obtained by Gao et al. [ 71, but in contradiction to studies reported in Refs. [ 4,10,13-l 5 I. Measurements of the reflection intensities were performed using coupled w-28 step scans. The minimum number of steps in each scan was 96, the step length varied from 0.009” (0) at small 20 angles up to 0.025” at large angles, and the measuring time was l-3 s/step. The reflection profiles were corrected for Lorentz and polarization effects, and the inte-

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Table 1 Unit cell parameters a and c (in A), fractional atomic coordinates A* ), and extinction parameter g ( x lo@ ) Temperature

T

Unit cell

a C

X

0.513(4) 0.537(l)

Tl(xyZ)

3.8490(3)

3.8498(3)

3.8501(3)

3.8545(3)

29.241(2)

29.249(2)

29.261(2)

29.317(2)

0.509 (4) 0.538(l) 0.21360(2)

0.512(4) 0.537(l) 0.21360(3) 0.67 (4) 1.68(10)

0.513(3) 0.541(l) 0.21365(2)

0.57(3) 1.53(9)

0.510(4) 0.538(l) 0.21359(3) 0.67(4) 1.46(10)

v13

0.61(2) 0.93(8) 0.17(10)

0.71(2) 0.77(9) 0.21(12)

0.75(2)

0.82(8) 0.13(11)

u23

0.28(5)

0.27(3)

0.24(4)

0.23(5)

0.13(9) 0.23 (4)

Z

0.12145(2)

0.12141(2)

0.12144(2)

0.12144(2)

0.12160(2)

VII

0.41(l)

0.37(l)

0.43(l)

0.95(l)

u33

0.86(2)

0.84(2)

0.41(l) 0.94(2)

1.00(2)

1.45(2)

0.45 (4) 0.61(6)

0.40(4) 0.67(6)

0.41(4) 0.76(6)

0.52(4)

0.87(4)

0.80(6)

1.22(6)

0.05394(4) 0.13(2) 0.74(4)

0.05396(5) 0.13(3) 0.87(5)

0.05395(5) 0.11(3)

0.05400(4) 0.48(2)

u33

0.05394(5) 0.17(3) 0.74(5)

0.94(5)

1.38(4)

Z

0.0524(2)

0.0526 (2)

0.0525(2)

0.0525(2)

0.0525(2)

VI1

0.5(2)

0.3(2)

0.4(2)

v22

0.7(2) 0.9(2)

0.3(l) 0.6(2)

0.7(2) 1.1(2)

0.6(l) 1.2(2)

0.8(2)

0.6(2) 1.3(2)

0.1453(3) 1.1(2) 1.2(3)

0.1455(3) 1.1(2) 1.1(3)

0.1456(3) 1.4(2)

u33

0.1457(3) 1.1(2) 1.1(3)

1.3(3)

1.8(2) 1.8(3)

Z

0.2199(7)

0.2184(5)

0.2189(6)

0.2195(6)

0.2194(5)

&I u33

14(2) 2.0(8)

15(2) 0.5(5)

13(2) 1.3(6)

15(2) 1.1(6)

14(2) 1.4(5)

g

1.1(2)

2.2(2)

1.7(2)

2.7(2)

3.8(2)

R(F)

0.0307

0.0262

0.0287

0.0283

0.0270

wR(F)

0.0329

0.0286

0.0323

0.0310

0.0267

u22

0.21362(3) 0.53(4) 1.65(11)

u33

0.63(2)

VII u33 Z VII

01 (Oiz)

v33

oZ(t$z)

Z VII

03 (OOZ)

Extinction

Temperature factor expression is exp(-2x2 F&,)*1

C

296 K

3.8486(3)

u12

cu(f+)

160K

29.232(4)

Ull

Ca/Tl(OOO)

Vtj (in lo-*

130K

Z

Ba(OOz)

thermal parameters

90 K

Y

60 K

x, Y and z, anisotropic

cij

hthjafa;Vtj).

0.81(8) 0.26(11)

The agreement factors are defined as wR(F)

1.12(3) 2.19(9) 1.10(2) 0.92(7)

1.6(2) 0.1457(3)

= [x

w (Fobs -

wF&ll’* and R(F) = c IFobs- FcJl C Fob, where Fobsand Foalsare the observed and calculated structure

factors. Unit weights w were chosen.

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KN. Molchanov et al. Physica C 229 (1994) 331-345

grated intensities were determined using the method of Lehmann and Larsen [ 261. The absorption correction factors for a spherical sample were interpolated from the tabulated values of Weber [ 271. The stability of the primary beam and the equipment was monitored by systematic measurements of intensities of three test reflections. In the experiments performed at 296, 160, 130 and 90 K, the test reflection intensities did not show any systematic time dependence. The experiment at 60 K was conducted in two stages, six days each, and between these periods the sample was kept at room temperature. The test reflection intensities changed about 4% from the starting values during both of these periods. The intensity of the standard reflections versus time could be expressed as quadratic polynomials, which were used to calculate the proper scale factors for the data. The maximum sin f3/n was 1.22 A-’ for the 160 K data set and 1.OOA-’ for the other sets. The observed intensity data contained 1844 (296 K), 1408 ( 160 K), 2664 (130 K), 3154 (90 K) and 1482 (60 K) reflections, of which 6 19, 89 1,627,626 and 620 reflections were unique. Averaging the symmetry equivalent reflections and rejecting discordant reflections led to Rfactors of 0.040, 0.024, 0.037, 0.034 and 0.027.

3. Structure model and refinements The structure model was refined by a least-squares method with the program system PROMETHEUS [28]. Since the number of independent reflections in each data set exceeds considerably the number of refined parameters, only the 466 most reliably measured reflections, present in all data sets, were used in the refinements. In the starting model the atoms were placed on special positions of the space group 14/mmm (see Fig. 1) according to the data reported earlier [ 5,9,10], with the exception that the oxygen atom of the Tl-0 layer (03) was placed in its ideal position at the four-fold axis. The atomic scattering factors and dispersion corrections were taken from the International Tables for Crystallography [ 291. The corrections for extinction were calculated following the theory of Becker and Coppens [ 301. The best agreement was achieved using the model of isotropic extinction (type I, Gaussian distribution). Refinement of the site occupancies yielded a seem-

BaW)

Tl0(3) Tm3)

Fig. 1. Fragment of the Tl-2212 structure (T = 60 K). The numbering scheme and the Cu-0 bonds are shown. The thermal ellipsoids are drawn as 95W surfaces. In the upper part of the figure the 03 atoms in the double Tl-0 layers are presented as large flattened ellipsoids. In the lower part an alternative presentation of disordered 03 atoms enclosed in an ellipsoidal cavity is given. For clarity, the dimensions of the isotropic spheres are reduced by a factor of two. ing excess of calcium and a deficit of thallium, indicating partial substitution of Tl with a lighter atom and Ca with a heavier atom. Isomorphous replace-

ment of Ca by Tl proved to be the best model. This has been suggested in most other studies [5-l I], although a full Ca site occupancy has also been reported [ 121. According to previous structural studies, the Tl sites are partially either vacant [ 7,8,10,12] or isomorphously replaced by Ca [ 5,9,10,12] or Cu atoms [ 6,251. From crystallochemical reasons, discussed in detail in Ref. [ 25 1, Cu seems a better choice than Ca. However, placing Cu in the Tl site did not result in a significant lowering of the R-factors, and the subsequent refinements of our structure model included the Tl site deficiency, without any additional atoms. Refinements from the data measured at different temperatures showed that the mean Tl site occupancy was 92.6(6)% of the full occupancy and that 12.5(3)%

335

V.N.Molchanovet al. PhysicaC 229 (1994) 331-345

of the Ca sites were occupied by Tl atoms. The differences of the site occupancies from the mean occupancy were within two standard deviations for both the Ca site and the Tl site. According to the refined site occupancies, the chemical formula of the single CryGil of our study is Tli.ssBaz (Ca0.s7T1a.i3)Cu2Gs, with a possible occupation of Cu atoms in the main Tl atom site. The site occupancies were fixed to their average values in the final refinements of all data sets. Refinement of the above model leads to unusually large anisotropy in the thermal motion of Tl (91 = 0.028 w2, U33 = 0.011 A2 at 296 K), as observed also in all previous studies. The thermal-vibration ellipsoid is squeezed along the c-axis while the ellipsoids of the other metal atoms are elongated. Since it is doubtful if this large thermal motion is physically reasonable for a heavy atom like thallium, the possibility of static disorder was considered. Estimating the static contribution to the Uij, like in Ref. [ 71, from the results at the two highest temperatures, 296 and 160 K, gives a Tl atom shift of about 0.11 A in the direction of the u-axis (or b-axis). Refinements of alternative models with thallium atoms displaced off the site 4e to the sites 16m or 16n yielded a significant lowering of the agreement factor (equal for both models). The difference electron density maps, constructed using the model with Tl at the site 4e, showed eight poorly defined maxima (see Fig. 2), suggesting that the Tl atoms are displaced from their average site ($, 4, z) to a general site (i + Ax, f + Ay, z). This model did not sustain refinement, but restricting Tl in comers of a regular octagon (Ax = 0.4142Ay) led to good convergence. According to statistical significance tests [ 3 11 of the R-factor ratio on the level 0.005, this model was clearly better than the other models mentioned above. However, probably due to severe correlations between the parameters, both the static displacements (Ax, Ay ) and the thermal parameters of Tl showed very irregular temperature dependencies, indicating ambiguousness in the separation between the static and dynamic effects. Therefore, an alternative two-step refinement was performed: first with an unrestricted general position and an isotropic thermal parameter of Tl, then with the fixed Tl position and anisotropic thermal parameters. This procedure reduced the correlation problems substantially and led to more normal temperature dependence of the parameters and to clearly smaller (though possibly

-0.5

0 x(A)

0.5



Fig. 2. Difference electron density around the Tl site in the xy-plane (T = 60 K). Contour intervals 0.25 e Am3, negative contours dashed, zero contours omitted. Eight maxima (2.6 e Aw3) at comers of a nearly regular octagon. The radius of the remainder electron density ring is about 0.167 (0.64 A). The estimated standard deviation of the electron density in the ring is 0.2 e k3. underestimated)

standard

deviations

of the parame-

ters. The R-factors are practically the same as for the octagon-restricted model. The obtained room temperature displacements are Ay = 0.16 A and Ax = 0.05

A, i.e. the total displacement is about 0.17 A. Sasaki et al. [32] reported the existence of anharmanic thermal vibrations for Tl and Ba atoms in Tl2212 at room temperature. They described successfully the nonspherical effects observed in the difference Fourier maps around Tl and Ba by using the Gram-Charlier series expansion of the Gaussian density function. The difference density around Tl obtained in the present study resembles closely to the one presented by Sasaki et al. As for the Ba atom surroundings, the similarity is not so obvious. Retinement of anharmonic temperature parameters of Tl and Ba up to the fourth rank yielded large values for cl i3 and di I 1I, in accordance with the results reported in Ref. [ 321, and in addition, also for di 122. It is well-known that anharmonic temperature factors and split positions are two alternative ways of structure evaluation. Usually anharmonicity drops substantially upon cooling. However, we did not observe any essential changes in the Tl atom shifts upon cooling the sample from room temperature down to 60 K. Further, the Gram-Charlier formalism used for X-ray data analysis may successfully represent

336

KN. Molchanov et al. Physica C 229 (1994) 331-345

bonding effects in the valence charge density, in addition to - or instead of - the thermal motion [ 331. The 160 K data, which was collected up to 1.22 A-’ in sin e/n, provided a possibility to a rough division between valence and core scattering by refining the low-order data separately from the high-order data. A cut-off value of 0.85 A-’ was chosen. The anharmanic parameters of Tl obtained from the two subsets of data did not differ significantly from each other, while the clearly non-zero parameters of Ba refined from the low-order data changed to values differing insignificantly from zero, when obtained from the high-order data. So, in conclusion, we believe that static disorder of the Tl (and 03) atoms is a more realistic model than anharmonic thermal motion, although anharmonic effects may contribute to the structure to a certain extent. According to the Fourier and difference Fourier maps of the 03 atom surroundings, there is no doubt that these atoms are highly disordered in the thallium-oxygen layers. Refinement with 03 at the average site 4e (00~) leads to abnormally large and highly anisotropic thermal parameters ( ~711= 0.14 A*, U33 = 0.014 A2 at 296 K). Introducing displacements from the ideal site to multiple positions with partial occupancies leads to more normal values of the thermal parameters. For example, refinement of the model with 03 at the site 16n (Oyz), using the room temperature data, results in the displacement y = 0.39 A and the isotropic thermal parameter B = 2.3 A*, while the equivalent isotropic thermal parameter of 03 at site 4e is Beq = 7.7 A*. The model with 03 at the site 16m (xxz) yields displacements with x = 0.25 A (i.e. 0.35 A along (110)) and the thermal parameter B = 2.6 A*. Unfortunately, choosing the best displacement model is not possible on the ground of the R-factor value, which is almost completely insensitive to the 03 atom shifts. However, especially in the case of simultaneous shifts to positions 16n and 16m, a visible depletion of the difference Fourier maps takes place around 03. Introducing of the 03 atom shifts has practically no effect on the values of the other relined parameters, and in the final retinements - in the study of the temperature dependence of the parameters - 03 was placed in the site 4e. Most authors [5,7-121 report 03 atom displacements from the average site by 0.34-0.60 A to the site 16n (Oyz ). Cox et al. [ 9 ] refined also an alterna-

tive model with the 03 atom shifted by 0.38 A to the site 16m (xxz), but this model yielded a poorer fit. Muradyan et al. [ 251 reported displacements of both 03 and Tl atoms along the (110) direction; the 03 atoms were shifted by 0.26-0.32 A and the Tl atoms by 0.14 A to the sites 16m. Dmowski et al. [ 341 found strongly correlated local displacements of both Tl and 03 atoms from the high-symmetry sites using atomicpair-distribution analysis of pulsed-neutron scattering data. The reported displacements were 0.32 A for Tl and 0.37 A for 03, both shifts approximately along the (110) direction. The 03 atom displacements obtained in our study agree well with these results, but the Tl atom displacement is about one half of the value reported in Ref. [ 341. As pointed out by Dmowski et al. [ 341, it is reasonable to assume that the Tl and 03 atoms are not displaced randomly from the high-symmetry positions. They proposed two different atomic contigurations, where the thallium and oxygen atom displacements lower the local symmetry of the structure to orthorhombic. Since these configurations are equally likely, the resulting structure would be a mixture of these two structures, and the local ordering would not develop into long-range order. In another model, suggested by Simonov et al. [ 351 for a statistically tetragonal Y-123, the crystal on the whole would retain its tetragonal symmetry due to a statistical combination of locally orthorhombic regions rotated 90” relative to each another. Formally, this situation does not differ from usual twinning and it should thus lead to broadening or splitting of the reflection profiles. However, the analysis of the reflection profiles of the studied Tl-22 12 sample did not reveal such behaviour. The Tl atom bonds to six oxygen atoms with average in-plane bond lengths of about 2.7 A (Tl-03 1 and outof-plane distances of about 2.0 A (Tl-03, Tl-021. The average in-plane Tl-03 distance is significantly longer than the sum of ionic radii (2.28 A). When the Tl and (or) 03 atoms are shifted from their ideal sites, shorter Tl-03 bonds are allowed. If 03 is shifted to the 16n sites, two short (2.4 A) and two long (3.0 A) bonds are formed. Thus the first oxygen coordination of thallium would contain three pairs of oxygen atoms, with distances about 2.0, 2.4 and 3.0 A, typical for all thallium oxide high-TC superconductors. Shifting both Tl and 03 atoms gives even more choices, and if the (locally) ordered configuration of Dmowski et

VW.Molchanovet al.PhysicaC 229(1994)331-345 al. [34] is assumed, the nearest-neighbour in-plane distances come very close to the expected values. The Cu atoms are located in tetragonal oxygen pyramids, similar to those in Y-123, except that the apical oxygen is located at a larger distance from the copper atom. The oxygen atoms are arranged in the opposite way to the coordination of thallium: the in-plane Cu-01 distance ( 1.9 A) is much shorter than the apical distance Cu-02 (2.7 A). The Ca atoms are surrounded by eight oxygen atoms forming a tetragonal prism, and the Ba atoms are coordinated by nine oxygen atoms (capped square-antiprism) . Before a detailed description of the possible structural changes in the vicinity of T,, it must be emphasized that all our results concern the averaged structure. Correlated local shifts or movements, as well as partial ordering of atoms in the mixed sites, which were not taken into account in our structural model, may still be accumulated in the refined parameters. Changes in the local atomic arrangements near T, (as detected by Toby et al. [ 361 for the same compound) would affect the centre-of-mass positions and could, in principle, be seen in the average structure model as small changes in the atomic positions and thermal parameters.

4. Temperature

dependence of the structure

Comparison of the data measured at various temperatures did not reveal any substantial changes in the structure during the superconducting phase transition. The symmetry of the crystal, as well as the metrics of the lattice, were retained in the transition. The temperature dependence of the unit cell volume did not show any discontinuities, which agrees with a secondorder phase transition. A more detailed analysis of the temperature dependence of the lattice parameters for another crystal of the same compound [ 371 did not reveal any significant discontinuities, either. However, these results indicated a small (of same order as the experimental error) anomaly in the length of the caxis near the critical temperature of superconductivity. The effect was of the same type as the one observed by Srinivasan et al. [ 201 for Y- 123, where the lattice parameter c was observed to increase abruptly at the transition temperature, recovering its original value as the temperature was reduced below T,. In the mea-

337

surements of Ref. [ 37 ] for Tl-22 12 the effect was too faint to be identified as a discontinuous change, and more experimental points would have been required in the very vicinity of Tc. However, some interesting features were observed in the temperature dependencies of the structure parameters, especially the thermal parameters and interatomic distances, which will be discussed in the following. 4.1. Atomic positions and thermal parameters The relative positions of atoms in the unit cell and the thermal parameters are presented in Table 1. In order to eliminate the effect of thermal contraction of the unit cell, it is most convenient to compare the relative positional parameters. The relative z-coordinates of the metal atoms decrease clearly, when the temperature is lowered from room temperature to 160 K. Below this temperature the changes are less pronounced and mainly within the experimental errors. It seems, however, that the z-coordinates have a minimum value near Tc. Despite of the lower experimental accuracy in determining the z-coordinates of the oxygen atoms, it can be seen that the temperature dependence of the z-coordinates of the 02 and 03 atoms is very similar to that of the metal atoms, showing a minimum for z near Tc. The z-coordinate of the 0 1 atom behaves differently, it has a maximum value in the vicinity of T,. For all oxygen atoms, the z-coordinates are almost equal at the lowest temperature and at room temperature. In conclusion, in the vicinity of Tc the oxygen pyramid of copper is slightly compressed along the c-axis, while the double thallium-oxygen layer is expanded. The most striking changes in the thermal parameters Uij occur for the 01 atom (Fig. 3a). When the temperature is lowered from 130 to 90 K, the parameter U3s shows an abrupt decrease. The corresponding drop in the thermal vibration amplitude, u3 = 6, is about 20%. This observation is, at least qualitatively, in accordance with the results of Toby et al. [ 361, who reported correlated Cu and 01 atom displacements perpendicular to the Cu-0 planes and a difference in the oxygen atom arrangement above and below T,. They also suggested that the 01 atom displacements are of dynamic origin. The thermal parameters of Ca (Fig. 3b) show same kind of temperature dependencies as the parameters of 01: the differ-

338

KN. Molchanov et al. Physica C 229 (1994) 331-345

x

16 14 12 210 d

8 6 4 2

t

0

50

100

150

200

250

300

200

250

300

T 6)

x 10 12.

-3

(b)

Ca

I

0

;

I

I

50

1OfJ

1.50

T (K)

Fig. 3. Temperature dependence of the thermal parameters of 01 (a) and Ca (b). The error bars equal to one standard deviation. ence between the axial (c) and in-plane (ab) components tends to increase in the vicinity Tc.Similarity is expected, since the Ca cation is situated in a cage of eight 01 atoms, and it is therefore probable that the thermal vibrations of Ca and 0 1 are, to some extent, correlated. The decrease in the Us3 of 0 1 is clearly higher than the corresponding changes for the metal atoms. As for the other oxygen atoms, the thermal parameter Us3 of the 03 atom behaves very similarly to that of 01, especially above T,,where the parameters are practically equal to each other. Below T,it shows first an abrupt decrease, then an abrupt increase. It must be noticed, however, that due to the poor localization of the 03 atom, the estimated standard deviations of the parameters are much higher than for the 01 atom. Further, the parameters of the 03 atom are extremely sensitive to small changes in the refinement proce-

dure (e.g. different weighting scheme of reflections), while the parameters of the other atoms are quite stable. The values of Us3 of the 02 atom are generally slightly higher than those of the 0 1 atom. Below Tcthe changes in Uss of the 02 and 03 atoms occur in opposite directions. The thermal motion of 02 is markedly isotropic in comparison to the thermal motion of the other atoms. Ion channelling experiments for single crystals of high-Tc superconductors, e.g. Y-123 [22] and (Bi,Pb)-22 12 [ 381, have shown an abrupt change near Tcin the thermal vibration amplitude of Cu in the ab-plane, while in neutron powder diffraction measurements no anomaly has been observed. No abrupt changes were observed in the present study, either, but some other interesting features can be seen. The Ull of Cu decreases to its minimum value already at 160 K and below this temperature it is nearly constant, increasing slightly at the lowest measured temperatures. This behaviour is similar to that observed for the Cu-0 bonds of Tl-2223 [39]. Further, Cu has clearly the smallest in-plane thermal vibrations of all atoms in the structure. The Uii of barium and calcium, which are almost equal to each other at all temperatures, have values at least two times those of copper UI1.Thallium seems to be the most prominent atom to have a jump-like decrease in the in-plane thermal vibration amplitude during the temperature lowering through Tc.However, since the thermal parameters of Tl are severely correlated with the positional parameters, they are also the most uncertainly determined. The ion channelling experiments [22,38] probed only the in-plane thermal vibrations, but according to our results it seems that abrupt changes in the vicinity of Tccould rather occur in the axial vibrations. The thermal parameters Us3 of the metal atoms continue decreasing below 160 K, while the parameters lJl1 are already close to their minimum values. The average amplitude ratios dm for Ba and Ca atoms are about 1.4 and 1.2, respectively, while for the Cu atom it is substantially larger, about 2.3. The highest values of U33 are found for the Ba atom, the values for Cu are slightly smaller, and the smallest Us3 are found for the Ca and Tl atoms. Practically all U,,, even those of the oxygen atoms, show changes in the slopes of the temperature curves in the vicinity of Tc.Although the number of experi-

339

V.N. Molchanov et al. Physica C 229 (1994) 331-345

mental points in defining the temperature dependencies of the thermal parameters is too small for any firm conclusions, it seems that accurate measurements of thermal parameters might be a unique method for investigation of second order, or nearly second order, phase transitions. Experiments in this direction are in progress. 4.2. Interatomic

distances

1.928 (a)

I

8 9 t; s

1.926

2-m 1.921

cu-01

II

1.925

Selected interatomic and interlayer distances are listed in Tables 2 and 3. The copper atom is situated in a square pyramid of oxygen and it deviates slightly off the pyramid base. The deviation (Cu-01 in Table 3) stays approximately constant during the temperature lowering. However, due to the changes in the 01 atom position, small abrupt variations in the vicinity of T, can be seen. The in-plane distance Cu01 shows a clear shortening during the transition to superconducting state (Fig. 4a). Curves fitted independently to the experimental points above and below TC do not meet when extrapolated to the transition point. Since the Cu and 01 atoms have almost identical z-coordinates, the temperature dependence of the interatomic distance is practically that of the lattice parameter a. The distance from the Cu atom to the apical oxygen 02 has a minimum near the critical temperature, and below T, it is abruptly increased (Fig. 4b). The minimum in the Cu-02 distance might be related to the cusp-like behaviour observed in the vibration frequency of the 02 atom in Tl-2212 [40]. Because of the relatively large standard deviations in comparison to the magnitudes of the effects and because of the very small number of different experimental temperatures, further studies at temperatures closer to the phase transition would be required to confirm the behaviour of the copper-oxygen bonds. The significance of the observed effects will be discussed in more details in Section 5. It is highly probable that the shortening of the Cu-01 distance is a unique signal of changes in the copper-oxygen chemical bonding, correlating with changes in the electronic structure during the transition to the superconducting state. The temperature dependence of the Ba-0 distances is shown in Fig. 5. All these distances exhibit a minimum near T,. The Ba-03 distance shows the most anomalous behaviour, while changes in the other dis-

4+ 0

50

100

150

200

250

300

200

250

300

T(K)

0

50

100

150

T W)

Fig. 4. Temperature dependence ror bars as in Fig. 3.

of the Cu-0 distances. Er-

tances (Ba-01, Ba-02) are clearly smaller, although visible. The results indicate a contraction of the oxygen polyhedron of Ba in the vicinity of TC. The deviation of the 02 layer from the Ba layer (Table 3) is practically constant within the whole measured temperature range. The Tl-02 and Tl-03 (x 1) distances (Table 2) show a weak tendency for a maximum near TC. The former distance is related to the distance Cu-02 and the latter one to the distance Ba-03, which both have a minimum near the critical temperature. When comparing the distances from a metal atom to the 03 atom, one has to keep in mind that in the refined model the 03 atom was placed in its average site. If the 03 atom displacements would be taken into account, the Tl-03 ( x 4) distances would have a much broader range of possible values. The separation between the oxygen layers 03-03 (along the c-axis) increases very clearly in the vicinity of Tc (Fig. 6). The

KN. Molchanovet al. PhysicaC 229 (1994) 331-345

340 Table 2 Interatomic

distances

Temperature

T

(8) 60 K

90 K

130K

160K

296 K

2.004(9)

1.999(10) 1.980(17) 2.599-2.856( 11)

1.996(10) 1.962(16)

1.998(9) 1.971(13) 2.583-2.880(9) 2.797(5)

Tl-02 Tl-03

x1 x1

1.990(10) 1.949(21)

Tl-03 Ba-01 Ba-02

x4 x4 x4

2.594-2.863(11) 2.788(5)

Ba-03 Ca-01

xl x8

cu-01

x4

cu-02

xl

cu-cu 01-01

x1 xl

2.812(3) 2.878(21) 2.460(4) 1.9248(2) 2.683(11) 3.154(2) 3.065 (7)

1.995(14) 2.599-2.853( 2.784(5) 2.810(2)

11)

2.835( 14) 2.464(3)

2.788(5) 2.811(3) 2.851(17)

1.9249(2)

2.463(4) 1.9254(2)

2.670( 10)

2.676( 10)

3.155(2) 3.078(6)

3.157(2) 3.072(7)

2.595-2.863(11) 2.789(5) 2.812(3) 2.871(16) 2.462(4) 1.9255(2) 2.681(11) 3.157(2) 3.071(7)

2.816(2) 2.866( 13) 2.466(3) 1.9278(2) 2.689(9) 3.166(2) 3.075 (6)

Table 3 Interlayer distances along c-axis (A) Temperature Ca-Cu Cu-Ba Ba-Tl Tl-Tl 03-03 cu-0

1

T

60 K

90 K

130 K

160 K

296 K

1.5769(15) 1.9735(17) 2.6944( 11)

1.5773(13)

1.5783(15) 1.9738(17) 2.6953(11)

1.5787( 15) 1.9749(16) 2.6964(10)

1.5831(13) 1.9818(14)

2.1297(11) 1.82(2)

2.1304(11) 1.78(2)

0.042(6)

0.043(6) 0.706( 10) 0.17(2)

1.9728(15)

2.1266(12)

2.6959(9) 2.1285(10)

1.76(3) 0.044(6)

1.85(2) 0.038(5)

Ba-02

0.710(10)

0.696(9)

0.702( 10)

Tl-03

0.18(2)

0.14(l)

0.16(2)

Tl-Tl interlayer distance decreases only slightly with decreasing temperature, since the relative Tl-Tl distance (OS-2z(Tl)) is increasing. Thus, in comparison to the 03-03 distance, it is almost constant. The difference in the magnitudes of these changes causes the abrupt variations in the buckling of the thalliumoxygen layers (Tl-03 distances in Table 3). The metal-metal distances can be determined more accurately than the metal-oxygen or oxygen-oxygen distances, and in addition to the Tl-Tl distances, also other metal-metal distances along the c-axis are listed in Table 3. For studying the temperature dependence of the distances, only the components parallel to the caxis are needed, since the perpendicular components depend solely on the size of the unit cell and follow the temperature dependence of the lattice parameter a. It

2.6987(9) 2.1313(11) 1.80(2) 0.045(5) 0.711(9) 0.17(l)

can be seen that the metal-metal distances along the c-axis reduce naturally with decreasing temperature. The Ca-Cu (Cu-Cu) and Cu-Ba distances decrease rapidly to almost constant values while the Ba-Tl and Tl-Tl distances behave just the opposite way, decreasing first slowly, then more rapidly. The total relative reduction in the Ca-Cu and Cu-Ba distances is about twice the reduction of the Ba-Tl and Tl-Tl distances (Fig. 7).

5. Correlation between structure and superconductivity The similarity of the layered structures and crystallochemical properties of all copper oxide superconductors has led to the general conception that the superconducting behaviour is linked to the presence of

KN. Molchanov et al. Physica C 229 (1994) 331-345

341

2.90 I

(a) 2.88 3

B 2.86 E 2.84

2.82 0.996 T (W

/

I

0 2.82

I

50

100

150 200 T W

250

300

Fig. 7. Metal-metal interlayer distances relative to the their room temperature values. 2.81 9 8 f 2.8a s 2.19

2.78

50

loo

150 200 T(K)

Fig. 5. Temperature dependence ror bars as in Fig. 3.

2.2 0 2.1 -

=,=

I ! I I

250

300

of the Ba-0 distances. Er-

0

= Tl-Tl

03-03 t

I 0

50

100

150 200 T W)

250

I 300

Fig. 6. Temperature dependence of the Tl-Tl and 03-03 interlayer distances in the double Tl-0 layers. Error bars as in Fig. 3 (for the Tl-Tl distance smaller than the size of the symbols).

the copper-oxygen layers, while the other layers (or chains) serve as charge reservoirs. A good description of the charge transfer concept in the case of Y123 is presented in Ref. [41]. In the case of Tl-2212 (see Fig. 1), the charge reservoir block of the structure involves two thallium-oxygen layers packed according to a rock-salt motive. The superconducting perovskite-like blocks consist of two CUOS pyramid layers, with Ca cations in between and Ba cations located at both sides. These two different blocks are alternating in the structure. It is generally accepted that the charge carriers in thallium oxide high-T’. superconductors are holes in the CUOZ planes, and charge transfer occurs from these planes to the TlO planes, leaving holes in the former. The replacement of some Ca atoms by Tl atoms, as well as vacancies or Cu atoms at the main site of Tl in Tl-2212, perturb the stoichiometry and alter the charge carrier concentration of the compound, thus affecting the value of T,. The observed increase in the interlayer distance 03-03 near T, (Fig. 6) may indicate a change in the degree of charge transfer between the thallium-oxygen and copperoxygen layers. The two interlayer distances Tl-Tl and 03-03 are proposed as characteristics for the charge reservoir block in Tl-22 12. The Ba ions are believed to participate in the charge transfer and, moreover, in the chemical bonding with the nearest oxygens [ 421. The close location of the Ba atom to the copper-oxygen planes makes it sensitive to changes in the superconducting part of

342

KN. Molchanov et al. Physica C229 (1994) 331-345

the structure. In the present study we observed the movement of Ba cations towards the copper-oxygen planes: the relative contraction of the Cu-Ba distance in the direction of the c-axis was larger than that of the other metal-metal distances (Fig. 7). Further, the observed stiffening of the barium atom surroundings in the vicinity of Tc (Fig. 5) may reflect the role of this atom in the charge transfer process. In the analysis of the temperature dependencies of the structure parameters, special attention was paid to the atoms in the copper-oxygen layers and close to them. In the following we shall consider the origin of the irregular changes observed in our study in the Cu-0 distances of Tl-2212 near the phase transition (Fig. 4), and discuss the possible connection of these effects to the superconducting coupling of the charge carriers. It should be pointed out that, despite of the large number of both experimental and theoretical studies of the phenomenon of high-Tc superconductivity, there is no generally accepted mechanism of the coupling of the charge carriers. In particular, it is discussed whether the coupling occurs in the impulse space (i.e. according to the BCS mechanism) or in the real space, with the formation of Bose-particles of the bipolaron type and their subsequent Bosecondensation [43]. We attempt to provide a qualitative explanation - without regard to the detailed mechanism of the coupling - of the observed structural changes of Tl-22 12 near Tc. However, before formulating the model, we will briefly review some essential properties of the high-T, superconductors. All the copper-oxide high-T, superconductors contain plane-square CuOZ nets as a common structural element. The oxygen atoms form a net of squares, half-filled with copper atoms in a staggered arrangement. In part of the structures there are oxygen atoms also above and beneath the Cu atoms, completing the squares of the main net to elongated CuO6 octahedra, while e.g. in Y-123 and in Tl-2212 oxygen atoms are located only on one side of the square to form a tetragonal CuOs pyramid about the copper atom, and in some structures the copper atom remains coordinated by a flat oxygen square, CuO.,. Since these structural fragments contain divalent copper ions in a pseudo-octahedral site, possibly with one or two oxygen vacancies, they can be regarded as Jahn-Teller centres. Each CuOz net can be inter-

preted as a co-operative Jahn-Teller system, which is at a ferrodistortive state with uniformly distorted (extended along the c-axis) pseudo-octahedral structural fragments. The local symmetry of such fragments is close to tetragonal. The typical Cu-0 bond lengths in the basic plane are about 1.9 A, while the distances up to the apical oxygen atoms are in the range 2.22.8 A (see e.g. Ref. [3]). Such distances are characteristic also to other oxygen compounds of divalent copper, containing distorted pseudo-octahedral JahnTeller centres. In a single regular CuO6 octahedron the local crystal field about the central copper ion splits the fivefold degenerate 3d-level of this ion into the lower three-fold degenerate level T2, (orbitals 3d,,, 3dX, and 3d,,) and the upper two-fold degenerate level Eg (orbitals 3dX2_y2and 3d,2). There are six electrons at the level Tzg and three electrons at the level Eg. Tetragonal distortion at the Jahn-Teller centre, as well as one or two oxygen vacancies in the axial positions for the CUOS or CuO4 centres, eliminates the degeneracy of the orbital doublet Eg. As a result, the 3d,2 orbital of the Cu2+ (3d9) ion is stabilized and filled by two electrons, while the 3dX2_,,2orbital is destabilized and filled by a single electron. It is known from the Jahn-Teller theory (see e.g. Ref. [ 441) that the symmetry and amplitude of distortion of the coordination sphere are closely related to the electron populations of the Jahn-Teller orbitals, because these orbitals are characterized by an anisotropic electron density distribution. Therefore, due to the antibonding character of both the 3d,2_r2 and the 3d,2 orbitals in a local CuO, centre (n = 4, 5, 6), an increase in the population of the 3d,2 orbital would result in elongation of the axial Cu-0 distances and in shortening of the Cu-0 distances in the CuO2 plane. An increase in the population of the 3d X2_y~ orbital would result in just the opposite effect, i.e. shortening of the axial bonds and elongation of the equatorial ones. The correlation between the relative populations of the 3d ,I_~z and 3d,2 orbitals and the variation in the Cu-0 distances in a single CuO, polyhedron is retained in the condensed CuOz sheets of the high-T, superconductors, where the populations of these orbitals are no longer integers. In other words, any variation in the populations of these orbitals should cause some structural changes in the first coordination sphere of

VW Molchanovet al. PhysicaC 229 (1994) 331-345

each copper ion. Thus, the reduction of the Cu-0 bonds in the CuO2 plane, observed experimentally for Tl-2212 in this work, as well as the possible simultaneous increase of the apical Cu-0 distance, upon the transition from the normal phase to the superconducting one - and similar effects observed for YBazCus0-r [ 171 - could be accounted for by a decrease in the effective population of the 3dX2_,,2 orbitals of copper. In the following we shall discuss how this decrease can be related with the superconducting phase transition. Experimental studies using photoelectron spectroscopy indicate that doping, or an increase in the oxygen content, does not lead to a further oxidation of the divalent copper to the trivalent state, but to the formation of holes in the 2p orbitals of the oxygen atoms in the CUOZ nets [45]. Due to the alternating arrangement of the copper and oxygen atoms, the corresponding oxygen 2p band is not very wide (less than 1 eV). Thus the 2p orbitals in neighbouring oxygen atoms can interact only indirectly via the 3d states of copper. Accordingly, the process of quantum jump of a hole from a 2p orbital of one oxygen atom to a 2p orbital of another oxygen atom occurs through an intermediate virtual state of hole migration to a copper atom (trivalent copper, Cu3+ ( 3d8 ), is formed) and a subsequent movement of the hole to the 2p orbital of the other oxygen atom, i.e.: 0’-...cu2+

. ..02-+02-...cu3+...02-

o*-

+

. . . (p+

. . . o’-.

The hole movement along the oxygen band in the CUOZ plane brings about a decrease in the population of the copper 3d orbitals, which play the role of virtual intermediate hole acceptors. As known from the experimental and theoretical data available, in particular from the numerous band structure calculations of various high-Tc superconductors, e.g. Refs. [46,47], the 2p orbitals of oxygen and the 3d X~_y~, 3d,z orbitals of copper make the largest contribution to the band states near the Fermi level. The role of the 3d X~_y2orbital turns out to be much more important than that of the 3d,2 orbital, because the former one is higher in energy (consequently, populated only by one electron) and overlaps better with the 2p orbitals of oxygen than the latter one. Therefore, any variations of the charge carrier system in the CuOz plane, including the superconducting phase

343

transition, should first of all be reflected in the population of the copper 3d,2_y2 orbitals. It is also reasonable to assume, that an increase in the hole concentration would cause a greater depopulation of the 3d,z_y2 orbitals. Another important fact to be pointed out is, that the coherence length and the characteristic size of the superconducting pairs in the CuO2 sheets are only a few angstroms [ 451, which is much less than in the ordinary superconductors. That is, the 2p holes which form the pair should be located on oxygen atoms belonging to one or a few neighbouring unit cells. This fact plays a key role in the model we formulate in the following. In the superconducting phase, where the hole motion within the CUOZ planes is strongly correlated, the presence of a 2p hole about a given copper ion should, due to the small size of the pair, mean an enhanced probability (as compared to the normal phase with non-correlated hole motion) of a simultaneous presence of another hole nearby. This can be interpreted as an increase of the local effective hole concentration during the transition from the normal phase to the superconducting one. The total average hole concentration remains, of course, unchanged upon the transition. Because of the above-mentioned sensitivity of the population ofthe copper 3dXz_y2orbital to the hole concentration variation, the average effective population of this orbital should be decreased below T,. This leads, consequently, to a reduction of the Cu-0 distances in the CuO2 plane and a simultaneous increase of the Cu-0 distance along the c-axis. The former effect was clearly observed in our structural study. As for the latter effect, any firm conclusions could not be made. Finally, two important comments should be noted. First of all, the considered qualitative model can be applied to all high-Tc superconductors containing CUOZ planes, since only these structural elements are essential to the model. Furthermore, the model does not include any details of the pairing mechanism and is based only on the fact that the effective size of the superconducting pairs is comparable with the cell size. In conclusion, the irregular temperature dependence of the structure parameters of Tl-2212 near T, invokes examination of analogous effects in other related layered high-T, superconductors. As pointed out above, a similar effect has previously been observed

344

KN. Molchanov et al. Physica C229 (1994) 331-345

only in Y- 123 [ 17 1. Therefore, it would be very important and interesting to carry out a series of direct experimental measurements of the electron density of the copper 3d,z_,z orbitals. Various precision techniques, including construction of deformation electron density maps from diffraction data above and below T,, should be used to reveal the predicted jump of the effective population of the 3d,z_,2 orbitals.

Acknowledgements The single crystals of Tl-22 12 were grown at the Institute of Solid State Physics (Russian Academy of Sciences) and were kindly supplied for this structural investigation. The authors thank R.P. Shibaeva and I.F. Schegolev for cooperation and for fruitful discussions of problems connected to high-Tc superconductivity. The work carried out at Brookhaven National Laboratory was supported under contract DEAC02-76CHOOO 16 with the US Department of Energy by its Division of Chemical Sciences, Office of Basic and Energy Sciences. T. Koetzle and J. Hanson are gratefully acknowledged for providing the X7B beamline facilities for use of one of the authors (M.K.B.). The Academy of Finland, the Russian Academy of Sciences and the Russian Fund for Fundamental Research (Grant No. 93-02-2002) are acknowledged for financial support.

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