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ySnx(Na,Tl)yS [2], and indicates that the electron exchange between the centers of Sn2+ and Sn4+ is implemented using state of the valence band. In favor of such a mechanism is evidenced by the fact that the exchange is observed at low concentrations of tin, when the process can not be a direct exchange of electrons between the centers of the tin.
REFERENCES
1. Anderson P. W. Model for electronic structure of amorphous semiconductors // Physical Review Letters. 1975. V. 34. No 15. R 953-955.
2. Bordovsky G., Marchenko A. and Seregin P Mossbauer of Negative U Centers in Semiconductors and Superconductors. Identification, Properties, and Applicaton. Academic Publishing GmbH & Co. 2012. 499 p.
3. Bordovskii G A., Castro R. A., Marchenko A.V., Seregin P P Thermal stability of tin charge states in the structure of the (As2Se3)0.4(SnSe)0.3(GeSe)0.3 glass // Glass Physics and Chemistry. 2007. V. 33. No. 5. R 467-470.
А. Shaldenkova, P Seregin
CORRELATIONS OF THE 63Cu NMR DATA WITH THE 67Cu (67Zn)
AND THE 61Cu (61Ni) EMISSION MOSSBAUER DATA FOR CERAMIC SUPERCONDUCTORS
A linear correlation between the quadrupole coupling constant ССи measured by the 63Cu NMR technique on the one hand and the quadrupole coupling constants С2п and CNi measured by the 67Cuf7Zn) and 6ICu(6INi) emission Mossbauer spectroscopy on the other hand has been found for ceramic superconductors.
Keywords: Mossbauer spectroscopy, NMR, electric field gradient.
А. В. Шалденкова, П. П. Серегин* Победитель конкурса поддержки публикационной активности молодых исследователей (проект 3.1.2, ПСР РГПУ им. А. И. Герцена)
КОРРЕЛЯЦИОННЫЕ СООТНОШЕНИЯ МЕЖДУ ДАННЫМИ ЯМР 63Cu И ЭМИССИОННОЙ МЕССБАУЭРОВСКОЙ СПЕКТРОСКОПИИ 67Cu(67Zn) И 61Cu(61Ni)
ДЛЯ КЕРАМИЧЕСКИХ СВЕРХПРОВОДНИКОВ
Установлена линейная корреляция между постоянной квадрупольного расщепления CCu, измеренной методом ЯМР 63Cu и постоянными квадрупольного расщепления CZn и CNi,, измеренные методом эмиссионной мессбауэровской спектроскопии 67Cuf7Zn) и 6ICu(6INi) для керамических сверхпроводников.
Ключевые слова: мессбауэровская спектроскопия, ЯКР, градиент электрического
поля.
1. Introduction
One of the main problems in physics of high-temperature (high-Tc) superconductors is the determination of the spatial distribution of electronic defects in the lattices of copper metal oxides. A potentially effective method to solve this problem is to compare the experimentally determined and calculated parameters of the electric field gradient (EFG) tensor for specific lattice sites [2]. Copper sites are of utmost interest in such work because these atoms are found in the
composition of all high-Tc superconductors, and now it is considered as an established fact that superconductivity is activated along the Cu-O2 planes.
Of all the methods used to determine the EFG at copper sites, special recognition is accorded nuclear magnetic resonance (NMR) using 63Cu [1], along with 67Cu(67Zn) and 61Cu(61Ni) emission Mossbauer spectroscopy (EMS) [2]. The measurement results are presented in the form of parameters of the quadrupole interaction tensor the quadrupole interaction constant C= eQUzz
and the asymmetry parameter n = --------~. Here Q is the quadrupole moment of the probe nu-
UUzz
cleus (Q =- 0.211 b for 63Cu, Q = 0.17 b for 67Zn, and Q = 0.162 b for 61Ni), Uxx, Uyy, and Uzz are the components of the diagonalized EFG tensor at the probe nucleus, where Uxx + Uyy + Uzz = 0 and |Uxx| <|Uyy| < |Uzz| and x, y, and z refer to the principal axes of the EFG tensor.
For the 63Cu2+ and 61Ni2+ probes EFG on nuclei is generated by lattice ions (crystal EFG) and by the aspherical valence shell of the probe atom (valence EFG); when the orientations of the principal axes of all the tensors coincide, the equation is
eQUzz = eQ(1 - y) Vzz + eQ(1 - R) Wzz, (1)
where Uzz, Vzz, and Wzz are the principal components of the total, crystal, and valence EFG tensors for Cu and Ni , and y and R are the Sternheimer coefficients for the Cu2+ and Ni2+ ions.
The situation is simplified when 67Cu(67Zn) EMS is used for the experimental determination of the parameters of the EFG tensor at copper sites, because aspherical valence electrons do not contribute to the EFG for a 67Zn2 + probe; as a result, we have
eQUzz * eQ(1 - y) Vzz, (2)
where Uzz and Vzz are the principal components of the total and crystal EFG tensors for 67Zn2+, and y is the Sternheimer coefficient of the Zn2+ ion.
However, even in the case of 67Cu(67Zn) EMS the number of experimentally measured parameters falls short of the number of charges to be determined, and auxiliary fitting parameters still need to be introduced [2]. In this light it is crucial to find general functional relations between 63Cu NMR and 67Cu(67Zn) and 61Cu(61Ni) EMS data, thereby providing a means for qualitatively assessing the charge state of atoms in high-Tc superconductor lattices. In this article we establish such relations between the quadrupole interaction constants for the 63Cu (CCu), 67Zn (CZn), and 61Ni (CNi) nuclei, and from a discussion of previously proposed [1] model distributions of the charge states of atoms in copper metal oxide lattices we identify these distributions.
2. Correlation between CCu and CZn
Fig. 1 summarizes experimental data obtained on |CCu| and CZn for copper metal oxides both by the 63Cu NMR method [1] and by the 67Cu(67Zn) EMS method [2]. We see that points corresponding to the divalent-copper compounds fit a straight line, where
Ccu = 195 - 11 CZn. (3)
All quantities are given in megahertz.
It follows from relations (1) that the linear relation (3) is a consequence of the fact that the valence component of the EFG for Cu2 + is identical in the divalent-copper compounds.
The points for Cu2O and Nd185Ce015CuO4 and the Cu(l) sites in YBa2Cu3O6 and YBa2Cu3O7 are situated away from the line (3). At least two reasons account for this: 1) a deviation of the valence of copper from the standard +2 (copper in Cu2O and copper at Cu(l) sites of the YBa2Cu3O6 lattice are monovalent, whereas in Nd185Ce015CuO4 the valence of copper differs
significantly from +2 [3]); 2) different orientations of the principal axes of the total and crystal
EFG tensors (for 63Cu(l)2+ centers in YBa2Cu3O6 we have Uzz=Ubb and Vzz = Vaa [3]).
Fig. 1. |C(Cu)| — C(Zn) diagram for copper sites.
The straight line is the least squares fit through points corresponding to divalent copper. The numbering of the points corresponds to Table
The numbering of the points in fig. 1-4
№ Lattice site Coupling № Lattice site Coupling
1 Cu Cu2O 26 Cu2 SmBa2Cu3O7
2 Cu CuO 27 Cu2 EuBa2Cu3O7
3 Cu La1.85Sro.15CuO4 28 Cu2 YBa2Cu3O7
4 Cu La2CuO4 29 Cu2 GdBa2Cu3O7
5 Cu Nd:.85Ceo.15CuO4 30 Cu2 DyBa2Cu3O7
6 Cu Nd2CuO4 31 Cu2 HoBa2Cu3O7
7 Cu1 NdBa2Cu3O6 32 Cu2 ErBa2Cu3O7
8 Cu1 GdBa2Cu3O6 33 Cu2 TmBa2Cu3O7
9 Cu1 YBa2Cu3O6 34 Cu2 YbBa2Cu3O7
10 Cu1 YbBa2Cu3O6 35 Cu1 SmBa2Cu4O8
11 Cu2 NdBa2Cu3O6 36 Cu1 YBa2Cu4O8
12 Cu2 GdBa2Cu3O6 37 Cu1 ErBa2Cu4O8
13 Cu2 YBa2Cu3O6 38 Cu2 SmBa2Cu4O8
14 Cu2 YbBa2Cu3O6 39 Cu2 YBa2Cu4O8
15 Cu1 NdBa2Cu3O7 40 Cu2 ErBa2Cu4O8
16 Cu1 SmBa2Cu3O7 41 Cu1 Y2Ba4Cu7O:5
17 Cu1 EuBa2Cu3O7 42 Cu2 Y2Ba4Cu7O15
18 Cu1 YBa2Cu3O7 43 Cu3 Y2Ba4Cu7O:5
19 Cu1 GdBa2Cu3O7 44 Cu4 Y2Ba4Cu7O15
20 Cu1 DyBa2Cu3O7 45 Cu Tl2Ba2CuO6
21 Cu1 HoBa2Cu3O7 46 Cu Tl2Ba2CaCu2O8
22 Cu1 ErBa2Cu3O7 47 Cu1 Tl2Ba2Ca2Cu3O:0
23 Cu1 TmBa2Cu3O7 48 Cu2 Tl2Ba2Ca2Cu3O:0
24 Cu1 YbBa2Cu3O7 49 Cu Bi2Sr2CuO6
25 Cu2 NdBa2Cu3O7 50 Cu Bi2Sr2CaCu2O8
3. Correlation between CCu and Vzz
The CCu - Vzz diagram is analogous to the |Ccu| - CZn diagram, since CZn, according to (2), is proportional to Vzz, but contains a larger number of points, since the values of CZn have been measured for a limited number of oxides. We determine the sign of CZn from the |CCu|-CZn diagram as described above and, when this is not feasible, from a comparison of the orientations of the principal axes of the total, crystal, and valence EFG tensors.
It is evident from Fig. 2 that for a large part of the data the points of the CCu - Vzz fit the straight line
Ccu = 188 - 204 Vz:
(4)
As in Fig. 1, the points for Cu2O, for Cu(l) in YBa2Cu3O6 and YBa2Cu3O7, and for NdL85Ce0.15CuO4 deviate from the line (4) in Fig. 2. The causes of these deviations have already been discussed. More significant is the fact that the CCu - Vzz discloses another reason for the deviation from the straight line (4): the incorrect value calculated for Vzz. This disclosure can be exploited to choose from several possible model charge distributions one that will satisfy relation (4). For an incorrect choice of model a point representing a give copper site is found on the line (3) in Fig. 1, but away from the line (4) in Fig. 2. From Figs. 1 and 2, it is evident that this situation occurs for Cu(1) sites in YBa2Cu4O8 and Y2Ba4Cu7O15. Figure 2 shows that the calculated value of Vzz is somewhat too large for Cu(1). This fact underscores the need to introduce modifications in proposed earlier model for the charge distribution among the sites of YBa2Cu4O8 and Y 2Ba4Cu7015.
Fig. 2. C(Cu) - Vzz diagram for copper lattice sites.
The straight line is the least squares fit through points 1-13 corresponding to divalent copper. The numbering of the points corresponds to Table
4. Correlations between CNi and Vzz and CNi and CZn
Figs. 3, 4 present a CNi vs. Vzz and CNi vs. CZn graphs for the divalent-copper compounds. The quadrupole coupling constant CNi was measured for the 61Ni probe in cuprous oxides by EMS [2]. It is readily seen that the experimental points fit straight lines
CNi = -80 + 48 Vzz (5)
for CNi - Vzz diagram and for CNi - CZn diagram.
CNi = -79 +2 CZn
(6)
Fig. 3. CNi - Vzz diagram for copper lattice sites. The straight line is the least squares fit through points corresponding to divalent copper. The numbering of the points corresponds to Table
-20
-30
-40 I-
50
-60
24 23 22 21 12 13 14 15 16 17 18 19 20
C-’zn, МГц
Fig. 4. CNi - CZn diagram for copper lattice sites.
The straight line is the least squares fit through points corresponding to divalent copper. The numbering of the points corresponds to Table
As in Figs. 3 and 4, the points for Cu2O, for Cu(l) in YBa2Cu3O6 deviate from the lines (5) and (6). The reasons of these deviations have already been discussed. It follows from relations (1) and (2) that the linear relations (5) and (6) are a consequence of the fact that the valence component of the EFG for Ni2+ is identical in the divalent-copper compounds.
Thus, using diagrams CNi - Vzz and CNi - CZn the divalent-copper compounds can be selected. The |CCu| - CZn diagram is therefore used to select such copper centers without invoking any kind of model.
5. Correlation between CCu and CNi
Fig. 5 presents a CCu vs. CNi graph for the divalent-copper compounds. It is readily seen that the experimental points fit a straight line
Ccu = -193 - 5 Ccu, (7)
This linear dependence can be understood if we recall that the EFG at nucleus sites for the Ni2+ and Cu2+ centers is generated both by the lattice ions (the crystal field EFG) and by the nonspherical valence shell of the ion itself (the valence EFG), so the quad-rupole coupling constant for the probe can be cast as relation (1).
The linear relation |C(Ni)| vs.
|C(Cu)| is actually a consequence of the linear relations C(Ni) vs. Vzz and C(Cu) vs. Vzz, which were observed for compounds of divalent copper.
Since the data obtained for the Cu(2) sites in the RBa2Cu3O7 and RBa2Cu3O6 compounds are on the straight line, one may conclude that copper in these sites is in the divalent state.
From fig. 5 it is seen that the points obtained for the copper sites in Cu2O and for the Cu(1) sites in RBa2Cu3O6 and RBa2Cu3O7 deviate from a linear relationship. There are two reasons for this deviation, namely, the copper valence state being other than
61 2+ 63 2+
2+ and different orientations of the total and valence EFG axes for the Ni and Cu probes. The first reason is valid for the Cu(1) sites in RBa2Cu3O6 and for the copper sites in Cu2O [the copper in Cu2O and in the Cu(1) sites of the RBa2Cu3O6 compounds is univalent], and the second applies to the Cu(1) sites in the RBa2Cu3O7 compounds (it is known that, at least for the Cu(1) sites in YBa2Cu3O7, the z axis of the total EFG tensor is directed along the b crystallographic axis, whereas the z axis of the crystal-field EFG is aligned with the a crystallographic axis).
The CNi - CCu diagram is therefore used to select such copper centers without invoking any kind of model.
Fig. 5. CCu - CNi diagram for copper lattice sites. The straight line is the least squares fit through points corresponding to divalent copper. The numbering of the
points corresponds to Table
6. Conclusion
Thus, a linear relation between CCu (63Cu NMR data) and CZn and CNi (67Cu(67Zn) and 61Cu(61Ni) EMS data) holds for the majority of metal oxides of divalent copper, indicating the similarity of the electronic structure of copper (Cu2+, 3d9) in these lattices. The data for copper in Cu2O and for copper at Cu(l) sites of the YBa2Cu3O6 are naturally excluded from this relation [owing to the monovalence of the copper (Cu+, 3d10) in these lattices], as are the data for Cu(l) in YBa2Cu3O7 (since the principal axes of the total and crystal EFG have different orientations). An analogous linear relation obtains between CCu (63Cu NMR data) and Vzz (calculated in the approximation of the point-charge model) for a much larger number of metal oxides of copper except the already mentioned ones. The latter relation can be used to assess the validity of proposed model charge distributions among the lattice sites for superconducting ceramics.
References
1. Asayama K., Kitaoka Y., Zheng G.-Q., Ishida K., Magishi K. NMR study of high-TC superconductors // Physica B: Condensed Matter. 1996. V. 223-224. № 1-4. P 478-483.
2. Bordovsky G., Marchenko A., and Seregin P Mossbauer of Negative Centers in Semiconductors and Superconductors. Identification, Properties, and Applicaton. Academic Publishing GmbH & Co. 2012. 499 p.
3. Seregin P. P., Masterov V F., Nasredinov F. S., Seregin N. P. Correlations of the 63Cu NQR/NMR data with the 67Cu(67Zn) emission Mossbauer data for htsc lattices as a tool for the determination of atomic charges // Physica Status Solidi (B): Basic Solid State Physics. 1997. V. 201. No. 1. P 269-275.
А. В. Ляпцев
СИММЕТРИЯ В ЗАДАЧАХ НЕЛИНЕЙНОЙ ДИНАМИКИ. ПРОЯВЛЕНИЕ СВОЙСТВ СИММЕТРИИ В ПОЛЯРИЗАЦИИ ИЗЛУЧЕНИЯ
Исследовано проявление свойств симметрии хаотического движения в случае, когда система описывается уравнениями классической динамики, а точечная группа симметрии системы содержит некоммутирующие элементы и, как следствие, имеет двумерные неприводимые представления. Численными расчетами показано, что излучение такой системы полностью деполяризовано, в то время как при понижении симметрии системы излучение становится частично поляризованным. Такие поляризационные характеристики полностью соответствуют характеристикам, получаемым при квантово-механическом описании аналогичной системы.
Ключевые слова: нелинейная динамика, динамический хаос, симметрия, поляризация излучения.
А. Liaptcev
Symmetry in Problems of Nonlinear Dynamics. The Manifestation of The Properties of The Symmetry in The Polarization of Radiation
Manifestation of symmetry properties of chaotic motions is investigated in a case when the system is described by equations of classical dynamics. The considered group of symmetry contains non-commuting elements and as consequence has two-dimensional irreducible representations. Numerical calculation shows, that radiation of this system are fully depolarized, at the same time at a lower symmetry of the system, radiation becomes partially polarized. Such
