Novel study on the electron density distribution projection maps calculated via the discrete cosine transform

It is already known that a curve estimated via the discrete cosine transform (DCT) always passes through all the measured points without using imaginary numbers in the DCT coefficients, unlike the discrete Fourier transform. Moreover, owing to its character, the DCT can be used instead of the nonlinear least-squares method to express various theoretical curves. Because the DCT is a kind of Fourier transform, there is a possibility that the DCT could be employed to draw electron density distribution maps of crystals. If so, the probability that the DCT could be used to investigate the internal structure of materials by analysing the theoretical curves would increase. This article reports an attempt to draw the electron density distribution maps of the Mg3BN3 low-pressure phase [Mg3BN3(L)] by using the DCT in order to confirm the utility of the DCT for analysing the internal structure of materials. It is found that the DCT can provide mirror-symmetric electron density distribution projection maps and a modified DCT can be used to calculate whole standard electron density distribution projection maps for the surface plane of the unit cell. Moreover, a real crystal structure that has a centre of symmetry can be determined by the DCT by transforming a 1/4 part of the mirror-symmetric electron density distribution projection map.

Simplicity Out of Complexity: Band Structure for W20O58 Superconductor

The band structure, density of states, and the Fermi surface of a recently discovered superconductor, oxygen-deficient tungsten oxide WO2.9 that is equivalent to W20O58, is studied within the density functional theory (DFT) in the generalized gradient approximation (GGA). Here we show that despite the extremely complicated structure containing 78 atoms in the unit cell, the low-energy band structure is quite feasible. Fermi level is crossed by no more than 10 bands per one spin projection (and even 9 bands per pseudospin projection when the spin-orbit coupling is considered) originating from the t2g 5d-orbitals of tungsten atoms forming zigzag chains. These bands become occupied because of the specific zigzag octahedra distortions. To demonstrate the role of distortions, we compare band structures of W20O58 with the real crystal structure and with the idealized one. We also propose a basis for a minimal low-energy tight-binding model for W20O58.

Tancaite-(Ce), ideally FeCe(MoO₄)₃ ● 3H₂O: description and average crystal structure

Tancaite-(Ce), ideally FeCe(MoO4)3⚫3H2O, is a new mineral occurring within cavities in the quartz veins which cut the granite at Su Seinargiu, Sarroch (CA), Sardinia, Italy. It is a secondary mineral formed in the oxidation zone of a sulfide ore vein. Associated minerals are quartz, muscovite, molybdenite, pyrite, and a mendozavilite-like phase. Tancaite-(Ce) is red or pale brown in colour, with a vitreous to adamantine lustre. Electron microprobe analyses give (wt %) SiO2 0.34, CaO 0.09, Fe2O3 11.29, SrO 0.02, La2O3 5.04, Ce2O3 10.35, Pr2O3 1.07, Nd2O3 3.66, Sm2O3 0.19, ThO2 2.58, UO2 0.17, MoO3 58.62, and H2O (calculated) 7.43, with a sum of 100.85, from which the empirical formula is calculated. The empirical formula Fe1.033+(Ce0.46La0.23Nd0.16Pr0.05Sm0.01U0.01Th0.07)Σ=0.99(Mo2.96Si0.04)Σ=3.00O12⚫3H2O can be simplified as Fe3+(REE)(MoO4)3⚫3H2O and idealized as FeCe(MoO4)3⚫3H2O. The presence of H2O was confirmed by micro-Raman spectrometry (stretching and bending vibrations of O–H). The calculated density is 3.834 g cm−3. The X-ray diffraction pattern of tancaite-(Ce) is characterized by a set of strong reflections, which point to a cubic subcell with a=6.870(1) Å and space group Pm3¯m, plus a set of superstructure reflections. Tancaite-(Ce) displays a new structure type not previously reported in natural and synthetic molybdates. By considering only the strong reflections, it was possible to solve and refine its average structure (R1=0.038 for 192 unique reflections with I>2σ(I)). The crystal structure consists of FeO6 octahedra centred at the origin of the cubic subcell and linked together through MoO4 tetrahedra by corner sharing. The Mo-centred tetrahedra are statistically distributed in four symmetry-related positions, with one-fourth occupancy. In the centre of the cubic unit cell the REE cations exhibit a 6+3 coordination, bonding six oxygen atoms and three H2O molecules, each of them being disorderly distributed in four symmetry-related positions. One of the possible supercells, with a 48-fold volume with respect to the primitive cubic small subcell, corresponded to a rhombohedral lattice, with a≈19.43 and c≈47.60 Å in the hexagonal setting. Several unsuccessful trials were performed to solve the real crystal structure of tancaite, by indexing the additional superstructure reflections and using their intensities to refine an ordered structural model. The new mineral has been approved by the IMA CNMNC (no. 2009-097). The name comes from Giuseppe Tanca, an Italian amateur mineralogist, who discovered the mineral and gave it to us for studying.

The thermal expansion of gold: point defect concentrations and pre-melting in a face-centred cubic metal

On the basis ofab initiocomputer simulations, pre-melting phenomena have been suggested to occur in the elastic properties of hexagonal close-packed iron under the conditions of the Earth's inner core just before melting. The extent to which these pre-melting effects might also occur in the physical properties of face-centred cubic metals has been investigated here under more experimentally accessible conditions for gold, allowing for comparison with future computer simulations of this material. The thermal expansion of gold has been determined by X-ray powder diffraction from 40 K up to the melting point (1337 K). For the entire temperature range investigated, the unit-cell volume can be represented in the following way: a second-order Grüneisen approximation to the zero-pressure volumetric equation of state, with the internal energy calculatedviaa Debye model, is used to represent the thermal expansion of the `perfect crystal'. Gold shows a nonlinear increase in thermal expansion that departs from this Grüneisen–Debye model prior to melting, which is probably a result of the generation of point defects over a large range of temperatures, beginning atT/Tm> 0.75 (a similar homologousTto where softening has been observed in the elastic moduli of Au). Therefore, the thermodynamic theory of point defects was used to include the additional volume of the vacancies at high temperatures (`real crystal'), resulting in the following fitted parameters:Q= (V0K0)/γ = 4.04 (1) × 10−18 J,V0= 67.1671 (3) Å3,b= (K0′ − 1)/2 = 3.84 (9), θD= 182 (2) K, (vf/Ω)exp(sf/kB) = 1.8 (23) andhf= 0.9 (2) eV, whereV0is the unit-cell volume at 0 K,K0andK0′ are the isothermal incompressibility and its first derivative with respect to pressure (evaluated at zero pressure), γ is a Grüneisen parameter,θDis the Debye temperature,vf,hfandsfare the vacancy formation volume, enthalpy and entropy, respectively, Ω is the average volume per atom, andkBis Boltzmann's constant.

A method for visualization of the variation of noncovalent interactions in crystal structures of conformational polymorphs

A method for clear visualization of the variation of noncovalent interactions in crystal structures of conformational polymorphs is developed and introduced. The first stage of the method establishes the characteristics of all, without exception, noncovalent interactions in all crystal structures under discussion. This is possible using a strict and objective method of construction of Voronoi–Dirichlet polyhedra within the framework of the stereoatomic model of crystal structures. The second stage of the method then involves plotting of diagrams, showing the relation between parameters characterizing interatomic interactions and chosen geometric parameters of molecules. Application of the title method to highly polymorphic systems of ROY and flufenamic acid allows several imperceptible features of real crystal structures to be revealed and determines the value of different types of interactions in their conformational polymorphs. The method is universal as it can be readily adapted to any system of crystal structures in which noncovalent interactions change as a function of any parameters. Employment of the title method along with quantum chemical calculations offers opportunities for the correlation of potential energy of crystalline materials with noncovalent interactions in their structures, which is a giant step forward towards a more complete understanding of the relationship between the structure and properties of compounds.

Influence of lithium and magnesium on the real structure and dielectric properties of Ca9Y(VO4)7 single crystals

The real crystal structure was oxyaminated by complex methods; the influence of impurity and point defects is shown.

Solution of the heavily stacking faulted crystal structure of the honeycomb iridate H3LiIr2O6

The idealized and real crystal structure of the heavily faulted honeycomb iridate H3LiIr2O6 was solved from XRPD and PDF data.