Finite Displacement Research Articles

Electronic, Thermal, and Thermoelectric Transport Properties of ε-Ga2O3 from First Principles.

The electronic, thermal, and thermoelectric transport properties of ε-Ga2O3 have been obtained from first-principles calculation. The band structure and electron effective mass tensor of ε-Ga2O3 were investigated by density functional theory. The Born effective charge and dielectric tensor were calculated by density perturbation functional theory. The thermal properties, including the heat capacity, thermal expansion coefficient, bulk modulus, and mode Grüneisen parameters, were obtained using the finite displacement method together with the quasi-harmonic approximation. The results for the relationship between the Seebeck coefficient and the temperature and carrier concentration of ε-Ga2O3 are presented according to the ab initio band energies and maximally localized Wannier function. When the carrier concentration of ε-Ga2O3 increases, the electrical conductivity increases but the Seebeck coefficient decreases. However, the figure of merit of thermoelectric application can still increase with the carrier concentration.

First-principles phonon calculations for lattice dynamics, thermal expansion and lattice thermal conductivity of CoSi in the high temperature region

This study presents the first-principles phonon calculations to understand the experimental thermal expansion () and lattice thermal conductivity of CoSi in the high temperature region. Phonon dispersion is computed using the finite displacement method and supercell approach by taking the equilibrium crystal structures obtained from DFT. The calculation of is done under quasi-harmonic approximation. The is calculated using first-principle anharmonic lattice dynamics calculations under single-mode relaxation time approximation. The calculated in the temperature range 0–1300 K gives a good match with existing experimental data. The calculated value of (∼8.0 W/mK) at 300 K is found to be in good agreement with the experimental value of ∼8.3 W/mK. The temperature dependence of phonon lifetime due to phonon-phonon interaction is calculated to understand the behaviour of . The present study suggests that ground state phonon dispersion obtained from DFT-based methods gives reasonably good explanation of experimental and .

Effect of Nonequilibrium Transient Electronic Structures on Lattice Stability in Metals: Density Functional Theory Calculations

The electronic structures of metals undergo transient nonequilibrium states during the photoexcitation process caused by isochoric heating of X-ray free-electron laser, and their lattice stability is, thus, significantly affected. By going beyond frozen core approximation, we manually introduced nonequilibrium electron distribution function in finite-temperature density functional theory with the framework of Kohn–Sham–Mermin to investigate such transient states, and their effect on lattice stability in metals is demonstrated by phonon dispersion calculated using the finite displacement method. We found that the perfect lattice of a metal collapses due to the exotic electronic structure of nonequilibrium transient state created by isochoric heating of X-ray free-electron laser. Further increase of the number of holes created in the sample (i.e., an increase of laser fluence) still results in lattice instability for aluminum, while for copper, it results in phonon hardening. The potential energy surface is calculated for the extreme case of both Al and Cu with exactly one hole created in its inner shell for each one of the atoms. A double-well structure is clearly observed for Al, while the potential energy surface becomes steeper for Cu.

Finite displacement screw-based group analysis of 3PRS parallel mechanisms

When limbs of a parallel mechanism have been selected, the geometric relation among limbs determines the mechanism's motion. The limb arrangement which affects the mechanism's motion raises a fundamental and significant issue. If a mechanism only owns limbs with Lie group motions, it is convenient to predict how a limb arrangement determines the mechanism's motion. However, if a mechanism is mainly or purely constituted by limbs with motions of general differential manifolds, it is difficult to find the influence of a limb arrangement. On this regard, this paper provides an in-depth investigation by focusing on motion analysis of parallel mechanisms consisting of three PRS limbs with planar-spherical manifolds. By formulating and comparing the motion characteristics of these mechanisms which though could be modeled difficultly by a mathematical tool without using the finite displacement screw, a finite displacement screw-based group method is proposed in this paper to resolve the raised issue. The novel approach presents results in expressions of new types of manifold motions, providing a foundation for design and application of parallel mechanisms having the various three-planar-spherical manifolds’ intersection motions.

Spin-Polarized Nematic Order, Quantum Valley Hall States, and Field-Tunable Topological Transitions in Twisted Multilayer Graphene Systems.

We theoretically study the correlated insulator states, quantum anomalous Hall (QAH) states, and field-induced topological transitions between different correlated states in twisted multilayer graphene systems. Taking twisted bilayer-monolayer graphene and twisted double-bilayer graphene as examples, we show that both systems stay in spin-polarized, C_{3z}-broken insulator states with zero Chern number at 1/2 filling of the flat bands under finite displacement fields. In some cases these spin-polarized, nematic insulator states are in the quantum valley Hall (QVH) phase by virtue of the nontrivial band topology of the systems. The spin-polarized insulator state is quasidegenerate with the valley polarized state if only the dominant intravalley Coulomb interaction is included. Such quasidegeneracy can be split by atomic on-site interactions such that the spin-polarized, nematic state become the unique ground state. Such a scenario applies to various twisted multilayer graphene systems at 1/2 filling, thus can be considered as a universal mechanism. Moreover, under vertical magnetic fields, the orbital Zeeman splittings and the field-induced change of charge density in twisted multilayer graphene systems would compete with the atomic Hubbard interactions, which can drive transitions from spin-polarized zero-Chern-number states to valley-polarized QAH states with small onset magnetic fields.

First-principles study of stability and electronic properties of single-element 2D materials

We have estimated stability of single-element 2D materials (C2, N2, Si2, P2, Ge2, As2, Sn2, Sb2, Pb2, and Bi2) by ab initio calculations. The calculations of structural and mechanical properties of 2D materials were performed using the VASP software package. The results of calculations of stiffness tensors, Young's modulus, and Poisson's ratios show that all studied single-element 2D materials are mechanically stable. Dynamic stability was investigated by calculating the phonon dispersion of the materials using the finite displacement method. Only Pb2 has imaginary modes in the phonon dispersion curves and therefore it has dynamic unstable structure at low temperatures. The analysis of the band structures indicates the presence of insulators (N2), semiconductors (P2, As2, Bi2, Sb2), semimetals, and metals among the studied group of single-element 2D materials.

The effect of finite element division and incremental displacement size on the inelastic analysis results of the composite beam

The authors have developed a finite element analysis (FEA) program based on an explicit method, including a modified incremental technique. Moreover, it has been modified to consider the elasto-plastic (EP) behavior of refractories in the compression stress-strain curve. Firstly, this paper verifies its validity through EP analysis of the steel beam with similar mechanical properties to the bottom steel plate of the composite beam. Secondly, we show the results of FE analysis by considering the materially non-linearity of the composite beam. Finally, we indicate that the effect of finite element division and incremental displacement size on the inelastic analysis results of the composite beam consisted of refractory and steel plate subject to bending load.

On blocks detection in unilateral masonry-like structures: a rigid-elastic displacement approach

In the present paper, a rigid block model for detection and identification of the cracks' pattern in a masonry-like structure subjected to dead loads and finite displacements is presented. The equilibrium problem is formulated by means of a suitable variational formulation for the boundary value problem of normal elastic no-tension material. Specifically, static equilibrium states of masonry-like structures are obtained through the linear conic optimisation of total potential energy. The independent variables of the optimisation problem are elastic strains and displacements, both assumed to be continuous. Indeed, the displacement and the strain fields are described in terms of nodal values through a FEM-like formulation and both of them are treated as independent variables of the optimisation problem. The study provides the basis for future developments in the field of mechanics and mechanisms of fracture. Two simple case studies are also discussed in order to tap the promising potential of the proposed approach.

Phonon Simulations and Its Applications

Computation of phonons using first principles has many applications for understanding crystal properties. This review provides an overview of the present capabilities of such simulations using finite displacement supercell approach.

Light-control of materials via nonlinear phononics

Nonlinear phononics is the phenomenon in which a coherent dynamics in a material along a set of phonons is launched after its infrared-active phonons are selectively excited using external light pulses. The microscopic mechanism underlying this phenomenon is the nonlinear coupling of the pumped infrared-active mode to other phonon modes present in a material. Nonlinear phonon couplings can cause finite time-averaged atomic displacements with or without broken crystal symmetries depending on the order, magnitude and sign of the nonlinearities. Such coherent lattice displacements along phonon coordinates can be used to control the physical properties of materials and even induce transient phases with lower symmetries. Light-control of materials via nonlinear phononics has become a practical reality due to the availability of intense mid-infrared lasers that can drive large-amplitude oscillations of the infrared-active phonons of materials. Mid-infrared pump induced insulator–metal transitions and spin and orbital order melting have been observed in pump–probe experiments. First principles based microscopic theory of nonlinear phononics has been developed, and it has been used to better understand how the lattice evolves after a mid-infrared pump excitation of infrared-active phonons. This theory has been used to predict light-induced switching of ferroelectric polarization as well as ferroelectricity in paraelectrics and ferromagnetism in antiferromagnets, which have been partially confirmed in recent experiments. This review summarizes the experimental and theoretical developments within this emerging field.

Finite deformation of a random array of rigid spheres in an elastic matrix at high concentration

We consider some modifications to the linear elastic deformation of an array of rigid spheres in an elastic medium to include an affine but finite displacement of the sphere, up to but not including elastic contact stresses between them. The subsequent and constitutive problem involves the load transfer problems between the spheres and illustrates the linkages between the microstructures and the macro-finite deformation stress incurred at the macro-level. The results represent a new class of finite deformation brought about by an array of rigid spheres in an otherwise perfectly elastic matrix.

Vibration Control of a Two-Link Flexible Robot Arm with Time Delay through the Robust Receptance Method

This paper proposes a method for active vibration control to a two-link flexible robot arm in the presence of time delay, by means of robust pole placement. The issue is of practical and theoretical interest as time delay in vibration control can cause instability if not properly taken into account in the controller design. The controller design is performed through the receptance method to exactly assign a pair of pole and to achieve a given stability margin for ensuring robustness to uncertainty. The desired stability margin is achieved by solving an optimization problem based on the Nyquist stability criterion. The method is applied on a laboratory testbed that mimic a typical flexible robotic system employed for pick-and-place applications. The linearization assumption about an equilibrium configuration leads to the identification of the local receptances, holding for infinitesimal displacements about it, and hence applying the proposed control design technique. Nonlinear terms, due to the finite displacements, uncertainty, disturbances, and the coarse encoder quantization, are effectively handled by embedding the robustness requirement into the design. The experimental results, and the consistence with the numerical expectations, demonstrate the method effectiveness and ease of application.

Insertion and diffusion of N and C in [formula omitted]–TiAl: Theoretical study and comparison with O

Nitrogen and carbon play an important role in the oxidation of Ti-Al intermetallic alloys in air. The insertion and diffusion of these elements in the γ-TiAl phase are investigated by first-principle computations. The accommodation of C and N atoms in several likely interstitial positions has been evaluated using density functional theory (DFT) calculations. The results show that both carbon and nitrogen prefer Ti-rich environments. Then, considering the possible jumps among the stable and metastable interstitial sites, the diffusion coefficients have also been obtained from ab initio calculations. According to the Transitional State Theory, in order to compute atomic jump rates, diffusion energy barriers and vibrational modes need to be known. Herein, barrier energies are obtained using the Climbing Image Nudged Elastic Band method. Vibrational properties are computed using the finite displacement method. Finally, diffusion coefficients are obtained solving the transport equation in the infinite time limit, using an analytical approach. The obtained results are compared to the diffusion of oxygen in γ-TiAl, investigated in previous studies. An anisotropic diffusion is obtained for all the interstitial species.

Study on CO2 foam fracturing model and fracture propagation simulation

CO2 foam fracturing fluid has the advantages of water saving and environmental protection, which has been widely used in unconventional oil and gas reservoir. However, there are still many technical difficulties in fracture propagation model and numerical calculation method of CO2 foam fracturing. In this paper, a CO2 foam fracturing fracture propagation model with temperature-pressure-phase coupling is established. Physical parameters of CO2 are calculated by Span-Wagner method, and the finite difference and displacement discontinuity methods are used to solve the model. Moreover, we compare the results of this model with the field measured data, KGD model and EFRAC-3D model to verify the model. The computation results show that in the process of fracturing, improving the CO2 foam quality can significantly enhance the fracturing effect. When the quality increased from 0.5 to 0.8, the fracture width raised by more than 2 times. In addition, the fracture propagation is significantly affected by injection temperature. With the increase of injection temperature, fracture width decreases continuously, and if the CO2 foam is supercritical phase state, it is not conducive to increase the fracture width.

Geometrical nonlinearities and shape effects in electromechanical models of piezoelectric bridge structures

We consider nonlinear shape effects appearing in the lumped electromechanical model of a bimorph piezoelectric bridge structure due to the interaction between the electromechanical constitutive model and the geometry of the structure. At finite proof-mass displacement and electrode voltage, the shape of the beams is no longer given by Euler-Bernoulli theory which implies that shape effects enter in both the electrical and mechanical domains and in the coupling between them. Accounting for such effects is important for the accurate modelling of, e.g., piezoelectrical energy harvesters and actuators in the regime of large deflections and voltages. We present a general method, based on a variational approach minimizing the Gibbs enthalpy of the system, for computing corrections to the nominal shape function and the associated corrections to the lumped model. The lowest order correction is derived explicitly and is shown to produce significant improvements in model accuracy, both in terms of the Gibbs enthalpy and the shape function itself, over a large range of displacements and voltages. Furthermore, we validate the theoretical model using large deflection finite element simulations of the bridge structure and conclude that the lowest order correction substantially improve the model, obtaining a level of accuracy expected to be sufficient for most applications. Finally, we derive the equations of motion for the lowest order corrected model and show how the coupling between the electromechanical properties and the geometry of the bridge structure introduces nonlinear interaction terms.

АНИЗОТРОПИЯ РАДИАЛЬНОЙ ЖЕСТКОСТИ РАСТОЧКИ КОРПУСА ПОД ОПОРЫ ШПИНДЕЛЯ ТОКАРНОГО СТАНКА

In the paper there are considered problems connected with the radial stiffness anisotropy of body borings for lathe spindle bearings. Factors having an influence upon stability of its operation characteristics of a machine-tool during idling are considered. 
 The analysis of force factors having an influence upon bearings of a spindle unit during lathe idling is carried out. The work purpose is to determine a quantitative and qualitative situation in the changes of boring forms for spindle bearings under the impact of loads mentioned. As an object of investigations there is chosen the lathe “Vector” manufactured at the Middle-Volga machine-tool plant. A finite element modeling is carried out for deformation investigations in the body boring of the spindle unit under the impact of forces caused by weight and imbalance of the rotating spindle. There is shown a geometrical model of a spindle carrier body, the peculiarities of a finite element model formation and a procedure for the fulfillment of a numerical experiment are described, and approaches of boundary conditions setting are also considered. As a result of a finite element there are obtained values of finite element unit displacements lying on the surface of the body boring of the spindle carrier under the impact of the mentioned power factors. The results found are presented for illustration in the form of solid and flat graphical dependences. The analysis of numerical experiment results has confirmed the presence of the stiffness anisotropy in spindle unit bearings. The phenomenon of stiffness anisotropy in bearings was already under consideration in investigations carried out earlier. But the results of the numerical experiments carried out by us have shown that along with other factors the imbalance forces together with design peculiarities of body parts have an influence upon the constancy of elastic characteristics of bearings. 
 The matter obtained can be used during development of measures for design changes in a spindle unit body with the purpose of stiffness anisotropy decrease in the borings for bearing.

Displacement Analyses for a Natural Slope Considering Post-Peak Strength of Soils

A natural slope undergoing recurrent movements caused by rainfall-induced groundwater table rises is studied using a novel method. The strength and displacement parameters are back-calculated using a force-equilibrium-based finite displacement method (FFDM) based on the first event of slope movement recorded in the monitoring period. Slope displacements in response to subsequent rainfall-induced groundwater table rises are predicted using FFDM based on the back-calculated material parameters. Important factors that may influence the accuracy of slope displacement predictions, namely, the curvature of the Mohr-Coulomb (M-C) failure envelope and post-peak strength softening, are investigated. It is found that the accuracy of slope displacement predictions can be improved by taking into account post-peak stress-displacement relationship in the analysis. The accuracy of slope displacement predictions is not influenced by the curvature of the M-C failure envelope in the displacement analysis.

Computational Amperometry of Nanoscale Capacitors in Molecular Simulations.

In recent years, constant applied potential molecular dynamics has allowed researchers to study the structure and dynamics of the electrochemical double-layer of a large variety of nanoscale capacitors. Nevertheless, it has remained impossible to simulate polarized electrodes at fixed total charge. Here, we show that combining a constant potential electrode with a finite electric displacement fills this gap by allowing us to simulate open-circuit conditions. The method can be extended by applying an electric displacement ramp to perform computational amperometry experiments at different current intensities. As in experiments, the full capacitance of the system is obtained at low intensity, but this quantity decreases when the applied ramp becomes too fast with respect to the microscopic dynamics of the liquid.

Piezoelectricity in monolayer BxCyNz structures: A first principles study

A new family of layered two-dimensional materials, borocarbonitrides (BxCyNz), is derived from the graphene and h-BN structures. Although there is quite a lot of studies about the synthesis, characterization, electronic and structural properties of BxCyNz structures, there is a lack of information about their piezoelectric capabilities in the literature. First, twenty different BxCyNz formations were taken into consideration and the structures with space group symmetry that could show piezoelectricity were determined among them. Then, density functional theory based theoretical calculations were used to investigate the electronic, elastic, and piezoelectric properties of these materials. Dynamical stability of these materials were investigated via phonon calculations. To compare the effect of the selected method and the functional on piezoelectric stress and strain coefficients, LDA and PBE functionals were used crosswise via finite displacement (FD) and density functional perturbation theory (DFPT) methods. DFPT calculations in which PBE and LDA were used showed that e11 and e12 piezoelectric stress coefficient results do not affected by the selected function. Although, FD calculations for e12 values give close results to DFPT methods, e11 values calculated via this method differs from the other two by %10–30. It was observed that BxCyNz structures are promising piezoelectric materials which their piezoelectricity can be tuned by changing x, y, and z ratios and atomic conformations. The effect of atomic bonding types on the piezoelectric properties of these materials were revealed. The lowest e11 and e12 piezoelectric coefficients calculated for the BCN2 structure, which has an undesired N-N bond. The highest relaxed-ion e11 values were calculated for BC2N structures,5 × 10−10 C/m. B2CN structure gives the highest relaxed-ion e12 value 5.5 × 10−10 C/m. B3C2N3 formations give close results to each other for e11 and e12 values around 4.5 × 10−10 C/m. Our calculations reveal that BxCyNz structures are strong candidates for future atomically thin piezoelectric applications.

Wrist singularity avoidance with a robot end-effector adding an oblique, redundant axis

Novel high-order procedures follow finite displacements avoiding the adverse effects of the wrist singularity of a serial robot manipulating a curved tool. In robotic welding, this type of end effector is commonly applied to right-angle seams. This tool is symmetric about a line emanating from its tip, which adds an effective revolute-joint axis line to the robot. The curve in the tool places this axis line oblique to the third joint in the robot wrist. When the second wrist axis is out of the plane containing the third joint and tool axes, the tool axis supplies useful kinematic redundancy for mitigating the loss of mobility in a 3-axis wrist on approach to its singularity. A new method plans a path encountering the wrist singularity while satisfying limits on joint rate and acceleration under a constant rate of tool traversal. This method maintains precise position of the tool tip with the seam while allowing rotation of the tool about its symmetry axis. This is accomplished with either zero or nearly zero deviation in pointing direction.