On the dimorphism of Pr₆Mo₁₀O₃₉

3.1.1 The triclinic structure of A-type Pr₆Mo₁₀O₃₉

The triclinic modification of Pr₆Mo₁₀O₃₉ crystallizes in space group P1̅ (a=945.25(1), b=1058.49(2), c=1815.16(3) pm; α=104.149(1), β=95.220(1), γ=102.617(1)°) with two formula units per unit cell and is thus isotypic to the cerium representative Ce₆Mo₁₀O₃₉ [27]. As this is both the denser phase as well as the one with the lighter lanthanides, it is henceforth named the A-type. All atoms in the unit cell are situated at Wyckoff positions 2i, therefore, the unit cell comprises as many crystallographic independent atoms as there are in the sum formula. The six Pr³⁺ cations are surrounded by seven (for Pr1) and eight (for Pr2–5) oxide anions, respectively, exhibiting rather irregular coordination polyhedra with shapes of mono- and bicapped trigonal prisms as well as square antiprisms (Fig. 1).

Fig. 1:

Oxide anion coordination environment around the six crystallographically independent Pr³⁺ cations in the crystal structure of triclinic A-type Pr₆Mo₁₀O₃₉ (ellipsoid representation at the 95% probability level).

The Pr–O interatomic distances range between 233 and 275 pm (Table 2) and therefore correspond very well with those in A-type Pr₂O₃, which show values between 234 and 267 pm [36]. According to the structure formula Pr₆[MoO₄]₈[Mo₂O₇] eight ortho-oxidomolybdate units are found in the unit cell with a cationic surrounding of five Pr³⁺ atoms around each tetrahedron. The Mo–O bond lengths are in the range of 173–182 pm (Table 2), which are in good agreement to those in lanthanum(III) sesquimolybdate(VI) La₂[MoO₄]₃ (d(Mo–O)=173–182 pm [3]). The O–Mo–O angles in these tetrahedra differ with values from 104 to 118° (Table 3) a maximum of 8% from the ideal tetrahedral angle of 109.47° (Table 3). The [Mo₂O₇]²⁻ anions exhibit staggered conformation with a Mo9–O36–Mo10 angle of about 162° (Fig. 2, bottom) and a coordination environment of seven praseodymium cations (Fig. 2, top). The bond lengths within both tetrahedra lie between 171 and 174 pm while the ones to the bridging (O36)²⁻ atoms show values of 185–187 pm (Table 2), which is typical for compounds bearing [Mo₂O₇]²⁻ anions (e.g. Mg[Mo₂O₇]: d(Mo–O_br)=185–188 pm [37], br=bridging). The O–Mo–O angles within the dimolybdate anions (105–116°) are again close to the one found in ideal tetrahedral environments.

Fig. 2:

Cationic coordination environment around the [Mo₂O₇]²⁻ anions (top) and view at their staggered conformation (bottom) in the crystal structure of triclinic A-type Pr₆Mo₁₀O₃₉ (ellipsoid representation at the 95% probability level).

Both the ortho- and the dimolybdate entities are loosely distributed in a layer along the crystallographic ac plane in the lower half of the unit cell (centering around y/b≈¼), and in the upper half (centering around y/b≈¾) the same build-up is found inversely (Fig. 3). The Pr³⁺ cations are found between the two aforementioned sheets of oxidomolybdate anions at y/b≈0 and ½.

Fig. 3:

View at the unit cell of triclinic A-type Pr₆Mo₁₀O₃₉ along [100].

3.1.2 The monoclinic structure of B-type Pr₆Mo₁₀O₃₉

The monoclinic modification of Pr₆Mo₁₀O₃₉ crystallizes in space group C2/c (a=1247.93(3), b=1989.68(6), c=1392.52(4) pm, β=100.505(2)°, Z=4) isotypic to Nd₆Mo₁₀O₃₉ [21], Eu₆Mo₁₀O₃₉ [23], and Gd₆Mo₁₀O₃₉ [28]. Its crystal structure is slightly less dense than the previously described triclinic phase and henceforth referred to as B-type. Except for (O20)²⁻, all atoms are situated at the general Wyckoff positions 8f, therefore three crystallographically distinguishable praseodymium cations are found in the crystal structure, which show coordination numbers of seven (Pr1) and eight (Pr2 and Pr3) oxide anions, again building up irregular polyhedra. While those around (Pr1)³⁺ and (Pr3)³⁺ can be regarded as distorted mono- and bicapped trigonal prisms, respectively, the coordination environment around (Pr2)³⁺ is best described as distorted pentagonal bipyramidal with an additional, second vertex below the pentagonal plane (Fig. 4).

Fig. 4:

Oxide anion coordination environment around the three crystallographically independent Pr³⁺ cations in the crystal structure of monoclinic B-type Pr₆Mo₁₀O₃₉ (ellipsoid representation at the 95% probability level).

The interatomic distances within these polyhedra range between 228 and 263 pm (Table 4) which correspond very well with those in the A-type of the title compound, as well as in A-type Pr₂O₃ [36]. Even a distance as short as 228 pm is found in several praseodymium compounds (e.g. G-type Pr₂[Si₂O₇]: d_min(Pr–O)=227 pm [38]). Furthermore, the crystal structure comprises four crystallographically independent [MoO₄]²⁻ tetrahedra with a cationic surrounding of five Pr³⁺ around each of these units. The Mo–O bond lengths lie between 173 and 181 pm, which represents the same range as found in the triclinic phase of Pr₆Mo₁₀O₃₉. The O–Mo–O angles differ by about ±6% from the ideal value of 109.47° in tetrahedral units, ranging between 103 and 115° (Table 5). The [Mo₂O₇]²⁻ entities exhibit the bridging O20 atom at Wyckoff position 4e (symmetry 2), a skew conformation (Fig. 5, bottom) with a Mo5–O20–Mo5 bridging angle of 146°, and a cation coordination of six Pr³⁺ cations (Fig. 5, top). Typically for these units, the Mo–O bond lengths to the terminal oxide anions remain rather short (172–173 pm, Table 4), while those to the bridging ones are as large as 187 pm (Table 4) as already seen in A-type Pr₆Mo₁₀O₃₉. The same applies for the angles within each tetrahedron of the dimolybdate unit with values ranging from 107 to 115° (Table 5).

Fig. 5:

Cation coordination environment around the [Mo₂O₇]²⁻ anions (top) and view at their skew conformation (bottom) in the crystal structure of monoclinic B-type Pr₆Mo₁₀O₃₉ (ellipsoid representation at the 95% probability level).

The Pr³⁺ cations, the [MoO₄]²⁻, and the [Mo₂O₇]²⁻ anions are arranged layer-like parallel to the ab plane in the crystal structure of the monoclinic B-type modification of Pr₆Mo₁₀O₃₉ (Fig. 6).

Fig. 6:

View at the unit cell of monoclinic B-type Pr₆Mo₁₀O₃₉ along [010].

3.1.3 Structural comparison of the triclinic A-type and the monoclinic B-type of Pr₆Mo₁₀O₃₉

Both structure types exhibit several similarities, such as comparable coordination environments around the praseodymium cations and the isolated [MoO₄]²⁻ anions. However, the ratio of seven-fold to eight-fold coordinated Pr³⁺ cations is 1:2 in the monoclinic and 1:5 in the triclinic phase. The differences between the two structures increase as the [Mo₂O₇]²⁻ entities are regarded. The cation coordination numbers decrease from seven in the triclinic A-type to six in the monoclinic B-type. Therefore, together with the higher ratio of eight-fold coordinated Pr³⁺ it is quite comprehensible that the triclinic phase has to be the denser one, if only by about 3%. Furthermore, the conformation of the aforementioned dimolybdate units differ from staggered with an almost linear Mo–O–Mo bridging angle of 163° to skew with a much smaller angle of 146°. All these distinctions substantially reduce the possibility to find a correlation between the two structures via a group-subgroup relationship. The best comparison is achieved by contemplating the crystal structure of the triclinic A-type along [010] (Fig. 7) and the monoclinic B-type along [001] (Fig. 8).

Fig. 7:

View at the crystal structure of triclinic A-type Pr₆Mo₁₀O₃₉ along [010] with special emphasis on the layer sequence.

Fig. 8:

View at the crystal structure of monoclinic B-type Pr₆Mo₁₀O₃₉ along [001] with special emphasis on the layer sequence.

These views allow both structures to be described with a layer-like arrangement, however different to the ones in Figs. 3 and 6. In triclinic A-type Pr₆Mo₁₀O₃₉ half of the crystallographically distinguishable [MoO₄]²⁻ tetrahedra are arranged together with the [Mo₂O₇]²⁻ anions in sheets A around x/a=0, while the other four [MoO₄]²⁻ anions are also set up in sheets B, however, around x/a=½. The overall stacking of these layers can be considered as AB. The Pr³⁺ cations are distributed between these anions to fill voids and provide for electroneutrality (Fig. 7). A similar arrangement is found in the crystal structure of monoclinic B-type Pr₆Mo₁₀O₃₉ if viewed along [001]. The [Mo₂O₇]²⁻ containing layers A are set up around y/b=¼ and ¾ while the others B are situated at y/b=0 and ½. Hence, a layer stacking according to B AB′ A′ is found with A′ being the respective inverted layer and B′ shifted by ½ along [010] (Fig. 8). Again, the praseodymium cations are distributed in the voids between the anions to ensure electroneutrality.