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INTRODUCTION. This publication completes the series of papers. [1−4] on obtainment and study of the structure and some properties of CdF2 crystals and Cd1 ...

ISSN 1063-7745, Crystallography Reports, 2008, Vol. 53, No. 4, pp. 565–572. © Pleiades Publishing, Inc., 2008. Original Russian Text © E.A. Sul’yanova, V.N. Molchanov, B.P. Sobolev, 2008, published in Kristallografiya, 2008, Vol. 53, No. 4, pp. 605–611.

STRUCTURE OF INORGANIC COMPOUNDS

Crystal Growth and Defect Crystal Structure of CdF2 and Nonstoichiometric Phases Cd1 – x R xF2 + x (R = Rare Earth Element or In). 5. Crystal Structure of As-Grown Cd0.9R0.1F2.1 (R = La–Nd) Single Crystals: Nanoclusters of Structural Defects E. A. Sul’yanova, V. N. Molchanov†, and B. P. Sobolev Shubnikov Institute of Crystallography, Russian Academy of Sciences, Leninskiœ pr. 59, Moscow, 119333 Russia e-mail: [email protected] Received July 20, 2007

Abstract—As-grown Cd0.9R0.1F2.1 (R = La–Nd) crystals were assigned to the CaF2 structure type and their structure was determined by X-ray diffraction. A new octacubic cluster of structural defects in Cd0.9R0.1F2.1 phases is proposed. The changes in the anionic motif of the Cd0.9R0.1F2.1 phase can be explained as a result of the formation of tetrahedral [Cd4 – nRnF26] and inverse octacubic [Cd14 – nRnF68] clusters with, respectively, tetrahedral and cuboctahedral anionic groups as cores. It is established that fluctuations of the La concentration in the cross section of a Cd0.9La0.1F2.1 crystal boule do not exceed 2.7%. PACS numbers: 61.66.Fn, 61.72.Dd DOI: 10.1134/S1063774508040068

INTRODUCTION

EXPERIMENTAL

This publication completes the series of papers [1−4] on obtainment and study of the structure and some properties of CdF2 crystals and Cd1 – xRxF2 + x fluorite solid solutions on the basis of cadmium fluorite with the entire series of available rare earth elements (REEs). The purpose of this study was to analyze the crystal structure of as-grown (grown from a melt without additional annealing) Cd0.9R0.1F2.1 crystals with the cerium REE subgroup (R = La–Nd). All fluorides of these elements belong to the morphotropic group of trifluorides RF3, which are crystallized in the tysonite structure (LaF3) in the range from the melting temperature to room temperature. It was established in [3] that two samples cut from the same portion of a Cd0.9Yb0.1F2.1 crystal boule have different crystal structures. Previously, different defect structures were observed for Ba0.8Yb0.2F2.2 crystals cut from the same boule [5]: two samples had unit cells of different types (sp. grs. Pm3m and Fm3m). The structure of different regions of a crystal boule within the same cross section can be different owing to the nonuniform distribution of R3+ impurity [1]. Therefore, we analyzed in this study for the first time the fluctuation of the R3+ concentration in Cd0.9R0.1F2.1 crystals in the cross section of a crystal boule with a step comparable with the size of samples used in a diffraction experiment.

Cd0.9R0.1F2.1 (R = La–Nd) single crystals were grown from a melt by the Bridgman method in an atmosphere of helium and products of tetrafluoroethylene pyrolysis [1]. Disks with a thickness of 3 mm were cut perpendicularly to the growth direction from the middle parts of crystal boules, 10 mm in diameter and 30 mm long. After optical polishing, the disks were investigated in polarized light. The growth technique, morphology of crystals, and their preparation were described in [1]. X-ray diffraction analysis was performed on optically uniform portions of disks, which were rolled off into spheres 150 μm in diameter. The diffraction experiment was carried out on a CAD-4 automatic X-ray diffractometer (Enraf Nonius) in MoKα radiation (graphite monochromator) at a temperature of 295 K. The numbers of measured reflections with sinθ/ λ ≤ 1.2 for each crystal are listed in Table 1. The structure was refined using the JANA2000 program [6]. Absorption corrections for a spherical sample, polarization, and Lorentz factor were introduced into the experimental array of intensities. Analysis of the diffraction data for all single crystals did not reveal any deviations from cubic symmetry. On the basis of the data obtained, the affiliation of the crystals studied to the CaF2 structure type was beyond question, and further structure refinement was performed within the sp. gr. Fm3m. The results of the structure refinement confirmed that it was a correct choice. During refine-

†Deceased.

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Table 1. Main characteristics of the diffraction experiments on the as-grown Cd0.9R0.1F2.1 (R = La–Nd) single crystals R

La (no. 1)

La (no. 2)

Ce

Pr

Nd

CAD-4 Enraf Nonius

Diffractometer Radiation T, K Sample diameter, μm Absorption coefficient, mm–1 Interval of ω/2θ scanning, deg Maximum value of sinθ/λ, Å–1 Number of measured reflections Number of independent reflections Rav(I), % Symmetry group Unit-cell parameter, Å

142(5) 14.27

1170 89 3.29 5.461(5)

ment, the isotropic secondary extinction correction was introduced in the Becker–Coppens approximation [7] (I type, angular distribution of mosaic blocks according to the Lorentz law). The anharmonic components of the atomic displacement tensor were refined using expansion of the temperature factor in the Gram–Charlier series [8]. Refinement by the least-squares method was performed over the moduli |F | using the atomic scattering curves and corrections for anomalous scattering [8]. The parameters of the diffraction experiment for Cd0.9R0.1F2.1 (R = La–Nd) are listed in Table 1. The fluctuation of the La concentration in the cross section of the Cd0.9La0.1F2.1 crystal boule was investigated with a JEOL JSM-6460LV scanning electron microscope in the high-vacuum mode with an accelerating voltage of 10 kV, using a wave attachment

MoKα , λ = 0.71069 295 150(5) 178(5) 142(5) 14.32 14.46 14.74 0.80 ± 0.35tanθ 1.2 2415 2421 1002 89 89 89 2.36 2.25 3.33 Fm3m 5.454(5) 5.457(5) 5.449(5)

(Oxford Instruments) version 4.02.

with

156(5) 14.94

990 88 2.26 5.448(5)

INCA

software,

Figure 1a shows a photograph of a part of the cross section of the Cd0.9La0.1F2.1 crystal boule in polarized light. The composition was determined in three regions of the cross section: two at the disk edges and one at the center (Fig. 1b). Ten measurements along a straight line with a step of ~200 μm were performed within each region. This step is comparable with the size of the samples used in the diffraction experiment. The error in measuring concentration was 0.5 mol %. The measurement results are shown in Fig. 1c. At the disk edges, the average La concentration is ~10.0(5) and ~11.3(5); at the center, it is ~11.8(5) mol %. Thus, the difference in the La concentrations in the samples selected from the cross section of the Cd0.9La0.1F2.1 boule did not exceed 2.7 mol %. x, mol % La

(a)

(b)

(c) 11.5 11.0 10.5 10.0 9.5

1 mm

9.0

0

0.4

0.8

1.2

1.6 L, μm

Fig. 1. (a) Cross section of a disk (thickness 3 mm, polarized light) cut from the middle part of a Cd0.9La0.1F2.1 crystal boule; (b) the region in which the La concentration was determined; and (c) the La concentration measured with a step of ~200 μm in the corresponding regions of the Cd0.9La0.1F2.1 disk: , × at the edges and  in the middle. CRYSTALLOGRAPHY REPORTS

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[001]

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(b) Fint(48i)

Fint(32f)3

0.5 0.4

0.4

0.3

Fint(48g)

0.3

0.2

0.2

0.1

0.1

0

0.2

0.1

0

La no. 1

0.2

La no. 2 (e)

(d)

(c) [001]

0.1

(a + b)/4

[110]

Fint(32f)3

Fint(48i)

0.5 0.4

0.4

0.3

0.3 Fint(48g)

0.2

0.2

0.1

0.1

0

0.1

0

0.2

0.1

0.2

0

0.1

0.2

(a + b)/4

[110]

ëe

Pr

Nd

Fig. 2. Difference and zero electron density maps in the (110) plane for the as-grown Cd0.9R0.1F2.1 (R = La–Nd) crystals. The (Cd2+, R3+) and F(8c) ions are subtracted. The step of isolines is 0.05 e/Å3. The solid and dotted lines show, respectively, the positive and negative electron densities; the dashed lines indicate zero level.

REFINEMENT OF THE STRUCTURE OF AS-GROWN Cd0.9R0.1F2.1 (R = La–Nd) CRYSTALS During refinement of the structure of all Cd0.9R0.1F2.1 (R = La–Nd) solid solutions under study, the composition was taken to be in correspondence with the initial charge: 10% RF3. Refinement of the structure of as-grown Cd0.9La0.1F2.1 single crystals. Figures 2a and 2b show the difference electron-density maps in the (110) plane for two Cd0.9La0.1F2.1 samples. The difference maps CRYSTALLOGRAPHY REPORTS

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were constructed after subtraction of (Cd2+, La3+) cations and F anions in the main position 8c. The anharmonicity of atomic displacements was taken into account up to the fourth and third orders for cations and F(8c) anions, respectively. The occupancy of the main position of fluorine ions, F(8c), was also refined. The electron density peaks observed in the difference maps belong to interstitial fluorine ions. The difference map for sample 1 exhibits electron density peaks in the 48i (Fint(48i)) and 48g (Fint(48g)) positions. The difference map for sample 2, along with the peaks

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Table 2. Results of the final structure refinement of the as-grown Cd0.9R0.1F2.1 (R = La–Nd) single crystals R

La (no. 1)

La (no. 2)

Ce

Pr

Nd

B11 × 103 D1111 × 108 D1122 × 108 F(8c) *Q, atoms/unit cell (1/4, 1/4, 1/4) B11 × 102 C123 × 106 Fint(48g) Q, atoms/unit cell (y, 1/4, 1/4) y Biso , Å2 Q, atoms/unit cell Fint(32f)1 (u, u, u) u Biso , Å2 Fint(32f)3 Q, atoms/unit cell (w, w, w) w Biso , Å2 Fint(48i) Q, atoms/unit cell (v, v, 0.5) v Biso , Å2 Number of independent structural amplitudes Number of refined parameters R Rw , %

11.02(5) 7.8(5) 0 6.47 1.41(3) 2.6(4) 0.63(27) 0.188(22) 1.5(5)

10.70(4) 8.4(5) 0 6.57 1.35(8) 3.0(3) 0.64(27) 0.188(24) 1.7(5)

10.2(1) 7.3(9) –0.8(3) 6.36 1.33(8) 3.2(3) 0.72(24) 0.186(20) 1.8(9)

9.4(2) 5.3(9) –0.9(3) 6.97 1.33(2) 2.8(4)

8.55(9) 2.3(4) –1.6(2) 7.07 1.29(1) 2.6(3)

0.83(29) 0.312(7) 2.8(8) 0.60(27) 0.400(6) 2.7(8)

0.71(13) 0.318(3) 2.3(4) 0.62(11) 0.412(3) 1.9(4)

85 13 0.40 0.54

85 13 0.28 0.39

(Cd0.9R0.1) (0, 0, 0)

1.30(18) 0.093(4) 2.9(4) 84 13 0.38 0.50

0.39(24) 0.404(8) 2.5(9) 0.80(27) 0.100(5) 2.5(6) 83 16 0.33 0.44

0.37(19) 0.415(6) 1.8(9) 0.95(23) 0.407(4) 2.5(5) 85 16 0.41 0.47

* Q(Fint(8c)) = 4(2 + x) – Q(Fint(48i)) – Q(Fint(32f)3) – Q(Fint(32f)1) – Q(Fint(48g)).

in the 48i and 48g positions, contains a peak in the 32f position (Fint(32f )3). The electron density peak in the Fint(48g) position is not eliminated upon introduction of anharmonicity of third-order atomic oscillations for F(8c) anions. We believe this peak to be due to the displacement of some fraction of F(8c) anions along the fourfold symmetry axis to the 48g position. The coordinate of the Fint(48g) ion was refined in the last stage of the least-squares procedure. There is a strong correlation between the refined parameters of the F(8c) and Fint(48g) ions. Therefore, the coordinate of the Fint(48g) ion was changed with a step of 0.005 and fixed in each refinement. Table 2 contains the coordinate corresponding to the refinement version with the minimum reliability factor R. The refined coordinate Fint(48g) does not correspond to the electron density peak in the difference map, in which, owing to the small displacement F(8c) Fint(48g), only the bases of the Fint(48g) peaks can be seen. Refinement of the structure of as-grown Cd0.9R0.1F2.1 (R = Ce, Pr, Nd) single crystals. Figures 2c– 2e show the difference electron-density maps in the

(110) plane after subtraction of (Cd2+, R3+) cations and F(8c) ions. For F(8c), the position occupancies are refined and the atomic-displacement anharmonicity is taken into account up to the third order; for (Cd2+, R3+) cations, the anharmonicity is taken into account up to the fourth order. In the difference maps for the single crystal with R = Ce, the electron density is observed in the 32f (Fint(32f )3) and 48i (Fint(48i)) positions, while in the maps of the single crystals with R = Pr or Nd, the electron density is present only in the 32f position (Fint(32f )1 and Fint(32f )3). In the last stage of refinement, the total occupancy of all fluorine ions was fixed according to the composition of each solid solution at a level of 8.4 atoms per cell. The results of the final structure refinement of Cd0.90R0.10F2.10 (R = La–Nd) single crystals are listed in Table 2. RESULTS AND DISCUSSION The electron density observed in the difference maps (Fig. 2) after subtraction of (Cd2+, R3+) cations and 8c (F(8c)) anions is related to interstitial fluorine CRYSTALLOGRAPHY REPORTS

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ions. They are present in the structure of the Cd0.9R0.1F2.1 solid solution to compensate for the excess positive charge formed as a result of heterovalent isomorphous replacement of Cd2+ cations with R3+. We suggest that the transformation of the anionic structural motif of fluorite upon formation of the Cd0.9R0.1F2.1 solid solution leads to aggregation of interstitial fluorine ions into tetrahedral and cuboctahedral anionic groups. The interaction of the excess positive charge of R3+ with the excess negative charge of the anionic groups produces preferred local charge compensation, as a result of which complexes (clusters) should arise. This prediction was confirmed for the ordered Ca2RF7 [9] and Ba4R3F17 (R = Y, Yb) [10] phases, where cation–anion groups [R6F36] were experimentally found. They are structurally ordered (shortrange order) blocks, referred to as octahedral rare earth clusters. The number of cluster configurations proposed by different researchers, predominantly on the basis of investigation of physical properties, exceeds 30. The most widespread are the following two: [R4F26] [11] and [R6F36] [9] (Fig. 3), which are referred to as tetrahedral and octahedral, respectively, according to the location of REE ions in tetrahedron and octahedron vertices. New octacubic nanocluster in the M1 – xRxF2 + x solid solution. Cations in [R4F26] and [R6F36] clusters have a noncubic environment of fluorine ions and the coordination numbers (CN) 10 and 8 (Thomson cube), respectively. Eight more M2+ cations, located in the vertices of the fluorite unit cell, along with their nearest environment of F ions, should be added to the rare earth cluster [R6F36], because these cations have CN = 10 (i.e., their coordination differs from that of fluorite) and are structural defects with respect to the basic (fluorite) structure. As a result, a 14-cation complex [M8{R6F36}F32] is obtained (Fig. 3), in which all types of structural defects are localized. It was previously proposed to refer to such a complex as a supercluster [12]. It is in fact, as well as the tetrahedral cluster, an elementary structural formation. To unify the cluster classification, a new name was proposed for it: octacubic cluster (OCC) [13], according to the configurations of 14 cations entering its composition. In contrast to the cations of the tetrahedral and octahedral clusters, OCC cations do not form a polyhedron. The cationic motif of OCC is a face-centered cube, which is formed by the cations entering the octahedron {R6F36} and cube [R8F32]. Interchanging the positions of R3+ and M2+ cations, we obtain a cluster of the [R8{M6F36}F32] composition in the OCC. We propose to refer to it as an inverted octacubic cluster (Fig. 3). Its size is about 1 nm. The limiting compositions of the OCC and inverted OCC are [M8{R6F36}F32] and [R8{M6F36}F32], respectively. They are implemented as ordered phases. The number of R3+ cations in the OCC may change in CRYSTALLOGRAPHY REPORTS

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F(8c) [M6F32]

Fint(48i)

[M6F36] [R6F36]

[M2+] R3+

[M8{R6F36}F32] Octacubic cluster

R3+ M2+

{R8{M6F36}F32] Inverted octacubic cluster

Fig. 3. Octacubic and inverted octacubic nanoclusters in MxR1 − xF2 + x crystals.

M1 − xRxF2 + x solid solutions. Furthermore, we will use the general formula [M14 – nRnF68] for these two OCC types. The electron density in the 48i position corresponds to Fint(48i) ions, which form the cuboctahedral anionic group {F12}; this group is the core of the cation–anion OCC. The electron density in the 32f position (with the maximum displacement with respect to the 8c position) belongs to Fint(32f )3 ions, which form the tetrahedral anionic group {F4}, serving as a core of the cation– anion tetrahedral cluster [Cd4 – nRnF26]. To conserve the local charge balance in the tetrahedral cluster [Cd4 − nRnF26], the value of n should be smaller than 4; for the OCC [Cd6 – nRnF36], n should be smaller than 5. In all fluorite solid solutions M1 – xRxF2 + x that have been studied to date, the OCC (cluster based on the cuboctahedral anionic group) is formed at the following ratio of the ionic radii of isomorphous substituted cations of different valence: r(R3+)/r(M2+) < 0.95 [11]. In the OCC, cations are divided into two groups, having

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+ [Cd6F32]

+ [F12]

[Cd4F23]

[Cd6F36]

[F4]

[Cd4–nRnF26]

Cd2+ R3+

[Cd14–nRnF68]

R = Pr, Nd Tetrahedral cluster

F(8c) Fint(48g) R = La, ëe Inverted octacubic cluster

Fint(32f)1

Fig. 4. Cluster structure of the as-grown Cd0.9R0.1F2.1 (R = La–Nd) crystals and the relaxation of the anion sublattice of the fluorite matrix around clusters.

different coordination polyhedra. For the cations located at the centers of faces of the fluorite unit cell, CN = 8, while for the cations located in the unit-cell vertices, CN = 10. In all the investigated fluorite solid solutions M1 – xRxF2 + x, where the cuboctahedral anionic group was found, an OCC is formed, in which R3+ cations are located in the polyhedra with CN = 8 and M2+ cations are in the polyhedra with CN = 10. In LaF3 (CeF3) fluorides, the CN of La3+ (Ce3+) cations is 11. The value CN = 8 is not characteristic of these large cations. The presence of the cuboctahedral anionic group in the Cd1 – xRxF2 + x (R = La, Ce) phases is also atypical of the fluorite solid solutions M1 − xRxF2 + x formed on the basis of RF3 of the first morphotropic group (R = La–Nd) [14]. Large La3+ and Ce3+ cations cannot be located in the polyhedra with CN = 8. We suggest that,

in the Cd0.9R0.1F2.1 (R = La, Ce) phases, inverted OCCs are formed, in which R3+ and M2+ cations are located in the polyhedra with CN = 10 and 8, respectively. In all studied crystals with R = La–Nd, fluorine ions Fint(32f )3 were found, which form tetrahedral anionic groups; tetrahedral clusters [Cd4 – nRnF26] are formed on the basis of these groups. Relaxation of the anion sublattice in the Cd0.9R0.1F2.1 R = La–Nd solid solutions. The electron density peaks in the 32f (Fint(32f )1) and 48g (Fint(48g)) positions correspond to the main fluorine ions F(8c) displaced (relaxed) from their positions. Figure 4 shows the scheme of relaxation of the anion sublattice in single crystals with R = La–Nd. We suggest relaxation of Fint(48g) ions (in Fig. 4, they are shown as large hatched spheres) in crystals with R = La or Ce; these ions are in CRYSTALLOGRAPHY REPORTS

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contact with the unlike (ëd2+, R3+) cations entering the composition of the inverted OCC [Cd14 – nRnF68]. The F(8c) Fint(48g) relaxation leads to equalization of the distances F(8c) – F(8c) and Fint(48i) – Fint(48g). The presence of weak peaks in the Fint(32f )1 and Fint(32f )2 positions in the difference electron-density maps of the Cd0.9Ce0.1F2.1 crystal corresponds to the presence of a small amount of fluorine relaxed into the 32f position. We failed to perform least-squares refinement taking into account these positions. In the Cd0.9La0.1F2.1 crystal, which contains tetrahedral clusters, no relaxed fluorine ions in the Fint(32f )1 and Fint(32f )2 positions were found. We suggest that, in the as-grown solid solutions with R = Pr or Nd, the anions (shown as large black spheres in Fig. 4) contacting like (R3+) and unlike (ëd2+, R3+) cations are displaced from the main positions. The Fint(32f )1 relaxation ensures equalization of the F(8c) Fint(32f )3 – Fint(32f )3 and Fint(32f )3 – Fint(32f )1 distances. The F(8c) ions, which are in contact with like Cd2+ cations in the as-grown crystals with R = Pr or Nd, do not relax. Analysis of the fluctuation of the La concentration in the cross section of the Cd0.9La0.1F2.1 crystal boule showed that it does not exceed 2.7%. The average La concentration is 10.0 mol % at one edge of the disk and 11.3 mol % at the other edge. At the center of the disk, the La concentration is 11.8 mol %. Thus, the fluctuation of the La concentration in the disks used to prepare samples 1 and 2 for structural analysis does not exceed 2.7 mol %. On the basis of such a small difference in the REE concentration, one cannot draw an unambiguous conclusion about a correlation between the crystal structure and composition of the Cd0.9La0.1F2.1 samples. To answer this question, it is necessary to investigate the behavior of the crystal structure of the Cd0.9R0.1F2.1 solid solutions with a change in the R3+ concentration in a wide range. CONCLUSIONS It has been shown by X-ray diffraction analysis that as-grown Cd0.9R0.1F2.1 (R = La–Nd) crystals belong to the CaF2 structure type. The interstitial fluorine ions (Fint) in these crystals are located in four positions: two 32f (w, w, w) positions (Fint(32f )1 and Fint(32f )3), 48i (Fint(48i)), and 48g (Fint(48g)). In the crystals with R = La or Ce, interstitial fluorine ions were found in the 48i (Fint(48i)) and 48g (Fint(48g)) positions. The fluorine ions in the 32f position (Fint(32f )3) are found in all crystals under consideration, whereas Fint(32f )1 ions were revealed only in the crystals with R = Pr or Nd. It is suggested that the main group of anionic defects (Fint) in the as-grown Cd0.9R0.1F2.1 (R = La–Nd) crystals is the tetrahedral anionic group, which is formed by CRYSTALLOGRAPHY REPORTS

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Fint(32f )3 ions, maximally displaced with respect to the main anionic position 8c. In the crystals with R = La or Ce, along with the tetrahedral group, a cuboctahedral anionic group is formed, which is characteristic of the structure of most previously studied M1 – xRxF2 + x phases. The changes in the anionic motif of the Cd0.9R0.1F2.1 (R = La–Nd) phases can be interpreted as a result of formation of the tetrahedral cluster [Cd4 – nRnF26] and inverted octacubic cation–anion cluster [Cd14 – nRnF68]. Both types of clusters can be simultaneously present in a crystal. Regions having different defect structures have been isolated in the same Cd0.9La0.1F2.1 crystal boule. One of such structures is formed by inverted octacubic clusters [Cd14 − nRnF68]. The other structure contains simultaneously both tetrahedral [Cd4 – nRnF26] and inverted octacubic [Cd14 – nRnF68] clusters. The formation of different defect structures in the same thin (3 mm) cut of a crystal can be due to the impurity concentration fluctuation in the crystal cross section and thermal stress. In [2, 3], the cationic composition of the [Cd4 − nRnF26] clusters was calculated on the basis of the occupancy of the position of interstitial fluorine ions. The number of vacancies beyond the clusters was also calculated. However, correlations between the refined structure parameters do not make it possible to reach high precision in determining the occupancies of the positions of interstitial fluorine ions. Thus, the proposed model of cluster structure of the Cd0.9R0.1F2.1 solid solution requires additional investigations. ACKNOWLEDGMENTS We are grateful to V.I. Simonov for the helpful participation in the discussion of the results and to N.V. Snegirev for the investigation of the Cd0.9La0.1F2.1 single crystal composition. This study was supported in part by the International Scientific and Technical Center, project no. 2136; Russian Foundation for Basic Research, project nos. 04-0216241, 07-02-01145, and 05-02-16101; and Grant NSh-2192.2008.5 of the President of the Russian Federation for Support of Leading Scientific Schools. REFERENCES 1. I. I. Buchinskaya, E. A. Ryzhova, M. O. Marychev, et al., Kristallografiya 49 (3), 544 (2004) [Crystallogr. Rep. 49, 500 (2004)]. 2. E. A. Ryzhova, V. N. Molchanov, and A. A. Artyukhov, Kristallografiya 49 (4), 668 (2004) [Crystallogr. Rep. 49, 591 (2004)]. 3. E. A. Sul’yanova, A. P. Shcherbakov, V. N. Molchanov, et al., Kristallografiya 50 (2), 235 (2005) [Crystallogr. Rep. 50, 203 (2005)].

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Translated by Yu. Sin’kov

CRYSTALLOGRAPHY REPORTS

Vol. 53

No. 4

2008

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