Equiatomic cerium intermetallics CeXX′ with two p elements

3.1.1 CeXX′ phases with α-ThSi₂-type structure

Most of the equiatomic CeXX′ compound crystallize with the tetragonal α-ThSi₂-type structure [43], space group I4₁/amd. As an example we present the CeGaSi structure [37] in Fig. 1. The gallium and silicon atoms statistically occupy the 8e silicon site of the α-ThSi₂ type and build up the three-dimensional network of three-connected atoms with Ga/Si–Ga/Si distances of 233 and 246 pm. The latter are compatible with the sum of the covalent radii [18] of 242 pm for Ga + Si. Within the [GaSi] network one observes parallel zig-zag chains that alternately run in x and y direction. Due to the tetragonal distortion, the bond angles within the network (118.4 and 120.8°) deviate slightly from the ideal value of 120°.

Fig. 1:

The crystal structures of CeGaSi and CeAlGa. Cerium and mixed occupied Ga/Si (Al/Ga) positions are drawn as light grey and magenta circles, respectively. The [GaSi] and [AlGa] networks are emphasized.

The near-neighbor coordination of the cerium atoms in CeGaSi is shown in Fig. 2. Each cerium atom has twelve nearest Ga/Si neighbors. The coordination geometry can be considered as two parallel distorted pentagons which are condensed by two further Ga/Si atoms. Additionally each cerium atom has eight cerium neighbors at 417 and 423 pm. These Ce–Ce distances are well above the Hill limit (340 pm) [44] for f-electron localization. This is consistent with the magnetic data discussed below. The crystal chemical description given for CeGaSi is also adequate for the isotypic ternaries listed in Table 1.

Fig. 2:

Coordination of the cerium atoms in the structures of CeAlGa and CeGaSi. Cerium and Al/Ga (Ga/Si) positions are drawn as light grey and magenta circles, respectively. Site symmetries and relevant Ce–Ce distances are indicated.

At this point arises the question on a possible ordering of the X and X′ atoms, especially if they are different in size and electron configuration. The α-ThSi₂ structure allows for a 1:1 ordering on the silicon site. This coloring pattern [45] is realized for the ternary silicide LaPtSi [46] (Fig. 3). The platinum-silicon ordering leads to a loss of the center of inversion. The space group symmetry is reduced via a translationengleiche transition of index 2 (t2) from I4₁/amd to I4₁md. The corresponding group subgroup scheme in the Bärnighausen formalism [47–50] is shown in Fig. 4. Although this symmetry reduction allows full ordering, even compounds with atoms of diffent chemical potential and size reveal residual disorder. An example is the structure refinement of CePt_0.97(1)Si_1.03(1) [51] which showed a small degree of mixing on both 4a sites.

Fig. 3:

The crystal structure of LaPtSi, space group I4₁md. Lanthanum, platinum, and silicon atoms are drawn as light grey, blue, and magenta circles, respectively. The three-dimensional [PtSi] network is emphasized.

Fig. 4:

Group-subgroup scheme in the Bärnighausen formalism [47–50] for α-ThSi₂, GdSi₂ and LaPtSi. The indices for the translationengleiche (t) symmetry reductions, the unit cell transformations and the evolution of the atomic coordinates are given.

The many tetragonal CeXX′ compounds described herein all contain the weak scatterers aluminum, gallium, silicon, and germanium which all have comparable covalent radii. Since the symmetry reduction is of the translationengleiche type, the ordering of the X and X′ atoms expresses itself only in small changes of the subcell intensities and this is hardly visible in the X-ray powder patterns. The similarity in size and electronegativity also explains the formation of extended solid solutions for the tetragonal CeXX′ phases.

A second kind of ordering is possible through an orthorhombic distortion which has first been observed for the gadolinium silicide GdSi₂ [52]. The space group symmetry is reduced from I4₁/amd to Imma (Fig. 4) and the ordering of the X and X′ atoms is possible on two crystallographically independent 4e sites. This distortion has so far only been reported for CeSiGe [34]. The electronic reasons for this kind of distortion are not yet known in detail.

Assuming trivalent cerium (see the magnetic properties discussed below), the valence electron concentration (VEC) for the fully ordered CeXX′ phases ranges from 8 to 11. Those with the α-ThSi₂ or GdSi₂ structure have 10 and 11. CeGaSi, CeAlSi, CeAlGe, and CeGaGe (all with VEC 10) can be described as electron precise Zintl phases with three-bonded Al^2–, Ga^2–, Si^–, and Ge^– which are isoelectronic with phosphorus and arsenic. This electronic situation is similar to that of LaAlGe [53–55] which shows semimetal behavior (the DOS tends to zero at the Fermi level). The corresponding polyanionic networks show three two-electron two-center bonds with almost equal bond lengths. Within the solid solutions, the Fermi level is either lowered (higher content of the group III element, e.g. CeAl_1.5Si_0.5) or increased (higher content of the group IV element, e.g. CeSiGe), tending to higher density of states and consequently an increase of the metallic character of the sample. This tendency is similar for the pair LaAlGe/La₂LiAlGe₂ [55].

3.1.2 CeXX′ phases with AlB₂-type structure

The second group of CeXX′ phases crystallizes with the AlB₂-type structure, space group P6/mmm. The structure of CeAlGa is shown as an example in Fig. 1. All X-ray powder diffraction experiments revealed a statistical distribution of the group III and group IV elements on the honeycomb network. The near neighbor coordination of the cerium atoms in the α-ThSi₂ and AlB₂ type is compared in Fig. 2. In both structure types the cerium atoms have twelve p-element neighbors, however, in a different arrangement: (i) two planar hexagons in the AlB₂-type phases and (ii) two planar, distorted pentagons which are condensed via two p-element atoms in the α-ThSi₂-type phases. As a consequence of the different site symmetry, in both types one observes two sets of distances, e.g. 12 × 333 pm in CeAlGa as compared to 8 × 321 pm + 4 × 322 pm for CeGaSi. Each cerium atom has eight cerium neighbors, 6 + 2 in CeAlGa and 4 + 4 in CeGaSi, again a consequence of the change in site symmetry. The p-element substructures are both three-connected nets with different conjugations. Detailed studies of chemical bonding were performed by Zheng and Hoffmann [56]. They showed that filling of the π* band with more than 4.5 electrons per p-element atom leads to stabilization of the α-ThSi₂ as compared to the AlB₂ type.

The arguments for a p-element ordering also hold for the AlB₂-type phases. The differences in the chemical potential should result in a coloring of the honeycomb networks. The many AlB₂ superstructures have been discussed on the basis of group–subgroup schemes [45, 57]. The two possibilities for the phases discussed herein are shown in Fig. 5. The pure equiatomic phases can exhibit a 1:1 ordering. This leads to a lowering of the space group symmetry. Several samples within the solid solutions (Table 1) have compositions CeX_1.5X′_0.5. This allows a 3:1 ordering with X₆ rings that are condensed via the X′ atoms (Fig. 5). Although these two ordering patterns are possible, all phases have been described with the structure of the disordered aristotype.

Fig. 5:

The 1:1 and 3:1 ordering (coloring) variants of honeycomb networks.

Most CeXX′ phases show pronounced homogeneity ranges, which were studied completely for the Al-Si [58], Al-Ge [59], and Al–Ga [60] systems where the whole ternary phase diagrams were constructed as isothermal sections.

3.1.3 CeMgX phases

The third group of CeXX′ phases covers the magnesium-based compounds CeMgX with X = Ga, In, Tl, Sn, or Pb. The gallide, indide, and thallide crystallize with the ZrNiAl-type structure. As an example we present the CeMgGa structure in Fig. 6. The magnesium and gallium atoms build up a three-dimensional [MgGa]^δ– polyanionic network which consists of distorted Mg₃Ga₂ pentagons which are condensed via further gallium atoms. Within the polyanion each cerium atom is coordinated by two Mg₃Ga₂ pentagons and a bridging gallium atom. The coordination number with respect to the main group element atoms is 11 as compared to 12 in the AlB₂- and α-ThSi₂-type phases. The more electronegative gallium atoms are the nearest neighbors to cerium. Electronic structure calculations underline the strongly bonding Ce–Ga interactions [61, 62]. For chemical bonding in the indide and the thallide we can safely assume a rigid band model. Further crystal chemical details on ZrNiAl-type cerium intermetallics have been summarized in [1].

Fig. 6:

The crystal structures of CeMgSn, CeMgGa and CeMgPb. Cerium, magnesium and tin (gallium, lead) atoms are drawn as light gray, blue and magenta circles, respectively. The three-dimensional [MgSn] and [MgGa] networks are emphasized. The layers of edge-sharing Ce_4/4 tetrahedra and corner-sharing Mg_4/2Pb₂ octahedra are drawn for CeMgPb.

CeMgSn adopts the orthorhombic TiNiSi type. The magnesium and tin atoms both have distorted tetrahedral coordination within the three-dimensional [MgSn]^δ– polyanionic network (Fig. 6). The cerium atoms are coordinated by two strongly titled and othorhombically distorted Mg₃Sn₃ hexagons (290–304 pm Mg–Sn). The structural chemistry of CeMgSn very much resembles that of the isopointal CeTX phases [2]. As expected from the course of the electronegativities, the tin atoms are the next nearest neighbors to cerium (i.e. one observes the inverse coloring within the polyanionic network). In total, the cerium and magnesium atoms can deliver five valence electrons. A Sn^4– stannide anion however can only carry four charges. This simple electron counting readily points to a metallic character for CeMgSn with the surplus electron within the conduction band. Accordingly, electronic structure calculations [63] point to negatively charged tin, underlining the stannide nature. Overlap population analyses show the Ce–Sn interactions as the strongest ones in the CeMgSn structure, as expected from the course of the electronegativities.

The last compound in this series is the plumbide CeMgPb which crystallizes with the tetragonal CeScSi-type structure, space group I4/mmm. From a purely geometrical point of view one can describe the CeMgPb structure with two basic building units, i.e. layers of corner-sharing Mg_4/2Pb₂ octahedra that are separated by layers of edge-sharing Ce_4/4 tetrahedra (Fig. 6). As a consequence of the body-centered lattice, every other of these layers is shifted by a/2 + b/2 with respect to each other. Within the octahedral layer the magnesium square nets have Mg–Mg distances of 321 pm and the capping lead atoms are at 315 pm Mg–Pb. The cerium coordination is shown in Fig. 7. Each cerium atom has five nearest lead neighbors at Ce–Pb distances of 320 (1×) and 326 (4×) pm in form of a square pyramid. The first coordination sphere is in agreement with the course of the electronegativities. The square face of the pyramid is capped by a square of magnesium atoms in staggered conformation. Similar to CeMgSn, charge analyses [63] reveal plumbide character for CeMgPb and the Ce–Pb interactions as the strongest ones in the structure.

Fig. 7:

Coordination of the cerium atoms in CeMgPb. Cerium, magnesium and lead atoms are drawn as light grey, blue and magenta circles, respectively. Relevant interatomic distances are indicated.