Re-entrant Angles Research Articles

The Vaults of St. John the Theologian at Ephesos

E ver since the first excavation of the remains of the church of St. John the Theologian on the hill of Ayasoluk, the reconstruction of the vaulted, sixth-century phase of the monument has been a major challenge in the field of early Byzantine architecture. This is partly due to the historic significance of the building. According to the contemporary account of Procopius, the church, rebuilt and enlarged under the auspices of Justinian, constituted the Ephesian counterpart to the Constantinopolitan church of the Holy Apostles.1 It was later to become the heart of medieval Ephesos and one of the most important pilgrimage churches in Asia Minor.2 Besides its historical interest, the reconstruction of St. John’s has a great significance for the study of early Byzantine vaulting technology. Indeed, reconstruction offers the only opportunity to recapture the form of the enormous brick vaults of the church, which are now lost. These sophisticated vaults, which seem to have survived in an earthquake-prone area for more than eight centuries, constitute a remarkable feat of structural engineering.3 They must have been a highly innovative structure, erected at a time when most churches were timber-roofed. The task of accurate and reasoned reconstruction through the scrutiny of archaeological evidence is more demanding than it may initially appear, in spite of the systematic exploration of the monument since its discovery in 1921. Eight decades of excavation and survey have made the ground plan of the aisled cruciform church as well as the footprint of its atrium, baptistery and skeuophylakion mostly clear (Figure 1).4 Some parts have even become the object of full-scale physical reconstruction (Figure 2). In addition to this, Hans Hormann, Mustafa Buyukkolanci, and Andreas Thiel have shed light on the building phases that preceded Justinian’s vaulted church.5 Still, in spite …

Texture control of fluorine-doped tin oxide thin film

The texture control of transparent oxide thin film, the crystalline orientation, is very important, because it is related to the electrical resistivity and the optical transparency. It is known that the crystal orientation could be controlled by varying precursor source, gas flow rate, and deposition temperature. We deposited fluorine-doped tin oxide (FTO) thin film on aluminoborosilicate glass by spraying water-based solution and ethyl alcohol-added solution. We showed in this research that (200) and (301) preferential orientation of FTO thin film can be controlled by the addition of ethyl alcohol to FTO coating solution. (200) oriented FTO thin film deposited from ethyl alcohol-added solution comprises of pyramidal crystallites with {111} polar faces, which contain {101} contact twin planes. {101} contact twin planes forms salient reentrant angle which provides nucleating sites and makes crystallites grow abnormally. (301) orientation is thought through Periodic Bond Chains of tin hydroxide which forms prismatic long crystallites. Prismatic crystallites are comprised of {110} crystal faces which contain {101} repeated contact twin. It is very helpful to control (200) or (301) oriented crystal formation in transparent conducting oxide film, because the texture affects the electrical and optical properties of transparent conducting oxide film. We suggest that ethyl alcohol addition plays a role to form crystallites with {111} polar faces corresponding to (200) preferential orientation. The crystal morphologies are changed by doping elements, precursor sources, deposition conditions like flow rate and temperatures, and solvents.

The UCM limit of the PTT equations at a re-entrant corner

We consider the Upper Convected Maxwell (UCM) limit of the Phan-Thien–Tanner (PTT) equations for steady planar flow around re-entrant corners. The PTT equations give the UCM equations in the limit of vanishing model parameter κ, this dimensionless parameter being associated with the quadratic stress terms in the PTT model. We show that the critical length scale local to the corner is r = O κ 1 2 ( 1 − α ) as κ → 0, where π/ α is the re-entrant corner angle with α ∈ [1/2, 1) and r the radial distance. On distances far smaller than this we obtain the PTT κ = 1 problem, whilst on distances greater (but still small) we obtain the UCM problem κ = 0. This critical length scale is that on which intermediate behaviour of the PTT model is obtained where both linear and quadratic stress terms are present in the wall boundary layer equations. The double limit κ → 0, r → 0 thus yields a nine region local asymptotic structure.

Slanted and Conical Electroplated Structures Created Using Photoresist Deformation

Electroplating structures with a reproducible slanted angle is difficult at the sub-micron scale. One application for this shape is in magnetic write heads, where a tapered magnetic pole near the surface of a magnetic head is desirable for writing magnetic media at higher areal densities. We will discuss a deep UV sensitive photoresist coupled with a shrink process which yields a convex shaped resist structure. Although the process is similar to a SAFIER process used in via hole applications, an altered thickness of the resist produced unexpected results. Furthermore, a metrology process will be presented to correlate resist deformation of a test structure with the reentrant angle at the base of the resist wall.

Silicon Surface Structure-Controlled Oleophobicity

Superoleophobic surfaces display contact angles >150 degrees with liquids that have lower surface energies than does water. The design of superoleophobic surfaces requires an understanding of the effect of the geometrical shape of etched silicon surfaces on the contact angle and hysteresis observed when different liquids are brought into contact with these surfaces. This study used liquid-based metal-assisted etching and various silane treatments to create superoleophobic surfaces on a Si(111) surface. Etch conditions such as the etch time and etch solution concentration played critical roles in establishing the oleophobicity of Si(111). When compared to Young's contact angle, the apparent contact angle showed a transition from a Cassie to a Wenzel state for low-surface-energy liquids as different silane treatments were applied to the silicon surface. These results demonstrated the relationship between the re-entrant angle of etched surface structures and the contact angle transition between Cassie and Wenzel behavior on etched Si(111) surfaces.

Bounds to eigenvalues of the Laplacian on L-shaped domain by variational methods

In this study, the bounds for eigenvalues of the Laplacian operator on an L-shaped domain are determined. By adopting some special functions in Goerisch method for lower bounds and in traditional Rayleigh–Ritz method for upper bounds, very accurate bounds to eigenvalues for the problem are obtained. Numerical results show that these functions can also be successfully used to solve the problem on the region with other reentrant angle.

Solution Growth and Structures of Semiconducting Distyryl-Oligothiophene

Large single crystals of 5,5′-distyryl-2,2′-bithiophene (DS-2T) were grown from tetrahydrofurane (THF) solution, and the crystal structure was analyzed by x-ray diffractometry. In-situ observation of crystal growth in solution was performed, and a unique change in the crystal habit depending on growth conditions is found. The change in crystal habit from a truncated parallelogram shape to a slender hexagonal shape with re-entrant angles at the both side can be explained as the consequence of kinetic roughing and Berg effect.

3-D vibration analysis of annular sector plates using the Chebyshev–Ritz method

The three-dimensional free vibration of annular sector plates with various boundary conditions is studied by means of the Chebyshev–Ritz method. The analysis is based on the three-dimensional small strain linear elasticity theory. The product of Chebyshev polynomials satisfying the necessary boundary conditions is selected as admissible functions in such a way that the governing eigenvalue equation can be conveniently derived through an optimization process by the Ritz method. The boundary functions guarantee the satisfaction of the geometric boundary conditions of the plates and the Chebyshev polynomials provide the robustness for numerical calculation. The present study provides a full vibration spectrum for the thick annular sector plates, which cannot be given by the two-dimensional (2-D) theories such as the Mindlin theory. Comprehensive numerical results with high accuracy are systematically produced, which can be used as benchmark to evaluate other numerical methods. The effect of radius ratio, thickness ratio and sector angle on natural frequencies of the plates with a sector angle from 120° to 360° is discussed in detail. The three-dimensional vibration solutions for plates with a re-entrant sector angle (larger than 180°) and shallow helicoidal shells (sector angle larger than 360°) with a small helix angle are presented for the first time.

Analytical solution for free vibration of transversely isotropic sector plates using a boundary layer function

The exact analytical solution based on the Mindlin's plate theory is presented for the free vibration of a transversely isotropic sector plate. The plate has simply supported radial edges and arbitrary conditions along the circular edge. By introducing a boundary layer function, the three coupled governing equations of motion have been converted into two uncoupled equations. Solving the uncoupled equations and satisfying the boundary conditions yields an eigenvalue problem for finding the natural frequencies. Non-dimensional frequency parameter is presented for over a wide range of salient ( α⩽180) and re-entrant (180< α⩽360) angles, some thickness–radius ratios and different boundary conditions along the circular edge.

THE CRYSTAL STRUCTURE OF MCKELVEYITE-(Y)-2M, A NEW MONOCLINIC POLYTYPE FROM VAL MALENCO, ITALIAN ALPS

A new monoclinic ( Cc ) polytype, mckelveyite-(Y)-2 M , NaBa 3 CaY(CO 3 ) 6 ·3H 2 O, was found in “Cava Fabi”, a talc quarry near Lanzada in Val Malenco, Lombardy, Italy, associated with anatase, brookite, brucite, calcite, dolomite, ilmenite, lindsleyite, magnesite, magnetite, pyrite, quartz, redledgeite and rutile, in hydrothermal carbonate veins intercalated in ultrabasic rocks and dolomitic marble in contact with serpentinites. The origin of the mineral is related to circulation of CO 2 -rich fluids in serpentinites, during the latest stages of Alpine metamorphism. The monoclinic mineral, space group Cc , has cell parameters a 15.8213(7), b 9.1364(4), c 13.7522(6) A, β 112.44(1)°, V 1837.35(15) A 3 , with marked pseudorhombohedral symmetry. The crystals are pseudopyramidal, up to 4 mm in length, with distinct trigonal character derived from intergrowth of three individuals twinned about a pseudo-threefold axis, in some cases showing re-entrant angles. The chemical analysis obtained by wavelengthdispersion electron-microprobe analysis, supplemented by structural data for CO 2 and H 2 O, gave (wt%): Na 2 O 3.50, CaO 5.68, SrO 3.45, BaO 45.33, Y 2 O 3 8.82, Sm 2 O 3 0.05, Gd 2 O 3 0.45, Dy 2 O 3 1.10, Er 2 O 3 0.85, Yb 2 O 3 0.08, CO 2 27.13, H 2 O 5.55, total 101.99, corresponding to the empirical formula (calculated on the basis of six metal sites in the asymmetric unit, as shown in the structure solution): Na 1.00 (Ca 0.83 Na 0.07 Sr 0.11 ) ∑1.01 (Ba 2.79 Sr 0.20 ) ∑2.99 (Y 0.74 REE 0.13 Ca 0.12 ) ∑0.99 [CO 3 ] 6 ·3H 2 O. The crystal structure has been refined to a final R = 0.0283 for 4454 observed reflections [ I > 2σ( I )], and corresponds to the first accurate determination of the structure of mckelveyite-(Y). The unit cell contains three independent atomic sites occupied by Ba plus minor Sr, and three sites occupied almost exclusively by Na + , Ca 2+ , and Y 3+ (plus the REE), respectively; there are alternate double layers of pseudohexagonal rings perpendicular to the c* axis containing either the Ba atoms or the other metal atoms, with no substantial disorder; each double layer is the mirror image on {010} of the adjacent ones. The strongest six lines in the X-ray powder-diffraction pattern [ d obs in A( I ) hkl ] are: 3.106(100)(312), 4.299(48)(310), 6.369(36)(002), 2.029(29)(602), 3.180(28)(004), 2.635(27)(602). The pattern shows significant differences with respect to type triclinic mckelveyite-(Y).

Experimental and Theoretical Morphology of Single and Twinned Crystals of Li2CO3 (Zabuyelite)

Crystals of lithium carbonate (monoclinic C2/c) have been synthesized from aqueous solution at room temperature and pressure. Their observed growth morphology, essentially made by {001}, {1̅01}, and {110} forms, has been compared with the theoretical one calculated applying the Hartman−Perdok method and using a formal charge potential function. Theoretical crystal equilibrium shape has also been obtained and compared with that resulting from ab initio calculations. The growth shape of the usually observed 100 contact twins is interpreted as well, on the basis of the energetic misfit of the 100 twin law and the kinetic effect due to the presence of salient and re-entrant angles at the twin original composition plane.

Reentrant cone angle dependence of the energetic electron slope temperature in high-intensity laser-plasma interactions

Energy spectra of fast electrons, generated when high-intensity laser pulses irradiated hollow conical targets, have been measured experimentally. It is shown here that the slope temperature of the fast electrons is strongly dependent on the opening angle of the cone, and has a maximum value at 25°. The data confirms optical guiding of the laser pulse, by comparison of the measured electron temperature with ray-tracing calculations that include absorption in plasmas. The enhanced energy flow and intensity induced by optical guiding of the laser pulse inside the cone as a function of the opening angle as well as the f-number of the focusing optics is discussed.

The Dependence of Thermal-Cycling-Induced Failure Mechanism on Topological Feature of Passivated Metallic Conductors in Plastic-Encapsulated Microelectronic Devices

This work presents how thermal-cycling-induced cracking in a device pattern is influenced by manipulating the topological feature of passivated metallic conductors. The modification of the topological feature is done by the variation of the sidewall slope of metallic conductors. In order to compare thermal-cycling reliability in two kinds of devices with different surface morphologies, each device is prepared to have pre-existing cracks along its edge region. The propagation behavior of the cracks is then investigated for each device. Discontinuous but fast crack propagation is observed for the device with the poor topological feature (i.e., 70°-sidewall slope) during thermal-cycling from -65 to 150 °C. On the other hand, continuous but limited crack growth is detected for the device with the improved topological feature (i.e., 130°-sidewall slope). The reason why cracking behavior differs, depending on the different re-entrant angle of each device pattern, is explained by numerical calculation. Finite-element method (FEM) work shows that the concentration of shear stress at the re-entrant corner of the passivated metallic conductor with the steep sidewall slope is responsible for such discontinuous crack propagation. Therefore, if the topological feature of passivated metallic conductors is improved, the rapid propagation of the pre-existing crack such as sawing-induced damage into the active device pattern will be effectively prevented to ensure thermal-cycling reliability.

A finite element method using singular functions for Poisson equations: Mixed boundary conditions

In [Z. Cai, S. Kim, A finite element method using singular functions for the Poisson equation: corner singularities, SIAM J. Numer. Anal. 39 (2001) 286–299], we proposed a new finite element method to compute singular solutions of Poisson equations on a polygonal domain with re-entrant angles. Singularities are eliminated and only the regular part of the solution that is in H 2 is computed. The stress intensity factor and the solution can be computed as a post-processing step. This method is extended to problems with crack singularities and to a higher-order method for smooth data in [Z. Cai, S. Kim, G. Woo, A finite element method using singular functions for the Poisson equation: crack singularities, Numer. Linear Algebra Appl. 9 (2002) 445–455]. In this paper, we study the Poisson equation with mixed boundary conditions. Examples with various singular points and numerical results are presented.

Abnormal Grain Growth of Pb(Mg1/3Nb2/3)O3-35 mol% PbTiO3 Ceramics Induced by the Penetration Twin

Pb(Mg 1/3 Nb 2/3 )O 3 -35 mol% PbTi0 3 (PMN-35PT) specimens with a 5 mol% excess PbO were prepared by excessive heat treatment at 1150°C to induce abnormal grain growth. Through electron backscatter diffraction analysis and the observation of a three-dimensional morphology, the abnormally grown PMN-35PT grains were found to be twinned crystals with penetration characteristics. The morphology of the PMN-35PT twinned crystal was crystallographically analyzed. The abnormal grain growth of PMN-35PT is suggested to be due to preferential growth at the reentrant angles formed by twins.

Growth of nordstrandite: effect of chloride on surface morphology

The effect of chloride on the growth of the Al(OH) 3 mineral nordstrandite in ethylenediamine solutions has been investigated. Atomic force microscopy (AFM) observations revealed a difference in the morphology of monolayer steps on the basal faces of the crystals. The steps are made up of straight segments, down to a horizontal resolution of a few nanometers. These segments are shorter for the crystals precipitated in the presence of chloride. However, they show no difference in crystallographic orientation compared to those of the crystals synthesized without added chloride. Double steps are more prevalent for crystals synthesized with higher chloride concentrations. For crystals synthesized in the control solutions, two-dimensional nucleation on the surfaces only occurred at a few points and concentric steps were commonly observed. However, for crystals synthesized in the presence of chloride, the nucleation sites were more evenly spread. The observations suggest that the differences in the step morphology between the nordstrandite crystals synthesized in the presence of chloride and those synthesized in the control solutions are due to the adsorption of chloride at the steps. For all twinned crystals, two-dimensional nucleation occurred preferentially at point sources within the re-entrant angles. Spiral growth was only observed in one case.

Ridged LiNbO&amp;lt;tex&amp;gt;$_3$&amp;lt;/tex&amp;gt;Modulators Fabricated by a Novel Oxygen-Ion Implant/Wet-Etch Technique

This paper demonstrates a new ion implantation and wet-etch technique for fabricating high-quality ridged optical waveguides for high-speed LiNbO/sub 3/-based optical modulators. In addition, the paper demonstrates the fabrication of optical waveguide ridges >3 /spl mu/m in height with 90/spl deg/, and even re-entrant sidewall angles for the first time. The modeling used indicates that 90/spl deg/ (and re-entrant) sidewall ridges can reduce the required modulator drive voltage by 10-20% over modulators with conventional trapezoidal ridge profiles fabricated with reactive ion etching. A 40-Gb/s modulator with a 30-GHz bandwidth, 5.1-V switching voltage at 1 GHz, and a 4.8-dB optical insertion loss is fabricated using the ion implantation/wet-etch process. Fabricated devices showed good stability against accelerated aging, indicating that this process could be used for commercial purposes.

Optimisation of the superplastic forming of a dental implant for bone augmentation using finite element simulations

Objectives. The phenomenon of superplasticity has made it possible to form complex shapes that require extremely high degrees of ductility in titanium alloy with minimal internal stresses. Combined with the use of an investment casting material as the die material, which makes possible the forming of re-entrant angles, it is possible to produce membranes for ridge augmentation. The aim is to characterise the metal alloy sheet and simulate the superplastic forming process in three dimensions to produce process parameters, namely gas pressure as a function of time, to accurately adapt the titanium sheet to the bone surface. Method. The surface of the die was digitised using a 3D laser scanning system (UBM-Keyence LC2450). Ti-6Al-4V sheet of 140 mm diameter was modelled using a grid of triangular membrane elements. This mesh was automatically refined during the simulations. Finite element simulation was carried out using the Superflag software program (University of Wales Swansea) Three different options for gas pressure control were adopted, namely, target flow stress, target strain rate and target energy dissipation. The pressure cycles produced from the simulation were used to form titanium alloy sheet at 900 °C using argon gas. The deformed regions of the formed sheet were then examined to determine the regions of contact with the die and to characterise surface damage. Results. Comparison of the simulations with experiment showed that there was good agreement between simulated and experimental thickness distributions in most parts of the sheet that were examined. Interrupted tests showed that in the intermediate positions of the forming sheet the simulations were slightly ahead of the experiment. The target stress option was found to produce the best degree of adaptation and the sheet formed using this cycle showed good surface quality, whereas in highly deformed regions using the other target options, the sheet was found to have formed microcracks. The use of a solid lubricant on the surface of the forming sheet was not found to have a significant influence on the adaptation of the titanium alloy sheet except in areas of high deformation where the sheet perforated. Significance. The finite element membrane formulation is well adapted to the superplastic forming of a ridge augmentation membrane prosthesis. The simulation accurately describes the evolution of the shape of the prosthesis and its thickness distribution with time, which allows the manufacturer to select an appropriate initial thickness of titanium alloy sheet prior to attempting to form the component. The investment dies are found to have sufficient strength to withstand the forming operation if a suitable orientation of the titanium sheet with respect to the die is adopted. A metal surface of good quality can be produced in the formed prosthesis using the appropriate gas control option.

Grain Growth and Twin Formation in 0.74PMN·0.26PT

The mechanisms controlling normal and exaggerated grain growth in lead magnesium niobate–lead titanate (PMN–PT) ceramics have been investigated by varying the PbO-based liquid-phase volume fraction from 0.03 to 0.6 and sintering temperature from 900° to 1100°C. There is a transition in matrix grain growth rate and matrix grain shape with liquid fraction; samples with liquid volume fractions less than ∼0.15 show relatively small equiaxed grains resulting from grain-to-grain impingement. Samples with higher liquid fractions show significantly larger, facetted, cube-shaped grains, whose size is independent of liquid fraction, indicating that a surface nucleation rate mechanism controls growth in this regime. Exaggerated grains were found in the high liquid fraction samples. Electron backscatter diffraction showed that all of the exaggerated grains contained 60°〈111〉 twins but none of the normal matrix grains contained twins. The reentrant angles in the twinned grains give them a growth advantage over untwinned grains, resulting in a population of exaggerated grains.

Geometric effects on micropolar elastic honeycomb structure with negative Poisson's ratio using the finite element method

A two-dimensional triangular finite element formulation including an extra degree of freedom was derived on the basis of Eringen's micropolar elasticity theory. The linear triangular element and a corresponding computer program were developed to investigate the relation between the Poisson's ratio of re-entrant honeycomb structure using various structural geometric parameters. According to our numerical results, the honeycomb structure can exhibit a negative Poisson's ratio with the appropriate re-entrant angle. We also found that the Poisson's ratio values varied when changing the honeycomb structure cell rib length and width.