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Crystals, Volume 12, Issue 11 (November 2022) – 183 articles

Cover Story (view full-size image): Three true polymorphs of a trinuclear triangular Cu(II) pyrazolato complex of formula (Bu4N)2[Cu33-Cl)2(μ-4-NO2-pz)3Cl3] (pz = pyrazolato anion) have been isolated by recrystallization from three different alcoholic solutions. Whereas the trimeric copper pyrazolate frame is by and large the same in the three polymorphic forms, the two capping μ3-Cl atoms float to different positions over the Cu3 plane, resulting in distinctly different packing in their respective lattices, resulting from different cation–cation, cation–anion and anion–anion interactions in the solid state. Single-crystal X-ray structure determination, DFT calculations and Hirshfeld surface analysis highlight the details of the three different 3D lattices. View this paper
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15 pages, 4075 KiB  
Article
Tunable Sensing and Transport Properties of Doped Hexagonal Boron Nitride Quantum Dots for Efficient Gas Sensors
Crystals 2022, 12(11), 1684; https://doi.org/10.3390/cryst12111684 - 21 Nov 2022
Cited by 9 | Viewed by 1580
Abstract
The electronic, sensing, and transport properties of doped square hexagonal boron nitride (shBN) quantum dots were investigated using density functional theory calculations. The electronic and magnetic properties were controlled by substitutional doping. For instance, heterodoping with Si and C atoms decreased the energy [...] Read more.
The electronic, sensing, and transport properties of doped square hexagonal boron nitride (shBN) quantum dots were investigated using density functional theory calculations. The electronic and magnetic properties were controlled by substitutional doping. For instance, heterodoping with Si and C atoms decreased the energy gap to half its value and converted the insulator shBN quantum dot to a semiconductor. Doping with a single O atom transformed the dot to spin half metal with a tiny spin-up energy gap and a wide spin-down gap. Moreover, doping and vacancies formed low-energy interactive molecular orbitals which were important for boosting sensing properties. The unmodified shBN quantum dot showed moderate physical adsorption of NO2, acetone, CH4, and ethanol. This adsorption was elevated by doping due to interactions between electrons in the low-energy orbitals from the doped-shBN dot and π-bond electrons from the gas. The transport properties also showed a significant change in the current by doping. For instance, the spin-up current was very high compared to the spin-down current in the shBN dots doped with an O atom, confirming the formation of spin half metal. The spin-up/down currents were strongly affected by gas adsorption, which can be used as an indicator of the sensing process. Full article
(This article belongs to the Special Issue Crystalline Magnetic Compounds)
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17 pages, 7187 KiB  
Article
Influential Factors of a Reactive Materials Projectile’s Damage Evolution Behavior
Crystals 2022, 12(11), 1683; https://doi.org/10.3390/cryst12111683 - 21 Nov 2022
Cited by 2 | Viewed by 1377
Abstract
To determine the mechanism of penetration of multi-layer aluminum targets (MLAT) by a reactive materials projectile (RMP), AUTODYN-3D numerical simulations and experimental tests were carried out. The Powder Burn equation of the state ignition model was introduced for the reactive core activation under [...] Read more.
To determine the mechanism of penetration of multi-layer aluminum targets (MLAT) by a reactive materials projectile (RMP), AUTODYN-3D numerical simulations and experimental tests were carried out. The Powder Burn equation of the state ignition model was introduced for the reactive core activation under different projectile–target interaction conditions, which effectively simulated the deflagration reaction damage effects behavior of the RMP and the damage evolution behavior of the MLAT. The activation rate of the reactive core increased significantly when the thickness of the steel target was 8–15 mm; a significant combined destructive effect of kinetic and chemical energy was produced on the MLAT. The initial velocity was proportional to the penetration and destruction effect of the front-layer aluminum target. For the rear-layer aluminum target, the detonation damage showed a tendency to increase and then decrease. If the head metal block was too thick, the penetration ability would be improved at the same time, and the deflagration reaction damage effects ability of the steel target would be significantly reduced. In order to achieve good battlefield damage efficacy, all of the influencing factors should be comprehensively considered. Full article
(This article belongs to the Special Issue Dynamic Behavior of Materials)
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11 pages, 1934 KiB  
Article
Research on Brownian Thermal Noise Limit of a Cylindrical Ultra-Stable Cavity with Support Pads
Crystals 2022, 12(11), 1682; https://doi.org/10.3390/cryst12111682 - 21 Nov 2022
Viewed by 1047
Abstract
Brownian thermal noise (TN) of ultra-stable cavities (USCs) imposes a fundamental limitation on the frequency stability of ultra-narrow linewidth lasers. This work investigates the TN in cylindrical USCs with the four support pads in detail through theoretical estimation and simulation. To evaluate the [...] Read more.
Brownian thermal noise (TN) of ultra-stable cavities (USCs) imposes a fundamental limitation on the frequency stability of ultra-narrow linewidth lasers. This work investigates the TN in cylindrical USCs with the four support pads in detail through theoretical estimation and simulation. To evaluate the performance of state-of-the-art ultra-narrow linewidth lasers, we derive an expression of the TN for a cylindrical spacer according to the fluctuation–dissipation theorem, which takes into account the front face area of the spacer. This estimation is more suitable for the TN of the cylindrical USC than the previous one. Meanwhile, we perform detailed studies of the influence of the four support pads on the TN in cylindrical USCs for the first time by numerical simulations. For a 400 mm long cylindrical USC with an ultra-low expansion spacer and fused silica substrates, the displacement noise contributed from the four support pads is roughly four times that of the substrates and the GaAs/AlGaAs crystalline coating. The results show that the four support pads are the primary TN contributors under some materials and geometries of USCs. Full article
(This article belongs to the Special Issue Crystals in Laser Systems)
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11 pages, 3088 KiB  
Article
A New Zero-Dimensional (CsK2)BiCl6 Metal Halide: Boosting Emission via B-Site Mn-Doping
Crystals 2022, 12(11), 1681; https://doi.org/10.3390/cryst12111681 - 21 Nov 2022
Cited by 2 | Viewed by 1878
Abstract
The A site of zero-dimensional (0D) metal halides A3BiCl6 can be replaced by Cs and/or K, thus, four possible 0D A3BiCl6 forms exist, such as (Cs2K)BiCl6, (CsK2)BiCl6, K3 [...] Read more.
The A site of zero-dimensional (0D) metal halides A3BiCl6 can be replaced by Cs and/or K, thus, four possible 0D A3BiCl6 forms exist, such as (Cs2K)BiCl6, (CsK2)BiCl6, K3BiCl6 and Cs3BiCl6. It is well known that Cs3BiCl6 has been reported. We predict that both (Cs2K)BiCl6 and K3BiCl6 do not have enough structural and thermodynamic stability, but (CsK2)BiCl6 should be a 0D stable A3BiCl6 candidate based on density functional theory (DFT). Furthermore, 0D (CsK2)BiCl6 metal halide was experimentally prepared by the solvothermal method. Though (CsK2)BiCl6 metal halide exhibits an indirect bandgap and poor luminescence properties, the emission can be boosted by B-site Mn-doping due to the efficient energy transfer from self-trapped excitons (STE) to the d-state of Mn ions. Our results enrich the family of 0D bi-based metal halides and provide guidance for the regulation of the structural and optical properties of metal halides. Full article
(This article belongs to the Section Materials for Energy Applications)
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17 pages, 2168 KiB  
Article
Hall Current Effect of Magnetic-Optical-Elastic-Thermal-Diffusive Non-Local Semiconductor Model during Electrons-Holes Excitation Processes
Crystals 2022, 12(11), 1680; https://doi.org/10.3390/cryst12111680 - 21 Nov 2022
Cited by 8 | Viewed by 1166
Abstract
This paper investigates a theoretical model for the interaction between electrons and holes (E/H) in elastic non-local semiconductors. When the medium is activated by photo-energy because of high temperatures, an optical-elastic-thermal-diffusion (OETD) process occurs and is described by this mathematical-physical model. A study [...] Read more.
This paper investigates a theoretical model for the interaction between electrons and holes (E/H) in elastic non-local semiconductors. When the medium is activated by photo-energy because of high temperatures, an optical-elastic-thermal-diffusion (OETD) process occurs and is described by this mathematical-physical model. A study is conducted on the impact of the Hall current brought on by the collapse of a strong magnetic field on the exterior of the non-local semiconductor medium. A Hall effect is brought on by the magnetic field’s effect on the density of magnetic flux. The Laplace transform with initial conditions of the dimensionless main physical fields in one dimension (1D) is used to demonstrate this. Mathematically, in the Laplace domain, the generic linear solutions for the strain and temperature distributions, as well as charge carrier holes and electrons, are derived. The key physical fields’ complete solutions in the time domain are obtained by numerically simulating a few thermal, mechanical, and optical conditions at the free surface of the semiconductor using the Laplace inverse approximation technique. For silicon material, the photo-thermoelasticity theory’s Hall current effect, non-local parameter, and effects of thermal relaxation durations are graphically displayed and analyzed. Full article
(This article belongs to the Section Materials for Energy Applications)
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15 pages, 8089 KiB  
Article
Structure and Bonding in CsNa2Hg18, a New Ternary Amalgam with Strong Coulombic Bonding Contributions
Crystals 2022, 12(11), 1679; https://doi.org/10.3390/cryst12111679 - 21 Nov 2022
Cited by 3 | Viewed by 1577
Abstract
The new ternary amalgam CsNa2Hg18 was synthesised from the elements in an unconventional low-temperature procedure. It crystallises in a tetragonal structure type (space group I4/mmm, a = 7.3054(7) and c = 20.046 Å) and combines ionic and [...] Read more.
The new ternary amalgam CsNa2Hg18 was synthesised from the elements in an unconventional low-temperature procedure. It crystallises in a tetragonal structure type (space group I4/mmm, a = 7.3054(7) and c = 20.046 Å) and combines ionic and metallic bonding contributions. In the crystal structure, Cs and Na atoms are embedded in a Hg scaffold with highly covalent Hg–Hg bonding. The alkali metal atoms are coordinated exclusively by Hg atoms in unusual environments with coordination numbers CN = 24 for Cs and CN = 16 for Na. Polar amalgams are suitable model systems for studying the parameters influencing the ’bad metal behaviour’ in polar intermetallic phases. We present structural studies on the basis of powder and single crystal diffraction data together with measurements of the specific resistivity and DFT calculations of the electronic structure. For CsNa2Hg18, a high specific resistivity can be observed, but the Ioffe–Regel saturation of the resistivity is expressed much less than in other polar amalgams. Full article
(This article belongs to the Special Issue Compounds with Polar Metallic Bonding Volume II)
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13 pages, 5826 KiB  
Article
Carbon Nanotubes (CNTs) Reinforced CoCrMoNbTi0.4 Refractory High Entropy Alloy Fabricated via Laser Additive Manufacturing: Processing Optimization, Microstructure Transformation and Mechanical Properties
Crystals 2022, 12(11), 1678; https://doi.org/10.3390/cryst12111678 - 21 Nov 2022
Cited by 3 | Viewed by 1283
Abstract
Refractory high-entropy alloys (RHEAs) exhibit outstanding softening resistance and thermal stability at elevated temperatures. Unfortunately, poor ductility at room temperature has remained the critical issue for their processability and practical application. In this study, an original-type fabrication method of RHEA was proposed, using [...] Read more.
Refractory high-entropy alloys (RHEAs) exhibit outstanding softening resistance and thermal stability at elevated temperatures. Unfortunately, poor ductility at room temperature has remained the critical issue for their processability and practical application. In this study, an original-type fabrication method of RHEA was proposed, using multi-walled carbon nanotubes (MWCNTs) to enhance the alloy prepared via laser melting deposition (LMD) technology. The processing optimization, microstructure evolution and mechanical properties were systematically investigated for LMD processing of CNTs/CoCrMoNbTi0.4 RHEA. The results have shown that CNTs/CoCrMoNbTi0.4 RHEA have a polycrystalline structure (BCC, HCP, and TiC). As the optimal LMD-processing parameters of laser linear energy density of 3.6 J/mm were applied, owing to the formation of high densification and an ultrafine microstructure, the fully dense LMD-processed alloy exhibited high microhardness of 1015 HV0.5, fracture strength of 2110.5 MPa, and fracture strain of 2.39%. The solid solution strengthening and load transfer are considered as the main strengthening mechanisms occurring simultaneously during compressive tests at room temperature, leading to excellent mechanical properties of LMD-processed CNTs/CoCrMoNbTi0.4 RHEA, which explores the potential application of RHEAs. Full article
(This article belongs to the Special Issue Advances of High Entropy Alloys)
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14 pages, 4579 KiB  
Article
Variation in Gemological Characteristics in Tsavorites with Different Tones from East Africa
Crystals 2022, 12(11), 1677; https://doi.org/10.3390/cryst12111677 - 20 Nov 2022
Cited by 3 | Viewed by 1606
Abstract
In this paper, the influencing factors of the color and the gemological changes of tsavorites with different tones from East Africa were studied. The gemological characteristics of 35 different green tones in tsavorites were collected based on the results of color measurement, X-ray [...] Read more.
In this paper, the influencing factors of the color and the gemological changes of tsavorites with different tones from East Africa were studied. The gemological characteristics of 35 different green tones in tsavorites were collected based on the results of color measurement, X-ray fluorescence, ultraviolet–visible, infrared and Raman spectroscopy. V and Cr are responsible for the samples’ color: with the increase of vanadium content, lightness L* and chroma C* decreased while hue h° increased, and the hue tends to blueish green. The color of tsavorite is related significantly to the absorption bands at about 430 nm and 605 nm through the UV-VIS spectrum. Under long-wave ultraviolet light, the samples show inert or red fluorescence. The G, H, and I peaks of the infrared spectrum are shifted towards the long-wave direction with the reduction of the V content. The peaks at 275 nm, 412 nm and 545 nm on the Raman spectrum tend to move towards the direction of decreasing wavelength with the increase of V content. Full article
(This article belongs to the Special Issue Diamonds: Growth, Properties and Applications)
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14 pages, 4401 KiB  
Article
Prediction of Lattice Volumes of Crystal Samples by Computer Image Recognition on the X-ray Diffraction Patterns
Crystals 2022, 12(11), 1676; https://doi.org/10.3390/cryst12111676 - 20 Nov 2022
Cited by 2 | Viewed by 1394
Abstract
Computer image recognition (CIR) on the diffraction patterns of X-ray single crystal diffractometer was used to assist the analysis of the unit cell parameters in terms of lattice volume. This method can improve the prediction accuracy of unit cell parameters in the pre-experiment [...] Read more.
Computer image recognition (CIR) on the diffraction patterns of X-ray single crystal diffractometer was used to assist the analysis of the unit cell parameters in terms of lattice volume. This method can improve the prediction accuracy of unit cell parameters in the pre-experiment step since erroneous prediction by the software may occur for 5% tested crystal samples, which may critically affect the complete crystal data quality and cause unnecessary testing time. In the imaging processing, the diffraction pattern images saved as .img format files were firstly batch transferred into .jpg format with high quality for further treatment. Specific features of the crystal diffraction points or zones in the images were extracted for the recognition processing by color mode. The Findcontour algorithm and the Canny algorithm based on Gaussian filtering were used for the diffraction peak points and area detection. The relationship between the distribution of crystal diffraction points (DCDP) and the lattice volumes based on reciprocal lattice theory was established for the users to judge the reasonable location range of the lattice volumes. A Density model was proposed to correlate the dependence of the DCDP and the experimental data. Special crystal samples were chosen to test the CIR performance, and its accuracy for the lattice volume prediction was evaluated. The CIR method can be used for the assistance in the analysis of the lattice volume location range and for crystal structure solving. Full article
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9 pages, 2482 KiB  
Article
Tunable, High-Power, Narrow-Linewidth Diode Laser for Potassium Alkali Metal Vapor Laser Pumping
Crystals 2022, 12(11), 1675; https://doi.org/10.3390/cryst12111675 - 20 Nov 2022
Cited by 1 | Viewed by 1706
Abstract
This work proposes a method of compressing spectral linewidth and tuning the central wavelength of multiple high-power diode laser arrays in an external cavity feedback structure based on one volume Bragg grating (VBG). Through the combination of beam collimation and spatial beam technologies, [...] Read more.
This work proposes a method of compressing spectral linewidth and tuning the central wavelength of multiple high-power diode laser arrays in an external cavity feedback structure based on one volume Bragg grating (VBG). Through the combination of beam collimation and spatial beam technologies, a diode laser source producing 102.1 W at an operating current of 40 A is achieved. This laser source has a central wavelength of 766 nm and a narrow spectral linewidth of 0.164 nm. Moreover, a tuning central wavelength ranging from 776–766.231 nm is realized by precisely controlling the temperature of the VBG, and the locked central wavelength as a function of temperature shifts at the rate of approximately 0.0076 nm/°C. The results further prove that the smile under 1 μm can restrain the self-excitation effect of the emitting laser, which can influence the efficiency of the potassium alkali metal vapor laser pumping. Full article
(This article belongs to the Special Issue Frontiers of Semiconductor Lasers)
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16 pages, 3600 KiB  
Article
Direct Phasing of Coiled-Coil Protein Crystals
Crystals 2022, 12(11), 1674; https://doi.org/10.3390/cryst12111674 - 20 Nov 2022
Cited by 2 | Viewed by 1332
Abstract
Coiled-coil proteins consisting of multiple copies of helices take part in transmembrane transportation and oligomerization, and are used for drug delivery. Cross-alpha amyloid-like coiled-coil structures, in which tens of short helices align perpendicular to the fibril axis, often resist molecular replacement due to [...] Read more.
Coiled-coil proteins consisting of multiple copies of helices take part in transmembrane transportation and oligomerization, and are used for drug delivery. Cross-alpha amyloid-like coiled-coil structures, in which tens of short helices align perpendicular to the fibril axis, often resist molecular replacement due to the uncertainty to position each helix. Eight coiled-coil structures already solved and posted in the protein data bank are reconstructed ab initio to demonstrate the direct phasing results. Non-crystallographic symmetry and intermediate-resolution diffraction data are considered for direct phasing. The retrieved phases have a mean phase error around 30∼40°. The calculated density map is ready for model building, and the reconstructed model agrees with the deposited structure. The results indicate that direct phasing is an efficient approach to construct the protein envelope from scratch, build each helix without model bias which is also used to confirm the prediction of AlphaFold and RosettaFold, and solve the whole structure of coiled-coil proteins. Full article
(This article belongs to the Special Issue Feature Papers in Biomolecular Crystals in 2022-2023)
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14 pages, 3469 KiB  
Article
Nanoindentation on the Transformation of LPSO Phases during Different Solution Heat Treatments in an Mg-Dy-Nd-Zn-Zr Alloy
Crystals 2022, 12(11), 1673; https://doi.org/10.3390/cryst12111673 - 20 Nov 2022
Cited by 4 | Viewed by 1129
Abstract
The objective of this study is the investigation of nanomechanical properties using nanoindentation of extruded and heat-treated Mg-Dy-Nd-Zn-Zr, with an emphasis on the transformation of long-period stacking-ordered (LPSO) phases. Solution heat treatment was performed with different heat treatment for durations on hot extruded [...] Read more.
The objective of this study is the investigation of nanomechanical properties using nanoindentation of extruded and heat-treated Mg-Dy-Nd-Zn-Zr, with an emphasis on the transformation of long-period stacking-ordered (LPSO) phases. Solution heat treatment was performed with different heat treatment for durations on hot extruded Mg-Dy-Nd-Zn-Zr to monitor the transformation of LPSO phases, as well as to keep track of microstructural changes. The initial fine-grained microstructure, with blocky and lamellar LPSO structures within the matrix, first transformed into coarser grains with fewer LPSO lamellae, which then increased in amount again at higher annealing duration. The blocky LPSO phases, which have the highest hardness compared to the matrix grains with and without LPSO lamellae, consistently decrease in quantity, as so does the trend in their hardness value. The Mg matrix grains with LPSO lamellae show a lower hardness compared to the Mg matrix grains without or with a just few lamellar LPSO phases, and increase in quantity at long annealing durations. The overall hardness of the microstructure is essentially determined by the LPSO lamellae-containing grains and reaches a peak at 24 h. There is another peak found for the grain size values; however, this is at later annealing duration, at 72 h. The reduction in grain size towards longer annealing durations goes along with a reactivated formation of LPSO lamellae. Full article
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17 pages, 6196 KiB  
Article
End-of-Life Liquid Crystal Displays Recycling: Physico-Chemical Properties of Recovered Liquid Crystals
Crystals 2022, 12(11), 1672; https://doi.org/10.3390/cryst12111672 - 19 Nov 2022
Cited by 2 | Viewed by 3548
Abstract
This report focuses particularly on liquid crystals display (LCD) panels because they represent a significant amount of all WEEE collected. Technologies involving liquid crystals (LCs) have enjoyed considerable success since the 1970s in all fields of LC displays (LCDs). This currently provokes the [...] Read more.
This report focuses particularly on liquid crystals display (LCD) panels because they represent a significant amount of all WEEE collected. Technologies involving liquid crystals (LCs) have enjoyed considerable success since the 1970s in all fields of LC displays (LCDs). This currently provokes the problem of waste generated by such equipment. Based on current statistical data, the LC amount represents approximately 1.3 g for a 35-inch diameter LCD panel unit possessing a total weight of 15 kg. In France, a recent study revealed LCD waste to represent an average of 5.6 panels per household. This represents an important quantity of LCs, which are generally destroyed by incineration or washed out with detergents during the recycling processes of end-of-life (EOL) LCDs. Hence, the aim of this study is to show that it is possible to remove LC molecules from EOL-LCD panels with the goal of valorizing them in new sectors. EOL-LCD panels have undergone various stages of dismantling, chemical treatments and characterization. The first stage of manual dismantling enables the elimination of the remaining physical components of the panels to process LC molecules only, sandwiched between the two glass plates. Mechanical treatment by scraping allows us to obtain a concentrate of LCs. The results obtained from chemical and physical techniques show that these molecules retain the characteristics essential for their operation in the field of optical and electro-optical devices. As the use of LCD surfaces continues to rise significantly, the amounts and economic stakes are huge, fully justifying the development of an LC recovery process for used panels. Many potential uses have been identified for these LC molecules: in new flat LCD panels after purification of the LCs concentrate, in PDLC systems, as lubricants or in thermal applications. Full article
(This article belongs to the Special Issue Advances in Liquid Crystal Optical Device)
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16 pages, 2315 KiB  
Review
Understanding Cysteine Chemistry Using Conventional and Serial X-ray Protein Crystallography
Crystals 2022, 12(11), 1671; https://doi.org/10.3390/cryst12111671 - 19 Nov 2022
Viewed by 2304
Abstract
Proteins that use cysteine residues for catalysis or regulation are widely distributed and intensively studied, with many biomedically important examples. Enzymes where cysteine is a catalytic nucleophile typically generate covalent catalytic intermediates whose structures are important for understanding mechanism and for designing targeted [...] Read more.
Proteins that use cysteine residues for catalysis or regulation are widely distributed and intensively studied, with many biomedically important examples. Enzymes where cysteine is a catalytic nucleophile typically generate covalent catalytic intermediates whose structures are important for understanding mechanism and for designing targeted inhibitors. The formation of catalytic intermediates can change enzyme conformational dynamics, sometimes activating protein motions that are important for catalytic turnover. However, these transiently populated intermediate species have been challenging to structurally characterize using traditional crystallographic approaches. This review describes the use and promise of new time-resolved serial crystallographic methods to study cysteine-dependent enzymes, with a focus on the main (Mpro) and papain-like (PLpro) cysteine proteases of SARS-CoV-2, as well as on other examples. We review features of cysteine chemistry that are relevant for the design and execution of time-resolved serial crystallography experiments. In addition, we discuss emerging X-ray techniques, such as time-resolved sulfur X-ray spectroscopy, that may be able to detect changes in sulfur charge states and covalency during catalysis or regulatory modification. In summary, cysteine-dependent enzymes have features that make them especially attractive targets for new time-resolved serial crystallography approaches, which can reveal both changes to enzyme structures and dynamics during catalysis in crystalline samples. Full article
(This article belongs to the Special Issue Novel Structural Studies of Coronavirus Proteins)
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18 pages, 4108 KiB  
Article
Mechanical and Microstructural Behavior of Tempered CPM® 3V High-Density Sintered Tool Steel
Crystals 2022, 12(11), 1670; https://doi.org/10.3390/cryst12111670 - 19 Nov 2022
Cited by 2 | Viewed by 1532
Abstract
The tempering response of CPM® 3V tool steel was investigated via a hardening and tempering heat treatment, tensile testing, fractography, and microstructural evaluation. CPM® 3V tool steel is manufactured using Crucible Particle Metallurgy (CPM®), a proprietary high-density sintering technique [...] Read more.
The tempering response of CPM® 3V tool steel was investigated via a hardening and tempering heat treatment, tensile testing, fractography, and microstructural evaluation. CPM® 3V tool steel is manufactured using Crucible Particle Metallurgy (CPM®), a proprietary high-density sintering technique developed by Crucible Industries. The hardening and tempering heat treatments were applied to ASTM E8 standard test specimens. Tempering temperature was the experimental variable. The following samples were prepared: As-Hardened (no tempering); tempered at 450 °C, 550 °C, 650 °C, and 700 °C; and As-Received (annealed). Ultimate tensile strength and the yield strength of each treatment was determined using the ASTM E8 standard tensile test. The failed specimens were examined for mode of fracture at macro- and microscopic scales. Reflected light microscopy and a scanning electron microscope (SEM) was used for microstructural characterization. Testing and analysis established the samples tempered at <550 °C were dominated by brittle failure while samples tempered at >550 °C experienced ductile failure. The 550 °C treatment showed mixed ductile and brittle fracture features. This study found that CPM® 3V can be optimized for strength, with good tensile toughness, at a 550 °C tempering temperature. This is consistent with Crucible Industries’ recommended tempering temperature for good wear resistance and toughness. Full article
(This article belongs to the Special Issue Advances in High Strength Steels)
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10 pages, 6457 KiB  
Article
High Temperature Fatigue Behavior and Failure Mechanism of Ti-45Al-4Nb-1Mo-0.15B Alloy
Crystals 2022, 12(11), 1669; https://doi.org/10.3390/cryst12111669 - 19 Nov 2022
Viewed by 875
Abstract
Strain-controlled low cycle fatigue experiments were carried out on the TiAl alloy Ti-45Al-4Nb-1Mo-0.15B at 400 °C and 750 °C to reveal the cyclic mechanical behavior and failure mechanism. The TiAl alloy presents stable cyclic characteristics under fatigue loading at elevated temperatures. No obvious [...] Read more.
Strain-controlled low cycle fatigue experiments were carried out on the TiAl alloy Ti-45Al-4Nb-1Mo-0.15B at 400 °C and 750 °C to reveal the cyclic mechanical behavior and failure mechanism. The TiAl alloy presents stable cyclic characteristics under fatigue loading at elevated temperatures. No obvious cyclic softening or cyclic hardening was manifested during experiments. The cyclic stress–strain relationship is well described by the Ramberg–Osgood equation. The fatigue lifetime at different temperatures has a log-linear relationship with the total strain ranges. The fracture morphology indicates the main fracture mode of fatigue specimens at 400 °C is a brittle fracture, while there is a ductile fracture at 750 °C. Meanwhile, the trans-lamellar fracture is dominant for the lamellar microstructure and the percentages of the inter-lamellar fracture decreases with the strain amplitude. Full article
(This article belongs to the Special Issue Processing, Structure and Properties of TiAl Alloys)
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13 pages, 9829 KiB  
Article
Synthesis, Evolution of Morphology, Transport Properties for Bi2Te3 Nanoplates
Crystals 2022, 12(11), 1668; https://doi.org/10.3390/cryst12111668 - 19 Nov 2022
Cited by 3 | Viewed by 1294
Abstract
Bi2Te3 has an extensive application as thermoelectric materials. Here, large scale Bi2Te3 single-crystal hexagonal nanoplates(NPs) with size of 0.4–0.8 μm were synthesized successfully by hydro-thermal method. X-ray diffraction (XRD), scanning electron microscope (SEM), and transmission electron microscope [...] Read more.
Bi2Te3 has an extensive application as thermoelectric materials. Here, large scale Bi2Te3 single-crystal hexagonal nanoplates(NPs) with size of 0.4–0.8 μm were synthesized successfully by hydro-thermal method. X-ray diffraction (XRD), scanning electron microscope (SEM), and transmission electron microscope (TEM) were used to characterize the Bi2Te3 nanoplates, which confirm the single crystal quality and smooth surface morphology with large size. We discussed the morphology-evolution in detail the influence of various reaction factors which including: the reaction temperature, the reaction time, the surfactants of the polyvinyl pyrrolidone (PVP) and pH value. The synthesis method is not only green, but also shortens the reaction time and improves the reaction efficiency. The Bi2Te3 nanopowders were hot-pressed into solid state pellets through spark plasma sintering (SPS). The values of the electrical conductivity σ were about 0.16 × 10−5 Sm−1 and 0.22 × 10−5 Sm−1 at room temperature and 530 K, respectively. The values of the Seebeck coefficient S were around −81 μVK−1 and −118 μVK−1 at room temperature and 530 K, respectively. Full article
(This article belongs to the Special Issue Raman Scattering in Optical Crystals)
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19 pages, 5650 KiB  
Article
Auto-Encoder Classification Model for Water Crystals with Fine-Tuning
Crystals 2022, 12(11), 1667; https://doi.org/10.3390/cryst12111667 - 19 Nov 2022
Viewed by 870
Abstract
Water is one of the important, though scarce, resources on earth. The 2021 World Water Resource Report claims that environmental challenges threaten the sustainability of water resources. Therefore, it is vital to screen water quality to sustain water resources. Water quality is related [...] Read more.
Water is one of the important, though scarce, resources on earth. The 2021 World Water Resource Report claims that environmental challenges threaten the sustainability of water resources. Therefore, it is vital to screen water quality to sustain water resources. Water quality is related to water crystal structure in its solid state. Intelligent models classify water crystals to predict their quality. Methods to analyze water crystals can aid in predicting water quality. Therefore, the major contribution of our research is the prediction of water crystal classes. The proposed model analyzes water crystals in solid states, employing image analysis and the deep learning method. The model specifies several feature groups, including crystal shape factors, solid-state features, crystal geometry and discrete cosine transform coefficients. The model utilizes feature fusion for better training. The proposed model utilized the EP water crystal dataset from the WC image depository and its accuracy was tested with the multi-feature Validation technique. The nature of our data inclined us to utilize F-Measure and sensitivity for the testing phase. Our proposed model outperformed other state of the art water crystal classification models by more than 6% in accuracy and 7% in f-measures, with performance exceeding 11% for triple feature fusion. Furthermore, our model was faster in training time (10% of the training time of the comparative models) and had 1.42 s classification time. Full article
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12 pages, 2998 KiB  
Review
Summary of the Basic Free Electron Transport Characteristics in Donor Doped Silicon
Crystals 2022, 12(11), 1666; https://doi.org/10.3390/cryst12111666 - 19 Nov 2022
Cited by 2 | Viewed by 1123
Abstract
A present summary is assigned to present the transport characteristics of the free randomly moving (RM) electrons in silicon at any doping level by phosphorous donors. The application of the Fermi-Dirac statistics and stochastic description of the free RM electrons lead to obtaining [...] Read more.
A present summary is assigned to present the transport characteristics of the free randomly moving (RM) electrons in silicon at any doping level by phosphorous donors. The application of the Fermi-Dirac statistics and stochastic description of the free RM electrons lead to obtaining the general expressions of conductivity, the effective density of the free RM electrons, their diffusion coefficient and the drift mobility, which are valid for silicon with any doping level. It is shown that drift mobility of the free RM electrons considerably exceeds the Hall mobility at heavy doping, and that the Einstein relation is fundamental and is conserved at any level of degeneracy. It is estimated what part of electrons in the conduction band of heavily doped silicon is not free and is coupled with phosphorous ions. The main conclusions and formulations can be applicable for holes in acceptor-doped silicon, and other homogeneous materials with one type of the free RM charge carriers as well. Full article
(This article belongs to the Special Issue Phase Engineering of Two-Dimensional Lattices)
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30 pages, 20113 KiB  
Article
Effect of the Strength of Initial Aluminium on the Bonding Properties and Deformation Coordination of Ti/Al Composite Sheets by the Cold Roll Bonding Process
Crystals 2022, 12(11), 1665; https://doi.org/10.3390/cryst12111665 - 18 Nov 2022
Cited by 2 | Viewed by 1169
Abstract
Ti/Al composite sheets were prepared using the cold rolling process, and different initial aluminium strengths were considered. The results showed that the peel strength of the Ti/Al composite sheet increased with the increasing initial strength of aluminium under the same reduction. A higher [...] Read more.
Ti/Al composite sheets were prepared using the cold rolling process, and different initial aluminium strengths were considered. The results showed that the peel strength of the Ti/Al composite sheet increased with the increasing initial strength of aluminium under the same reduction. A higher strength of the initial aluminium corresponds to better deformation coordination between titanium and aluminium, where the strain hardening of titanium and aluminium plays an important role. The change degree of the components of twins on the titanium side for the Ti/Al composite sheet with a low aluminium strength is stronger than that for the Ti/Al composite sheet with a high aluminium strength. The strong change in the components of twins may result in the low uniformity of the microstructure on the titanium side. The analysis of the peeling surface shows aluminium residue on the titanium side, while there was almost no titanium residue on the aluminium side. At the same reduction, a higher strength of aluminium corresponds to less aluminium residue on the titanium side. The bonding properties of Ti/Al cold-rolled composite sheets were determined by four strong bonding areas. The strength of the initial aluminium was the main factor, and the residual amount of aluminium on the titanium side of the peeling surfaces was a secondary factor. Full article
(This article belongs to the Special Issue Advances in Laminated Metallic Composites)
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11 pages, 1737 KiB  
Article
(Z)-2-(2-(Anthracen-9-ylmethylene)hydrazineyl)pyrimidine-rhodium(III): Crystal Structure and DNA Binding Property
Crystals 2022, 12(11), 1664; https://doi.org/10.3390/cryst12111664 - 18 Nov 2022
Viewed by 772
Abstract
A new rhodium(III) complex of a 9-anthrahydrazone ligand ((Z)-2-(2-(Anthracen-9-ylmethylene)hydrazineyl)pyrimidine, 9-PMAH) is six-coordinated respectively by one bidentate ligand, one solvent DMSO, and three chlorides, to form a distorted octahedral coordination geometry. The ligand chelates to Rh(III) via the hydrazone N atom (N1) and pyrimidine [...] Read more.
A new rhodium(III) complex of a 9-anthrahydrazone ligand ((Z)-2-(2-(Anthracen-9-ylmethylene)hydrazineyl)pyrimidine, 9-PMAH) is six-coordinated respectively by one bidentate ligand, one solvent DMSO, and three chlorides, to form a distorted octahedral coordination geometry. The ligand chelates to Rh(III) via the hydrazone N atom (N1) and pyrimidine N atom (N3), whereas DMSO coordinates to Rh(III) via the S atom. The three chloride ligands (Cl1, Cl2, and Cl3) are in a mer-configuration of the octahedron, with the DMSO cis- to the pyrimidine nitrogen. In solution, the complex may exist in the positively charged species, [RhIIICl2(DMSO)(9-PMAH)]+, but can be stable in this mode for no less than 48 h. It was suggested by the fluorescence spectroscopic analysis that the complex showed much higher intercalative binding ability with ct-DNA than the typical DNA intercalator, EtBr. Full article
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10 pages, 1703 KiB  
Article
Crystal Growth and Electronic Properties of LaSbSe
Crystals 2022, 12(11), 1663; https://doi.org/10.3390/cryst12111663 - 18 Nov 2022
Cited by 1 | Viewed by 1556
Abstract
The ZrSiS-type materials have gained intensive attentions. The magnetic version of the ZrSiS-type materials, LnSbTe (Ln = Lanthanide), offers great opportunities to explore new quantum states owing to the interplay between magnetism and electronic band topology. Here, we report the growth [...] Read more.
The ZrSiS-type materials have gained intensive attentions. The magnetic version of the ZrSiS-type materials, LnSbTe (Ln = Lanthanide), offers great opportunities to explore new quantum states owing to the interplay between magnetism and electronic band topology. Here, we report the growth and characterization of the non-magnetic LaSbSe of this material family. We found the metallic transport, low magnetoresistance and non-compensated charge carriers with relatively low carrier density in LaSbSe. The specific heat measurement has revealed distinct Sommerfeld coefficient and Debye temperature in comparison to LaSbTe. Such addition of a new LnSbSe selenide compound could provide the alternative material choices in addition to LnSbTe telluride materials. Full article
(This article belongs to the Section Inorganic Crystalline Materials)
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17 pages, 2972 KiB  
Article
Study on Thermodynamics and Kinetics of Cephalexin Enzymatic Hydrolysis and Its Process Development to Prepare 7-ADCA
Crystals 2022, 12(11), 1662; https://doi.org/10.3390/cryst12111662 - 18 Nov 2022
Viewed by 1503
Abstract
Cephalosporin enzymatic hydrolysis technology is a green technology for recovering 7-amino-3-deacetoxycephalosporanic acid (7-ADCA) from cephalosporin mother liquor. Solubility is critical for the production and purification of 7-ADCA. In this paper, the solubility of 7-ADCA and phenylglycine was measured. Solubility-temperature correlation model and solubility-pH [...] Read more.
Cephalosporin enzymatic hydrolysis technology is a green technology for recovering 7-amino-3-deacetoxycephalosporanic acid (7-ADCA) from cephalosporin mother liquor. Solubility is critical for the production and purification of 7-ADCA. In this paper, the solubility of 7-ADCA and phenylglycine was measured. Solubility-temperature correlation model and solubility-pH correlation model were investigated, and Akaike information criterion (AIC) analysis was performed. The kinetic parameters of the enzymatic hydrolysis reaction of cephalexin, cefradine, and cefadroxil were determined, and the reaction rates under different substrate concentrations were measured, and the Lineweaver–Burk double-reciprocal equation was used to draw a graph. The Michaelis constants Km/(mg/mL) were 73.98, 583.84, 38.66, Vmax/(mg/mL·min) 4.20, 16.00, 1.96, respectively. The experimental results show that amphoteric compounds and buffers can prompt the reaction, low concentration of methanol promotes the reaction, while high concentration of methanol inhibits the reaction, and ethanol, isopropanol, tetrahydrofuran (THF), dimethyl sulfoxide (DMSO), ethylene glycol (EG), 1,4-dioxane all have different degrees of inhibition on the reaction speed. Finally, based on thermodynamic and kinetic studies, a process technology for the preparation of 7-ADCA by hydrolysis catalyzed of cephalexin was developed. It was confirmed that the proposed process route of preferential removal of phenylglycine by elution and/or cooling crystallization was reasonable and effective. The 7-ADCA crystal products obtained by crystallization were characterized by PXRD, thermal analysis, infrared, electron microscope, and high-performance liquid chromatography (HPLC). Full article
(This article belongs to the Special Issue Pharmaceutical Crystal and Process Engineering)
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14 pages, 6509 KiB  
Review
Spintronics Based Terahertz Sources
Crystals 2022, 12(11), 1661; https://doi.org/10.3390/cryst12111661 - 18 Nov 2022
Cited by 3 | Viewed by 2199
Abstract
Terahertz (THz) sources, covering a range from about 0.1 to 10 THz, are key devices for applying terahertz technology. Spintronics-based THz sources, with the advantages of low cost, ultra-broadband, high efficiency, and tunable polarization, have attracted a great deal of attention recently. This [...] Read more.
Terahertz (THz) sources, covering a range from about 0.1 to 10 THz, are key devices for applying terahertz technology. Spintronics-based THz sources, with the advantages of low cost, ultra-broadband, high efficiency, and tunable polarization, have attracted a great deal of attention recently. This paper reviews the emission mechanism, experimental implementation, performance optimization, manipulation, and applications of spintronic THz sources. The recent advances and existing problems in spintronic THz sources are fully present and discussed. This review is expected to be an introduction of spintronic terahertz sources for novices in this field, as well as a comprehensive reference for experienced researchers. Full article
(This article belongs to the Special Issue Nonlinear Crystals for Terahertz Generation)
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17 pages, 4881 KiB  
Article
Experimental Analysis of Polycaprolactone High-Resolution Fused Deposition Manufacturing-Based Electric Field-Driven Jet Deposition
Crystals 2022, 12(11), 1660; https://doi.org/10.3390/cryst12111660 - 18 Nov 2022
Cited by 2 | Viewed by 1240
Abstract
Polycaprolactone (PCL) scaffolds have been widely used in biological manufacturing engineering. With the expansion of the PCL application field, the manufacture of high-resolution complex microstructure PCL scaffolds is becoming a technical challenge. In this paper, a novel PCL high-resolution fused deposition 3D printing [...] Read more.
Polycaprolactone (PCL) scaffolds have been widely used in biological manufacturing engineering. With the expansion of the PCL application field, the manufacture of high-resolution complex microstructure PCL scaffolds is becoming a technical challenge. In this paper, a novel PCL high-resolution fused deposition 3D printing based on electric field-driven (EFD) jet deposition is proposed to manufacture PCL porous scaffold structures. The process principle of continuous cone-jet printing mode was analyzed, and an experimental system was constructed based on an electric field driven jet to carry out PCL printing experiments. The experimental studies of PCL-fused deposition under different gas pressures, electric field voltages, motion velocities and deposition heights were carried out. Analysis of the experimental results shows that there is an effective range of deposition height (H) to realize stable jet printing when the applied voltage is constant. Under the stretching of electric field force and viscous drag force (FD) with increasing movement velocities (Vs) at the same voltage and deposition height, the width of deposition lines was also gradually decreased. The width of the deposition line and the velocity of the deposition platform is approximately a quadratic curve. The bending phenomenon of deposition lines also gradually decreases with the increase of the movement velocities. According to the experiment results, a single layer linear grid structure was printed under the appropriate process parameters, with compact structure, uniform size and good straightness. The experimental results verify that the PCL porous scaffold structure can be accurately printed and manufactured. Full article
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15 pages, 2803 KiB  
Article
VOLDIS: A Direct Search for the Size Distribution of Nanoparticles from Small-Angle Scattering Data and Stability of the Solution
Crystals 2022, 12(11), 1659; https://doi.org/10.3390/cryst12111659 - 18 Nov 2022
Cited by 2 | Viewed by 1147
Abstract
The paper considers an algorithm for the direct search for a nonparametric smooth histogram of the particle size distribution from small-angle X-ray and neutron scattering data. The features and details of the implementation of the method, which consists in the sequential search for [...] Read more.
The paper considers an algorithm for the direct search for a nonparametric smooth histogram of the particle size distribution from small-angle X-ray and neutron scattering data. The features and details of the implementation of the method, which consists in the sequential search for several solutions with different degrees of smoothness of the distribution contour, are considered. Methods for evaluating the stability of both the whole distribution contour and its individual parts are discussed. The work of the program is illustrated by examples of the analysis of polydisperse spherical particles in silicasol solutions. Full article
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19 pages, 11035 KiB  
Article
Machining Performance Analysis of Rotary Ultrasonic-Assisted Drilling of SiCf/SiC Composites
Crystals 2022, 12(11), 1658; https://doi.org/10.3390/cryst12111658 - 17 Nov 2022
Cited by 3 | Viewed by 1548
Abstract
An SiCf/SiC composite has the following excellent properties: high strength, low specific gravity, and high temperature resistance, which has great prospects in the combustion chamber of rockets or aero engines. Hole-making in SiCf/SiC parts is an important processing method. [...] Read more.
An SiCf/SiC composite has the following excellent properties: high strength, low specific gravity, and high temperature resistance, which has great prospects in the combustion chamber of rockets or aero engines. Hole-making in SiCf/SiC parts is an important processing method. Generally, water-based or oil-based coolants are avoided, so dry drilling is the primary hole-making approach for SiCf/SiC. However, the abrasion resistance and high hardness of SiCf/SiC often lead to fast tool wear as well as serious damage to the fiber and matrix during dry drilling. This study proposes an innovative strategy for hole-making in SiCf/SiC parts—rotary ultrasonic-assisted drilling (RUAD) using an orderly arranged brazed diamond core drill. The influence of tool life and wear on drilling accuracy is analyzed. Additionally, the impacts of the process parameters of conventional drilling (CD) and RUAD on drilling force, torque, the surface roughness of the hole wall, and the exit tearing factor are investigated. The results show that the orderly arranged brazed diamond core drill exhibits longer tool life and higher accuracy in hole-making. Meanwhile, compared with CD, RUAD with the proposed core drill effectively improves the drilling quality and efficiency, and reduces the force and torque of drilling. The range of process parameters for dry drilling is broadened. Full article
(This article belongs to the Special Issue Processing Technology of Brittle Crystal Materials)
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12 pages, 498 KiB  
Article
Mathematical Modeling of the Solid–Liquid Interface Propagation by the Boundary Integral Method with Nonlinear Liquidus Equation and Atomic Kinetics
Crystals 2022, 12(11), 1657; https://doi.org/10.3390/cryst12111657 - 17 Nov 2022
Viewed by 936
Abstract
In this paper, we derive the boundary integral equation (BIE), a single integrodifferential equation governing the evolutionary behavior of the interface function, paying special attention to the nonlinear liquidus equation and atomic kinetics. As a result, the BIE is found for a thermodiffusion [...] Read more.
In this paper, we derive the boundary integral equation (BIE), a single integrodifferential equation governing the evolutionary behavior of the interface function, paying special attention to the nonlinear liquidus equation and atomic kinetics. As a result, the BIE is found for a thermodiffusion problem of binary melt crystallization with convection. Analyzing this equation coupled with the selection criterion for a stationary dendritic growth in the form of a parabolic cylinder, we show that nonlinear effects stemming from the liquidus equation and atomic kinetics play a decisive role. Namely, the dendrite tip velocity and diameter, respectively, become greater and lower with the increasing deviation of the liquidus equation from a linear form. In addition, the dendrite tip velocity can substantially change with variations in the power exponent of the atomic kinetics. In general, the theory under consideration describes the evolution of a curvilinear crystallization front, as well as the growth of solid phase perturbations and patterns in undercooled binary melts at local equilibrium conditions (for low and moderate Péclet numbers). In addition, our theory, combined with the unsteady selection criterion, determines the non-stationary growth rate of dendritic crystals and the diameter of their vertices. Full article
(This article belongs to the Special Issue Phase Transition in External Fields)
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16 pages, 8829 KiB  
Article
Wet Chemical Synthesis and Characterization of Au Coatings on Meso- and Macroporous Si for Molecular Analysis by SERS Spectroscopy
Crystals 2022, 12(11), 1656; https://doi.org/10.3390/cryst12111656 - 17 Nov 2022
Cited by 8 | Viewed by 1357
Abstract
Porous silicon (PS) is a promising material for nanostructure fabrication providing a precise control over its size, shape, and spatial distribution. This makes it an excellent candidate for constructing highly sensitive, reproducible, and low-cost platforms for surface enhanced Raman scattering (SERS) spectroscopy. In [...] Read more.
Porous silicon (PS) is a promising material for nanostructure fabrication providing a precise control over its size, shape, and spatial distribution. This makes it an excellent candidate for constructing highly sensitive, reproducible, and low-cost platforms for surface enhanced Raman scattering (SERS) spectroscopy. In this work, we connect the PS structural parameters with the morphology of the gold nanostructures fabricated on its surface, placing the emphasis on the SERS response. Two different types of PS are considered here, namely meso- and macro-PS. The former is prepared by Si electrochemical etching, applying three different current densities: 100 mA cm−2, 60 mA cm−2, and 30 mA cm−2, while the technological parameters for the latter are selected to mimic metal nanovoids’ (Me NVs) configuration. The gold-coated PS surfaces are produced via an electroless chemical deposition method for different time periods. By performing comprehensive structural, morphological, and optical characterization, we show the importance of the size and density of the PS pore openings, which govern the Au growth kinetics. The results presented in this work assure a simple yet flexible approach for the fabrication of large-area plasmonic gold nanostructures, which are not only suitable for advanced SERS spectroscopy studies but can also serve for a wider range of plasmonic applications. Full article
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11 pages, 3104 KiB  
Article
Design Method of Acoustic Metamaterials for Negative Refractive Index Acoustic Lenses Based on the Transmission-Line Theory
Crystals 2022, 12(11), 1655; https://doi.org/10.3390/cryst12111655 - 17 Nov 2022
Viewed by 1338
Abstract
The design theory for electromagnetic metamaterials with negative refractive indices by using a distributed transmission-line model is introduced to the design of acoustic metamaterials, and a negative refractive index (NRI) acoustic lens is designed theoretically. Adjustments to the negative refractive indices of metamaterials [...] Read more.
The design theory for electromagnetic metamaterials with negative refractive indices by using a distributed transmission-line model is introduced to the design of acoustic metamaterials, and a negative refractive index (NRI) acoustic lens is designed theoretically. Adjustments to the negative refractive indices of metamaterials have been carried out by calculations with numerical simulators in conventional design methods. As the results show, many calculations are needed to determine the shape of the unit structures and there are issues in that it is difficult to design those rigorously, meaning that limitations regarding the degree of freedom in the designs are many. On the other hand, the transmission-line model can rigorously design the unit cell structures of both the negative refractive index metamaterials and the background media with the positive refractive indices by calculations with the design formulas and modifying the error from the theory with a small calculation. In this paper, a meander acoustic waveguide unit cell structure is proposed in order to realize a structure with characteristics equivalent to the model, and the waveguide width and length for realizing an NRI acoustic lens are determined from the design formula of the model. The frequency dispersion characteristics of the proposed structure are also computed by eigenvalue analysis and the error in the waveguide length from the theoretical value is modified by a minor adjustment of the waveguide length. In addition, the NRI acoustic lens is constituted by periodically arranging the proposed unit cell structure with the calculated parameters, and the full-wave simulations are carried out to show the validity of the design theory. The results show that the designed lens operates at 2.5 kHz. Full article
(This article belongs to the Special Issue Anisotropic Acoustic Metamaterials)
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