X-ray electron density investigation of chemical bonding in van der Waals materials.

Van der Waals (vdW) solids have attracted great attention ever since the discovery of graphene, with the essential feature being the weak chemical bonding across the vdW gap. The nature of these weak interactions is decisive for many extraordinary properties, but it is a strong challenge for current theory to accurately model long-range electron correlations. Here we use synchrotron X-ray diffraction data to precisely determine the electron density in the archetypal vdW solid, TiS2, and compare the results with density functional theory calculations. Quantitative agreement is observed for the chemical bonding description in the covalent TiS2 slabs, but significant differences are identified for the interactions across the gap, with experiment revealing more electron deformation than theory. The present data provide an experimental benchmark for testing theoretical models of weak chemical bonding.

Low-Barrier Hydrogen Bonds in Negative Thermal Expansion Material H3 [Co(CN)6 ].

The covalent nature of the low-barrier N-H-N hydrogen bonds in the negative thermal expansion material H3 [Co(CN)6 ] has been established by using a combination of X-ray and neutron diffraction electron density analysis and theoretical calculations. This finding explains why negative thermal expansion can occur in a material not commonly considered to be built from rigid linkers. The pertinent hydrogen atom is located symmetrically between two nitrogen atoms in a double-well potential with hydrogen above the barrier for proton transfer, thus forming a low-barrier hydrogen bond. Hydrogen is covalently bonded to the two nitrogen atoms, which is the first experimentally confirmed covalent hydrogen bond in a network structure. Source function calculations established that the present N-H-N hydrogen bond follows the trends observed for negatively charge-assisted hydrogen bonds and low-barrier hydrogen bonds previously established for O-H-O hydrogen bonds. The bonding between the cobalt and cyanide ligands was found to be a typical donor-acceptor bond involving a high-field ligand and a transition metal in a low-spin configuration.

High-Temperature Crystal Structure and Chemical Bonding in Thermoelectric Germanium Selenide (GeSe).

The discovery of the ultra-high thermoelectric figure of merit of 2.6 in SnSe has drawn attention to other lead-free IV-VI orthorhombic semiconductors. GeSe has been predicted to possess thermoelectric performances comparable to SnSe. Here, a complete structural study is reported of GeSe with temperature by means of high-resolution synchrotron powder X-ray diffraction. In the orthorhombic phase, the evolution of the bond distances with temperature is shown to deviate significantly with respect to SnSe. Analysis of the chemical bonding within the Quantum Theory of Atoms in Molecules shows that GeSe is ionic with van der Waals interlayer interactions. The signature of the N shell lone pair of Ge is also evident from both the electron density Laplacian and the ELF topologies.

Low-Temperature Anharmonicity in Cesium Chloride (CsCl).

Anharmonic lattice vibrations govern heat transfer in materials, and anharmonicity is commonly assumed to be dominant at high temperature. The textbook cubic ionic defect-free crystal CsCl is shown to have an unexplained low thermal conductivity at room temperature (ca. 1 W/(m K)), which increases to around 13  W/(m K) at 25 K. Through high-resolution X-ray diffraction it is unexpectedly shown that the Cs atomic displacement parameter becomes anharmonic at 20 K.

Structural disorder, anisotropic micro-strain and cation vacancies in thermo-electric lead chalcogenides.

Thermoelectric materials can interconvert heat and electricity, and the extraordinary thermoelectric properties of lead chalcogenides (PbX, X = S, Se, Te) attract immense scientific interest. A key topic is the role of the cation in reaching a very low thermal conductivity necessary for efficient energy conversion. Here we present new structural insights about the deceptively simple rock-salt lead chalcogenides through a comparative multi-temperature synchrotron powder X-ray diffraction study. For the first time, the presence of anisotropic microstrain broadening as well as lead vacancies are quantified for all three compounds. The microstrain implies extended breakage of cubic symmetry as a sign of the incipient ferroelectric nature of PbX. The degree of microstrain is correlated to the transition pressure of a symmetry reducing phase transition, and this trend can be explained by anion mediated s-p hybridization on lead. The observed number of vacancies is greatest for PbS (4-8%), but two samples of PbS show different cation occupancy, and thus sample-dependent vacancies might be the property that unifies conflicting results reported for PbX. Gram-Charlier analysis identifies a local non-spherical distribution of Pb; however, model unbiased maximum entropy analysis indicates that any static displacement of Pb, if present, is less than 0.2 Å at 100 K.

Chemical bonding origin of the unexpected isotropic physical properties in thermoelectric Mg3Sb2 and related materials.

The Mg3Sb2 structure is currently being intensely scrutinized due to its outstanding thermoelectric properties. Usually, it is described as a layered Zintl phase with a clear distinction between covalent [Mg2Sb2]2- layers and ionic Mg2+ layers. Based on the quantitative chemical bonding analysis, we unravel instead that Mg3Sb2 exhibits a nearly isotropic three-dimensional bonding network with the interlayer and intralayer bonds being mostly ionic and surprisingly similar, which results in the nearly isotropic structural and thermal properties. The isotropic three-dimensional bonding network is found to be broadly applicable to many Mg-containing compounds with the CaAl2Si2-type structure. Intriguingly, a parameter based on the electron density can be used as an indicator measuring the anisotropy of lattice thermal conductivity in Mg3Sb2-related structures. This work extends our understanding of structure and properties based on chemical bonding analysis, and it will guide the search for and design of materials with tailored anisotropic properties.

Crystal structure and phase transition of thermoelectric SnSe.

Tin selenide-based functional materials are extensively studied in the field of optoelectronic, photovoltaic and thermoelectric devices. Specifically, SnSe has been reported to have an ultrahigh thermoelectric figure of merit of 2.6 ±â€…0.3 in the high-temperature phase. Here we report the evolution of lattice constants, fractional coordinates, site occupancy factors and atomic displacement factors with temperature by means of high-resolution synchrotron powder X-ray diffraction measured from 100 to 855 K. The structure is shown to be cation defective with a Sn content of 0.982 (4). The anisotropy of the thermal parameters of Sn becomes more pronounced approaching the high-temperature phase transition (∼ 810 K). Anharmonic Gram-Charlier parameters have been refined, but data from single-crystal diffraction appear to be needed to firmly quantify anharmonic features. Based on modelling of the atomic displacement parameters the Debye temperature is found to be 175 (4) K. Conflicting reports concerning the different coordinate system settings in the low-temperature and high-temperature phases are discussed. It is also shown that the high-temperature Cmcm phase is not pseudo-tetragonal as commonly assumed.

Carrier concentration dependence of structural disorder in thermoelectric Sn1-x Te.

SnTe is a promising thermoelectric and topological insulator material. Here, the presumably simple rock salt crystal structure of SnTe is studied comprehensively by means of high-resolution synchrotron single-crystal and powder X-ray diffraction from 20 to 800 K. Two samples with different carrier concentrations (sample A = high, sample B = low) have remarkably different atomic displacement parameters, especially at low temperatures. Both samples contain significant numbers of cation vacancies (1-2%) and ordering of Sn vacancies possibly occurs on warming, as corroborated by the appearance of multiple phases and strain above 400 K. The possible presence of disorder and anharmonicity is investigated in view of the low thermal conductivity of SnTe. Refinement of anharmonic Gram-Charlier parameters reveals marginal anharmonicity for sample A, whereas sample B exhibits anharmonic effects even at low temperature. For both samples, no indications are found of a low-temperature rhombohedral phase. Maximum entropy method (MEM) calculations are carried out, including nuclear-weighted X-ray MEM calculations (NXMEM). The atomic electron densities are spherical for sample A, whereas for sample B the Te electron density is elongated along the 〈100〉 direction, with the maximum being displaced from the lattice position at higher temperatures. Overall, the crystal structure of SnTe is found to be defective and sample-dependent, and therefore theoretical calculations of perfect rock salt structures are not expected to predict the properties of real materials.

Quantitative analysis of intermolecular interactions in orthorhombic rubrene.

Rubrene is one of the most studied organic semiconductors to date due to its high charge carrier mobility which makes it a potentially applicable compound in modern electronic devices. Previous electronic device characterizations and first principles theoretical calculations assigned the semiconducting properties of rubrene to the presence of a large overlap of the extended π-conjugated core between molecules. We present here the electron density distribution in rubrene at 20 K and at 100 K obtained using a combination of high-resolution X-ray and neutron diffraction data. The topology of the electron density and energies of intermolecular interactions are studied quantitatively. Specifically, the presence of Cπ⋯Cπ interactions between neighbouring tetracene backbones of the rubrene molecules is experimentally confirmed from a topological analysis of the electron density, Non-Covalent Interaction (NCI) analysis and the calculated interaction energy of molecular dimers. A significant contribution to the lattice energy of the crystal is provided by H-H interactions. The electron density features of H-H bonding, and the interaction energy of molecular dimers connected by H-H interaction clearly demonstrate an importance of these weak interactions in the stabilization of the crystal structure. The quantitative nature of the intermolecular interactions is virtually unchanged between 20 K and 100 K suggesting that any changes in carrier transport at these low temperatures would have a different origin. The obtained experimental results are further supported by theoretical calculations.