Four-parameter Semi-quantum Model Research Articles

Crystal structures, lattice vibrational characteristics, and dielectric responses of ZnWO4 microwave dielectric ceramics sintered at different temperatures

The study meticulously examined the impact of varying sintering temperatures on the phase transformations, crystallographic configurations, dielectric response mechanisms, and lattice vibrational characteristics of the ZnWO4 ceramics. Far-infrared reflectance spectra were fitted using a four-parameter semiquantum model to obtain the intrinsic dielectric properties. Moreover, the contribution to the dielectric properties for each vibrational mode was analyzed, indicating that the lower-frequency mode had the most contribution. The relationship linking the structural aspects to the properties of ZnWO4 ceramics was elucidated through an analysis of the Raman spectral modes across a range of sintering temperatures, overcoming the limitation of solely textual description without mathematical quantification. When sintered at 1070 °C, the ZnWO4 ceramic had the best dielectric properties: εr = 14.81, Q×f = 34,239 GHz (f = 9.69 GHz), with the highest relative density of 96.95 %.

Crystal structures, dielectric properties, and lattice vibrational characteristics of Zn1-xCaxWO4 (x = 0–0.25) composite ceramics

In this work, Zn1-xCaxWO4 (x=0–0.25, ZCWO) composite ceramics were prepared by using the conventional solid-state sintering method at 1070 ℃. The impact of Ca2+ substitution on the lattice vibrational characteristics and dielectric responses of the ZCWO composite ceramics was investigated in detail. The formation of composite ceramics was verified by the Rietveld refined X-ray diffraction data of the ZCWO samples. The lattice vibrational characteristics were also identified and analyzed by the Raman and infrared reflection spectra combined with the theoretical simulations. The vibrational modes analysis of the Raman spectra showed that the internal modes of the ZCWO ceramics correspond to the vibrations of the W-O octahedrons. From the Fourier transform infrared reflectance spectra, the existence of three new vibrational modes of Au (315 cm−1), Au (834 cm−1), and Eu (885 cm−1) at x = 0.15–0.25 was observed, which belong to the modes of the CaWO4 ceramic. In addition, the intrinsic dielectric properties fitted by the four-parameter semiquantum model were in direct agreement with the theoretical values obtained from the Clausius-Mossotti & damping equations and the measured values. Besides, the contribution of each lattice vibrational mode to the intrinsic properties of the ZCWO ceramics was thoroughly studied, which shows that external mode 1 contributes the most to the intrinsic properties. The structure-property relationships of the ZCWO ceramics were established using the Raman modes as a media. The optimum dielectric properties of the ZCWO ceramics were obtained when x = 0.25: εr =13.98 (10.48 GHz), Q × f = 32,188 GHz.

Effects of sintering temperatures on crystal structures, dielectric properties, and phonon characteristics of Sr2V2O7 microwave ceramics

Sr2V2O7 (SVO) microwave dielectric ceramics were fabricated through a conventional solid-state synthesis method and sintered at 900–1000 °C for 10 h. The crystal structures and morphologies of the SVO samples were examined via X-ray diffraction and scanning electron microscopy. These analyses revealed that the SVO sample sintered at 950 °C exhibited high crystallinity and a triclinic crystal system. Through the lens of lattice dynamics, the phonon characteristics of the SVO samples were investigated via Raman spectroscopy and far-infrared spectroscopy to elucidate the dielectric response mechanics and microstructural origins of these responses. Raman spectra were classified into three sections corresponding to the vibration of Sr2+ ions, the V–O or V–O–V telescopic vibration, and the internal elongation of the tetrahedral structure composed of V–O, respectively. The inherent dielectric properties obtained from the far-infrared spectra were analyzed using a four-parameter semi-quantum model with the assistance of the Focus software. This analysis aligned with the measured property values. The relationships between the crystal structures and the dielectric properties were established using the Raman modes. Particularly, the SVO sample sintered at 950 °C exhibited excellent dielectric properties, characterized by a dielectric constant (εr) of 9.49, a quality factor (Q × f) of 35,189 GHz, and a resonant frequency (f) of 12.48 GHz.

Crystal structures, lattice vibrational characteristics, and dielectric response of Mg3(VO4)2 microwave dielectric ceramics sintered at different temperatures

Mg3(VO4)2 (MVO) microwave dielectric ceramics were fabricated by a conventional solid-state sintering method at different sintering temperatures (Ts) between 1000 °C and 1100 °C. The effects of Ts on the phase evolution, the crystal structures, the dielectric responses, and the lattice vibrational characteristics of MVO were investigated. XRD patterns after Rietveld refinement were applied to analyze the phase evolution and the crystal structures of the samples, which shows the orthorhombic structure with the space group of Cmca for the MVO ceramics. Micrograph from scanning electron microscopy shows a uniform and dense crystal structure with the highest bulk density for the MVO sample sintered at 1050 °C. Raman scattering spectroscopy and infrared reflectance spectroscopy were used to dissect the lattice vibrational characteristics of the MVO ceramics. There are two types of vibrational modes of the MVO samples, i.e., the external modes caused by the deformation of [VO4]3- and the rotational and translational vibrations of the lattices, the internal modes attributed to the asymmetric stretching vibrations of V-O bonds. The intrinsic dielectric properties were determined by fitting the data with a four-parameter semi-quantum (FPSQ) model. Modes 1, 2, and 4, associated with the external modes, have the greatest contribution coefficient of 65.58% to the dielectric constant, and Mode 1 has the greatest contribution coefficient of 51.40% to the dielectric loss. The structure-property relationships were semi-quantitatively mathematically established according to the Raman modes. The MVO sample sintered at 1050 °C has the best dielectric properties of εr = 9.59 and Q × f = 41,193 GHz (f = 13.69 GHz).

Lattice vibrational characteristics and structure-property relationships of SrWO4- x wt.% LiF (x = 0.5–3.0) microwave dielectric ceramics

SrWO4-x wt.% LiF (SWL, x = 0.5–3.0) ceramics were obtained by a conventional solid-state reaction at 850 °C. The effects of the LiF additive on the phase evolution and dielectric response mechanism of the SWL ceramics were comprehensively studied. The densification temperature of the SWL ceramics was successfully reduced to 850 °C by adding LiF as the sintering additive. The X-ray diffraction data indicated that the SWL ceramics were composite ceramics. The lattice vibrational properties were investigated in depth by Raman scattering and Fourier transform infrared reflectance. The intrinsic dielectric property values fitted by the four-parameter semi-quantum model agreed well with the measured dielectric property values and the theoretical values obtained from the Clausius-Mossotti & damping equations. Moreover, structure-property relationships were obtained by studying the lattice vibrational modes of the SWL ceramics. The SWL ceramic achieved the optimum dielectric property at x = 2.0, with εr = 9.03 and Q × f = 47,830 GHz.

Dielectric responses and structure-property relationships of Ca1-xBaxWO4 composite microwave dielectric ceramics

Ca1-xBaxWO4 (x = 0–0.25, CBWO) composite microwave dielectric ceramics were obtained after sintering at 1200 °C for 4 h. X-ray diffraction and X-ray photoelectron spectroscopy were used to determine their complex phase structures. The lattice vibrational properties were revealed by Raman scattering and Fourier-transform infrared (FTIR) spectroscopy. The Raman spectra showed that phase-pure CaWO4 had eight active vibrational modes when x = 0.15–0.25. A new vibrational mode appeared near 927 cm−1, which was attributed to BaWO4. The intrinsic properties were fitted and simulated by the four-parameter semi-quantum model according to the FTIR spectra. The low-frequency vibrational modes made a greater contribution to the intrinsic properties than the high-frequency modes. Structure-property relationships of the CBWO ceramics were obtained using Raman spectroscopy, and their dielectric responses wereelucidated. The CBWO ceramic at x = 0.25 had excellent dielectric properties with εr = 7.43 and Q × f = 56,929 GHz.

Effects of LiF additive on crystal structures, lattice vibrational characteristics and dielectric properties of CaWO4 microwave dielectric ceramics for LTCC applications

In this paper, CaWO4-x wt.% LiF (x = 0.5–3.0) microwave dielectric ceramics are prepared by conventional solid-state reaction at 850 °C. All the X-ray diffraction peaks are attributed to CaWO4, combined with the results of X-ray photoelectron spectroscopy and scanning electron microscope. They indicate that LiF forms liquid phase at high temperature, exists in amorphous phase, and the CaWO4-x wt.% LiF samples belong to the composite ceramics. With the increase of the LiF content, the liquid phase fills the pores of the ceramics and increases the compactness. Therefore, the quality factor increases from 59,055 GHz (x = 0.5) to 77,855 GHz (x = 3.0), and the dielectric constant decreases from 9.26 (x = 0.5) to 8.41 (x = 3.0). The lattice vibration characteristics of the CaWO4-x wt.% LiF samples are studied by Raman and infrared spectroscopy. The external modes associated with the vibration of the Ca–O bonds have the greatest influence on the dielectric response, as shown by the fitting results based on the four-parameter semi-quantum (FPSQ) model. In addition, the simulated intrinsic properties and measured values are in general agreement. When the x value increases, the dielectric constant decreases with the decrease of the bond length. The quality factor has a negative correlation with the FWHM value of the Bg mode and a positive correlation with the packing fraction. Finally, the CaWO4-3 wt.% LiF sample has good compatibility with the silver powders at 850 °C, and high application value in the LTCC field.

Lattice vibrational characteristics and structure-property relationships of Ca(Mg1/2W1/2)O3 microwave dielectric ceramics with different sintering temperatures

Ca(Mg 1/2 W 1/2 )O 3 (CMW) microwave dielectric ceramics were synthesized by the solid state reaction method and were sintered at the temperatures in the range of 1450–1550 °C for 4 h. X-ray diffraction and Rietveld refinement results confirmed that the main phase of the samples belongs to the monoclinic crystal structure (P2 1 /c space group). The vibrational modes were determined using the Raman scattering and Fourier transform infrared reflection (FTIR) spectra, and the lattice vibrational characteristics were revealed in detail. The fitting curves of FTIR spectra were obtained by the four-parameter semi-quantum model that was used to calculate the intrinsic properties of samples, and the influence of the infrared mode on the intrinsic properties was elucidated. The structure-property relationships were constructed based on the Raman modes. The optimal dielectric properties of CMW ceramics are of ε r = 18.37, tanδ = 2.71 × 10 −4 and were obtained for the sintering temperature of 1500 °C.

Crystal structure, lattice vibrational characteristics, and dielectric properties of Ba(Mg1/2Mo1/2)O3 ceramics sintered at different temperatures

Double perovskite structured Ba(Mg1/2Mo1/2)O3 (BMM) ceramics were prepared by traditional solid sintering methods at different sintering temperatures (Ts=1250–1325 °C). X-ray diffraction (XRD) data proved a 1:1 ordered face-centered cubic lattice (Fm-3 m), and the ceramic sintered at 1300 °C obtained maximum relative density. The lattice vibration characteristics were identified by Raman spectroscopy and far-infrared reflection spectroscopy. Based on the far-infrared data, a four-parameter semi-quantum model (FPSQ) was applied to calculate the intrinsic properties of BMM ceramics, and the obtained results approximated the measured values. The Raman shift of the BMM F2g(B) mode (attributed to the centrosymmetric vibration of Ba atom) was shown to be negatively correlated with the corrected permittivity and Ba-O bond length. With increasing sintering temperature (Ts), the relative density is positively correlated with the quality factor (Q × f), and the change of Ba-O bond length leads to distortion of the oxygen octahedron, which is positively correlated with the dielectric constant. The sintered BMM ceramics obtained their best dielectric properties at 1300 °C (εr= 4.987, Q × f = 23,069 GHz, f = 11.16 GHz).

Optical phonon modes, static and high-frequency dielectric constants, and effective electron mass parameter in cubic In2O3

A complete set of all optical phonon modes predicted by symmetry for bixbyite structure indium oxide is reported here from a combination of far-infrared and infrared spectroscopic ellipsometry, as well as first principles calculations. Dielectric function spectra measured on high quality, marginally electrically conductive melt grown single bulk crystals are obtained on a wavelength-by-wavelength (also known as point-by-point) basis and by numerical reduction of a subtle free charge carrier Drude model contribution. A four-parameter semi-quantum model is applied to determine all 16 pairs of infrared-active transverse and longitudinal optical phonon modes, including the high-frequency dielectric constant, ε∞=4.05±0.05. The Lyddane–Sachs–Teller relation then gives access to the static dielectric constant, εDC=10.55±0.07. All experimental results are in excellent agreement with our density functional theory calculations and with previously reported values, where existent. We also perform optical Hall effect measurements and determine for the unintentionally doped n-type sample a free electron density of n=(2.81±0.01)×1017cm−3, a mobility of μ=(112±3)cm2/(Vs), and an effective mass parameter of (0.208±0.006)me. Density and mobility parameters compare very well with the results of electrical Hall effect measurements. Our effective mass parameter, which is measured independently of any other experimental technique, represents the bottom curvature of the Γ point in In2O3 in agreement with previous extrapolations. We use terahertz spectroscopic ellipsometry to measure the quasi-static response of In2O3, and our model validates the static dielectric constant obtained from the Lyddane–Sachs–Teller relation.

Sintering behavior, crystal structures, phonon characteristics and dielectric properties of LiZnPO4 microwave dielectric ceramics

Single phase LiZnPO4 (LZP) microwave dielectric ceramics were synthesized via a conventional solid-state ceramic route at different temperatures. Their sintering behavior, crystal structures, phonon characteristics and dielectric properties were studied in detail so as to further expound their physical mechanism of the dielectric respond. The results indicate that the LZP ceramic sintered at 825 °C exhibits a relative dielectric constant of 5.50 and a fine quality factor of 47,207 (f = 15 GHz). Raman vibrational modes below 600 cm−1 are classified as the external modes, which are associated with Li+ and Zn2+ ions, and the internal modes above 600 cm−1 are related to the vibration of the [PO4]3- tetrahedron. On the light of the infrared reflection spectrum, the dielectric properties simulated via the four-parameter semi-quantum model are similar to the measured property values, which demonstrate that the modes of low-frequency are the main factors affecting the dielectric properties. The dielectric constant is inversely related to the P–O bond length and the Raman shift of mode 13 ([PO4]3−tetrahedral vibration). The Q × f value owns a negative correlation with packing fraction and full width at half maximum values of modes 13. That is, the semi-quantitative relationships between the structures and the properties of the LZP ceramics were successfully established as a function of the sintering temperature.

Lattice vibrational characteristics and structures-properties relationships of non-stoichiometric Nd[Mg0.5Sn0.5(1+x)]O3 ceramics

Non-stoichiometric Nd[Mg0.5Sn0.5(1+x)]O3 (− 0.04 ≤ x ≤ + 0.04)—type samples were prepared using a traditional two-step solid-state sintering process. Their crystal structures, phase compositions, dielectric properties and lattice vibrational characteristics were identified in detail. The double perovskite Nd(Mg0.5Sn0.5)O3 with a monoclinic structure was distinguished as the main crystalline phase, and pure phase was obtained when x < 0. The sample [Nd(Mg0.5Sn0.49)O3] at x = − 0.02 shows the excellent dielectric properties: er = 18.74, Q × f = 47,979 GHz. The lattice vibrational characteristics were clarified with Raman and infrared active mode spectroscopy. The intrinsic properties were fitted by four-parameter semi-quantum model, which show that the low-frequency infrared modes yield a more significant contribution to permittivity and dielectric loss. Raman shifts of modes F2g(A) and F2g(B) correlate with dielectric constants negatively, which implies that the bond length has a positive correlation with permittivity. Full widths at half maximum of vibrational modes A1g(O) correlate with dielectric loss values positively and correlate with the degree of order (S) negatively.

Brillouin zone center phonon modes in ZnGa2O4

Infrared-active lattice mode properties of melt-grown high-quality single bulk crystals of ZnGa2O4 are investigated by combined spectroscopic ellipsometry and density functional theory computation analysis. The normal spinel structure crystals are measured by spectroscopic ellipsometry at room temperature in the range of 100 cm–1–1200 cm–1. The complex-valued dielectric function is determined from a wavenumber-by-wavenumber approach, which is then analyzed by the four-parameter semi-quantum model dielectric function approach augmented by impurity mode contributions. We determine four infrared-active transverse and longitudinal optical mode pairs, five localized impurity mode pairs, and the high frequency dielectric constant. All four infrared-active transverse and longitudinal optical mode pairs are in excellent agreement with results from our density functional theory computations. With the Lyddane–Sachs–Teller relationship, we determine the static dielectric constant, which agrees well with electrical capacitance measurements performed on similarly grown samples. We also provide calculated parameters for all Raman-active and for all silent modes and, thereby, provide a complete set of all symmetry predicted Brillouin zone center modes.

Lattice vibrational characteristics, crystal structures and dielectric properties of non-stoichiometric Nd(1+x)(Mg1/2Sn1/2)O3 ceramics

Non-stoichiometric Nd(1+x)(Mg1/2Sn1/2)O3 (−0.04 = x ≤ 0.04, NMS) ceramics were fabricated via a conventional solid-state reaction method. Crystal structures and morphologies were investigated by X-ray diffraction (XRD) and scanning electron microscopy (SEM), respectively. The main crystalline phase is monoclinic Nd(Mg1/2Sn1/2)O3 with a double perovskite structure (P21/n space group) for the NMS system proved by XRD. The sample at x = 0.01 has the best crystallinity and evenly distributed crystal grains observed by SEM. The optimum performances (εr = 19.87, Q×f = 41840 GHz, f = 12.05 GHz) are obtained at x = 0.01. Lattice vibrational modes of the Raman spectra were assigned and illustrated, in detail. The dielectric properties obtained by fitting infrared reflectance spectra with the help of four-parameter semi-quantum model are consistent with the calculated values by microscopic polarization and damping coefficients. The reverse translational vibration of the NdMgO6, the F5u(5) mode, provides the greatest contribution to the dielectric response. The relationships between crystal structures and dielectric properties were mainly established using lattice vibrational modes as a media.

Phonon characteristics and intrinsic properties of single phase ZnWO4 ceramic

Single phase ZnWO4 microwave dielectric ceramic was prepared by a traditional solid-state method, which possesses the monoclinic wolframite structure. The lattice vibrational modes were obtained by Raman and Fourier-transform infrared (FTIR) spectra, whose phonon characteristics were analyzed by identification and description of the vibrational modes. Furthermore, the intrinsic properties of Single phase ZnWO4 was simulated based on FTIR data, and the contribution of each vibrational mode to the intrinsic properties was analyzed, in particular. The theoretical property values, calculated by the Clausius–Mossotti and damping equations, agree well with the data fitted by the four-parameter semi-quantum model according to FTIR spectrum.

Phonon characteristics and dielectric properties of a phase pure CoWO4 ceramic

A phase pure CoWO4 ceramic was prepared using the conventional solid-state reaction method and sintering at 1150 °C for 2 h. The sintered sample exhibited a tetragonal wolframite structure (space group P2/c) without impurity phases according to X-ray diffraction analysis. The Raman and infrared spectra of the CoWO4 ceramic were studied based on Lorentz fitting, a first-principles calculation, the four-parameter semiquantum (4-P) model and the Kramers-Krönig (K-K) transformation to reveal the local structure and intrinsic properties. The infrared spectrum was fitted based on the 4-P model, which showed that the simulated properties are similar to the experimental results and that the largest contribution to the dielectric response comes from the Bu(1) mode, which is related to the stretching vibration of the WO6 octahedra.

Intrinsic properties and lattice vibrational characteristics of NiWO4 ceramic

NiWO4 ceramic was prepared by solid-state synthesis, which was confirmed to be monoclinic wolframite structure (P12/c) by X-ray diffraction pattern. The vibrational modes were identified and illustrated at length by Raman scattering spectroscopy and far-infrared reflection spectroscopy to study the lattice vibrational characteristics. The tested properties are consistent well with the theoretical values obtained by Clausius-Mossotti & damping equations and four-parameter semi-quantum model, and the infrared vibrational mode Bu(263 cm−1) has the greatest contribution to the dielectric properties.

Phonon characteristics and intrinsic properties of phase-pure CaMoO4 microwave dielectric ceramic

Phase-pure CaMoO4 microwave dielectric ceramic was sintered at 1150 ℃ for 4 h via a conventional solid-state reaction method, which was indicated as a tetragonal scheelite structure (space group I41/a) by XRD analysis. Raman scattering and infrared spectra of the phase-pure CaMoO4 were investigated based on Lorentz function, four-parameter semiquantum model and Kramers–Kronig transformation to reveal the local structure and intrinsic properties. External modes of Raman spectrum are vibration of Ca2+ ions relative to the rigid [MoO4]2− tetrahedron, internal modes corresponded to vibration inside [MoO4]2−. Fitting infrared spectrum show that the dielectric properties are similar to the experimental results and the main source of contribution to dielectric response comes from Eu modes, i.e., translational vibration of Ca–O bonds in the CaMoO4 ceramic.

Crystal structures, dielectric properties, and lattice vibrational characteristics of (1-x)CaWO4-xTiO2 composite ceramics

(1-x)CaWO4-xTiO2 (CWT) ceramics were fabricated by conventional solid-state sintering method at 1200 °C for 4 h. X-ray diffraction data show that CaWO4 and TiO2 coexist as composite ceramics and Rietveld refinement reveals the change in crystal structures of CWT system. There are seven Raman vibrational modes for CaWO4, two Raman modes for TiO2, and eight infrared vibrational modes for CaWO4, whose intensities decrease with increasing TiO2 content. The theoretical properties obtained from four-parameter semiquantum model coincide with those calculated from C-M and damping equations. The structure-property relationships of CWT system were established based on the lattice vibrational modes. When x = 0.15, the sample achieves the optimum dielectric properties with εr = 10.86, Q × f = 16046 GHz (f = 15.51 G), τf = −15.99 ppm/°C.

Crystal structures, intrinsic properties and phonon characteristics of non-stoichiometric Nd[Mg1/2(1+x)Sn1/2]O3 ceramics

The non-stoichiometric Nd[Mg1/2(1+x)Sn1/2]O3 (NMS, − 0.04 ≤ x ≤ 0.04) were synthesized through a routine solid-state reaction process. The phase composition, phonon characteristics, and microwave dielectric properties were investigated by X-ray diffraction patterns, Scanning electron microscopy Raman and Fourier transform far-infrared reflection. The best crystallinity with uniformly distributed grains and clear grain boundaries at x = 0.01. The intrinsic properties were calculated by four-parameter semi-quantum model based on far-infrared reflectivity data, which agree well with those values obtained from the microscopic polarizabilities & damping coefficient angle. The correlations between intrinsic properties and lattice vibrational modes were discussed in particular.