Structure variations within RSi₂ and R ₂Si₃ silicides. Part II. Structure driving factors

Abstract

To gain an overview of the various structure reports on RSi 2 and R 2 TSi 3 compounds (R is a member of the Sc group, an alkaline earth, lanthanide or actinide metal, T is a transition metal), compositions, lattice parameters a and c, ratios c/a, formula units per unit cell, and structure types are summarized in extensive tables and the variations of these properties when varying the R or T elements are analyzed. Following the structural systematization given in Part I, Part II focuses on revealing the driving factors for certain structure types, in particular, the electronic structure. Here, concepts of different complexity are presented, including molecular orbital theory, the principle of hard and soft acids and bases, and a Bader analysis based on Density Functional Theory calculations for representatives of the reported structure types. The potential Si/T ordering in different structures is discussed. Additionally, the influences from intrinsic and extrinsic properties (e.g. elemental size and electronics as well as lattice parameters and structure type) are investigated on each other using correlation plots. Thermal treatment is identified as an important factor for the ordering of Si/T atoms. Nentwich et al. RSi 2 and R 2 Si 3 silicides. Part II. 379 research papers 380 Nentwich et al. RSi 2 and R 2 Si 3 silicides. Part II. Acta Cryst. (2020). B76, 378-410Figure 2R-T diagram of the RSi 2 and R 2 TSi 3 compounds. (a) normalized lattice parameter a, (b) normalized lattice parameter c, (c) normalized ratio c/a of lattice parameters, (d) shortest Si-T bonds, (e) ratio of atomi radii r T,Si /r R , (f) electronegativity difference EN(Si,R), (g) range of ordering, (h) thermal treatment, (i) density and (j) valence electron concentration. The used markers symbolize the crystal system: hexagon -hexagonal AlB 2 -like systems, open star -orthorhombic, AlB 2 -like systems, diamond -tetragonal ThSi 2 systems, elongated diamond -orthorhombic GdSi 2 systems. The lattice parameters a and c of the subplots (a) and (b) are normalized to the R-R distances within a/b and along c, respectively, to provide comparability.Accordingly, the ratio c/a in subplot (c) is also based on these normalizations. The shortest Si/T bonds in subplot (d) are calculated based on the formula (1). Subplot (e) depicts the ratio of atomic radii q rad , which is based on equation (2). Subplot (f) shows the electronegativity difference for the evaluation of the Zintl conditions. For the range of ordering n in subplot (g), a structure with disordered Si/T sites is marked with a black symbol, otherwise the color stands for the range of ordering n. For the thermal treatment (h), the color represents the temperature and the circle size the time of the treatment (triangle if unknown). Application of the floating zone method is marked with a black dot *, while no treatment is marked with a cross Â. The plots for the theoretical properties vec and ratio of radii were completed for not experimentally determined compounds (small circles) (Riedel & Janiak, 2011...

Entropy-Assisted, Long-Period Stacking of Honeycomb Layers in an AlB2-Type Silicide

“…Figure builds up the long-period stacking sequence of Gd 2 PdSi 3 , starting from the AlB 2 -type with random occupation on the honeycomb layer. This hypothetical Gd­(Pd 1/4 Si 3/4 ) 2 is unfavorable due to effective Coulomb repulsion between Pd–Pd. − Instead, Pd–Si ordering emerges in the honeycomb plane, where Pd atoms occupy positions of maximal mutual distance [Figure (b)]. Given the geometry of the honeycomb lattice with six sites for Pd/Si, four types of layers, A, B, C, and D, are possible [Figure , Figure (e)].…”

“…Alloying experiments are suitable to shed light on the hitherto elusive origin of the 8M stacking sequence in stoichiometric Gd 2 PdSi 3 , which is the longest-period polytype in AlB 2 -derived silicides. , All data are consistent with the notion that the fundamental building blocks of Gd 2 Pd­(Si 1– x Ge x ) 3 , at least up to x = 0.5, are the 1H layers A–D depicted in Figure (e). We compare several ordered stacking sequences, or polytypes built from 1H, based on energetic and entropic considerations.…”

“…We control long-period polytype formation by alloying Gd 2 Pd­(Si 1– x Ge x ) 3 (GPSG) and use high-resolution synchrotron X-ray scattering to determine the stacking sequence. The eight-layer stack of R 2 PdSi 3 , shown in Figure , is the longest-period polytype out of all AlB 2 -derived silicides. − Its thermodynamic origins remain mysterious, especially because Coulomb interactions between distant layers are strongly suppressed by charge screening in metals. Instead, configurational entropy is found to tip the balance between short- and long-period polytypes of Gd 2 PdSi 3 .…”

Griffiths-like behavior and magnetocaloric properties of rare-earth silicide Tb2Co0.8Si3.2

“…This distinction is likely due to the significant influence of the 4f electrons of rare-earth atoms on the stabilization of crystal structures, interatomic distances, and magnetic interactions. In rareearth silicides, this influence, in addition to the ordering of T/Si atoms, annealing, and stoichiometry, leads to the unique magnetic properties of each compound, without any shared trends [18].…”