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Correlations between the structural distortion of LaCuO3 lattice and the resulting physical properties
Solid State Communications, Printed in Great Britain.
003%1098/93$6.00+.00 Pergamon Press Ltd
Vol. 85, No. 11, pp. 961-965, 1993.
CORRELATIONS BETWEEN THE STRUCTURAL OF LaCu03 LATTICE AND THE RESULTING PROPERTIES
DISTORTION PHYSICAL
S. Darracq, S. Matar and G. Demazeau Laboratoire de Chimie du Solide du CNRS et Interface Hautes Pressions E.N.S.C.P.B. Universitb BORDEAUX I 33405 Talence Cedex (France)
Received
LaCu03
can
tetragonal In
order
present
1992,
two
6 January
in revised form
structural
types
versus
form for P < 50 kbar and a rhombohedral to
approaches structure
IO October
precise have
based
measurements
the
been on
the
physical developed A.S.W.
properties
: an “ab method,
of initio”
the
1993 by P. Burlet
oxygen
pressure
one for the highest both
structures
calculation
experimental
of
magnetic
value,
two the
a
pressures. different electronic
and
electric
on both forms.
I/ INTRODUCTION During these last five years, copper oxides with mixed valencies weie intensively studied after the discoverv bv K.A. MULLER and J.G. BEDNORZ of high tempeiature superconductivity (1). This behaviour seems to be induced by different factors, in particular the dimensionality of the lattice and the mixed valency for copper [for example Cu(lll)/Cu(ll)l... Copper (III) was pointed out in different oxygen In 1959 and 1969. ACuOl oxides lattices. A = Na, K, Rb, Cs and Na3Cu03 (2-3) were prepared, (Cu041 square planes with shared edges characterizing these lattices. In 1972-73, G. DEMAZEAU et al. have stabilized Cu(lll) in sixperovskite-type lattice coordinated sites in [LaCu03 (411 or in the K2NiF -type structure (4) and trLaCu04 (511. [La2Li0.50CU0.5004 LaCuO was prepared under high oxygen pressure (65 i: bar, 900°C) using in a belt-type apparatus the “in situ” thermal decomposition of KCIO, [KC103 -+ KCI + 3/202 (611. ‘Under these experimental conditions this oxide showed a small rhombohedral distor$on of the perovskite lattice (a = 5.431 f0.002 A, a = 60.85 rtO.02”) (4). In 1989, WEBB er a/. using the same synthetic route confirmed such a structure for LaCu03 (7). Recently the rhombohedral structure of LaCu03 was refined by neutron diffraction [CURRIE and WELLER (811. The Cu(lll) site is a pure octahedron with a Cu-0 distance eaual to 1.951 l(3) A. such a distance is close .‘to that calduiated by DEMAZEAU er a/. (Cu-0 = 1.94 Al (6) from an X.R.D. refinement on powder. In 1990, J.F. BRINGLEY et al. reported on 961
LaCu03_s prepared under much lower oxygen pressures (0.2 to 1 kbar) (9) than those used Three different previously (65-70 kbar) (4). structures have been pointed out versus oxygen (0.5 Z 6 > 0.43), stoichiometry : orthorhombic monoclinic (0.4 2 6 2 0.2) and tetragonal (0.2 2 6 t 0). For 6 equal to zero, the structure still remained tetragonal (9). Such a structure has been described through a simple tetragonal distortion of $ cubic perovskite (with 6 = 0, a = 3.81875 A and c = 3.9727 A, space groupe P4/m) (9). From BRINGLEY et al. this distortion would result from a slight local Jahn-Teller-like elongation of the (CL&) octahedra with four eauatorial Cu-O-bonds close to 1.909 A and two apical bonds at 1.986 8, (9). This result led to conclude that stoichiometric oxide adopt two different LaCu03 could structures. The comparison of the volume per formula unit for both structures (Table I) would suggest that the rhombohedral form would be the high pressure variety of LaCu03, in agreement with the elaboration conditions. In order to precise this point, recently a common research work [DARRACQ et al. (IO)] has underlined that the tetragonal form can be stable and prepared under oxygen pressure up till TABLE I : Comparison of cell parameters for both phases
and V/Z
962
STRUCTURAL
DISTORTION
50 kbar. But due to the small AV value between both formular volumes, the direct transformation (tetragonal -+ rhombohedral) using only high pressure is difficult to achieve. This phenomenon has been observed several years ago, the kinetics of the structural transformation being dependent on the AV value (11). differences The small structural observed for the distortion of the (CuOej Site could modify the physical properties of such LaCuOg oxides. The isotropic (CuOe) octahedron in the rhombohedral form is in agreement with the previously by metallic behaviour observed DEMAZEAU et al. (41. The small (CuOe) elongation associated with the tetragonal form would suggest an increase of the electronic localization inducing a local Jahn-Teller-type distortion. The measurements of the magnetic and electric properties of LaCuOg are not so easy due to many factors such as : (i) prepared under oxygen pressure, the thermal instability of such an oxide, due to Cu(lll), hinders at high temperature and the the sintering preparation of good ceramics for electrical study, (ii) the small value of the magnetic susceptibility and the small quantity of powder prepared under make difficult an conditions such pressure accurate magnetic characterization. In order to precise the physical behaviour of both structures two different approaches have been developed : (a) an “ab-initio” calculation of the electronic and magnetic properties on the basis of the A.S.W. method (I 21, (b) an experimental investigation of the magnetic and electrical properties.
II/ “AB INITIO” CALCULATION OF THE ELECTRONIC PROPERTIES OF LaCuO3 The present calculations of LaCuOg were achieved in a preliminary objective of checking the effects of local distortion on its electronic structure. This was firstly done in the hypothetical structure of a cubic perovskite with local non-distorted cue - obviously octahedron. &h a feature is close to the6 rhombohedral variety (4,8). The a cell constant used throughout the calculations was derived from the experimental value of the volume obtained from the literature. A second calculation was carried out within the tetragonal structure known for this material, this latter structure resulting from a slight elongation of the CuOe octahedron along c with a c/a ratio of 1.0403 (9). The radii of the atomic spheres 0 were taken surrounding La, Cu and proportionally to their experimental values without further search of a different choice that would minimize the energy whence the non-unique choice of the radii. Method of calculation. “Ab initio” band structure calculations were undertaken for LaCuOq usina the A.S.W. (augmented spherical wave) method (12). In this work a scalar relativistic version (13) was used due to the presence of a lanthanide. This method
OF LaCu03 LATTICE
Vol. 85, No. 11
is based on the local spin density approximation for the treatment of exchange and correlation effects within the scheme of von BARTH and HEDIN (14) and JANAK (15). In as far as A.S.W. calculations assume the sum of the volumes of the atomic spheres to be equal to the cell volume within the atomic sphere approximation, overlapping spheres cannot be avoided. Calculations and results. For both structural setups the Brillouinzone integration was carried out on a uniform mesh of points in the irreducible wedge. The number of k points was progressively increased in the iterative process until no more changes in charge transfer and total energy could be observed. The final numbers of independent kpoints were 84 and 126 k-points for the cubic and tetragonal structures respectively. The matrix elements were constructed involving solutions of the Schrbdinger equation up to f? + 1 where cmax = 3, 2 and 1 for La, Cu and?%espectively. The contributions associated with e + 1 are used for the internal 3-center terms summations. The self consistent cycle was carried out until energy convergence on a scale better than 1 mRyd was achieved. Charge distribution. The local partial charges for the cubic and the tetragonal varieties are given at Table II (a and b respectively). For each atomic species, QToT, and AQ give the final valence charge and the charge difference with respect to starting valence charge respectively. From this table it can be seen that major charge transfer occurs between the spheres of Cu and 0 ; i.e. the charge AQ on Cu is nearly three times the value of AQ on 0. This suggests a strong mixing between the states of these atoms on a one hand and little mixing between them and those of La on another hand whose sphere undergoes little charge transfer. It is interesting to note that the charge slightly higher than 1.5 in both on Cu, calculations, tends to give this element a divalent character rather than the trivalent one that would be expected from a totally ionic picture of the material. This feature finds support in recent X.A.N.E.S. studies of LaCuOg where a divalent character of Cu is suggested (16). Moreover this result suggests that the electron-hole would be localized on oxygen in agreement with the strong covalency of the Cu-0 bond in this lattice. Densities of States. The densities of states (D.O.S.) are given at Figs. Icr(a, b, c) and lj3(a, b, c) for La, Cu and 0 in the two structures respectively. In both cases there is a vanishing D.O.S. at Fermi level (E, = 7.189 and 7.243 eV, respectively) for La (Figs. Icta and I pa). On the contrary a nonvanishing D.O.S. at E, is observed for Cu and 0 sites [Figs. la(b,c) and lP(b,c)l which is higher in the tetragonal phase (16.8 states/e\/) than in the cubic one (15.5 states/e\/). However the close magnitudes of the two D.O.S. cannot allow to address the respective electrical conductivities. As stated above there is little mixing between La states on a one hand and those of Cu and 0 the other hand. In these structures characterized by nearly cubic (small rhombohedral distortion) and tetragonally distorded octahedra, the D.O.S. can
STRUCTURAL
Vol. 85, No. 11
TABLE
DISTORTION
II :Local
OF La&O3
partial charges
963
LATTICE
for LaCu03
a) Cubic perovskite
Qvalence EF.=
0.528
b) Tetragonally
0
Ryd.
EVAR
distorted
1 1.85211
=
-20725.27236
=
31.953
=
0.533
perovskite
4.69511
Ryd.
32.000
Ryd.
0.06811
-
-
1
Qvalence* EF
/
; EVAR= -20725.45710
6.6151
+0.615
32.001
/
32.000
Ryd.
F..:.:::::.,, 1 ,,:.: ::......_ ) ,VE!”
-
“;,mm”
A
M
[y=5”I
X.,,
I-=+
‘--ih,,_J/
b
E-B
(N)
Fig. Fig. 1 :
1.a.
E-EC Fig.
(W 1.8.
Site projected densities of states [a) La ; b) Cu ; c) 01 for LaCu03 in the cubic perovskite (Fig. lo) and tetragonnaly distorted perovskite (Fig. 1 PI.
r Fig 2:
r
A
R
X
r
z
Energy bands for LaCu03 along main directions in the first Brillouin zone of a) simple cubic and b) simple tetragonal lattices.
964
STRUCTURAL
DISTORTION
be approximated to those solely produced by a {CuOe} arrangement with hardly any role played by La. Consequently any changes at EF would be induced by the distortion of such an octahedron when the lattice is tetranonally distorted. In as far as little difference can be .observed from the analysis of the DOS, this could be shown by the plot of the band structures in both structural setups of LaCuOg. Band structures of LaCu03. The plot of the bands along the major symmetry lines in the simple cubic and simple Brillouin-zones respectively are tetragonal represented at Figs. 2(a, b). For clarity only those bands close to EF are shown i.e. the low lying s states are discarded. Although a full analysis of the bands necessitates a group theoretical treatment and a plot of the Fermi surface, a simple preliminary analysis can be undertaken. For whereas the lanthanum the cubic structure antibonding states all lie above EF , one can count 14 bands along the F...M line below EF (Fig. 2a. lower panel). They arise from 5 Cu states and 9 (3 x 3) states of oxygen. Moreover from EF downwards from the F point one can count 3, 5, 3 then 3 bands respectively. States of Cu and 0 can be seen to mix along the F...M and F...Fi lines Fermi level is crossed by below EF . However, two of the first 3 bands which seem to arise from oxygen with no crossing of EF by bands from copper. The other 0-2~ states lie low in energy with respect to EF and contribute little if not at all to the bonding with Cu. For the tetragonally distorted cell the band structure is more complicated especially at EF where more bands are crossing with a consequence of a larger D.O.S. as stated above. With a similar band count as above a major difference seems to arise from states of Cu-0 mixing crossing EF i.e. along F...A and A...R directions for instance. Further analysis will be provided in a more thorough forthcoming investigation of lanthanum-copper oxides. In this preliminary study it was shown the major contribution to a non that in LaCuO vanishing D.O. 8 . at EF arises from a strong mixing between Cu and 0 states whereas those of La are involved. An oxidation state of Cu less 5.0
/
Vol. 85, No. 11
OF LaCu03 LATTICE
approaching a divalent character was suggested, in agreement with a strong covalent bond inducing a charge transfer. The band structure analysis seems to assign a role to 0-2~ states at EF which would modify the transport properties of the oxide. Before closing this section, we should say that there is a qualitative agreement between our calculations for-the cubic variety and recent investiaations bv TAKEGAHARA 1171 of LaCuOl by the- APW method, a work we came acros6 during the redaction of this paper. This agreement stands for the DOS, the band structure as well as to the magnitude of the atomic spheres occupations.
Ill/ EXPERIMENTAL INVESTIGATION PHYSICAL PROPERTIES OF LaCuOB 1. The rhombohedral
OF THE
form
the magnetic Twenty years ago properties of the rhombohedral form nave been measured between room temperature and 77 K by G. DEMAZEAU et al. (4). More recentlv such properties have been re-investigated (Fig. 3). The magnetic properties versus temperature underlined a Pauli paramagnetism. This behaviour with suggested a metallic character the delocalization of the e electrons in a o* band. This experimental resul? is in agreement with the previous “ab initio” calculation of the electronic structure using in a first approximation a non distorded cubic lattice. The electric measurements have been carried out on compressed pellets (1.2 kbar) at room temperature. They confirm the magnetic properties (Fig. 4). Recently a qeneral study of the.Lat_,Y,C& rhombohedral phases (x < 6.20) [F. TRESSE, G. DEMAZEAU, K.A. MULLER (1811 increase of suggested an the electronic localization with the structural distortion when La(lll) is reolaced bv the smaller Y(IIII cation in the rhombohedral lattice. 3.0 2.5_
: :
b
1.0 I0.0
I
0
I
50
100
150
200
250
300 T
Fig. 3 :
Thermal magnetic a) 70 Kb b) 40 Kb
0
50
100
150
200
250
T
(K)
(Xl
variation of the reverse molar susceptibility of LaCuOs rhombohedral structure tetragonal structure
resistance of LaCu03 Fig. 4 : Normalized temperature a) 70 Kb rhombohedral structure b) 40 Kb tetragonal structure
versus
Vol. 85, No. 11 2. The tetragonal
STRUCTURAL
DISTORTION
form
The variation of the inverse of the magnetic susceptibility versus temperature between 300 and 4.2 K for the tctragonal LaCuQg prepared at 40 kbar (a = 3,817 A, c = 3,974 A), is given in Fig. 3. This high value of oxygen pressure (40 kbar), near the upper limit of stability for this structural variety, was chosen in order to eliminate the formation of oxygen vacancies. The thermal variation of the reciprocal magnetic susceptibility is of the same order of magnitude for the rhombohedral and the tetragonal forms. At room temperature, the magnetic susceptibility is higher for the tetragonal form than that of the rhombohedral one. Such a behaviour is in agreement with an increase of the electronic localization. The electrical measurement versus temperature for both forms is given in Fig. 4. The observed result suggests a semi-conducting behaviour with a small band gap for the tetragonal form compared to the metallic character characterizing the rhombohedral one.
OF LaCu03 LATTICE
965
Electric measurement on powder take into account the average conductivity. The difference between the electrical behaviour of the tetragonal form and the rhombohedral one could be due to the anisotropy of Cu-0 bonds in the first form and the isotropy of the Cu-0 bonds for the second one (8,9). Due to the local elongation of (CuQ6) in octahedra the tetragonal structure the conductivity must be enhanced in the xOy planes but largely reduced along the Oz axis leading to semi-conducting properties of the ceramics. CONCLUSION LaCu03 can present two different structures versus the pressure conditions used for the synthesis. In both structures the strong covalent character of the Cu-0 bond, induces a partial electronic transfer from oxygen to copper and modifies the electronic properties. In the tetragonal form, due to the local structural distortion -the electronic transfer Q2p --j d,2.,2Cu(lll) could be enhanced in the xOy planes and reduced along the Oz axis.
References
J.G. Bednorz K.A. Mi.iller 2. Phys. B. r%ndensed Matter 64 189-193 (1’9863 2) W. Klemm, G.’ Wehrmeyer and H.’ Bade, 2. elektrochem. Ber. Bunsenges physik Chem., 53, 56 (1959) 3) K. Hestermann and R. Hoppe, 2. anorg. allg. them., 367, 249;261;270 (1969). 4) G. Demazeau, C. Parent, M. Pouchard, P. Hagenmuller, Mat. Res. Bull., 7. 913 (1972). 5) J.B. Goodenough, G. Demazeau, M. Pouchard et P. Hagenmuller, J. Solid State Chem,, 8, 325330 (1973). 6) G. Demazeau, These de doctorat es Science, Bordeaux, 1973. 7) A.W. Webb, E.F. Skelton, S.B. Qadri, E.R. Carpenter, J.M.S. Osefoky, R.J. Soulenand, V. Letourneau, Physics Letters A, Vol. 137, N4,5 15 may 1989. 8) D.B. Currie and M.T. Weller, Acta. Cryst., C47, 696-698 (1991). 9) J.F. Bringley, B.A. Scott, S.J. La Placa, R.F. Boehme, T.M. Shaw, M.W. MC. Elfrech, S.S. Frail
and D.E. Cost, Nature, 347, 263-265 (1990). IO) S. Darracq, A. Largeteau, G. Demazeau, B.A. Scott and J.F. Bringley, Eur. J. Solid State and Inora. Chem., 29, 585-591 (1992). 11) 3. Demazeau, F. Menil, J. Portier et P. Hagenmuller, C.R. Acad. SC., 273, 1641-1644 (1971). 12) A.R. Williams, J. Kubler and C.D. Gelatt, J. Phvs. Rev.. B19. 6094 (1979). 13i D.D. Koelling~ and B.N. Harmon, J. Phys., CIO, 3107 (1977). 14) J. van Barth and D. Heden, J. Phys., C5, 1629 (1972). 15) J.F. Janak, Solid State Comm., 25, 52 (1978). 16) A.W. Webb, K.M. Kim and C. Bouldin, Solid State Comm., 79, N6, 507 (1991). 17) Katsuhiko TAKEGAHARA, Japanese J. of Aool. Phvs.. 26. L437 (19871. 18i F. ire&e, ‘G. Demazeau, K.A. Muller, High Pressure Research, 7, 61, 1991.
003%1098/93$6.00+.00 Pergamon Press Ltd
Vol. 85, No. 11, pp. 961-965, 1993.
CORRELATIONS BETWEEN THE STRUCTURAL OF LaCu03 LATTICE AND THE RESULTING PROPERTIES
DISTORTION PHYSICAL
S. Darracq, S. Matar and G. Demazeau Laboratoire de Chimie du Solide du CNRS et Interface Hautes Pressions E.N.S.C.P.B. Universitb BORDEAUX I 33405 Talence Cedex (France)
Received
LaCu03
can
tetragonal In
order
present
1992,
two
6 January
in revised form
structural
types
versus
form for P < 50 kbar and a rhombohedral to
approaches structure
IO October
precise have
based
measurements
the
been on
the
physical developed A.S.W.
properties
: an “ab method,
of initio”
the
1993 by P. Burlet
oxygen
pressure
one for the highest both
structures
calculation
experimental
of
magnetic
value,
two the
a
pressures. different electronic
and
electric
on both forms.
I/ INTRODUCTION During these last five years, copper oxides with mixed valencies weie intensively studied after the discoverv bv K.A. MULLER and J.G. BEDNORZ of high tempeiature superconductivity (1). This behaviour seems to be induced by different factors, in particular the dimensionality of the lattice and the mixed valency for copper [for example Cu(lll)/Cu(ll)l... Copper (III) was pointed out in different oxygen In 1959 and 1969. ACuOl oxides lattices. A = Na, K, Rb, Cs and Na3Cu03 (2-3) were prepared, (Cu041 square planes with shared edges characterizing these lattices. In 1972-73, G. DEMAZEAU et al. have stabilized Cu(lll) in sixperovskite-type lattice coordinated sites in [LaCu03 (411 or in the K2NiF -type structure (4) and trLaCu04 (511. [La2Li0.50CU0.5004 LaCuO was prepared under high oxygen pressure (65 i: bar, 900°C) using in a belt-type apparatus the “in situ” thermal decomposition of KCIO, [KC103 -+ KCI + 3/202 (611. ‘Under these experimental conditions this oxide showed a small rhombohedral distor$on of the perovskite lattice (a = 5.431 f0.002 A, a = 60.85 rtO.02”) (4). In 1989, WEBB er a/. using the same synthetic route confirmed such a structure for LaCu03 (7). Recently the rhombohedral structure of LaCu03 was refined by neutron diffraction [CURRIE and WELLER (811. The Cu(lll) site is a pure octahedron with a Cu-0 distance eaual to 1.951 l(3) A. such a distance is close .‘to that calduiated by DEMAZEAU er a/. (Cu-0 = 1.94 Al (6) from an X.R.D. refinement on powder. In 1990, J.F. BRINGLEY et al. reported on 961
LaCu03_s prepared under much lower oxygen pressures (0.2 to 1 kbar) (9) than those used Three different previously (65-70 kbar) (4). structures have been pointed out versus oxygen (0.5 Z 6 > 0.43), stoichiometry : orthorhombic monoclinic (0.4 2 6 2 0.2) and tetragonal (0.2 2 6 t 0). For 6 equal to zero, the structure still remained tetragonal (9). Such a structure has been described through a simple tetragonal distortion of $ cubic perovskite (with 6 = 0, a = 3.81875 A and c = 3.9727 A, space groupe P4/m) (9). From BRINGLEY et al. this distortion would result from a slight local Jahn-Teller-like elongation of the (CL&) octahedra with four eauatorial Cu-O-bonds close to 1.909 A and two apical bonds at 1.986 8, (9). This result led to conclude that stoichiometric oxide adopt two different LaCu03 could structures. The comparison of the volume per formula unit for both structures (Table I) would suggest that the rhombohedral form would be the high pressure variety of LaCu03, in agreement with the elaboration conditions. In order to precise this point, recently a common research work [DARRACQ et al. (IO)] has underlined that the tetragonal form can be stable and prepared under oxygen pressure up till TABLE I : Comparison of cell parameters for both phases
and V/Z
962
STRUCTURAL
DISTORTION
50 kbar. But due to the small AV value between both formular volumes, the direct transformation (tetragonal -+ rhombohedral) using only high pressure is difficult to achieve. This phenomenon has been observed several years ago, the kinetics of the structural transformation being dependent on the AV value (11). differences The small structural observed for the distortion of the (CuOej Site could modify the physical properties of such LaCuOg oxides. The isotropic (CuOe) octahedron in the rhombohedral form is in agreement with the previously by metallic behaviour observed DEMAZEAU et al. (41. The small (CuOe) elongation associated with the tetragonal form would suggest an increase of the electronic localization inducing a local Jahn-Teller-type distortion. The measurements of the magnetic and electric properties of LaCuOg are not so easy due to many factors such as : (i) prepared under oxygen pressure, the thermal instability of such an oxide, due to Cu(lll), hinders at high temperature and the the sintering preparation of good ceramics for electrical study, (ii) the small value of the magnetic susceptibility and the small quantity of powder prepared under make difficult an conditions such pressure accurate magnetic characterization. In order to precise the physical behaviour of both structures two different approaches have been developed : (a) an “ab-initio” calculation of the electronic and magnetic properties on the basis of the A.S.W. method (I 21, (b) an experimental investigation of the magnetic and electrical properties.
II/ “AB INITIO” CALCULATION OF THE ELECTRONIC PROPERTIES OF LaCuO3 The present calculations of LaCuOg were achieved in a preliminary objective of checking the effects of local distortion on its electronic structure. This was firstly done in the hypothetical structure of a cubic perovskite with local non-distorted cue - obviously octahedron. &h a feature is close to the6 rhombohedral variety (4,8). The a cell constant used throughout the calculations was derived from the experimental value of the volume obtained from the literature. A second calculation was carried out within the tetragonal structure known for this material, this latter structure resulting from a slight elongation of the CuOe octahedron along c with a c/a ratio of 1.0403 (9). The radii of the atomic spheres 0 were taken surrounding La, Cu and proportionally to their experimental values without further search of a different choice that would minimize the energy whence the non-unique choice of the radii. Method of calculation. “Ab initio” band structure calculations were undertaken for LaCuOq usina the A.S.W. (augmented spherical wave) method (12). In this work a scalar relativistic version (13) was used due to the presence of a lanthanide. This method
OF LaCu03 LATTICE
Vol. 85, No. 11
is based on the local spin density approximation for the treatment of exchange and correlation effects within the scheme of von BARTH and HEDIN (14) and JANAK (15). In as far as A.S.W. calculations assume the sum of the volumes of the atomic spheres to be equal to the cell volume within the atomic sphere approximation, overlapping spheres cannot be avoided. Calculations and results. For both structural setups the Brillouinzone integration was carried out on a uniform mesh of points in the irreducible wedge. The number of k points was progressively increased in the iterative process until no more changes in charge transfer and total energy could be observed. The final numbers of independent kpoints were 84 and 126 k-points for the cubic and tetragonal structures respectively. The matrix elements were constructed involving solutions of the Schrbdinger equation up to f? + 1 where cmax = 3, 2 and 1 for La, Cu and?%espectively. The contributions associated with e + 1 are used for the internal 3-center terms summations. The self consistent cycle was carried out until energy convergence on a scale better than 1 mRyd was achieved. Charge distribution. The local partial charges for the cubic and the tetragonal varieties are given at Table II (a and b respectively). For each atomic species, QToT, and AQ give the final valence charge and the charge difference with respect to starting valence charge respectively. From this table it can be seen that major charge transfer occurs between the spheres of Cu and 0 ; i.e. the charge AQ on Cu is nearly three times the value of AQ on 0. This suggests a strong mixing between the states of these atoms on a one hand and little mixing between them and those of La on another hand whose sphere undergoes little charge transfer. It is interesting to note that the charge slightly higher than 1.5 in both on Cu, calculations, tends to give this element a divalent character rather than the trivalent one that would be expected from a totally ionic picture of the material. This feature finds support in recent X.A.N.E.S. studies of LaCuOg where a divalent character of Cu is suggested (16). Moreover this result suggests that the electron-hole would be localized on oxygen in agreement with the strong covalency of the Cu-0 bond in this lattice. Densities of States. The densities of states (D.O.S.) are given at Figs. Icr(a, b, c) and lj3(a, b, c) for La, Cu and 0 in the two structures respectively. In both cases there is a vanishing D.O.S. at Fermi level (E, = 7.189 and 7.243 eV, respectively) for La (Figs. Icta and I pa). On the contrary a nonvanishing D.O.S. at E, is observed for Cu and 0 sites [Figs. la(b,c) and lP(b,c)l which is higher in the tetragonal phase (16.8 states/e\/) than in the cubic one (15.5 states/e\/). However the close magnitudes of the two D.O.S. cannot allow to address the respective electrical conductivities. As stated above there is little mixing between La states on a one hand and those of Cu and 0 the other hand. In these structures characterized by nearly cubic (small rhombohedral distortion) and tetragonally distorded octahedra, the D.O.S. can
STRUCTURAL
Vol. 85, No. 11
TABLE
DISTORTION
II :Local
OF La&O3
partial charges
963
LATTICE
for LaCu03
a) Cubic perovskite
Qvalence EF.=
0.528
b) Tetragonally
0
Ryd.
EVAR
distorted
1 1.85211
=
-20725.27236
=
31.953
=
0.533
perovskite
4.69511
Ryd.
32.000
Ryd.
0.06811
-
-
1
Qvalence* EF
/
; EVAR= -20725.45710
6.6151
+0.615
32.001
/
32.000
Ryd.
F..:.:::::.,, 1 ,,:.: ::......_ ) ,VE!”
-
“;,mm”
A
M
[y=5”I
X.,,
I-=+
‘--ih,,_J/
b
E-B
(N)
Fig. Fig. 1 :
1.a.
E-EC Fig.
(W 1.8.
Site projected densities of states [a) La ; b) Cu ; c) 01 for LaCu03 in the cubic perovskite (Fig. lo) and tetragonnaly distorted perovskite (Fig. 1 PI.
r Fig 2:
r
A
R
X
r
z
Energy bands for LaCu03 along main directions in the first Brillouin zone of a) simple cubic and b) simple tetragonal lattices.
964
STRUCTURAL
DISTORTION
be approximated to those solely produced by a {CuOe} arrangement with hardly any role played by La. Consequently any changes at EF would be induced by the distortion of such an octahedron when the lattice is tetranonally distorted. In as far as little difference can be .observed from the analysis of the DOS, this could be shown by the plot of the band structures in both structural setups of LaCuOg. Band structures of LaCu03. The plot of the bands along the major symmetry lines in the simple cubic and simple Brillouin-zones respectively are tetragonal represented at Figs. 2(a, b). For clarity only those bands close to EF are shown i.e. the low lying s states are discarded. Although a full analysis of the bands necessitates a group theoretical treatment and a plot of the Fermi surface, a simple preliminary analysis can be undertaken. For whereas the lanthanum the cubic structure antibonding states all lie above EF , one can count 14 bands along the F...M line below EF (Fig. 2a. lower panel). They arise from 5 Cu states and 9 (3 x 3) states of oxygen. Moreover from EF downwards from the F point one can count 3, 5, 3 then 3 bands respectively. States of Cu and 0 can be seen to mix along the F...M and F...Fi lines Fermi level is crossed by below EF . However, two of the first 3 bands which seem to arise from oxygen with no crossing of EF by bands from copper. The other 0-2~ states lie low in energy with respect to EF and contribute little if not at all to the bonding with Cu. For the tetragonally distorted cell the band structure is more complicated especially at EF where more bands are crossing with a consequence of a larger D.O.S. as stated above. With a similar band count as above a major difference seems to arise from states of Cu-0 mixing crossing EF i.e. along F...A and A...R directions for instance. Further analysis will be provided in a more thorough forthcoming investigation of lanthanum-copper oxides. In this preliminary study it was shown the major contribution to a non that in LaCuO vanishing D.O. 8 . at EF arises from a strong mixing between Cu and 0 states whereas those of La are involved. An oxidation state of Cu less 5.0
/
Vol. 85, No. 11
OF LaCu03 LATTICE
approaching a divalent character was suggested, in agreement with a strong covalent bond inducing a charge transfer. The band structure analysis seems to assign a role to 0-2~ states at EF which would modify the transport properties of the oxide. Before closing this section, we should say that there is a qualitative agreement between our calculations for-the cubic variety and recent investiaations bv TAKEGAHARA 1171 of LaCuOl by the- APW method, a work we came acros6 during the redaction of this paper. This agreement stands for the DOS, the band structure as well as to the magnitude of the atomic spheres occupations.
Ill/ EXPERIMENTAL INVESTIGATION PHYSICAL PROPERTIES OF LaCuOB 1. The rhombohedral
OF THE
form
the magnetic Twenty years ago properties of the rhombohedral form nave been measured between room temperature and 77 K by G. DEMAZEAU et al. (4). More recentlv such properties have been re-investigated (Fig. 3). The magnetic properties versus temperature underlined a Pauli paramagnetism. This behaviour with suggested a metallic character the delocalization of the e electrons in a o* band. This experimental resul? is in agreement with the previous “ab initio” calculation of the electronic structure using in a first approximation a non distorded cubic lattice. The electric measurements have been carried out on compressed pellets (1.2 kbar) at room temperature. They confirm the magnetic properties (Fig. 4). Recently a qeneral study of the.Lat_,Y,C& rhombohedral phases (x < 6.20) [F. TRESSE, G. DEMAZEAU, K.A. MULLER (1811 increase of suggested an the electronic localization with the structural distortion when La(lll) is reolaced bv the smaller Y(IIII cation in the rhombohedral lattice. 3.0 2.5_
: :
b
1.0 I0.0
I
0
I
50
100
150
200
250
300 T
Fig. 3 :
Thermal magnetic a) 70 Kb b) 40 Kb
0
50
100
150
200
250
T
(K)
(Xl
variation of the reverse molar susceptibility of LaCuOs rhombohedral structure tetragonal structure
resistance of LaCu03 Fig. 4 : Normalized temperature a) 70 Kb rhombohedral structure b) 40 Kb tetragonal structure
versus
Vol. 85, No. 11 2. The tetragonal
STRUCTURAL
DISTORTION
form
The variation of the inverse of the magnetic susceptibility versus temperature between 300 and 4.2 K for the tctragonal LaCuQg prepared at 40 kbar (a = 3,817 A, c = 3,974 A), is given in Fig. 3. This high value of oxygen pressure (40 kbar), near the upper limit of stability for this structural variety, was chosen in order to eliminate the formation of oxygen vacancies. The thermal variation of the reciprocal magnetic susceptibility is of the same order of magnitude for the rhombohedral and the tetragonal forms. At room temperature, the magnetic susceptibility is higher for the tetragonal form than that of the rhombohedral one. Such a behaviour is in agreement with an increase of the electronic localization. The electrical measurement versus temperature for both forms is given in Fig. 4. The observed result suggests a semi-conducting behaviour with a small band gap for the tetragonal form compared to the metallic character characterizing the rhombohedral one.
OF LaCu03 LATTICE
965
Electric measurement on powder take into account the average conductivity. The difference between the electrical behaviour of the tetragonal form and the rhombohedral one could be due to the anisotropy of Cu-0 bonds in the first form and the isotropy of the Cu-0 bonds for the second one (8,9). Due to the local elongation of (CuQ6) in octahedra the tetragonal structure the conductivity must be enhanced in the xOy planes but largely reduced along the Oz axis leading to semi-conducting properties of the ceramics. CONCLUSION LaCu03 can present two different structures versus the pressure conditions used for the synthesis. In both structures the strong covalent character of the Cu-0 bond, induces a partial electronic transfer from oxygen to copper and modifies the electronic properties. In the tetragonal form, due to the local structural distortion -the electronic transfer Q2p --j d,2.,2Cu(lll) could be enhanced in the xOy planes and reduced along the Oz axis.
References
J.G. Bednorz K.A. Mi.iller 2. Phys. B. r%ndensed Matter 64 189-193 (1’9863 2) W. Klemm, G.’ Wehrmeyer and H.’ Bade, 2. elektrochem. Ber. Bunsenges physik Chem., 53, 56 (1959) 3) K. Hestermann and R. Hoppe, 2. anorg. allg. them., 367, 249;261;270 (1969). 4) G. Demazeau, C. Parent, M. Pouchard, P. Hagenmuller, Mat. Res. Bull., 7. 913 (1972). 5) J.B. Goodenough, G. Demazeau, M. Pouchard et P. Hagenmuller, J. Solid State Chem,, 8, 325330 (1973). 6) G. Demazeau, These de doctorat es Science, Bordeaux, 1973. 7) A.W. Webb, E.F. Skelton, S.B. Qadri, E.R. Carpenter, J.M.S. Osefoky, R.J. Soulenand, V. Letourneau, Physics Letters A, Vol. 137, N4,5 15 may 1989. 8) D.B. Currie and M.T. Weller, Acta. Cryst., C47, 696-698 (1991). 9) J.F. Bringley, B.A. Scott, S.J. La Placa, R.F. Boehme, T.M. Shaw, M.W. MC. Elfrech, S.S. Frail
and D.E. Cost, Nature, 347, 263-265 (1990). IO) S. Darracq, A. Largeteau, G. Demazeau, B.A. Scott and J.F. Bringley, Eur. J. Solid State and Inora. Chem., 29, 585-591 (1992). 11) 3. Demazeau, F. Menil, J. Portier et P. Hagenmuller, C.R. Acad. SC., 273, 1641-1644 (1971). 12) A.R. Williams, J. Kubler and C.D. Gelatt, J. Phvs. Rev.. B19. 6094 (1979). 13i D.D. Koelling~ and B.N. Harmon, J. Phys., CIO, 3107 (1977). 14) J. van Barth and D. Heden, J. Phys., C5, 1629 (1972). 15) J.F. Janak, Solid State Comm., 25, 52 (1978). 16) A.W. Webb, K.M. Kim and C. Bouldin, Solid State Comm., 79, N6, 507 (1991). 17) Katsuhiko TAKEGAHARA, Japanese J. of Aool. Phvs.. 26. L437 (19871. 18i F. ire&e, ‘G. Demazeau, K.A. Muller, High Pressure Research, 7, 61, 1991.