Thermal Conductivity of Pyroclastic Soil (<Emphasis Type="BoldItalic">Pozzolana</Emphasis>) from the Environs of Rome

The paper reveals the experimental procedure and thermo-physical characteristics of a coarse pyroclastic soil (Pozzolana), from the neighborhoods of Rome, Italy. The tested samples are comprised of 70.7 % sand, 25.9 % silt, and 3.4 % clay. Their mineral composition contained 38 % pyroxene, 33 % analcime, 20 % leucite, 6 % illite/muscovite, 3 % magnetite, and no quartz content was noted. The effective thermal conductivity of minerals was assessed to be about \(2.14\,\hbox {W}{\cdot } \hbox {m}^{-1}{\cdot } \hbox {K}^{-1}\). A transient thermal probe method was applied to measure the thermal conductivity (\(\lambda \)) over a full range of the degree of saturation \((S_{\mathrm{r}})\), at two porosities (n) of 0.44 and 0.50, and at room temperature of about \(25\,^{\circ }\hbox {C}\). The \(\lambda \) data obtained were consistent between tests and showed an increasing trend with increasing \(S_{\mathrm{r}}\) and decreasing n. At full saturation (\(S_{\mathrm{r}}=1\)), a nearly quintuple \(\lambda \) increase was observed with respect to full dryness (\(S_{\mathrm{r}}=0\)). In general, the measured data closely followed the natural trend of \(\lambda \) versus \(S_{\mathrm{r}}\) exhibited by published data at room temperature for other unsaturated soils and sands. The measured \(\lambda \) data had an average root-mean-squared error (RMSE) of \(0.007\,\hbox {W}{\cdot } \hbox {m}^{-1}{\cdot } \hbox {K}^{-1}\) and \(0.008\,\hbox {W}{\cdot } \hbox {m}^{-1}{\cdot } \hbox {K}^{-1}\) for n of 0.50 and 0.44, respectively, as well as an average relative standard deviation of the mean at the 95 % confidence level \((\hbox {RSDM}_{0.95})\) of 2.21 % and 2.72  % for n of 0.50 and 0.44, respectively.     

Thermodynamic Properties at Saturation Derived from Experimental Two-Phase Isochoric Heat Capacity of 1-Hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide

New measurements are reported for the isochoric heat capacity of the ionic liquid substance 1-hexyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]imide ([C6mim][NTf2]). These measurements extend the ranges of our earlier study (Polikhronidi et al. in Phys Chem Liq 52:657, 2014) by 5 % of the compressed liquid density and by 75 K. An adiabatic calorimeter was used to measure one-phase \((C_{\mathrm{V1}})\) liquid and two-phase \((C_{\mathrm{V2}})\) liquid + vapor isochoric heat capacities, densities \((\rho _s)\), and phase-transition temperatures \((T_s)\) of the ionic liquid (IL) substance. The combined expanded uncertainty of the density \(\rho \) and isochoric heat capacity \(C_\mathrm{V}\) measurements at the 95 % confidence level with a coverage factor of \(k = 2\) is estimated to be 0.15 % and 3 %, respectively. Measurements are concentrated in the immediate vicinity of the liquid + vapor phase-transition curve, in order to closely observe phase transitions. The present measurements and those of our earlier study are analyzed together and are presented in terms of thermodynamic properties \((T_s\), \(\rho _s\), \(C_{\mathrm{V1}}\) and \(C_{\mathrm{V2}})\) evaluated at saturation and in terms of key-derived thermodynamic properties \(C_\mathrm{P}\), \(C_\mathrm{S}\), \(W_\mathrm{S}^{{\prime }}\), \(K_{\mathrm{TS}}^{{\prime }}\), \(\left( {\partial P/\partial T} \right) _{\mathrm{V}}^{\prime }\), and \(\left( {\partial V/\partial T} \right) _\mathbf{P}^{\prime })\) on the liquid + vapor phase-transition curve. A thermodynamic relation by Yang and Yang is used to confirm the internal consistency of measured two-phase heat capacities \(C_{\mathrm{V2}} \), which are observed to fall perfectly on a line as a function of specific volume at a constant temperature. The observed linear behavior is exploited to evaluate contributions to the quantity \(C_{\mathrm{V2}} = f(V, T)\) from chemical potential \(C_{{\mathrm{V}\upmu }} =-T\frac{\mathrm{d}^{{2}}\mu }{\mathrm{d}T^{2}}\) and from vapor pressure \(C_{\mathrm{VP}} =VT\frac{\mathrm{d}^{2}P_{\mathrm{S}} }{\mathrm{d}T^{2}}\). The physical nature and specific details of the temperature and specific volume dependence of the two-phase isochoric heat capacity and some features of the other derived thermodynamic properties of IL at liquid saturation curve are considered in detail.     

Magnetism in Solid Oxygen Studied by High-Pressure Neutron Diffraction

A systematic modification of the entropy trajectory (\(S_\mathrm{m}(T)\)) is observed at very low temperature in magnetically frustrated systems as a consequence of the constraint (\(S_\mathrm{m}\ge 0\)) imposed by the Nernst postulate. The lack of magnetic order allows to explore and compare new thermodynamic properties by tracing the specific heat (\(C_\mathrm{m}\)) behavior down to the sub-Kelvin range. Some of the most relevant findings are: (i) a common \(C_\mathrm{m}/T|_{T\rightarrow 0} \approx 7\) J/mol K\(^2\) ‘plateau’ in at least five Yb-based very-heavy-fermions (VHF) compounds; (ii) quantitative and qualitative differences between VHF and standard non-Fermi-liquids; (iii) entropy bottlenecks governing the change of \(S_\mathrm{m}(T)\) trajectories in a continuous transition into alternative ground states. A comparative analysis of \(S_\mathrm{m}(T\rightarrow 0)\) dependencies is performed in compounds suitable for adiabatic demagnetization processes according to their \(\partial ^2 S_\mathrm{m}/\partial T^2\) derivatives.     

Electrochemical impedance studies of capacity fading of electrodeposited ZnO conversion anodes in Li-ion battery

Electrodeposited ZnO coatings suffer severe capacity fading when used as conversion anodes in sealed Li cells. Capacity fading is attributed to (i) the large charge transfer resistance, \(R_{\mathrm{ct}}\) (300–700 \(\Omega \)) and (ii) the low \(\hbox {Li}^{+}\) ion diffusion coefficient, \(D_{\mathrm{Li}}^{+}\ (10^{-15}\) to \(10^{-13}\hbox { cm}^{2}\hbox { s}^{-1})\). The measured value of \(R_{\mathrm{ct}}\) is nearly 10 times higher and \(D_{\mathrm{Li}}^{+}\) 10–100 times lower than the corresponding values for \(\hbox {Cu}_{2}\hbox {O}\), which delivers a stable reversible capacity.     

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.     

Further Estimates of $$(T-T_{90})$$ Close to the Triple Point of Water

Recent advances in primary acoustic gas thermometry (AGT) have revealed significant differences between temperature measurements using the International Temperature Scale of 1990, \(T_{90}\), and thermodynamic temperature, T. In 2015, we published estimates of the differences \((T-T_{90})\) from 118 K to 303 K, which showed interesting behavior in the region around the triple point of water, \(T_\mathrm{TPW}=273.16\) K. In that work, the \(T_{90}\) measurements below \(T_\mathrm{TPW}\) used a different ensemble of capsule standard platinum resistance thermometers (SPRTs) than the \(T_{90}\) measurements above \(T_\mathrm{TPW}\). In this work, we extend our earlier measurements using the same ensemble of SPRTs above and below \(T_\mathrm{TPW}\), enabling a deeper analysis of the slope \(\mathrm{d}(T-T_{90})/\mathrm{d}T\) around \(T_\mathrm{TPW}\). In this article, we present the results of seven AGT isotherms in the temperature range 258 K to 323 K. The derived values of \((T-T_{90})\) have exceptionally low uncertainties and are in good agreement with our previous data and other AGT results. We present the values \((T-T_{90})\) alongside our previous estimates, with the resistance ratios W(T) from two SPRTs which have been used across the full range 118 K to 323 K. Additionally, our measurements show discontinuities in \(\mathrm{d}(T-T_{90})/\mathrm{d}T\) at \(T_\mathrm{TPW}\) which are consistent with the slope discontinuity in the SPRT deviation functions. Since this discontinuity is by definition non-unique, and can take a range of values including zero, we suggest that mathematical representations of \((T-T_{90})\), such as those in the mise en pratique for the kelvin (Fellmuth et al. in Philos Trans R Soc A 374:20150037, 2016. doi: 10.1098/rsta.2015.0037), should have continuity of \(\mathrm{d}(T-T_{90})/\mathrm{d}T\) at \(T_\mathrm{TPW}\).     

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.     

Inhomogeneous Superconducting Behaviour in $$\hbox {La}_{5}\hbox {Ni}_{2}\hbox {Si}_{3}$$

The superconducting phase transition at \(T_\mathrm{c} = 2.3\) K was observed for the electrical resistivity \(\rho ({T})\) and magnetic susceptibility \(\chi (T)\) measurements in the ternary compound La\(_{5}\hbox {Ni}_{2}\hbox {Si}_{3}\) that crystallizes in the hexagonal-type structure. Although a single-phase character with the nominal stoichiometry of the synthesized sample was confirmed, a small trace of the La–Ni phase was found, being probably responsible for the superconducting behaviour in the investigated compound. The magnetization loop recorded at \({T} = 0.5\) K resembles a star-like shape which indicates that the density of the critical current can be strongly suppressed by a magnetic field. The low-\(T _{\rho }(T)\) and specific heat \({C}_\mathrm{p}({T})\) data in the normal state reveal simple metallic behaviour. No clear evidence of a phase transition to any long- or short-range order was found for \(C_\mathrm{p}(T)\) measurements in the T-range of 0.4–300 K.     

Temperature and Heat Flow Rate Calibration of a Calvet Calorimeter from $$0\,{^{\circ }}\hbox {C}$$ to $$190 \,{^{\circ }}\hbox {C}$$19

This study describes the temperature and heat flow rate calibrations of a Calvet calorimeter (SETARAM, BT2.15) in the temperature range of 0–190 \({^{\circ }}\hbox {C}\). Temperature calibration is carried out using three reference materials, namely water, gallium, and indium, as specified in the International Temperature Scale of 1990 (ITS-90). The sample temperature of the Calvet calorimeter is corrected by the obtained mean value, \(-0.489 \,{^{\circ }}\hbox {C}\), of the measured extrapolated peak onset temperature (\(T_{e})\) when the heating rate (\(\upbeta )\) is zero (\(\Delta T_\mathrm{corr }(\upbeta ~=~0\))). The heat flow rate is calibrated using a reference material with a known heat capacity, namely SRM 720 \(\alpha \)-\(\hbox {Al}_{2}\hbox {O}_{3}\) (synthetic sapphire), which is traceable to the National Institute of Standards and Technology. From the heat flow rate measurements of the blank baseline and SRM 720, the proportional calibration factor, \(\hbox {K}_{\Phi }\), in the 0–190\( \,{^{\circ }}\hbox {C}\) temperature range was determined. The specific heat capacity of copper was measured with the obtained calibration values, and the measured data show consistency with the reference value.     

Spin-orbit coupling in graphene,silicene and germanene: dependence on the configuration of full hydrogenation and fluorination

We investigate the effect of full hydrogenation and fluorination on the spin-orbit coupling (SOC) in graphene, silicene and germanene. In chair conformation, the fluorination of graphene increases the spin-orbit splitting (\(E_{\mathrm{so}})\), while the hydrogenation and fluorination of other structures reduce the \(E_{\mathrm{so}}\) at the \(\Gamma \)-point. In case of boat conformation, the hydrogenation and fluorination reduce the symmetry of honeycomb structure, which in turn remove the degeneracy of valence band maximum at the \(\Gamma \)-point. The change in band gaps due to SOC is very small in boat conformation structures as compared to that in the corresponding chair conformation structures.     

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.     

Characterization and optical properties of $$\hbox {Pr}_{2}\hbox {O}_{3}$$-doped molybdenum lead-borate glasses

\(\hbox {Pr}^{3+}\) doped molybdenum lead-borate glasses with the chemical composition 75PbO?[25–(x \(+\) y)\(\hbox {B}_{2}\hbox {O}_{3}]\)–\(y\hbox {MoO}_{3}\)–\(x\hbox {Pr}_{2}\hbox {O}_{3}\) (where \(x = 0.5\) and 1.0 mol% and \(y = 0\) and 5 mol%) were prepared by conventional melt-quenching technique. Thermal, optical and structural analyses are carried out using DSC, UV and FTIR spectra. The physical parameters, like glass transition \((T_{\mathrm{g}})\), stability factor \((\Delta T)\), optical energy band gap \((E_{\mathrm{gopt}})\), of these glasses have been determined as a function of dopant concentration. The \({T}_{\mathrm{g}}\) and optical energy gaps of these glasses were found to be in the range of 290–350\({^{\circ }}\hbox {C}\) and 2.45–2.7 eV, respectively. Stability of the glass doped with \(\hbox {Pr}^{3+}\) is found to be moderate (\(\sim \)40). The results are discussed using the structural model of Mo–lead-borate glass.     

New formulations of the ship-motion Green function

The ship-motion Green function representing the potential flow generated by a time-harmonically pulsating source with unit strength advancing beneath a free surface along a straight path at a constant speed is studied in the paper. Starting with the form of a double Fourier integral with respect to wavenumber k and polar angle \(\theta \) on the Fourier plane, one alternative formulation based on the single integral along dispersion curves for the wave component, and the integrals in polar angle after having evaluated integration in wavenumber, is first presented. Another new formulation based on performing the integral with respect to polar angle \(\theta \) prior to the wavenumber k is developed afterward. Analytical formulations of the \(\theta \)-integral defined as \(g_{\ell }\left( k\right) \) are obtained by applying the theorem of residue. The behaviours of poles located in the integration contour are analyzed, and a method to efficiently evaluate the integral of \(g_{\ell }\left( k\right) \) for different values of Brard number \(\tau \) is outlined. Furthermore, numerical calculation is implemented. On comparing with the results obtained by means of the existing formulation, an excellent agreement is achieved with a maximum of difference in the order of \(10^{-6}\) which shows that two formulations are intrinsically consistent. The new formulation based on the polar angle integration is shown to be suitable for the study of the spatial integration of the Green function.     

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.     

Physical,optical and structural studies of copper-doped lead oxychloro borate glasses

Bluish coloured glasses are obtained from the composition PbCl\(_{2}\)–PbO–B\(_{2}\)O\(_{3}\) doped with Cu\(^{2+}\) ions. Basic physical properties and spectroscopic studies (optical absorption, electron paramagnetic resonance, Fourier transform infrared and Raman spectroscopies) were carried out on these samples. The increase in PbCl\(_{2}\) content resulted in the decrease in density and increase in molar volume. At optical frequencies, band gaps and Urbach energies were evaluated and their variation is explained. Spin-Hamiltonian parameters (SHP) obtained from the EPR spectra suggest that the ligand environment around Cu\(^{2+}\) is tetragonally distorted octahedral sites and the orbital \(d_{x^{2}-{y}^{2}} \) is the ground state. The characteristics broad bands in the optical absorption spectra are assigned to the \(^{2}\)B\(_{\mathrm{1g}}\,\rightarrow \, {}^{2}\)B\(_{\mathrm{2g}}\) transition. The bonding coefficient values were evaluated using optical data and SHP. FTIR studies suggested that the glass structure is built up of BO\(_{3}\) and BO\(_{4}\) units. The presence of diborate, pyroborate, pentaborate groups, etc. in the glass network was confirmed from Raman spectra.     

Research on Intelligent Control System of DC SQUID Magnetometer Parameters for Multi-channel System

In a multi-channel SQUID measurement system, adjusting device parameters to optimal condition for all channels is time-consuming. In this paper, an intelligent control system is presented to determine the optimal working point of devices which is automatic and more efficient comparing to the manual one. An optimal working point searching algorithm is introduced as the core component of the control system. In this algorithm, the bias voltage \(V_\mathrm{bias}\) is step scanned to obtain the maximal value of the peak-to-peak current value \(I_\mathrm{pp}\) of the SQUID magnetometer modulation curve. We choose this point as the optimal one. Using the above control system, more than 30 weakly damped SQUID magnetometers with area of \(5 \times 5 \, \hbox {mm}^2\) or \(10 \times 10 \, \hbox {mm}^2\) are adjusted and a 36-channel magnetocardiography system perfectly worked in a magnetically shielded room. The average white flux noise is \(15 \, {\upmu \Phi }_0/\hbox {Hz}^{1/2}\).     

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.     

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.     

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 \(K_{\mathrm{p}} = 27\%\).