The Structure and Microwave Dielectric Properties of MgTi_1−x(Mn_1/3Nb_2/3)_xO₃ Ceramics

Abstract

MgTi_1−x(Mn_1/3Nb_2/3)_xO₃ (x = 0–0.30) ceramics were prepared via the solid-state reaction method. The phase composition, microstructure, bond characteristics, and microwave dielectric properties of MgTi_1−x(Mn_1/3Nb_2/3)_xO₃ (x = 0–0.30) were systematically investigated. The MgTi_1−x(Mn_1/3Nb_2/3)_xO₃ ceramics presented an ilmenite type with an R-3 space group, and the secondary-phase MgTi₂O₅ only existed at x = 0 and 0.30. The introduction of (Mn_1/3Nb_2/3)⁴⁺ effectively suppressed the formation of the MgTi₂O₅ phase. The variation trend of the dielectric constant (ε_r) was the same as relative density. The quality factor (Qf) value was enhanced by the stable microstructure, which was caused via the lattice energy of Ti/(Mn_1/3Nb_2/3)-O bonds. And a high Qf value (353,000 GHz) was obtained for MgTi_1−x(Mn_1/3Nb_2/3)_xO₃ (x = 0.04) ceramics sintered at 1250 °C. In addition, the introduction of Mn²⁺ ions with a larger ionic radius exacerbates the distortion of TiO₆ octahedra, leading to significant fluctuations in the temperature coefficient of the resonance frequency (τ_f) value.

1. Introduction

As 5G communication technology gradually shifts towards the millimeter wave band, the trend towards higher frequencies has further raised the performance requirements for microwave devices. There is an increasing demand for the miniaturization, integration, and lightweight design of microwave circuits. Compared to traditional metallic cavity resonators, dielectric resonators possess advantages such as miniaturization, low cost, high reliability, and high stability. The microwave dielectric performance of materials plays a crucial role in determining their overall performance. To meet this requirement, it is generally necessary to have a moderate dielectric constant (ε_r), high quality factor (Qf), and near-zero temperature coefficient of resonance frequency (τ_f).

MgTiO₃ is an ABO₃ ilmenite-type structure, which has garnered considerable attention from numerous researchers due to its relatively high Qf value (Qf ~ 160,000 GHz). In general, the microwave dielectric properties of MgTiO₃ are affected by intrinsic structural characteristics such as bond characteristics and octahedron distortion [1]. These characteristics can be modified by varying cations at Mg or Ti sites. Researchers have investigated the variations in the Qf value caused by the addition of 36 different dopants in TiO₂ ceramics [2]. It was found that significant improvements in the Qf value occur when the Ti site is substituted with low-valence cations. However, the introduction of low-valence cations solely for Ti substitution may lead to lattice defects. Therefore, to improve the microwave dielectric properties of MgTiO₃ ceramics, the intrinsic structural characteristics were tailored via the substitution of the Ti site [3,4,5,6,7,8,9,10,11]. The substitution of the Ti site in a MgTiO₃ ceramic with (Mn_1/2W_1/2)⁴⁺ reveals that the presence of Mn²⁺ eliminates the detrimental effect of Ti³⁺ on the Qf value of the ceramic and suppresses the formation of the secondary-phase MgTi₂O₅. However, the continuous introduction of Mn²⁺ and W⁶⁺ ions, while suppressing Ti³⁺, does not significantly enhance the Qf value compared to pure MgTiO₃ ceramics. In addition, we have found that (Zn_1/3Nb_2/3)⁴⁺ can enhance the microwave dielectric properties, especially the Qf value, and lower the sintering temperature of MgTiO₃ ceramics [12]. And the τ_f value was related to the structural distortion. Meanwhile, in previous works, there are some relationships between ionic radii and the structure distortion, which relates to the microwave dielectric properties. Furthermore, the existence of Nb⁵⁺ could suppress Ti⁴⁺ to Ti³⁺ and therefore enhance the Qf value [5]. Hence, based on the inhibition of Ti⁴⁺ reducibility by Nb⁵⁺ and Mn²⁺ ions and their larger ionic radii, the (Mn_1/3Nb_2/3)⁴⁺ were considered as an alternative ion to improve the microwave dielectric properties of MgTiO₃. In the present work, MgTi_1−x(Mn_1/3Nb_2/3)_xO₃ (x = 0–0.30) ceramics were synthesized via solid-state reactions, and their phase composition, microstructure, bond characteristics, and microwave dielectric properties were investigated. Furthermore, the correlations among them were analyzed and established in detail.

2. Experimental Procedures

High-purity MgO, TiO₂, MnCO₃, and Nb₂O₅ powders were employed as the raw materials to synthesize the MgTi_1−x(Mn_1/3Nb_2/3)_xO₃ (x = 0, 0.04, 0.12, 0.20 and 0.30) ceramics via the solid state reaction. The raw material was weighed according to the stoichiometric ratio. Next, the mixed powder was placed into the ball milling jar and milled for 4 h. The slurry was dried. Subsequently, the mixed powder was calcined at 1100 °C for 4 h. After calcination, the powder was ball-milled to break the agglomerates and dried again. Subsequently, the powder was mixed with PVA (10 wt%) and pressed into pellets under the pressure of 20 MPa. These pellets were 12 mm in diameter and 6–7 mm in thickness. The pressed disks were pre-heated at 600 °C for 4 h to evaporate PVA and then sintered at 1250–1350 °C for 4 h. The x = 0 sample served as a control sample.

An X-ray diffractometer (XRD) is used to determine the phase composition and crystal structure of a sample under the conditions of Cu-Kα radiation and a scanning range of 10° to 120°. Scanning electron microscopy (SEM) is used to observe the microscopic morphology of ceramic surfaces and is usually shared with Energy Dispersive Spectroscopy (EDS) to analyze the elemental composition and content of the sample surface. The bulk density (ρ_bulk) is measured using Archimedes’ drainage method. Here, the microwave dielectric properties of the ceramic samples were measured based on the Hakki–Coleman method, and the τ_f values were calculated from the resonance frequencies at 25 °C and 85 °C:

$${\tau }_f=\frac{f\left(85 °\mathrm{C}\right)-f\left(25 °\mathrm{C}\right)}{60\times f\left(25 °\mathrm{C}\right)}\times {10}^6$$

(1)

3. Results and Discussion

3.1. Phase Composition and Structure Analysis

Figure 1a shows the XRD patterns of the MgTi_1−x(Mn_1/3Nb_2/3)_xO₃ (x = 0–0.30) ceramics obtained via sintering at 1250 °C. It can be observed that the major phase of MgTiO₃ (R-3, PDF #06-0494) was present in all samples, while the secondary-phase MgTi₂O₅ (PDF #76-2373) appeared only at x = 0 and 0.30 [13]. The results indicated that appropriate amounts of Mn²⁺ and Nb⁵⁺ ions could effectively suppress the formation of the MgTi₂O₅ phase. Figure 1b shows the crystal structure of MgTiO₃, from which it can be seen that this structure consists of two kinds of octahedra, MgO₆ and TiO₆, which are arranged alternately in the order of Mg-Ti-Mg-Ti-...... in the z-axis direction.

In order to further analyze the crystal structure of samples, the XRD patterns of the MgTi_1−x(Mn_1/3Nb_2/3)_xO₃ (x = 0–0.30) ceramics were refined by FullProf software (FullProf 2020.6) [14], and the refinement results are plotted in Figure 2. The refinement curves and XRD patterns agreed well, indicating that the refinement results are reliable. The structural parameters are listed in

Table 1. Lattice parameters of MgTi_1−x(Mn_1/3Nb_2/3)_xO₃ (x = 0–0.30) ceramics at 1250 °C.

x	0	0.04	0.12	0.20	0.30
a (Å)	5.059	5.060	5.067	5.071	5.074
b (Å)	5.059	5.060	5.067	5.071	5.074
c (Å)	13.910	13.915	13.941	13.961	13.991
V (Å3)	308.31	308.55	309.98	310.86	312.00
Wf1 (%)	95.75	100	100	100	91.88
Wf2 (%)	4.25	/	/	/	8.12
Mg-O(1) 1 (Å)	2.034	2.055	2.050	2.031	2.058
Mg-O(1) 2 (Å)	2.175	2.167	2.175	2.171	2.170
Ti/(Mn1/3Nb2/3)-O(1) 1 (Å)	1.878	1.868	1.875	1.891	1.884
Ti/(Mn1/3Nb2/3)-O(1) 2 (Å)	2.093	2.089	2.092	2.110	2.093

W_f1: weight fraction of MgTiO₃ phase; W_f2: weight fraction of MgTi₂O₅ phase. ¹, ² represent two distinct types of chemical bonds that are exported using the FullProf software.

. The cell parameters (a, b, c) and cell volume (V) kept increasing with increasing x. The main contribution to the ionic radius of (Mn_1/3Nb_2/3)⁴⁺ (0.703 Å), which was larger than that of Ti (0.605 Å), entered into the lattice and resulted in the expansion of the lattice [9,15]. By further observation, it was found that the bond lengths showed irregular variations. There was a correlation between these chemical bond changes and microwave dielectrics [16,17].

3.2. Micromorphology

Figure 3 shows the microscopic morphology of MgTi_1−x(Mn_1/3Nb_2/3)_xO₃ ceramics sintered at different temperatures. In comparison to the x = 0 sample (refer to Supplementary Figure S1), a discernible trend was observed where the grain size progressively increased and the number of pores gradually diminished with the increasing value of x. This indicated that the incorporation of Mn²⁺ and Nb⁵⁺ ions imparted a denser structure to the ceramics while simultaneously resulting in the formation of delicate specks on the surface of the samples. Upon further observation, the grain size gradually increased with the increase in temperature at the same x. Abnormal grain growth occurred at 1350 °C, indicating that the temperature had a promoting effect on the grain growth. It also demonstrated that the introduction of Mn²⁺ and Nb⁵⁺ ions could reduce the sintering temperature of the system and improve the sintering behaviors of the ceramics.

In order to analyze the elemental species and content of the ceramic surface, EDS analysis was performed on the surface of MgTi_0.96(Mn_1/3Nb_2/3)_0.04O₃ ceramics sintered at 1250 °C. The test areas of the ceramic surface and the elemental composition of each test area are marked in Figure 4, from which it can be seen that both areas contained only Mg, Ti, Mn, Nb and O elements, and Mg:(Ti, Mn, and Nb) = 1:1, which also confirms the XRD analysis results that Mn and Nb ions enter into the lattice and form a solid solution.

3.3. Microwave Dielectric Properties

Figure 5 illustrates the trends of the ε_r values of MgTi_1−x(Mn_1/3Nb_2/3)_xO₃ ceramics at 1250 °C, along with the associated influencing factors. A variation in ε_r is typically closely intertwined with factors such as relative density, the presence of a second phase, and the total distortion [18,19]. When examining the impact of relative density on the ε_r value of ceramics, it is often crucial to account for the influence of porosity. To address this, a correction was applied to the ε_r value, yielding the corrected dielectric constant (ε_c), using the following equation [20]:

$$P=1-{\rho }_r$$

(2)

$${\epsilon }_c={\epsilon }_r(1+1.5P)$$

(3)

where P is the porosity and ρ_r is the relative density.

Through a careful analysis of Figure 5, it becomes evident that both the actual dielectric constant (ε_r) and the corrected dielectric constant (ε_c) exhibited an inverse trend compared to the total distortion within the phase range from x = 0 to x = 0.04. Notably, this observation can be attributed to the presence of a second phase, MgTi₂O₅, at x = 0, which displayed a dielectric constant of ε_r = 17.4, while MgTiO₃ exhibited ε_r = 17 [21,22]. Therefore, we can infer that the influence of the second phase during this range was responsible for this phenomenon. In order to investigate the impact of the second phase (MgTi₂O₅) on the ε_r value of MgTi_1−x(Mn_1/3Nb_2/3)_xO₃ ceramics, we employed a mixed law equation to calculate the theoretical permittivity (ε_theo) of the ceramics. The equation utilized is as follows [23]:

$$\ln {\epsilon }_{theo}=V_1\ln {\epsilon }_{theo1}+V_2\ln {\epsilon }_{theo2}$$

(4)

where V₁, V₂, ε_theo1, and ε_theo2 denote the volume fraction and theoretical dielectric constant of each phase.

In the depicted range from x = 0.04 to x = 0.3, as observed in Figure 5, we observed remarkable alignment between the actual dielectric constant (ε_r) and the total distortion (δ). This alignment strongly suggests that the total distortion (δ) exerted the most dominant influence on the ε_r value within this interval. This phenomenon can be attributed to the direct relationship between an increase in total distortion and a subsequent rise in the ion polarization rate, ultimately resulting in a larger dielectric constant (ε_r) value. Conversely, a decrease in total distortion led to a lower ion polarization rate, consequently resulting in a smaller ε_r value. The total distortion of MgO₆ and TiO₆ could be quantified by employing the following equation [23]:

$$\delta =\frac{1}{6}{{\displaystyle \sum \left(\frac{R_i-\stackrel{-}{R}}{\stackrel{-}{R}}\right)}}^2$$

(5)

An intriguing observation arises from the analysis of Figure 5, where a distinct inverse relationship emerged between the actual dielectric constant (ε_r) and the modified dielectric constant (ε_c) within the interval ranging from x = 0.2 to x = 0.3. The underlying disparity could likely be attributed to the influence of porosity on the relative density of the ceramics, consequently impacting the variability in ε_r values. Moreover, it is worth highlighting the close correspondence between the fluctuation in ε_r values within this range and the variation in total distortion (δ). This suggests that the changes in ε_r values during this specific interval were governed by both δ and porosity. Although the presence of a secondary phase did contribute to the alteration in ε_r values, its influence appeared to be of secondary significance.

Figure 6a demonstrates the trend of Qf values of MgTi_1−x(Mn_1/3Nb_2/3)_xO₃ (x = 0–0.30) ceramics sintered at different temperatures, and it can be seen from the figure that the sample presented the highest Qf at x = 0.04 and a sintering temperature of 1250 °C. In addition, Qf showed a decreasing trend when the x value or the temperature increased, which indicates that Mn and Nb ions were introduced to lower the sintering temperature of the system and also increase the Qf of the system. To further analyze the factors affecting the Qf in this experiment, the Qf of MgTi_0.96(Mn_1/3Nb_2/3)_0.04O₃ ceramics obtained via sintering at 1250 °C was investigated to explore the influencing factors.

There have been numerous studies that have delved into the factors influencing microwave dielectric properties [24,25,26,27]. In general, Qf is mainly affected by both intrinsic and non-intrinsic factors. Both intrinsic and extrinsic factors contribute to the total loss of a material, where intrinsic losses primarily depend on the crystal structure, while extrinsic losses arise from second phases, crystal defects, and porosity, among others [8,9,11,28]. In this section, the impact of chemical bond properties on crystal structure and microwave dielectric properties is investigated using the complex chemical bond theory.

According to the complex chemical bond theory, each compound crystal can be decomposed into a superposition of several binary crystal sub-formulas (A_mB_n), where A and B represent different types of cations and anions, respectively [17]. Thus, MgTi_1−x(Mn_1/3Nb_2/3)_xO₃ (x = 0–0.30) can be decomposed into the following binary crystal sub-formulas:

$$\begin{array}{l}MgT{i}_{1-x}{\left(M{n}_{1/3}N{b}_{2/3}\right)}_x{O}_3=M{g}_{1/2}O{(1)}^1{}_{3/4}+M{g}_{1/2}O{(1)}^2{}_{3/4}+T{i}_{1-x/2}O{(1)}^1{}_{3-3x/4}\\ +T{i}_{1-x/2}O{(1)}^2{}_{3-3x/4}+{\left(M{n}_{1/3}N{b}_{2/3}\right)}_{x/2}O{(1)}^1{}_{3x/4}+{\left(M{n}_{1/3}N{b}_{2/3}\right)}_{x/2}O{(1)}^2{}_{3x/4}\end{array}$$

(6)

In general, lattice energy is defined as the energy required to separate one mole of a crystal into gaseous free ions, reflecting the vibrational energy of ions and the stability of chemical bonds within the crystal [29]. Higher lattice energy (U) results in lower internal losses caused by lattice polarization under an electric field, leading to a higher Qf [30]. For this purpose, we calculated the lattice energy equation based on Equations (7)–(10).

$$U_{cal}={\displaystyle {\sum }_{\mu }{U}_b^{\mu }}$$

(7)

$$U_b^{\mu }=U_{bc}^{\mu }+U_{bi}^{\mu }$$

(8)

$$U_{bc}^{\mu }=2100m\frac{{\left(Z_{+}^{\mu }\right)}^{1.64}}{{\left(d^{\mu }\right)}^{0.75}}{f}_c^{\mu }$$

(9)

$$U_{bi}^{\mu }=1270\frac{\left(m+n\right)Z_{+}^{\mu }{Z}_{-}^{\mu }}{d^{\mu }}\left(1-\frac{0.4}{d^{\mu }}\right)f_i^{\mu }$$

(10)

The Qf value variations in MgTi_0.96(Mn_1/3Nb_2/3)_0.04O₃ ceramics obtained via sintering at 1250 °C are presented in Figure 6b. Meanwhile, the lattice energy and total lattice energy of the Mg-O bond and Ti/(Mn_1/3Nb_2/3)-O bond in each component are plotted in Figure 6b. It can be observed that the lattice energy of the Mg-O bond showed minimal variation, whereas the lattice energy of the Ti/(Mn_1/3Nb_2/3)-O bond and the overall total lattice energy decreased with increasing x. In addition, the lattice energy of the Ti/(Mn_1/3Nb_2/3)-O bond was higher compared with that of the Mg-O bond, indicating that the Ti/(Mn_1/3Nb_2/3)-O bond made a significant contribution to the total lattice energy and had more influence on the Qf when sintered at 1250 °C [17]. The sample with x = 0.04 had the highest Qf value; however, the corresponding total lattice energy was lower at this time compared to the sample with x = 0. In general, the higher the lattice energy, the higher the Qf, but the Qf of the sample with x = 0 was lower than that of the sample with x = 0.04 due to the presence of the second-phase MgTi₂O₅ (Qf = 47,000 GHz) in the sample with x = 0 [17,31]. At x > 0.04, the trends of lattice energy and Qf were in agreement, indicating that lattice energy and the second phase are the main factors that affected Qf in this experiment.

τ_f is an essential consideration in the practicality of microwave dielectric ceramics, which represents the temperature stability of microwave components in the operating environment. According to Equation (11), the variation in τ_f is closely related to the dielectric constant temperature coefficient (τ_ε), and Equation (12) is the expression for τ_ε obtained by differentiating the Clausius–Mossotti equation [32,33].

$${\tau }_f=-\left(\frac{{\tau }_{\epsilon }}{2}+{\alpha }_L\right)$$

(11)

$$\begin{array}{ll}{\tau }_{\epsilon }& =\frac{\left(\epsilon -1\right)\left(\epsilon +2\right)}{\epsilon }\left[\frac{1}{{\alpha }_D}{\left(\frac{\partial {\alpha }_D}{\partial T}\right)}_V+\frac{1}{{\alpha }_D}{\left(\frac{\partial {\alpha }_D}{\partial V}\right)}_T{\left(\frac{\partial V}{\partial T}\right)}_P-\frac{1}{V}{\left(\frac{\partial V}{\partial T}\right)}_P\right]\\ & =\frac{\left(\epsilon -1\right)\left(\epsilon +2\right)}{\epsilon }\left(A+B+C\right)\end{array}$$

(12)

where α_L is considered as a constant, 10 ppm/°C. α_D and V represent the polarizability of the sample and the volume of a small sphere. Part A is a dependence of polarizability on temperature; Part B represents an increase in the polarizability of a constant number of particles with the increment in the available volume while the temperature increases; Part C presents the decrease in the number of polarizable particles per unit volume while the temperature increases [34]. Since the Parts B and C have similar magnitudes and opposite signs, τ_ε is generally determined by Part A. In addition, Part A is related to the restoring force of chemical bonds, which is in turn correlated with the degree of structural distortion [33]. And this structural alteration will have an impact on τ_f. In this section, we analyze the effect of TiO₆ octahedral distortion (∆_Ti) on τ_f. Therefore, we calculate ∆_Ti in the system using Equation (13) and judge the magnitude of the bond-restoring force in its different states according to the degree of distortion of the TiO₆ octahedra, which is related to the polarizability and thus affects the value of τ_ε, which is finally reflected in τ_f.

$${\Delta }_{Ti}=\frac{1}{6}\times \sum {\left(\frac{R_i-R_{ave}}{R_{ave}}\right)}^2$$

(13)

Figure 7 plots the trends of τ_f and ∆_Ti for MgTi_1−x(Mn_1/3Nb_2/3)_xO₃ (x = 0–0.30) ceramics sintered at 1250 °C. From Figure 7, it can be observed that the trends of τ_f and ∆_Ti were opposite, with a decrease in distortion indicating an increase in recovery. Recovery is inversely proportional to polarization capacity. Therefore, an increase in recovery leads to a decrease in polarization capacity, resulting in a decrease in the value of Part A. This decrease in Part A also causes a decrease in τ_f, thereby affecting its value and causing it to shift in the positive direction.

Figure 8 provides a comparative analysis of various MgTiO₃-based ceramics [3,4,5,6,7,8,9,10,12,35]. However, in the case of most ion-substituted MgTiO₃ ceramics, achieving high Qf values typically requires modifications to the structure of the oxygen octahedra. In our study, we successfully adjusted the structure of TiO₆ octahedra by introducing (Mn_1/3Nb_2/3)⁴⁺ substitutions. This resulted in significantly higher Qf values and improved τ_f values, all while using lower sintering temperatures. Notably, the MgTi_1−x(Mn_1/3Nb_2/3)_xO₃ ceramics with x = 0.04, sintered at 1250 °C, exhibited the most exceptional performance. These findings indicate that by precisely adjusting the crystal structure, it becomes possible to modify the microwave dielectric properties, offering promising prospects for practical applications.

4. Conclusions

The investigation of MgTi_1−x(Mn_1/3Nb_2/3)_xO₃ (x = 0–0.30) ceramics revealed the presence of the MgTiO₃ phase, while MgTi₂O₅ was exclusively detected at x = 0 and x = 0.30. The observed variations in ε_r values demonstrated a correlation with the relative density and molecular polarization rate. The P-V-L theory supports the notion that higher lattice distortion leads to enhanced Qf values, which was evident at x = 0.04. Consequently, the substitution of Ti sites with (Mn_1/3Nb_2/3)⁴⁺ ions emerged as a promising strategy for improving the microwave dielectric properties of the ceramics. This substitution induced significant distortions in the TiO₆ octahedra, resulting in increased bond-restoring power. These structural modifications led to the emergence of τ_ε effects, ultimately manifested in τ_f values. Remarkably, the x = 0.04 MgTi_1−x(Mn_1/3Nb_2/3)_xO₃ ceramics exhibited outstanding microwave dielectric properties when sintered at 1250 °C, with ε_r = 17, Qf = 353,000 GHz, and τ_f = −69 ppm/°C. Consequently, these MgTi_1−x(Mn_1/3Nb_2/3)_xO₃ ceramics hold substantial potential for applications in microwave communications. The findings presented in this paper also inspire novel research directions aimed at enhancing Qf values in future ceramic products.