Effects of LiF-Addition on Sintering Behavior and Dielectric Response of LaPO 4 Ceramics at Microwave and Terahertz Frequency for LTCC Applications

: This paper reports on the successful preparation of LaPO 4 - x wt.% LiF ( x = 0–5) ceramics using the traditional solid-state reaction method. The crystal structures, sintering behaviors, and dielectric response at microwave and terahertz frequencies were investigated. XRD results indicate that all the diffraction peaks were attributed to LaPO 4 , and no secondary phase was observed. Rietveld reﬁnement was conducted to analyze the variation of the crystal structure of LaPO 4 - x wt.% LiF. SEM indicates that the addition of LiF signiﬁcantly decreased the grain size while increasing the apparent density of the ceramics. When x = 3, the optimum microwave dielectric properties ε r = 10.03, Q × f = 81,467 GHz, and τ f = − 43.79 ppm/ ◦ C were achieved in LaPO 4 -3 wt.% LiF ceramic at 750 ◦ C. The infrared reﬂectance spectrum and terahertz time-domain spectroscopy were analyzed and compared with the dielectric properties measured at microwave frequency to investigate the inherent dielectric response. The ﬁndings indicate that the dielectric constant attributed to ionic displacement polarization and oxygen vacancy is an essential factor affecting dielectric loss. Moreover, it is worth noting that the LaPO 4 -3 wt.% LiF ceramic demonstrates excellent compatibility with silver powders, suggesting its immense potential as a dielectric material in LTCC applications.


Introduction
With the development of wireless communication and the arrival of the 5G era, the demand for high-speed, high-capacity wireless technology in 5G communications is soaring [1][2][3]. In the future communication field, the operating frequency will be expanded to micron and millimeter waves. Microwave dielectric ceramics, which are essential components in passive devices, have garnered more attention due to their exceptional performance. The main parameters to measure the properties of microwave dielectric ceramics are the dielectric constant (ε r ), quality factor (Q × f ), and temperature coefficient (τ f ). Among these, ε r is a physical quantity that characterizes polarizability. High-frequency communication is characterized by low signal delay and therefore requires a low dielectric constant in the material. Q × f described the dielectric loss of materials [4]. A high-quality factor means high signal quality. τ f determines the stability of signals and requires a value near zero to ensure operating stability at work. In addition, to realize the device application of materials, low-temperature co-firing technology (LTCC) is necessary [5][6][7][8][9].
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Experimental Procedure
The LaPO 4 -x wt.% LiF (x = 0, 1, 2, 3, 4, and 5) system was prepared by the traditional solid-state reaction method. High-purity powders of La 2 O 3 (99.99%), NH 4 H 2 PO 4 (99%), and LiF (99%) as the primary raw materials were weighted stoichiometrically. The raw powders were mixed with zirconium balls and alcohol for 24 h. Then the slurry was dried in an oven at 80 • C and passed through a 60-mesh screen. The dried powders were calcined at 1200 • C to form the main crystal phase. Whereafter, LiF was added as a sintering aid and for secondary ball milling. Before being pressed into a pellet with a diameter of 10 mm and a height of 6 mm. To bind the pellets, 12 wt.% paraffin was added. Finally, the pellets were sintered with a heating rate of 5 • C/min.
The phase composition of the sample was identified using an X-ray diffractometer (Model D/MAX-B, Rigaku Co., Tokyo, Japan) at room temperature with Cu Kα radiation. The signals were collected in the range of 10 • -80 • . Archimedes' drainage method was carried out to measure the apparent density of the samples. Scanning electron microscopy (S-4800, Hitachi, Tokyo, Japan) was implemented to observe the microstructure. The microwave dielectric properties (ε r , Q × f, and τ f ) of the samples were measured by a network analyzer (3656D, Ceyear Co., Qingdao, China) with the Hakki-Coleman method [19]. The ε r and τ f were determined by the parallel plate method, and the Q × f was determined by the resonant cavity method. The temperature coefficient can be calculated using Equation (1). where the resonant frequencies f 1 and f 2 are measured at T 1 (25 • C) and T 2 (85 • C), respectively. The infrared reflectance spectrum was measured using a far infrared spectrometer (FTIR, Bruker IFS66v, Bruker Optics, Ettlingen, Germany) at the National Synchrotron Radiation Laboratory. The terahertz time-domain spectroscopy was measured by a THz-TD spectrometer (Z3, Zomega, Plano, TX, USA) in the State Key Laboratory of New Ceramics and Fine Technology, Tsinghua University [20][21][22]. The dielectric properties and loss in the terahertz band are calculated as follows: Equations (2)-(7) [23][24][25].
where n*(ω) is the complex refractive index at terahertz frequency, n(ω) is the index of refraction, k(ω)is the coefficient of extinction, v is the propagation speed of an electromagnetic wave at terahertz, ω is the frequency of Angle, and α(ω) is the coefficient of absorption. Figure 1 shows the XRD diffraction pattern of LaPO 4 -x wt.% LiF ceramic. The figure's diffraction peaks are consistent with the standard PDF card (PDF#83-0651), indicating that the crystal structure is a single monoclinic structure with a space group of P2 1 /c. The absence of the diffraction peak of the second phase demonstrates that the addition of LiF does not affect the formation of the LaPO 4 main stage. Figure 1b shows that with increasing doping of LiF, the diffraction peaks corresponding to the (200) crystal orientations are shifted towards. According to the Bragg equation, the lattice parameters and cell volume change as the angle shifts. The lattice parameters and cell volume also change as the angle shifts; with increasing x, the cell volume increases from 306.115 Å 3 to 306.339 Å 3 as x increases. Figure 2 exhibits the refined XRD data using Full Prof software (FullProf_Suite Windows (64 bits)). Table 1 summarizes lattice parameters and reliability factors. The smooth red line represents the difference between the measured and theoretical values, while the lower R-factors indicate that the refined results are reliable [26][27][28]. Figure 3 Figure 1 shows the XRD diffraction pattern of LaPO4-x wt.% LiF ceramic. The figure's diffraction peaks are consistent with the standard PDF card (PDF#83-0651), indicating that the crystal structure is a single monoclinic structure with a space group of P21/c. The absence of the diffraction peak of the second phase demonstrates that the addition of LiF does not affect the formation of the LaPO4 main stage.   Figure 1b shows that with increasing doping of LiF, the diffraction peaks corresponding to the (200) crystal orientations are shifted towards. According to the Bragg equation, the lattice parameters and cell volume change as the angle shifts. The lattice parameters and cell volume also change as the angle shifts; with increasing x, the cell volume increases from 306.115 Å 3 to 306.339 Å 3 as x increases. Figure 2 exhibits the refined XRD data using Full Prof software (FullProf_Suite Windows (64 bits)). Table 1 summarizes lattice parameters and reliability factors. The smooth red line represents the difference between the measured and theoretical values, while the lower R-factors indicate that the refined results are reliable [26][27][28]. Figure 3 Figure 4 displays the SEM image, which illustrates the changes in the apparent morphology of LaPO4 ceramics with the increase in the amount of LiF. As shown in Figure  4a-e, when x = 1,2, the grain size is relatively large and the grain boundary is distinct. However, when x ≥ 3, the grain size begins to refine, indicating that adding LiF is condu-  Table 1. The refinement patterns of the LaPO 4 -x wt.% LiF ceramics at the optimal sintering temperatures.  Figure 4 displays the SEM image, which illustrates the changes in the apparent morphology of LaPO 4 ceramics with the increase in the amount of LiF. As shown in Figure 4a-e, when x = 1,2, the grain size is relatively large and the grain boundary is distinct. However, when x ≥ 3, the grain size begins to refine, indicating that adding LiF is conducive to grain refinement. It is worth noting that due to the melting point of LiF at 845 • C, a part of LiF melts to form a liquid phase during the ceramic sintering process. When x ≥ 4, grain boundaries begin to soften, and macroscopic defects such as pores between grains and cracks appear on the surface, which particularly impacts the apparent density and performance [29][30][31]. When the amount of LiF continues to increase, the sintering temperature does not change significantly. Excessive LiF exists on the grain surface in an amorphous state, and a small number of pores and cracks appear, which has an adverse effect on the densification of ceramics. This is consistent with the trend of relative density change and further indicates that an appropriate amount of LiF can effectively reduce the sintering temperature and porosity. Improve the relative density of ceramics. Figure 5 shows the apparent density of LaPO 4 -x wt.% LiF (x = 0-5) ceramics. Between 1250 • C and 1450 • C, the apparent density of the LaPO 4 ceramic matrix increases from 4.13 g/cm −1 to 4.40 g/cm −1 with the increase in temperature, indicating that temperature is an essential factor. Furthermore, the sintering interval of the LaPO 4 -x wt.% LiF ceramics is 650 • C-1000 • C, meaning that the addition of LiF successfully reduces the sintering temperature of ceramics. The sintering temperature decreases further with the increase in LiF content. When x = 3, the temperature is reduced to 750 • C. At different x values, the apparent density increases first and then decrease. Figure 5b shows the relative density of ceramic samples. The shrinkage increases initially with the increase of x and reaches its maximum value at x = 3. Figure 6 is the dielectric constant (ε r ) of LaPO 4 -x wt.% LiF (x = 0-5) ceramics. As the sintering temperature increases, the ε r first increases and then decreases. It takes x = 3 as an example. When the temperature increases from 700 • C to 750 • C, the ε r increases from 7.08 to 10.03. However, as the temperature rises, the ε r begins to decrease slowly. The ε r is affected by several factors, such as dielectric polarization, porosity, and second equality [24,32,33]. However, the X-ray shows that the LaPO 4 -x wt.% LiF (x = 0-5) ceramic is a single pure phase. The change in apparent density is the same as the dielectric constant, so the density is the main factor affecting the dielectric constant of LaPO 4 ceramics. Adding LiF reduces the sintering temperature and promotes the densification of ceramics. Therefore, as the temperature increases, giant permittivity is obtained. Still, when the temperature exceeds the optimal sintering temperature, the increase in grain size destroys the crystal structure, leading to a decrease in density and a consequent reduction in permittivity.

Results and Discussion
performance [29][30][31]. When the amount of LiF continues to increase, the sintering te ature does not change significantly. Excessive LiF exists on the grain surface in an phous state, and a small number of pores and cracks appear, which has an adverse on the densification of ceramics. This is consistent with the trend of relative density c and further indicates that an appropriate amount of LiF can effectively reduce the ing temperature and porosity. Improve the relative density of ceramics.   Figure 5 shows the apparent density of LaPO4-x wt.% LiF (x = 0-5) ceramics. Be 1250 °C and 1450 °C, the apparent density of the LaPO4 ceramic matrix increases fro g/cm −1 to 4.40 g/cm −1 with the increase in temperature, indicating that temperatur essential factor. Furthermore, the sintering interval of the LaPO4-x wt.% LiF ceram 650 °C-1000 °C, meaning that the addition of LiF successfully reduces the sinterin perature of ceramics. The sintering temperature decreases further with the increase content. When x = 3, the temperature is reduced to 750 °C. At different x values, t parent density increases first and then decrease. Figure 5b shows the relative den ceramic samples. The shrinkage increases initially with the increase of x and reac maximum value at x = 3.   Figure 5 shows the apparent density of LaPO4-x wt.% LiF (x = 0-5) ceramics. Betw 1250 °C and 1450 °C, the apparent density of the LaPO4 ceramic matrix increases from 4 g/cm −1 to 4.40 g/cm −1 with the increase in temperature, indicating that temperature is essential factor. Furthermore, the sintering interval of the LaPO4-x wt.% LiF ceramic 650 °C-1000 °C, meaning that the addition of LiF successfully reduces the sintering te perature of ceramics. The sintering temperature decreases further with the increase in content. When x = 3, the temperature is reduced to 750 °C. At different x values, the parent density increases first and then decrease. Figure 5b shows the relative density ceramic samples. The shrinkage increases initially with the increase of x and reaches maximum value at x = 3.  Figure 6 is the dielectric constant (εr) of LaPO4-x wt.% LiF (x = 0-5) ceramics. As sintering temperature increases, the εr first increases and then decreases. It takes x = 3 an example. When the temperature increases from 700 °C to 750 °C, the εr increases fr 7.08 to 10.03. However, as the temperature rises, the εr begins to decrease slowly. The ε affected by several factors, such as dielectric polarization, porosity, and second equa [24,32,33]. However, the X-ray shows that the LaPO4-x wt.% LiF (x = 0-5) ceramic is a  Figure 7 is the quality factor (Q × f) of LaPO4-x wt.% LiF (x = 0-5) ceramics. The quality factor has the same variation as the dielectric constant. For instance, when x = 3, as an example. With the temperature increasing, the Q × f increases significantly from 15,946 GHz at 700 °C to 81,467 GHz at 750 °C, and the Q × f begins to decrease as the temperature continues to rise. Many factors affect the Q × f. These factors fall into two categories: inherent losses and external losses. The lattice vibration mode and crystal structure influence the inherent losses [34,35]. The sintering additive effectively reduces the sintering temperature of LaPO4 ceramics, but the phase composition is not affected. Thus, the main factor affecting the quality factor is density. Before reaching the optimum temperature point (750 °C), the increase in temperature is beneficial to reduce the number of pores in the ceramic, improve the density, and reduce the material loss inside the ceramic. As the temperature continues to rise, especially to 800 °C, several macroscopic cracks and pores make the interior loose, leading to the Q × f dropping to 68,791 GHz. The quality factor finally stabilizes within the range of 68,000 GHz to 77,000 GHz. The temperature coefficient characterizes the thermal stability of materials. Figure 8 summarizes the trend of the temperature coefficient. The temperature coefficients are all negative, and the change of x and τf does not change significantly. It fluctuates between  Figure 7 is the quality factor (Q × f ) of LaPO 4 -x wt.% LiF (x = 0-5) ceramics. The quality factor has the same variation as the dielectric constant. For instance, when x = 3, as an example. With the temperature increasing, the Q × f increases significantly from 15,946 GHz at 700 • C to 81,467 GHz at 750 • C, and the Q × f begins to decrease as the temperature continues to rise. Many factors affect the Q × f. These factors fall into two categories: inherent losses and external losses. The lattice vibration mode and crystal structure influence the inherent losses [34,35]. The sintering additive effectively reduces the sintering temperature of LaPO 4 ceramics, but the phase composition is not affected. Thus, the main factor affecting the quality factor is density. Before reaching the optimum temperature point (750 • C), the increase in temperature is beneficial to reduce the number of pores in the ceramic, improve the density, and reduce the material loss inside the ceramic. As the temperature continues to rise, especially to 800 • C, several macroscopic cracks and pores make the interior loose, leading to the Q × f dropping to 68,791 GHz. The quality factor finally stabilizes within the range of 68,000 GHz to 77,000 GHz.  Figure 7 is the quality factor (Q × f) of LaPO4-x wt.% LiF (x = 0-5) ceramics. The quality factor has the same variation as the dielectric constant. For instance, when x = 3, as an example. With the temperature increasing, the Q × f increases significantly from 15,946 GHz at 700 °C to 81,467 GHz at 750 °C, and the Q × f begins to decrease as the temperature continues to rise. Many factors affect the Q × f. These factors fall into two categories: inherent losses and external losses. The lattice vibration mode and crystal structure influence the inherent losses [34,35]. The sintering additive effectively reduces the sintering temperature of LaPO4 ceramics, but the phase composition is not affected. Thus, the main factor affecting the quality factor is density. Before reaching the optimum temperature point (750 °C), the increase in temperature is beneficial to reduce the number of pores in the ceramic, improve the density, and reduce the material loss inside the ceramic. As the temperature continues to rise, especially to 800 °C, several macroscopic cracks and pores make the interior loose, leading to the Q × f dropping to 68,791 GHz. The quality factor finally stabilizes within the range of 68,000 GHz to 77,000 GHz. The temperature coefficient characterizes the thermal stability of materials. Figure 8 summarizes the trend of the temperature coefficient. The temperature coefficients are all negative, and the change of x and τf does not change significantly. It fluctuates between The temperature coefficient characterizes the thermal stability of materials. Figure 8 summarizes the trend of the temperature coefficient. The temperature coefficients are all negative, and the change of x and τ f does not change significantly. It fluctuates between −46.40 ppm/ • C and −34.71 ppm/ • C, indicating that adding LiF has little effect on the temperature coefficient. Table 2 shows the microwave dielectric properties of LaPO 4 -x wt.% LiF ceramics. In conclusion, when x = 3, the optimum microwave dielectric    Infrared spectroscopy is an effective technique for characterizing the dielectric loss and response of ceramics. Figure 9a displays the fit of the infrared reflectance spectrum, obtained using the Reffit software and the classical resonator model with three parameters. The fitted values are in good agreement with the measured values. The complex permittivity (ε*) and reflectance (R) can be calculated using Equations (8) and (9) in the harmonic oscillator mode [36,37]: In the formula, ε ∞ is the optical permittivity, ω pj and ω oj are the plasma frequency and transverse frequency, respectively, γ j is the damping factor, and i is the imaginary  Infrared spectroscopy is an effective technique for characterizing the dielectric loss and response of ceramics. Figure 9a displays the fit of the infrared reflectance spectrum, obtained using the Reffit software and the classical resonator model with three parameters. The fitted values are in good agreement with the measured values. The complex permittivity (ε*) and reflectance (R) can be calculated using Equations (8) and (9) in the harmonic oscillator mode [36,37]: Crystals 2023, 13, 1035 9 of 13 obtained by infrared spectrum fitting is 2.341. Figure 9 represents the real (ε′) and imaginary (ε″) parts. The scattering of phonons and the overlap of peaks make the real part (ε′ = 6.83) less than the measured dielectric constant (εr = 10.04) [37][38][39]. Figure 9c shows the observed dielectric loss (2.16 × 10 −4 ) in the same order of magnitude as the measured dielectric loss (1.72 × 10 −4 ), indicating that phonon vibration affects dielectric loss. Moreover, external factors such as porosity, density, and grain distribution also affect dielectric loss. Pores can be reduced or processes optimized to minimize losses.  In the formula, ε ∞ is the optical permittivity, ω pj and ω oj are the plasma frequency and transverse frequency, respectively, γ j is the damping factor, and i is the imaginary unit. Table 3 shows the vibration modes of 16 different phonons. The optical permittivity obtained by infrared spectrum fitting is 2.341. Figure 9 represents the real (ε ) and imaginary (ε ) parts. The scattering of phonons and the overlap of peaks make the real part (ε = 6.83) less than the measured dielectric constant (ε r = 10.04) [37][38][39]. Figure 9c shows the observed dielectric loss (2.16 × 10 −4 ) in the same order of magnitude as the measured dielectric loss (1.72 × 10 −4 ), indicating that phonon vibration affects dielectric loss. Moreover, external factors such as porosity, density, and grain distribution also affect dielectric loss. Pores can be reduced or processes optimized to minimize losses. Infrared fitting results are easily limited by infrared pattern recognition. Terahertz timedomain spectroscopy technology investigates the effect of lattice vibration on properties. Figure 10 shows the dielectric response of LaPO 4 -3 wt.% LiF sintered at 750 • C in the frequency band of 0.5 THz~1.1 THz. The dielectric properties of the terahertz band are derived from the refractive index and extinction coefficient. Infrared fitting results are easily limited by infrared pattern recognition. Terahertz time-domain spectroscopy technology investigates the effect of lattice vibration on properties. Figure 10 shows the dielectric response of LaPO4-3 wt.% LiF sintered at 750 °C in the frequency band of 0.5 THz~1.1 THz. The dielectric properties of the terahertz band are derived from the refractive index and extinction coefficient.  Figure 11 shows the change curve of the refractive index (n). The refractive index does not increase significantly with the increase in frequency and is stable between 3.17  Figure 11 shows the change curve of the refractive index (n). The refractive index does not increase significantly with the increase in frequency and is stable between 3.17 and 3.21. The absorption coefficient (α) increases with the increase in frequency, which is associated with the unit volume polarizability. The dielectric constant which extrapolated from terahertz time-domain spectrum was in line with the value at microwave frequency [1,21,35]. At 7 GHz, the dielectric constant of ceramics is 10.03. At 0.5 THz, the dielectric constant of the ceramic is 10.04. Therefore, it can be inferred that the polarization mechanism of dielectric ceramic does not change in the terahertz frequency band, in which the ionic polarization is still dominant.  The fitted line in Figure 11 is the linear relationship between dielectric loss and frequency, and the slope of the matched line is 0.010, representing the vibration of the lattice. Considering the defect in the sample, it may be the oxygen vacancy that affects the dielectric loss. When x = 3, S.T. = 750 °C, the excellent optical and dielectric properties are: n = The fitted line in Figure 11 is the linear relationship between dielectric loss and frequency, and the slope of the matched line is 0.010, representing the vibration of the lattice. Considering the defect in the sample, it may be the oxygen vacancy that affects the dielectric loss. When x = 3, S.T. = 750 • C, the excellent optical and dielectric properties are: n = 3.17, ε r = 10.03, α = 1.28 cm −1 , tan δ = 0.0039. Therefore, LaPO 4 -3 wt.% LiF ceramics with low absorption coefficients and dielectric losses are optional for dielectric filters and lenses applied in the terahertz band.
The low-temperature co-firing ceramic (LTCC) technology has garnered significant attention due to its exceptional high-frequency characteristics, low energy consumption, and compact size. Among the various components of LTCC, the focus of research has been on LTCC materials. LaPO 4 ceramics have a high sintering temperature (1400 • C). Adding 3 wt.% LiF reduces the sintering temperature to 750 • C and has excellent dielectric properties. In this study, 20 wt.% Ag powder (10 µm) and LaPO 4 -3 wt.% LiF ceramic powder at 750 • C are mixed and co-fired at 750 • C for 2 h. Figure 11 shows the XRD results. The results show that no chemical reaction occurs after co-firing LaPO 4 -3 wt.% LiF ceramic and Ag, and the co-firing is a success, which provides a new idea for the future application of LTCC [29].

Conclusions
In this paper, the LaPO 4 -x wt.% LiF (x = 0~5) ceramics are prepared by the traditional solid-state reaction method, and the microwave dielectric properties at different frequency bands are studied. The XRD patterns show that the ceramics crystallized in single phase LaPO 4 , no secondary phase observed. Rietveld refinement by using Fullprof software. The results show that the crystal structure of the ceramics is monoclinic and that the phase composition of the mixture has not changed. LiF exists in the liquid phase and fills the void in ceramic. Therefore, with the increase of LiF, the relative density of ceramic is greatly improved compared with the matrix, the sintering temperature reduces to 750 • C, and the quality factor rises to 81,466 GHz. The dielectric constant increases by 10.03, and the temperature coefficient is −43.78 ppm/ • C (x = 3). In the microwave frequency band, the ion shift polarization determines the dielectric constant, and the dielectric loss is mainly due to the lattice vibration. In the THz frequency band, the main factor affecting the dielectric constant is the ion displacement polarization, while the oxygen vacancy is the main factor affecting the dielectric loss. At 750 • C, LaPO 4 -3 wt.% LiF ceramic powder does not react with Ag, and the co-firing is successful, indicating that LaPO 4 -x wt.% LiF ceramic is an alternative material for future LTCC technology.

Data Availability Statement:
The data and materials supporting this study's findings are available from the corresponding author upon reasonable request.