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This study investigates the pressure-dependent thermal and mechanical properties of solid bromine through density functional theory (DFT) calculations used in conjunction with the quasi-harmonic approximation (QHA). At ambient pressure, bromine crystallizes as a molecular crystal of Cmca symmetry. Previous studies have indicated that upon compression, this polymorph should undergo a bandgap closure at 80 GPa followed by a phase transition to a nonmolecular phase at 90 GPa. By employing QHA, we model the lattice vibrations and calculate the free energy, thermal expansion, and specific heat capacities of solid molecular bromine over a temperature range from 0 to 1000 K and pressures up to 90 GPa. Furthermore, mechanical properties such as bulk modulus and elastic constants are also analyzed. The results reveal the significant impact that pressure has on the thermal properties, mechanical stability, and dynamical stability of a molecular crystal. These findings contribute to a deeper understanding of such systems under extreme conditions, potentially guiding future experimental and theoretical investigations. [ABSTRACT FROM AUTHOR]

General derivation of the well-known Ren–Otsuka relationship, 1 α d T o d x = − α β (where T o , x, α and β (> 0) are the transformation temperature and composition, as well as the composition and temperature coefficient of the critical shear constant, c′, respectively) for shape memory alloys, SMAs, is provided based on the similarity of interatomic potentials in the framework of dimensional analysis. A new dimensionless variable, t o x = T o x T m x , describing the phonon softening (where Tm is the melting point) is introduced. The dimensionless values of the heat of transformation, ΔH, and entropy, ΔS, as well as the elastic constants c′, c44, and A = c 44 c ′ are universal functions of to(x) and have the same constant values at to(0) within sub-classes of host SMAs having the same type of crystal symmetry change during martensitic transformation. The ratio of d t o d x and α has the same constant value for all members of a given sub-class, and relative increase in c′ with increasing composition should be compensated by the same decrease in to. In the generalized Ren–Otsuka relationship, the anisotropy factor A appears instead of c′, and α as well as β are the differences between the corresponding coefficients for the c44 and c′ elastic constants. The obtained linear relationship between h and to rationalizes the observed empirical linear relationships between the heat of transformation measured by differential scanning calorimetry (DSC) (QA⟶M) and the martensite start temperature, Ms. [ABSTRACT FROM AUTHOR]

Improving ferro-piezoelectric properties of niobate-based perovskites is highly desirable for developing eco-friendly high-performance sensors and actuators. Although electro-strain coupling is usually obtained by constructing multiphase boundaries via complex chemical compositions, defect engineering can also create opportunities for novel property and functionality advancements. In this work, a representative tetragonal niobate-based perovskite, i.e., KNbO3, is studied by using first-principles calculations. Two intrinsic types of Nb antisite defect complexes are selected to mimic alkali-deficiency induced excess Nb antisites in experiments. The formation energy, electronic profiles, polarization, and piezoelectric constants are systematically analyzed. It is shown that the structural distortion and chemical heterogeneity around the energetically favorable antisite pair defects, i.e., ( Nb K 4 · + K Nb 4 ′ ), lower the crystal symmetry of KNbO3 from tetragonal to triclinic phase, and facilitate polarization emergence and reorientation to substantially enhance intrinsic ferro-piezoelectricity (i.e., spontaneous polarization Ps of 68.2 μC/cm2 and piezoelectric strain constant d33 of 228.3 pC/N) without complicated doping and alloying. [ABSTRACT FROM AUTHOR]

A metaheuristic algorithm named the Crystal Structure Algorithm (CrSA), which is inspired by the symmetric arrangement of atoms, molecules, or ions in crystalline minerals, has been used for the accurate modeling of Mono Passivated Emitter and Rear Cell (PERC) WSMD-545 and CS7L-590 MS solar photovoltaic (PV) modules. The suggested algorithm is a concise and parameter-free approach that does not need the identification of any intrinsic parameter during the optimization stage. It is based on crystal structure generation by combining the basis and lattice point. The proposed algorithm is adopted to minimize the sum of the squares of the errors at the maximum power point, as well as the short circuit and open circuit points. Several runs are carried out to examine the V-I characteristics of the PV panels under consideration and the nature of the derived parameters. The parameters generated by the proposed technique offer the lowest error over several executions, indicating that it should be implemented in the present scenario. To validate the performance of the proposed approach, convergence curves of Mono PERC WSMD-545 and CS7L-590 MS PV modules obtained using the CrSA are compared with the convergence curves obtained using the recent optimization algorithms (OAs) in the literature. It has been observed that the proposed approach exhibited the fastest rate of convergence on each of the PV panels. [ABSTRACT FROM AUTHOR]

Rules that control the arrangement of chemical species within crystalline arrays of different symmetry and structural complexity are of fundamental importance in geoscience, material science, physics, and chemistry. Here, the volume of crystal phases is normalized by their ionic volume and an algebraic index that is based on their space-group and crystal site symmetries. In correlation with the number of chemical formula units Z, the normalized volumes exhibit upper and lower limits of possible structures. A bottleneck of narrowing limits occurs for Z around 80 to 100, but the field of allowed crystalline configurations widens above 100 due to a change in the slope of the lower limit. For small Z, the highest count of structures is closer to the upper limit, but at large Z, most materials assume structures close to the lower limit. In particular, for large Z, the normalized volume provides rather narrow constraints for the prediction of novel crystalline phases. In addition, an index of higher and lower complexity of crystalline phases is derived from the normalized volume and tested against key criteria. [ABSTRACT FROM AUTHOR]

The computation of the rotation barriers of the methyl groups (Me) of tribromomesitylene (TBM) crystals has been carried out. Experimentally, the barriers of the three Me groups of TBM are found to be high and different. These groups do not experience the same hindering environment in the crystal state. For an isolated TBM molecule, the three barriers are equal and very low. We found that a cluster of 21 TBM molecules permits the reproduction of the crystal symmetry and structure of the bulk, with a central molecule surrounded by six molecules in the same plane and seven other molecules in two planes above and below. DFT computations including dispersion corrections have been carried out using the ONIOM procedure. The Me groups of the central TBM molecule were rotated step by step to determine the conformations of lowest and highest energy for each Me, thus allowing estimation of the rotation barriers as the difference between these energies. In doing so, we found the following barrier values, namely 105, 173, and 205 cm−1, whereas the experimental values were 111, 180 and 200 cm−1. [ABSTRACT FROM AUTHOR]

In recent years, the phenomenon of optical second harmonic generation (SHG) has attracted significant attention as a pivotal nonlinear optical effect in research. Notably, in low-dimensional materials (LDMs), SHG detection has become an instrumental tool for elucidating nonlinear optical properties due to their pronounced second-order susceptibility and distinct electronic structure. This review offers an exhaustive overview of the generation process and experimental configurations for SHG in such materials. It underscores the latest advancements in harnessing SHG as a sensitive probe for investigating the nonlinear optical attributes of these materials, with a particular focus on its pivotal role in unveiling electronic structures, bandgap characteristics, and crystal symmetry. By analyzing SHG signals, researchers can glean invaluable insights into the microscopic properties of these materials. Furthermore, this paper delves into the applications of optical SHG in imaging and time-resolved experiments. Finally, future directions and challenges toward the improvement in the NLO in LDMs are discussed to provide an outlook in this rapidly developing field, offering crucial perspectives for the design and optimization of pertinent devices. [ABSTRACT FROM AUTHOR]

The endohedral lithium fulleride, Li+@C60•−, is a potential precursor for new families of molecular superconducting and electronic materials beyond those accessible to date from C60 itself. Solid Li@C60 comprises (Li@C60)2 dimers, isostructural and isoelectronic with the (C59N)2 units found in solid azafullerene. Here, we investigate the structural and vibrational properties of Li@C60 samples synthesized by electrolytic reduction routes. The resulting materials are of high quality, with crystallinity far superior to that of their antecedents isolated by chemical reduction. They permit facile, unambiguous identification of both the reduced state of the fulleride units and the interball C-C bonds responsible for dimerization. However, severe orientational disorder conceals any crystal symmetry lowering due to the presence of dimers. Diffraction reveals the adoption of a hexagonal crystal structure (space group P63/mmc) at both low temperatures and high pressures, typically associated with close-packing of spherical monomer units. Such a situation is reminiscent of the structural behavior of the high-pressure Phase I of solid dihydrogen, H2. [ABSTRACT FROM AUTHOR]

This document discusses the prediction of crystal systems or space groups using machine learning based on databases. It highlights the development of algorithms for predicting space groups from chemical composition, with a focus on their application in powder X-ray diffraction analysis. The document also explores the statistics of space groups for inorganic and organic crystals, as well as the differences in databases for inorganic compounds, organic compounds, and protein crystallography. It concludes by discussing the influence of molecular and supramolecular symmetry on the symmetry of supramolecular aggregations and the potential for future developments in theories and data utilization methods. [Extracted from the article]

In addition to graphene, the transition metal dichalcogenides, black phosphorus and multiple other layered materials have undergone immense investigations. Among them, metal thiophosphates (MPSx) have emerged as a promising material for various applications. While several layered metal thiophosphates with general-formula MPSx have been scrutinized extensively, van der Waals (vdW) CdPS3 has been overlooked in the literature. Here we report on the extensive Raman scattering of layered CdPS3, showing structural phase transition at a low temperature. The emergence of multiple new peaks at low frequency and a significant shift in peak position with temperature implied a probable change in crystal symmetry from trigonal D3d to triclinic Ci below the phase transition temperature, TK~180 K. In addition, we also showed a p-type performance of CdPS3 FET fabricated using Au electrodes. This work adds CdPS3 to the list of potential layered materials for energy application. [ABSTRACT FROM AUTHOR]

Many enzymes are composed of several identical subunits, which are arranged in a regular fashion and usually comply with some definite symmetry. This symmetry may be approximate or exact and may or may not coincide with the symmetry of crystallographic packing. Purine nucleoside phosphorylases (PNP) are a class of oligomeric enzymes that show an interesting interplay between their internal symmetry and the symmetry of their crystal packings. There are two main classes of this enzyme: trimeric PNPs, or "low-molecular-mass" proteins, which are found mostly in eukaryotic organisms, and hexameric PNPs, or "high-molecular-mass" proteins, which are found mostly in prokaryotic organisms. Interestingly, these two enzyme classes share only 20–30% sequence identity, but the overall fold of the single monomer is similar, yet this monomeric building block results in a different quaternary structure. To investigate this interplay of symmetry in this class of enzymes, a comprehensive database of all PNPs is constructed, containing their local symmetries and interface information. [ABSTRACT FROM AUTHOR]

It is well known that the properties of polycrystalline metals are related to grain boundaries (GBs), which are fundamental structural elements where crystallographic orientations change abruptly and often exhibit some degree of symmetry. Grain boundaries often exhibit unique structural, chemical, and electronic properties that differ from bulk crystalline domains. Their effects on material properties, including mechanical strength, corrosion resistance, and electrical conductivity, make grain boundaries a focus of intense scientific investigation. In this study, the microstructural transformation of an AlSi10Mg alloy subjected to KoBo extrusion and subsequent annealing is investigated. A notable discovery is the effectiveness of a strain-annealing method for grain boundary engineering (GBE) of the LPBF AlSi10Mg alloy. In particular, this study shows a significant increase in the population of coincidence site lattice boundaries (CSL), which embody the symmetry of the crystal lattice structure. These boundaries, which are characterised by a high degree of symmetry, contribute to their special properties compared to random grain boundaries. The experimental results emphasise the crucial role of strain-induced boundary migration (SIBM) in the development of a brass texture in the microstructure of the alloy after annealing. In addition, the presented results demonstrate the feasibility of applying GBE to materials with high stacking fault energy (SFE), which opens up new possibilities for optimizing their properties. [ABSTRACT FROM AUTHOR]

Obtaining a suitable chemical composition for high-entropy alloys (HEAs) with superior mechanical properties and good biocompatibility is still a formidable challenge through conventional trial-and-error methods. Here, based on a large amount of experimental data, a machine learning technique may be used to establish the relationship between the composition and the mechanical properties of the biocompatible HEAs. Subsequently, first-principles calculations are performed to verify the accuracy of the prediction results from the machine learning model. The predicted Young's modulus and yield strength of HEAs performed very well in the previous experiments. In addition, the effect on the mechanical properties of alloying an element is investigated in the selected Ti-Zr-Hf-Nb-Ta HEA with the high crystal symmetry. Finally, the Ti8-Zr20-Hf16-Nb35-Ta21 HEA predicted by the machine learning model exhibits a good combination of biocompatibility and mechanical performance, attributed to a significant electron flow and charge recombination. This work reveals the importance of these strategies, combined with machine learning and first-principles calculations, on the development of advanced biocompatible HEAs. [ABSTRACT FROM AUTHOR]

In recent years, there have been intense studies on hybrid organic–inorganic compounds (HOIPs) due to their tunable and adaptable features. This present study reports the vibrational, structural, and elastic properties of mixed halide single crystals of MAxFA1-xPbCl3 at room temperature by introducing the FA cation at the A-site of the perovskite crystal structure. Powder X-ray diffraction analysis confirmed that its cubic crystal symmetry is similar to that of MAPbCl3 and FAPbCl3 with no secondary phases, indicating a successful synthesis of the MAxFA1-xPbCl3 mixed halide single crystals. Structural analysis confirmed that the FA substitution increases the lattice constant with increasing FA concentration. Raman spectroscopy provided insight into the vibrational modes, revealing the successful incorporation of the FA cation into the system. Brillouin spectroscopy was used to investigate the changes in the elastic properties induced via the FA substitution. A monotonic decrease in the sound velocity and the elastic constant suggests that the incorporation of large FA cations causes distortion within the inorganic framework, altering bond lengths and angles and ultimately resulting in decreased elastic constants. An analysis of the absorption coefficient revealed lower attenuation coefficients as the FA content increased, indicating reduced damping effects and internal friction. The current findings can facilitate the fundamental understanding of mixed lead chloride perovskite materials and pave the way for future investigations to exploit the unique properties of mixed halide perovskites for advanced optoelectronic applications. [ABSTRACT FROM AUTHOR]

Bi2Se3, one of the most extensively studied topological insulators, has received significant attention, and abundant research has been dedicated to exploring its surface electronic properties. However, little attention has been given to its piezoelectric properties. Herein, we investigate the piezoelectric response in a five-layer Bi2Se3 nanosheet using scanning probe microscopy (SPM) techniques. The piezoelectricity of Bi2Se3 is characterized using both conventional piezoresponse force microscopy (PFM) and a sequential excitation scanning probe microscopy (SE-SPM) technique. To confirm the linear piezoelectricity of Bi2Se3 two-dimensional materials, measurements of point-wise linear and quadratic electromechanical responses are carried out. Furthermore, the presence of polarization and relaxation is confirmed through hysteresis loops. As expected, the Bi2Se3 nanosheet exhibits an electromechanical solid response. Due to the inevitable loss of translational symmetry at the crystal edge, the lattice of the odd-layer Bi2Se3 nanosheet is noncentrosymmetric, indicating its potential for linear piezoelectricity. This research holds promise for nanoelectromechanical systems (NEMS) applications and future nanogenerators. [ABSTRACT FROM AUTHOR]

Ceramics of the quasi-binary concentration section (0.1 ≤ x ≤ 0.2, Δx = 0.025) of the ternary solid solution system (0.5 − x)BiFeO3-0.5PbFe0.5Nb0.5O3-xPbTiO3 were prepared by the conventional solid-phase reaction method. An X-ray study at different temperatures revealed that (0.5 − x)BF-0.5PFN-xPT ceramics have a cluster morphology. Clusters have different modulation, crystal lattice symmetry, and chemical composition. The presence of a cluster structure in a solid solution with heterovalent substitution, consisting of regions rich in Ti+4, Nb+5, or Fe3+, has led to the appearance of Maxwell–Wagner polarization in the studied ceramics. The study of the dielectric characteristics revealed the relaxor-like behavior of the studied ceramics. The grain morphology, dielectric, pyroelectric, and piezoelectric properties of the selected solid solutions were investigated. The highest piezoelectric coefficient, d33 = 280 pC/N, was obtained in the 0.3BiFeO3-0.5PbFe0.5Nb0.5O3-0.2PbTiO3 ceramics. Study of the dielectric characteristics of all samples revealed relaxor ferroelectric behavior and a region of diffuse phase transition from the paraelectric to ferroelectric phase in the temperature range of 140–170 °C. [ABSTRACT FROM AUTHOR]

The Raman scattering, infrared absorption, and reflection spectra of hexagonal non-centrosymmetric BaZnBO3F and BaAlBO3F2 and centrosymmetric BaZn3BO3F2 and BaZnCO3F2 are calculated using the standard procedures of the CRYSTAL package with the basis of localized orbitals and the B3LYP hybrid functional within the framework of the Hartree-Fock conjugate perturbation method. It is shown that the layered structure of crystals manifests itself in the spectra of vibrational modes polarized along and perpendicular to the c axis with wavenumbers for the lattice region formed by displacements of atoms in [BaF]∞ and [MAO3]∞ (M: Zn, Al; A: B, C) layers, for molecular deformation outside and in the plane of anions BO3 and CO3. The quantitative and qualitative composition of the spectra is determined by the symmetry of the crystal lattice. [ABSTRACT FROM AUTHOR]

This study focused on electron microscopy studies of microstructural defects formed in an additively manufactured (AM) AlSi10Mg alloy as a result of post-deformation by equal channel angular pressing (ECAP), with the aim of elucidating the fundamental deformation mechanisms that govern the plasticity of both the aluminium matrix and the silicon phase. This article focused on the process of grain refinement, metastable phase transformations, and microstructural defects such as stacking faults or amorphous areas that severely disrupt the face-centred cubic (FCC) crystal lattice symmetry. The findings presented in this study imply that deformation twinning, phase transformation, and amorphization are not mutually exclusive modes of Si phase deformation. Both can occur at an ECAP temperature of 150 °C. At a deformation temperature of 100 °C, amorphization is the dominant deformation mode of the Si phase. It was also discovered that dislocation slip was the predominant deformation mode of Al matrix at 150 °C, while at 100 °C, additionally stacking faults were formed within the Al matrix. The present findings provide not only a fundamental understanding of the deformation micro-mechanism of the SLMed AlSi10Mg alloy but also open a new horizon for the development of the next generation of structural materials. [ABSTRACT FROM AUTHOR]

The (001) plate-like BaTiO3 piezoelectric micromaterials are synthesized by topochemical microcrystal conversion technique. BaTiO3 plates with a length of 2~10 μm and thickness of 0.5~1.3 μm are obtained. The dependence of morphology on synthesis conditions is discussed in detail. The crystal symmetry and multiscale domain structures of BaTiO3 plates are systematically investigated by various characterizations. X-ray diffraction (XRD) and Raman spectra analyses demonstrate the tetragonal symmetry of the (001) oriented BaTiO3 plates at room temperature. The domain configurations of the micron BaTiO3 are investigated with a polarized light microscope (PLM) and piezoresponse force microscopy (PFM). The single-crystal-like quality and uniformity are supported by PLM observations. More importantly, the classical 90° banded ferroelectric domains of ~125 nm width are observed for the first time in such BaTiO3 plates. The domain features in the mesoscale BaTiO3 plate are discussed and compared with its bulk counterparts. The results may provide insights into understanding and designing the mesoscale BaTiO3 functional materials. [ABSTRACT FROM AUTHOR]

We conducted a systematic investigation using state-of-the-art techniques on the electronic and optical properties of two crystals of alkaline earth metal fluorides, namely rutile MgF 2 and cubic SrF 2 . For these two crystals of different symmetry, we present density functional theory (DFT), many-body perturbation theory (MBPT), and Bethe–Salpeter equation (BSE) calculations. We calculated a variety of properties, namely ground-state energies, band-energy gaps, and optical absorption spectra with the inclusion of excitonic effects. The quantities were obtained with a high degree of convergence regarding all bulk electronic and optical properties. Bulk rutile MgF 2 has distinguished ground-state and excited-state properties with respect to the other cubic fluoride SrF 2 and the other members of the alkaline earth metal fluoride family. The nature of the fundamental gaps and estimates of the self-energy and excitonic effects for the two compounds are presented and discussed in detail. Our results are in good accordance with the measurements and other theoretical–computational data. A comparison is made between the excitation and optical properties of bulk rutile MgF 2 , cubic SrF 2 , and the corresponding clusters, for which calculations have recently been published, confirming strong excitonic effects in finite-sized systems. [ABSTRACT FROM AUTHOR]

In this paper, an analysis of gain properties of a single primitive cell of a one-dimensional photonic crystal with parity–time symmetry is demonstrated for the first time. The proposed simple model makes it possible to study the transmission and amplification properties of the investigated cell made of a wide range of optical materials, taking into account the refractive index of the surrounding medium. This analysis is carried out with the use of a transfer matrix method. The obtained characteristics allow indicating the optimal size of the studied structure providing wave amplification, i.e., a transmittance greater than unity. In this case, the increase in the wave intensity in the gain layer exceeds its decrease in the loss layer. This effect is illustrated with the distributions of the electromagnetic field of waves propagating inside the cell. [ABSTRACT FROM AUTHOR]

Topological indices are numbers that are applied to a graph and can be used to describe specific graph properties through algebraic structures. Algebraic graph theory is a helpful tool in a range of chemistry domains. Because it helps explain how the different symmetries of molecules and crystals affect their structure and dynamics, it is a powerful theoretical approach for forecasting both the common and uncommon characteristics of molecules. A topological index converts the chemical structure into a number and contributes a lot in chemical graph theory. In this article, we compute the Wiener index, Zagreb indexes, Wiener polynomial, Hyper-Wiener index, ABC index and eccentricity-based topological index of a nonzero component union graph from vector space. [ABSTRACT FROM AUTHOR]

Monoclinic potassium rare-earth crystals are known as efficient materials for solid-state lasers and acousto-optic modulators. A number of specific configurations for acousto-optic devices based on those crystals have recently been proposed, but the acousto-optic effect of those crystals has only been analyzed fragmentarily for some interaction directions. In this work, we numerically searched for the global maxima of an acousto-optic figure of merit for isotropic diffraction in KGd(WO4)2 and KY(WO4)2 crystals. It was demonstrated that the global maxima of the acousto-optic figure of merit in those crystals occur in the slow optical mode propagating along the crystal's twofold symmetry axis and in the acoustic wave propagating orthogonally, both for quasi-longitudinal and quasi-shear acoustic modes. The proposed calculation method can be readily used for the optimization of the acousto-optic interaction geometry in crystals with arbitrary symmetry. [ABSTRACT FROM AUTHOR]

The optical and magneto-optical characteristics of KTb3F10 crystals in the transition region of 5D4 → 7F6 4f8 configurations of the Tb3+ ion at temperatures of 90 and 300 K were studied. The schemes of the optical transitions in the KTb3F10 crystals were constructed, and the energies of most of the Stark sublevels of the ground 7F6 and excited 5D4 multiplets of the Tb3+ ion split by the C4v symmetry crystal environment were determined. The presence of three- and two-doublet states in the energy spectra of the Tb3+ion multiplets 7F6 and 5D4, respectively, was established, which is in good agreement with theoretical predictions. The use of the wavefunctions of the Stark sublevels of multiplets split by a tetragonal crystal field and combining in the studied optical transition made it possible to explain some of the magnetic and magneto-optical features observed in the KTb3F10 single crystals. [ABSTRACT FROM AUTHOR]

The structures of 2-(3-hydroxy-5-methylphenoxy)-N-(4-nitrophenyl)acetamide), B1, and 2-(3-hydroxy-5-methylphenoxy)-N-(4-(trifluoromethyl)phenyl)acetamide, B2, are crystallized in the crystal symmetry of the monoclinic structure and in the space group of P21/c. For the different structures of B1 and B2, B1 displays an absolute planarity conformation with torsion angles of 172.2–179.1. The two molecules of B1 are linked by a hydrogen bond of N–H...O–N–O, where a hydrogen atom of amide is bound to an oxygen atom of the nitro-substituted group. In the case of B2, the molecules are connected to each other through the hydrogen bonding interaction of C=O...H–O. DFT calculations reveal that the transition from HOMO to LUMO of B1 and B2 shows the absorption bands B1 and B2 at 314 and 240 nm, respectively. Upon the addition of an OH− ion, the absorption bands of B1 and B2 shift to a longer wavelength than the original bands of B1 and B2. According to the 1H-NMR results, the NH proton of B1 and B2 disappears due to the deprotonation process. The methylene group and aromatic region move to upfield shift when adding an OH− ion. [ABSTRACT FROM AUTHOR]

The spin–Hamiltonian parameters g–factors ( g | | and g ⊥ ) of the Ce3+ paramagnetic centers in BaWO4: Ce and BaWO4: Ce, Na single crystals with axial symmetry are investigated using the superposition model (SPM) via complete diagonalization procedure of energy matrix (CDM method). The calculated g–factors are in reasonable agreement with the experimental values. The fitted intrinsic parameters are comparable with data from other publications for rare-earth paramagnetic centers in a similar environment. The angular distortions of the cerium dodecahedron [CeO8] are also studied. Structural analysis of paramagnetic centers with axial symmetry through the postulated cerium barium tetrahedron [CeBa4] connected via oxygens bridges was carried out. The mechanism of the charge compensation and the role of the second dopant (Na+) is also discussed. [ABSTRACT FROM AUTHOR]

Unconventional superconductivity in heavily boron-doped nanocrystalline diamond films (HBDDF) produced a significant amount of interest. However, the exact pairing mechanism has not been understood due to a lack of understanding of crystal symmetry, which is broken at the grain boundaries. The superconducting order parameter (Δ) of HBDDF is believed to be anisotropic since boron atoms form a complex structure with carbon and introduce spin-orbit coupling to the diamond system. From ultra-high resolution transmission electron microscopy, the internal symmetry of the grain boundary structure of HBDDF is revealed, which can explain these films' unconventional superconducting transport features. Here, we show the signature of the anisotropic Δ in HBDDF by breaking the structural symmetry in a layered microstructure, enabling a Rashba-type spin-orbit coupling. The superlattice-like structure in diamond describes a modulation that explains strong insulator peak features observed in temperature-dependent resistance, a transition of the magnetic field-dependent resistance, and their oscillatory, as well as angle-dependent, features. Overall, the interface states of the diamond films can be explained by the well-known Shockley model describing the layers connected by vortex-like structures, hence forming a topologically protected system. [ABSTRACT FROM AUTHOR]

In this paper, the elastic constitutive relation of polycrystals contains the effect of the mesostucture coefficients. We consider a general case and derive the average elastic constitutive relation pertaining to polycrystals of cubic crystals with any symmetry of crystalline orientation in their statistical distribution. Following Budiansky and Wu, we used self-consistent estimates of eigenstrain to obtain the effective elastic constitutive relation of polycrystals in an explicit form. For the Voigt assumption and the Reuss assumption, the effective elastic constitutive relation of polycrystals on cubic crystals contains the the mesostructure coefficients up to linear terms. In general, the linear term expression works well for materials such as aluminum, the single crystal of which has weak anisotropy. However the same expression (which allows the anisotropic part of the effective elastic constitutive relation to depend only linearly on the mesostructure coefficients) does not suffice for materials such as copper, in which the single crystal is strongly anisotropic. Per the Taylor theorem, we expand the expression based on the self-consistent estimates with respect to the mesostructure coefficients up to quadratic terms for anisotropic polycrystals of cubic crystals. While our numerical data are very close to those of Morris, our expression is much simpler. [ABSTRACT FROM AUTHOR]

The symmetry of crystals is an extremely important property of crystals. Crystals can be divided into centrosymmetric and non-centrosymmetric crystals. In this paper, an infrared (IR) nonlinear optical (NLO) material AgGaGeSe4 was synthesized. The related performance analysis, nonlinear optical properties, and first-principle calculation of AgGaGeSe4 were also introduced in detail. In the AgGaGeSe4 structure, Ge4+ was replaced with Ga3+ and produced the same number of vacancies at the Ag+ position. The low content of Ge doping kept the original chalcopyrite structure and improved its optical properties such as the band gap. The UV-Vis diffuse reflection spectrum shows that the experimental energy band gap of AgGaGeSe4 is 2.27 eV, which is 0.48 eV larger than that of AgGaSe2 (1.79 eV). From the perspective of charge-transfer engineering strategy, the introduction of Group IV Ge elements into the crystal structure of AgGaSe2 effectively improves its band gap. The second harmonic generation (SHG) effect of AgGaGeSe4 is similar to that of AgGaSe2, and at 1064 nm wavelength, the birefringence of AgGaGeSe4 is 0.03, which is greater than that of AgGaSe2 (∆n = 0.02). The results show that AgGaGeSe4 possessed better optical properties than AgGaSe2, and can been broadly applied as a good infrared NLO material. [ABSTRACT FROM AUTHOR]

Understanding the relationships between the local structures and physical properties of low-dimensional ferroelectrics is of both fundamental and practical importance. Here, pressure-induced enhancement in the photocurrent of SbSI is observed by using pressure to regulate the lone-pair electrons (LPEs). The reconfiguration of LPEs under pressure leads to the inversion symmetry broken in the crystal structure and an optimum bandgap according to the Shockley–Queisser limit. The increased polarization caused by the stereochemical expression of LPEs results in a significantly enhanced photocurrent at 14 GPa. Our research enriches the foundational understanding of structure–property relationships by regulating the stereochemical role of LPEs and offers a distinctive approach to the design of ferroelectric-photovoltaic materials. [ABSTRACT FROM AUTHOR]

Transition metal dichalcogenides exhibit rich phase diagrams dominated by the interplay of superconductivity and charge density waves, which often result in anomalies in the electric transport properties. Here, we employ the ionic gating technique to realize a tunable, non-volatile organic ion intercalation in bulk single crystals of molybdenum disulphide (MoS 2 ). We demonstrate that this gate-driven organic ion intercalation induces a strong electron doping in the system without changing the pristine 2 H crystal symmetry and triggers the emergence of a re-entrant insulator-to-metal transition. We show that the gate-induced metallic state exhibits clear anomalies in the temperature dependence of the resistivity with a natural explanation as signatures of the development of a charge-density wave phase which was previously observed in alkali-intercalated MoS 2 . The relatively large temperature at which the anomalies are observed (∼150 K), combined with the absence of any sign of doping-induced superconductivity down to ∼3 K, suggests that the two phases might be competing with each other to determine the electronic ground state of electron-doped MoS 2 . [ABSTRACT FROM AUTHOR]

Fully compensated ferrimagnets do not create any magnetic stray field and allow for a completely polarized current of charges. As a result, these alloys show promising prospects for applications as spintronic devices. In this paper, we investigated the phase stability, the site preference, the tetragonal distortion and the influence of symmetry from the crystal structure and chemical environments of magnetic ions on the magnetic properties of Cr2YZ and Mn2YZ (Y = void, Ni, Cu, and Zn; Z = Ga, Ge, and As) full Heusler alloys by first-principles calculations. We found that the selected Cr2-based alloys, except for Cr2NiGa and Cr2NiGe, prefer to crystallize in the centrosymmetric L21-type structure, while the selected Mn2-based alloys, except for Mn2CuAs, Mn2ZnGe and Mn2ZnAs, tend to crystallize in the non-centrosymmetric XA-type structure. Due to the symmetry, the antiferromagnetism of the selected L21-type alloys is very stable, and no spin-polarized density of states could be generated. In contrast, the magnetic moment of the selected XA-type alloys depends heavily on the number of valence electrons and tetragonal distortion, and spin-polarized density of states is generated. Therefore, the selected alloys with L21-type structures and their tetragonal-distorted structure are potential candidates for conventional antiferromagnets, while those with XA-type structure and their tetragonal-distorted structure are promising candidates for (fully) compensated ferrimagnets. [ABSTRACT FROM AUTHOR]

Discreditation of the monoclinic tourmaline mineral species luinaite-(OH), ideally (Na,▯)(Fe2+,Mg)3Al6(BO3)3Si6O18(OH)4 was approved by the IMA-CNMNC (proposal 21-L) and is described. We analyzed two luinaite-(OH) samples: one from the type locality Cleveland tin mine, Luina, Waratah, Tasmania, Australia, and the other from Blue Mountain Saddle (Bald Hornet Claim), North Bend, King County, Washington, DC, USA. Biaxial (−) crystals representative of the studied samples were spectroscopically (Mössbauer, polarized Fourier transform infrared, optical absorption spectroscopy), chemically (nuclear microprobe analysis and electron microprobe analysis), and structurally characterized (single-crystal X-ray diffraction). Results show the occurrence of a triclinic structure for the studied luinaite-(OH) samples, which differs only in terms of a slight structural distortion from typical trigonal tourmaline structure (the topology of the structure is retained). As a result, following the IMA-CNMNC and tourmaline nomenclature rules, the triclinic luinaite-(OH) from the type locality (Australia) can be considered as the triclinic dimorph of schorl, as its chemical composition corresponds to schorl, and thus it should be referred as schorl-1A. Similarly, the triclinic sample from the USA can be considered as the triclinic dimorph of oxy-dravite, as its chemical composition corresponds to oxy-dravite, and then is referred to as oxy-dravite-1A. [ABSTRACT FROM AUTHOR]

The monoclinic YCOB crystal still maintains good piezoelectric properties at 800 °C; thus, it has a good application prospect in high-temperature piezoelectric acoustic wave sensors. However, due to the lower symmetry compared crystals in trigonal and tetragonal systems, the exciting characteristics of piezoelectric plates based on monoclinic YCOB crystals are more complicated. The vibration analysis model of lateral-field-excitation (LFE) devices based on monoclinic crystals is scarce; thus, the coupling relationships between different vibration modes and energy-trapping characteristics of the devices are unclear, which hinders the optimal design of devices. In this paper, by using Mindlin plate theory, the high-frequency vibrations of piezoelectric resonators based on monoclinic YCOB crystal plates excited by a lateral electric field are modeled and analyzed. The coupling relationships between the vibration modes of the device are clarified. The influences of the electrode width, electrode/plate mass ratio and electrode gap value on resonances and energy-trapping characteristics of the device are achieved. In addition, the effects of the structure parameters on the mass sensitivity of the monoclinic YCOB LFE devices are investigated, which are further verified by FEM simulations. The results are crucial to obtaining good resonance and sensing characteristics for LFE high-temperature piezoelectric sensors based on crystals with monoclinic symmetry. [ABSTRACT FROM AUTHOR]

Generally, a liquid crystal device confines liquid crystal molecules in a cell and achieves a desired liquid crystal alignment by interfacial force. Currently, the scale of the global liquid crystal industry is approximately USD 75 billion, most of which is for display applications using nematic liquid crystals (including chiral nematic liquid crystals). Liquid crystals are aggregates of individual molecules due to moderate intermolecular interactions, which are roughly divided into lyotropic liquid crystals and thermotropic liquid crystals. [Extracted from the article]

It is much easier to determine a protein's sequence than to determine its three dimensional structure and consequently homology modeling will be an essential aspect of most studies that require 3D protein structure data. Homology modeling templates tend to be PDB files. About 88% of all protein structures in the PDB have been determined with X-ray crystallography, and thus are based on crystals that by necessity hold non-natural packing contacts in accordance with the crystal symmetry. Active site residues, residues involved in intermolecular interactions, residues that get post-translationally modified, or other sites of interest, normally are located at the protein surface so that it is particularly important to correctly model surface-located residues. Unfortunately, surface residues are just those that suffer most from crystal packing artifacts. Our study of the influence of crystal packing artifacts on the quality of homology models reveals that this influence is much larger than generally assumed, and that the evaluation of the quality of homology models should properly account for these artifacts. [ABSTRACT FROM AUTHOR]

Where are the atoms in complex crystals such as quasicrystals or periodic crystals with one hundred or more atoms per unit cell? How did they get there? The first of these questions has been gradually answered for many materials over the quarter-century since quasicrystals were discovered; in this paper we address the second. We briefly review a history of proposed models for describing atomic positions in crystal structures. We then present a revised description and possible growth model for one particular system of alloys, those containing Tsai-type clusters, that includes an important class of quasicrystals. [ABSTRACT FROM AUTHOR]

In this work, a set of nanoparticles of Nb2O5 nanoparticles were grown by both the Pechini and the sol-gel methods. The amorphous materials were calcined at 650°C or at 750°C. X-ray diffraction, scanning electron microscopy, luminescence and Raman spectroscopy were used in order to characterize the materials. From the study, it is possible to state that the method of production of nanoparticles, beyond the temperature of synthesis, has a great influence on whether the phase produced is hexagonal or orthorhombic. Additionally, compared to de Sol-gel method, the Pechini method produced samples with smaller particle sizes. The photoluminescence spectra of niobium pentoxide nanostructure materials show that the emission peaks are positioned between 334 to 809 nm and there is a change of intensity which varies depending on the synthesis route used. High pressure Raman spectra at room temperature were obtained from two samples grown by the sol-gel method. Up to 6 GPa, where it is possible to observe the Raman bands, no modification other than the increase of disorder was observed, and this can be associated with a change of phase. [ABSTRACT FROM AUTHOR]

NLPs are disc-shaped particles composed of a patch of lipid bilayer surrounded by a belt of apolipoproteins, which are typically used in the structural characterization of membrane proteins by inserting them within the lipid bilayer. The successful adaptation of the serial macromolecular crystallography approach at most 3rd generation synchrotron facilities allows a fruitful synergy between synchrotrons and XFELs that have accelerated the access and impact of this approach to an even larger community. The review article by Golub et al. [[4]] discusses the principles and prototypical applications of small-angle neutron and X-ray scattering (SANS and SAXS, respectively) applied to the photosynthetic pigment-protein complexes phycocyanin (PC) and Photosystem I (PSI) as model systems for a water-soluble protein and a membrane protein, respectively. [Extracted from the article]

Currently, an intensive search for high-performance lead-free ferroelectric materials is taking place. ABO3 perovskites (A = Ba, Bi, Ca, K and Na; B = Fe, Nb, Ti, and Zr) appear as promising candidates. Understanding the structure-function relationship is mandatory, and, in this field, the roles of long-and short-range crystal orders and interactions are decisive. In this review, recent advances in the global and local characterization of ferroelectric materials by synchrotron light diffraction, scattering and absorption are analyzed. Single-and poly-crystal synchrotron diffraction studies allow high-resolution investigations regarding the long-range average position of ions and subtle global symmetry break-downs. Ferroelectric materials, under the action of electric fields, undergo crystal symmetry, crystallite/domain orientation distribution and strain condition transformations. Methodological aspects of monitoring these processes are discussed. Two-dimensional diffraction clarify larger scale ordering: polycrystal texture is measured from the intensities distribution along the Debye rings. Local order is investigated by diffuse scattering (DS) and X-ray absorption fine structure (XAFS) experiments. DS provides information about thermal, chemical and displacive low-dimensional disorders. XAFS investigation of ferroelectrics reveals local B-cation off-centering and oxidation state. This technique has the advantage of being element-selective. Representative reports of the mentioned studies are described. [ABSTRACT FROM AUTHOR]

The crystalline structure of two biodegradable odd-odd polyesters (i.e., poly(nonamethylene pimelate) (PES 9,7) and poly(nonamethylene azelate) (PES 9,9)) was investigated by means of electron and X-ray diffraction of single crystals and oriented fibers, respectively. Truncated rhombic crystals were obtained with an aspect ratio that was strongly depended on the supercooling degree. The crystalline structure of both homopolyesters was defined by an orthorhombic P21ab space group and a large unit cell containing four molecular segments with an all-trans conformation. Nevertheless, the structure in the chain axis projection was equivalent to a simpler cell containing only two segments. Crystalline lamellae were effectively degraded by lipases, starting the enzymatic attack on the lamellar surfaces. The random copolymer constituted by an equimolar amount of pimelate and azelate units (COPES 9,7/9) crystallized according to regular lamellae with a similar molecular arrangement in the chain axis projection. The structure of this copolymer was preferably conditioned by the azelate component as could be deduced from both, diffraction and spectroscopic data. Analysis of small angle X-ray scattering patterns pointed out that less crystalline lamellae with higher amorphous thickness had developed in the copolymer. This feature was interpreted as a consequence of the preferential incorporation of pimelate comonomer units in the folding surface. [ABSTRACT FROM AUTHOR]

An overview is given of the use of symmetry considerations for aperiodic crystals. Superspace groups were introduced in the seventies for the description of incommensurate modulated phases with one modulation vector. Later, these groups were also used for quasi-periodic crystals of arbitrary rank. Further extensions use time reversal and time translation operations on magnetic and electrodynamic systems. An alternative description of magnetic structures to that with symmetry groups, the Shubnikov groups, is using representations of space groups. The same can be done for aperiodic crystals. A discussion of the relation between the two approaches is given. Representations of space groups and superspace groups play a role in the study of physical properties. These, and generalizations of them, are discussed for aperiodic crystals. They are used, in particular, for the characterization of phase transitions between aperiodic crystal phases. [ABSTRACT FROM AUTHOR]

Several materials science type research topics are described in which advantageous use of crystal symmetry considerations has been helpful in ferreting the essential elements of dislocation behavior in determining material properties or for characterizing crystal/polycrystalline structural relationships; for example: (1) the mechanical strengthening produced by a symmetrical bicrystal grain boundary; (2) cleavage crack formation at the intersection within a crystal of symmetrical dislocation pile-ups; (3) symmetry aspects of anisotropic crystal indentation hardness measurements; (4) X-ray diffraction topography imaging of dislocation strains and subgrain boundary misorientations; and (5) point and space group aspects of twinning. Several applications are described in relation to the strengthening of grain boundaries in nanopolycrystals and of multiply-oriented crystal grains in polysilicon photovoltaic solar cell materials. A number of crystallographic aspects of the different topics are illustrated with a stereographic method of presentation. [ABSTRACT FROM AUTHOR]

It is well understood that nonlinear optical (NLO) phenomena are deeply related to the material's symmetry. Mathematically, the material symmetry can be described in terms of the nonzero parameters in the nonlinear susceptibility tensors. Generally, more complex structures involve more nonzero parameters in the tensor. The number of parameters increases rapidly if higher NLO orders are considered, complicating the physical analysis. Conventionally, these parameters are obtained via abstract symmetry analysis, e.g., group theory (GT). This work presents a novel theoretical analysis to approach the nonlinear tensor using the simplified bond hyperpolarizability model (SBHM) and compare it with GT. Our analysis is based on a light–matter interaction classical phenomenological physical framework. Rather than just looking at the symmetry of the crystal, the model applies physical considerations requiring fewer independent parameters in the tensor than GT. Such a simplification significantly improves the determination of the surface–bulk SHG contribution factors, which cannot be extracted from the experiment alone. We also show for the case of perovskite that the SHG contribution can be addressed solely from their surface dipoles with only one independent component in the tensor. Therefore, this work may open the path for a similar analysis in other complicated semiconductor surfaces and structures in the future, with potential applications to nanoscale surface characterization and real-time surface deposition monitoring. [ABSTRACT FROM AUTHOR]

High-order harmonic generation (HHG) is a fundamental process which can be simplified as the production of high energetic photons from a material subjected to a strong driving laser field. This highly nonlinear optical process contains rich information concerning the electron structure and dynamics of matter, for instance, gases, solids and liquids. Moreover, the HHG from solids has recently attracted the attention of both attosecond science and condensed matter physicists, since the HHG spectra can carry information of electron-hole dynamics in bands and inter- and intra-band current dynamics. In this paper, we study the effect of interlayer coupling and symmetry in two-dimensional (2D) material by analyzing high-order harmonic generation from monolayer and two differently stacked bilayer hexagonal boron nitrides (hBNs). These simulations reveal that high-order harmonic emission patterns strongly depend on crystal inversion symmetry (IS), rotation symmetry and interlayer coupling. [ABSTRACT FROM AUTHOR]

Three-layer iron-rich Fe3+xSi1−x/Ge/Fe3+xSi1−x (0.2 < x < 0.64) heterostructures on a Si(111) surface with Ge thicknesses of 4 nm and 7 nm were grown by molecular beam epitaxy. Systematic studies of the structural and morphological properties of the synthesized samples have shown that an increase in the Ge thickness causes a prolonged atomic diffusion through the interfaces, which significantly increases the lattice misfits in the Ge/Fe3+xSi1−x heterosystem due to the incorporation of Ge atoms into the Fe3+xSi1−x bottom layer. The resultant lowering of the total free energy caused by the development of the surface roughness results in a transition from an epitaxial to a polycrystalline growth of the upper Fe3+xSi1−x. The average lattice distortion and residual stress of the upper Fe3+xSi1−x were determined by electron diffraction and theoretical calculations to be equivalent to 0.2 GPa for the upper epitaxial layer with a volume misfit of −0.63% compared with a undistorted counterpart. The volume misfit follows the resultant interatomic misfit of |0.42|% with the bottom Ge layer, independently determined by atomic force microscopy. The variation in structural order and morphology significantly changes the magnetic properties of the upper Fe3+xSi1−x layer and leads to a subtle effect on the transport properties of the Ge layer. Both hysteresis loops and FMR spectra differ for the structures with 4 nm and 7 nm Ge layers. The FMR spectra exhibit two distinct absorption lines corresponding to two layers of ferromagnetic Fe3+xSi1−x films. At the same time, a third FMR line appears in the sample with the thicker Ge. The angular dependences of the resonance field of the FMR spectra measured in the plane of the film have a pronounced easy-axis type anisotropy, as well as an anisotropy corresponding to the cubic crystal symmetry of Fe3+xSi1−x, which implies the epitaxial orientation relationship of Fe3+xSi1−x (111)[0−11] || Ge(111)[1−10] || Fe3+xSi1−x (111)[0−11] || Si(111)[1−10]. Calculated from ferromagnetic resonance (FMR) data saturation magnetization exceeds 1000 kA/m. The temperature dependence of the electrical resistivity of a Ge layer with thicknesses of 4 nm and 7 nm is of semiconducting type, which is, however, determined by different transport mechanisms. [ABSTRACT FROM AUTHOR]

Properties of FeTe0.65Se0.35 single crystals, with the onset of critical temperature (Tconset) at 15.5 K, were modified via hydrogenation performed for 10–90 h, at temperatures ranging from 20 to 250 °C. It was found that the tetragonal matrix became unstable and crystal symmetry lowered for the samples hydrogenated already at 200 °C. However, matrix symmetry was not changed and the crystal was not destroyed after hydrogenation at 250 °C. Bulk Tcbulk, determined at the middle of the superconducting transition, which is equal to 12–13 K for the as grown FeTe0.65Se0.35, rose by more than 1 K after hydrogenation. The critical current density studied in magnetic field up to 70 kOe increased 4–30 times as a consequence of hydrogenation at 200 °C for 10 h. Electron paramagnetic resonance measurements also showed higher values of Tcbulk for hydrogenated crystals. Thermal diffusion of hydrogen into the crystals causes significant structural changes, leads to degeneration of crystal quality, and significantly alters superconducting properties. After hydrogenation, a strong correlation was noticed between the structural changes and changes in the parameters characterizing the superconducting state. [ABSTRACT FROM AUTHOR]

A comparative analysis of crystal structure, Raman spectra, and dielectric hysteresis loops was carried out for organic ferroelectric crystals of 2-methylbenzimidazole (MBI) grown from ethanol (MBIet), acetone (MBIac), deuterated acetone (MBId-ac), or prepared by sublimation from gas phase (MBIgas). Raman spectroscopy shows identical frequencies of molecular vibrations in all studied crystals, proving the same molecular structure. At the same time, a detailed analysis of the asymmetry of the powder XRD reflection profiles indicates the presence of nano-scaled regions with the same MBI symmetry and crystal structure but slightly different sizes and unit cell parameters. The formation of the MBI modifications is associated with possible penetration of solvent molecules into the voids of the MBI crystal structure. Dielectric hysteresis loops in MBIet and MBId-ac crystals at room temperature demonstrate significantly different values of coercive fields Ec. Analysis of hysteresis loops within the framework of the Kolmogorov-Avrami-Ishibashi (KAI) model shows that the polarization switching in MBId-ac occurs much faster than in MBIet crystals, which in the KAI model is associated with different values of the characteristic frequency ω0 and the activation field Ea of the domains wall motion. [ABSTRACT FROM AUTHOR]

All possible experimental geometries of the piezo-optic effect in crystals of trigonal symmetry are studied in detail through the interferometric technique, and the corresponding expressions for the calculation of piezo-optic coefficients (POCs) πim and some sums of πim based on experimental data obtained from the samples of direct and X/45°-cuts are given. The reliability of the values of POCs is proven by the convergence of πim obtained from different experimental geometries as well as by the convergence of some sums of POCs. Because both the signs and the absolute values of POCs π14 and π41 are defined by the choice of the right crystal-physics coordinate system, we here use the system whereby the condition S14 > 0 is fulfilled (S14 is an elastic compliance coefficient). The absolute value and the sign of S14 are determined by piezo-optic interferometric method from two experimental geometries. The errors of POCs are calculated as mean square values of the errors of the half-wave stresses and the elastic term. All components of the matrix of elasto-optic coefficients pin are calculated based on POCs and elastic stiffness coefficients. The technique is tested on LiTaO3 crystal. The obtained results are compared with the corresponding data for trigonal LiNbO3 and Ca3TaGa3Si2O14 crystals. [ABSTRACT FROM AUTHOR]

Herein, the spontaneous polarization in crystals with hexagonal symmetry are calculated as a function of the number of monolayers composing a nanostructure by adding the dipole moments for consecutive units of the nanostructure. It is shown that in the limit of a large numbers of monolayers that the spontaneous polarization saturates to the expected bulk value of the spontaneous polarization. These results are relevant to understanding the role of the built-in spontaneous polarizations in a variety of nanostructures since these built-in polarizations are generally quite large, on the order of 1 × 108 to 1 × 1010 V/m. Using these formulations, we come to the prediction that small nanolayered structures are theoretically capable of having larger spontaneous polarizations than their bulk counterparts due to how the dipole moments of the anions and cations within a wurtzite lattice cancel out with one another more in larger structures. [ABSTRACT FROM AUTHOR]