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48ISSN 2072-5981 doi: 10.26907/mrsej
aänetic Resonance in Solids
Electronic Journal
Volume 21 Special Issue 4 Paper No 19408 1-6 pages
2019
doi: 10.26907/mrsej-19408
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Boris Malkin (KFU, Kazan) Alexander Shengelaya (Tbilisi State University, Tbilisi) Jörg Sichelschmidt (Max Planck Institute for Chemical Physics of Solids, Dresden) Haruhiko Suzuki (Kanazawa University, Kanazava) Murat Tagirov (KFU, Kazan) Dmitrii Tayurskii (KFU, Kazan) Valentine Zhikharev (KNRTU,
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Short cite this: Magn. Reson. Solids 21, 19408 (2019)
doi: 10.26907/mrsej-19408
To the structure of the trigonal center of Yb3+ ion in hexagonal perovskite crystal RbMgF3
A.M. Leushin
Kazan Federal University, Kremlevskaya 18, Kazan 420008, Russia
E-mail: amleushin@gmail.com (Received May 9, 2019; accepted May 28, 2019; published June 6, 2019)
EPR and optical spectra are used for the analysis of distortions of a crystal lattice in the vicinity of an impurity ion Yb3+ of trigonal symmetry in RbMgF3 crystal. Within the framework of the superposition model, it is established that three F- ions of the nearest-neighboring octahedron, located symmetrically along the threefold axis of the trigonal center, move away from the impurity ion and have considerable angular deviations from the symmetry axis of the center. The next three F- ions, which enter the other octahedra, shift towards the paramagnetic ion and, on the contrary, come a bit closer to the axis.
PACS: 71.70.Ch, 75.10.Dg, 76.30.Kg.
Keywords: perovskite RbMgF3, crystal field, syperposition model, rare earth. Preface
Author expresses deep gratitude to B.Z.Malkin, who often advised him during their collaboration on the projects related to the analysis of the structure of impurity centers, and who performed such researches at the highest level, taking into account both static and dynamic effects.
1. Introduction
Resently, EPR and optical spectroscopy data of the trigonal paramagnetic centers (Ttrig) of Yb3+ ion in RbMgF3 crystal have been published [1]. The results of these experiments make it possible to conclude that Yb3+ ions replace two different host cation sites of Mg2+ forming three different types of paramagnetic centers (PC). In RbMgF3 [2,3] there are two nonequivalent sites (Mgi and Mgii), both with C3v symmetry (Fig. 1), and Yb3+ resides in both sites, forming three kinds of centers. Two kinds of trigonal Yb3+ centers (Yb3+ (I) Ttrig and Yb3+ (II) Ttrig) with Yb3+ ions in a single MgF6 unit (MgI site) were identified. One of them Yb3+ (I) Ttrig may be ascribed to the Yb3+ ion simply substituting at the MgI site without any charge compensators in its immediate neighborhood, while the other Yb3+ (II) Ttrig was identified as the substitution with the Yb3+ ion at the Mgi site with the nearest Rb+ vacancy. The center of the third type Yb3+ (III) Ttrig is formed by the Yb3+ ion when it substitutes another Mg2+ site in the Mg2Fg unit composed of two face-sharing fluorine octahedra (MgII site). In [1] the crystal field parameters Bq of a Hamiltonian of interaction of the Yb3+ ions with the crystal field (CF) of all centers were determined from the schemes of energy levels and g-factors of the ground Kramers doublets. The value and sign of the parameter B0 was used to qualitatively describe the nearest surrounding of the Yb3+ ion.
In this work, the found parameters Bqk (except B0) of CF trigonal symmetry were used in order to obtain more detailed information on the structure of the basic Yb3+ (I) center Ttrig ((I) Ttrig). The quantitative assessment of distortions of a crystal lattice near Yb3+ was carried out on the basis of superposition model (SM) taking into account only the nearest F- ions forming a deformed octahedron.
2. Structure of the (I) Ttrig
Interaction of an ion of Yb3+ with CF Ttrig is described by a Hamiltonian
Hcr(C3v ) = B2oO0 + B°4O°4 + b|o3 + B0O0 + b|o| + B66O66. (1)
Parameters found in work [1] B^ = Aqk (rq) incorporating the relevant radial integrals (rq) are presented in Table 1 (the line "(I) Ttrig (exp.)"). Operators Oqq = Y1 i Oq(Qi,&) are extended Steven's operators [4] depending on polar coordinates 6i, 0i of i-th electron of the paramagnetic ion (PI) defined in relation to trigonal axes of the PC. An arrangement of these axes (X, Y, Z) in relation to hexagonal axes of a crystal (a, a, c) is shown in Fig. 1.
Table 1. CF parameters Bq (in cm-1) of (I) Ttrig in RbMgF3 crystal.
Parameters B20 B42 B43 R 2 B2 b3 B6
(I) Ttrig (exp.) 413 -175 -4763 19 433 -844
(I) Ttrig (theory) -99 -4827 14 377 -157
Figure 1. Unit cell of RbMgF3 [5], where the Z axis is parallel to the hexagonal crystal axis. 2 Magnetic Resonance in Solids. Electronic Journal. 2019, Vol. 21, No 4, 19408 (6 pp.)
For the analysis of quantitative distortions of a crystal lattice near Yb3+ we will use SM [6-10]. In this model, it is postulated that full CF is a linear superposition of the fields created by each ion of a crystal. The resulting CF parameters are then presented in the form
Bk = ££ K (8i, $i)Bfc (Rl),
(2)
where Kk(0j, $j) are the structural factors depending on angular coordinates (determined by spherical angles ©j and $j) of all ions located at the distance RL from PI, and Bk (Rl) are the "intrinsic" parameters depending on ligand type. Summation in (2) is performed over the coordination spheres of ligands (sum over L) and over all the ligands of each area (sum on i). After performance of summation over i, expression (2) can be written as
Bl =
£ Kl(L)Bk (RL),
(3)
where Kq(L) is the structural factor of the coordination sphere L. The dependence of parameters Bk(Rl) on Rl in limited ranges of distances obeys a power law of the form
Bk (Rl) = Bk (Rl)(Rl/Rl )tk, (4)
where tk is the exponent, and Bk(RL)is the intrinsic model parameter relating to some average distance RL which is often accepted equal to the sum of ionic radii of the magnetic ion and ligand.
In our modeling using the expression (4), in accordance to the majority of works which use SM, we will be accounting the contributions from only the first coordination sphere of fluorine ions F-.
Fluorine ions 1, 2, 3 of the nearest octahedron of the Mg2+ ion in the system of coordinates of the trigonal center shown on Fig. 2 occupy positions with coordinates: Ri = R2 = R3 = R°a = 2.034 A [3], ©i = ©2 = ©a = = 56.16° [3], = 60°, = 180°, $3 = 300°, while coordinates of the last three ions (4, 5, 6) are as follows: R4 = R5 = R6 = R0 = 2.034 A [3], ©a = ©5 = ©6 = ©0 = 123.84° [3], $4 = 0°, $5 = 120°, $6 = 240°. Comparing the angles ©i and ©4 with the corresponding angles ©i = 54.74° and ©4 = 125.36° in regular octahedron, one can see that the MgiF6 octahedron of RbMgF3 crystal is slightly compressed along the c-axis.
Figure 2. A structural fragment of the RbMgF3: Yb3+ crystal containing the trigonal center (I) Ttrig.
During formation of (I) Ttrig in the RbMgF3 crystal, radial R0 and angular 6° coordinates of all six ions of fluorine change. However, owing to the symmetry of the center, Ri, R2 and R3 distances and the corresponding angles remain equal among themselves. We will designate them further through Ra and 6a, respectively. The same belongs to R4, R5 and R6 distances and the corresponding angles of the last three ions of fluorine, which become equal to Rb and 6b, respectively. The experimental CF B' Yb3+ (I) Ttrig parameters found from (3) and (4) and with the use of an explicit form of the structural factors K'k(6i; [4] are described by the following system of the equations:
3 3
B4° = - B4(Ra)K'°(6a) + 3 B4(R6)K/0(66),
o o
B43 = -105B4 (Ra )K'3(6a) + 105B4(Rb )K'3(6b),
3 3
B° = - B6(Ra)K'0(6a) + - B6(Rb)K/0 (6b), (5)
Be = - ^ B (Ra )K'3(6a) + ^ B6(Rb)K'6(6b),
B6 = 6923 B6(Ra)K'6(6a) + 6923 B6(Rb)K'6(6b), in which the factors K'qk(6) are defined by expressions:
K'0(6) = 35 cos4 6 - 30cos2 6 + 3, K'4(6) = sin3 6 cos 6,
K'0(6) = 231 cos6 6 - 315 cos4 6 + 105 cos2 6 - 5, (6)
K'3(6) = sin3 6cos 6(11 cos 6 - 3), K'6(6) = sin6 6.
The values tk and Bk(RF) can be taken the same as values of elpasolite Rb2NaYF6 [11] (BB4 = 105.57cm-1, t4 = 5.49, B6 = -13.49cm-1, t6 = 13.10) besause Yb3+ ion substituting at the Y3+ site in Rb2NaYF6 as well as at the Mgj site in RbMgF3 is surrounded by an octahedron of F- ions and by a cube of Rb+ ions.
From system (5) it is possible to find the parameters Ra, 6a, Rb, 6b characterizing structure of (I) Ttrig. Despite that the number of variables does not exceed the number of equations, the system (5) has many solutions, the majority of which are not satisfactory from the physical point of view. These are such solutions which lead either to very large, or to very small distances between ligands and PI, either to very big, or to very small changes of angular ligand coordinates. To select the satisfactory solutions, we were guided by requirements that the structure of the Ttrig should be similar to that in which the first three fluorine ions can move from a PI or approach it, and free to deviate from the symmetry axis of the center, as it is not connected with the nearby ions of the lattice. The last three ions, on the contrary, will be restrained in their displacements because they are structurally (see Fig. 1) included in other octahedra that are surrounding the ions Mg2+ at Mgu sites.
The self-consistent solution which follows these requirements leads to the values Ra, 6a, Rb, 6b presented in Table 2 (line "(I) Ttrig (theory)". This solution is not the best one from the mathematical point of view, i.e. not giving the smallest value of the merit function of the system of equations. Comparing the values Ra, 6a, Rb, 6b to coordinates in an undistorted crystal lattice (2.034 A, 56.16°, 2.034 A, 123.84°, respectively, line 2 in Table 2), we see that three F- ions of the nearest octahedron which are situated symmetrically along the threefold axis of the trigonal center (I) Ttrig in RbMgF3 crystal move away from PI by 0.231 AA and deviate from the axis by 18.52°. Another three F- ions move away too from PI by 0.061 A and deviate by
Table 2. Structural parameters of undoped RbMgF3 crystal and of (I) Ttrig in RbMgF3 crystal. Distances are in A, and angles in degrees.
Parameter Ra 00 a r0 0o 0b
Undoped crystal 2.034 56.16 2.034 123.84
Parameter Ra 0a Rb 0b
(I) Ttrig (theory) 2.265 74.68 2.095 138.22
14.38° from the axis. The theoretical values of the parameters B^ of the CF (I) Ttrig which are obtained with these values Ra, 0a, Rb, 0b are given in Table 1 (line "Ttrig (theory)"). Comparing them to experimental values of the Table 1 (line "Ttrig (exp.)"), we see that the structure of PC satisfactory corresponds to the CF experimental parameters. All parameters have the correct signs, but parameters B4 and B| strongly differ by their absolute value. It is also not surprising, as the parameters of SM which are used in our calculations vere found for interpretation of interactions of ions Yb3+ and F- in interval of distances near to rYb3+_f- = 2.206 A of elpasolite Rb2NaYbF6 [12], while in RbMgF3 crystal rYb3+-F- = 2.034 A [2,3]. Note that the solution of the system of equations (5) gives the parameter B66 almost equal to its experimental value (845cm-1), but the value of axial parameter B° diminishes almost by an order of magnitude. This implies large deviation of the first three F- ions from the symmetry axis of the center 34°), as well as shift of all the fluorine ions towards PI by approximately 0.016 A.
The structure of (I) Ttrig established as a result of the carried-out analysis is given in Fig. 3 where the section of the center is represented by the plane passing through its axes Z and X and F2, F4 fluorine ions which are in this plane. The other two corresponding ions are located in the planes passing through each of these two fluorine ions perpendicular to axis Z of the center at the vertices of the corresponding triangles. At formation of (I) Ttrig from the MgiF6 octahedron the triangles of ions F- are displaced in the opposite direction to the three F- ions not bounding with the other ions. Shifts of the corresponding planes of the triangles are defined by values: 5a = R0 cos 0a - Ra cos 0a = 0.534 A, 5b = R0 cos 00 - Rb cos 0b = 0.429 A.
center is represented by the plane passing through its axes Z and X and F2, F4 fluorine ions which are in this plane. Dotted circles are the positions of ions in the undoped RbMgF3 crystal.
3. Conclution
Analysis of an environment of the Yb3+ ion substituting at the Mgi site of RbMgF3 crystal without any charge compensators in its immediate neighborhood demonstrated that the nearest surrounding octahedron is considerably deformed from its form in undoped crystal. The CF theoretical parameters calculated for the found structure of the center on the basis of SM satisfactorily correspond to experimental values. Structures of two other centers of ions of Yb3+, found in the RbMgF3 crystal, will be more difficult for an analysis, as in a center (II) Yb3+ the already distorted octahedron of (I) Yb3+ is additionally exposed to the action of a nearest Rb+ vacancy, and in (III) Yb3+ to the field of the distorted octahedron the effects of three ions of F-symmetrically located in relation to the axis of center and of nearby axial ion of Mg2+ are added.
Acknowledgments
This study was supported by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities (project 3.672.2017/8.9).
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