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24Physics of Complex Systems, 2022, vol. 3, no 2. _www.physcomsys.ru
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Physics of Semiconductors. Semiconductors
UDC 538.945.9
EDN NFNKXG
https://www.doi.org/10.33910/2687-153X-2022-3-2-86-99
Electronic defects in lattices of YBa0Cu0O7 and La Sr CuO,
2 3 2 - x x 4
A. V. Marchenko1, P. P. Seregin™ V. S. Kiselev1
1 Herzen State Pedagogical University of Russia, 48 Moika Emb., Saint Petersburg 191186, Russia
Authors
Alla V. Marchenko, ORCID: 0000-0002-9292-2541, e-mail: al7140@rambler.ru Pavel P. Seregin, ORCID: 0000-0001-5004-2047, e-mail: ppseregin@mail.ru Valentin S. Kiselev, e-mail: kiselev.valentin@gmail.com
For citation: Marchenko, A. V., Seregin, P. P., Kiselev, V. S. (2022) Electronic defects in lattices of YBa2Cu3O7 and La2 _ xSrxCuO4. Physics of Complex Systems, 3 (2), 86-99. https://www.doi.org/10.33910/2687-153X-2022-3-2-86-99. EDN NFNKXG
Received 28 February 2022; reviewed 28 March 2022; accepted 28 March 2022. Funding: The study did not receive any external funding.
Copyright: © A. V. Marchenko, P. P. Seregin, V. S. Kiselev (2022). Published by Herzen State Pedagogical University of Russia. Open access under CC BY-NC License 4.0.
Abstract. Using emission Mossbauer spectroscopy data for the 67Zn isotope and nuclear quadrupole resonance data for the 17O isotope, as well as calculations of the lattice electric field gradient, the effective charges of all atoms in superconducting copper metal oxide YBa2Cu3O7 and La2 _ xSrxCuO4 crystal lattices were determined. The effective charges of metal atoms and most oxygen atoms correspond to their standard oxidation states (Y3+, La3+, Ba2+, Sr2+, Cu2+ and O2_). However, the atoms of chain oxygen (in YBa2Cu3O7) and planar oxygen (in YBa2Cu3O7 and La2 _ xSrxCuO4) show a reduced charge, which is explained by the localisation of holes in the corresponding sublattices.
Keywords: Mossbauer spectroscopy, nuclear quadrupole resonance, electric field gradient tensor, atomic charges, high-temperature superconductors
Introduction
The discovery of the high-temperature superconductivity phenomenon in copper metal oxides (Bed-norz, Muller 1986) resulted in a large number of studies of nuclear quadrupole interaction (NQI) in typical materials of this kind—YBa2Cu3O7 _ x and La2 _ xSrxCuO4—through nuclear quadrupole resonance (nQr) method with probe nuclei 17O (Ishida et al. 199X1; Takigawa et al. 1989), 63Cu (Ohsugi et al. 1994; Pennington et al. 1989), 137Ba (Shore et al. 1992), 139La (Ohsugi 1995), as well as through absorption Mossbauer spectroscopy (MS) with probe nuclei 57Fe, 119Sn, 151Eu, 155Gd, 161Dy, 166Er, 169Tm, 170Yb (Masterov et al. 1995) and emission MS with probe nuclei 67Cu(67Zn) and 67Ga(67Zn) (Marchenko et al. 2018a; 2018b; Terukov et al. 2018). NQI tensor parameters (the quadrupole interaction constant and the asymmetry parameter) provide information on the spatial distribution of electronic defects in various sublattices within high-temperature superconductors (HTSC). This information makes it possible to determine the effective charges of their atoms, which, in turn, naturally limits the number of models that should be used in quantum mechanical calculations of HTSC electronic properties. A reliable method for finding the effective charges of atoms is to compare the calculated and the experimental parameters of the NQI tensor.
In crystal lattices with high chemical bond ionicity, which includes copper metal oxides YBa2Cu3O7 _ x and La2 _ xSrxCuO4, two sources of the electric field gradient (EFG) on probe nuclei can be distinguished: crystal lattice ions (lattice EFG) and nonspherical valence shells of the probe atoms (valence EFG). The total EFG on the probe nucleus is determined by the parameters (Marchenko et al. 2018a; 2018b)
Ua = (1 -r)Vzz + (1 - R )WZZ, (l)
_ (1 - rKMat + (1 - R Wn , (2)
n U22
U -U V - V W -W
n_ V xx V yy n xx y yy n xx " yy (3)
1 U V 'lval W
zz zz zz
where U.,, V., and W.. are the components of the diagonalised total, lattice and valence EFG tensors,
ll' IV ll c O ' '
Uz, Vz, and Wz are the principal components of these tensors, n, nlat, nval are the asymmetry parameters of these tensors, y, R0 are the Sternheimer coefficients, that should consider antiscreening and screening processes of the probe nucleus by the internal electron shells of the probe atom from external charges.
Blaha et al., suggested the full potential linearised-augmented-plane-wave (LAPW) method for the theoretical calculation of the parameters of the total EFG tensor using the local-density-approximation (LDA) (Blaha et al. 1985). This calculation is carried out without additional approximations such as the Sternheimer antishielding coefficients. Using this approach, EFG calculations "from first principles" based on LDA for high-temperature superconductors YBa2Cu3O7 (Schwarz et al. 1990) were performed. When using the X-ray diffraction data (Beno et al. 1987) for YBa2Cu3O7 and the nuclear quadrupole moment Q = -0.211 b for 63Cu and Q = -0.026 b for 17O while converting NQR frequencies to EFG, the calculated EFGs were in good agreement with the experimental NQR measurements with 63Cu (Pennington et al. 1989), 170 (Takigawa et al. 1989) and 137Ba (Shore et al. 1992) for Ba, Cu, and O sites, with the exception of the planar copper Cu(2) nodes, where the main component of the experimental EFG tensor is more than twice the calculated value. Similar results were also presented in (Yu et al. 1991). In connection with this discrepancy, the authors of (Ambrosch-Draxl et al. 1991) reported on EFG calculations for YBa2Cu3O7, in which the ambiguities presented in LAPW were eliminated. Despite the changes in the calculations, the calculated EFG at the Cu(2) site is similar to the values obtained in earlier LAPW studies. This means that the discrepancy between the EFG calculated within the LDA framework and the experimental one cannot be explained by a computational artefact and confirms the assumption made in (Schwarz et al. 1990), that the discrepancy is a real LDA error. It is emphasised that the EFG tensor components are only the second derivatives of the Coulomb potential and thus represent well-defined properties of the ground state, uniquely determined by the charge density.
It can be noted here that the studies of La2 _ xSrxCuO4 performed in (Sun et al. 2015; 2016) demonstrate how the doping electronic structures of high-temperature cuprate superconductors can be accurately modelled based on the first principles developed in (Lee et al. 2021). These calculations correctly predict the key experimentally observed features of the electronic structure and magnetism of La2 _ xSrxCuO4 without involving any free parameters. Thus, studies (Lee et al. 2021; Sun et al. 2016) open a new way to investigate the first principles of electronic structures and broader properties of correlated materials in general.
It is possible to just compare the theoretical and experimental parameters of the lattice EFG tensor to determine the effective charges of atoms (Marchenko et al. 2018a; 2018b; Terukov et al. 2018). If the electron shells of the probe atom are completely (or half) filled, then the electron cloud can be considered as consisting of several concentric spheres. The strength of the electrostatic field from such spheres on the nucleus is zero, so only the charges of the neighbouring atoms should be taken into consideration when calculating the EFG at the nucleus of an atom-probe (lattice probe).
The method of making lattice EFG tensor calculations using the point charge model is quite simple and clear. For such a calculation, only the unit cell parameters are required, which are known for most HTSCs from X-ray diffraction studies. The term "effective charges" refers to the charges that are required to describe the electric field of ions using the Coulomb potential. Effective charges accurately present the valence states of ions at the lattice sites and the significant deviations from their standard valence states (Seregin, Masterov, Nasredinov 1992; Seregin, Marchenko, Seregin et al. 1992; 2015). Such calculations for the YBa2Cu3O7 and La2 _ xSrxCuO4 lattices have been carried out in many works (see, for example, (Adrian 1989; Garcia, Bennemann 1989; Lyubutin et al. 1989; Seregin et al. 1992; 2015; Shimizu 1993)), but their results are in poor agreement with experimental data (Ishida et al. 1991; Masterov et al. 1995; Ohsugi 1995; Ohsugi et al. 1994; Pennington et al. 1989; Shore et al. 1992; Takigawa et al. 1989).
This is explained by the fact that copper metal oxides YBa2Cu3O7 and La2 _ xSrxCuO4 predominantly contain atoms that do not form lattice probes.
This study describes effective charge determination for atoms in the copper metal oxides YBa2Cu3O7 and La2 _ xSrxCuO4. The calculated EFG tensor parameters are compared with the experimental NQI tensor parameters measured by NMR/NQR or MS using the lattice probes located at the lattice sites. The EFG tensor parameters are the main components of the lattice EFG tensors at the i-sites of the lattice Vzzi and the asymmetry parameters of these tensors nlati. The parameters of the NQI tensors are the quadrupole interaction constants C . = Q.(1 _ v.) V . = a, V . and the asymmetry parameters n . (here
^ £ expi ' v zzi i zzi ' It »expi x
ai = Qi(1 _ yi) is the electron-nuclear parameter of the lattice i-probe located at the i-site of the lattice, Yi is the Sternheimer coefficient of the i-probe and Q. is the quadrupole moment of the atomic nucleus of the i-probe).
Requirements for lattice probes
There are several requirements for the lattice probes (Seregin et al. 2015):
• it is necessary to use such probes that their position in the lattice is known a priori;
• the possibility of uncontrolled appearance of point defects in the lattice (such as vacancies or atoms displaced into interstitial spaces) is excluded during probe introduction. Such defects distort the results of EFG tensor calculations;
• to eliminate any uncertainties in the theoretical values of nucleus quadrupole moments and Sternheimer coefficients, as well as to determine the effective charges of atoms in units of electron charge, it is necessary to experimentally determine the coefficient a = eQ(1 _ y) for at least one probe that is used;
• to reduce the influence that coefficient a uncertainties have on the values of the obtained effective charges, it is appropriate to use the minimum number of probes and, in the ideal case, use one probe each in the cationic and anionic sublattices (of course, each probe should replace as many crystallographically nonequivalent sites of the crystal lattice as possible);
• for crystals containing one lattice probe in two crystallographically non-equivalent positions, one should not compare the values V . and C . = eQ. (1 _ y ) V , but the values of the ratios V JV „
£ zzi expi ^-i x m7 zzr zz1 zz2
and Cexp1/Cexp2, where Vzz1, Vzz2 are the principal components of the lattice EFG tensor at structurally nonequivalent sites 1 and 2 occupied by the lattice probe atom, and Cexp1 and Cexp2 are the quadrupole interaction constants for the lattice probe at these sites (i.e., it is proposed to exclude quadrupole moments of probe nuclei and Sternheimer coefficients of probe atoms);
• All of these conditions for YBa2Cu3O7 and La2 _ xSrxCuO4 are satisfied for the 67Zn2+ probe using emission MS (Seregin et al. 2015);
• when using emission MS with 67Cu(67Zn) isotopes, copper atoms form a lattice probe of divalent zinc 67Zn2+ after beta decay of 67Cu at the sites of divalent copper Cu2+ in the YBa2Cu3O7 and La2 _ xSrxCuO4 lattices;
• when using emission MS with 67Ga(67Zn) isotopes, trivalent gallium atoms 67Ga3+ replace trivalent yttrium atoms Y3+ in the YBa2Cu3O7 lattice or trivalent lanthanum atoms La3+ in the La2 _ xSrxCuO4 lattice, and the lattice probe of bivalent zinc 67Zn2+ stabilises at trivalent yttrium (or trivalent lanthanum) sites after the electron capture in 67Ga.
The results of Mossbauer spectroscopy of the YBa2Cu3O7 compound (Seregin et al. 2015) show that in some structural positions the oxygen atom can be considered a 17O2_ lattice probe, making it possible to determine the effective charges of all atoms in the YBa2Cu3O7 and La2 _ xSrxCuO4 crystal lattices using the NQR data with the 170 isotope (Masterov et al. 1995; Terukov et al. 2018).
To confirm the validity of the effective charges determined in La2 _ xSrxCuO4, other lattice probes can also be introduced:
• when using emission MS with 57Co(57mFe) isotopes, the atoms of bivalent cobalt Co2+ replace the atoms of bivalent copper Cu2+ in the La2 _ xSrxCuO4 lattice, and the lattice probe of trivalent iron 57mFe3+ is stabilised at the sites of bivalent copper after electron capture in 57Co;
• when using emission MS with 155Eu(155Gd) isotopes, the trivalent europium atoms 155Eu3+ replace the atoms of trivalent lanthanum La3+ in the La2 _ xSrxCuO4 lattice, and the lattice probe of trivalent gadolinium 155Gd3+ is stabilised at the sites of trivalent lanthanum after the decay of 155Eu.
Experimental techniques
EFG tensors calculations
Copper oxide Cu2O and superconducting YBa2Cu3O7 and La2 _ ^Sr^CuO4 ceramics were chosen as objects of study.
The Cu2O compound crystallises in a cubic lattice (Wells 1984). The YBa2Cu3O7 compound has an orthorhombic structure (see Fig. 1a) (Yvon, Francois 1989). The La2_^Sr^CuO4 solid solutions crystallise in a lattice of the K2NiF4 type (a weakly distorted orthogonal structure; for x > 0.1, the lattice becomes tetragonal (see Fig. 1b) (Yvon, Francois 1989).
Fig. 1. Unit cells of YBa2Cu3O7 (a) and La2 _ xSrCuO4 (b)
The components of the lattice EFG tensor were calculated using the point-charge model with the relations (Seregin et al. 2015).
e>X^^ -1] _XetG,
i rki rki
aak '
V -V eV 3 akiPki eG
V a/} ¿_t /t ¿_t 5 / ^k^aBk.
k i rki k
(4)
k
k
where k is the summation index over sublattices, i is the summation index over sublattice sites, a, p are the Cartesian coordinates, ek are the effective charges of atoms of the k-sublattice (in units of the electron charge e), rk. is the distance from the i-ion of the k-sublattice to node where the EFG is calculated.
The lattice of the Cu2O compound was represented as Cu4O2, and the atomic coordinates c and unit cell parameters were set according to (Wells 1984).
According to (Yvon, Francois 1989), a unit cell of the YBa2Cu3O7 compound contains nodes of yttrium, barium, chain copper Cu(1), planar copper Cu(2), apical oxygen O(1), planar oxygen O(2), O(3) and chain O(4) oxygen (see Fig. 1a). The YBa2Cu3O7 lattice was represented as YBa2Cu(1)Cu(2)2O(1)2O(2)2O(3)2O(4), and the summation index over sublattices in the formula (3) took the following values:
k =1 2 3 4 5 6 7 8
atom Y Ba Cu(1) Cu(2) O(1) O(2) O(3) O(4)
According to (Yvon, Francois 1989), a unit cell of La2—xSrxCuO4 solid solution contains nodes of lanthanum (strontium), copper, apical O(1) and planar oxygen O(2) (see Fig. 1b). The La2 _ xSrxCuO4 lattice was represented as in the form (La,Sr)2CuO(l)2O(2)2, with the crystallographic parameters taken from (Yvon, Francois 1989; Tarascon et al. 1987); the summation index over sublattices in the formula (3) took the following values:
k = 1 2 3 4 5
atom La Sr Cu O(1) O(2)
The tensors Gaa and were calculated inside spheres with a radius of 30 A, and the obtained parameters of the tensors are consistent with the literature data (Seregin et al. 2015).
Sample synthesis and Mossbauer spectra measurement
Cu2O copper oxide was obtained by calcining CuO in vacuum. YBa2Cu3O7 and La2—xSrxCuO4 compounds (x = 0 ^ 1) were prepared using ceramic technology (Seregin et al. 2015). The YBa2Cu3O7 samples had an orthorhombic structure, while the La2 _ xSrxCuO4 samples had a K2NiF4 type structure. The obtained materials were single-phase with superconducting transition temperatures of 91 K for YBa2Cu3O7 and 25, 37, 32 K for La2 _ xSrxCuO4 (where x = 0.1, 0.15, 0.2). Ceramics were alloyed with isotopes 67Cu, 67Ga, 57Co and 155Eu during diffusion annealing (Seregin et al. 2015).
Mossbauer spectra were recorded at 80 K (57Co, 155Eu) and 4.2 K (67Cu, 67Ga) with K457Fe(CN)6.3H2O, 155GdPd„ and 67ZnS absorbers.
Table 1. Experimental NQI parameters at the lattice sites of YBa2Cu3O7, La185Sr015CuO4, and Cu2O
Compound Node Probe Method С ,MHz exp n exp z-axis of the EFG tensor Reference
Y 67Zn MS 67Ga(67Zn) -2.2(3) 0.8(1) c [*]
Ba 137Ba NQR 137Ba |56.4(1)| 0.94(2) c [6]
Cu(1) 67Zn MS 67Cu(67Zn) +20.1(3) 0.95(3) [*]
YBa2Cu3O7 Cu(2) 67Zn MS 67Cu(67Zn) +11.8(3) < 0.2 [*]
O(1) 17O NMR 17O |7.3(1)| 0.32(2) c [2]
O(2) 17O NMR 17O |6.4(1)| 0.24(2) b [2]
O(3) 17O NMR 17O |6.6(1)| 0.21(2) a [2]
O(4) 17O NMR 17O |10.9(1)| 0.41(2) b [2]
La,Sr 67Zn MS 67Cu(67Zn) —2.7(2) < 0.2 [*]
La1.85Sr0.15CuO4 Cu 67Zn MS 67Cu(67Zn) 11.4(5) < 0.2 [*]
O(1) 17O NMR 17O |1.33(5)| 0.0 [3]
O(2) 17O NMR 17O |4.6(1)| 0.36(2) [3]
Cu2O Cu 67Zn MS 67Cu(67Zn) —22.0(3) < 0.2 [*]
[*]—the results of this work.
Experimental results and discussion
MS data
The Mossbauer spectra of 67Zn are shown in Figs. 2-4, the results of their processing are summarised in Table 1. The same table shows NQR data for barium (Shore et al. 1992) and oxygen (Ishida et al. 1991; Takigawa et al. 1989) sites.
Fig. 2. 67Cu(67Zn) and 67Ga(67Zn) Mossbauer spectra of YBa2Cu3O7 and Cu2O compounds at 4.2 K
Fig. 3. 67Cu(67Zn) Mossbauer spectra of La2 _ Sr CuO4 solid solutions for x = 0.1, 0.5, and 1.0 at 4.2 K
Fig. 4. 67Ga(67Zn) Mossbauer spectra of La2_xSrxCuO4 solid solutions for x = 0.1, 0.5, and 1.0 at 4.2 K
The Mossbauer emission spectra of 67Cu(67Zn) and 67Ga(67Zn) of all studied materials are either well-resolved quadrupole triplets (spectra of Cu2O:67Cu, YBa2Cu3O7:67Ga (see Fig. 2), La2 _ xSrxCuO4:67Cu (see Fig. 3), and 2 _ xSrxCuO4:67Ga (see Fig. 4)), or a superposition of two quadrupole triplets (YBa2Cu3O7:67Cu spectrum (see Fig. 2)). According to the values of isomer shifts, these spectra correspond to the lattice centres of divalent zinc 67Zn2+ either at copper sites (67Cu(67Zn) spectra) or at yttrium and lanthanum sites (67Ga(67Zn) spectra). The number of quadrupole triplets in the experimental spectra is determined by the number of crystallographic positions occupied by the substituting atoms.
The 57Co(57mFe) and 155Eu(155Gd) Mossbauer emission spectra of La2 _ xSrxCuO4 solid solutions are quadrupole triplets (see Figs. 5 and 6). According to the values of isomeric shifts, these spectra correspond to the lattice centres of trivalent iron 57mFe3+ and trivalent gadolinium 155Gd3+ at lanthanum sites.
The noncubic symmetry of the local environment of copper, yttrium, and lanthanum atoms leads to the splitting of the spectra into quadrupole triplets (67Cu(67Zn) and 67Ga(67Zn) spectra) or quadrupole doublets (57Co(57mFe) and 155Eu(155Gd) spectra).
57Co(57mFe), 80 K
-2-10 1 2
Velocity, mm/s
Fig. 5. 57Co(57mFe) Mossbauer spectra of La2 _ xSrxCuO/7Co for x = 0.1, 0.5, and 1.0 at 80 K
• 155Eu(155Gd), 80 K
-4 -2 0 2 4
Velocity, mm/s
Fig. 6. 155Gd Mossbauer spectra of La2 _ xS^CuO4:155Eu solid solutions for x = 0.1, 0.5, and 1.0 at 80 K
Determining the aZn = eQZn (1 - yZJ coefficient for the 67Zn2+ probe
For the Cu+2O2- model, the calculation for copper sites yields Vz = -1.093 e/À3, which leads to a equal to 20.1(3) MHz.À3/e for 67Zn=- centres at copper sites in the Cu2O lattice.
Determining effective atom charges in the YBa2Cu3O7 lattice
To determine the effective charges of YBa2Cu3O7 lattice atoms, emission MS data on the isotopes 67Cu(67Zn) and 67Ga(67Zn) and NQR data on the isotope 17O were used (Takigawa et al. 1989). A system of equations was compiled, including
• the equation of electroneutrality:
e1 + 2e2 + e3 + 2e4 + 2e5 + 2e6 + 2e7 + e8 = 0, (5)
• the equation relating the quantities Vzz1. and C1 for the 67Zn2+ probe at yttrium nodes:
k=8
aZn Z ekGzzkl = C1, (6)
k=1
• the equation relating the quantities Vzz3/Vzz4 and P34 = C3/C4 for the 67Zn2+ probe at the Cu(1) and Cu(2) sites:
k=8
Z ek Kk3 - P34Gzzk4 ] = 0 (7)
k=1
• equation relating the values Vzz5/Vzz6 and P56 = C5/C6 for the 17O2- probe at the O(5) and O(7) nodes:
Z ek [Gzk5 - PG,6 ] = 0, (8)
k=i
four equations relating the calculated and experimental values of the asymmetry parameters of the EFG tensors for the 67Zn2+ probe at the copper sites and for the 17O2- probe at the O(1) and O(2) sites:
k=8
X ek [Gxxkl - Gyykl - hGzzkl ] = 0 (9)
k=1
where l = 3, 4, 5, 6.
Additional factors that were taken into account are as follows:
• the principal axes of the EFG tensors for the 17O2- centres at the O(1) and O(2) sites coincide with the crystallographic axes c and b, respectively (Takigawa et al. 1989);
• the main axis of the EFG tensor for 137Ba2+ centres is directed along the crystallographic c axis (Shore et al. 1992);
• the main axis of the EFG tensor for 155Gd3+ centres at Y sites is directed along the crystallographic c axis (Wortmann et al. 1989);
• solutions with negative charges of cations or positive charges of anions were rejected as having no physical meaning.
The accuracy of effective charge ek values obtained from the system of equations (5-9) is limited by the assumption that there is no valence electric field on probe nuclei. As an example, Table 2 shows the atom charges obtained using the experimental values from Table 1 and various structural data (Capponi et al. 1987; Francois et al. 1988; Konstatntinovic et al. 1989; Le Page et al. 1987; Yvon, Francois 1989). The reduced values of the O(4) and O(3) charges reflect charge distribution in the YBa2Cu3O7 lattice,
while the deviations of remaining atoms' charges from the standard oxidation states are random and are associated with the difference in the temperatures for determining the NQI parameters and the parameters of the YBa2Cu3O7 crystal lattice structure, and also with the errors in the latter.
Table 2. Effective charges of atoms of the YBa2Cu3O7 lattice obtained by solving the system of equations (5-9) with different structural data at different temperatures
Structural data T, K el e2 e3 e4 e5 e6 e7 e8 Model
[28] 5 K 2.92 2.04 1.96 2.00 -2.09 -1.93 -1.81 -1.28 1
[28] 320 K 2.80 1.90 1.88 1.92 -1.99 -1.83 -1.71 -1.22 2
[29] 5 K 2.91 2.01 1.88 1.99 -2.05 -1.92 -1.80 -1.25 3
[31] 298 K 3.03 2.06 2.13 2.14 -2.18 -2.00 -1.91 -1.36 4
[30] 9 K 2.99 2.00 2.01 2.00 -2.00 -2.00 -1.80 -1.40 5
[25] 295K 3.00 1.99 2.00 2.01 -2.00 -2.00 -1.85 -1.30 6
The models given in Table 2 satisfy the assumption made in (Baryshev et al. 2011; Mitsen, Ivanenko 2007) about the localisation of holes in YBa2Cu3O7 _ x around Cu ions in CuO3 chains on oxygen ions (O(4) crystallographic position).
For all models from Table 2, the calculated parameters of the lattice EFG tensors with different structural data turn out to be similar. For model 6, these values are shown in Table 3.
Table 3. Components of lattice EFG tensors for YBa2Cu3O7 crystal sites (model 6)
Node Vaa, e/À3 Vbb, e/À3 Vcc, e/À3 nlat
Y 0.006 0.107 - 0.113 0.89
Ba - 0.118 - 0.003 0.121 0.94
Cu(1) 0.982 - 0.036 - 0.946 0.97
Cu(2) - 0.263 - 0.324 0.587 0.10
O(1) - 0.158 - 0.331 0.489 0.35
O(2) - 0.153 0.385 - 0.232 0.21
O(3) 0.439 - 0.206 - 0.233 0.06
O(4) - 0.086 0.575 - 0.489 0.70
The obtained parameters of the lattice EFG tensors can be used to interpret NQR data on the 137Ba isotope, for which the value Cexp = 56.4MHz, nexp = 0.94 was found in YBa2Cu3O7 (Shore et al. 1992). We calculated the lattice EFG tensor at Ba nodes for model 6 in Table 3. For the 137Ba2+ probe, the value aBa = e Q (1 - y) = 470(9) MHz.e/À3 was obtained.
Similarly, the value a0 = e Q (1 - y) can be determined for lattice centres 17O2-. Using the values Vzz5 (see Table 3) and C5 (see Table 1) for the 17O2_ centers at the nodes O(1) of the YBa2Cu3O7 lattice, we obtained a0 = 14.9(2) MHz.À3/e.
Finally, we obtained z || c and Uzz < 0 for the 155Gd3+ lattice probe in the YBa2Cu3O7 compound within the framework of the point charge model (see Table 3). This is in agreement with MS results (Wortmann et al. 1989) obtained on the 155Gd isotope for the compound GdBa2Cu3O7.
Effective atom charges in the lattices of La2 _ SrCuO4 solid solutions
To determine the effective atom charges in the La2 _ xSrxCuO4 lattice, we used emission MS data on the 67Cu(67Zn) and 67Ga(67Zn) isotopes, as well as nQr data on the 17O isotope (Ishida et al. 1991). It should be noted that according to the data on the 17O isotope, the asymmetry parameter of the EFG tensor for planar oxygen O(2) lattice La185Sr015CuO4 is different from zero (see Table 1), whereas according to the calculations of the lattice EFG tensor for this oxygen, n4 = 0. In other words, the crystal probe can only be the apical oxygen centre O(1).
Thus, the following system of equations was compiled:
• the equation of electroneutrality:
2e1 + e2 +2e3 + 2e4 = 0, (10)
• the equation relating the quantities Vzz1. and C1 for the 67Zn2+ probe at lanthanum nodes:
Z ekGzzkl = C, (11)
k=1
• the equation relating the quantities Vzz2. and C2 for the 67Zn2+ probe at copper nodes;
"z„ Z efizkk 2 = 0, (12)
k=1
where aZn = 20.1(3) MHz.A3/e.
• the equation relating the quantities Vzz3. and C3 for the 17O2- probe at O(1) nodes;
k=4
a Z efizkk3 = 0, (13)
k=1
where aO = 14.9(2) MHz.A3/e.
The effective charges of metal atoms and apical oxygen atoms of the La2 _ xSrxCuO4 lattice, as in the case of the YBa2Cu3O7 lattice, correspond to the standard oxidation states of these atoms. However, for planar oxygen atoms, a reduced charge of planar oxygen atoms is observed, which is consistent with the authors' assumption (Baryshev et al. 2011; Mitsen, Ivanenko 2007) about the localisation of a hole in the energy zone formed by the electronic states of O(2) atoms. Taking into account the error in determining the parameters of the lattice GAP tensors, the distribution of atomic charges in the La2 _ xSrxCuO4 lattice can be represented as
(La1.85Sr0J5)2-925+Cu2+O(1)2-2 ( 2)1-925-2. (13)
To confirm the model (13), we performed a co-representation of the calculated P(x) = [ Vzz]x/[ Vzz]x=01 and experimental Pexp = [eQUzz]x/[eQUzz]x01 dependencies in lanthanum nodes (see Fig. 7) and copper (see Fig. 8) lattices of La2 _ xSrxCuO4 solid solutions. MS was used on isotopes 57Co(57mFe), 67Cu(67Zn) (see Fig. 7) and 67Ga(67Zn), 155Eu(155Gd) (see Fig. 8). The indicated permutations were carried out for four models of hole localisation: the hole is located in the sublattice of copper; in the sublattice of apical oxygen; in the sublattice of planar oxygen and the hole is distributed between sublattices of apical and planar oxygen. The dependences of P(x) in Figs. 7 and 8 can be explained if the hole is localised mainly in the positions of planar oxygen.
Conclusion
Using only crystallographic data, Mossbauer spectroscopy data on the 67Zn isotope and nuclear quadrupole resonance on the 17O isotope, as well as calculations of lattice EFG tensors, the effective charges of all atoms of superconducting copper metal oxide YBa2Cu3O7 and La2 _ xSrxCuO4 lattices were determined. These charges correspond to the standard degrees of atom oxidation, with the exception of the chain and planar oxygen atoms in the YBa2Cu3O7 lattice and planar oxygen atoms in the La2 _ xSrxCuO4 lattice. The reduced charge of these atoms is explained by the localisation of holes in the corresponding sublattices.
Fig. 7. Dependences of Рexp on x for La2 _ xSrxCuO4 for copper sites: (1) the hole is located in the copper sublattice; (2) the hole is in the O(1) sublattice; (3) the hole is in the O(2) sublattice; (4) the hole is distributed between the O(1) and O(2) sublattices; open and filled squares are experimental MS data with the S7Co(S7mFe ) (1) and
67Cu(67Zn) (2) isotopes
Fig. 8. Dependences of Pexp on x for La2 _ xSrxCuO4 for lanthanum sites: 1—the hole is localised in Cu positions; 2—the hole is localised in positions O(1); 3—the hole is localised in positions O(2); 4—the hole is localised in positions O(1) and O(2); open and filled squares are experimental data with the 67Ga(67Zn) (1) and 1ssEu(1ssGd)
(2) isotopes
Conflict of Interest
The authors declare that there is no conflict of interest, either existing or potential.
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