Ying
Chen
abc,
Qingyang
Pang
bc,
Genshui
Wang
c,
Zhaoquan
Zhang
c,
Chenxi
Zhu
c,
Xin
Li
c,
Liangcai
Wu
*a and
Zhitang
Song
*a
aNational Key Laboratory of Materials for Integrated circuits, Shanghai Institute of Micro-system and Information Technology, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050, P. R. China. E-mail: lcwu@dhu.edu.cn; ztsong@mail.sim.ac.cn
bUniversity of Chinese Academy of Sciences, 19 A Yuquan Rd, Shijingshan District, Beijing 100049, P. R. China
cShanghai Institute of Ceramics, Chinese Academy of Sciences, 1295 Dingxi Road, Shanghai 200050, P. R. China
First published on 7th September 2023
Double-site yttria-doped (Ca,Sr)z(Zr,Ti)O3−δ (CSZTY) ceramics were synthesized using the solid-state reaction method. The correlation among the crystal structure, microstructure and microwave dielectric properties was investigated. Their structures were characterized by X-ray diffraction (XRD), transmission electron microscopy (TEM) and Raman spectroscopy. CSZTY ceramics have a perovskite structure with coexisting orthorhombic and cubic phases; the main phase is the orthorhombic Pnma phase. Rietveld refinement, atomic-resolved high angle annular dark field (HAADF) STEM images and energy dispersive spectroscopy (EDS) for elemental mapping revealed that Y3+ cations occupy both A and B-sites in the perovskite structure (ABO3). Upon increasing Y3+ cations distributed on A and B-sites in CSZT ceramics, the factor of tolerance t decreases and the tilting angle of BO6 octahedra and the unit-cell volume increase. Superlattice reflections appearing along the [100]c, [110]c and [012]c zone axes are observed in the selected area electron diffraction (SAED) patterns as a result of cell doubling caused by the octahedral tilt transitions. Raman spectra show that upon increasing the doping amount of yttria, before and after 450 cm−1, the frequencies of some vibrational modes correlated with B ion movement in the BO6 octahedron blue shift and red shift, respectively. Upon increasing the octahedral tilting angle, the polarizability of the ions produces corresponding changes, the dielectric constant εr decreases, the value of Q × f increases, and the temperature coefficient of dielectric permittivity τc increases while the resonant frequency temperature coefficient τf decreases. At x = 0.15, the CSZTY ceramics show optimized microwave dielectric properties: εr = 29.8, Q × f = 23528 GHz, τc = 0.50 ppm °C−1, and τf = −4.25 ppm °C−1. This work provides a method to optimize the microwave dielectric properties of perovskite structure materials.
To date, no literature reported the crystal structure dependence of the microstructure and microwave dielectric properties of the same element double substituted at the A-site and B-site in CSZT perovskite ceramics. In this paper, double-site yttria-doped (Ca,Sr)z(Zr,Ti)O3−δ (CSZTY) perovskite ceramics were synthesized via the conventional solid-state reaction method. The effects of double-site substitution of the trivalent cation on the crystal structure, microstructure and microwave dielectric properties were investigated. The introduction of trivalent cation Y3+ decreases the dielectric constant, improves the quality factor Q × f value and decreases the temperature coefficient of resonant frequency of the CSZT perovskite ceramics. Meanwhile, the relationship between the structures and microwave dielectric properties was investigated in detail. The purpose of adding little magnesium oxide is to promote the densification of ceramics due to the stress produced by the difference of the thermal expansion coefficients of MgO (13.6 × 10−6 °C−1) and CaZrO3 (5–6 × 10−6 °C−1) during annealing treatment. In order to simplify the difficulty of the analysis, the role of Mg doping is ignored in this paper.
The crystalline structures of the ceramics were determined using an X-ray diffractometer (XRD, CuKα1, λ = 1.54056 Å, 40 kV 40 mA, Bruker D8 Advance) in the range of 10–90° with a step size of 0.02° and a step time of 1.5 s. Rietveld refinements were performed using the TOPAS software. The microstructures and chemical elements were analyzed using a field emission scanning electron microscope (FESEM, Magellan400, USA) with an energy dispersive X-ray spectrometer (EDS), a transmission electron microscope (TEM, JEM-2100F, JEOL) with an energy dispersive X-ray spectrometer (EDS) and a high-resolved scanning transmission electron microscope (HRSTEM, Hitachi HF 5000) combined with an EDS. For FESEM, Magellan400, resolution is 0.9 nm. For TEM, JEM-2100F, point resolution is 0.19 nm and line resolution is 0.14 nm. For HRSTEM, Hitachi HF 5000, point resolution is 0.23 nm, line resolution is 0.13 nm, and the STEM resolution is 78 pm. The EDS analysis is carried out for minerals with atomic numbers greater than 11. The relative error of quantitative analysis is as follows: for the mass fraction greater than 20%, the relative error is within 5%; for the mass fraction ranging from 3% to 20%, the relative error is within 10%; for the mass fraction ranging from 1% to 3%, the relative error is within 20%; for the mass fraction ranging from 0.5% to 1%, the relative error is within 30%; and for the mass fraction ranging from 0.1% to 0.5%, the relative error is within 50%. The specimens for TEM analysis were prepared by mechanical thinning and finally Ar+ milling in a Gatan Precision Ion Polishing System. Raman spectra were measured using the Renishaw in via Reflex Raman spectrometer with an excitation laser of 532 nm. The spectral resolution is within 0.025 nm, and the repetition rate is within ±0.02 cm−1. A vector network analyzer (Agilent E8362B) and a temperature chamber were used to measure the microwave dielectric properties of the samples. The quality factor Q × f and dielectric constant εr at resonant frequency were estimated using the TE01δ mode dielectric resonator method. The measurement range of the microwave dielectric constant is 5–100, and the relative error is within 1%. The measurement range of the microwave loss is 2 × 10−4–6 × 10−3, and the relative error is within ∼5%. The resonant frequency temperature coefficient τf was calculated using the following equation:
(1) |
The temperature coefficient of dielectric permittivity τC was evaluated using a broad-band dielectric spectrometer (Novocontrol Technologies, Germany) at 1 MHz. The value of τC was calculated using the following equation:
(2) |
Fig. 2 shows the cross-sectional backscattering electron (BSE) images of the CSZT and CSZTY (x = 0.01, 0.05, 0.10, 0.15, 0.20) ceramics at 10000x magnification obtained using a field emission scanning electron microscope (FESEM). It can be seen that for the CSZT ceramic, the cross-section exhibits an intergranular fracture, the grain boundaries are clear, and the grain sizes are uniform. With the doping of 0 to 0.025 of Y2O3, the mean grain sizes become smaller, which may be attributed to two reasons: (1) the MgO phase at the grain boundary which can effectively reduce the grain boundary movement rate and inhibit the rapid growth of grains; (2) the stress generated by the thermal expansion difference between the MgO phase (∼13.6 × 10−6 °C−1) and the CSZTY phase (∼5–6 × 10−6 °C−1) during the sintering process. With the continuous doping of Y2O3, the proportion of MgO in stoichiometry is reduced; there was a noteworthy change in the microstructure. The cross-section of CSZTY ceramics exhibits a more trans granular fracture, the grain boundaries become unclear, the grain growth is promoted greatly and the small grains gradually disappear, which indicate that the continuous doping of Y2O3 increases the surface energy of the grains, promotes grain boundary migration, and increases the degree of ceramic densification. But, at x = 0.20, the mean grain size suddenly gets smaller. It is due to the forming of impurity phase Y2O3 which blocks the movement of the crystal boundaries resulting in fine grains.
Fig. 3(a) shows the cross-sectional SEM-BSE image of the CSZTY (x = 0.1) ceramic at 10000x magnification. The sample was surface polished and heat treated at 1400 °C for 1 h. Fig. 3(b) and (d–j) are the corresponding EDS elemental maps. Two differently colored grains can be clearly seen in Fig. 3(a). The smaller black grains are tightly embedded at the gray grain boundaries. Based on the corresponding EDS elemental mapping, the components of black grains are the Mg element and O element. The components of gray grains are Y, Zr, Ti, Sr, Ca, and O elements which are evenly distributed without agglomeration. Fig. 3(c) shows the TEM-BSE image of the CSZTY (x = 0.1) ceramic. Fig. 4 shows the EDS line scanning of O, Mg, Y, Ti, Zr, Sr, and Ca elements from the MgO grain to the CSZTY grain (red arrow region in Fig. 3(c)). On the grain boundary, no obvious element diffusion was observed.
Fig. 4 The EDS line scanning of O, Mg, Y, Ti, Zr, Sr, and Ca elements from the MgO grain to CSZTY grain (red arrow region in Fig. 3(c)). |
Fig. 5 shows the selected area electron diffraction (SAED) patterns, atomic-resolved high angle annular dark field (HAADF) STEM images and energy dispersive spectroscopy (EDS) elemental maps viewed along the [012]c zone axis for the CSZTY (x = 0.1) ceramic. Superlattice reflections were observed along the [012]c zone axis in the SAED pattern, which resulted from cell doubling caused by the octahedral tilt transitions. According to the grayscale in Fig. 5(b) and (c) and the distribution of elements in Fig. 5(d)–(h), the position of the A-site and B-site atomic columns can be identified. Zr and Ti atoms occupy the B-site, and the Sr and Ca atoms occupy the A-site in the ABO3 structure. The Y atom occupies both A and B sites. It is difficult to identify the position of the Mg atom in the ABO3 structure because of the low doping amount. The effect of Mg doping is not considered in this paper to simplify the analysis.
Rietveld refinement is used to characterize the phase content and cell parameters of the materials and determine the crystal structure. The lattice parameters and mass percentage of each phase of all samples were calculated using TOPAS software based on the Rietveld refinement results, which are shown in Fig. 6 and Table 1. Fig. 6(a)–(g) show the Rietveld refinement patterns of CSZT and CSZTY (x = 0.01, 0.05, 0.10, 0.15, and 0.20) ceramics. The goodness of fit values (Rp, Rwp, and Rexp) indicate the high reliability of the refinement results. Fig. 6(h) shows the correlations among t, Φ, and V with variations of x.
Fig. 6 (a)–(g) Rietveld refinement patterns of CSZTY (x = 0, 0.01, 0.05, 0.10, 0.15, and 0.20) ceramics. (h) The correlations among t, Φ, and V with variations of x. |
Composition | Phase | a (Å) | b (Å) | c (Å) | V (Å3) | Φ (°) | |
---|---|---|---|---|---|---|---|
x = 0 | Ca0.7Sr0.3Zr0.913Ti0.048O2.92 | Orthorhombic | 5.647767(15) | 8.05770(2) | 5.75441(18) | 261.868 (13) | 13.42 |
Cubic | 4.03190(3) | — | — | 65.541 (16) | |||
x = 0.01 | Ca0.7Sr0.3Zr0.912Ti0.048Y0.02Mg0.01O2.96 | Orthorhombic | 5.64712(14) | 8.06930(2) | 5.76678(14) | 262.783 (11) | 14.31 |
Cubic | 4.03620(3) | — | — | 65.752 (14) | |||
x = 0.025 | Ca0.6965Sr0.2985Y0.005Zr0.912Ti0.048Y0.04O2.9825 | Orthorhombic | 5.64849(17) | 8.07050(3) | 5.76593(19) | 262.845 (15) | 14.19 |
Cubic | 4.03670(4) | — | — | 65.780 (2) | |||
x = 0.05 | Ca0.679Sr0.291Y0.03Zr0.8835Ti0.0465Y0.07O2.98 | Orthorhombic | 5.64695(16) | 8.07560(2) | 5.77261(17) | 263.246 (13) | 14.71 |
Cubic | 4.03920(4) | — | — | 65.90 (2) | |||
x = 0.10 | Ca0.651Sr0.279Y0.07Zr0.855Ti0.045Y0.1O2.985 | Orthorhombic | 5.64726(15) | 8.07570(2) | 5.77280(17) | 263.273 (13) | 14.70 |
Cubic | 4.03930(4) | — | — | 65.903 (18) | |||
x = 0.15 | Ca0.623Sr0.267Y0.11Zr0.8075Ti0.0425Y0.15O2.98 | Orthorhombic | 5.64473(15) | 8.08270(2) | 5.78254(17) | 263.824 (13) | 15.44 |
Cubic | 4.0420(5) | — | — | 66.040 (3) | |||
x = 0.20 | Ca0.595Sr0.255Y0.15Zr0.779Ti0.041Y0.18O2.985 | Orthorhombic | 5.64540(13) | 8.08510(12) | 5.78455(14) | 264.029 (11) | 15.52 |
Y2O3 | Cubic | 5.27310(3) | — | — | 146.620 (2) |
For CSZT and CSZTY (x = 0.01, 0.05, 0.10, 0.15, and 0.20) ceramics, the perovskite structure exhibits Pnma orthorhombic and a small amount of Pmm cubic phases. As x increases from 0 to 0.15, the Pnma orthorhombic phase increases from 98.0 wt% to 98.7 wt%, and the Pmm cubic phase decreases from 2.0 wt% to 1.3 wt%. At x = 0.20, there are only a Pnma orthorhombic phase (94.71 wt%) and a cubic Y2O3 phase (5.29 wt%) in CSZTY.
Table 1 summarizes the lattice parameters of CSZT and CSZTY (x = 0.01, 0.05, 0.10, 0.15, and 0.20) ceramics. For the main phase (the Pnma orthorhombic phase), the unit cell is anisotropic in the tilted structures. As x increases, lattice parameter b increases from 8.058 Å to 8.085 Å, lattice parameter c increases from 5.754 Å to 5.785 Å, while lattice parameter a varies little. The lattice volume V increases from 261.87 Å3 to 264.03 Å3. Therefore, it is not a simple increase in dimensions of the dodecahedra but also a distortion of the crystal lattice. Here, we use changes in the tilt angle of the BO6 octahedra (Φ) and tolerance factor (t) to characterize the distortion process of the lattice structure. The tilt angle of the BO6 octahedra, Φ, can be deduced from the unit cell parameters a, b and c according to the relation:12
(3) |
(4) |
Ion | Ca2+ | Sr2+ | Zr4+ | Ti4+ | Y3+ | Mg2+ | O2− | |
---|---|---|---|---|---|---|---|---|
Coordination | XII | XII | VI | VI | VIII | VI | VI | VI |
Ionic radius (Å) | 1.34 | 1.44 | 0.72 | 0.605 | 1.02 | 0.90 | 0.72 | 1.4 |
Composition | R A (Å) | R B (Å) | R o (Å) | t | |
---|---|---|---|---|---|
x = 0 | Ca0.7Sr0.3Zr0.913Ti0.048O2.92 | 1.370 | 0.686 | 1.400 | 0.939 |
x = 0.01 | Ca0.7Sr0.3Zr0.912Ti0.048Y0.02Mg0.01O2.96 | 1.370 | 0.711 | 1.400 | 0.928 |
x = 0.025 | Ca0.6965Sr0.2985Y0.005Zr0.912Ti0.048Y0.04O2.9825 | 1.368 | 0.722 | 1.400 | 0.923 |
x = 0.05 | Ca0.679Sr0.291Y0.03Zr0.8835Ti0.0465Y0.07O2.98 | 1.360 | 0.727 | 1.400 | 0.917 |
x = 0.1 | Ca0.651Sr0.279Y0.07Zr0.855Ti0.045Y0.1O2.985 | 1.346 | 0.733 | 1.400 | 0.910 |
x = 0.15 | Ca0.623Sr0.267Y0.11Zr0.8075Ti0.0425Y0.15O2.98 | 1.332 | 0.742 | 1.400 | 0.902 |
x = 0.2 | Ca0.595Sr0.255Y0.15Zr0.779Ti0.041Y0.18O2.985 | 1.318 | 0.748 | 1.400 | 0.895 |
As the Y2O3 doping amount increases from x = 0 to x = 0.2, the mean size of the A-cation decreases from 1.370 Å to 1.318 Å, the mean size of the B-cation increases from 0.686 Å to 0.748 Å, so the factor of tolerance t decreases from 0.939 to 0.895 according to the formula (4). The values of t for all components are less than 0.965, which confirms the presence of the oxygen octahedron tilt.23,25Fig. 6(h) shows the correlations among the factor of tolerance t, the tilt angle of BO6 octahedra Φ, and unit-cell volume V with variation of x. It can be observed that with the increase of x, the factor of tolerance t has an approximately linear decreasing trend, while the tilt angle of the BO6 octahedra and unit-cell volume has a synchronous increasing trend overall. The distribution of Y3+ on the A-site induces an increase in the tilting of octahedra due to the decrease of the A cation size in the dodecahedra; the distribution of Y3+ on the B-site produces an increase in the tilting of the octahedra due to the increase of the B cation size. With a decrease in the size of the A-cation and an increase in the size of the B cation, the volume of octahedra increases. The analysis is verified by the observation of superlattice reflections in the SAED patterns. Superlattice reflections are caused by the octahedral tilt transitions. Fig. 7 shows the SAED patterns viewed along the [110]c and [100]c zone axis for the CSZTY (x = 0.1) ceramic. α and β superlattice reflections from antiphase tilting and antiparallel shifts of A-site species are observed in the [110]c and [100]c zone axis diffraction patterns, respectively. This phenomenon has also been observed in other perovskite compounds.23
Raman spectroscopy is a tool to study the lattice dynamics of dielectric ceramics. From the Raman spectra, some information on the composition, crystal structure and dielectric properties of materials can be obtained. The primitive cell of the orthorhombic phase perovskite (Pnma) contains 20 atoms. Through group theory analysis, it is found that there are a total of 24 Raman active modes.11–13,18,19Fig. 8 presents the Raman spectra of the CSZTY (x = 0, 0.01, 0.025, 0.05, 0.10, 0.15, 0.20) ceramics in the 100 cm−1 to 900 cm−1 frequency range. The number of Raman-active modes is lower than the 24 expected modes of vibrations. Some modes cannot be detected. As the Y2O3 doping amount increases from x = 0 to x = 0.2, the number of Raman modules that can be observed decreases from 13 to 7. It could be due to the decrease of dielectric polarizability with the continuous distribution of the Y3+ trivalent cation at the A- or B-site; it is also possible for some predicted modes to hide behind other intense bands, and thus may overlap as previously suggested for other perovskites.12,25
Table 4 shows the Raman frequencies and mode assignments in CSZTY ceramics in this study and previous literature.11–13,18,19 Based on previous studies on perovskite zirconate-based oxides,11–13,18,19 the vibration modes of CSZTY ceramics are divided into five regions: the region (100–190 cm−1) related to the A-BO6 octahedron inverted translational vibrations; the region (190–300 cm−1) related to the O–B–O bending motion, which is the inverted B ion movement in the BO6 octahedron; the region (300–450 cm−1) correlated with the B–O torsion modes; the 450–600 cm−1 region associated with B–O stretching; and the high-frequency region (above 600 cm−1) corresponding to second-order Raman scattering. Here, Raman data show that vibrational spectra are strongly affected by the cation substitution at the A and B-sites. From Fig. 8, it can be seen that compared with the CSZT (x = 0) ceramic, the vibration modes (124–432 cm−1) blue shift and Raman vibration modes (473–732 cm−1) red shift with the increasing doping content of Y3+. The rules of frequency shifts of vibrational modes are similar to those in Ca(Sr)ZrO3 and CaZr(Sn)O3 solid solutions.12Fig. 9 shows the relationships between the A and B-site ionic radii and frequency shifts of some vibrational modes of CSZTY ceramics with variations of x.
Raman shifts | (cm−1) | Mode | Assignments |
---|---|---|---|
This work | Literature11–13,18,19 | ||
124–129 | 117, 124 | B2g | Second order |
197–206 | 190, 193 | B2g | B–O bending |
239–246 | 239, 242 | Ag | B–O bending |
276–281 | 278, 283 | Ag | B–O bending |
336–340 | 338, 340 | Torsional mode | |
380–390 | 392, 395 | B2g | Torsional mode |
432–435 | 435, 439 | Ag + B1g or B2g | Torsional mode |
482–462 | 468, 473 | B2g | B–O stretching |
549–540 | 543, 551 | Ag + B1g or B3g | B–O stretching |
594–596 | 603 | Second-order scattering: the superposition of different combinations modes | |
651 | 666, 685 | ||
721–734 | 765 |
Fig. 9 The A and B-site ionic radii and frequency shifts of some vibrational modes of CSZTY ceramics with variations of x. |
In perovskite ceramics, the dielectric properties are related to the structural features. The vibrational modes at low frequencies have larger contributions to the permittivity and dielectric loss.18 With the decrease of t from 0.939 to 0.895, the Raman modes below 450 cm−1 blue shift, and the increase of the octahedral tilting angle produces a change in polarizability of the ions. The dielectric properties also undergo corresponding changes. Fig. 10 shows the relationship among the factor of tolerance t, unit-cell volume V, the tilt angle of BO6 octahedra, A-site ionic radius RA, B-site ionic radius RB, temperature coefficient of permittivity τc (@1 MHz, −55 °C to 125 °C), temperature coefficient of resonant frequency τf (@7 GHz, 25 °C to 85 °C), dielectric constant εr (@7 GHz), and factor of merit Q × f (@7 GHz) of CSZTY ceramic with variations of x. With the decrease of the factor of tolerance t from 0.939 to 0.895, εr decreases linearly from 33.45 to 29.09, while Q × f increases from 18232 GHz to 23528 GHz, τc increases from −23.78 ppm °C−1 to 4.28 ppm °C−1, and τf decreases from 14.92 ppm °C−1 to −6.05 ppm °C−1. Except for the CSZTY ceramic at x = 0.2, Q × f slightly decreases for the formation of impurity phase Y2O3. The relationship between t and τc observed in this work is similar to the work of Chae-Il Cheon and Jeong-Seog Kim,26 which reported that τc increases with the decrease of t from 0.96 to 0.92. In our work, t is in the range from 0.895 to 0.939, and as t decreases from 0.939 to 0.928, τc quickly tends to zero and flattens out as t decreases from 0.928 to 0.895. At x = 0.15, the CSZTY ceramic presents optimized microwave dielectric properties: εr = 29.8, Q × f = 23528 GHz, τc = 0.50 ppm °C−1, and τf = −4.25 ppm °C−1. Table 5 lists the values of t, εr (@7 GHz), Q × f (@7 GHz), τc (@1 MHz, −55 °C to 125 °C), and τf (@7 GHz, 25 °C to 85 °C) of the CSZTY ceramic and the data from the literature on (Ca,Sr)(Zr,Ti)O3 ceramics with a similar preparation process.
Composition | t | ε | Qxf (GHz) | τ c (ppm °C−1) | τ f (ppm °C−1) |
---|---|---|---|---|---|
CSZTY(x = 0) | 0.939 | 33.45 | 18232 | −23.78 | 14.92 |
CSZTY(x = 0.01) | 0.928 | 31.61 | 18007 | −13.59 | 1.30 |
CSZTY(x = 0.025) | 0.923 | 31.41 | 19062 | −1.20 | −1.90 |
CSZTY(x = 0.05) | 0.917 | 31.23 | 20340 | −0.80 | −1.73 |
CSZTY(x = 0.1) | 0.910 | 30.42 | 22495 | −0.92 | −4.15 |
CSZTY(x = 0.15) | 0.902 | 29.83 | 23528 | 0.50 | −4.25 |
CSZTY(x = 0.2) | 0.895 | 29.09 | 22511 | 4.28 | −6.05 |
Ca0.6Sr0.4Zr0.95Ti0.05O311 | 0.930 | 35.74 | 15734 | −28.26 | 5.62 |
Ca0.75Sr0.25Zr0.95Ti0.05O311 | 0.920 | 35.16 | 17306 | −48.79 | 16.06 |
Ca0.8Sr0.2Zr0.92Ti0.08O326 | 0.933 | 38 | 7403 | −62 | — |
Ca0.8Sr0.2Zr0.96Ti0.04O326 | 0.931 | 34 | 10938 | −15 | — |
Ca0.8Sr0.2ZrO326 | 0.929 | 31 | 15006 | 67 | — |
CaZrO310 | 0.914 | 27 | 16543 | — | −19.98 |
From our work and literature reports, it can be seen that the changes in the ion radius, unit-cell volume, and the tilt angle of BO6 octahedra in the perovskite structure have a significant impact on ion polarization. For (Ca,Sr)(Zr,Ti)O3 ceramics, with the increase of the Ca/Sr ratio, the radius of A-site ions decreases, the tolerance factor decreases, and the dielectric constant decreases; with the increase of the Zr/Ti ratio, the radius of B-site ions increases and t and εr decrease. εr of the CaZrO3 ceramic is the smallest among those of (Ca,Sr)(Zr,Ti)O3 ceramics, and the value is 27. But τf is −19.98 ppm °C−1, which is far from zero. With the increase of the Ti/Zr ratio, τf gradually changes from negative to positive, while εr increases and the value of Q × f decreases significantly. In order to obtain materials with εr of 30, higher value of Q × f, and near zero τf or τc simultaneously, changing the ratios of Ca/Sr and Ti/Zr is not enough. The substitution of Y3+ at the A and B-sites in (Ca,Sr)(Zr,Ti)O3 ceramics can reduce εr, improve the value of Q × f, and quickly regulate τf or τc to near zero, making up for the shortcomings of pure (Ca,Sr)(Zr,Ti)O3 ceramics.
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