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Crystal structure of the low pressure modification of BaSn (TlI-type crystal structure) and the high-pressure modification (CsCl type): The phase transition can be described as a shift of columns of trigonal prisms relative to neighboring columns and synchronous dis- placements of atoms (indicated by arrows).
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Effects of high pressure on intermetallic com- pounds are reviewed with regards to structural stability and phase transitions. Changes of bonding properties and electronic structure are examplified by means of the ele- mental metals caesium and titanium, the latter forming an internal intermetallic compound at high pressures. After a short systemat...
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... crystal structure of the low-pressure modification of BaSn is isostructural to TlI (Fig. 6). The atomic pattern can be regarded as an arrangement of trigonal prisms Sn [Ba] 6 and empty tetragonal pyramids [Ba] 5 resulting in a coordination number of 7 for both atom types. At high pressure there is a phase transition into the CsCl-type with CN 8 for both atom types. Formally, the transition can be described as a shifting of ...
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Citations
... Lower row: corresponding coordination environment of SiH 6 2− octahedra by K + ions. 38 and Si in the diamond structure (Fd3̅ m) up to 9.7 GPa and in the β-Sn structure (I4 1 /amd) above. Hydrogen at zero pressure was calculated as a molecule H 2 and at higher pressures as a solid P6 3 /m phase with 16 atoms in the unit cell, following Pickard and Needs. ...
K2SiH6, crystallizing in the cubic K2PtCl6 structure type (Fm3̅m), features unusual hypervalent SiH62- complexes. Here, the formation of K2SiH6 at high pressures is revisited by in situ synchrotron diffraction experiments, considering KSiH3 as a precursor. At the investigated pressures, 8 and 13 GPa, K2SiH6 adopts the trigonal (NH4)2SiF6 structure type (P3̅m1) upon formation. The trigonal polymorph is stable up to 725 °C at 13 GPa. At room temperature, the transition into an ambient pressure recoverable cubic form occurs below 6.7 GPa. Theory suggests the existence of an additional, hexagonal, variant in the pressure interval 3-5 GPa. According to density functional theory band structure calculations, K2SiH6 is a semiconductor with a band gap around 2 eV. Nonbonding H-dominated states are situated below and Si-H anti-bonding states are located above the Fermi level. Enthalpically feasible and dynamically stable metallic variants of K2SiH6 may be obtained when substituting Si partially by Al or P, thus inducing p- and n-type metallicity, respectively. Yet, electron-phonon coupling appears weak, and calculated superconducting transition temperatures are <1 K.
... High pressure (hp) can induce phase transitions and may lead to new compounds with new structures, especially for elements with valence fluctuations, such as Ce. A useful compilation of the binary high pressure compounds can be found in Ref. [16]. High pressure synthesis of CeGe 3 [17] was reported under a pressure of 5 GPa at 1600°C. ...
Sub-oxides with the anti-perovskite structure constitute a large part of the interstitial stabilized compounds with novel chemical and physical properties, especially in the systems containing rare earth elements and/or early transition metal elements. A new sub-oxide compound, (Ce$_{0.85}$Ti$_{0.15}$)Ge$_3$O$_{0.5}$, is synthesized by flux growth. The compound crystallizes in a cubic structure which can be considered as an ordered vacancy variant of anti-perovskite-structure or an ordered interstitial variant of the Cu$_3$Au type, with a space group of Fm-3m (225). The structure is refined from X-ray single crystal methods. The compound may be considered as a compound stabilized by chemical pressure generated by the substitution and the interstitials atoms. The stability of the compounds in RTr$_3$ systems (R = rare earth elements except Pm and Sc, Tr = tetrel elements such as Si, Ge, Sn, Pb) seem to be highly correlated to the ratio of the rare earth elements' radii to the main group elements' atomic radii. The magnetic property of the compound confirms the 4$^+$ valence of the Ce atoms. The resistivity measurement of the compound shows that it is metallic.
... Some quite peculiar systems exhibiting Laves phases or Laves-phase-like structure elements such as van der Waals compounds, irradiated metals, polymer particles and pressurized van der Waals compounds were already mentioned in Sect. 2. In a couple of more 'ordinary' binary metallic systems, which do not contain Laves phases at ambient pressure, they may form at high pressure as summarized in a review [70]. Notable examples of such Laves phases, which are only stable at elevated pressures, pressure as a stable phase instead of the Laves phase. ...
Laves phases with their comparably simple crystal structure are very common intermetallic phases and can be formed from element combinations all over the periodic table resulting in a huge number of known examples. Even though this type of phases is known for almost 100 years, and although a lot of information on stability, structure, and properties has accumulated especially during the last about 20 years, systematic evaluation and rationalization of this information in particular as a function of the involved elements is often lacking. It is one of the two main goals of this review to summarize the knowledge for some selected respective topics with a certain focus on non-stoichiometric, i.e., non-ideal Laves phases. The second, central goal of the review is to give a systematic overview about the role of Laves phases in all kinds of materials for functional and structural applications. There is a surprisingly broad range of successful utilization of Laves phases in functional applications comprising Laves phases as hydrogen storage material (Hydraloy), as magneto-mechanical sensors and actuators (Terfenol), or for wear- and corrosion-resistant coatings in corrosive atmospheres and at high temperatures (Tribaloy), to name but a few. Regarding structural applications, there is a renewed interest in using Laves phases for creep-strengthening of high-temperature steels and new respective alloy design concepts were developed and successfully tested. Apart from steels, Laves phases also occur in various other kinds of structural materials sometimes effectively improving properties, but often also acting in a detrimental way.
... [13] Thereby, high pressure-high temperature (HP-HT) preparation was found to be a very efficient tool for the preparation of new modifications of the members of this family and new intermetallic phases in general. [14,15] Among the monogermanides, the representatives of the heavy rare-earth metals are less studied. This was the reason to apply the HP-HT technique for the preparation of LuGe, which is not known in the published phase diagram. ...
The monogermanide LuGe is obtained via high‐pressure high‐temperature synthesis (5–15 GPa, 1023–1423 K). The crystal structure is solved from single‐crystal X‐ray diffraction data (structure type FeB, space group Pnma, a=7.660(2) Å, b=3.875(1) Å, and c=5.715(2) Å, RF=0.036 for 206 symmetry independent reflections). The analysis of chemical bonding applying quantum‐chemical techniques in position space was performed. It revealed—beside the expected 2c‐Ge‐Ge bonds in the germanium polyanion—rather unexpected four‐atomic bonds between lutetium atoms indicating the formation of a polycation by the excess electrons in the system Lu³⁺(2b)Ge²⁻×1 e⁻. Despite the reduced VEC of 3.5, lutetium monogermanide is following the extended 8‐N rule with the trend to form lutetium‐lutetium bonds utilizing the electrons left after satisfying the bonding needs in the anionic Ge‐Ge zigzag chain.
... [13] Die Hochdruck-Hochtemperatur-Synthese (HP-HT) erwies sich dabei als ein sehr effizientes Werkzeug für die Präparation neuer Vertreter dieser Familie und neuer intermetallischer Phasen im Allgemeinen. [14,15] Die Vertreter der schweren Seltenerdmetalle waren im Falle der Monogermanide weniger untersucht. Dies war der Grund, die HP-HT-Technik zur Herstellung der Verbindung LuGe anzuwenden, die im verçffentlichten Phasendiagramm nicht bekannt war. ...
Das Germaniummonogermanid wird durch Hochdruck‐ und Hochtemperatur‐Synthese dargestellt. Die chemische Bindung in LuGe wird als kovalent gebundene Zickzackketten von Ge‐Atomen und Lu4‐Polykationen beschrieben, die mit Hilfe „überschüssiger“ Elektronen im Sinne der Zintl‐Bilanz Lu³⁺(2b)Ge²⁻ × 1 e⁻ gebildet werden. Die homonukleare Bindung in dem Polykation in LuGe ähnelt der Bindungssituation in Ga2Se2.
Abstract
Das Monogermanid LuGe wurde durch Hochdruck‐Hochtemperatursynthese (5–15 GPa, 1023–1423 K) erhalten. Die Kristallstruktur wurde aus Einkristall‐Röntgenbeugungsdaten gelöst und verfeinert (Strukturtyp FeB, Raumgruppe Pnma, a=7.660 (2) Å, b=3.875 (1) Å und c=5.715 (2) Å, RF=0.036 für 206 symmetrie‐unabhängige Reflexe). Die Analyse der chemischen Bindung wurde mit Hilfe quantenchemischer Techniken im Ortsraum durchgeführt. Neben den erwarteten 2c‐Ge‐Ge‐Bindungen im Germaniumpolyanion wurde eine eher unerwartete vieratomige Wechselwirkung zwischen Lutetium‐Atomen gefunden, was auf die Bildung eines Polykations durch die überschüssigen Elektronen im System Lu³⁺(2b)Ge²⁻×1 e⁻ hinweist. Trotz der reduzierten Valenzelektronen‐Konzentration von 3.5 folgt Lutetium‐Monogermanid der erweiterten 8‐N‐Regel durch die Bildung von Lutetium‐Lutetium‐Bindungen unter Verwendung der Elektronen, die nach der Bindungssättigung in der anionischen Ge‐Ge‐Zickzackkette übrigbleiben.
... S8). In previous studies of Zintl phases, bidimensional polymorphic transitions between 3D and 2D structures have been only observed under high pressure (29,30). The present bidimensional polymorphism between 3D-ZnSb and 2D-ZnSb thus emphasizes the potential and broad availability of such an electron transfer that manipulates a hybridized bonding state, transforming the crystal structure even in a bulk scale. ...
The discovery of new families, beyond graphene, of two-dimensional (2D) layered materials has always attracted great attention. However, it has been challenging to artificially develop layered materials with honeycomb atomic lattice structure composed of multicomponents such as hexagonal boron nitride. Here, through the dimensional manipulation of a crystal structure from sp ³ -hybridized 3D-ZnSb, we create an unprecedented layered structure of Zintl phase, which is constructed by the staking of sp ² -hybridized honeycomb ZnSb layers. Using structural analysis combined with theoretical calculation, it is found that the 2D-ZnSb has a stable and robust layered structure. The bidimensional polymorphism is a previously unobserved phenomenon at ambient pressure in Zintl families and can be a common feature of transition metal pnictides. This dimensional manipulation of a crystal structure thus provides a rational design strategy to search for new 2D layered materials in various compounds, enabling unlimited expansion of 2D libraries and corresponding physical properties.
... For example, the densest packings of hard-sphere mixtures are intimately related to high-pressure phases of compounds for a range of temperatures. 66,67 Another natural extension of the hard-sphere model that will be surveyed is hard nonspherical particles in two and three dimensions. Asphericity in particle shape is capable of capturing the salient features of phases of molecular systems with anisotropic pair interactions (e.g., liquid crystals) and is also a more realistic characteristic of real granular media. ...
... The densest packings of spheres with a size distribution are of great interest in crystallography, chemistry, and materials science. It is notable that the densest packings of hard-sphere mixtures are intimately related to high-pressure phases of molecular systems, including intermetallic compounds 66 and solid rare-gas compounds 67 for a range of temperatures. ...
... These structures may correspond to currently unidentified stable phases of certain binary atomic and molecular systems, particularly at high temperatures and pressures. 66,67 Reference 155 provides details about the structural characteristics of these densest-known binary sphere packings. ...
Packing problems have been a source of fascination for millennia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure and bulk properties of condensed phases of matter, including low-temperature states (e.g., molecular and colloidal liquids, crystals, and glasses), multiphase heterogeneous media, granular media, and biological systems. The densest packings are of great interest in pure mathematics, including discrete geometry and number theory. This perspective reviews pertinent theoretical and computational literature concerning the equilibrium, metastable, and nonequilibrium packings of hard-particle packings in various Euclidean space dimensions. In the case of jammed packings, emphasis will be placed on the “geometric-structure” approach, which provides a powerful and unified means to quantitatively characterize individual packings via jamming categories and “order” maps. It incorporates extremal jammed states, including the densest packings, maximally random jammed states, and lowest-density jammed structures. Packings of identical spheres, spheres with a size distribution, and nonspherical particles are also surveyed. We close this review by identifying challenges and open questions for future research.
... For example, the densest packings of hard-sphere mixtures are intimately related to high-pressure phases of compounds for a range of temperatures. 59,60 Another natural extension of the hard-sphere model that will be surveyed are hard nonspherical particles in two and three dimensions. Asphericity in particle shape is capable of capturing salient features of phases of molecular systems with anisotropic pair interactions (e.g., liquid crystals) and is also a more realistic characteristic of real granular media. ...
... The densest packings of spheres with a size distribution is of great interest in crystallography, chemistry and materials science. It is notable that the densest packings of hard-sphere mixtures are intimately related to high-pressure phases of molecular systems, including intermetallic compounds 59 and solid rare-gas compounds 60 for a range of temperatures. ...
... These structures may correspond to currently unidentified stable phases of certain binary atomic and molecular systems, particularly at high temperatures and pressures. 59,60 Reference 148 provides details about the structural characteristics of these densest-known binary sphere packings. ...
Packing problems have been a source of fascination for millenia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure and bulk properties of condensed phases of matter, including low-temperature states (e.g., molecular and colloidal liquids, crystals and glasses), multiphase heterogeneous media, granular media, and biological systems. The densest packings are of great interest in pure mathematics, including discrete geometry and number theory. This perspective reviews pertinent theoretical and computational literature concerning the equilibrium, metastable and nonequilibrium packings of hard-particle packings in various Euclidean space dimensions. In the case of jammed packings, emphasis will be placed on the "geometric-structure" approach, which provides a powerful and unified means to quantitatively characterize individual packings via jamming categories and "order" maps. It incorporates extremal jammed states, including the densest packings, maximally random jammed states, and lowest-density jammed structures. Packings of identical spheres, spheres with a size distribution, and nonspherical particles are also surveyed. We close this review by identifying challenges and open questions for future research.
... Sphere packings with a polydispersity in size have a richer phase diagram than their monodisperse counterparts and enable a greater control of their structural characteristics, such as density and degree of order. Polydisperse sphere packings have served as structural models for a variety of solid states matter including high temperature and pressure phases of various binary intermetallic and rare-gas compounds [29,30], alloys [31], solid propellants [32], concrete [33], and ceramics [34]. It has been recently suggested that the packing fraction at which the viscosity of hard-sphere suspensions diverges is closely related to the MRJ density [35]. ...
Disordered jammed packings under confinement have received considerably less
attention than their \textit{bulk} counterparts and yet arise in a variety of
practical situations. In this work, we study binary sphere packings that are
confined between two parallel hard planes, and generalize the Torquato-Jiao
(TJ) sequential linear programming algorithm [Phys. Rev. E {\bf 82}, 061302
(2010)] to obtain putative maximally random jammed (MRJ) packings that are
exactly isostatic with high fidelity over a large range of plane separation
distances $H$, small to large sphere radius ratio $\alpha$ and small sphere
relative concentration $x$. We find that packing characteristics can be
substantially different from their bulk analogs, which is due to what we term
"confinement frustration". Rattlers in confined packings are generally more
prevalent than those in their bulk counterparts. We observe that packing
fraction, rattler fraction and degree of disorder of MRJ packings generally
increase with $H$, though exceptions exist. Discontinuities in the packing
characteristics as $H$ varies in the vicinity of certain values of $H$ are due
to associated discontinuous transitions between different jammed states. We
also apply the local volume-fraction variance $\sigma_{\tau}^2(R)$ to
characterize confined packings and find that these packings possess essentially
the same level of hyperuniformity as their bulk counterparts. Our findings are
generally relevant to confined packings that arise in biology (e.g., structural
color in birds and insects) and may have implications for the creation of
high-density powders and improved battery designs.
... Rare-earth intermetallic compounds exhibit diversified structural behavior upon the application of hydrostatic pressure [1,2]. For instance, rare-earth digallides undergo structural phase transitions from ambient AlB 2 type structure to orthorhombic (LaGa 2 ), AlB 2 to AlB 2 with reduced c/a ratio (CeGa 2 , HoGa 2 and GdGa 2 ) [3][4][5][6]. ...
