Energy Considerations for Parabolic Cyclides in SmA Liquid Crystals

The fully harmonic lattice approximation derived in a previous paper is used to calculate the elastic interaction energies in the niobium-hydrogen system. The permanent-direct, permanent-indirect, induced-direct, and induced-indirect forces calculated previously each give rise to a corresponding elastic interaction between hydrogen atoms. The latter three interactions have three- and four-body terms in addition to the usual two-body terms. These quantities are calculated and compared with the corresponding two-body permanent elastic interactions obtained in the harmonic-approximation treatment of Horner and Wagner. The results show that the total induced elastic energy is approximately (1/3) the size of the total permanent elastic energy and opposite to it in sign. The total elastic energy due to three-body interactions is approximately (1/4) the size of the total two-body elastic energy, while the total four-body elastic energy is approximately 5% of the total two-body energy. These additional elastic energies are expected to have a profound effect on the thermodynamic and phase-change behavior of a metal hydride.

Smectic-A nucleating in the isotropic phase presents various bulk focal conic defects close to the interface, within the “bâtonnets” first described by Friedel and Grandjean in 1910. We experimentally study the stability of the “bâtonnets” in a high-frequency aligning electrical field. Although the external shape appears out-of-equilibrium, the focal conic texture is found stable. We build a model explaining the general interfacial focal conic texture : it participates in the minimization of the interfacial energy by orienting the smectic layers almost perpendicular to the interface, above a critical size ℓ0 comparing layer curvature and surface energies. This model explains new arborescent textures that we observe inside capillary tubes. We then discuss equilibrium shapes of size ∼L. We discuss three regimes : L ≪ℓ0 yields 3D-cristal-like “Wulf” shapes. For L > ℓ0, equilibrium shapes must contains focal conics, although we cannot solve the general solution. In the asymptotic limit L ↦∞, we predict fractal textures of dimension 1 < d < 2 inside “optimal” configurations, spherical as for 3D-liquids. Finally focal conics can be considered as “bulk facets” which pile up to decorate “bâtonnet” and more general interfacial textures. Focal conics appear then an intrinsic defects of Smectic-A materials in contact with their isotropic phase.

By using Eshelby’s method for the determination of the stresses and strains generated in a transformation, the shape and orientation of an ellipsoidal region of transformed phase that minimizes the elastic strain energy accompanying the transformation are calculated together with the change in elastic strain energy. The orientation of minimum total energy describes the habit plane. The applicability of the approach is demonstrated by showing that the habit planes of twins in cubic crystals, and martensitic plates in In-20 pct TI and Fe-31 pct Ni, which have been calculated by other methods, can alternatively be determined by this method. It is then used to calculate that the habit plane for martensitic plates in bulk, high density, oriented orthorhombic polyethylene should be (4.67,1,0) orthorhombic. As a consequence of these calculations it is shown that minimization of the total elastic strain energy must be the dominating factor in the nucleation event of transformed products in most metals.

Universal theorems for total energy of the dynamics of linearly elastic heterogeneous solids

Focal conics consisting of an ellipse and a hyperbola in chiral smectic C liquid crystals aligned in surface‐stabilized cells of medium thickness (about 25 µm cell gap) were characterized in relation to the chevron structure by synchrotron X‐ray microdiffraction. The focal conic texture is embedded in the chevron structure with a relatively sharp interface. The deformed layer of the focal conics is a kinked bookshelf consisting of a few slightly bent segments for small focal conics, whereas it is a bookshelf layer for large focal conics. Around the focus of the ellipse toward the hyperbola, a complicated layer structure appears, although the core region of small layer curvature has been hardly observed within the present experimental sensitivity. The broad and narrow walls of a zigzag defect in the same cell are analyzed for comparison.

Reorientation of planets with lithospheres: The effect of elastic energy

An energy balance in crack propagation and arrest

It is commonly known that the magnetostriction of grain oriented silicon steel for electric transformers, is strongly influenced by applied stress on the steel as well as coating stress of the steel and is dominated exclusively by the formation of 90/spl deg/ domain walls. A new concept on a condition for the formation of 90/spl deg/ domain wall considers the total elastic energy which consists of both strain elastic energy and magnetoelastic energy in axes of easy magnetization of Goss texture {110} <001>. It is proposed that 90/spl deg/ domain wall is formed under the condition that the total elastic energies in the three easy axes of magnetization are related by the expression Ex([100])<Ey([010]), Ez([001]). This was confirmed by electron microscopy, and calculated in various stress conditions including applied stress to a specimen and coating stress as well. The calculation by this new assumption could satisfactorily explain not only previous magnetostriction results by many researchers in silicon steel, such as the harmful effect of compressive applied stress on magnetostriction which is reduced by higher coating stress, but also an excellent study of magnetostriction under sophisticated complex superimposed longitudinal and transverse stress reported by Moses et al. as well as their study in coating removal and on the effects of increased temperature. In the new concept, strain elastic energy is dominant in the total elastic energy, which results in good agreement with past data on the influence of stress on magnetostriction even under sophisticated complex stress conditions and coating stress as well.<<ETX>>

The method of thermomigration of liquid zones based on aluminum makes it possible to create complex structures of closed channels with boundaries formed from p-n junctions in single-crystal silicon wafers. The channels are characterized by the uniformity of their properties, and the pn junctions are characterized by their sharpness. Such structures are used in high-current electronics, photovoltaics, and microelectromechanical converters. Volumetric deformation inside and outside the channel due to alloying of silicon with aluminum leads to the formation of mechanical stresses. The equilibrium shape of the channels formed at high temperatures is determined by the minimum elastic energy and depends on the material parameters and geometry of the structure. Within the framework of the linear theory of elasticity, the behavior of elastic energy during the formation of the structure of thermomigration channels at high temperatures doped with aluminum in a single-crystalline (001) cut disk was studied. The simulation was performed using the finite element method in the COMSOL Multiphysics mathematical package. The study was carried out for practically important structures in which the direction of the edges is oriented along the diagonal of the square. Only such structures do not have breaks during the process of thermomigration. Based on the calculation results, it was revealed that the minimum elastic energy corresponds to structures with different crystalline orientations inside the channel and outside it – in the main silicon matrix. The direction of the crystalline axes inside the channel, corresponding to the minimum elastic energy, is rotated by 45 degrees in the plane of the disk relative to the direction of the axes of the main matrix of the silicon crystal. In addition, calculations showed that with such a turn, the shape of the channels changes. The minimum elastic energy corresponds not to vertical structures, but to inclined ones. The angle of inclination of the pyramids depends on the width of the channels and the distance between them.

Damage characteristics and energy-dissipation mechanism of frozen–thawed sandstone subjected to loading

Crystallography and elastic energy analysis of VN precipitates in Fe–Mn–Si–Cr shape memory alloys

Nowadays, more and more unmanned aerial vehicles are used in the logistics industry. Yet these delivery drones are heavy, needing to be charged very often and can’t transport many packages. We hope to solve these issues by reducing the weight of wings and slightly increasing the size of the drone by using elastic transportation network based on energy optimization. This would help extend the work time of these drones and allowing for maximum transportation amount. We first figured out the total elastic potential energy of the wings and the gravity potential energy. Then we minimized the total energy to find the best geometric value (radius of each pipelines within the wings). Next simulated on MATLAB, wings were built according to the pipeline wing radius and the total energy result was updated continuously to constantly minimize the energy with a more ideal pipeline radiuses. We expect a final pipeline elastic structure similar to that of a dragonfly’s wing with minimum total energy that will significantly help reduce the weight of large drone wings. This project will help design significantly lighter wings of drones based on elastic transportation network mainly through MATLAB simulations. Drones can then be expanded in size to transport more products and fly for longer periods.

We perform analysis of several key aspects of the extended defect formation and their impact on silicon and GaN transistors. Heterogeneous epitaxy has been an enabling technique in transistor design since 90 nm technology node. The most widely used stress engineering technique is based on introducing crystal lattice mismatch stress by growing SiGe on Si. Depending on Ge content and on the size and shape of the selectively grown SiGe islands, the lattice mismatch stress can be high enough to introduce edge dislocations and stacking faults. Once the dislocations are created, they can move, driven by stress gradients towards more energetically favorable locations. An example of creating geometrical features to attract dislocations towards certain area has been demonstrated experimentally for epitaxial SiGe layers exceeding critical thickness on non-planar Si surfaces [1]. We reproduce such behavior by numerical minimization of elastic strain energy of an ensemble of {111} stacking faults (Fig. 1). Whenever dislocations manage to escape such herding and encroach into sensitive transistor areas, we perform quantum transport analysis to estimate the impact of a dislocation on electron scattering, on-state and off-state currents for Si nanowires with 5nm design rules. Another area where extended defect monitoring is essential is the GaN power switches. To achieve low buffer leakage in AlGaN/GaN HEMT for high voltage applications, it has been proposed to intentionally dope the GaN buffer with carbon [2]. This creates acceptor traps in the buffer to pin the Fermi Level at ~0.86 eV above the valence band [3]. A p-type buffer is thus formed and isolated from the Two-Dimensional Electron Gas (2DEG), which aggravates current collapse [3][4]. However, experimental results show that the magnitude of current collapse is less than suggested by modeling which can be attributed to the buffer being connected to the 2DEG through threading dislocations [3]. In this work, we perform 3D TCAD analysis of the impact of threading dislocations on the buffer trapping/de-trapping and current collapse. [1] R. Gatti, F. Boioli, M. Grydlik, M. Brehm, H. Groiss et al., Appl. Phys. Lett., 98, 121908 (2011) [2] E. Bahat-Treidel, F. Brunner, O. Hilt et al., IEEE Trans. Electron Devices, 57(11), 3050–3058 (2010) [3] M. J. Uren, M. Silvestri, M. Cäsar, G. A. M. Hurkx, J. A. Croon, J. Šonský, and M. Kuball, IEEE Electron Device Lett. 35(3), 327–329 (2014) [4] M. J. Uren, J. Möreke, and M. Kuball, IEEE Trans. Electron Devices 59 (12), 3327–3333 (2012) Fig. 1. Dislocations in epitaxial SiGe layer move towards the bottom of a V-shaped trench in Si wafer (a). Each additional dislocation reduces the total elastic strain energy of the structure (b). Figure 1

Energy evolution of brittle granite under different loading rates

The growth process of isolated focal conics is investigated under orthogonal electric and magnetic fields. It is found that isolated focal conics elongate parallel to the magnetic field. This results in the monodomain of densely packed focal conics having the helical axis perpendicular to the orthogonal fields.