Two-Dimensional Substitution: Towards a Better Understanding of the Structure-Transport Correlations in the Li-Superionic Thio-LISICONs

A deeper understanding of the relationships among composition‒structure‒transport properties in inorganic solid ionic conductors is of paramount importance to develop highly conductive phases for future employment in solid‒state Li‒ion battery applications. In order to shed light on the mechanisms that regulate these relationships, in this work we perform a “<i>two-dimensional</i>” substitution series in the thio-LISICON family Li₄Ge_1‒<i>x</i>Sn<i>_x</i>S_4‒<i>y</i>Se<i>_y</i>. The structural modifications brought up by the elemental substitutions were investigated via Rietveld refinements against high‒resolution neutron diffraction data that allowed a precise characterization of the anionic framework and the lithium substructure. The analyses show that the anionic and cationic substitutions influence the polyhedral and unit cell volumes in different fashions and that the size of the polyanionic groups alone is not enough to describe lattice expansion in these materials. Moreover, we show that the lithium disorder that is crucial to achieve fast ionic mobility may be correlated to the lithium polyhedral volumes. The correlation of these structural modifications with the transport properties, investigated via electrochemical impedance spectroscopy and ⁷Li nuclear magnetic resonance spin-lattice relaxation measurements, shows a non-monotonic behavior of the ionic conductivity and activation energy against the lithium polyhedral volumes, hinting to an optimal size of the conduction pathways for the ionic diffusion. Ultimately, the results obtained in this work will help to establish new guidelines for the optimization of solid electrolytes and to gain a more profound understanding of the influence of the substituents on the structure and transport properties of Li‒ion conductors

Two-Dimensional Substitution: Towards a Better Understanding of the Structure-Transport Correlations in the Li-Superionic Thio-LISICONs

A deeper understanding of the relationships among composition‒structure‒transport properties in inorganic solid ionic conductors is of paramount importance to develop highly conductive phases for future employment in solid‒state Li‒ion battery applications. In order to shed light on the mechanisms that regulate these relationships, in this work we perform a “<i>two-dimensional</i>” substitution series in the thio-LISICON family Li₄Ge_1‒<i>x</i>Sn<i>_x</i>S_4‒<i>y</i>Se<i>_y</i>. The structural modifications brought up by the elemental substitutions were investigated via Rietveld refinements against high‒resolution neutron diffraction data that allowed a precise characterization of the anionic framework and the lithium substructure. The analyses show that the anionic and cationic substitutions influence the polyhedral and unit cell volumes in different fashions and that the size of the polyanionic groups alone is not enough to describe lattice expansion in these materials. Moreover, we show that the lithium disorder that is crucial to achieve fast ionic mobility may be correlated to the lithium polyhedral volumes. The correlation of these structural modifications with the transport properties, investigated via electrochemical impedance spectroscopy and ⁷Li nuclear magnetic resonance spin-lattice relaxation measurements, shows a non-monotonic behavior of the ionic conductivity and activation energy against the lithium polyhedral volumes, hinting to an optimal size of the conduction pathways for the ionic diffusion. Ultimately, the results obtained in this work will help to establish new guidelines for the optimization of solid electrolytes and to gain a more profound understanding of the influence of the substituents on the structure and transport properties of Li‒ion conductors

The High-Pressure Structural Evolution of Olivine along the Forsterite–Fayalite Join

Structural refinements from single-crystal X-ray diffraction data are reported for olivine with a composition of Fo100 (forsterite Mg2SiO4, synthetic), Fo80 and Fo62 (~Mg1.6Fe0.4SiO4 and ~Mg1.24Fe0.76SiO4, both natural) at room temperature and high pressure to ~8 GPa. The new results, along with data from the literature on Fo0 (fayalite Fe2SiO4), were used to investigate the previously reported structural mechanisms which caused small variations of olivine bulk modulus with increasing Fe content. For all the investigated compositions, the M2 crystallographic site, with its bonding configuration and its larger polyhedral volume, was observed to control the compression mechanisms in olivine. From Fo100 to Fo0, the compression rates for M2–O and M1–O bond lengths were observed to control the relative polyhedral volumes, resulting in a less-compressible M1O6 polyhedral volume, likely causing the slight increase in bulk modulus with increasing Fe content.

Haar-LikeWavelets over Tetrahedra

In this paper we define a Haar-like wavelets basis that form a basis for L2(T,S,μ), μ being the Lebesgue measure and S the σ -algebra of all tetrahedra generated from a subdivision method of the T tetrahedron. As 3D objects are, in general, modeled by tetrahedral grids, this basis allows the multiresolution representation of scalar functions defined on polyhedral volumes, like colour, brightness, density and other properties of an 3D object.

The effect of non-stoichiometry on the high-temperature behaviour of MgAl2O4 spinel

The effect of cation vacancies upon the thermal expansion and crystal structure of a synthetic defect spinel with composition Mg0.4Al2.4☐0.2O4 was investigated by X-ray diffraction, in situ, at temperatures up to 1273 K. No evidence of symmetry violations from the Fd3m evenat the highest temperature were noted. The volume thermal expansion is markedly less than that of stoichiometric MgAl2O4 spinel, regardless of the degree of inversion. The u oxygen atomic coordinate remains constant throughout the temperature range investigated, with the M–O an dT–O bond lengths showing identical rates of expansivities. An analysis of the evolution of polyhedral volumes with temperature indicates that at 1273 K the octahedron inflates by 0.099 Å3 and the tetrahedron by 0.056 Å3. The expansion of the octahedron is significantly greater than in stoichiometric MgAl2O4 spinel, whereas the expansion of the tetrahedron is similar. The results demonstrate that an excess of Al in the spinel structure accompanied by the formation of cation vacancies strongly affect an important thermodynamic property, in this case, thermal expansion. Such an effect must be considered for those phases stable inthe Earth’s mantle where 4–5 wt.% Al2O3 is thought to be present.

Crystal chemistry of aegirine as an indicator of P-T conditions

One metamorphic and four magmatic aegirines, together with two end-member aegirines synthesized at atmospheric pressure and different temperatures, were investigated by single-crystal X-ray diffraction. The limited compositional differences allow the polyhedral volumes to be almost constant in all the aegirines investigated( VM1 ≈ 11.0 Å3; VM2 ≈ 26.3 Å3; VT ≈ 2.21 Å3). However, differences in polyhedral distortions are responsible for the cell-volume variations, reflected mainly in the change of a and β cell parameters. Cell volume is only partly related to the composition of these aegirines: with increasing formation temperature, an increase in the unit-cell volume of ~1.2 Å3 is observed, while a significant contraction of the cell volume occurs during high-pressure formation. As the difference in cell volume between the two synthetic aegirines is ascribed to the different conditions of synthesis temperature, the same interpretation could be adopted for the differences observed in natural aegirines.

Structural changes induced by cation ordering in ferrotapiolite

Structural modifications as a function of the degree of order (Q) in FeTa2O6 ferrotapiolite have been characterized by means of single-crystal X-ray diffraction (SC-XRD). A total of 26 datasets covering the range of Q between 0.154 and 1 have been obtained by thermal treatments followed by quenching of natural tapiolite crystals. Ordering of Fe2+ at the A sites and of Ta5+ at the B sites causes a linear increase in the a/c lattice constants ratio, as a consequence of a linear decrease of the c dimension and only slight modifications of the a parameter. Calibration of a/c vs. Q represents a very useful tool for a rapid determination of the degree of order of tapiolite samples. Polyhedral volumes of the two octahedral sites vary linearly with Q as a consequence of the different ionic radii of the two species. Both the sites remain almost regular at all Q values but the B site shows an increasing off-centre displacement of the cation with increasing Q. Observed structure factors of supercell reflections, characterized by l ≠ 3n, increase linearly as a function of Q, thus representing a further tool for a quick evaluation of the degree of order.

Temperature dependence of polyhedral cage volumes in clathrate hydrates

The polyhedral cage volumes of structure I (sI) (carbon dioxide, methane, trimethylene oxide) and structure II (sII) (methane–ethane, propane, tetrahydrofuran, trimethylene oxide) hydrates are computed from atomic positions determined from neutron powder-diffraction data. The ideal structural formulas for sI and sII are, respectively, S2L6 · 46H2O and S16L'8 · 136H2O, where S denotes a polyhedral cage with 20 vertices, L a 24-cage, and L' a 28-cage. The space-filling polyhedral cages are defined by the oxygen atoms of the hydrogen-bonded network of water molecules. Collectively, the mean cage volume ratio is 1.91 : 1.43 : 1 for the 28-cage : 24-cage : 20-cage, which correspond to equivalent sphere radii of 4.18, 3.79, and 3.37 Å, respectively. At 100 K, mean polyhedral volumes are 303.8, 227.8, and 158.8 Å3 for the 28-cage, 24-cage, and 20-cage, respectively. In general, the 20-cage volume for a sII is larger than that of a sI, although trimethylene oxide is an exception. The temperature dependence of the cage volumes reveals differences between apparently similar cages with similar occupants. In the case of trimethylene oxide hydrate, which forms both sI and sII, the 20-cages common to both structures contract quite differently. From 220 K, the sII 20-cage exhibits a smooth monotonic reduction in size, whereas the sI 20-cage initially expands upon cooling to 160 K, then contracts more rapidly to 10 K, and overall the sI 20-cage is larger than the sII 20-cage. The volumes of the large cages in both structures contract monotonically with decreasing temperature. These differences reflect reoriented motion of the trimethyelene oxide molecule in the 24-cage of sI, consistent with previous spectroscopic and calorimetric studies. For the 20-cages in methane hydrate (sI) and a mixed methane–ethane hydrate (sII), both containing methane as the guest molecule, the temperature dependence of the 20-cage volume in sII is much less than that in sI, but sII is overall larger in volume. PACS Nos.: 82.75, 61.66H, 65.40D, 61.12

The compositional dependence of octahedral tilting in orthorhombic and tetragonal perovskites

A new parameterization is defined for the quantitative description of octahedral tilting in orthorhombic and tetragonal perovskites. It contains six parameters, s 1, s 2, s 3, θx , θy and θz . s 1, s 2 and s 3 refer to the lengths of the lines or `stalks' joining pairs of opposite octahedral vertices, and θx , θy and θz to the angles subtended by these stalks with pseudo-cubic axes x, y and z. An equation is derived for the dependence of polyhedral volume ratio, Va / VB , on these parameters: Va / VB = 6cos2 θm cos θz − 1, where θm = (θx + θy )/2. To a good approximation, lengths s 1, s 2 and s 3 do not affect Va / VB . The validity of this equation is tested by reference to the known crystal structures of 48 ternary oxide and fluoride perovskites, and its versatility demonstrated by application to the structures of some ternary palladium and platinum hydrides. The relationship of the approach to Glazer's system of nomenclature for octahedral tilting in perovskites is considered, in particular concerning the numbers of tilts operative in a given structure. A comparison is also made with the parameterization proposed for octahedral tilting and distortion in rhombohedral perovskites [Thomas & Beitollahi (1994). Acta Cryst. B50, 549–560]. Factors governing the choice of rhombohedrai or orthorhombic symmetry are discussed, with the significance of rhombohedral symmetry in obtaining ferroelectric properties brought out. Through the compilation of a table of AO12 and BO6 polyhedral volumes, the prospect is identified of predicting both the degree of octahedral tilting and the likelihood of ferroelectric behaviour for novel, hypothetical oxide compositions.

Zaoyang chondrite cooling history from Fe2+-Mg intracrystalline ordering in pyroxenes

The crystal chemistry of clinopyroxene, orthopyroxene and olivine from a crushed fragment of the H5 Zaoyang chondrite has been investigated by X-ray structure refinement and detailed microprobe analysis. The meteoritic pyroxenes have cell and polyhedral volumes which compare well with such data from terrestrial pyroxenes that typically crystallize at low-pressure. Fe2+ and Mg are rather disordered in M1 and M2 sites of clino- and orthopyroxenes; the closure temperatures of the exchange reaction are 600 and 512°C respectively, which is consistent with a reasonably fast cooling rate, estimated to be of the order of 1°C/day.The closure temperature for the intercrystalline Ca-Mg exchange reaction for clino- and orthopyroxenes is 900°C as calculated from clino- and orthopyroxene intergrowth.The cooling rates obtained from Fe2+-Mg intracrystalline partitioning suggest a cooling of the order of degrees per day at temperatures of 600–500°C due to a strong loss of heat by irradiation.