Temperature Stable Cold Sintered (Bi0.95Li0.05)(V0.9Mo0.1)O4-Na2Mo2O7 Microwave Dielectric Composites

Dense (Bi0.95Li0.05)(V0.9Mo0.1)O4-Na2Mo2O7 (100−x) wt.% (Bi0.95Li0.05)(V0.9Mo0.1)O4 (BLVMO)-x wt.% Na2Mo2O7 (NMO) composite ceramics were successfully fabricated through cold sintering at 150 °C under at 200 MPa for 30 min. X-ray diffraction, back-scattered scanning electron microscopy, and Raman spectroscopy not only corroborated the coexistence of BLVMO and NMO phases in all samples, but also the absence of parasitic phases and interdiffusion. With increasing NMO concentration, the relative pemittivity (εr) and the Temperature Coefficient of resonant Frequency (TCF) decreased, whereas the Microwave Quality Factor (Qf) increased. Near-zero TCF was measured for BLVMO-20wt.%NMO composites which exhibited εr ~ 40 and Qf ~ 4000 GHz. Finally, a dielectric Graded Radial INdex (GRIN) lens was simulated using the range of εr in the BLVMO-NMO system, which predicted a 70% aperture efficiency at 26 GHz, ideal for 5G applications.

Bulk densities of ceramic pellets were calculated by the geometric method. Crystal structure, phase assemblage, microstructures of ceramic pellets were characterised by X-ray powder diffraction (XRD, D2 Phaser, Bruker, Billerica, MA, USA) using CuKα radiation, scanning electron microscopy (SEM, Inspect F, FEI, Hillsboro, OR, USA) and Raman spectroscopy (inVia Raman microscope, Renishaw, Wotton-under-Edge, UK) using a green laser with 514.5 nm at room temperature, respectively. Microwave properties of ceramic pellets were determined by a TE 01δ dielectric resonator method using a vector network analyzer (R3767CH, Advantest Corporation, Tokyo, Japan). A Peltier device heated the cavity to measure the resonant frequency (f ) from 25 • C to 85 • C. TCF was calculated according to: where the f T and f T 0 were the TE 01δ resonant frequencies at temperature T and T 0 , respectively.

Results and Discussion
The bulk and relative densities of CSP BLVMO are 4.98 g/cm 3 and 73%, respectively, which increase to 6.04 g/cm 3 and 98% with the addition of NMO ( Figure 1 and Table 1). Following an initial increase for x = 0.05, bulk densities decreased linearly due to a lower theoretical density of NMO compared with BLVMO (6.85 g/cm 3 and 3.69 g/cm 3 for BLVMO and NMO, respectively) [25][26][27][28]. The relative densities of (100−x) wt.% BLVMO-x wt.% NMO ceramics are >90% (except pure BLVMO), attaining 98% for 40 wt.% NMO, confirming that dense (100−x) wt.% BLVMO-x wt.% NMO composites could be readily fabricated by CSP.  Room-temperature XRD patterns of CSP BLVMO, NMO and (100−x) wt.% BLVMO-x wt.% NMO samples in the 10°-50° 2θ range are shown in Figure 2. BLVMO has a tetragonal scheelite structure (PDF 48-0744) [26−28], with no evidence of splitting of main diffraction peaks. NMO has an orthorhombic structure with symmetry described by the space group Cmca (PDF 01-073-1797, a = 7.164 Å, b = 11.837 Å, c = 14.713 Å, Z = 8) [25]. All reflections in the XRD data for BLVMO-NMO ceramic composites can be ascribed to BLVMO and NMO and the intensity of NMO diffraction peaks increases with the concentration of NMO, as marked in Figure 2. Coexistence of peaks corresponding to BLVMO and NMO appear in all compositions with 0 < x < 1, and there is no apparent shift in peak position, indicating no interaction between these two end-members.
Room-temperature Raman spectra of CSP BLVMO, NMO and (100−x) wt.% BLVMO-x wt.% NMO ceramics are shown in Figure 3. According to group theory and irreducible representations, there are 15 and 129 different vibrational modes in BLVMO and NMO [26][27][28][29], respectively, given as follows: In BLVMO, nine 3A g + 6B g modes are Raman active and six 2A u + 4B u modes are IR active [26][27][28]. In NMO, translations of Na and Mo atoms give 3A g + 2A u + 3B 1g + 4B 1u + 3B 2g + 4B 2u + 3B 3g + 2B 3u and 3A g + 2A u + 3B 1g + 4B 1u + 2B 2g + 3B 2u + 4B 3g + 3B 3u modes, respectively. Three B 1u + B 2u + B 3u modes are acoustic active and the remaining 12A g + 9A u + 9B 1g + 12B 1u + 9B 2g + 12B 2u + 19B 3g + 9B 3u modes correspond to stretching and bending modes of MoO 4 and MoO 6 octahedra [29]. The Raman spectra of (100−x) wt.% BLVMO-x wt.% NMO composites consist of a superposition of the spectral features exhibited by each individual phase, further confirming the coexistence of BLVMO and NMO in composite ceramics. Furthermore, the intensity of the NMO Raman modes increases with increasing NMO concentration. Several Raman bands in NMO (~86, 832, 872, 920 and 937 cm −1 ) are visible in all (100−x) wt.% BLVMO-x wt.% NMO compositions, confirming the coexistence of BLVMO and NMO in the composites.   Back-Scattered Electron (BSE) scanning electron microscope images of fracture surfaces of conventionally-sintered BLVMO, cold-sintered BLVMO-20wt.%NMO and NMO are revealed in Figure 4. Dense microstructures are visible in all three compositions, in agreement with the data presented in Figure 1 and Table 1. The average grain size of BLVMO (1-2 μm, Figure 4a) is smaller than that of NMO (2-5 μm, Figure 4b), consistent with previous reports [25 −28]. Figure 4c,d shows the composites to be composed two chemically distinct and discrete phases with EDS confirming the dark and light contrast to be NMO and BLVMO, respectively, in agreement with XRD and Raman (Figures 2 and 3).   Back-Scattered Electron (BSE) scanning electron microscope images of fracture surfaces of conventionally-sintered BLVMO, cold-sintered BLVMO-20wt.%NMO and NMO are revealed in Figure 4. Dense microstructures are visible in all three compositions, in agreement with the data presented in Figure 1 and Table 1. The average grain size of BLVMO (1-2 μm, Figure 4a) is smaller than that of NMO (2-5 μm, Figure 4b), consistent with previous reports [25 −28]. Figure 4c,d shows the composites to be composed two chemically distinct and discrete phases with EDS confirming the dark and light contrast to be NMO and BLVMO, respectively, in agreement with XRD and Raman (Figures 2 and 3). Back-Scattered Electron (BSE) scanning electron microscope images of fracture surfaces of conventionally-sintered BLVMO, cold-sintered BLVMO-20wt.%NMO and NMO are revealed in Figure 4. Dense microstructures are visible in all three compositions, in agreement with the data presented in Figure 1 and Table 1. The average grain size of BLVMO (1-2 µm, Figure 4a) is smaller than that of NMO (2-5 µm, Figure 4b), consistent with previous reports [25][26][27][28]. Figure 4c,d shows the composites to be composed two chemically distinct and discrete phases with EDS confirming the dark and light contrast to be NMO and BLVMO, respectively, in agreement with XRD and Raman (Figures 2 and 3). The microwave properties of (100−x) wt.% BLVMO-x wt.% NMO as a function x are presented in Figure 5 and also listed in Table I. Low relative density (73%) of CSP BLVMO is observed which gives rise to lower εr (30) and Qf (1300 GHz) than for conventionally-sintered BLVMO, Table 1. εr and TCF values decrease linearly from 48 and +41 ppm/°C, respectively, for BLVMO-5 wt.%NMO to 12.7 and −99 ppm/°C for NMO. Near-zero TCF (−4 ppm/°C) is obtained for BLVMO-20 wt.%NMO. Qf increases from 1300 GHz for BLVMO to 12,000 GHz for NMO, as shown in Figure 5 and Table 1.  The microwave properties of (100−x) wt.% BLVMO-x wt.% NMO as a function x are presented in Figure 5 and also listed in Table I. Low relative density (73%) of CSP BLVMO is observed which gives rise to lower ε r (30) and Qf (1300 GHz) than for conventionally-sintered BLVMO, Table 1. ε r and TCF values decrease linearly from 48 and +41 ppm/ • C, respectively, for BLVMO-5 wt.%NMO to 12.7 and −99 ppm/ • C for NMO. Near-zero TCF (−4 ppm/ • C) is obtained for BLVMO-20 wt.%NMO. Qf increases from 1300 GHz for BLVMO to 12,000 GHz for NMO, as shown in Figure 5 and Table 1. The microwave properties of (100−x) wt.% BLVMO-x wt.% NMO as a function x are presented in Figure 5 and also listed in Table I. Low relative density (73%) of CSP BLVMO is observed which gives rise to lower εr (30) and Qf (1300 GHz) than for conventionally-sintered BLVMO, Table 1. εr and TCF values decrease linearly from 48 and +41 ppm/°C, respectively, for BLVMO-5 wt.%NMO to 12.7 and −99 ppm/°C for NMO. Near-zero TCF (−4 ppm/°C) is obtained for BLVMO-20 wt.%NMO. Qf increases from 1300 GHz for BLVMO to 12,000 GHz for NMO, as shown in Figure 5 and Table 1.  Provided there are no chemical reactions between phases, the ε r in composites may be predicted by different mixing laws, as follows [22]: where ε 1 , ε 2 and ε 0 are the ε r of phase 1, phase 2 and air, respectively and V 1 , V 2 and V 0 (V 1 + V 2 + V 0 = 1) are their respective volume fractions. As shown in Figure 5, ε r for (100−x) wt.% BLVMO-x wt.% NMO composite ceramics is within the range of calculated values for Equations (4) and (5), and close to the values obtained using Equation (6), indicating that ε r follows a logarithmic mixing law with x. TCF of composites is predicted with a simple mixing rule, which is derived from the Equation (6) [30]: where TCF 1 and TCF 2 correspond to the TCF of the two phases. TCF is consistent with calculated values using Equations (7), as shown in Figure 5b, suggesting they can be predicted using simple rules of mixture.
A GRIN lens is an antenna component for transforming a spherical to a planar wavefront, and enables highly directive antennas and shaped beams. A lightweight, flat lens may be used in the proximity of the feed to realise a compact system that is desired by 5G applications. For practical fabrication, the index profile of a flat lens is usually graded to several tight-fitted rings with radially reduced ε r . GRIN lenses may be fabricated from concentric dielectric cylindrical rings with graded ε r , Figure 6a. The simulated electric field of a ceramic GRIN lens is displayed in Figure 6b, transforming a spherical to a planar wavefront at 26 GHz.
A GRIN lens is an antenna component for transforming a spherical to a planar wavefront, and enables highly directive antennas and shaped beams. A lightweight, flat lens may be used in the proximity of the feed to realise a compact system that is desired by 5G applications. For practical fabrication, the index profile of a flat lens is usually graded to several tight-fitted rings with radially reduced εr. GRIN lenses may be fabricated from concentric dielectric cylindrical rings with graded εr, Figure 6a. The simulated electric field of a ceramic GRIN lens is displayed in Figure 6b, transforming a spherical to a planar wavefront at 26 GHz. The design parameters of a lens are shown in Tables 3 and 4. The dielectric lens is comprised of six concentric rings; the outermost has the lowest effective εr (12.7), while the centre has the highest εr (48). The high εr ceramic reduces the thickness of the lens (miniaturises) compared with low εr materials such as polymers. Table 3. Designed parameters of a 3D-printed lens.

Parameter
Value Diameter R = 12.5 mm Focal length F = 12.5 mm Thickness T = 1.53 mm Lens performance was simulated using CST Microwave Studio. An open-ended Ka-band waveguide (7.112 mm × 3.556 mm) was used to illuminate the lens. The boresight directivity is increased across the whole frequency range from 26 to 40 GHz. The relative increase compared to the case with no lens is between 4.6 and 8.5 dB. The aperture efficiency of the lens is ~70% at 26 GHz. The simulated E-plane (i.e., the plane containing the electric field vector) and H-plane (the plane containing the magnetic field vector, normal to the E-plane) radiation patterns of the lens are illustrated in Figure 7. The design parameters of a lens are shown in Tables 3 and 4. The dielectric lens is comprised of six concentric rings; the outermost has the lowest effective ε r (12.7), while the centre has the highest ε r (48). The high ε r ceramic reduces the thickness of the lens (miniaturises) compared with low ε r materials such as polymers. Table 3. Designed parameters of a 3D-printed lens.

Parameter Value
Diameter R = 12.5 mm Focal length F = 12.5 mm Thickness T = 1.53 mm Lens performance was simulated using CST Microwave Studio. An open-ended Ka-band waveguide (7.112 mm × 3.556 mm) was used to illuminate the lens. The boresight directivity is increased across the whole frequency range from 26 to 40 GHz. The relative increase compared to the case with no lens is between 4.6 and 8.5 dB. The aperture efficiency of the lens is~70% at 26 GHz. The simulated E-plane (i.e., the plane containing the electric field vector) and H-plane (the plane containing the magnetic field vector, normal to the E-plane) radiation patterns of the lens are illustrated in Figure 7.

Conclusions
The (100−x) wt.% BLVMO-x wt.% NMO ceramics with relative density of 92%-98% were fabricated by cold sintering process at 150 °C/30 min/200 MPa. No evidence of chemical interaction was observed in composites, except BLVMO and NMO phases, by means of SEM, XRD and Raman spectroscopy. As x increased, TCF and εr decreased, while Qf increased. Near-zero TCF ~ +4 ppm/°C was measured for BLVMO-20wt%NMO with εr ~ 40 and Qf ~ 4000 GHz. A dielectric GRIN lens was designed and simulated exhibiting 70% aperture efficiency at 26 GHz, which we propose may be fabricated using (100−x) wt.% BLVMO-x wt.% NMO composites.

Conclusions
The (100−x) wt.% BLVMO-x wt.% NMO ceramics with relative density of 92%-98% were fabricated by cold sintering process at 150 • C/30 min/200 MPa. No evidence of chemical interaction was observed in composites, except BLVMO and NMO phases, by means of SEM, XRD and Raman spectroscopy. As x increased, TCF and ε r decreased, while Qf increased. Near-zero TCF~+4 ppm/ • C was measured for BLVMO-20wt%NMO with ε r~4 0 and Qf~4000 GHz. A dielectric GRIN lens was designed and simulated exhibiting 70% aperture efficiency at 26 GHz, which we propose may be fabricated using (100−x) wt.% BLVMO-x wt.% NMO composites.