Search

Intermetallics contribute significantly to our current demand for high-performance functional materials. However, understanding their chemistry is still an open and debated topic, especially for complex compounds such as approximants and quasicrystals. In this work, targeted topological data mining succeeded in (i) selecting all known Mackay-type approximants, (ii) uncovering the most important geometrical and chemical factors involved in their formation, and (iii) guiding the experimental work to obtain a new binary Sc–Pd 1/1 approximant for icosahedral quasicrystals containing the desired cluster. Single-crystal X-ray diffraction data analysis supplemented by electron density reconstruction using the maximum entropy method, showed fine structural peculiarities, that is, smeared electron densities in correspondence to some crystallographic sites. These characteristics have been studied through a comprehensive density functional theory modeling based on the combination of point defects such as vacancies a...

The new intermetallic compound Eu2Pd2Sn has been investigated. A single crystal was selected from the alloy and was analyzed by single-crystal X-ray diffraction, revealing that this compound possesses the noncentrosymmetric Ca2Pd2Ge structure type being, so far, the only rare-earth-based representative. Bonding analysis, performed on the basis of DOS and (I)COHP, reveals the presence of strong covalent Sn–Pd bonds in addition to linear and equidistant Pd–Pd chains. The incomplete ionization of Eu leads to its participation in weaker covalent interactions. The magnetic effective moment, extracted from the magnetic susceptibility χ(T) is μeff = 7.87 μB, close to the free ion Eu2+ value (μeff = 7.94 μB). The maximum of χ(T) at TN ∼ 13 K indicates an antiferromagnetic behavior below this temperature. A coincident sharp anomaly in the specific heat CP(T) emerges from a broad anomaly centered at around 10 K. From the reduced jump in the heat capacity at TN a scenario of a transition to an incommensurate antiferromagnetic phase below TN followed by a commensurate configuration below 10 K is suggested., A new intermetallic compound, Eu2Pd2Sn, is so far the only rare-earth representative of the Ca2Pd2Ge structure type. Synthesis and characterization of the structure, together with magnetic properties, are discussed.

A comparative chemical bonding analysis for the germanides La2 MGe6 (M=Li, Mg, Al, Zn, Cu, Ag, Pd) and Y2 PdGe6 is presented, together with the crystal structure determination for M=Li, Mg, Cu, Ag. The studied compounds adopt the two closely related structure types oS72-Ce2 (Ga0.1 Ge0.9 )7 and mS36-La2 AlGe6 , containing zigzag chains and corrugated layers of Ge atoms bridged by M species, with La/Y atoms located in the biggest cavities. Chemical bonding was studied by means of the quantum chemical position-space techniques QTAIM (quantum theory of atoms in molecules), ELI-D (electron localizability indicator), and their basin intersections. The new penultimate shell correction (PSC0) method was introduced to adapt the ELI-D valence electron count to that expected from the periodic table of the elements. It plays a decisive role to balance the Ge-La polar-covalent interactions against the Ge-M ones. In spite of covalently bonded Ge partial structures formally obeying the Zintl electron count for M=Mg2+ , Zn2+ , all the compounds reveal noticeable deviations from the conceptual 8-N picture due to significant polar-covalent interactions of Ge with La and M ≠ Li, Mg atoms. For M=Li, Mg a formulation as a germanolanthanate M[La2 Ge6 ] is appropriate. Moreover, the relative Laplacian of ELI-D was discovered to reveal a chemically useful fine structure of the ELI-D distribution being related to polyatomic bonding features. With the aid of this new tool, a consistent picture of La/Y-M interactions for the title compounds was extracted.

The new intermetallic phase SrPt3In2 was synthesized by induction-melting of the elements in a sealed tantalum ampoule followed by long-term annealing for crystal growth. The SrPt3In2 structure was refined from single crystal X-ray diffraction data: Imma, a = 1674.7(6), b = 921.2(4), c = 971.2(4) pm, wR2 = 0.0551, 1192 F2 values and 55 variables. Electronic structure calculations indicate strong covalent Pt–In bonding and a substantial charge transfer from the strontium atoms to the three-dimensional [Pt3In2]δ− polyanionic network. The strontium atoms fill larger cavities within the network and the bonding of strontium to the polyanion is of the electrostatic type. The Bader charge calculations classify SrPt3In2 as a ternary platinide. The close relationship between the SrPt3In2 structure and the aristotype CaCu5 is discussed on the basis of a group–subgroup scheme in the Barnighausen formalism along with other CaCu5 coloring variants and superstructures.

The two La2Pd3Ge5 and Nd2Pd3Ge5 compounds, crystallizing in the oI40-U2Co3Ge5 crystal structure, were targeted for analysis of their chemical bonding and physical properties. The compounds of interest were obtained by arc melting and characterized by differential thermal analysis, scanning electron microscopy, and X-ray diffraction both on powder and on a single crystal (for the La analogue), to ensure the high quality of the samples and accurate crystallographic data. Chemical bonding was studied by analyzing the electronic structure and effective QTAIM charges of La2Pd3Ge5. A significant charge transfer mainly occurs from La to Pd so that Ge species assume tiny negative charges. This result, together with the -(I)COHP analysis, suggests that, in addition to the expected homopolar Ge bonds within zigzag chains, heteropolar interactions between Ge and the surrounding La and Pd occur with multicenter character. Covalent La–Pd interactions increase the complexity of chemical bonding, which could not be adequately described by the simplified, formally obeyed, Zintl–Klemm scheme. Electric resistivity, specific heat, magnetization, and magnetic susceptibility as a function of temperature indicate for both compounds a metallic-like behavior. For Nd2Pd3Ge5, two low-temperature phase transitions are detected, leading to an antiferromagnetic ground state., The chemical bonding and physical properties of the two isotypic R2Pd3Ge5 (R = La and Nd) intermetallics are presented. La2Pd3Ge5 shows polar Ge−Pd/La multicenter interactions in addition to covalent Ge−Ge bonds. The bonding scenario is further complicated by the fact that Pd and La are also covalently interacting. For Nd2Pd3Ge5, an antiferromagnetic ground state is established after a long-range magnetic ordering (at ∼7.5 K) followed by a spin-reorientation transition (at ∼6.2 K).

The two La2Pd3Ge5 and Nd2Pd3Ge5 compounds, crystallizing in the oI40-U2Co3Ge5 crystal structure, were targeted for analysis of their chemical bonding and physical properties. The compounds of interest were obtained by arc melting and characterized by differential thermal analysis, scanning electron microscopy, and X-ray diffraction both on powder and on a single crystal (for the La analogue), to ensure the high quality of the samples and accurate crystallographic data. Chemical bonding was studied by analyzing the electronic structure and effective QTAIM charges of La2Pd3Ge5. A significant charge transfer mainly occurs from La to Pd so that Ge species assume tiny negative charges. This result, together with the -(I)COHP analysis, suggests that, in addition to the expected homopolar Ge bonds within zigzag chains, heteropolar interactions between Ge and the surrounding La and Pd occur with multicenter character. Covalent La-Pd interactions increase the complexity of chemical bonding, which could not be adequately described by the simplified, formally obeyed, Zintl-Klemm scheme. Electric resistivity, specific heat, magnetization, and magnetic susceptibility as a function of temperature indicate for both compounds a metallic-like behavior. For Nd2Pd3Ge5, two low-temperature phase transitions are detected, leading to an antiferromagnetic ground state.

The Sc2Ru compound, obtained by high-temperature synthesis, was found to crystallize in a new trigonal hP45 structure type [space group P3̅m1; a = 9.3583(9) Å and c = 11.285(1) Å]: Ru@Sc8 cubes, Ru@Sc12 icosahedra, and uncommon Ru@Sc10 sphenocoronae are the building blocks of a unique motif tiling the whole crystal space. According to density functional theory studies, Sc2Ru is a metallic compound characterized by multicenter interactions: a significant charge transfer occurs from Sc to Ru, indicating an unexpectedly strong ionic character of the interactions between the two transition metals. Energy calculations support our experimental results in terms of stability of this compound, contributing to the recurrent discussion on the limits of the high-throughput first-principles calculations for metallic materials design., A strong metal (Sc) to metal (Ru) charge transfer occurs for the new Sc2Ru compound, indicating a significant ionic contribution to the bond. The Sc2Ru trigonal crystal structure features a unique structural motif built up by Ru-centered simple cubes and icosahedra connected through hybrid sphenocorona polyhedra. This investigation represents also a little food for thought on the interplay between the experiments and theoretical prediction in metallic materials design.

The new intermetallic compound Eu2Pd2Sn has been investigated. A single crystal was selected from the alloy and was analyzed by single-crystal X-ray diffraction, revealing that this compound possesses the noncentrosymmetric Ca2Pd2Ge structure type being, so far, the only rare-earth-based representative. Bonding analysis, performed on the basis of DOS and (I)COHP, reveals the presence of strong covalent Sn-Pd bonds in addition to linear and equidistant Pd-Pd chains. The incomplete ionization of Eu leads to its participation in weaker covalent interactions. The magnetic effective moment, extracted from the magnetic susceptibility χ(T) is μeff = 7.87 μB, close to the free ion Eu2+ value (μeff = 7.94 μB). The maximum of χ(T) at TN ∼ 13 K indicates an antiferromagnetic behavior below this temperature. A coincident sharp anomaly in the specific heat CP(T) emerges from a broad anomaly centered at around 10 K. From the reduced jump in the heat capacity at TN a scenario of a transition to an incommensurate antiferromagnetic phase below TN followed by a commensurate configuration below 10 K is suggested.

Gold intermetallic chemistry is very rich, covering different classes of compounds ranging from the Hume-Rothery to Zintl phases to polar intermetallics to quasicrystals. Au's relativistic effects are frequently mentioned as responsible for the peculiar structural and physical properties of its compounds, nonetheless the aspects of chemical bonding are far to be clearly understood. In this work, the La–Au–Mg system was targeted for the discovery of new gold intermetallics and their structural and chemical bonding characterization. Studies on solid state interactions resulted in the construction of a partial La–Au–Mg isothermal section at 400 °C. The high reactivity between the constituents is reflected by the formation of five intermetallic compounds in the concentration range of less than 50 at% of Au. A complete crystallographic study was conducted for four of them, namely La1.82Au3+xMg14.36−x (0 ≤ x ≤ 0.90, hP42-3.64-CeMg10.3), La3Au4−xMg12+x (0 ≤ x ≤ 0.75, hP38-Gd3Ru4Al12), LaAuMg2 (oS16-MgCuAl2) and LaAu1+xMg1−x (0 ≤ x ≤ 0.15, hP9-ZrNiAl). A unifying description based on the different stacking sequences of equal slabs along the c-axis is proposed for these intermetallics. Chemical bonding in LaAuMg2 was studied by following the position space approach and including relativistic effects. Among the peculiarities of this LaMg2Au auride, there are two-atomic La–Au bonds showing a classical polar covalent character and that form distorted hexagonal planar layers and multi-atomic bonds involving Mg species. One of these is interpreted as a Mg–Mg bond supported by the neighbouring La and Au atoms, explaining the Mg reduced oxidation state (close to +1) in this compound.

The 500 °C isothermal section of the La–Mg–Sn ternary system was established by scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDXS) and powder X-ray diffraction (XRPD) on more than fifty alloys synthesized by induction melting and annealed. A few boundary binary compounds were found to dissolve the third element, forming ternary solid solutions, among which La(MgxSn1−x)3 (0≤x≤0.14, cP4-AuCu3) is the most extended. The existence and crystal structure of three ternary compounds were confirmed, and their homogeneity ranges at 500 °C determined: La3Mg4−xSn2+x (0.12≤x≤0.40, hP9-Zr3Cu4Si2), LaMg3−xSn2 (0.33≤x≤0.78, hP34-LaMg3−xGe2) and LaMgSn (oP12-TiNiSi). The crystal structures of two novel ternary stoichiometric compounds, found during this work, were determined from powder X-ray diffraction pattern analysis and refined using the Rietveld method: La6Mg23Sn ( F m 3 ¯ m , cF120-Zr6Zn23Si, a =1.47107(1) nm) and LaMgSn2 ( I 4 ¯ 2 m , tI32-LaMgSn2, a =0.83325(3) nm, c =1.24385(5) nm). The latter is the first representative of a new structure type and can be presented as composed by a complex Mg-Sn network hosting the bigger La atoms.

The new intermetallic phase SrPt

A systematic study on the existence of R2Pd3Ge5 intermetallics with heavy rare earth metals (R = Gd–Lu) was conducted; only the Yb2Pd3Ge5 was revealed to exist. Its crystal structure was established by X-ray powder diffraction and refined by means of Rietveld method. This compound crystallizes in the orthorhombic U2Co3Si5 structure type (Ibam, oI40, Z = 4, a = 10.2628(1), b = 12.0580(1), and c = 5.98251(6) A), which represents an ordered derivative of the tI10-ThCr2Si2 prototype, ubiquitous among intermetallics. Magnetization and susceptibility measurements indicate that Yb2Pd3Ge5 is a paramagnet with μeff close to 0.8 μB/Yb-atom, suggesting a nearly divalent Yb state. Electrical resistivity and Seebeck coefficient of the studied compound as a function of temperature confirm its metallic-like behavior.

We present a machine learning approach for evaluating thermodynamic properties within model compositional/configurational spaces (CCSs) of complex intermetallics with Mackay-type building units. Recently, by performing high-throughput density functional theory calculations, we determine and analyze the formation energies for the recently synthesized 1/1 approximant of icosahedral quasicrystals in the Sc-Pd system possessing structural disorder. Here, sequentially increasing training sets are used in regression models based on compositional and topological descriptors for predicting formation enthalpies. We investigate different learning strategies. The obtained R2 dependencies show higher learning rates for the models using real features (composition and contact counters of defects) with small training set sizes, whereas using categorical features (topological types of defect structure fragments) result in a slightly higher prediction quality when the training set size increases. In connection with the obtained results, the proposed approach is considered as a tool for investigations of disordering phenomena in complex intermetallics as well as for a subsequent searching for new stable phases of Mackay-type approximants of quasicrystals.

Atom order in the crystal structures of Yb2Cu2-xMg (x = 0.17; Mo2FeB2-type; P4/mbm; a = 0.75592(2) nm; c = 0.40282(1) nm) and Yb9+xCuMg4-x (x = 0.034; Hf9Mo4B-type; P63/mmc; a = 1.0169(5) nm; c = 1.0290(5) nm) was determined from powder and X-ray single-crystal counter data analyses supported by electron probe microanalyses. Among the group of the so-called κ-phases, Yb9+xCuMg4-x is the first representative formed by a lanthanoid element. The structure of this κ-phase can be viewed as a typical network of corner-connected empty Yb6-octahedra, which encompass Yb6Mg6-icosahedra (filled by a mix of Mg/Yb atoms) and Yb6-trigonal prisms centered by Cu atoms to complete the three-dimensional metal framework. From another point of view, the same structure is considered as built from infinite polyicosahedral columns of Yb9Mg4 composition with Cu atoms located in trigonal prismatic interstices, highlighting similarities with other Yb-rich Yb-Cu-Mg phases. Density functional theory (DFT) calculations classify Yb9CuMg4 as a polar intermetallic. Metallic-like behavior is inferred from the Sommerfeld constant, γ = 49.2 mJ/mol·K(2), derived from the electronic density of states, calculated at the Fermi level. DFT integration of the f-density of states indicates almost completely filled f-states, revealing 13.6 and 13.7 electrons in the valence band for Yb1 and Yb2 atoms, respectively, close to the Yb(2+) ground state ((1)S0) for both Yb atoms. Magnetic susceptibility data recorded on the same compound are consistent with a nonmagnetic divalent Yb(2+) state. Temperature-dependent heat capacity data display a metallic behavior characterized by a small Sommerfeld constant γ = 64.8 mJ/mol·K(2) and a rather low Debye temperature ΘD = 140 K as typical for soft materials.

The crystal structure of the new Er6Zn23Ge intermetallic compound was established by X-ray diffraction analysis on a twinned crystal (space group Fm3̅m, Wyckoff sequence: f2edba, cF120–Zr6Zn23Si, a =12.7726(6) Å). The crystal is composed of two nearly equal size domains, whose mutual orientation is described by a 180° rotation around the cubic [111] axis, i.e. a spinel-type twinning law, not common for intermetallics. Applying the nanocluster approach, Er6Ge octahedra and centered two-shell Zn45 clusters were found as structural building blocks, filling the crystal space in a NaCl-like arrangement. This description was adopted to interpret the twinning in terms of stacking faults in the fcc cubic close packed arrangement. Moreover, the assembly of the nanocluster units is proposed as a possible mechanism for crystal growth and twin formation, in agreement with the principle of the interface energy minimization. Experimental conditions such as supersaturation and co-formation of other phases are also considered as favorable factors for Er6Zn23Ge twin formation.

In this study, two novel Lu5Pd4Ge8 and Lu3Pd4Ge4 polar intermetallics were prepared by direct synthesis of pure constituents. Their crystal structures were determined by single crystal X-ray diffraction analysis: Lu5Pd4Ge8 is monoclinic, P21/m, mP34, a = 5.7406(3), b = 13.7087(7), c = 8.3423(4) Å, β = 107.8(1), Z = 2; Lu3Pd4Ge4 is orthorhombic, Immm, oI22, a = 4.1368(3), b = 6.9192(5), c = 13.8229(9) Å, Z = 2. The Lu5Pd4Ge8 analysed crystal is one more example of non-merohedral twinning among the rare earth containing germanides. Chemical bonding DFT studies were conducted for these polar intermetallics and showing a metallic-like behavior. Gathered results for Lu5Pd4Ge8 and Lu3Pd4Ge4 permit to described both of them as composed by [Pd–Ge]δ– three dimensional networks bonded to positively charged lutetium species. From the structural chemical point of view, the studied compounds manifest some similarities to the Zintl phases, containing well-known covalent fragment i.e., Ge dumbbells as well as unique cis-Ge4 units. A comparative analysis of molecular orbital diagrams for Ge26– and cis-Ge10– anions with COHP results supports the idea of the existence of complex Pd–Ge polyanions hosting covalently bonded partially polarised Ge units. The palladium atoms have an anion like behaviour and being the most electronegative cause the noticeable variation of Ge species charges from site to site. Lutetium charges oscillate around +1.5 for all crystallographic positions. Obtained results explained why the classical Zintl-Klemm concept can’t be applied for the studied polar intermetallics.

The R

The R2PdGe6 series (R = rare earth metal) was structurally characterized, and the results achieved were extended for a comprehensive study on R2MGe6 (M = another metal) compounds, employing symmetry-based structural rationalization and energy calculations. Directly synthesized R2PdGe6 exists for almost all R-components (R = Y, La–Nd, Sm and Gd–Lu) and even if with La is probably metastable. Several single crystal X-ray analyses (R = Y, Ce, Pr, Nd, Er and Lu) indicated oS72-Ce2(Ga0.1Ge0.9)7 as the correct structure. The alternative In-flux method, once optimized, produced three good quality R2PdGe6 single crystals: La2PdGe6 and Pr2PdGe6 turned out to be mS36-La2AlGe6-type non-merohedrally twinned crystals and Yb2PdGe6 is of oS72-Ce2(Ga0.1Ge0.9)7-type. The vacancy ordering phenomenon was considered as a possible cause of the symmetry reduction relations connecting the most frequently reported 2 : 1 : 6 structural models (oS18, oS72 and mS36) with the oS20-SmNiGe3 aristotype. The detected twin formation is consistent with the symmetry relations, which are discussed even considering the validity of the different structural models. DFT total energy calculations were performed for R2PdGe6 (R = Y and La) in the three abovementioned structural models, and for La2MGe6 (M = Pt, Cu, Ag and Au) in the oS18 and oS72 modifications. The results indicate that the oS18-Ce2CuGe6 structure, prevalently proposed in the literature, is associated with the highest energy and thus it is not likely to be realized in these series. The oS72 and mS36 polytypes are energetically equivalent, and small changes in the synthetic conditions could easily stabilize any of them, in agreement with experimental results obtained by direct and flux syntheses.

Phase equilibria in the Yb−Pd−Sn ternary system at 600 °C were established in the Pd ≤ 75 at.% concentration range employing X-ray diffraction (XRD), scanning electron microscopy (SEM) and electron probe micro-analysis (EPMA). Besides the known intermetallic compounds, three new ternary intermetallics were revealed in the system, together with homogeneity ranges into the ternary field for some binary phases. Magnetic properties for the new compounds were investigated revealing stable Yb states Yb3+ for Yb3Pd4Sn13 and Yb2+ for Yb5Pd39Sn56, whereas for Yb13Pd40Sn31 an unstable valency of Yb is suggested.

The novel isostructural series of phases RMgSn2 (R = Y, La–Nd, Sm, Gd–Tm, Lu) is presented. They were prepared by direct synthesis in an induction furnace and subsequently annealed at 500 °C. Their crystal structures were determined through single-crystal X-ray diffraction analysis of the Ce representative [I42m, tI32-LaMgSn2, Z = 8, a = 0.82863(3) nm, c = 1.23129(5) nm] and confirmed by powder X-ray diffraction analysis of the other members of the series. Rietveld refinements were also performed on the homologues with R = Pr, Tm, and Y. The title phases show a unique space distribution of atoms, characterized by the presence of a Sn–Sn dumbbell distanced at around 0.29 nm. Their structures are related to those of a few binary AeTt3 (Ae = alkaline earth; Tt = Si, Ge; I4/mmm, tI32-YbSi3) compounds that are stable at high pressure, characterized by a more complex 3D covalently bonded Tt network. Compounds CeMgSn2 and TbMgSn2 were magnetically characterized; they show paramagnetic behavior with the presence of ferromagnetic interactions, more pronounced in the case of TbMgSn2, as suggested by the Curie–Weiss temperatures, determined in the high-temperature range, of 0.96 and 27.6 K for CeMgSn2 and TbMgSn2, respectively.

The title compounds are prepared by melting mixtures of the elements twice at 1100 °C followed by annealing (Ta crucible, 700 °C, 14 d).

Direct synthesis and structural characterization of a series of polar rare earth palladium germanides of R2Pd3Ge5 composition (R = La–Nd, Sm) is reported. The crystal structure of the Nd representative was determined by single-crystal X-ray diffraction analysis (U2Co3Si5-type, SG: Ibam, oI40, Z = 4, a = 10.1410(6), b = 12.0542(8), c = 6.1318(4) A, wR 2 = 0.0306, 669 F 2 values, 31 variables). The crystal structures of the other homologues were ensured by powder X-ray diffraction pattern analysis. A smooth variation of the cell dimensions is observed through the rare earth series. The structure of the studied compounds can be interpreted as consisting of a complex three-dimensional [Pd3Ge5]δ− network spaced by the rare earth cations. Within the concept of symmetry reduction, a Barnighausen tree is used to rationalize the related crystal structures of the RPd2Ge2, RPdGe3 and R2Pd3Ge5 ternary compounds, enriching the large family of the BaAl4 derivatives. Moreover, syntheses with metal fluxes were performed, some of which were successful to obtain large crystals of La2Pd3Ge5 (using Bi as solvent) and Nd2Pd3Ge5 (using Pb as solvent) stoichiometry.

The crystal chemical features of the new series of compounds R6Mg23C with R = La-Sm or Gd and Ce6Mg23Z with Z = C, Si, Ge, Sn, Pb, P, As, or Sb have been studied by means of single-crystal and powder X-ray diffraction techniques. All phases crystallize with the cubic Zr6Zn23Si prototype (cF120, space group Fm3̅m, Z = 4), a filled variant of the Th6Mn23 structure. While no Th6Mn23-type binary rare earth-magnesium compound is known to exist, the addition of a third element Z (only 3 atom %), located into the octahedral cavity of the Th6Mn23 cell (Wyckoff site 4a), stabilizes this structural arrangement and makes possible the formation of the ternary R6Mg23Z compounds. The results of both structural and topological analyses as well as of LMTO electronic structure calculations show that the interstitial element plays a crucial role in the stability of these phases, forming a strongly bonded [R6Z] octahedral moiety spaced by zeolite cage-like [Mg45] clusters. Considering these two building units, the crystal structure of these apparently complex intermetallics can be simplified to the NaCl-type topology. Moreover, a structural relationship between RMg3 and R6Mg23C compounds has been unveiled; the latter can be described as substitutional derivatives of the former. The geometrical distortions and the consequent symmetry reduction that accompany this transformation are explicitly described by means of the Bärnighausen formalism within group theory.

Synthesis and structural characterization of the two new lanthanum–magnesium–stannides La3Mg4−xSn2+x (0.12≤x≤0.40) and LaMg3−xSn2 (0.33≤x≤0.78) are reported. The crystal structures of these intermetallics were determined by single crystal X-ray diffraction analysis and confirmed by Rietveld refinement of powder X-ray diffraction patterns of the corresponding samples. The La3Mg4−xSn2+x phase crystallizes in the hexagonal Zr3Cu4Si2 structure type (P6¯2m, hP9, Z=3, x=0.12(1), a=7.7974(7), c=4.8384(4) A), which represents an ordered derivative of the hP9-ZrNiAl prototype, ubiquitous among equiatomic intermetallics. The LaMg3–xSn2 phase is the second representative of the trigonal LaMg3−xGe2 type, which is a superstructure of the LaLi3Sb2 structure type (P3¯1c, hP34-0.12, Z=6, x=0.35(1), a=8.3222(9), c=14.9546(16) A). The scheme describing the symmetry reduction/coloring with respect to the parent type is reported here with the purpose to discuss the LaMg3−xSn2 off-stoichiometry from the geometrical point of view. Structural relationships between the La–Mg–Sn ternary phases, including the already known equiatomic LaMgSn compound (oP12-TiNiSi), are presented in the framework of the AlB2-related compounds family and discussed with the aid of group-subgroup relations in the Barnighausen formalism.

The crystal structures of three new La–Ag–Mg ternary phases were solved and refined from X-ray diffraction data recorded on single crystals. All the studied phases show wide homogeneity regions extending at a constant La concentration. The Mg-rich compound La(AgxMg1–x)12 (0.11 ≤ x ≤ 0.21) crystallises with a large tetragonal unit cell [I, I41/amd, tI208, own str. type, Z = 16, a = 10.1686(10), c = 46.539(5) A, R1 = 0.013, wR2 = 0.025, x = 0.12]. The Ag-rich phase LaAg4+xMg2–x (–0.15 ≤ x ≤ 1.05) shows two structural modifications: body-centred tetragonal for an Ag content lower than ca. 70 at.-% [II, I4/mmm, tI14, YbAl4Mo2-type, Z = 2, a = 7.1995(3), c = 5.5996(2) A, R1 = 0.031, wR2 = 0.081, x = 0.4] and primitive tetragonal for a higher Ag-content [III, P4/nmm, tP14, own str. type, Z = 2, a = 7.2227(4), c = 5.4433(9) A, R1 = 0.013, wR2 = 0.030, x = 0.9]. These two structural models are group-subgroup related (LaAg5Mg is the k2 subgroup of LaAg4Mg2) as usual for second-order transformations. The LaAg2+xMg2–x phase (0 < x ≤ 0.45) crystallises with an orthorhombic unit cell [IV, Cmcm, oS20, own str. type, Z = 4, a = 4.805(1), b = 17.258(4), c = 5.527(1) A, R1 = 0.029, wR2 = 0.081, x = 0.25]. In order to gain insights into their bonding peculiarities, calculations of the electronic structures (LMTO approach) were performed on idealised stoichiometric models of the studied compounds representing a chemical modelling of mixed occupations. We also computed the structural parameters of the Ag-rich phases and the vibrational properties of LaAg4+xMg2–x within the pseudopotential approach in generalised-gradient approximation (GGA).

The crystal structures of two new ternary phases, La{sub 4}Ag{sub 10}Mg{sub 3} and La{sub 4}Ag{sub 10.3}Mg{sub 12}, were refined from X-ray single crystal diffraction data. La{sub 4}Ag{sub 10}Mg{sub 3} crystallizes in the Ca{sub 4}Au{sub 10}In{sub 3} structure type, an ordered variant of the binary Zr{sub 7}Ni{sub 10} compound: orthorhombic, Cmce, oS68, a=14.173(5), b=10.266(3), c=10.354(3) A, Z=4, wR{sub 2}=0.0826, 676 F{sup 2} values, 50 variables. La{sub 4}Ag{sub 10.3}Mg{sub 12} represents a new structure type: orthorhombic, Cmmm, oS116-10.32, a=9.6130(3), b=24.9663(8), c=9.6333(2) A, Z=4, wR{sub 2}=0.0403, 1185 F{sup 2} values, 101 variables. The structural analysis of both compounds, highlighting a significant contraction of the Ag-Mg distances, suggests the existence of three-dimensional [Ag-Mg] networks hosting La atoms. LMTO calculations applied to La{sub 4}Ag{sub 10}Mg{sub 3} indicate that the strongest bonds occur for Ag-Ag and Ag-Mg interactions, and confirm the presence of a 3D{sub {infinity}}[Ag{sub 10}Mg{sub 3}]{sup {delta}}{sup -} polyanionic framework balanced by positively charged La atoms. -- Graphical abstract: An independent fragment of the 3D [Ag-Mg] framework in La{sub 4}Ag{sub 10}Mg{sub 3} together with an ELF section (1/2 0 0 basal plane). Display Omitted

Synthesis and characterization of about fifty alloys were performed in order to construct the isothermal section of the Y–Cu–Mg ternary system at 400 °C in the 0–66.7 at.% Cu concentration range. Scanning electron microscopy (SEM), energy dispersive X-ray spectroscopy (EDXS) and X-ray powder diffraction (XRPD) techniques were used to examine microstructures, identify phases and define their compositions and crystal structures. Phase equilibria in the investigated compositional region are characterized by the absence of extended ternary solid solutions and by the presence of at least ten ternary phases. Crystal structures of the previously reported Y 2 Cu 2 Mg, Y 5 Cu 5 Mg 8 , Y 5 Cu 5 Mg 13 , Y 5 Cu 5 Mg 16 and YCuMg 4 phases were confirmed. A ternary phase with homogeneity range around the YCu 4 Mg stoichiometry was found, crystallizing in the cF24--MgCu 4 Sn structure type; at 400 °C this phase coexists with a ternary solid solution based on the binary Laves phase Cu 2 Mg, which dissolves about 5 at.% Y. The equiatomic YCuMg phase was also found to exist: from the analysis of X-ray powder patterns it is suggested to crystallize in the hP9--ZrNiAl structure type ( a = 0.74449(4) nm, c = 0.39953(2) nm). Two other stoichiometric ternary phases were detected, of approximate compositions Y 25 Cu 18 Mg 57 and Y 13 Cu 9 Mg 78 , whose crystal structures are still unknown. In the Mg-rich region, a ternary phase forms characterized by a large homogeneity region.

The isothermal section of the La–Ni–Zn system at 400 °C was studied from 16.7 to 100 at.% La, by coupling X-ray powder diffraction and SEM–EDXS analyses on induction melted samples. Several binary phases were found to dissolve an appreciable amount of the third element forming ternary solid solutions which extend along lines at a constant La content. Particularly, a continuous solid solution was detected between the LaNi5 and LaZn5 isostructural compounds. Seven ternary phases were found to exist at 400 °C, both stoichiometric and showing homogeneity ranges at a constant La concentration. The crystal structures of LaNiZn (hP9-ZrNiAl), La2Ni2Zn (oI10-Pr2Ni2Al) and La3Ni3Zn (oS28-Y3Co3Ga) were confirmed; quite extended homogeneity ranges were detected for the last two phases. The crystal structure of the new phase of stoichiometry La7Ni2Zn was solved ab initio from X-ray powder diffraction data: it crystallizes in its own structure type, tetragonal, P4/mbm, tP20, a = 1.24104(9) nm, c = 0.38256(3) nm. A phase of general formula La(Ni,Zn)3 extends from about 2.5 to 9 at.% Zn whose crystal structure corresponds to the hexagonal CeNi3 type: a negligible addition of Zn is likely to stabilize this structure instead of the analogue rhombohedral PuNi3 type, which the binary compound LaNi3 crystallizes in. Two more ternary phases were found in the isothermal section at 400 °C: the stoichiometric ∼La3Ni4Zn3 and the LaNi1+xZn2−x (0

The crystal structures of the new ternary compounds LaCuMg4 and TbCuMg4 were studied by X-ray powder diffraction and single-crystal methods, respectively. Scanning electron microscopy (SEM) coupled with energy dispersive X-ray spectroscopy (EDXS) was used for examining microstructure and phase composition. LaCuMg4 crystallizes in the UCoAl4 structure type (space group P6¯2m, Pearson code hP18, a=1.03911(1), c=0.45126(1) nm, Z=3, RF=0.0654), while TbCuMg4 exhibits a new structure (space group Cmmm, Pearson code oS48, a=1.35797(6), b=2.03333(9), c=0.39149(2) nm, Z=8, wR2=0.0426). Both structures represent a family of two-layer compounds. All interatomic distances indicate metallic type bonding. The structural peculiarities of these compounds and their relations are discussed.

Single crystals of diterbium dinickel trimagnesium, Tb2Ni2Mg3, were synthesized from the elements by induction melting. The novel compound crystallizes in the space group Cmmm with one Mg atom of site symmetry mmm and the Tb, Ni and other Mg atom in m2m positions. This ternary compound represents a new structure type that is derived from Ru3Al2B2 by way of Wyckoff site distribution. The two-layer structure of Tb2Ni2Mg3 is a new representative of a homologous linear structure series of general formula R′k+nX2nR′′2m+k based on structural fragments of the α-Fe, CsCl and AlB2 structure types. The Tb atoms in the structure are enclosed in 17-vertex polyhedra, while rhombododeca­hedra and distorted rhombododeca­hedra surround the Mg atoms, and equatorially tricapped trigonal prisms form around the Ni atoms. All inter­atomic distances indicate metallic type bonding.

The new compounds Ln2Zn1-xGe6 (Ln: La—Nd, Sm, Gd—Ho) are prepared from the elements (Ta crucible, 950 °C) and characterized by single crystal XRD.

Synthesis and structural characterization of the new compounds R2Zn1-xGe6 (R = La-Nd, Sm, Gd-Ho) is reported. A structural change was revealed along this series by careful analysis of single-crystal X-ray diffraction data. For light rare earths up to Tb the orthorhombic oS72-Ce2(Ga0.1Ge0.9)7 model was established; instead, the Dy compound represents a new structure type (P21/m, mP34, Z = 4, a = 7.9613(3) Å, b = 8.2480(4) Å, c = 10.5309(5) Å, β = 100.861(1)°) being a superstructure of the mS36-La2AlGe6 prototype. The established structural models support the increase of Zn deficiency along the series, suggested by microprobe analysis, and its key role in governing structural changes. The vacancy ordering criterion was applied as a successful approach to find a general scheme including the structures of the ∼R2MGe6 compounds known up to now (R = rare-earth metal, M = transition metal, Mg, Al, Ga) and highlighting the subtle structural differences within this family. According to this scheme, these structures are obtained from a common aristotype (oS20-SmNiGe3) via symmetry reduction based on group-subgroup relations accompanied by ordering of vacancies. This approach was optimized with the help of the ToposPro software and extended to the R2Zn3Ge6 series, enriched with new members (R = Sm, Gd-Ho) during this work. Electronic structure calculations on La2ZnGe6 confirm the presence of infinite covalent germanium zigzag chains and three-bonded corrugated layers connected via Zn atoms to form a polyanionic network stabilized by La atoms.

The isothermal section of the Ce–Cu–Zn phase diagram was constructed at 200 °C over the whole concentration range as a result of X-ray powder diffraction, wavelength dispersive spectrometry and electron probe microanalysis. The existence of one new ternary compound Ce2Cu5–5.7Zn2–1.3 was observed at this temperature and its crystal structure was refined from X-ray single crystal data (structure type Ce2Ni5Zn2, space group R 3 ¯ m , Pearson code hR18, a = 0.4998(1)–0.5078(1) nm, c = 3.6924(5)–3.6987(4) nm). The homogeneity regions were determined for a number of solid solutions on the basis of binary phases.

Investigations of the solid solution of CeCu 5− x Zn x composition (CaCu 5 structure type) are presented in this article. We refined the XPD patterns for the series of alloys of the CeCu 5 –CeZn 5 pseudobinary system. The crystal structure of this solid solution was determined by means of the single crystal and powder X-ray methods. Besides, the limit of the measured solid solution has been determined. WDS and EPMA were used for examining the number of phases and the phase content.

The limited solid solution CeCu6−xZnx, x=0÷0.84 (structure type CeCu6, space group Pnma, Pearson code oP28, a=0.8112(1)÷0.8154(2), b=0.5102(1)÷0.5056(1), c=1.0162(2)÷1.0185(2) nm) was observed in the Ce–Cu–Zn ternary system at 200 °C. The homogeneity range of the solid solution was investigated by X-ray powder diffraction, wavelength dispersive spectrometry (WDS) and electron probe microanalysis (EPMA). X-ray single crystal diffraction was used for the detailed refinement of the crystal structure of CeCu5.16Zn0.84.

The crystal structure of new RTZn 2 intermetallic compounds (R = La, Ce, Tb; T = Co, Cu) was determined. The X-ray diffraction data showed that these compounds are isostructural to the new ternary compound ErCuCd 2 , which was found to crystallize with a superstructure of the ErCd 3 structure type (space group Cmcm, Pearson code oS16, a = 0.7097(1) nm, b = 1.0659(3) nm, c = 0.4471(1) nm, V = 0.3382(2) nm 3 , Z = 4). The obtained reliability factors are R F = 0.0240 and R W = 0.1127 for 235 unique reflections (|F 0 | > 4.00σ|F 0 |).

The 500 °C isothermal section of the phase diagram of the title system is constructed over the whole composition range.

The whole 500 °C isothermal section of the La–Mg–Ge ternary system was constructed. The existence and crystal structure of three ternary compounds were confirmed: La2+xMg1−xGe2 (τ2, P4/mbm, tP10–Mo2FeB2, 0≤x≤0.25), La4Mg5Ge6 (τ3, Cmc21, oS60–Gd4Zn5Ge6) and La4Mg7Ge6 (τ4, C2/m, mS34, own structure type). Five novel compounds were identified and structurally characterized: La11Mg2Ge7 (τ1, P42/ncm, tP88-8, own structure type, a=1.21338(5), c=1.57802(6) nm), LaMg3−xGe2 (τ5, P 3 ¯ 1c, hP34-0.44, own structure type, x=0.407(5), a=0.78408(4), c=1.45257(7) nm), La6Mg23Ge (τ6, Fm 3 ¯ m, cF120–Zr6Zn23Si, a=1.46694(6) nm), La4MgGe10−x (τ7, x=0.37(1), C2/m, mS60-1.46, own structure type, a=0.88403(8), b=0.86756(8), c=1.7709(2) nm, β=97.16°(1) and La2MgGe6 (τ8, Cmce, oS72–Ce2(Ga0.1Ge0.9)7, a=0.8989(2), b=0.8517(2), c=2.1064(3) nm). Disordering phenomena were revealed in several La–Mg–Ge phases in terms of partially occupied sites. The crystal structures of La11Mg2Ge7 and LaMg3−xGe2 are discussed in details. The latter is a √3a×√3a×2c superstructure of the LaLi3Sb2 structure type; the symmetry reduction scheme is shown in the Barnighausen formalism terms.

The isothermal section of the La-Co-Mg system at 400 °C was determined by characterization of about thirty ternary alloys synthesised by induction melting in sealed Ta crucibles and then annealed. Scanning electron microscopy (SEM) coupled with energy dispersive x-ray spectroscopy (EDXS) and x-ray powder diffraction (XRPD) were used to analyze microstructures, identify phases, measure their compositions and determine their crystal structures. Phase equilibria are characterized by the absence of ternary solid solutions and by the presence of three ternary phases. The existence and the crystal structure of the La4−x CoMg1 + x (τ1, 0 ≤ x ≤0.15, cF96-Gd4RhIn) were confirmed and its homogeneity region determined; the new phases La23−x Co7Mg4 + x (τ2, −0.50≤ x ≤0.60, hP68-Pr23Ir7Mg4) and ~La38Co55Mg7 (τ3, unknown crystal structure) were detected.

The title phases illustrate the tendency of Ag and Mg to substitute each other, forming compounds with extended homogeneous regions.

The structures of MgNi nanoparticles are searched for by a computational methodology combining atomistic modeling, global optimization searches and density-functional theory (DFT) calculations. Sizes of up to 45 atoms are considered for several different compositions. Core-shell structures are found in most cases. However, there are also exceptions, such as the three-shell high-symmetry matryoshka clusters Mg@Ni-12@Mg-32 (of anti-Mackay icosahedral geometry) and Mg@Ni-12@Mg-14 (of tetrahexahedral geometry). Other high-symmetry structures comprise the core-shell cubic Mg8Ni6, the tetrahexahedral cluster Mg14Ni13 and the pentadocahedral cluster Mg21Ni12. The results of the atomistic models are compared with DFT calculations, obtaining a good agreement.

Single crystals of the title compounds are prepared by induction-melting of the elements (nominal compositions La20Mg38Ge42 and La16Mg57Ge27, resp.) in Ta crucibles, followed by annealing at 500 °C for 25 d.