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X-ray single-crystal structure analysis was performed for the novel compound V1.84Fe1.16B2 ≡ (V1-xFex)2FeB2 at x = 0.08 (P4/mbm; a = 0.555931(9) nm, c = 0.306781(5) nm; U3Si2-type). Consequently, structural identity is obvious between (V0.92Fe0.08)2FeB2 and the precipitates V∼2Fe∼1B2 earlier identified in the UGISTAB215XH permanent magnet. Magnetic and 57Fe Mossbauer studies of (V0.92Fe0.08)2FeB2 reveal a magnetically ordered ground state with Tc∼110 K. Mossbauer spectra point towards a ferrimagnetic spin arrangement. Enthalpy of formations (DFT calculations) for (Fe,V), VB, V3B2, and the hypothetical solution V3-xFexB2 (x Calculation of the electron localization function elf yielded a very high value (ϒ ∼0.75) between boron atoms documenting strong covalent bonding. The Young's modulus E (from nano-indentation) for V1.84Fe1.16B2 is 442 GPa. The higher anisotropy in the ternary boride V2FeB2 is concluded from the significantly higher difference between C11 and C33 in V2FeB2 (192.1 GPa) with respect to V3B2 (117.0 GPa).

We synthesized a new ternary stannide CePd 3 Sn 2 and determined its crystal structure from single crystal x-ray diffraction. This compound crystallizes in the orthorhombic structure with space group Pnma (No.62). One-dimensional chains of the shortest Ce-Ce contacts at 0.47663(1) nm run along the b axis. Both specific heat C and susceptibility χ of polycrystalline samples show a pronounced peak at T N = 0.6 K indicating an antiferromagnetic order. An obvious tail in C ( T ) appears in the temperature range from T N up to 3 K where the magnetic entropy S m reaches Rln2. Meanwhile, the electrical resistivity ρ exhibits an upward curvature without showing any sign of Kondo scattering. The unusual behaviors of C ( T ) and ρ ( T ) above T N are attributed to antiferromagnetic short-range correlations in the Ce-Ce chain.

The phase equilibria in the Gd–Ni–Sb and Lu-Ni-Sb ternary systems were studied at 873 K by X-ray and metallographic analyses in the whole concentration range. The interaction of the elements in the Gd–Ni–Sb system results the formation of five ternary compounds at investigated temperature: Gd5Ni2Sb (Mo5SiB2-type), Gd5NiSb2 (Yb5Sb3-type), GdNiSb (MgAgAs-type), Gd3Ni6Sb5 (Y3Ni6Sb5-type), and GdNi0.72Sb2 (HfCuSi2-type). At investigated temperature the Lu-Ni-Sb system is characterized by formation of the LuNiSb (MgAgAs-type), Lu5Ni2Sb (Mo5SiB2-type), and Lu5Ni0.56Sb2.44 (Yb5Sb3-type) compounds. The disordering in the crystal structure of half-Heusler GdNiSb and LuNiSb was revealed by EPMA and studied by means of Rietveld refinement and DFT modeling. The performed electronic structure calculations are in good agreement with electrical transport property studies.

International audience; Phase relations in the Th-Pd-B system were determined via electron microprobe and X-ray powder diffraction analyses of similar to 20 ternary alloys. Phase equilibria are dominated by the two high-melting thorium borides ThB4, Th1-yB6 and one ternary compound, namely tau(1)-Th2Pd14+xB5, with a structure deriving from the Sc4Ni29B10-type. Th1-yB6 is the binary starting point of a continuous solid solution up to ThPd0.53B4.28 closely corresponding to the superconducting phase Th1-yPdxB6-2x (x

Phase equilibria in the isothermal sections of the ternary systems Sr-{Ag, Au}-{Si, Ge} were determined in the (Si) or (Ge) rich part up to 33.3 at % Sr after annealing at 700 °C (Sr-{Ag, Au}-Ge) or 800 °C (Sr-{Ag, Au}-Si). Tentative liquidus projections were constructed for the Si, Ge-rich part of all the four phase diagrams. These systems are characterized by a series of ternary compounds, exhibiting in some cases extended homogeneity regions at a constant Sr content. Compounds in the Si, Ge-rich region essentially form along two sections: at 33.3 at % Sr (AlB2-family) and at 20 at % Sr (BaAl4-family of structure types). The crystal structures of the novel equilibrium phases were derived by X-ray single crystal diffraction: Sr2Ag1+xSi3–x–y□y [Sr2LiSi3 type; x = 0.17, y = 0.43: a = 8.4488(2), b = 14.6376(2), c = 18.4018(2) A], SrAg2–xSi2+x [ThCr2Si2 type; x = 0.1: a = 4.37664(6), c = 10.4517(2) A], Sr(Au1–y□y)(Si1–xAux)3 [BaNiSn3 type; x = 0.59, y = 0.64: a = 4.4594(2), c = 10.1013(6) A] and SrAu5–x□xSi2 [BaAu5Si2 type; x = 0.7: a = 8.7557(3), b = 6.9945(2), c = 9.8873(3) A]. The crystal structures of Sr(AgxGe1–x)2 [AlB2 type; x = 0.25: a = 4.3431(2), c = 4.5938(1) A], SrAg2–xGe2+x [ThCr2Si2 type; x = 0.2: a = 4.4476(2), c = 10.822(1) A] and Sr(AuxGe1–x)2 [AlB2 type; x = 0.25: a = 4.3263(2), c = 4.5852(7) A] were evaluated by X-ray powder Rietveld analysis. Composition dependent polymorphism was observed among the BaAl4-type derivative structures for SrAu2–xGe2+x: CaBe2Ge2 type [x = 0.45: a = 4.4796(2), c = 10.6315(5) A], BaCu2Sb2 type [x = 0.35: a = 4.4866(2), c = 31.808(1) A] and ThCr2Si2 type [x = 0.2: a = 4.5214(4), c = 10.336(1) A]. Similarly, Sr(AuxSi1–x)2 exhibits the Ca2AgSi3 structure type [x = 0.25: a = 8.3407(2), b = 14.4465(2) and c = 9.2664(3) A] and the AlB2 type [x = 0.375: a = 4.2241(2), c = 4.5799(3) A]. The structural chemistry of the BaAl4 derivative structures within the sections SrT2–xX2+x is discussed.

Phase equilibria of the system Ti–Ni–Sn have been determined for the isothermal section at 950 °C based on X-ray powder diffraction (XPD) and electron probe microanalysis (EPMA) of about 60 ternary alloys in as cast and annealed state. The section is characterized by the formation of four ternary compounds labelled τ1 to τ4. Whereas two of the ternary compounds are found without significant homogeneity regions: τ1-TiNiSn (half Heusler phase, MgAgAs-type), τ3-Ti2Ni2Sn (U2Pt2Sn-type), τ4-(Ti1−x−ySnxNiy)Ni3 with AuCu3-type exhibits a solution range (0.22 ≤ x ≤ 0.66 and 0.22 ≥ y ≥ 0.02) and a particularly large homogeneity region is recorded for τ2-Ti1+yNi2−xSn1−y (Heusler phase, MnCu2Al-type). Extended solid solutions starting from binary phases at 950 °C have been evaluated for Ti5Ni1−xSn3 (filled Mn5Si3 = Ti5Ga4-type; 0 ≤ x ≤ 1), Ti1−xSnxNi3 (TiNi3-type; 0 ≤ x ≤ 0.27) and (Ti1−xNix)1−ySny (CsCl-type) reaching a maximum solubility at x = 0.53, y = 0.06). From differential thermal analysis (DTA) in alumina crucibles under argon a complete liquidus surface has been elucidated revealing congruent melting for τ2-TiNi2Sn at 1447 °C, but incongruent melting for τ1-TiNiSn (pseudobinary peritectic formation: + τ2 ↔ τ1 at 1180 °C), τ3-Ti2Ni2Sn (peritectic formation: L + τ2 + Ti5NiSn3 ↔ τ3 at 1151 °C) and τ4-Ti1−xSnxNi3 (peritectic formation: L + TiNi3 + (Ni) ↔ τ4 at 1157 °C). A Schultz–Scheil diagram for the solidification behavior was constructed for the entire diagram involving 20 isothermal four-phase reactions in the ternary. For a thermodynamic CALPHAD assessment of the ternary diagram we relied on the binary boundary systems as modelled in the literature. As thermodynamic data in the ternary system were only available in the literature for the compounds TiNi2Sn and TiNiSn, heat of formation data were supplied by our density functional theory (DFT) calculations for Ti2Ni2Sn, as well as for the solid solutions, which were modelled for Ti1−xSnxNi3, Ti5Ni1−xSn3 and (Ti1−xNix)1−ySny. Thermodynamic calculation was performed with the Pandat software and finally showed a reasonably good agreement for all the 20 invariant reaction isotherms involving the liquid.

Phase relations have been established by electron probe microanalysis (EPMA) and X-ray powder diffraction (XPD) for the Sr-poor part of four ternary systems: Sr–{Pd,Pt}–Si at 900 °C and Sr–{Pd,Pt}–Ge at 700 °C. In the Sr–Pd–Si system the formation of the silicide SrPdSi 3 (BaNiSn 3 -type) was confirmed and a small homogeneity region was found. Furthermore, two novel compounds were detected and their crystal structure was refined from X-ray powder patterns: SrPd 0.3 Si 1.7 (AlB 2 -type) and SrPd 5.9 Si 6.1 (own-type). In the Sr–Pt–Si ternary system a novel compound with AlB 2 -type was discovered (SrPt 0.3 Si 1.7 ), whereas SrPtSi 3 with the BaNiSn 3 -type was confirmed. Two more compounds were detected by EPMA, but their crystal structure remains unknown. In the Sr–{Pd,Pt}–Ge systems no new compounds were observed, but the existence of SrPdGe 3 and SrPtGe 3 (both adopt the BaNiSn 3 structure type), and SrPt 4 Ge 12 , crystallizing in the LaFe 4 Sb 12 structure type, was corroborated. For selected ternary silicides the electronic structure was evaluated by DFT calculations.

The phase relations in the Ge-rich corner of the Sr–Ni–Ge system are investigated at 700 °C by X-ray powder diffraction and electron probe microanalysis. The formation of one ternary compound, SrNiGe 3 , crystallizing in the BaNiSn 3 -structure type, is observed. No clathrate-I compound was detected in as cast or annealed state. Theoretical calculations based on density functional theory (DFT) were performed to gain information on the heat of formation for three different clathrate-I compounds, Sr 8 T 6 Ge 40 (T = Ni, Cu, Zn) and relevant other Ge-rich ternary compounds, namely SrT 2 Ge 2 (T = Cu, Zn) and SrNiGe 3 . Based on these data and the phase relations at 700 °C energies of formation of the clathrate-I phases were calculated and predictions of the phase equilibria at 0 K are provided.

The phase equilibria in the Zr–Co–Sb ternary system were studied at 873 K by means of X-ray and metallographic analyses in the whole concentration range. The interaction between the elements results the formation of four ternary compounds at investigated temperature: ZrCoSb (MgAgAs-type), Zr6CoSb2 (K2UF6-type), Zr5CoSb3 (Hf5CuSn3-type) and Zr5Co0.5Sb2.5 (W5Si3-type). The limited composition Zr5CoSb3 of the solid solution based on the Zr5Sb3−4 binaries is considered as compound with Hf5CuSn3 structure type. The influence of the disordering and defects in the crystal structure of ZrCoSb on the physical properties was analyzed. The performed electronic structure calculations are in good agreement with electrical and magnetic studies.

Phase relations for the Ba-poor part of the ternary system Ba–Zn–Sn at 500 °C were established by electron probe microanalysis (EPMA) and X-ray powder diffraction (XPD). Besides the already known compounds BaZnSn (ZrBeSi type) and BaZn 2 Sn 2 (CaBe 2 Ge 2 type), a novel ternary compound BaZnSn 2 was found to crystallize with the CeNiSi 2 -type. The precise determination (EPMA) of the homogeneity region at 500 °C for the compound BaZn 1− x Sn 1+ x with the ZrBeSi type (0.22 ⩽ x ⩽ 0.35) excludes the stoichiometric composition. The stannide BaZn 2− x Sn 2+ x ( x = 0.05) is characterized by mixed occupancy of Zn and Sn atoms in the 2 c site; accordingly the composition is slightly shifted from stoichiometry 1:2:2. Structural effects in the Ba–Zn–Sn compounds were explained on the basis of crystal chemistry analyses and electronic structure calculations employing the electron localization function ELF. The solubility of Sn in the clathrate phase Ba 8 Zn 7 Si 39 was found to be insignificant (around 1 at.%; 800 °C).

Constitution of the ternary systems Nb-Co-B and Ta-Co-B was studied, employing optical and electron microscopy, x-ray powder, single crystal diffraction, electron probe microanalysis, DTA and Pirani melting point measurements. Ternary phase equilibria were determined within an isothermal section at 1100 °C. For the Co-rich part (≥50 at.% Co) of the system, a liquidus surface projection and a corresponding Schulz-Scheil reaction scheme were constructed in combination with data for primary crystallization from as-cast samples determined by SEM and EPMA measurements. The crystal structures of novel ternary compounds have been elucidated by x-ray powder and single crystal diffraction and were supported by TEM. {Nb,Ta}CoB with NbCoB-type exhibits a high temperature modification (ZrAlNi-type, a = 0.5953 nm, c = 0.3248 nm; a = 0.5926 nm, c = 0.3247 nm for Nb and Ta respectively), which was only present in as-cast alloys, but found to be stabilized by the addition of Fe to annealing temperatures of 1400 °C. Ta3Co4B7 (a = 0.3189 nm, b = 1.8333 nm, c = 0.8881 nm) was proven to be isotypic with Nb3Co4B7. The novel orthorhombic compounds {Nb,Ta}Co2B3 (TaCo2B3-type with space group Pnma; a = 0.53628 nm, b = 0.32408 nm, c = 1.24121 nm for TaCo2B3; a = 0.53713 nm, b = 0.32442 nm, c = 1.2415 nm for NbCo2B3) adopt unique structure types with branched boron zig-zag chains. {Nb,Ta}Co2B were found to crystallize in a unique monoclinic structure type (space group P21/c; a = 0.9190 nm, b = 0.64263 nm, c = 0.63144 nm; β = 109.954°, for Nb) very close to an orthorhombic setting (Cmce, a = 0.63162 nm, b = 1.72810 nm, c = 0.64270 nm, for Nb). Substitution of Co by Ni stabilizes a smaller orthorhombic lattice with Re3B-type structure (Cmcm) although no homologue compound in the Ni-system exists. The crystallographic relations among the structure types of Re3B and pseudo-orthorhombic as well as monoclinic {Nb,Ta}Co2B were defined in terms of a Barnighausen scheme. DFT calculations revealed very close stabilities for the three competing structure types for {Nb,Ta}Co2B. Detailed transmission electron microscopy (TEM) for Nb(Co,Fe)B, {Nb,Ta}Co2B, {Nb,Ta}(Co,Ni)2B, and Ta3Co4B7 confirmed lattice geometries and crystal symmetry. Vickers hardness was measured for {Nb,Ta}Co2B, {Nb,Ta}(Co,Ni)2B, {Nb,Ta}2−xCo21+xB6 and {Nb,Ta}Co2B3 exhibiting the highest value of hardness of HV = 22.4 ± 1.1 GPa for TaCo2B3. Magnetic, specific heat and electrical resistivity measurements on the compounds TaCo2B and Ta2Co21B6 reveal paramagnetic and ferromagnetic metallic ground states, respectively.

Phase relations in the {Si,Ge}-rich part of the three systems Ba–Ir–Ge and Ba–{Rh,Ir}–Si were investigated by means of X-ray single crystal (SC) and powder diffraction (XPD), EPMA and DTA measurements. For Ba–Ir–Ge, partial isothermal sections were constructed at 800 °C and 700 °C. The clathrate solid solution extends from binary Ba8Ge43□3 to Ba8Ir0.4Ge43□2.6 with a slightly enlarged lattice parameter a = 2.13402(2) nm ( I a 3 ¯ d , Ba8Ge43□3-type). Two new ternary stoichiometric compounds were found and their crystal structures were determined by X-ray diffraction: τ1-BaIr2Ge7 (Pmna, own type, a = 3.7782(1), b = 0.64099(2), c = 0.64401(2) nm; RF = 0.0331, SC-data) and τ2-Ba3Ir4Ge16 (P4/mmm, Ba3Rh4Ge16-type, a = 0.653948(6), c = 2.22849(3) nm; RF = 0.0388, XPD-Rietveld analysis). The isothermal sections of the Ba–{Rh,Ir}–Si systems were investigated at 950 °C. Whereas in the Ba–Rh–Si system a clathrate-type I solid solution κI-Ba8RhxSi46−x extends within 2.6 ≤ x ≤ 2.9, the corresponding clathrate-I phase in the Ba–Ir–Si system, κI-Ba8Ir1.8Si44.2 ( P m 3 ¯ n , Na4Si23-type, a = 1.0346(1) nm), is not stable at this temperature, but was clearly observed in the as cast state. The analysis of temperature dependent atomic displacement parameters (100–300 K) of guest and framework atoms for κI-Ba8IrxGe46−x−y□y revealed Debye (θD) and Einstein (θE) temperatures of θD = 244 K, θE,11 = 85 K, and θE,22,33 = 64 K proving the rattling nature of the Ba-atoms in the large Ge-based tetrakaidecahedral cages. A similar analysis for κI-Ba8RhxSi46−x yields significantly higher Debye and Einstein temperatures, θD = 508 K, θE,11 = 115 K, θE,22,33 = 99 K, i.e. a tight bonding of Ba-atoms to the smaller Si-based cages. This behavior is further reflected by the pronounced difference in the thermal expansion coefficients: α100–300 K = 13.7 × 10−6 K−1 (κI-Ba8IrxGe46−x−y□y) and α100–300 K = 7.3 × 10−6 K−1 (κI-Ba8RhxSi46−x).

Phase relations for the system Ni–Zn–B have been established in the isothermal section at 800 °C based on X-ray powder diffraction and electron microprobe analyses of about 60 samples, which have been prepared by hot pressing of pre-annealed powder compacts of arc-melted master alloys NixBy and Zn-filings. Six ternary compounds (labeled τ1 to τ6) were found to exist, which in some cases exhibit considerable mutual solid solubilities mostly as an exchange of Ni–Zn at constant B-content, but in the case of the so-called τ-phase τ1-(Ni1−xZnx)21[Zn1−y−z□y(B4)z]2B6 (0.07≤x≤0.11, 0.07≤y≤0.53, 0≤z≤0.3) also with Zn/B substitution. Single crystal X-ray data analysis for the composition x=0.07, y=0.125, z=0.30, and a=1.05800(3) nm confirmed the Cr23C6 type with space group F m 3 ¯ m , but revealed partial replacement of Zn-atoms by B4-tetrahedra (RF=0.014). Whereas Ni/Zn exchange (at constant B-content) ranges at about 4–5 at% for τ4-Ni3ZnB2 and τ5-Ni48Zn32B20, it is below 3 at% for τ2-Ni12ZnB8−x (x=0.43), τ3-Ni21Zn2B20 and τ6-Ni47Zn23B30. The crystal structures of τ2-Ni12ZnB8−x (x=0.43; Ni12AlB8 type), τ3-Ni21Zn2B20 (own type) and τ4-Ni3ZnB2 (own type) have been determined in our foregoing paper [8] . Due to the non-availability of suitable single crystals, the crystal structures of τ5-Ni48Zn32B20 (body-centered orthorhombic; a=1.6(2) nm, b=0.63(7) nm, and c=0.27(0) nm, determined from TEM) and of τ6-Ni47Zn23B30 have not been elucidated yet. Phase equilibria at 800 °C are dominated by a large three-phase field (βB)+Ni2Zn11+τ3, as practically all ternary compounds form at compositions with less than about 50 at% Ni. Furthermore, precise data on atom site distribution and positional parameters have been provided from X-ray single crystal refinements for Ni-borides, for which crystal structures hitherto have only been derived from X-ray diffraction photographs: o-Ni4B3−x (x=0.19; Pnma, a=1.9665(4) nm, b=0.29852(1) nm, c=0.65750(2) nm; RF=0.015) and m-Ni4B3 (C2/c, a=0.64356(3) nm, b=0.48867(3) nm, c=0.78267(3) nm, β=103.288(3)°, RF=0.021).

The phase equilibria of the Ti-Ni-Sn and Ti-Ni-Sb ternary systems have been studied in the whole concentration range by means of X-ray and EPM analyses at 1073 K and 873 K, respectively. Four ternary intermetallic compounds TiNiSn (MgAgAs-type), TiNi{sub 2-x}Sn (MnCu{sub 2}Al-type), Ti{sub 2}Ni{sub 2}Sn (U{sub 2}Pt{sub 2}Sn-type), and Ti{sub 5}NiSn{sub 3} (Hf{sub 5}CuSn{sub 3}-type) are formed in Ti-Ni-Sn system at 1073 K. The TiNi{sub 2}Sn stannide is characterized by homogeneity in the range of 50-47 at% of Ni. The Ti-Ni-Sb ternary system at 873 K is characterized by formation of three ternary intermetallic compounds, Ti{sub 0.8}NiSb (MgAgAs-type), Ti{sub 5}Ni{sub 0.45}Sb{sub 2.55} (W{sub 5}Si{sub 3}-type), and Ti{sub 5}NiSb{sub 3} (Hf{sub 5}CuSn{sub 3}-type). The solubility of Ni in Ti{sub 0.8}NiSb decreases number of vacancies in Ti site up to Ti{sub 0.91}Ni{sub 1.1}Sb composition. - Graphical abstract: Isothermal section of the Ti-Ni-Sn phase diagram and DOS distribution in hypothetical TiNi{sub 1+x}Sn solid solution. Highlights: Black-Right-Pointing-Pointer Ti-Ni-Sn phase diagram was constructed at 1073 K. Black-Right-Pointing-Pointer Four ternary compounds are formed: TiNiSn, TiNi{sub 2-x}Sn, Ti{sub 2}Ni{sub 2}Sn, and Ti{sub 5}NiSn{sub 3}. Black-Right-Pointing-Pointer Three ternary compounds exist in Ti-Ni-Sb system at 873 K. Black-Right-Pointing-Pointer The TiNi{sub 2}Sb compound is absent.

The liquidus and solidus projection has been constructed for the Ag-Ba-Ge system up to 33.3 at% Ba, using electron micro probe analysis (EPMA), X-ray powder diffraction (XRD) and differential thermal analysis (DSC/DTA). Eight different primary crystallization regions were found: (Ge), Ba{sub 8}Ag{sub x}Ge{sub 46-x-y}{open_square}{sub y} ({kappa}{sub I}) ({open_square} is a vacancy), Ba{sub 6}Ag{sub x}Ge{sub 25-x} ({kappa}{sub Ix}), BaGe{sub 2}, Ba(Ag{sub 1-x}Ge{sub x}){sub 2} ({tau}{sub 1}), BaAg{sub 2-x}Ge{sub 2+x} ({tau}{sub 2}) BaAg{sub 5} and (Ag). The ternary invariant reactions have been determined for the region investigated and are the basis for a Schulz-Scheil diagram. The second part of this work provides a comprehensive compilation of melting points of ternary A{sub 8}T{sub x}M{sub 46-x} and quaternary (A=Sr, Ba, Eu; T=Ni, Pd, Pt, Cu, Ag, Au, Zn, Cd, B, Al, Ga; M=Si, Ge, Sn) clathrate type-I compounds and decomposition temperatures of inverse clathrate type-I Ge{sub 38}{l_brace}P,As,Sb{r_brace}{sub 8}{l_brace}Cl,Br,I{r_brace}{sub 8}, Si{sub 46-x}P{sub x}Te{sub y} and tin based compounds. - Graphical Abstract: Partial liquidus projection of the Ag-Ba-Ge system. Highlights: Black-Right-Pointing-Pointer The liquidus and solidus projection has been constructed for the Ag-Ba-Ge system up to 33.33 at% Ba. Black-Right-Pointing-Pointer Eight different primary crystallization fields have been found. Black-Right-Pointing-Pointer All the ternary compounds form congruently from themore » melt. Black-Right-Pointing-Pointer The ternary invariant reactions have been determined and are the basis for a Schulz-Scheil diagram.« less

As the Ti-Mn phase diagram is part of numerous ternary and higher order systems of technological importance, the present paper defines phase relations which have been experimentally established throughout this work from 800 °C to the melting range based on Differential Thermal Analyses (DTA), X-ray powder diffraction, metallography and Electron Probe Micro Analysis (EPMA) techniques on ∼50 alloys, which were prepared by arc melting or high frequency melting under high purity argon starting from freshly cleaned metal ingots. Novel compounds were identified and reaction isotherms were redefined accordingly. In the Ti-rich region a novel compound TiMn was detected, sandwiched between the known phases: TiMn1-x (∼45 at% Mn) and TiMn1+x (∼55 at% Mn). In the Mn-rich region the hitherto unknown crystal structure of TiMn∼3 was solved from X-ray single crystal diffraction data and found to be of a unique structure type Ti6(Ti1-xMnx)6Mn25 (x = 0.462; space group Pbam (#55); a = 0.79081(3) nm, b = 2.58557(9) nm, c = 0.47931(2) nm), which consists of two consecutive layers of the hexagonal MgZn2-type Laves phase (TiMn2) and a combined layer of alternate structure blocks of MgZn2 type and Zr4Al3 type. Whereas TiMn can be considered as a line compound (solubility range

Phase relations have been established for the system Ce–Ni–Zn in the isothermal section at 800 °C using electron microprobe analysis and X-ray powder diffraction. Phase equilibria at 800 °C are characterized by a large region for the liquid phase covering most of the Ce-rich part of the diagram, whereas a Zn-rich liquid is confined to a small region near the Zn-corner of the Gibbs triangle. Whereas solubility of Ce in the binary Ni-Zn phases is negligible, mutual solubilities of Ni and Zn at a constant Ce content are large at 800 °C for most Ce–Zn and Ce–Ni compounds. The solid solution Ce(Ni1−xZnx)5 with the CaCu5-type is continuous throughout the entire section and for the full temperature region from 400 to 800 °C. Substitution of Zn by Ni is found to stabilize the structure of CeZn11 to higher temperatures. At 800 °C Ce(NixZn1−x)11 (0.03≤x≤0.22) appears as a ternary solution phase. Similarly, a rather extended solution forms for Ce2(NixZn1−x)17 (0≤x≤0.53). Detailed data on atom site occupation and atom parameters were derived from X-ray structure analyses for single crystals of Ce2+y(NixZn1−x)17, y=0.02, x=0.49 (a=0.87541(3), c=1.25410(4) nm; Th2Zn17 type with space group R 3 ¯ m , R F 2 = 0.018 ) and Ce(Ni0.18Zn0.82)11 (a=1.04302(2), c=0.67624(3)nm, BaCd11 type with space group I41/amd, R F 2 = 0.049 ).

X-ray single crystal (XSC) and neutron powder diffraction data (NPD) were used to elucidate boron site preference for five ternary phases. Ta{sub 3}Si{sub 1-x}B{sub x} (x=0.112(4)) crystallizes with the Ti{sub 3}P-type (space group P4{sub 2}/n) with B-atoms sharing the 8g site with Si atoms. Ta{sub 5}Si{sub 3-x} (x=0.03(1); Cr{sub 5}B{sub 3}- type) crystallizes with space group I4/mcm, exhibiting a small amount of vacancies on the 4a site. Both, Ta{sub 5}(Si{sub 1-x}B{sub x}){sub 3}, x=0.568(3), and Nb{sub 5}(Si{sub 1-x}B{sub x}){sub 3}, x=0.59(2), are part of solid solutions of M{sub 5}Si{sub 3} with Cr{sub 5}B{sub 3}-type into the ternary M-Si-B systems (M=Nb or Ta) with B replacing Si on the 8h site. The D8{sub 8}-phase in the Nb-Si-B system crystallizes with the Ti{sub 5}Ga{sub 4}-type revealing the formula Nb{sub 5}Si{sub 3}B{sub 1-x} (x=0.292(3)) with B partially filling the voids in the 2b site of the Mn{sub 5}Si{sub 3} parent type. - Graphical abstract: The crystal structures of a series of compounds have been solved from X-ray single crystal diffractometry revealing details on the boron incorporation. Highlights: Black-Right-Pointing-Pointer Structure of a series of compounds have been solved by X-ray single crystal diffractometry. Black-Right-Pointing-Pointer Ta{sub 3}(Si{sub 1-x}B{sub x}) (x=0.112) crystallizes with the Ti{sub 3}P-type,more » B and Si atoms randomly share the 8g site. Black-Right-Pointing-Pointer Structure of Nb{sub 5}Si{sub 3}B{sub 1-x} (x=0.292; Ti{sub 5}Ga{sub 4}-type) was solved from NPD.« less

Phase relations have been evaluated for the Ta-V-Si system at 1500 and 1200 degrees C. Three ternary phases were found: tau(1)-(Ta,V)(5)Si-3 (Mn5Si3-type), tau(2)-Ta(Ta,V,Si)(2) (MgZn2-type) and tau(3)-Ta(Ta,V,Si)(2) (MgCu2-type). The crystal structure of tau(2)-Ta(Ta,V,Si)(2) was solved by X-ray single crystal diffraction (space group P6(3)/mmc). Atom order in the crystal structures of tau(1)-(Ta,V)(5)Si-3 (Mn5Si3 type) and tau(3)-Ta(Ta,V,Si)(2) was derived from X-ray powder diffraction data. A large homogeneity range was found for tau(1)-(TaxV1-x)(5)Si-3 revealing random exchange of Ta and V at a constant Si content. At 1500 degrees C, the end points of the tau(1)-phase solution (0.082

We report on (i) the phase relations at 800 °C within the ternary system Au–Ba–Si up to 33.3 at.% Ba, (ii) on the crystallographic data of new ternary compounds, (iii) on details of the clathrate type I solid solution, (iv) on electrical and thermal transport measurements for Ba8Au5.1Si40.9 supported by (v) density functional theory calculations. The clathrate type I solid solution Ba8AuxSi46−x at 800 °C extends from Ba8Au4Si42 (a = 1.039 nm) to Ba8Au6Si40 (a = 1.042 nm). The cubic primitive symmetry (space group Pm 3 ¯ n ) was confirmed by X-ray powder diffraction in the whole homogeneity region. The lattice parameters of the solid solution show an almost linear increase with increasing gold content and site preferences from X-ray refinement confirm that gold atoms preferably occupy the 6d site in random mixture with Si atoms. The phase equilibria at 800 °C are characterized by seven ternary phases in the investigated region up to 33.3 at.% Ba. The homogeneity range has been established for Ba(Au1−xSix)2 (AlB2 type, extending from BaAu0.4Si1.6 to BaAu0.9Si1.1). BaAu2+xSi2−x (unknown structure type) exhibits a very small homogeneity range (x = 0.6–0.7) and two other ternary phases exist at about 22 at.% Ba, 52 at.% Au and 28 at.% Si and 20 at.% Ba, 58 at.% Au and 22 at.% Si (structure types for both unknown). The crystal structures of two further novel phases in the gold-rich part have been determined from single crystal X-ray data: BaAu3+xSi1−x of BaAu3Ge type (x = 0–0.3, space group P4/nmm, x = 0: a = 0.6488(2), c = 0.5305(2) nm) and BaAu5−xSi2+x (x = 0–0.2, own structure type, space group Pnma, x = 0: a = 0.8935(2), b = 0.6939(2), c = 1.0363(2) nm). The proximity of Ba8AuxSi46−x to a metal to insulator transition is corroborated by density functional theory electronic structure calculations. A gap in the electronic density of states, located near the Fermi energy, gives rise to distinct features of the temperature-dependent electrical resistivity and Seebeck effect.

Phase relations have been established by electron probe microanalysis (EPMA) and X-ray powder diffraction (XPD) for the Sr-poor part of the ternary systems Sr–Zn–Si at 800 °C and Sr–Zn–Ge at 700 °C. In the Sr–Zn–Si system one new ternary compound SrZn 2+ x Si 2− x (0≤ x ≤0.45) with CeAl 2 Ga 2 structure and a statistical mixture of Zn/Si in the 4 e site was found. Neither a type-I nor a type-IX clathrate phase was encountered. This system is characterized by formation of two further phases, i.e. SrZn 1− x Si 1+ x with ZrBeSi-type (0.16≤ x ≤0.22) and SrZn 1− x Si 1+ x with AlB 2 -type (0.35≤ x ≤0.65) with a random distribution of Zn/Si atoms in the 2 c site. For the Sr–Zn–Ge system, the homogeneity regions of the isotypic phases SrZn 1− x Ge 1+ x with ZrBeSi-type (0≤ x ≤0.17) and AlB 2 -type (0.32≤ x ≤0.56), respectively, have been determined. Whereas the germanide SrZn 2+ x Ge 2− x (CeAl 2 Ga 2 -type) is characterized by a homogeneity region (0≤ x ≤0.5), the clathrate type-I phase Sr 8 Zn 8 Ge 38 shows a point composition.

The crystal structures of three Al-rich compounds have been solved from X-ray single crystal diffractometry: τ(1)-MoPd(2-x)Al(8+x) (x = 0.067); τ(7)-Zr(Cu(1-x)Al(x))(12) (x = 0.514) and τ(9)-ZrCu(1-x)Al(4) (x = 0.144). τ(1)-MoPd(2-x)Al(8+x) adopts a unique structure type (space group Pbcm; lattice parameters a = 0.78153(2), b = 1.02643(3) and c = 0.86098(2) nm), which can be conceived as a superstructure of the Mo(Cu(x)Al(1-x))(6)Al(4) type. Whereas Mo-atoms occupy the 4d site, Pd(2) occupies the 4c site, Al and Pd(1) atoms randomly share the 4d position and the rest of the positions are fully occupied by Al. A Bärnighausen tree documents the crystallographic group-subgroup relation between the structure types of Mo(Cu(x)Al(1-x))(6)Al(4) and τ(1). τ(7)-Zr(Cu(1-x)Al(x))(12) (x = 0.514) has been confirmed to crystallize with the ThMn(12) type (space group I4/mmm; lattice parameters a = 0.85243(2) and c = 0.50862(3) nm). In total, 4 crystallographic sites were defined, out of which, Zr occupies site 2a, the 8f site is fully occupied by Cu, the 8i site is entirely occupied by Al, but the 8j site turned out to comprise a random mixture of Cu and Al atoms. The compound τ(9)-ZrCu(1-x)Al(4) (x = 0.144) crystallizes in a unique structure type (space group P4/nmm; lattice parameters a = 0.40275(3) and c = 1.17688(4) nm) which exhibits full atom order but a vacancy (14.4%) on the 2c site, shared with Cu atoms. τ(9)-ZrCu(1-x)Al(4) is a superstructure of Cu with an arrangement of three unit cells of Cu in the direction of the c-axis. A Bärnighausen tree documents this relationship. The ZrCu(1-x)Al(4) type (n = 3) is part of a series of structures which follow this building principle: Cu (n = 1), TiAl(3) (n = 2), τ(5)-TiNi(2-x)Al(5) (n = 4), HfGa(2) (n = 6) and Cu(3)Pd (n = 7). A partial isothermal section for the Al-rich part of the Mo-Pd-Al system at 860 °C has been established with two ternary compounds τ(1)-MoPd(2-x)Al(8+x) and τ(2) (unknown structure). The Vickers hardness (H(v)) for τ(1) was found to be 842 ± 40 MPa.

On the basis of a detailed study applying X-ray single-crystal and powder diffraction, differential scanning calorimetry, and scanning electron microscopy analysis, it was possible to resolve existing uncertainties in the Pt-rich section (≥65 atom % Pt) of the binary Pt-B phase diagram above 600 °C. The formation of a unique structure has been observed for Pt2B [X-ray single-crystal data: space group C2/m, a = 1.62717(11) nm, b = 0.32788(2) nm, c = 0.44200(3) nm, β = 104.401(4)°, RF2 = 0.030]. Within the homogeneity range of "Pt3B", X-ray powder diffraction phase analysis prompted two structural modifications as a function of temperature. The crystal structure of "hT-Pt3B" complies with the hitherto reported structure of anti-MoS2 [space group P63/mmc, a = 0.279377(2) nm, c = 1.04895(1) nm, RF = 0.075, RI = 0.090]. The structure of the new "[Formula: see text]T-Pt3B" is still unknown. The formation of previously reported Pt∼4B has not been confirmed from binary samples. Exploration of the Pt-rich section of the Pt-Cu-B system at 600 °C revealed a new ternary compound, Pt12CuB6-y [X-ray single-crystal data: space group Im3̅, a = 0.75790(2) nm, y = 3, RF2 = 0.0129], which exhibits the filled WAl12-type structure accommodating boron in the interstitial trigonal-prismatic site 12e. The isotypic platinum-aluminum-boride was synthesized and studied. The solubility of copper in binary platinum borides has been found to attain ∼7 atom % Cu for Pt2B but to be insignificant for "[Formula: see text]T-Pt3B". The architecture of the new Pt2B structure combines puckered layers of boron-filled and empty [Pt6] octahedra (anti-CaCl2-type fragment) alternating along the x axis with a double layer of boron-semifilled [Pt6] trigonal prisms interbedded with a layer of empty tetrahedra and tetragonal pyramids (B-deficient α-T[Formula: see text]I fragment). Assuming boron vacancies ordering (space group R3), the Pt12CuB6-y structure exhibits serpentine-like columns of edge-connected boron-filled [Pt6] trigonal prisms running infinitely along the z axis and embedding the icosahedrally coordinated Cu atom. Pt2B, (Pt1-yCuy)2B (y = 0.045), and Pt12CuB6-y (y = 3) behave metallically, as revealed by temperature-dependent electrical resistivity measurements.

The isothermal section for the system Ce–Zn–B has been established at 800 °C using electron microprobe analysis and X-ray powder diffraction. No ternary compounds exist and mutual solid solubilities of binary phases are negligible. In the concentration range of 10.0–10.5 at% Ce two structural modifications have been confirmed: high temperature βCe2Zn17 above ∼750 °C with the Th2Zn17 type (R3m, a=0.90916(4) nm, c=1.3286(1) nm) and low temperature αCeZn7 (Ce1−xZn5+2x; x∼0.33) up to 750 °C for which we attributed the TbCu7 type (P6/mmm, a=0.52424(2), c=0.44274(1) nm). The crystal structure of CeZn7 was derived from the Rietveld refinement of X-ray powder intensities. Precise data on atom site distribution and positional parameters have been furthermore provided from X-ray single crystal refinements for two compounds, for which crystal structures hitherto have only been derived from X-ray diffraction photographs: Ce3Zn11 (Immm, a=0.45242(2) nm, b=0.88942(3) nm, c=1.34754(4) nm) and Ce3Zn22 (I41/amd; a=0.89363(2) nm, c=2.1804(5) nm).

The crystal structures of three ternary Ni-Zn borides have been elucidated by means of X-ray single-crystal diffraction (XSC) and X-ray powder diffraction techniques (XPD) in combination with electron microprobe analyses (EMPA) defining the Ni/Zn ratio. Ni(21)Zn(2)B(24) crystallizes in a unique structure type (space group I4/mmm; a = 0.72103(1) nm and c = 1.42842(5) nm; R(F)(2) = 0.017), which contains characteristic isolated cages of B(20) units composed of two corrugated octogonal boron rings, which are linked at four positions via boron atoms. The B(20) units appear to have eight-membered rings on all six faces like the faces of a cube. Each face is centered by a nickel atom. The six nickel atoms are arranged in the form of an octahedron nested within the B(20) unit. Such a boron aggregation is unique and has never been encountered before in metal-boron chemistry. The crystal structure of Ni(12)ZnB(8-x) (x = 0.43; space group Cmca, a = 1.05270(2) nm, b = 1.45236(3) nm, c = 1.45537(3) nm; R(F)(2) = 0.028) adopts the structure type of Ni(12)AlB(8) with finite zigzag chains of five boron atoms. The compound Ni(3)ZnB(2) crystallizes in a unique structure type (space group C2/m, a = 0.95101(4) nm, b = 0.28921(4) nm, c = 0.84366(3) nm, β = 101.097(3)°, and R(F)(2) = 0.020) characterized by B(4) zigzag chain fragments with B-B bond lengths of 0.183-0.185 nm. The Ni(3)ZnB(2) structure is related to the Dy(3)Ni(2) type.

In the Au-Ba-Ge system the clathrate type I solid solution, Ba8Au x Ge46−x−y □ y , extends at 800 °C from binary Ba8Ge43□3 (□ is a vacancy) to Ba8Au6Ge40. For the clathrate phase (1 ≤ x ≤ 6) cubic primitive symmetry (space group $$ Pm{\bar{{3}}}n $$ ) was confirmed by x-ray powder diffraction assisted by x-ray single crystal analyses of Ba8Au4.6Ge40.3□1.1. The lattice parameters of the solid solution show an almost linear increase with increasing gold content. Site preference from x-ray refinement shows that gold atoms preferably occupy the 6d site in random mixture with Ge and vacancies, which vanish at the solubility limit. Clathrate type ΙX (Ba6Ge25 type) has a maximum solubility of 2.7 at.% gold at 800 °C. Phase equlilibria at 800 °C are characterized by four ternary phases in the investigated region up to 33.3 at.% barium. The homogeneity range of Ba(Au1−x Ge x )2 (AlB2-type) and BaAu1+x Ge3−x has been established: Ba(Au1−x Ge x )2 extends from BaAu0.5Ge1.5 to BaAu0.9Ge1.1 and BaAu1+x Ge3−x from BaAu1.1Ge2.9 (BaNiSn3-type) to BaAu2.7Ge1.3 (Ce(Ni,Sb)4-type). The crystal structures of two phases in the gold-rich part have been determined from single crystal x-ray data and were found to form new structure types: BaAu3Ge with BaAu3Ge-type (space group P4/nmm, a = 0.6459(2), c = 0.5487(2) nm) and BaAu5+x Ge2−x (x = 0, BaAu5Si2-type, space group Pnma, a = 0.8981(2), b = 0.7106(2) and c = 1.0363(2) nm), the latter revealing with increasing gold content a closely related derivative structure type (BaAu5.3Ge1.7, $$ a = a_{{{\text{BaAu}}_{5} {\text{Si}}_{2} }} ,\;b = b_{{{\text{BaAu}}_{5} {\text{Si}}_{2} }} ,\;c = 2c_{{{\text{BaAu}}_{5} {\text{Si}}{}_{2}}} $$ ). Transport properties and particularly the thermoelectric behavior were studied for Ba8Au6Ge40.

Phase equilibria within the isothermal section of the ternary system Nd–Fe–Sb were derived at 800 °C by using X-ray powder diffraction, light optical microscopy and electron probe microanalysis. Crystal structures of the ternary compounds Nd2Fe7−xSb6−y (τ2-orthorhombic), Nd2Fe5−xSb10−y (τ2-tetragonal) Nd3Fe3Sb7 (τ3) and NdFeSb3 (τ4) were determined by single crystal X-ray diffraction and by Rietveld X-ray powder data refinement. The phase τ2 was found to exhibit two modifications, orthorhombic (Nd2Fe7−xSb6−y-type, S.G. Immm, a = 0.42632(6) nm, b = 0.43098(7) nm, c = 2.5823(3) nm) and tetragonal (La2Fe5−xSb10−y-type, S.G. I4/mmm, a = 0.42897(2) nm, c = 2.5693(4) nm). Tetragonal and orthorhombic modifications form a crystallographic group–subgroup relation and are closely related to the Zr3Cu4Si6-type. Nd3Fe3Sb7 (τ3) crystallizes with a unique structure type (S.G. P63/m, a = 1.31808(3) nm, c = 0.41819(3) nm), which is isopointal to the Cu10Sb3-type. NdFeSb3 (τ4) adopts the LaPdSb3-type. Physical properties comprising magnetization, resistivity and specific heat were measured for RE2Fe5−xSb10−y (RE = Ce, Nd), NdFeSb3 and Nd3Fe3Sb7. NdFeSb3 orders antiferromagnetically below 3.0 K due to the presence of magnetic moments on Nd sites. For the other compounds a more complex magnetic behaviour is observed at low temperatures that may be related to the contributions coming from both the rare earth and iron sublattices.

Phase equilibria in the system Si–U–V were established at 1100 °C by optical microscopy, EMPA and X-ray diffraction. Two ternary compounds were observed, U 2 V 3 Si 4 and (U 1− x V x ) 5 Si 3 , for which the crystal structures were elucidated by X-ray powder data refinement and found to be isotypic with the monoclinic U 2 Mo 3 Si 4 -type (space group P 2 1 / c ; a = 0.6821(3), b = 0.6820(4), c = 0.6735(3) nm, β = 109.77(1)°) and the tetragonal W 5 Si 3 -type (space group I 4/ mcm , a = 1.06825(2), c = 0.52764(2) nm), respectively. (U 1− x V x ) 5 Si 3 appears at 1100 °C without any significant homogeneity region at x ∼ 0.2 resulting in a formula U 4 VSi 3 which corresponds to a fully ordered atom arrangement. DTA experiments clearly show decomposition of this phase above 1206 °C revealing a two-phase region U 3 Si 2 + V 3 Si. At 1100 °C U 4 VSi 3 is in equilibrium with V 3 Si, V 5 Si 3 , U 3 Si 2 and U(V). At 800 °C U 4 VSi 3 forms one vertex of the tie-triangle to U 3 Si and V 3 Si. Due to the rather high thermodynamic stability of V 3 Si and the corresponding tie-lines V 3 Si + liquid at 1100 °C and V 3 Si + U(V) below 925 °C, no compatibility exists between U 3 Si or U 3 Si 2 and vanadium metal.

Phase relations in the system Ce–Zn–Si have been determined for the isothermal section at 800 °C using electron microprobe analysis and X-ray powder diffraction. Phase equilibria are characterized by extended solid solutions along the section CeSi 2 –CeZn 2 , which form a structurally related sequence of structure types: Ce(Zn x Si 1− x ) 2 (αThSi 2 -type, 0 ≤ x ≤ 0.32), τ 2 -Ce(Zn x Si 1− x ) 2 (AlΒ 2 -type, 0.36 ≤ x ≤ 0.76) and Ce(Zn 1− x Si x ) 2 (CeCu 2 -type, 0 ≤ x ≤ 0.18). Silicon stabilizes the ternary compound τ 1 -Ce 7 Zn 21 (Zn 1− x Si x ) 2 , (0.28 ≤ x ≤ 0.98) for which the crystal structure was derived from X-ray diffraction data for a single crystal of Ce 7 Zn 21 (Zn 1− x Si x ) 2 ( x = 0.28; unique structure type, Pbam ; a = 1.55722(3) nm, b = 1.71942(3) nm, c = 0.44772(1) nm; R F = 0.029). The structure of Ce 7 Zn 21 (Zn 1− x Si x ) 2 can be considered as an arrangement of slightly distorted building blocks of Cu 3 Au-type (Zn[Ce 4 Zn 8 ]) and BaAl 4 -type (Ce[Ce 2 Zn 10 M 4 ] and Ce[Ce 2 Zn 13 M 2 ]), arranged in form of a zig-zag string of face-sharing units…Cu 3 Au–BaAl 4 –BaAl 4 –BaAl 4 –Cu 3 Au… running parallel to the b -axis. Structural analyses proved isotypism for homologous La 7 Zn 21 (Zn 1− x Si x ) 2 ( x = 0.27), Ce 7 Zn 21 (Zn 1− x Si x ) 2 -type, Pbam ; a = 1.56817(2) nm, b = 1.72923(3) nm, 0.450887(7) nm; X-ray single crystal data and La(Zn x Si 1− x ) 2 , ( x = 0.56, AlΒ 2 -type, P6/ mmm , a = 0.42775(4) nm, c = 0.42832(4) nm; X-ray powder data). The structure types of the ternary compounds τ 3 -Ce(Zn x Si 1− x ), 0.17 ≤ x ≤ 0.23, and τ 4 -Ce 40 Zn 37 Si 23 (in at.%) are still unknown.

The formation and crystal chemistry of ternary clathrates in the Ba-Cu-Si system were investigated on a series of compounds Ba8Cu x Si46−x (3 ≤ x ≤ 8). The phase diagram around the clathrate phase was constructed at 800°C, revealing a homogeneity range from Ba8Cu3.4Si42.6 to Ba8Cu4.8Si41.2. Structural investigations confirmed that the clathrates in this system crystallize with cubic primitive symmetry, in the type I clathrate structure (space group Pm $$ \bar{3} $$ n). Single-crystal x-ray diffraction indicates that the Cu atoms partially substitute for Si atoms on the 6d site; no vacancies are observed.

Phase equilibria and crystal structures of ternary compounds were determined in the systems Ce–Pd–B and Yb–Pd–B at 850 °C in the concentration ranges up to 45 and 33 at% of Ce and Yb, respectively, employing X-ray single crystal and powder diffraction. Phase relations in the Ce–Pd–B system at 850 °C are governed by formation of extended homogeneity fields, τ2-CePd8B2−x (0.10 The Yb–Pd–B system is characterized by one ternary compound, τ1-Yb2Pd14B5, forming equilibria with extended solution YbPd3Bx, YbB6, Pd5B2 and Pd3B. The crystal structures of both Yb2Pd14B5 and isotypic Lu2Pd14B5 were determined from X-ray Rietveld refinements and found to be closely related to the Y2Pd14B5-type (I41/amd). The crystal structure of binary Yb5Pd2−x (Mn5C2-type) was confirmed from X-ray single crystal data and a slight defect on the Pd site (x=0.06) was established. The three structures τ1-Ce6Pd47−xB6, τ2-CePd8B2−x and τ3-Ce3Pd25−xB8−y are related and can be considered as the packings of fragments observed in Nd2Fe14B structure with different stacking of common structural blocks. Physical properties for Yb2Pd13.6B5 (temperature dependent specific heat, electrical resistivity and magnetization) yielded a predominantly Yb-4f13 electronic configuration, presumably related with a magnetic instability below 2 K. Kondo interaction and crystalline electric field effects control the paramagnetic temperature domain.

The phase diagram of the Dy–Ni–Sn ternary system was constructed at 870 K (0–50 at.% Sn) and 770 K (more than 50 at.% Sn) using X-ray analysis and scanning electron microscopy. The interaction of the elements results the formation of 11 ternary compounds—Dy6Ni2Sn (Ho6Co2Ga-type), DyNi5Sn (CeCu4.38In1.62-type), DyNiSn2 (LuNiSn2-type), DyNiSn (TiNiSi-type), Dy2Ni2Sn (W2CoB2-type), DyNiSn4 (LuNiSn4-type), DyNi3Sn2 (HoGa2.4Ni2.6-type), Dy2Ni7Sn3 (own structure type), DyNi2−xSn (YbNi2−xSn-type), Dy3Ni4Sn6 (Ce3Pd4Sn6-type), and Dy4Ni12Sn25 (Ce4Pt12Sn25-type). The formation of Dy2NiSn6 compound with Lu2NiSn6 type structure was found at 670 K. The crystal chemistry analysis of ternary compounds formed in the Dy–Ni–Sn system was done.

Phase relations in the ternary system Ce–Pd–Si have been established for the isothermal section at 8001C based on X-ray powder diffraction and EMPA techniques on about 130 alloys, which were prepared by arc-melting under argon or powder reaction sintering. Eighteen ternary compounds have been observed to participate in the phase equilibria at 8001C. Atom order was determined by direct methods from X-ray single-crystal counter data for the crystal structures of t8—Ce3Pd4Si4 (U3Ni4Si4type, Immm; a ¼ 0.41618(1), b ¼ 0.42640(1), c ¼ 2.45744(7) nm), t16—Ce2Pd14Si (own structure type, P4/nmm; a ¼ 0.88832(2), c ¼ 0.69600(2) nm) and also for t18—CePd1� xSix (x ¼ 0.07; FeB-type, Pnma; a ¼ 0.74422(5), b ¼ 0.45548(3), c ¼ 0.58569(4) nm). Rietveld refinements established the atom arrangement in the structures of t5—Ce3PdSi3 (Ba3Al2Ge2-type, Immm; a ¼ 0.41207(1), b ¼ 0.43026(1), c ¼ 1.84069(4) nm) and t13—Ce3� xPd20+xSi6 (0rxr1, Co 20Al3B6-type, Fm3 ¯ m; a ¼ 1.21527(2) nm). The ternary compound Ce2Pd3Si3 (structure-type Ce2Rh1.35Ge4.65, Pmmn; a ¼ 0.42040(1), b ¼ 0.42247(1), c ¼ 1.72444(3) nm) was detected as a high-temperature compound, however, does not participate in the equilibria at 8001C. Phase equilibria in Ce–Pd–Si are characterized by the absence of cerium solubility in palladium silicides. Mutual solubility among cerium silicides and cerium–palladium compounds are significant whereby random substitution of the almost equally sized atom species palladium and silicon is reflected in extended homogeneous regions at constant Cecontent such as for t2—Ce(PdxSi1� x)2 (AlB2-derivative type), t6—Ce(PdxSi1� x)2 (ThSi2-type) and t7—CePd2� xSi2+x. The crystal structures of compounds t4—Ce� 8Pd� 46Si� 46, t12—Ce� 29Pd� 49Si� 22, t15—Ce� 22Pd� 67Si� 11, t17—Ce� 5Pd� 77Si� 18 and t18—CePd1� xSix (x� 0.1) are still unknown.

The crystal structures of ternary compounds RPt3−xSi1−y(R=Y, Tb, Dy, Ho, Er, Tm, Yb) have been elucidated from X-ray single crystal CCD data. All compounds are isotypic and crystallize in the tetragonal space group P4/mbm. The general formula RPt3−xSi1−y arises from defects: x≈0.20, y≈0.14. The crystal structure of RPt3−xSi1−y can be considered as a packing of four types of building blocks which derive from the CePt3B-type unit cell by various degrees of distortion and Pt, Si-defects.

Phase relations at 700 deg. C, 800 deg. C and solidus temperatures have been derived for the clathrate system Ba{sub 8}Cu{sub x}Ge{sub 46-x-y}square{sub y} via X-ray single crystal and powder diffractometry combined with electron probe micro analysis and differential thermal analysis. The ternary clathrate phase derives from binary Ba{sub 8}Ge{sub 43}square{sub 3} and extends up to x=6. Structure investigations define cubic primitive symmetry with the space group type Pm3-barn consistent with a clathrate type I structure throughout the entire homogeneity region 0 =5.5. - Graphical Abstract: Cages and atom thermal displacement parameters in clathrate Ba{sub 8}Cu{sub x}Ge{sub 46-x-y}square{sub y} for Ba{sub 8}Cu{sub 2}Ge{sub 42}square{sub 2} and Ba{sub 8}Cu{sub 6}Ge{sub 40}.

Formation and crystal structure of Laves phases in the systems Ti–{Pd,Pt}–Al were investigated employing XPD (X-ray powder diffraction), XSCD (X-ray single crystal diffraction) and EPMA (electron probe microanalysis) techniques. Laves phases with MgZn 2 type (space group: P 6 3 / mmc ) and its variant with the Nb(Ir,Al) 2 -type ( a √3 × a √3 × c supercell of MgZn 2 -type, space group: P 6 3 / mcm ) were found in both systems. Formation of a particular structure type is dependent on temperature and composition. Laves phases with the Nb(Ir,Al) 2 -type form around 25 at.% of Pd,Pt at 950 °C. The MgZn 2 -type Laves phase Ti(Pt,Al) 2 was not observed at 950 °C, but it forms in as-cast alloys at a slightly lower Pt content, Ti 37.8 Pt 19.0 Al 43.2 . In the Ti–Pd–Al system at 950 °C the MgZn 2 -type phase exists at the Pd-poor side of the homogeneity region whilst the Nb(Ir,Al) 2 -type phase is slightly richer in Pd. Phase relations associated with the Ti–Pt–Al Laves phase were established at 950 °C and reveal a new compound TiPtAl that derives from hexagonal ZrBeSi-type (ordered Ni 2 In-type, a = 0.43925(4) nm, c = 0.54844(5); space group P 6 3 / mmc ; R F2 = 0.015 from single crystal data). Atom distribution in the compound shows a slight deviation from full atom order Ti(Pt 0.97 Al 0.03 )(Al 0.98 Pt 0.02 ).

Phase relations in the ternary systems Ce–M–Sb (M=Si, Ge, Sn) in composition regions CeSb2–Sb–M were studied by optical and electron microscopy, X-ray diffraction, and electron probe microanalysis on arc-melted alloys and specimens annealed in the temperature region from 850 to 200 °C. The results, in combination with an assessment of all literature data available, were used to construct solidus surfaces and a series of isothermal sections. No ternary compounds were found to form in the Ce–Si–Sb system whilst Ce12Ge9−xSb23+x (3.3

Alloys with nominal composition Nb(Ni1−xAlx)2 (xAl=0.15, 0.23, 0.30, 0.38, 0.46, 0.54, 0.62, 0.69, 0.77, 0.85) were investigated by means of X-ray powder and single crystal diffraction, optical microscopy, electron probe microanalysis (EPMA) concentrating on structural details of the C14 MgZn2-type Laves phase. Rietveld refinements of X-ray powder data ( 0.23 x Al 0.77 ) revealed that Nb atoms fully occupy the 4f sites, whereas Ni and Al atoms share 6h and 2a sites in a random fashion. Single crystal refinement for Nb(Ni0.54Al0.46)2 confirmed structure type and atom order in line with results from powder diffraction. The characteristic site preferences throughout the series of alloys serve as a basis for the interpretation of the non-linear dependence of unit cell parameters with Al content.

Phase relations in the ternary system Ce–Pt–Si have been established for the isothermal section at 800 °C based on X-ray powder diffraction, metallography, scanning electron microscopy (SEM) and electron probe microanalysis (EPMA) techniques on about 120 alloys, which were prepared by various methods employing arc-melting under argon or powder reaction sintering. Nineteen ternary compounds were observed. Atom order in the crystal structures of τ18-Ce5(Pt,Si)4 (Pnma; a=0.77223(3) nm, b=1.53279(8) nm c=0.80054(5) nm), τ3-Ce2Pt7Si4 (Pnma; a=1.96335(8) nm, b=0.40361(4) nm, c=1.12240(6) nm) and τ10-CePtSi2 (Cmcm; a=0.42943(2) nm, b=1.67357(5) nm, c=0.42372(2) nm) was determined by direct methods from X-ray single-crystal CCD data and found to be isotypic with the Sm5Ge4-type, the Ce2Pt7Ge4-type and the CeNiSi2-type, respectively. Rietveld refinements established the atom arrangement in the structures of Pt3Si (Pt3Ge-type, C2/m, a=0.7724(2) nm, b=0.7767(2) nm, c=0.5390(2) nm, β=133.86(2)°), τ16-Ce3Pt5Si (Ce3Pd5Si-type, Imma, a=0.74025(8) nm, b=1.2951(2) nm, c=0.7508(1) nm) and τ17-Ce3PtSi3 (Ba3Al2Ge2-type, Immm, a=0.41065(5) nm, b=0.43221(5) nm, c=1.8375(3) nm). Phase equilibria in Ce–Pt–Si are characterised by the absence of cerium solubility in platinum silicides. Cerium silicides and cerium platinides, however, dissolve significant amounts of the third component, whereby random substitution of the almost equally sized atom species platinum and silicon is reflected in extended homogeneous regions at constant Ce content such as for τ13-Ce(PtxSi1−x)2, τ6-Ce2Pt3+xSi5−x or τ7-CePt2−xSi2+x.

A series of isotypic RE 1.9 Cu 9.2 Sn 2.8 compounds, where RE are Y, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Lu, was synthesized by arc-melting and the crystal structure was determined by X-ray powder diffraction. The structure is a partly disordered substitution variant of the CeNi 5 Sn structure type (space group P 6 3 / mmc ), which consists of CaCu 5 -type fragments of composition RE 0.9 Cu 4.2 Sn 0.8 and fragments of a hypothetical structure of composition RECu 5 Sn 2 . All the RE 1.9 Cu 9.2 Sn 2.8 compounds obtained here are paramagnets and characterized by metal-like conductivity.

The phase diagram of the Nd–Ni–Sn ternary system was constructed at 770 K (more than 50 at.% Sn) and 870 K (0–50 at.% Sn) using X-ray and partially metallographic analyses. The interaction between the elements results the formation of 13 ternary intermetallic compounds. The existence of the substitutional solid solution NdNi5−xSnx (up to 10 at.% Sn) was observed.

Phase relations at 900 °C, crystal chemistry, electrical and thermal transport measurements, and heat capacity data are reported for the clathrate systems: Ba 8 {Pd,Pt} x Si 46- x . For both systems a ternary clathrate phase was identified with a small homogeneity region extending at 900 °C for 2.5≤ x Pd ≤4.1 and 2.8≤ x Pt ≤4.9, respectively. Structural investigations of these clathrate phases at 300, 200 and 100 K define cubic primitive symmetry with the space group type P m 3 n consistent with clathrate type I. Studies of electronic and thermal transport groups both series of compounds close-by a semiconducting state. An sizeable charge carrier concentration in these systems, however, prevents sufficiently large thermopower values. In comparison to isostructural type I clathrates based on Ge, thermal conductivity – dominated by the lattice contribution – is larger due to the smaller mass of Si.

Alloys with composition Ti(Mn1−xAlx)2 (xAl = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.55, 0.6, and 0.67) were studied by X-ray powder diffraction (XPD), optical microscopy, electron probe microanalysis (EPMA) and electronic density functional theory. EPMA and XPD defined an extensive solid solution of up to xAl = 0.64 at 900 °C. Structure determination from Rietveld refinements of X-ray powder diffraction data for Ti(Mn1−xAlx)2 (0 ≤ xAl ≤ 0.60) and from single crystal X-ray counter data for xAl = 0.2 revealed a C14-MgZn2-type Laves phase, where Ti atoms fully occupy the 4f sites, whereas Mn and Al atoms share the 6h and 2a sites in various ratios. By means of density functional theory, the structural stabilities and site preferences of nine ternary compositions, Ti(Mn1−xAlx)2 (xAl = 0, 0.125, 0.25, 0.375, 0.500, 0.625, 0.750, 0.875, 1.00), were further calculated for a large number of structural models. The derived Al content dependent structural stabilities, lattice parameters, and site occupations as well as enthalpies of formations are in nice agreement with experimental results. Based on the calculated data, we analyzed the occupation behaviour of Al atoms substituting for Mn atoms at the 2a and 6h sites: up to concentrations xAl

The ternary intermetallic Ce 16 Ru 8 In 37 was synthesized by arc-melting from elemental Ce, Ru, and In under an argon atmosphere. The crystal structure of Ce 16 Ru 8 In 37 was determined from the single-crystal X-ray diffraction data: a = 4.7451(1) A, b = 9.3518(2) A, c = 32.6162(7) A; space group Immm , Z = 1. The architecture of the crystal structure of Ce 16 Ru 8 In 37 is based on CeIn 3 units with cubic Cu 3 Au-type and can be presented as consisting of two different slabs: CeIn 3 -like slab of composition Ce 4 In 14.5 and a slab of composition Ce 4 Ru 4 In 4 .

The 700 °C isothermal sections of the phase diagrams of the ternary systems Sr—Ag—Ge and Sr—Au—Ge and the 800 °C isothermal sections of Sr—Ag—Si and Sr—Au—Si are determined in the Ge,Si-rich region for Sr contents up to33.3 at%.

Phase equilibria of the system Ce–Zn–Si have been determined for the isothermal section at 600 °C for

The extended ternary solid solution for the G-phase in the Ti–Co–Al system, Ti6+xCo7+yAl17−x−y, has been investigated by neutron powder diffraction of the as-cast alloys in order to elucidate the precise atom-site distribution. A concentration-dependent structural transformation has been observed between two crystal structures. Whilst the aluminium-rich G-phase crystallizes with the centrosymmetric, filled variant of the Th6Mn23-type (SG F m 3 ¯ m ), Ti-rich alloys adopt a new non-centrosymmetric structure (SG F 4 ¯ 3 m ) for compositions with more than 34 at.% Ti. Three states of high atomic order were denoted for the G-phase. The unit cells containing 24Ti–28Co–68Al atoms (x=0, y=0, SG F m 3 ¯ m ) and 56Ti–32Co–32Al atoms (x=8, y=1, SG F 4 ¯ 3 m ) represent fully ordered structures. The unit cell containing 40Ti–30Co–50Al atoms (x=4, y=0.5, SG F 4 ¯ 3 m ) shows partial atom order with a statistical distribution of atoms in the 4b site, whilst all other atom sites are completely ordered. A corresponding transition from centrosymmetric SG F m 3 ¯ m to non-centrosymmetric SG F 4 ¯ 3 m was furthermore established in the Ti–Fe–Al ternary system. Al-rich compositions of the G-phase crystallise in the filled variant of the Th6Mn23-type (SG F m 3 ¯ m ). The crystal structure of the Ti-rich G-phase adopts the non-centrosymmetric structure (SG F 4 ¯ 3 m ).

Combined refinement of neutron powder, X-ray single crystal and powder diffraction data allows precise evaluation of symmetry and atom site occupation for the MgZn2-type Laves phase. For compositions Ti(Ni1–x,Alx)2 titanium atoms were found to fully occupy the 4f site, whilst Ni- and Al-atoms randomly share the 2a and 6h sub-lattice sites of space group P63/mmc. At higher Ti-concentrations, Ti-atoms tend to enter the 2a and 6h site. Compositional dependences of the site occupations were used to explain the curved shape of the homogeneity region of the Laves phase. Investigation of the phase relations around the Ti-rich side of the ternary Laves phase was based on LOM, EPMA and X-ray diffraction experiments on argon arc-melted bulk alloys, which were annealed at 1000 °C in vacuum-sealed silica capsules for 100 h. The Ti-rich end of the homogeneity region of the ternary Laves phase at 1000 °C was derived from EMPA to be at Ti0.463Ni0.273Al0.264. Heat of formation data, derived from adiabatic drop calorimetry, were Δ298 H 0 = –57.9 ± 3.5 kJ/mol for Ti0.34Ni0.18Al0.48and –61.6 ± 3.3 kJ/mol for Ti0.36Ni0.24Al0.40. For the ab initio density functional theory applications a large number of structural models were investigated in order to calculate the concentration dependent heats of formation, structural stabilities, lattice parameters, bulk moduli and site occupancies, which are in good agreement with experiment. The theoretical analysis revealed that there are no Ni—Ni nearest neighbours when the concentration of Ni is smaller than that of Al. With increasing Al concentration, Al starts to fill 2a sites, and then continues occupying 6h sites. In compounds with Ti concentration larger than 33.3 at% the 4f sites are fully occupied by Ti, and the excessive Ti prefers 6h sites. The Al concentration of the Al-rich end of the homogeneity region of the ternary Laves phase was predicted to be 57 at%.

Site preference and thermodynamic properties of the ternary Laves phase Ti(Fe1–xAlx)2 with MgZn2-type have been studied employing Rietveld refinement of X-ray and neutron powder diffraction data, X-ray single crystal data, and isoperibolic drop calorimetry techniques. A detailed relation between lattice parameters of Ti(Fe1–xAlx)2 and the Al content in the Laves phase has been presented. The Rietvelt refinement revealed that Ti atoms occupy the 4f site in the MgZn2-type, whilst Fe and Al atoms randomly share the 2a and 6h site. Heat of formation has been measured for Ti(Fe0.5Al0.5)2. For the ab initio density functional theory applications, a large number of structural models were investigated to calculate the concentration dependent (Al) heats of formation, magnetic structural stabilities, lattice parameters, and site occupancies, which are in good agreement with experiment.