The Reciprocal Lattice in Hierarchic Quasicrystals

Initially, all that was known about diffraction in quasicrystals was its point group symmetry;nothing was known about the mechanism. The structure was more evident, and was called quasiperiodic. From mapping the Mn atoms by phase-contrast, optimum-defocus, electron microscopy, the progress towards identifying unit cell, cluster, supercluster and extensive hierarchic structure is evident. The structure is ordered and uniquely icosahedral. From the known structure, we could calculate structure factors. They were all zero. The quasi structure factor is an iterative procedure on the hierarchic structure that correctly calculates diffraction beam intensities in 3-dimensional space. By a creative device, the diffraction is demonstrated to occur off the Bragg condition;the quasi-Bragg condition implies a metric that enables definition and measurement of the lattice constant. The reciprocal lattice is the 3-dimensional diffraction pattern. Typically, it builds on Euclidean axes with coordinates in geometric series, but it also transforms to Cartesian coordinates.

Electronic structures and properties of Ti, Zr and Hf metals

The electronic structures of pure Ti, Zr and Hf metals with hcp structure were determined by one atom (OA) theory. According to the electronic structures of these metals,their potential curves, cohesive energies, lattice constants, elasticities and the temperature dependence of linear thermal expansion coefficients were calculated. The electronic structures and characteristic properties of these metals with bcc and fcc structures and liquids were also studied. The results show that the electronic structures of Ti, Zr and Hf metals are respectively [Ar](3d n) 0.481 0 (3d c) 2.085 7 (4s c) 1.000 0 (4s f) 0.433 3 , [Kr](4d n) 0.396 8 (4d c) 2.142 8 (5s c) 1.262 0 (5s f) 0.198 4 , [Xe](5d n) 0.368 0 (5d c) 2.041 4 (6s c) 1.406 6 (6s f) 0.184 0 . It is explained why the pure Ti, Zr and Hf metals with hcp and bcc structures can exist naturally, while those with fcc structure can not.

ELECTRONIC STRUCTURE AND PROPERTIES OF Au METAL

Using the new developed valence bond theory of metals,the electronic structure,crystal structure and physical properties of Au metal have been systematically analysed.It has been determined that its electronic structure is(5d_(n))^(4.65)(5d_(c))^(4.71)(6s_(c))^(0.62)(6s_(f))^(1.02).According to this electronic structure,lattice constant,cohesive energy.potential curve,bulk modulus and temperature dependence of liner thermal expansion coeCHcient have been calculated.The theoretical values of properties are all in good agreement with experimental results.This electronic structure has been verified in part by linear rigorous cellular method of band theory.It shows that the valence bond theory has been reached perfectly.

The Mechanical and Electronic Properties of Ternary Rare-Earth Hexaboride LaxNd8-xB6 (x = 0, 1, 7, 8) Materials

We have carried out density functional theory to study the lattice constants and electronic properties of LaB6, NdB6, Nd-doped LaB6, and La-doped NdB6. The lattice constant, intra-octahedral bond, inter-octahedral boron bond, and positional parameter (z) were calculated for LaB6, La7Nd1B6, La1Nd7B6, and NdB6. Our results show that the doped Nd increases the lattice constant of La7Nd1B6. Likewise, La-doping leads to an increase in the lattice constant of the La1Nd7B6. The PDOSs of LaB6, B of LaB6, La7Nd1B6, B of La7Nd1B6, La1Nd7B6, B of La1Nd7B6, NdB6, and B of NdB6 were calculated. La d-electron bands cross the Fermi energy, showing classical conductor behavior. The charge density results indicate that light and dark colors show high and low-intensity zones, respectively. La1Nd7B6 has a low-density region and LaB6 has a high-density region. The LaB6 midpoint has strong charge density peaks. Weak peaks are also observed for La1Nd7B6. Thus, ternary REB6 has good potential for many applications. This article reports an investigation of the electronic features and structural parameters of binary and ternary hexaborides.

Automatic Measurement of Silicon Lattice Spacings in High-Resolution Transmission Electron Microscopy Images Through 2D Discrete Fourier Transform and Inverse Discrete Fourier Transform

Line width(i.e.,critical dimension,CD)is a crucial parameter in integrated circuits.To accurately control the CD in manufacturing,a reasonable CD measurement algorithm is required.We develop an automatic and accurate method based on a two-dimensional discrete Fourier transform for measuring the lattice spacings from high-resolution transmission electron microscopy images.Through the two-dimensional inverse discrete Fourier transform of the central spot and a pair of symmetrical diffraction spots,an image containing only a set of lattice spacings is obtained.Then,the pixel span of the lattice spacing is calculated through the centre of gravity method.Finally,we estimate the standard CD value according to the half-intensity method.The silicon crystal lattice constant guarantees the accuracy and traceability of the CD value.Through experiments,we demonstrate the efficiency of the proposed method,which can be conveniently applied to accurately measure CDs in practical applications.

Microscopic insights into hydrophobicity of cerium oxide:Effects of crystal orientation and lattice constant

Cerium oxide possesses intrinsic hydrophobic properties ascribed to the unique electronic structure.However,the relationship between the crystal structure and hydrophobicity of cerium oxide has not been systematically studied.Herein,it is experimentally and theoretically demonstrated that the water contact angle(105.9°)of the(111)surface is higher than that(91.7°)of the(220)surface,associated with the lower surface free energy(28.44 mN/m)of(111)surface than that(38.48 mN/m)of(220)surface.Furthermore,cerium oxide films with(111)-terminated surface are annealed at 300℃ and 600℃ for1 h,respectively.The lattice constant increases(5.4594Å<5.4613Å<5.4670Å)with decreasing the annealing temperature(600℃>300℃>the as-deposited),leading to the increased water contact angle(96.7°<96.8°<99.0°).The First-principles calculation provides microscopic insights into the wetting mechanism,originating from the weakened adsorption capacity of the(111)surface for water molecules with the increasing lattice constant.

Band Structure Characteristics of Two-Dimensional Si-A (Ge, Pb, Sn) Alloy-Air Holes Thermal Crystals

This paper designs the thermal crystals composed of alloy materials with air holes and analyzes their properties of band structures,heat transmission,and flux spectra.Thermal crystals composed of Si-A(A=Ge,Sn,Pb)alloys as background materials and air holes with square array are used to construct an elastic-constant periodic structure and their high-frequency phononic band is calculated by deploying finite element methods.Moreover,this paper investigates heat transmission through a finite array of thermally excited phonons and presents the thermal crystal with maximum heat transport.The results show that a wider bandgap could be achieved by increasing the air hole radius and decreasing the lattice constant.In the alloy materials,with increasing atomic radius and thus atomic mass(Ge,Sn,Pb),the frequency range(contributed to thermal conductivity)shifts towards lower frequency.Hence,the bandgap frequencies also shift toward low frequency,but this decreasing rate is not constant or in order,so former may have a faster or slower decreasing rate than the later.Thus,the frequency range for the contribution of heat transportation overlaps with the bandgap frequency range.The development of thermal crystals is promising for managing heat and controlling the propagation of the thermal wave.

Electronic structure of Ag-Cu alloys

According to the correlativity between energy, volume and electronic structure of characteristic crystals and bound conditions of OA theory, the Gibbs energy function, atomic volume function and electronic structure of Ag Cu alloys have been determined. Then the electronic structure and properties of disordered alloys with any composition and ordered alloys with any ordering degree can be calculated. The number of d c covalent electrons in the states of Ag characteristic atoms decreases with the increase of Cu atoms in the nearest neighbouring shell. The number of d c covalent electrons in the states of Cu characteristic atoms decreases with the increase of Ag atoms in the nearest neighbouring shell. Such changes lead to the tendencies of atomic segregation and partition into two phases in the Ag Cu system.

Atomic volumes and volume functions for Ag-Cu alloys

Nine functions of atomic volume interaction have been established. The values of average atomic volumes and lattice constants of Ag-Cu alloys obtained from each V-function are, respectively, equal to each other and in good agreement with experimental values. But the average atomic volumes of components and the volumes of characteristic atoms obtained from each V-function are different from each other. Only after the correlative study of energy, volume and electronic structure is carried out, can the V-function be correctly chosen, can a knowledge system about the alloys be established, thus providing the base for scientific design of new alloys. The relationships between lattice parameters of metastable phases of Ag-Cu alloys and composition and between average properties and partial molar properties of components are discussed.