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Crystal chemistry of superconductors: A guide to the tailoring of new compounds
Physica C 156 (1988) 693-700 North-Holland, A m s t e r d a m
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CRYSTAL CHEMISTRY OF SUPERCONDUCTORS: A GUIDE TO T H E TAILORING OF NEW C O M P O U N D S A. SANTORO and F. BEECH Reactor Division, National Bureau o f Standards, Gaithersburg, MD 20899, USA
M. MAREZIO * and R.J. CAVA Bell Laboratories, Murray Hill. NJ 07974, USA Received 9 September 1988 Revised manuscript received 24 October 1988
The crystal structures of the known superconducting copper oxides can be described in terms of two basic structural types. The seriesLa2Ca._ tCu.O2. + 2, (TI,Bi)_~(Ba,Sr) :Ca~_ ~Cu.O2~ + 4 and TIBa2Ca._ aCunO2. + 3 can be viewed as made of alternatingslices having the rock saltand perovskite structure.The compounds Ba:YCu,Os and Ba,Y2Cu7OI4+.~, on the other hand, comprise of perovskite blocks alternatingwith blocks in which a crystallographicshear is present. The effectof this shear is that of forming double chains of edge sharing squares with oxygen atoms at the comers and copper atoms at the center. The superconductor Ba.~YCu307 can be described in terms of both structuraltypes and may be considered as an intermediate type between the other two. The basic building blocks of these superconducting materials can be furtherbroken down into constituent nets (or meshes). This description allows one to envisage new structuresbuiltfrom these meshes containing the key structuralelements present in the currently known superconductors. As such, the structural schemes used in this description may be used as a guide in the preparation of new materials with interestingelectronicproperties.
1. Introduction
The structures of the oxide superconductors are in general classified in terms of well known structural types. For example, the structure of Ba_.YCu307 [ 1 ] (Tc = 93 K) is related to that of perovskite with specific oxygen atoms removed from the structure, while the arrangement of Ba- or St-doped La2CuO4 ( Tc ~ 40 K) is identical to that of K2NiF4 [2]. The superconductors belonging to the systems Bi2Sr2Ca,_lCunO2n+4 [3] (T~=80 to 110 K) and Tl2Ba2Ca,,_]Cu,O2,÷4 [4] (To=80 to 125 K) have been compared to the Aurivillius phases [5], although these phases have a number of important structural features significantly.different from those reported for the superconductors. These simple descriptions are useful for purposes of classification, but are in general inadequate when * Also Laboratoire de Crystailographie. C.N.R.S., 166X, 38042 Grenoble, France.
complex structures must be compared to one another in order to find common structural features. The number o f superconductors (and of materials crystallographically or chemically related to them) discovered so far is fairly large. Therefore, it is vital to establish relationships between the various structures not only to provide a meaningful basis for theoretical studies, but also to outline a coherent scheme for the search o f new compounds that may exhibit interesting electronic properties.
2. Materials with the rock sait-perovskite structure The structures of oxide superconductors and related compounds can be easily analyzed and compared to one another if we describe them in terms of layers having composition AX and BX~. For example, in the structure of an ABX3 perovskite, shown in fig. la, the first layer perpendicular to the c-axis has the composition BX2. The B atoms are located
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A. Santoro et al. / Crystal chemistry of superconductors
¢
~b (a) ABX 3
/ b'
C
.jQ.f// Qx
a'
©A •
@
I/
/
e
......
,
1
© U
Such formulation allows one to derive in a simple way the coordination of the atoms. For example, in the case of perovskite, the atom A at the center of the mesh is surrounded by twelve X atoms. Four are at the corners of the same mesh and eight at the midpoints of the mesh's edges of the BX2 layers above and below. The configuration of the coordination polyhedron is that of a cuboctahcdron. There are cases in which some or all of the atoms X of the BX2 or AX layers are missing. These layers are called "defective" and have composition BX and A (the case of a BX2 layer with all the atoms X removed is similar to that of a layer of composition A). An illustration of all the possible meshes of full or defective layers BX2 and AX is given in fig. 2. The relationship between perovskite and Ba2YCu307, illustrated in fig. 3, can be easily under-
B (AX)o
(AX)ox
(A)o
(A)ox
(AX)c
(AX)cx
(A)c
(A)cx
(BX2)o
(BX2)ox
(BX)o
(BX)ox
(BX2)c
(BX2)cx
(BX)c
(BX)cx
~b
(b) AX
a
Fig. 1. Crystalstructures of (a) perovskiteand (b) rock salt. The conventional unit cell of rock salt is face centered and it is defined by the axes, a'. b', and c. at the corners of a square mesh, that is, at the origin of the reference system, and the X atoms at the midpoints of the edges. This configuration may be represented with the symbol (BX2)o expressing the composition of the layer as well as the choice of origin. The next layer has composition AX and this time the A atom is located at the center of the mesh, while the X atoms are at the corners. This geometry may be expressed by the symbol (AX)c so that the structure of perovskite is represented by the formula [ (BX:)o(AX)c] (BX2)o(AX)c
•
cation (A or B)
in which the layers contained in one unit cell are enclosed in brackets. In a similar way we may represent the structure of rock-salt (fig. I b ) with the sequence:
O
anion (X)
(AX)c[ (AX)o(AX)¢] (AX)o
Fig. 2. All possible meshes used to describe the structures of superconductors and related compounds.The configurationof the defective B layers is identical to that of the A layer.
A. ~ioPo et at )Cry~tal chemistry of supereonduetors
695
•
Cu
®Y aa
~o
:::::OiieilKii) ....
ABX 3
Ba2Y Cu3 07
Ba2Y Cu3 O6
.... [(BX2)o (AX)c] (BX2)o (AX)c (BXQo (AX)c (BX2)o .... .... [(CuO)o (BaO)c (CuO2)o (Y)c (CuC~)o (BaO)c] (CuO) o .... .... [(Cu) o (BaO)c (CuOQo(Y)c (CuO=)o (BaO)c] (Cu)o ....
Fig. 3. Relationship between the structure o f perovskite (left), Ba2YCu30~ ( middle ) and Ba2YCu30+ (right). The scheme at the bottom is a description o f the structures layer by layer.
stood in terms of defective layers. In this case B = C u and X = O , while A represents yttrium and barium atoms in an ordered sequence. This order induces the tripling of the c-axis of the perovskite unit cell. The structure of Ba2YCu307 has two oxygen-deficient layers: the first is the CuO layer at z = 0 which has the configuration of a BX., layer in which two oxygen atoms at the mid-points of opposite edges have been removed, and the other is the yttrium layer in which all the oxygen atoms are missing. The structure of LaeCuO, (K,NiF4-type) is illustrated in fig. 4, where A = L a , B = C u , and X = O . There are six layers in the unit cell of this structural type and they can be divided in two sets of three perovskite layers each. The first set (AX)o(BX2)¢(AX)o is related to the second (AX)c(BX2)o(AX)c by a shift of the origin oft= 1/ 2 ( = + b ) . This structure has also been regarded as containing alternate layers of perovskite and rock-salt with the A atoms surrounded by nine X atoms, that is the average between the coordination the A atoms would have in perovskite (twelve) and in rock-salt
°T
IO+o. Jol
!+:++++ I
a
J
9 .....+
.+
AX IABX)3
.... [(BX2)o (AX)c (AX)o (BX2)c (AX)o (AX)c] (BX=)o(AX)c .... . . . .
(CuO2)o(Ca)c (CuOz)o.... (CuO2)c(Ca)o (CuO2)c .... (CuOzlo(Ca)c (C.O2)o .... Fig. 4. Structural type A X ( A B X 3 ) . The scheme at the bottom is a description layer by layer and the structural is compared with that o f the homologous series La2Ca._iCu.O2.+2. The higher terms o f the series are obtained from LazCuO+ by substituting the CuO2 layers with sequences CuO2 Ca CuO2....
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A. Santoro et aL / Crystal chemist~ of superconductors
(MO)c (NO)o (NO)c (MO)o]
[
]
[(MO)o (NO)c (NO)o (MO)c ] [
icoc
] ....
l.o
(CuO2)c (Ca)o (CuO2)c (CuO2)c (Ca)o (CuO2)c (Ca)o (CuO2)c
~ (CuO2)o (Ca)c (CuO2)o l,(CuO2)o (Ca)c (CuO2)o (Ca)c (CuO2)o
1
M = Ba, Sr ; N = T.I, Bi Fig. 5. Schematicrepresentationof the series (TI.Bi) 2(Ba,Sr),Ca,-, Cu.O2,+4with n = 1, 2. 3. (six). For this reason the formula is sometimes written as AX(ABX3). This composition is the end member of a homologous series of formula AX (ABX3),, with n-- 1, 2, 3. These two descriptions are possible because the role of the AX layers in the structure is ambiguous, in the sense that they can be considered either as part of the rock-salt slice or as a part of the perovskite slice. The homologous series AX(ABX3), was first described by Ruddlesden and Popper [ 6] and later by Longo and Raccah [ 7 ] as an alternate layering of rock-salt and perovskite blocks. Subsequently, this description was generalized by Smyth [ 8 ] who proposed the formula m A X nABX3 for the structures of a number of high-To superconductors. The series with A f L a , B--Cu, and X = O , La,+,Cu,O3,+,, has been observed experimentally by Davies and Tilley [ 9 ]. The homologous series La.,Ca,_ iCu,O2,+ 2 can be generated from the structure of La:CuO4. For example, the second member can be generated by replacing the CuO2 layers with blocks of CuO2 Ca CuO2 as indicated in fig. 4. The existence and structure of the Sr analogue, La,SrCu206, have been reported by Nguyen et al. [10,111. As mentioned in the Introduction, the crystal structures of the compounds of the series belonging to the systems ( TI,Bi ): (Ba,Sr) 2 Ca,_, Cu ,02, + 4 have been described as related to the Aurivillius phases. Precise structural determinations [ 12,13 ], however, have shown that this analogy is not entirely correct since in the Aurivillius phases the oxygen atoms of the Bi and 1"1 layers are not located on, or close to, the layers, but rather between them. Furthermore, the positions occupied by the Sr and Ba atoms in the Aurivillius phases are empty. The structures of the Bi and T1 superconductors are illustrated in a sche-
matic fashion in fig. 5. They can be properly described as a sequence of four layers with the rock-salt structure followed by a variable number of layerswith the perovskite configuration. In analogy with the series La2Ca._ ~Cu.O2.+4, the unit ceilsof the bismuth and thallium compounds are made up of two identical halves, shifted one with respect to the other by the translation vector t= I/ 2 (a + b ). The previous analysis shows that many structures of superconductors can be described in terms of a structural type comprising A X and BX2 layers arranged in slices with the rock-salt and perovskite structure. The chemical nature and the number of layers in each slice may vary considerably, thus accounting for the large number of existing materials that belong to this family. Examples of structures of this type are schematically represented in fig.6. The general formula is given in the firstline of the figure. The integer n indicates the number of layers forming the perovskite slice and the integer r the number of those forming the rock-salt slice. The perovskite blocks have the composition Cu.A._,O2. and are represented with the symbol P.(A) which indicates the sequence C u O 2 - A - C u O 2 - A .... in which the CuO2 layers alternate with oxygen-deficient layers of type AX. The layers AX at both ends of each rocksalt slice have been written explicitly to emphasize the fact that they can be considered part of the rocksalt structure or part of the perovskite structure. The number s is given by s--- 1 - [ l / r ] , where [ l/r] represents the largest integer contained in 1/r. Thus, for r = 1 it is s = 0 on the layers (AX), and (AX)~,_e~, do not exist (case of BaYFcCuOs, sixth line in fig. 6), for r = 2 it is s = 1 and the layer (AX)sffil exists while the layers (AX) ~,_ 2~, are missing, and for r > 2, s = 1 and both (AX)sffil and (AX)~,_z), exist. The
A. ~hibJ'o et aL / CO~talchemist'~. ~ft~pet'conduetOrs
697
"
jinx) }[l~o/,.I ] .... ]~..Olo }[l~oc] ....
(AX)s
(SrO)o
[ ] (LaO)c }[ (P.(Ca))o [ (BiO)c(BiO)o] (SrO)c} [ (Pn(Ca))o
]{(LaO)c [ ] { (SrO)c [ (BiO)o(BiO)c ]l~,O~o
(BaO) o
[/T'O~:'OIo ]l~,Olo }[ I~olOa,o
]{l~aOlo [(T-~O)o(T'O)c ](BaO)o }[(Pn(Ca))c] ....
(BaO) o
[/T'O~c
]{
(LaO) o
{ { {
[ [
] ]
]
}[
}[/~:~o~>~ ]{ } [ (P')°(Ca.asSr-'s)c] {
} [(~o(c.~>c] ....
[
] (BaO)o } [(P3(Ca))c] ....
[ [
] ] ]
}[ }[ )[
] .... ] .... ] ....
Fig. 6. Comparison of the structures of La2Ca._lCunO2n+2 (second line); Bi2Sr2Ca._ iCu.O2.+4 (third line), TI2Ba2Ca._ ~Cu.O2.+4 (fourth line), TIBa2Ca2Cu309 (fifth line), BaYFeCuOs (sixth line), Ba2YCu307 (seventh line) and Cao.ssSro.]sCuO2 (last line). In the first line is given the general formula of the structural type. The symbol P.(A' ) represents the sequence CuO2 A' CuO2--"etc, P2~FC)(Y) represents the three layers (Cuo.sFeo.5)02 Y (Cuo.sFeo.5)02, and K the sequence BaO CuO BaO. The asterisk indicates that the CuO layer may be oxygen deficient. In the general formula, the thickness of the rock salt slice is indicated by the integer r, while the integer s is defined in the text.
values
r=2
and
r = 4 generate the series ka2Ca._iCunO2n+2 and (TI,Bi)2(Ba,Sr)2Ca,_l02,+4, respectively. For r=3 and n=3, the compound TIBa2Ca2Cu309 isgenerated [14 ] and for r= I and n=2, BaY(FeCu)Os [15]. Finally compounds such as Ba2YCu307 and (Cao.ssSro.~5)CuO2 [ 16] can only bc described with this scheme as purely perovskite sequences of layers.From fig.6 it is clearthat structures with r even have unit cellscontaining two identical halves of the structure shifted one with respect to the other by a translation vector t= I/ 2(a+b). O n the contrary, when r is odd this does not happen and as a consequence these unit cellshave a much smaller length of the parameter c.
coordination. Following the scheme of fig. 6, we may write the most general formula for these compounds as
(AO).,.(A'O),,(A"),_~ (CuO2), Because of the presence of the AO layers, the Cu atoms at the end of the perovskite slices have a pyramidal coordination. If the valence of the A and A' cations is taken as p and q, respectively, and that of A' and Cu as 2 +, we must have
2 n + x + y = ( p x + q y ) / 2 + 2 n - 1, that is
x(p-2)+y(q-2)=2. 3. General formulas of homologous series Let us assume that in the general formula 1he perovskite slices are comprised of AX and BX2 layers having the following sequence: (CuO2) ( A " ) (CuO2) (A" ) (CuO2) namely all the AX-type layers are oxygen deficient and, consequently, all the Cu atoms have a square
For p=3 and q--2 (case of thallium and barrium, for example), it must be x = 2, while y is not defined. We have then the following set of series of compounds: A2A"_ i Cu,O2,+2
for y = 0
A2A'A~_ICunO2n+3
for y = 1
A2 Af,A~_ l CunO2.+4
for y = 2
A2A~A~_ICu.O2.+5
fory=3
etc.
A. Santoro et al. / Crystal chemistry of superconductors
698
The series corresponding to y = 0 and y = 2 do exist and they are La2Can_tCu,02,+2 and (Bi,TI)2(Sr, Ba)_,Ca,_tCu,O2,+4, respectively. By changing the cation valences and the parameters p and q, all sorts of different compounds can be foreseen. The above series have been derived assuming that the oxidation state of Cu is 2 +. More in general, if the valence of copper is m + , the relationship of equality between cation and anion valences becomes 2 n + x + y = (px+qy)/2+ ( n - 1)+mn/2. Assuming as before p = 3 and q = 2 , and x = 1, the value of y is not defined and we have
m= (l +2n)/ n, i.e., the oxidation state of copper is a function of n. The resulting series can be written:
and 40 K, respectively. The structures of these compounds arc closely related to that of Ba2YCu3OT, and can be described with the mechanism based on the stacking of AX and BX2 layers used previously. The main difference between these materials and those having the rock salt-perovskite structure is that in this case there exist two consecutive, oxygen deficient, layers CuO whose stacking is accompanied by a shift of origin of ( ½, 0, 0 ) [ or (0, ½, 0), as the case may be ]. This configuration may be represented with a sequence such as (CuO)o(CuO)ox in which the symbol (CuO)ox means that the layer is the same as (CuO)o with a shift of origin of 1/2a (the symbol (CuO)or would indicate a shift of origin of l / 2 b ) .
(AO) (A' O),,A;;_ ~(CuO:). that is
Cu 0
AA; A:_, Cu.O2.+ l +.,,
Cu 0
For y = 0, 1, 2 .... we have the series AA~_ ,Cu. O2.+1, AA'A;;_,Cu,,O_,.+2, AA~A;;_ICu.O2.+3,..., respectively. The series TIBa_.Ca._ ,Cu.O2.+3 is obtained for y = 2 . For n = 3, the value of copper is 2.33+ and we have
BaO
AA~Cu307
Cu O= ¥
Cu O=
y=O
AA'A'_4Cu3Os y = 1 AA;_A~Cu309 y = 2
etc.
The compound TIBa2Ca_,Cu~O9 corresponds to y = 2. Note that the member with y = 0 is not Ba2YCu3OT, the well known 93 K superconductor, but a compound with a different structure in which the oxygen atoms of the A"O layers are all missing (which is not the case for the BaO layers in the superconductor BaEYCu3OT).
I
~c_~---¢_-7_Z I
~
BaO
i~
Cu 0
i~
Cu 0
-~ [
aa o
---.I
Cu O= y
I~
Cu O= e= o
4. Materials with crystallographic shear Recently, two new compounds have been discovered in the B a - Y - C u - O quaternary system, namely Ba_,YCu4Os [ 17,18 ] and Ba4Y2CuTOt4+.,- [ 19 ]. They exhibit superconducting transitions at about 80 K
~__----_-~ ~'
Cu 0
Fig. 7. Schematic representation of the crystal structure of Ba2YCu4Os showing two successive C u O layers shifted one with respect to the other by I/2a. This shift induces a crystallographic shear with the consequent formation o f double chains o f edgesharing squares with the copper at the center and the oxygen at the corners.
A. Santoro et al. I C~. stal chemistry of superconductors
{
[
l
}[
{(,,,o>o[o(o,,O>ox](,,ao>ox
1{
[
699
]
;1
1{(,,.O>o. [(o,,O>ox(O,,o>o](BaO>o}[(.:(',>>o ]
{ (8,.O)o[(OuO)c(OUO)cx](BaO)o×} [(Pa(V))cx(K)o×(P:(Y))cx ] { (BaO)o×[(OI.K))cx(CuO)c](BaO)o} [(Pl(V))c(K)o(Pi(V))c] Fig. 8. Schematic representation of the structures of Ba2YCu3OT, Ba2YCu4Os, and Ba4Y2Cu7Ol4+x. The symbols are the same as those defined for fig. 6. As indicated in the text and in fig. 2, a symbol such as (BX2)ox indicates a mesh identical to (BX2)o, but shifted 1/2 in the direction ofthe a axis.
As we know, the sequence (BaO)c(CuO)o(BaO)c is associated with the presence of corner sharing squares as those existing in the structure of Ba2YCu3OT. It is easy to visualize, then, that the sequence (BaO)c(CuO)o(CuO)ox(BaO)c~ is associated with the existence of double chains of edgesharing squares of the type shown in fig. 7 for Ba2YCu408. The shift of origin of (1/2, 0, 0), and the consequent formation of edge sharing between the squares of adjacent chains is in general referred to as a crystallographic shear. As we have mentioned previously, the structures of Ba2YCu3OT, Ba2YCu4Os, and Ba4Y2Cu7Ot4+x are related to one another. The nature of this relationship is illustrated by the scheme of fig. 8. From the figure it is clear that the structure of Ba4Y2Cu70~4+x is built of single Ba2YCu307 type blocks alternating with single Ba2YCu4Os type blocks. The materials containing layers of CuO not involved in the formation of double chains of edge-sharing squares may be "oxygen deficient (case of Ba2YCu307_x and Ba4Y2Cu70~4+x), while a compound such as Ba2YCu4Os is stoichiometric. The presence of these CuO layers is marked with an asterisk in fig. 8. As we have done for the rock salt-perovskite structural type, also in this case we may build different theoretical structures by changing the composition a n d / o r the ordering of the constituent blocks. For example, a compound in which single blocks of BazYCu30~ alternate with double blocks of Ba2YCu4Os can be envisaged using the scheme indicated in fig. 8. Its formula would be Ba6Y3Cul IO23 (or more precisely, Ba6Y3Cul iO22+x since the blocks of Ba2YCu307 may have additional oxygen vacan-
cies in the CuO layers not involved in the formation of double chains). Attempts to prepare this and other compounds will be made in the near future. 5. Conclusions In this paper we have shown that all the superconductors discovered so far can be described in terms of two basic structural types. One is made by alternating slices having the rock salt and perovskite structure. The thickness and the chemical nature of these slices may vary significantly, thus accounting for the large number of compounds prepared to the present day. The other structural type comprises blocks with the perovskite structure alternating with blocks in which a crystallographic shear is present. This description allows one to envisage new structures built by using blocks containing the key structural elements present in all the currently known superconductors. References [ I ] See, e.g.J.E. Greedan, A. O'Reilly and C.V. Stager, Phys. Rev. B 35 (1987) 8770. [2] R.J. Cava, A. Santoro, D.W. Johnson and W.W. Rhodes, Phys. Rev. B 35 (1987) 6716. [3] M.A. Subramanian, C.C. Tarardi, J.C. Calabrese, J. Gopalakrishnan, K.J. Morrissey, T.R. Askew, R.B. Flippen, U. Chowdhry and A.W. Sleight, Science 239 (1988) 1015. [4]C.C. Torardi, M.A. Subramanian, J.C. Calabrese, J. Gopalakrishnan, K.J. Morrissey, T.R. Askew, R.B. Flippen, U. Chowdhry and A.W. Sleight, Science 240 ( 1988 ) 631.
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A. Santoro et al. / Crystal chemist~ o f superconductors
[5] B. Aurivillius, Arkiv Kemi 1 (1949) 463; Arkiv Kemi 2 (1950) 519. [6] S.N. Ruddlesden and P. Popper, Acta Crystallogr. 10 ( 1957 ) 538;ibid. 11 (1958) 54. [7] J.M. Longo and P.M. Raccah, J. Solid State Chem. 6 (1973) 526. [8 ] D.M. Smyth, 90th Annual Meeting of the American Ceramic Society. Cincinnati, USA (1988). [9] A.H. Davies and R.J.D. Tilley, Nature 326 (1987) 859. [10] N. Nguyen, L. Er-Rakho, C. Michel, J. Choisinet and B. Raveau, Mat. Res. Bull. 15 (1980) 891. [ 11 ] N. Nguyen, C. Michel, F. Studer and B. Raveau, Mater. Chem. 7 (1982) 413. [ 12 ] P. Bordet, J.J. Capponi, C. Chaillout, J. Chenavas, A.W. Hewat, E.A. Hewat, J.L. Hodeau, M. Marezio, J.L. Tholence and D. Tranqui, Physica C 156 (1988) 189. [13] D.E. Cox, C.C. Torardi, M.A. Subramanian, J. Gopalakrishnan and A.W. Sleight, Phys. Rev., submitted.
[ 14] S.S.P. Parkin, V.Y. Lee, A.I. Nazzal, E.M. Engler, R. Savoy, R, Beyers and S.J. LaPlaca, Jpn. J. Appl. Phys. 27 (1988) L837. [ 15 ] T, Siegrist, personel communication. [16]T. Siegrist, S.M. Zahurak, D.W. Murphy and R.S. Roth, Nature 334 (1988) 231. [ 17 ] K. Char, M. Lee, R.W. Barton, A.F. Marshall, 1. Bozovic, R,H. Hammond, M.R. Beasley, T.H. Geballe, A. Kapitulnik and S.S. Laderman, Phys. Rev. B 38 (1988) 834. [ 18] P. Marsh, R.M. Fleming, M.L. Mandich, A.M. DeSantolo, J. Kwo, M. Hong and L.J. Martinez-Miranda, Nature 334 (1988) 141. [19]P. Bordet, C. Chaillout, J. Chenavas, J.L. Hodeau, M. Marezio, J. Karpinski and E. Kaldis, Nature 334 (1988) 596.
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"
CRYSTAL CHEMISTRY OF SUPERCONDUCTORS: A GUIDE TO T H E TAILORING OF NEW C O M P O U N D S A. SANTORO and F. BEECH Reactor Division, National Bureau o f Standards, Gaithersburg, MD 20899, USA
M. MAREZIO * and R.J. CAVA Bell Laboratories, Murray Hill. NJ 07974, USA Received 9 September 1988 Revised manuscript received 24 October 1988
The crystal structures of the known superconducting copper oxides can be described in terms of two basic structural types. The seriesLa2Ca._ tCu.O2. + 2, (TI,Bi)_~(Ba,Sr) :Ca~_ ~Cu.O2~ + 4 and TIBa2Ca._ aCunO2. + 3 can be viewed as made of alternatingslices having the rock saltand perovskite structure.The compounds Ba:YCu,Os and Ba,Y2Cu7OI4+.~, on the other hand, comprise of perovskite blocks alternatingwith blocks in which a crystallographicshear is present. The effectof this shear is that of forming double chains of edge sharing squares with oxygen atoms at the comers and copper atoms at the center. The superconductor Ba.~YCu307 can be described in terms of both structuraltypes and may be considered as an intermediate type between the other two. The basic building blocks of these superconducting materials can be furtherbroken down into constituent nets (or meshes). This description allows one to envisage new structuresbuiltfrom these meshes containing the key structuralelements present in the currently known superconductors. As such, the structural schemes used in this description may be used as a guide in the preparation of new materials with interestingelectronicproperties.
1. Introduction
The structures of the oxide superconductors are in general classified in terms of well known structural types. For example, the structure of Ba_.YCu307 [ 1 ] (Tc = 93 K) is related to that of perovskite with specific oxygen atoms removed from the structure, while the arrangement of Ba- or St-doped La2CuO4 ( Tc ~ 40 K) is identical to that of K2NiF4 [2]. The superconductors belonging to the systems Bi2Sr2Ca,_lCunO2n+4 [3] (T~=80 to 110 K) and Tl2Ba2Ca,,_]Cu,O2,÷4 [4] (To=80 to 125 K) have been compared to the Aurivillius phases [5], although these phases have a number of important structural features significantly.different from those reported for the superconductors. These simple descriptions are useful for purposes of classification, but are in general inadequate when * Also Laboratoire de Crystailographie. C.N.R.S., 166X, 38042 Grenoble, France.
complex structures must be compared to one another in order to find common structural features. The number o f superconductors (and of materials crystallographically or chemically related to them) discovered so far is fairly large. Therefore, it is vital to establish relationships between the various structures not only to provide a meaningful basis for theoretical studies, but also to outline a coherent scheme for the search o f new compounds that may exhibit interesting electronic properties.
2. Materials with the rock sait-perovskite structure The structures of oxide superconductors and related compounds can be easily analyzed and compared to one another if we describe them in terms of layers having composition AX and BX~. For example, in the structure of an ABX3 perovskite, shown in fig. la, the first layer perpendicular to the c-axis has the composition BX2. The B atoms are located
0921-4534/88/$03.50 © Elsevier Science Publishers B.V. ( North-Holland Physics Publishing Division )
694
A. Santoro et al. / Crystal chemistry of superconductors
¢
~b (a) ABX 3
/ b'
C
.jQ.f// Qx
a'
©A •
@
I/
/
e
......
,
1
© U
Such formulation allows one to derive in a simple way the coordination of the atoms. For example, in the case of perovskite, the atom A at the center of the mesh is surrounded by twelve X atoms. Four are at the corners of the same mesh and eight at the midpoints of the mesh's edges of the BX2 layers above and below. The configuration of the coordination polyhedron is that of a cuboctahcdron. There are cases in which some or all of the atoms X of the BX2 or AX layers are missing. These layers are called "defective" and have composition BX and A (the case of a BX2 layer with all the atoms X removed is similar to that of a layer of composition A). An illustration of all the possible meshes of full or defective layers BX2 and AX is given in fig. 2. The relationship between perovskite and Ba2YCu307, illustrated in fig. 3, can be easily under-
B (AX)o
(AX)ox
(A)o
(A)ox
(AX)c
(AX)cx
(A)c
(A)cx
(BX2)o
(BX2)ox
(BX)o
(BX)ox
(BX2)c
(BX2)cx
(BX)c
(BX)cx
~b
(b) AX
a
Fig. 1. Crystalstructures of (a) perovskiteand (b) rock salt. The conventional unit cell of rock salt is face centered and it is defined by the axes, a'. b', and c. at the corners of a square mesh, that is, at the origin of the reference system, and the X atoms at the midpoints of the edges. This configuration may be represented with the symbol (BX2)o expressing the composition of the layer as well as the choice of origin. The next layer has composition AX and this time the A atom is located at the center of the mesh, while the X atoms are at the corners. This geometry may be expressed by the symbol (AX)c so that the structure of perovskite is represented by the formula [ (BX:)o(AX)c] (BX2)o(AX)c
•
cation (A or B)
in which the layers contained in one unit cell are enclosed in brackets. In a similar way we may represent the structure of rock-salt (fig. I b ) with the sequence:
O
anion (X)
(AX)c[ (AX)o(AX)¢] (AX)o
Fig. 2. All possible meshes used to describe the structures of superconductors and related compounds.The configurationof the defective B layers is identical to that of the A layer.
A. ~ioPo et at )Cry~tal chemistry of supereonduetors
695
•
Cu
®Y aa
~o
:::::OiieilKii) ....
ABX 3
Ba2Y Cu3 07
Ba2Y Cu3 O6
.... [(BX2)o (AX)c] (BX2)o (AX)c (BXQo (AX)c (BX2)o .... .... [(CuO)o (BaO)c (CuO2)o (Y)c (CuC~)o (BaO)c] (CuO) o .... .... [(Cu) o (BaO)c (CuOQo(Y)c (CuO=)o (BaO)c] (Cu)o ....
Fig. 3. Relationship between the structure o f perovskite (left), Ba2YCu30~ ( middle ) and Ba2YCu30+ (right). The scheme at the bottom is a description o f the structures layer by layer.
stood in terms of defective layers. In this case B = C u and X = O , while A represents yttrium and barium atoms in an ordered sequence. This order induces the tripling of the c-axis of the perovskite unit cell. The structure of Ba2YCu307 has two oxygen-deficient layers: the first is the CuO layer at z = 0 which has the configuration of a BX., layer in which two oxygen atoms at the mid-points of opposite edges have been removed, and the other is the yttrium layer in which all the oxygen atoms are missing. The structure of LaeCuO, (K,NiF4-type) is illustrated in fig. 4, where A = L a , B = C u , and X = O . There are six layers in the unit cell of this structural type and they can be divided in two sets of three perovskite layers each. The first set (AX)o(BX2)¢(AX)o is related to the second (AX)c(BX2)o(AX)c by a shift of the origin oft= 1/ 2 ( = + b ) . This structure has also been regarded as containing alternate layers of perovskite and rock-salt with the A atoms surrounded by nine X atoms, that is the average between the coordination the A atoms would have in perovskite (twelve) and in rock-salt
°T
IO+o. Jol
!+:++++ I
a
J
9 .....+
.+
AX IABX)3
.... [(BX2)o (AX)c (AX)o (BX2)c (AX)o (AX)c] (BX=)o(AX)c .... . . . .
(CuO2)o(Ca)c (CuOz)o.... (CuO2)c(Ca)o (CuO2)c .... (CuOzlo(Ca)c (C.O2)o .... Fig. 4. Structural type A X ( A B X 3 ) . The scheme at the bottom is a description layer by layer and the structural is compared with that o f the homologous series La2Ca._iCu.O2.+2. The higher terms o f the series are obtained from LazCuO+ by substituting the CuO2 layers with sequences CuO2 Ca CuO2....
696
A. Santoro et aL / Crystal chemist~ of superconductors
(MO)c (NO)o (NO)c (MO)o]
[
]
[(MO)o (NO)c (NO)o (MO)c ] [
icoc
] ....
l.o
(CuO2)c (Ca)o (CuO2)c (CuO2)c (Ca)o (CuO2)c (Ca)o (CuO2)c
~ (CuO2)o (Ca)c (CuO2)o l,(CuO2)o (Ca)c (CuO2)o (Ca)c (CuO2)o
1
M = Ba, Sr ; N = T.I, Bi Fig. 5. Schematicrepresentationof the series (TI.Bi) 2(Ba,Sr),Ca,-, Cu.O2,+4with n = 1, 2. 3. (six). For this reason the formula is sometimes written as AX(ABX3). This composition is the end member of a homologous series of formula AX (ABX3),, with n-- 1, 2, 3. These two descriptions are possible because the role of the AX layers in the structure is ambiguous, in the sense that they can be considered either as part of the rock-salt slice or as a part of the perovskite slice. The homologous series AX(ABX3), was first described by Ruddlesden and Popper [ 6] and later by Longo and Raccah [ 7 ] as an alternate layering of rock-salt and perovskite blocks. Subsequently, this description was generalized by Smyth [ 8 ] who proposed the formula m A X nABX3 for the structures of a number of high-To superconductors. The series with A f L a , B--Cu, and X = O , La,+,Cu,O3,+,, has been observed experimentally by Davies and Tilley [ 9 ]. The homologous series La.,Ca,_ iCu,O2,+ 2 can be generated from the structure of La:CuO4. For example, the second member can be generated by replacing the CuO2 layers with blocks of CuO2 Ca CuO2 as indicated in fig. 4. The existence and structure of the Sr analogue, La,SrCu206, have been reported by Nguyen et al. [10,111. As mentioned in the Introduction, the crystal structures of the compounds of the series belonging to the systems ( TI,Bi ): (Ba,Sr) 2 Ca,_, Cu ,02, + 4 have been described as related to the Aurivillius phases. Precise structural determinations [ 12,13 ], however, have shown that this analogy is not entirely correct since in the Aurivillius phases the oxygen atoms of the Bi and 1"1 layers are not located on, or close to, the layers, but rather between them. Furthermore, the positions occupied by the Sr and Ba atoms in the Aurivillius phases are empty. The structures of the Bi and T1 superconductors are illustrated in a sche-
matic fashion in fig. 5. They can be properly described as a sequence of four layers with the rock-salt structure followed by a variable number of layerswith the perovskite configuration. In analogy with the series La2Ca._ ~Cu.O2.+4, the unit ceilsof the bismuth and thallium compounds are made up of two identical halves, shifted one with respect to the other by the translation vector t= I/ 2 (a + b ). The previous analysis shows that many structures of superconductors can be described in terms of a structural type comprising A X and BX2 layers arranged in slices with the rock-salt and perovskite structure. The chemical nature and the number of layers in each slice may vary considerably, thus accounting for the large number of existing materials that belong to this family. Examples of structures of this type are schematically represented in fig.6. The general formula is given in the firstline of the figure. The integer n indicates the number of layers forming the perovskite slice and the integer r the number of those forming the rock-salt slice. The perovskite blocks have the composition Cu.A._,O2. and are represented with the symbol P.(A) which indicates the sequence C u O 2 - A - C u O 2 - A .... in which the CuO2 layers alternate with oxygen-deficient layers of type AX. The layers AX at both ends of each rocksalt slice have been written explicitly to emphasize the fact that they can be considered part of the rocksalt structure or part of the perovskite structure. The number s is given by s--- 1 - [ l / r ] , where [ l/r] represents the largest integer contained in 1/r. Thus, for r = 1 it is s = 0 on the layers (AX), and (AX)~,_e~, do not exist (case of BaYFcCuOs, sixth line in fig. 6), for r = 2 it is s = 1 and the layer (AX)sffil exists while the layers (AX) ~,_ 2~, are missing, and for r > 2, s = 1 and both (AX)sffil and (AX)~,_z), exist. The
A. ~hibJ'o et aL / CO~talchemist'~. ~ft~pet'conduetOrs
697
"
jinx) }[l~o/,.I ] .... ]~..Olo }[l~o
(AX)s
(SrO)o
[ ] (LaO)c }[ (P.(Ca))o [ (BiO)c(BiO)o] (SrO)c} [ (Pn(Ca))o
]{(LaO)c [ ] { (SrO)c [ (BiO)o(BiO)c ]l~,O~o
(BaO) o
[/T'O~:'OIo ]l~,Olo }[ I~olOa,o
]{l~aOlo [(T-~O)o(T'O)c ](BaO)o }[(Pn(Ca))c] ....
(BaO) o
[/T'O~c
]{
(LaO) o
{ { {
[ [
] ]
]
}[
}[/~:~o~>~ ]{ } [ (P')°(Ca.asSr-'s)c] {
} [(~o(c.~>c] ....
[
] (BaO)o } [(P3(Ca))c] ....
[ [
] ] ]
}[ }[ )[
] .... ] .... ] ....
Fig. 6. Comparison of the structures of La2Ca._lCunO2n+2 (second line); Bi2Sr2Ca._ iCu.O2.+4 (third line), TI2Ba2Ca._ ~Cu.O2.+4 (fourth line), TIBa2Ca2Cu309 (fifth line), BaYFeCuOs (sixth line), Ba2YCu307 (seventh line) and Cao.ssSro.]sCuO2 (last line). In the first line is given the general formula of the structural type. The symbol P.(A' ) represents the sequence CuO2 A' CuO2--"etc, P2~FC)(Y) represents the three layers (Cuo.sFeo.5)02 Y (Cuo.sFeo.5)02, and K the sequence BaO CuO BaO. The asterisk indicates that the CuO layer may be oxygen deficient. In the general formula, the thickness of the rock salt slice is indicated by the integer r, while the integer s is defined in the text.
values
r=2
and
r = 4 generate the series ka2Ca._iCunO2n+2 and (TI,Bi)2(Ba,Sr)2Ca,_l02,+4, respectively. For r=3 and n=3, the compound TIBa2Ca2Cu309 isgenerated [14 ] and for r= I and n=2, BaY(FeCu)Os [15]. Finally compounds such as Ba2YCu307 and (Cao.ssSro.~5)CuO2 [ 16] can only bc described with this scheme as purely perovskite sequences of layers.From fig.6 it is clearthat structures with r even have unit cellscontaining two identical halves of the structure shifted one with respect to the other by a translation vector t= I/ 2(a+b). O n the contrary, when r is odd this does not happen and as a consequence these unit cellshave a much smaller length of the parameter c.
coordination. Following the scheme of fig. 6, we may write the most general formula for these compounds as
(AO).,.(A'O),,(A"),_~ (CuO2), Because of the presence of the AO layers, the Cu atoms at the end of the perovskite slices have a pyramidal coordination. If the valence of the A and A' cations is taken as p and q, respectively, and that of A' and Cu as 2 +, we must have
2 n + x + y = ( p x + q y ) / 2 + 2 n - 1, that is
x(p-2)+y(q-2)=2. 3. General formulas of homologous series Let us assume that in the general formula 1he perovskite slices are comprised of AX and BX2 layers having the following sequence: (CuO2) ( A " ) (CuO2) (A" ) (CuO2) namely all the AX-type layers are oxygen deficient and, consequently, all the Cu atoms have a square
For p=3 and q--2 (case of thallium and barrium, for example), it must be x = 2, while y is not defined. We have then the following set of series of compounds: A2A"_ i Cu,O2,+2
for y = 0
A2A'A~_ICunO2n+3
for y = 1
A2 Af,A~_ l CunO2.+4
for y = 2
A2A~A~_ICu.O2.+5
fory=3
etc.
A. Santoro et al. / Crystal chemistry of superconductors
698
The series corresponding to y = 0 and y = 2 do exist and they are La2Can_tCu,02,+2 and (Bi,TI)2(Sr, Ba)_,Ca,_tCu,O2,+4, respectively. By changing the cation valences and the parameters p and q, all sorts of different compounds can be foreseen. The above series have been derived assuming that the oxidation state of Cu is 2 +. More in general, if the valence of copper is m + , the relationship of equality between cation and anion valences becomes 2 n + x + y = (px+qy)/2+ ( n - 1)+mn/2. Assuming as before p = 3 and q = 2 , and x = 1, the value of y is not defined and we have
m= (l +2n)/ n, i.e., the oxidation state of copper is a function of n. The resulting series can be written:
and 40 K, respectively. The structures of these compounds arc closely related to that of Ba2YCu3OT, and can be described with the mechanism based on the stacking of AX and BX2 layers used previously. The main difference between these materials and those having the rock salt-perovskite structure is that in this case there exist two consecutive, oxygen deficient, layers CuO whose stacking is accompanied by a shift of origin of ( ½, 0, 0 ) [ or (0, ½, 0), as the case may be ]. This configuration may be represented with a sequence such as (CuO)o(CuO)ox in which the symbol (CuO)ox means that the layer is the same as (CuO)o with a shift of origin of 1/2a (the symbol (CuO)or would indicate a shift of origin of l / 2 b ) .
(AO) (A' O),,A;;_ ~(CuO:). that is
Cu 0
AA; A:_, Cu.O2.+ l +.,,
Cu 0
For y = 0, 1, 2 .... we have the series AA~_ ,Cu. O2.+1, AA'A;;_,Cu,,O_,.+2, AA~A;;_ICu.O2.+3,..., respectively. The series TIBa_.Ca._ ,Cu.O2.+3 is obtained for y = 2 . For n = 3, the value of copper is 2.33+ and we have
BaO
AA~Cu307
Cu O= ¥
Cu O=
y=O
AA'A'_4Cu3Os y = 1 AA;_A~Cu309 y = 2
etc.
The compound TIBa2Ca_,Cu~O9 corresponds to y = 2. Note that the member with y = 0 is not Ba2YCu3OT, the well known 93 K superconductor, but a compound with a different structure in which the oxygen atoms of the A"O layers are all missing (which is not the case for the BaO layers in the superconductor BaEYCu3OT).
I
~c_~---¢_-7_Z I
~
BaO
i~
Cu 0
i~
Cu 0
-~ [
aa o
---.I
Cu O= y
I~
Cu O= e= o
4. Materials with crystallographic shear Recently, two new compounds have been discovered in the B a - Y - C u - O quaternary system, namely Ba_,YCu4Os [ 17,18 ] and Ba4Y2CuTOt4+.,- [ 19 ]. They exhibit superconducting transitions at about 80 K
~__----_-~ ~'
Cu 0
Fig. 7. Schematic representation of the crystal structure of Ba2YCu4Os showing two successive C u O layers shifted one with respect to the other by I/2a. This shift induces a crystallographic shear with the consequent formation o f double chains o f edgesharing squares with the copper at the center and the oxygen at the corners.
A. Santoro et al. I C~. stal chemistry of superconductors
{
[
l
}[
{(,,,o>o[
1{
[
699
]
;1
1{(,,.O>o. [(o,,O>ox(O,,o>o](BaO>o}[(.:(',>>o ]
{ (8,.O)o[(OuO)c(OUO)cx](BaO)o×} [(Pa(V))cx(K)o×(P:(Y))cx ] { (BaO)o×[(OI.K))cx(CuO)c](BaO)o} [(Pl(V))c(K)o(Pi(V))c] Fig. 8. Schematic representation of the structures of Ba2YCu3OT, Ba2YCu4Os, and Ba4Y2Cu7Ol4+x. The symbols are the same as those defined for fig. 6. As indicated in the text and in fig. 2, a symbol such as (BX2)ox indicates a mesh identical to (BX2)o, but shifted 1/2 in the direction ofthe a axis.
As we know, the sequence (BaO)c(CuO)o(BaO)c is associated with the presence of corner sharing squares as those existing in the structure of Ba2YCu3OT. It is easy to visualize, then, that the sequence (BaO)c(CuO)o(CuO)ox(BaO)c~ is associated with the existence of double chains of edgesharing squares of the type shown in fig. 7 for Ba2YCu408. The shift of origin of (1/2, 0, 0), and the consequent formation of edge sharing between the squares of adjacent chains is in general referred to as a crystallographic shear. As we have mentioned previously, the structures of Ba2YCu3OT, Ba2YCu4Os, and Ba4Y2Cu7Ot4+x are related to one another. The nature of this relationship is illustrated by the scheme of fig. 8. From the figure it is clear that the structure of Ba4Y2Cu70~4+x is built of single Ba2YCu307 type blocks alternating with single Ba2YCu4Os type blocks. The materials containing layers of CuO not involved in the formation of double chains of edge-sharing squares may be "oxygen deficient (case of Ba2YCu307_x and Ba4Y2Cu70~4+x), while a compound such as Ba2YCu4Os is stoichiometric. The presence of these CuO layers is marked with an asterisk in fig. 8. As we have done for the rock salt-perovskite structural type, also in this case we may build different theoretical structures by changing the composition a n d / o r the ordering of the constituent blocks. For example, a compound in which single blocks of BazYCu30~ alternate with double blocks of Ba2YCu4Os can be envisaged using the scheme indicated in fig. 8. Its formula would be Ba6Y3Cul IO23 (or more precisely, Ba6Y3Cul iO22+x since the blocks of Ba2YCu307 may have additional oxygen vacan-
cies in the CuO layers not involved in the formation of double chains). Attempts to prepare this and other compounds will be made in the near future. 5. Conclusions In this paper we have shown that all the superconductors discovered so far can be described in terms of two basic structural types. One is made by alternating slices having the rock salt and perovskite structure. The thickness and the chemical nature of these slices may vary significantly, thus accounting for the large number of compounds prepared to the present day. The other structural type comprises blocks with the perovskite structure alternating with blocks in which a crystallographic shear is present. This description allows one to envisage new structures built by using blocks containing the key structural elements present in all the currently known superconductors. References [ I ] See, e.g.J.E. Greedan, A. O'Reilly and C.V. Stager, Phys. Rev. B 35 (1987) 8770. [2] R.J. Cava, A. Santoro, D.W. Johnson and W.W. Rhodes, Phys. Rev. B 35 (1987) 6716. [3] M.A. Subramanian, C.C. Tarardi, J.C. Calabrese, J. Gopalakrishnan, K.J. Morrissey, T.R. Askew, R.B. Flippen, U. Chowdhry and A.W. Sleight, Science 239 (1988) 1015. [4]C.C. Torardi, M.A. Subramanian, J.C. Calabrese, J. Gopalakrishnan, K.J. Morrissey, T.R. Askew, R.B. Flippen, U. Chowdhry and A.W. Sleight, Science 240 ( 1988 ) 631.
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A. Santoro et al. / Crystal chemist~ o f superconductors
[5] B. Aurivillius, Arkiv Kemi 1 (1949) 463; Arkiv Kemi 2 (1950) 519. [6] S.N. Ruddlesden and P. Popper, Acta Crystallogr. 10 ( 1957 ) 538;ibid. 11 (1958) 54. [7] J.M. Longo and P.M. Raccah, J. Solid State Chem. 6 (1973) 526. [8 ] D.M. Smyth, 90th Annual Meeting of the American Ceramic Society. Cincinnati, USA (1988). [9] A.H. Davies and R.J.D. Tilley, Nature 326 (1987) 859. [10] N. Nguyen, L. Er-Rakho, C. Michel, J. Choisinet and B. Raveau, Mat. Res. Bull. 15 (1980) 891. [ 11 ] N. Nguyen, C. Michel, F. Studer and B. Raveau, Mater. Chem. 7 (1982) 413. [ 12 ] P. Bordet, J.J. Capponi, C. Chaillout, J. Chenavas, A.W. Hewat, E.A. Hewat, J.L. Hodeau, M. Marezio, J.L. Tholence and D. Tranqui, Physica C 156 (1988) 189. [13] D.E. Cox, C.C. Torardi, M.A. Subramanian, J. Gopalakrishnan and A.W. Sleight, Phys. Rev., submitted.
[ 14] S.S.P. Parkin, V.Y. Lee, A.I. Nazzal, E.M. Engler, R. Savoy, R, Beyers and S.J. LaPlaca, Jpn. J. Appl. Phys. 27 (1988) L837. [ 15 ] T, Siegrist, personel communication. [16]T. Siegrist, S.M. Zahurak, D.W. Murphy and R.S. Roth, Nature 334 (1988) 231. [ 17 ] K. Char, M. Lee, R.W. Barton, A.F. Marshall, 1. Bozovic, R,H. Hammond, M.R. Beasley, T.H. Geballe, A. Kapitulnik and S.S. Laderman, Phys. Rev. B 38 (1988) 834. [ 18] P. Marsh, R.M. Fleming, M.L. Mandich, A.M. DeSantolo, J. Kwo, M. Hong and L.J. Martinez-Miranda, Nature 334 (1988) 141. [19]P. Bordet, C. Chaillout, J. Chenavas, J.L. Hodeau, M. Marezio, J. Karpinski and E. Kaldis, Nature 334 (1988) 596.