Octahedral Lattice Research Articles

Defect Chemistry of Spinel Cathode Materials-A Case Study of Epitaxial LiMn2O4 Thin Films.

Spinels of the general formula Li2-δM2O4 are an essential class of cathode materials for Li-ion batteries, and their optimization in terms of electrode potential, accessible capacity, and charge/discharge kinetics relies on an accurate understanding of the underlying solid-state mass and charge transport processes. In this work, we report a comprehensive impedance study of sputter-deposited epitaxial Li2-δMn2O4 thin films as a function of state-of-charge for almost the entire tetrahedral-site regime (1 ≤ δ ≤ 1.9) and provide a complete set of electrochemical properties, consisting of the charge-transfer resistance, ionic conductivity, volume-specific chemical capacitance, and chemical diffusivity. The obtained properties vary by up to three orders of magnitude and provide essential insights into the point defect concentration dependences of the overall electrode potential. We introduce a defect chemical model based on simple concentration dependences of the Li chemical potential, considering the tetrahedral and octahedral lattice site restrictions defined by the spinel crystal structure. The proposed model is in excellent qualitative and quantitative agreement with the experimental data, excluding the two-phase regime around 4.15 V. It can easily be adapted for other transition metal stoichiometries and doping states and is thus applicable to the defect chemical analysis of all spinel-type cathode materials.

Effect on magnetic behaviour of Ag and Cd doped cobalt ferrite nanoparticles prepared by glycine-assisted sol-gel auto combustion method

The nanocomposites of the Silver (Ag) and cadmium (Cd) based, cobalt ferrite having formula AgxCdxCo1–2xFe2O4 (where x = 0.0, 0.05, and 0.1) have been successfully prepared by glycine-assisted Sol-gel derived auto combustion technique. The synthesized samples were analyzed by X-ray diffraction (XRD), scanning electron microscopy (SEM), Fourier Transform Infrared Spectroscopy (FT-IR), UV–visible spectrum, and Vibrating Sample Magnetometer (VSM). The XRD and FTIR results reveal the formation of a single-phase cubic spinel structure with crystallite sizes 14–19 nm. SEM analysis of surface morphology revealed spherical and cubic-shaped nano-particles. FTIR spectra indicated two fundamental absorption peaks around 580 cm-1 and 460 cm−1. This confirmed the existence of m-o bonding in the synthesized products corresponding to the stretching vibration of tetrahedral (A) and octahedral (B) lattice sites. According to UV-Visible analysis, it is observed that the optical band gap energies vary from 1.88 eV to 1.52 eV as the Ag/Cd concentration increased. From VSM data, the magnetic behavior of prepared specimens is studied and the corresponding variations in the (Ms), (Hc), (Mr), and Mr/Ms values are analyzed. This prepared composites materials are recommended for magnetic storage applications.

Modification of BCZT piezoelectric ceramics by modulating oxygen vacancies in different sintering atmospheres

In this work, we regulated the oxygen vacancy concentration by sintering BCZT + 0.1 mol % Y + 0.1 mol % Nb [BCZT-0.1 mol % (Y + Nb)] ceramics under air, oxygen, argon, and vacuum atmospheres and examined the effect of oxygen vacancy concentration on phase composition, crystal structure, microstructure, and electrical properties. X-ray photoelectron spectrometry and X-ray diffraction Rietveld refinement showed that the air- and oxygen-sintered ceramic samples had lower oxygen vacancy concentrations, and the oxygen octahedral lattice distortion in the samples was stable when the R-O-T phases coexisted, forming a multiphase coexistence structure with more spontaneous polarization directions. The oxygen-sintering atmosphere is important in oxygen compensation, which promotes the formation of dense microstructure, thereby increasing the Curie temperature (TC). Oxygen vacancy formation energy was low in the argon and vacuum atmospheres, and some oxygen vacancies increased the mass transfer effect and grain growth. Nevertheless, excess oxygen vacancies increased the leakage current during polarization resulting in poor polarity, which prevents directional deflection of domains and degrades performance. The vacuum-sintered sample was calcined in 1000 °C air for oxygen supplementation sintering, and as the sintering time increased, the oxygen vacancy concentration decreased, the grains grew further, the density increased, and the piezoelectric properties improved. The oxygen-sintered BCZT-0.1 mol % (Y + Nb) samples had good comprehensive electrical properties (d33 = 547 pC/N, kp = 55%, εr = 5355, Pr = 10.63 µC/cm2, EC = 1.89 kV/cm, tan δ = 0.02, and TC = 102 °C).

Compression Behavior of Pilar Octahedral Lattice Structures

Lattice structures have a great potential in the fields like aerospace and biomedical, due to their outstanding properties like high strength, low mass, and good energy absorption capacity. With the development of the Additive Manufacturing technologies, there was an increasing attention towards these structures. The compressive behavior of the pilar octahedral lattice structure, which has the high strength to weight ratio was analyzed in this work. Lattice structures with three strut diameters of 1.5, 1.75, and 2 mm were built using Fused Filament Fabrication from Tough Polylactic Acid (PLA) plastic. Quasi-static compression tests were performed and two finite element models using beam elements with and without nodal beam diameter correction were proposed. It was found that as the diameter of the strut increases strength and elastic moduli are increased as well, while specific mechanical properties almost do not change. It was also confirmed from numerical and experimental results that lattice structure fails by forming a diagonal shear band. The relative error of the simulation without nodal correction in predicting the strength of the lattice with a 1.5 mm strut diameter was 1.58%. However, due to the inability of the beam element to model the behavior at the nodes properly its accuracy decreases for larger diameters. By modifying the model and using a nodal beam diameter correction, it has been possible to achieve a relative error of 0.58% and 12.15% for strut diameters of 1.75 and 2 mm respectively.

Quantum Effects on Unconventional Pinch Point Singularities.

Fracton phases are a particularly exotic type of quantum spin liquids where the elementary quasiparticles are intrinsically immobile. These phases may be described by unconventional gauge theories known as tensor or multipolar gauge theories, characteristic for so-called type-I or type-II fracton phases, respectively. Both variants have been associated with distinctive singular patterns in the spin structure factor, such as multifold pinch points for type-I and quadratic pinch points for type-II fracton phases. Here, we assess the impact of quantum fluctuations on these patterns by numerically investigating the spin S=1/2 quantum version of a classical spin model on the octahedral lattice featuring exact realizations of multifold and quadratic pinch points, as well as an unusual pinch line singularity. Based on large scale pseudofermion and pseudo-Majorana functional renormalization group calculations, we take the intactness of these spectroscopic signatures as a measure for the stability of the corresponding fracton phases. We find that in all three cases, quantum fluctuations significantly modify the shape of pinch points or lines by smearing them out and shifting signal away from the singularities in contrast to effects of pure thermal fluctuations. This indicates possible fragility of these phases and allows us to identify characteristic fingerprints of their remnants.

Thermomechanical behavior of lattice structures: An analytical, numerical, and experimental study

In this study, thermomechanical behavior of regular porous materials is studied using analytical, numerical, and experimental approaches. Analytical relationships for octahedral lattice structure have been obtained based on Euler-Bernoulli beam theory. Three types of finite element models, two based on beam elements and one based on volumetric elements, are made. Additive manufacturing technique is also used to fabricate lattice structures with different relative densities. The manufactured samples are heated to a certain temperature in a closed chamber, and the displacements are measured and compared to their analytical and numerical counterparts. Based on the results, the analytical, numerical, and experimental results are in excellent agreement with each other. The methodologies introduced in this study would be beneficial for further studies on porous materials and lattice structure with other topologies and higher degrees of freedom.

Effect of Sb-induced oxygen octahedral distortion on piezoelectric performance and thermal stability of Pb(In,Nb)O3-Pb(Hf,Ti)O3 ceramics

The combination of excellent thermal stability and outstanding electrical performance is of great significance for piezoelectric ceramics. Herein, we have prepared 0.11Pb(In0.5Nb0.5)O3-0.89Pb(Hf0.47Ti0.53)O3-Sb2O5 (PIN-PHT-xSb) ceramics by solid-phase method and investigated the effect of oxygen octahedral lattice distortion on microstructure and macroscopic electrical properties. The distortion index of oxygen octahedra is studied by Rietveld refinement, showing that optimal octahedral distortion can soften B-O repulsion, disrupt long-range ordered ferroelectric domains, and enhance local heterogeneities, significantly increasing piezoelectric properties. Moreover, outstanding thermal stability and ultrahigh piezoelectric response of PIN-PHT-1.2Sb ceramics are realized under the synergistic influence of octahedral distortion, excellent density, and large grain size. Compared with PIN-PHT ceramics, PIN-PHT-1.2Sb ceramics exhibit ultrahigh piezoelectric responses (d33 = 706 pC/N, kp = 0.68, εr = 3244), a high Curie temperature (TC) of 300 °C, excellent thermal stability, and anti-fatigue properties.

Influence of the hierarchical architecture of multi-core iron oxide nanoflowers on their magnetic properties

Magnetic properties of superparamagnetic iron oxide nanoparticles are controlled mainly by their particle size and by their particle size distribution. Magnetic properties of multi-core iron oxide nanoparticles, often called iron oxide nanoflowers (IONFs), are additionally affected by the interaction of magnetic moments between neighboring cores. The knowledge about the hierarchical structure of IONFs is therefore essential for understanding the magnetic properties of IONFs. In this contribution, the architecture of multi-core IONFs was investigated using correlative multiscale transmission electron microscopy (TEM), X-ray diffraction and dynamic light scattering. The multiscale TEM measurements comprised low-resolution and high-resolution imaging as well as geometric phase analysis. The IONFs contained maghemite with the average chemical composition gamma-Fe_{2.72pm 0.02}O_4. The metallic vacancies located on the octahedral lattice sites of the spinel ferrite structure were partially ordered. Individual IONFs consisted of several cores showing frequently a specific crystallographic orientation relationship between direct neighbors. This oriented attachment may facilitate the magnetic alignment within the cores. Individual cores were composed of partially coherent nanocrystals having almost the same crystallographic orientation. The sizes of individual constituents revealed by the microstructure analysis were correlated with the magnetic particle sizes that were obtained from fitting the measured magnetization curve by the Langevin function.

Structural, optical, magnetic and anti-bacterial properties of green synthesized spinel zinc ferrite by microwave-assisted method

Spinel structured zinc ferrite (ZF) has been green synthesized using microwave-assisted solution combustion method. Toxic free Hibiscus leaves extract was used as a reducing agent in the synthesis process. Rietveld refinement analysis of high-resolution X-ray diffraction (XRD) pattern confirmed that the ZF has cubic spinel structure with the average crystallite size of 10.47 nm. Agglomerated spherical shapes were observed in green synthesized spinel ZF by scanning electron microscope. The estimated average particle size was found to be 11.52 nm by high resolution transmission electron microscopy imaging. The Zn, Fe and O are the main elements present in spinel ZF, analysed from energy dispersion X-ray analysis. Tetrahedral and octahedral lattice sites which are related to Zn–O and Fe–O bonds were identified by Fourier transform infra-red and Raman spectra. The estimated optical energy bandgap of spinel ZF is found to be 2.17 eV using diffuse reflectance spectroscopy. The Vibrating sample magnetometer results showed single domain superparamagnetic nature of spinel ZF at room temperature. In addition, antibacterial properties of spinel ZF were tested using agar dispersion and agar well diffusion methods on gram negative bacteria Escherichia coli DH5α, after 24 h the bacterial growth completely inhibited.

Experimental investigation of mechanical properties and energy absorption capabilities of hybrid lattice structures manufactured using fused filament fabrication

Hybrid lattice structures are composed of several dissimilar unit cells arranged in specific patterns. Unlike their one-phase counterparts, hybrid lattices remain relatively unexplored. In this work, novel hybrid lattice structures composed of Pillar Octahedral (PO) and Rhombic Dodecahedron (RD) lattices having variable strut diameters are arranged in different orders to form hybrid vertical piles (HVP), 2D and 3D chessboard order (HCh2D and HCh3D), are proposed, and their mechanical properties, energy absorption characteristics, and deformation modes are investigated under quasistatic compression. The empirical results indicated that the mechanical properties of hybrid lattice structures are the average of those of their parent lattices. HVP lattice structure has a high yield stress of 1.2, 2.22, and 3.54 MPa when strut diameter is 1.5, 1.75, and 2 mm respectively, and stable post-buckling region. It was also observed that hybrid lattice structures are more efficient in absorbing the energy of the deformation. When strut diameter is 1.5 mm, PO lattice structure has an efficiency of 50%, while HVP, HCh2D, and HCh3D lattices have an efficiency of about 70–80%. Finally, Gibson-Ashby models were proposed to predict the mechanical properties of lattice structures as the function of relative density.

Landau theory and self-assembly of spherical nanoclusters and nanoparticles with octahedral symmetry

Spherical nanoclusters and nanoparticles are rising materials whose functional design provides many useful applications ranging from catalysis, molecular sensing, gas storage to drug targeting and delivery. Here, we develop phenomenological crystallization theory of such spherical structures with octahedral symmetries O and O_h. Within the developed theory, we propose a method, which is based on constructing irreducible octahedral density functions and allows to predict the positions of structural units in the spherical nanoobjects. The proposed theory explains the structures of the simplest known metal nanoclusters, some metal-organic polyhedra and membrane protein polyhedral nanoparticles, and also predicts more complex chiral spherical structures and achiral assemblies characterized by the geometry of semiregular polyhedra. A relationship between the constructed irreducible octahedral functions and spherical lattices, obtained by mapping a plane hexagonal order onto a spherical surface through an octahedron net, is discussed as well.

Impact of the organic cation on the band-edge emission of two-dimensional lead-bromide perovskites.

Organic-inorganic low-dimensional layered metal-halide perovskites are semiconductors in which the optoelectronic properties can be tuned by the material composition and the design of the layered architecture. While the electronic band structure is mainly determined by the inorganic octahedra lattice, the binding and conformation of the organic cations induces related lattice distortions that can break the symmetry and lead to the splitting of the exciton energy levels, and influence the dielectric confinement. Furthermore, organic-induced lattice deformations lead to offsets in k-space (where k is the wavevector) that go along with the exciton energy level splitting. Hence, the electronic transitions between these levels require the momentum contribution of phonons, and contributions of phonons in the exciton recombination dynamics result in thermal broadening of the emission linewidth. In this work, we investigate the band-edge emission of two-dimensional Ruddlesden-Popper lead-bromide perovskites synthesized with different organic cations that vary in their binding head group and their alkyl chain length. We find several peaks in the low-temperature photoluminescence spectra, and the number of peaks in the band-edge emission and their decay dynamics depend strongly on the type of organic cation in the material, which we relate to the difference in the inorganic lattice distortions that the cations induce. For two-dimensional layered perovskites with mainly in-plane distortions, induced by short primary ammonium molecules, we find a two-fold splitting of the band edge emission at low temperatures. If also out-of-plane distortions are present, as for the long-chain primary ammoniums, a three-fold splitting is observed. Interestingly, the low-energy peaks of the split series merge into the highest energy peak with increasing temperature. Thermal broadening analysis of the temperature-dependent photoluminescence linewidth in the structures with out-of-plane distortions yields energies that are larger than those reported for the inorganic lattice phonons. This indicates the involvement of either high-frequency oscillations involving the organic cations, or the broadening might be related to higher order phonon scattering processes in the excitonic recombination process. The strong directionality of the phonon modes in the octahedral lattice could promote the involvement of multiple electron-phonon scattering processes in the exciton relaxation dynamics, for example involving modes with orthogonal directionality.

Optical and electrical properties of Sb-doped β-Ga2O3 crystals grown by OFZ method

Sb-doped β-Ga2O3 crystals were grown using the optical floating zone (OFZ) method. X-ray diffraction data and X-ray rocking curves were obtained, and the results revealed that the Sb-doped single crystals were of high quality. Raman spectra revealed that Sb substituted Ga mainly in the octahedral lattice. The carrier concentration of the Sb-doped single crystals increased from 9.55×1016 to 8.10×1018 cm-3, the electronic mobility depicted a decreasing trend from 153.1 to 108.7 cm2 ·V-1 ·s-1, and the electrical resistivity varied from 0.603 to 0.017 Ω·cm with the increasing Sb doping concentration. The un-doped and Sb-doped β-Ga2O3 crystals exhibited good light transmittance in the visible region; however, the evident decrease in the infrared region was caused by increase in the carrier concentration. The Sb-doped β-Ga2O3 single crystals had high transmittance in the UV region as well, and the cutoff edge appeared at 258 nm.

Impact of gadolinium doping into the frustrated antiferromagnetic lithium manganese oxide spinel

Cubic spinel LiMn2O4 (LMO) are promising electrode materials for advanced technological devices owing to their rich electrochemical properties. Here, a series of Gd3+-doped LiMn2O4 were synthesized using a simple one-step sol-gel synthesis, and a systematized study on the effect of increasing Gd3+ concentration on magnetic properties is conferred. The Raman and density functional theory (DFT) calculations of the synthesized materials were correlated with the magnetic properties; we observed a high coercivity value for the doped LMO compared to pristine LMO, which scales down from 0.57T to 0.14T with an increase in Gd concentration. The samples exhibited paramagnetic (at 300K) to antiferromagnetic (at 5K) transition and variation in the magnetic moment due to the replacement of Mn+2 or Mn+3 ion by Gd+3 ion from the octahedral 16d lattice site. The observed phase transitions in the hysteresis curve below the Neel temperature (TN) at 5K are found to be due to the superexchange mechanism.

Influence of interaction-generated anisotropy on the antiferromagnetic spin system on the octahedral lattice

The phase diagram of the antiferromagnetic spin-1/2 Ising-like model on the octahedral lattice with different strength of the nearest-neighbor interactions in all horizontal planes of the lattice in comparison to all nearest-neighbor interactions between them is investigated in the appropriate recursive lattice approximation. The existence of the intermediate phase that separates two dominant antiferromagnetic phases is shown and the nature of all phase transitions between various phases is determined. The sublattice as well as total magnetization properties of all phases of the model are studied. It is shown that the introduced interaction-generated anisotropy has strong impact on the very existence of the phenomenon of the weak ferromagnetism as well as on its magnetization properties in such pure antiferromagnetic spin systems.

Influence of Ce-Mn co-doping on the structure and magnetic properties of cobalt ferrites

In this study, we selected Ce3+ and Mn2+ as co-doped ions in order to improve the magnetic properties of cobalt ferrite. The nominal composition Co1−xMnxFe2−xCexO4 (x = 0, 0.05, 0.10, and 0.20) nanoparticles were prepared by facile co-precipitation technique, and the effect of co-doping content on the structural and magnetic properties of cobalt ferrite was investigated. The structural result confirmed the formation of cubic spinel structure for all co-doped samples, although secondary phase of CeO2 was detected in the high co-doping content ones. Fourier transform infrared spectroscopy confirmed the presence of metal-oxygen bonding. All samples exhibited two frequency bands corresponding to the phonon vibrational stretching in the octahedral and tetrahedral lattice positions, respectively. The surface morphology analysis revealed the spherical shape of the ferrite nanoparticles. After co-doped with Ce3+ and Mn2+ ions, the magnetic parameters of cobalt ferrite were significantly improved. The maximum magnetization saturation is 66.5 emu/g when x = 0.05, and the maximum coercivity is 2288 Oe when x = 0.10. The two values are approximately 29% and 47% higher than that of the un-doped one. At the same time, the maximum energy product reaches 0.72 MG·Oe, which is about 118% higher than that for pure cobalt ferrite, i.e. 0.33 MG·Oe. The reasons may be related to the substitution of Fe3+ and Co2+ with Ce3+ and Mn2+, and also the resulting changes in crystallite sizes of the samples. These results demonstrate the effectivity of Ce-Mn co-doping in improving the magnetism of cobalt ferrite.

Investigation of the Performance of Ti6Al4V Lattice Structures Designed for Biomedical Implants Using the Finite Element Method

The development of medical implants is an ongoing process pursued by many studies in the biomedical field. The focus is on enhancing the structure of the implants to improve their biomechanical properties, thus reducing the imperfections for the patient and increasing the lifespan of the prosthesis. The purpose of this study was to investigate the effects of different lattice structures under laboratory conditions and in a numerical manner to choose the best unit cell design, able to generate a structure as close to that of human bone as possible. Four types of unit cell were designed using the ANSYS software and investigated through comparison between the results of laboratory compression tests and those of the finite element simulation. Three samples of each unit cell type were 3D printed, using direct metal laser sintering technology, and tested according to the ISO standards. Ti6Al4V was selected as the material for the samples. Stress–strain characteristics were determined, and the effective Young’s modulus was calculated. Detailed comparative analysis was conducted between the laboratory and the numerical results. The average Young’s modulus values were 11 GPa, 9 GPa, and 8 GPa for the Octahedral lattice type, both the 3D lattice infill type and the double-pyramid lattice and face diagonals type, and the double-pyramid lattice with cross type, respectively. The deviation between the lab results and the simulated ones was up to 10%. Our results show how each type of unit cell structure is suitable for each specific type of human bone.

Systemic development of Mn4+-activated double perovskite red phosphors for plant growth applications

Developing efficient and stable red phosphor has always been considered as important academic research of LED plant-growth lamps. In this study, Mn4+-activated double perovskite red phosphors, A2BB’O6:Mn4+ (A = Sr, Ba; B = Lu, Gd; B’ = Nb, Ta), were successfully synthesized by solid-phase method. To elucidate the structure-activity relationship between the double perovskite structure and the luminescence of Mn4+, the crystal structure, electronic structure and luminescence properties of Sr2LuNbO6:Mn4+ were first studied in detail using X-ray powder diffraction data, density functional theory calculations and spectroscopy data. The coordination environment of Mn4+ was analyzed by investigating the crystal-field parameters, Racah parameters and nephelauxetic parameter. Then, the effect of structural evolution on the luminescence of Mn4+ was investigated by regulating the local coordination environment of Mn4+ through cationic modification. The results demonstrate that Mn4+ enters the octahedral lattice site with a strong crystal field and covalent environment, which can be excited by a near-ultraviolet LED chip to emit narrow-band far-red light in the double perovskite oxides. Moreover, the Mn–O bond length, octahedral distortion and crystal-system type all affect the luminescence of Mn4+. This systemic development provides some guidance for the exploration of novel Mn4+-activated double perovskite red phosphors.

High energy storage performance of Ca0.15(Sr0.6Ba0.4)0.85Nb2-xTaxO6 relaxor ferroelectric ceramics

A series of lead-free Ca0.15(Sr0.6Ba0.4)0.85Nb2-xTaxO6 (CSBNTx) unfilled tetragonal tungsten bronze (TTB) ferroelectric ceramics were fabricated via a traditional solid-state reaction process by substituting Ta5+ for Nb5+ in B sites to enhance relaxor behavior. The introduction of Ta5+, which has a strong refractory character, resulted in pronounced grain size reduction and improvement of the breakdown strength. The distortion of the BO6 octahedral lattice promoted the movement of the relaxor transition peak toward lower temperatures. The weakening of the covalency of the B–O bond destroyed the ferroelectric domain structure, resulting in a more slender P-E hysteresis loop, ultimately improving the efficiency at higher ratios of Ta. Finally, a relatively good recoverable energy-storage density of 1.42 J/cm3 and a high energy storage efficiency of 81.9% were obtained for Ca0.15(Sr0.6Ba0.4)0.85Nb1.4Ta0.6O6. Optimal charging-discharging performance, with a discharge time of τ0.9 = 69 ns, a current density (CD) of 1110.9 A/cm2, and a power density (PD) of 94.43 MW/cm3, was achieved in CSBNT0.6 ceramics.

Ca2+ doping effects on the structural and electrical properties of Na0.5Bi4.5Ti4O15 piezoceramics

Bismuth layer structured Na0.5Bi4.5Ti4O15 (NBT) ferroelectric is one of the most promising materials for potential applications at high temperature. However, it is challenged to achieve a balance between high Curie temperature piezoelectric coefficient and excellent thermal stability for NBT piezoceramics. Here, through chemical modification at the A site of NBT with Ca2+, novel (Na0.5Bi0.5)1-xCaxBi4Ti4O15 piezoceramics with excellent properties fabricated by solid state reaction were studied. After doping of Ca2+, the Curie temperature TC increased from 648 °C to 662 °C while the piezoelectric coefficient d33 increased from 14 pC/N to 22 pC/N which can be attributed to the intrinsic contribution of TiO6 octahedral lattice distortion (tilting and rotation) and the extrinsic contribution of the increased density of domain walls. The composition of (Na0.5Bi0.5)0.95Ca0.05Bi4Ti4O15 ceramics with x = 0.05 has the optimal performance with high TC of 655 °C, large d33 of 22 pC/N, high electrical resistivity ρ close to 107 Ω cm at 500 °C and especially excellent thermal stability of d33 only about 5% reduction after being annealed at 625 °C. The work effectively reveals the great potential of CNBT-5 ceramics for high-temperature piezoelectric applications.