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The nuclear density of YBCO by the maximum entropy method using neutron powder data
PHYSICA© ELSEVIER
Physica C 263 (1996) 176-179
The nuclear density of YBCO by the maximum entropy method using neutron powder data Masaki Takata a, *, Eiji Nishibori a, Takashi Takayama a, Makoto Sakata a, Katsuaki Kodama b Masatoshi Sato b C.J. Howard c a Department of Applied Physics, Nagoya University, Nagoya 464-01, Japan b Department of Physics, Nagoya University, Nagoya 464-01, Japan c ANSTO, Lucas Heights. NSW 2234, Australia
Abstract
In order to examine the nature of thermal motions of the YBCO superconductor, particularly in the CuO 2 and CuO planes, the nuclear density distribution was observed by the maximum entropy method (MEM) using neutron powder diffraction data measured at 15 K. The characteristic squarish deformation of the nuclear density due to anharmonic thermal motion was found even at such a low temperature for the Cu atom in the CuO z plane but not in the CuO plane. The obtained MEM nuclear density is consistent with the existence of strong Cu-O bonds in the CuO 2 plane and not in the CuO plane.
I. Introduction
The thermal vibrational feature, which is often associated with the bonding nature of atoms in a crystal, can be investigated by neutron diffraction experiments [1,2]. In the structure determination of high-Tc superconductors, Rietveld analysis of neutron powder data has played a central role. The Rietveld method is an extremely good way to determine aspects of the basic crystal structure at the atomic level, such as atomic coordinates and hence bond lengths. However, Rietveld analysis cannot provide further structural information beyond the presumed crystal structural model of an atomic arrangement.
* Corresponding author. Fax: + 81 52 789 3724; e-mail: [email protected].
The fine features of thermal vibration including anharmonicity should provide important complementary information on the bonding nature in a crystal of a high-T~ superconductor. Such a detailed structural study has not been carried out so far. Recently, the maximum entropy method (MEM) [3-5] has been successfully applied to the model-free reconstruction of the nuclear density distribution from neutron powder data, and has revealed significant anharmonic thermal vibrational features of atoms [6]. It is well known that the superconducting behaviour of high-Tc superconductors is governed by the two-dimensional network of the CuO 2 conduction plane which is known to be a path of the doped holes or electrons in the superconducting state. Therefore, one of the central points of interest for the fine structure in a high-T~ superconductor is the bonding nature of the CuO z plane. The M E M charge densities of YBa2Cu306.97 (YBCO) given elsewhere [7] showed
0921-4534/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0921-4534(96)00082-2
M. Takata et al. / Physica C 263 (1996) 176-179 Table 1 The structural parameters of YBCO by the Rietveld analysis
that there is a strong C u - O bond on the CuO 2 plane. The main interest of this paper is to reveal atomic thermal vibrational features of YBCO in the superconducting phase by the MEM nuclear density obtained from neutron powder data; these features must be related to the bonding nature of this substance.
YBa2Cu306.97 Space Group Pmmm a = 3.81550(8) ~., b = 3.88203(9) ,g,, c = 11.6458(3) ,g, Site x y z Occupancy Y Ba Cu(l) Cu(2) 0(1) 0(2) 0(3) 0(4) R I = 3.2%
2. Data analysis The powder sample of YBa2Cu307_ ~ was prepared by solid-state reaction with appropriate amounts of Y203 (3N), BaO 2 (2N) and CuO (3N). Two intermediate grindings were made to optimize homogeneity. Annealing and cooling in oxygen ensured that the oxygen content was close to 7.0. Neutron powder data were collected at 15 K on HRPD at ANSTO [8]. The wavelength of incident neutrons was 1.884 ,~. The powder pattern was obtained up to a 20 value of 147°.
I'
I
177
lh 2t la 2q 2q 2s 2r le
0.5 0.5 0.0 0.0 0.0 0.5 0.0 0.0
0.5 0.5 0.0 0.0 0.0 0.0 0.5 0.5
0.5 0.1841(3) 0.0 0.3551(2) 0.1586(2) 0.3775(3) 0.3778(3) 0.0
1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.97(1)
In order to analyse the neutron powder data, a new method is employed, which is the combination of Rietveld analysis and MEM. Very recently, this method has been successfully applied for the X-ray structural determination of the metallofullerene Y@C82 [9]. In the Rietveld analysis, which is con-
T
T
1
16oI ..~
1
140 t-
>, 120 • ~.-,4
,.o
100
j
80 ~r~
60
°
40
°~"i
20
,,.g,
0
I
I
IIII U Ill I II
1
Illlllllllllllllllll
IIIIIll IIIIIIIIIl~lltlll Ill Illlllll IIII Illl
I
I
I
j
8
28
48
j.
1
68 88 20 (degree)
1
1
108
128
Fig. 1. The Rietveld fitting result of the neutron powder pattern.
178
M. Takata et al./Physica C 263 (1996) 176-179
sidered as a pre-analysis in the present study, the anisotropic harmonic model was used only for temperature factors of the 0(4) atom. The determined parameters are listed in Table 1. The reliability factor (R-factor) based on Bragg intensities, R t, was 3.2%. The fitting result of the Rietveld analysis is shown in Fig. l(a) in which Rp, Rwp and Rexp are 4.4%, 5.7% and 3.2%, respectively. Observed structure factors were evaluated by dividing the observed intensities at each data point according to the calculated contributions of individual reflections by a modified Rietveld-refinement program [9]. The number of structure factors derived in this analysis was 138, which were used for further MEM analysis.
l
3. MEM nuclear density YBCO After Rietveld pre-analysis, the MEM analysis was carried out with the computer program MEED [10], using 40 × 40 × 100 pixels. In the MEM analysis, the structure factors were all treated independently as phased values. The R-factor based on the structure factors, R F, in the MEM analysis was 6.0%. The obtained MEM nuclear densities are shown in Fig. 2 for the CuO 2 and CuO planes. The contour lines are drawn in logarithmic scale. At first glance, the obtained MEM densities represent physically reasonable features as nuclear densities; the densities are concentrated around the atomic sites only. Anisotropic features can be found very clearly, especially for the Cu atom in the CuO 2 plane, denoted Cu(2). In the Rietveld pre-analysis, the isotropic harmonic model was used for the temperature factor of Cu(2). For the harmonic vibration, the feature of nuclear density should be a circle on this plane. The MEM analysis succeeded in revealing such a fine structure of thermal vibrations on the CuO z plane. In contrast to Cu(2), the shape of the nuclear density of the Cu atom in the CuO plane, denoted Cu(1), is rather spherical, which is expected from the harmonic thermal vibration. The nuclear density distribution of the Cu(2) atom is deformed towards the voids in the C u - O network and shows squarish distortion which can be interpreted as being caused by anharmonic vibrations. It is well known that the anharmonic deformation is
I
2A
(a)
~ O 4
~ l
I
(b) Fig. 2. The MEM nuclear density distributions for (a) CuO 2 and (b) CuO planes. The contour lines are drawn in logarithmic scale of 0.04)<2" (n = 1.-20) [ × 10- 13 cm/,~3].
oppositely directed to the bonding distribution since the atom spends more time towards the hole than towards the bond. In the Si case, the anharmonic distortion of the nuclear density, which is the tetrahedral distribution with robes towards the holes, is
M. Takata et al. / P hysica C 263 (1996) 176-179
oppositely directed to the tetrahedral bonding distribution [11]. Similar oppositely directed deformation in nuclear and charge densities caused by anharmonic motion and bonding electrons has been revealed for metallic Be by the M E M analysis [1]. The MEM charge density of the CuO 2 plane is given elsewhere by Takata et al. [7]. In the MEM charge density, the fundamental C u - O bonding feature was found clearly in the CuO a plane corresponding to the overlapping of the electron density of Cu 3d~2_y~ and O 2p~. In conclusion, the squarish deformation of the Cu(2) nuclear density can be interpreted as an anharmonic effect due to the existence of the bonding by superexchange interaction of Cu(2)-O(2) and Cu(2)-O(3) in the CuO 2 plane. If the anharmonicity is suppressed at a low temperature, the anharmonicity of Cu(2) atoms at 15 K in YBCO may be one of the characteristics of the CuO 2 plane in high-Tc superconductors. The present MEM study reveals the fine features of atomic thermal vibration in YBCO far beyond the model assumed in the Rietveld analysis. From the methodological viewpoint, the present method involving the Rietveld analysis and M E M has a great potential for the structural study of high-T~ superconductors in which the Rietveld analysis of powder data is leading.
179
Acknowledgements The authors thank S. Kumazawa for his help in the computer program, MEED. This work was supported by a Grant-in-aid for Scientific Research from the Ministry of Education, Science and Culture in Japan, to which the authors' thanks are due.
References [1] M. Takata, M. Sakata, S. Kumazawa, F.K. Larsen and B.B. Iversen, Acta Crystallogr. A 50 (1994) 330. [2] M. Sakata, M. Takagi, M. Takata and C.J. Howard, Physica B 213&214 (1995) 384. [3] D.M. Collins, Nature (London) 298 (1982) 49. [4] G. Bricogne, Aeta Crystallogr. A 44 (1988) 517. [5] M. Sakata and M. Sato, Acta Crystallogr. A 46 (1990) 263. [6] M. Sakata, T. Uno, M. Takata and C.J. Howard, J. Appl. Crystallogr. 26 (1993) 159. [7] M. Takata, T. Takayama, M. Sakata, S. Sasaki, K. Kodama and M. Sato, in: Proc. Int. Syrup. on Frontiers of High-Tc Superconductivity, Morioka, Japan; Physica C 263 (1996) 340 (this issue). [8] C.J. Howard, CJ. Ball, R.L. Davis and M.M. Elcomhe, Aust. J. Phys. 36 (1983) 503. [9] M. Takata, B. Umeda, E. Nishibori, Y. Saito, M. Ohno and H. Shinohara, Nature (London) 377 (1995) 46. [10] S. Kumazawa, Y. Kubota, M. Takata, M. Sakata and Y. Ishibashi, J. Appl. Crystallogr. 26 (1993) 453. [I 1] B.T.M. Willis and A.W. Pryor, Thermal Vibrations in CrystaUography, (Cambridge Univ. Press, Cambridge, 1975).
Physica C 263 (1996) 176-179
The nuclear density of YBCO by the maximum entropy method using neutron powder data Masaki Takata a, *, Eiji Nishibori a, Takashi Takayama a, Makoto Sakata a, Katsuaki Kodama b Masatoshi Sato b C.J. Howard c a Department of Applied Physics, Nagoya University, Nagoya 464-01, Japan b Department of Physics, Nagoya University, Nagoya 464-01, Japan c ANSTO, Lucas Heights. NSW 2234, Australia
Abstract
In order to examine the nature of thermal motions of the YBCO superconductor, particularly in the CuO 2 and CuO planes, the nuclear density distribution was observed by the maximum entropy method (MEM) using neutron powder diffraction data measured at 15 K. The characteristic squarish deformation of the nuclear density due to anharmonic thermal motion was found even at such a low temperature for the Cu atom in the CuO z plane but not in the CuO plane. The obtained MEM nuclear density is consistent with the existence of strong Cu-O bonds in the CuO 2 plane and not in the CuO plane.
I. Introduction
The thermal vibrational feature, which is often associated with the bonding nature of atoms in a crystal, can be investigated by neutron diffraction experiments [1,2]. In the structure determination of high-Tc superconductors, Rietveld analysis of neutron powder data has played a central role. The Rietveld method is an extremely good way to determine aspects of the basic crystal structure at the atomic level, such as atomic coordinates and hence bond lengths. However, Rietveld analysis cannot provide further structural information beyond the presumed crystal structural model of an atomic arrangement.
* Corresponding author. Fax: + 81 52 789 3724; e-mail: [email protected].
The fine features of thermal vibration including anharmonicity should provide important complementary information on the bonding nature in a crystal of a high-T~ superconductor. Such a detailed structural study has not been carried out so far. Recently, the maximum entropy method (MEM) [3-5] has been successfully applied to the model-free reconstruction of the nuclear density distribution from neutron powder data, and has revealed significant anharmonic thermal vibrational features of atoms [6]. It is well known that the superconducting behaviour of high-Tc superconductors is governed by the two-dimensional network of the CuO 2 conduction plane which is known to be a path of the doped holes or electrons in the superconducting state. Therefore, one of the central points of interest for the fine structure in a high-T~ superconductor is the bonding nature of the CuO z plane. The M E M charge densities of YBa2Cu306.97 (YBCO) given elsewhere [7] showed
0921-4534/96/$15.00 © 1996 Elsevier Science B.V. All rights reserved SSDI 0921-4534(96)00082-2
M. Takata et al. / Physica C 263 (1996) 176-179 Table 1 The structural parameters of YBCO by the Rietveld analysis
that there is a strong C u - O bond on the CuO 2 plane. The main interest of this paper is to reveal atomic thermal vibrational features of YBCO in the superconducting phase by the MEM nuclear density obtained from neutron powder data; these features must be related to the bonding nature of this substance.
YBa2Cu306.97 Space Group Pmmm a = 3.81550(8) ~., b = 3.88203(9) ,g,, c = 11.6458(3) ,g, Site x y z Occupancy Y Ba Cu(l) Cu(2) 0(1) 0(2) 0(3) 0(4) R I = 3.2%
2. Data analysis The powder sample of YBa2Cu307_ ~ was prepared by solid-state reaction with appropriate amounts of Y203 (3N), BaO 2 (2N) and CuO (3N). Two intermediate grindings were made to optimize homogeneity. Annealing and cooling in oxygen ensured that the oxygen content was close to 7.0. Neutron powder data were collected at 15 K on HRPD at ANSTO [8]. The wavelength of incident neutrons was 1.884 ,~. The powder pattern was obtained up to a 20 value of 147°.
I'
I
177
lh 2t la 2q 2q 2s 2r le
0.5 0.5 0.0 0.0 0.0 0.5 0.0 0.0
0.5 0.5 0.0 0.0 0.0 0.0 0.5 0.5
0.5 0.1841(3) 0.0 0.3551(2) 0.1586(2) 0.3775(3) 0.3778(3) 0.0
1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.97(1)
In order to analyse the neutron powder data, a new method is employed, which is the combination of Rietveld analysis and MEM. Very recently, this method has been successfully applied for the X-ray structural determination of the metallofullerene Y@C82 [9]. In the Rietveld analysis, which is con-
T
T
1
16oI ..~
1
140 t-
>, 120 • ~.-,4
,.o
100
j
80 ~r~
60
°
40
°~"i
20
,,.g,
0
I
I
IIII U Ill I II
1
Illlllllllllllllllll
IIIIIll IIIIIIIIIl~lltlll Ill Illlllll IIII Illl
I
I
I
j
8
28
48
j.
1
68 88 20 (degree)
1
1
108
128
Fig. 1. The Rietveld fitting result of the neutron powder pattern.
178
M. Takata et al./Physica C 263 (1996) 176-179
sidered as a pre-analysis in the present study, the anisotropic harmonic model was used only for temperature factors of the 0(4) atom. The determined parameters are listed in Table 1. The reliability factor (R-factor) based on Bragg intensities, R t, was 3.2%. The fitting result of the Rietveld analysis is shown in Fig. l(a) in which Rp, Rwp and Rexp are 4.4%, 5.7% and 3.2%, respectively. Observed structure factors were evaluated by dividing the observed intensities at each data point according to the calculated contributions of individual reflections by a modified Rietveld-refinement program [9]. The number of structure factors derived in this analysis was 138, which were used for further MEM analysis.
l
3. MEM nuclear density YBCO After Rietveld pre-analysis, the MEM analysis was carried out with the computer program MEED [10], using 40 × 40 × 100 pixels. In the MEM analysis, the structure factors were all treated independently as phased values. The R-factor based on the structure factors, R F, in the MEM analysis was 6.0%. The obtained MEM nuclear densities are shown in Fig. 2 for the CuO 2 and CuO planes. The contour lines are drawn in logarithmic scale. At first glance, the obtained MEM densities represent physically reasonable features as nuclear densities; the densities are concentrated around the atomic sites only. Anisotropic features can be found very clearly, especially for the Cu atom in the CuO 2 plane, denoted Cu(2). In the Rietveld pre-analysis, the isotropic harmonic model was used for the temperature factor of Cu(2). For the harmonic vibration, the feature of nuclear density should be a circle on this plane. The MEM analysis succeeded in revealing such a fine structure of thermal vibrations on the CuO z plane. In contrast to Cu(2), the shape of the nuclear density of the Cu atom in the CuO plane, denoted Cu(1), is rather spherical, which is expected from the harmonic thermal vibration. The nuclear density distribution of the Cu(2) atom is deformed towards the voids in the C u - O network and shows squarish distortion which can be interpreted as being caused by anharmonic vibrations. It is well known that the anharmonic deformation is
I
2A
(a)
~ O 4
~ l
I
(b) Fig. 2. The MEM nuclear density distributions for (a) CuO 2 and (b) CuO planes. The contour lines are drawn in logarithmic scale of 0.04)<2" (n = 1.-20) [ × 10- 13 cm/,~3].
oppositely directed to the bonding distribution since the atom spends more time towards the hole than towards the bond. In the Si case, the anharmonic distortion of the nuclear density, which is the tetrahedral distribution with robes towards the holes, is
M. Takata et al. / P hysica C 263 (1996) 176-179
oppositely directed to the tetrahedral bonding distribution [11]. Similar oppositely directed deformation in nuclear and charge densities caused by anharmonic motion and bonding electrons has been revealed for metallic Be by the M E M analysis [1]. The MEM charge density of the CuO 2 plane is given elsewhere by Takata et al. [7]. In the MEM charge density, the fundamental C u - O bonding feature was found clearly in the CuO a plane corresponding to the overlapping of the electron density of Cu 3d~2_y~ and O 2p~. In conclusion, the squarish deformation of the Cu(2) nuclear density can be interpreted as an anharmonic effect due to the existence of the bonding by superexchange interaction of Cu(2)-O(2) and Cu(2)-O(3) in the CuO 2 plane. If the anharmonicity is suppressed at a low temperature, the anharmonicity of Cu(2) atoms at 15 K in YBCO may be one of the characteristics of the CuO 2 plane in high-Tc superconductors. The present MEM study reveals the fine features of atomic thermal vibration in YBCO far beyond the model assumed in the Rietveld analysis. From the methodological viewpoint, the present method involving the Rietveld analysis and M E M has a great potential for the structural study of high-T~ superconductors in which the Rietveld analysis of powder data is leading.
179
Acknowledgements The authors thank S. Kumazawa for his help in the computer program, MEED. This work was supported by a Grant-in-aid for Scientific Research from the Ministry of Education, Science and Culture in Japan, to which the authors' thanks are due.
References [1] M. Takata, M. Sakata, S. Kumazawa, F.K. Larsen and B.B. Iversen, Acta Crystallogr. A 50 (1994) 330. [2] M. Sakata, M. Takagi, M. Takata and C.J. Howard, Physica B 213&214 (1995) 384. [3] D.M. Collins, Nature (London) 298 (1982) 49. [4] G. Bricogne, Aeta Crystallogr. A 44 (1988) 517. [5] M. Sakata and M. Sato, Acta Crystallogr. A 46 (1990) 263. [6] M. Sakata, T. Uno, M. Takata and C.J. Howard, J. Appl. Crystallogr. 26 (1993) 159. [7] M. Takata, T. Takayama, M. Sakata, S. Sasaki, K. Kodama and M. Sato, in: Proc. Int. Syrup. on Frontiers of High-Tc Superconductivity, Morioka, Japan; Physica C 263 (1996) 340 (this issue). [8] C.J. Howard, CJ. Ball, R.L. Davis and M.M. Elcomhe, Aust. J. Phys. 36 (1983) 503. [9] M. Takata, B. Umeda, E. Nishibori, Y. Saito, M. Ohno and H. Shinohara, Nature (London) 377 (1995) 46. [10] S. Kumazawa, Y. Kubota, M. Takata, M. Sakata and Y. Ishibashi, J. Appl. Crystallogr. 26 (1993) 453. [I 1] B.T.M. Willis and A.W. Pryor, Thermal Vibrations in CrystaUography, (Cambridge Univ. Press, Cambridge, 1975).