LaTe1.82(1): modulated crystal structure and chemical bonding of a chalcogen-deficient rare earth metal polytelluride

Small finite telluride anions are found as dominant species in the anionic layers of modulated LaTe1.82(1), corresponding to its semiconducting properties.


Introduction
The structural chemistry of the rare earth metal chalcogenides REX 2-(RE = Y, La-Nd, Sm, Gd-Lu; X = S, Se or Te; 0 0.2) with trivalent RE metals has attracted attention because of their structural variety in a quite small compositional range. The sulfides and selenides of this class of compounds have been intensively investigated, illuminating several different (super)structures due to different amounts of defects and the formation and arrangements of chalcogenide X 2À and polychalcogenide X n 2À anions for charge balancing. A comprehensive overview discussing these aspects can be found in Doert & Mü ller (2016). At the beginning of the 21st century, the structures of four rare earth metal polytellurides RETe 2-(RE = La-Nd) (Stö we, 2000a(Stö we, ,b,c, 2001, were thoroughly (re)investigated, revealing considerable differences to the sulfides and selenides of analogous compositions, while still maintaining the same general structural motif. This general structural motif of all binary polychalcogenides REX 2-of trivalent rare earth metals is closely related to the structure of ZrSSi (space group P4/nmm, No. 129; a 0 ' 3.80 and c 0 ' 8.00 Å ) (Onken et al., 1964;Klein Haneveld & Jellinek, 1964), which shows an alternating stacking of puckered [ZrS] slabs and square-planar [Si] layers along [001]. The binary rare earth metal chalcogenides REX 2-(RE = Y, La-Nd, Sm, Gd-Lu; X = S, Se or Te; 0 0.2) comprise puckered [REX] + slabs and planar chalcogenide layers, which can formally be stated as [X] À (Doert & Mü ller, 2016). For electronic reasons, the chalcogenide layers of the stoichiometric REX 2 compounds, especially the disulfides RES 2 and diselenides RESe 2 , feature only X 2 2À dianions, resulting in a distortion from an idealized square-planar net towards a planar herringbone pattern; for ditellurides RETe 2 , the structural situation is not that uniform (Stö we, 2000a,b,c). Going to the off-stoichiometric REX 2-(0 < 0.2) compounds, vacancies in the planar chalcogenide layers are observed, together with X 2À to maintain the overall net charge [X] À for the layer. This structural change is obvious for the CeSe 1.9 structure type, but can also be seen for the related, intrinsically disordered Gd 8 Se 15 -type structures Doert, Dashjav et al., 2007). Hence, the two most important factors accounting for structural differences are the amount of vacancies in the chalcogenide layer and the ionic radii of the trivalent rare earth metal cations, as they largely determine the Coulomb repulsion between the anions in the [X] À layers in this series. In addition, in accordance with the Zintl-like electron localization, the polysulfides RES 2-and polyselenides RESe 2-are semiconductors.
To distinguish between different anionic fragments in the chalcogenide layer, classical electron counting has been proven a simple but powerful way to describe these structures, as briefly explained for the CeSe 1.9 structure type; the CeSe 1.9 type is a ffiffi ffi 5 p Â ffiffi ffi 5 p Â 2 superstructure of the basic ZrSSi unit cell and crystallizes in the space group P4 2 /n (No. 86) . The planar [Se] layer of this compound is built up by four dinuclear Se 2 2À anions, forming a pinwheel-like arrangement around a vacancy. The complementary isolated Se 2À anion is surrounded by four Se 2 2À anions in a spoke-like manner (Lee & Foran, 1994). Assuming only trivalent rare earth metal cations, ten positive charges per [REX] + layer and unit cell need to be balanced by nine atoms of the planar [X] À layer. This is achieved by four Se 2 2À anions and one isolated Se 2À anion. This kind of charge-ordered superstructure has only been reported once for a rare earth metal telluride, namely for CeTe 1.9 (Ijjaali & Ibers, 2006), whereas many examples are known for the rare earth metal polysulfides and polyselenides (Doert, Graf, Lauxmann et al., 2007;Grupe & Urland, 1991;Plambeck-Fischer et al., 1989;Urland et al., 1989;Dashjav et al., 2000;Mü ller et al., 2012).
An unusual case of charge balancing for the deficient REX 2-compounds has been reported for structures with a composition of RETe 1.8 (Sm, Gd-Dy) by forming larger anionic fragments (Ijjaali & Ibers, 2006;Wu et al., 2002;Gulay et al., 2007;Poddig et al., 2018). Here, a similar enlargement of the basic lattice parameters of ffiffi ffi 5 p Â ffiffi ffi 5 p Â 2 is observed, and the compounds crystallize in a 10-fold superstructure of the aristotype in P4/n (No. 85). In contrast to the respective sulfides and selenides, a motif of statistically disordered Te 2   2À   anions and linear Te 3  4À anions are found here. Linear Te 3   4À anions have rarely been reported in REX 2-compounds, although the presence of an Se 3 4À anion was discussed for DySe 1.84 , but neglected after computational studies (van der Lee et al., 1997). The bonding situation in such linear trinuclear anions, like Te 3 4À or I 3 À , requires the occupation of nonbonding states, similar to the situation of the prominent XeF 2 molecule. Within the concept of molecular orbital (MO) theory, this situation can be described as a 3c-4e bond (Rundle, 1963;Assoud et al., 2007). A density functional theory (DFT)-based study clearly evidenced such a linear Te 3 unit in GdTe 1.8 (Poddig et al., 2018) and confirmed an alternative method of electron localization for this composition of REX 1.8 : ten positive charges of one puckered [REX] + layer per unit cell are balanced by two Te 3 4À anions and one Te 2 2À anion.
Starting from the results of the RETe 1.8 (RE = Sm, Gd-Dy) compounds, we were interested in identifying the structural motifs of the early rare earth metal tellurides RETe 2-with > 0. This was especially motivated by the reported differences between the structures of LaTe 2 , CeTe 2 and PrTe 2 (Stö we, 2000a,b,c), and the corresponding sulfides and selenides. Structural data on tellurides RETe 2-with a comparable low chalcogen content have rarely been reported; RETe 1.8 (RE = Sm, Gd-Dy) are a few examples (Ijjaali & Ibers, 2006;Wu et al., 2002;Gulay et al., 2007;Poddig et al., 2018). The first results on the lanthanum compound LaTe 1.82(1) are presented in the following.

Synthesis
All preparation steps were carried out in an argon-filled (5.0, Praxair) glove-box (MBraun, Garching, Germany). Crystals were grown by the addition of a small amount of I 2 to the reaction mixture in closed silica ampoules. In a standard synthesis, 500 mg of a stoichiometric mixture of lanthanum (99.9%, Edelmetall Recycling m&k GmbH) and tellurium (Merck, >99.9%, reduced in a H 2 stream at 673 K) were placed in a quartz tube and flame sealed under dynamic vacuum (p 1 Â 10 À3 mbar). The ampoule was heated slowly with a ramp of 2 K min À1 to 1073 K. The reaction takes place in a gradient from 1123 to 1073 K with I 2 (Roth, >99.8%, purified by sublimating twice prior to use) as transporting agent. After 7 d, the ampoule was cooled to room temperature. As we observed a slow degrading of the compounds under atmospheric conditions, the samples were stored under argon.

Powder diffraction
Data collection was performed at 296 (1) K with an Empyrean diffractometer (PANalytical) equipped with a curved Ge(111) monochromator using Cu K 1 radiation ( = 1.54056 Å ). The scans covered the angular range from 5 to 90 2. Rietveld refinement using the fundamental parameter approach was performed with TOPAS (Version 5; Coelho, 2018).

Single-crystal diffraction
Crystal data, data collection and structure refinement details are summarized in Table 1. Data for the modulated structure were integrated and corrected for Lorentz and polarization factors, before applying a numerical absorption correction with the program JANA2006 (Petříček et al., 2014).
The structure was solved using the charge-flipping method of the program SUPERFLIP (Palatinus & Chapuis, 2007) implemented in the JANA2006 software; the atomic positions were synchronized with those of the average structure. Structure refinement was performed with JANA2006 against F 2 including anisotropic displacement parameters for all atoms. Second-order satellites were neglected because of their low intensity (about 99% of these reflections were found with intensities below 3) and two harmonic waves have been used for the fit of the atomic modulation functions.

Scanning electron microscopy (SEM) and EDS
SEM was performed with an SU8020 (Hitachi) with a tripledetector system for secondary and low-energy backscattered electrons (U a = 5 kV). The composition of selected single crystals was determined by semiquantitative energy dispersive X-ray analysis (U a = 20 kV) with a Silicon Drift Detector (SDD) X-Max N (Oxford).

Computational methods
Solid-state calculations were performed with the all-electron code FHI-aims (Blum et al., 2009) for three ordered structural models of LaTe 1.82(1) . The FHI-aims calculations for subsequent real-space analysis were performed with a (2 Â 2 Â 2) k-point grid (model in P1) and a (3 Â 2 Â 2) k-point grid  Table 1 Crystallographic data and refinement details for LaTe 1.82(1) .

Model Pmmn
Model Pm2  (model in Amm2 and A2) using the zeroth-order scalar relativistic zora correction, collinear spins, the numerical atomcentred basis of light level and the PBE functional (Perdew et al., 1996). Real-space properties were evaluated subsequently with the help of the program package DGrid (Kohout, 2016). Hereby, the electron localizability indicator (ELI-D) was calculated on a grid with a 0.1 Bohr mesh size.
2.6. Temperature-dependent electrical resistance The electrical resistance of LaTe 1.82(1) was measured between 7 and 345 K with a mini-CFMS (Cryogenic Ltd, London). Four gold contacts were attached to the surface of a single crystal in a linear set-up with a carbon conductive composite 7105 (DuPont) to establish the electrical contact between the crystal and the gold wires.

Synthesis
Black plate-like single crystals of previously unreported LaTe 1.82(1) were obtained starting from the elements by alkali halide flux reactions or solid-state reactions with a small amount of I 2 for mineralization in fused-silica ampoules. Temperatures above 1173 K in the presence of I 2 lead to an attack on the ampoule wall, whereas temperatures of about 1073 to 1123 K are well suited for crystal growth, without noticeable side reactions with the ampoule material. The best results were achieved in a small gradient from 1123 to 1073 K, where crystals of about 0.3 mm in length were grown. The amount of added I 2 needs to be compensated by excess La when preparing the experiment due to the formation of LaI 3 during and after the experiment, which in turn alters the composition slightly. Solid LaI 3 was mainly found at the sink of the ampoule, whereas the desired product was found at the source of the ampoule. A similar procedure at higher temperatures was chosen, e.g. for RETe 1.8 (RE = Gd, Tb or Dy) (Poddig et al., 2018).

Diffraction image
The strong reflections of the powder pattern can be indexed with a tetragonal unit cell with a = b ' 4.50 Å and c ' 9.17 Å . As a starting point for the Rietveld refinement, the space group (P4/nmm, No. 129) and the atom sites of the aristotype, the ZrSSi type, were chosen. The fit shows some additional unindexed reflections, which are not compatible with the space group P4/nmm and its most prominent lower symmetric subgroups (Fig. 1).
The diffraction image of a single crystal at ambient temperature reveals, as already indicated by powder diffraction, additional weak reflections in the layers (hkn) with n = 0, AE1, AE2, . . . (Fig. S1 in the supporting information). Slightly stronger reflections can be observed in the layers (hkn) with n = AE0.5, AE1.5, . . . (Fig. S1). These additional reflections cannot be indexed with a commensurate superstructure of the basic unit cell and were treated as satellites. Moreover, the distribution of the satellites with respect to the main reflec-tions suggest a two-dimensional modulation. The whole diffraction image can then be indexed with five indices hklm 1 m 2 according to: The modulation wave vector components and were determined to be 0.272 (1) and 0.314 (1), respectively. A schematic image of the relative positions of the satellite reflections with respect to the main reflections is displayed in Fig. 2 and reconstructed precession images are shown in Fig. S1 (see supporting information). The schematic figure illustrates also that two different q vectors are necessary to index the complete diffraction image. Equivalent satellites are linked by a twofold rotational axis ( Fig. S1), pointing towards orthorhombic (or lower) symmetry for the modulated structure. Furthermore, the weak additional reflections in the (hkn) (n = AE1, AE2, . . . ) plane correspond to the linear combinations of q 1 and q 2 , which cannot be explained by twinning and are, thus, evidencing a true [3 + 2]-dimensional modulated structure.

Average crystal structure
Single-crystal data collected at ambient temperature indicated the same lattice parameters for a and b within standard deviations so that a tetragonal unit cell of a = 4.4996 (5) and c = 9.179 (1) Å was chosen. The main reflections are clearly compatible with high tetragonal Laue symmetry and the space group P4/nmm (No. 129) was chosen for structure refinement of the average structure according to the reflection condition h+k = 2n. The refinement resulted in a reasonable structural model (Table S1 in   EDS (energy-dispersive X-ray spectroscopy) measurements points towards a composition of LaTe 1.79 (1) . Throughout the article, we will refer to this compound as LaTe 1.82(1) , based on the refined composition of the modulated structure.
The average structure of LaTe 1.82(1) can be described with puckered [LaTe] layers sandwiched by square-planar [Te] layers. The partial occupation of the Te position in the [Te] layer, together with its large oblate anisotropic displacement parameters (ADPs) in the ab plane and prolate ADPs of the La atom along the [001] direction already give hints towards the modulation (Fig. 3).

Refinement of the modulated structure
The tetragonal symmetry of the average structure discussed above is violated by the modulation vectors, as mentioned before. The observed satellite positions are incompatible with a fourfold rotational axis (Fig. 2), resulting in a lower symmetric Laue class. To establish a suitable basic structure as starting model, orthorhombic and monoclinic subgroups of the space groups of the average structure were considered. The highest possible orthorhombic space group would then be Pmmn, which is a translationengleiche subgroup of the index 2 (t2) of P4/nmm, as displayed in Fig. 4. However, a very similar basic structure has been used for DySe 1.84 , with similar modulation wave vectors q 1 = a* + b* + 1 2 c* and q 2 = a* À  Lee et al., 1997) and the final model for DySe 1.84 was established in the noncentrosymmetric space group Pm2 1 n(,, 1 2 )000(,À, 1 2 )000 (No. 31.2.51.35). We therefore decided to establish a second structure model for LaTe 1.82(1) in Pm2 1 n(,, 1 2 )000(À,, 1 2 )000, too, and evaluate it against the centrosymmetric one in Pmmn(,, 1 2 )000(À,, 1 2 )000. The group-subgroup relationship between these two space groups of the basic structures is displayed in Fig. 4, indicating a t2 group-subgroup relationship between them. The limits of both models shall be discussed in the following and the crystallographic details of the refinements are given in Table 1.
The main reflections meet the conditions for a primitive tetragonal lattice nearly perfectly, the data derived by powder diffraction and single-crystal diffraction give no hint of an orthorhombic or even monoclinic distortion of the lattice within standard uncertainties. However, taking the symmetry of the satellite reflections into account, the final unit-cell parameters were restrained to the conditions of an orthorhombic unit cell and were used for the integration of the intensities, as well as for structure refinements. According to the two modulation vectors and reflection conditions, the proper superspace group is Pmmn(,, 1 2 )000(À,, 1 2 )000 (No.  Average crystal structure of LaTe 1.82(1) . Displacement ellipsoids are drawn with a probability level of 99.9%.

Figure 4
Group-subgroup relationship between the space group of the aristotpye ZrSSi (P4/nmm) and the chosen orthorhombic space groups of the basic structures.
around the position of the main reflections in layers hkl, l = AE0.5, AE1.5, . . . (Fig. S2 in the supporting information). The reconstructed precession images, however, reveal only the four expected satellite reflections corresponding to AEq 1 and AEq 2 .
A second model in superspace group Pm2 1 n(,, 1 2 )-000(À,, 1 2 )000 (No. 31.2.51.35; we keep the nonstandard setting for a concise structure description) has been evaluated against the centrosymmetric model to check if there are also differences in the structural model, as in the case of DySe 1.84 . For simplicity, we will use the three-dimensional space-group symbols during the structure descriptions to distinguish between the two different modulated structures in the following.
The refinement in Pm2 1 n has been adjusted by considering inversion twinning. The refinement converged with a twin volume fraction of about 40% for the second domain.
The atomic modulation functions (amf) were stepwise included in both refinements, by first modelling the positional displacement of all atoms, before including an additional occupational modulation for the Te2 atom. As already expected from the average structure, the La1 and Te1 position show mainly shifts in the c direction, whereas the Te2 atom in the [Te] layer shows a strong displacement in the ab plane, as displayed in the two t plots in Fig. 5. Note, that there is a small difference for the positional modulation along [001] for the Te2 atom between the models in Pmmn and Pm2 1 n, as a result of the higher degree of freedom in the noncentrosymmetric space group. In Pm2 1 n, the t plot shows a slightly sinusoidal curve in the c direction with a very small amplitude.
The displacement in the [LaTe] layer along c can be explained as a reaction to the modulation in the [Te] layer; the La atom aims to compensate the missing Te atoms in the coordination sphere by getting closer to the [Te] layer. Consequently, the Te1 atom reacts accordingly to the La1 dislocation by adjusting its position along c as well. The displacement of the Te2 atom in the [Te] layer is slightly more pronounced (Fig. 5), due to vacancy formation and the creation of different Te anions. This holds for both models, as mentioned before. As a second step in the refinement, the occupational modulation in the [Te] layer was introduced by adding two harmonic functions. This improved the structural model in Pmmn and Pm2 1 n considerably and the areas of low electron density at certain points in the Fourier map around Te2 are now also covered by the atomic modulation function (Fig. 6).
The Fourier sections in Fig. 6 also reveal a partially discontinuous behaviour of the electron density around Te2, although it is not very pronounced (see also Fig. S3 in the supporting information for a two-dimensional plot of the Te occupancy). The drawback in modelling this with harmonic functions are some overshooting and truncation effects in the final structure model, which we assume to be one major reason for the large residual electron-density maxima (see Table 1). The interatomic distances are, nevertheless, in good agreement with previously reported distances for Te anions and the refined composition matches that of the semiquantitative EDS analysis. In the second evaluated model in Pm2 1 n, harmonic functions, as well as crenel functions, have been utilized. The refinement with harmonic waves in Pm2 1 n converged with slightly better R values and a similar residual electron density compared to the refinement in Pmmn, mainly due to the greater number of independently refined parameters. The use of discontinuous functions, such as crenel or sawtooth functions (Petříček et al., 2016), failed in Pmmn but refined stably in Pm2 1 n, although they did not improve the structural model. The comparison between both types of functions suggests that treating the occupational and positional modulation of Te2 by harmonic functions is suitable. The large residual peaks in the difference Fourier (F o -F c ) maps decrease considerably if two modulation functions are applied to the ADPs of Te2 as well. However, this leads to nonpositive-definite values for U min at some values of t and has hence been rejected for the final structure model. The structure model derived in Pmmn(,, 1 2 )000(À,, 1 2 )000 for LaTe 1.82(1) is used in the following paragraph for the discussion of the structural features as the structural differences between both models are negligible, as stated before.
The displacement of the La atoms along the c direction, as expected from the average structure. The motif of the puckered layer is very stable and does not show large deviations between different REX 2-compounds, whereas the planar [X] layer is the more interesting structural feature and will be discussed in the following.
The change of the occupation and the variations of the Te-Te distances for the model in Pmmn are shown in Fig. 7. The t-plot for the occupational modulation displays a static behaviour along t, which is shifted for different u values. The changes of the Te-Te distances in the modulated [Te] layer are displayed in the second t plot (Fig. 7). Short distances with a lower limit of 2.801 (4) Å correspond to a Te-Te single bond (see above) and medium distances up to 2.959 (1) Å are in good agreement with distances reported for a linear Te 3 4À anion (see, for example: Poddig et al., 2018), as well as the often observed Te 2 2À anions (see, for example: Stö we, 2000a). Larger distances of 2.984 (1) to 3.563 (4) Å are mainly considered as nonbonding interactions between Te entities. Compared to the known rare earth metal polysulfides and selenides, the interpretation of the Te-Te distances from a purely crystallographic viewpoint is more difficult as we face a much larger variety of distances, and boundaries between bonding and nonbonding interactions in the RETe 2-system are floating. Reported Te-Te distances in dinuclear Te 2 2À anions ranging from 2.868 (1) Å in GdTe 1.8 (Poddig et al., 2018) to 3.036 (2) Å in LaTe 2 (Stö we, 2000a) have been interpreted as single bonds. Nevertheless, the observed distances in the modulated structure of LaTe 1.82(1) are in good agreement with the distances found in comparable compounds.
In the modulated [Te] layer of LaTe 1.82(1) , a Te 4 square is apparent additionally when choosing small cut-off values for the approximant crystal structure for visualization (see, for example: Fig. S5 in the supporting information). As all four atoms in these fragments have an occupation value of about 0.52 (5), the presence of all four at the same time seems unrealistic. Instead, an unresolved superposition of a dinuclear Te 2 2À anion with two adjacent vacancies is the most likely explanation. Moreover, there is no evidence for anionic [Te 4 ] squares with Te-Te distances of 2.80 Å in the literature. Cationic Te 4 2+ and the corresponding Se 4 2+ entities, on the other hand, are well known (see, for example: Barr et al., 1968;Beck et al., 1997;Forge & Beck, 2018;Ruck & Locherer, 2015) and their bonding situation has been investigated by computational methods in 1980 already (Rothman et al., 1980). The typical Te-Te distance in Te 4 2+ is about 2.65 to 2.70 Å (Ruck & Locherer, 2015) and the Te-Te-Te angles are often close to 90 , which results in a slight distortion from idealized D 4h symmetry. Taking the EDS results and the site-occupation  factor from the average structure (both resulting in a composition of about LaTe 1.8 ) into account, a substantial number of voids in the [Te] layer is expected, which also supports the idea of a disordered motif of dinuclear Te 2 2À anions and adjacent vacancies instead.
A similar discussion of apparent structure motifs and possible (super)positions due to unresolved disorder shall be deduced for the apparent Te 8 rings (Fig. 8). Arrangements of disordered X 2 2À anions have been identified as the constituents of eight-membered ring-like motifs in the sulfides RE 8 S 15-(RE = Y, Tb-Ho; Doert et al., 2012) and selenides RE 8 Se 15-(RE = Y, Gd-Er; = 0 0.3; Doert, Dashjav et al., 2007). In LaTe 1.82(1) , these apparent eight-membered rings may also consist of different disordered constituents, like Te 3 2À and Te 3 4À anions, along with the more common Te 2À and Te 2 2À motifs, around central vacancies. However, this is hard to resolve solely from the diffraction data. To gain more insight into this structural motif and the chemical bonding situation in the modulated [Te] layers in general, chemical bonding analyses were performed for three different commensurate approximants.

Bonding analysis
Quantum mechanical calculations based on density functional theory (DFT) and bonding analyses with the electron localizability indicator (ELI-D) (Kohout, 2004(Kohout, , 2006Pendá s et al., 2012) have been performed for three approximant structures of LaTe 1.82(1) in order to provide additional information on the bonding situation in the Te layers, especially regarding the (presumably disordered) Te 4 and Te 8 entities. As these calculations require three-dimensional commensurate structure models as bases, a suitable commensurate orthorhombic B-centred 4 Â 3 Â 2 supercell of the basic ZrSSi-type structure was chosen by approximating the q vector components and by 1 4 and 1 3 , respectively. The respective three-dimensional space groups and the atomic positions were derived by the JANA2006 software package (Petříček et al., 2014) by enabling the commensurate option, after the final refinement of the modulated structure. According to the previously reported structures of RESe 1.875-compounds (Doert, Dashjav et al., 2007;Stö we, 2001), this cell was transformed into an A-centred setting for a better comparison, resulting in a 3 Â 4 Â 2 supercell with unit-cell dimensions of a = 13.4859 (4), b = 17.9812 (4) and c = 18.3446 (8) Å . As the highest possible symmetry, space group Amm2 (No. 38), the space group of the RE 8 Se 15-compounds, was chosen for one approximant. The respective Amm2 structure model exhibits bent Te 3 units in the Te 8 ring, as well as a Te 4 square, which cannot be resolved due to the symmetry restrictions in this space group (Fig. S6 in the supporting information). A second model has been established in the space group A2 (No. 5), i.e. removing the two perpendicular mirror planes. This space group has also been used to describe the disorder in the structures of the compounds RE 8 S 15-. Here, only Te 2 2À anions with alternating short (bonding) and longer (nonbonding) distances are considered as building units of the Te 8 rings (Fig. S7 in the supporting information), enabling a direct comparison between the bent X 3 fragments in Amm2, and the X 2 2À patterns known from different REX 1.9 and RE 8 X 15-structures (cf. above). A third model in the space group P1 (No. 1) was developed starting from the previous model in A2 to lift the symmetry restrictions completely. The disorder of the apparent Te 4 unit can then be resolved by assuming two t-plots of (a) the occupation and (b) the distances shown for LaTe 1.82(1) .

Figure 8
Section of the modulated Te layer, with a cut-off occupancy at 0.5. Blackframed squares emphasize the voids in the layer. Solid lines are drawn from 2.801 to 2.981 Å and dashed lines are drawn for distances between 2.984 to 3.282 Å .
vacancies and a single Te 2 2À anion (Fig. S8 in the supporting information). Bear in mind that energetic comparisons are only possible between models with the same number of atoms. This is the case for the models in Amm2 and A2, but not for P1, due to the additional vacancies when taking the occupational disorder of the Te 4 square into account. This means that an identification of the favoured structure is not possible based on the computed net energies only.
The calculated band gaps for all models are finite, but small, e.g. 0.04 eV for the model in A2, so that semiconducting electronic properties are expected (see below). The corresponding stoichiometric LaTe 2 was reported as metallic (Stö we, 2000a).
Regarding the large Te 8 entities, the (disordered) structure model in Amm2 shows a lower energy than the corresponding (ordered) model in A2 (ÁE = 0.16 eV). The Amm2 structure would imply the existence of bent Te 3 entities with bond angles of about 90.0 (1) in the planar Te layer, as mentioned before. Angular Te 3 2À anions are well known, e.g. from the binary dialkali metal tritellurides A 2 Te 3 with A = K, Rb or Cs (Eisenmann & Schä fer, 1978;Bö ttcher, 1980) and have Te-Te distances of about 2.80 Å , but significantly larger bond angles of about 100 . These Te 3 2À anions are, however, more or less isolated in the structures and no interactions amongst them or with other anionic fragments are expected. Bent Te 3 entities with Te-Te-Te angles close to 90 were described as parts of the anionic substructure in disordered polytellurides like KRE 3 Te 8 (Stö we et al., 2003;Patschke et al., 1998) and RbUSb 0.33 Te 6 (Choi & Kanatzidis, 2001), and in the modulated structures of K 1/3 Ba 2/3 AgTe 2 (Gourdon et al., 2000), LnTe 3 (Malliakas et al., 2005) and RESeTe 2 (Fokwa et al., 2002;Fokwa Tsinde & Doert, 2005), for example.
Orthoslices of the ELI-D within the [Te] layers of the Amm2 and the P1 approximant are shown in Fig. 9. The isolines of both ELI-D images within the [Te] plane discriminates most of the observed Te atoms in three groups: isolated Te 2À , dinuclear Te 2 2À and bent trinuclear Te 3 2À anions. The ELI-D in the P1 model suggest a slightly more pronounced tendency to form Te 2 2À dumbbells as main polynuclear building units, in accordance with the reported structures of rare earth metal sulfides and selenides (Doert & Mü ller, 2016) and with theoretical considerations for the rare earth metal selenides (Lee & Foran, 1994). As discussed above, these entities are expected to represent the dominant bonding interactions in the planar layer, but the local bonding situation and the stability of the corresponding fragment are also influenced by interactions with other telluride anions in the [Te] layers, as well as by the surrounding La atoms in the layers below and above. Indeed, substantial interactions between these small anionic fragments in the [Te] layer have to be considered based on relatively high isovalues of the ELI-D between the dominating species in all models (Fig. 9). For nonbonding or antibonding interactions, deep valleys (depicted in blue) would be expected, like, for example, the dark-blue regions between strongly localized lone-pair regions in P1.
The ELI-D slices in Fig. 9 show some additional interesting features. Significant localized lone-pair regions are found for those Te atoms located directly adjacent to vacancies. This may be taken as evidence for the anionic character of the [Te] layers. The respective lone pairs are localized in the structural voids with no hint of bonding interactions between Te fragments encasing the voids. The additional vacancies of the P1  model (Fig. 9b) seem to be used to accommodate the lone pairs of different anionic Te fragments, again supporting the ionic description of the [Te] layer and in accordance with the calculated band gap and the measured semiconducting properties of LaTe 1.81 (2) (see below). Note, that the evaluated approximant structures indicate compositions of about LaTe 1.95 (Amm2 and A2) and LaTe 1.875 (P1), i.e. a higher tellurium content as compared to the actual composition LaTe 1.82(1) . Thus, additional vacancies would be necessary to get a more realistic image of the Te substructure. The bonding features between different constituents should nevertheless be comparable.

Electrical resistance of LaTe 1.82(1)
The temperature-dependent electrical resistance of LaTe 1.82(1) has been recorded by a four-point measurement between 7 and 345 K. The observed temperature dependence of the resistance of LaTe 1.82(1) is characteristic for a semiconductor (Fig. 10). The band gap, E g , can be estimated from the highest temperature values using a fit of the form = 0 exp(E g / 2k B T), where k B is the Boltzmann constant and T is the absolute temperature. The estimated E g value is 0.17 eV for LaTe 1.82(1) , which is slightly larger than the calculated value for the model in A2 (cf. above). However, comparable compounds like NdTe 1.89 (1) , GdTe 1.8 and SmTe 1.84 show similar band gaps of 0.14 (Stö we, 2001), 0.19 (Poddig et al., 2018) and 0.04 eV (Park et al., 1998), respectively, in contrast to LaTe 2 , which was reported to be metallic (Stö we, 2000a).

Conclusions
The modulated structure of the rare earth metal polytelluride LaTe 1.82(1) has been solved and refined using the superspace approach. The diffraction pattern evidences that the tetragonal symmetry of the average structure is not preserved in the modulation. Two different models evaluated in superspace groups Pmmn(,, 1 2 )000(À,, 1 2 )000 (No. 59.2.51.39) and Pm2 1 n(,, 1 2 )000(À,, 1 2 )000 (No. 31.2.51.35) show only slightly different results, suggesting that the highest possible superspace group Pmmn(,, 1 2 )000(À,, 1 2 )000 should describe the structure accordingly. In the regime of the different REX 2compounds, LaTe 1.82(1) may be best described as a depleted REX 1.9 or REX 1.875 structure. For the latter two structure types, it is possible to accommodate the respective anionic vacancies structurally isolated, i.e. separated between different (poly)telluride anions and in a commensurate superstructure. In the title compound, 18% of the Te2 positions are unoccupied, which leads to two obvious consequences: a commensurate ordering of vacancies and remaining anions is not possible anymore, and a considerable number of adjacent anion defects occur. In other words, LaTe 1.82(1) exhibits a higher propensity for missing Te 2 2À dianions. This description deviates significantly from the structures described for RETe 1.8 (RE = Sm, Gd-Dy; Ijjaali & Ibers, 2006;Wu et al., 2002;Gulay et al., 2007;Poddig et al., 2018). However, this different structure fits well with the overall trend for the rare earth metal tellurides RETe 2-, where different structures have been observed for a similar composition, as pointed out for the stoichiometric RETe 2 (RE = La, Ce or Pr) compounds. Quantum mechanical calculations based on DFT with subsequent ELI-D-based bonding analysis for the ionic Te layer reveal Te 2 2À units as dominant species, however, with significant long-range interactions amongst them. Temperaturedependent resistance measurements suggest a semiconducting behaviour with a band gap of about 0.17 eV, which is in good agreement with comparable rare earth metal compounds.  (Dolomanov et al., 2009) and DIAMOND (Brandenburg, 2019). Software used to prepare material for publication: OLEX2 (Dolomanov et al., 2009)