Rectangular Quartz Research Articles

Narrow bandwidth spectral beam combining of cm bar in a short external resonator based on rhombic prism combinations

A novel narrow bandwidth spectral beam combining structure of cm bar with a short external resonator based on rhombic prism combinations is proposed and demonstrated. A pair of rhombic prism combinations are employed between the LDA and the transform lens in the external resonator, which consists of a rectangular quartz plate in the middle and two quartz rhombic prisms on either side in opposite orientations in each combination. The beam emitted from a standard cm bar is segmented and rearranged, and spectral beam combining is carried out along the slow axis. A spectral bandwidth of about 5.46 nm is obtained by employing a transform lens with a short focal length of 150 mm, which is only about 1/3 of that of the conventional spectral beam combining, and a narrow spectral bandwidth of 1.14 nm is obtained when a 5x de-magnifying telescope is employed in the above external resonator, the distance between LDA and diffraction grating is 500 mm while that between LDA and output coupler is 650 mm. This novel structure provides a compact external resonator scheme for narrow bandwidth spectral beam combining.

Design of a torque sensor based on piezoelectric torsional effect of quartz pillar

PurposeTorque is one of the main parameters reflecting the operation status and detection of a mechanical rotation system. The use of quartz pillar to design torque sensors has advantage over the use of quartz disk, but research into the torsional effect of quartz pillar is rare. This paper aims to investigate a novel type of torque sensor based on piezoelectric torsional effect.Design/methodology/approachBased on the theory of anisotropic elasticity and the Maxwell electromagnetism, the torsion stress and distribution of surface charge of a rectangular quartz pillar are calculated. Using finite element analysis, the polarized electric field of the piezoelectric pillar is solved. According to the theoretical calculation of torsional effect of piezoelectric quartz pillar, detection electrodes are mounted on the surface of the quartz pillar and a new type of torque sensor is designed.FindingsThe calibration experimental results show that the bound charges are proportional to the torque applied, and the torque sensor has fully reached the dynamometer standard.Originality/valueThis paper shows that the torsional effect of the developed piezoelectric quartz pillar can be used to create a new type of piezoelectric torque sensor.

The Force-Frequency Characteristics of Quartz Wafers under a Cantilever Beam Structure.

This study investigated the force-frequency characteristics of quartz wafers inside a cantilever beam frame. Firstly, the force-frequency coefficient formula of quartz wafers with fixed ends under axial force was analyzed. Firstly, the formula for the force-frequency coefficient of quartz wafers with fixed ends under axial force was analyzed. A force-frequency coefficient formula suitable for cantilever beam structures was derived by considering the changes in surface stress and stiffness of quartz wafers with fixed ends and one end under force on the other. Subsequently, the formula's accuracy was verified by experiments, and the accuracy was more than 92%. In addition, strain simulation analysis was performed on three different shapes of quartz wafers, and experimental verification was carried out on two of them. The results revealed that trapezoidal quartz wafers and cantilever beam structures exhibited superior stress distribution to rectangular chips. Furthermore, by positioning electrodes at various locations on the surface of the quartz chip, it was observed that, as the electrodes moved closer to the fixed end, the force-frequency coefficient of the rectangular quartz chip increased, along with an increase in chip strain under the cantilever structure. In summary, this study provides a new approach for designing cantilever quartz resonator sensors in the future.

Application of TiO2 Supported on Nickel Foam for Limitation of NOx in the Air via Photocatalytic Processes.

TiO2 was loaded on the porous nickel foam from the suspended ethanol solution and used for the photocatalytic removal of NOx. Such prepared material was heat-treated at various temperatures (400-600 °C) to increase the adhesion of TiO2 with the support. Obtained TiO2/nickel foam samples were characterized by XRD, UV-Vis/DR, FTIR, XPS, AFM, SEM, and nitrogen adsorption at 77 K. Photocatalytic tests of NO abatement were performed in the rectangular shape quartz reactor, irradiated from the top by UV LED light with an intensity of 10 W/m2. For these studies, a laminar flow of NO in the air (1 ppm) was applied under a relative humidity of 50% and a temperature of 28 °C. Concentrations of both NO and NO2 were monitored by a chemiluminescence NO analyzer. The adsorption of nitrogen species on the TiO2 surface was determined by FTIR spectroscopy. Performed studies revealed that increased temperature of heat treatment improves adhesion of TiO2 to the nickel foam substrate, decreases surface porosity, and causes removal of hydroxyl and alcohol groups from the titania surface. The less hydroxylated surface of TiO2 is more vulnerable to the adsorption of NO2 species, whereas the presence of OH groups on TiO2 enhances the adsorption of nitrate ions. Adsorbed nitrate species upon UV irradiation and moisture undergo photolysis to NO2. As a consequence, NO2 is released into the atmosphere, and the efficiency of NOx removal is decreasing. Photocatalytic conversion of NO to NO2 was higher for the sample heated at 400 °C than for that at 600 °C, although coverage of nickel foam by TiO2 was lower for the former one. It is stated that the presence of titania defects (Ti3+) at low temperatures of its heating enhances the adsorption of hydroxyl groups and the formation of hydroxyl radicals, which take part in NO oxidation. Contrary to that, the presence of titania defects in TiO2 through the formation of ilmenite structure (NiTiO3) in TiO2/nickel foam heated at 600 °C inhibits its photocatalytic activity. No less, the sample obtained at 600 °C indicated the highest abatement of NOx due to the high and stable adsorption of NO2 species on its surface.

Elastic, piezoelectric coefficients, and internal frictions of a single alpha-quartz crystal determined by partial-electrode electromechanical impedance spectroscopy.

In this work, all independent elastic coefficients, piezoelectric coefficients, and internal frictions of a single alpha-quartz crystal are determined at room temperature using our recently proposed partial-electrode electromechanical impedance spectroscopy (PE-EMIS). In PE-EMIS, the rectangular parallelepiped quartz sample with two small partial electrodes fabricated on a corner is self-excited/sensed. The conductance spectrum (equivalent to the acoustic resonance spectrum) measured by an impedance analyzer under a free boundary condition is noiseless, allowing the first 100 eigenmodes ranging from 50 to 310kHz to be accurately fitted. To avoid mode misidentification, the off-plane displacement distributions of the quartz sample under different eigenmodes are determined using a scanned-laser vibrometer. The resonance spectrum measured by a traditional sandwich-like RUS apparatus is also presented for comparison, and the results show that the clamping force in sandwich-like RUS shifts the sample's resonance frequencies, causing 13% and 75% overestimations for the piezoelectric coefficients e11 and e14, respectively. In comparison with the RUS, our proposed PE-EMIS is more effective and convenient, and will be widely used for characterization of piezoelectric crystals.

Novel flame dynamics in rich mixture of premixed propane–air in a planar microcombustor

This paper reports the first experimental observations of various novel unsteady flame propagation modes in a two-dimensional, high-aspect ratio rectangular quartz channel with a positive wall temperature gradient for rich premixed propane–air mixtures. Various flame propagation modes are observed on progressively increasing the mixture velocity, while keeping the equivalence ratio fixed: FREI (Flame with Repetitive Extinction and Ignition) mode, oscillating FREI mode, oscillating flame mode, and wavy flame mode. The FREI mode resembles the classical FREI flame propagation reported earlier in the literature. In the oscillating FREI mode, the flame front oscillates in the transverse direction between the upper and lower walls of the channel, while propagating upstream as in the classical FREI mode. A sudden peak in flame intensity is observed in this mode before its extinction at an upstream location. In the oscillating flame propagation mode, the flame front anchors itself at an axial location and exhibits periodic oscillations in the transverse direction without extinction. In the wavy flame mode the flame anchoring happens at a location close to the downstream end of the channel. The flame front exhibits visibly irregular fluctuations, while anchored at this axial location. A Fast Fourier transform analysis of the flame intensity data shows that FREI and oscillating FREI modes consist of a single dominant frequency of ∼100 Hz, whereas multiple dominant frequencies are present for oscillating and wavy flame modes. The appearance of these multiple oscillating and propagating flame modes is attributed to flame bifurcation behavior due to thermal-wall coupling in the channel.

Continuous Photocatalysis Based on Layer‐by‐Layer Assembly of Separation‐Free TiO2/Reduced Graphene Oxide Film Catalysts with Increased Charge Transfer and Active Site

Although photodegradation is the most widely studied method for the purification of water, the challenges for the post‐separation of catalysts from water make the technique unsuitable for practical applications. In this study, separation‐free TiO2/reduced graphene oxide (rGO) multilayer films were first prepared through layer‐by‐layer (LbL) assembly of TiO2 and graphene oxide (GO) on quartz slides, followed by a reduction of the assembled GO to rGO. For a proof‐of‐concept demonstration of novel continuous photocatalysis with potential for scaled‐up production, these quartz slides with TiO2/rGO film catalysts were further assembled into slide arrays in a home‐made rectangular quartz reactor and a model pollutant Rhodamine B (RhB) solution was circularly pumped over the slide surface under UV irradiation. It was found that the as‐prepared TiO2/rGO film catalysts show excellent enhanced photocatalytic activity for this pumping‐based continuous photocatalysis, with a photodegradation rate constant of 2.6 × 10–2 min–1 exceeding the corresponding TiO2/GO and TiO2 (TiO2/PSS) samples by a factor of 11.3 and 13, respectively. The enhanced performance is attributed to the formation of Ti–O–C bonds in film catalysts bridging TiO2 and rGO to enable efficient charge separation and transfer, the Ti–O–C bond bridged electron transfer leading to increase in ·O2– active sites on the rGO surface, and the porous‐like multilayer structure. The recycling experiments showed the film catalysts are stable and could be reused with the same efficiency for at least 8 cycles.

Kinetic spectrophotometric method for real-time monitoring of ultraviolet photoreactions: A mini-photoreactor.

It is proposed a new approach to evaluate the performance of ultraviolet photoreactions by integrating UV-LED and a UV-Vis cuvette as a mini-reactor for kinetic monitoring in a spectrophotometer not influenced by external light. This system uses only 3.0 mL of solutions in a rectangular quartz cuvette with a mini-bar magnetic stirrer in a cell holder and a UV-LED of 5 W with λmax at 370 nm was positioned on the top of the cuvette and maintained at 25.0 oC. The effectiveness of this photoreactor was demonstrated by measuring the real-time degradation of two model compounds, salicylic acid and methylene blue, in homogeneous and heterogenous systems. Photolysis of MB with H2O2 results in increasing of rate constants as [H2O2] increased. Heterogeneous photocatalysis of MB and SA was fastest achieved in ZnO dosage of 0,20 g.L-1. This mini-photoreactor allows monitoring the real-time kinetic performance collecting almost a thousand points in each experiment, leading to accurate rate constants. Moreover, this system presented positive environmental aspects such as: lower reactants and catalyst amounts, lower cost and waste amounts, use of the UV-LED radiation and labor time saving. This is a novel approach to determine the photoreaction effectiveness and it can be applied to systematic studies especially for the kinetic parameter determinations.

(Invited) Singularity in Chemistry: Digitally Controlled Kinetics of Titania-Photocatalyzed Oxygen Evolution

Oxygen evolution (EO) from water in heterogeneous photocatalyses is one of the most significant chemical reactions. It has been believed that number of electrons in this multielectron-transfer (MET) process is four with standard electrode potential (SEP) 1.23 V (vs SHE), but there seems to be no effective method to determine the number for any OE reactions, not limited to photocatalysis, except for electrolytic OE in which its electrode potential might suggest n et. Here we present the light intensity-dependent kinetics of titanium(IV) oxide (titania)-photocatalyzed OE and show, for the first time for non-electrochemical METs, n et depending on the titania photocatalysts and reaction conditions. This also suggests that MET kinetics depends digitally on its thermodynamics, i.e. possible SEPs, as a novel concept, to result in the appearance of "singularity" in chemical kinetics. Digitally controlled kinetics is important to clarify the true mechanism and to design, for example, highly efficient photocatalytic artificial photosynthetic systems. Highly intense 365-nm UV-LEDs (NS Lighting ULEDN-101 (NSL) and Hamamatsu Photonics L11921-400 (HMP)) were used in this study. The maximum power of focused NSL light beams and that of unfocused HMP light beams from those LEDs measured by a Hioki 3664 power meter with a 9742 optical sensor through a 1 cm-square aperture in front of a rectangular quartz cell were ca. 340 mW and 500 mW, respectively. Light intensities were adjusted by changing the LED-cell distance or source power. Those maximum intensities were more than one-order of magnitude higher than those of UV light from ordinary mercury or xenon arc lamps (ca. several tens of mW cm-2). Commercial titania powder (30 mg) was suspended in aqueous 0.05 mol-L–1 sodium iodate (pH 10) or iron(III) chloride (pH ca. 2) solution (3.0 mL) in a quartz cell. Air was purged off from the head space by argon, and the cell was tightly sealed with a rubber septum. UV irradiation on such titania suspensions containing strong electron acceptors (EAs), as photoexcited-electron scavengers, induced OE, and the observed OE rate (R a/µmol h–1) was measured by gas chromatography. Figure 1 shows the I L-dependent OE rate (r) for suspensions of two sets of anatase and rutile titania samples, including small anatase ("SA"; 4 nm), small rutile ("SR"; 13 nm), large anatase ("LA"; 170 nm) and large rutile ("LR"; 360 nm), using iodate (IO3 –) as an EA. Although all of the samples except for LR showed an almost linear correlation, i.e., r was almost proportional to I L, at the middle I L region (0.5 < I L < 2), plots for small particles (SA and SR) at the lower I L region seemed to be deviated downward from the straight lines. From the simulation curves of double logarithmic LID, the order of LID for SA and SR can be presumed to be 2 at the lower limit of I L and the order was gradually decreased to 1. In addition to this bimodal "spoon-like" behavior, r for SA showed a sudden increase, i.e., singularity, at ca. 2.3 W cm-2, and the order seemed to be suddenly changed from 1 to 4, i.e., "singularity" was observed . To the best of the authors’ knowledge, this is the first report of such higher-order LIDs for photoreaction induced by ordinary (non laser) continuous-light irradiation. The former second-order LIDs were also observed when iron(III) (Fe3+) was used as an EA with threshold I L (I thr), at which the LID order is changed from 2 to 1, higher than that for IO3 –, though fourth-order LID could not be observed even for SR (One of the possible reasons for SR not showing a fourth-order LID even at higher I L is shorter lifetime of one positive-hole bearing particle (t 1) which is presumed from the I thr of SR being higher than that of SA for IO3 – EA as discussed later. Therefore, at further higher I L, fourth-order LID may be observed.). The reactions of those EAs are assumed to be one-electron and six-electron processes as: Fe3+ + e– = Fe2+ and IO3 – + 3H2O + 6e– = 6OH– + I–, but bimodal (second-to-first order) LIDs were commonly observed, suggesting that the hole-transfer (oxidation) step, i.e, OE from water (See SI.), is attributable to the bimodal LIDs. The observed multimodal (unimodal) LIDs can be interpreted using a model in which the number of accumulated positive holes in each photocatalyst particle is counted, taking the individual action of each particle into account. The detailed mechanism and effect of particle size in this OE reactions are discussed. Figure 1

Coupling Vibration Analysis of Trapped-Energy Rectangular Quartz Resonators by Variational Formulation of Mindlin's Theory.

Mindlin’s two-dimensional theory has been derived and applied to research on quartz resonators for a long time. However, most works have focused on vibrations varying only in two directions, including thickness direction, while the effect of other directions like the length or width direction is normally neglected. Besides, researchers often model quartz resonators as fully electroded plates because of the resulting simplicity. Since a real device is finite in all directions and is only centrally electroded, results obtained in such works cannot offer quantitative information on vibrations with enough accuracy. In this paper, a theoretical analysis of a rectangular trapped-energy resonator of AT-cut quartz is studied using the Ritz method, associated with the variational formulation of Mindlin’s first-order equations. Frequency spectra and mode shapes of a real-scaled trapped-energy resonator, which is finite in all directions, are obtained with the consideration of mode couplings among thickness-shear mode, thickness-twist mode, and flexural mode. Results show the existence of an energy-trapping and coupling phenomenon and are helpful for thorough and accurate understanding of quartz resonator vibrations. Detailed discussions on the effects of structural parameters on mode couplings and energy trapping are provided, and the results can helpfully guide the selection of aspect ratio, length/thickness ratio, and electrode inertia in device design.

Electrically Forced Vibrations of Partially Electroded Rectangular Quartz Plate Piezoelectric Resonators

Electrically Forced Vibrations of Partially Electroded Rectangular Quartz Plate Piezoelectric Resonators

Thickness-shear and thickness-twist vibrations of rectangular quartz crystal plates with nonuniform thickness

ABSTRACTAn analysis was performed on the vibration of a rectangular contoured quartz plate resonator. The surface of the resonator has different curvatures in the two in-plane directions. The analysis was based on the equation by Tiersten and Smythe, which has variable coefficients. The power series method was used. Thickness-shear and thickness-twist vibration frequencies and modes were obtained. The effects of the curvatures of the resonator surface were examined. Two types of boundary conditions were considered from which the proper size of the resonator was determined. The results are useful in the understanding of these resonators and their design.

Design and analysis of higher harmonic cantilever based on finite element analysis

Recently, the developing multi-frequency atomic force microscopy, not only can characterize more physical properties of samples with a remarkable spatial resolution, but also detect non-linear force with time-resolved. Its basic principle is that multiple vibrating frequencies of micro cantilever probe is motivated and detected, which is closely related to higher harmonics or eigenmodes of micro cantilever. In order to realize this new technology, it is very important and necessary to design special micro cantilever. Generally, silicon cantilever and quartz cantilever are widely used in traditional AFM. For rectangular silicon cantilever, the ratio of the second order eigenmode and basic frequency is 6.27, and for quartz tuning micro-cantilever, it also isn’t an integral value, so it is almost impossible to study the MF-AFM using the conventional cantilevers directly. Based on the resonant amplification effect, in this article, we discussed the corresponding eigenvibration of traditional rectangular silicon micro-cantilever and quartz tuning micro-cantilever by the method of changing the mass distribution of micro cantilever, namely changing its geometric size and shape. Finally we designed some special cantilevers, which the ratio of second mode frequency and basic frequency are all integer times by theoretical calculation and Finite Element Analysis, including some discussions between flexural resonant and basic frequency.

Fundamental properties of a planar type of inductively coupled thermal plasma with current modulation

A novel planar type of induction thermal plasma system with current modulation has been developed using a rectangular quartz vessel instead of a conventional cylindrical tube for thermal plasma processing for large-area material surface. To expand the generated thermal plasma laterally, the rectangular coil is used around the planar torch. Electrical properties including effective electrical impedance and instantaneous effective power of the thermal plasma at a pressure of 30 Torr at an input power about 10 kW were studied for the developed Ar planar type of induction thermal plasma. The spatial distribution of Ar excitation temperature in a planar torch was measured to elucidate fundamental aspects of a planar thermal plasma. Furthermore, the effect of coil current modulation was studied for changes in electrical properties and temperature, and their controllability in a planar thermal plasma.

Fundamentals of planar-type inductively coupled thermal plasmas on a substrate for large-area material processing

In this work, the fundamentals of planar-type Ar inductively coupled thermal plasmas (ICTPs) with oxygen molecular gas on a substrate have been studied. Previously, aiming at large-area material processing, we developed a planar-type ICTP torch with a rectangular quartz vessel instead of a conventional cylindrical tube. For the adoption of such planar-type ICTP to material processing, it is necessary to sustain the ICTP with molecular gases on a substrate stably and uniformly. To determine the uniformity of the ICTP formed on the substrate, spectroscopic observation was carried out at 3 mm above the substrate. Results showed that the radiation intensities of specified O atomic lines were almost uniformly detected along the surface of the substrate. This means that excited O atoms, which are important radicals for thermal plasma oxidation, are present in the planar-type ICTP uniformly on the substrate.

Thickness-shear Modes and Energy Trapping in a Rectangular Piezoelectric Quartz Resonator with Partial Electrodes

We analyze thickness-shear vibrations of a rectangular plate of quartz piezoelectric crystal for acoustic wave resonator application. The plate is partially electroded in the central region. The scalar differential equation derived by Tiersten and Smythe is employed. Exact solution for the free vibration resonant frequencies and modes are obtained. Trapped modes with vibrations mainly under the electrodes are found. The results are useful to the understanding and design optimization of crystal resonators.

Variational formulation of the Stevens-Tiersten equation and application in the analysis of rectangular trapped-energy quartz resonators

The two-dimensional scalar differential equation for transversely varying thickness modes in quartz crystal resonators operating with thickness-shear modes is formulated into variational form for trapped-energy resonators with both electroded and unelectroded regions. A theoretical analysis of rectangular trapped-energy resonators of singly rotated quartz is performed using the Ritz method based on the variational formulation. Free vibration resonant frequencies and modes are obtained. The results show the existence of trapped modes under the electrodes. The effects of various geometric and physical parameters on the trapped modes are examined. It is also found that the classical frequency prediction given by Tiersten and Smythe from an approximate analysis using the scalar differential equation has an inaccuracy on the order of 100 ppm for the fundamental mode, significant in resonator design.

Thickness-shear vibration analysis of rectangular quartz plates by a numerical extended Kantorovich method

Thickness-shear vibration analysis of rectangular quartz plates was carried out by a numerical extended Kantorovich method (NEKM) proposed in this paper. Thickness-shear vibration is characterized by high frequency vibration that needs huge computational cost. The NEKM reduced the two-dimensional elasticity problem into two one-dimensional ones and then solved them iteratively as the Kantorovich method. But all the processes of reduction and solvation in NEKM were carried out by using a differential quadrature finite element method (DQFEM). Therefore, the NEKM is much simpler than the Kantorovich method that does all the processes analytically with great complexity. Because the two-dimensional problem was reduced to one-dimensional ones and the DQFEM was very accurate, the NEKM was very efficient and accurate. The correctness and high accuracy of the NEKM were validated through numerical comparison with the results of the Kantorovich method in literature.

Thickness-shear vibration of a rectangular quartz plate with partial electrodes

We study free vibration of a thickness-shear mode crystal resonator of AT-cut quartz. The resonator is a rectangular plate partially and symmetrically electroded at the center with rectangular electrodes. A single-mode, three-dimensional equation governing the thickness-shear displacement is used. A Fourier series solution is obtained. Numerical results calculated from the series show that there exist trapped thickness-shear modes whose vibration is mainly under the electrodes and decays rapidly outside the electrodes. The effects of the electrode size and thickness on the trapped modes are examined.

In-situ observation of eutectic growth in Al-based alloys by light microscopy

An experimental method for the in-situ observation of solidification in eutectic metallic alloys growing at moderate temperatures, i.e. 500–600°C was developed. It is based on unidirectional solidification of thin samples (200 to 700μm thick) contained in rectangular quartz glass tubes allowing for in-situ observation of growth on the sample surface by means of light microscopy using a long-distance microscope. The method is illustrated for two-phase eutectic growth in Al–17.5Cu–1.0Ag, Al–11.8Si and Al–11.8Si–0.025Sr as well as for three phase growth in Al–13.3Cu–5.7Si, all at%.Coupled growth of lamellar Al–Al2Cu eutectic in Al–17.5Cu–1.0Ag was investigated in more detail with regard to spacing selection: experiments were performed in a temperature gradient of 38±1Kcm−1 using different, but constant withdrawal velocities ranging from 0.025 to 1.8μms−1. Measured spacing was compared with literature data and discussed with reference to the Jackson–Hunt theory and the recent amendment proposed by Akamatsu, Faivre, Karma and Plapp. In-situ observations were complemented by post-mortem metallographic analysis using SEM and EBSD in transverse sections.