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Structural architecture of superconducting oxides
Physica C 161 (1989) 512-516 North-Holland
STRUCTURAL ARCHITECTURE OF SUPERCONDUCTING OXIDES J. H A U C K and K. M I K A Institut ~ r Festk6rperforschung,, KFA, D-5170 Jiilich, Fed. Rep. Germany Received 27 July 1989 Revised manuscript received 2 October 1989
The crystal structures of Ba2YCu307, Lan~-lCunO3n+t, Bi2Sr2Can_lCUnO2n+4 and TIBa2Can_lCunO2n+3 (n= 1-3) can be considered as a combination of structural subunits with (Ca, Sr)CuO2, CaTiO3 and VH structure. The VH and (Ca, Sr)CuO2 units are linked to CaTiO3 units in symmetrical combinations. The oxygen content and formal valence of metal atoms vary with the number of CaTiO3 structural units. Eight different formulas MxOy (x-< 8 ) with twenty-three different crystal structures and formal valence of M atoms are suggested for possible candidates in addition to the fifteen experimental structures.
1. Introduction
2. Combination of CaCuO2, CaTiO3 and V H
subunits The crystal structures o f the superconducting oxides Ba2YCu307, (Ba,K)BiO3, La2_rSrrCuO4, Pb2Sr2(Y, Ca)Cu3Os, Bi2Sr2Can_lCUnOEn+4 and T1Ba2Can_lCu~O2n+3 with n = 1-4 [ 1 ] can be compared, if the metal a t o m s M = B a , Bi, Cu, etc. and oxygen atoms are shifted to the positions of a bodycentered metal lattice M with oxygen a t o m s at octahedral interstices [2]. It has been d e m o n s t r a t e d that the structures can be described as a c o m b i n a t i o n o f structural subunits with (Ca, Sr)CuO2, CaTiO3 and VH structure in the ratio u, v, w. The oxygen atoms of these oxides are as far apart as possible. The structures are on a hyperbolic triangle as the limiting surface o f a three-dimensional Ising model, which considers oxygen-oxygen interactions for three coo r d i n a t i o n shells [2 ]. This extremal surface contains only structures f o r m e d by c o m b i n a t i o n o f structural elements u, v, w. The present investigation shows how to combine these structural subunits and how to vary the o x y g e n / m e t a l ratio r = y / x in MxOy in order to yield new structures. The large n u m b e r o f possible c o m b i n a t i o n s (several t h o u s a n d s ) can be reduced to thirty-eight structures in the present case. This information should be useful in the quest for new superconducting compounds.
0921-4534/89/$03.50 © Elsevier Science Publishers B.V. ( North-Holland )
The crystal structures o f tetragonal or pseudotetragonal superconducting oxides can be constructed by c o m b i n a t i o n o f u CaCuO2 (short for (Ca, Sr)CuO2), /9 CaTiO3 and w VH structural subunits shown in fig. 1. The cubic or tetragonal subunits can have different origin o f metal a t o m s and different orientation o f oxygen a t o m s as specified by u', u", etc. They can be c o m b i n e d at c o m m o n interfaces as indicated by arrows. The smallest unit for combination contains ½ o f the cubic or pseudocubic unit cells o f CaCuO2, CaTiO3 and VH, which are considered as u, v, w unities in this investigation. They are indicated by different shading for identification. Fig. 2 shows the crystal structures o f superconducting oxides, some non-superconducting oxides such as BaYCuFeOs, La2SrCu206, LaaCu207, La4Cu3Olo [ 2 ] and twelve theoretical structures with a m a x i m u m o f eight metal atoms. The comparison o f the experimental structures indicates that the architecture o f superconducting oxides is limited by the following rules (see fig. 2 and table I): ( a ) The v CaTiO3 subunits must be an even n u m b e r per formula unit. This is because the three oxygen atoms at v = 2 cannot be split. (b) The v=O, 2, 4, 6 CaTiO3 units are combined with
J. Hauck, K. Mika / Structural architecture of superconducting oxides ^
,^
v,w u=O
u=2
513
u=t,
u,6
CoTi'03 BaYCuFeOs BazYCu307
Laz.Cu0~i
LazSrCq206
TL'B°zCuOs i ~
B
i
~
Doz i
u207
Md09
M70a
tBaa(.~:~w3 9
z
z
Sr2CazCu301o
2,~
N A
M607
Me09 2,6
2,5 ~ n
L.Q3Cuz07 '
M709
6,1 ~
6,2 t
ha4Cu3010 Fig. I. Projection ofu (Ca, Sr)CuO2, v CaTiO3 and w VH structures in different settings u, u', etc. The metal atoms occupy the origin and the center of the cubic or pseudocubic unit cells. The oxygen atoms at octahedral interstices are at projection height 0 ( • ) or 0.5 (tD). Arrowsindicate common interfaces.
Fig. 2. Combination of the structural subunits of fig. 1 to MxOy (x<8) oxide structures as indicated by the u, v, w values and different shadings. Bi2Sr2Ca2Cu3Otowith x= 9 is added.
(g) (c) (d)
(e)
(f)
w = 0 , 1, 2, ... 5 VH units in the vertical row of fig. 2 at u = 0 CaCuO 2 and u = 2 , 4 or 6 CaCuO2 subunits are added to these structures in the horizontal rows. All crystal structures contain mirror planes, which are indicated by the dashed lines in fig. 2. This is only possible for even values of u as implied by (c). The c o m p o u n d s MxOy with x = 3 , 5, 7 possess I centered cells with translations a / 2 , b/2, c / 2 of all atoms. Only half of the unit cells are shown in fig. 2. The VH units in the center interface with CaTiO3 units on each side. CaCuO2 units are at the extremes. Crystal structures with w = 0 are centered by CaCuO2 units (table I).
Me011
(h)
The w, w", u* and u** structural units do not occur in superconducting oxides. The c o m p o u n d s MxOy with x = 3, 5, 7 possess an even n u m b e r of M atoms in symmetrical positions plus one M atom on a mirror plane, e.g. the Cu atom of Bi2Sr2CuO6. C o m p o u n d s MxOy with x = 4 , 6, 8 are with two M atoms on mirror planes, e.g. T1 and Ca of T1Ba2CaCu2OT.
The superconducting transition temperatures from ref. [1] are plotted for different percentages of CaTiO3 v / ( v + w ) and different u values (fig. 3). By what is known today high-To values are found at ~ 50 and 100% CaTiO3. Crystal structures with small unit cells occur at 0, 50 and 100% CaTiO3. The combinations of w and u' at v = 0 form one-dimensional M - O - M ribbons (fig. 2). All other structures pos-
514
J. Hauck, K. Mika / Structural architecture o f superconducting oxides
Table I Sequence of u, u', u" or u" (Ca, Sr)CuO2, vor v' CaTiO3 and w or w' VH structural subunits per given formula M~Oy, x = u + v + w , y = x + v / 2 at increased x, w and v, resp. The neighbouring units follow in symmetric setting, e.g. vw' v' v' w'v for
(La, Sr)zCuO4. MxOy
uvw units
(Ca, Sr)CuO 2
u2 v2 w2
CaTiO3
VH (La, Sr)2CuO4
vw'v'
M405
vu~v
BaYCuFeO5
v' u ~v'
TIBa2CuO5
vw'2 v u" v' w' vu
La2Srfu206 La3Cu207 BizSr2CuO6 M607 M607 BazYCu307 Ba2LaCu308 M608 TIBazCaCu207
u2 w' l)2 vw'3 v'
vu~,v V' U'~V' u' VUzVU' v2uzv2 V'2U~U~'V'2 u" v' w'2 v' u"
U
8
122
6.
4.
•
2.
•
0
.
• .
.
.
110 110
•
90
90
+
12
70
•
90 •
40
+
" *
+
30 i
;
'
o12'
'
0'6
'
o18
'
vl(v+w) Fig. 3. T¢/K values [1] of Bi2Sr2Ca~_lCUnO2n+4, TIBa2Can_lCunO2n+3 ( n = 1-4), (La, Sr)2CuO4, (Ba, K)BiO3 and Ba2YCu307 (from left to right), at different percentage o f u, v, w structural subunits. + and • are non-superconducting oxides and theoretical structures of fig. 2, resp.
3. Oxygen content and coordination numbers The general formula for the oxides is M~+~OLsv+,, n = u + w with u, v, w being the number of CaCuO2, CaTiO3 and VH structural subunits. The oxygen content/metal atom increases from MnOn to
M6Os
v~w~v~
M607 MTOs M709
VW'4V U2VW' V' U'~ U' V2w' v'2u"
La4Cu3Olo
v3 w' v]
M2+nO3+n, M4+nO6+n, M 6 + n O 9 + n ( n = 0 ,
Bi2Sr2CaCu2Os M709 MTOs MsO9 MsO 9 M809 M809 MsOlo MsO,o MsOll MsOl~
u" v' w'3 vu vt2we3v 2 vw's v"
the number v=O, 2, 4, 6 of CaTiO3 structural subunits/formula increases. The increased oxygen content/metal atom can be correlated to an increased formal valence of metal atoms. We have chosen the elements Ti, La, Cu for the formal valence + 4 , + 3 and +2, resp. and have selected formulas with a maximum of eight M atoms. In MnOn i.e. v = 0 , for example CaCuOz, all M atoms have a formal valence of +2. There are two series of compounds at v=2: TiCul+nO3+n and LazCu~O3+n. SrTiO3 belongs to the first series, La2CuO4, Ba2YCu3OT, TIBa2Can_iCunO2n+3and Bi2Sr2Can_ iCunO2~+4 to the second series. One Cu atom of BaEYCu3 and T1BazCa._ ICunO2n+3is at the trivalent state. Three series can be formulated at v=4: TiLa/Cu~+,O6+,, Ti2Cu2+nO6+n and La4CunO6+,, four at v=6; TiLa4Cul +nOg+~, Ti2La2Cu2+nO9+n,La6CunO9+nand T i 3 C u 3 + n O 9 + n. The oxides La3Cu207 and Ba2LaCu3Os with v = 4 and La4Cu3Olo with v = 6 (table I) are within the series La4Cu,O6+n ( v = 4 ) and La6CUnOg+n(/)=6). Part of the Ti, La and Cu atoms are exchanged by other atoms with the same valence but different coordination. The local ge-
T1Ba2Ca2Cu309
Ms01o
MsOII MsO9 MsOio M809
VU~V V'U'~V'
U2VU~UU2 U'~'V'U'~ v2u4v2 v'zu~' v'2 v'3v' u'~' v'3 v3u'2v3 u2 vw'2 tru2 U' U2Wt2U2u' V3 W'2U3 U" U' W'aF'U"
v~w~V~ VW'6V
sess M - O - M planes linked either in two dimensions or three dimensions. The two-dimensional Cu-O-Cu sheets, which occur in u or u" CaCuO2 and/) or v' CaTiO3 subunits, are believed to be crucial for high temperature superconductivity [ 1 ].
1, 2 ...) a s
•1. Hauck, K. Mika / Structural architecture of superconducting oxides ometry and c o o r d i n a t i o n n u m b e r m a y be correlated to the size and the preference in known compounds. For example, divalent Cu favors five or six fold coordination, Ca favors eight fold and Ba from ten to twelve fold coordination. F o r a new superconducting candidate, at least one C u - O - C u plane o f the u, u", v or v' subunits should be present. The other positions o f divalent M can be occupied by alcaline earths, Pb 2+, etc. This latter substitution depends on size and coordination. M o n o v a l e n t atoms such as K might be introduced in c o m b i n a t i o n s with other atoms. F o r example, K + La could substitute for 2 Cu or 2 K + T i could substitute for 3 Cu. The oxygen content can be increased, if two u units are filled up to v units. An example o f this would be the sequence u' vu2vu' for Ba2YCu307 going to/32u2u2 for Ba2LaCu308 ( " s t o i c h i o m e t r i c " tetragonal Ba2YCu3Ox) (table I).
515
VH
x "VH2 x'
"VH3
"VHo. 5
Ndz Cu Ol,
Pb 2 Sr2 (Y, Ccl) Cu? 0 a
Fig. 4. Schematic crystal structures of T' and T* (Nd, Ce, Sr)2CuO4 and Pb2Sr2 (Y, Ca)Cu308 containing the new structural subunits VH2 and VHo.5. ( x ' u ~ ) interface with half o f the (La, structure (v' w' v).
Sr)2CuO4
5. Conclusion 4. Other combinations The T' and T* phases o f (Nd, Ce, S r ) z C u O 4 [3] and Pb2Sr2(Y, Ca)Cu308 [ 1 ] can be considered as interstitial c o m p o u n d s with b o d y centered M lattices. The (Nd, Ce, Sr)eCu metal lattice is similar to the Hf2Cu lattice (MoSi2 structure). The oxygen sublattices possess new structural elements. T* and T' Nd2CuO4 contain x ' = 1 or 2 subunits o f VH2, respectively. Pb2Sr2 (Y, Ca)Cu308 contains y = 2 VHo.5 subunits. The VHz structure has interstitial H a t o m s at sites which are e m p t y in the VH structure. Occupation o f all octahedral sites in the bcc V lattice would yield the VH 3 composition. The oxygen a t o m s in the x ' VH2 subunit o f NdzCuO4 are shifted towards the CaCuO2 units as indicated by the arrows in fig. 4. In the experimental VHz structure (CaF2structure t y p e ) the shift o f H a t o m s gives rise to a tetragonal elongation in c direction by a factor c/ a = x / 2 . Besides this the H a t o m s o f experimental VH2 are shifted to tetrahedral interstices by c/4. The three superconducting oxides o f fig. 4 with combinations u"v'w'y2w'v'u" (Pb2Sr2(Y, C a ) C u 3 O s ) , u2x'2u2 or x ' u g x ' ( T ' ) a n d x ' u ~ v ' w ' v (T*) can be c o m p a r e d with the oxides lg"U'W'U'2W'V'U " (M809) , v'u'~v' (M607) a n d vw'v' ( ( L a , Sr)ECuO4). The c o m b i n a t i o n o f T* structure is not symmetrical. H a l f o f the T ' structure
The crystal structures o f superconducting oxides and some structurally related c o m p o u n d s can be considered as a c o m b i n a t i o n o f u, u', u" and u " CaCuO2, v and v' CaTiO 3 and w or w' VH structural subunits as listed in table I. u', u", v', w', etc. differ from u, v, w by the shift o f origin or different orientation (fig. 1 ). Each subunit with the a p p r o x i m a t e lattice constants a = b = a o , c = a o / 2 (ao0.4 n m ) contains one metal a t o m and one oxygen a t o m ( 1.5 oxygen for C a T i O 3 / 2 unit). The composition o f the oxides MxOy with x = u + v + w and y = x + v / 2 can be o b t a i n e d from the u, u' etc. values o f table I. Different c o m b i n a t i o n s o f u, v, w etc. subunits can be constructed with v # 0 as observed in superconducting oxides. F o u r structures are obtained at c--2ao, twenty-one at c = 3 a o , one h u n d r e d a n d eight at c-- 4ao and six hundred and fifty-one at c = 5ao. These numbers decrease to 4, 16, 49 and 147, resp., if only symmetrical structures are selected. A further reduction to 3, 9, 14 and 22, resp. is obtained, if the subunits are c o m b i n e d similarly to the experimental oxides. The crystal structures o f experimental oxides, which have w # 0 as listed in table I are symmetric with w' units in the middle, v or v' units as nearest neighbours and u, u', u" or u"' units at the extremes (table I). W i t h w = 0, the BaYCuFeO5 and Ba2YCu307 structures have u units as their centers.
516
J. Hauck, K. Mika / Structural architecture of superconducting oxides
All c o m p o u n d s MxOy with o d d numbers o f metal atoms x, e.g. (La, Sr)2CuO4 with x = 3 or Bi2Sr2CuO6 with x = 5 possess I centered unit cells twice as long as listed in table I. In these cases the second half is symmetric to the first, e.g. v w ' v ' v ' w ' v for (La, Sr)2CuO4. The subunits w, w", u* and u** do not occur in the superconducting compounds. Twentythree new structures with a m a x i m u m o f eight M atoms are closely related to the fifteen experimental structures. They are listed in table I. N i n e o f these twenty-three are shown in fig. 2. The structures M709, v'2w'3v2 and MaOm, v'zw'4v'2 have been reported very recently for the new c o m p o u n d s (Bi, Pb) 2Sr2BiFe209 and Bi2SraFe2Olo, resp. [4]. Other c o m p o u n d s like Bi2Sr2Ca2Cu3Olo [ 1 ], (Bi, Pb)2SrzBi2Fe3Ol2 and (Bi, Pb)2Sr2Bi3Fe40~5 [4] are with the same structural architecture U2UWf3U'U~ (fig. 2), UI3W~3U3 and v'4W'aV4 but with x > 8 M atoms.
The formal valence o f metal a t o m s o f superconducting c o m p o u n d s containing v = 2 CaTiO3 subunits can be correlated in two series: T i C u l + , O 3 + n and La2CunO3+n. Here Ti, La and Cu stand for tetra-, tri- and divalent atoms, resp. Three formulas were derived for v = 4 , four formulas for v = 6 . In order to obtain a new stable structure type o f particular composition, one would substitute a t o m s o f suitable size, valence and c o o r d i n a t i o n n u m b e r for the various metal atoms o f the theoretical structures.
References [ 1] A.W. Sleight, Science 242 ( 1988 ) 1519. [2] J. Hauck, D. Henkel and K. Mika, Solid State Commun. 70 (1989) 735. [3 ] Y. Tokura, H. Takagi and S. Uchida, Nature 337 (1989) 345. [4 ] T. Fries, G. Mayer-von Kiirthy, A. Ehmann and S. KemmlerSack, J. Less Common Metals, preprint.
STRUCTURAL ARCHITECTURE OF SUPERCONDUCTING OXIDES J. H A U C K and K. M I K A Institut ~ r Festk6rperforschung,, KFA, D-5170 Jiilich, Fed. Rep. Germany Received 27 July 1989 Revised manuscript received 2 October 1989
The crystal structures of Ba2YCu307, Lan~-lCunO3n+t, Bi2Sr2Can_lCUnO2n+4 and TIBa2Can_lCunO2n+3 (n= 1-3) can be considered as a combination of structural subunits with (Ca, Sr)CuO2, CaTiO3 and VH structure. The VH and (Ca, Sr)CuO2 units are linked to CaTiO3 units in symmetrical combinations. The oxygen content and formal valence of metal atoms vary with the number of CaTiO3 structural units. Eight different formulas MxOy (x-< 8 ) with twenty-three different crystal structures and formal valence of M atoms are suggested for possible candidates in addition to the fifteen experimental structures.
1. Introduction
2. Combination of CaCuO2, CaTiO3 and V H
subunits The crystal structures o f the superconducting oxides Ba2YCu307, (Ba,K)BiO3, La2_rSrrCuO4, Pb2Sr2(Y, Ca)Cu3Os, Bi2Sr2Can_lCUnOEn+4 and T1Ba2Can_lCu~O2n+3 with n = 1-4 [ 1 ] can be compared, if the metal a t o m s M = B a , Bi, Cu, etc. and oxygen atoms are shifted to the positions of a bodycentered metal lattice M with oxygen a t o m s at octahedral interstices [2]. It has been d e m o n s t r a t e d that the structures can be described as a c o m b i n a t i o n o f structural subunits with (Ca, Sr)CuO2, CaTiO3 and VH structure in the ratio u, v, w. The oxygen atoms of these oxides are as far apart as possible. The structures are on a hyperbolic triangle as the limiting surface o f a three-dimensional Ising model, which considers oxygen-oxygen interactions for three coo r d i n a t i o n shells [2 ]. This extremal surface contains only structures f o r m e d by c o m b i n a t i o n o f structural elements u, v, w. The present investigation shows how to combine these structural subunits and how to vary the o x y g e n / m e t a l ratio r = y / x in MxOy in order to yield new structures. The large n u m b e r o f possible c o m b i n a t i o n s (several t h o u s a n d s ) can be reduced to thirty-eight structures in the present case. This information should be useful in the quest for new superconducting compounds.
0921-4534/89/$03.50 © Elsevier Science Publishers B.V. ( North-Holland )
The crystal structures o f tetragonal or pseudotetragonal superconducting oxides can be constructed by c o m b i n a t i o n o f u CaCuO2 (short for (Ca, Sr)CuO2), /9 CaTiO3 and w VH structural subunits shown in fig. 1. The cubic or tetragonal subunits can have different origin o f metal a t o m s and different orientation o f oxygen a t o m s as specified by u', u", etc. They can be c o m b i n e d at c o m m o n interfaces as indicated by arrows. The smallest unit for combination contains ½ o f the cubic or pseudocubic unit cells o f CaCuO2, CaTiO3 and VH, which are considered as u, v, w unities in this investigation. They are indicated by different shading for identification. Fig. 2 shows the crystal structures o f superconducting oxides, some non-superconducting oxides such as BaYCuFeOs, La2SrCu206, LaaCu207, La4Cu3Olo [ 2 ] and twelve theoretical structures with a m a x i m u m o f eight metal atoms. The comparison o f the experimental structures indicates that the architecture o f superconducting oxides is limited by the following rules (see fig. 2 and table I): ( a ) The v CaTiO3 subunits must be an even n u m b e r per formula unit. This is because the three oxygen atoms at v = 2 cannot be split. (b) The v=O, 2, 4, 6 CaTiO3 units are combined with
J. Hauck, K. Mika / Structural architecture of superconducting oxides ^
,^
v,w u=O
u=2
513
u=t,
u,6
CoTi'03 BaYCuFeOs BazYCu307
Laz.Cu0~i
LazSrCq206
TL'B°zCuOs i ~
B
i
~
Doz i
u207
Md09
M70a
tBaa(.~:~w3 9
z
z
Sr2CazCu301o
2,~
N A
M607
Me09 2,6
2,5 ~ n
L.Q3Cuz07 '
M709
6,1 ~
6,2 t
ha4Cu3010 Fig. I. Projection ofu (Ca, Sr)CuO2, v CaTiO3 and w VH structures in different settings u, u', etc. The metal atoms occupy the origin and the center of the cubic or pseudocubic unit cells. The oxygen atoms at octahedral interstices are at projection height 0 ( • ) or 0.5 (tD). Arrowsindicate common interfaces.
Fig. 2. Combination of the structural subunits of fig. 1 to MxOy (x<8) oxide structures as indicated by the u, v, w values and different shadings. Bi2Sr2Ca2Cu3Otowith x= 9 is added.
(g) (c) (d)
(e)
(f)
w = 0 , 1, 2, ... 5 VH units in the vertical row of fig. 2 at u = 0 CaCuO 2 and u = 2 , 4 or 6 CaCuO2 subunits are added to these structures in the horizontal rows. All crystal structures contain mirror planes, which are indicated by the dashed lines in fig. 2. This is only possible for even values of u as implied by (c). The c o m p o u n d s MxOy with x = 3 , 5, 7 possess I centered cells with translations a / 2 , b/2, c / 2 of all atoms. Only half of the unit cells are shown in fig. 2. The VH units in the center interface with CaTiO3 units on each side. CaCuO2 units are at the extremes. Crystal structures with w = 0 are centered by CaCuO2 units (table I).
Me011
(h)
The w, w", u* and u** structural units do not occur in superconducting oxides. The c o m p o u n d s MxOy with x = 3, 5, 7 possess an even n u m b e r of M atoms in symmetrical positions plus one M atom on a mirror plane, e.g. the Cu atom of Bi2Sr2CuO6. C o m p o u n d s MxOy with x = 4 , 6, 8 are with two M atoms on mirror planes, e.g. T1 and Ca of T1Ba2CaCu2OT.
The superconducting transition temperatures from ref. [1] are plotted for different percentages of CaTiO3 v / ( v + w ) and different u values (fig. 3). By what is known today high-To values are found at ~ 50 and 100% CaTiO3. Crystal structures with small unit cells occur at 0, 50 and 100% CaTiO3. The combinations of w and u' at v = 0 form one-dimensional M - O - M ribbons (fig. 2). All other structures pos-
514
J. Hauck, K. Mika / Structural architecture o f superconducting oxides
Table I Sequence of u, u', u" or u" (Ca, Sr)CuO2, vor v' CaTiO3 and w or w' VH structural subunits per given formula M~Oy, x = u + v + w , y = x + v / 2 at increased x, w and v, resp. The neighbouring units follow in symmetric setting, e.g. vw' v' v' w'v for
(La, Sr)zCuO4. MxOy
uvw units
(Ca, Sr)CuO 2
u2 v2 w2
CaTiO3
VH (La, Sr)2CuO4
vw'v'
M405
vu~v
BaYCuFeO5
v' u ~v'
TIBa2CuO5
vw'2 v u" v' w' vu
La2Srfu206 La3Cu207 BizSr2CuO6 M607 M607 BazYCu307 Ba2LaCu308 M608 TIBazCaCu207
u2 w' l)2 vw'3 v'
vu~,v V' U'~V' u' VUzVU' v2uzv2 V'2U~U~'V'2 u" v' w'2 v' u"
U
8
122
6.
4.
•
2.
•
0
.
• .
.
.
110 110
•
90
90
+
12
70
•
90 •
40
+
" *
+
30 i
;
'
o12'
'
0'6
'
o18
'
vl(v+w) Fig. 3. T¢/K values [1] of Bi2Sr2Ca~_lCUnO2n+4, TIBa2Can_lCunO2n+3 ( n = 1-4), (La, Sr)2CuO4, (Ba, K)BiO3 and Ba2YCu307 (from left to right), at different percentage o f u, v, w structural subunits. + and • are non-superconducting oxides and theoretical structures of fig. 2, resp.
3. Oxygen content and coordination numbers The general formula for the oxides is M~+~OLsv+,, n = u + w with u, v, w being the number of CaCuO2, CaTiO3 and VH structural subunits. The oxygen content/metal atom increases from MnOn to
M6Os
v~w~v~
M607 MTOs M709
VW'4V U2VW' V' U'~ U' V2w' v'2u"
La4Cu3Olo
v3 w' v]
M2+nO3+n, M4+nO6+n, M 6 + n O 9 + n ( n = 0 ,
Bi2Sr2CaCu2Os M709 MTOs MsO9 MsO 9 M809 M809 MsOlo MsO,o MsOll MsOl~
u" v' w'3 vu vt2we3v 2 vw's v"
the number v=O, 2, 4, 6 of CaTiO3 structural subunits/formula increases. The increased oxygen content/metal atom can be correlated to an increased formal valence of metal atoms. We have chosen the elements Ti, La, Cu for the formal valence + 4 , + 3 and +2, resp. and have selected formulas with a maximum of eight M atoms. In MnOn i.e. v = 0 , for example CaCuOz, all M atoms have a formal valence of +2. There are two series of compounds at v=2: TiCul+nO3+n and LazCu~O3+n. SrTiO3 belongs to the first series, La2CuO4, Ba2YCu3OT, TIBa2Can_iCunO2n+3and Bi2Sr2Can_ iCunO2~+4 to the second series. One Cu atom of BaEYCu3 and T1BazCa._ ICunO2n+3is at the trivalent state. Three series can be formulated at v=4: TiLa/Cu~+,O6+,, Ti2Cu2+nO6+n and La4CunO6+,, four at v=6; TiLa4Cul +nOg+~, Ti2La2Cu2+nO9+n,La6CunO9+nand T i 3 C u 3 + n O 9 + n. The oxides La3Cu207 and Ba2LaCu3Os with v = 4 and La4Cu3Olo with v = 6 (table I) are within the series La4Cu,O6+n ( v = 4 ) and La6CUnOg+n(/)=6). Part of the Ti, La and Cu atoms are exchanged by other atoms with the same valence but different coordination. The local ge-
T1Ba2Ca2Cu309
Ms01o
MsOII MsO9 MsOio M809
VU~V V'U'~V'
U2VU~UU2 U'~'V'U'~ v2u4v2 v'zu~' v'2 v'3v' u'~' v'3 v3u'2v3 u2 vw'2 tru2 U' U2Wt2U2u' V3 W'2U3 U" U' W'aF'U"
v~w~V~ VW'6V
sess M - O - M planes linked either in two dimensions or three dimensions. The two-dimensional Cu-O-Cu sheets, which occur in u or u" CaCuO2 and/) or v' CaTiO3 subunits, are believed to be crucial for high temperature superconductivity [ 1 ].
1, 2 ...) a s
•1. Hauck, K. Mika / Structural architecture of superconducting oxides ometry and c o o r d i n a t i o n n u m b e r m a y be correlated to the size and the preference in known compounds. For example, divalent Cu favors five or six fold coordination, Ca favors eight fold and Ba from ten to twelve fold coordination. F o r a new superconducting candidate, at least one C u - O - C u plane o f the u, u", v or v' subunits should be present. The other positions o f divalent M can be occupied by alcaline earths, Pb 2+, etc. This latter substitution depends on size and coordination. M o n o v a l e n t atoms such as K might be introduced in c o m b i n a t i o n s with other atoms. F o r example, K + La could substitute for 2 Cu or 2 K + T i could substitute for 3 Cu. The oxygen content can be increased, if two u units are filled up to v units. An example o f this would be the sequence u' vu2vu' for Ba2YCu307 going to/32u2u2 for Ba2LaCu308 ( " s t o i c h i o m e t r i c " tetragonal Ba2YCu3Ox) (table I).
515
VH
x "VH2 x'
"VH3
"VHo. 5
Ndz Cu Ol,
Pb 2 Sr2 (Y, Ccl) Cu? 0 a
Fig. 4. Schematic crystal structures of T' and T* (Nd, Ce, Sr)2CuO4 and Pb2Sr2 (Y, Ca)Cu308 containing the new structural subunits VH2 and VHo.5. ( x ' u ~ ) interface with half o f the (La, structure (v' w' v).
Sr)2CuO4
5. Conclusion 4. Other combinations The T' and T* phases o f (Nd, Ce, S r ) z C u O 4 [3] and Pb2Sr2(Y, Ca)Cu308 [ 1 ] can be considered as interstitial c o m p o u n d s with b o d y centered M lattices. The (Nd, Ce, Sr)eCu metal lattice is similar to the Hf2Cu lattice (MoSi2 structure). The oxygen sublattices possess new structural elements. T* and T' Nd2CuO4 contain x ' = 1 or 2 subunits o f VH2, respectively. Pb2Sr2 (Y, Ca)Cu308 contains y = 2 VHo.5 subunits. The VHz structure has interstitial H a t o m s at sites which are e m p t y in the VH structure. Occupation o f all octahedral sites in the bcc V lattice would yield the VH 3 composition. The oxygen a t o m s in the x ' VH2 subunit o f NdzCuO4 are shifted towards the CaCuO2 units as indicated by the arrows in fig. 4. In the experimental VHz structure (CaF2structure t y p e ) the shift o f H a t o m s gives rise to a tetragonal elongation in c direction by a factor c/ a = x / 2 . Besides this the H a t o m s o f experimental VH2 are shifted to tetrahedral interstices by c/4. The three superconducting oxides o f fig. 4 with combinations u"v'w'y2w'v'u" (Pb2Sr2(Y, C a ) C u 3 O s ) , u2x'2u2 or x ' u g x ' ( T ' ) a n d x ' u ~ v ' w ' v (T*) can be c o m p a r e d with the oxides lg"U'W'U'2W'V'U " (M809) , v'u'~v' (M607) a n d vw'v' ( ( L a , Sr)ECuO4). The c o m b i n a t i o n o f T* structure is not symmetrical. H a l f o f the T ' structure
The crystal structures o f superconducting oxides and some structurally related c o m p o u n d s can be considered as a c o m b i n a t i o n o f u, u', u" and u " CaCuO2, v and v' CaTiO 3 and w or w' VH structural subunits as listed in table I. u', u", v', w', etc. differ from u, v, w by the shift o f origin or different orientation (fig. 1 ). Each subunit with the a p p r o x i m a t e lattice constants a = b = a o , c = a o / 2 (ao0.4 n m ) contains one metal a t o m and one oxygen a t o m ( 1.5 oxygen for C a T i O 3 / 2 unit). The composition o f the oxides MxOy with x = u + v + w and y = x + v / 2 can be o b t a i n e d from the u, u' etc. values o f table I. Different c o m b i n a t i o n s o f u, v, w etc. subunits can be constructed with v # 0 as observed in superconducting oxides. F o u r structures are obtained at c--2ao, twenty-one at c = 3 a o , one h u n d r e d a n d eight at c-- 4ao and six hundred and fifty-one at c = 5ao. These numbers decrease to 4, 16, 49 and 147, resp., if only symmetrical structures are selected. A further reduction to 3, 9, 14 and 22, resp. is obtained, if the subunits are c o m b i n e d similarly to the experimental oxides. The crystal structures o f experimental oxides, which have w # 0 as listed in table I are symmetric with w' units in the middle, v or v' units as nearest neighbours and u, u', u" or u"' units at the extremes (table I). W i t h w = 0, the BaYCuFeO5 and Ba2YCu307 structures have u units as their centers.
516
J. Hauck, K. Mika / Structural architecture of superconducting oxides
All c o m p o u n d s MxOy with o d d numbers o f metal atoms x, e.g. (La, Sr)2CuO4 with x = 3 or Bi2Sr2CuO6 with x = 5 possess I centered unit cells twice as long as listed in table I. In these cases the second half is symmetric to the first, e.g. v w ' v ' v ' w ' v for (La, Sr)2CuO4. The subunits w, w", u* and u** do not occur in the superconducting compounds. Twentythree new structures with a m a x i m u m o f eight M atoms are closely related to the fifteen experimental structures. They are listed in table I. N i n e o f these twenty-three are shown in fig. 2. The structures M709, v'2w'3v2 and MaOm, v'zw'4v'2 have been reported very recently for the new c o m p o u n d s (Bi, Pb) 2Sr2BiFe209 and Bi2SraFe2Olo, resp. [4]. Other c o m p o u n d s like Bi2Sr2Ca2Cu3Olo [ 1 ], (Bi, Pb)2SrzBi2Fe3Ol2 and (Bi, Pb)2Sr2Bi3Fe40~5 [4] are with the same structural architecture U2UWf3U'U~ (fig. 2), UI3W~3U3 and v'4W'aV4 but with x > 8 M atoms.
The formal valence o f metal a t o m s o f superconducting c o m p o u n d s containing v = 2 CaTiO3 subunits can be correlated in two series: T i C u l + , O 3 + n and La2CunO3+n. Here Ti, La and Cu stand for tetra-, tri- and divalent atoms, resp. Three formulas were derived for v = 4 , four formulas for v = 6 . In order to obtain a new stable structure type o f particular composition, one would substitute a t o m s o f suitable size, valence and c o o r d i n a t i o n n u m b e r for the various metal atoms o f the theoretical structures.
References [ 1] A.W. Sleight, Science 242 ( 1988 ) 1519. [2] J. Hauck, D. Henkel and K. Mika, Solid State Commun. 70 (1989) 735. [3 ] Y. Tokura, H. Takagi and S. Uchida, Nature 337 (1989) 345. [4 ] T. Fries, G. Mayer-von Kiirthy, A. Ehmann and S. KemmlerSack, J. Less Common Metals, preprint.