Poole Ch.P., Jr. Handbook of Superconductivity
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Chapter 8
Crystal Structures of
H igh-/' Superconducting
Cuprates
Roman Gladyshevskii
D~partement de Physique de la Mati&e Condens~e, Universit~ de Gen~ve,
Geneva, Switzerland
Philippe Galez
Laboratoire d'Instrumentation et de Mat&iaux d'Annecy, Universit~ de
Savoie~ Annecy~ France
A. Introduction 268
B. Perovskite-Type Structures 269
C. Atom Layers and Stacking Rules 271
a. Definition of Atom Layer 271
b. Stacking Rules 273
c. Basic Structures 275
d. Limiting Structures 276
e. Intergrowth of Basic Structures 277
f. Four-Digit Codes 277
D. High-T c Superconductor Family Tree 278
a. Structural Operations 278
b. Application of the Three Structural Operations
c. Generation of the Family Tree 283
278
ISBN: 0-12-561460-8
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HANDBOOK OF SUPERCONDUCTIVITY
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267
268
Chapter 8: Crystal Structures of High-Tc Superconducting Cuprates
E. Symmetry 285
a. Plane Groups for Individual Atom Layers 285
b. Space Groups for Basic Structures 285
c. Space Groups for Limiting Structures 290
d. Space Groups for Intergrowth Structures 291
E Ideal and Real Cation Coordinations 293
a. Coordination Polyhedra 293
b. Interatomic Distances 296
G. Chemical Families 297
a. Rare-Earth-Alkaline-Earth Cuprates 298
b. BaY Cuprates 299
c. Bi-Based Cuprates 299
d. T1- and Ga-Based Cuprates 300
e. Pb-Based Cuprates 301
f. Hg-Based Cuprates 302
g. C-Based Cuprates 302
h. Cuprates with Halogens 303
i. Ladder Compounds 304
H. Crystallographic Data Sets 305
a. Conventions Used 305
b. Data Sets 309
I. Conclusions 413
Acknowledgement 413
References 413
A
Introduction
Knowledge of crystal chemistry is essential for understanding and influencing the
synthesis and properties of materials. Intense studies of the crystal structures of
high-T c superconducting oxides, reflected in an exceptionally high number of
publications, have greatly contributed to the development of these materials. The
efforts invested since the discovery of superconductivity in the La-Ba-Cu-O
system by Bednorz and Miiller in 1986 have led to the synthesis of hundreds of
different superconducting cuprates, some of them suitable for applications. It
appeared early that these compounds have common structural features, such as a
pronounced layered character, and can be grouped not only into chemical but also
into structural families. Multiple cation substitutions, variable oxygen contents,
and distortions make the crystal structures appear complicated, but the main
features are simple. All structures of superconducting cuprates known up to now
are based on the stacking of a limited number of different kinds of atom layer, one
of these always being a square-mesh layer containing copper and oxygen atoms.
B. Perovskite-Type Structures
269
This work is a critical compilation of crystallographic data of structures
found among high-T c superconducting cuprates, reported up to January 1997.
After a brief description of the structure of perovskite, four kinds of atom layer
are defined, and stacking rules for these layers are formulated. Based on these, a
high-T c superconductor family tree is generated, and the space groups for
undistorted structures are derived. Cation coordinations, interatomic distances,
and structural peculiarities of the main chemical families are then discussed.
Finally, representative crystallographic data sets with drawings, followed by
tables for selected compounds, are given.
The term "structure type" is commonly used for structures of inorganic
compounds to denote a specific geometrical arrangement of atoms. Following the
definition proposed in Parth6
et al.
(1993/1994), 1 two structures with similar
atom arrangements crystallize with different structure types, if a slight distortion
or a change in the ordering of the atoms leads to a description in a different space
group, or if additional, fully or partly occupied, atom sites are present in one of
the structures. In the case ofhigh-T c superconducting cuprates, a strict application
of this definition would result in an artificially large number of "structure types,"
since in some cases the structure of the same compound has been refined in
different space groups or with different Wyckoff sites occupied. For this reason,
in the present work, the term "structure type" is used to denote the ideal,
undistorted, generally tetragonal structure with the a-parameter similar to that of
cubic perovskite. These structure types will be referred to by generalized
chemical formulas where the cations are represented by the letters A, B, C, and D.
The data sets contain complete crystallographic data for selected high-T c
superconducting cuprates, lists of cell parameters, and critical temperatures for
related compounds. They are ordered according to a classification scheme based
on the widely used four-digit code, which gives a general view of the structural
relationships. It is our hope that this work may be a help in finding systematic
trends in the physical properties related to the structural features and thereby
provide hints for the preparation of new compounds.
Perovskite-Type Structures
It was noticed at an early stage that the structures of high-T c superconducting
cuprates are related to that of perovskite. The first structural studies of the mineral
perovskite, CaTiO3, revealed a cubic cell with a ~ 3.8 ,~ (Barth, 1925; Levi and
Natta, 1925). The proposed structure with five atoms in the unit cell respects the
1Two structures
are considered isotypic if they have the same stoichiometry, the same space
group, the same Wyckoff sites with the same or similar positional coordinates, and the same or similar
values of the unit cell axial ratios and cell angles.
270
Chapter 8: Crystal Structures of High-T~ Superconducting Cuprates
symmetry of space group
Pm3m,
calcium atoms being situated at the comers of
the cube, a titanium atom at the center of the cube, and oxygen atoms at the
centers of the cube faces (Fig. 8.1). The Ca site is surrounded by 12 equidistant
oxygen atoms that form a cuboctahedron, and the Ti site is located between six
oxygen atoms forming a perfect octahedron. The TiO6 octahedra share comers to
form a three-dimensional framework. Two kinds of layer, of composition CaO
and TiO2, respectively, may be considered. These layers are stacked along
[0 0 1] and build up the structure completely (note that for a cubic structure,
similar layers may also be considered perpendicular to [1 0 0] or [0 1 0]).
The cubic structure of perovskite, denoted E21 (originally G5) in the
Strukturbericht notation (see chapter on classical superconductors), represents
only an average structure for the mineral CaTiO3, the real structure being a
distortion to orthorhombic or monoclinic. The name perovskite is, however, used
to designate not only the mineral, but also the simple cubic structure and, in a
larger sense, all distorted variants of this. Such structures are formed by a large
range of M(1)2+M(2)4+O3 and M(1)+M(2)2+F3 (rM(1) > rM(2) ) compounds,
where the M(2) cations center the corner-sharing octahedra. Only a few
compounds, such as SrTiO3 (room-temperature modification) and BaTiO3
(high-temperature modification), crystallize with the truly cubic structure.
Owing to its ferroelectric properties, BaTiO3 is one of the most studied materials.
Upon cooling, it undergoes successive phase transitions: At 393 K the structure
becomes tetragonal, at 278K orthorhombic (see data sets) and at 183 K
rhombohedral (Megaw, 1947; Kwei
et al.,
1993). The structures of the super-
conducting pervoskites Bal_xKxBiO 3 and BaPbl_xBixO 3 are discussed in the
chapter on classical superconductors.
Fig. 8.1.
The average structure of perovskite CaTiO3
(Pm~3m).
The unit cell is indicated with dotted
lines; a CaO12 cuboctahedron and
a TiO6
octahedron are presented (see also data set for cubic
BaTiO3 in Section H,b).
C. Atom Layers and Stacking Rules 271
C
Atom Layers and Stacking Rules
The crystal structures of the high-T c superconducting cuprates have essentially a
layered character, confirmed by the anisotropy of their properties, and are
conveniently described as a stacking of atom layers. Basically four kinds of
atom layer can be considered, two of which are identical to those found in the
perovskites. The translation period within the undistorted layers remains that of
the ideal structure of perovskite (~ 3.85 A for cuprates), whereas the periodicity
in the third direction depends on the number and kind of atom layers in the
stacking unit, the average interlayer distance being ~ 2.0 A.
a. Definition of Atom Layer
To understand the structures of high-T c superconducting cuprates it is convenient
to distinguish four kinds of layers, which have different "functions" in the
structure. The notations used here will allow a direct correspondence with the
conventional four-digit codes, described later on. The layers are presented in Fig.
8.2.
DO 2
(conducting
layers): Superconductivity is believed to take place in these
layers, which are present as CuO2 layers in all superconducting cuprates.
They consist of a regular square mesh of copper atoms with oxygen atoms
centering the square edges. In the (nonsuperconducting) perovskites
discussed earlier, the corresponding layers have the composition TiO2.
C (separating
layers typically Ca or Y): The structure of pervoskite does not
contain this kind of layer, which consists of a simple regular square mesh of
metal atoms. The insertion of a C layer into perovskite will "split" the TiO6
octahedron into two TiO5 square pyramids, the basal planes of which will
be separated by the new layer. Consecutive C layers in superconducting
cuprates are always intercalated by O2 layers, where the oxygen atoms are
arranged as in the DO 2 layers, that is, centering the edges of the square
lattice. (~
BO (bridging
layers typically BaO, LaO or SrO): These layers are located next to
a DO2 layer and contain the apical oxygen atom of the octahedron or square
pyramid coordinating the copper atom. They are present in perovskite (CaO
or BaO above) and in all basic structures as defined here (see Section C,c).
They consist of a regular square mesh of metal atoms with oxygen atoms
centering the squares.
AO (additional
layers typically BiO, HgO or T10): In contrast to the C and the
BO layers, these layers are never in direct contact with the DO2 layers, but
272
Chapter 8: Crystal Structures of High-Tr Superconducting Cuprates
separated from these by a
bridging BO
layer. They can have different
oxygen contents, leading to compositions ranging from A to AO 2. In all
cases the cations are arranged in a regular square mesh, whereas the oxygen
atoms may occupy different positions: A, none; AO, centering the squares;
AO', centering square edges in one direction; AO2, centering square edges
in two directions; AO", centering square edges with partial occupancy. For
simplicity, unless specified,
additional
layers will hereafter be represented
by AO layers.
It may be noted that from a geometrical point of view the BO layer is
identical to the AO layer (as well as C and DO 2 to A and AO2, respectively), but
Fig. 8.2.
Schematic drawings of the atom layers building up the structures of high-Tr superconducting
cuprates. Except for the 02 layer, each layer is shown twice. For layers with labels starting
(e.g., DO2) and ending (e.g., O2D ) with D, C, B, or A, solid lines delimit two-dimensional cells
with the cation (shaded circles) located at the comer (0 0) and at the center (89 89 of the square,
respectively. Cells shifted by 89 89 (dashed lines) are indicated to emphasize the equivalence.
Open circles represent oxygen atoms. All atom layers (except
AO')
are described in plane
group
p4mm.
C. Atom Layers and Stacking Rules 273
that the former acquires its specificity from the position in the structure, next to a
DO2
layer. All layers have a square lattice, except the AO' layer, where the
presence of oxygen atoms along only one of the cell edges leads to a rectangular
lattice (see Section E,a).
b. Stacking Rules
In the structures of most high-T e superconducting cuprates, the atom layers just
defined are stacked on top of each other, so that the cation sites in neighboring
layers are shifted by 89 1 with respect to each other. There are, however, two
notable exceptions, BazYCu408 and Ba4YzCu7014.94, for which the cation
positions in consecutive
additional AO'
(CuO) layers are shifted by 0 89 As a
consequence of these systematic shifts, the translation period in the stacking
direction must contain an even number of layers. This means that for an odd
number of layers in what we define as the stacking unit, the translation period in
1 1
the stacking direction has to be doubled. As shown in Fig. 8.2, a shift by 2 2
respects the 4-fold symmetry, and therefore undistorted structures that do not
contain AO' layers will have tetragonal symmetry (see Section E,b). It may be
noted that the presence of an O2 layer between consecutive C layers does not
modify the relative shift of the cation sites.
Not all stacking combinations are possible. Stacking rules that are
respected in all structures of superconducting cuprates are illustrated in Fig.
8.3 and may be formulated as follows for each kind of layer. They lead to a
limited number of coordinations characteristic of the different cation sites.
Conducting
DO 2 layers (i.e. CoO 2 layers) cannot be stacked directly upon
each other. They can have as closest neighbors either two BO layers, one
BO and one C layer, or two C layers. In the first case the D atom will be
surrounded by six oxygen atoms forming an octahedron, in the second case
by five oxygen atoms forming a square pyramid, and in the third case by
four oxygen atoms, belonging to the
DO 2
layer itself, forming a square.
Copper atoms are always present in this layer at the D position, but may
exceptionally be partly replaced by a 3d-transition metal.
Separating C
layers may be inserted between two DO 2 layers. Consecutive
C layers, sandwiched between DO 2 layers, are always intercalated by O2
layers. In all cases, the coordination polyhedron formed by the oxygen
atoms around the C atom is a tetragonal prism. The C layers are generally
built up by Ca or Y, and sometimes by La or rare-earth metal atoms.
Since, by definition, a BO layer must be in direct contact with a DO 2 layer,
one, or at most two,
bridging BO
layers can be placed between two DO 2
layers. When AO layers are present, a single BO layer makes the bridge to
the neighboring DO 2 layer. When a BO layer is surrounded by two DO 2
layers, as in perovskite, the B atom is coordinated by 12 oxygen atoms
274
Chapter 8: Crystal Structures of High-Tc Superconducting Cuprates
Fig. 8.3.
Possible stacking combinations for DO2, C, BO and AO (A) layers, corresponding to stacking
rules 1, 2, 3, and 4 (Section C,b), respectively.
,
located at the comers of a cuboctahedron. In all other cases, the coordina-
tion is reduced, generally to nine oxygen atoms forming a monocapped
square antiprism, but other coordinations may also occur, depending on the
exact type of neighboring
additional layer. Typical B atoms are large,
ionized, and spherical like Ba, Sr, and La.
Several
additional A O layers can be stacked on each other to form slabs
that are always delimited by a BO layer on each side. The coordination of
the A cation depends on the actual composition and geometry of the
additional layers. Considering, for example, an additional layer stacked
between two AO layers, the coordination of the cation in a central layer of
type AO will be octahedral, in a layer of type A linear, and in a layer of type
AO' square planar. Cations in
additional layers are usually main group
elements, such as T1, Pb, Bi, or C, but can also be Cu or Hg, the cations of
the latter elements preferring low coordination numbers.
C. Atom Layers and Stacking Rules 275
In summary DO 2
are CuO2,
C layers are Ca (or Y), BO layers are BaO,
LaO or SrO and AO layers are BiO, HgO or T10 in most common cuprates.
c Basic Structures
Any basic structure, as defined here, must contain at least one DO 2 layer and one
BO layer, like the structure of perovskite. It derives from the stacking rules just
formulated, that A O and BO layers are never in direct contact with C layers, nor
are AO layers in contact with DO 2 layers. Two kinds of thicker structural slab may
thus be considered, one built up of DO 2 (and C) layers, the other by BO (and AO)
layers. The former is sometimes referred to as "conduction" and the latter as
"charge reservoir" slab. The stacking unit of a basic structure will contain one
slab of each kind.
Slabs formed by DO 2 and C layers: In its simplest version, the slab will contain a
single DO 2 layer. When there is more than one DO 2 layer (n of them), then
together with m C layers a slab of composition
CmOn Ozm+2
is formed.
Since the outside layers of the slab must always be DO 2 layers, when
consecutive DO 2 layers are separated by single C layers the formula of the
slab becomes Cn_lDnOzn. A grouping of p consecutive C layers, inter-
calated by O2 layers and sandwiched between two DO 2 layers, is described
by the formula
CpD202p+2.
Following the definition used here, groupings
between two DO 2 layers in a basic structure contain a constant number (p)
of C layers. The general formula for the slab, considering groupings of p C
and (p- 1)O2 layers, intercalated between n consecutive DO 2 layers,
becomes
Cp(n_l)DnO2p(n_a)+2.
The stacking sequence inside the slab can
be written as
DO2- (n- 1){C-(p- 1)[O 2 - C]-DO2 }.
Slabs formed by BO and AO layers: In the simplest case, the slab is reduced to the
expression BzO z, where I can only take the values 1 or 2. When there is
more than one, k A O layers are stacked directly upon each other, between
two BO layers, to form a slab of composition
AkBzOk+ 2.
Note that the total
number of oxygen atoms in the additional layers may differ from k and
consequently the oxygen content of the slab may show large variations.
In a basic structure, conduction
CmOnO2m+2
and charge reservoir AkBzOk+ l
slabs alternate, so that the general formula can be written as
A kB lCmDn Ok+l+Zm+2.
The outer conducting DO 2 layers of the former slab are in direct contact with the
bridging BO layers of the latter. As a consequence of the definition of a basic
structure and of the stacking rules formulated earlier, the following relations are