Site-Preference among Three Anions in the Quaternary BaAl₄-Type Structure: Experimental and Computational Investigations for BaLi_1.09(1)In_0.91Ge₂

Experimental

Each element in the stoichiometric ratio of 1:2:2:2 for Ba:Li:In:Ge was loaded in an one end-sealed Nb-tubing inside an argon-filled glove box. The other end of Nb-tubing was sealed by arc-welding under a partial argon atmosphere, then the tubing was subsequently sealed in a fused-silica jacket under vacuum to avoid any contact with oxygen during the reaction at the elevated temperature. The mixture of reactants was initially heated up to 950 ℃ by 200 ℃/h, kept at the temperature for 5 h, then cooled down to 890 ℃ by 5 ℃/h.

After then, the reactants were naturally cooled down to room temperature by turning off the furnace. Block-shaped products with metallic luster were obtained. The products were air- and moisture-stable for at least one month.

Table 1.aR1 = Σ||Fo| − |Fc||/Σ|Fo|; wR2 = [Σ[w(Fo 2 − Fc 2]/Σ[w(Fo 2)2]]1/2, where w = 1/ [σ2Fo 2 + (A – P)2 + B – P], and P = (Fo 2 + 2Fc 2)/3; A and B – weight coefficients.

Single-crystal X-ray diffraction data was collected at room temperature using Bruker SMART APEX2 CCD-based diffractometer equipped with Mo Kα1 radiation (λ = 0.71073 Å). The selected crystal was mounted on a glass fiber, and data collection was carried out using the Bruker’s APEX2 software.26 The structure was solved by direct method and refined to full convergence by full matrix least-squares method on F2 using SHELXTL.27 During the initial stage of structure refinement, the apical-site (Wyckoff site 4e) was refined as a full occupation of Ge, whereas the basal-site (Wyckoff site 4d) was assigned by In with an electron deficiency of ca. 52%. Thus, we eventually allowed a mixedoccupation of Li with In at the 4d-site, and this lead to the final composition of BaLi1.09(1)In0.91Ge2. In the last stage of refinement, program STRUCTURE TIDY28 was exploited to standardize atomic positions. Important crystallographical data are displayed in Tables 1-3 and deposited with FIZ, Eggenstein-Leopoldshafen, Germany (Deposition No. CSD-426587).

Quantum theoretical calculations were conducted by TBLMTO method29 using the LMTO47 program.30 The program package employs the atomic sphere approximation (ASA) method, in which space is filled with overlapping Wigner- Seitz (WS) atomic spheres.31 The WS radii are as follows: Ba = 2.378 Å, Li = 1.655 Å, In = 1.655 Å, and Ge = 1.427 Å. The basis sets included 6s, 6p, 5d and 4f orbitals for Ba; 2s, 2p and 3d orbitals for Li; 5s, 5p, 5d and 4f orbitals for In; and 4s, 4p and 4d orbitals for Ge. The Ba 6p, Li 2p and 3d, In 5d and 4f, and Ge 4d orbitals were treated by the Löwdin downfolding technique.31 The k-space integration was conducted by the tetrahedron method32 using 262 irreducible k-points in the Brillouin zone.

 

Results and Discussion

BaLi1.09(1)In0.91Ge2 crystallized in the BaAl4-type (or the ternary ThCr2Si2-type) structure adopting the tetragonal space group I4/mmm with Z = 2 (Pearson code tI10).910 Detail crystallographic information including lattice parameters, atomic coordinates and selected bond distances are displayed in Tables 1-3. Since the BaAl4-structure type is one of the most prominent structure types observed in the binary MTr4 and ternary phases MTxTr4-x/MTxPn4-x (M = alkali-earth metals or rare-earth metals; T = transition metals; Tr = triels; and Pn = pnictogens) series,13-1521 detail discussions of the given crystal structure can be found elsewhere.1113 Therefore, we will provide a simple structural description, then pay more attention to the site-preference among three anionic elements within the 3D frameworks in this report.

Table 2.aUeq is defined as one third of the trace of the orthogonalized Uij tensor. bRefined as a statistical mixture of Li and In.

Table 3.aRefined as a statistical mixture of Li and In.

The overall crystal structure of BaLi1.09(1)In0.91Ge2 is shown in Figure 1(a). There exists three crystallographically independent atomic sites including one cationic and two different anionic sites. In particular, the local coordination environments for two anionic sites are clearly distinctive: 1) the basal-site (Wyckoff site 4d) is coordinated to four identical apical-sites forming a distorted tetrahedron (Figure 1(b)), whereas 2) the apical-site (Wyckoff site 4e) is surrounded by one apical- and four basal-sites forming a distorted square-pyramid (Figure 1(c)). These anionic sites eventually form the 3D polyanionic frameworks, which can be considered as stacks of Federov polyhedra3334 along all directions in space (Figure 1(d)). Relatively larger Ba atoms are situated at the center of each Fedorov polyhedron having the total coordination number of 18.

Interestingly, in the given structure type, three anionic elements display a distinctive site-preference over two available sites within the anionic frameworks. As can be seen in Figure 1, Ge atoms show an exclusive occupation for the 4e-site, whereas the mixed-occupation of Li and In (ca. 55% vs 45%) was observed at the 4d-site. This type of site-preference among three anionic elements in the 3D frameworks can be described as if two steps of consecutive substitutions, respectively, by Ge and Li occur for its parental binary phase BaIn4.25 Firstly, as Ge atoms having the larger electronegativity and the smaller size than In atoms (Pauling scale: Ge = 2.01 vs In = 1.63; and rGe = 1.23 Å vs rIn = 1.63 Å)3536 are introduced to the anionic frameworks in BaIn4, the site occupation between Ge an In seems to follow the sitepreference rules reported by Miller and Häussermann et al.: the more electronegative atom should prefer to occupy the 4e-site over the 4d-site.1113

Figure 1.(a) Crystal structure of BaLi1.09(1)In0.91Ge2 illustrated by a combination of ball-and-stick and polyhedral representations. (b) The local coordination environment around the Li/In mixed-site, (c) the Ge site, and (d) the Ba-site.

Figure 2.Four structure models of BaLiInGe2. The relative total electronic energy of each model (eV/cell) compared to the Model 1 is also shown. See text for further detail.

There have been numerous reported examples supporting this argument: EuMgxGa4–x (0 ≤ x ≤ 1.95),11 AEMg1.7(1)Ga2.3 (AE = Sr, Ba),13 BaAuIn3,18 AEMgxIn4–x (AE = Sr, 0.85 ≤ x ≤ 1.53; AE = Ba, 0 ≤ x ≤ 1.79)14 and REZnxAl4-x (RE = Yb, x = 1.65; RE = Nd, x = 2.3).17 In addition, Corbett et al. also proved that in the case like SrZnIn3, where only a small electronegativity difference existed between anionic elements, the geometric factor would play a major role to decide the preferred anionic sites.14

Based on these criteria, the site-occupation of Ge in the title compound is fully understandable. Secondly, if we apply the same criteria for the site-occupation of Li, it seems to be rational that Li atoms having the smallest electronegativity among three anions and the larger size than Ge but similar size to In (Pauling scale: Li = 0.98, rLi = 1.52 Å)3536 should prefer to occupy the 4d-site resulting in a mixed-occupation with In. Therefore, we can conclude that the site-preference among three anions reasonably follows the site-preference rules with respect to the electronic- and geometric-factors. Further analysis for electronic structures and chemical bonding within the polyanionic frameworks will be discussed in the subsequent section.

A series of quantum theoretical calculations have been conducted 1) to understand the observed site-preference among anionic elements from the electronic perspective, and 2) to investigate an overall electronic structure of the title compound. Initially, four structure models with various anionic arrangements were designed and exploited for calculations - Model 1: refined crystal structure, and Model 2, 3, 4: hypothetical model structures (Figure 2). After then, total electronic energy of each model was compared in order to find out energetically the most favorable structure, and the model with the lowest energy was further analyzed to interrogate its electronic structure based on DOS and COHP plots. TB-LMTO-ASA method29-31 was the method of our calculation choice. The ideal composition of BaLiInGe2 was adopted for the practical reason. In addition, to apply the given stoichiometric composition, a space group was lowered from I4/mmm (no. 139) to Imm2 (no. 44). Model 1 showed an atomic arrangement resembling that of the refined structure, in which the 4e-site was exclusively occupied by Ge, whereas the 4d-site was alternatively occupied by Li and In. On the other hand, Model 2 located Ge at the 4d-site exclusively, while the mixture of Li and In was situated at the 4e-site. Model 3 and 4 were designed based on the hypothesis what if Li was mixed with Ge either at the 4e-site or at the 4d-site, respectively.

Figure 3.DOS and COHP curves of Model 1. (a) Total DOS - solid line; partial DOS of Ba, In, Ge, and Li – gray, blue, orange, and green area, respectively. EF (solid line) is the energy reference at 0 eV, and the DOS value corresponding the refined composition is also marked with a dashed line. Four COHP curves representing various interatomic interactions are also shown in (b) and (c). The region with the “+” sign represents bonding interactions, whereas the region with the “-” sign represents antibonding interactions.

After a series of calculations, the total electronic energy comparison proved that Model 1 based on the refined crystal structure was energetically the most favorable structure (Figure 2). Thus, the quantum theoretical approach provided a consistent result to the experimental observation.

Total and partial DOS plots shown in Figure 3(a) were obtained using Model 1. Throughout the whole range of energy, a strong orbital mixing of components was observed. In particular, the valence region implying interatomic interactions among four elements can be divided into three sections. The region between -10.5 and -7 eV is mostly contributed by In 5s and Ge 4s orbitals with a small amounts of Li 2s orbital participation. In particular, the lower peak corresponds to the σ bonding, whereas the upper peak is related to σ* anti-bonding interactions among three components. The next region between -6 and -3.5 eV contains the major contributions from Ge 4pz and In 5pz orbitals. The last region from −3.5 eV up to the Fermi level (EF) also includes the largest contributions from Ge and In, but those are descended from 4px and 4py, and 5px and 5py orbitals, respectively, as well as some contributions from Li orbital. EF for the ideal composition BaLiInGe2 (corresponding to 14 ve-) and for the refined composition BaLi1.09(1)In0.91Ge2 (corresponding to 13.82 ve-) were found near the local DOS minimum (also known as pseudogap) indicating that the title compound having a given chemical composition is energetically stable with the BaAl4-type structure. Interestingly, the significantly sharp DOS peaks are observed just above EF, and these are closely related to the anti-bonding characters found in COHP curves.

Total four COHP curves representing interatomic interactions within the polyanionic frameworks are shown in Figure 3(b) and (c). Two COHP curves representing strong interactions around the 4e-site (Ge-Ge (4e-4e) and Ge-In (4e-4d)) show relatively larger integrated COHP (iCOHP) values with shorter bond distances (Table 3). Some antibonding characters of Ge-Ge COHP curve near EF were compensated by Ba-Ge and Ba-In/Li bonding characters (Supporting Information Figure S1). Two other COHP curves representing In-Li (4d-4d) and Ge-Li (4e-4d) interactions display relatively weaker bonding characters with smaller iCOHP values (Table 3). However, both curves are well optimized at EF indicating energetically stable interactions. Thus, total DOS and various COHP curves clearly indicate that the title compound is energetically stable with a given chemical composition BaLi1.09(1)In0.91Ge2 and the BaAl4-type crystal structure.