Elastic Dipole Research Articles

Step-induced elastic relaxation and surface structure of the Si(7710) surface

We have studied by Grazing Incidence X-ray Diffraction (GIXD) the strain field induced by periodic triple steps on a Si(7710) surface that is a vicinal of Si(111) surface 10° misoriented towards the [11¯2] direction. We find that the strain field induced by the triple steps is well described by an elastic model in which the steps are modelized by parallel rows of buried elastic dipoles. The best fit of the experimental results is reached on the basis of the (7710) surface structure model proposed by Teys et al. (Surface Science 600 (2006) 4878). The so-obtained dipole characteristics are the dipole amplitude (decomposed in a stretch component PT=1.5nN and a torque component PS=0.2nN) as well as the lever arm Ω=170° and force Φ=81° orientations of the dipole. We also determine the prefactor of the elastic interaction energy between triple steps Ael.=0.52eVÅ we discuss in the light of other independent measurements.

A new cluster model interpretation of the anomalous lifetime of 14C

A new cluster model solution to the long-standing nuclear structure problem of describing the anomalously long lifetime of 14C is presented. Related beta-decay data for 14O to states in 14N, gamma-decay data between low-lying positive parity states in 14N and the elastic and inelastic magnetic dipole electron scattering from 14N data are all shown to be very accurately described by the model. The shapes of the beta spectra for the A = 14 system are also well reproduced by the model. The model invokes four-nucleon tetrahedral symmetric spatial correlations arising from three- and four-nucleon interactions, which yields a high degree of SU(4) singlet structure for the clusters and a tetrahedral intrinsic shape for the doubly magic 16O ground state. The large quadrupole moment of the 14N ground state is obtained here for the first time and arises because of the almost 100% d-wave deuteron-like-hole cluster structure inherent in the model.

Colloidal structures in confined nematic liquid crystals

Colloidal structures in confined nematics offer novel routes for designing complex optical materials with micrometre and submicrometre functionality. In this paper, we review some of our recently assembled colloidal structures that form in confined nematic cells. We present effective elastic binding via nematic distortion as a mechanism for the assembly of two-dimensional colloidal crystals of elastic dipoles and elastic quadrupoles. We introduce entangled colloids as novel types of structures, where particles are topologically bound by delocalised defect loops, producing robust and possibly chiral structures. The concept of hierarchical assembly is demonstrated in colloids with particles of various scales. In cholesteric blue phases, the assembly of three-dimensional colloidal crystals is shown based on naturally occurring three-dimensional arrays of trapping sites produced by blue phases.

Dipolar colloids in nematostatics: Tensorial structure, symmetry, different types, and their interaction

In spite of the analogy to the electrostatics, the three-dimensional colloidal nematostatics is substantially different in both its mathematical structure and its physical implications. The general tensorial structure of elastic multipoles derived in V. M. Pergamenshchik and V. O. Uzunova [Eur. Phys. J. E 23, 161 (2007); Phys. Rev. E 76, 011707 (2007)] allows for a classification of different types of colloids in the nematostatics. In comparison to their electrostatic counterparts, the elastic multipoles have one extra tensorial index. Based on this structure, we identify possible types of elastic dipoles. An elastic dipole is characterized by three coefficients--isotropic strength, anisotropy, and chirality--and a two-component vector along the unperturbed director. The relationship between the dipole type and symmetry groups is established and sketches of various representative types of dipolar colloids are given. Instead of a single electric dipole, in the nematostatics there are four different pure types (dipolar singlets) and eight mixed types of elastic dipoles (one quintet, one quartet, two triplets, and four doublets). It is shown that the full symmetry of the colloid-induced director field and the colloid's shape (body) symmetry determine different dipole components. For instance, a helicoidal component of the anchoring easy axes can make a chiral elastic dipole of a colloid with the quadrupolar shape symmetry. The interaction potentials for different singlet and doublet dipoles are derived and illustrated in terms of the dipolar dyads and elastic Coulomb law. We argue that multipole parameters must be found by pure numerical means, as from ansatz director distributions one can find only orders of their magnitudes.

Low-frequency mechanical relaxation in CoO crystals

Internal friction Q−1 was studied in nominally pure and Li-doped CoO crystals at frequencies of about a few Hz in the temperature range from −180 to 20°C. Doping Co crystals with Li results in a new relaxation maximum of Q−1 at −115°C at a frequency of 3 Hz. The occurrence of this maximum is related to the reorientation of the Co3+-Li1+ elastic dipole under external stress.

Kinetic Monte-Carlo simulation of self-point defect diffusion in dislocation elastic fields in bcc iron and vanadium

Simulation of self-point defects (SPDs) diffusion in elastic fields of edge and screw dislocations in slip systems 〈111〉{110}, 〈111〉{112}, 〈100〉{100}, 〈100〉{110} in the temperature range 293–1000K has been performed by the object kinetic Monte-Carlo method for bcc iron and vanadium crystals with dislocation density ∼3×1014m−2. Interaction energies of SPDs (elastic dipoles) with dislocations were calculated by means of the anisotropic theory of elasticity. These elastic interactions significantly change dislocation sink efficiencies. Dislocation sink efficiencies decrease as the temperature increases and tend to the limit value for linear sink without interaction field. The dislocations are more efficient sinks for self-interstitial atoms (SIAs) than for vacancies. The difference between the sink efficiencies for SIAs and vacancies is several times less for screw dislocations than for edge dislocations.

Strain screening by mobile oxygen vacancies in SrTiO3

Recently, Freedman et al. [Phys. Rev. B 80, 064108 (2009)] calculated the elastic dipole tensor for several types of point defects in SrTiO3 and showed that it is nearly traceless for oxygen vacancies. Thus, mobile oxygen vacancies are predicted to screen elastic strain fields. Here, we report detailed diffuse x-ray scattering measurements of bulk SrTiO3 crystals prepared with controlled oxygen vacancy distributions. We verify the traceless nature of the elastic dipole tensor of an oxygen vacancy and demonstrate both correlations between oxygen vacancies and elastic strain screening by oxygen vacancies.

Shadowing in Compton scattering on nuclei

We evaluate the shadowing effect in deeply virtual and real Compton scattering on nuclei in the framework of the color dipole model. We rely on the soft photon wave function derived in the instanton vacuum model, and employ the impact parameter dependent phenomenological elastic dipole amplitude. Both the effects of quark and the gluon shadowing are taken into account.

Step interactions on Pt(111) vicinal surfaces determined by grazing incidence X-ray diffraction: Influence of the step orientation

We have studied the step–step interactions on the Pt(997) vicinal surface. Grazing incidence X-ray diffraction (GIXD) allowed us to measure the elastic atomic relaxations near the surface due to the steps. By means of the model of buried elastic dipoles, within the framework of anisotropic linear elasticity (ALE) calculations, the surface stress of Pt(111), and the elastic interaction between steps are deduced. The values so-obtained are compared to the values previously measured on the Pt(779) surface with the same technique. The comparison shows the strong influence of step geometry on step interactions.

Elastic displacements and step interactions on metallic surfaces: Grazing-incidence x-ray diffraction andab initiostudy of Au(332)

We have studied the energetics, relaxation, and interactions of steps on the Au(332) vicinal surface using a combination of grazing incidence x-ray diffraction, anisotropic linear elasticity theory, and ab initio density-functional theory. We find that the initial force distribution on a bulk-truncated surface, as well as the resulting pattern of atomic relaxations, can be reproduced excellently by a buried dipole elastic model. The close agreement obtained between experimental and calculated x-ray diffraction profiles allows us to precisely determine the value of the elastic dipole density at the steps. We also use these results to obtain an experimental estimate of the surface stress on an unreconstructed Au(111) facet, ${\ensuremath{\tau}}_{\text{Au}(111)}=2.3\ifmmode\pm\else\textpm\fi{}0.4\text{ }{\text{Nm}}^{\ensuremath{-}1}$, and the value of the step-step elastic interaction energy $A=950\ifmmode\pm\else\textpm\fi{}150\text{ }\text{meV}\text{ }\text{\AA{}}$.

Diffusion of self-point defects in body-centered cubic iron crystal containing dislocations

The energetic, crystallographic, and diffusion characteristics of self-point defects (SPDs) (vacancies and self-interstitial atoms (SIAs)) in body-centered cubic (bcc) iron crystal in the absence of stress fields have been obtained by the molecular statics and molecular dynamics methods. The effect of elastic stress fields of dislocations on the characteristics of SPDs (elastic dipoles) has been calculated by the methods of the anisotropic linear theory of elasticity. The SPD diffusion in the elastic fields of edge and screw dislocations (with Burgers vectors 1/2 〈111〉 and 〈100〉) at 293 K has been studied by the kinetic Monte Carlo method. The values of the SPD sink strength of dislocations of different types are obtained. Dislocations are more effective sinks for SIAs than for vacancies. The difference in the sink strengths for SIAs and vacancies in the case of edge dislocations is larger than the screw dislocations.

Acoustic emission and dielectric studies of phase transitions within the morphotropic phase boundary of xPb(Zr1/2Ti1/2)O3-(1−x)Pb(Ni1/3Nb2/3)O3 relaxor ferroelectrics

We have carried out a combined acoustic emission (AE) and dielectric permittivity study of the xPb(Zr1/2Ti1/2)O3-(1−x)Pb(Ni1/3Nb2/3)O3 relaxor ferroelectric ceramics with compositions x=0.7–0.9 corresponding to its morphotropic phase boundary. Temperatures of all phase transitions occurring on heating are identified accurately by AE, and a direct transition between the low-temperature (rhombohedral) and high-temperature (pseudocubic) relaxor phases is found. The AE peak intensity is generally proportional to the temperature derivative of the dielectric permittivity, in agreement with a model proposed for a thermally cycled small elastic dipole.

On modeling the mechanical behavior of heterostructures with quantum dots

The problems on simulation of a stressed-strained state in epitaxial quantum-dot heterostructures with and without coating are considered. Within the framework of the continuum approach, a mechanical-mathematical model of a quantum dot is developed. The stressed-strained state in a heterostructure with a quantum dot located under the coating is simulated within the developed model using the well-known analytical solution to the problem on inclusion of the corresponding shape. An isolated quantum dot in the absence of coating is simulated by a set of elastic dipoles uniformly distributed over the region of elastic half-space matching the quantum dot base. Within the model, the problem on deformation of the quantum-dot heterostructure without coating is analytically solved. The analytical solution is used to analyze the stressed-strained state in the structure under consideration.

Interaction of the Torque-Induced Elastic Charge and Elastic Dipole with a Wall in a Nematic Liquid Crystal

We show that the elastic charge of colloids in a nematic liquid crystal can be generated by the vector of external torque. The torque components play the role of two component charge (dyad) and give rise to the Coulomb-like potential, while their conservation law plays the role similar to that of Gauss' theorem in the electrostatics. The theory is applied to the colloid-surface interaction. A wall with homeotropic or planar director is shown to induce a repulsive 1/r4 force on the elastic dipole. The external torque, however, induces the elastic charge in this colloid and triggers switching to the 1/r2 repulsion

Real Compton scattering via color dipoles

We study the photoabsorption reaction and real Compton scattering within the color dipole model. We rely on a photon wave function derived in the instanton-vacuum model and on the energy-dependent phenomenological elastic dipole amplitude. Data for the photoabsorption cross section at high energies agree with our parameter-free calculations. We also provide predictions for the differential real Compton scattering cross section. Although no data for small angle Compton scattering are available so far, this process can be measured in ultraperipheral hadronic and nuclear collisions at the LHC.

The orientation dependent electromigration induced healing on the surface cracks and roughness caused by the uniaxial compressive stresses in single crystal metallic thin films

The first order unified linear instability analysis (ULISA) of the governing equation for evolutions of surfaces and interfaces under the capillary, electromigration, and elastostatic forces including the thermomigration (Soret effect) is developed very recently by the author. In the present application of the theory, the concurrent effects of uniaxial applied stresses and the electrostatic field on the sidewall morphological evolution of a single crystal thin metallic film are explored by dynamic computer simulations by taking the surface drift diffusion anisotropy fully into account. These computer experiments, which are supported by ULISA, clearly show that only the applied elastic compressive stresses are primary agents responsible for the morphological instability of the surface undulations through the elastic dipole tensor interactions but not the uniaxial tension loading in thin solid films. It is also demonstrated that these morphological instabilities manifested themselves as formations of the surface cracks and thus one may fully control the roughness. To do that, one needs to select crystal orientations properly with respect to the applied field so that a counteraction of the applied electrostatic fields (healing effect) is created above well defined threshold levels of electromigration. On the contrary to the healing effects, the improper selection of crystal orientations may drastically enhance the instability and eventually may cause catastrophic interconnect failure. At large normalized surface undulation amplitudes (a¯≥0.20), the drastic reductions in the decay rate constants (i.e., the strain relaxation rate) are detected in the nonlinear uniaxial tension regime compared to the ULISA theory regardless of the intensity of the normalized stress by analyzing the data obtained from the computer simulations. This situation is contrary to the results deduced from the low to moderate normalized amplitude (a¯≤0.10) measurements, where one finds that the decay rate constant closely obeys the prediction of the ULISA theory even for very high stress intensities.

Elastic effects of vacancies in strontium titanate: Short- and long-range strain fields, elastic dipole tensors, and chemical strain

We present a study of the local strain effects associated with vacancy defects in strontium titanate and report the first calculations of elastic dipole tensors and chemical strains for point defects in perovskites. The combination of local and long-range results will enable determination of x-ray scattering signatures that can be compared with experiments. We find that the oxygen vacancy possesses a special property---a highly anisotropic elastic dipole tensor which almost vanishes upon averaging over all possible defect orientations. Moreover, through direct comparison with experimental measurements of chemical strain, we place constraints on the possible defects present in oxygen-poor strontium titanate and introduce a conjecture regarding the nature of the predominant defect in strontium-poor stoichiometries in samples grown via pulsed laser deposition. Finally, during the review process, we learned of recent experimental data, from strontium titanate films deposited via molecular-beam epitaxy, that show good agreement with our calculated value of the chemical strain associated with strontium vacancies.

Hopping and clustering of oxygen vacancies in [formula omitted

It is shown that O vacancies ( V O ) in SrTiO 3 − δ with δ < 0.01 give rise to at least three anelastic relaxation processes associated with hopping of isolated vacancies (activation energy of 0.60 eV), reorientation of pairs (0.97 eV) and formation/dissolution of pairs and other clusters. Most of the V O are aggregated already at δ < 0.01 , so explaining why an activation energy of 1 eV is generally found in experiments probing the O mobility. The anelastic spectra are well interpreted in terms of a model taking into account the formation of pairs and chains of length ≤ 4 , whose concentrations are calculated with a method based on the construction of an approximated grand-partition function. The anisotropic component of the elastic dipole of an isolated O vacancy is rather small: Δ λ = 0.026 .

Interactions between solute atoms in Fe–Si–Al–C alloys as studied by mechanical spectroscopy

In Fe–Si–Al–C alloys, point-defect relaxation includes both the interstitial carbon Snoek-type relaxation, split into a “pure iron” (Fe–C–Fe) Snoek peak and an “interstitial–substitutional” (Fe–C–Me; Me = Al, Si) peak, and the substitutional Zener relaxation. The influence of Al and Si, with varying Al/Si ratio, on these effects is used to study the qualitative characteristics of substitutional–interstitial (Si–C, Al–C) and substitutional–substitutional (Al–Al, Si–Si, Al–Si) interactions in these alloys. Concerning the latter, there is a mutual compensation of the elastic distortion fields, produced in the Fe matrix by the relatively bigger Al and smaller Si atoms, respectively, which largely suppresses the Zener relaxation in the ternary Fe–Si–Al alloys, probably without affecting the elastic dipole strength of interstitial carbon. From the kinetic behavior of the two components of the Snoek-type relaxation, it is concluded that the substitutional–interstitial interaction is generally attractive and sufficient for modifying the distribution of the C atoms, but not for trapping to become dominant.

Colloid-wall interaction in a nematic liquid crystal: The mirror-image method of colloidal nematostatics

The new area of nematic colloidal systems (or nematic emulsions) has been greatly guided by the fruitful analogy between the colloidal nematostatics and electrostatics. The elastic charge density representation of the colloidal nematostatics [V. M. Pergamenshchik and V. O. Uzunova, Eur. Phys. J. E 23, 161 (2007); Phys. Rev. E 76, 011707 (2007)] develops this analogy at the level of charge density and Coulomb interaction. It shows, however, that the colloidal nematostatics in three dimensions substantially differs from the electrostatics both in its mathematical structure and physical implications: the elastic charge and multipoles are dyads; similar charges attract while opposite charges repel each other, and so on. In this paper we consider the interaction between an elastic charge and elastic dipole with a nematic surface (wall) at which the director alignment is fixed. Using the mirror image method of electrostatics as a guiding idea, we develop the mirror image method in the nematostatics for arbitrary director tilt at the wall. A wall is shown to induce a repulsive 1R{4} force on the elastic dipole which, in general, is accompanied by its reorientation. External torque on the colloid induces an elastic charge therein and triggers switching to the 1R{2} repulsion. The dyadic nature of an elastic dipole is shown to be essential: a particle-wall interaction potential cannot be obtained in phenomenological theories with a single component dipole. In the introductory sections we discuss connection between the director-mediated interaction in two and three dimensions and the electrostatic interaction and consider different symmetries of elastic dipoles. Conservation of the torque components exerted upon colloids is shown to play the role of Gauss' theorem and determines the elastic charge dyad.