Lattice vibrational characteristics, crystal structures, and dielectric properties of LiMnPO4 microwave dielectric ceramics as a function of sintering temperature

LiMnPO4 (LMP) microwave dielectric ceramics were manufactured at different temperatures via a standard solid-state reaction method and the LMP ceramic sintered at 750 °C displayed dielectric properties of εr = 7.82 and Q × f = 29,189 (f = 12.7 GHz). The lattice vibrational characteristics of LMP ceramics were studied utilizing both infrared reflection and Raman scattering spectroscopy to clarify the basic principle of the dielectric response. The intrinsic properties that were fitted and simulated based on the infrared spectra agreed with the measured property values. The low-frequency vibrational modes contributed more to the dielectric properties than the high-frequency modes. Upon increasing the temperature, the permittivity was positively correlated with the bond length but showed the opposite trend of the Raman shift of mode 9 Ag(υ1). The Q × f value was positively correlated with the packing fraction but negatively correlated with the FWHM of mode 10 Ag(υ3). Thus, the structure–property relationships of LMP ceramics were established as a function of sintering temperature.


Introduction
The progress and revolutionary development of modern communication products toward generalization, miniaturization, and high efficiency have increased the requirements and demand for highperformance microwave dielectric ceramics (MWDCs) [1,2]. Specifically, the substrates used to fabricate integrated circuits must have a low dielectric constant (e r ) to reduce transmission delays, a high quality factor (Q 9 f) to obtain favorable filter characteristics and communication quality. Some MWDCs exhibit excellent dielectric properties, but they require high sintering temperatures and have other shortcomings that severely limit their applications. To save energy and reduce costs, the sintering temperatures of ceramics must be decreased to achieve better sintering characteristics, therefore MWDCs with low inherent sintering temperatures have attracted attention. [1,[3][4][5][6].
For lithium-transition metal phosphates LiRPO 4 (R = Ni, Mn, Zn, Mg)-series ceramics [7][8][9][10][11], different atoms at the R position affect the crystal structures and inherent properties of the materials. They are generally investigated as cathode materials for lithium-ion batteries and do not display microwave dielectric properties. But there have been studying the microwave dielectric properties of LiRPO 4 -series ceramics by adjusting the sintering temperature, doping, substitution, and other methods. So, they have received considerable attention as microwave dielectric ceramics.
Few studies have been conducted on the lattice vibrational characteristics of MWDCs, which can be used to interpret their microphysical mechanisms, i.e., the dielectric response mechanism. Xiao et al. revealed the inherent attributes of LiNiPO 4 (LNP) and LiZnPO 4 (LZP) ceramics [15,16], including their intrinsic dielectric properties and the corresponding dielectric response mechanisms, which were affected by the composition, process parameters, and crystal structures of samples. The intrinsic dielectric properties and the dielectric response mechanisms of MWDCs are closely related to their lattice vibrational characteristics, which can be studied using Raman scattering and infrared reflection (IR) spectroscopy.
Compared with LNP and LZP, there is no research on the inherent attributes or the lattice vibrational characteristics of LMP ceramics, which limit the indepth understanding of these kinds of ceramics. Thus, additional research on LMP ceramics is necessary to articulate their physical dielectric response mechanism. Having a theoretical foundation for lithium-transition metal phosphate (LiRPO 4 )-series MWDCs can further promote their engineering applications.
In this work, a conventional solid-state reaction was used to manufacture LMP ceramics at different sintering temperatures. The structures of the LMP ceramics were determined by X-ray diffraction and their microstructures were studied by scanning electron microscopy. The Raman and infrared reflection spectroscopy analyzed the lattice vibrational characteristics. The dielectric performances were calculated using the four-parameter semi-quantum (FPSQ) model combined with IR spectroscopy. The structure-property relationships were established using the Raman and infrared reflection spectroscopy. which provide a theoretical reference for the design of new MWDCs, especially for controlling their structures and properties.

Experimental
The LMP ceramics were fabricated using analytically pure Li 2 CO 3 (AR, Kelon Chemical), MnCO 3 (AR, Macklin), and NH 4 H 2 PO 4 (AR, Kelon Chemical) powders as raw materials by a conventional solidstate reaction. First, the raw materials were weighed J Mater Sci: Mater Electron (2022) 33:7708-7717 in a stoichiometric ratio and milled with ZrO 2 balls in distilled water for 6 h. After drying, the powders were sintered at 600°C for 3 h and then ball milled and dried again. The prepared powders were uniformly mixed with 5 wt% polyvinyl alcohol (PVA) solution and pressed into samples under a pressure of 100 MPa. The LMP pellets were divided into six parts and sintered at 700, 725, 750, 775, 800, and 825°C for 4 h. In addition, the LMP specimens were polished with micron Al 2 O 3 slurry ahead of all characterization and measurements to form a mirror to reduce the impact of surface defects.
The crystal structures and main phases of the specimens were studied by XRD (Rigaku D/max-2000, Japan) equipped with a Cu-Ka radiation source in step-and-scan mode. The XRD data were obtained over the diffraction angle range of 10-80°with a wavelength of 1.542 Å , a scanning speed of 4°/min. SEM (Nova-Nano-SEM 450, USA) was used to analyze the microscopic surface topographies of the pellet cross-sections. The Raman scattering spectra were collected by a Raman spectrometer (LabRAM HR Evolution) with a liquid-N 2 -cooled device at room temperature. FTIR spectrometry (Bruker Optik GmbH, IFS 66v/s, Germany) was used to gather the infrared reflectivity spectra at room temperature. To collect the far-infrared spectra (50-700 cm -1 ), a PE-DTGS detector and a Mylar beamsplitter were applied under vacuum, and the mid-infrared (500-4500 cm -1 ) spectra were obtained by a device composed of a DTGS detector with a Ge-coated KBr beamsplitter.
Archimedes' method was applied to obtain the bulk densities of the LMP samples. The permittivity and quality factors were measured using a network analyzer (E8363B, Agilent Technologies Inc., Palo Alto, CA) via the open cavity and resonant cavity methods, respectively.

Results and discussion
The XRD patterns of the LiMnPO 4 (LMP) samples sintered at different temperatures are shown in Fig. 1, which were recognized as pure LiMnPO 4 phase (JCPDS#74-0375), belonging to an olivine structure with an orthogonal structure and the Pnmb space group (No. 62). The XRD baselines are flat, and the diffraction peaks are sharp, indicating that all samples have good crystallinity. To further analyze the crystal structures of the LMP ceramics, the XRD data were refined via Rietveld refinement utilizing TOPAS software. The refined lattice parameters of the LMP ceramics are listed in Table 1. The quality of the refined results was characterized by the R-factors (R wp , R p , and R exp ), which indicated the reliability and credibility of the refinements. Taking the LMP sample sintered at 750°C as an example, the experimental data (pink circle) were consistent with the fitting curve (black curve), as shown in Fig. 2, which were demonstrated by the relatively smooth difference curve (green line). Figure 3 displays the unit cell structure of olivine LMP, which belongs to the orthorhombic crystal system with the Pmnb space group. The unit cell has center symmetry and is composed of four  Figure 4 shows the variations in the relative density, permittivity, and Q 9 f values of LMP ceramics as a function of the sintering temperature. As the sintering temperature increased, these data first increased and then decreased. The dielectric constant reached a minimum at 700°C (e r = 7.63), the Q 9 f value reached the minimum at 825°C (23,556 GHz), and the two reached the maximum at 750°C (e r = 7.82, Q 9 f = 29,189 GHz). The LMP ceramic sintered at 750°C achieved the highest dielectric properties and also had the highest relative density of 95.90%. Compared with other ceramics, its Q 9 f value was better than at a lower sintering temperature.
The surface micromorphology of the LMP ceramics in Fig. 5 shows that the pores were gradually sealed upon increasing the sintering temperature. The ceramics displayed a better micromorphology, the relative density gradually increased, and the quality factor also increased progressively. Above 750°C, the grain boundaries became fuzzy and abnormal grain growth appeared due to over-sintering, which decreased the quality factor.
Infrared reflectance spectroscopy and room-temperature Raman spectroscopy are used to study the lattice vibrations and intrinsic dielectric properties [17,18]. Based on the group theory analysis, theoretically, 81 optical vibrational modes exist for LMP  ceramics with the Pmnb space group, whose specific information can be stated as follows: [15] C The A and B modes represent a single-degenerate state of symmetric eigenfrequency with respect to the main axis and a single-degenerate state of eigenfrequency with respect to the main axis, respectively. The g represents the central symmetric vibrational mode and the u represents the central antisymmetric vibrational mode. All A g and B g vibrational modes are Raman active, which are attributed to changes in the polarizability. The infrared-active modes include 13B 1u , 9B 2u , and 13B 3u , which are related to vary of the dipole moment. When analyzing the vibrational spectra of phosphates, the vibration (stretching and deformation) of the [PO 4 ] 3tetrahedron and the vibration of the Li ? and Mn 2? ions are usually considered because the P-O bond is much stronger than the other ionic bonds.
The Raman spectra of the LMP samples at different temperatures are presented in Fig. 6. In total, 11 peaks were identified and assigned according to group theory, which allowed them to be classified into two regions: an internal mode with a frequency higher than 400 cm -1 and the external lattice oscillations corresponding to frequencies lower than 400 cm -1 . The Raman peak with the strongest intensity appeared at 948 cm -1 (mode 9), assigned as mode A g (t 1 ), which represents the symmetric tensile oscillation of the [PO 4 ] 3tetrahedron, where each tetrahedron in the unit cell has the same phase (A g symmetry) [19]. The A g mode observed around 948 cm -1 belongs to the asymmetric vibration of tetrahedral [PO 4 ] 3-, consistent with a previous report (948.5 cm -1 ) [19]. It does not include the movement of metal ions due to its symmetry, so the A g mode of other phosphates has a similar frequency, i.e., 946-950 cm -1 in LiNiPO 4 [20] and 944 cm -1 in LiCdPO 4 [19]. The A g (t 1 ) mode represents the Fig. 4 Relationship between the relative density, permittivity, and Q 9 f value, as a function of sintering temperature symmetric tensile vibration of tetrahedral [PO 4 ] 3-, and the A g (t 2 ) mode corresponds to symmetric bending vibrations. The A g (t 3 ) (mode 10) and A g (t 4 ) mode (mode 11) are the stretching and bending vibrations of the P-O bond, respectively, and both modes are antisymmetric [21].
The dielectric constant is affected by pores in the ceramics, which can be corrected according to the porosity (P) and measured permittivity (e r ), according to Eq. (2). The calculation results are summarized in Table 2. [15] e r ¼ e rc 1 À 3P e rc À 1 ð Þ 2e rc þ 1 ð2Þ The corrected dielectric constant (e rc ) and other properties are summarized in Table 2. As shown in the table, e rc and e r have opposite trends. e r is affected by the ceramics compactness and followed the same trend as the relative density. The relative density was the highest at 750°C, so e r was the largest at this time. e rc eliminates the influence of pores, and the crystal structure is the decisive factor. The lower the relative density is, the greater the increase in the dielectric constant after correction.
Infrared spectroscopy can be used to study the dielectric response mechanism. The infrared reflection spectrum of LMP fabricated at 750°C is shown in Fig. 7, where the vibrational modes corresponding to t 1 -t 2 are as described above. Within the microwave frequency range, the complex dielectric function e * and the optical reflectance R satisfy the Fresnel Eq. (3): [22] R ¼ The FPSQ model is often performed to infer the corresponding parameters of the oscillator from the infrared reflection spectrum. Eq. (4) of the complex dielectric constant related to infrared phonons is as follows: [23] where e ? is the optical permittivity caused by highfrequency electron polarization, the number of phonon modes is indicated by n, the j-th frequency of transverse and vertical modes is represented by X jTO and X jLO , respectively. The damping factor of the transverse and vertical modes is expressed as c jTO and c jLO , respectively. The contribution of each infrared vibration mode to the dielectric performance can be calculated by the following formulae: [24] The intrinsic dielectric constant and dielectric loss can be obtained by summing the oscillator strength  and the loss of all modes, using the following equations: [15] The detailed simulation results of the LMP samples sintered at 750°C are listed in Table 3. The low-frequency vibrational modes have a major contribution to the dielectric properties. The intrinsic dielectric constant value of LMP fitted from the FPSQ model was 7.94, which is close to the measured permittivity of 7.82 and the corrected value e rc of 8.23, which implies that the effect of defective phonon scattering is weak. The simulated dielectric loss was 3.07 9 10 -4 , which is lower than the measured value of 4.36 9 10 -4 (f = 12.7 GHz) because defects on the sample surface will inevitably produce defects in the optical signal. With respect to the permittivity, the dielectric loss is more susceptible to these defects [25], so the dielectric loss can only be estimated from the IR spectra.
Figures 8 illustrates the relationship between the corrected dielectric constant, the P-O bond length (in Table 4, calculated using FullProf software), and a Raman shift of mode 9 upon increasing the sintering temperature. As the temperature increased, the corrected dielectric constants were positively correlated with the P-O bond length, i.e., longer bonds are more easily polarized. This will enhance the dielectric constant, which may indicate that the vibrational frequency of the mode is proportional to its bond energy. The center frequency corresponding to the  strongest mode 9 (representing the asymmetric stretching vibration of the P-O tetrahedron) in the LMP Raman diagrams falls and then rises upon increasing the sintering temperature, which is the opposite of the P-O bond length and the corrected dielectric constant trends. The energy of the P-O bond increased and the bond length decreased when the vibration frequency increased upon increasing the sintering temperature. Accordingly, a shorter bond length has a larger bond energy. An inflection point appeared at 750°C, where the bond length increased at temperatures higher than 750°C. The quality factor of ceramics is only related to external factors, such as internal stress, pores, impurities, and various defects, as well as to internal factors, such as phonons. The packing fraction of ceramics can be calculated by the following formula: [26] Packing fraction % where Z is the number of atomic in the unit cell. As depicted in Fig. 9, the quality factor and packing fraction exhibited similar trends. This may be because an increase in the packing fraction weakened lattice vibrations, which increased the quality factor [27]. Changes in the Q 9 f value were negatively correlated with the full width at half maximum (FWHM) value of mode 10 (antisymmetric vibration of the tetrahedron [PO 4 ] 3-). The FWHM value reflects changes in the degree of order of the crystal structure.  Table 4 The bond lengths of LiMnPO 4 ceramics Upon changing the P-O bond length, the [PO 4 ] 3tetrahedron was distorted, which affected the ordering degree. A lower ordering degree indicates greater damping, which results in a larger dielectric loss, i.e., a lower Q 9 f value.

Conclusion
The feasibility of synthesizing LiMnPO 4 ceramics by a solid-state method was studied, and the lattice vibrational characteristics and structure-property relationships of LMP samples were analyzed. The prepared pure-phase LMP possessed fine crystallization and clear grain boundaries. Both Raman and IR spectroscopies were obtained to clarify the lattice vibrational characteristics. The Raman and far-infrared modes were also analyzed to investigate the phonon characteristics. IR spectroscopy was used to consider the contribution of each mode to the dielectric performance in combination with the FPSQ model. The results showed that low-frequency vibrational modes exhibited a greater impact than the high-frequency modes. The relationships between the dielectric properties, FWHM, and Raman shifts, as well as the fine structural parameters, such as packing fraction and bond length, were determined. The permittivity was positively correlated with the P-O bond length but negatively correlated with the Raman shift of mode 9. As the temperature increased, the Q 9 f value was positively correlated with the packing fraction. In contrast, the negative correlation with the FWHM of mode 10 was related to the ordering degree of the P-O tetrahedron. The IR data simulated according to the FPSQ model indicated that the low-frequency vibrational modes have a major contribution to the dielectric properties. LMP sintered at 750°C possessed excellent dielectric properties of e r = 7.82, Q 9 f = 29,189 (f = 12.7 GHz) and the highest relative density of 95.90%.