Distorted Te nets in the modulated crystal structures of RETe1.94(1) (RE = La, Pr, Nd)

The two-dimensionally incommensurately modulated crystal structures of the compounds RETe1.94 (1) (RE = La, Pr, Nd) were investigated by single-crystal X-ray diffraction. The compounds crystallize in the tetragonal superspace group P4/n( 12)00( 12)00 (No. 85.2.58.2) with q1 = a*+ b*+12c* and q2 = a*+ b*+12c* and share a common motif of an alternating stacking of a puckered [RETe] layer and a planar [Te] layer. This basic structural motif is observed for all reported compounds with unusually large anisotropic displacement parameters in the planar [Te] layer. Taking the modulation into account, a distortion from this perfect square planar net is noted along with vacancies in the planar [Te] layer. The distortion leads to the formation of different discrete anions, like Te , Te2 2 and Te3 2 , similar to previously reported structures for REX2– compounds (RE = trivalent rare earth metal, X = S, Se, Te). The Te–Te distances in the modulated [Te] layer are found in a narrow range as compared to those in the corresponding sulfides and selenides.


Introduction
The crystal structures observed for the rare earth metal polychalcogenides REX 2-(RE = Y, La-Nd, Sm, Gd-Lu; X = S, Se, Te; 0 0.2) show a broad variety of different patterns, including conventional commensurate and incommensurately modulated superstructures based on a common basic unit cell. The basic unit cell features an alternating stacking of a [REX] layer and a [X] layer. This kind of motif is shared by a variety of matlockite-related structures (Nuss & Jansen, 2002;Nuss et al., 2006), where the ZrSSi structure is usually referred to as the common aristotype for the REX 2compounds. The ZrSSi structure features a puckered [ZrS] double layer, which is sandwiched by square planar layers of [Si]. The structure of the REX 2 compounds adopts the same puckered [REX] layer with a slightly different planar chalcogenide layer. As only trivalent RE 3+ cations and divalent X 2À anions are assumed to be present in the puckered layer, the chalcogen atoms of the planar layers carry a formal charge of À1 which leads to a distortion from the ideal square net by forming different polychalcogenide anions, most prominently X 2 2À anions. The phase width of the REX 2-compounds adds another parameter to the distortion in the planar [X] layer by introducing vacancies and forcing the layer to compensate the charge of the missing X atoms. This is usually achieved by forming a more or less isolated X 2anion for every vacancy along the X 2 2À anions, resulting in an average charge of [X] 1-À , as described for the CeSe 1.9 -type and the Gd 8 Se 15--type structures (Doert & Mü ller, 2016). However, ISSN 2052-5206 in contrast to the sulfides and selenides, where this rule of thumb is satisfied for all structures, a different scenario has been observed for the tellurides with a composition of RETe 1.8 (RE = Sm, Gd-Dy) (Ijjaali & Ibers, 2006;Poddig et al., 2018). Here, a larger polyanionic telluride fragment, an XeF 2 analogous Te 3 4À anion, compensates for a less dense [Te] layer (Poddig et al., 2018). Motivated by this unique situation, structure investigations of further deficient rare earth metal tellurides seem promising.
Aside from conventional commensurate superstructures of the basic ZrSSi unit cell, like CeSe 1.9 -or GdTe 1.8 -type structures, several incommensurately modulated structures have been reported, e.g. GdS 1.82 (Tamazyan et al., 2003), RESe 1.84 (1) (RE = La-Nd, Sm) (Graf & Doert, 2009;Doert et al., 2007), or DySe 1.84 (van der Lee et al., 1997). Interestingly, most of the listed compounds are described in superspace group P4/n( 1 2 )00(À 1 2 )00 (No. 85.2.58.2), though with different values for and , resulting in their unique structural features. These structures show a similar pattern of X 2À and X 2 2À anions along with some vacancies as observed for the commensurate superstructures of the sulfides and selenides. However, one recent report for LaTe 1.82 (1) describes an incommensurately modulated superstructure for the tellurides, featuring larger polyanionic Te m nÀ fragments along with isolated Te 2À and Te 2 2À anions (Poddig et al., 2020). The existence of incommensurately modulated structures for the tellurides is not surprising, when looking at the related RETe 3 compounds, which feature an additional planar [Te] layer. The structure observed for these compounds show a one-dimensional modulation, affecting the bonding situation in the planar [Te] layers. Here, mostly V-shaped Te 'trimers' and Nshaped 'tetramers' have been observed along with isolated Te 2À anions (Malliakas et al., 2005). Similar results were also reported for mixed RESeTe 2 (La-Nd, Sm) compounds, which again show a distortion from a perfect square [Te] net (Fokwa Tsinde & Doert, 2005).
These hints from literature gave reason to investigate some further Te-deficient compounds RETe 2-compounds in detail. We report in the following on the Te-deficient compounds of the composition RETe 1.94 (1) (RE = La, Pr, Nd), which highlights a significant difference to the corresponding sulfide and selenide systems where this composition is not documented.

Synthesis
All preparation steps were carried out in an argon (purity of 5.0; Praxair Deutschland GmbH, Dü sseldorf, Germany) filled glovebox (MBraun, Garching, Germany). Crystals were grown by flux reaction in an alkali halide flux. In a standard synthesis, 500 mg of a stoichiometric mixture of the rare earth metal (RE: 99.5%, MaTecK) and tellurium (Merck, > 99.9%, reduced in H 2 stream at 400 C) was thoroughly mixed with KI (1.5 g, AppliChem, p.a., dried at 200 C under vacuum prior to use) before placing the mixture in a glassy carbon crucible inside a quartz ampoule. The quartz container was flame sealed under dynamic vacuum (p 1 Â 10 À3 mbar) and the sample was heated with a ramp of 2 K min À1 to 1073 K and kept at this temperature for seven days. After this time, the ampoule was slowly cooled with a rate of 0.5 K min À1 to 673 K, followed by quick cooling to room temperature. The product was washed with deionized water to remove the alkali halide flux, before washing with ethanol and drying under vacuum. The obtained black crystals can be handled under atmospheric conditions, although we observed a slow degrading of the compounds. Therefore, the samples were stored under an argon atmosphere and the experiments were prepared and realized under atmospheric conditions.
A second approach to synthesize the rare earth metal tellurides is utilizing I 2 in a chemical transport reaction. In a standard synthesis, 500 mg of a stoichiometric mixture of the rare earth metal and tellurium were placed in a quartz tube and flame sealed under dynamic vacuum (p 1 Â 10 À3 mbar). The ampoule was slowly heated with a ramp of 2 K min À1 to 1173 K. The transport takes place in a gradient from 1173 K to 1073 K with I 2 (Roth, > 99.8%, purified by sublimating twice prior to use) as transporting agent. After seven days, the ampoule was cooled to room temperature.

Single crystal
Single crystal X-ray diffraction was performed with the twocircle diffractometer IPDS II (STOE & Cie, Darmstadt, Germany) equipped with an image plate detector using graphite-monochromated Mo K radiation ( = 0.71073 Å ) at 296 (1) K. The software package X-Area (STOE & Cie, 2009) was used for data collecting, determination and refinement of the lattice parameters as wells as the modulation wavevector components, data integration and correction for Lorentz and polarization factors. A numerical absorption correction based on refined crystal shapes has been performed again with the X-Area software package for the average structures, whereas the data of the (3+2)D modulated crystal structure has been corrected with the routine implemented in Jana2006 (Petříček et al., 2014). The average structures were solved using the dual space approach of the program package SHELXT (Sheldrick, 2015b). Structure refinement was performed with the program package SHELXL against F 2 including anisotropic displacement parameters for all atoms (Sheldrick, 2015a). The average crystal structures of the data sets of the (3+2)D modulated crystal structures were solved using the charge-flipping method of the program Superflip (Palatinus & Chapuis, 2007) implemented in the Jana2006 software and the subsequent refinement has been performed with the Jana2006 software (Petříček et al., 2014). Structure refinement was performed 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 3I/) and two harmonic waves have been used for the fit of the atomic modulation functions. The two different domains were integrated and corrected independently, as the absorption correction of a (3+2)D hklf5 file was unsatisfactory. The second domain was added to the refinement in Jana2006 as a separate reflection file. Structure images were created with DIAMOND (Brandenburg, 2019). Further details on the crystal structure investigations can be obtained from the Fachinformationszentrum Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: (+49)7247-808-666; e-mail: crysdata@fiz-karlsruhe.de), on quoting the depository numbers 2012376 (LaTe 1.94 (1) ), 2012379 (NdTe 1.93 (1) ), 2012380 (PrTe 1.94 (1) ).

Scanning electron microscopy and EDS
Scanning electron microscopy (SEM) was performed with a Hitachi SU8020 microscope with a triple detector system for secondary and low-energy backscattered electrons (U a = 5 kV). The composition of selected single crystals was determined by semi-quantitative energy-dispersive X-ray analysis (U a = 20 kV) with a silicon drift detector (SDD) X-Max N (Oxford).

Temperature-dependent electrical resistance
The electrical resistance of LaTe 1.94 (1) was measured between 2.5 and 360 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 silver conductive composite ACHESON 1415 (Plano GmbH) to establish the electrical contact between the crystal and the gold wires.

Results and discussion
Black, plate-like single crystals of LaTe 1.94 (1) , PrTe 1.94 (1) and NdTe 1.93 (1) were obtained by either alkali halide flux reactions or mineralization with I 2 as transporting agent and showed different advantages. The mineralization experiments yielded larger crystals compared to alkali halide flux reactions, which proved to be useful to grow crystals for a physical characterization. The crystals grown by molten alkali halide flux, on the other hand, were better suited for single-crystal diffraction experiments, as less intergrowth of several individuals has been observed. Side phases, e.g. compounds with a lower Te content like NdTe 1.89 (1) , can be avoided by controlling the ratio of the rare earth metal and tellurium. Special care has to be taken when performing the mineralization experiments, as the Te-richer RETe 3 compounds can be formed if the initial ratio of the rare earth metal and tellurium is not corrected for the amount of REI 3 formed due to the addition of I 2 (Poddig et al., 2018). Powder and single-crystal diffraction clearly indicate a tetragonal basic unit cell for all compounds with a ' 4.4 Å and c ' 9.1 Å , as also seen for LaTe 1.82 (1) (Poddig et al., 2020). The EDS analysis of different single crystals, give a ratio RE:Te of about 1:1.9 (Table 1), which was later on confirmed by the structure refinements.
Single crystal diffraction at ambient temperature revealed additional weak reflections in the hkn (n = 0, 1, 2 . . . ) layer and slightly stronger reflections in the hkn (n = AE0.5, AE1.5 . . . ) layer, with respect to the basic tetragonal unit cell. A similar situation has been observed for the recently reported compound LaTe 1.82 (1) , where additional reflections are noted in the hkn (n = AE0.5, AE1.5 . . . ) layers. However, unlike for LaTe 1.82 (1) , eight strong satellite reflections, alongside several weak reflections, are essentially present around one main reflection in the hkn.5 layers of the title compounds ( Fig. S1). Only half of the satellite reflections can be described with two q vectors, i.e. by a two-dimensional modulation, for the description of all other reflections an additional twinning phenomenon needs to be taken into account (Fig. 1). Considering two merohedral twin domains with Laue symmetry 4/m yields a fully indexable diffraction pattern, making an intergrowth compound unlikely (van Smaalen & Petříček, 1992). The symmetry reduction is necessary, as the modulation wavevector components and are different and, thus, not compatible with 4/mmm Laue symmetry but match the conditions for the Laue class 4/m. The modulated RESe 1.84 (1) (RE = La-Nd, Sm) compounds showed a similar twinning, although a comparable clear differentiation between the two domains from the diffraction images has not been reported (Graf & Doert, 2009;Doert et al., 2007).
Using the superspace approach, the modulation wavevectors q 1 and q 2 for indexing of the diffraction patterns of the compounds RETe 1.94 (1) (RE = La, Pr, Nd) are q 1 = a* + b* + 1 2 c* and q 2 = Àa* + b* + 1 2 c* with components , and given in Table 2     supports our assumption of a [3+2] dimensional superstructure (Fig. S1). As mentioned above, the observed satellite reflections are compatible with a fourfold rotational axis, which is shown in an idealized, schematic diffraction image in Fig. 1. In contrast to the similarly twinned modulated rare earth metal selenides RESe 1.84 (1) (RE = La-Nd, Sm) with nearly identical modulation wavevector components ' ' 0.293 (1) (Doert et al., 2007;Graf & Doert, 2009), and are clearly distinguishable in the case of the tellurides RETe 1.94 (1) (RE = La, Pr, Nd), resulting in two separate and distinguishable sets of satellite reflections.

Average crystal structure
As the diffraction patterns and, hence, the modulated structures of the three title compounds are very similar, the discussion of the structural data will be outlined on LaTe 1.94 (1) in detail. The main reflections of all compounds can be indexed with a basic tetragonal unit cell and the dimensions of the unit-cell parameters deviate slightly for each rare earth element as shown in Table 3. Structure solution and refinements have been performed in space group P4/nmm (No. 129) in accordance with the space group of the ZrSSi aristotype. Note that the general reflection condition observed (reflections hk0 only present if h + k = 2n) is also compatible with P4/n (No. 85), which is a t2 subgroup of P4/nmm. The refined average structure shows an alternating stacking of a puckered [LaTe] layer and a square planar [Te] layer. EDS results point towards a ratio La:Te of about 1:1.9 (Table 1), indicating a reduced site occupancy on one Te site. In accordance with previous results on other commensurate superstructures as e.g. CeTe 1.9 (Ijjaali & Ibers, 2006) and incommensurately modulated structures such as e.g. LaTe 1.82 (1) (Poddig et al., 2020) a reduced site occupancy should only be present in the planar Te layer. Hence, a freely refined site occupancy factor of Te2 converged with about 0.93 (1) as expected.
The average structure of LaTe 1.94 (1) is displayed in Fig. 2. Compared to the previously reported structure of LaTe 1.82 (1) (Poddig et al., 2020) and the compounds of the series RESe 1.84 (1) (RE = La-Nd, Sm) (Graf & Doert, 2009;Doert et al., 2007), the anisotropy of the atomic displacement parameters (ADPs) is less pronounced for the respective atoms of the title compounds, but hint towards similar effects of the modulation in the crystal structures. The elongated ADPs in the ab plane of Te2 point towards a displacement of Te inside the [Te] layer, forming different (poly)anions. The reduced site occupancy factor is a result of vacancies in the planar [Te] layer of the modulated structure. The average structure of LaTe 1.94 (1) shows a Te-Te distance of 3.1980 (4) Å , which is larger than the usual observed bond length for a Te 2 2À anion with about 2.80 Å (Bö ttcher et al., 1993). However, larger Te-Te distances are expected for the average structure, as similar distances of 3.1821 (4) Å have been observed for LaTe 1.82 (1) (Poddig et al., 2020). The ADPs of La1 and Te1 are only slightly elongated along the [001] direction, most probably as a reaction of the metal cation to the modulation in the [Te] layer. Due to the small amount of vacancies, this tendency is less pronounced as compared to LaTe 1.82 (1) or the RESe 1.84 (1) (RE = La-Nd, Sm) compounds. The coordination polyhedron around the La atom only is a nearly undistorted capped square antiprism formed by five Te atoms from the [LaTe] layers with distances of 4 Â 3.3121 (5) Å and 1 Â 3.303 (1) Å , and by four additional Te atoms from the planar layer with distances of 3.3643 (6) Å .

Modulated crystal structure
The development of a structural model was performed analogous to the procedure for LaTe 1.82 (1) reported recently (Poddig et al., 2020) by considering first group-subgroup relations starting from the highest possible three-dimensional space group P4/nmm (No. 129). The components of the two different q vectors do not meet the conditions of a superspace group in the high Laue class 4/mmm and enforce a symmetry reduction to 4/m or lower symmetry. A similar symmetry reduction has been reported for RESe 1.84 (1) (RE = La-Nd, Sm) (Graf & Doert, 2009;Doert et al., 2007), resulting in space group P4/n (No. 85) for the basic structure. In contrast to the reported selenides, the c axis has not been doubled for the tellurides to meet the conditions of an X-centred unit cell, where the main reflections in the hkn.5 layer are treated as systematically absent. Considering the modulation wavevec-  Table 3 Unit-cell parameters, Te2 occupation and refinement indicators of the RETe 1.94 (1) average structures.

Figure 2
Average structure of LaTe 1.94 (1) refined in P4/nmm. Ellipsoids are drawn with a probability of 99.9%.
tors and their components (see above) results in the superspace group P4/n( 1 2 )00(À 1 2 )00 (No. 85.2.58.2) (Stokes et al., 2011). As pointed out in the discussion of the diffraction image, twinning was taken into account, which is likely due to the t2 symmetry reduction. The twin law (010 100 001) has been introduced for all three structures, converging to a twin volume of about 44% for LaTe 1.94 (1) .
The atomic modulation functions (AMF) have been added stepwise to the refinement. The positional displacement of all atoms has been modelled first, before introducing the occupational modulation function for the Te2 atoms and finally adding modulation functions to the ADPs. For all parameters, two harmonic modulation functions were used. Introducing AMFs for the ADPs was especially crucial for modelling the Te2 atom in the [Te] layer to compensate for overshooting and truncation effects, which greatly reduced the residual electron density. Details on the refinement are given in Table 4.
The displacements of all atoms along a, b and c are displayed in Fig. 3 [see Fig. S4 for PrTe 1.94 (1) and NdTe 1.93 (1) ]. The most pronounced displacement in the [LaTe] layer is seen along the [001] direction, as already hinted at by the average structure. Additionally, this plot emphasizes the larger influence of the modulation on La1 as compared to Te1, which can best be seen along the c direction, where Te1 follows the movement of La1, however, with a smaller displacement. The different amounts of the displacements can also be seen in the corresponding F obs plots in Figs. S2 and S3, respectively. From a crystal-chemically point of view, this is not surprising, as La1 tries to maintain its coordination sphere which is partly fragmented by vacancies in the planar [Te] layer and the respective re-arrangement of the telluride anions. This is achieved by getting closer to the [Te] layer, which in return forces the Te1 atom to react to the displacement of La1. A different situation is observed for Te2 in the [Te] layer, where only a displacement in the ab plane is observed and the displacement along the [001] direction is negligible. Moreover, the comparison of the displacements with LaTe 1.82 (1) shows another interesting feature. The total displacement for LaTe 1.94 (1) , as shown in Figs. 3(a) and 3(b), is considerably smaller (roughly by a factor of two) than in LaTe 1.82 (1) . This can mainly be attributed to the higher Te content in the [Te] layer of the RETe 1.94 (1) compounds, resulting in less void space for their displacements, but also a reduced need for structural reorganization. For a fully occupied [Te] layer in LaTe 2 , a double-herringbone pattern of dinuclear Te 2 2À dianions was reported (Stö we, 2000a) with only small differences between bonding and nonbonding TeÁ Á ÁTe distances. Introducing even small amounts of vacancies results in the formation of charge-compensating Te 2À anions and, hence, changes the local environment of the remaining Te 2 2À anions while maintaining a more or less close packed [Te] layer. As more and more vacancies are introduced, this close packing of dinuclear anions falls apart, allowing for a higher degree of freedom and increases the displacement of the Te2 atoms with respect to the basic ZrSSi-  Table 4 Crystallographic data and refinement details on the compounds RETe 1.94 (1) . For all structures: space group P4/n( 1 2 )00(À 1 2 )00 (No. 85.2.58.2), modulation wavevectors q 1 = a*+b*+ 1 2 c*, q 2 = Àa*+b*+ 1 2 c*, Z = 2. All experiments carried out at 296 (1) K on a STOE IPDS II diffractometer with Mo K radiation ( = 0.71073 Å ). type structure. Going along with the increasing number of vacancies, different ordering patterns have been found, like the patterns in CeTe 1.9 , crystallizing in the CeSe 1.9 -type (Ijjaali & Ibers, 2006) Fig. 4(a)] with an average distance of 3.206 (2) Å . These distances match the observed distances for LaTe 2 quite well, where Te-Te distances between 2.988 (2) Å and 3.406 (2) Å are reported (Stö we, 2000a). As mentioned in the discussion of the average structure, these distances are quite large compared to isolated Te 2 2À anions, e.g. (Bö ttcher et al., 1993), although very common for the stoichiometric rare earth metal tellurides LaTe 2 , CeTe 2 and PrTe 2 (Stö we, 2000a,b,c).
The investigation of the different t-plots of Te2 showed two extreme values of u, respectively x5, at 0 and 0.5, which is best visualized in the F obs maps for Te2 (Fig. 5). At u = 0.5 the lowest electron density is observed, consistent with the lowest occupation probability of Te2. However, in contrast to the selenides RESe 1.84 (1) and LaTe 1.82 (1) , a real gap indicating zero occupation between two maxima in the F obs plots is not observed for any t and u or respectively x4 and x5. This, on the one hand reflects the higher chalcogen content of this compound but may also indicate an underlying, unresolved atomic disorder.
Using a cut-off value of about 0.825 for the occupation of the Te2 position as indicated in Fig. 4(b) and used in the F obs maps (Fig. 5), the Te2-Te2 distance plot [ Fig. 4(a), see Figs. S5 for PrTe 1.94 (1) and NdTe 1.93 (1) ] allows for an interpretation as isolated Te 2À anions. For u = 0.5, the largest Te2-Te2 distances can be observed with distances ranging from about 3.003 Å to 3.473 Å [ Fig. 4(a)], which could be interpreted as a region containing mainly isolated Te 2À anions. In the interval from 0.5 u 0.65, the observed distances spread again, indicating shorter, bonding interactions and larger, non-bonding interactions for the different Te2 atoms [ Fig. 4(a)]. Looking at the plot of the occupancy of Te2 against t reveals, that this is mainly a consequence of the rising Te content in the planar [Te] layer, forcing the Te atoms to get closer to each other.
3.3. Discussion of the modulated crystal structure of LaTe 1.94 (1) A representative section of the modulated crystal structure of LaTe 1.94 (1) is displayed in Fig. 6 and Fig. S6   for different RETe 2-compounds, like CeTe 2 , PrTe 2 and LaTe 1.82 (1) (Stö we, 2000b,c;Poddig et al., 2020). However, these Te 4 fragments are presumably the result of an unresolved disorder of two differently orientated Te 2 2À anions and two adjacent vacancies in the [Te] layer.
The observed bent Te 3 fragments are part of a larger Te 8 ring, emphasized in Fig. S6, as already reported for NdTe 1.89 (1) (Stö we, 2001) and LaTe 1.82 (1) . The ordering pattern of a Te 8 ring around a vacancy by four Te 2 2anions with alternating short and long distances is additionally observed. The latter resembles the pattern of the CeSe 1.9 structures very well. Because the title compounds are compositionally intermediate between the stoichiometric ditellurides RETe 2 and the RETe 1.9 phases, their structures may be rationalized as a combination of the double herringbone pattern of Te 2 2À anions observed in RETe 2 , and a CeSe 1.9 -type pattern, which shows a regular ordering of an eight-membered Te ring around a central vacancy plus an isolated Te 2À anion. A combination of these motifs is indeed visible in the modulated Te layer, where a double herringbone like distribution of the Te 2 2À anions is observed complemented by isolated Te 2À anions and a few Te 3 2À -shaped anions (Fig. S6). This motif seems to have its origin at an eight-membered Te ring, as displayed in Fig. 6(b).
As the reported RETe 1.9+ compounds show a comparably low amount of vacancies, their influence on the shape on the [Te] layer will be discussed with regard to the recently published tellurides and the analogous sulfides and selenides. Vacancy ordering is quite fundamental to these structures, as the chalcogenide layer of the commensurate superstructures of CeSe 1.9 -and Gd 8 Se 15 -type structures can be rationalized by vacancies, isolated X 2À anions and X 2 2À dianions (Doert & Mü ller, 2016). The tellurides show a more ambiguous behaviour compared to the sulfides and selenides, as e.g. GdTe 1.8type structures do not fit into this scheme and exhibit a less dense [Te] layer due to a larger polyanionic Te 3 4À fragment and no obvious vacancy in the chalcogenide layer (Poddig et al., 2018). The structure of LaTe 1.82 (1) , however, matches partly the motif observed for Gd 8 Se 15 -type structures as vacancies are situated within eight-membered Te rings. Furthermore, larger dumbbell-shaped vacancies dominate the motif in between the Te rings additionally to larger poly-anionic fragments. The higher Te content present in LaTe 1.94 (1) results in considerably fewer vacancies, which are mostly situated inside Te 8 rings, resembling quite well the motif observed for the sulfides and selenides. This observation of very similar structures and vacancy ordering for all three chalcogenides is only noticed for a low vacancy concentration as observed for e.g. CeTe 1.9 and NdTe 1.89 (1) . Although vacancies are found in a very similar environment for all three chalcogenides, the tellurides still show a distinct tendency to form larger anions, as e.g. Te 3 2À anions are found in NdTe 1.89 (1) and LaTe 1.94 (1) .

Electrical resistance of LaTe 1.94 (1)
The electrical resistance of LaTe 1.94 (1) has been measured as a function of the temperature between 2.5 and 360 K by a four-point measurement. As expected from previous reports on these compounds, the electrical resistance increases with decreasing temperature, indicating semiconducting behaviour. Estimating the band gap, E g , from the recorded data has been done by fitting the high-temperature region according to the Arrhenius-like equation = 0 exp(E g /2k B T), where k B is the    Boltzmann constant and T is the absolute temperature. The band gap of LaTe 1.94 (1), according to this fit, is 0.14 eV (Fig. 7), which is similar to the reported band gaps of NdTe 1.89 (1) (0.14 eV) (Stö we, 2001), LaTe 1.82 (1) (0.17 eV) (Poddig et al., 2020), GdTe 1.8 (0.19 eV) (Poddig et al., 2018) and SmTe 1.84 (0.04 eV) (Park et al., 1998). As expected, the band gap of LaTe 1.94 (1) is slightly smaller than the one reported for LaTe 1.82 (1) , but matches that of NdTe 1.89 (1) very well, hinting towards a more metallic behaviour with an increasing Te content in the RETe 2-series. The only metallic behaviour in this series has been reported for LaTe 2 (Stö we, 2000a).

Conclusion
The modulated crystal structures of the compounds RETe 1.94 (1) (RE = La, Pr, Nd) have been solved and refined in superspace group P4/n( 1 2 )00(À 1 2 )00 (No. 85.2.58.2) from single crystal data. Unlike the previously reported LaTe 1.82 (1) , the tetragonal symmetry is preserved for all compounds. The average crystal structure resembles the structure of the commonly shared aristotype, ZrSSi, with a reduced site occupancy of the Te2 atom to about 94% for LaTe 1.94 (1) . Taking the modulation into account, a displacement of both atoms in the [RETe] layer along the [001] direction and, apart from a similar displacive modulation in the ab plane, an occupational modulation is observed for the Te2 atoms in the planar [Te] layer. The puckered [RETe] double layer is less affected by the modulation, whereas the modulation leads to vacancies and the formation of different anionic Te fragments in the planar [Te] layer. As expected for a compound of this composition, many similarities with the well known REX 2 and REX 1.9 structures are observed, like eight-membered Te fragments, isolated Te 2À anions along with Te 2 2À anions and vacancies. In this sense, the new structures fit well into the series of rare earth metal polychalcogenides REX 2-.