Quantitative Advances in the Zintl–Klemm Formalism

Fragment Orbitals Extracted from First-Principles Plane-Wave Calculations

Decomposing extended structures into smaller, molecular, even functional groups or simple fragments has a long tradition in chemistry because it allows for understanding certain electronic peculiarities in truly chemical terms. By doing so, invaluable property information is chemically accessible, for example, needed to rationalize catalytic or magnetic or optical nature. In order to also follow that train of thought for periodic materials, we have developed a tool which in a straightforward manner derives fragment molecular orbitals from plane-wave electronic-structure data of whatever kind of solid-state material. We here report on the mathematical apparatus of the method dubbed linear combination of fragment orbitals (LCFO) used for that purpose, implemented within the LOBSTER code. The method is illustrated from various sorts of molecular entities contained in such crystalline materials, together with an assessment of both accuracy and robustness of the new tool.

Twists and Puckers: Tuning Crystal Chemistry in the La(AuxGe1-x)2 Compositional Series

The physical properties of solid-state materials are closely tied to their crystal structure, yet our understanding of how competing structural arrangements energetically compare is limited. In this work, we explore how small differences in composition affect the structure in the La(AuxGe1-x)2 series of compounds, which comprises four unique structure types between LaGe2 and LaAu2. This family includes the previously unknown AlB2-type compound with stoichiometry La(Au0.375Ge0.625)2 as well as La(Au0.25Ge0.75)2, an intergrowth of the AlB2 and ThSi2 structure types. We then study the chemical forces driving the structure changes and use phonon band structure calculations and DFT-Chemical Pressure to evaluate atomic-size effects. These calculations show that the parent AlB2 structure type is disfavored in Au-rich compounds due to soft atomic motions along the c axis. The instability of AlB2-type LaAuGe is confirmed by the presence of imaginary modes in the phonon band structure that correspond to a "puckering" of the hexagonal AlB2-type lattice, resulting in the experimentally observed LiGaGe structure type. The impact of size effects is less clear for Au-poor compositions; instead, twisting the AlB2 structure type to form the ThSi2 type opens a pseudogap at the Fermi level in the electronic density of states. This investigation demonstrates how crystal structure in solid-state materials can be compositionally tuned based on balancing size and electronics when multiple structure types are in close thermodynamic competition.

Zintl Phases: From Curiosities to Impactful Materials

The synthesis of new compounds and crystal structures remains an important research endeavor in pursuing technologically relevant materials. The Zintl concept is a guidepost for the design of new functional solid-state compounds. Zintl phases are named in recognition of Eduard Zintl, a German chemist who first studied a subgroup of intermetallics prepared with electropositive metals combined with main-group metalloids from groups 13-15 in the 1930s. Unlike intermetallic compounds, where metallic bonding is the norm, Zintl phases exhibit a combination of ionic and covalent bonding and are typically semiconductors. Zintl phases provide a palette for iso- and aliovalent substitutions that can each contribute uniquely to the properties. Zintl electron-counting rules can be employed to interrogate a structure type and develop a foundation of structure-property relationships. Employing substitutional chemistry allows for the rational design of new Zintl compounds with technological properties, such as magnetoelectronics, thermoelectricity, and other energy storage and conversion capabilities. Discovering new structure types and compositions through this approach is also possible. The background on the strength and innovation of the Zintl concept and a few highlights of Zintl phases with promising thermoelectric properties in the context of structural and electronic design will be provided.

Exploring the Interdependence between Electronically Unfavorable Situations and Pressure in a Chalcogenide Superconductor

The development of solids with the requested chemical and physical properties requires a thorough understanding of their electronic structures, as proper knowledge of the electronic structure of a given solid provides invaluable information regarding its properties. In this context, recent research on two competing sorts of electronic instabilities in chalcogenide superconductors stimulated us to explore the interdependence between these instabilities and another aspect, pressure, which was previously shown to influence the presence of a superconducting state in diverse solids. To accomplish our goal, we carried out pressure-dependent examinations of the electronic structures of two tellurides, YTe and YTe0.97, which were inspected as prototypes in our explorations based on quantum-chemical means. In addition to our pressure-dependent explorations of the electronic structures, we also performed chemical bonding analyses to reveal the subtle interplay between pressure and two sorts of electronically unfavorable situations.

Flux Growth, Crystal Structure, and Chemical Bonding of Yb2PdGe3, an AlB2 Superstructure within the Rare-Earth Series

The complete structure revision of the RE₂PdGe₃ (RE = rare-earth metal) series revealed that Yb₂PdGe₃ is the only AlB₂ ordered superstructure. Good-quality single crystals of this compound were successfully grown from molten indium flux, enabling accurate single-crystal investigations. Yb₂PdGe₃ crystallizes with the Ce₂CoSi₃-type structure in the hexagonal space group P6/mmm (no. 191) with lattice parameters a = 8.468(1) Å and c = 4.0747(7) Å. This structure is a four-order derivative of AlB₂, composed of planar _∞²[PdGe₃] honeycomb layers spaced by Yb species, located at the center of Ge₆ and Ge₄Pd₂ hexagons. A superconducting transition is observed below the critical temperature of 4 K. A divalent state of Yb is deduced from magnetic susceptibility measurements below room temperature, which indicate an almost nonmagnetic behavior. A charge transfer from Yb to Pd and Ge was evidenced by the Quantum Theory of Atoms in Molecules (QTAIM) effective charges; polar four-atomic Ge-Pd/Yb and two-atomic Pd-Yb bonds were observed from the ELI-D (electron localizability indicator), partial ELI-D, and ELI-D/QTAIM intersections. The bonding interactions between Ge atoms within regular Ge₆ hexagons are found to be intermediate between single bonds, as in elemental Ge, and higher-order bonds in the hypothetic Ge₆H₆ and Ge₆^6- aromatic molecules.

Exploring the subtle factors that control the structural preferences in Cu7Te4

In the quest for materials suited as components in future technologies, the copper-rich regions of the binary Cu-Te system have been of great interest. In this context, several explorative efforts were also focused on Cu₇Te₄which was reported to crystallize with different types of structure. To explore the structural preferences for two Cu₇Te₄structure models, both experimental as well as quantum-chemical means were employed. The crystal structures of both Cu₇Te₄types are composed of hexagonal closest packed layers of tellurium atoms, and differ in the respective distributions of the copper atoms between these layers. The analysis of the electronic structures was accomplished based on the densities-of-states, Mulliken charges, projected crystal orbital Hamilton populations, and electron localization functions of both structure models, and its outcome indicates that the factors that control the formation of a respective type of structure are rather subtle.

Examination of a Structural Preference in Quaternary Alkali-Metal (A) Rare-Earth (R) Copper Tellurides by Combining Experimental and Quantum-chemical Means

In the quest for materials addressing the grand challenges of the future, there is a critical need for a broad understanding of their electronic structures because the knowledge of the electronic structure of a given solid allows us to recognize its structural preferences and to rationalize its properties. As previous research on quaternary chalcogenides containing active metals (a group-I- or -II-element), early transition-metals, and late transition-metals indicated that such materials could pose as alluring systems in the developments of thermoelectrics, our impetus was stimulated to probe the suitability of tellurides belonging to the prolific A₃R₄Cu₅Te₁₀-family. In doing so, we first used quantum-chemical techniques to explore the electronic and vibrational properties of representatives crystallizing with different A₃R₄Cu₅Te₁₀ structure types. The outcome of these explorations indicated that the aspects that control the formation of a given type of A₃R₄Cu₅Te₁₀ structure are rather subtle so that transitions between different types of A₃R₄Cu₅Te₁₀ structures could be induced by manipulating the ambient conditions. To probe this prediction, we explored the thermal behavior for the example of one quaternary telluride, that is, Rb₃Er₄Cu₅Te₁₀, and thereby identified a new type of A₃R₄Cu₅Te₁₀ structure. Because understanding the structural features of the A₃R₄Cu₅Te₁₀ family plays an important role in the analyses of the aforementioned explorations, we also present an overview about the structural features and the members of this class of quaternary tellurides. In this connection, we also provide a structural report of four tellurides, that is, K₃Tb₄Cu₅Te₁₀ and Rb₃R₄Cu₅Te₁₀ (R = Tb, Dy, Ho), which have been obtained from high-temperature solid-state reactions for the very first time.

From simple to complex crystal chemistry in the RE-Au-Tt systems (RE = La, Ce, Pr, Nd; Tt = Ge, Pb)

Polar intermetallics are an intriguing class of compounds with complex relationships between composition and structure that are not fully understood. This work reports a systematic study of the underexplored ternary composition space RE-Au-Tt (RE = La, Ce, Pr, Nd; Tt = Ge, Pb) to expand our knowledge of the intriguing chemistry and diversity achievable with these metallic constituents. These composition spaces are particularly interesting because of the potential to find Au-bearing, highly polar intermetallic compounds. The elements were first reacted through arc welding under an inert atmosphere, followed by annealing at 850 °C. X-ray diffraction of the products identified seven unreported compounds ranging from the simple NaTl-type compounds La_1.5Au₂Pb_0.5 and Nd_2-x Au₂Pb _x to the more structurally complex La₅AuPb₃ in the Hf₅CuSn₃-type structure and Pu₃Pd₄-type RE₃Au₃Ge (RE = La, Ce, Pr, Nd). First-principles electronic structure calculations investigate the combination of Fermi surface-Brillouin zone interactions, electrostatic interactions, and delocalized metallic bonding that contributes to the formation of these phases. These calculations show that a mixture of electrostatic and metallic bonding plays a dominant role in these phases. The RE-Au-Tt composition space remains full of potential for discovering materials with relevant magnetic and quantum properties, provided the crystal chemistry can be comprehended.

From Three-Dimensional Clathrates to Two-Dimensional Zintl Phases AMSb2 (A = Rb, Cs; M = Ga, In) Composed of Pentagonal M-Sb Rings

Three new antimonide Zintl phases, RbGaSb₂, CsGaSb₂, and CsInSb₂, were discovered during exploration of corresponding A-M-Sb (A = Rb, Cs; M = Ga, In) ternary systems while searching for new clathrates. The AGaSb₂ phases crystallize in the tetragonal space group P4₂/nmc (No. 137) in the LiBS₂ structure type, while CsInSb₂ crystallizes in lower symmetry in the orthorhombic space group Cmce (No. 64) in the KGaSb₂ structure type with additional disorder of one of the Cs sites. The crystal structures of all three reported AMSb₂ compounds are composed of two-dimensional [MSb₂]^- tetrahedral layers separated by Rb⁺ or Cs⁺ cations. [MSb₂]^- layers are built from fused M-Sb pentagons and hexagons, which are also the main structural units for A₈M₂₇Sb₁₉ clathrate cages. The semiconductor nature of AMSb₂ was suggested by band structure calculations and confirmed by transport property characterization. CsGaSb₂ is a rare example of an n-type pnictide Zintl phase. All reported compounds exhibit low thermal conductivity typical for complex antimonides of heavy elements.

Exploring the frontier between polar intermetallics and Zintl phases for the examples of the prolific ALnTnTe3-type alkali metal (A) lanthanide (Ln) late transition metal (Tn) tellurides

Understanding electronic structures is important in order to interpret and to design the chemical and physical properties of solid-state materials. Among those materials, tellurides have attracted an enormous interest, because several representatives of this family are at the cutting edge of basic research and technologies. Despite this relevance of tellurides with regard to the design of materials, the interpretations of their electronic structures have remained challenging to date. For instance, most recent research on tellurides, which primarily comprise post-transition elements, revealed a remarkable electronic state, while the distribution of the valence electrons in tellurides comprising group-I/II elements could be related to the structural features by applying the Zintl-Klemm-Busmann concept. In the cases of tellurides containing transition metals the applications of the aforementioned idea should be handled with care, as such tellurides typically show characteristics of polar intermetallics rather than Zintl phases. And yet, how may the electronic structure look like for a telluride that consists of a transition metal behaving like a p metal? To answer this question, we examined the electronic structure for the quaternary RbTbCdTe3 and provide a brief report on the crystal structures of the isostructural compounds RbErZnTe3 and RbTbCdTe3, whose crystal structures have been determined by means of X-ray diffraction experiments for the very first time.

p-Type Double Doping and the Diamond-like Morphology Shift of the Zintl Phase Thermoelectric Materials: The Ca11-xAxSb10-yGez (A = Na, Li; 0.06(3) ≤ x ≤ 0.17(5), 0.19(1) ≤ y ≤ 0.55(1), 0.13(1) ≤ z ≤ 0.22(1)) System

Five ternary and quaternary Zintl phases in the solid-solution Ca_11-xA_xSb_10-yGe_z (A = Na, Li; 0.06(3) ≤ x ≤ 0.17(5), 0.19(1) ≤ y ≤ 0.55(1), 0.13(1) ≤ z ≤ 0.22(1)) system have been successfully synthesized by both of the arc-melting and the molten Pb metal-flux reactions. The crystal structure of these title compounds was characterized by powder and single-crystal X-ray diffractions analyses, and all title compounds crystallized in the Ho₁₁Ge₁₀-type phase in the tetragonal space group I4/mmm (Z = 4, Pearson code tI84). The complex crystal structure can be described as an assembly of 1) three kinds of cationic polyhedra centered by three different Sb and 2) the cage-shaped anionic frameworks built through the connection of two types of Sb. The newly substituted p-type double dopants of the cationic (Na and Li) and anionic (Ge) elements displayed particular site preferences, which were successfully explained by either the size-factor criterion based on the atomic size or the electronic-factor criterion based on the electronegativity of an element. Quite interestingly, as the reaction conditions were changed, the morphology shift of single crystals in Ca_10.94(3)Na_0.06Sb_9.58(1)Ge_0.21 occurred from a cubic-shaped to a hummocky-type, to a hopper-type, and eventually to an octahedral-shaped crystal, just like the Yakutian kimberlite diamonds. Moreover, we firmly believe that the inclusion of the p-type Ge dopant for Sb was crucial to trigger this type of morphology shift and complete the octahedral-shaped morphology in the overall crystal-growth mechanism. The theoretical calculations using a DFT method rationalized the observed site preference of Na and the electronic effect of the p-type Ge dopants. The Seebeck coefficient measurements for Ca_10.88(4)Li_0.12Sb_9.45(1)Ge_0.21 indicated that some portions of electron charge carriers were effectively eliminated by the p-type double dopants using Li and Ge.

Bonding diversity in rock salt-type tellurides: examining the interdependence between chemical bonding and materials properties

Future technologies are in need of solid-state materials showing the desired chemical and physical properties, and designing such materials requires a proper understanding of their electronic structures. In this context, recent research on chalcogenides, which were classified as ‘incipient metals’ and included phase-change data storage materials as well as thermoelectrics, revealed a remarkable electronic behavior and possible state (dubbed ‘metavalency’) proposed for the frontier between entire electron localization and delocalization. Because the members of the family of the polar intermetallics vary widely in their properties as well as electronic structures, one may wonder if the aforementioned electronic characteristics are also achieved for certain polar intermetallics. To answer this question, we have employed quantum-chemical tools to examine the electronic structures of the rock salt-type YTe and SnTe belonging to the families of the polar intermetallics and incipient metals, respectively. To justify these classifications and argue as to why an application of the Zintl–Klemm concept (frequently employed to relate the structural features of tellurides to their electronic structures) could be misleading for YTe and SnTe, the electronic structures of YTe and SnTe were first compared to that of the rock salt-type SrTe. In addition, we carried out a Gedankenexperiment by subsequently modifying the chemical composition from YTe to SnTe, and, by doing so, we shed new light on the interdependence between chemical bonding and materials properties. Gradual changes in the former do not necessarily translate into the latter which may undergo discontinuous modifications.

Future technologies are in need of solid-state materials showing the desired chemical and physical properties, and designing such materials requires a proper understanding of their electronic structures.

Revealing the Bonding Nature in an ALnZnTe3-Type Alkaline-Metal (A) Lanthanide (Ln) Zinc Telluride by Means of Experimental and Quantum-Chemical Techniques

Tellurides have attracted an enormous interest in the quest for materials addressing future challenges, because many of them are at the cutting edge of basic research and technologies due to their remarkable chemical and physical properties. The key to the tailored design of tellurides and their properties is a thorough understanding of their electronic structures including the bonding nature. While a unique type of bonding has been recently identified for post-transition-metal tellurides, the electronic structures of tellurides containing early and late-transition-metals have been typically understood by applying the Zintl−Klemm concept; yet, does the aforementioned formalism actually help us in understanding the electronic structures and bonding nature in such tellurides? To answer this question, we prototypically examined the electronic structure for an alkaline metal lanthanide zinc telluride, i.e., RbDyZnTe3, by means of first-principles-based techniques. In this context, the crystal structures of RbLnZnTe3 (Ln = Gd, Tb, Dy), which were obtained from high-temperature solid-state syntheses, were also determined for the first time by employing X-ray diffraction techniques.

Probing the Validity of the Zintl-Klemm Concept for Alkaline-Metal Copper Tellurides by Means of Quantum-Chemical Techniques

Understanding the nature of bonding in solid-state materials is of great interest for their designs, because the bonding nature influences the structural preferences and chemical as well as physical properties of solids. In the cases of tellurides, the distributions of valence-electrons are typically described by applying the Zintl-Klemm concept. Yet, do these Zintl-Klemm treatments provide adequate pictures that help us understanding the bonding nature in tellurides? To answer this question, we followed up with quantum-chemical examinations on the electronic structures and the bonding nature of three alkaline-metal copper tellurides, i.e., NaCu3Te2, K2Cu2Te5, and K2Cu5Te5. In doing so, we accordingly probed the validity of the Zintl-Klemm concept for these ternary tellurides, based on analyses of the respective projected crystal orbital Hamilton populations (-pCOHP) and Mulliken as well as Löwdin charges. Since all of the inspected tellurides are expected to comprise Cu-Cu interactions, we also paid particular attention to the possible presence of closed-shell interactions.

Revealing the Nature of Chemical Bonding in an ALn2Ag3Te5-Type Alkaline-Metal (A) Lanthanide (Ln) Silver Telluride

Although the electronic structures of several tellurides have been recognized by applying the Zintl-Klemm concept, there are also tellurides whose electronic structures cannot be understood by applications of the aforementioned idea. To probe the appropriateness of the valence-electron transfers as implied by Zintl-Klemm treatments of ALn2Ag3Te5-type tellurides (A = alkaline-metal; Ln = lanthanide), the electronic structure and, furthermore, the bonding situation was prototypically explored for RbPr2Ag3Te5. The crystal structure of that type of telluride is discussed for the examples of RbLn2Ag3Te5 (Ln = Pr, Nd), and it is composed of tunnels which are assembled by the tellurium atoms and enclose the rubidium, lanthanide, and silver atoms, respectively. Even though a Zintl-Klemm treatment of RbPr2Ag3Te5 results in an (electron-precise) valence-electron distribution of (Rb+)(Pr3+)2(Ag+)3(Te2−)5, the bonding analysis based on quantum-chemical means indicates that a full electron transfer as suggested by the Zintl-Klemm approach should be considered with concern.

Synthesis and Characterization of K and Eu Binary Phosphides

The synthesis, structural characterization, and optical properties of the binary Zintl phases of α-EuP₃, β-EuP₃, EuP₂, and α-K₄P₆ are reported in this study. These crystal structures demonstrate the versatility of P fragments with dimensionality varying from 0D (P₆ rings in α-K₄P₆) to 1D chains (EuP₂) to 2D layers (both EuP₃). EuP₂ is isostructural to previously reported SrP₂ and BaP₂ compounds. The thermal stabilities of the EuP₂ and both EuP₃ phases were determined using differential scanning calorimetry (DSC), with melting temperatures of 1086 K for the diphosphide and 1143 K for the triphosphides. Diffuse reflectance spectroscopy indicated that EuP₂ is an indirect semiconductor with a direct bandgap of 1.12(5) eV and a smaller indirect one, less than 1 eV. Both EuP₃ compounds had bandgaps smaller than 1 eV.

Development of a robust tool to extract Mulliken and Löwdin charges from plane waves and its application to solid-state materials

Chemically understanding the electronic structure of a given material provides valuable information about its chemical as well as physical nature and, hence, is the key to designing materials with desired properties. For example, to rationalize the structures of solid-state materials in terms of the valence-electron distribution, highly schematic, essentially non-quantum-mechanical electron-partitioning models such as the Zintl–Klemm concept have been introduced by assuming idealized ionic charges. To go beyond the limits of the aforementioned concept, a Mulliken and Löwdin population analytical tool has been developed to accurately calculate the charges in solid-state materials solely from first-principles plane-wave-based computations. This population analysis tool, which has been implemented into the LOBSTER code, has been applied to diverse solid-state materials including polar intermetallics to prove its capability, including quick access to Madelung energies. In addition, a former weakness of the population analysis (namely, the basis-set dependency) no longer exists for the present approach which therefore represents a comparatively fast and accurate wave-function-based alternative for plane-wave calculations for which density-based charge approaches (e.g., Bader like) have been very popular.

A robust tool to extract Mulliken and Löwdin charges for (extended) solids from plane waves has been developed and applied.

Polyanionic Gold-Tin Bonding and Crystal Structure Preference in REAu1.5Sn0.5 (RE = La, Ce, Pr, Nd)

During a systematic search of the RE-Au-Sn (RE = La, Ce, Pr, Nd) ternary phase space, a series of compounds with the general formula REAu_1.5Sn_0.5 have been identified. These phases can be synthesized by arc melting the elemental metals, followed by annealing. The crystal structures were solved using single-crystal X-ray diffraction, with the composition confirmed by energy-dispersive X-ray spectroscopy. All four compounds crystallize in orthorhombic space group Imma with the CeCu₂-type structure. Most notable in these compounds is the polyanionic backbone composed of a single statistically mixed Au/Sn position, which creates a puckered hexagonal bonding network separated by the rare-earth atoms. Electronic structure calculations indicate that the Au 5d bands are dominant in the density of states, while the crystal orbital Hamilton population (-COHP) curves demonstrate Au-Au and Au-Sn interactions, which stabilize the crystal structure. Likewise, a qualitative electron localization function analysis supports the existence of a polyanionic network, and a Bader charge analysis implies anionic character on Au and Sn. The preference for these compounds to adopt the simple CeCu₂-type structure is also determined using density functional theory calculations and compared to related compounds to establish a better picture of the unusual behavior of Au in polar intermetallic compounds.

The Crystal Orbital Hamilton Population (COHP) Method as a Tool to Visualize and Analyze Chemical Bonding in Intermetallic Compounds

Recognizing the bonding situations in chemical compounds is of fundamental interest for materials design because this very knowledge allows us to understand the sheer existence of a material and the structural arrangement of its constituting atoms. Since its definition 25 years ago, the Crystal Orbital Hamilton Population (COHP) method has been established as an efficient and reliable tool to extract the chemical-bonding information based on electronic-structure calculations of various quantum-chemical types. In this review, we present a brief introduction into the theoretical background of the COHP method and illustrate the latter by diverse applications, in particular by looking at representatives of the class of (polar) intermetallic compounds, usually considered as “black sheep” in the light of valence-electron counting schemes.

AAuAl (A = Ca, Sc, and Ti): Peierls Distortion, Atomic Coloring, and Structural Competition

Using density functional theory, the crystal structure variation of AAuAl (A = Ca, Sc, and Ti) from orthorhombic Co₂Si-type to distorted hexagonal Fe₂P-type and then Ni₂In-type structures is shown to correlate with their electronic structures and valence electron counts, sizes of the active metals A, and site preferences for Au and Al atoms, which are arranged to maximize Au-Al nearest neighbor contacts. An evaluation of chemical pressure imposed by the varying A metals using total energy vs volume calculations indicates that larger unit cell volumes favor the orthorhombic structure, whereas smaller volumes favor the hexagonal structures. The electronic origin of the Mg₂Ga-type crystal structure of ScAuAl, refined as a distorted Fe₂P-type supercell doubled along the c-axis, indicates a Peierls-type distortion mechanism of the Au chains along the c-axis.

Ba and Sr Binary Phosphides: Synthesis, Crystal Structures, and Bonding Analysis

Synthesis, crystal structures, and chemical bonding are reported for four binary phosphides with different degrees of phosphorus oligomerization, ranging from isolated P atoms to infinite phosphorus chains. Ba3P2 = Ba4P(2.67)□(0.33) (□ = vacancy) crystallizes in the anti-Th3P4 structure type with the cubic space group I4̅3d (no. 220), Z = 6, a = 9.7520(7) Å. In the Ba3P2 crystal structure, isolated P(3-) anions form distorted octahedra around the Ba(2+) cations. β-Ba5P4 crystallizes in the Eu5As4 structure type with the orthorhombic space group Cmce (no. 64), Z = 4, a = 16.521(2) Å, b = 8.3422(9) Å, c = 8.4216(9) Å. In the crystal structure of β-Ba5P4, one-half of the phosphorus atoms are condensed into P2(4-) dumbbells. SrP2 and BaP2 are isostructural and crystallize in the monoclinic space group P2₁/c (no. 14), Z = 6, a = 6.120(2)/6.368(1) Å, b = 11.818(3)/12.133(2) Å, c = 7.441(2)/7.687(2) Å, β = 126.681(4)/126.766(2)° for SrP2/BaP2. In the crystal structures of SrP2 and BaP2, all phosphorus atoms are condensed into ∞(1)P(1-) cis-trans helical chains. Electronic structure calculations, chemical bonding analysis via the recently developed solid-state adaptive natural density partitioning (SSAdNDP) method, and UV-vis spectroscopy reveal that SrP2 and BaP2 are electron-balanced semiconductors.

mP-BaP₃: a new phase from an old binary system

A polyphosphide, mP-BaP3, with a unique two-dimensional phosphorus layer has been discovered and characterized. It crystallizes in the monoclinic space group P2₁/c with unit-cell parameters a=6.486(1), b=7.710(1), c=8.172(2) Å; β=104.72(3)°; Z=4. Its phosphorus polyanion can be derived from the strong elongation of 2/3 of the P-P bonds present in the layers of black phosphorus. The unit-cell volume of the mP-BaP3 phase is 1.4% larger than the volume of another polymorph, mS-BaP3, reported more than 40 years ago. The latter phase features the presence of one-dimensional phosphorus chains separated by Ba atoms. The differences in the structures of the phosphorus fragments in both polymorphs of barium triphosphide result in large differences in both the thermal stability of these materials as well as in their properties as evidenced by DSC, (31)P solid-state MAS NMR, UV/Vis, and surface photovoltage spectroscopies, alongside quantum-chemical calculations.

Clathrate Ba8Au16P30: the "gold standard" for lattice thermal conductivity

A novel clathrate phase, Ba8Au16P30, was synthesized from its elements. High-resolution powder X-ray diffraction and transmission electron microscopy were used to establish the crystal structure of the new compound. Ba8Au16P30 crystallizes in an orthorhombic superstructure of clathrate-I featuring a complete separation of gold and phosphorus atoms over different crystallographic positions, similar to the Cu-containing analogue, Ba8Cu16P30. Barium cations are trapped inside the large polyhedral cages of the gold-phosphorus tetrahedral framework. X-ray diffraction indicated that one out of 15 crystallographically independent phosphorus atoms appears to be three-coordinate. Probing the local structure and chemical bonding of phosphorus atoms with (31)P solid-state NMR spectroscopy confirmed the three-coordinate nature of one of the phosphorus atomic positions. High-resolution high-angle annular dark-field scanning transmission electron microscopy indicated that the clathrate Ba8Au16P30 is well-ordered on the atomic scale, although numerous twinning and intergrowth defects as well as antiphase boundaries were detected. The presence of such defects results in the pseudo-body-centered-cubic diffraction patterns observed in single-crystal X-ray diffraction experiments. NMR and resistivity characterization of Ba8Au16P30 indicated paramagnetic metallic properties with a room-temperature resistivity of 1.7 mΩ cm. Ba8Au16P30 exhibits a low total thermal conductivity (0.62 W m(-1) K(-1)) and an unprecedentedly low lattice thermal conductivity (0.18 W m(-1) K(-1)) at room temperature. The values of the thermal conductivity for Ba8Au16P30 are significantly lower than the typical values reported for solid crystalline compounds. We attribute such low thermal conductivity values to the presence of a large number of heavy atoms (Au) in the framework and the formation of multiple twinning interfaces and antiphase defects, which are effective scatterers of heat-carrying phonons.