Isotropic Substrate Research Articles

Effect of the electric field induced birefringence on the slab waveguide evanescent-wave sensor sensitivity

We have investigated the potential of using the E-field induced birefringence for improving the sensitivity of uniaxial anisotropic slab waveguide sensor based on evanescent wave interactions. LiNbO3 waveguide core was used as an example. We have calculated the sensor sensitivity formulas for the two kinds of modes propagating simultaneously in the waveguide sensor. In our study, we have distinguished between two different cases. The first case when the electric field is applied along the optic axis (+c) of the LiNbO3 wave guiding film (positive electric field); the second case when the electric field is applied opposite to the optic axis (−c) of such uniaxial crystal (negative electric field). The obtained results showed that, for positive electric field, increasing the electric field induces an increasing of the total anisotropy which causes decreasing on sensor sensitivity. However, for negative electric field, the increase of absolute values of negative electric field induces a decrease of the total anisotropy, the latter increases the sensor sensitivity. On the other hand, the study of the physical parameters on the sensor sensitivity showed that, to maximize the sensor sensitivity, it is advisable to use isotropic substrate that has a refractive index as closer as possible to the measurand index.

Study of an Inverted Rectangular Patch Printed on Anisotropic Substrates

ABSTRACTThe resonant frequencies and bandwidths of the inverted rectangular patch over anisotropic substrates are investigated in this paper. A rigorous analysis is performed using dyadic Green’s function formulation in the vector Fourier transform domain. The Galerkin’s technic is then used in the resolution of the integral equation; the complex resonance frequencies for the TM01 mode are studied with sinusoidal basis functions. The numerical results obtained are compared with previously published numerical results computed by means of the electromagnetic simulator “IE3D software”. Good agreement is found in all cases among all sets of results. For an isotropic substrate, it is confirmed that the bandwidth decreases with increasing of air-gap layer for high permittivity and low thickness of the substrate. Also, we show that the resonant frequencies and bandwidths are highly dependent on the permittivity variations alongside the optical axis. Other theoretical results attained display that the resonant frequencies downtrend monotonically with increasing substrate thickness, the diminution being larger for the uniaxial anisotropy of the substrate. Finally, numerical results for the effects of uniaxial anisotropy in the substrate on the radiation of the inverted rectangular microstrip structure are also presented.

The effect of orthotropic material gradation on the plane sliding frictional contact mechanics problem

With the advent of new functional and intelligent non-conventional materials, understanding the behavior of these materials in different contact conditions over the conventional materials is one of the most crucial aspects in early design process for coated systems. Therefore, the sliding contact problem for a functionally graded orthotropic coating–substrate system and a rigid cylindrical punch is considered in this article to study the aforementioned aspects. The functionally graded orthotropic coating is modeled to be bonded to an isotropic substrate of finite thickness and is loaded by a sliding rigid cylindrical punch under plane strain conditions. For the material orthotropy, five different real orthotropic materials are utilized and the stiffness coefficients of each principal direction are graded separately. Navier’s equations are converted to ordinary differential equations using the Fourier integral transformation technique. Then, the algebraic equations are solved and the problem is cast into a singular integral equation. A parametric finite element analysis based on augmented contact method is also conducted. The normalized surface stress distributions and the normalized contact boundaries obtained from finite element analysis are validated with the results obtained from singular integral equation approach. The results of this study may be helpful for engineers in design and optimization of the characteristics of non-conventional coatings that are used as thermal or structural barriers and wear-resistant surfaces in engineering applications.

Analytical Study on Propagation of G-Type Waves in a Transversely Isotropic Substrate beneath a Stratum considering Couple Stress

The present paper is framed to study analytically the propagation characteristics of the G-type wave through a functionally graded transversely isotropic substrate beneath a stratum with the consideration of couple stress. The couple stress theory concerned with size-dependent continuum mechanics, with additional parameter-characteristic length, accounts for the internal microstructure of materials, which provides deeper insight into the analysis of wave propagation aspects. Elastodynamic equations are laid down for the two media (stratum and substrate), and the frequency equation is derived by enforcing admissible boundary conditions. The solution process involves separation of variable technique and the method of infinite determinants. The frequency equation is reduced and found to fairly match with the classical Love-wave equation. The expression of group velocity of the G-type wave is also deduced in closed form. Numerical simulation and graphic illustration of the phase velocity as well as group velocity profiles of G-type waves are performed taking into account three different rocks in the functionally graded transversely isotropic substrate, i.e., granite (igneous rock), sandstone (sedimentary rock), and marble (metamorphic rock). The substantial effects of characteristic length associated with couple stress stratum, anisotropy, and functional gradedness on phase velocity is revealed and also traced out graphically. Comparative analysis of phase velocity and group velocity profiles of G-type waves for the three distinct previously mentioned rocks is one of the finest features of this study.

Analytical and finite element solution of the sliding frictional contact problem for a homogeneous orthotropic coating‐isotropic substrate system

AbstractIn this study, the contact problem for a homogeneous orthotropic coating‐isotropic substrate system is considered. The rigid stamp slides over the orthotropic coating whose bottom surface is bonded to a homogeneous isotropic substrate. The bottom surface of the substrate is fixed to the ground. By using Fourier integral transforms, the partial differential equations are converted to ordinary differential equations (ODEs). The displacement components for coating and substrate are obtained by solving the corresponding ODEs. A numerical study based on finite element analysis (FEA) is also conducted. The results from the analytical formulation are directly compared with the FEA results. The effects of orthotropic and isotropic material properties, coefficient of friction between the sliding surfaces, geometrical properties on the contact stresses and contact widths are presented. The results of this study may help tribology engineers to understand the deformation characteristics of the coating‐substrate systems and enhance their knowledge on friction and wear mechanisms of sliding surfaces.

Highly sensitive wearable 3D piezoresistive pressure sensors based on graphene coated isotropic non-woven substrate

Piezoresistive pressure sensors are deemed as a critical sensing component in wearable devices, and various polymer assembly with different structures are selected as flexible sensor substances. In this paper, low cost, commercial three-dimensional polyester non-woven fabrics (PNWFs) were employed as the sensor substrate whose advantages were elucidated through mathematical analysis. The effects of structure parameters (fiber diameter and fiber volume fraction) of 3D non-woven sensors on the sensing performance were analyzed. Reduced graphene oxide (rGO) and polydimethylsiloxane (PDMS) were deposited on the substrate to form the piezoresistive pressure sensor with a high conductivity 0.29 S/m after thermal reduction treatment. The assembled pressure sensors in general possessed excellent sensing characteristics, including excellent sensitivities of compressing (S = 23.41 kPa−1) and bending (S = 35.37 kPa−1), short response time (120 ms) and recovery time (240 ms), favorable resolutions (18 Pa under compressing and 21 Pa under bending) and low hysteresis value (0.8%). Finally, the pressure sensor has demonstrated successfully in detecting various physiological activities and subtle physiological signals, including walking, running, elbow flexing, finger bending, breathing, speaking and blood pulse beating.

Rigorous computation of a compact square patch antenna with notches using the moment method

A new rigorous computation of a square microstrip patch antenna with dual square notches at the two corners of the diagonal using Galerkin’s method in the spectral domain is presented; the dyadic Green’s functions of the problem are well resolved by the (TM, TE) representation. The spectral domain formulation of this square patch antenna with square notches for circular polarization and printed on an isotropic substrate is developed and calculated based on the study of a simple square patch antenna. Comparisons of the left hand circular polarization (LHCP) and right hand circular polarization (RHCP) patterns at various planes with different frequencies are also presented. Moreover, the effect of some parameters on the radiation characteristics of this proposed square patch with square notches has been investigated. The proposed structure is attractive and do not require exterior circuitry or large space compared to other designs that impose stacked multilayer configurations or a complex matching system to create circular polarization. Furthermore, this proposed structure exhibits the advantage of the simplicity of the design which needs only the cutting of two identical squares at the two opposite edges of the square patch, and; hence, requires only the same dimensions of the square notches at two corners of the diagonal to be determined.

A full-field crystal plasticity study on how texture and grain structure influences hydrostatic stress in thermally strained β-Sn films

The present study uses full-field thermo-mechanically coupled crystal plasticity to simulate the stress distribution in thermally strained β-Sn films to better understand the conditions causing the generally rare nucleation of whiskers from such films. Following the notion that stress-driven diffusion along the grain boundary network is leading to and supporting whisker formation, the goal is to identify critical factors of crystallographic and/or geometric nature that influence the hydrostatic stress in such films prior to the onset of actual whisker formation. Approximating the film as a periodic structure of around a hundred columnar grains on an isotropic substrate, the simulations reveal a strong spatial variation of hydrostatic stress over distances comparable to the grain size but without apparent long-range gradients, suggesting whisker nucleation to be a phenomenon that depends on specifics within a relatively small neighborhood of grains. Furthermore, neither the grain size distribution nor the presence of oblique surface grains alters the width of the stress distribution by much. In contrast, the variation of hydrostatic stress notably depends on the crystallographic texture of the film, where β-Sn films for which the film normal is aligned with ⟨0 0 1] show a narrower distribution than films with ⟨1 0 0] parallel to the normal. The former film texture, therefore, is predicted to be less prone to whisker formation than the latter.

Stiffness Measurement of Soft Silicone Substrates for Mechanobiology Studies Using a Widefield Fluorescence Microscope.

Soft tissues in the human body typically have stiffness in the kilopascal (kPa) range. Accordingly, silicone and hydrogel flexible substrates have been proven to be useful substrates for culturing cells in a physical microenvironment that partially mimics in vivo conditions. Here, we present a simple protocol for characterizing the Young's moduli of isotropic linear elastic substrates typically used for mechanobiology studies. The protocol consists of preparing a soft silicone substrate on a Petri dish or stiff silicone, coating the top surface of the silicone substrate with fluorescent beads, using a millimeter-scale sphere to indent the top surface (by gravity), imaging the fluorescent beads on the indented silicone surface using a fluorescence microscope, and analyzing the resultant images to calculate the Young's modulus of the silicone substrate. Coupling the substrate's top surface with a moduli extracellular matrix protein (in addition to the fluorescent beads) allows the silicone substrate to be readily used for cell plating and subsequent studies using traction force microscopy experiments. The use of stiff silicone, instead of a Petri dish, as the base of the soft silicone, enables the use of mechanobiology studies involving external stretch. A specific advantage of this protocol is that a widefield fluorescence microscope, which is commonly available in many labs, is the major equipment necessary for this procedure. We demonstrate this protocol by measuring the Young's modulus of soft silicone substrates of different elastic moduli.

Indexing of grazing-incidence X-ray diffraction patterns: the case of fibre-textured thin films.

Crystal structure solutions from thin films are often performed by grazing-incidence X-ray diffraction (GIXD) experiments. In particular, on isotropic substrates the thin film crystallites grow in a fibre texture showing a well defined crystallographic plane oriented parallel to the substrate surface with random in-plane order of the microcrystallites forming the film. In the present work, analytical mathematical expressions are derived for indexing experimental diffraction patterns, a highly challenging task which hitherto mainly relied on trial-and-error approaches. The six lattice constants a, b, c, α, β and γ of the crystallographic unit cell are thereby determined, as well as the rotation parameters due to the unknown preferred orientation of the crystals with respect to the substrate surface. The mathematical analysis exploits a combination of GIXD data and information acquired by the specular X-ray diffraction. The presence of a sole specular diffraction peak series reveals fibre-textured growth with a crystallographic plane parallel to the substrate, which allows establishment of the Miller indices u, v and w as the rotation parameters. Mathematical expressions are derived which reduce the system of unknown parameters from the three- to the two-dimensional space. Thus, in the first part of the indexing routine, the integers u and v as well as the Laue indices h and k of the experimentally observed diffraction peaks are assigned by systematically varying the integer variables, and by calculating the three lattice parameters a, b and γ. Because of the symmetry of the derived equations, determining the missing parameters then becomes feasible: (i) w of the surface parallel plane, (ii) the Laue indices l of the diffraction peak and (iii) analogously the lattice constants c, α and ß. In a subsequent step, the reduced unit-cell geometry can be identified. Finally, the methodology is demonstrated by application to an example, indexing the diffraction pattern of a thin film of the organic semiconductor pentacenequinone grown on the (0001) surface of highly oriented pyrolytic graphite. The preferred orientation of the crystallites, the lattice constants of the triclinic unit cell and finally, by molecular modelling, the full crystal structure solution of the as-yet-unknown polymorph of pentacenequinone are determined.

A new approach to analyze a resistive patch antenna excited by a microstrip line and printed on an anisotropic substrate with superstrate

An improved model is presented to study the effect of a superstrate on a resistive rectangular microstrip antenna fed by a microstrip line and printed on anisotropic substrate. A new accurate computation with different unknown currents of the electric field on overlap, feed line and resistive patch is studied by the Fourier transform, considering the Galerkin’s method and entire domain basis functions. Additionally, the scattering radar cross section (RCS) was studied for this novel resistive patch taking into account the effect of the nonzero surface resistance, the superstrate and the anisotropic substrate. To determine the unknown current modes on the patch, the electric field integral equation can be discretized into a matrix form that incorporates the effect of the superstrate, the anisotropic substrate and the currents on the feed line which are efficiently developed. Moreover, the necessary terms to represent the resistive patch are derived and are included in the equation in the form of a resistance matrix. RCS reduction is obtained for high superstrate thicknesses and low superstrate permittivities. Also, the addition of a resistance on the surface of the patch antenna provides a scattered energy diminution. Moreover, the RCS of this novel structure is affected by both $$\varepsilon _z $$ and $$\varepsilon _x $$ permittivities change, however, has drastically changed due to the $$\varepsilon _x $$ permittivity change. In order to validate the theoretical results, a study has been achieved for a perfectly conducting patch on isotropic substrate, without superstrate and excitation, and the results were compared well with other papers. This subject has not been treated or reported previously in the literature, and there has been very little work on the scattering RCS of only simple perfectly conducting patch antennas.

Superconducting pairing of topological surface states in bismuth selenide films on niobium.

A topological insulator film coupled to a simple isotropic s-wave superconductor substrate can foster helical pairing of the Dirac fermions associated with the topological surface states. Experimental realization of such a system is exceedingly difficult, however using a novel "flip-chip" technique, we have prepared single-crystalline Bi2Se3 films with predetermined thicknesses in terms of quintuple layers (QLs) on top of Nb substrates fresh from in situ cleavage. Our angle-resolved photoemission spectroscopy (ARPES) measurements of the film surface disclose superconducting gaps and coherence peaks of similar magnitude for both the topological surface states and bulk states. The ARPES spectral map as a function of temperature and film thickness up to 10 QLs reveals key characteristics relevant to the mechanism of coupling between the topological surface states and the superconducting Nb substrate; the effective coupling length is found to be much larger than the decay length of the topological surface states.

Optimized dynamic design of laminated piezocomposite multi-entry actuators considering fiber orientation

Laminated piezocomposite actuators (LAPA) are structures composed of piezoelectric and non-piezoelectric materials layers. Due to several parameters and the multiphysics domain involved in the design of LAPA, simple forms are commonly found in industrial applications. However, its design can be systematized by using the topology optimization method (TOM) that permits the solution of complex problems. The design of LAPA with TOM has traditionally considered the optimization of piezoelectric materials over an isotropic substrate, yet some previous researches suggest that LAPA including fiber-reinforced composite layers can increase the performance of these transducers. In addition, works dealing with fiber-based composite focus on static or harmonic analysis with sinusoidal excitations, although other signal inputs are used in practice. In fact, the design of fiber-based LAPA in transient regime has not been assessed before. Thus, a methodology is proposed here to design LAPA with TOM. The actuator is electrically excited with a combined waveform: a sine wave treated as a harmonic problem and a step excitation addressed as a transient problem. Both waves have the same frequency, however they are not applied at the same time. This approach allows the development of a multi-entry actuator since it generates the same level of output displacement independently of the type of excitation input. Consequently, the optimization problem is formulated with the purpose of distributing the material in all layers, the polarization sign in piezoelectric layers and the fiber orientation angle in composite layers, in which the objective function simultaneously seeks for the maximization of the vibration amplitude at certain points of the actuator and its response speed. Eight-node shell elements taking into account the piezoelectric effects are used in the finite element method (FEM) and the “layer wise theory is adopted to model the laminated structure. The Generalized-α method is used to solve the transient problem. In order to optimize the material distribution and the polarization sign, the classical SIMP and PEMAP-P models are used respectively, while to optimize the fiber orientation angles in the composite material, a novel self-penalizable interpolation model is proposed. This optimization problem is solved by using the sequential linear programming (SLP) technique with the CVX solver and the sensitivity analysis is performed with the adjoint method. Discrete signal processing concepts are applied to solve the adjoint problem involving specific points of curves obtained by time integration methods in transient analysis. Numerical techniques are implemented to avoid TOM instabilities. Finally, the potential of this approach is demonstrated with two numerical examples.

The sliding contact problem for an orthotropic coating bonded to an isotropic substrate

We consider the sliding contact problem of an orthotropic coating/substrate system. The coating/substrate system is pressed by a rigid flat or cylindrical stamp. For the orthotropic coating, the principal material directions are assumed to be parallel and perpendicular to the contact surface. The governing integral equations corresponding to the mentioned contact problem are extracted by means of the Fourier transform technique. Later, the numerical solution of the singular integral equations is provided by applying the Gauss-Chebyshev integration method. The main goal of this study is to obtain analytical benchmark solutions in order to examine the effect of material orthotropy parameters, relative stiffness, the coefficient of friction and the coating thickness on the stress distribution at the surface of the orthotropic coating. The behavior of the surface in-plane stress intensity factor is analyzed as well. For a constant value of the applied load, the results indicate that the stiffness ratio and the shear parameter have a more pronounced effect on the surface stress components than the effective Poisson's ratio. Also, the stress intensity factor at sharp edges of the flat punch decreases as the coating softens with respect to the substrate and/or the coating thickness decreases.

Fano line shapes of leaky surface acoustic waves extending from supersonic surface wave points

This paper highlights the close connection between two issues that are attracting considerable attention in diverse areas of physics including photonics, acoustics, fluid dynamics and the dynamical properties of periodic structures, namely bound states in a continuum (BIC), and asymmetric Fano resonance line shapes. The discussion is framed in the context of solid state acoustics, with supersonic surface acoustic waves (supersonic-SAW) taken as representative examples of BIC. One of these pertains to the surface of an anisotropic solid and the other to an isotropic layer on an isotropic substrate. These are surface modes lying within a continuum of bulk radiating states, which at isolated values of the system parameters become uncoupled from these states. We demonstrate how for generic non-symmetry-protected supersonic-SAW, varying these parameters leads to the unfolding of this mode into a leaky pseudo-SAW, with the resonance line shape conforming accurately to the Fano expression. With passage through the SSAW point in parameter space, the Fano q parameter diverges and changes sign. It is anticipated that this is a fairly general feature of the unfolding of BIC with variation of relevant control parameters.

Quenched disorder of a nematic liquid crystal under a magnetic field

We report measurements and theoretical predictions on the effect of an aligning magnetic field on the orientational disorder of a nematic liquid crystal in contact with isotropic solid substrates. Different types of substrates present a similar disorder and a similar dependency on the magnetic field amplitude, i.e. a decreasing of the angular distribution widths and spatial correlation lengths. Measurements are in qualitative agreement with a theory where the orientational disorder emerges from the competition between the aligning magnetic torque and the disorienting thermal fluctuations during the adsorption of the liquid crystal molecules on the substrate.

Stripe domains in epitaxial BiFeO3 thin films on (100) SrTiO3 substrates

Highly crystallized ferroelectric BiFeO3 thin films were deposited on various miscut (100) SrTiO3 substrates. The domain structure of the films varies with substrate miscut angles and atomic-layer termination at the surface. The BiFeO3 thin films grown on 4° miscut substrates exhibit 71° periodic stripe domains consisting of two downward polarization variants. In contrast, four downward variants coexist in the films deposited on 0.2° miscut substrates, regardless of atomic-layer termination at the surface of the substrate. The introduction of an additional SrTiO3 repair layer on the same substrate results in a step-flow growth mode of the film. It is believed that the improved mobility of the BiFeO3 atomic species during the film growth leads to the appearance of preferred ferroelectric variants at the step edges. These preferred variants eventually form stripe domains. Our results reveal that both the miscut angle and the step-flow growth promote the formation of the two variant striped domains in BiFeO3 films deposited on decorated isotropic SrTiO3 substrates.

On the influence of lipid-induced optical anisotropy for the bioimaging of exo- or endocytosis with interference microscopic imaging.

Some implementations of interference microscopy imaging use digital holographic measurements of complex scattered fields to reconstruct three-dimensional refractive index maps of weakly scattering, semi-transparent objects, frequently encountered in biological investigations. Reconstruction occurs through application of the object scattering potential which assumes an isotropic refractive index throughout the object. Here, we demonstrate that this assumption can in some circumstances be invalid for biological imaging due to the presence of lipid-induced optical anisotropy. We show that the nanoscale organization of lipids in the observation of cellular endocytosis with polarized light induces a significant change in far-field scattering. We obtain this result by presenting a general solution to Maxwell's equations describing light scattering of core-shell particles near an isotropic substrate covered with an anisotropic thin film. This solution is based on an extension of the Bobbert-Vlieger solution for particle scattering near a substrate delivering an exact solution to the scattering problem in the near field as well as far field. By applying this solution to study light scattering by a lipid vesicle near a lipid bilayer, whereby the lipids are represented through a biaxial optical model, we conclude through ellipsometry concepts that effective amounts of lipid-induced optical anisotropy significantly alter far-field optical scattering in respect to an equivalent optical model that neglects the presence of optical anisotropy.

Asymmetric Green’s functions for exponentially graded transversely isotropic substrate–coating system

By virtue of a complete set of two displacement potentials, an analytical derivation of the elastostatic Green’s functions of an exponentially graded transversely isotropic substrate–coating system is presented. Three-dimensional point–load and patch–load Green’s functions for stresses and displacements are given in line-integral representations. The formulation includes a complete set of transformed stress–potential and displacement–potential relations, with utilizing Fourier series and Hankel transforms. As illustrations, the present Green’s functions are degenerated to the special cases such as an exponentially graded half-space and a homogeneous two-layered half-space Green’s functions. Because of complicated integrand functions, the integrals are evaluated numerically and for numerical computation of the integrals, a robust and effective methodology is laid out which gives the necessary account of the presence of singularities of integration. Comparisons of the existing numerical solutions for homogeneous two-layered isotropic and transversely isotropic half-spaces are made to confirm the accuracy of the present solutions. Some typical numerical examples are also given to show the general features of the exponentially graded two-layered half-space Green’s functions that the effect of degree of variation of material properties will be recognized.

A theoretical model describing the one-dimensional growth of single crystals on free sustained substrates

We develop a theoretical model that interprets the growth mechanism of zinc (Zn) crystal nanorods on a liquid substrate by thermal evaporation. During deposition, Zn atoms diffuse randomly on an isotropic and quasi-free sustained substrate, the nucleation of the atoms results in the primary nanorod (or seed crystal) growth. Subsequently, a characteristic one-dimensional atomic aggregation is proposed, which leads to the accelerating growth of the crystal nanorod along its preferential growth direction until the growth terminates. The theoretical results are in good agreement with the experimental findings.