Predictions Of Elasticity Theory Research Articles

Advanced Analysis of Total Energies of Fullerenes

A comparison study has been conducted to compare the accuracy of the used methods, the global and local definitions, in order to calculate the cage radii of fullerene, by which the total energies of fullerene have been analyzed. It was found that the local definition method is more accurate in calculating the cage radii of fullerene than the global definition basing on correlation coefficients and standard deviation values in addition to the agreement of the elasticity theory predictions with local definition method results.

Atomistic simulations of screw dislocations in bcc tungsten: From core structures and static properties to interaction with vacancies

Atomistic simulations have been used to investigate the core structures, static properties of isolated 1/2 <111> screw dislocations, and their interaction with vacancies in bcc tungsten (W) based on three empirical interatomic potentials. Differential displacement maps show that only one embedded atom method potential is able to reproduce the compact non-degenerate core as evidenced by ab initio calculations. The obtained strain energy and stress distribution from atomistic simulations are, in general, consistent with elasticity theory predictions. In particular, one component of the calculated shear stress, which is not present according to elasticity theory, is non-negligible in the core region of our dislocation model. The differences between the results calculated from three interatomic potentials are in details, such as the specific value and the symmetry, but the trend of spatial distributions of static properties in the long range are close to each other. By calculating the binding energies between the dislocations and vacancies, we demonstrate that the dislocations act as vacancy sinks, which may be important for the nucleation and growth of hydrogen bubbles in W under irradiation.

Emission of full and partial dislocations from a crack in BCC and FCC metals: An atomistic study

The behavior of crack propagation and blunting at different strain rates, temperature and crack geometry in BCC-Fe, W, and FCC-Ni, Cu has been studied by molecular dynamics under load mode I. Large scale atomistic simulations coupled with a structural analysis have been performed to reveal conditions at which dislocations can be emitted from a semi-infinite crack. In FCC metals the crack tip is blunted by the plastic deformation due to the nucleation and emission of dislocations. These processes, however, occur in a different manner in Ni and Cu. It can be concluded that the formation of stacking faults and twins at a crack tip is particularly important for brittle cleavage. In BCC crystals the crack was found to open without plastic deformation, however, the strain work hardening has a significant dependence on temperature. The critical stress intensity factor for brittle cleavage or dislocation emission was calculated from the stress tensor measured on atoms located at the crack tip. The obtained results are discussed and compared with predictions of elasticity theory.

Dislocation–vacancy interactions in tungsten

We systematically investigate the interaction between a monovacancy and various lattice dislocations in body-centered cubic (bcc) metal tungsten by means of atomistic simulations. Two models with a different level of sophistication have been employed for the description of interatomic interactions—the empirical Finnis–Sinclair potential, which is a central-force scheme, and the bond-order potential, which is able to describe correctly unsaturated directional covalent bonds that are crucial for the cohesion and structure of bcc transition metals. Our simulation results show that the vacancy–dislocation interaction depends sensitively on the separation distance and orientation of the two defects. A comparison of the simulation results with the predictions of elasticity theory shows excellent agreement between the two approaches when the separation between the vacancy and the dislocation core is above 0.5 nm. Large deviations from the elastic limit are found at close distances, when the vacancy enters the dislocation core.

Point defects in two-dimensional colloidal crystals: simulation vs. elasticity theory

Using numerical and analytical calculations we study the structure of vacancies and interstitials in two-dimensional colloidal crystals. In particular, we compare the displacement fields of the defect obtained numerically with the predictions of continuum elasticity theory for a simple defect model. In such a comparison it is of crucial importance to employ corresponding boundary conditions both in the particle and in the continuum calculations. Here, we formulate the continuum problem in a way that makes it analogous to the electrostatics problem of finding the potential of a point charge in periodic boundary conditions. The continuum calculations can then be carried out using the technique of Ewald summation. For interstitials, the displacement fields predicted by elasticity theory are accurate at large distances, but large deviations occur near the defect for distances of up to 10 lattice spacings. For vacancies, the elasticity theory predictions obtained for the simple model do not reproduce the numerical results even far away from the defect.

Critical Analysis of Different Techniques for Measuring Strain in Si1-yCy Layers Grown by CVD on a Si Substrate

In this work, we performed quantitative measurements of strain in structures consisting of a 30 nm-thick Si1-yCy layer grown by chemical vapour deposition (CVD) on a Si (001) substrate. Total C concentrations vary from 0.67 to 2%. Geometric phase analysis (GPA) of high-resolution transmission electron microscopy (HR TEM) cross-section images and convergent-beam electron diffraction (CBED) with a nanometer resolution as well as Raman spectroscopy and high-resolution X-ray diffraction with a micro- and millimeter resolutions, respectively, were used to deduce the strain within these Si1-yCy layers. These results were compared with the predictions of elasticity theory. Particular interest is paid to the formation of the structural defects within Si1-yCy layers as a function of C concentration, growth temperature and incorporated strain.

Dislocation interaction with C in α-Fe: A comparison between atomic simulations and elasticity theory

The interaction of C atoms with a screw and an edge dislocation is modelled at an atomic scale using an empirical Fe–C interatomic potential based on the embedded atom method and molecular statics simulations. Results of atomic simulations are compared with predictions of elasticity theory. It is shown that a quantitative agreement can be obtained between both modelling techniques as long as anisotropic elastic calculations are performed and both the dilatation and the tetragonal distortion induced by the C interstitial are considered. Using isotropic elasticity allows the prediction of the main trends of the interaction, whereas considering only the interstitial dilatation will lead to a wrong interaction.

Determination of strain within Si1-yCy layers grown by CVD on a Si Substrate

AbstractIn this work, we performed quantitative measurements of strain in structures consisting of a 30 nm-thick Si1-yCy layer grown by chemical vapour deposition (CVD) on a Si (001) substrate at 550 or 600°C. The total C concentration varies from 0.67 to 1.97% that was measured by SIMS. Geometric phase analysis (GPA) of high resolution transmission electron microscopy (HR TEM) cross-section images and convergent beam electron diffraction (CBED) were used to deduce the strain within these Si1-yCy layers. Finite-element simulations were carried out to estimate the impact of strain relaxation in thin areas of a specimen. These results were compared with the data obtained by high resolution X-ray diffraction and Raman spectroscopy and with the predictions of elasticity theory. Particular interest is paid to the formation of the structural defects within Si1-yCy layers as a function of a C concentration, growth temperature and incorporated strain. Both cross-sectional and plan-view TEM specimen configurations were used to obtain quantitative information on the defect size distribution, their density and structure.

Quantitative local strain measurements in compressive strained Ge/tensile strained Si bi-layers grown on top of relaxed Si0.5Ge0.5 virtual substrates

This paper reports on quantitative measurements of strain in a 7.5nm compressive strained Ge/5.1nm tensile strained Si bi-layer grown by reduced pressure chemical vapour deposition on top of a relaxed Si0.5Ge0.5 virtual substrate. Geometric phase analysis of high resolution transmission electron microscopy images acquired using the SACTEM-Toulouse, an aberration-corrected transmission electron microscope, is used to quantify the strain within s-Ge and s-Si layers. Finite element simulations are carried out to estimate the impact of strain relaxation in thin areas of a TEM specimen. Experimental results are compared with the predictions of elasticity theory and finite element simulations.

Hysteresis effects studied by numerical simulations: Cyclic loading-unloading of a realistic sand model

When Hertz-Mindlin force laws are considered in the context of the effective-medium theory, the predictions yield a constant Poisson coefficient and bulk/shear elastic moduli that scale with pressure with a 1/3 power law exponent [Formula: see text]. This prediction contradicts early and recent experimental findings that conclude moduli grow faster with a 1/2 power law exponent ([Formula: see text]). Such a conclusion is also reached by recent second-order corrections to linear elastic theory. In this work we use a discrete-particle method to study the elastic response of a model of sand that is unconsolidated because of cyclic loading. We use a detailed molecular dynamics simulation that accounts for Hertz-type grain interactions and history-dependent shear forces. The porous sand model is constructed from spherical particles whose size distribution mimics well-sorted unconsolidated sands. The geometry of the model is obtained by simulating critical processes in sedimentary rock formations. Hysteretic behavior and relations between the sample bulk modulus, strain, and stress are obtained. The simulated sample reproduces experimental transient and stationary loading-unloading behavior. We find good correspondence of pressure and strain dependence of elastic moduli in our model with semilinear elasticity theory predictions. Simple arguments explain low coordination numbers observed on force-transmitting samples and the tendency to reduce dissipation under cyclic loading. Our approach clearly shows that a Hertz-Mindlin grain interaction is not inconsistent with the experimental [Formula: see text] behavior of the bulk modulus.

Quantitative strain and stress measurements in Ge/Si dual channels grown on a Si 0.5Ge 0.5 virtual substrate

The incorporation of compressive strained Ge/tensile strained Si bi-layers in the active regions of MOSFETs is a promising route for creating ultimate Si-based devices due to the considerable increase of the mobility of spatially confined holes/electrons. The main challenge in device application is to be able to control and manipulate strain within such thin layers. This paper reports on quantitative measurements of strain in a structure consisting of a 8 nm Ge/5 nm Si heterostructure grown by chemical vapour deposition on top of a relaxed Si 0.5Ge 0.5 buffer layer. Geometric phase analysis of high resolution TEM images is used to measure the strain within Ge and Si layers. The in-plane stress within each layer is deduced. Experimental results are compared with the predictions of elasticity theory and discussed in terms of effect of defect formation.

Characteristics of the interaction of Cu-rich precipitates with irradiation-produced defects in α-Fe

The interaction between copper-rich precipitates in α-iron and either vacancies or self-interstitial atoms and their clusters is studied by atomic-scale modelling. Results are compared with predictions of elasticity theory and interpreted in terms of size misfit of precipitates and defects, and the modulus and cohesive energy differences between iron and copper. Interstitial defects are repelled by precipitates at large distance but, like vacancies, attracted at small distance. Hence, copper precipitates in iron can be sinks for both vacancy and interstitial defects, and can act as strong recombination centres under irradiation conditions. This leads to a tentative explanation for the mixed Cu–Fe structure of precipitates and the absence of precipitate growth under neutron irradiation conditions. More generally, both vacancy and interstitial defects may be strongly bound to precipitates with weaker cohesion than the matrix.

InGaAs/GaAs nanotubes simulation: Comparison between continual and molecular dynamics approaches

The results of InGaAs/GaAs nanotubes synthesis on atomic scale using molecular dynamics are presented. On basis of the comparison with mechanics of continua it is shown that the values of nanotubes radius obtained by molecular dynamics calculations are less then elasticity theory predicts with the discrepancy exceeding 30% for a few monolayer thick heterostructure. The influence of discreteness of matter and surface energy to this discrepancy was considered. The proposed simple discrete model produces estimation of the correction to elasticity theory formula due to the discreteness of matter. Though this correction also predicts decrease for equilibrium heterostructure radius of curvature, its value is not sufficient for the explanation of molecular dynamics results. Comparison of the potential energy distribution with elasticity theory predictions shows the importance of heterostructure surface layers contribution to this discrepancy. Introduction of surface energy to the elasticity theory model expands the limits of continuum mechanics application for nanoscale simulations.

An XPD and LEED study of highly strained ultrathin Ni films on Pd(1 0 0)

The epitaxial growth of ultrathin Ni films on the Pd(100) surface was studied by means of X-ray photoelectron diffraction (XPD) and LEED experiments. In excellent numerical agreement with the predictions of elasticity theory, the data indicate the formation of tetragonally strained Ni epitaxial layers, which subsequently turns into a bulk-like Ni structure as the thickness of approximately 12MLE is exceeded. This study demonstrates that LEED and XPD methodologies are rather complementary in order to have a detailed picture of the evolution of the overlayer structure in different thickness regimes.

X-ray studies of Si/Ge/Si(001) epitaxial growth with Te as a surfactant

X-ray standing waves (XSW) and grazing incidence x-ray diffraction (GIXD) were used to investigate the crystallinity of ultrathin Ge films grown by molecular-beam epitaxy on Si(001) with and without Te as a surfactant. The Ge layer thickness ranged from 1 to 10 ML. The results clearly indicate that Ge films grown with Te have a higher degree of crystallinity compared to those grown without Te. For example, GIXD shows that 9 ML Ge grown on Si(001) with Te is strained in plane; while the same film grown without Te is relaxed. The (004), (022), and (008) XSW results are used to determine the registry of the Ge atoms with respect to the Si lattice. This is compared with macroscopic continuum elasticity theory predictions for Ge/Si(001).

Strain determination in ultrathin bcc Fe layers on Si(001) by x-ray diffraction

Good quality body-centered cubic iron layers can be grown on Si(001) at room temperature using thin ${\mathrm{FeSi}}_{2}$ or ${\mathrm{CoSi}}_{2}$ silicide buffer layers. The in-plane and out-of-plane strains are measured by x-ray diffraction (XRD). Due to the difference in Fe and Si parameters of +5.6%, the thin Fe layers undergo a strong tetragonal distortion. For the samples deposited on ${\mathrm{FeSi}}_{2},$ the measured biaxial in-plane compressive strain ranges from values as large as -3.8% in the thinnest films (25 ML) to -1% in the thicker layers (&gt;40 ML). In the samples deposited on ${\mathrm{CoSi}}_{2},$ a part of the iron layer clearly observable up to 40 ML, apparently grows in pseudomorphy with the silicon, whereas another dominant part above 15 ML partly relaxes and behaves as on ${\mathrm{FeSi}}_{2}$ templates but with systematically larger strains. The evolution of the in-plane cubic effective magnetic anisotropy constant versus Fe film thickness observed in previous work, can be explained by means of fourth-order (in spin) magnetoelastic coupling in the iron lattice with the strain components determined by XRD. Finally, the observed ratio between the perpendicular and in-plane strain components differs substantially from linear elasticity theory predictions and indicates the importance of anharmonic effects and/or defects in the description of the elastic properties of such films.

Measurement of the twist elastic constant by phase retardation technique

We have extended the experimental approach, used by Yu. A. Nastyshyn et al. [J. Appl. Phys. 86 , 4199 (1999)] for measuring polar anchoring strength, to measure the twist elastic constant in nematic liquid crystal. The method implies measurements of phase retardation changes in liquid crystal under the action of magnetic field. The obtained experimental data were fitted with the predictions of elastic theory. We found that the value of the measured elastic constant, K_{22} , is in good agreement with those described in literature.

Green's Function Probe of a Static Granular Piling

We present an experiment which aims to investigate the mechanical properties of a static granular assembly. The piling is a horizontal 3D granular layer confined in a box. We apply a localized extra force at the surface and the spatial distribution of stresses at the bottom is obtained (the mechanical Green's function). For different types of granular media, we observe a linear pressure response whose profile shows one peak centered at the vertical of the point of application. The peak's width increases linearly with increasing depth. This Green's function seems to be in at least qualitative agreement with predictions of elastic theory.

Surface extrapolation length and director structures in confined nematics

We report the results of Monte Carlo simulations of the Lebwohl-Lasher model of nematic liquid crystals confined to cylindrical cavities with homeotropic anchoring. We show that the ratio of the bulk to surface couplings is not in general equal to the corresponding parameter K/W used in elastic theory (where K is the Frank elastic constant in the one-constant approximation and W is the surface anchoring strength). By measuring the temperature dependence of K/W (which is equivalent to the surface extrapolation length) we are able to reconcile the results of our simulations as well as others with the predictions of elastic theory. We find that the rate at which we cool the system from the isotropic to nematic phase plays a crucial role in the development of the final director structure, because of a large free energy barrier separating different director structures as well as the temperature dependence of K/W. With a suitably fast cooling rate we are able to keep the system out of a metastable planar state and form an escaped radial structure for large enough systems. Copyright 2000 The American Physical Society.

Nematic structures in cylindrical cavities

We present the results of Monte Carlo simulations of a nematic liquid crystal confined to a cylinder with homeotropic surface anchoring. The nematic is modelled using the LebwohlLasher model. For low values of the cylinder radius or anchoring strength, a stable planar polar configuration with two line defects is readily formed, consistent with the predictions of elastic theory. At larger values of the radius or anchoring strength we observe a metastable escaped radial configuration. However, this structure eventually collapses to a planar configuration, contrary to the predictions of elastic theory.