Comment

Following the discovery of giant magnetocaloric effects in Gd₅Si₂Ge₂ in 1997 (Pecharsky & Gschneidner, 1997a), great effort has been devoted to the synthesis and study of the structures and physical properties of rare earth silicides and germanides with the Gd₅Si₄ or Sm₅Ge₄ structure types, and also of their intermediates (Kyunghan et al., 1997; Misra & Miller, 2008). In this paper, we report the syntheses and single-crystal structures of three compounds with the Sm₅Ge₄ structure type, namely Sm_3.97Li_1.03Ge₄, Nd_3.97Li_1.03Ge₄ and Gd_3.96Li_1.03Ge₄.

Many articles have already discussed the structural similarities and differences between the Gd₅Si₄ and Sm₅Ge₄ structures, which are isopointal but not isostructural (Pecharsky & Gschneidner, 1997b) (Fig. 1). Summarizing these findings briefly, we must point out that there are two pairs of Si-Si bonds in Gd₅Si₄ but only one type of Ge-Ge bond in Sm₅Ge₄ (Pecharsky & Gschneidner, 1997b). Furthermore, there are many factors, such as temperature, pressure and chemical make-up, which can cause one of the interslab bonds to form or cleave reversibly (Levin et al., 2002; Magen et al., 2003).

Our previous work on Mg substitutions in RE₅Ge₄ has already demonstrated that the structure is amenable to variations. For brevity, RE will denote a rare earth metal throughout this article. Note that RE³⁺ ions are replaced with Mg²⁺, which allows for structural changes that are also coupled with the magnetic properties of the resultant RE_5-xMg_xGe₄ materials (Tobash et al., 2009). Importantly, our study has also shown that Mg first replaces the rare earth metal at the 4c site. Mg also replaces some of the RE2 at site 8d, leading to the final formula RE_5-xMg_xGe₄ (x 2).

The `phase width' can be easily understood from the point of view of the Zintl-Klemm concept (Kauzlarich, 1996). In RE₅Ge₄ (Sm₅Ge₄ type), two of the Ge atoms are dimerized and two remain as isolated Ge atoms. The Ge dimer needs six electrons (three on each Ge) to satisfy the octet rule and the isolated Ge atom needs four electrons. Accordingly, the overall electron count for the RE₅Ge₄ structure will be (RE³⁺)₅(Ge^3-)₂(Ge^4-)₂(e^-). For RE₃Mg₂Ge₄, the total number of valence electrons contributed by the cations decreases, leading to a structural distortion that brings the isolated Ge atoms together to form an additional dimer. The electronic structure change here can be rationalized as (RE³⁺)₃(Mg²⁺)₂(Ge^3-)₄(e^-). The ideal electron count will be realised for the formula RE₂Mg₃Ge₄, but our studies have not shown evidence for extending the stoichiometry much beyond RE_5-xMg_xGe₄ (x 2) (Tobash et al., 2009). This suggests that metal-metal bonding and efficient packing are also critical for the stabilization of the phase, and the Zintl-Klemm concept is just a good starting point for consideration. Nonetheless, the ideas above can help to explain the fewer substitutions of RE³⁺ by Li⁺ cations, as will now be discussed.

Since Li⁺ is very similar to Mg²⁺ in terms of ionic size (Shannon, 1976), it is not surprising that the crystal chemistry observed when replacing the rare earth metal with Li mirrors the results obtained with Mg. The RE_5-xLi_xGe₄ structure (Gd₅Si₄ type) is the same as that of RE_5-xMg_xGe₄ and has been considered in detail elsewhere (Pavlyuk et al., 1990; Xie et al., 2008; Peter et al., 2012; Fornasini et al., 2012). It can be broken down into two simpler building units (Fig. 2). One is the framework made by the rare earth metals, which is a combination of trigonal prisms and parallelepipeds, with Ge atoms located at the centres of the trigonal prisms. The second building unit is the pentagonal ring (Fig. 2c) made by Li and Ge atoms (paired in the ac plane). The interatomic distances within the Ge1-Ge1(-x, -y, -z + 1) and Ge2-Ge3(x, y, z - 1) dumbbells fall in the range 2.633 (2)-2.528 (3) Å. There does not appear to be any correlation between the refined Ge-Ge contacts and the decreasing unit-cell volumes due to the lanthanide contraction. We also note that the Ge-Ge distances are slightly longer than the sum of the corresponding Pauling radii (Pauling, 1960), which suggests the Ge-Ge interactions are best regarded as covalent two-centre-two-electron bonds. Therefore, the electron count for the RE₄LiGe₄ structure can be represented as (RE³⁺)₄(Li⁺)(Ge^3-)₄(e^-). Such an electronic structure also accounts for the different homogeneity range of RE_5-xLi_xGe₄ compared with RE_5-xMg_xGe₄. For instance, if we apply the same electron count for RE₃Li₂Ge₄, we now have only 11 electrons from the cations, which are not sufficient to supply the electrons needed to form two pairs of Ge-Ge dimers (12 negative charges).

Li substitutions in RE₅Ge₄ were known before our work commenced, the first report being the example of Tm₄LiGe₄, which was characterized by Pavlyuk et al. (1990) on the basis of single-crystal X-ray diffraction data. The same paper also identifies the isotypic RE₄LiGe₄ (RE = Y, Gd, Er Lu) from powder X-ray diffraction data without discussing the possible homogeneity range. Very recently, Fornasini et al. (2012) reported the Nd₄LiGe₄ structure, also refined from single-crystal X-ray diffraction data, but they also did not comment on the small RE/Li disorder we have identified in our sample. The compound Yb₂Li_0.5Ge₂ (Yb₄LiGe₄) has been studied twice in the last four years, first by Xie et al. (2008) and then by Peter et al. (2012). Yb₄LiGe₄ was suggested to be a mixed-valent Yb²⁺/Yb³⁺ system, similar to Yb_5-xMg_xGe₄ (Tobash & Bobev, 2006), but again with no mention of the homogeneity range.

It should also be noted that we have chosen to discuss the present structures not as stoichiometric compounds RE₄LiGe₄, as done previously, but rather as RE_5-xLi_xGe₄. The deviation from the idealized formula RE₄LiGe₄ is very small indeed, making it not very conspicuous, but the following two signs of the narrow phase width cannot be ignored.

Firstly, powder patterns of the products of reactions with different amounts of lithium metal as a starting material reveal peak shifts, which indicate that the unit-cell volumes change as a function of the nominal composition. Unfortunately, these were not phase-pure materials and further structural analysis was severely hindered. Fornasini et al. (2012) also commented on the heterogeneity of the samples. Some of the common RE-Li-Ge phases identified in this process include RELiGe₂ (RE = La-Nd, Sm and Eu; Pavlyuk et al., 1986; Bobev et al., 2012), RE₂Li₂Ge₃ and RE₃Li₄Ge₄ (Pavlyuk et al., 1989; Guo, You & Bobev, 2012), and RE₇Li₈Ge₁₀ and RE₁₁Li₁₂Ge₁₆ (RE = La-Nd, Sm; Guo, You, Jung & Bobev, 2012). The fact that Pavlyuk et al. (1990) reported a smaller unit cell for their Gd₄LiGe₄ sample than ours is yet another indicator that the amount of Li in RE_5-xLi_xGe₄ can be varied within a certain range. The major difficulty in establishing the solubility limits arises from the fact that Li and the rare earth metals have very different melting points, so obtaining equilibrium conditions is nearly impossible. Since the studied crystals were chosen from reactions with an excess of Li, we may speculate that RE_5-xLi_xGe₄ (x 1) most likely represents the most Li-rich compositions that can be synthesized under the given conditions.

Secondly, when the occupancy factors of the Wyckoff sites 8d were freed to vary during trial refinements, for RE1 in all three cases the freed variable was always close to 100%, while the RE2 site consistently refined with 97% occupancy. A very similar observation was made with regard to the RE_5-xMg_xGe₄ (x 2) structure (Tobash et al., 2009), so we have assumed that Li can also partially substitute the RE2 atoms just like Mg does. The single-crystal X-ray data for the latter metal showed that the substitution effect was well pronounced and easy to identify, while the very light Li makes it hard to detect or characterize. However, the refinement of a mixed occupied RE2/Li2 site was found to be statistically significant according to the Hamilton test (Hamilton, 1965). Specifically, at a significance level of 0.005, for models A (RE_5-xLi_xGe₄) and B (RE₄LiGe₄), the hypothesis that the former is better than the latter can be verified based on R = 1.004 < R_B/R_A = 1.013, where R is the interpolated value at the given significance level.

All of the above confirms that the title compounds are better described as solid solutions RE_5-xLi_xGe₄ (x 1) with narrow homogeneity ranges, rather than stoichiometric compounds RE₄LiGe₄.

Figure 1 Side-by-side comparison of the Sm5Ge4 and Gd5Si4 structures (Pecharsky & Gschneidner, 1997b). The rare earth metals are shown as large spheres (green in the electronic version of the paper), Ge/Si atoms as light spheres (orange in the electronic version) and Li atoms as dark spheres (blue). The `interslab' dimers and broken dimers are outlined.

Figure 2 (a) A representation of the Sm5-xLixGe4 structure, viewed approximately down the [100] direction. The rare earth metals are shown as large spheres (green in the electronic version of the paper), Ge atoms as medium spheres (orange) and Li atoms as small spheres (blue). (b) A representation of the first building unit, comprising a trigonal prism (shaded; orange in the electronic version) and a parallelepiped (hollow framework of rare earth metals). (c) A view of the chain of vertex/edge-shared pentagonal rings built by Li atoms and Ge-Ge dimers.

Experimental

All starting materials were purchased from common chemical vendors [pure elements from Alfa or Aldrich (>99.9 wt%)] and stored and handled in an argon-filled glove-box to prevent their deterioration due to moisture and oxygen. All reactions were carried out by loading stoichiometric amounts of the respective elements into Nb containers, which were then sealed with an arc welder. Subsequently, the Nb containers were flame sealed in evacuated (ca 10^-5 Torr; 1 Torr = 133.322 Pa) fused silica jackets. The synthesis followed the conventional solid-state route through direct fusion, but the process was somewhat complicated due to the very high melting points of the rare earth metals. The general synthetic route was that the reactions were heated in a tube furnace to 1358 K at a rate of 200 K h^-1, kept there for 5 h and then cooled slowly to 573 K at a rate of 10 K h^-1. The title compounds were first identified as side products of reactions aimed at synthesizing NdLiGe₂ and SmLiGe₂. As mentioned in our previous work (Bobev et al., 2012), due to the high melting points of Nd (1300 K) and Sm (1315 K) it is necessary to increase the synthetic temperature. However, this also increases the possibility of Li leaking out of the Nb container, which would destroy the stoichiometric ratio and could lead to other phases. If Li were to leak outside the Nb tube and condense in the silica tube, it could be dangerous and the furnace should be stopped immediately.

Crystals were selected under an optical microscope and cut under oil to the desired small dimensions. They were then mounted on glass fibres and quickly placed under a cold nitrogen stream (ca 200 K) on the diffractometer.

The crystals diffracted strongly and an exposure time of 8-12 s per frame was sufficient. Refined parameters included the scale factor, extinction coefficients and atomic positions, with the corresponding anisotropic displacement parameters. Li had to be refined with an isotropic displacement parameter in the case of the Nd and Gd compounds, likely because of the inferior crystal quality compared with the Sm analogue. This is not without precedent for elements with such a low Z number in structures dominated by very heavy elements. The atomic positions were standardized using STRUCTURE TIDY (Gelato & Parthé, 1987) prior to the final refinement step.

Structure refinements using the coordinates from the parent Sm₅Ge₄ type did not converge and it was obvious that the RE3 site (site 4c) was occupied by a much lighter atom. Therefore, in the next least-squares refinement cycles, RE3 was assigned as Li1 and its occupancy factor was allowed to vary. This time the refinements converged, and the site-occupancy factor for Li1 was very close to the full value. In the next round of least-squares refinement, all atoms (except Li in the case of the Nd and Gd compounds) were refined with anisotropic displacement parameters (ADPs) and fixed occupancies. Refinements converged at much lower R values. Subsequent refinement with free RE and Ge site-occupancy factors (done for an individual site, while the remaining site-occupancy factors were kept fixed) proved that the RE2 sites in all three structures are slightly underoccupied (within 6-8). All remaining crystallographic sites proved to be fully occupied, with the corresponding deviations from full occupancy less than 2.

Since Li is too light when refined together with RE atoms at the RE2 sites, its occupancy factor was very small. The actual solubility limits were not investigated, as obtaining phase-pure samples was hindered by the very different melting points of Li and the rare earth metals. However, we note that such a stoichiometry breadth (and substitution pattern) is not unusual for germanide compounds with this structure type, as evidenced by studies of RE_5-xMg_xGe₄ (Tobash et al., 2009).

The highest residual density for the Sm compound is located 1.86 Å from Ge1 and the deepest hole is 1.84 Å from Ge2. For the Nd and Gd analogues, the peaks are close to Nd2 (1.9 Å) and Gd1 (0.85 Å), while the holes are located near Nd1 (0.84 Å) and Ge2 (0.72 Å), respectively.

For all compounds, data collection: SMART (Bruker, 2002); cell refinement: SMART; data reduction: SAINT (Bruker, 2002); program(s) used to solve structure: SHELXS97 (Sheldrick, 2008b); program(s) used to refine structure: SHELXL97 (Sheldrick, 2008b); molecular graphics: SHELXTL (Sheldrick, 2008b); software used to prepare material for publication: SHELXTL.

Supplementary data for this paper are available from the IUCr electronic archives (Reference: FN3120 ). Services for accessing these data are described at the back of the journal.