Linear Muffin-tin Orbital Calculations Research Articles

Eleven new compounds in the RE–Cd–Ge systems (RE=Pr, Nd, Sm, Gd–Yb; Y): Crystal chemistry of the RE2CdGe2 series

A large new family of rare-earth metal–cadmium–germanides RE2CdGe2 (RE=Y, Pr, Nd, Sm, Gd–Yb) has been synthesized and structurally characterized. All eleven structures have been established from single-crystal X-ray diffraction data and have been found to belong to the tetragonal Mo2FeB2 structure type (ordered ternary variant of the U3Si2 structure type—space group P4/mbm (No. 127), Z=2; Pearson symbol tP10). The structural variations among the three series of isostructural RE2MgGe2, RE2InGe2, and RE2CdGe2 compounds are discussed, as well as the crystal chemistry changes as a function of the decreasing size of the rare-earth metals (lattice constants a=7.176(2)–7.4589(12)Å and c=4.1273(14)–4.4356(13)Å). The experimental results have been complemented by tight-binding linear muffin-tin orbital (TB–LMTO) electronic structure calculations.

Experimental and theoretical investigations of the novel ternary compound Ca4InGe4

A new polar intermetallic compound with a novel structure type has been synthesized and characterized by both powder and single-crystal X-ray diffraction. Ca(4)InGe(4) crystallizes in the monoclinic crystal system (space group C2/c, Z = 4, Pearson symbol mS36) with five crystallographically unique atomic positions in the asymmetric unit. The corresponding lattice parameters at 200(2) K are a = 18.452(8) Å, b = 5.819(2) Å, c = 8.339(3) Å, and β = 99.330(6)°. The overall crystal structure can be described as a linear intergrowth of two imaginary fragments--Ca(2)InGe(2) with the Gd(2)AlGe(2) type- and CaGe with the FeB type-structures. Another way to rationalize the bonding is to focus on the polyanionic framework, which in this case is made up of unique nets of "seesaw"-shaped [InGe(4)] units. They are interconnected via Ge-Ge dimers into an open three-dimensional framework with Ca(2+) cations occupying the voids within it. Tight-binding linear muffin-tin orbital (LMTO) calculations provide a rationale for the unique local coordination geometry around In and the two distinct types of Ge-Ge bond distances.

New Ternary Germanides La4Mg5Ge6 and La4Mg7Ge6: Crystal Structure and Chemical Bonding

The synthesis, structural characterization, and chemical-bonding peculiarities of the two new polar lanthanum-magnesium germanides La(4)Mg(5)Ge(6) and La(4)Mg(7)Ge(6) are reported. The crystal structures of these intermetallics were determined by single-crystal X-ray diffraction analysis. The La(4)Mg(5)Ge(6) phase crystallizes in the orthorhombic Gd(4)Zn(5)Ge(6) structure type [Cmc2(1), oS60, Z = 4, a = 4.5030(7) Å, b = 20.085(3) Å, c = 16.207(3) Å, wR2 = 0.0451, 1470 F(2) values, 93 variables]. The La(4)Mg(7)Ge(6) phase represents a new structure type with a monoclinic unit cell [C2/m, mS34, Z = 2, a = 16.878(3) Å, b = 4.4702(9) Å, c = 12.660(3) Å, β = 122.25(3)°, wR2 = 0.0375, 1466 F(2) values, 54 variables]. Crystallographic analysis together with linear muffin-tin orbital band structure calculations reveals the presence of strongly bonded 3D polyanionic [Mg-Ge] networks balanced by positively charged La atoms in both stoichiometric compounds. The La(4)Mg(5)Ge(6) compound is related to Zintl phases, showing a prominent density of states pseudogap at the Fermi level. A distinctive feature of the La(4)Mg(5)Ge(6) structure is the presence of Ge-Ge covalent dumbbells; in La(4)Mg(7)Ge(6), the higher Mg content generates a polyanionic network consisting exclusively of Mg-Ge heterocontacts. Nevertheless, the frameworks of the two phases are structurally similar, as is highlighted in this work.

Synthesis, Structure, Chemical Bonding, and Magnetism of the Series RELiGe2 (RE = La–Nd, Sm, Eu)

This article focuses on the synthesis and the crystal chemistry of six members of a series of rare-earth metal based germanides with general formula RELiGe(2) (RE = La-Nd, Sm, and Eu). The structures of these compounds have been established by single-crystal X-ray diffraction (CaLiSi(2) structure type, space group Pnma, Z = 4, Pearson symbol oP16). The chemical bonding within this atomic arrangement can be rationalized in terms of anionic germanium zigzag chains, conjoined via chains of edge-shared LiGe(4) tetrahedra and separated by rare-earth metal cations. The structure can also be viewed as an intergrowth of AlB(2)-like and TiNiSi-like fragments, or as the result of the replacement of 50% of the rare-earth metal atoms by lithium in the parent structure of the REGe monogermanides. Except for LaLiGe(2) and SmLiGe(2), the remaining four RELiGe(2) phases exhibit Curie-Weiss paramagnetism above about 50 K. In the low temperature regime, the localized 4f electrons in CeLiGe(2), PrLiGe(2), and SmLiGe(2) order ferromagnetically, while antiferromagnetic ordering is observed for NdLiGe(2) and EuLiGe(2). The calculated effective magnetic moments confirm RE(3+) ground states in all cases excluding EuLiGe(2), in which the magnetic response is consistent with Eu(2+) configuration (J = S = 7/2). The experimental results have been complemented by tight-binding linear muffin-tin orbital (TB-LMTO) band structure calculations.

First-principles study of structural, electronic and magnetic properties in Cd1−xFexS diluted magnetic semiconductors

In this paper, we report theoretical investigations of structural, electronic and magnetic properties of ordered dilute ferromagnetic semiconductors Cd1−xFexS with x=0.25, 0.5 and 0.75 in zinc blende (B3) phase using all-electron full-potential linear muffin tin orbital (FP-LMTO) calculations within the density functional theory and the generalized gradient approximation. The analysis of band structures, density of states, total energy, exchange interactions and magnetic moments reveals that both the alloys may exhibit a half-metallic ferromagnetism character. The value of calculated magnetic moment per Fe impurity atom is found to be 4μB. Moreover, we found that p–d hybridization reduces the local magnetic moment of Fe from its free space charge value of 4μB and produces small local magnetic moments on Cd and S sites.

Eight-Coordinated Arsenic in the Zintl Phases RbCd4As3 and RbZn4As3: Synthesis and Structural Characterization

Reported are two new series of Zintl phases, ACd(4)Pn(3) and AZn(4)Pn(3) (A = Na, K, Rb, Cs; Pn = As, P), whose structures feature complex atomic arrangements based on four- and eight-coordinated arsenic and phosphorus. A total of 12 compounds have been synthesized from the corresponding elements via high temperature reactions, and their structures have been established by X-ray diffraction. RbCd(4)As(3), KCd(4)As(3), NaCd(4)As(3), NaZn(4)As(3), KCd(4)P(3), and KZn(4)P(3) crystallize with a new rhombohedral structure (space group R3m, Z = 3, Pearson symbol hR24), while the isoelectronic RbZn(4)As(3), CsCd(4)As(3), CsZn(4)As(3), KZn(4)As(3), CsZn(4)P(3), and RbZn(4)P(3) adopt the tetragonal KCu(4)S(3)-type structure (space group P4/mmm, Z = 1, Pearson symbol tP8). Both structures are very closely related to the ubiquitous CaAl(2)Si(2) and ThCr(2)Si(2) structure types, and the corresponding relationships are discussed. The experimental results have been complemented by linear muffin-tin orbital (LMTO) tight-binding band structure calculations. Preliminary transport properties measurements on polycrystalline samples suggest that the compounds of these families could be promising thermoelectric materials.

Complete Titanium Substitution by Boron in a Tetragonal Prism: Exploring the Complex Boride Series Ti3−xRu5−yIryB2+x (0 ≤ x ≤ 1 and 1 < y < 3) by Experiment and Theory

Polycrystalline samples and single crystals of four members of the new complex boride series Ti(3-x)Ru(5-y)Ir(y)B(2+x) (0 ≤ x ≤ 1 and 1 < y < 3) were synthesized by arc-melting the elements in a water-cooled copper crucible under an argon atmosphere. The new silvery phases were structurally characterized by powder and single-crystal X-ray diffraction as well as energy- and wavelength-dispersive X-ray spectroscopy analyses. They crystallize with the tetragonal Ti(3)Co(5)B(2) structure type in space group P4/mbm (No. 127). Tetragonal prisms of Ru/Ir atoms are filled with titanium in the boron-poorest phase (Ti(3)Ru(2.9)Ir(2.1)B(2)). Gradual substitution of titanium by boron then results in the successive filling of this site by a Ti/B mixture en route to the complete boron occupation, leading to the boron-richest phase (Ti(2)Ru(2.8)Ir(2.2)B(3)). Furthermore, both ruthenium and iridium share two sites in these structures, but a clear Ru/Ir site preference is found. First-principles density functional theory calculations (Vienna ab initio simulation package) on appropriate structural models (using a supercell approach) have provided more evidence on the stability of the boron-richest and -poorest phases, and the calculated lattice parameters corroborate very well with the experimentally found ones. Linear muffin-tin orbital atomic sphere approximation calculations further supported these findings through crystal orbital Hamilton population bonding analyses, which also show that the Ru/Ir-B and Ru/Ir-Ti heteroatomic interactions are mainly responsible for the structural stability of these compounds. Furthermore, some stable and unstable phases of this complex series could be predicted using the rigid-band model. According to the density of states analyses, all phases should be metallic conductors, as was expected from these metal-rich borides.

Experimental determination of the state-dependent enhancement of the electron-positron momentum density in solids

The state-dependence of the enhancement of the electron-positron momentum density is investigated for some transition and simple metals (Cr, V, Ag and Al). Quantitative comparison with linearized muffin-tin orbital calculations of the corresponding quantity in the first Brillouin zone is shown to yield a measurement of the enhancement of the s, p and d states, independent of any parameterizations in terms of the electron density local to the positron. An empirical correction that can be applied to a first-principles state-dependent model is proposed that reproduces the measured state-dependence very well, yielding a general, predictive model for the enhancement of the momentum distribution of positron annihilation measurements, including those of angular correlation and coincidence Doppler broadening techniques.

Isolated ∞1[ZnPn2]4− Chains in the Zintl Phases Ba2ZnPn2 (Pn = As, Sb, Bi)—Synthesis, Structure, and Bonding

Reported are the synthesis of three new Zintl phases, Ba2ZnAs2 (I), Ba2ZnSb2 (II), Ba2ZnBi2 (III) and their structural characterization by single-crystal X-ray diffraction. They are isoelectronic and isotypic and crystallize in the orthorhombic space group Ibam, with four formula units per cell (Pearson symbol oI20; K2SiP2 type). Lattice parameters are as follows: a = 13.399(9)/14.133(3)/14.325(6); b = 6.878(5)/7.1919(15)/7.280(3); and c = 6.541(4)/6.9597(15)/7.089(3) A for I/II/III, respectively. The structure can be viewed as polyanionic chains, infinity1[ZnPn2]4- (Pn = As, Sb, Bi), running parallel to the c-axis, with Ba2+ cations separating them. The chains are made of edge-shared ZnPn4 tetrahedra, which are isosteric with the infinity1[SiS4/2] chains in SiS2. This and some other structural parallels with known Zintl phases have been discussed. The experimental results have been complemented by tight-binding linear muffin-tin orbital electronic structure calculations.

Synthesis and structural characterization of A3In 2Ge 4 and A5In 3Ge 6 ( A=Ca, Sr, Eu, Yb)—New intermetallic compounds with complex structures, exhibiting Ge–Ge and In–In bonding

Reported are the synthesis and the structural characterization of four new polar intermetallic phases, which exist only with mixed alkaline-earth and rare-earth metal cations in narrow homogeneity ranges. (Sr 1– x Ca x ) 5In 3Ge 6 and (Eu 1– x Yb x ) 5In 3Ge 6 ( x≈0.7) crystallize in the orthorhombic space group Pnma with two formula units per unit cell (own structure type, Pearson symbol oP56). The lattice parameters are as follows: a=13.109(3)–13.266(3) Å, b=4.4089(9)–4.4703(12) Å, and c=23.316(5)–23.557(6) Å. (Sr 1– x Ca x ) 3In 2Ge 4 and (Sr 1– x Yb x ) 3In 2Ge 4 ( x≈0.4–0.5) adopt another novel monoclinic structure-type (space group C2 /m, Z=4, Pearson symbol mS36) with lattice parameters in the range a=19.978(2)–20.202(2) Å, b=4.5287(5)–4.5664(5) Å, c=10.3295(12)–10.3447(10) Å, and β=98.214(2)–98.470(2)°, depending on the metal cations and their ratio. The polyanionic sub-structures in both cases are based on chains of InGe 4 corner-shared tetrahedra. The A 5In 3Ge 6 structure ( A=Sr/Ca or Sr/Yb) also features Ge 4 tetramers, and isolated In atoms in nearly square-planar environment, while the A 3In 2Ge 4 structure ( A=Sr/Ca or Eu/Yb) contains zig-zag chains of In and Ge strings with intricate topology of cis- and trans-bonds. The experimental results have been complemented by tight-binding linear muffin-tin orbital (LMTO) band structure calculations.

Mixed Cations and Structural Complexity in (Eu1−xCax)4In3Ge4 and (Eu1−xCax)3In2Ge3—The First Two Members of the Homologous Series A2[n+m]In2n+mGe2[n+m] (n, m = 1, 2, ...∞; A = Ca, Sr, Ba, Eu, or Yb)

Reported are the synthesis and the structural characterization of two members of a new homologous series of polar intermetallic compounds, which exist only with mixed alkaline-earth and rare-earth metal cations. Crystals of (Eu(1-x)Ca(x))(4)In(3)Ge(4) (0.35(1) <or= x <or= 0.70(1)) and (Eu(1-x)Ca(x))(3)In(2)Ge(3) (0.78(1) <or= x <or= 0.90(1)) have been grown using a molten In metal flux and structurally characterized by single-crystal X-ray diffraction. (Eu(1-x)Ca(x))(4)In(3)Ge(4) adopts the monoclinic Mg(5)Si(6)-type structure (space group C2/m, Z = 2, Pearson symbol mS22) with lattice parameters a = 16.874(1)-17.024(2) A, b = 4.496(3)-4.556(1) A, c = 7.473(4)-7.540(1) A, and beta = 107.306(10)-105.631(3) degrees . (Eu(1-x)Ca(x))(3)In(2)Ge(3) crystallizes with a novel orthorhombic structure (space group Pnma, Z = 4, Pearson symbol oP32) with lattice parameters in the ranges a = 7.382(2)-7.4010(9) A, b = 4.452(1)-4.4640(6) A, and c = 23.684(6)-23.734(3) A, depending on the Eu/Ca ratio. The polyanionic substructures in both cases are related and are based on InGe(4) edge-shared tetrahedra, Ge(2) dimers, and bridging In atoms in a nearly square-planar environment. The (Eu(1-x)Ca(x))(4)In(3)Ge(4) structure can be viewed as a 1:1 intergrowth of Mo(2)FeB(2)-like and TiNiSi-like fragments, whereas (Eu(1-x)Ca(x))(3)In(2)Ge(3) can be rationalized as a 2:1 intergrowth of the same structural motifs. Both phases exhibit fairly wide homogeneity ranges and exist only with mixed cations. The experimental results have been complemented by linear muffin-tin orbital tight-binding band structure calculations, as well as an analysis of the observed cationic site preferences.

Electronic structure and magnetic properties of RuFe 3N nitride

Self-consistent band structure calculations were performed on nitride RuFe 3N in order to investigate its magnetic and ground state properties. The Linear Muffin-Tin Orbital (LMTO) method was employed and calculations were performed at several lattice parameters so as to obtain the RuFe 3N equilibrium volume. Nonmagnetic and ferromagnetic LMTO calculations have shown that the RuFe 3N stable stage is ferromagnetic with constant lattice equilibrium of 7.2502 atomic units (a.u.). At equilibrium volume the LMTO calculations have given magnetic moments of 1.25 and 1.63 μ B at Ru and Fe sites, respectively, and no magnetic moment at N sites. The analysis of states density at equilibrium volume as well as the results for charge transfer illustrates why this ruthenium nitride is ferromagnetic. The LMTO calculations anticipate that the magnetic moment, the hyperfine field (the Fermi contact) and the isomer shift show a strong dependence on the lattice spacing.

Nitridogermanate Nitrides Sr7[GeN4]N2 and Ca7[GeN4]N2: Synthesis Employing Sodium Melts, Crystal Structure, and Density-Functional Theory Calculations

The alkaline earth nitridogermanate nitrides AE(7)[GeN(4)]N(2) (AE = Ca, Sr) have been synthesized using a Na flux technique in sealed Ta tubes. According to single-crystal X-ray diffraction the isotypic compounds crystallize in space group Pbcn (No. 60) with Z = 4, (Sr(7)[GeN(4)]N(2): a = 1152.6(2), b = 658.66(13), c = 1383.6(3) pm, V = 1050.5(4) x 10(6) pm(3), R1 = 0.049; Ca(7)[GeN(4)]N(2): a = 1082.6(2), b = 619.40(12), c = 1312.1(3) pm, V = 879.8(3) x 10(6) pm(3), R1 = 0.016). Owing to the high N/Ge ratio, the compounds contain discrete N(3-) ions coordinated by six AE(2+) besides discrete [GeN(4)](8-) tetrahedrons. One of the AE(2+) ion is coordinated by only four N(3-) ions, which is rather an unusual low coordination number for Sr(2+). Together with the isolated [GeN(4)](8-) tetrahedrons, these Sr(2+) ions form chains of alternating cation centered edge sharing tetrahedrons. The electronic structure and chemical bonding in Sr(7)[GeN(4)]N(2) has been analyzed employing linear muffin-tin orbital (LMTO) band structure calculations.

Magnetic exchange interactions in the gadolinium pnictides from first principles

The magnetic exchange interactions in the Gd-pnictide series are analyzed from various points of view. First, a Heisenberg Hamiltonian between the $4f$ induced local moments on the Gd only is used and the corresponding exchange interactions between first and second-nearest neighbors are derived from total-energy differences between the ferromagnetic (FM) and antiferromagnetic AFM-I and AFM-II configurations, as calculated from a full-potential-linearized muffin-tin orbital method in the local-density approximation with Hubbard-$U$ corrections $(\text{LSDA}+U)$. The induced magnetic moments on $\text{Gd}\text{ }d$ and N in the different configurations are found to differ and to favor the AFM-II for the P-Bi compounds while the FM configurations is favored for GdN. The extracted ${J}_{2}$ parameter determines the N\'eel temperature of the AFM-II compounds in good agreement with experimental values. The Curie-Weiss temperature involves both ${J}_{1}$ and ${J}_{2}$ in this model and is also in good agreement with experiment. The FM state of GdN can be viewed as an antiferromagnetic arrangement of the small moments induced on $\text{Gd}\text{ }d$ and N on the rocksalt lattice, which in this case happen to cancel each other exactly because of the semiconducting nature of GdN. This locks the $\text{Gd}\text{ }4f$ moments into a FM arrangement through the on-site $f\text{\ensuremath{-}}d$ coupling. Linear response calculations in the atomic sphere approximation, including empty sphere sites, provide an alternative decomposition of the magnetic ordering energy in Gd-Gd, Gd-N, and Gd-empty sphere exchange interactions. The latter can be viewed as representing the tails of the ${t}_{2g}$ orbitals on Gd. This analysis shows that the magnetic ordering arises from the small induced moments on the $\text{Gd}\text{ }d$, N, and empty sphere sites rather than from direct interactions between $4f$ moments. The Curie temperature for GdN is found to be significantly smaller than previous calculations estimated and than experimental values and may indicate that the latter are influenced by defects. For GdP, GdAs, GdSb, and GdBi, the linear-response calculations around the AFM-II ground state give results in good agreement with the full-potential linearized muffin-tin orbital calculations. The linear-response approach also gives a reasonable value for the Curie temperature of metallic Gd.

First-principles study of correlation effects inVO2

We present a first-principles study of ${\text{VO}}_{2}$ in the rutile and monoclinic $({M}_{1})$ phases by means of all-electron full-potential linear muffin-tin orbital GW calculation. Full frequency dependence and off-diagonal matrix elements of the self-energy are taken into account. As a result of dynamical correlations, a satellite structure is found above the ${t}_{2g}$ quasiparticle peak, although not below, in both the rutile and monoclinic phases. For the monoclinic structure, the insulating state is not obtained within the usual one-shot GW calculation. We have performed a simplified ``self-consistent'' GW scheme by adding a uniform shift to the conduction-band levels and recalculating the quasiparticle wave functions accordingly. An insulating solution with a gap of approximately 0.6 eV is obtained, in agreement with experiments.

High pressure structural phase transition in zircon(ZrSiO4)

We report on a full potential linear muffin-tin orbital calculation of the electronicstructure of zircon at ambient conditions as well as under high pressure. The calculationsreproduce the experimentally observed pressure induced phase transition from the zircon toscheelite structure. The calculated transition pressure of 8 GPa compares very well with theexperimental value of about 10 GPa. Our calculated equation of state and the volume collapseassociated with the crystallographic change are also in very good agreement with experiment.

Angle-resolved photoemission study of the evolution of band structure and charge density wave properties inRTe3(R=Y, La, Ce, Sm, Gd, Tb, and Dy)

We present a detailed angle-resolved photoemission spectroscopy (ARPES) investigation of the $R{\text{Te}}_{3}$ family, which sets this system as an ideal ``textbook'' example for the formation of a nesting driven charge density wave (CDW). This family indeed exhibits the full range of phenomena that can be associated to CDW instabilities, from the opening of large gaps on the best nested parts of Fermi surface (up to 0.4 eV), to the existence of residual metallic pockets. ARPES is the best suited technique to characterize these features, thanks to its unique ability to resolve the electronic structure in $k$ space. An additional advantage of $R{\text{Te}}_{3}$ is that the band structure can be very accurately described by a simple two dimensional tight-binding (TB) model, which allows one to understand and easily reproduce many characteristics of the CDW. In this paper, we first establish the main features of the electronic structure by comparing our ARPES measurements with the linear muffin-tin orbital band calculations. We use this to define the validity and limits of the TB model. We then present a complete description of the CDW properties and of their strong evolution as a function of $R$. Using simple models, we are able to reproduce perfectly the evolution of gaps in $k$ space, the evolution of the CDW wave vector with $R$, and the shape of the residual metallic pockets. Finally, we give an estimation of the CDW interaction parameters and find that the change in the electronic density of states $n({E}_{F})$, due to lattice expansion when different $R$ ions are inserted, has the correct order of magnitude to explain the evolution of the CDW properties.

Cation Substitution Effects in the System Sr2−xBaxBi3 (0 ≤ x ≤ 1.3): Structural Distortions Induced by Chemical Pressure

Crystals of the composition Sr(2-x)Ba(x)Bi(3) (0 < or = x < or = 1.3) have been synthesized from the elements and were characterized by single-crystal and powder X-ray diffraction methods. The compounds crystallize for x = 0, 0.45, 0.86, 1.08, 1.28 in the structure type of the parent compound Sr 2Bi 3 with space group Pnna (No. 52) and Z = 4. Substitution of Sr by Ba leads to a site preference for Ba. The anionic Bi substructures in the pseudoternary system simultaneously distort under remarkable elongation of one distinct Bi-Bi contact. Magnetic measurements for samples with x = 0, 0.45 and 1.08 reveal superconducting transitions at low temperatures. Linear muffin-tin orbital band structure calculations of Sr(2)Bi(3) show strong cation-anion interactions that greatly stabilize the structure. Besides showing characteristics of a typical metal, the band structure plot unveils the co-instantaneous occurrence of flat and steep bands around the Fermi level indicative for superconductivity.

Similar K@Au10Sn10 Polyhedra in the Markedly Different Structures of KAu4Sn6 and KAu3Sn3. Syntheses and Characterization

These compounds were synthesized by high-temperature reactions of the elements in welded Ta tubes and characterized by X-ray diffraction methods and linear muffin-tin orbital (LMTO) calculations. AAu4Sn6 (A = K, Rb) have a new structural type (Fddd, Z = 8), and KAu3Sn3 (Pmmn, Z = 2) is isostructural with SrAu3In3. Both orthorhombic structures contain similar condensed K@Au10Sn10 polyhedral building blocks, which can be described as overall 6-8-6 arrangements of planar rings or, alternatively, as hexagonal prisms centered by K and augmented about the waists by 8-rings of Au and Sn. However, the 3D Au-Sn networks differ appreciably in both composition and the modes of condensation. In KAu3Sn3, the prisms stack by sharing both hexagonal faces with like neighbors along a, whereas those in KAu4Sn6 condense in a complex zigzag network. Compared with related indium systems, the structure change from KAu4In6 ( P_6m2, Z = 1) to KAu4Sn6 apparently illustrates the effect of complex factors such as atom size and valence electron counts on structure, whereas the SrAu3In3 and KAu3Sn3 pair are isotypic. Both compounds are Pauli-paramagnetic and inert to water at room temperature for several days. Tight-binding electronic structure (LMTO) calculations emphasize the dominance and strength of the heteroatomic Au-Sn bonding.

An Application of the “Coloring Problem”: Structure−Composition−Bonding Relationships in the Magnetocaloric Materials LaFe13-xSix

The LaFe(13)-(x)Si(x) (1.0 < or = x < or = 5.0) series is studied experimentally and theoretically to gain possible understanding for the relationships among geometrical structure, chemical composition, magnetic behavior, and physical properties as related to the magnetocaloric effect in these compounds. As the Si concentration increases, LaFe(13)-(x)Si(x) exhibits a structural transformation from the cubic NaZn(13) structure type to a tetragonal derivative due primarily to preferential ordering of Fe and Si atoms. At room temperature, LaFe(13)-(x)Si(x) crystallize in the cubic structure for the range 1 < or = x < or = 2.6 and in the tetragonal for 3.2 < or = x < or = 5. In the range 2.6 < or = x < or = 3.2, it shows a two-phase mixture. Temperature-dependent single-crystal X-ray diffraction experiments near the corresponding Curie temperatures were performed on the room-temperature cubic phases to examine the origin of the large isothermal magnetic entropy changes. A thorough statistical and structural analysis of the data indicates that the noncentrosymmetric F43c space group provides a more adequate atomic arrangement than the centrosymmetric Fm3c space group. This change in space group leads to divergence for specific sets of Fe-Fe distances below the Curie temperature that arises from tilting of Fe-centered [Fe(12)-(x)Si(x)] icosahedra. The noncentrosymmetric space group also agrees with the predominance of icosahedral clusters lacking local inversion symmetry. From extended Hückel and tight-binding linear muffin-tin orbital (TB-LMTO) electronic structure calculations on various model structures, the F43c model is more energetically favorable than the Fm3c model. Extended Hückel calculations on various icosahedral [Fe(12)-(n)Si(n)] (n = 1-5) clusters and TB-LMTO calculations on "LaFe(13)," LaFe(11)Si(2), and LaFe(9)Si(4) have also been carried out to study the effects of a main group element (Si) on stabilizing the cubic NaZn(13)-type structure, influencing the transformation between cubic and tetragonal symmetries, and to study relationships among their chemical bonding and magnetic properties.