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Coulomb interactions in superconducting oxides, hydrides and carbides
PhysicaC153-155 (1988) 1173-1174 North-Holland, Amsterdam
C O U L O M B I N T E R A C T I O N S IN S U P E R C O N D U C T I N G OXIDES, H Y D R I D E S AND C A R B I D E S
Jfirgen H A U C K , D o r o t h e a H E N K E L and Klaus M I K A Institut f~r Festkhrperforschung, KFA, D-5170 Jfilich, F R G
Ba2YCu3Oz, La2Cu04, SrTi03 and interstitial alloys M Z z , e.g. F e T i H z , V H z , Y C o C with Z = O, H or C at octahedral sites of the bcc M lattice are analyzed for Coulomb interactions. 1. I N T R O D U C T I O N Superconducting B a 2 Y C u 3 0 z, z = 6 - 8 , La2CuO 4 and the perovskites SrTiO3_z/Ba(Pb, Bi)O 3 can be considered as interstitial alloys M Z z similar to V H z , F e T i H z or Y C o C with Z = O , H or C atoms at octahedral sites of the bcc metal lattice. The interstitial Z atoms have a high mobility because of m a n y vacant interstitial sites with substantial disorder at high temperatures and substantial order at low t e m p e r a t u r e s e.g. below 480K for VHo. 5. Similar to that, the oxygen content of B a 2 Y C u 3 0 z varies in the tetragonal high t e m p e r a t u r e phase between 5.8 < z < 7 and is restricted to small ranges at decreased t e m p e r a t u r e s (1). The structures of the ordered sublattice of Z atoms can be characterized by the coordination numbers T 1 - T 3 of Z atoms with Z atoms at distance a/2, ax/~/2 and ax/~/2 of the bcc lattice constant a and the ratio r = Z / M : (T 1 T 2 T3;r). The m a x i m u m coordination numbers (4 8 8; 3) at occupation of all octahedral sites are reduced by a factor r/3 at reduced r, if the vacant sites are distributed randomly. The number T 1 of nearest neighbors is decreased at Coulomb repulsion of Z atoms, 2"2 and T 3 at attractive interactions. The analysis of ordered superconducting interstitial alloys with fcc M lattice had shown m i n i m u m numbers of T1 values (2). The present investigation compares derivative structures of Z atoms with bcc M lattice. 2. O R D E R I N G O F I N T E R S T I T I A L A T O M S A b o u t 350 structures with Z atoms at octahedral sites of the bcc M lattice were obtained similar as for the fcc M lattice (2). Fig. 1 shows all (0 772 T3; r) structures with m a x i m u m r and few structures for r >_ 0.5. The T3 values of (0 0 8;1), (0 1 6;1), (0 2 4;1), (0 3 2; 1) and (0 4 0; 1) vary with T 2 by 2T2 + T3 = 8 and cannot be increased further at increased r. These structures are identical to tetrahedral site sublattices of e.g. (0 2 4; la) NbH or (0 0 4; 0.5) TaHo.5, if the Z sublattice is lifted by a/4 in projection height. A further increase of r is possible in perovskite related structures
0921 4534/88/$03.50 © ElsevierSciencePublishers B.V. (North-Holland Physics Publishing Division)
(0 4 2; 1), (0 6 1; 1.2) and (0 8 0;1.5) CaTiO 3 with T 2 + 2T 3 = 8. The different O atoms of B a 2 Y C u 3 0 z , z = 6, 7, 8 and La2CuO 4 exhibit two or more different coordinations (Fig. 1). Other structures related to perovskite are (0 4 0/0 5 0;1.125) Ba4YCu309, (0 5 0/0 8 0; 1.125) BasY3CuhOl8 (3) and (0 0 0; 0.hb) Y C o C (4). 3. C O M P A R I S O N W I T H ISING M O D E L The Cowley-Warren short-range order parameters
a i can be obtained from the T i by T(nazai = Ti (T[ nax - Ti)r/(3 - r) with T~naz = 4, 8, 8 at i = 1, 2, 3, resp.. The a i values ( - 1 < a i _< 1) were chosen for comparison with the Ising model of nearest and nextnearest neighbor interactions V/, i = 1, 2 with a i = 0 at Vi = 0, e.g. at r a n d o m distribution, positive a i for attractive interactions (Vi > 0) e.g. cluster formation and segregation (Fig. 2), negative al at repulsive interactions, e.g. Coulomb repulsion. Fig. 2 shows the variation of al, 2 for different series (0 T 2 T3; r) of Fig. 1 with a 1 = - 0 . 5 at m a x i m u m r = 1 and 9 a l + 4 a 2 -- - 5 for perovskite related structures. The upper limit of the fcc M lattice is 4a 1 + a 2 = - 1 . These limits depend also on a3 : a l + a3 = 0 for fcc M , 2a 2 + a 3 -- 0 for bcc M. The superconducting M Z r with fcc or bcc M lattice (Fig. 2) are on or close to the limits. The Z atoms in the fcc M lattice are as far apart as possible with m a x i m u m Coulomb energy. In the bcc M lattice the Coulomb energy decreases with increasing T 2. The Madelung factor (refering to relative prime charges (5)) has a m a x i m u m e.g. for (0 0 8; 1) V H ( M F = 1.484) and decreases ~ 1 % , if T2 is increased by 1. The loss of Coulomb energy of (0 4 0/0 6 0;1) Ba2YCu306 w i t h M F = 1.300 should be compensated by the crystal field stabilization energy. The coordination of M atoms with Z atoms is rather asymmetrical in (0 1 6; 1), (0 2 4; l a ) and (0 4 2; 1) with 6 Z neighbors, (0 2 4; lb) with 5,7, (0 3 2; 1) with 4, 6, 8, (0 5 0; 1) with 4, 8, (0 6 0; 1) with 3, 6,9 Z neighbors. The M coordinations of (0 0 8;1) (6 fold), (0 4 0;1) (4 + 8 fold) and (0 8 0;1.5) (6 + 12 fold) are symmetrical and are probably favourable for crystal field stabilization.
J. Hauck et a L / Coulomb interactions
1174 1
4A
V-0--] 2
2
LoiI 000; 0.5b
Matoms I,, ,)I 008;1
006 0.8
006 ~0.67
004;0.5
_
O"
014;0.67
016;1
1
1~,
;
1 0
/ I'0.
~/I\0~
)1
"1 ------'0,~_
012;0.5
t/\
024.1a
000;0.50
024.1b
I
022.067
020;0.5
o O,o >
032;1
.0./
I
0.
030;0.67
~-,o,3~
040;1
O~;O.5b
9=0,5~
042:10x*~'6 O, ~;OY50'~- 040;0.60~'~1_0 0L,0;0.50,6_ 1.
,6
O;\ \ / i~
I[Igl
•,0~-+5-:.;2 ~-+5r-J,9
"~,4,6_
050;I 15-0 24-J 5 'Ira/ '\ I1'
,i
These structures contain 1,2 and 3 dimensional linked M - Z - M chains, resp., which are often disrupted by vacancies at lower Z content r. The (0 4 0;1) structure is identical to Model 1 Ba2YCu306 (6). The coordination n u m b e r s of Ba, Y, Cu(1) and Cu(2) atoms in Ba2YCu3Ox, x = 6 : 8 , 8 , 2 , 5 , z = 7 : 1 0 , 8 , 4 , 5 , x = 8 : 1 2 , 8 , 6 , 5 and of La (9 fold) and Cu (6 fold) in La2Cu04 are different from the values given above and seem to be i m p o r t a n t for size, valence and crystal field of Ba, Y or La and Cu to stabilize the structure. Crystal field effects are not i m p o r t a n t in (0 0 8; 1) V H with m a x i m u m Coulomb energy.
']l / "%,
02 2. ~0 ~"!
•o ,5,8,1_o 061;1.2 060;I 15,-24,=15 15~4~15 '1/'
v o 13
Fig2: Short range order parameters al,2 of Z atoms in MZr with bcc (solid lines, x) or fcc M lattice (dashed lines, 0).
il/'\fi
REFERENCES ',6
080;1.5 1.5=03=15 iX i-1~¢i("
02:~ 02~6 0,2,~ ~2~,6 2/.,, 7;4.6 0~i~,,0~3.~ '1 JIt ~--
(I) J. Hauck, K. Bickmann and F. Zucht, Z. Phys. B. 67, 299 (1987).
I,~,2,~45 I,~-'~,~-[5- i,~-2,~,5- i:5-~,f~-,5
(2) J. Hauck, D. Henkel and K. Mika, Z. Phys. B., in print. (3) M. Klee, Aachen, private communication.
0601080;1.33 0/,01060;1.17 0401060;I 0441080;1.33 Ba2Y CU30x Lo2Cu0~,
(4) M.H. Gerss and W. Jeitschko, Z. Kristallogr. 174, 63 (1986).
Fig.l: [001] projection of Z atom sublattice in (0 T2 T3; r) MZr with bcc M lattice, a = 2. The T2, T3 neighbors of Z atoms are connected by solid and dashed lines, resp., underlined # gives periodicity in [0011.
(5) W. Van Gool and A.G. Piken, J. Mat. Science 4, 95 (1969). (6) A. Santoro et al., Mat. (1987).
Res.
Bull.
22, 1007
C O U L O M B I N T E R A C T I O N S IN S U P E R C O N D U C T I N G OXIDES, H Y D R I D E S AND C A R B I D E S
Jfirgen H A U C K , D o r o t h e a H E N K E L and Klaus M I K A Institut f~r Festkhrperforschung, KFA, D-5170 Jfilich, F R G
Ba2YCu3Oz, La2Cu04, SrTi03 and interstitial alloys M Z z , e.g. F e T i H z , V H z , Y C o C with Z = O, H or C at octahedral sites of the bcc M lattice are analyzed for Coulomb interactions. 1. I N T R O D U C T I O N Superconducting B a 2 Y C u 3 0 z, z = 6 - 8 , La2CuO 4 and the perovskites SrTiO3_z/Ba(Pb, Bi)O 3 can be considered as interstitial alloys M Z z similar to V H z , F e T i H z or Y C o C with Z = O , H or C atoms at octahedral sites of the bcc metal lattice. The interstitial Z atoms have a high mobility because of m a n y vacant interstitial sites with substantial disorder at high temperatures and substantial order at low t e m p e r a t u r e s e.g. below 480K for VHo. 5. Similar to that, the oxygen content of B a 2 Y C u 3 0 z varies in the tetragonal high t e m p e r a t u r e phase between 5.8 < z < 7 and is restricted to small ranges at decreased t e m p e r a t u r e s (1). The structures of the ordered sublattice of Z atoms can be characterized by the coordination numbers T 1 - T 3 of Z atoms with Z atoms at distance a/2, ax/~/2 and ax/~/2 of the bcc lattice constant a and the ratio r = Z / M : (T 1 T 2 T3;r). The m a x i m u m coordination numbers (4 8 8; 3) at occupation of all octahedral sites are reduced by a factor r/3 at reduced r, if the vacant sites are distributed randomly. The number T 1 of nearest neighbors is decreased at Coulomb repulsion of Z atoms, 2"2 and T 3 at attractive interactions. The analysis of ordered superconducting interstitial alloys with fcc M lattice had shown m i n i m u m numbers of T1 values (2). The present investigation compares derivative structures of Z atoms with bcc M lattice. 2. O R D E R I N G O F I N T E R S T I T I A L A T O M S A b o u t 350 structures with Z atoms at octahedral sites of the bcc M lattice were obtained similar as for the fcc M lattice (2). Fig. 1 shows all (0 772 T3; r) structures with m a x i m u m r and few structures for r >_ 0.5. The T3 values of (0 0 8;1), (0 1 6;1), (0 2 4;1), (0 3 2; 1) and (0 4 0; 1) vary with T 2 by 2T2 + T3 = 8 and cannot be increased further at increased r. These structures are identical to tetrahedral site sublattices of e.g. (0 2 4; la) NbH or (0 0 4; 0.5) TaHo.5, if the Z sublattice is lifted by a/4 in projection height. A further increase of r is possible in perovskite related structures
0921 4534/88/$03.50 © ElsevierSciencePublishers B.V. (North-Holland Physics Publishing Division)
(0 4 2; 1), (0 6 1; 1.2) and (0 8 0;1.5) CaTiO 3 with T 2 + 2T 3 = 8. The different O atoms of B a 2 Y C u 3 0 z , z = 6, 7, 8 and La2CuO 4 exhibit two or more different coordinations (Fig. 1). Other structures related to perovskite are (0 4 0/0 5 0;1.125) Ba4YCu309, (0 5 0/0 8 0; 1.125) BasY3CuhOl8 (3) and (0 0 0; 0.hb) Y C o C (4). 3. C O M P A R I S O N W I T H ISING M O D E L The Cowley-Warren short-range order parameters
a i can be obtained from the T i by T(nazai = Ti (T[ nax - Ti)r/(3 - r) with T~naz = 4, 8, 8 at i = 1, 2, 3, resp.. The a i values ( - 1 < a i _< 1) were chosen for comparison with the Ising model of nearest and nextnearest neighbor interactions V/, i = 1, 2 with a i = 0 at Vi = 0, e.g. at r a n d o m distribution, positive a i for attractive interactions (Vi > 0) e.g. cluster formation and segregation (Fig. 2), negative al at repulsive interactions, e.g. Coulomb repulsion. Fig. 2 shows the variation of al, 2 for different series (0 T 2 T3; r) of Fig. 1 with a 1 = - 0 . 5 at m a x i m u m r = 1 and 9 a l + 4 a 2 -- - 5 for perovskite related structures. The upper limit of the fcc M lattice is 4a 1 + a 2 = - 1 . These limits depend also on a3 : a l + a3 = 0 for fcc M , 2a 2 + a 3 -- 0 for bcc M. The superconducting M Z r with fcc or bcc M lattice (Fig. 2) are on or close to the limits. The Z atoms in the fcc M lattice are as far apart as possible with m a x i m u m Coulomb energy. In the bcc M lattice the Coulomb energy decreases with increasing T 2. The Madelung factor (refering to relative prime charges (5)) has a m a x i m u m e.g. for (0 0 8; 1) V H ( M F = 1.484) and decreases ~ 1 % , if T2 is increased by 1. The loss of Coulomb energy of (0 4 0/0 6 0;1) Ba2YCu306 w i t h M F = 1.300 should be compensated by the crystal field stabilization energy. The coordination of M atoms with Z atoms is rather asymmetrical in (0 1 6; 1), (0 2 4; l a ) and (0 4 2; 1) with 6 Z neighbors, (0 2 4; lb) with 5,7, (0 3 2; 1) with 4, 6, 8, (0 5 0; 1) with 4, 8, (0 6 0; 1) with 3, 6,9 Z neighbors. The M coordinations of (0 0 8;1) (6 fold), (0 4 0;1) (4 + 8 fold) and (0 8 0;1.5) (6 + 12 fold) are symmetrical and are probably favourable for crystal field stabilization.
J. Hauck et a L / Coulomb interactions
1174 1
4A
V-0--] 2
2
LoiI 000; 0.5b
Matoms I,, ,)I 008;1
006 0.8
006 ~0.67
004;0.5
_
O"
014;0.67
016;1
1
1~,
;
1 0
/ I'0.
~/I\0~
)1
"1 ------'0,~_
012;0.5
t/\
024.1a
000;0.50
024.1b
I
022.067
020;0.5
o O,o >
032;1
.0./
I
0.
030;0.67
~-,o,3~
040;1
O~;O.5b
9=0,5~
042:10x*~'6 O, ~;OY50'~- 040;0.60~'~1_0 0L,0;0.50,6_ 1.
,6
O;\ \ / i~
I[Igl
•,0~-+5-:.;2 ~-+5r-J,9
"~,4,6_
050;I 15-0 24-J 5 'Ira/ '\ I1'
,i
These structures contain 1,2 and 3 dimensional linked M - Z - M chains, resp., which are often disrupted by vacancies at lower Z content r. The (0 4 0;1) structure is identical to Model 1 Ba2YCu306 (6). The coordination n u m b e r s of Ba, Y, Cu(1) and Cu(2) atoms in Ba2YCu3Ox, x = 6 : 8 , 8 , 2 , 5 , z = 7 : 1 0 , 8 , 4 , 5 , x = 8 : 1 2 , 8 , 6 , 5 and of La (9 fold) and Cu (6 fold) in La2Cu04 are different from the values given above and seem to be i m p o r t a n t for size, valence and crystal field of Ba, Y or La and Cu to stabilize the structure. Crystal field effects are not i m p o r t a n t in (0 0 8; 1) V H with m a x i m u m Coulomb energy.
']l / "%,
02 2. ~0 ~"!
•o ,5,8,1_o 061;1.2 060;I 15,-24,=15 15~4~15 '1/'
v o 13
Fig2: Short range order parameters al,2 of Z atoms in MZr with bcc (solid lines, x) or fcc M lattice (dashed lines, 0).
il/'\fi
REFERENCES ',6
080;1.5 1.5=03=15 iX i-1~¢i("
02:~ 02~6 0,2,~ ~2~,6 2/.,, 7;4.6 0~i~,,0~3.~ '1 JIt ~--
(I) J. Hauck, K. Bickmann and F. Zucht, Z. Phys. B. 67, 299 (1987).
I,~,2,~45 I,~-'~,~-[5- i,~-2,~,5- i:5-~,f~-,5
(2) J. Hauck, D. Henkel and K. Mika, Z. Phys. B., in print. (3) M. Klee, Aachen, private communication.
0601080;1.33 0/,01060;1.17 0401060;I 0441080;1.33 Ba2Y CU30x Lo2Cu0~,
(4) M.H. Gerss and W. Jeitschko, Z. Kristallogr. 174, 63 (1986).
Fig.l: [001] projection of Z atom sublattice in (0 T2 T3; r) MZr with bcc M lattice, a = 2. The T2, T3 neighbors of Z atoms are connected by solid and dashed lines, resp., underlined # gives periodicity in [0011.
(5) W. Van Gool and A.G. Piken, J. Mat. Science 4, 95 (1969). (6) A. Santoro et al., Mat. (1987).
Res.
Bull.
22, 1007