ABSTRACT
A series of Yb-substituted Zintl phases in the Ca3-xYbxAlSb3 (0 ≤ x ≤ 0.81(1)) system has been synthesized by initial arc melting and post-heat treatment, and their isotypic crystal structures were characterized by both powder and single crystal X-ray diffraction analysis. All four title compounds adopted the Ca3AlAs3-type structure (space group Pnma, Pearson code oP28, Z = 4). The overall structure can be described as a combination of the 1-dimensional (1D) infinite chain of ∞1[Al(Sb2Sb2/2)] formed by two vertices sharing [AlSb4] tetrahedral moieties and three Ca2+/Yb2+ mixed sites located in between these 1D chains. The charge balance and the resultant independency of the 1D chains in the title system were explained by the Zintl-Klemm formalism [Ca2+/Yb2+]3[(4b-Al1-)(1b-Sb2-)2(2b-Sb1-)2/2]. A series of DFT calculations proved that (1) the band overlap between the d-orbital states from two types of cations and the p-orbital states from Sb at the high symmetry Γ point implied a heavily doped degenerate semiconducting behavior of the quaternary Ca2YbAlSb3 model and (2) the site preference of Yb for the M1 site was due to the electronic-factor criterion based on the Q values of each atomic site. The electron localization function calculations also proved that the two different shapes of lone pairs of the Sb atomsâthe "umbrella-shape" and the "C-shape"âare determined by local geometry and the coordination environment on the anionic frameworks. Thermoelectric measurements of the quaternary title compound Ca2.19(1)Yb0.81AlSb3 showed an approximately two times larger ZT value than that of ternary Ca3AlSb3 at 623 K due to increased electrical conductivity and ultralow thermal conductivity originated from Yb substitution for Ca.
ABSTRACT
Three Li- and Mg-cosubstituted compounds in the Gd5-x(Li/Mg)xGe4 (x = 1.04(2), 1.17(2), 1.53(2)) system have been successfully prepared by conventional high-temperature reactions. According to powder and single-crystal X-ray diffraction analyses, all three compounds adopt a Gd5Si4-type phase with the orthorhombic Pnma space group (Pearson code oP16, Z = 4) and six crystallographically independent atomic sites. The crystal structure can be described as a combination of two-dimensional Mo2FeB2-type ∞2[Gd2(Li/Mg)Ge2] layers and [Ge2] dimers. Interestingly, as 64% of Li and 26% of Gd at the RE3 and RE2 sites, respectively, were exclusively substituted by Mg in Gd3.47(1)Li0.36(2)Mg1.17(3)Ge4, the lattice parameter b was selectively shortened as a result of the RE3-Ge1 bond shrinkage in comparison to that in Gd4LiGe4, while lattice parameters a and c remained nearly intact. A series of theoretical calculations using the tight-binding linear muffin-tin orbital (TB-LMTO) method indicated that the reduction of the particular RE3-Ge1 bond distance in the title compounds could also be explained by an optimization of bonding based on the corresponding RE3-Ge1 crystal orbital Hamilton population (COHP) curve. Moreover, the specific site preference of Mg for the RE3 site was supported by both size-factor as well as electronic-factor criteria on the basis of the smallest atomic size and the highest electronegativity of Mg among the three cations. Therefore, the overall electronic structure was further interrogated by a density of states (DOS) analysis. The influence of nonmagnetic Li/Mg cosubstitution for the magnetic Gd atoms in the title Gd5-x(Li/Mg)xGe4 system on the magnetic characteristics was also thoroughly studied by isofield magnetization at 100 Oe and 10 kOe and isothermal magnetization measurements at 4 K using two of the title compounds: Gd3.83(1)Li0.48Mg0.69(3)Ge4 and Gd3.47(1)Li0.36(2)Mg1.17(3)Ge4.
ABSTRACT
Centrosymmetric skutterudite RhP3 was converted to a nonsymmorphic and chiral compound RhSi0.3 P2.7 (space group P21 21 21 ) by means of partial replacement of Si for P. The structure, determined by a combination of X-ray crystallography and solid state 31 Pâ NMR, exhibits branched polyanionic P/Si chains that are unique among metal phosphides. A driving force to stabilize the locally noncentrosymmetric cis-RhSi2 P4 and fac-RhSi3 P3 fragments is π-electron back-donation between the Rh t2g -type orbitals and the unoccupied antibonding Si/P orbitals, which is more effective for Si than for P. In situ studies and total energy calculations revealed the metastable nature of RhSi0.3 P2.7 . Electronic structure calculations predicted centrosymmetric cubic RhP3 to be metallic which was confirmed by transport properties measurements. In contrast, the electronic structure for chiral orthorhombic RhSi0.3 P2.7 contained a bandgap, and this compound was shown to be a narrow gap semiconductor.
ABSTRACT
Complex polymorphic relationships in the LnSiP3 (Ln = La and Ce) family of compounds are reported. An innovative synthetic method was developed to overcome differences in the reactivities of the rare-earth metal and refractory silicon with phosphorus. Reactions of atomically mixed Ln + Si with P allowed for selective control over the reaction outcomes resulting in targeted isolation of three new polymorphs of LaSiP3 and two polymorphs of CeSiP3. In situ X-ray diffraction studies revealed that the developed method bypasses formation of the thermodynamic dead-end, the binary SiP. Careful re-determination of the crystal structure ruled out the previously reported ordered centrosymmetric structure of CeSiP3 and showed that the main LnSiP3 polymorphs crystallize in the non-centrosymmetric Pna21 and Aea2 space groups featuring distinct distortions of the regular P square net to yield either cis-trans 1D phosphorus chains (Pna21) or disordered-2D phosphorus layers (Aea2). The disordered 2D nature of the P layers in the Aea2 LaSiP3 polymorph was confirmed by Raman spectroscopy. A unique centrosymmetric P21/c polymorph was observed for LaSiP3 and has a completely different crystal structure lacking P layers. Consecutive polymorphic transformations at increasing temperatures for LaSiP3(Pna21 â P21/c â Aea2) were derived from optimized synthetic profiles and confirmed by a combination of phonon computations and experimental in situ and ex situ annealings. Crystal structures of the LaSiP3 polymorphs were verified via advanced solid state NMR analysis using 31P MAS and 31P{139La} double resonance techniques. A combination of phonon and electronic structure calculations, NMR T1 relaxation times, UV/Vis/NIR spectroscopy, and resistivity measurements revealed that all the reported polymorphs are semiconductors with resistivities and thermal conductivities strongly dependent on the degree of distortion of P square layers in the crystal structure. Reported here, non-centrosymmetric LnSiP3 polymorphs with tunable resistivity and thermal conductivity provide a platform for the development of novel functional materials with a wide range of applications.
ABSTRACT
The electronic and magnetic structures of tetragonal, Cu2 Sb-type CrMnAs were examined using density functional theory. To obtain reasonable agreement with reported atomic and low-temperature magnetic ordering in this compound, the intra-atomic electron-electron correlation in term of Hubbard U on Mn atoms are necessary. Using GGA + U, calculations identify four low-energy antiferromagnetically ordered structures, all of which adopt a magnetic unit cell that contains the same direct CrCr and CrMn magnetic interaction, as well as the same indirect Mnâ â â Mn magnetic interaction across the Cr planes. One of these low-energy configurations corresponds to the reported case. Effective exchange parameters for metal-metal contacts obtained from SPRKKR calculations indicate both direct and indirect exchange couplings play important roles in tetragonal CrMnAs. © 2018 Wiley Periodicals, Inc.
ABSTRACT
Using density functional theory, the crystal structure variation of AAuAl (A = Ca, Sc, and Ti) from orthorhombic Co2Si-type to distorted hexagonal Fe2P-type and then Ni2In-type structures is shown to correlate with their electronic structures and valence electron counts, sizes of the active metals A, and site preferences for Au and Al atoms, which are arranged to maximize Au-Al nearest neighbor contacts. An evaluation of chemical pressure imposed by the varying A metals using total energy vs volume calculations indicates that larger unit cell volumes favor the orthorhombic structure, whereas smaller volumes favor the hexagonal structures. The electronic origin of the Mg2Ga-type crystal structure of ScAuAl, refined as a distorted Fe2P-type supercell doubled along the c-axis, indicates a Peierls-type distortion mechanism of the Au chains along the c-axis.
ABSTRACT
Intermetallic compounds represent an extensive pool of candidates for energy related applications stemming from magnetic, electric, optic, caloric, and catalytic properties. The discovery of novel intermetallic compounds can enhance understanding of the chemical principles that govern structural stability and chemical bonding as well as finding new applications. Valence electron-poor polar intermetallics with valence electron concentrations (VECs) between 2.0 and 3.0 e-/atom show a plethora of unprecedented and fascinating structural motifs and bonding features. Therefore, establishing simple structure-bonding-property relationships is especially challenging for this compound class because commonly accepted valence electron counting rules are inappropriate. During our efforts to find quasicrystals and crystalline approximants by valence electron tuning near 2.0 e-/atom, we observed that compositions close to those of quasicrystals are exceptional sources for unprecedented valence electron-poor polar intermetallics, e.g., Ca4Au10In3 containing (Au10In3) wavy layers, Li14.7Mg36.8Cu21.5Ga66 adopting a type IV clathrate framework, and Sc4MgxCu15-xGa7.5 that is incommensurately modulated. In particular, exploratory syntheses of AAu3T (A = Ca, Sr, Ba and T = Ge, Sn) phases led to interesting bonding features for Au, such as columns, layers, and lonsdaleite-type tetrahedral frameworks. Overall, the breadth of Au-rich polar intermetallics originates, in part, from significant relativistics effect on the valence electrons of Au, effects which result in greater 6s/5d orbital mixing, a small effective metallic radius, and an enhanced Mulliken electronegativity, all leading to ultimate enhanced binding with nearly all metals including itself. Two other successful strategies to mine electron-poor polar intermetallics include lithiation and "cation-rich" phases. Along these lines, we have studied lithiated Zn-rich compounds in which structural complexity can be realized by small amounts of Li replacing Zn atoms in the parent binary compounds CaZn2, CaZn3, and CaZn5; their phase formation and bonding schemes can be rationalized by Fermi surface-Brillouin zone interactions between nearly free-electron states. "Cation-rich", electron-poor polar intermetallics have emerged using rare earth metals as the electropositive ("cationic") component together metal/metalloid clusters that mimic the backbones of aromatic hydrocarbon molecules, which give evidence of extensive electronic delocalization and multicenter bonding. Thus, we can identify three distinct, valence electron-poor, polar intermetallic systems that have yielded unprecedented phases adopting novel structures containing complex clusters and intriguing bonding characteristics. In this Account, we summarize our recent specific progress in the developments of novel Au-rich BaAl4-type related structures, shown in the "gold-rich grid", lithiation-modulated Ca-Li-Zn phases stabilized by different bonding characteristics, and rare earth-rich polar intermetallics containing unprecedented hydrocarbon-like planar Co-Ge metal clusters and pronounced delocalized multicenter bonding. We will focus mainly on novel structural motifs, bonding analyses, and the role of valence electrons for phase stability.
ABSTRACT
The irreversible transformation from an icosahedral quasicrystal (i-QC) CaAu4.39Al1.61 to its cubic 2/1 crystalline approximant (CA) Ca13Au56.31(3)Al21.69 (CaAu4.33(1)Al1.67, Pa3Ì (No. 205); Pearson symbol: cP728; a = 23.8934(4)), starting at â¼570 °C and complete by â¼650 °C, is discovered from in situ, high-energy, variable-temperature powder X-ray diffraction (PXRD), thereby providing direct experimental evidence for the relationship between QCs and their associated CAs. The new cubic phase crystallizes in a Tsai-type approximant structure under the broader classification of polar intermetallic compounds, in which atoms of different electronegativities, viz., electronegative Au + Al vs electropositive Ca, are arranged in concentric shells. From a structural chemical perspective, the outermost shell of this cubic approximant may be described as interpenetrating and edge-sharing icosahedra, a perspective that is obtained by splitting the traditional structural description of this shell as a 92-atom rhombic triacontahedron into an 80-vertex cage of primarily Au [Au59.86(2)Al17.14â¡3.00] and an icosahedral shell of only Al [Al10.5â¡1.5]. Following the proposal that the cubic 2/1 CA approximates the structure of the i-QC and on the basis of the observed transformation, an atomic site analysis of the 2/1 CA, which shows a preference to maximize the number of heteroatomic Au-Al nearest neighbor contacts over homoatomic Al-Al contacts, implies a similar outcome for the i-QC structure. Analysis of the most intense reflections in the diffraction pattern of the cubic 2/1 CA that changed during the phase transformation shows correlations with icosahedral symmetry, and the stability of this cubic phase is assessed using valence electron counts. According to electronic structure calculations, a cubic 1/1 CA, "Ca24Au88Al64" (CaAu3.67Al2.67) is proposed.
ABSTRACT
Planar hydrocarbon-like metal clusters may foster new insights linking organic molecules with conjugated π-π bonding interactions and inorganic structures in terms of their bonding characteristics. However, such clusters are uncommon in polar intermetallics. Herein, we report two polar intermetallic phases, Pr5 Co2 Ge3 and Pr7 Co2 Ge4 , both of which feature such planar metal clusters, namely, ethylene-like [Co2 Ge4 ] clusters plus the concatenated forms and polyacene-like [Co2 Ge2 ]n ribbons in Pr5 Co2 Ge3 , and 1,2,4,5-tetramethylbenzene-like [Co4 Ge6 ] cluster in Pr7 Co2 Ge4 . Just as in the related planar organic structures, these metal-metalloid species are dominated by covalent bonding interactions. Both compounds magnetically order at low temperature with net ferromagnetic components: Pr5 Co2 Ge3 through a series of transitions below 150â K and Pr7 Co2 Ge4 through a single ferromagnetic transition at 19â K. Spin-polarized electronic structure calculations for Pr7 Co2 Ge4 reveal strong spin-orbit coupling within Pr and considerable magnetic contributions from Co atoms. This work suggests that similar structural chemistry can emerge for other rare-earth/late-transition-metal/main-group systems.
ABSTRACT
The first example of polytypism in the I-II-V semiconductors has been demonstrated with the synthesis of cubic LiZnSb by a low-temperature solution-phase method. This phase exhibits a unique coloring pattern that is novel for this class of compounds. The choice of site configuration has a considerable impact on the band structure of these materials, which in turn affects the transport properties. While the hexagonal polytype has been suggested as a promising n-type and extremely poor p-type thermoelectric material, the cubic analogue is calculated to have high efficiencies for both the n- and p-type derivatives (1.64 and 1.43, respectively, at 600 K). Furthermore, the cubic phase is found to be the energetically favored polytype. This surprising result provides a rationale for the lack of success in synthesizing the hexagonal polytype in either stoichiometric or n-type compositions.
ABSTRACT
A new icosahedral quasicrystalline phase, CaAu4.5-xAl1.5+x [0.11 ≤ x ≤ 0.40(6); CaAu4.4Al1.6, aQC = 5.383(4) Å, and Pm3Ì â¯5Ì ], and its lowest-order 1/0 cubic crystalline approximant phase, CaAu3+xAl1-x [0 ≤ x ≤ 0.31(1); a = 9.0766(5)-9.1261(8) Å, Pa3Ì (No. 205), and Pearson symbol cP40], have been discovered in the Ca-poor region of the Ca-Au-Al system. In the crystalline approximant, eight [Au3-xAl1+x] tetrahedra fill the unit cell, and each tetrahedron is surrounded by four Ca atoms, thus forming a three-dimensional network of {Ca4/4[Au3-xAl1+x]} tetrahedral stars. A computational study of Au and Al site preferences concurs with the experimental results, which indicate a preference for near-neighbor Au-Al interactions over Au-Au and Al-Al interactions. Analysis of the electronic density of states and the associated crystal orbital Hamilton population curves was used to rationalize the descriptions of CaAu4.5-xAl1.5+x [0.11 ≤ x ≤ 0.46(6)] and CaAu3+xAl1-x [0 ≤ x ≤ 0.31(1)] as polar intermetallic species, whereby Ca atoms engage in polar covalent bonding with the electronegative, electron-deficient [Au3-xAl1+x] tetrahedral clusters and the observed phase width of the crystalline approximant.
ABSTRACT
Spin-frustrated chains of Cr3 triangles are found in the new metal boride TiCrIr2B2 by synergistic experimental and theoretical investigations. Although magnetic ordering is found at 275 K, competing ferro- and anti-ferromagnetic interactions coupled with spin frustration induce a rather small total magnetic moment (0.05 µB at 5 T), and density functional theory (DFT) calculations propose a canted, nonlinear magnetic ground-state ordering in the new phase. TiCrIr2B2 crystallizes in the hexagonal Ti1+xOs2-xRuB2 structure type (space group P6Ì 2m, No. 189, Pearson symbol hP18). The structure contains trigonal planar B4 boron fragments with B-B distances of 1.76(3) Å alternating along the c-direction with Cr3 triangles with intra- and intertriangle Cr-Cr distances of 2.642(9) and 3.185(1) Å, respectively. Magnetization measurements of TiCrIr2B2 reveal ferrimagnetic behavior and a large, negative Weiss constant of -750 K. DFT calculations demonstrate a strong site preference of Cr for the triangle sites, as well as magnetic frustration due to indirect anti-ferromagnetic interactions within the Cr3 triangles.
ABSTRACT
Cluster chemistry of intermetallics with valence electron counts (VECs) in the range of 2.0-3.0 is intriguing. Lithiation of polar intermetallics in this VEC region is found to be an effective chemical route to produce new complex structures with different stability mechanisms. In this work, two new complex intermetallic structures have been discovered in the Ca-Li-Zn system: Ca12LixZn59-x and Ca15LixZn75-x. Ca12LixZn59-x, x ≈ 5.65(3)-14.95(3), forms in the trigonal space group R3Ì m, with a = 9.074(1)-9.1699(2) Å, c = 53.353(1)-53.602(1) Å, and Z = 3. In comparison, Ca15LixZn75-x, x ≈ 19.07(2), crystallizes in the space group P63/mmc, with a ≈ 9.183(1) Å, c ≈ 45.191(5) Å), and Z = 2. Both structures are members of a large intergrowth family featuring slabs of dimers (D) and trimers (T) stacking along [001], with the sequences DTDDTDDTD for Ca12LixZn59-x and TDDDTDDD for Ca15LixZn75-x. Each dimer consists of two face-sharing Zn-centered hypho-icosahedra, and each trimer comprises a Li-centered icosahedron sandwiched by two hypho-icosahedra. This intergrowth family includes several known intermetallic structure types involving very electropositive metals, e.g., SrMg5.2, Ba2Li4.21Al4.79, and Sr9Li17.5Al25.5. Because of cluster defects and condensation, both Ca12LixZn59-x and Ca15LixZn75-x are electronically akin to close-packed metals, and their structural stabilities can be interpreted by a Hume-Rothery mechanism rather than the Zintl-Klemm concept.
ABSTRACT
We report the synthesis and characterization of nanocrystalline LiZnP. The reaction proceeds through a zinc metal intermediate followed by rapid incorporation of lithium and phosphorus. We demonstrate flexibility in the selection of Li, Zn, and P precursors, as well as extension of this method to other half-Heusler phases.
ABSTRACT
Four complex intermetallic compounds BaAu(6±x)Ga(6±y) (x = 1, y = 0.9) (I), BaAu(6±x)Al(6±y) (x = 0.9, y = 0.6) (II), EuAu6.2Ga5.8 (III), and EuAu6.1Al5.9 (IV) have been synthesized, and their structures and homogeneity ranges have been determined by single crystal and powder X-ray diffraction. Whereas I and II originate from the NaZn13-type structure (cF104-112, Fm3Ì c), III (tP52, P4/nbm) is derived from the tetragonal Ce2Ni17Si9-type, and IV (oP104, Pbcm) crystallizes in a new orthorhombic structure type. Both I and II feature formally anionic networks with completely mixed site occupation by Au and triel (Tr = Al, Ga) atoms, while a successive decrease of local symmetry from the parental structures of I and II to III and, ultimately, to IV correlates with increasing separation of Au and Tr on individual crystallographic sites. Density functional theory-based calculations were employed to determine the crystallographic site preferences of Au and the respective triel element to elucidate reasons for the atom distribution ("coloring scheme"). Chemical bonding analyses for two different "EuAu6Tr6" models reveal maximization of the number of heteroatomic Au-Tr bonds as the driving force for atom organization. The Fermi levels fall in broad pseudogaps for both models allowing some electronic flexibility. Spin-polarized band structure calculations on the "EuAu6Tr6" models hint to singlet ground states for europium and long-range magnetic coupling for both EuAu6.2Ga5.8 (III) and EuAu6.1Al5.9 (IV). This is substantiated by experimental evidence because both compounds show nearly identical magnetic behavior with ferromagnetic transitions at TC = 6 K and net magnetic moments of 7.35 µB/f.u. at 2 K. The effective moments of 8.3 µB/f.u., determined from Curie-Weiss fits, point to divalent oxidation states for europium in both III and IV.
ABSTRACT
Low-dimensional cuprous nitride (Cu3N) was synthesized by nitridation (ammonolysis) of cuprous oxide (Cu2O) nanocrystals using either ammonia (NH3) or urea (H2NCONH2) as the nitrogen source. The resulting nanocrystalline Cu3N spontaneously decomposes to nanocrystalline CuO in the presence of both water and oxygen from air at room temperature. Ammonia was produced in 60% chemical yield during Cu3N decomposition, as measured using the colorimetric indophenol method. Because Cu3N decomposition requires H2O and produces substoichiometric amounts of NH3, we conclude that this reaction proceeds through a complex stoichiometry that involves the concomitant release of both N2 and NH3. This is a thermodynamically unfavorable outcome, strongly indicating that H2O (and thus NH3 production) facilitate the kinetics of the reaction by lowering the energy barrier for Cu3N decomposition. The three different Cu2O, Cu3N, and CuO nanocrystalline phases were characterized by a combination of optical absorption, powder X-ray diffraction, transmission electron microscopy, and electronic density of states obtained from electronic structure calculations on the bulk solids. The relative ease of interconversion between these interesting and inexpensive materials bears possible implications for catalytic and optoelectronic applications.
ABSTRACT
Five new polar intermetallic compounds in the Ae-Ga-Au system (Ae = Ba, Eu), BaAu(5)Ga(2) (I), BaAu(4.3)Ga(2.7) (II), Ba(1.0)Au(4.5)Ga(2.4 )(III), EuAu(4.8)Ga(2.2) (IV), and Eu(1.1)Au(4.4)Ga(2.2) (V), have been synthesized and their crystal structures determined by single-crystal X-ray diffraction. I crystallizes in the orthorhombic crystal system with a large unit cell [Pearson symbol oP64; Pnma, Z = 8, a = 8.8350(5) Å, b = 7.1888(3)Å, c = 20.3880(7) Å], whereas all other compounds are hexagonal [hP24; P6Ì 2m, Z = 3, a = 8.54-8.77(1) Å, c = 7.19-7.24(1) Å]. Both structures contain mutually orthogonal layers of Au(6) hexagons in chair and boat conformations, resulting in a hexagonal diamond-like network. Ae atoms and additional (Au/Ga)(3) groups are formally encapsulated by (Au(6))(2) distorted hexagonal prisms formed of three edge-sharing hexagons in the boat conformation or, alternatively, lie between two Au(6) hexagons in the chair conformation. The (Au/Ga)(3) groups can be substituted by Ae atoms in some of the hexagonal structures with no change to the structural symmetry. Tight-binding electronic structure calculations using linear-muffin-tin-orbital methods on idealized models "BaAu(5)Ga(2)" and "BaAu(4)Ga(3)" show both compounds to be metallic with evident pseudogaps near the corresponding Fermi levels. The integrated crystal orbital Hamilton populations are dominated by Au-Au and Au-Ga orbital interactions, although Ba-Au and Ba-Ga contributions are significant. Furthermore, Au-Au interactions vary considerably along different directions in the unit cells, with the largest values for the hexagons in the boat conformation and the lowest values for those in the chair conformation. II revealed that partial substitution of Au atoms in the hexagonal diamond net by a post-transition element (Ga) may occur in this family, whereas the sizes of the (Au/Ga)(3) groups and strong Ba-Au covalent interactions allow for their mutual replacement in the voids.
ABSTRACT
Three ordered structures of the tetragonal BaAl4 type were identified in the Ba-Au-Sn system, from which a unified view of the interplay between the valence electron counts (VECs) and phase stabilities of these three types of derivatives can be developed. The BaNiSn3 (I4mm), ThCr2Si2 (I4/mmm), and CaBe2Ge2 (P4/nmm) type BaAu(x)Sn(4-x) phases occurred respectively at x = 0.78(1)-1, 1.38(1)-1.47(1), and 1.52(1)-2.17(1), consistent with theoretical atomic "coloring" analyses that reveal an optimal VEC of â¼14 for the ThCr2Si2 type but larger and smaller values respectively for the BaNiSn3- and CaBe2Ge2-type structures.