Zinc-lead ordering in equiatomic rare earth plumbides REZnPb (RE=La–Nd and Sm–Tb)

1 Introduction

Of the rare earth (RE)-transition metal (T)-tetrel (tr) systems [1], [2], [3], [4], [5], [6], [7], [8], [9], those with lead have only scarcely been investigated. Although, meanwhile more than 240 RE_xT_yPb_z plumbides are known [10], [11], [12] only few isothermal sections have completely been studied with respect to phase formation. Data have been published for the RE-Ni-Pb systems with RE=Y, La, Ce, Sm, Gd and Dy [13], [14], [15], [16], [17], [18], the RE-Cu-Pb systems with RE=Y, La, Ce, Nd, Sm, Gd and Dy [16], [17], [19], La-Zn-Pb and Tb-Zn-Pb [20].

The zinc containing systems comprise so far only 19 compounds, i.e. the series of zinc-rich phases RE₇Zn₂₁Pb₂ [21] und RE₂Zn₅Pb [22] both with RE=La, Ce, Pr, and Nd that both contain isolated lead atoms, La₅ZnPb₃ with Hf₅CuSn₃ type [23], the Cu₃Au type phase LaZnPb₂ [20], the solid solutions La₅Zn_1.6Pb_1.4 [20] and La₅Zn_0.4Pb_2.6 [24] which are derived from the Mo₅SiB₂ and Nb₅Sn₂Si types, LaZn_1.78Pb_0.22 with a disordered AlB₂ type [20] and the zinc-poor phase ~Tb₁₀ZnPb₉ with a so far unknown structure [20].

In the present contribution we focus on the equiatomic plumbides REZnPb. The large and famous family of equiatomic RETtr tetrelides has intensively been studied since these compounds are interesting model systems for detailed investigations of the various magnetic ground states of the respective rare earth cation [25], [26]. For the REZnPb series, so far, structural data have only been reported for LaZnPb [20], CeZnPb [27], NdZnPb [28], EuZnPb [29], and YbZnPb [29]. While the CeZnPb structure was refined from single crystal X-ray diffractometer data, the remaining plumbides were characterized on the basis of X-ray powder data. The YPtAs and LiGaGe types were correctly assigned to LaZnPb [20], respectively YbZnPb [29], while NdZnPb [28] and EuZnPb [29] were described with the CaIn₂, respectively KHg₂ types, with Zn/Pb statistics. Keeping the substantially different chemical potentials of lead and zinc in mind, complete Zn/Pb disorder is questionable. Herein we present the synthesis of the complete series of REZnPb plumbides and report on the Zn/Pb ordering within the two-, respectively three-dimensional [ZnPb] substructures.

2 Experimental

3 Crystal chemistry

The present study focused on the completion of the REZnPb series. Our phase analytical studies showed that these plumbides form for RE=La–Nd and Sm–Tb. The course of the cell volume per formula unit is presented in Fig. 1 along with the literature data of the series REZnSi, REZnGe and REZnSn [10]. This plot shows four relevant features: (i) the cell volumes in the four series decrease with increasing atomic number as expected from the lanthanide contraction, (ii) in the europium compounds the RE element is divalent giving rise to a significant positive deviation from the smooth curve (the same holds true for YbZnGe and YbZnSn), (iii) the volumes of the yttrium compounds are slightly smaller than those of the terbium compounds (for the REZnPb series no representative with yttrium and the smaller rare earth elements has been observed), and (iv) the volumes increase from the REZnSi to the REZnPb series, a consequence of the increase of the covalent radius of the tetrel: Si (117 pm), Ge (122 pm), Sn (140 pm) and Pb (154 pm) [30].

Fig. 1:

Course of the cell volume per formula unit for the series of REZnSi, REZnGe, REZnSn, and REZnPb tetrelides. Literature data were taken from the Pearson data base [10].

The present investigation focused on the existence range of the REZnPb plumbides as well as on the Zn/Pb ordering. Our X-ray powder and single crystal data clearly show that all of these plumbides are fully ordered (in contrast to the statistical descriptions for NdZnPb [28] and EuZnPb [29] based on powder diffraction data). In the following crystal chemical discussion we start with the hexagonal YPtAs type [35] phases and refer to NdZnPb when we quote interatomic distances. The unit cell of NdZnPb is presented in Fig. 2. The zinc and lead atoms form ordered Zn₃Pb₃ hexagons that show a significant degree of puckering. The Zn–Pb distances of 277 pm are close to the sum of the covalent radii of 279 pm for Zn+Pb [30], indicating covalent Zn–Pb bonding within these layers. The layers of Zn₃Pb₃ hexagons show a stacking sequence AA′BB′. The layers A and A′ as well as B and B′ are related by the mirror planes perpendicular to the c axis at z=1/4 and z=3/4 (an equivalent description relates the layers through the inversion centres of space group P6₃/mmc). The layers A and B as well as A′ and B′ are related by the 6₃ screw axis. The NdZnPb structure is reminiscent of the AlB₂ type structure. Indeed, the prototype YPtAs is a superstructure of the aristotype AlB₂ and the underlying group-subgroup relationship is discussed in review articles [36], [37].

Fig. 2:

The crystal structure of NdZnPb. The puckered Zn₃Pb₃ hexagons and their stacking sequence are emphasized. Displacement ellipsoids of the zinc and lead atoms are drawn at 90% probability.

The zinc atoms within the Zn₃Pb₃ network show a slight anisotropy, and this is also the case for PrZnPb and the previously studied plumbide CeZnPb [27]. The U₃₃ displacement parameter is about two times larger than the U₁₁ parameter. The zinc atoms of adjacent layers show a shorter Zn–Zn distance of 296 pm, slightly longer than the Zn–Zn distances (6×266 and 6×291 pm) in hcp zinc [38]. Thus, the formation of weak Zn–Zn bonding is a driving force for the puckering of the Zn₃Pb₃ layers. Nevertheless we need to discuss this feature in more detail. The puckering of the layers and the interlayer Zn–Zn bonding have been compared for the series CeZnGe (373 pm Zn–Zn)→CeZnSn (323 pm Zn–Zn)→CeZnPb (305 pm Zn–Zn) [27]. On going from the germanide to the plumbide one observes increasing puckering paralleled by decreasing Zn–Zn distances. The even smaller value in NdZnPb is a consequence of the lanthanide contraction.

The different orientation of the puckered Zn₃Pb₃ hexagons leads to drastic differences in the coordination of the two crystallographically independent neodymium sites. The Nd1 atoms have six closest lead neighbours (324 pm) and six further Nd1–Zn contacts (374 pm) while the Nd2 atoms have six closer contacts to zinc (304 pm) and much longer Nd2–Pb distances of 345 pm. The different hybridization of the two crystallographic rare earth sites substantially influences the magnetic ground state as demonstrated for CeZnPb [27].

Next we turn to the valence electron count of the REZnPb plumbides. The trivalent rare earth elements and divalent zinc supply five valence electrons but plumbide formation can only accommodate four electrons, leading to a formulation RE³⁺Zn²⁺Pb⁴⁻·e⁻. The excess electron can either fill the conduction band or allow metal-metal bonding (i.e. Zn–Zn in the present case). Keeping the comparison of CeZnGe, CeZnSn and CeZnPb in mind, notable Zn–Zn contacts only occur in the plumbide.

This peculiar behaviour is directly associated with the valence electron count (VEC) of the YPtAs type phases. The series RENiP, RENiAs and REPtAs have VEC=18 while the zinc series REZnGe, REZnSn and REZnPb [10] and the antimonides REAuSb [39] have VEC=19. Especially the antimonide series shows pronounced Au–Au interlayer bonding with 298 pm Au–Au in NdAuSb and this dimer formation is supported by the crystal orbital Hamilton population analyses.

The enhanced electron count of the zinc series leads to a facile hydride formation, exemplarily shown for REZnSnH_1.5 (RE=Ce, Pr, Nd) [40], [41], capturing the excess electron. Hydrogen incorporation leads to a flattening of the Zn₃Sn₃ hexagons along with drastic changes in the magnetic properties. To give an example, the Curie temperature increases from 4.8 (CeZnSn) to 7.3 K (CeZnSnH_1.5) [40].

The YPtAs type is also formed for a variety of compounds with alkaline earth cations as well as with divalent europium and ytterbium: CaGaGe, CaGaSn, SrGaGe, SrGaSn, BaGaGe, EuGaGe, EuGaSn, YbGaGe and YbGaSn [10]. These tetrelides are the main group analogues to the transition metal compounds discussed above and we deal with VEC=9. The electron-precise VEC=8 compound is the Zintl phase LiGaGe [42] where the Ga⁻ and Ge⁰ entities build up a tetrahedral network with wurtzite type topology. An increase of the VEC through the divalent cations leads to a switch of the structure type to YPtAs, and the puckered [GaGe]²⁻, respectively [GaSn]²⁻, layers show a tendency to Ga–Ga contacts with distances of 300 pm in YbGaSn [43], 318 pm in EuGaSn [44] and 330 pm in SrGaSn [45], [46]. These Ga–Ga distances are all longer than in gallium metal (1×244+6×270–279 pm Ga–Ga) [38]. Furthermore, the Zintl-related description seems to be too superficial. The bonding situation is more sophisticated since detailed electronic structure calculations for EuGaSn [44] revealed essentially nonbonding Ga–Ga contacts.

Finally we turn to the Zintl phase EuZnPb. This plumbide was originally described with a KHg₂ type structure (space group Imma) with Zn/Pb statistics [29]. Since the lattice parameters determined by Merlo et al. [29] compare well with our data, both samples apparently have the same composition. A solid solution EuZn_1±xPb_1±x towards higher zinc or lead content would lead to different cell parameters. In Fig. 3 we present the X-ray powder pattern of our EuZnPb sample along with a simulation. The latter was performed with the EuZnPb lattice parameters and the atomic parameters of TiNiSi type [47] EuZnSn [48], space group Pnma. We clearly observe three stronger superstructure reflections 111, 102 and 311 which violate the body-centered lattice. The intensities of the calculated pattern perfectly match the experimental values and we can thus assume full Zn/Pb ordering, i.e. the TiNiSi type structure for EuZnPb. The sample contained a small amount of residual lead as impurity phase (marked by a green arrow within the powder pattern). The crystal chemistry of the europium-containing TiNiSi representatives has been discussed in detail and we refer to these reviews [36], [37], [49] for further reading.

Fig. 3:

Experimental and simulated X-ray powder pattern (CuKα₁ radiation) of EuZnPb. The three strongest reflections that violate the extinction conditions of a body-centered lattice (and thus manifest the Zn/Pb ordering of the TiNiSi type) are marked in magenta. The sample contains a small amount of residual lead. The 200 reflection is marked in green. The 111 reflection of lead overlaps with the triple around 2θ=31°.