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Site distribution of Cu (2a, 2c, or 4d) can vary from Cu2ZnSnS4 to Cu2HgSnS4. Leveraging the analytical capabilities of 65Cu solid-state NMR spectroscopy, we solved the site distribution ambiguity between two reported structural models.

The ternary rare-earth-metal nickel indides RE23Ni7In4 (RE = Gd, Tb, Dy) were prepared by arc-melting mixtures of the elements followed by annealing at 870 K. They adopt the Yb23Cu7Mg4-type structure (space group P63/mmc, Pearson symbol hP68, Z = 2), as determined by laboratory and synchrotron powder diffraction methods for RE = Gd (a = 9.6435(10) A, c = 22.118(3) A) and Tb (a = 9.5695(8) A, c = 21.983(3) A), and single-crystal X-ray diffraction methods for RE = Dy (a = 9.533(5) A, c = 21.890(13) A). The centrosymmetric Yb23Cu7Mg4-type structure is closely related to the noncentrosymmetric Pr23Ir7Mg4-type structure. Triangular In3 clusters within RE23Ni7In4 represent a rare type of cluster found among metal-rich indides; the reasons for their formation were investigated by density functional theory methods.

The oxyselenide La

Mixed Sn–Pb halide perovskites are more stable at ambient conditions and can be tuned to give narrower band gaps than the all-Pb-containing counterparts (APbX3) used as photovoltaic materials. In t...

Accurate density functional theory calculations of the interrelated properties of thermoelectric materials entail high computational cost, especially as crystal structures increase in complexity and size. New methods involving ab initio scattering and transport (AMSET) and compressive sensing lattice dynamics are used to compute the transport properties of quaternary CaAl2Si2-type rare-earth phosphides RECuZnP2 (RE = Pr, Nd, Er), which were identified to be promising thermoelectrics from high-throughput screening of 20 000 disordered compounds. Experimental measurements of the transport properties agree well with the computed values. Compounds with stiff bulk moduli (>80 GPa) and high speeds of sound (>3500 m s−1) such as RECuZnP2 are typically dismissed as thermoelectric materials because they are expected to exhibit high lattice thermal conductivity. However, RECuZnP2 exhibits not only low electrical resistivity, but also low lattice thermal conductivity (∼1 W m−1 K−1). Contrary to prior assumptions, polar-optical phonon scattering was revealed by AMSET to be the primary mechanism limiting the electronic mobility of these compounds, raising questions about existing assumptions of scattering mechanisms in this class of thermoelectric materials. The resulting thermoelectric performance (zT of 0.5 for ErCuZnP2 at 800 K) is among the best observed in phosphides and can likely be improved with further optimization.

Heusler compounds form a diverse group of intermetallic materials encompassing many compositions and structures derived from cubic prototypes, and exhibiting complicated types of disorder phenomena...

The quaternary rare-earth-metal hafnium copper arsenides REHfCu2+δAs3 (where RE = La-Nd; δ ≈ 0.17) were obtained by direct reactions of the elements at 1073 K. They adopt a noncentrosymmetric orthorhombic crystal structure (space group Pmn21; a = 397.73(3)-392.37(2) pm, b = 1062.68(8)-1055.23(6) pm, c = 1307.25(9)-1291.40(7) pm for RE = La-Nd), which can be considered to be a Cu-deficient superstructure of the ternary Zr2Ni3P3-type structure found among metal-rich pnictides with a metal-to-nonmetal ratio close or equal to 2:1. The RE atoms occupy trigonal prismatic (CN6) and monocapped trigonal prismatic (CN7) sites, the latter resulting from the occurrence of Cu vacancies, the Hf atoms occupy octahedral sites (CN6), and the Cu atoms occupy tetrahedral sites (CN4). Band structure calculations on idealized models LaHfCu2As3 and LaHfCu2.5As3 suggest that the bonding situation improves by fractional occupation of the Cu3 site via depopulation of antibonding Cu-As states.

Accurate density functional theory calculations of the interrelated properties of thermoelectric materials entail high computational cost, especially as crystal structures increase in complexity and size. New methods involving ab initio scattering and transport (AMSET) and compressive sensing lattice dynamics are used to compute the transport properties of quaternary CaAl

The ternary rare-earth-metal nickel indides RE

Tin halide perovskites are promising candidates for lead-free photovoltaic and optoelectronic materials, but not all of them have been well characterized. It is essential to determine how the bulk photophysical properties are correlated with their structures at both short and long ranges. Although CsSnCl3 is normally stable in the cubic perovskite structure only above 379 K, it was prepared as a metastable phase at room temperature. The transition from the cubic to the monoclinic phase, which is the stable form at room temperature, was tracked by solid-state 133Cs NMR spectroscopy and shown to take place through a first-order kinetics process. The complete solid solution CsSn(Cl1−xBrx)3 (0 ≤ x ≤ 1) was successfully prepared, exhibiting cubic perovskite structures extending between the metastable CsSnCl3 and stable CsSnBr3 end-members. The NMR spectra of CsSnBr3 samples obtained by three routes (high-temperature, mechanochemical, and solvent-assisted reactions) show distinct chemical shift ranges, spin-lattice relaxation parameters and peak widths, indicative of differences in local structure, defects and degree of crystallinity within these samples. Variable-temperature 119Sn spin-lattice relaxation measurements reveal spontaneous mobility of Br atoms in CsSnBr3. The degradation of CsSnBr3, exposed to an ambient atmosphere for nearly a year, was monitored by NMR spectroscopy and powder X-ray diffraction, as well as by optical absorption spectroscopy., Unravelling the atomic-level chemical structure, slow phase conversion or degradation pathways and rapid halogen hopping of cesium tin(ii) halide perovskites using solid-state 119Sn and 133Cs NMR spectroscopy.

An innovative application of metal-organic frameworks (MOFs) is in biomedical materials. To treat bone demineralization, which is a hallmark of osteoporosis, biocompatible MOFs (bioMOFs) have been proposed in which various components, such as alkaline-earth cations and bisphosphonate molecules, can be delivered to maintain normal bone density. Multicomponent bioMOFs that release several components simultaneously at a controlled rate thus offer an attractive solution. We report two new bioMOFs, comprising strontium and calcium ions linked by p-xylylenebisphosphonate molecules that release these three components and display no cytotoxic effects on human osteosarcoma cells. Varying the Sr2+/Ca2+ ratio in these bioMOFs causes the rate of ions dissolving into simulated body fluid to be unique; along with the ability to adsorb proteins, this property is crucial for future efforts in drug-release control and promotion of mineral formation. The one-pot synthesis of these bioMOFs demonstrates the utility of MOF design strategies.

Four Hg-based IR nonlinear-optical materials, AHgSnQ4 (A = Sr, Ba; Q = S, Se), were discovered and investigated systematically. Their structures are built of two-dimensional [HgSnQ4]2- layers, which are assembled alternately by distorted (HgQ4 and SnQ4) tetrahedra and separated by eight-coordinated A2+ cations. The two sulfides AHgSnS4 (A = Ba, Sr) exhibit large second-harmonic-generation (SHG) responses (2.8 and 1.9 × AgGaS2 at 2.09 μm), as well as large band gaps (2.77 and 2.72 eV). The two selenides AHgSnSe4 (A = Ba, Sr) show even stronger SHG responses, about 5 times that of AgGaS2. Furthermore, all four compounds show phase-matching behavior, and the results of first-principles calculation elucidate the key role of the HgQ4 group in the enhanced SHG effect in β-BaHgSnS4 and BaHgSnSe4.

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.

New practically usable infrared (IR) nonlinear optical (NLO) crystals, especially those suitable for highly efficient pumping of the commercial 1 μm laser, are in urgent demand. However, only a few new IR NLO materials have been grown into bulk crystals and realized IR laser output during the past 20 years due to the extreme difficulty in achieving the coexistence of various strongly correlated properties. In this work, on the basis of the bonding characteristics of the Hg element and an efficient screening strategy for high-performance new crystals, we identified two new Hg-based IR NLO materials, BaHgGeSe4 and SrHgGeSe4. They crystallize in polar space group Ama2 with the distorted HgSe4 and GeSe4 tetrahedra aligned in parallel. They exhibit exceptional balance in terms of all of the preferred properties for practical applications, especially for highly efficient pumping of the commercial 1 μm laser. Their large band gap (∼2.5 eV) can avoid the two-photon absorption of the 1 μm laser and increase the la...

The quaternary chalcogenides SrCdGeS4 and SrCdGeSe4 were prepared by high-temperature reactions in the form of single crystals (at 1223 and 1123 K, respectively) or microcrystalline samples (at 1023 K). They adopt non-centrosymmetric structures (orthorhombic, space group Ama2, Z = 4; a = 10.3352(14) A, b = 10.2335(14) A, c = 6.4408(9) A for SrCdGeS4; a = 10.8245(8) A, b = 10.6912(8) A, c = 6.6792(5) A for SrCdGeSe4) consisting of anionic [CdGeCh4]2– layers separated by Sr2+ cations. Although the structure is closely related to the BaZnSiSe4-type, the substitution of Cd for Zn is accompanied by a significant displacement away from an ideal tetrahedral site toward a trigonal pyramidal geometry. Relationships to other similar structures are also elucidated. Large optical band gaps of 2.6 eV for SrCdGeS4 and 1.9 eV for SrCdGeSe4 were deduced from the absorption edges, consistent with the light yellow and red colors, respectively, of crystals of these compounds. Nonlinear optical measurements on powder samples...

The series of quaternary rare-earth phosphides REMnCuP2 (RE = Y, La–Nd, Sm, Gd–Tm, Lu), which had previously been limited to the Yb member, has been prepared by reaction of the elements at 800 °C. These phosphides adopt the CaAl2Si2-type structure (trigonal, space group P 3 ¯ m 1 , Z = 1) with Mn and Cu atoms disordered over the tetrahedral M sites within [M2P2] slabs. However, single-crystal X-ray diffraction studies, carried out on some of these members (RE = Tb, Dy, Er, Tm), provide evidence for an interstitial octahedral site being partially occupied by Cu atoms, resulting in the nonstoichiometric formulation REMnCu1+xP2 (x = 0.10–0.16). A second polymorph of LaMnCuP2 adopting the BaCu2S2-type structure (orthorhombic, space group Pnma, Z = 4) was also identified in the course of these investigations. Electronic structure calculations on a ordered superstructure model of YMnCuP2 indicate the absence of a band gap.

The quaternary rare-earth-metal hafnium copper arsenides REHfCu

A total of 73 new quaternary rare-earth germanides RE4 M2 XGe4 ( RE = rare-earth metal; M = Mn-Ni; X = Ag, Cd) were prepared through reactions of the elements. The solid solution Nd4Mn2Cd(Ge1- ySi y)4 was also prepared under the same conditions and found to be complete over the entire range. All of these compounds adopt the monoclinic Ho4Ni2InGe4-type structure (space group C2/ m, a = 14.2-16.7 A, b = 4.0-4.6 A, c = 6.8-7.5 A, β = 106-109°), as revealed by powder X-ray diffraction analysis and single-crystal X-ray diffraction analysis on selected members. The structure determination of Nd4(Mn0.78(1)Ag0.22(1))2Ag0.83(1)Ge4 disclosed disorder of Mn and Ag atoms within the tetrahedral site and Ag deficiencies within the square planar site. Within the solid solution Nd4Mn2Cd(Ge1- ySi y)4, the end-members and two intermediate members were structurally characterized; as the Si content increases, the Cd sites become less deficient and the individual [Mn2 Tt2] layers contract but become further apart from each other. Electronic band structure calculations confirm that the Ag-Ge or Cd-Ge bonds are the weakest in the structure and thus prone to distortion. Thermal property measurements confirm expectations from machine-learning predictions that these quaternary germanides should exhibit low thermal conductivity, which was found to be

The quaternary sulfide Ba5Cd2Ga2S10 was prepared by reaction of BaS, CdS, and Ga2S3 at high temperatures. Single-crystal X-ray diffraction analysis revealed that it adopts a new orthorhombic structure type (space group Pccn, Z = 4, a = 12.7664(7) A, b = 12.8060(7) A, c = 12.1265(7) A) consisting of one-dimensional anionic chains [CdGaS5]5– built from edge- and corner-sharing tetrahedra centred by Cd and Ga atoms in an ordered fashion, with Ba2+ cations located between the chains. The UV–vis–NIR diffuse reflectance spectrum reveals two optical transitions at 1.92(2) and 3.29(2) eV, the latter being consistent with the yellow colour of the crystals.

Twelve quaternary rare-earth selenides Ba2REGaSe5 and Ba2REInSe5 were prepared in the form of single crystals from reactions of BaSe, RE, M2Se3 (M = Ga, In), and Se at 1373 K. The compounds Ba2REGaSe5 fall into two separate series adopting an orthorhombic (RE = La, Ce; space group Pnma, Z = 4, a = 12.49–12.50 A, b = 9.60–9.63 A, c = 8.74 A) or a triclinic structure (RE = Tb, Ho, Tm, Yb, Lu; space group P 1 ¯ , Z = 2, a = 7.28–7.31 A, b = 8.61–8.72 A, c = 9.37–9.43 A, α = 103.4–103.5°, β = 103.0–103.1°, γ = 107.3–107.5°). The compounds Ba2REInSe5 adopt an orthorhombic structure (RE = Pr, Tb, Ho, Tm, Lu; space group Cmc21, Z = 4, a = 4.23–4.33 A, b = 18.75–18.96 A, c = 13.29–13.31 A). All structures contain anionic M-centred tetrahedra, isolated Se2– anions, Ba2+ cations in eight-fold coordination, and RE3+ cations in either six- or seven-fold coordination. A structure map developed based on radius ratios involving the RE3+, M3+, and Ch2– ions is effective in segregating four structures (in space groups Cmc21, P 1 ¯ , Pnma, and I4/mcm) found for Ba2REMCh5 (M = Ga, In; Ch = S, Se, Te). Bond valence sum calculations reveal that the upper limit for the largest RE components that can be substituted within a given structural series is set by the need to avoid overbonding of the RE atoms. An optical band gap of 1.34(2) eV was measured for the compound Ba2LaGaSe5, slightly less than a value of 1.76 eV obtained from electronic band structure calculations, which suggest an indirect transition.

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...

Two missing members, K3Bi2Cl9 and K3Bi2Br9, within the series of Bi-containing defect perovskite halides A3Bi2X9 were sought. K3Bi2Cl9 could not be obtained, but the previously identified but uncharacterized compound K2BiCl5 was prepared. K3Bi2Br9 was successfully prepared. K2BiCl5 and K3Bi2Br9 were synthesized by reactions of binary halides at 450–500 ​°C and their structures were determined by single-crystal X-ray diffraction methods. K2BiCl5 adopts the K2PrCl5-type structure in orthorhombic space group Pnma with Z ​= ​4 and cell parameters of a ​= ​12.5461(7) A, b ​= ​8.7630(5) A, and c ​= ​7.9865(5) A. This structure features one-dimensional columns of edge-sharing BiCl7 capped octahedra. K3Bi2Br9 adopts the Tl3Bi2Br9-type structure in monoclinic space group P21/c with Z ​= ​4 and cell parameters of a ​= ​18.718(3) A, b ​= ​8.1148(13) A, c ​= ​13.154(2) A, and β ​= ​91.329(2)°. In this defect perovskite variant, Bi atoms occupy two-thirds of the octahedral sites formed by close-packed arrays of the K and Br atoms, and the BiBr6 octahedra are connected by corner-sharing within slabs. Among defect perovskite halides A3Bi2X9 containing corner-sharing octahedra, K3Bi2Br9 exhibits the greatest degree of distortion from the ideal cubic perovskite structure observed so far. The band gaps, as measured from optical diffuse reflectance spectra, are 2.8 ​eV for K2BiCl5 and 2.2 ​eV for K3Bi2Br9. Electronic structure calculations indicate an indirect gap for K2BiCl5 and a direct gap with rather flat bands for K3Bi2Br9.

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.

Intermetallic compounds are bestowed by diverse compositions, complex structures, and useful properties for many materials applications. How metallic elements react to form these compounds and what structures they adopt remain challenging questions that defy predictability. Traditional approaches offer some rational strategies to prepare specific classes of intermetallics, such as targeting members within a modular homologous series, manipulating building blocks to assemble new structures, and filling interstitial sites to create stuffed variants. Because these strategies rely on precedent, they cannot foresee surprising results, by definition. Exploratory synthesis, whether through systematic phase diagram investigations or serendipity, is still essential for expanding our knowledge base. Eventually, the relationships may become too complex for the pattern recognition skills to be reliably or practically performed by humans. Complementing these traditional approaches, new machine-learning approaches may be a viable alternative for materials discovery, not only among intermetallics but also more generally to other chemical compounds. In this Account, we survey our own efforts to discover new intermetallic compounds, encompassing gallides, germanides, phosphides, arsenides, and others. We apply various machine-learning methods (such as support vector machine and random forest algorithms) to confront two significant questions in solid state chemistry. First, what crystal structures are adopted by a compound given an arbitrary composition? Initial efforts have focused on binary equiatomic phases AB, ternary equiatomic phases ABC, and full Heusler phases AB

Reaction of BaSe, Ga2Se3, and Sb2Se3 yielded the quaternary selenide Ba23Ga8Sb2Se38 in the form of single crystals (at 1223 K) and phase-pure powder (at 1073 K). Ba23Ga8Sb2Se38 is isostructural to the sulfide analogue Ba23Ga8Sb2S38, crystallizing in the noncentrosymmetric orthorhombic space group Cmc21 with a = 9.9825(4) A, b = 33.4658(13) A, c = 13.3856(5) A, and Z = 2. The structure consists of isolated GaSe4 tetrahedra and SbSe3 trigonal pyramids, separated by Ba cations. An optical band gap of 2.31(2) eV, consistent with the red-brown colour of the crystals, was deduced from the UV–vis–NIR diffuse reflectance spectrum. Nonlinear optical measurements using a fundamental laser wavelength of 2090 nm indicated that Ba23Ga8Sb2Se38 exhibits a moderate powder second harmonic generation signal and non-type-I phase-matching behaviour.

A method to predict the crystal structure of equiatomic ternary compositions based only on the constituent elements was developed using cluster resolution feature selection (CR-FS) and support vector machine (SVM) classification. The supervised machine-learning model was first trained with 1037 individual compounds that adopt the most populated ternary 1:1:1 structure types (TiNiSi-, ZrNiAl-, PbFCl-, LiGaGe-, YPtAs-, UGeTe-, and LaPtSi-type) and then validated using an additional 519 compounds. The CR-FS algorithm improves class discrimination and indicates that 113 variables including size, electronegativity, number of valence electrons, and position on the periodic table (group number) influence the structure preference. The final model prediction sensitivity, specificity, and accuracy were 97.3%, 93.9%, and 96.9%, respectively, establishing that this method is capable of reliably predicting the crystal structure given only its composition. The power of CR-FS and SVM classification is further demonstrated by segregating the crystal structure of polymorphs, specifically to examine polymorphism in TiNiSi- and ZrNiAl-type structures. Analyzing 19 compositions that are experimentally reported in both structure types, this machine-learning model correctly identifies, with high confidence (0.7), the low-temperature polymorph from its high-temperature form. Interestingly, machine learning also reveals that certain compositions cannot be clearly differentiated and lie in a "confused" region (0.3-0.7 confidence), suggesting that both polymorphs may be observed in a single sample at certain experimental conditions. The ensuing synthesis and characterization of TiFeP adopting both TiNiSi- and ZrNiAl-type structures in a single sample, even after long annealing times (3 months), validate the occurrence of the region of structural uncertainty predicted by machine learning.