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1.
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%.  相似文献   

2.
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.  相似文献   

3.
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.  相似文献   

4.
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 Cij. 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.  相似文献   

5.
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.  相似文献   

6.
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.  相似文献   

7.
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.  相似文献   

8.
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.  相似文献   

9.
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  相似文献   

10.
Kaplan G  Darling TW  McCall KR 《Ultrasonics》2009,49(1):139-8235
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.  相似文献   

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