III. RESULTS AND DISCUSSION

XRD patterns of (1 − x)Ba(Mg_1/3Ta_2/3)O₃–xBa(Co_1/3Nb_2/3)O₃ ceramics (BMT–BCN, x = 0.0, 0.20, 0.25, 0.30, 0.40) as a function of x value are shown in Fig. 1(a), in which the indices of the peaks in the range 2θ ≤ 120° are labeled. There are (001) and (100) super-lattice diffraction peaks, whose intensities decrease with the increase in the BCN content. A small amount of new phase appears, which was indicated as Ba₅Ta₄O₁₅ (No. 18-0193); moreover, the BCN (No. 46-0997) phase appears especially at x = 0.30 and 0.40.

FIG. 1.

(a) XRD patterns of the BMT–BCN ceramic samples and (b) refinement profile for x = 0 sample.

As shown in the inset figure, the (306) peak drifts to lower angle when x ≤ 0.25 and drift to higher angle when x ≥ 0.25, i.e., x = 0.25 is the turning point for the crystal structures of the samples and the sample at x = 0.25 has the lowest angle. With the increase of BCN content, the new phase decreases in the content and almost disappears at x = 0.25, which may be related to the lower evaporation of Mg²⁺ ions (Co²⁺ ions can enter into the vacancies in B′-sites due to their small ionic radius as compared to that of Mg²⁺ ions). Mg²⁺ ions and Ta⁵⁺ ions in the inside of the grains cannot diffuse to the crystal surfaces due to the existence of BCN, that is, the addition of BCN decreases the amount of the Ba₅Ta₄O₁₅ phase. With the increase in the BCN content, the intensities of the ordered diffraction peaks decrease gradually, and when x = 0.4, the ordered phase almost disappears, which implies that phase transition occurs due to the replacement of ions.

The lattice parameters of BMT–BCN ceramics were refined by Topas software based on the XRD data, and the refined XRD patterns are shown in Fig. 1(b). Table I shows the refined XRD parameters, the lattice constants, and the values of the ordered degree with different BCN contents.

TABLE I.

Refined XRD parameters, lattice constants, ordered degree, and packing fraction of BMT–BCN ceramics.

Weighted profile R-factor: R _wp. Profile R-factor: R _p.

Studies have shown that the bigger the discrepancy of the charge and radius in B-site ions, the larger the ordered degree. The ionic radii of both Nb⁵⁺ and Ta⁵⁺ are similar to each other, which cannot affect the ordered degree. The ionic radii discrepancy between Co²⁺ ions and Ta⁵⁺ ions is less than that of Mg²⁺ ions and Ta⁵⁺ ions, thus it is difficult to form an ordered structure with more BCN added. Accordingly, the ordered degree (S) of the BMT–BCN ceramics decreases with the increase in the BCN content. The ratio of lattice parameters (c/a) deviates from the ideal hexagonal structure date of 1.2274, and the maximum appears at x = 0.25, which complies with the lowest angle at x = 0.25 stated above.

Figures 2(a)–2(e) exhibit SEM images taken from the fractured surfaces of the BMT–BCN ceramics. When 0 ≤ x ≤ 0.3, the grain size increases slightly with x value, from 0.5 μm at x = 0 to 0.8 μm at x = 0.25, 0.3, and the number of pores also gradually decreases. However, at x = 0.4, grain boundaries become indistinct as shown in Fig. 2(e), different from those of other samples. Blurred grain boundaries come from the liquid phase,^{Reference Ahn, Jang, Nahm, Park and Lee7} indicated by the arrow in Fig. 2(e).

FIG. 2.

SEM images of the fractured surface of the BMT–BCN ceramics: (a) BMT; (b) 0.8BMT–0.2BCN; (c) 0.75BMT–0.25BCN; (d) 0.7BMT–0.3BCN; (e) 0.6BMT–0.4BCN.

The Raman spectra of the BMT–BCN within the range of 50–1000 cm⁻¹ are shown in Fig. 3, which were assigned according to the related compound of Ba(Mg_1/3Ta_2/3)O₃.^{Reference Wang, Jing, Wang and Lu5} In Fig. 3, seven main Raman vibrational modes are observed,^{Reference Shi, Wang and Sun4} and each mode was fitted with the Lorentzian model and the related parameters are listed in Table II.

FIG. 3.

Raman spectrum of BMT–BCN ceramic samples from 50 to 1000 cm⁻¹.

TABLE II.

Parameters of the phonon modes (frequency and FWHM) of Raman active modes and the dielectric properties.

^a ×10⁻⁴.

As shown in Fig. 3, the spectra were divided into four main assigned zones,^{Reference Wang, Jing, Wang and Lu5} i.e., (i) the F_2g(Ba) phonon modes near 108 cm⁻¹, which are mainly ascribed to the vibrations of Ba atoms, (ii) the degenerated F_2g(O) phonon modes near 380–410 cm⁻¹, (iii) the E_g(O) phonon modes near 430 cm⁻¹, and (iv) the A_1g(O) phonon modes, i.e., stretching vibration of the oxygen octahedra, near 800 cm⁻¹. Three extra active modes are assigned, i.e., mode E_g(O) at x =160 cm⁻¹, mode E_g(Ta) at 213 cm⁻¹, and mode A_1g(Ta) at 270 cm⁻¹, which were indexed as the 1:2 ordered structure-related vibrations. The E _g (580 cm⁻¹) mode also originated from the vibrations of O atoms, i.e., antisymmetric breathing vibrations.

According to Fig. 4 and Tables I and II, the sample with higher ordered degree shows higher intensities of Raman peaks, and the change of Raman active modes depends on long-range and short-range ordered symmetry.^{Reference Richtmyer11} The intensities of BMT Raman peaks are stronger than those of other samples and the intensities of Raman peaks decrease with increasing BCN content, which was consistent with the results of the XRD analysis.

FIG. 4.

Raman spectra of BMT–BCN ceramics. (a) phonon mode related to Ba²⁺ near 108 cm⁻¹, (b) phonon mode at 125–350 cm⁻¹, and (c) phonon mode related to O²⁻ at 350–460 cm⁻¹ (d) stretching mode of the O octahedron near 800 cm⁻¹.

As shown in Fig. 4(a), the modes at about 108 cm⁻¹ corresponding to Ba²⁺ ions in A-site are identified as F_2g(Ba) modes. According to the analysis of crystal symmetry, when the 1:2 ordered structure appears, F_2g modes can split into two vibrational modes, that is, A_1g and E_g modes.^{Reference Roessler12} However, F_2g(Ba) modes in Raman spectra of BMT–BCN ceramics do not split, which shows that A_1g(Ba) and E_g(Ba) modes overlap. Moreover, a blue-shift occurs with increasing BCN content.

As shown in Fig. 4(b), the modes of E_g(O), E_g(Ta), and A_1g(Ta) are identified as the 1:2 ordered structure-related vibrations. Their intensities decrease with increasing BCN content. According to previous studies,^{Reference Wang, Jing, Wang and Lu5} Raman-active vibrational modes are assigned as the short-range symmetry and long-range symmetry, while high-intensity peaks and flat baselines are observed in the high-ordered specimens, and thus, the decrease in intensities of E_g(O), E_g(Ta), and A_1g(Ta) modes show the ordered degree decrease with the increase in the BCN content. Moreover, there is a slight deviation in the relative equilibrium position between the positive and negative ions. In other words, the O octahedral distortion decreases with increasing BCN content, causing the E_g(Ta) and A_lg(Ta) modes to move to higher angles.

As shown in Fig. 4(c), F_2g(O) modes shift to low frequencies with increasing BCN content, which complies with the change of the cell volume. Unapparent change is observed in frequencies of E_g(O) Raman modes.

As shown in Fig. 4(d), the A_1g(O) stretching modes with the highest intensity correlate with the vibration of the oxygen octahedra. According to Fig. 4(d) and Table II, FWHM values of A_1g(O) modes show nonlinear variation and the A_1g(O) modes drift to low frequencies with increasing BCN content, which implies the weakening of the lattice distortion.

The measured dielectric properties are shown in Table II. As shown in Fig. 5(a), the ε_r value of BMT (25) is smaller than that of BCN (32.6); thus, the dielectric constant increases with increasing BCN content, which applies with the logarithmic mixing law. There is a negative correlation between the Raman shifts of E_g(O) phonon modes and the dielectric constants at x ≤ 0.25, while a positive correlation at x ≥ 0.25, which shows that the Raman shifts of E_g(O) phonon modes have close relationship with the dielectric constants.

FIG. 5.

Correlation between Raman shift of E_g(O) and dielectric constant (a), the FWHM of F_2g(O) and A_1g(O) phonon mode and dielectric loss (b), and packing fraction and dielectric loss (c) as a function of BCN content.

Figure 5(b) shows that there are negative correlations between the FWHM values of F_2g(O)/A_1g(O) phonon modes and the dielectric loss at x ≤ 0.25, while positive correlations exist at x ≥ 0.25, which shows that the FWHM values of F_2g(O) and A_1g(O) phonon modes have close relationship with the dielectric losses.

To better analyze the dielectric properties of the BMT–BCN ceramics, Fig. 6 exhibits 12 IR active vibrational modes assigned based on the related system of Ba(Mg_1/3Nb_2/3)O₃^{Reference Akbas and Davies13} and Ba(Mg_1/3Ta_2/3)O₃.^{Reference Wang, Jing, Wang and Lu5} The infrared spectra of BMT–BCN ceramics are divided into three regions according to the mode vibrations: (i) the peaks below 180 cm⁻¹ are assigned as the vibrations of Ba²⁺ with respect to (Mg Ta)O₆ and (Co Ta)O₆ octahedra; (ii) the modes between 180 and 500 cm⁻¹ are considered to be the twisting vibrations of (Mg Ta)–O or (Co Ta)–O; (iii) the phonons above 500 cm⁻¹ are considered to be the stretching vibrational modes of (Mg Ta)–O or O–(Co Ta)–O. As shown in Figs. 6, A_2u⁽¹⁾ and E_u⁽²⁾ appear when x ≥ 0.2, and their intensities gradually increase as a function of x value. According to the previous study,^{Reference Wang, Jing, Wang and Lu5} when the specimens become more disordered, their local symmetry will be changed, so some of the original Raman inactive patterns may be activated. Therefore, with increasing BCN content, the ordered degree of the samples decreases step by step, which is confirmed by the intensities of A_2u⁽¹⁾ and E_u⁽²⁾. It can be observed that the A_2u⁽³⁾ mode became broaden with increasing BCN content and then disappeared when x = 0.4, which may be attributed to the weakening of the distortion for (Mg Ta)O₆ or (Co Ta)O₆ octahedra.

FIG. 6.

Measured (red circles) and fitted (solid lines) IR spectra for the BMT–BCN ceramics.

In the microwave frequency range, the complex dielectric constant ε* can be deduced by the IR reflectivity (R(ω)) based on the Fresnel equation, which can be obtained by the FPSQ model as follows^{Reference Qiao, Sun, Li, Chen, Xing, Yang, Dong, Wang, Yin, Qi and Shi14}:

(1)$$R\left( \omega \right) = {\left| {{{\sqrt {{\varepsilon ^ * } - 1} } \over {\sqrt {{\varepsilon ^ * } + 1} }}} \right|^2}\quad ,$$

(2)$${\varepsilon ^ * }\left( \omega \right) = \varepsilon '\left( \omega \right) - {\rm{i}}\varepsilon ''\left( \omega \right) = {\varepsilon _\infty }\prod\limits_{j = 1}^n {{{\Omega _{j{\rm{LO}}}^2 - {\omega ^2} + {\rm{i\omega }}{{\rm{\gamma }}_{j{\rm{LO}}}}} \over {\Omega _{j{\rm{TO}}}^2 - {\omega ^2} + {\rm{i}}\omega {\gamma _{j{\rm{TO}}}}}}} \quad ,$$

where ε_∞ is the optical dielectric constant due to the electron polarization at high frequencies; n is the number of polar phonons; Ω_jTO (Ω_jLO) and γ_jTO (γ_jLO) are the frequency and damping factor of the jth transverse (longitude) bands, respectively.^{Reference Shi, Yang, Liu, Qi and Sun3} The results are listed in Table II.

It is essential to calculate the contribution of each mode to the microwave dielectric response. The dielectric constant (ε_j) and dielectric loss (tan δ_j/ω) were calculated according to the following formulae:

(3)$${\varepsilon _j} = {{{\varepsilon _\infty }\prod\limits_k {\left( {\Omega _{k{\rm{LO}}}^2 - \Omega _{j{\rm{TO}}}^2} \right)} } \over {\Omega _{j{\rm{TO}}}^2\prod\limits_{k \ne j} {\left( {\Omega _{k{\rm{TO}}}^2 - \Omega _{j{\rm{TO}}}^2} \right)} }}\quad ,$$

(4)$${{\tan \;{\delta _j}} / \omega } = {{{{{\varepsilon _j}{\gamma _{j{\rm{TO}}}}} / {\Omega _{j{\rm{TO}}}^2}}} \over {{\varepsilon _\infty } + \sum\limits_j {{\varepsilon _j}} }}\quad .$$

Here, the ε_j and tan δ_j/ω represent the contributions to the dielectric constants and dielectric losses, respectively.

The dielectric contributions of every mode are listed as ∆ε_j and tan δ_j/ω in Table III (taking x = 0 as an example). The main contributions of the dielectric constants coming from the first two modes, which are below 180 cm⁻¹, can reach 15.96 and about 64% of the total value, while the contributions to the dielectric losses are 3.349 and about 87% of the total loss value, which means that vibrations of Ba²⁺ with respect to (MgTa)O₆ and (CoTa)O₆ octahedra play a vital role in the dielectric properties. The results correspond well with previous studies.^{Reference Zhou, Guo, Li, Pang, Yao, Wang and Reaney15}

TABLE III.

Fitting parameters of infrared reflectivity spectra of BMT ceramic.

ε_∞ = 4.8. x = 0.

The real part ε′ and imaginary part ε″ of the complex dielectric properties were also obtained from the fitting process, which are shown in Fig. 7 (taking x = 0, 0.3, 0.4 as an example). It is worth noting that the calculated values match well with the measured data (@3.8 GHz), which means that most of dielectric contribution to the system may be ascribed to the absorption of structural phononic oscillations at the infrared region. The contribution from the scattering of the defective phonons is small.

FIG. 7.

IR Reflectivity and fitted line as well as real part ε′ and imaginary part ε″ of the complex dielectric properties of BMT (a), 0.7BMT–0.3BCN (b), and 0.6BMT–0.4BCN (c) ceramics calculated by the FPSQ model.

The dielectric loss of ceramics depends not only on the intrinsic factors such as lattice phonon vibration but also on extrinsic factors such as pores, lattice defects, grain size, and internal stress.^{Reference Kim, Kim, Kim and Yoon16} It is widely accepted that the dielectric loss was related to the packing fraction of the structure.^{Reference Kim, Chun, Freer and Cernik17} The packing fraction of BMT–BCN ceramics was calculated from the following equation^{Reference Tseng18} and the results are shown in Table I.

(5)$${\rm{Packing}}\;{\rm{fraction}} = {{{\rm{Volume}}\;{\rm{of}}\;{\rm{the}}\;{\rm{atoms}}\;{\rm{in}}\;{\rm{the}}\;{\rm{cell}}} \over {{\rm{Volume}}\;{\rm{of}}\;{\rm{primitive}}\;{\rm{unit}}\;{\rm{cell}}}}\quad .$$

As confirmed in Fig. 5(c), there is a negative relationship between the dielectric loss and the packing fraction. There would be a reduction in lattice vibrations as the increase in packing fraction, which tends to decrease the dielectric loss (tan δ).