Clausius-Mosotti Equation Research Articles

Relationship between bond characteristics and microwave dielectric properties of REVO4 (RE = Yb, Ho) ceramics

Two novel low- ε r REVO 4 (RE = Yb, Ho) microwave dielectric ceramics with the symmetry of the zircon structure, space group I 4 1 / amd , were prepared using the solid-state method. Dense REVO 4 (RE = Yb, Ho) ceramics sintered at 1200 °C and 1160 °C performed ε r ∼ 12.3 ± 0.1 and 13.3 ± 0.1, Q × f ∼ 28,200 ± 300 GHz and 24,100 ± 300 GHz, τ f ∼ −18.8 ± 0.5 ppm/°C and −17.4 ± 0.5 ppm/°C, along with thermal expansion coefficient ( α L ) of 9.0 ppm/°C and 8.1 ppm/°C, respectively. Bond valence results indicated that the slightly rattling RE 3+ cations at the A-site and compressed V 5+ at the B-site occurred in both ceramics. The positive deviations ( Δε r ) of porosity corrected ε r (Corr) from those calculated by the Clausius-Mosotti equation ε r (C-M) , 8.1% for YbVO 4 and 17.7% for HoVO 4 , were observed, implying that the rattling effect of RE 3+ in dodecahedral A-site were greater than those of compressed V 5+ in tetrahedral B-site. Rattling effect also led REVO 4 (RE = Yb, Ho) to develop higher ε r , and smaller τ ε and τ αm , then closer to zero τ f values than other zircon-structured REVO 4 (RE = Ce, Nd, Sm, Eu) ceramics with large negative τ f . The differences in sintering temperature and microwave dielectric performance of both ceramics were discussed using the packing fraction, full width at half maximum (FWHM) of Raman modes and Phillips-Van Vechten-Levine (P–V-L) theory.

Combined effect of rattling and compression on the microwave dielectric properties of B-site 1:3 ordered Li6A7Ti11O32 (A = Zn, Mg) spinels

Dense ceramics of two B-site 1:3 ordering spinels Li6A7Ti11O32 (A = Zn, Mg) with space group P4332 were prepared by solid-state reaction. Raman spectroscopy and XRD analysis revealed why the lattice parameters and volume of Li6Mg7Ti11O32 are abnormally greater than those of Li6Zn7Ti11O32. Li6Zn7Ti11O32 exhibits outstanding microwave dielectric properties (Q × f = 129,600 GHz (8.9 GHz), εr = 20.7, τf = −45 ppm/°C) and a low thermal expansion coefficient (αL) of 5.5 ppm/°C. While Mg-analogue displayed a lower Q × f ∼108,600 GHz (9.1 GHz), a lower αL ∼ 4.9 ppm/°C, a higher εr ∼ 21.9, and a slightly positive offset τf ∼ −21 ppm/°C relative to Li6Zn7Ti11O32. A significant positive deviation of 91.6% was observed between the corrected εr(corr) by the porosity and the calculated εr(C-M) by the Clausius-Mosotti (C-M) equation in the Li1.33xA2-2xTi1+0.67xO4 solid solution. The variation in εr and τf values of Li6A7Ti11O32 (x = 0.5625) compared to Li2ATi3O8 (x = 0.75) might be attributed to the combined effect of rattling and compression cations at A-site and B-site. Moreover, the negative τf of Li6A7Ti11O32 (A = Zn, Mg) ceramics was balanced to near zero by adding CaTiO3.

Growth and characterization of semi-organic non-linear optical L-threonine doped ZTS crystal

Single crystals of L-threonine doped zinc tris thiourea sulphate, a semi-organic nonlinear optical material was successfully grown by the slow evaporation technique. The crystalline nature and structural parameters of L-threonine doped ZTS crystal have been confirmed by single-crystal XRD analysis. The substantial enhancement in mechanical strength of ZTS crystal due to the incorporation of L-threonine has been carried out with Vicker’s microhardness analysis. The second harmonic generation (SHG) efficiency of the crystal has been confirmed by standard Kurtz-Perry powder analysis. Further, the electrical properties, such as plasma energy, Penn energy, Fermi energy, and electronic polarizability of the grown crystals have been theoretically calculated and compared with the classical Clausius–Mosotti equation.

Induced permittivity increment of electrorheological fluids in an applied electric field in association with chain formation: A Brownian dynamics simulation study.

We report Brownian dynamics simulation results for the relative permittivity of electrorheological (ER) fluids in an applied electric field. The relative permittivity of an ER fluid can be calculated from the Clausius-Mosotti (CM) equation in the small applied field limit. When a strong field is applied, however, the ER spheres are organized into chains and assemblies of chains in which case the ER spheres are polarized not only by the external field but by each other. This manifests itself in an enhanced dielectric response, e.g., in an increase in the relative permittivity. The correction to the relative permittivity and the time dependence of this correction is simulated on the basis of a model in which the ER particles are represented as polarizable spheres. In this model, the spheres are also polarized by each other in addition to the applied field. Our results are qualitatively similar to those obtained by Horváth and Szalai experimentally [Phys. Rev. E 86, 061403 (2012)PLEEE81539-375510.1103/PhysRevE.86.061403]. We report characteristic time constants obtained from biexponential fits that can be associated with the formation of pairs and short chains as well as with the aggregation of chains. The electric field dependence of the induced dielectric increment reveals the same qualitative behavior that experiments did: three regions with different slopes corresponding to different aggregation processes are identified.

A Novel Linear Capacitive Temperature Sensor Using Polydimethylsiloxane

A linear, simple, and reliable capacitive temperature sensor is fabricated with inexpensive materials. The sensor is a parallel plate capacitor, in which the dielectric material polydimethylsiloxne (PDMS) is sensitive to temperature. The sensor works on the principle that the density of sensing layer decreases with an increase in temperature following the Clausius–Mosotti equation, because of which the permittivity also decreases. Moreover, the thickness of the sensing layer also increases with an increase in temperature due to a positive coefficient of linear expansion. The sensor is tested in the range of 20 °C–200 °C and shows a mean sensitivity ( $\mu$ ) of 156 fF/°C with standard deviation ( $\sigma$ )± 0.037 pF. It shows a linear characteristic with the coefficient of correlation ( $R^{2})~0.99$ , and maximum nonlinearity is 1.11% at 10 kHz. The measured resolution of the sensor is 0.08 °C, and the time constant for a unit step input is 0.6 s/°C. The average repeatability index ( $\Re$ ) of the sensor is 0.51% over a month. Finally, an interfacing circuit based on the integrator and instrumentation amplifier is designed, which gives a DC output with a sensitivity of 67.9 mV/°C.

Phonon characteristics, crystal structures and intrinsic properties of non-stoichiometric Ba1+xWO4 ceramics

Scheelite-type non-stoichiometric Ba1+xWO4 (0 ≤ x ≤ 0.04) ceramics were synthesized by a conventional solid-state reaction method. X-ray diffraction patterns showed that the main phase is a tetragonal scheelite structure with space group I41/a. The vibrational modes were obtained from Raman spectra, which were assigned and illustrated. The intrinsic properties were obtained by Clausius-Mosotti equation (C–M) and the damping equation, and there is a positive relationship between the FWHM values of the Bg(Ba) modes and the dielectric losses (calculated by the damping equation), as well as a negative correlation between the Raman shifts of the Eg (near 355 cm−1) and the dielectric constants (deduced by C–M equation). The far-infrared reflectivity spectra were analyzed by the four-parameter semi-quantum (FPSQ) model to calculate the intrinsic properties of the samples, which agreed well with those values obtained by the measured data.

Effects of ZrO2 substitution on crystal structure and microwave dielectric properties of Zn0.15Nb0.3(Ti1-xZrx)0.55O2 ceramics

In this study, the influence of substitution of Zr for Ti on crystal structure and microwave dielectric properties of Zn0.15Nb0.3(Ti1-xZrx)0.55O2 (0 ≤ x ≤ 0.7) ceramics were discussed through Rietveld refinement, normalized bond analysis and complex chemical bond theory. Rietveld refinement analysis indicated that a composite could be formed for x ≤ 0.22. Pure orthorhombic type (O-type) solid solutions are prepared in the region of x = 0.3–0.7. With the increasing amount of ZrO2, cell volume of O-type phase increases, and it results in the enlarging and compressing behaviors of chemical bonds. Under the circumstances, the dielectric polarizability is deteriorated because of the reducing chemical bond covalency value (fc), and this finding is also confirmed by Clausius-Mosotti equation. Lattice energy of Zr–O1 bonds and grain size distribution of sintered specimens are mainly responsible for the variations of quality factor (Q × f) value. Chemical bond energy (E) is closely related with the temperature coefficient of resonant frequency value (τf). Typical microwave dielectric properties of Zn0.15Nb0.3(Ti1-xZrx)0.55O2 ceramics (x = 0.22) were obtained when sintered at 1100 °C: εr = 46.31, Q × f = 30,297 GHz, τf = -8.24 ppm/°C.

Crystal structure, lattice vibrational characteristic, and dielectric property of Nd(Mg1/2Sn1/2)O3 ceramic

Nd(Mg1/2Sn1/2)O3 (NMS) ceramic was synthesized using a conventional solid-state reaction method. Crystal structure and morphology were investigated through X-ray diffraction (XRD) and scanning electron microscopy (SEM), respectively. Lattice vibrational modes were obtained through Raman scattering and Fourier transform far-infrared reflection spectroscopy. The main phase is NMS with monoclinic P21/n1 symmetry proved by XRD. SEM shows sample is dense and well-crystallized ceramic. The Raman spectrum with active modes were fitted with Lorentzian function, then these modes were assigned and illustrated, respectively. For example, the highest wavenumber mode above 650 cm−1 is attributed to A1g-like mode that corresponds to the symmetric breathing of oxygen octahedra. The far-infrared spectrum with seven infrared active modes was fitted by using four-parameter semiquantum models to calculate intrinsic properties, which agree well with the data calculated from Clausius-Mosotti equation, as well as the relationship between the damping coefficient and the intrinsic loss. F2u(2) yielded the greatest contribution to dielectric constant and loss, which is primarily represented as the inverted translational vibration of NdMgO6 octahedron. A1g(Nd) Raman mode in A-site has an enormous effect on the dielectric loss. The imaginary and real parts of the dielectric constant were obtained with the Kramers-Krönig analysis.

Dielectric properties of MgO–ZnO–TiO2-based ceramics at 1 MHz and THz frequencies

The dielectric properties (e and tan δ) of MZT-based ceramics can be tailored at both 1 MHz and the terahertz (THz) frequencies (0.2–2 THz) by CaTiO3 (CT) doping. CT was formed liquid phase during the sintering process and accelerated the densification of the ceramics. Doped with CT, the increase of the e at 1 MHz could be explained by Lichtenecker expressions equation, and the tan δ is decreased at 1 MHz due to the high density. By doping with CT, the THz dielectric properties of ceramics can be modified, due to the variation of the lattice parameter and microstructure (porosity). At THz frequencies, ion displacement polarization is difficult to achieve, so that e at THz is smaller than e at 1 MHz according to Clausius–Mosotti equation. According to the four-parameter factorized oscillator model, the tan δ is increased with frequency up to THz frequencies. The power absorption of the MZT-based ceramics is lower than 10 cm−1 below 1 THz, and it is a good choice as a transparent material at terahertz domain, which may promote the development of terahertz devices.

The dielectric constant and quality factor calculation of the microwave dielectric ceramic solid solutions

The dielectric constant of the microwave dielectric ceramic solid solution is usually predicted by the Clausius-Mosotti equation but the quality factor (Q) cannot be precisely calculated. In this paper, it finds that the dielectric constant of the solid solutions also could be well calculated by the Maxwell-Wagner formula, and that the Q of solid solutions can be precisely calculated, by assuming a solid solution as a two or more materials’ mixture.

Quantitative diffusion and swelling kinetic measurements using large-angle interferometric refractometry.

The uptake and release of sorbates into films and coatings is typically accompanied by changes of the films' refractive index and thickness. We provide a comprehensive model to calculate the concentration of the sorbate from the average refractive index and the film thickness, and validate the model experimentally. The mass fraction of the analyte partitioned into a film is described quantitatively by the Lorentz-Lorenz equation and the Clausius-Mosotti equation. To validate the model, the uptake kinetics of water and other solvents into SU-8 films (d = 40-45 μm) were explored. Large-angle interferometric refractometry measurements can be used to characterize films that are between 15 μm to 150 μm thick and, Fourier analysis, is used to determine independently the thickness, the average refractive index and the refractive index at the film-substrate interface at one-second time intervals. From these values the mass fraction of water in SU-8 was calculated. The kinetics were best described by two independent uptake processes having different rates. Each process followed one-dimensional Fickian diffusion kinetics with diffusion coefficients for water into SU-8 photoresist film of 5.67 × 10(-9) cm(2) s(-1) and 61.2 × 10(-9) cm(2) s(-1).

Growth, structural, optical, thermal and dielectric properties of a novel semi-organic nonlinear optical crystal: Dichloro-diglycine zinc II

Dichloro-diglycine zinc II (DCDGZ II), a semi-organic nonlinear optical material has been synthesized and single crystals were grown from the aqueous solution up to dimensions 20×10×3mm3. The title compound, DCDGZ II (C4H10Cl2N2O4Zn·H2O) crystallizes into monoclinic structure with the space group of C2/c. The unit-cell parameters were found to be a=14.4191(7), b=6.9180(2), c=12.9452(6)Å and Z=4. In the crystal structure, DCDGZ II layer is building up alternatingly with layers of water in which the zinc ions lie on a twofold axis. Theoretical calculations for polarizability, which are useful for device fabrication were made using Clausius–Mosotti equation and Penn analysis and the results were compared. Fourier transform infrared (FTIR) spectroscopic studies were performed for the identification of the different functional groups presented in the compound. The UV–vis–NIR absorption spectrum reveals that the lower UV cut-off wavelength is 240nm. The optical band gap of the crystal was estimated as 2.2eV. The surface morphology, thermal behaviour, dielectric properties have been studied using SEM, TG/DTA and LCR HITESTER analyzer. The nonlinear optical property of the crystal was also confirmed using Kurtz powder technique.

Extending the applicability of the Tkatchenko-Scheffler dispersion correction via iterative Hirshfeld partitioning.

Recently we have demonstrated that the applicability of the Tkatchenko-Scheffler (TS) method for calculating dispersion corrections to density-functional theory can be extended to ionic systems if the Hirshfeld method for estimating effective volumes and charges of atoms in molecules or solids (AIM's) is replaced by its iterative variant [T. Bučko, S. Lebègue, J. Hafner, and J. Ángyán, J. Chem. Theory Comput. 9, 4293 (2013)]. The standard Hirshfeld method uses neutral atoms as a reference, whereas in the iterative Hirshfeld (HI) scheme the fractionally charged atomic reference states are determined self-consistently. We show that the HI method predicts more realistic AIM charges and that the TS/HI approach leads to polarizabilities and C6 dispersion coefficients in ionic or partially ionic systems which are, as expected, larger for anions than for cations (in contrast to the conventional TS method). For crystalline materials, the new algorithm predicts polarizabilities per unit cell in better agreement with the values derived from the Clausius-Mosotti equation. The applicability of the TS/HI method has been tested for a wide variety of molecular and solid-state systems. It is demonstrated that for systems dominated by covalent interactions and/or dispersion forces the TS/HI method leads to the same results as the conventional TS approach. The difference between the TS/HI and TS approaches increases with increasing ionicity. A detailed comparison is presented for isoelectronic series of octet compounds, layered crystals, complex intermetallic compounds, and hydrides, and for crystals built of molecules or containing molecular anions. It is demonstrated that only the TS/HI method leads to accurate results for systems where both electrostatic and dispersion interactions are important, as illustrated for Li-intercalated graphite and for molecular adsorption on the surfaces in ionic solids and in the cavities of zeolites.

Optical and dielectric studies on organic nonlinear optical 2-furoic acid single crystals

Single crystals of 2-furoic acid were grown by slow evaporation method within a period of 5 weeks at room temperature. The grown crystal was subjected to single crystal X-ray diffraction, UV–vis-NIR analysis, dielectric and surface analysis. The band gap energy is also calculated from UV studies. Theoretical calculations for polarizability which are useful for device fabrication are also made using Clausius–Mosotti equation and Penn analysis and their results are compared.

Organic Solvents for Separating Ethyl Acetate-Ethanol by Extractive Distillation

The azeotropic mixture ethyl acetate-ethanol (EA-EtOH) enables effective separation by extractive distillation. The effectiveness of an extractive distillation process depends on the solvent selection, so the single and mixed solvent for separating ethyl acetate-ethanol by extractive distillation were examined. The results showed that the volatility of the ethyl acetate relative to ethanol increased with an increase of the ratio of any given solvent. The selectivity of the mixed solvent is superior to the single solvent. The measured data were correlated well using modified UNIFAC model. Simultaneously, the influence of temperature on solvent selectivity was proposed by using the Clausius-Mosotti equation.

Carbon-induced extreme ultraviolet reflectance loss characterized using visible-light ellipsometry

Carbon deposition on extreme ultraviolet (EUV) optics was observed due to photon-induced dissociation of hydrocarbons in a EUV lithography environment. The reflectance loss of the multilayer mirror is determined by the carbon layer thickness and density. To study the influence of various forms of carbon, EUV-induced carbon, hot filament and e-beam evaporated carbon were deposited on EUV multilayer mirrors. Spectroscopic ellipsometry was used to determine the carbon layer thickness and the optical constants ranging from ultraviolet to near infrared. The carbon density (and thus reflectance loss) was determined from the optical constants using both Bruggeman's effective medium approximation and the Clausius–Mosotti equation. Both approaches result in a similar EUV reflectance loss, with an accuracy of about 4%. The application of this process to ultrathin carbon films is further discussed.

Local electric field investigation of Si 2N 2O and its electronic structure, elastic and optical properties

This paper demonstrates that the Clausius–Mosotti equation cannot be used for Si 2N 2O since the Lorenz approximation is invalid therein. Therefore a modified definition for the Lorenz electric field is suggested which can be derived from the optical dielectric constant calculated using the plane-wave pseudopotential method. In addition, other parameters of Si 2N 2O such as the energy band gap, density of states, elastic and optical properties are also given in this paper. Based on the new expression for local electric field, the modified Clausius–Mosotti equation is suggested, and then the dielectric constant of Si 2N 2O is discussed by using the additivity rule. It is found that the result of the phenomenological analysis of the dielectric constant is basically consistent with the experimental data and the first principles results, which explain the experimental observation that the dielectric constant of Si 2N 2O is enhanced with the increase of Li content. Also, the modified Clausius–Mosotti equation and the additivity rule are suggested to be used in predicting the dielectric behaviors of the new and complex compounds.

Relationships between lattice energy and electronic polarizability of A NB 8-N crystals

The correlations between the electronic polarizability, determined from Clausius–Mosotti equation based on dielectric constant ε, and the lattice energy density u have been established for A NB 8-N crystals, such as the systems of rock salt crystals (group I–VII, II–VI) and tetrahedral coordinated crystals (group II–VI, III–V). For the A NB 8-N crystals systems, our present conclusions suggest that lattice energy density u decreases exponentially with increasing electronic polarizability, and the normal mathematical expression between lattice energy density u and electronic polarizability is u = pα q, p and q depend on the type of crystals. For the same cation binary A NB 8-N crystals systems, curve fitting equations have been obtained, and the relevant squares of the correlation coefficient R 2 are larger than 0.99, which show all lattice energy density u are in good exponential relation with electronic polarizability. These empirical equations will give more information on calculating lattice energy or electronic polarizability. New data of lattice energy have been calculated on the above equation u = pα q, and a good linear trend in the calculating values along with the Zhang’s values has been obtained.

Correction to the Clausius–Mosotti equation: The dielectric constant of nonpolar fluids from Monte Carlo simulations

We examine the dielectric constant of nonpolar fluids by direct Monte Carlo simulations on the basis of the polarizable hard sphere (PHS) model, where the spheres carry molecular polarizabilities. Point dipoles are induced in the spheres partly by an external electric field and partly by other molecules. It has been known that the Clausius-Mosotti equation needs a correction due to mutual polarization between molecules. We reproduce the qualitative behavior found in experiments: the correction increases with increasing density, reaches a maximum, and decreases at high densities. We show that the classic theory of Kirkwood and Yvon is quantitatively correct for the PHS model.

Charge transportation and permittivity in electron beam irradiated polymethyl methacrylate

The charging phenomenon in the insulating dielectrics often occurs in the radiative environments such as in the outer space and in the nuclear reactor. Both surface charging and bulk charging have various influences on the dielectric properties. Understanding electrical properties of e-beam irradiated dielectrics is of great significance in order to maintain the stability and reliability of the related operating system. In this work, the effect of electron beam irradiation on the permittivity of polymethyl methacrylate (PMMA) samples was investigated. It was found that the variance of permittivity in e-beam irradiated PMMA is mainly determined by two factors. One is the porosity of the material. The irradiating process could increase the porosity of PMMA due to the escape of the small molecule (e.g., CO, CO2, and CH4) produced during material degradation caused by e-beam irradiation. The enhanced higher porosity corresponds to lower permittivity. The distribution of the implanted charge is the other factor that influences the permittivity. When the distribution of electric field generated by the accumulating charge is asymmetric for the middle thickness of the sample, the PMMA sample with polar groups would be subjected to extra polarization by the field, which could lead to the increase in permittivity. Combining with the model of Wakino et al. [J. Am. Ceram. Soc. 76, 2588 (1993)] on permittivity of mixture materials, the Clausius–Mosotti equation was utilized to analyze the variation in permittivity in the e-beam irradiated PMMA samples.