Cu²⁺-Ion-Substitution-Driven Microstructure and Microwave Dielectric Properties of Mg_1−xCu_xAl₂O₄ Ceramics

Abstract

In this work, Cu-substituted MgAl₂O₄ ceramics were prepared via solid-state reaction. The crystal structure, cation distribution, and microwave dielectric properties of Mg_1−xCu_xAl₂O₄ ceramics were investigated. Cu²⁺ entered the MgAl₂O₄ lattice and formed a spinel structure. The substitution of Cu²⁺ ions for Mg²⁺ ions contributed to Al³⁺ ions preferential occupation of the octahedron and changed the degree of inversion. The quality factor (Qf) value, which is correlated with the degree of inversion, increased to a maximum value at x = 0.04 and then decreased. Ionic polarizability and relative density affected the dielectric constant (ε_r) value. The temperature coefficient of the resonant frequency (τ_f) value, which was dominated by the total bond energy, generally shifted to the positive direction. Satisfactory microwave dielectric properties were achieved in x = 0.04 and sintered at 1550 °C: ε_r = 8.28, Qf = 72,800 GHz, and τ_f = −59 ppm/°C. The Mg_1−xCu_xAl₂O₄ solid solution, possessing good performance, has potential for application in the field of modern telecommunication technology.

1. Introduction

The microwave dielectric ceramics have been extensively applied in various fields, including fifth-generation wireless systems, intelligent transmission systems, and ultrahigh-speed wireless local area networks [1,2,3]. In the application of millimeter waves, there is an urgent requirement for microwave dielectric ceramics with excellent performance in the following areas: a high quality factor (Qf) to enable microwave frequency selectivity, a low dielectric constant (ε_r) to shorten the delay time of signal propagation, and a near-zero temperature coefficient of resonant frequency (τ_f) to ensure the stability of frequency against temperature changes [4,5]. However, few single-phase materials can meet these requirements simultaneously due to the mutual restrictions of the three parameters. In general, ideal ε_r and Qf values can be obtained by selecting material systems, whereas the near-zero τ_f value is tailored through two materials with opposite τ_f values [6,7,8,9]. However, this approach tends to deteriorate the ε_r and Qf values.

Previous studies have found that the τ_f value is related to octahedral distortion in some ceramic crystals [10,11]. Microwave dielectric ceramics with superior τ_f values can be obtained by adjusting the distortion of the octahedron without deteriorating the ε_r and Qf values [4]. Therefore, it is important to improve the microwave dielectric properties utilizing the crystal structure. In general, the spinel structural degrees of freedom, such as the cell parameters, the oxygen fractional coordinates, and degrees of inversion, can be tailored via substitution [12]. MgAl₂O₄ is known to have a typical cubic spinel belonging to symmetry group Fd-3m (227); the molecular formula is [Mg_1−λAl_λ]^IV[Al_2−λMg_λ]^VIO₄, where λ value, which is related to the degree of inversion [13,14], represents the occupation of Al³⁺ cations at tetrahedral site.

MgAl₂O₄ ceramic, which generally exhibits a Qf value of ~68,900 GHz (the highest Qf value is over 200,000 [15]) and a low ε_r value (~8.75), is one of the candidate material for a millimeter-wave communication substrate [16]. However, it has a large negative τ_f value (~−75 ppm/°C). It has been reported that MgAl₂O₄-based composite dielectric ceramics, such as MgAl₂O₄-TiO₂ and MgAl₂O₄-(Ca_0.8Sr_0.2)TiO₃, have near-zero τ_f values [6,7]. However, the ε_r and Qf values are also deteriorated in this system. It is worth mentioning that the τ_f value in MgAl₂O₄ can be improved through the crystal structure [17,18]. Previously, in MgAl₂O₄ ceramics, it has been shown that the enhancement in Qf value corresponds to the cation distribution [19]. Moreover, the degree of inversion in MgAl₂O₄ ceramics, prepared by the solid-state reaction or molten-salt reaction routes, has also been investigated [15]. A high degree of inversion represents a high Qf value, and the preferential occupation of Al³⁺ could enhance the covalency of M-O bonds in a [MO₄] tetrahedron of MgAl₂O₄ (M = Mg and Al). Consequently, the cation distribution of Al³⁺ in MgAl₂O₄ can be discussed to ameliorate the microwave dielectric properties.

In general, the ionic radius of Cu²⁺ ion is close to that of Mg²⁺ ions [4,20,21], which is beneficial for forming Mg_1−xCu_xAl₂O₄ solid solutions. Additionally, a significant Jahn–Teller effect can be observed when Cu²⁺ ions occupy the octahedral site in a spinel structure [22]. This can contribute to the regulation of the microstructure of MgAl₂O₄. In addition, CuO can also reduce the sintering temperature of ceramics [4,21]. Therefore, in this work, the Cu²⁺ ion was considered as a substitution of the Mg²⁺ ion in MgAl₂O₄. Mg_1−xCu_xAl₂O₄ ceramics were synthesized through a solid-state route. The phase composition, microstructure, and microwave dielectric properties were investigated in detail.

2. Experimental Procedure

Mg_1−xCu_xAl₂O₄ (x = 0, 0.04, 0.08, 0.12, 0.16, and 0.20) ceramics were synthesized via the conventional solid-state route. Analytic-grade purity MgO, CuO, and Al₂O₃ powders (Shanghai Macklin Biochemical Co., Ltd., Shanghai, China) with the range of particle size at 45–80 μm were used as starting materials, which were weighed and wet-mixed in deionized water using zirconia balls in a plastic container at 300 rpm for 4 h. The obtained slurries were dried and calcined in alumina crucibles at 1450 °C for 4 h. Subsequently, the calcined powders were ground into a fine form and pressed under a uniaxial pressure of 10 MPa into cylindrical disks with 12 mm diameter and 5–6 mm height. Samples were sintered at temperature levels ranging from 1450 to 1600 °C for 4 h.

To confirm the crystalline phase of the Mg_1−xCu_xAl₂O₄ ceramics, X-ray diffraction (XRD, Miniflex600, Rigaku, Tokyo, Japan), using Cu K_α radiation (λ = 1.54 Å) at room temperature, was measured in the 2θ angle range between 10° and 120° with a step of 0.01°, and counting time for 5 s per step. Based on the XRD results, the crystal structure was analyzed using the Rietveld refinement method using FullProf software (FullProf Suite May2021 64b, The FullProf Team, Grenoble, France) [23]. The microstructures and morphologies of the samples were analyzed by a scanning electron microscope (SEM, JSM-6490; JEOL, Tokyo, Japan) at an accelerating voltage of 20 kV. The Al³⁺ ion distributions of Mg_1−xCu_xAl₂O₄ were investigated through ²⁷Al solid-state magic-angle spinning nuclear magnetic resonance (MAS-NMR) with a spinning frequency of 12 kHz (Avance II 600 MHz, Bruker, Fällanden, Switzerland).

Microwave dielectric properties (ε_r, Qf, and τ_f) of these samples were measured by the Hakki–Coleman dielectric resonator with a vector network analyzer (N5230A, Agilent Technologies, Santa Clara, CA, USA). The τ_f value was calculated based on the resonant frequencies at 25 and 85 °C:

$${\mathsf{\tau }}_{\mathrm{f}}=\frac{f_{85}-f_{25}}{60\times f_{25}}\times {10}^6\left(\mathrm{ppm}/°\mathrm{C}\right)$$

(1)

where $f_t$ represents the resonant frequency at t °C.

3. Results and Discussion

Figure 1 shows the microwave dielectric properties of Mg_1−xCu_xAl₂O₄ ceramics sintered at 1450–1600 °C. Good microwave dielectric properties were obtained at x = 0.04 with sintering at 1550 °C: ε_r = 8.28, Qf = 72,800 GHz, and τ_f = −59 ppm/°C. With the sintering temperature at 1550 °C, the τ_f value experienced a significant increase in the negative direction to about −59 ppm/°C at 0 ≤ x ≤ 0.04; then, the rapid fall was witnessed and a steady rise was observed at 0.08 ≤ x ≤ 0.20. Figure 1b shows the ε_r value, which increased first up to x = 0.12 and then presented a modest downward trend when the sintering temperatures were 1450 and 1500 °C, whereas it remained virtually unchanged at 1550 and 1600 °C. In addition, it is well known that Qf values are determined by both intrinsic and extrinsic factors. Intrinsic factor is mainly caused by lattice vibration, while extrinsic factor is dominated by grain boundary, secondary phase, and densification [24,25]. With the increase in the x value, the Qf values of the samples with different sintering temperatures increased initially and then showed a steady drop. The maximum Qf value was acquired at x = 0.04 with sintering at 1550 and 1600 °C. Compared with previous studies (see

Table 1. Microwave dielectric properties and preparation condition of MgAl₂O₄-based and ZnAl₂O₄ ceramics.

Sample	τf (ppm/°C)	Qf (GHz)	εr	Ts (°C)	Milling Time (h)	Preparation Method	Ref.
Mg0.96Cu0.04Al2O4	−59	72,800	8.28	1550	4	solid state reaction	This work
MgAl2O4	N/A	82,000	7.9	1550–1700	24	solid state reaction	[26]
ZnAl2O4	N/A	106,000	8.6	1550–1700	24	solid state reaction	[26]
Mg(Al0.4Ga0.6)2O4	−16	107,000	8.87	1285–1535	6	solid state reaction	[27]
MgAl1.94(Mg0.5Ti0.5)0.06O4	−61.36	98,000	9.1	1425	6	solid state reaction	[28]
Mg0.25Zn0.75Al2O4	−60	222,600	8.40	1600	24	solid state reaction	[29]
0.75MgAl2O4-0.25TiO2	−12	105,400	11.04	1400–1460	24	solid state reaction	[6]
(Mg0.75Ni0.25)Al2O4	−53.5	130,000	8.21	1480–1600	24	solid state reaction	[17]
(Mg0.95Zn0.05)Al2O4	−64~−70	156,000	8.1	1480–1600	12	solid state reaction	[30]
Zn0.4Al2.4O4	−66	202,468	8.2	1500–1600	24	molten salt method	[31]
MgAl2O4	−62.4	201,690	7.8	1600	24	molten salt method	[15]
Mg0.7Al2.2O4	−60	201,111	7.7	1600	24	molten salt method	[32]
Mg0.4Al2.4O4	−60	232,301	7.5	1600	24	molten salt method	[32]
Mg0.8Co0.2Al2O4	−60	49,300	8.46	1475–1500	12	reaction-sintering process	[18]
Transparent MgAl2O4	N/A	52,640	8.20	1350	N/A	spark plasma sintering	[33]

Note: N/A is not applicable.

) [6,15,17,18,26,27,28,29,30,31,32,33], the sintering temperature and τ_f value of this work can be improved. However, Qf is lower than the best reported value [15], one of the reasons may be the different experimental conditions, such as preparation method, sintering temperature and ball milling time, etc. To understand the microstructure and microwave dielectric properties of Mg_1−xCu_xAl₂O₄ ceramics, the phase composition, relative density, and cation distribution were investigated in this study.

XRD analysis is often carried out to identify phases. The XRD patterns of Mg_1−xCu_xAl₂O₄ ceramics sintered at 1550 °C are illustrated in Figure 2. All the diffraction peaks can be assigned to those for the standard MgAl₂O₄ (PDF # 21-1125) pattern with a space group Fd-3m (227). Meanwhile, there is no apparent peak corresponding to any additional secondary phase containing Cu or structural phase transitions observed from Figure 2, indicating the successful formation of Mg_1−xCu_xAl₂O₄ solid solutions [34].

Figure 3 displays the Rietveld refinement of the XRD patterns for Mg_1−xCu_xAl₂O₄ ceramics, and the refinement results are presented in

Table 2. The cell parameters, density, and reliable factors were obtained based on the Rietveld refinements of XRD.

	x = 0	x = 0.04	x = 0.08	x = 0.12	x = 0.16	x = 0.20
a = b = c (Å)	8.0849	8.0864	8.0869	8.0838	8.0817	8.0828
V (Å3)	528.467	528.775	528.857	528.259	527.841	528.060
Rp (%)	6.35	6.51	5.41	4.76	4.35	3.99
Rwp (%)	8.54	8.88	7.19	6.10	5.63	5.17
Rexp (%)	4.72	4.60	4.29	3.94	3.70	3.56
χ2	3.27	3.73	2.81	2.40	2.32	2.10
ρm (g∙cm−3)	3.379	3.454	3.465	3.491	3.484	3.503
ρt (g∙cm−3)	3.577	3.614	3.652	3.696	3.738	3.776
ρr (%)	94.49	95.59	94.90	94.49	93.22	92.79

Note: The ρ_m, ρ_t, and ρ_r are the measured density, the measured density, and the relative density, respectively.

. Both the Bragg positions models are well within the standard indexed peaks, indicating that the refinement result is acceptable. According to the refinement, the Cu²⁺ ions occupied the tetrahedral site, with the exception of a small amount of the octahedral site. Figure 4 shows the schematic diagram of a crystal structure from MgAl₂O₄ to Mg_1−xCu_xAl₂O₄. The Mg²⁺ and Cu²⁺ ions significantly occupy the 8a Wyckoff position, and the Al³⁺ ions mainly occupy the 16d Wyckoff position. They form a [Mg(T)/Cu(T)O₄] tetrahedron and an [Al(M)O₆] octahedron, respectively. In general, Al³⁺ ions preferentially occupy tetrahedra, which can effectively improve the Qf value (~232,301 GHz) [19,26]. However, Al³⁺ ions mainly occupy the octahedron, which is consistent with low Qf values (~72,800 GHz) of the Mg_1−xCu_xAl₂O₄ system. The cell parameters showed a nonlinear trend with an increase in Cu²⁺ ions content; that is, they first increased, then decreased, and finally increased. On the one hand, the radius of a Cu²⁺ ion (r = 0.73 Å) is slightly larger than that of a Mg²⁺ ion (r = 0.72 Å) [20], which may have led to the increase in cell parameters. On the other hand, the Cu²⁺ ions’ octahedral coordination has a significant Jahn–Teller effect. The Jahn–Teller distortion can enhance the polarizing effect of Cu²⁺ ions [22]. Therefore, the hybridization of Cu²⁺ ions is responsible for a decrease in average cell parameters [22]. Consequently, the two mechanisms were in competition with each other, resulting in a nonlinear variation trend of cell parameters. The cation distribution, which is a significant variation, had no obvious effect on the microwave dielectric properties.

For further analysis of the effects of the introduction of Cu²⁺ ions on microwave dielectric properties, the variations in the cation distribution in Al³⁺ were measured via the ²⁷Al solid-state MAS-NMR measurement, which was used to evaluate the Al³⁺ sites in Mg_1−xCu_xAl₂O₄ ceramics. Figure 5a shows the ²⁷Al NMR spectra of Mg_1−xCu_xAl₂O₄ ceramics sintered at 1550 °C. The spectra indicate three signals with chemical shifts at ca. 10, 17, and 71 ppm. They correspond to octahedrally coordinated aluminum (AlO₆), pentahedrally coordinated aluminum (AlO₅), and tetrahedrally coordinated aluminum (AlO₄), respectively [35,36]. For the emergence of AlO₅, a dynamic disorder occurred between the twisted tetrahedral structure and octahedral structure and froze some Al ions stuck in the pentahedral structure at high temperatures [37]. In Figure 5a, the peak intensities of AlO₄ at 71 ppm gradually weakened, whereas the peaks of AlO₆ at 10 ppm and AlO₅ at 17 ppm first increased and then decreased with the increase in Cu²⁺ content. This result indicated that the redistribution of Al³⁺ ions in the lattice occurred by the substitution of Cu²⁺ for Mg²⁺. Moreover, the peaks transferred to low chemical shifts on account of the second-order quadrupolar-order shifts with the increase in Cu²⁺ content [31,38]. On the whole, the peak intensity of AlO₆ is significantly larger than that of AlO₄, which indicates that Al³⁺ ions mainly occupied octahedral sites. This was in accordance with the XRD results. The different peaks indicated the existence of an intermediate spinel structure in the system. The intermediate spinel structure can be described as [Mg_1−λ²⁺Al_λ³⁺]^IV[Al_2−λ³⁺Mg_λ²⁺]^VIO₄, where λ is the degree of the inversion of spinel structure, corresponding to the fraction of Al³⁺ ions in the tetrahedral site. The value of λ ranges from 0 (normal spinel: (Mg²⁺)^IV(Al₂³⁺)^VIO₄) to 1 (inverse spinel: (Al³⁺)^IV(Al³⁺Mg²⁺)^VIO₄) [13,14]. It is known that the microwave dielectric properties are related to λ [14,15,39]. The value of λ can be calculated with the following formula [40]:

$$\mathsf{\lambda }=\frac{2I\left({\mathrm{AlO}}_4\right)}{I\left({\mathrm{AlO}}_4\right)+I\left({\mathrm{AlO}}_6\right)}$$

(2)

where I(AlO₄) and I(AlO₆) are the intensities of tetrahedral and octahedral resonances, respectively. The λ values are displayed in Figure 5b. Considering the trend of λ in Figure 5b, the Al³⁺ cations preferentially occupied the octahedral sites. It has been reported that the preferential tetrahedron site occupation of Al³⁺ could enhance the Qf value of the system [19,26]. Consequently, when 0.04 < x < 0.16, the Qf values reduce with the decrease in the λ value in Mg_1−xCu_xAl₂O₄ ceramics (see Figure 5b). In addition, the entry of Cu²⁺ ions into the MgAl₂O₄ lattice can lead to disordered charge distribution, which can cause a decrease in Qf value at high Cu²⁺ ions content [41].

The relative density can be calculated according to measured and theoretical density. The theoretical density can be derived from XRD refinements. The results are presented in Table 2. The relative density first increased and then gradually decreased, and the maximum value, which was obtained at x = 0.04, was 95.59%. The SEM shows that the densification was consistent with the relative density (see Figure S1). It also indicates that the moderate amount of CuO can promote the sintering of MgAl₂O₄ ceramics, which is beneficial for obtaining uniform and dense microstructures (see Figure S1). The relationship between the ε_r value and the relative density is presented in Figure 6, which shows that the ε_r value and relative density showed the same trend when x ≤ 0.12. With the increase in Cu²⁺ at x > 0.12, the pores in ceramics also played an important role for the ε_r value. To further investigate the effect of porosity on the ε_r value, the porosity-corrected dielectric constant (ε_rc) can be calculated by a spherical-pore model [42]:

$${\mathsf{\epsilon }}_{\mathrm{r}}={\mathsf{\epsilon }}_{\mathrm{rc}}\left(1-\frac{3P\left({\mathsf{\epsilon }}_{\mathrm{rc}}-1\right)}{2{\mathsf{\epsilon }}_{\mathrm{rc}}+1}\right)$$

(3)

where ε_r and P (1 − ρ_relative) are the measured ε_r and the porosity, respectively. The calculated results are listed in

Table 3. Measured dielectric constant (ε_r) and porosity-corrected dielectric constant (ε_rc) of Mg_1−xCu_xAl₂O₄ ceramics sintered at 1550 °C.

x Value	x = 0	x = 0.04	x = 0.08	x = 0.12	x = 0.16	x = 0.2
P	0.055	0.044	0.051	0.055	0.068	0.072
εr	8.14	8.28	8.23	8.22	8.26	8.29
εrc	8.75	8.76	8.80	8.83	9.04	9.12
εtheo	7.79	7.92	8.05	8.23	8.40	8.54

. The ε_rc value was higher than the ε_r value, which indicated that the air trapped in the pores contributed to the decrease in the dielectric constant [43]. It is worth mentioning that, with the increase in Cu²⁺ at x > 0.12, the relative density maintained a declining trend, while the ε_r value had a slight growth. In response to this difference, apart from the relative density and pores, the variation in the ε_r value can be evaluated by the Clausius–Mosotti equation [44]:

$${\mathsf{\epsilon }}_{\mathrm{theo}}=\frac{3V_{\mathrm{m}}+8\pi {\alpha }_{\mathrm{theo}}}{3V_{\mathrm{m}}-4\pi {\alpha }_{\mathrm{theo}}}$$

(4)

where V_m and α_theo represent the molecular volume and theoretical ionic polarizabilities, respectively. α_theo can be calculated as follows [45,46]:

$${\alpha }_{\mathrm{theo}}=\left(1-x\right)\alpha \left(M{g}^{2+}\right)+x\alpha \left(C{u}^{2+}\right)+2\alpha \left(A{l}^{3+}\right)+4\alpha \left(O^{2-}\right)$$

(5)

where the α_i value corresponds to the individual ionic dielectric polarizabilities. The results are listed in Table 3. The theoretical ionic polarizabilities of Mg_1−xCu_xAl₂O₄ ceramics, which increased linearly from 10.94 to 11.10, are shown in Figure 6. In general, the increase in polarizabilities led to the increase in the ε_r value, and the expected variation only occurred at x ≥ 0.12 [47]. This indicates that the ionic polarizabilities have a more significant impact on the ε_r value than that of the relative density at x > 0.12.

In order to clarify the correlation between the chemical bonds and the microwave dielectric properties of Mg_1−xCu_xAl₂O₄ ceramics at 1550 °C, the complex chemical bond theory analysis was carried out, which was contributed by Phillips, Van Vecten, and Levine (P-V-L) [48,49,50,51,52]. The detailed process of the P-V-L theory analysis is presented in the Supplementary Materials. The bond length, lattice energy, and bond energy, which are calculated through P-V-L theory, are shown in Tables S1–S4, respectively. The τ_f value is the combined result of the bonding strength and the crystal structure. In general, the binding force between the ions in the unit cell was stronger, the restoring force that affected the tilt of the oxygen octahedron was higher, the unit cell was less affected at high temperatures, and the τ_f value was closer to zero [21,53]. Figure 7 shows the τ_f value and the total bond energy as a function of the x value. When x ≤ 0.04 and x ≥ 0.08, the τ_f value shifted to zero with the increase in total bond energy, indicating that the system tended to be stable.

4. Conclusions

A single-phase Mg_1−xCu_xAl₂O₄ ceramic with a spinel structure was formulated and analyzed. The Cu²⁺ ions occupied the tetrahedral site, whereas the Al³⁺ ions preferentially occupied octahedral site, resulting in a low the Qf value. In addition, the entry of Cu²⁺ ions into the MgAl₂O₄ lattice lead to disordered charge distribution, which can cause a decrease in Qf value at high Cu²⁺ ions content. The Cu substitution had the high bond energy, which contributed to the temperature stability of the samples at x ≤ 0.04 and x ≥ 0.08. Then, the τ_f value moved toward the positive direction. Good microwave dielectric properties were achieved at x = 0.04, sintered at 1550 °C: ε_r = 8.28, Qf = 72,800 GHz, and τ_f = −59 ppm/°C. Therefore, the Qf and τ_f values of the Mg_1−xCu_xAl₂O₄ solid solution were improved, maintaining a low ε_r value. This study suggests that Mg_1−xCu_xAl₂O₄ is a promising candidate ceramic, possessing a high Qf value and a low dielectric constant, for use in modern communication systems.