Raman spectra and microwave dielectric properties of Na5Tm1 − x(Y1/3Yb2/3)x(MoO4)4 ceramics with ultra-low sintering temperature

XRD and SEM analysis

Figure 1a shows XRD patterns of Na₅Tm_0.91Y_0.03Yb_0.06(MoO₄)₄ ceramics sintered at 550–650 °C. The higher (132) diffraction peak suggests a more consistent orientation or a predominant number of this crystal plane, enhancing its diffraction effect. Figure 1b and Fig. S1 (SI, Supplementary Information) compare the XRD patterns of samples with different Y/Yb content sintered at 575 °C and 600 °C. The XRD patterns of all samples match well with Na₅Y_0.5Tm_0.5(MoO₄)₄ (PDF# 00-054-0897, a=b=11.415 Å, c=11.46 Å, V=1493.17 ų, Z=4), confirming the formation of a pure tetragonal scheelite-type structure with the space group I41/a (88)²¹. Additionally, based on Rietveld refinement, the Na₅Tm_1 − x(Y_1/3Yb_2/3)_x(MoO₄)₄ ceramics sintered at 575 °C and 600 °C show refinement results in Fig. 1c, with supplementary data in Fig. S2 (SI, Supplementary Information) and Table S1(SI, Supplementary Information).Table S1 presents detailed refinement outcomes for the ceramics sintered at 600 °C, with R_wp values ranging from 4.559 to 5.296% and R_p values between 2.97% and 3.34%. All of these values fall below 10%, thereby confirming the reliability of the obtained results²². The crystal structure of Na₅Tm_1 − x(Y_1/3Yb_2/3)_x(MoO₄)₄ ceramics, as illustrated in Fig. 1d, features right angles (α, β, γ=90°) and is characterized by Tm/Y/Yb ions that are surrounded by four O3 and four O4 atoms, forming a distorted dodecahedron²³. Na1 and Na2 occupy distinct Wyckoff sites: Na1 coordinates with four O2 atoms to form a tetrahedron, whereas Na2 and Mo1 occupy sites that form an octahedron and a tetrahedron, respectively, involving O1, O2, O3, and O4 atoms. The coordination numbers for these ions are as follows: 8 for Tm/Y/Yb, 4 for Na1, 6 for Na2, and 4 for Mo.

The SEM images and average grain sizes (A.G.) of Na₅Tm_0.91Y_0.03Yb_0.06(MoO₄)₄ ceramics sintered at 550–650 °C are presented in Fig. 2a–e. An appropriate sintering temperature favors grain growth, leading to a reduction in porosity and a tighter grain boundary. However, excessively high sintering temperatures can cause grain melting, resulting in distinct grain boundaries that enhance microwave scattering and adversely affect dielectric properties^24,25. Figure 2j clearly demonstrates that the A.G. of the samples increases from 1.472 μm to 4.03 μm, indicating that an elevation in sintering temperature promotes grain growth. Additionally, Na₅Tm_1 − x(Y_1/3Yb_2/3)_x(MoO₄)₄ ceramics sintered at 575 °C (with average grain sizes ranging from 1.612 to 1.997 μm, as shown in Fig. S3 in the Supplementary Information) and 600 °C (Fig. 2f-i, with A.G. ranging from 2.172 μm to 2.424 μm) suggest that the incorporation of a small amount of Y and Yb elements may be beneficial for grain growth^26,27,28. Notably, the EDS spectrum of Na₅Tm_1 − x(Y_1/3Yb_2/3)_x(MoO₄)₄ ceramics in Fig. 2k reveals an atomic ratio of Na, Tm, Mo, and O close to 5:1:4:24, confirming the successful synthesis of the desired crystalline phase and validating the corresponding XRD data analysis.

Microwave dielectric properties

The microwave dielectric properties of ceramics are typically influenced by a combination of intrinsic factors (such as crystal structure, oxygen octahedral distortion, ionic polarizability, and lattice energy) and extrinsic factors (such as porosity, presence of secondary phases, and grain size)^29,30. The dielectric properties of Na₅Tm_1 − x(Y_1/3Yb_2/3)_x(MoO₄)₄ ceramics are illustrated in Fig. 3, with a consistent trend observed between apparent density and ε_r (relative permittivity), as well as Q×f value. Na₅Tm(MoO₄)₄ ceramics exhibit peak values for apparent density, ε_r, Q×f, and τ_f at 625 °C, which are 3.98 g/cm³, 8.025, 18,967 GHz, and − 101ppm/°C, respectively. In contrast, Na₅Tm_0.91Y_0.03Yb_0.06(MoO₄)₄ ceramics doped with Y and Yb can achieve densification at a lower temperature of 600 °C, with respective values of 3.95 g/cm³, 7.82, 34,752 GHz, and an improved τ_f. Clearly, the incorporation of appropriate amounts of (Y_1/3Yb_2/3)³⁺ not only reduces the sintering temperature but also significantly improves the Q×f and τ_f values. Therefore, a discussion on ion substitution modification is necessary.

Shannon’s research indicates that the dielectric constant of Na₅Tm_1 − x(Y_1/3Yb_2/3)_x(MoO₄)₄ ceramics is influenced by ionic polarizability. Based on the ionic polarizabilities (α(Na⁺)=1.8 ų, α(Tm³⁺)=3.82 ų, α(Y³⁺)=3.81 ų, α(Yb³⁺)=3.58 ų, α(Mo⁶⁺)=3.28 ų, and α(O²⁻)=2.01 ų), combined with Shannon’s additive rule (Eq. (2))³¹ and the Clausius-Mossotti equation (Eq. 3))³², the theoretical ionic polarizability (α_th) and measured ionic polarizability (α_obs, Eq. (4)) were estimated, along with the measured ε_r, as shown in Fig. 4a. Notably, the αth of the samples at the optimal sintering temperature of 600 °C remains approximately constant at 58.08 ų, while the α_obs calculated from ε_r falls within the range of 58.01–60.85 ų, demonstrating minimal difference between the two values. Both α_th, α_obs, ε_r, and ε_rcorr (corrected ε_r using the Bosman-Havinga Equation (Eq. (5))^33,34, where p represents porosity (P=1-ρ_re)) decrease consistently with increasing x content, indicating that the ε_r of the samples is a result of the combined effects of ionic polarizability and relative density (ρ_re). Additionally, the ρ_re of Na₅Tm_1 − x(Y_1/3Yb_2/3)_x(MoO₄)₄ ceramics is closely related to Q×f, with ρ_re positively correlated with Q×f as shown in Fig. 4b. The highest ρ_re value reaches 94.9%. A discussion on the ε_r and Q×f of the samples at 575 °C can be found in the Supplementary Information.

Park et al.‘s research reveals a correlation between τ_f and the total bond valence of the samples. The formula for calculating the total bond valence is provided as follows³⁵:

In the equation above, R₀ represents the reference bond length for a specific bond type, di is the calculated bond length of the i-th bond, and the b value is 0.37 ų⁶. Figure 4c depicts the functional relationship between τ_f and V_total at 600 °C as a function of the x content. When x=0.09, τ_f = -71.9 ppm/°C. According to the bond valence theory³⁵, an increase in bond valence values suggests shorter bond lengths and stronger bond energies, resulting in a decrease in the τ_f value. Consequently, bond valence in Na₅Tm_1 − x(Y_1/3Yb_2/3)_x(MoO₄)₄ becomes a crucial factor affecting its τ_f value.

The impact of P-V-L theory on microwave dielectric properties

In 1991, Zhang et al. expanded the P-V-L theory by decomposing complex multi-component crystals into binary (A_mB_n) components^37,38. This provided theoretical support for studying how chemical bond properties influence the microwave dielectric properties of ceramics. Based on this expansion, Na₅Tm_1 − x(Y_1/3Yb_2/3)_x(MoO₄)₄ can be represented as²³:

The bond ionicity (f_i) is closely related to ε_r, as described in Eq. (12)³⁹. In the compound Na₅Tm_1-x(Y_1/3Yb_2/3)_x(MoO₄)₄, the coordination numbers for Na(1), Na(2), Tm, Mo, O(1), O(2), O(3), and O(4) are 4, 6, 8, 4, 3, 4, and 3, respectively. Based on these coordination numbers, the average bond ionicity (Ave f_i) of the compound was calculated and is presented in Fig. 5a. Notably, Ave f_i (Tm-O) is higher than Ave f_i (Mo-O) and Ave f_i (Na-O). Therefore, the f_i of the Tm-O bond makes a significant contribution to ε_r. The equations for calculating f_i are provided in Eqs. 5–8 (SI, Supplementary Information)³⁹.

Figure 6a illustrates the correlation between Ave f_i (Tm-O) and ε_r. When 0.09 ≤ x ≤ 0.12, a negative association between ε_r and Ave f_i (Tm-O) is observed, potentially attributed to the porosity of the samples. However, within the range of 0.12 to 0.18, Ave f_i (Tm-O) and ε_r exhibit a concurrent decreasing trend, clearly suggesting that the f_i of the Tm-O bond has a notable influence on ε_r.

The lattice energy of chemical bonds in ceramics significantly influences the Q×f. Based on Eqs. (9–11)^40,41 (SI, Supplementary Information), the average lattice energies of Na-O, Tm-O, and Mo-O in Na₅Tm_1-x(Y_1/3Yb_2/3)_x(MoO₄)₄ ceramics were calculated and presented in Fig. 5b. Notably, the relationship Ave U(Na-O) 6b precisely illustrates the relationship between the Q×f value of the samples and Ave U(Mo-O). The results show that when 0.12 ≤ x ≤ 0.18, the Q×f value and Ave U(Mo-O) exhibit similar trends, suggesting that a higher lattice energy correlates with enhanced stability of the ionic crystal and, consequently, lower dielectric loss. However, within the range of 0.09 ≤ x ≤ 0.12, the Q×f values show a contrasting trend to the increase in Ave U(Mo-O), which may be attributed to the effect of the porosity of the samples⁴².

It is reported that the τ_f value is influenced by a combination of bond valence, the temperature coefficient of permittivity (τ_ε), and the linear thermal expansion coefficient (α_L), as described by Eq. (10)⁴³. The average linear expansion coefficient of Na₅Tm_1-x(Y_1/3Yb_2/3)_x(MoO₄)₄ has been calculated using Eqs. (12–15) (detailed in the Supplementary Information, SI), with the results presented in Fig. 5c. Among them, the Mo-O bond shows a negative linear expansion coefficient between − 0.635 10^− 6/K to -0.576 10^− 6/K, which helps to improve the stability of the ceramic.In contrast, the Na-O bond, characterized by lower lattice energy and bond energy, adversely impacts the thermal stability of the samples^44,45,46. Further analysis of the total bond energies of Na-O, Tm-O, and Mo-O bonds in this ceramic (Fig. 5d) reveals that the Mo-O bond possesses the highest total bond energy, reaching 1,685 kJ/mol, and that there is a positive correlation between bond energy and thermal stability. The bond energy of the Mo-O bond follows the same trend as the τ_f value (Fig. 6c), suggesting that it significantly contributes to the thermal stability of Na₅Tm_1-x(Y_1/3Yb_2/3)_x(MoO₄)₄.

Raman spectra analysis

Raman spectrum is a valuable tool for exploring crystal structure, short-range order, phase changes, and vibrational modes^47,48. According to group theory analysis^19,23, the Raman-active modes of Na₅Tm_1 − x(Y_1/3Yb_2/3)_x(MoO₄)₄ ceramics can be represented as Γ_Raman=18A_g + 20B_g + 20¹E_g + 20²E_g. Additional vibrational modes, such as optical, acoustic, infrared-active, and hyper-Raman-active modes, can be found in the Supplementary Information. Figure 7a presents the deconvoluted Raman spectra of Na₅Tm_1 − x(Y_1/3Yb_2/3)_x(MoO₄)₄ ceramics at room temperature, revealing characteristic peaks in the lower frequency range. Specifically, the peak at 225 cm⁻¹ is associated with the rotation of Na⁺, Tm³⁺, and the MoO₄ octahedra²². The peak at 327 cm^− 1 corresponds to the asymmetric bending vibration of [MoO₄]²⁻, while those at 370 cm^− 1 and 388 cm^− 1 represent its symmetric bending vibrations. The peaks at 766 cm^− 1, 804 cm^− 1, 841 cm^− 1, and 868 cm^− 1 are attributed to the asymmetric stretching vibrations of [MoO₄]²⁻, and the peak at 914.11 cm⁻¹ corresponds to its symmetric stretching vibration⁴⁹. Additionally, due to the broadness and overlap of weaker bands, the number of observed vibrational modes is fewer than predicted by group theory analysis⁵⁰. Figure 7b shows the Raman spectra of Na₅Tm_1 − x(Y_1/3Yb_2/3)_x(MoO₄)₄ ceramics, sintered optimally at 600 °C for 6 h. Figure 7c reveals a gradual blue shift of the peak at 917.03 cm^− 1 as x increases, suggesting a decline in molecular polarization. This, in turn, leads to a lower ε_r, as illustrated in Fig. 7d^30,51. The full width at half maximum (FWHM) of Raman spectroscopy can indicate the intrinsic dielectric loss of ceramic materials^33,52. As shown in Fig. 7e, as the x value increases, the FWHM value also increases, accompanied by a decrease in the Q×f value. Conversely, as the FWHM decreases, lattice damping weakens, leading to a reduction in intrinsic dielectric loss.

Table 1 compares the microwave dielectric properties of Na₅RE(MoO₄)₄ ceramics (RE=rare earth elements), revealing optimal sintering temperatures below 660 °C. Notably, Na₅Y(MoO₄)₄ and Na₅Yb(MoO₄)₄ exhibit the lowest dielectric loss at 600 °C and 570 °C, respectively, with Q×f values of 56,800 GHz and 43,400 GHz. In this study, Na₅Tm(MoO₄)₄ showed optimal dielectric properties at 625 °C, with ε_r=8.025, Q×f=18,967 GHz, and τ_f = -101 ppm/°C. Remarkably, Na₅Tm_0.91Y_0.03Yb_0.06(MoO₄)₄ ceramics doped with (Y_1/3Yb_2/3)³⁺ exhibited excellent performance at 600 °C, with ε_r=7.82, Q×f=34,752 GHsz, and a significantly improved τ_f of -71.9 ppm/°C. This indicates that the substitution of (Y_1/3Yb_2/3)³⁺ not only reduces the sintering temperature but also significantly improves Q×f and τ_f.