Hexagonal Unit Cell Research Articles

Synthesis and structural study of the partially disordered complex hexagonal phase δ1-MnZn9.7.

A detailed structural analysis of the Zn-rich δ1-MnZn9.7 phase using single-crystal X-ray diffraction is presented. The δ1 phase has been synthesized by the high-temperature synthetic route. The structure crystallizes in space group P63/mmc (Pearson symbol hP556) with unit-cell parameters: a = b = 12.9051 (2) Å and c = 57.640 (1) Å. The 556 atoms are distributed over 52 Wyckoff positions in the hexagonal unit cell: seven ordered Mn sites, 37 ordered Zn sites and eight positionally disordered Zn sites. The structure predominantly consists of Frank-Kasper polyhedra (endohedral icosahedra Zn12 and icosioctahedron Zn16) and four distinct types of glue Zn atoms. The structure comprises a 127-atom supercluster (Mn13Zn114), a 38-atom extended Pearce cluster (Mn3Zn35), a 46-atom L-tetrahedron (Mn4Zn42), a Friauf polyhedron (Zn17), a disordered icosahedral cluster (MnZn12) and four glue Zn atoms. Positionally disordered Zn sites around an Mn site can be visualized as the superimposition of three differently oriented Zn12 icosahedra.

Bio-Mediated Synthesis of ZnO Nano Photocatalyst using C. gigantea (L.): Microstructural Study for Rapid Degradation of Organic Pollutants from Aqueous Medium

The purpose of this paper was to synthesize ZnO nanoparticles (NPs) from Calotropis gigantea (L.) and use them as photocatalyst for the elimination of wastewater contaminants, methyl orange (MO), and paracetamol (PCM) by UV irradiation. The UV-Vis absorption spectra show a peak at a wavelength of 374 nm with excitonic band gap of 3.41 eV. The hexagonal unit cell with mean crystallite size of 29.13 nm was found from the XRD pattern. The FESEM images confirms the formation of nanostructures. The bio-mediated nanoparticles are used as nano photocatalysts to eliminate MO and PCM. The effects of irradiation time, photocatalyst dose, dye concentration, and solution pH on photodegradation were studied in MO. Furthermore, the photodegradation of paracetamol was also investigated.

Enhanced electrochemical performance of K0.67[Ni0.3Mn0.6Co0.1] O2 as a cathode material for secondary K-Ion batteries: Improved K-Ion insertion and reduced charge transfer barrier

Potassium-ion batteries, with their high operating voltage and cost-efficiency, emerged as promising contenders for large-scale energy storage system. Nevertheless, the practical application is hindered by the significant challenges of achieving high capacity and good rate capability in cathodes. Herein, a novel layered oxide cathode, K0.67[Ni0.3Mn0.6Co0.1] O2 (KNMCO), has been synthesized via solid-state (S-KNMCO) and co-precipitation (C-KNMCO) routes. The X-Ray diffraction (XRD) peaks of KNMCO are identified in R3 m space group and well-indexed to hexagonal unit cell. The FE-SEM shows non-spherical morphologies for both samples. Additionally, high-resolution transmission electron microscopy (HR-TEM) images of the synthesized cathode materials shows the interlayer spacing of S-KNMCO is higher than that of C-KNMCO. Furthermore, the electrochemical performance of S-KNMCO and C-KNMCO is characterized using K-metal as anode and electrolyte KPF6 in EC/DEC (1:1, v/v). The S-KNMCO and C-KNMCO exhibit the maximum specific discharge capacity of ∼101 mAhg-1 and ∼66 mAhg-1 at the current rate of C/20 respectively. Additionally, these cells show the good rate capability and coulombic efficiency (∼94%). This research offers novel perspectives on the development of cathode substances for KIBs.

Mechanical Properties of Re-Entrant Hybrid Honeycomb Structures for Morphing Wings.

The exceptional energy absorption, deformability, and tuneable Poisson's ratio properties of negative Poisson's ratio (NPR) honeycomb biomimetic structures make them highly suitable for applications in aerospace, medical, and acoustic stealth industries. The present study proposes a re-entrant hybrid honeycomb (REHH) structure comprising a re-entrant octagonal unit cell and a re-entrant hexagonal unit cell. Theoretical models of the in-plane elastic modulus and Poisson's ratio are established based on beam theory, and these models are validated through finite element (FE) simulations and tensile experiments conducted on the REHH samples. The influence of the cell geometry parameters on the in-plane elastic behaviours is investigated. The results indicate that the NPR performance of the REHH structure exhibits superior deformation capability compared with the four-point star hybrid honeycomb (FSHH) structure. The experimental REHH structure samples exhibit significant tensile displacement capabilities in the x-direction.

Diatom Cribellum-Inspired Hierarchical Metamaterials: Unifying Perfect Absorption Toward Subwavelength Color Printing.

Diatom exoskeletons, known as frustules, exhibit a unique multilayer structure that has attracted considerable attention across interdisciplinary research fields as a source of biomorphic inspiration. These frustules possess a hierarchical porous structure, ranging from millimeter-scale foramen pores to nanometer-scale cribellum pores. In this study, this natural template for nanopattern design is leveraged to showcase metamaterials that integrates perfect absorption and subwavelength color printing. The cribellum-inspired hierarchical nanopatterns, organized in a hexagonal unit cell with a periodicity of 300nm, are realized through a single-step electron beam lithography process. By employing numerical models, it is uncovered that an additional induced collective dipole mode is the key mechanism responsible for achieving outstanding performance in absorption, reaching up to 99%. Analysis of the hierarchical organization reveals that variations in nanoparticle diameter and inter-unit-cell distance lead to shifts and broadening of the resonance peaks. It is also demonstrated that the hierarchical nanopatterns are capable of color reproduction with high uniformity and fidelity, serving as hexagonal pixels for high-resolution color printing. These cribellum-inspired metamaterials offer a novel approach to multifunctional metamaterial design, presenting aesthetic potential applications in the development of robotics and wearable electronic devices, such as smart skin or surface coatings integrated with energy harvesting functionalities.

Enhanced properties of multi‐element soluted (Nb0.8Ti0.05Zr0.05Mo0.05M0.05)4AlC3 (M = Hf, Ta) ceramics

AbstractRecently multielements solid solution has shown significant improvement to the mechanical properties of parent MAX phases. Therefore, in this work, five elements with different radii were incorporated to check the effect on properties of MAX phases. (Nb0.8Ti0.05Zr0.05Mo0.05Hf0.05)4AlC3 (MAXHf) and (Nb0.8Ti0.05Zr0.05Mo0.05Ta0.05)4AlC3 (MAXTa) ceramics were successfully synthesized using the spark plasma sintering technique. The microstructure and elemental map analysis results further confirmed that the five transition metals were successfully solid soluted at the M‐sites of the hexagonal M4AlC3 unit cell. The mean elemental compositions for M‐site elements were achieved as Nb0.85Ti0.052Zr0.035Mo0.027Hf0.036 and Nb0.847Ti0.051Zr0.043Mo0.025Ta0.033 for MAXHf and MAXTa ceramics, respectively. The electrical and thermal conductivities of multielement solid solution MAX phases were decreased compared to pure Nb4AlC3. However, Mechanical properties were significantly increased with the solid solution of five transition metals. The fracture toughness, flexural strength, compressive strength and Vickers hardness (10 N) of MAXHf and MAXTa ceramics were achieved as 8.87 MPa m1/2, 448 MPa, 867 MPa, 6.5 GPa and 10.36 MPa m1/2, 557 MPa, 1039 MPa, 8.2 GPa, respectively. The enhanced mechanical properties suggest the effectiveness of the solid solution strengthening effect and provide new opportunities to further tailor the mechanical properties of the MAX phase ceramics.

Phase transition, structural and magnetic parameters of vanadium-substituted Bi0.9Sm0.1FeO3 multiferroic ceramics

ABSTRACT The inorganic multiferroic compounds Bi0.9Sm0.1Fe1 − x V x O3 (x = 0.0, 0.015, 0.03, and 0.045) were prepared by the solid-state reaction method. X-ray diffraction analysis confirmed the rhombohedral perovskite-like structure with minor traces of the impurity phases Bi2Fe4O9 and Bi25FeO40. The lattice parameters a and c, and the volume of the hexagonal unit cell were extracted from the X-ray diffraction data and found to increase as the V5+ content is increased. The average crystallite size was estimated to be in the range 380–415 Å. Fourier transform infrared spectroscopy confirmed the rhombohedral perovskite-like structure via the vibration bands of the octahedral FeO6 group observed between 410 and 570 cm−1. A differential scanning calorimeter was used to record the thermal scans which revealed that the compounds have undergone crystalline phase transitions at temperatures in the range 300–320°C. A 4.5% V + 5 substitution has shifted the transition peak by 20°C. The magnetic hysteresis loops taken at room temperature with a vibrating sample magnetometer revealed the ordinary ferromagnetic behavior. The V5+ substitution enhanced the remanent magnetization, but the magnetic coercivity was found to fluctuate around an average value of about 1000 Oe. The compound Bi0.9Sm0.1Fe0.955V0.045O3 exhibited the maximum remanent magnetization.

CVT grown CuSe single crystals: Unveiling photodetection advancements and thermoelectric promise

Over the past few decades, transition metal chalcogenides garnered global recognition for their noteworthy contributions to the modeling and engineering of electronic, optoelectronic, and thermoelectric devices to improve overall device performance. In the current investigation, the first ever growth of CuSe single crystals is achieved utilizing the chemical vapor transport technique with iodine serving as a transporting medium. The ascertainment of the hexagonal unit cell configuration in the grown CuSe crystals with the P63/mmc space group is substantiated via powder X-ray diffraction examination. The micro-surface characteristics exhibited planar facets outlined by layer boundaries, signifying crystal development through a mechanism reliant on layer growth. The direct optical bandgap of 1⋅64 eV for CuSe single crystals is unveiled by optical reflectance spectrum, demonstrating its aptitude for incorporation into photodetectors. The Raman spectrum manifested a prominent peak at 259 cm−1, aligning to Ag1 vibrational mode. The exploration of temperature-induced fluctuations in the power factor and figure of merit unveiled a progressive increase with rising temperatures. The optimal ZT parameter for the CuSe single crystals attains 0⋅058 at 523 K. The thermogravimetric patterns of CuSe single crystals exhibited singular step decomposition, exemplified by an average weight reduction of 25⋅49 % across the temperature spectrum from ambient to 813 K. The current−voltage (I–V) features of the fabricated CuSe single crystal photodetector are assessed under biasing voltage set at 20 mV at ambient temperature. Under a bias voltage of 20 mV and a polychromatic light intensity of 50 mW/cm2, the achieved responsivity is 4335⋅57 μA/W and a detectivity of 135 × 106 Jones. The photoresponse and thermoelectric examination of CuSe crystals alludes to their potential utility in innovative applications on the horizon.

In-situ synchrotron X-ray diffraction investigation of martensite decomposition in Laser Powder Bed Fusion (L-PBF) processed Ti–6Al–4V

Laser powder bed fusion (L-PBF) processed Ti–6Al–4V components present two substantial challenges: the presence of tensile residual stress and brittleness of the as-fabricated component due to the formation of the martensite (α′) phase. Industrially, post-heat treatment is performed to improve the quasi-static mechanical properties of the Ti–6Al–4V component through martensite (α′) decomposition and residual stress relaxation. However, detailed insights into the martensite decomposition and stress relaxation mechanisms are still lacking. To address this, in-situ high-energy synchrotron x-ray diffraction (HEXRD) was employed to simultaneously track: (I) martensite (α′) decomposition into a mixture of hexagonal α and body-centered cubic β phases, (II) residual stress relaxation process during heating. Rietveld refinement of 2D diffraction patterns recorded over a temperature range spanning from 25 to 1000°C revealed a three-stage evolution in the α′ unit cell parameters. Unit cell parameter analysis combined with the phase fraction analysis based on the diffraction patterns and the chemical composition profiles predicted by Thermocalc simulation gave detailed insight into the martensite (α′) decomposition process. In Stage 1 (until 375°C), the α′ phase unit cell exhibited linear expansion without indications of any phase transformation or stress relaxation. Upon commencement of stage II at 375°C, an increased expansion rate of the martensite (α′) unit cell was observed, attributed to the enhanced outward diffusion of vanadium (V), succeeded by β phase nucleation at 575°C. Simultaneously, during stage II, residual stress relaxation was observed at both macro and micro scale, culminating in a stress-free state achieved at approximately 750–800°C. Lastly, α-to-β phase transformation was observed in stage 3. The thermal evolution of the hexagonal unit cell dimensions was compared between martensitic and mill-annealed α+β microstructures. This comparison unraveled the link between the initial microstructure and the thermal expansion behavior of the hexagonal α′ and α phase.

A rasterized plane wave expansion method for complex 2-D phononic crystals

This paper introduces a computer image processing-based method called the rasterized plane wave expansion method (RPWEM). This method improves the conventional plane wave expansion method (CPWEM) and reduces its formula derivation cost in the case of 2-D phononic crystals with complex inclusions. In addition, for 2-D phononic crystals with arbitrary multiphase materials, this method can also simplify the calculation process. By employing the proposed RPWEM, successful calculations of band gaps are conducted for planar phononic crystals with the hexagonal unit cell as well as phononic crystals featuring integrated circuit-like structures. The results further validate the expanded applicability of the RPWEM in comparison to the CPWEM. In the end, a potential application similar to DIC (Digital Image Correlation) for predicting band structures of phononic crystals is proposed, and its feasibility is briefly validated.

Effect of strontium fluoride on mechanical and remineralization properties of enamel: An in-vitro study on a modified orthodontic adhesive

ObjectivesEvaluate the ability of strontium fluoride on bond strength and enamel integrity after incorporation within orthodontic adhesive system as a delivery vehicle. MethodsExperimental orthodontic adhesive system Transbond™ XT were modified with 1% Sr2+, 0.5% SrF2, 1% strontium, 0.5% Sr2+, 1% F-, 0.5% F-, and no additions were control. Mixing of formulation was monitored using Fourier transform infrared spectroscopy. Small-molecule drug-discovery suite was used to gain insights into Sr2+, F-, and SrF2 binding. Shear bond testing was performed after 6-months of ageing. Enamel blocks were cut, and STEM pictures were recorded. Specimens were indented to evaluate elastic modulus. Raman microscope was used to collect Raman spectra and inspected using a scanning electron microscope. Crystal structural analysis was performed using X-ray diffraction. Effect of material on cellular proliferation was determined. Confocal was performed to evaluate the effect of formulation on biofilms. ResultsFTIR of modified adhesives depicted peak changes within range due to various functional groups existing within samples. TEM represented structurally optimized hexagonal unit-cell of hydroxyapatite. Mean shear bond strength is recorded highest for Transbond XT with 1% SrF2. Dead bacterial percentage appeared higher in 0.5% SrF2 and 1% F- specimens. Crystal lengths showed an increase in 0.5% and 1% SrF2 specimens. Phase contrast within TEM images showed a union of 0.5% SrF2 crystal with enamel crystal with higher elastic modulus and highly mineralized crystalline hydroxyapatite. Intensity of ν1 PO43- and ν1 CO32- along with carbonate - / ν1PO43- ratio displayed good association with strontium fluoride. The formulation showed acceptable cell biocompatibility (p < 0.353). All specimens displayed characteristic diffraction maxima of different apatite angles within XRD. SignificanceExperimental results suggested good biocompatibility, adequate mechanical strength, and far-ranging crystallization ability. This would provide a new strategy to overcome the two major challenges of fixed orthodontics, biofilm growth, and demineralization of enamel.

Synthesis of ZnO nanopowder using zinc Zamak dross and adsorption of Pb

In this study, zinc oxide nanopowder (ZnONPDs) was successfully recovered from zinc die casting alloys’ (ZAMAK) dross using a facile dissolution and pH-controlled precipitation approach for removal of lead (II) ions from aqueous solutions. XRD patterns showed that ZnONPDs, calcined at 240°C, exhibited a hexagonal unit cell structure with an average crystallite size of 36.46 nm. FE-SEM micrographs revealed that the ZnONPDs are spherical and hexagonal in shape. TEM images showed the morphology and particle size of synthesized ZnONPDs with an average size of 23.81 nm. XRF and EDS analyses confirmed the high purity of the prepared ZnONPDs. The BET surface area of ZnONPDs was 33.85 m²/g. Adsorption experiments exhibited the maximum removal of Pb2+ ions 100% at the optimal conditions (25 ppm Pb2+ ions, 20 min contact time, 30 mg adsorbent per 100 ml of solution). The pH and zeta potential confirmed that a pH range from 5 to 9 was optimal for the adsorption study. The zeta potential within this range indicated a high level of stability for the particles in the suspensions, effectively preventing flocculation and agglomeration. XPS results conclusively demonstrated the successful adsorption of Pb onto the surface of ZnONPDs. The ZnONPDs synthesized in this study were shown to be promising candidates for use in adsorption processes, indicating that they could be highly useful in wastewater treatments removing toxic metal ions.

Optical and structural characterization of zinc oxide thin films upon ion beam assisted smoothing

Wurtzite zinc oxide (ZnO) has a preferential growth direction along the c-axis of the hexagonal unit cell, which, especially in combination with underlying (amorphous) heterostructures, can lead to a high surface roughness for the ZnO layers. This poses a significant challenge to the construction of e.g. photonic waveguides or gratings. Here, we propose an efficient way for smoothing ZnO surfaces after deposition using a collimated beam of Argon ions. Furthermore, the influence of this treatment at different angles of incidence and fluence of the ions on the morphological, structural and linear optical emission properties is investigated using atomic force microscopy, X-ray diffraction, spectroscopic ellipsometry and photoluminescence (PL) experiments. Our results suggest that using an ion beam incident at an angle of 85° reduces the surface roughness by around 70% while keeping the ZnO crystal structure intact. Though such a treatment leads to a reduced intensity and to a broadening of the PL-emission, excitonic transitions are still prominently observable.

Carbon-Related Quantum Emitter in Hexagonal Boron Nitride with Homogeneous Energy and 3-Fold Polarization.

Most hexagonal boron nitride (hBN) single-photon emitters (SPEs) studied to date suffer from variable emission energy and unpredictable polarization, two crucial obstacles to their application in quantum technologies. Here, we report an SPE in hBN with an energy of 2.2444 ± 0.0013 eV created via carbon implantation that exhibits a small inhomogeneity of the emission energy. Polarization-resolved measurements reveal aligned absorption and emission dipole orientations with a 3-fold distribution, which follows the crystal symmetry. Photoluminescence excitation (PLE) spectroscopy results show the predictability of polarization is associated with a reproducible PLE band, in contrast with the non-reproducible bands found in previous hBN SPE species. Photon correlation measurements are consistent with a three-level model with weak coupling to a shelving state. Our ab initio excited-state calculations shed light on the atomic origin of this SPE defect, which consists of a pair of substitutional carbon atoms located at boron and nitrogen sites separated by a hexagonal unit cell.

Modifying the valence phase transition in Eu2Al15Pt6 by the solid solutions Eu2Al15(Pt1−x T x )6 (T = Pd, Ir, Au; x = 1/6)

Abstract The solid solutions Eu2Al15(Pt1−x T x )6 with T = Pd, Ir, Au and x = 1/6 were prepared by arc-melting the stoichiometric mixture of the elements, and subsequent annealing. For x = 1/6, all three solid solutions adopt the same structure type as Eu2Al15Pt6 according to powder X-ray diffraction data. Since the platinide Eu2Al15Pt6 exhibits a (3 + 1)D modulated structure (approximant in space group P121/m1), only the averaged hexagonal unit cell (P63/mmc, Sc0.6Fe2Si4.9 type) was refined by the Rietveld method. Scanning electron microscopy in combination with energy-dispersive X-ray spectroscopy (SEM/EDX) showed that the degree of substitution is in line with the weighed amounts. For values of x &gt; 1/6, no phase-pure samples could be obtained. The results of the magnetic susceptibility measurements indicate that the isoelectronic substitution of Pd for Pt lowers the temperature of the first-order valence phase transition from T trans = 45 K in Eu2Al15Pt6 to T trans = 42 K in Eu2Al15(Pt5/6Pd1/6)6. For Eu2Al15(Pt5/6Ir1/6)6 and Eu2Al15(Pt5/6Au1/6)6 a change in the electronic situation occurs since the Ir substituted compound exhibits one electron less compared to the pristine Pt compound, while Eu2Al15(Pt5/6Au1/6)6 has one additional electron. As a consequence, Eu2Al15(Pt5/6Ir1/6)6 shows a higher valence phase transition temperature of T trans = 52 K while for Eu2Al15(Pt5/6Au1/6)6 no such transition is obvious.

Full-field characterizations of additively manufactured composite cellular structures

Honeycomb structures possess unique mechanical and structural behaviors, including high specific strength, superior energy absorption, and potential for multifunctionality. The advantages of such structures are bolstered by their realization through additive manufacturing, enabling cellular geometries beyond traditionally fabricated hexagons and facilitating a pathway for hybridization using composite materials to tune the response. This research synthesized photocurable, particulate-reinforced resins using mechanically compliant matrix and glass microballoons reinforcement. The modified resins were used to additively manufacture lattice structures with circular and hexagonal unit cell geometries at different glass microballoons reinforcement weight ratios, ranging from neat to 20 wt.%. The 3D printed structures were tested under quasi-static and impact loading scenarios to elucidate the interrelationships between the cell geometry, induced deformations, and strain rates. The mechanical testing was coupled with digital image correlation (DIC) to reveal the deformation-geometry interrelationship on the global (macroscale) and local (mesoscale) levels. The multiscale analyses allowed for extensive characterization of the effect of cell geometry and increased weight reinforcement on the mechanical response at a global, sub-cellular, and cellular level, i.e., elucidating the hierarchical dependency. The novelty leading to the current study stems from probing and revealing the deformation state of cellular structures subjected to two loading scenarios using DIC. This study intended to provide mechanistic insights for engineering lattice structures for impact mitigation applications by offering a viable approach to additive manufacturing composite materials.

Topological edge and corner states in biphenylene photonic crystal.

The biphenylene network (BPN) has a unique two-dimensional atomic structure, where hexagonal unit cells are arranged on a square lattice. Inspired by such a BPN structure, we design a counterpart in the fashion of photonic crystals (PhCs), which we refer to as the BPN PhC. We study the photonic band structure using the finite element method and characterize the topological properties of the BPN PhC through the use of the Wilson loop. Our findings reveal the emergence of topological edge states in the BPN PhC, specifically in the zigzag edge and the chiral edge, as a consequence of the nontrivial Zak phase in the corresponding directions. In addition, we find the localization of electromagnetic waves at the corners formed by the chiral edges, which can be considered as second-order topological states, i.e., topological corner states.

Comprehensive understanding of the crystal structure of perovskite-type Ba3Y4O9 with Zr substitution: a theoretical and experimental study.

We previously reported that Zr substitution improves the chemical stability of Ba3Y4O9 and nominally 20 mol% Zr-substituted Ba3Y4O9 is an oxide-ion conductor at intermediate temperatures (500-700 °C). However, the influence of Zr substitution on the structural properties of Ba3Y4O9 was poorly understood. This paper aims to comprehensively understand the crystal structure of Ba3Y4O9 with Zr substitution by powder X-ray diffraction (XRD), extended X-ray absorption fine structure (EXAFS) measurements, and first-principles calculations. From the results, firstly we found that the hexagonal unit cell of Ba3Y4O9 reported in the database should be revised as doubled along the c-axis in terms of the periodicity of oxide-ion positions. The revised unit cell of Ba3Y4O9 consists of 18 layers of BaO3 and 24 layers of Y which periodically stack along the c-axis. In this work, we focused on the cationic lattice and noticed that the periodical stacking of Ba and Y layers comprises a similar sequence to that in the body-centered cubic (BCC) structure. There are two regions in the Ba3Y4O9 structure: one is a hetero-stacking region of Ba and Y layers (Ba-Y-Ba-Y-Ba) and the other is a homo-stacking region (Ba-Y-Y-Ba). It is noteworthy that the former region is similar to a cubic perovskite. In Zr-substituted Ba3Y4O9, Zr ions preferentially substitute for Y ions in the hetero-stacking region, and therefore the local environment of Zr ions in Ba3Y4O9 is quite similar to that in BaZrO3. Besides, the Zr substitution for Y in Ba3Y4O9 increases the fraction of the cubic-perovskite-like region in the stacking sequences. The structural change in the long-range order strongly affects the other material properties such as chemical stability and the ionic-conduction mechanism. Our adopted description of perovskite-related compounds based on the stacking sequence of the BCC structure should help in understanding the complex structure and developing new perovskite-related materials.

An inverse application of unit cells for extracting fibre properties from effective properties of composites

A semi-analytical solution is obtained in this paper for the micromechanical analysis of the square and hexagonal unit cells using complex potentials. It provides a means of numerical characterisation of unidirectionally fibre-reinforced composites for their effective properties. This process is considered as the forward problem and its inverse counterpart is also established in this paper to extract fibre properties from effective properties of composites. It is formulated into a mathematical optimisation problem in which the difference between predicted and provided effective properties is employed as the objective function with the fibre properties as the optimisation variables. The attempt of such an inverse problem is to address the lack of fibre properties for many types of composites commonly in use. The novelty of the paper lies in both sides of the analyses, forward and inverse, as none is available in the literature in the forms as presented in this paper and, more importantly, in the objective of this paper as an attempt to address the pressing and yet long-standing issue of lack of fibre properties. As a verification of the forward analysis, the predicted effective properties of a composite match perfectly with the finite element method (FEM) results. The same case is also employed to verify the inverse analysis by turning the prediction the other way round. Both the forward and inverse analyses have been validated against a series of experimental data. While the forward analysis is generally applicable to any input data as the properties of the constituents, the inverse analysis is sensitive to the input data. Potentially, the inverse analysis would offer a much-needed and also effective tool for the characterisation of fibres. However, reasonable predictions of fibre properties can only be obtained if input data are reasonably consistent.

Synthesis and optical properties of novel red-emitting phosphors Ba3Lu1–xEuxB9O18 (x = 0–0.85)

The novel red-emitting phosphors Ba3Lu1–xEuxB9O18 (x = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.85) belonging to the Ba3REEB9O18 (REE – Y, Pr–Lu) family were successfully obtained by a multistep solid-phase synthesis. X-ray diffraction experiments revealed no phase transitions caused by the Eu3+ → Lu3+ isomorphic substitution in this series of solid solutions. An increase in the Eu3+ content leads to an expectable increase of hexagonal unit cell parameters and volume. Optical properties of the Ba3Lu1–xEuxB9O18 (x = 0–0.85) phosphors were investigated. The highest emission intensity was demonstrated by Ba3Lu0.6Eu0.4B9O18. The concentration quenching of luminescence was revealed for the x(Eu3+) > 0.4 samples. Concentration quenching, quantum yield and structural data were compared between three red-emitting Ba–Lu borates-phosphors (BLBO:Eu3+) containing independent crystallographic sites for the REE ions (n = 1–3) in crystal structure. It was revealed that the higher the number of nonequivalent cationic REE sites suitable for the Eu3+ → Lu3+ substitution, the higher the quantum yield taking into account practically equal amount of an optimal concentration of the activator-ion. Such an observation could be useful for a crystal chemical design of novel phosphors.