46 structure types of binary and ternary intermetallic compounds have been derived from the well known, simple aristotype AlB 2 . Many compounds with the general compositions RX 2 , RT 2 , R7X, and R 2 TX 3 (R = alkaline earth, rare earth or actinoid metal: T = transition metal; X = main group element) belong to this family. The structural similarities between these compounds are manifested by an ordering of the transition metal atoms and main group element atoms on the boron positions of the AlB 2 type. Also an ordering of vacancies on the boron positions occurs in some compounds. Striking structural motifs of the RX 2 , RT 2 , RTX, and R 2 TX 3 compounds are planar or puckered six-membered rings consisting of X 6 , T 6 . T 3 X 3 , and T 2 X 4 separated by the respective R atoms The crystal chemical relationships between these compounds are discussed on the basis of a group-subgroup scheme in the concise and compact Barnighausen formalism with respect to the aristotype AlB 2 . Two different branches of AlB 2 related structures are discussed. In the first, the hexagonal/trigonal branch, six-membered rings carry at least a three-fold axis, while in the orthorhombic/ monoclinic branch the distortions are more pronounced. The pseudo-hexagons show significant tilting and a loss of hexagonal/trigonal symmetry. Significant variations of the chemical bonding occur for some structure types, and therefore they may only be considered to be isopointal rather than isotypic. These isopointal conversions are based on a gradual changeover from two- to three-dimensionally infinite polyanions. Besides the group theoretical group-subgroup scheme we also discuss chemical bonding in these AlB 2 related intermetallic compounds.

AlB2-related intermetallic compounds – a comprehensive view based on group-subgroup relations

Review on magnetic and related properties of RTX compounds

The crystallochemistry of and the bonding in the orthorhombic four-connected nets of BaIn2 (CeCu2 structure) and of CaPtSn (TiNiSi structure, a derivative of the CeCu2 structure) are analyzed with approximate molecular orbital calculations. Following the Zintl concept, in BaIn2 the In- ions are isoelectronic with group IV tin and should adopt a four-connected structure. In contrast to α-tin, which has a cubic diamond structure, the indium ions in BaIn2 build up an orthorhombic three-dimensional four-connected net containing distorted tetrahedra and ladder polymers of four-membered rings. In the CeCu2 structure (space group Imma) two bond angles in these distorted tetrahedra are fixed at 90°. The four-connected net in the CeCu2 structure is topologically related to the layers in black phosphorus (space group Cmca). In CaPtSn (TiNiSi structure) the orthorhombic four-connected net is formed by (PtSn)2- ions in an ordered arrangement. Calculations on BaIn2 and CaPtSn show that the four-connected nets are incr...

The Four-Connected Net in the CeCu2 Structure and Its Ternary Derivatives. Its Electronic and Structural Properties

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 demonstrat...

Disentangling Structural Confusion through Machine Learning: Structure Prediction and Polymorphism of Equiatomic Ternary Phases ABC.

Structural and transport properties of some UTX compounds where T = Fe, Co, Ni and X = Si, Ge

Over 100 new equiatomic ternary rare earth (R)-transition metal (T) silicides, germanides and gallides were synthesized and structurally analysed either by evaluating powder diffraction photographs or in the case of ScRhSi, ScPtSi, YNiSi, ScRuGe and PrPtGe by refining single-crystal diffraction data. The hexagonal ZrNiAl type, an Fe2P-type derivative, was found for ScRuSi and ScTGe (T ≡ Ru, Rh, Pd, Os). The orthorhombic TiNiSi type, a PbCl2-type derivative, was assigned to RRhGa (R ≡ Er, Y), RPdGa (R ≡ La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Lu, Y, Sc), RIrGa (R ≡ Er, Y), RPtGa (R ≡ La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu, Y, Sc), YNiSi, RRhSi (R ≡ Er, Y, Sc), ScPdSi, RIrSi (R ≡ Gd, Er, Y, Sc), RPtSi (R ≡ Tb, Dy, Ho, Er, Tm, Lu, Y, Sc), RRhGe (R ≡ Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Y, Sc), RIrGe (R ≡ Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Y, Sc) and RPtGe (R ≡ Sm, Gd, Tb, Dy, Ho, Er, Tm, Y, Sc). The CeCu2 type, which is related to TiNiSi, was found for R(Pd0.5Ge0.5)2 (R ≡ La, Ce, Pr, Nd, Sm, Gd, Tb, Dy, Ho, Er, Tm, Y) and R(Pt0.5Ge0.5)2 (R ≡ Ce, Pr, Nd) where the palladium or platinum and germanium atoms are arranged at random on the copper sites. The tetragonal LaPtSi type, a ThSi2-type derivative, was found for RPtSi (R ≡ La, Ce, Pr, Nd, Sm, Gd), LaIrGe and LaPtGe. Finally the cubic LaIrSi type, an SrSi2-type derivative, was found for LaIrSi. The occurrence and structural features of these five structure types together with the tetragonal PbFCl type, an Fe2As-type derivative found earlier for RFeSi and RCoSi compounds, are discussed.

Equiatomic ternary rare earth-transition metal silicides, germanides and gallides

The structures of the FeB-CrB stacking variants and their homogeneity ranges in the pseudobinary systems R1−xR′xNi (Gd1−xR′xNi (R′ ≡ Tb, Dy, Ho, Er, Tm, Lu, Y) and Sm1−x R′xNi (R1 ≡ Tb, Dy, Ho, Er, Y)) and RT1−x T′x (GdNi1−xPtx, DyPd1−xPtx and DyPd1−xNix) were investigated. The structures of four new monoclinic (space group P21/m) intermediate phases were determined from single-crystal diffractometer data. Gd0.5Er0.5Ni and DyPd0.65Ni0.35 are new examples of h2c base structure stacking (Gd0.7Y0.3 Ni structure type), GdNi0.9Pt0.1 is a new representative of h2c2 base structure stacking (Gd0.55Dy0.45Ni-type structure) and Gd0.7Er0.3Ni is a new example of h2c3 base structure stacking (Gd0.75Y0.25Ni-type structure). The low temperature form of DyPd was established to have an FeB-type structure with α = 6.921(3) A , b = 4.561(2) A and c = 5.532(3) A . The sequence of the different FeB-CrB stacking variants in a given pseudobinary R1−xR'xNi (rR >rTb ⩾ rR') with increasing x is accompanied by a systematic increase in the percentage of hexagonal stacking of their base structures. Since the formation of mixed stacking variants requires rather subtle geometric conditions, their range of existence rapidly decreases when the difference between the radii of the rare earth elements is increased until no intermediate stacking occurs.

K. Klepp

Papers

Equiatomic ternary rare earth-transition metal silicides, germanides and gallides

Phase relationship of ternary rare earth-transition metal alloys with CrB and FeB structures or stacking variants