Structural Evolution and Microwave Dielectric Properties of Ba_1–xSr_xTi₄O₉, (0.0 ≤ x ≤ 0.06) Ceramics

Abstract

The structural, microstructural, and microwave dielectric properties of Ba_1–xSr_xTi₄O₉, (0.0 ≤ x ≤ 0.06) ceramics samples synthesized by a conventional route were investigated. These structural, microstructural, and dielectric properties were recorded using X-ray diffraction (XRD), scanning electron microscopy (SEM), and Fourier transform infrared (FTIR) and impedance analyzer spectroscopies. Ti–O octahedral distortion was observed due to Sr²⁺ addition. The microwave dielectric properties were interrelated with various Sr²⁺ concentrations. Excellent microwave dielectric properties, i.e., high relative permittivity (ϵ_r = 71.50) and low dielectric loss (tan δ = 0.0006), were obtained.

Introduction

Microwave dielectric devices are used in advanced technological systems such as radar, satellite receiver modules, and mobile telephones.¹ The dielectric material, which is used in telecommunication devices, is termed dielectric resonators (DRs). Dielectric resonators may be used to stabilize microwave oscillators and microwave filter frequencies. Barium titanate (BaTiO₃) and barium tetratitanate (BaTi₄O₉) are candidate materials for DRs in microwave telecommunication and satellite broadcasting.² Microwave DRs provide important advantages in terms of temperature stability, compactness, light weight, and comparatively low costs in the processing of high-dependence frequency devices.³ The physical characteristics required for DRs are as follows.

• (i)High relative permittivity (ε_r) to attain reduction of modules in the interpretation of (1/ε_r²), i.e., size dependence.
• (ii)High quality factor (Q × f) values to reduce tangent loss.
• (iii)Small temperature coefficient of resonant frequency (τ_f) for stabilization of resonant frequency.

BaTiO₃, BaTi₄O₉, and doped BaTi₄O₉ compounds meet these basic requirements for the application of DRs; for example, ε_r = 39.11, Q × f = 10,700 GHz, and τ_f = + 14.2 ppm/°C.⁴ However, it is essential for the synthesized dielectric ceramics to have the required microwave dielectric properties. Thus, the processing of single-phase ceramics is necessary to investigate different characterizations. The mixed oxide route involves a high calcination temperature during the reaction of BaCO₃ and TiO₂ (raw materials), and secondary phases may also be formed during the calcination process.⁵⁻⁷ Additionally, the product may be contaminated with impurities from grinding media. Nagas et al. reported the effects of different additives on the phase and microwave dielectric properties of BaTiO₃ and BaTi₄O₉ ceramics.⁸ The dielectric and structural properties of BaTi₄O₉ with different dopants have been studied in the microwave-frequency range.⁹⁻¹³ The different types of additives, i.e., Sr in BaTi₄O₉ ceramics, result in multiple phases including BaTi₄O₉, Ba₂Ti₉O₂₀, and TiO₂.¹¹ Kolar et al.¹⁴ and Negas et al.¹⁵ determined the phases and investigated the microwave dielectric properties with a relatively lower frequency at 1 MHz. Several studies have been executed to improve the microwave dielectric properties of BaTi₄O₉ ceramics by doping different additives, i.e., Sr²⁺, Ca²⁺, Pb²⁺, and Bi²⁺ ions for Ba²⁺ site-ion and Zr⁴⁺ and Sn⁴⁺ ions for Ti⁴⁺ site-ion.^16,17 Other synthesis routes such as sol gel and co-precipitation may also use to synthesize these products.^18,19

Barium tetratitanate (BaTi₄O₉) ceramics is one of the well-known dielectric materials and has been studied by numerous researchers for use in dielectric resonators, thermistors, and electro-optic devices.²⁰ Due to its importance, in the present work, we studied the effect of Sr on phase, surface morphology, and the dielectric properties of BaTi₄O₉ ceramics using a controlled mixed oxide solid-state processing route to prepare (Ba_1–xSr_x)Ti₄O₉, 0.0 ≤ x ≤ 0.06. These products have been analyzed using X-ray diffraction (XRD), scanning electron microscopy (SEM), and Fourier transform infrared (FTIR) spectroscopy. The dielectric properties of products were measured using impedance spectroscopy.

Results and Discussion

Phase Analysis

The XRD pattern of (Ba_1–xSr_x) Ti₄O₉, 0.0 ≤ x ≤ 0.06 sintered ceramics is shown in Figure 1. The XRD studies revealed the formation of the orthorhombic (Amm2) structured base composition of barium tetratitanate (BaTi₄O₉), which matches with ICDD/PDF card # 034-0070. It is suggested that Sr²⁺ is incorporated in the lattice of the base composition to partially replace Ba²⁺ ions. A shift of XRD peaks was detected toward higher Bragg-angle (2θ) values with increasing Sr²⁺ content in (Ba_1–xSr_x)Ti₄O₉. The shifting may be due to the substitution of relatively smaller cations of Sr²⁺ (R_Sr = 1.44 Å) for Ba²⁺(R_Ba = 1.61 Å) following the Brags diffraction law (2d Sin θ = mλ).^21,22 A peak at 32.4° emerges with an increase in Sr²⁺, which is attributed to the transformation of the structure from orthorhombic (Amm2) at x = 0.0 to tetragonal (I4/m) at x = 0.02, 0.04 and then to cubic (Pm3m) at x = 0.06. The variation in lattice parameters with increasing Sr²⁺ content is attributed to the phase transition from orthorhombic to tetragonal and then to the cubic structure as listed in Table 1, while Table 2 represents the XRD data of the base composition (BaTi₄0₉).

Figure 1.

XRD pattern of (Ba_1–xSr_x) Ti₄O₉, 0.0 ≤ x ≤ 0.06 ceramics.

Table 1. Structural Data of (Ba_1–xSr_x) Ti₄O₉, 0.0 ≤ x ≤ 0.06 Ceramics.

X	structure	space group	a (Å)	b (Å)	c (Å)
0.00	orthorhombic	Amm2	6.29400	14.5324	3.79720
0.02	tetragonal	I4/m	10.1434	10.1434	2.96795
0.04	tetragonal	I4/m	10.1434	10.1434	2.96795
0.06	cubic	Pm3m	3.89800	3.89800	3.89800

Table 2. X-ray Diffraction Data for the Base Composition (BaTi₄0₉) at λ = 0.154 nm.

2θexp	2θcalc	Iexp	h	k	l	dexp	dcalc
18.85	18.63	105.82	1	2	0	4.70211	4.75713
22.45	23.14	140.18	1	3	0	3.95557	3.83916
24.55	24.20	366.33	0	1	1	3.62176	3.67334
28.20	28.34	163.72	2	0	0	3.16072	3.14543
32.30	33.15	303.62	1	3	1	2.76826	2.69921
35.30	36.08	184.69	2	0	1	2.53956	2.48643
38.39	37.61	174.98	2	1	1	2.34196	2.38872
42.55	42.32	195.27	2	5	0	2.12212	2.13312
43.60	43.06	168.88	3	0	0	2.07342	2.09816
45.65	45.99	206.25	1	7	0	1.98496	1.97107
47.75	47.30	179.09	2	6	0	1.90244	1.91949
49.60	49.59	156.41	0	2	2	1.83573	1.83607
54.80	54.51	174.53	0	4	2	1.67319	1.68141
56.85	56.56	199.23	2	0	2	1.61762	1.62522

The particle size and lattice strain of the Ba_1–xSr_xTi₄O₉, (0.00 ≤ x ≤ 0.06) sample were determined using the Williamson–Hall (W–H) technique from the broadening of the XRD peaks.²³

1

The equation represents a straight line, where ε is the gradient (slope) of the line and kλ/D is the y-intercept.

Consider the standard equation of a straight line,

2

Now, we plot 4 sin θ on the x-axis and β cos θ on the y-axis.

The value of the strain (ε_W-H) is given by the value of “m”, which represents the gradient (slope) of the line, and the crystallite size can be calculated from the y-intercept kλ/D.

Figure 2a–d shows Williamson–Hall (W–H) plots for Ba_1–xSr_xTi₄O₉, (0.00 ≤ x ≤ 0.06) ceramics. The W–H is used for deconvoluting shapes (crystalline shapes) and strain that contributes to X-ray line broadening because Scherrer’s formula does not take into account the strain contribution.

Figure 2.

Williamson–Hall plot of Ba_1–xSr_xTi₄O₉ with Sr content (a) X = 0.00, (b) X = 0.02, (c) X = 0.04, and (d) X = 0.06.

Therefore, the average crystallite size, dislocation density, and strain of W–H lie in the 2.9449–11.6128 Å, 0.74152 × 10^–6–271.667 × 10^–6, and 1.1949 × 10^–3–22.871 × 10^–3 ranges for Ba_1–xSr_xTi₄O₉, (0.00 ≤ x ≤ 0.06) ceramics, respectively, as shown in Table 3.

Table 3. Williamson–Hall (W–H) Calculated Crystallite Size (D_W-H), Dislocation Density (δ_W-H), and Strain (η_W-H) Ba_1–xSr_xTi₄O₉, (0.00 ≤ x ≤ 0.06).

composition	DW-H (nm)	δW-H (×10–6 nm–2)	ηW-H (×10–3)
0.00	0.29449	11.5301	4.7118
0.02	0.06067	271.667	22.871
0.04	0.13191	57.4710	10.519
0.06	1.16128	0.74152	1.1949

Mathematically, the dislocation density (δ) was calculated using the equation²⁴

3

Dislocation strongly influences many other properties of materials. As the dopant element perfectly replaces the host ions in the crystal lattice, it improves the crystal structure and produces very small crystal defects that can be negligible.

The lattice strain (η) was calculated through the equation^25,26

4

In Table 3, the deviation in the calculated lattice strain and crystallite sizes of all prepared Ba_1–xSr_xTi₄O₉, (0.00 ≤ x ≤ 0.06) ceramics samples with compositions is shown. When the concentration of the dopant element is increased, the microstrain decreases due to the size of the dopant element being greater than the host ions, as shown in Table 3.

Microstructural Analysis

The SEM images of (Ba_1–xSr_x) Ti₄O₉, 0.0 ≤ x ≤ 0.06 ceramics sintered at 1300 °C in air for 2 h, polished, and thermally etched are shown in Figure 3. The SEM images indicated a dense microstructure with no obvious pores and grains, exhibiting elongated platelike morphologies for the base composition (x = 0.00), which is consistent with previous reports for the orthorhombic-structured BaTi4O₉.^27,28 The grain morphologies were observed to change from elongated to rectangular with an increase in the Sr²⁺ content. The grain size for x = 0.00 is about 10 × 1 μm² and decreases with increasing Sr²⁺ content. The variation of relative densities (ρ_r) with increasing Sr²⁺ content is shown in Table 4. The maximum theoretical density achieved is 4.94 g/cm³ as listed in Table 3. The increase in density may affect the value of the dielectric constant.¹¹

Figure 3.

SEM images of (Ba_1–xSr_x) Ti₄O₉, 0 ≤ x ≤ 0.06 ceramics polished and thermally etched: (a) x = 0.00, (b) x = 0.02, (c) x = 0.04, and (d) x = 0.06 indicating a decrease in grain size and change in grain morphologies with an increase in Sr²⁺ content.

Table 4. Density Parameters and Dielectric Properties of (Ba_1–xSr_x) Ti₄O₉, 0.0 ≤ x ≤ 0.06 Ceramics^a.

X	ρa (g/cm3)	ρt (g/cm3)	ρr (%)	tan δ	εr
0.00	4.26	4.402	96.77	0.0008	21.93
0.02	4.40	4.840	90.90	0.0006	47.84
0.04	4.40	4.940	89.07	0.0043	71.50
0.06	4.07	4.540	89.64	0.0044	52.50

^aNote: ρ_a = apparent density, ρ_t = theoretical density, and ρ_r = relative density.

FTIR Spectroscopy

The FTIR spectra of (Ba_1–xSr_x) Ti₄O₉, 0.0 ≤ x ≤ 0.06 ceramics have been studied as shown in Figure 4. Very strong absorption peaks appear near 800 and 1400 cm^–1 at x = 0.00, while minor peaks are also observed at x > 0.00 near 1600 cm^–1. These peaks revealed the Ti–O octahedral vibrations according to previous studies on titanates.²⁹ Due to the addition of Sr²⁺, the concentration in the solid solution of BaT₄O₉ ceramics is been shifted to higher wavenumbers. Sun et al. reported that only one oxygen vacancy can be used to replace Ba²⁺ ion, while the remaining three oxygen vacancies were used to replace the produced Ti⁴⁺ ion using respective additives.³⁰ Therefore, Ti–O octahedra are easily distorted or damaged in this way. Some vibrational modes were observed in the FTIR spectrum. Therefore, relative studies of the FTIR spectrum further support the development of redispersibility of polycrystalline BaT₄O₉ ceramic dielectrics.

Figure 4.

FTIR spectra of (Ba_1–xSr_x) Ti₄O₉, 0.0 ≤ x ≤ 0.06 ceramics.

Microwave Dielectric Properties

The microwave dielectric properties of (Ba_1–xSr_x) Ti₄O₉, 0.0 ≤ x ≤ 0.06 ceramics have also been investigated, as shown in Figure 5. The dielectric constant (ε_r) varies from 21.9 3 to 71.50, while the variation in dielectric loss (tan δ) with Sr²⁺ is shown in Table 4. The maximum value of tan δ (0.0006) was observed. The frequency-dependent quality factor (Q) is a dimensionless physical quantity, and quantitatively, it is expressed in terms of Q × f.³¹⁻³⁵

Figure 5.

Variation of ε_r with the frequency of (Ba_1–xSr_x) Ti₄O₉, 0.0 ≤ x ≤ 0.06 ceramic.

The variations of tan(δ) with frequency (f) for various Sr²⁺ contents in (Ba_1–xSr_x) Ti₄O₉, 0.0 ≤ x ≤ 0.06 are shown in Figure 6. The orientation polarization decreases with increasing frequency and results in an increase in dielectric loss, which may be attributed to the time lag between flipping dipoles and the applied electric field.^1,36−38 Microwave dielectric material is usually characterized by high relative permittivity and a low tangent loss. The theoretical justification is very important for this case in which ionic crystals with an optical mode of vibrations resonate at a frequency of (10¹³ Hz). In the frequency range from approximately 10⁹ to 10¹¹ Hz, the dielectric dispersion theory shows the contribution to polarization from the ionic displacement to be nearly constant and the loss to increase with frequency.³⁹

Figure 6.

Variation of tan δ with frequency (f) for various Sr²⁺ contents in (Ba_1–xSr_x) Ti₄O₉, 0.0 ≤ x ≤ 0.06 ceramics.

Conclusions

The structural, microstructural, and microwave dielectric properties of (Ba_1–xSr_x)Ti₄O₉, 0.0 ≤ x ≤ 0.06 sintered ceramics were investigated via a solid-state route. It is found that the dielectric constant (ε_r) and dielectric loss (tan δ) values improved with Sr²⁺ content. The (Ba_0.98Sr_0.02)Ti₄O₉ ceramics was found to have the best ε_r and tan δ values. The microwave dielectric properties of (Ba_0.98Sr_0.02)Ti₄O₉ ceramics intensely depend upon density. Outstanding microwave dielectric properties of ε_r ∼ 47.84 and tan δ ∼ 0.0006 were obtained for (Ba_0.98Sr_0.02)Ti₄O₉ ceramics sintered at 1300 °C for 2 h. We obtained excellent microwave dielectric properties in this study for the application of microwave wireless communication systems.

Experimental Procedure

BaCO₃ (purity 99.0%, Chemdad, China), SrCO₃ (purity 99.5%, ABSCO, U.K.), and TiO₂ (purity 99.9%, Sigma) were chosen as raw starting materials to prepare (Ba_1–xSr_x)Ti₄O₉, 0.0 ≤ x ≤ 0.06 ceramics material for microwave dielectric devices. The raw materials, i.e., BaCO₃, SrCO₃, and TiO₂, were thoroughly mixed according to the (Ba_1–xSr_x) Ti₄O₉, 0 ≤ x ≤ 0.06 stoichiometric ratios, where the mole ratio of A site-ion and B site-ion was 1:4. Distilled water was added to the weighed raw material powder in a polyethylene jar container along with 5 mm diameter zirconia balls and then milled by horizontal ball milling for 24 h. The mixture powders were dried at 100 °C for 24 h in an air atmosphere, and after drying, the reactant mixture was loaded in an alumina crucible and calcined at 1000 °C for 3 h in air at 10 °C/min in a heating/cooling rate. After calcination, the product powder was ground and then pressed into green body discs (5 mm thickness and 10 mm diameter) under a pressure of 80 MPa using a manual pellet press (CARVER). The pellet samples were sintered at 1300 °C for 2 h in air with a heating/cooling rate of 10 °C/min. The crystalline phases of the calcined (Ba_1–xSr_x) Ti₄O₉, 0.0 ≤ x ≤ 0.06 ceramics samples were identified using X-ray diffraction (XRD) (JDX-3532, JEOL, Japan) with a Cu Kα (λ = 0.15406 nm) radiation source operated at 40 mA and 40 kV in a wide range of Braggs angle 2θ (20° < 2θ < 80°) at a scanning rate of 2°/min. The surface morphology information was obtained using SEM (JSM-5910, JEOL Japan), while the microwave dielectric properties of the sintered samples were measured at microwave frequencies using impedance spectroscopy (Agilent 4287A).

Author Contributions

This work was carried out in collaboration with all authors. A.A. prepared samples and wrote the original draft of the manuscript. A.Z. performed the final writing review, corrections, and editing. M.A. helped in methodology and measurements. S.A.A. and M.M. prepared content analysis and graphical arrangements. K.B. helped with software and validation. K.A. and M.A. helped with formal analysis and provided funding acquisition. All authors have read and approved the final manuscript.

The authors declare no competing financial interest.