Diamond-type Lattice Research Articles

Improved Tribological Performance of MOF@MXene/PI under High Temperature.

High-temperature-resistant and self-lubricating polymer composites with long life and high reliability are increasingly indispensable in the aerospace field. Herein, ZIF-67 grown on the MXene lamella was successfully prepared, and ZIF-67@MXene/PI composites with a regular layered structure were obtained by a hot-pressing three-dimensional network aerogel. It was revealed that incorporating ZIF-67@MXene into PI dramatically reduced the friction and abrasion with elevated temperatures. Largely, aerogel walls always paralleled the sliding direction by compressing, providing a significant antifriction effect. More notably, the presence of a vigorous tribofilm composed of a PI matrix and a diamond-type lattice MOF-modified MXene provided rolling and sliding interface friction under high temperatures, simultaneously. In addition, the uniform tribofilm with a thickness of about 200 nm can effectively avoid the direct contact of the friction pair during the sliding process. Hence, the combination of the constructed multiscale nanocomposites and nanostructured tribofilm with outstanding tribological performance endow the material potentially useful in reducing energy consumption, thus addressing the energy wastage problem caused by friction.

Surface Modification Using Assisting Electrodes in Wire Electrical Discharge Machining for Silicon Wafer Preparation.

This paper outlines notable advances in the wire electrical discharge machining of polycrystalline silicon workpieces for wafer preparation. Our use of assisting electrodes permits the transfer of aluminum particles to the machined surface of the polycrystalline silicon workpieces, to enhance conductivity and alter surface topography regardless of the silicon’s crystallographic structure and diamond-type lattice. This in-process surface modification technique was shown to promote material removal and simultaneously preserve the integrity of the machined surfaces with preferable surface textures. In the validation experiment, the 25 mm-thick assisting electrodes deposited a notable concentration of aluminium on the machined surface (~3.87 wt %), which greatly accelerated the rate of material removal (~9.42 mg/s) with minimal surface roughness (Sa ~5.49 μm) and moderate skewness (−0.23). The parameter combination used to obtain the optimal surface roughness (Sa 2.54 μm) was as follows: open voltage (80 V), electrical resistance (1.7 Ω), pulse-on time (30 μs), and electrode thickness (15 mm). In multiple objective optimization, the preferred parameter combination (open voltage = 80 V, resistance = 1.4 Ω, pulse-on time = 60 μs, and assisting electrode thickness = 25 mm) achieved the following appreciable results: surface modification of 3.26 ± 0.61 wt %, material removal rate of 7.08 ± 2.2 mg/min, and surface roughness of Sa = 4.3 ± 1.67 μm.

Automorphism group of $L$-fuzzy topologies when $L$ is a diamond-type lattice

Automorphism group of $L$-fuzzy topologies when $L$ is a diamond-type lattice

Influence of Boundary Conditions on the Simulation of a Diamond-Type Lattice Structure: A Preliminary Study

Emergent additive manufacturing processes allow the use of metallic porous structures in various industrial applications. Because these structures comprise a large number of ordered unit cells, their design using conventional modeling approaches, such as finite elements, becomes a real challenge. A homogenization technique, in which the lattice structure is simulated as a fully dense volume having equivalent material properties, can then be employed. To determine these equivalent material properties, numerical simulations can be performed on a single unit cell of the lattice structure. However, a critical aspect to consider is the boundary conditions applied to the external faces of the unit cell. In the literature, different types of boundary conditions are used, but a comparative study is definitely lacking. In this publication, a diamond-type unit cell is studied in compression by applying different boundary conditions. If the porous structure’s boundaries are free to deform, then the periodic boundary condition is found to be the most representative, but constraint equations must be introduced in the model. If, instead, the porous structure is inserted in a rigid enclosure, it is then better to use frictionless boundary conditions. These preliminary results remain to be validated for other types of unit cells loaded beyond the yield limit of the material.

Excitation spectrum and superconductivity in diamond-type compounds

The occurrence of superconductivity in a diamond-type lattice is investigated. For each integer interval of electron concentration np, narrow concentration regions are discovered in which the superconducting transition temperature has the highest possible value. Analysis is carried out under the assumption that the energy of strong electron-electron correlations is the largest energy parameter. The results are in qualitative agreement with experimental data.

Critical behavior of the quantum Heisenberg model on three-dimensional diamond-type hierarchical lattice

With a real-space renormalization-group method, the anisotropic quantum Heisenberg model on three-dimensional diamond-type hierarchical lattice is studied, and the phase diagram and critical properties are obtained. For the ferromagnetic system, it is shown that there is a finite-temperature phase transition for Δ=0 where Δ is the anisotropy parameter. The order parameter and critical exponents are also calculated. For the antiferromagnetic model, we find that the critical temperature is not equal to zero for Δ=0 and there is not reentrant behavior on the critical line.

Structure of the boron nitride E-phase: Diamond lattice of B 12N 12 fullerenes

The molecular and crystal structures of the boron nitride E-phase are determined. Analysis of all calculated for the first time main peaks of X-ray diffraction patterns (6.28, 3.85, 3.28, 2.72, 2.50, 2.22, 2.09, 1.92 Å) in comparison with experimental ones indicates that E-BN has the diamond-type lattice (the cell constant a = 10.877 Å, the space group Fd3 m or O h 7) formed with T h symmetry B 12N 12 molecules copolymerized by the hexagonal faces. Hence we propose to mean “extradiamond” term instead of “explosion” term in the E-phase name. Extradiamond-B 12N 12 has a framework type of faujasite and can be referred to as [B 12N 12]- FAU zeolite. Ideal crystal of E-BN has 192 atoms per unit cell and theoretical density of 3.074 g/cm 3.

Critical properties of the S4 model on a special diamond-type hierarchical lattice

Using the renormalization-group transformation and cumulative expansion technique, the phase transition and critical properties of the S4 model on a special diamond-type hierarchical lattice are studied, and its fixed points and critical exponents are obtained. The results show that there exists a Wilson-Fisher fixed point besides the Gaussian fixed point, and compared with the Gaussian model of the special diamond-type hierarchical lattices, the critical exponents have changed.

Influence of Temperature on the Coefficient of Thermal Expansion of Monocrystals of Silicon

Using specimens of monocrystalline silicon with strict crystallographic orientation and insignificant (1.5°) off-orientation, we have studied changes in the value (up to 400%) and sign of the coefficient of thermal expansion for the crystallographic directions 〈111〉, 〈110〉, and 〈112〉. Experiments were carried out under conditions of permanent change in the temperature from 32 3 to 1473 K and under normal pressure. We have corroborated that the monomorphism of silicon (Fd3m, i.e., a diamond-type lattice) is retained over the entire temperature range. Specimens of crystallographic direction 〈110〉 are much less subjected to the influence of changes in the temperature than the others.

Critical properties of the model on diamond-type hierarchial lattices

We study the critical properties of the S-4 model on diamond-type hierarchical lattices in the presence of an external magnetic field. It is assumed that for this type of inhomogenous fractal lattice, the Gaussian distribution constant, the four-spins interaction parameter and the external magnetic field in the S4 model depend on the coordination number of the site on the fractal lattices. By combining the real-space renormalization-group scheme with the cumulative expansion method, we obtain the critical points and further calculate critical exponents according to the scaling theory. The results show that on diamond-type hierarchical lattices with branches m > 4 of 2 bonds, the critical point of the S4 model is just the Gaussian fixed point, and therefore critical exponents are in full agreement with those of the Gaussian model, and that on those with m <= 4, the Wilson-Fisher fixed point as well as the Gaussian fixed point is obtained. The Wilson-Fisher fixed point has a decisive influence on the critical behavior of the system, and critical exponents are related to the fractal dimensionality. We found that the S4 model on the fractal lattices and that on the translation symmetric lattices show similar behaviors in the dependence of the critical properties on the dimensionality. (c) 2005 Elsevier B.V. All rights reserved.

Electronic and Optical Properties of SiGe alloys within first-principles schemes

ABSTRACTWe present first-principles calculated electronic and optical properties of some SiGe alloys. The ground-state, electronic excitations and optical properties have been calculated with Ge and Si atoms arranged in different ways among the sites of a diamond-type lattice. For the ground state a DFT-LDA scheme and for the electronic excitations a DFT-GW approach have been respectively used. For the optical properties the DFT-LDA-RPA scheme has been applied for alloys going in composition from Si(100%) to Ge(100%): obtained results have been compared with existing experimental and theoretical data. For the noticeable Si(50%)Ge(50%) alloy also two-particle effects have been evaluated using the Bethe-Salpeter equation.

Preparation, characterization, X-ray crystal structure, and energetics of cesium 5-cyano-1,2,3,4-tetrazolate: Cs[NCCNNNN

Cesium 5-cyano-1,2,3,4-tetrazolate, Cs[NCCNNNN] (Cs1), was prepared in 100% yield by a 3 + 2 cycloaddition reaction of CsN3 and (CN)2 in SO2. Cs1 forms monoclinic crystals (a = 8.297(2) A, b = 11.040(3) A, c = 6.983(2) A, beta = 120.31(2) degrees, space group C2/c, Z = 4, R1 = 0.048, wR2 = 0.120 for 1217 independent reflections). Cs1 is best described as a three-dimensional array of cations and anions connected by weak Cs(+)-N delta- contacts. The cations and anions each form a diamond-type lattice (tetrahedral arrangement of ions) with the counterions lying in hexagonal channels running parallel to the c-axis. The anions in the channels form stacks with the CN groups pointing in opposite directions in adjacent layers. The calculated (RB3PW91/6-311 + G*) geometry of 1 is in agreement with the X-ray crystal structure, and the calculated vibrational spectrum is in good agreement with the observed FT-IR and FT-Raman spectra. The lattice enthalpies and heats of formation of M1 (M = Cs, K) as well as the enthalpy of formation from MN3(s) and (CN)2(g) were estimated. The 13C and 14N NMR spectra of Cs1 are also reported. The ionization potential (450.7 kJ mol) and electron affinity (427.4 kJ/mol) of 1 were calculated. Attempts to oxidize 1 with AsF5 led to the formation of Cs1.xAsF5 (x approximately 2). The 7 pi dianion [NCCNNNN].2- is calculated to be a stable entity in the gas phase, but Cs(2)1 is estimated to be unstable with respect to dissociation to 2 CsCN and 3/2 N2 (delta Hdiss = -132.4 kJ/mol). The preparation of the potassium salt of 1 and the corresponding thermodynamic quantities are reported.

Critical behavior of the Gaussian model on a diamond-type hierarchical lattice with periodic and aperiodic interactions

The critical behavior of the Gaussian models on a diamond-type hierarchical lattice with periodic and aperiodic interactions according to a class of substitution sequences are studied by the exact renormalization-group approach and spin rescaling. For the periodic case with a two-letter general Fibonacci sequence given by the generating substitutions A→AB, B→AB and the aperiodic case with the generating substitutions A→AB, B→BA , the critical behaviors are found unchanged with respect to the uniform case and belong to the same universality of the uniform case. For the other aperiodic case with the generating substitutions A→AB, B→AA , the geometric fluctuation is relevant by Luck's criterion and the critical phenomena of the uniform and periodic cases are found to disappear.

Lattice dynamical Debye-Waller factor for silicon

The mean-square amplitude of vibration of silicon at 293 K has been determined by a lattice-dynamical procedure. A Born\char21{}von K\'arm\'an model has been used to fit phonon dispersion data from inelastic neutron-scattering measurements. The force-constant model included the first six nearest neighbors in the diamond-type lattice. The least-squares results from the fitting of the force constants were used to carry out variance analyses of properties dependent on the harmonic model. The density of phonon states was determined by sampling an even mesh of 5.7 billion points in the unique part of the Brillouin zone. Moments of the frequency distribution up to eighth order are tabulated. The frequency distribution function was used to calculate a $〈{u}_{\mathrm{LD}}^{2}〉$ for silicon. The result is $0.005941\ifmmode\pm\else\textpm\fi{}0.000021{\AA{}}^{2}.$ An Einstein-type potential of Dawson and Willis was used to extract an anharmonic force constant from the temperature dependence of neutron-diffraction measurements of silicon carried out by Batterman and co-workers. These measurements were restricted to the weak reflections from the (222), (442), and (622) diffracting planes. With the use of the lattice-dynamical value for the vibrational amplitude of silicon the result for the ${\ensuremath{\beta}}_{\mathrm{DW}}$ anharmonic constant is $18.58\ifmmode\pm\else\textpm\fi{}0.27{\mathrm{N}\mathrm{}\mathrm{m}}^{\mathrm{\ensuremath{-}}1}{\AA{}}^{\ensuremath{-}1}.$

Calculation of Spectral Dimension on Inhomogeneous Fractal Lattices**The project supported in part by the Nonlinear Science Project of China and the State Education Committee Grant for Doctor Study

We propose a scheme to derive the spectral dimension of inhomogeneous fractal lattice via renormalization procedure, in which the distribution of masses on the sites of fractals is introduced. The spectral dimension of diamond-type hierarchical lattice and Sierpinski gasket with are re-investigated in this way. Moreover, the variants of Sierpinski gasket-type fractals are studied, the results show that the spectral dimension is independent of the details of internal structure of fractal, and thus implies the existence of universality. The source of the universality is also analyzed.

Additional Long-Range Interactions on Diamond-Type Hierarchical Lattices11The project supported in part by the Nonlinear Science Project of China and the National Natural Science Foundation of China

The Ising model with additional next-nearest neighbour (n.n.n.) interactions in generator of diamond-type hierarchical lattice is studied. It is found that phase transition occurs only when the nearest neighbour (n.n.) interaction and n.n.n. interaction fulfils a certain relation and the universal class of phase transition is not changed by the long-range interactions.

Monte-Carlo studies of energy characteristics of carbon plasma fluxes at deposition of diamond-like films

Using the simulation by the Monte-Carlo method, the distribution of carbon plasma particles over the energies of their arrival at the substrate in the deposition of diamond-like films by the are evaporation of graphite in vacuum has been investigated. The conditions of separation of fluxes according to the particle energies have been established and the optimum substrate potential for the production of films with a diamond-type lattice has been found. A high-quality separation of fluxes necessitates their preliminary acceleration with the aid of the additional anode with a −10 V potential, placed between the cathode and the separator. The optimum substrate potential is at −18 V with a permissible drift±3V.

The theory of structural transitions in microsegregated systems with spherical domains

The possibility of a structural transition between different types of spatial packing of spherical domains is considered. It is supposed that the domains are formed in diblock copolymers with strongly incompatible blocks. With an increase in the parameter α = χN a (where χ is a parameter that characterizes the repulsion between opposite blocks and N a is the number of links in an A-block) any given spatial structure loses its stability; a simple cubic lattice of micelles will transform into a face-centred cubic lattice and a body-centred cubic lattice will transform into a diamond-type lattice. The transition occurs while the number of chains forming the domains remains constant.

Calculations of the free conformation energy of a polymer chain on a diamond-type lattice within wide ranges of chain lengths, elongations and temperatures

A method is proposed for calculating the partition function Z( r) of a chain on a diamond-type lattice on the basis of the Monte Carlo algorithm for simulating a chain ‘from point to point’ with allowance made for the statistical weight factor of the conformation. The free energy is calculated for chains with the parameters of polyethylene, polytetrafluoroethylene, polyoxymethylene and poly(ethylene oxide), within a wide range of elongations for various chain lengths and temperatures. Allowance is made for the effect of the limiting planes on the free energy, which is characteristic for chains in amorphous regions of semicrystalline polymers. The accuracy of the proposed method is shown to rise with increasing elongations and decreasing chain lengths. A simple analytical approximation of the free chain energy is proposed for all the polymers examined.

Nonlocal dipole model for the phonon dispersion in diamond-type lattices.

We present a potential model for diamond-structure crystals where the interatomic forces are split into a long-range part described by dipole forces and a residual short-range interaction treated within a customary force-constant model. The dipole forces arise from nonlocal dipole moments induced on an atom by the displacements of the atom itself and of its nearest neighbors. This nonlocality enables us to satisfy infinitesimal translational invariance explicitly. Within this model we calculate the bulk-phonon dispersion for diamond, silicon, germanium, and gray tin by fitting the two dipole parameters and the six force constants to the experimental data, obtaining a very good agreement. For silicon we present two additional models employing only six or five parameters, respectively, which show that the dipole forces represent the main contribution to the long-range interactions. Finally, we point out the main advantage of our model, that it allows for a physical interpretation of the dipole parameters, in contrast to many other phenomenological models. Thus, it can be applied to more complicated problems such as defect or anharmonic calculations in a comparatively easy manner without losing too much physical significance.