Crystal structure and phase transitions in R₂TeO₆ (R = La, Pr, Nd, Tb, Ho, Er, Tm, Lu) oxides: A neutron diffraction study

3.1 Crystallographic characterization

R₂TeO₆ (R = La, Pr, Nd, Tb, Ho, Er, Tm, Yb and Lu) oxides were synthesized as pure and well-crystallized powders, as checked by XRD diffraction measurements. Fig. 1 shows the XRD patterns obtained for each compound; for larger rare earth ions from R = La to Tm the patterns are characteristic of single-phase oxides that can be indexed in the Nd₂WO₆-type orthorhombic structure (space group P2₁2₁2₁) (Trömel et al., 1987). For Lu₂TeO₆ a different polytype is stabilized, belonging to the trigonal Na₂SiF₆ (space group P321) structural type (Zalkin et al., 1964). For our Yb₂TeO₆ sample, a mixture of orthorhombic and trigonal phases was found, as shown in Fig. 1. For R = La-Tm, NPD data at room temperature were successfully used to refine the crystal structure in the orthorhombic P2₁2₁2₁ space group, No. 19, Z = 4. All the atoms are located at 4a (x, y, z) sites, including two kinds of R atoms, R1 and R2, one Te and 6 types of O atoms, O1 to O6. The refinement of the oxygen occupancy factors for oxygen atoms converged to unity within the standard deviations. Tables S1 to S7 in the Supplementary Information contain the unit-cell, structural parameters, anisotropic displacement factors and reliability factors after each refinement, for R = La to Tm, respectively. An additional refinement for Tm₂TeO₆ from neutron data collected at 2 K shows no phase transition in the 2–295 K temperature range, since the structure at 2 K can perfectly be refined in the orthorhombic model; the structural parameters are collected in Table S8. The unit-cell parameters for Tm₂TeO₆ decrease rather isotropically upon cooling from a = 5.2062(2), b = 8.9868(4), c = 9.8793(4) Å, V = 462.22(3) ų at 295 K, to a = 5.2020(1), b = 8.9773(3), c = 9.8664(3) Å, V = 460.77(2) ų at 2 K.

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Figure 1

X-ray diffraction patterns for R₂TeO₆. They are all single crystallographic phases excepting for Yb₂TeO₆, where an admixture of orthorhombic and trigonal phases is observed.

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Fig. 2a–d illustrates the goodness of the fits for La, Nd, Tb, Tm at 295 K, respectively. A regular variation of the unit-cell parameters and interatomic distances is observed with the ionic radii of the rare-earth cations (Shannon, 1976), according to the well-known lanthanide contraction, as displayed in Fig. 3a. This graph also includes the values for Yb, obtained from a refinement from XRD data including both orthorhombic and trigonal phases. The main interatomic distances after the refinement are listed in Table 1.

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Figure 2

Observed (crosses), calculated (solid line) and difference (bottom) NPD Rietveld profiles for (a) La₂TeO₆; (b) Nd₂TeO₆; (c) Tb₂TeO₆; Tm₂TeO₆ at 295 K.

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Figure 3

Evolution of the (a) unit-cell parameters and (b) normalized volume V/Z for the R₂TeO₆ series with the R³⁺ ionic radius (Shannon, 1976).

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For Lu₂TeO₆ the structure was refined from NPD data in the trigonal P321 space group, No. 150, Z = 3. There are two inequivalent Lu1 and Lu2 atoms located at 3e (x, 0, 0) and 3f (x, 0, 1/2) Wyckoff sites; two independent Te1 and Te2 atoms placed at 1a (0, 0, 0) and 2d (1/3, 2/3, z) and three kinds of oxygen atoms, O1, O2 and O2, all placed at general 6g (x, y, z) positions. The refinement from 2 K data is also excellent, demonstrating the absence of phase transitions in the 2–295 K range. Tables S9 and S10 in the Supplementary Information contain the unit-cell, structural parameters, anisotropic displacement factors and reliability factors after each refinement, at RT and 2 K. Fig. 4a and b illustrates the goodness of the fits for Lu, at 295 and 2 K, respectively. The thermal evolution of the unit-cell parameters for Lu₂TeO₆, from a = 8.9528(2) Å, c = 5.0762(1) Å, V = 352.36(1) ų at 295 K, to a = 8.9547(2), c = 5.0706(1) Å, V = 352.13 ų at 2 K, is not isotropic since a slight increase is observed in a (=b) parameter, compensated by the expected contraction in c to give a subtle reduction in the unit-cell volume (by 0.06%), much smaller than that observed in the orthorhombic phase for Tm₂TeO₆ (by 0.3%) in the same temperature range, 295–2 K. The normalized V/Z volume (Fig. 3b) versus the ionic radius of R³⁺ ions shows an anomaly for the trigonal Yb phase and Lu, since the trigonal structure is considerably expanded (per unit formula) with respect to the orthorhombic arrangement, due to the lower coordination number for R³⁺ in the Na₂SiF₆ structural type. This anomaly corresponds to a morphotropic phase transition, defined as an abrupt change in the structure of a solid solution with variation in composition. In this case the driving force for the morphotropic transition is the change of ionic radius of R³⁺ due to the lanthanide contraction. The main interatomic distances for Lu₂TeO₆ at 295 K and 2 K are included in Table 2.

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Figure 4

Observed (crosses), calculated (solid line) and difference (bottom) NPD Rietveld profiles for Lu₂TeO₆ at (a) 295 K and (b) 2 K.

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Figs. 5 and 6 show different aspects of the orthorhombic structure. This crystal structure is stabilized for the larger rare-earth ions, from R = La to Tm, and contains octahedrally coordinated TeO₆ units sharing edges and vertices with R1O₇ and R2O₇ polyhedra, as displayed in Fig. 5. There are no contacts between TeO₆ polyhedra, which form discrete octahedral units. Both kinds of sevenfold oxygen coordinated RO₇ units form chains along the [1 0 0] direction; R1O₇ share edges via O5 and O6 oxygen atoms (Fig. 6a), whereas R2O₇ share vertices via O3 oxygens (Fig. 6b). Average <R1-O> and <R2-O> span from 2.496 to 2.333 Å and 2.493 to 2.316 Å from La to Tm, respectively, showing very similar sizes and relative variation upon the lanthanide contraction. Upon cooling down some R-O distances show a significant contraction, such as R1-O5 (2.472(7) Å at 295 K and 2.443(5) Å at 2 K), whereas other remain almost unchanged or slightly increase, resulting in a small average variation for both <R1-O> (2.333 Å at 295 K to 2.327 Å) and R2-O (2.316 Å at 295 K to 2.317 Å at 2 K). The <Te–O> bond lengths within the octahedra undergo a subtle compression along the series, varying between 1.929 and 1.918 Å from La to Tm, as a result of the chemical pressure as the unit-cell volume becomes smaller with the lanthanide contraction. These distances are close to that expected from the ionic radii sum for octahedrally coordinated Te⁶⁺ (0.56 Å) with three threefold and three fourfold coordinated O²⁻ ions (1.36 and 1.38 Å, respectively) (Shannon, 1976), of 1.93 Å. Fig. 5 also shows the anisotropic displacement ellipsoids; all of them are oblate ellipsoids, with the largest displacement plane perpendicular to the bonding directions, as it is normally observed for strongly covalent crystal structures.

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Figure 5

Representation of the orthorhombic R₂TeO₆ crystal structure; R atoms are in sevenfold coordination and TeO₆ form isolated octahedra.

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Figure 6

Chains of RO₇ polyhedra running along the [1 0 0] direction: (a) R1O₇ polyhedra sharing edges; (b) R2O₇ polyhedra sharing corners.

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For the trigonal crystal structure exhibited by Lu₂TeO₆ (Fig. 7), both Lu³⁺ and Te⁶⁺ are octahedrally coordinated with a distorted close-packed array of oxygens, with distortions lengthening the Lu–O distances and shortening the Te–O bond lengths from the ideal values [Malone et al., 1969]. In this compound Lu³⁺ shares the octahedral coordination with Te⁶⁺, although in general rare-earth ions often prefer a higher coordination number. The Na₂SiF₆ crystal structure is exhibited in A₂BO₆ oxides with fairly large A ions (i.r. ≈0.85 Å) for octahedral coordination and a large difference in valence between the A and B cations (Malone et al., 1969). All the oxygen atoms are threefold coordinated with 2 Lu and 1 Te, in such a way that every TeO₆ octahedra share edges with three LuO₆ polyhedra, and corners with three other LuO₆ octahedra.

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Figure 7

View of the trigonal Lu₂TeO₆ crystal structure, showing both kinds of RO₆ and TeO₆ octahedra.

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It is interesting to examine the valence of the cations and anions present in the solids, which can give hints on the stability of the structure and its evolution across the series. The Brown’s bond valence model (Brown, 1981; Brese and O’Keeffe, 1991) gives a phenomenological relationship between the formal valence of a bond and the corresponding bond length. In perfect nonstrained structures the bond valence sum (BVS) rule states that the formal charge of the cation (anion) is equal to the sum of the bond valences around this cation (anion). This rule is satisfied only if the stress introduced by the coexistence of different structural units can be relieved by the existence of enough degrees of freedom in the crystallographic structure. The departure of the BVS rule is a measure of the existing stress in the bonds of the structure. The overall stress can be quantified by means of a global instability index (GII) [Brown, 1992], calculated as the root mean of the valence deviations for the j = 1 … N atoms in the asymmetric unit, according to GII = (∑_j [∑_i(s_ij − V_j)²]/N^1/2. Table 3 lists the valences calculated for R, Te and O atoms from the individual R–O and Te–O distances of Tables 1 and 2, as well as GII along the three crystallographic axes. Several trends must be highlighted. In the orthorhombic structure the valences for rare-earth cations at R1 sites are always lower than those at R2, which are slightly overbonded, or under compressive stress (excepting for Tb). This stress is relieved upon the transition to the trigonal structure: Lu2 shows valence values very close to the expected 3+. Te ions always exhibit valences lower than 6+ (excepting Tm at 2 K); however, the transition to the trigonal structure for Lu shows a significant increment of the valence at Te1 sites (6.28 at 295 K), displaying an important compressive stress. It is thus remarkable that the stabilization of the trigonal polymorph is clearly driven by the trend of Lu to adopt a lower-coordination environment, despite the less suited environment exhibited by Te ions. It is noteworthy that the overall stress quantified by the global instability index (GII) does not significantly vary across the series, showing similar values for Tm and Lu (at both sides of the structural transition), since Te ions become overbonded (Te1) or underbonded (Te2) in the trigonal polymorph. It is again indicating that the coordination of Lu in a sixfold environment is the driving force for the stabilization of the Na₂SiF₄-type polymorph for Lu₂TeO₆.