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Transition metal chalcogenides (TMC) is a broad class of materials comprising binary, ternary, quaternary, and multinary oxides, sulfides, selenides, and tellurides. These materials have application in different areas such as solar cells, photocatalysis, sensors, photoinduced therapy, and fluorescent labeling. Due to the technological importance of this class of material, it is necessary to find synthetic methods to produce them through procedures aligned with the Green Chemistry. In this sense, this chapter presents opportunities to make the solution chemistry synthesis of TMC greener. In addition to synthesis, the chapter presents different techniques of experimental planning and analysis, such as design of experiments, life cycle assessment, and machine learning. Then, it explains how Green Chemistry can benefit from each one of these techniques, and how they are related to the Green Chemistry Principles. Focus is placed on binary chalcogenides (sulfides, selenides, and tellurides), and the quaternary sulfide Cu2ZnSnS4 (CZTS), due to its application in many fields like solar energy, photocatalysis, and water splitting. The Green Chemistry synthesis, characterization, and application of these materials may represent sustainable and effective ways to save energy and resources without compromising the quality of the produced material.

The rapidly growing interest in machine learning (ML) for materials discovery has resulted in a large body of published work. However, only a small fraction of these publications includes confirmation of ML predictions, either via experiment or via physics-based simulations. In this review, we first identify the core components common to materials informatics discovery pipelines, such as training data, choice of ML algorithm, and measurement of model performance. Then we discuss some prominent examples of validated ML-driven materials discovery across a wide variety of materials classes, with special attention to methodological considerations and advances. Across these case studies, we identify several common themes, such as the use of domain knowledge to inform ML models.

This Methods/Protocols article is intended for materials scientists interested in performing machine learning-centered research. We cover broad guidelines and best practices regarding the obtaining...

The rare-earth germanium sulfide iodides RE3Ge2S8I (RE = La, Ce, Pr) have been prepared by reaction of the elements at 900 °C. They adopt the monoclinic La3(SiO4)2Cl-type structure (space group C2/c, Z = 4; a = 16.156(4)–15.9760(9) A, b = 7.9776(18)–7.8786(5) A, c = 11.081(3)–10.9281(6) A, β = 98.192(5)–98.4525(10)° on progressing from La to Pr for the RE component) consisting of isolated thiogermanate tetrahedral groups [GeS4]4– separated by RE3+ and I− ions. The optical band gaps fall in the range of 2.7–3.1 eV. Magnetic measurements indicated simple paramagnetic behaviour for Ce3Ge2S8I and Pr3Ge2S8I.

This Editorial is intended for materials scientists interested in performing machine learning-centered research.We cover broad guidelines and best practices regarding the obtaining and treatment of data, feature engineering, model training, validation, evaluation and comparison, popular repositories for materials data and benchmarking datasets, model and architecture sharing, and finally publication.In addition, we include interactive Jupyter notebooks with example Python code to demonstrate some of the concepts, workflows, and best practices discussed.Overall, the data-driven methods and machine learning workflows and considerations are presented in a simple way, allowing interested readers to more intelligently guide their machine learning research using the suggested references, best practices, and their own materials domain expertise.

Two quantum dots, both alike in composition, but differing in structure, where we lay our scene. From broader classes, to bring deeper understanding, to the crystalline core that drives the quantum dot's sheen. In this contribution we examine two families of silicon quantum dots (SiQDs) that bring to mind the Capulets and the Montagues in Shakespeare’s Romeo and Juliet because of their stark similarities and differences. SiQDs are highly luminescent, heavy-metal-free and based upon earth-abundant elements. As such, they have attracted attention for far reaching applications ranging from biological imaging to luminescent solar concentrators to light-emitting diodes that rely on their size-dependent optical response. Unfortunately, correlating SiQD “size” to their photoluminescence maximum is often challenging. Herein, we provide essential structural insight into the correlation of SiQD dimension and PL maximum through a direct comparison of samples that exhibit statistically identical physical dimensions (dTEM) and chemical compositions, but different crystallite size (dXRD) and PL maxima. We then expand the scope of this investigation and systematically compare groupings of SiQDs: one in which the dXRD and dTEM agree and one where dXRD < dTEM. This latter comparison clearly shows dXRD better predicts SiQD optical response when using the well-established effective mass approximation.

Rare-earth substituted inorganic phosphors are critical for solid state lighting. New phosphors are traditionally identified through chemical intuition or trial and error synthesis, inhibiting the discovery of potential high-performance materials. Here, we merge a support vector machine regression model to predict a phosphor host crystal structure’s Debye temperature, which is a proxy for photoluminescent quantum yield, with high-throughput density functional theory calculations to evaluate the band gap. This platform allows the identification of phosphors that may have otherwise been overlooked. Among the compounds with the highest Debye temperature and largest band gap, NaBaB9O15 shows outstanding potential. Following its synthesis and structural characterization, the structural rigidity is confirmed to stem from a unique corner sharing [B3O7]5– polyanionic backbone. Substituting this material with Eu2+ yields UV excitation bands and a narrow violet emission at 416 nm with a full-width at half-maximum of 34.5 nm. More importantly, NaBaB9O15:Eu2+ possesses a quantum yield of 95% and excellent thermal stability., Identifying phosphors with good thermal stability and quantum efficiency is a prerequisite to improve the performance of white LED light sources. Here, a combined machine learning and density functional theory method is introduced to identify next generation inorganic phosphors.

Two new compounds in the Yb–Cu–Ga system were discovered. Yb6(CuGa)50 was obtained as single crystals grown from gallium metal flux, and Yb6(CuGa)51 was synthesized by high-frequency induction heating technique. Structure analysis reveals new structure type for Yb6(CuGa)50 (C2/m space group), while Yb6(CuGa)51 crystallizes in rhombohedral space group R3m adopting the Th2Zn17 structure type. Both structures could be derived from the simplest layered packing, through CaCu5-type structure, as a common parent. Physical properties of the Yb6(CuGa)51 sample obtained bulk quantity were explored. The magnetic susceptibility study of Yb6(CuGa)51 in the temperature range of 2–300 K suggests a valence fluctuation at lower temperatures. X-ray absorption near edge spectroscopy suggests that Yb exists in mixed-valent state in Yb6(CuGa)51. Electrical resistivity measurement reveals that Yb6(CuGa)51 is metallic in nature and shows Fermi-liquid behavior in the temperature range from 3.5 to 25 K.

Most discoveries in materials science have been made empirically, typically through one-variable-at-a-time (Edisonian) experimentation. The characteristics of materials-based systems are, however, neither simple nor uncorrelated. In a device such as an organic photovoltaic, for example, the level of complexity is high due to the sheer number of components and processing conditions, and thus, changing one variable can have multiple unforeseen effects due to their interconnectivity. Design of Experiments (DoE) is ideally suited for such multivariable analyses: by planning one’s experiments as per the principles of DoE, one can test and optimize several variables simultaneously, thus accelerating the process of discovery and optimization while saving time and precious laboratory resources. When combined with machine learning, the consideration of one’s data in this manner provides a different perspective for optimization and discovery, akin to climbing out of a narrow valley of serial (one-variable-at-a-time) experimentation, to a mountain ridge with a 360° view in all directions.

There remain 21 systems (out of over 3500 possible combinations of the elements) in which the existence of the simple binary equiatomic phases AB has not been established experimentally. Among these, the presumed binary phase HfIn is predicted to adopt the tetragonal CuAu-type structure (space group P4/mmm) by a recently developed machine-learning model and by structure optimization through global energy minimization. To test this prediction, the Hf−In system was investigated experimentally by reacting the elements in a 1:1 stoichiometry at 1070 K. Under the conditions investigated, the bulk and surface of the sample correspond to different crystalline phases but have nearly the same equiatomic composition, as revealed by energy-dispersive X-ray analysis. The structure of the bulk sample, which was solved from powder X-ray diffraction data through simulated annealing, corresponds to the γ-brass (Cu5Zn8) type (space group I43m) with Hf and In atoms disordered over four sites. The structure of crystals sel...

The germanides Ce3Rh11Ge5, Ce6Rh30Ge19.5, and CeRh3Ge2, which are new ternary Rh-rich phases in the Ce–Rh−Ge system, were prepared by reactions of the elements. Their crystal structures were determined by single-crystal and powder X-ray diffraction methods. Ce3Rh11Ge5 adopts the Gd3Ru4Al12-type structure, which represents the fully stoichiometric version of the defect Sc3Ni11Ge4-type structure, in hexagonal space group P63/mmc with Z ​= ​2 and cell parameters a ​= ​8.6964 (12) A and c ​= ​9.2209 (12) A. Ce6Rh30Ge19.5 is a filled derivative of the U6Co30Si19-type structure in hexagonal space group P63/m with Z ​= ​2 and cell parameters a ​= ​22.8480 (11) A and c ​= ​3.9208 (2) A. CeRh3Ge2 is derived from a symmetry-lowered distortion of the hexagonal CeCo3B2-type (or substitutionally ordered CaCu5-type) structure, and crystallizes in orthorhombic space group Fmmm with Z ​= ​16 and cell parameters a ​= ​7.392 (6) A, b ​= ​11.341 (9) A, and c ​= ​19.66 (2) A. As expected by their Rh-rich compositions, the three compounds exhibit extensive Rh–Rh bonding, but surprisingly, they also show some short Ge–Ge contacts. Analysis of the electron localization functions and Bader charges reveals that charge transfer takes place from Ce to Rh atoms, indicative of a polar character in the bonding in these intermetallic compounds.

The Li-containing intermetallic compounds LiCu2Al and LiCu2Ga were prepared by induction heating. Powder X-ray diffraction revealed cubic structures for these compounds: Li0·5CuAl0.5, CsCl-type ( P m 3 ¯ m , Z ​= ​1, a ​= ​2.9283 (2) A); LiCu2Ga, Heusler or Cu2MnAl-type ( F m 3 ¯ m , Z ​= ​4, a ​= ​5.8617 (4) A). Solid-state 7Li NMR spectra confirmed that the Li atoms are situated on a single site rather than being disordered over multiple sites. Optical reflectance spectra show absorption edges in the visible region consistent with the appearance of colour in these compounds: red for LiCu2Al, yellow for LiCu2Ga. Band structure calculations revealed the presence of completely filled Cu 3d states, and suggest that interband transitions from the top of this narrow band (located around 2.5 ​eV below the Fermi level) to empty bands are responsible for the colour.

A machine-learning model has been trained to discover Heusler compounds, which are intermetallics exhibiting diverse physical properties attractive for applications in thermoelectric and spintronic materials. Improving these properties requires knowledge of crystal structures, which occur in three subtle variations (Heusler, inverse Heusler, and CsCl-type structures) that are difficult, and at times impossible, to distinguish by diffraction techniques. Compared to alternative approaches, this Heusler discovery engine performs exceptionally well, making fast and reliable predictions of the occurrence of Heusler vs non-Heusler compounds for an arbitrary combination of elements with no structural input on over 400 000 candidates. The model has a true positive rate of 0.94 (and false positive rate of 0.01). It is also valuable for data sanitizing, by flagging questionable entries in crystallographic databases. It was applied to screen candidates with the formula AB$_{2}$C and predict the existence of 12 novel gallides MRu$_{2}$Ga and RuM$_{2}$Ga (M = Ti-Co) as Heusler compounds, which were confirmed experimentally. One member, TiRu$_{2}$Ga, exhibited diagnostic superstructure peaks that confirm the adoption of an ordered Heusler as opposed to a disordered CsCl-type structure.

Partial least-squares discriminant analysis (PLS-DA) and support vector machine (SVM) techniques were applied to develop a crystal structure predictor for binary AB compounds. Models were trained and validated on the basis of the classification of 706 AB compounds adopting the seven most common structure types (CsCl, NaCl, ZnS, CuAu, TlI, β-FeB, and NiAs), through data extracted from Pearson’s Crystal Data and ASM Alloy Phase Diagram Database. Out of 56 initial variables (descriptors based on elemental properties only), 31 were selected in as unbiased manner as possible through a procedure of forward selection and backward elimination, with the quality of the model evaluated by measuring the cluster resolution at each step. PLS-DA gave sensitivity of 96.5%, specificity of 66.0%, and accuracy of 77.1% for the validation set data, whereas SVM gave sensitivity of 94.2%, specificity of 92.7%, and accuracy of 93.2%, a significant improvement. Radii, electronegativity, and valence electrons, previously chosen i...

Solid-state phase equilibria have been established in the Ta–Cr–P system in the region of 0–67 at% P at 1070 K through powder X-ray diffraction analysis. Mutual substitution of Ta and Cr in binary phosphides gives rise to significant homogeneity ranges in Ta 1.00–0.66 Cr 0–0.34 P (NbAs-type; a =3.332(3)–3.1366(3) A, c =11.386(4)–11.364(2) A), Ta 3.0–2.1 Cr 0–0.9 P (Ti 3 P-type, a =10.156(2)–9.9992(2) A, c =5.015(1)–4.956(2) A), and Cr 3.0–2.4 Ta 0–0.6 P (Ni 3 P-type, a =9.186(5)–9.217(4) A, c =4.557(3)–4.5911(3) A). A limited homogeneity range is found in the ternary phase Ta 1.0–0.8 Cr 1.0–1.2 P (TiNiSi-type, a =6.2344(5)–6.141(2) A, b =3.5034(3)–3.3769(6) A, c =7.3769(6)–7.357(2) A). The OsGe 2 -type structures (space group C 2/ m ) of a new P-rich compound, Ta 0.92(2) Cr 0.08(2) P 2 ( a =8.8586(3) A, b =3.2670(2) A, c =7.4871(2) A, β =119.315(2)°) as well as of the Ti-containing analogue Ta 0.93(3) Ti 0.07(3) P 2 ( a =8.8592(5) A, b =3.2663(3) A, c =7.4870(5) A, β =119.309(2)°) were refined from powder X-ray diffraction data.

In this article we provide an overview of data mining, informatics, and machine learning approaches for thermoelectrics. We describe how the initial development of a thermoelectric materials database has enabled the creation of a recommendation engine governed by machine learning and how this engine introduces a new paradigm in thermoelectric materials development. Performance probability is generated based on training models. A demonstration of the data mining approach is set forth in a ternary intermetallic system, where we report new materials.

Despite numerous studies on three-dimensional topological insulators (3D TIs), the controlled growth of high quality (bulk-insulating and high mobility) TIs remains a challenging subject. This study investigates the role of growth methods on the synthesis of single crystal stoichiometric BiSbTeSe2 (BSTS). Three types of BSTS samples are prepared using three different methods, namely melting growth (MG), Bridgman growth (BG) and two-step melting-Bridgman growth (MBG). Our results show that the crystal quality of the BSTS depend strongly on the growth method. Crystal structure and composition analyses suggest a better homogeneity and highly-ordered crystal structure in BSTS grown by MBG method. This correlates well to sample electrical transport properties, where a substantial improvement in surface mobility is observed in MBG BSTS devices. The enhancement in crystal quality and mobility allow the observation of well-developed quantum Hall effect at low magnetic field.

Phase equilibria in the Hf–Ti–P system were investigated at T = 1070 K in the region 0–67 at.% of P, employing X-ray powder diffraction. The three ternary compounds exist in the Hf–Ti–P system at this temperature. Two of them have homogeneity regions and their compositions can be represented as Hf x Ti 2− x P (0.65 ⩽ x ⩽ 1.30; TiNiSi-type, space group Pnma , a = 6.130(3)–6.673(5), b = 3.508(2)–3.557(2), c = 8.050(5)–8.161(2) A) and Hf x Ti 2− x P 0.68 . (0.75 ⩽ x ⩽ 1.00; Zn 3 Cu-type, space group Р -6, a = 4.758(1)–4.803(1), c = 3.005(1)–3.035(1) A). The crystal structure of the new phosphide Hf 5.35 Ti 8.65 P 8.93 was determined by X-ray single crystal diffraction. This compound crystallizes with the Zr 14 P 9 -type structure (space group Pnnm , cell parameters a = 15.973(1), b = 26.335(2), c = 3.5281(2) A, R 1 = 0.0670; wR 2 = 0.0875). The majority of binary compounds form substitution type solid solutions, in their homogeneity ranges the substitution of Ti by Hf or Hf for Ti takes place.

Part of the quaternary Ce–Mn–In–Ge phase diagram has been examined through powder X-ray diffraction and energy-dispersive X-ray analysis. Two new quaternary (Ce 4 Mn 2 InGe 4 and Ce 2 Mn 2 InGe 2 ) and two ternary (Ce 3 Mn 2 Ge 3 and Ce 43 Mn 18 Ge 39 ) phases were found. The isothermal sections of the boundary ternary systems (Ce–Mn–In, Mn–In–Ge, Ce–In–Ge, and Ce–Mn–Ge) were determined at 800 °C. Among these, the Ce–Mn–Ge system deserves particular attention because the phase equilibria are complex. Relative to the previously reported phase diagram evaluated at a lower temperature (400 °C), three ternary phases (CeMn 2 Ge 2 , Ce 2 MnGe 6 , and CeMnGe) persist, Ce 2 MnGe 5 does not form, and two new phases with very close composition (Ce 3 Mn 2 Ge 3 and Ce 43 Mn 18 Ge 39 ) appear at 800 °C. Ce 3 Mn 2 Ge 3 (orthorhombic Hf 3 Ni 2 Si 3 -type) has a small homogeneity range (2%) deviating from the ideal composition, whereas Ce 43 Mn 18 Ge 39 (tetragonal La 2+ x MnGe 2+ y -type) has negligible homogeneity. Magnetic measurements on Ce 4 Mn 2 InGe 4 suggest ferromagnetic behaviour.

The ternary germanides RE 3 Mn 2 Ge 3 , which have been prepared by arc-melting and annealing at 800 °C, are formed with larger rare-earth components (RE = Ce–Nd), in contrast to other RE 3 M 2 Ge 3 series. They adopt the orthorhombic Hf 3 Ni 2 Si 3 -type structure (space group Cmcm , Z = 4). Single-crystal X-ray diffraction studies performed for the Ce member ( a = 4.3340(3) A, b = 11.6069(9) A, c = 14.6717(12) A) indicate an expanded structure relative to other RE 3 M 2 Ge 3 series, with essentially nonbonding Ge–Ge contacts between the [Mn 2 Ge 3 ] layers built up of double-chains of MnGe 4 tetrahedra. A minor oxidation product identified in the course of these investigations was proposed to be Nd 4 Mn 2 Ge 5 O 0.6 , in which a host monoclinic Yb 4 Mn 2 Sn 5 -type structure accommodates interstitial oxygen atoms partially occupying an octahedral void (space group C 2/ m , Z = 2, a = 16.275(3) A, b = 4.3779(8) A, c = 7.3783(14) A, β = 107.372(2)°). This structure also contains layers with double-chains of MnGe 4 tetrahedra which are now connected through Ge 2 dimers; isolated Ge atoms in square planar coordination are located between the layers. Magnetic measurements on RE 3 Mn 2 Ge 3 suggest complex antiferromagnetic ordering phenomena with several field-dependent transitions.

Six series of quaternary rare-earth transition-metal chalcogenides RE3MGaCh7 (M=Fe, Co, Ni; Ch=S, Se), comprising 33 compounds in total, have been prepared by reactions of the elements at 1050 °C (for the sulphides) or 900 °C (for the selenides). They adopt noncentrosymmetric hexagonal structures (ordered Ce3Al1.67S7-type, space group P63, Z=2) with cell parameters in the ranges of a=9.5–10.2 A and c=6.0–6.1 A for the sulphides and a=10.0–10.5 A and c=6.3–6.4 A for the selenides as refined from powder X-ray diffraction data. Single-crystal structures were determined for five members of the sulphide series RE3FeGaS7 (RE=La, Pr, Tb) and RE3CoGaS7 (RE=La, Tb). The highly anisotropic crystal structures consist of one-dimensional chains of M-centred face-sharing octahedra and stacks of Ga-centred tetrahedra all pointing in the same direction. Magnetic measurements on the sulphides reveal paramagnetic behaviour in some cases and long-range antiferromagnetic behaviour with low Neel temperatures (15 K or lower) in others. Ga L-edge XANES spectra support the presence of highly cationic Ga tetrahedral centres with a tendency towards more covalent Ga–Ch character on proceeding from the sulphides to the selenides. Band structure calculations on La3FeGaS7 indicate that the electronic structure is dominated by Fe 3d-based states near the Fermi level.

The four series of quaternary sulfides RE3Zn0.5SiS7 (RE = La–Nd, Sm, Gd–Er), RE3Zn0.5GeS7 (RE = La–Nd, Sm, Gd–Er), RE3Cd0.5SiS7 (RE = La–Nd, Sm, Gd–Ho), and RE3Cd0.5GeS7 (RE = La–Nd, Sm, Gd, Tb) were prepared by reactions of the elements at 1050 °C. Analysis of their powder X-ray diffraction patterns indicates that they adopt the noncentrosymmetric hexagonal La3Mn0.5SiS7-type structure (space group P63, Z = 2). The structures of two Cd-containing members were refined from single-crystal X-ray diffraction data (Gd3Cd0.5SiS7, a = 9.9737(8) A, c = 5.6287(4) A; Gd3Cd0.5GeS7, a = 9.9739(3) A, c = 5.7296(4) A). La3Zn0.5GeS7 melts incongruently above 1300 °C. Ce3Zn0.5GeS7 shows simple paramagnetic behaviour arising from non-interacting Ce3+ species. Optical band gaps of 2.7 eV for La3Cd0.5SiS7, 2.3 eV for La3Cd0.5GeS7, and 1.8 eV for Ce3Zn0.5GeS7 were measured. Band structure calculations on La3Cd0.5SiS7 and La3Cd0.5GeS7 confirm the presence of band gaps whose magnitude is controlled by Si–S or Ge–S bonding interactions.

Reactions of the elements through arc-melting and annealing at 800 °C have led to the ternary rare-earth manganese germanides RE2+xMnGe2+y (RE=La, Ce). The approximate composition is RE2.1MnGe2.2, as determined by single-crystal X-ray diffraction studies on the La member (space group P4/nmm, a=16.0491(4) A, c=8.1587(2) A, Z=16). Although this composition is close to other germanides RE2MGe2 (Sc2CoSi2-type), the structure is completely unrelated. Rather, La2.1MnGe2.2 contains layers built up of Mn-centred tetrahedra in two types of arrangements, four-membered rings and stellae quadrangulae, with La and additional Ge atoms in the intervening spaces. Disorder of La atoms, isolated Ge atoms, and Ge2 dimers takes place within tunnels in the structure. Electrical and magnetic measurements on La2.1MnGe2.2 indicate metallic behaviour and likely ferromagnetic ordering with a transition temperature above 300 K.

Abstract Phase equilibria was investigated in the Ti-Fe-P system at T = 1070 K in the region 0–67 at.% of P, employing X-ray powder diffraction. The two ternary compounds, namely Ti0.5–0.8Fe1.5−1.2P (Co2Si-type; space group Pnma; a = 0.5964(2)–0.6011(3), b = 0.3575(3)–0.3600(1), c = 0.6828(2)–0.6882(2) nm) and Ti0.85−1.25Fe1.15−0.75P (ZrNiAl-type; space group P-62m; a = 0.6071(4)–0.6117(1), c = 0.3510(9)–0.3506(1) nm) exist in the Ti-Fe-P system at this temperature. The crystal structure of the Ti0.85–1.25Fe1.15−0.75P compound was additionally determined by X-ray single crystal diffraction on the phase with stoichiometric composition. The substitutions of Ti by Fe were observed for Ti5P3.16, Ti3P and TiP phases, and Fe for Ti in the case of Fe3P, Fe2P binary compounds. Graphical abstract

Through arc-melting reactions of the elements and annealing at 800 °C, the ternary rare-earth germanides RE 3 Ru 2 Ge 3 and RE 3 Ir 2 Ge 3 have been prepared for most of the smaller RE components ( RE =Y, Gd–Tm, Lu). In the iridium-containing reactions, the new phases RE 2 IrGe 2 were also generally formed as by-products. Powder X-ray diffraction revealed orthorhombic Hf 3 Ni 2 Si 3 -type structures (space group Cmcm , Z =4) for RE 3 M 2 Ge 3 ( M =Ru, Ir) and monoclinic Sc 2 CoSi 2 -type structures (space group C 2/ m , Z =4) for RE 2 IrGe 2 . Full crystal structures were determined by single-crystal X-ray diffraction for all members of RE 3 Ru 2 Ge 3 ( a =4.2477(6) A, b =10.7672(16) A, c =13.894(2) A for RE =Y; a =4.2610(3)–4.2045(8) A, b =10.9103(8)–10.561(2) A, c =14.0263(10)–13.639(3) A in the progression of RE from Gd to Lu) and for Tb 3 Ir 2 Ge 3 ( a =4.2937(3) A, b =10.4868(7) A, c =14.2373(10) A). Both structures can be described in terms of CrB- and ThCr 2 Si 2 -type slabs built from Ge-centred trigonal prisms. However, band structure calculations on Y 3 Ru 2 Ge 3 support an alternative description for RE 3 M 2 Ge 3 based on [ M 2 Ge 3 ] layers built from linked M Ge 4 tetrahedra, which emphasizes the strong M –Ge covalent bonds present. The temperature dependence of the electrical resistivity of RE 3 Ru 2 Ge 3 generally indicates metallic behaviour but with low-temperature transitions visible for some members ( RE =Gd, Tb, Dy) that are probably associated with magnetic ordering of the RE atoms. Anomalously, Y 3 Ru 2 Ge 3 exhibits semiconductor-like behaviour of uncertain origin. Magnetic measurements on Dy 3 Ru 2 Ge 3 reveal antiferromagnetic ordering at 3 K and several unusual field-dependent transitions suggestive of complex spin reorientation processes.

The interaction between components in the Zr–Ti–P system in the range of up to 67 at.% P was analyzed and the isothermal section diagram at 1070 K was constructed from X-ray structural and EDS analysis. Solid substitutional solutions based on the binary phosphides M 3 P with the Ti 3 P-type structure (Ti 3.0−2.3 Zr 0−0.7 P and Zr 3.0−2.5 Ti 0−0.5 P) were found. The phosphide (Ti,Zr) 2 P with the Co 2 Si-type structure is homogeneous at the Zr 1.2−0.6 Ti 0.8−1.4 P composition. From powder X-ray diffraction methods, the crystal structure of ZrTiP 0.68 was shown to be of the Zn 3 Cu-type (space group P -6, a = 0.47600(1), c = 0.30038(1) nm, R I = 0.0444); HfTiP 0.68 is isostructural. These compounds are homogenous in the range Zr 1.0−1.5 Ti 1.0−0.5 P 0.68 and Hf 0.9−1.2 Ti 1.1−0.8 P 0.68 . From single-crystal methods, the structure of Zr 0.93 Ti 0.07 P 0.93 was determined to belong to the WC-type structure (space group P -6 m 2, a = 0.3004(2), c = 0.3117(3) nm, R F = 0.0228).

Attempts to prepare Gd12Co5Bi, a member of the rare-earth (RE) intermetallics RE12Co5Bi, which were identified by a machine-learning recommendation engine as potential candidates for thermoelectric materials, led instead to formation of the new compound Gd12Co5.3Bi with a very similar composition. Phase equilibria near the Gd-rich corner of the Gd-Co-Bi phase diagram were elucidated by both lab-based and variable-temperature synchrotron powder X-ray diffraction, suggesting that Gd12Co5.3Bi and Gd12Co5Bi are distinct phases. The higher symmetry structure of Gd12Co5.3Bi (cubic, space group Im3̅, Z = 2, a = 9.713(6) Å), as determined from single-crystal X-ray diffraction, is closely related to that of Gd12Co5Bi (tetragonal, space group Immm). Single Co atoms and Co-Co dumbbells are disordered with occupancies of 0.78(2) and 0.22(2), respectively, in Gd12Co5.3Bi, but they are ordered in Gd12Co5Bi. Consistent with this disorder, the electrical resistivity shows less dependence on temperature for Gd12Co5.3Bi than for Gd12Co5Bi. The thermal conductivity is low and reaches 2.8 W m(-1) K(-1) at 600 °C for both compounds; however, the temperature dependence of the thermal conductivity differs, decreasing for Gd12Co5.3Bi and increasing for Gd12Co5Bi as the temperature increases. The unusual trends in thermal properties persist in the heat capacity, which decreases below 2R, and in the thermal diffusivity, which increases at higher temperatures.