A new modelling approach to superconductor layered structures

PERGAMON

Solid State Communications 110 (1999) 387–392

A new modelling approach to superconductor layered structures L.E. Depero*, L. Sangaletti, B. Allieri, E. Bontempi Istituto Nazionale per la Fisica della Materia and Dipartimento di Ingegneria Meccanica, Universita di Brescia, Via Branze 38, 25133 Brescia, Italy Received 22 October 1998; accepted 8 February 1999 by C. Calandra

Abstract The analysis of the structural data of high Tc superconducting cuprates (HTSCs) shows that large differences exist in X-ray diffraction (XRD) patterns collected from powders and thin films with respect to the single crystal case, depending in many cases on the synthesis routes and material treatments. These differences are often disregarded and the assessment on the purity of the crystalline phase is made on the basis of XRD pattern indexing only. However, when relative intensities of XRD reflections belonging to the same family (e.g. (001)) differ from those obtained from the single crystal structure, the simple pattern indexing is not sufficient for the structural characterization and important structural features are missed. These might be helpful for discussing magnetic or electrical behaviour of specimens, as the related properties may depend on the structural correlation along the c axis. In this article a structural modelling of cuprates of the Bi–Sr–Ca–Cu–O family is proposed by considering the electronic density in the projection perpendicular to the layers of the structure. In particular, the structures of Bi2201, Bi-2212 and Bi-2223 HTSCs were reduced to monomers and intergrowth effects are simulated by generating polymers with different percentages of these phases. By using this model, much information in terms of intergrowth and site occupancy can be gained from a careful analysis of intensities and widths of 001 reflections. 䉷 1999 Elsevier Science Ltd. All rights reserved. Keywords: A. Disordered systems; A. High Tc superconductors; A. Thin films; C. X-ray scattering; D. Order–disorder effects

Superconductors of the Bi–Ca–Sr–Cu–O family (BCSCO) have structures based on BiO–SrO–CuO– CaO layers: a rocksalt-derived slab formed by two BiO layers and a perovskite-derived slab containing n CuO2 layers [1]. The ideal structure of these compounds is determined by the sequence of these layers. The frequent phases are Bi-2201, Bi-2212, and Bi-2223, where n is equal to 1, 2 and 3, respectively. While the average structures were readily identified, the real structures turned out to be complicated, containing displacive and substitutional modulations * Corresponding author. Fax: ⫹ 39-30-3715-788. E-mail address: [email protected] (L.E. Depero)

[2–5]. Moreover, in view of the strong two-dimensional (2D) character of the structure it is difficult to obtain single crystals and, therefore, the majority of the structural data are based on powder diffraction experiments. However, these powders are usually affected by strong preferred orientation. As a consequence, reflections corresponding to the periodicity perpendicular to the layers (here indicated as the c axis) are more intense than the general hkl. Sometimes the preferred orientation, which is usually desired in the film samples because of the anisotropy of the superconducting properties, is so strong that only 001 reflections are present in the pattern.

0038-1098/99/$ - see front matter 䉷 1999 Elsevier Science Ltd. All rights reserved. PII: S0038-109 8(99)00076-9

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Fig. 1. (a) Ideal Bi-2212 phase (left) and corresponding monomer (right). (b) Ideal monomers for Bi-2201, Bi-2212, and Bi-2223.

The starting points of this work are the following observations about the diffraction patterns reported in the literature: First, the relative intensities of the 001 reflections at the same 2u positions depend on the preparation of the powders (see, e.g., Ref. [6]). In the ideal case the ratio among the integrated intensities of reflections belonging to the same family of planes is fixed by the structure, independently on the preferred orientation. Then, changes in the 001 relative intensities mean that the projections of the electronic density on the c axis are different. In particular, the 002 reflection, that characterizes the layer periodicity, is often much lower than expected [7]. Therefore it is not correct to claim for the purity of the crystalline phase when the structure considered for the indexing does not account for changes in the relative intensity within the same family of reflections. Second, the broadening of the 001 reflections in some experiments is clearly not monotonic [8], while in the ideal case the reflection broadening within the same family of planes should increase with the 2u angle, as both size and second order distortions of the crystallites make the reflections width increase with 2u . The alterations in the X-ray diffraction (XRD) pattern concerning both line positions and widths have been studied on the basis of a Hendricks– Teller-type formalism [9,10] but can be applied only if a given type of defect dominates over other possible defects and a sufficiently large volume is affected by the dominant defect. Moreover, even if the intergrowth of different phases can be simulated by stacking fault defects [11] no specific study is reported for HTSCs materials.

While a large variety of studies has been published on structural modulations in HTSCs single crystal where reflections resulting from the modulation in the lattice planes are readily identified and consistently interpreted [2–5,12,13], no systematic investigation is reported on the simultaneous analysis of intensity ratio and line broadening of strongly oriented powders and thin films. XRD pattern indexing only is often considered in powder and thin film samples for evaluating the phase purity of materials that are used for electrical or magnetic measurements. In the present study it is shown that for HTSCs materials this is not sufficient. To assess the purity of the material and gain information on intergrowth and substitutional effects, a careful analysis of the broadening and the relative intensity of reflections belonging to the 001 family must be carried out. In particular, the structural correlation along the c axis is very important for the formation and stability of the vortex structure [14–16], and, as a consequence, a non-destructive evaluation of the intergrowth in oriented powders or thin films is mandatory. The modelling proposed here for polycrystalline BCSCO materials is based on the study of the projection of the structure along the axis perpendicular to the layer. By using the Cerius 2 program, developed by Molecular Simulations Incorporated, the structure is projected and a linear ‘monomer’ containing the structural information in terms of lattice plane spacing and charge density is defined, as shown in Fig. 1(a). In Fig. 1(b) the ‘monomers’ for Bi-2201, Bi-2212, and Bi-2223 structures are shown. The first application of this modelling is a simplified refinement of the structure projection perpendicular to the layers. In almost all the reported XRD patterns of polycrystalline Bi-2212 phase, the intensity of the 002 reflection is much lower than that simulated for the ideal structure. This fact may be determined by cation substitution in the Bi site and/ or by a low occupancy of this site. Accordingly, the electronic densities at the different lattice sites were properly normalized. In the ICSD database [17] Bi2212 structures with similar c axis, but different space group and/or different electronic distributions on the cation are present. In order to simplify the simulation, the same kind of atom (Bi) was put in all sites. The

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Fig. 3. Comparison among the electronic distribution obtained for Model I, Model II, the ideal, Bi2.06(Sr1.7Ca1.24)Cu2O8 (ICSD card number 63217), Bi2(Sr2Ca)Cu2O8 (ICSD card number 68188), and Bi2.1(Sr1.78Ca1.12)Cu2O8 (ICSD card number 203211).

Fig. 2. (a) Rietveld refinement of the pattern reported in Ref. [18]. Only the projection of the electronic distribution perpendicular to the layer was considered. The starting model is shown in the inset. The reflections due to the doubling of the periodicity are indicated by the arrows. (b) Rietveld refinement of the pattern reported in Ref. [18]. Only the projection of the electronic distribution perpendicular to the layers was considered. The starting model is shown in the inset.

refined structural parameters in this approach are, for each site, the atomic coordinate (z) and the occupancy. As an example, an XRD pattern previously reported has been used for the Bi-2212 case [18]. Even if all the peaks in this pattern can be indexed as 001 reflections ˚ , intenof the Bi-2212 phase with a c axis of 30.95 A sities are different from those obtained by an ‘ideal’ Bi-2212 structure or by Bi-2212 patterns found in the literature [17,19]. In particular: (i) the intensity of the experimental 002 reflection is very low while it should be the strongest reflection; (ii) unlike the ideal case, the 004 reflection is absent and the 006 is present; (iii) the relative intensities of 008, 0010 and 0012 are

different from those of the ideal case; (iv) in the experimental pattern odd reflections are present. To have a better model for Bi-2212 powder, Rietveld refinements were performed by considering only 001 reflections. The simplest model used in the refinement (Model I) is shown in the inset of Fig. 2(a), where the calculated and the observed patterns are compared. A peri˚ and the space group P-1 were set as odicity of 15.47 A input. As can be observed, several reflections (indicated by arrows) cannot be indexed with the present choice of periodicity. Indeed, by introducing a peri˚ a better agreement with the experiodicity of 30.95 A mental data is obtained, as shown in Fig. 2(b). Doubling the c axis, the odd reflections were simulated, but a large R-factor is still found (21.5) which is due to the shape of the peaks, that will be discussed later. In Fig. 3 the calculated electronic densities, normalized with that of Bi, obtained for the two refined models and for some reference structures are reported. The main difference in the electronic densities is related to the occupancies and positions in the Bi

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˚ . The non-monotonic structure, with c axis of 15.47 A behaviour detected in the broadening of the even reflections, as well as in that of the odd, will be discussed in the next section. By considering the ‘monomers’ of superconductor structures shown in Fig. 1(b), the effect of an intergrowth on the XRD pattern can be simulated using the module POLYMERS of the CERIUS program. A polymer is built by randomly generating sequences of different ‘monomers’ and the XRD pattern of the corresponding crystal structure can be calculated. The effects on the FWHMs of the 001 reflections due to the following defects have been simulated:

Fig. 4. (a) Simulation of the diffraction patterns of 10% of Bi-2201 intergrowth in Bi-2212 matrix; (b) Simulation of the diffraction patterns of 30% of Bi-2223 intergrowth in Bi-2212 matrix; (c) Simulation of the diffraction pattern of a structure containing two Bi–Bi distances along the c axes (dBi – Bi) randomly distributed; (d) Simulation of the diffraction pattern of 10% intergrowth of the Bi2201 phase with a c axis shorter than the ideal one (see the text).

sites. This fact can be predicted in view of the very low relative intensity of the 002 reflection (001 in the Model I), that can be attributed to a low electronic density in the Bi sites. The projection of the electronic distribution obtained in Model II is similar to that of card number 203211 [17], that corresponds to the best refinement obtained for the average Bi-2212 structure, except that, even if disordered over two positions, the Bi occupancy in the phase of card number 203211 around the ‘ideal’ Bi site is about 1 while in Model II is 0.6. A possible explanation for the very low intensity of the 002 reflection, that is the origin of the calculated low occupancy of the Bi site in the refinement, can be found in the presence of defects of the layer packing. Indeed, in the considered experimental pattern, significant differences are found in the relative broadening of the even and odd reflections: the full-widths at the half-maximum (FWHM) of the odd reflections are larger than those of the even ones. This fact can be ascribed to different coherence lengths of the ordered ˚ , and the average structure, with c axis of 30.95 A

1. the intergrowth of Bi-2201 phase in Bi-2212 matrix structure; 2. different distances between neighbouring Bi–O planes in the Bi-2212 structure; 3. different c axis length of the Bi-2201 phase. In these simulations the reflection intensities have not been refined. Intergrowth of Bi-2201 phase in Bi-2212 matrix structure: Five polymers were generated, each composed of a random sequence of forty Bi-2201 and Bi-2212 monomers with a fixed ratio. Then, the unit cell formed by a single polymer aligned along the c axis was built. The XRD pattern with only the 001 reflections was generated and the five patterns have been added. The XRD pattern in the 20–40⬚ 2u range calculated for 10 and 30% of intergrowth are shown in Fig. 4(a) and (b). The FWHM of the 0010 and 0020 (not reported in the figure) reflections are small and do not change with the percentage of the intergrowth, while the 008 and 0012 reflections become larger as the weight of the Bi-2201 phase increases. The simulated pattern obtained for 30% of random intergrowth is very similar to that obtained by Arrasmith et al. [8]. Similar results were obtained by considering the intergrowth of the Bi-2223 phase in the Bi-2212 phase, the main difference being the positions of some reflections, as for example the 008 and the 0012. Indeed, in the Bi-2201 intergrowth the 2u position of the 008 reflection shifts to higher angles and that of the 0012 reflection shifts to lower 2u . In turn, opposite shifts are obtained when the Bi-2223 intergrowth is simulated. Different distances between neighbouring Bi–O

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planes in the Bi-2212 structure: As different dBi–Bi distances between Bi–O layers are present in the single crystal of the Bi-2212 phase, a simulation of the effect of the disorder on dBi–Bi was performed. In particular, two monomers of the Bi-2212 phase were ˚ . As generated with Bi–Bi distance of 2.9 and 3.2 A shown in Fig. 4(c), the width of the reflection increases with 2u . Indeed, this effect is similar to that induced by microstrains. Different c axis length of the Bi-2201 phase: The broadening of the 001 reflection of the matrix Bi-2212 phase depends on the relative position of the 001 reflections of the intergrowing phase. For example, when the ideal Bi-2201 phase intergrows in the Bi2212 matrix, the 0010 reflection of the matrix almost coincides with the 008 reflection on the intergrowth. The broadening of the 001 reflections shown in Fig. 2 was evaluated by fitting the profiles with a Lorentian function and the FWHMs are shown in Fig. 5. In this figure the odd and the even reflections of the experimental pattern are reported in different curves, the odd reflections being larger than the even ones. A possible explanation for the broadening of the odd reflection is the difference in the coherence length of the average and the ordered structure. Both curves have a peculiar ‘up and down’ behaviour, while the sharpest reflection is the 008. The general behaviour of the experimental broadening can be simulated by introducing a Bi-2201 monomer with a length shorter than the ideal one ˚ instead of 24.6 A ˚ ). With the same procedure (23.1 A of point (i), polymers were generated by introducing a 10% intergrowth of the Bi-2201 (Fig. 3(d)). The reflections were fitted by a Lorentian function and the dependence of FWHMs on the reflection order is shown in Fig. 5 and compared with the experimental values. A possible origin of the different Bi-2201 monomer length is the presence of the Na ⫹ in the material. Indeed, X-ray photoelectron spectroscopy measurements performed on the same sample showed that Na substitutes Sr or Ca ions [18]. In view of the present result, it is possible that Na segregates in the intergrowth phase, causing the decrease of the Bi2201 monomer length. A last remark should be made on the intensities of XRD reflections. As the 002 reflection is related to the length of the ideal structure, variation of its intensity is usually assumed in the analysis of XRD pattern as a deviation from the ideal Bi site occupancy. In the light

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Fig. 5. Comparison of the FWHMs of the odd (W) and even (X) reflection of the experimental pattern in Fig. 2 with the FWHMs evaluated from the simulation of Fig. 4(d) (V).

of the present simulations, where the effect of intergrowth has been pointed out, the Rietveld results should be reconsidered by including as a cause of reduced intensity of the 002 reflection also the intergrowth effect. In the structure, the intergrowth phases may determine the presence at Bi sites of atoms lighter than Bi cation (e.g. Ca, Sr, or Cu). This results in a reduction of the average electronic density in the Bi site and, consequently, in a decrease of the intensity of the 002 reflection. In conclusion, it was shown that a modelling of the superconducting cuprate structure can be performed in strongly oriented powders or films, by refining only the projection of the electronic density along the c axis. The comparison among similar structures can be obtained by normalizing the electronic charge in each lattice site. Second, when odd and even reflections are present in the Bi-2212 phase, differences can be found in the average broadening of these two sets. In particular, it should be always checked if the even reflections are sharper than the odd ones, as this is an indication of a different coherence length for ˚ ) and average (c ˆ 15.97 A ˚) the ordered (c ˆ 30.95 A structures. Third, non-monotonic behaviour of the broadening in the 001 reflection of Bi-2212 phase can be due to intergrowing phases and can be simulated by

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considering the projection of the layer structure as the monomer. In perspective using this modelling a more qualitative study of the effect of the intergrowth can be performed and also introducing linking rules among superconductor monomers.

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