Constitutive modeling of polycarbonate over a wide range of strain rates and temperatures

The mechanical behavior of polycarbonate was experimentally investigated over a wide range of strain rates (\(10^{-4}\mbox{ to }5\times 10^{3}~\mbox{s}^{-1}\)) and temperatures (293 to 353 K). Compression tests under these conditions were performed using a SHIMADZU universal testing machine and a split Hopkinson pressure bar. Falling weight impact testing was carried out on an Instron Dynatup 9200 drop tower system. The rate- and temperature-dependent deformation behavior of polycarbonate was discussed in detail. Dynamic mechanical analysis (DMA) tests were utilized to observe the glass (\(\alpha \)) transition and the secondary (\(\beta \)) transition of polycarbonate. The DMA results indicate that the \(\alpha \) and \(\beta \) transitions have a dramatic influence on the mechanical behavior of polycarbonate. The decompose/shift/reconstruct (DSR) method was utilized to decompose the storage modulus into the \(\alpha \) and \(\beta \) components and extrapolate the entire modulus, the \(\alpha\)-component modulus and the \(\beta\)-component modulus. Based on three previous models, namely, Mulliken–Boyce, G’Sell–Jonas and DSGZ, an adiabatic model is proposed to predict the mechanical behavior of polycarbonate. The model considers the contributions of both the \(\alpha \) and \(\beta \) transitions to the mechanical behavior, and it has been implemented in ABAQUS/Explicit through a user material subroutine VUMAT. The model predictions are proven to essentially coincide with the experimental results during compression testing and falling weight impact testing.     

Study of $$\upbeta $$-phase development in spin-coated PVDF thick films

A study was conducted to ascertain the effect of variation in spin speed and baking temperature on \(\upbeta \)-phase content in the spin-coated poly(vinylidene fluoride) (PVDF) thick films (\({\sim }4{-}25\,\upmu \hbox {m}\)). Development of \(\upbeta \)-phase is dependent on film stretching and crystallization temperature. Therefore, to study the development of \(\upbeta \)-phase in films, stretching is achieved by spinning and crystallization temperature is adjusted by means of baking. PVDF films are characterized using Fourier transform infrared spectroscopy, X-ray diffraction, differential scanning calorimetry, and scanning electron microscopy. It is observed that crystallization temperature lower than \(60^{\circ }\hbox {C}\) and increase in spin speed increases the \(\upbeta \)-phase content in PVDF films. Crystallization temperature above \(60^{\circ }\hbox {C}\) reduces \(\upbeta \)-phase content and increases \(\upalpha \)-phase content. It was also observed that viscosity of the PVDF solution affects the \(\upbeta \)-phase development in films at a particular spin speed.     

Study of optical properties of potassium permanganate ($$\hbox {KMnO}_{4}$$) doped poly(methylmethacrylate) (PMMA) composite films

We have developed films of pure polymethylmethacrylate (PMMA) (0.5, 1, 2 and 5%) and potassium permanganate \((\hbox {KMnO}_{4})\)-doped PMMA composite films of thickness (\(\sim 100\, \upmu \hbox {m}\)) using the solution-cast technique. To identify the possible change that happen to the PMMA films due to doping, the optical properties were investigated for different concentrations of \(\hbox {KMnO}_{4}\) by recording the absorbance (A) and transmittance (\(T\%\)) spectra of these films using UV–Vis spectrophotometer in the wavelength range of 300–1100 nm. From the data obtained from the optical parameters viz. absorption coefficient (\(\alpha \)), extinction coefficient (\(\kappa \)), finesse coefficient (F), refractive index (\(\eta \)), real and imaginary parts of dielectric constant (\(\varepsilon _{\mathrm{r}}\) and \(\varepsilon _{\mathrm{i}})\) and optical conductivity (\(\sigma \)) were calculated for the prepared films. The indirect optical band gap for the pure and the doped-PMMA films were also estimated.     

Nonlinear Ultrasound Propagation in Solid $$^4\hbox {He}$$ Compared with Shear Modulus Experiments

Ultrasound attenuation (\(\alpha \)) and velocity (V) at 9.6 MHz are measured in polycrystalline hcp \(^4\hbox {He}\). The ultrasound signal above 200 mK is linear and understood in terms of resonant vibration of dislocation segments pinned between network nodes with an average pinning length of 3.7 \(\mu \hbox {m}\), much shorter than 59 \(\mu \hbox {m}\) estimated from a shear modulus measurement. Dramatic changes in \(\alpha \) and V are observed below 200 mK. The changes are strongly dependent on temperature and are nonlinear and hysteretic. These effects result from pinning of dislocations by \(^3\hbox {He}\) impurities (nominal concentration of 0.3 ppm). The dislocation damping constant due to thermal phonons, the binding energy between dislocation and \(^3\hbox {He}\), and the average network pinning length obtained from the ultrasound data are compared with those from the shear modulus experiments.     

Structural,dielectric and piezoelectric study of Ca-, Zr-modified $$\hbox {BaTiO}_{3}$$ lead-free ceramics

We prepared a lead-free ceramic (\(\hbox {Ba}_{0.85}\hbox {Ca}_{0.15})(\hbox {Ti}_{1-x}\hbox {Zr}_{x})\hbox {O}_{3}\) (BCTZ) using the conventional mixed oxide technique. The samples were prepared by an ordinary mixing and sintering technique. In this study we investigated how small amounts of \(\hbox {Zr}^{4+}\) can affect the crystal structure and microstructure as well as dielectric and piezoelectric properties of \(\hbox {BaTiO}_{3}\). X-ray diffraction analysis results indicate that no secondary phase is formed in any of the BCTZ powders for \(0 \le x \le 0.1\), suggesting that \(\hbox {Zr}^{4+}\) diffuses into \(\hbox {BaTiO}_{3}\) lattices to form a solid solution. Scanning electron microscopy micrographs revealed that the average grain size gradually increased with \(\hbox {Zr}^{4+}\) content from 9.5 \(\upmu \!\hbox {m}\) for \(x = 0.02\) to 13.5 \(\upmu \!\hbox {m}\) for \(x = 0.1\); Curie temperature decreased due to the small tetragonality caused by \(\hbox {Zr}^{4+}\) addition. Owing to the polymorphic phase transition from orthorhombic to tetragonal phase around room temperature, it was found that the composition \(x = 0.09\) showed improved electrical properties and reached preferred values of \(d_{33} = 148\) pC \(\hbox {N}^{-1}\) and \(K_{\mathrm{p}} = 27\%\).     

Bootstrap in semi-functional partial linear regression under dependence

This paper deals with the semi-functional partial linear regression model \(Y={{\varvec{X}}}^\mathrm{T}{\varvec{\beta }}+m({\varvec{\chi }})+\varepsilon \) under \(\alpha \)-mixing conditions. \({\varvec{\beta }} \in \mathbb {R}^{p}\) and \(m(\cdot )\) denote an unknown vector and an unknown smooth real-valued operator, respectively. The covariates \({{\varvec{X}}}\) and \({\varvec{\chi }}\) are valued in \(\mathbb {R}^{p}\) and some infinite-dimensional space, respectively, and the random error \(\varepsilon \) verifies \(\mathbb {E}(\varepsilon |{{\varvec{X}}},{\varvec{\chi }})=0\). Naïve and wild bootstrap procedures are proposed to approximate the distribution of kernel-based estimators of \({\varvec{\beta }}\) and \(m(\chi )\), and their asymptotic validities are obtained. A simulation study shows the behavior (on finite sample sizes) of the proposed bootstrap methodology when applied to construct confidence intervals, while an application to real data concerning electricity market illustrates its usefulness in practice.     

Thermo-transport properties of Zn-substituted layered Li-nickel oxide, $$\hbox {LiNiO}_{2}$$

The layered Li-TM-\(\hbox {O}_{2}\) materials have been investigated extensively due to their application as cathodes in Li batteries. The electrical properties of these oxides can be tuned or controlled either by non-stoichiometry or substitution. Hence the thermo-transport properties of Zn-substituted \(\hbox {LiNi}_{1-x}\hbox {Zn}_{x}\hbox {O}_{2}\) for \(0 \le x \le 0.16\) have been investigated in the temperature range of 300–900 K for potential application as a high-temperature thermoelectric material. For \(x < 0.08\), the compounds were of single phase belonging to the space group R-3mH while for \(x > 0.08\) an additional minority phase, ZnO forms together with the main layered phase. All the compounds exhibit a semiconducting behaviour with electrical resistivity, varying in the range of  \(\sim 10^{-4}\) to \(10^{-2}\,\,\Omega \hbox {m}\) between 300 and 900 K. The electrical resistivity is found to increase with increasing Zn-substitution predominantly due to a decrease in the charge carrier hole mobility. The activation energy remains constant, \(\sim \)10  meV, with Zn-substitution. The Seebeck coefficient of the compounds is found to decrease with increasing temperature and increase with increasing Zn-substitution. The Seebeck coefficient decreases from \(\sim \)95 to \(35\ \upmu \hbox {V K}^{-1}\) and the corresponding power factor is \(\sim \)12\(\ \upmu \hbox {W m}^{-1}\ {\hbox {K}}^{-2}\) for the \(x = 0.16\) compound.     

Shear-thinning and constant viscosity predictions for rotating sphere flows

The steady motion of a rotating sphere is analysed through two contrasting viscoelastic models, a constant viscosity (FENE-CR) model and a shear-thinning (LPTT) model. Giesekus (Rheol. Acta 9:30–38, 1970) presented an intriguing rotating viscoelastic flow, which to date has not been completely explained. In order to investigate this flow, sets of parameters have been explored to analyse the significant differences introduced with the proposed models, while the momentum-continuity-stress equations are solved through a hybrid finite-element/finite volume numerical scheme. Solutions are discussed for first, sphere angular velocity increase (\(\varOmega\)), and second, through material velocity-scale increase (\(\alpha\)). Numerical predictions for different solvent-ratios (\(\beta\)) show significant differences as the sphere angular velocity increases. It is demonstrated that an emerging equatorial anticlockwise vortex emerges in a specific range of \(\varOmega\). As such, this solution matches closely with the Giesekus experimental findings. Additionally, inside the emerging inertial vortex, a contrasting positive second normal stress-difference (\(N_{2} ( \dot{\gamma} ) = \tau_{rr} - \tau_{\theta\theta}\)) region is found compared against the negative \(N_{2}\)-enveloping layer.     

Measurement of the Nonlinearity of Heat-Flux Sensors Employing a $$\hbox {CO}_2$$ laser

Heat-flux sensors are widely used in industry to test building products and designs for resistance to bushfire, to test the flammability of textiles and in numerous applications such as concentrated solar collectors. In Australia, such detectors are currently calibrated by the National Measurement Institute Australia (NMIA) at low flux levels of 20 W \(\cdot \) m\(^{-2}\). Estimates of the uncertainty arising from nonlinearity at industrial levels (e.g. 50 kW \(\cdot \) m\(^{-2}\) for bushfire testing) rely on literature information. NMIA has developed a facility to characterize the linearity response of these heat-flux sensors up to 110 kW \(\cdot \) m\(^{-2}\) using a low-power \(\hbox {CO}_2\) laser and a chopped quartz tungsten–halogen lamp. The facility was validated by comparison with the conventional flux-addition method, and used to characterize several Schmidt–Boelter-type sensors. A significant nonlinear response was found, ranging from (\(3.2 \pm 0.9\))% at 40 kW \(\cdot \) m\(^{-2}\) to more than 8 % at 100 kW \(\cdot \) m\(^{-2}\). Additional measurements confirm that this is not attributable to convection effects, but due to the temperature dependence of the sensor’s responsivity.     

Probing the boundary effect in granular piles

We present in this paper a DEM study of the effect of boundary configuration on the formation of granular piles. We examine the macro and micro responses of granular piles formed in a two-wall boundary system consisting of a horizontal base and an inclined wall. The results show that the left inclined boundary wall does not exert a considerable impact on the angle of repose \(\alpha _{R}\) estimated by the right free surface of granular pile, but it has an obvious effect on the angle of repose \(\alpha _{L}\) obtained by the left free surface. We observe the shifting of pile apex to the left inclined wall, with the shift distance depending on the orientation angle \(\beta \) of inclined wall. The principal stress field of granular pile is characterized by two sub regions, in which the major principal stresses are oriented respectively in acute and obtuse angles relative to the horizontal axis. We propose an index \(\lambda \) relating to the distribution of the two sub regions of principal stress field, and identify a relationship between \(\lambda \) (\(=\,\sin \beta \)) and \(\beta \) to account for the effect of boundary configuration on the internal mechanical responses of granular pile. We also analyze the boundary responses at varying \(\beta \) values, and observe three modes for the friction mobilization along the inclined boundary wall, on the basis of which we preliminarily illuminate the effect of boundary configuration on the macro responses of granular piles.     

Indirect measurement of $$\mu (I)$$ relation from finite granular avalanche down an inclined narrow reservoir of smooth bed

This work examines the algebraic \(\mu -I\) relation proposed for steady uniform dry granular flows via unsteady granular avalanche experiments of finite nearly identical dry glass spheres down an inclined narrow reservoir of smooth bed. Lateral high-speed digital imaging permits particle tracking velocimetry with which we can evaluate bulk local instantaneous volume fraction and velocity components to conduct a quasi-two-dimensional control volume analysis of streamwise momentum assuming an internal shear stress based on the \(\mu -I\) rheology, a hydrostatic normal stress and a Coulomb yielding condition at lateral walls. Hence, the desired \(\mu \) is a function of flow dynamics and a wall friction coefficient \(\mu _w\). Complementary sliding table experiments were conducted to estimate an upper bound of \(\mu _w=0.17\) which was used with a chosen nonzero lower bound \(\mu _w=0.05\) to extract possible range of \(\mu \) at a local instantaneous inertial number I. The so-obtained local instantaneous \(\mu -I\) data conform to the non-linear monotonically increasing trend proposed for steady inertial flows above a crossover value \(I_c\approx 0.03\). Below \(I_c\), a peculiar segment of decaying \(\mu \) with I was revealed agreeing to the rheology tests in quasi-static regime.     

Evidence for Argon Content in Pure Oxygen from Thermal Data

Since many years it is known that argon impurities in oxygen change the temperature of the oxygen triple point by \(+12 \hbox { K}{\cdot }\mathrm{mol}^{-1}\) (positive, while most impurities decrease the temperature) without any effect on the melting range of this transition, for the impurity concentrations usually encountered in nominally pure gases. It has been hypothesized that thermal measurements on the \(\alpha -\beta \) solid-to-solid transition at 23.8 K or the \(\beta -\gamma \) solid-to-solid transition at 43.8 K may give reliable evidence regarding the argon content. However, such measurements require very long times for full completion of each transition (with prohibitive costs if liquid helium is used) and for the \(\alpha -\beta \) solid-to-solid transition the heat pulse method cannot be applied reliably. The availability of closed-cycle refrigerators permits the first obstacle to be surmounted. The automatic system earlier developed at INRIM during the EU Multicells project and used extensively for the project on the isotopic effect in neon is perfectly suited for such measurements. Thus, the uncertainties of the temperature measurements are similar to those obtained previously (of the order of 0.1 mK or less). Three argon-in-oxygen mixtures were prepared gravimetrically and certified at KRISS, just as was previously done for the work on the neon isotopic compositions. Results of continuous-current measurements on the \(\alpha -\beta \) solid-to-solid transition, along with the triple-point data obtained with the heat pulse method, are presented for one cell with a known doped argon content, to be compared with similar data from a cell with oxygen of very high purity. In addition, some preliminary data for the \(\beta -\gamma \) solid-to-solid transition are given. The measurements on the mixture with the highest argon content, about \(1002\, \upmu \hbox {mol}{\cdot } \mathrm{mol}^{-1}\), imply a (linear) sensitivity of \((116 \pm 7) \hbox {K}{\cdot }\mathrm{mol}^{-1}\) for the \(\alpha -\beta \) transition. This sensitivity may be different at much lower argon contents, and follow-up measurements with the other (smaller) mixtures will shed light on the linearity of this dependence.     

Investigation on the bulk growth of $${\upalpha }$$-$$\hbox {LiIO}_{3}$$LiIO3 single crystals and the influence of pH on its structural,morphological and optical characteristics

\(\upalpha \)-\(\hbox {LiIO}_{3}\) is an excellent optical material exhibiting strong nonlinear optical, piezoelectric and elasto-optic properties. However, its practical applications are limited by the insufficient reproducibility of the mentioned properties caused by the strong influence of the growth conditions, and, in particular, pH of the solution from which \(\upalpha \)-\(\hbox {LiIO}_{3}\) crystal is grown. Herein, we investigate to grow bulk size good quality crystals of \(\upalpha \)-\(\hbox {LiIO}_{3}\) based on the observed problems during its crystallization process. A systematic investigation was carried out to find the effect of pH on solubility, crystal growth, structural, surface and laser damage properties of \(\upalpha \)-\(\hbox {LiIO}_{3}\) single crystals. The structure and phase of \(\hbox {LiIO}_{3}\) were confirmed by powder X-ray diffractometer analysis. The functional groups of the compound were identified using Fourier transform infrared spectroscopy. Surface defects of the grown crystals were studied by etch patterns. The crystal grown at pH 10 showed 10% optical transmission enhancement in comparison to the crystals grown at pH 2. The indirect optical bandgap of the crystal was reinvestigated using ultraviolet–Visible–near-infrared transmittance spectrum. The laser damage threshold studies of the crystals grown at pH 10 reveal the higher optical radiation stability against 532 nm laser. The second-order nonlinear optical behaviour of \(\upalpha \)-\(\hbox {LiIO}_{3}\) crystals grown at different pH conditions have been investigated by using Kurtz and Perry powder technique with Nd:YAG laser pulses at the wavelength of 1064 nm.     

A Novel Vibrating Finger Viscometer for High-Temperature Measurements in Liquid Metals and Alloys

A novel vibrating finger viscometer for high-temperature measurement in liquid metals and alloys up to 1823 K was constructed. The dynamic viscosity (\(\eta \)) of the liquid fluid is measured as a product of \((\rho \cdot \eta )^{0.5}\) and the relative change of the field coil input for a constant amplitude recording at the resonant frequency of the oscillator. The viscometer was calibrated at 298 K using reference silicon oils with varying kinematic viscosities (\(\nu \)), \((0.79\hbox { to } 200)\times 10^{-6}\hbox { m}^{2}\cdot \hbox {s}^{-1}\). In the present study, the viscosity of liquid gold (\(99.99\,\%\) Au), silver (\(99.9\, \%\) Ag), and tin (\(99.9\,\%\) Sn) was measured. The viscosities expressed as an Arrhenius function of temperature are:

$$\begin{aligned} \hbox {for Au:}\quad \quad \hbox {ln }\eta= & {} -0.1990+\frac{2669}{T}\\ \hbox {for Ag:} \quad \quad \hbox {ln }\eta= & {} -0.4631+\frac{2089}{T}\\ \hbox {for Sn:} \quad \quad \hbox {ln }\eta= & {} -0.5472+\frac{671}{T} \end{aligned}$$

The viscosity values are consistent within the range of available literature data.

     

Mesoscale evolution of non-graphitizing pyrolytic carbon in aligned carbon nanotube carbon matrix nanocomposites

Polymer-derived pyrolytic carbons (PyCs) are highly desirable building blocks for high-strength low-density ceramic meta-materials, and reinforcement with nanofibers is of interest to address brittleness and tailor multi-functional properties. The properties of carbon nanotubes (CNTs) make them leading candidates for nanocomposite reinforcement, but how CNT confinement influences the structural evolution of the PyC matrix is unknown. Here, the influence of aligned CNT proximity interactions on nano- and mesoscale structural evolution of phenol-formaldehyde-derived PyCs is established as a function of pyrolysis temperature (\(T_{\mathrm {p}}\)) using X-ray diffraction, Raman spectroscopy, and Fourier transform infrared spectroscopy. Aligned CNT PyC matrix nanocomposites are found to evolve faster at the mesoscale by plateauing in crystallite size at \(T_{\mathrm {p}}\) \(\sim\)800 \(^{\circ }\hbox {C}\), which is more than \(200\,\,^{\circ }\hbox {C}\) below that of unconfined PyCs. Since the aligned CNTs used here exhibit \(\sim\)80 nm average separations and \(\sim\)8 nm diameters, confinement effects are surprisingly not found to influence PyC structure on the atomic-scale at \(T_{\mathrm {p}}\) \(\le \)1400 \(^{\circ }\hbox {C}\). Since CNT confinement could lead to anisotropic crystallite growth in PyCs synthesized below \(\sim\)1000 \(^{\circ }\hbox {C}\), and recent modeling indicates that more slender crystallites increase PyC hardness, these results inform fabrication of PyC-based meta-materials with unrivaled specific mechanical properties.     

Study of Lanthanide Complexes with BTFA in Silica Gels by Photoacoustic Spectroscopy

In this work, lanthanide \(\beta \)-diketonate complexes Ln(btfa)\({}_{3} \cdot 2\hbox {H}_{2}\)O (Ln\(^{3+}\): Eu\(^{3+}\), Sm\(^{3+ }\), and Tb\(^{3+}\); btfa: 4,4,4-trifluoro-l-phenyl-1,3-butanedione) were incorporated into silica gels by a sol–gel method. Photoacoustic (PA) spectra of these complex-doped silica samples were measured and studied. The PA intensity of the \(\beta \)-diketonate ligand is nearly the same for lanthanide complexes in wet gels. After heat treatment at 150 \(^{\circ }\)C, however, the PA intensity of the ligand increases for Eu\(^{3+}\), Sm\(^{3+}\), and Tb\(^{3+}\) complexes in silica gels, respectively. Different PA intensities of the samples are interpreted by comparison with their luminescence spectra. The luminescence result is consistent with the PA spectra. The result indicates that lanthanide \(\beta \)-diketonate complexes cannot be formed in silica gels without a suitable heat treatment. Moreover, the relaxation process model is proposed based on the PA and luminescence results.     

Microwave-hydrothermal synthesis of mesoporous $$\upgamma $$-$$\hbox {Al}_{2}\hbox {O}_{3}$$Al2O3 and its impregnation with AgNPs for excellent catalytic oxidation of CO

Mesoporous \(\upgamma \)-alumina was synthesized by the microwave-hydrothermal process with a shorter duration time at 150\({^{\circ }}\)C/2 h followed by calcination at 550\({^{\circ }}\)C/1 h. Ag nanoparticles (AgNPs) were impregnated into \(\upgamma \)-alumina under a reducing atmosphere at 450\({^{\circ }}\)C. The synthesized product was characterized by X-ray diffraction (XRD), thermogravimetric (TG)/differential thermal analysis (DTA), X-ray photoelectron spectroscopy (XPS), \(\hbox {N}_{2}\) adsorption–desorption study, field-emission scanning electron microscopy (FESEM) and transmission electron microscopy (TEM). The BET surface area values of \(\upgamma \)-alumina and Ag-impregnated \(\upgamma \)-alumina were found to be 258 and 230 m\(^{2}\) g\(^{-1}\), respectively. FESEM images showed the formation of grain-like particles of 50–70 nm in size with a flake-like microstructure. The XRD, XPS and TEM studies confirmed the presence of Ag in the synthesized product. Catalytic properties of the product for CO oxidation was studied with the \(T_{50}\) (50% conversion) and \(T_{100}\) (100% conversion) values of 118 and 135\({^{\circ }}\)C, respectively; the enhanced values were compared with the literature reported values.     

One weight $$\mathbb {Z}_2\mathbb {Z}_4$$ additive codes

We study one weight \(\mathbb {Z}_2\mathbb {Z}_4\) additive codes. It is shown that the image of an equidistant \(\mathbb {Z}_2\mathbb {Z}_4\) code is a binary equidistant code and that the image of a one weight \(\mathbb {Z}_2\mathbb {Z}_4\) additive code, with nontrivial binary part, is a linear binary one weight code. The structure and possible weights for all one weight \(\mathbb {Z}_2\mathbb {Z}_4\) additive codes are described. Additionally, a lower bound for the minimum distance of dual codes of one weight additive codes is obtained.     

Elastic and thermodynamic properties of zirconium- and hafnium-doped $$\hbox {Rh}_{3}\hbox {V}$$ intermetallic compounds: potential aerospace material

Structural, electronic, mechanical and thermodynamic properties of \(\hbox {Rh}_{3}\hbox {Zr}_{x}\hbox {V}_{1-x}\) and \(\hbox {Rh}_{3}\hbox {Hf}_{x}\hbox {V}_{1-x}\) (\(x = 0\), 0.125, 0.25, 0.75, 0.875 and 1) combinations are investigated by means of first-principles calculations based on the density functional theory within the generalized gradient approximation. Here, \(\hbox {Rh}_{3}\hbox {V}\) is chosen as the parent binary compound and the doping elements are zirconium and hafnium with the above-mentioned concentrations. The calculated lattice parameters and elastic modulus of binary \(\hbox {Rh}_{3}\hbox {Hf}\), \(\hbox {Rh}_{3}\hbox {V}\) and \(\hbox {Rh}_{3}\hbox {Zr}\) are in good agreement with the available experimental and other theoretical results. In this study, the following ternary materials viz., \(\hbox {Rh}_{3}\hbox {Zr}_{0.75}\hbox {V}_{0.25}\), \(\hbox {Rh}_{3}\hbox {Hf}_{0.25}\hbox {V}_{0.75}\) and \(\hbox {Rh}_{3}\hbox {Hf}_{0.75}\hbox {V}_{0.25}\) are found to be brittle/more brittle than the parent binary compound \(\hbox {Rh}_{3}\hbox {V}\), whereas the other ternary combinations, namely \(\hbox {Rh}_{3}\hbox {Zr}_{0.125}\hbox {V}_{0.875}\), \(\hbox {Rh}_{3}\hbox {Zr}_{0.25}\hbox {V}_{0.75}\), \(\hbox {Rh}_{3}\hbox {Zr}_{0.875}\hbox {V}_{0.125}\), \(\hbox {Rh}_{3}\hbox {Hf}_{0.125}\hbox {V}_{0.875}\) and \(\hbox {Rh}_{3}\hbox {Hf}_{0.875}\hbox {V}_{0.125}\) are found to be more ductile than \(\hbox {Rh}_{3}\hbox {V}\). The more brittle ternary combination, namely \(\hbox {Rh}_{3}\hbox {Hf}_{0.75}\hbox {V}_{0.25}\) (\(B = 229.32\,\hbox {GPa}\)) has the maximum Young’s modulus, shear modulus and hardness values; whereas the more ductile ternary \(\hbox {Rh}_{3}\hbox {Zr}_{0.25}\hbox {V}_{0.75}\) combination (\(B = 243.54\,\hbox {GPa}\)) is found to have the least values of Young’s modulus, shear modulus and hardness. The band structure, density of states histograms and charge density plots are drawn and discussed. Computed Debye temperature (\(\theta _{\mathrm{D}}\)), Grüneisen parameter (\(\zeta \)) and melting temperature (\(T_{\mathrm{m}})\) of the parent binary compound \(\hbox {Rh}_{3}\hbox {V}\), the more brittle \(\hbox {Rh}_{3}\hbox {Hf}_{0.75}\hbox {V}_{0.25}\) combination and the more ductile \(\hbox {Rh}_{3}\hbox {Zr}_{0.25}\hbox {V}_{0.75}\) combination are given by (895 K, 1.3491, 2788 K), (790 K, 1.2701, 2736 K) and (698 K, 1.7972, 2529 K), respectively.     

Crystal structure,thermal behaviour,vibrational spectroscopy and optical properties of new compounds K$$_{}$$Ca(HAsO$$_{4}$$4)$$_{}\cdot $$·H$$_{}$$O with kröhnkite-type chain

The new kröhnkite compound called potassium calcium-bis-hydrogen arsenate dihydrate K\(_{2}\)Ca(HAsO\(_{4})_{2}\cdot \)2H\(_{2}\)O was obtained by hydrothermal method and characterized by X-ray diffraction, infrared spectroscopy, Raman scattering, thermogravimetric analysis (TGA) and differential scanning calorimetry (DSC) analysis and optical (photoluminescence and absorption) properties. It crystallizes in the triclinic space group P\(\bar{1}\) and unit cell parameters \(a = 5.971(3)\) Å, \(b =6.634(3)\) Å, \(c = 7.856(4)\) Å, \(\alpha =104.532(9)\) \(^{\circ }\), \(\beta = 105.464(9)\) \(^{\circ }\) and \(\gamma = 109.698(9)\) \(^{\circ }\). The structure of K\(_{2}\)Ca(HAsO\(_{4})_{2}\cdot \)2H\(_{2}\)O built up from this infinite, (Ca(HAsO\(_{4})_{2}\)(H\(_{2}\)O)\(_{2})^{2+}\), was oriented along an axis resulting from the association of CaO\(_{6}\) octahedra alternating with each two HAsO\(_{4}\) tetrahedra by sharing corners. Each potassium atom links two adjacent chains by three oxygen atoms of HAsO\(_{4}\) tetrahedra. TGA and DSC have shown the absence of phase transition. The existence of vibrational modes corresponding to the kröhnkite is identified by the IR and Raman spectroscopies in the frequency ranges of 400–4000 and 20–4000 cm\(^{-1}\), respectively. The photoluminescence measurement show one peak at 507 nm, which is attributed to band–band (free electron–hole transitions) and (bound electron–hole transitions) emissions within the AsO\(_{4}\) inorganic part.