Elastic behavior of a screw dislocation in the wall of a hollow nanotube

The elastic behavior of a screw dislocation lying in the wall of a hollow cylindrical nanotube is studied theoretically. The corresponding boundary-value problem of the classical theory of elasticity is formulated and solved (for stresses) for a linear elastically isotropic or transversely isotropic body. The elastic energy of the nanotube with the dislocation and the image force exerted on this dislocation by the inner and outer nanotube surfaces are calculated. The internal space of the nanotube is shown to cause the following qualitative differences in the dislocation stress-field distribution: a change in the sign of stress-tensor components near the inner nanotube surface, a high stress concentration at this surface, and a strong stress gradient at this surface. The dislocation has only one position of unstable equilibrium in the nanotube wall, which is always shifted toward the inner nanotube surface. As the internal-space radius increases, the dislocation energy decreases and the position of its equilibrium shifts toward the outer nanotube surface; in the limiting case of a flat plate, it reaches the center of the plate. Near the nanotube free surfaces, the image force on the dislocation is large and can substantially affect the dislocation behavior.     

Extensivity and the Gibbs-Duhem equation

It is shown that the Gibbs-Duhem equation does not remain valid for system having inhomogeneous entropies. Some consequences of this are discussed, as are the generalised Gibbs-Duhem equations introduced in Weinhold's metric geometry of equilibrium thermodynamics.     

Phase stabilities of fcc Ti nanocrystals

A model for the equilibrium transition size and temperature between hcp and fcc structure of nanocrystals Ti has been established in terms of the effect of surface stress on the internal pressure of nanocrystals. It was found that as size and temperature decreased, the relative stability of fcc structure in comparison with hcp structure increased. The obtained result is consistent with other theoretical and experimental data.     

Stress anisotropy in liquid crystalline phases

Monte Carlo simulations of bulk liquid crystals in the isotropic, nematic and smectic phases were performed. The simulations were carried out using different box shapes. The diagonal components of the pressure tensor were calculated to verify that the system is in mechanical equilibrium. For simulations in cubic boxes it was found that the three components of the pressure tensor had the same values in the isotropic and nematic phases but they were different in the smectic phase, i.e. the system seemed to be under anisotropic stress. NVT and NPT simulations in the smectic phase were performed by allowing the box sides to fluctuate independently; in this case, the average diagonal components of the pressure tensor had the same value. Inaccurate calculation of the total pressure produces incorrect equilibrium boundaries in the phase diagram. Microphases and poorly defined layering can be found in simulations of smectic phases when they are performed on cubic boxes. Although the pressure anisotropy is relaxed out, the layering structure in smectic phases seems to depend on the initial configuration, regardless of the simulation method.     

High-pressure crystal structure of elastically isotropic CaTiO3 perovskite under hydrostatic and non-hydrostatic conditions

The structural evolution of orthorhombic CaTiO3 perovskite has been studied using high-pressure single-crystal x-ray diffraction under hydrostatic conditions up to 8.1 GPa and under a non-hydrostatic stress field formed in a diamond anvil cell (DAC) up to 4.7 GPa. Under hydrostatic conditions, the TiO6 octahedra become more tilted and distorted with increasing pressure, similar to other 2:4 perovskites. Under non-hydrostatic conditions, the experiments do not show any apparent difference in the internal structural variation from hydrostatic conditions and no additional tilts and distortions in the TiO6 octahedra are observed, even though the lattice itself becomes distorted due to the non-hydrostatic stress. The similarity between the hydrostatic and non-hydrostatic cases can be ascribed to the fact that CaTiO3 perovskite is nearly elastically isotropic and, as a consequence, its deviatoric unit-cell volume strain produced by the non-hydrostatic stress is very small; in other words, the additional octahedral tilts relevant to the extra unit-cell volume associated with the deviatoric unit-cell volume strain may be totally neglected. This study further addresses the role that three factors--the elastic properties, the crystal orientation and the pressure medium--have on the structural evolution of an orthorhombic perovskite loaded in a DAC under non-hydrostatic conditions. The influence of these factors can be clearly visualized by plotting the three-dimensional distribution of the deviatoric unit-cell volume strain in relation to the cylindrical axis of the DAC and indicates that, if the elasticity of a perovskite is nearly isotropic as it is for CaTiO3, the other two factors become relatively insignificant.     

强激光对燃烧室壳体的热-力毁伤研究

基于ANSYS有限元软件, 按有无内压作用, 分别对激光辐照下燃烧室壳体的温度场、热应力、应变与损伤进行了计算与分析.分析表明, 壳体的温度场分布与光束的功率分布一致, 光斑中心温度最高.壳体中应力最大值不在光斑中心, 而是位于光斑边缘处, 在壳体吸收的激光功率密度超过1 000 W/cm²时, 壳体中应力大于材料的强度极限, 壳体均会发生软化.在存在内部燃气压力的情况下, 壳体应力会产生局部集中, 沿壳体环向表面通过光斑中心中轴线区域很有可能裂口;相比较无内压的壳体, 存在内压的壳体中的应力和产生的形变均大于无内压时的壳体.因此, 为达到相同的毁伤效果, 在存在内压的情况下, 可以适当的降低激光的辐照强度.     

强激光对燃烧室壳体的热-力毁伤研究

基于ANSYS有限元软件,按有无内压作用,分别对激光辐照下燃烧室壳体的温度场、热应力、应变与损伤进行了计算与分析.分析表明,壳体的温度场分布与光束的功率分布一致,光斑中心温度最高.壳体中应力最大值不在光斑中心,而是位于光斑边缘处,在壳体吸收的激光功率密度超过1 000W/cm2时,壳体中应力大于材料的强度极限,壳体均会发生软化.在存在内部燃气压力的情况下,壳体应力会产生局部集中,沿壳体环向表面通过光斑中心中轴线区域很有可能裂口;相比较无内压的壳体,存在内压的壳体中的应力和产生的形变均大于无内压时的壳体.因此,为达到相同的毁伤效果,在存在内压的情况下,可以适当的降低激光的辐照强度.     

A dissipative particle dynamics study of the realignment of a nanodroplet of a nematic in a weak external magnetic field

We present a dissipative particle dynamics (DPD) approach for simulating the realignment of a nematic nanodroplet suspended in an isotropic fluid following a switch in the direction of an applied external magnetic field. The interaction of the mesogens with the external field is weak relative to the inter-molecular interactions. The simulations were used to investigate the way orientational equilibrium is re-established. The results reveal that the realignment process of the nanodroplet is consistent with its fluid structure. The reorientation of the nanodroplet as a whole is found to be caused by an internal structural rearrangement rather than a coherent rotation of the centres of mass of the mesogens about the centre of the nanodroplet. The switch in the field direction furthermore is found to induce a transient spatial variation in the orientational order of the long axes of the mesogens: the orientational order parameters decreases on moving from the core of the nanodroplet to the surface in contact with the isotropic environment. The results highlight differences between the time evolution of the orientation of the long molecular axes in the field and the rotations of the centres of mass of the mesogens about the centre of the nanodroplet.     

Surface pressure in clusters and small particles—is it real?

Using the methods of statistical mechanics and applying the conditions of thermal equilibrium for an ensemble of interacting molecules, it is proved that there is no excess pressure, nor internal and surface stresses, in clusters and small particles that are not subjected to the action of external forces. With this premise taken into account the thermodynamics of spherical and faceted small particles is developed. In a particle-vapour system surrounded by a rigid impervious shell, Kelvin's and Thomson's formulae and Wulff's rule are derived. For a particle-melt system at a constant external pressure it is expected that the melting points of a particle and a bulk solid should be equal. It is noted that, if a particle is not subjected to the action of external fields or bodies, its molecules occupy their natural equilibrium positions, and it is from them that deformations and internal stresses should be counted off. These equilibrium positions differ from those occupied by the same molecules in a bulk solid, which is what usually gives rise to the illusions of the stressed state of a small particle and its deformation caused by the “uncompensated” surface forces.     

Radiative sublimation of a homogeneous,relativistic model star

A relativistic model of a radiating star is constructed as a generalization of an exact, internal Schwarzschild solution. The version of radiative sublimation in which radiation appears at the stellar surface while the inner layers remain in hydrostatic equilibrium is considered. The generalization procedure presumes that Pascal's law is violated for the stress tensor. The model's behavior is studied for different values of the parameter that allows for the predominance of tangential or radial stresses. Upon a change in the sign of the parameter, the model dynamics reveals a bifurcation, reflected in the time dependence of the star's radius, pressure, and luminosity.Work carried out under financial support from the Krasnoyarsk Regional Fund for Science, Grant D (1F0019).Krasnoyarsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 13–17, October, 1994.     

Peculiarities of the amorphous-to-crystalline-state transition in intermetallic LaNi<Subscript>5</Subscript>

The peculiarities of the transition of LaNi₅ films from the metastable amorphous state to the equilibrium crystalline state have been studied. It is shown that surface coatings with a composition corresponding to LaNi₅ can be obtained, which have, depending on the deposition and treatment conditions, structures from amorphous to single-phase crystalline, free of internal stress.     

Elastic interaction of a dislocation array with a phase boundary

The equilibrium configuration of an array of dislocations in parallel equidistant slip planes under an external shear stress near a welded boundary between two isotropic half-spaces having different elastic constants is computed. For large external stress, the dislocations are arranged into an arc concave when seen from the boundary. It is concluded that such an arc is formed at the tip of a twin or of a martensitic plate near a phase boundary. The tensile stress across the boundary due to an edge dislocation array is discussed in connection with the formation of an interfacial crack.     

Prediction of dislocation formation in epitaxial multilayers subject to in-plane loading

A theoretical model is described to predict equilibrium distributions of misfit dislocations in one or more anisotropic epitaxial layers of a multilayered system deposited on a thick substrate. Each layer is regarded as having differing elastic and lattice constants, and the system is subject to biaxial in-plane mechanical loading. A stress transfer methodology is developed enabling both the stress and displacement distributions in the system to be estimated for cases where the interacting dislocations are of a pure edge configuration. Energy methods are used to determine equilibrium distributions of the dislocations for given external applied stress states. It is shown that the new model accurately reproduces known exact analytical solutions for the special case of just one isotropic epitaxial layer applied to an isotropic semi-infinite substrate having the elastic constants of the substrate but differing lattice constants. The model is used to consider equilibrium dislocation distributions in capped epitaxial systems with misfit dislocations. It is shown that the simplifying assumptions often made in the literature, regarding the uniformity of elastic properties and the neglect of anisotropy, can lead to critical thicknesses being underestimated by 15–18%. The application of uniaxial tensile stresses increases the value of critical thicknesses. The model can be used to analyse dislocations in various non-neighbouring layers provided the dislocation density has the same value in all layers in which dislocations have formed. This type of analysis enables the prediction of the deformation of metallic multilayers subject to mechanical and thermal loading.     

The Born-model and the effects of hydrostatic and non-hydrostatic stresses on rubidium halide structural phase transitions

An analytic Born-model, with the same set of repulsive parameters for both phases in each salt, has been used to calculate the properties of the NaCl-CaCl structural phase transformation in three rubidium halides. The treatment required a careful evaluation of the three repulsive parameters by comparison with equilibrium conditions in both phases and measured bulk moduli, and involved a self consistent analysis which takes into account the experimental uncertainties in reported values of CsCl-phase lattice parameters. Calculated values for the equilibrium transition pressure, lattice parameters and lattice energies are in satisfactory agreement with reported experimental results. The model has also been used to calculate the lattice energy continuously from the NaCl to the CsCl phases, as a function of both hydrostatic and non-hydrostatic stresses. These calculations give a semiquantitative estimate of an energy barrier between the two stable structures, which is consistent with reported measurements of elastic constant and hysteresis effects near the transition pressure. The calculated effects of a uniaxial stress are found to be as much as three times larger than those of a hydrostatic stress, and the effects of the uniaxial stress on the barrier height are found to be approximately the same as the effects on the equilibrium energy differences. Measurements of the effect of this uniaxial stress on the forward transition pressure of RbI were carried out and the measured variations were found to be in excellent agreement with the calculated change in equilibrium transition pressure—as expected from the energy barrier calculations.     

Isotropic-nematic transition in liquid-crystalline elastomers

In liquid-crystalline elastomers, the nematic order parameter and the induced strain vary smoothly across the isotropic-nematic transition, without the expected first-order discontinuity. To investigate this smooth variation, we measure the strain as a function of temperature over a range of applied stress, for elastomers cross-linked in the nematic and isotropic phases, and analyze the results using a variation on Landau theory. This analysis shows that the smooth variation arises from quenched disorder in the elastomer, combined with the effects of applied stress and internal stress.     

The Boltzmann equation from quantum field theory

We show from first principles the emergence of classical Boltzmann equations from relativistic nonequilibrium quantum field theory as described by the Kadanoff–Baym equations. Our method applies to a generic quantum field, coupled to a collection of background fields and sources, in a homogeneous and isotropic spacetime. The analysis is based on analytical solutions to the full Kadanoff–Baym equations, using the WKB approximation. This is in contrast to previous derivations of kinetic equations that rely on similar physical assumptions, but obtain approximate equations of motion from a gradient expansion in momentum space. We show that the system follows a generalized Boltzmann equation whenever the WKB approximation holds. The generalized Boltzmann equation, which includes off-shell transport, is valid far from equilibrium and in a time dependent background, such as the expanding universe.     

Geometrical formulation of equilibrium phenomenological thermodynamics

An abstract geometric formulation of equilibrium phenomenological thermodynamics which generalizes and unifies that of Gibbs, Carathéodory, and others is given. As done by Hermann, one adapts here a contact manifold as the basic mathematical structure. Such a manifold for a thermodynamic system is constructed. The empirical laws of thermodynamics have been reformulated in terms of this manifold and by means of exterior differential forms. Such concepts as Gibbs phase rule, Gibbs-Duhem equation and thermodynamic potentials have been reexamined within such a general scheme.     

Imaging of internal stress around a mineral inclusion in a sapphire crystal: application of micro‐Raman and photoluminescence spectroscopy

We developed a micro‐Raman and photoluminescence imaging technique for visualizing the internal stress fields in a sapphire crystal. The technique was applied to an Australian sapphire gemstone with a zircon inclusion. Considering piezospectroscopic effects on Raman and photoluminescence spectra, the Raman shifts of sapphire around the zircon inclusion were converted to hydrostatic pressure and deviatoric components of stress tensor. The internal stress was highly concentrated at the tips of the zircon crystal, where the deviatoric stress and the hydrostatic pressure component reached 700 and 470 MPa, respectively. Generation of compressive stress on the crystal surface of zircon can be explained by the difference in thermal expansion coefficients and elastic constants between sapphire and zircon. In general, internal stress fields induced by mineral inclusions reflect the pressure and temperature conditions at which the host sapphire gemstones were crystallized. Thus, the present technique can be utilized to identify the origin of gemstones. Copyright © 2012 John Wiley & Sons, Ltd.     

Mechanism of formation of the equilibrium domain structure in crystals undergoing thermoelastic phase transitions

The mechanism of formation of the equilibrium domain structure during a thermoelastic phase transition is proposed. This mechanism is related to long-range elastic strain fields created by “elastic charges” at the free crystal surface. It is assumed that, during a phase transition, there appears not only the nonzero primary (antiferromagnetic, martensitic) order parameter in the crystal but also an internal (quasi-plastic) stress rigidly related to the order parameter. The orientation of this stress with respect to the crystallographic axes can be changed by external fields. Elastic charges arise due to those components of the internal stress tensor whose flux across the crystal surface is nonzero. The nonlocal destressing energy is found. It is shown that, for a certain shape of a sample, an inhomogeneous distribution of the primary order parameter (a domain structure) is energetically more favorable. The characteristic field at which a sample becomes a single domain is shown to be dependent on the shape of the crystal.