Lattice EFG tensors at the rare-earth metal sites in RBа 2сu 3о 7 Текст научной статьи по специальности «Физика»

REFERENCES

1. Zaslavskij G M., Sagdeev R. Z. Vvedenie v nelinejnuju fiziku: ot majatnika do turbulentnosti i haosa. M., 1988.

2. Kondrat'ev A. S., Ljaptsev A. V. Dinamicheskij haos v dinamicheskih i opticheskih sistemah // Izves-tija RGPU im. A. I. Gertsena: Estestvennye i tochnye nauki. 2006. № 6 (15). S. 262-273.

3. Ljaptsev A. V. «Kvantovanie» v zadachah nelinejnoj dinamiki. Chislennyj eksperiment i interpretatsija // Izvestija RGPU im. A. I. Gertsena: Estestvennye i tochnye nauki. 2012. № 147. S. 50-61.

4. Ljaptsev A. V. Simmetrija reguljarnyh i haoticheskih dvizhenij v zadachah nelinejnoj dinamiki. Urav-nenie Duffinga // Izvestija RGPU im. A. I. Gertsena: Estestvennye i tochnye nauki. 2013. № 157.

5. Petrashen'M. I., Trifonov E. D. Primenenie teorii grupp v kvantovoj mehanike. M.: Knizhnyj dom «LIBROKOM», 2010. 280 s.

G. A. Bordovsky, A. V. Marchenko, T. Yu. Rabchanova, V. A. Doronin

LATTICE EFG TENSORS AT THE RARE-EARTH METAL SITES

IN RBа2СuзО7

Parameters of the tensors of the electric field gradient (EFG) created by lattice ions at the rare-earth metal (REM) sites in RBа2Сu3О7 (R is Pr, Nd, Sm, Eu, Gd, Dy, Y, Tm or Yb) have been determined by means of 155Euf55Gd) emission Mossbauer spectroscopy. The EFG tensors at the REM sites have been calculated in the point charge approximation. The experimental and calculated EFGs are shown to be in good agreement when holes are supposed to be mainly in sublattices of the chain oxygen for RBа2Сu3О7. It is shown that the anomalous behavior of the compound PrBa2Cu3O7 is caused by antistructural substitution of Pr3+ for Ba2+ at its orthorhombic lattice.

Keywords: Mossbauer spectroscopy, the electric field gradient.

Г. А. Бордовский, А. В. Марченко, Т. Ю. Рабчанова, В. А. Доронин

ТЕНЗОР КРИСТАЛЛИЧЕСКОГО ГЭП В УЗЛАХ РЕДКОЗЕМЕЛЬНЫХ МЕТАЛЛОВ В РЕШЕТКАХ RBа2СuзО7

Параметры тензора градиента электрического поля (ГЭП), создаваемого ионами кристаллической решетки в узлах редкоземельных металлов (РЗМ) в RBа2Сu3О7 (Я = Pr, Nd, Sm, Eu, Gd, Dy, Y, Тт или Yb), были определены методом эмиссионной мессбауэровской спектроскопии на изотопе 155Eu(155Gd). Тензор ГЭП в узлах РЗМ был рассчитан в приближении точечных зарядов. Экспериментальные и рассчитанные значения ГЭП находятся в хорошем согласии, если предположить, что дырки, как правило, находятся в подрешетке цепочечного кислорода решеток ЯВа2Си3О7. Показано, что аномальное поведение соединения РгВа2Си307 объясняется антиструктурным замещением Рг3+ на Ва2+ в его орторомбической решетке.

Ключевые слова: мессбауэровская спектроскопия, градиент электрического

поля.

1. Introduction

The spatial distribution of charges among sites in ionic lattices can be determined comparing the experimental and calculated parameters of the electric field gradient (EFG) tensors [9]. Generally, the Upp components of the diagonalized EFG tensor at a nucleus consist of two parts

eQUpp = eQ(1 - y) Vpp + eQ(1 - R0) Wpp , (1)

where Vpp and Wpp are tensor components of the EFG created by lattice ions (lattice EFG) and by valence electrons related to the nucleus (valence EFG), respectively; y and R0 are the Stern-heimer coefficients, p is the Cartesian coordinate.

The lattice EFG may be calculated using the point charge model, whereas the valence EFG is given by various quantum-mechanical methods [9]. The validity of the results of the latter might evoke some doubt, and, therefore, probe atoms with spherical electron shells, i.e. without valence contribution to equation (1), are preferable for measuring of EFG. The 67Cu(67Zn) emission Mossbauer spectroscopy was suggested as the technique for the experimental determination of the EFG tensor at the copper-based high-temperature superconductors (HTSCs) [1 - 4, 7]. In this technique a Zn2+ ion with a spherical 3d10 electron shell, and thus without valence EFG, appears at a copper site after the decay of the parent 67Cu nucleus [9].

The above described technique allowed us to find the effective charges of oxygen ions for YBa2Cu307 with certain assumptions made for the cation charges [5, 7]. The agreement between the calculated and experimental parameters of the lattice EFG tensors for YBa2Cu307 may be achieved using two kinds of models. Both imply the presence of a hole in the immediate vicinity of the chain copper, either at the chain oxygen (model A) or at the bridging (apical) oxygen (model B). Additional evidence is necessary to choose the model. The present work proposes 155Eu(155Gd) emission Mossbauer spectroscopy as a source of the necessary additional evidence for RBa2Cu307 compounds (R is a rare-earth metal (REM) or Y).

2. Experimental details

The principle of the used technique consists in extraction of a carrier-free preparation of the 155Eu parent activity followed by synthesis of 155Eu-doped ceramic samples and by 155Eu (I55Gd) emission Mossbauer spectra recording. 155Eu has been considered to occupy the REM sites in the substances mentioned above. It is supported by the chemical similarity of all rare-earth metals. Therefore, the 155Gd Mossbauer probe produced after the decay of 155Eu should also reside at a regular REM site [6, 8]. The carrier-free 155Eu preparation allows low Mossbauer impurity concentrations and enables one to use structural data for undoped RBa2Cu307 to analyze the results.

Typical for the Gd3+ ion is the 6S7/2 state with a half-filled spherical 4f7 shell. Due to this reason the EFG at 155Gd nuclei is expected to be created only by lattice ions.

The l55Eu activity was produced by the 154Sm(n, Y)155Sm reaction followed by decay of 155Sm. The carrier-free 155Eu preparation was separated chromatographically, since the half-lives of 155Eu and the intermediate nucleus 155Sm are 4.96 years and 23 min, respectively. The separation was carried out in six months after the reactor irradiation for the decay of the residual activity of 156Eu with a half-life of 15 d.

Ceramic samples of RBa2Cu307 (R is Pr, Nd, Sm, Eu, Gd, Dy, Y, Yb or Tm) were prepared sintering the corresponding oxides. The 155Eu activity was added to the starting mixture. Test samples of RBa2Cu307 had an orthorhombic structure and critical temperatures Tc of about 85 K.

The Mossbauer spectra (86.5 keV transition) were recorded at 80 K using a singlet GdPd3 absorber. The 86.5 keV radiation was detected by a NaI(Tl) detector with a Pb critical filter that

suppressed the 60 keV and 105 keV radiation of 155Eu and the rest of the 89 keV radiation of 155Eu. For this reason the 155Gd 86.5 keV spectra were recorded predominantly. The 155Gd 105 keV spectra were additionally suppressed due to the high measuring temperature. The 155Gd 60 keV spectra were not observed in the velocity range used because of their large line width of about 30 mm/s.

Typical spectra are shown in figures 1. The results of the processing of the spectra are shown in figures 2.

Fig. 1. 155Eu(155Gd) emission Mossbauer spectra of RBa2Cu307

Fig. 2. Dependence of the quadrupole splitting A of the RBa2Cu307:155Eu Mossbauer spectra on the rare-earth ion radius r and dependences of the calculated principal components Vzz of the lattice EFG tensors at the REM sites of the RBa2Cu307 compounds on r for models A and B.

3. Experimental results and discussion

3.1. RBa2Cu307 (R is Nd, Sm, Eu, Gd, Dy, Y, Tm or Yb) compounds

The emission Mossbauer spectra of the RBa2Cu307:155Eu samples are quadrupole doublets. It points to a non-cubic environment of the REM sites. The isomer shifts of all spectra correspond to Gd3+. The fact that the quadrupole splitting A increases with increasing radius r of the REM ion (see figure 2) is important to mention. The quadrapole splitting of the l55Gd Mossbauer spectra is determined by the ground state of the nucleus (spin I = 3/2, quadrupole moment Q = 1.59 b) and is described by the equation:

Г 2V/2

' n

(2)

A = 1 eQU:z\ 1 + ^

2 V 3 J

where Uzz is the principal component of the total EFG tensor at the 155Gd nucleus; n = (Ux Uyy)/Uzz is the asymmetry parameter of the total EFG tensor. For the tensor components the inequality Uxx\ < \ Uyy\ < | Uzz\ should be valid.

Thus, the value of A is proportional to | Uzz\ which is determined by the lattice EFG for the

Gd3+ probe

Uzz * (1-y) Vzz , (3)

where Vzz and y relate to the REM sites and Gd3+ ion, respectively.

We have calculated the lattice EFG tensor components Vpp for all sites of the RBa2Cu307 lattices using the point charge approximation. The lattice was considered as a superposition of eight sublattices according to the structural formula RBa2Cu(l)Cu(2)2O(l)2O(2)2O(3)2O(4). Since various versions of oxygen site numbering are accepted in the literature, our designations are shown in figure 3. The structural parameters used in calculation of the lattice EFG for the RBa2Cu3O7 compounds were taken from [10]. All the calculated EFG tensors proved to be diagonal in the crystal axes.

Previously [11] we used the results of the lattice EFG calculations for the Cu(l), Cu(2), O(1), O(2) and O(4) sites in YBa2Cu3O7 as well as the parameters of the quadrupole coupling tensors for 67Zn at the copper sites and for 17O at the oxygen sites to determine the charge distribution among the sites for both A and B models

R3+Ba2205+Cu(1)2.16+Cu(2)2.15+Q(1)2.17-O(2)2.01-O(3)12.90-Q(4)1.38-, (A)

R3+Ba32.25+Cu(1)1.32+Cu(2)2.48+O(1)2.49-O(2)2.02-O(3)2.90-O(4)2.98-. (B)

Then the lattice EFG tensors were calculated at the REM sites using both charge distributions. Figure 2 shows the slopes of the calculated Vzz(r) dependences having opposite signs for models A and B. The z-axes of the calculated EFG tensors are also different for different models. The z-axis coincides with the crystal axes c and a for models A and B, respectively. Unfortunately, our 155Eu(155Gd) data for ceramic samples are insensitive to the direction of the z-axis. A qualitative agreement between, the measured A(r) dependence and the calculated Vzz(r) one is found only for model A. Thus, the 155Eu(155Gd) emission Mossbauer data support model A for the RBa2Cu3O7 compounds.

Fig. 3. The unit cells of RBa2Cu307

by

Oi

However, this conclusion is valid only if the EFG at the Gd probe nuclei is created solely the lattice ions. To examine this condition we have plotted the dependence of A on

A

cr

V - V

yy

cr

ncr is the asymmetry parameter. Figure 4 shows

that for model A this dependence is satisfactorily described by a straight line. An extrapolation of the latter to Acr = 0 gives the value До = - (0.09 ± 0.02) mm/s. Compared with the experimental values of A this value is small. Therefore, in figure 4 the dependence could be considered as an approximately direct proportionality.

The quadrupole splitting of the l55Gd Mossbauer spectra is described by the following equation derived from equations (1) and (2)

A =1 eQ |(1 -у )V„ +(1 -R )W!:

2\1/2 1 + -П-

(4)

(1 - Y )V„n„. +(1 - R0 )W„n,al

(1 - Y)V1: +(1 - R)Wz

Here, y and R0 are the Sternheimer coefficients for Gd3+, nval is the asymmetry parameter of the valence EFG tensor. From equation (4) it can be seen that the direct proportionality in figure 4 gives evidence of the small valence EFG at the l55Gd nuclei. The valence contribution eQ(1 -R0)Wzz > 0, since Vzz < 0 and Ao < 0. Its magnitude can be estimated by the quantity |Ao/eQ| = 0.13 ± 0.10 e x Â-3. The slope of the straight line in figure 4 corresponds to the Sternheimer coefficient for the Gd3+ ion y =- (24 ± 2), which gives the values of the lattice contribution (1-y) Vzz in the range from -2.45 to - 4.60 e x Â- for the investigated compounds RBa2Cu307. It should be mentioned that the value y = -24 is only a rough estimation. For instance, it is considerably less than the value y = -60.87 resulted from quantum-mechanical calculations [9].

Асг,е/л

Fig. 4. Dependence of the quadrupole splitting A of the RBa2Cu307: 155Eu Mossbauer spectra on the parameters of the calculated lattice EFG tensor Acr at the REM sites.

The experimental data of PrBa2Cu3O7 were taken from Ref. 11

3.2. Charge distribution in the PrBa2Cu3O7 lattice

RBa2Cu3O7 compounds (R is a rare-earth metal or yttrium) with the perovskite structure are superconductors with a transition temperature Tc ~ 90 K. An exception to the rule is PrBa2Cu3O7, and its anomalous behavior is connected either with Pr being tetravalent, or with partial mutual substitution of the Pr3+ and Ba2+ ions. 155Cu(155Gd) Mossbauer emission spectroscopy data obtained by us for the R1-xEuxBa2Cu3O7 solid solutions (R is Nd, Sm, Eu, Gd, Dy, Y, Tm or Yb, with x< 10-3) and 155Gd Mossbauer absorption measurements made for GdBa2Cu3O7 (Ref. 12) and for gadolinium impurity atoms in Pr sites of the PrBa2Cu3O7 orthorhombic lattice [10] permit one to decide between these two models.

The crystal-field EFG tensor can be calculated in the point charge approximation using the lattice constants a, b, c, and the coordinates of atomic planes in the unit cell [z(Ba), z(Cu2), z(O1), z(O2, O3)] which are known. Such data are available for RBa2Cu3O7 compounds [10] (R = Tm, Y, Dy, Gd, Eu, Sm, Nd) with the orthorhombic structure, while for orthorhombic PrBa2Cu3O7 only lattice constants are known [6]. To determine the atomic coordinates in the orthorhombic cell of PrBa2Cu3O7, we assumed a linear relation between the atomic-plane coordinates and the ionic radius of R3+ ions. This assumption is supported by the fact that extrapolation of the dependences of the parameters a, b, and c on r to the ionic radius of Pr3+ (r = 1.013 A) yields a = 3.870 A, b = 3.916 A, and c = 11.75 A, that is in excellent agreement with the values [6] a = 3.874 A, b = 3.912 A, and c = 11.74 A (Fig. 5). We treated the data [10] on atomic-plane coor-

dinates by the least-squares technique and extrapolated the straight lines thus constructed to the ionic radius of Pr3+ to obtain for the PrBa2Cu3O7 lattice z(Ba) = 0.1831, z(Cu2) = 0.3511, z(O1) = 0.156, and z(O2, O3) = 0.371 (Fig. 5).

Necessary for calculation of the crystal-field EFG tensor the charge distribution over the lattice sites in RBa2Cu3O7 was taken (A). Figure 4 presents the dependence of the experimental value of Aexp on the calculated value of Alat = Vzz(1 + n2/3)12 for RBa2Cu3O7 compounds (R = Tm, Dy, Y, Gd, Eu, Sm, Nd). This dependence is described by the straight line, as expected for the 155Gd3+ probe, which feels only the EFG generated by lattice ions. Only the corresponding to PrBa2Cu3O7 point falls off of the linear relationship.

We have calculated the crystal-field EFG tensor at Pr sites of the PrBa2Cu3O7 lattice for the model assuming partial mutual substitution of the Pr3+ and Ba2+ ions:

[ Pr£Ba;;f ][ Ba2;905Pr„JI ] Cu(1)216+Cu(2)215+O(1)217-O(2)201-O(3)i-9<'-O(4)1J8- (C)

(charge states of the copper and oxygen atoms remain unchanged). As it is seen from Fig. 4, the calculated data agree with experiment for the PrBa2Cu3O7 compound. The assumption that Pr4+ ions are stabilized in the structure of PrBa2Cu307 (with the corresponding change of the charge state of the O(4) atoms to O2-) results in an increase of Alat and in a disagreement between experimental and calculated values for the PrBa2Cu307 compound.

£

S

5

О

Ы

>aa

12

11

4

3

0,38

0,33

0,23

■£—---------&--------¿s------"ft------ft£"

5 0,18

0,13

g}~-~ -p- ~ ~n—er -ga—— --.vfr-q № —- a a

1 *——++— zO(2,3)

ш-ш--и- -Щ. • • • - zCu(2)

zBa

c — O O- —CO -O -Q - о Z0(l)

0,85

1,00

Fig. 5.

0,90 0,95

r, A

Dependence of the lattice constants and atomic-plane coordinates on the rare-earth ion radius r

4. Conclusions

155Eu(,55Gd) emission Mossbauer spectroscopy has been shown to be applicable for determining the parameters of the lattice EFG tensor at the REM sites of RBa2Cu3O7. The experimental EFG can

be fitted by the calculated values if the holes are placed mainly at the chain and Cu-O plane oxygen sites of the RBa2Cu3O7 lattices.

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7. Серегин П. П., Серегин Н. П., Мастеров В. Ф., Насрединов Ф. С. Эффективные заряды атомов

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11. Bordovskii G A., Marchenko A. V., and Seregin P P Atomic Charges in YBa2Cu3O7, YBa2Cu4O8, and Y2Ba4Cu7O15 Ceramic Samples // Glass Physics and Chemistry 2009. V. 35. Вып. 6. P. 643-651.

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6. Masterov V. F., Nasredinov F. S., Seregin N. P., Seregin P P., Davydov A. V., Kumzerov Ju.A. Osoben-nosti zarjadovogo raspredelenija v reshetke PrBa2Cu3O7 // Fizika tverdogo tela. 1997. T. 39. Vyp. 7.

S. 1163-1164.

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YBa2Cu3O7, opredelennye metodom emissionnoj messbaujerovskoj spektroskopii // Sverhprovodimost': fizika, himija, tehnologija. 1991. T. 4. Vyp. 6. S. 1136-1143.

8. Seregin P P., Masterov V. F, Nasredinov F. S., Seregin N. P., Saidov Ch. S. Tenzor kristallicheskogo gradienta elektricheskogo polja v uzlah redkozemel'nyh metallov reshetok RBa2Cu3O7 i La2-xSrxCuO4 // Sverhprovodimost': fizika, himija, tehnologija. 1994. T. 7. Vyp. 3. S. 467-474.

9. Bordovsky G., Marchenko A., and Seregin P Mossbauer of Negative Tsenters in Semiconductors and Superconductors. Identification, Properties, and Applicaton. Academic Publishing GmbH & Co. 2012. 499 p.

10. Tarascon J. M., McKinnon W. R., Greene L. H., Hull G W., Vogel B. М. Oxygen and rare-earth doping of the 90 K superconducting RBa2Cu3O7. Phys. Rev. B. 1987. V. 36. P. 226-237; LePage Y., Siegrist Т., Sunshine S. A., Schneemeyer L. P., Murphy D. W., Zahurak S. M., Waszczak J.V., McKinnon W. R., Tarascon J. M., Hull G W., Greene L. H. Neutron diffraction of atomic displacements in RBa2Cu3O7. Phys. Rev. B. 1987. V. 36. P. 3617-3621.

11. Bordovskii G A., Marchenko A. V., and Seregin P P Atomic Charges in YBa2Cu3O7, YBa2Cu4O8, and Y2Ba4Cu7O15 Ceramic Samples // Glass Physics and Chemistry 2009. V. 35. Вып. 6. S. 643-651.

12. Wortmann G., and Felner I. Magnetic order of the Pr sublattice in tetragonal and orthorhombic Pr1-xGdxBa2Cu3O7-x observed by 155Gd-Mossbauer spectroscopy // Solid State Commun. 1990. V. 75. P. 981-985.

A. V. Nikolaeva, P. P. Seregin, A. B. Jarkoi

USING THE 57mFe3+ MOSSBAUER PROBE TO DETERMINE THE EFG TENSOR PARAMETERS IN THE COOPER SITES TO THE LATTICES OF CuO And La2-*Sr*CuO4

Mossbauer emission spectroscopy of the 57Co(57mFe) isotope has shown that the impurity iron atoms appearing at the CuO-lattice cation sites after the decay of 57Co2+ are donors and can become stabilized in two charge states,

57mFe3+ and 57mFe2+. A satisfactory agreement between the calculated and experimental values of the quadrupole splitting in Mossbauer spectra has been obtained for the 57mFe3+ centers. This permits one to consider the results obtained in the 57Co(57mFe) Mossbauer emission spectroscopy study of cuprates as reliable experimental data on the lattice electric-field gradient ( lattice EFG) tensor parameters at copper sites. The parameters of the lattice EFG tensor at the copper sites in the La2-xSrxCuO4 lattice (the main component of the EFG tensor Vzz and the asymmetry parameter) were determined experimentally by emission Mossbauer spectroscopy with 57Co(57Fe) isotopes. A comparison of the experimental and calculated dependences of Vzz on x shows that the holes arising from the substitution of La3+ by Sr2+ are localized mainly at the oxygen sites in the Cu-O2 plane.

Keywords: Mossbauer emission spectroscopy, electric field gradient tensor.