An empirical model for free surface energy of strained solids at different temperature regimes

We have developed an empirical formulation, based on the elastic theory, to calculate the variation of the surface free energy when a crystal is strained in the elastic regime. The model permits to obtain the variation of the surface energy at different strains and temperatures when are known the thermal dependence on the bulk and surface elastic constants. Molecular dynamics (MD) simulations were performed using the three low index surfaces of Al, to validate the accuracy of the model. The comparison between the empirical model and the MD simulations shows a good agreement for temperatures ranging between 0 and 900 K, and for deformation between −2% and 2%.     

Third-order elastic constants and pressure derivatives of the second-order elastic constants of β-tin

The second- and third-order elastic constants and pressure derivatives of second-order elastic constants of tetragonal β-tin have been obtained using the deformation theory. The strain energy density derived using the deformation theory is compared with the strain dependent lattice energy obtained from the elastic continuum model approximation to get the expressions for the second- and third-order elastic constants. Higher order elastic constants are a measure of the anharmonicity of a crystal lattice. The 12 non-vanishing third-order elastic constants and the six pressure derivatives of the second-order elastic constants in tetragonal β-tin are obtained in the present work and are compared with the available experimental values. The second-order elastic constant C₃₃ obtained in the present study is in reasonable agreement with the experimental values. The third-order elastic constants are generally one order of magnitude greater than the second-order elastic constants as expected of a crystalline solid. The third-order elastic constant C₃₃₃ is higher in magnitude than all other values. This shows a greater anharmonicity of β-tin along the c-axis direction of the crystal.     

Lie Symmetries and Conserved Quantities for Super-Long Elastic Slender Rod

DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. We study the Lie symmetries of a super-long elastic slender rod by using the methods of infinitesimal transformation. Based on Kirchhoff＇s analogue, generalized Hamilton canonical equations are analysed. The infinitesimal transformations with respect to the radian coordinate, the generalized coordinate, and the quasimomentum of the model are introduced. The Lie symmetries and conserved quantities of the model are presented.     

Third-order elastic constants of ZnS and ZnSe

The complete set of non-vanishing third-order elastic constants of the semiconductors ZnS and ZnSe is obtained theoretically. The strain energy density is estimated using finite strain elasticity theory by considering the interactions up to two nearest neighbours of each atom in the unit cell of these compounds. This energy density is compared with the strain dependent lattice energy density from the continuum model approximation. The second-order parameter of the potential function φ is obtained from the measured principal axis C_ij. The third-order potential parameter is estimated by assuming a Lennard-Jones type of interatomic potential. The interlattice displacements as well as the second-order elastic constants are evaluated along with the six third-order elastic constants of ZnS and ZnSe. Using these second- and third-order elastic constants of ZnS, the pressure derivatives of second-order elastic constants are evaluated. The second- and third-order elastic constants of ZnSe are compared with the available experimental values. The third-order elastic constants show anisotropy in different directions.     

Two-Photon-Exchange Correction to Elastic ep Scattering in the Forward Angle Limit

The two-photon-exchange （TPE） correction to elastic ep scattering in the forward angle region is discussed based on a simple hadronic model. It is found that the correction is exactly zero in the forward angle limit. This analytical result gives a good explanation of the previous numerical results and shows the clear power behavior of the TPE correction to elastic ep scattering in the forward angle region.     

Third-order elastic constants of the alloy Fe72Pt28

The complete sets of second- and third-order elastic constants of the cubic Fe₇₂Pt₂₈ have been obtained using the strain energy density derived from interactions up to three nearest neighbours of each atom in the unit cell. The finite strain elasticity theory has been used to get the strain energy density of Fe₇₂Pt₂₈. The strain energy density is compared with the strain-dependent lattice energy density obtained from the continuum model approximation and the expressions for the second- and third-order elastic constants of Fe₇₂Pt₂₈ are given. The second-order potential parameter is deduced from the measured second-order elastic constants of Fe₇₂Pt₂₈ and the third-order potential parameter is estimated from the Lennard-Jones inter-atomic potential for Fe₇₂Pt₂₈. The inter-lattice displacements; the three independent second-order elastic constants and the six independent third-order elastic constants of Fe₇₂Pt₂₈ are also determined. The second-order elastic constants are compared with the experimental elastic constants of Fe₇₂Pt₂₈. We also study the effect of pressure on the second-order elastic constants of Fe₇₂Pt₂₈.     

Elastic Interaction between a String of Cells and an Individual Cell

The elastic interaction between a string of cells and an individual cell on an elastic substrate is investigated numerically using the force-dipole model. This interaction is found to be of short range, and the cut-off distance is about 1.4 times of the length of the cell. The energy-minimization distance is about half the cellular length. The specific relationship between the cellular reorientation and the cellular position are obtained quantitatively. A critical distance is found, and the cellular orientation has an abrupt change at this transition point.     

Influence of elastic properties on superplasticity in doped yttria-stabilized zirconia

We report the first principles calculations of elastic and electronic properties of yttria-stabilized tetragonal zirconium dioxide (YZP) doped with GeO₂, TiO₂ and SiO₂. Electronic structure and isotropic elastic properties of YZP do not change upon addition of dopants. Addition of dopants affects the shear C₆₆ elastic constant that decreases with the increasing dopant concentration. A simple model that connects elastic softening to enhancement of superplasticity in doped fine-grained zirconia ceramics is proposed.     

Special interaction between quasiperiodic grain boundaries and lattice dislocations in crystalline solids

A theoretical model is suggested which describes phason imperfections (specific excitations) in a quasiperiodic grain boundary in a polycrystalline solid as dilatation flexes. In the framework of the model, an elastic stress field of the quasiperiodic grain boundary is calculated as a stress field created by an ensemble of dilatation flexes (phason imperfections) located in the boundary. It is shown that there is a special elastic interaction between crystal lattice defects and quasiperiodic grain boundaries comprising phason imperfections. The strengthening effect in plastically deformed polycrystalline solids is quantitatively described which is related to the special elastic interaction between lattice dislocations and quasiperiodic grain boundaries. Received: 29 October 1996 / Revised: 22 August 1997 / Accepted: 13 November 1997     

Resonant ultrasound spectroscopy and homogeneity in polycrystals

Resonant ultrasound spectroscopy (RUS) is capable of determining the bulk elastic properties of a solid from its characteristic vibration frequencies, given the dimensions, density and shape of the sample. The model used for extracting values of the elastic constants assumes perfect homogeneity, which can be approximated by average-isotropic polycrystals. This approximation is excellent in the small grain regime assumed for most averaging procedures, but for real samples with indeterminate grain size distributions, it is not clear where the approximation breaks down. RUS measurements were made on pure copper samples where the grain size distribution was changed by progressive heat treatments in order to find a quantitative limit for the loss of homogeneity. It is found that when a measure of the largest grains is 15% of the sample’s smallest dimension, the deviation in RUS fits indicates elastic inhomogeneity.     

First-Principles Calculations of Elastic and Thermal Properties of Molybdenum Disilicide

The first-principles plane-wave pseudopotential method using the generalized gradient approximation within the framework of density functional theory is applied to anaylse the equilibrium lattice parameters, six independent elastic constants, bulk moduli, thermal expansions and heat capacities of MoSi2. The quasi-harmonic Debye model, using a set of total energy versus cell volume obtained with the plane-wave pseudopotential method, is applied to the study of the elastic properties, thermodynamic properties and vibrational effects. The calculated zero pressure elastic constants are in overall good agreement with the experimental data. The calculated heat capacities and the thermal expansions agree well with the observed values under ambient conditions and those calculated by others. The results show that the temperature has hardly any effect under high pressure.     

Relating multichannel scattering and production amplitudes in a microscopic OZI-based model

Relations between scattering and production amplitudes are studied in a microscopic multichannel model for meson-meson scattering, with coupling to confined quark-antiquark channels. Overlapping resonances and a proper threshold behaviour are treated exactly in the model. Under the spectator assumption, it is found that the two-particle production amplitude shares a common denominator with the elastic scattering amplitude, besides a numerator consisting of a linear combination of all elastic and some inelastic matrix elements. The coefficients in these linear combinations are shown to be generally complex. Finally, the standard operator expressions relating production and scattering amplitudes, viz. , are fulfilled, while in the small-coupling limit the usual isobar model is recovered.     

Phase structure of a spherical surface model on fixed connectivity meshes

An elastic surface model is investigated by using the canonical Monte Carlo simulation technique on triangulated spherical meshes. The model undergoes a first-order collapsing transition and a continuous surface fluctuation transition. The shape of surfaces is maintained by a one-dimensional bending energy, which is defined on the mesh, and no two-dimensional bending energy is included in the Hamiltonian.     

Theoretical Study of Elastic Properties of Tungsten Disilicide

The plane-wave pseudopotential method using the generalized gradient approximation within the framework of density functional theory is applied to analyse the lattice parameters, elastic constants, bulk moduli, shear moduli and Young's moduli of WSi₂. The quasi-harmonic Debye model, using a set of total energy versus cell volume obtained with the plane-wave pseudopotential method, is applied to the study of the elastic properties and vibrational effects. The athermal elastic constants of WSi₂ are calculated as a function of pressure up to 35GPa. The relationship between bulk modulus and temperature up to 1200K is also obtained. Moreover, the Debye temperature is determined from the non-equilibrium Gibbs function. The calculated results are in good agreement with the experimental data.     

Non-linear elastic behavior of light fibrous materials

Light fibrous materials composed of elastic fibers display a non-linear elastic behavior, where the non-linearity is due to the increase in the number of contacts between fibers under compression. Testing glass wool under compression up to 95% shows such a strongly non-linear behavior. A model is proposed to account for the divergence of the compressive stress as the strain approaches a threshold compression , with . Quantitative analysis of the experimental data on glass wool is fully consistent with this result. Received 2 February 1999     

Elasticity and thermodynamic properties of RuB2 under pressure

First-principles calculations of the crystal structure and the elastic properties of RuB₂ have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values are in very good agreement with experimental data as well as with some of the existing model calculations. The elastic constants c_ij, the aggregate elastic moduli (B, G, E), Poisson's ratio, and the elastic anisotropy with pressure have been investigated. Through the quasi-harmonic Debye model considering the phonon effects, the isothermal bulk modulus, the thermal expansions, Grüneisen parameters, and Debye temperatures depending on the temperature and pressure are obtained in the whole pressure range from 0 to 60 GPa and temperature range from 0 to 1100 K as well as compared to available data.     

Elastic properties of the RIV-RIII rotator phases of alkanes

A model free energy has been constructed to describe the R_IV-R_III rotator phase transition in alkanes in terms of the elastic strains and order parameter. The conditions for the R_IV-R_III phase transition are discussed. From the free energy, the order parameter and the elastic strains are determined. The model free energy describes the first or second order character of the R_IV-R_III transition depending on the strength of the coupling. The elastic properties in the vicinity of the R_IV-R_III transition are discussed on the basis of a free energy expansion. The temperature dependence of the elastic constants is calculated on both sides of the transition. The coupling between the order parameter and elastic stains is shown to have a crucial influence on the phase behavior and the order of the transition.     

Does roughening of rock-fluid-rock interfaces emerge from a stress-induced instability?

Non-planar solid-fluid-solid interfaces under stress are very common in many industrial and natural materials. For example, in the Earth’s crust, many rough and wavy interfaces can be observed in rocks in a wide range of spatial scales, from undulate grain boundaries at the micrometer scale, to stylolite dissolution planes at the meter scale. It is proposed here that these initially flat solid-fluid-solid interfaces become rough by a morphological instability triggered by elastic stress. A model for the formation of these unstable patterns at all scales is thus presented. It is shown that such instability is inherently present due to the uniaxial stress that promotes them, owing to the gain in the total elastic energy: the intrinsic elastic energy plus the work of the external forces. This is shown explicitly by solving the elastic problem in a linear stability analysis, and proved more generally without having resort to the computation of the elastic field.     

First-principles calculations on elasticity of under pressure

First-principles calculations of the crystal structure and the elastic properties of OsN₂ have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values are in very good agreement with experimental data as well as with some of the existing model calculations. The dependence of the elastic constants c_ij, the aggregate elastic moduli (B,G,E), Poisson’s ratio, and the elastic anisotropy on pressure has been investigated. Moreover, the variation of the Debye temperature and the compressional and shear elastic wave velocities with pressure P up to 60 GPa at 0 K have been investigated for the first time.     

Dynamics of reorientation of a constrained nematic elastomer

A model is proposed for the reorientation dynamics of a confined nematic liquid crystal elastomer, where the effect of crosslinks is to couple the director to deformations of the elastic matrix. The model combines the (equilibrium) `neo-classical' theory of liquid crystal rubber elasticity with the simplest time evolution equations for a system described by two coupled, non-conserved order parameters. Relaxation from an orientation imposed by an electric field is studied as a function of elastic softness, starting angle, surface pretilt, and the relative mobilities of director and strain. Most importantly, the absence of a `semi-soft' elastic threshold changes the long-time behaviour of the effective refractive index of the medium from exponential to inverse power law decay. Predictions are compatible with recent experimental results by Chang, Chien and Meyer [Phys. Rev. E 56, 595 (1997)]. Received 22 June 1998