Fabrication of Temperature-Stable Low-Temperature Co-Fired Ceramics via Reaction Between Ba3(VO4)2 and Li2WO4

TL;DR

Scientists created a new type of ceramic material that can be fired at low temperatures and has stable microwave properties, making it suitable for electronic applications.

Contribution

A new glass-free ceramic composite with controllable microwave properties is developed using a reaction between Ba3(VO4)2 and Li2WO4.

Findings

The ceramics achieved high relative densities of ≈94–98% at 850 °C through reactive liquid-phase sintering.

Adjusting Li2WO4 content allows systematic control of τf and Q × f values.

The composite shows no detectable reaction with Ag electrodes, indicating good chemical compatibility.

Abstract

New glass-free low-temperature co-fired microwave dielectric composites with compositions (1–4x/3)Ba3(VO4)2–xBaWO4–(2x/3)Li3VO4 (x = 0.3–0.7) were fabricated by reactive liquid-phase sintering of (1–x)Ba3(VO4)2–xLi2WO4 mixtures at 850 °C. During sintering, Li2WO4 is fully consumed by reacting with Ba3(VO4)2 to form BaWO4 and Li3VO4 while providing a transient liquid phase that promotes densification. As a result, the sintered ceramics achieve high relative densities of ≈94–98% at 850 °C. The relative fractions of Ba3(VO4)2, BaWO4, and Li3VO4 can be systematically tailored by adjusting the initial Li2WO4 content, enabling effective control of the temperature coefficient of the resonant frequency (τf) and the quality factor (Q × f). With increasing Li2WO4 content, the τf values shift from +23.97 to −45.48 ppm/°C, owing to the increasing contributions of the negative τf phases BaWO4 and Li3VO4, while the Q × f values increase moderately from 44,300 to 47,300 GHz. The optimal microwave dielectric properties are obtained for x = 0.5, meaning εr = 9.19, Q × f = 45,900 GHz, and τf = −1.15 ppm/°C when sintering at 850 °C for 1 h. Chemical compatibility tests confirmed that the composites exhibit no detectable reaction with Ag electrodes, indicating that the Ba3(VO4)2–BaWO4–Li3VO4 system is a promising glass-free dielectric for LTCC applications requiring low firing temperature, near-zero thermal drift, and reliable electrode compatibility.

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Full text

1. Introduction

The development of the latest wireless communication systems, such as 5G communication systems or portable mobile phones, has created an increased demand for new dielectric substrate materials to fulfill the requirements of increased signal transmission speed, enhanced miniaturization, and improved integration of passive elements [1,2,3,4]. The key material requirements for such applications include a low dielectric permittivity ( $[eqn]$ ) to minimize signal propagation delay, a high quality factor (Q × f) to ensure frequency selectivity and reduce power consumption, a low temperature coefficient of resonant frequency ( $[eqn]$ ) to guarantee temperature-stable operation, and a sufficiently low sintering temperature to enable multilayer low temperature co-fired ceramics (LTCC) processing [5,6,7,8].

However, many commercial dielectric materials used in high-frequency devices require relatively high sintering temperatures and are therefore not well matched to LTCC processes. To lower the sintering temperature of dielectric ceramics, glasses are generally added to promote densification via liquid phase sintering. Unfortunately, the presence of a glassy phase can increase dielectric loss, as many glass-forming oxides exhibit higher dielectric loss than the crystalline phases used in microwave dielectrics [9,10,11]. The use of sintering aids is thus a cost-effective and simple way to reduce the firing temperature, but it tends to compromise the intrinsic microwave dielectric properties. For this reason, the exploration of glass-free, low-melting compounds suitable for LTCC applications has attracted considerable attention. Several low-temperature-melting ceramic systems, particularly those based on bismuth- or tellurium-containing compounds, have been investigated as glass-free LTCC materials [12,13,14,15]. Although these materials can be fired at relatively low temperatures, they often show limited chemical compatibility with Ag electrodes, which limits their use in multilayer devices.

Li_2_WO_4_ has attracted considerable attention as a low-melting additive because it exhibits reasonably good intrinsic microwave dielectric properties ( $[eqn]$ ≈ 5.5, Q × f ≈ 62,000 GHz, $[eqn]$ ≈ −145 ppm/°C) and has a relatively low melting temperature (~741 °C) [16]. These characteristics enable Li_2_WO_4_ to effectively reduce the sintering temperature of various microwave dielectric ceramics via liquid-assisted sintering [17,18,19,20,21]. Furthermore, owing to its large negative $[eqn]$ , Li_2_WO_4_ has also been employed in temperature-compensated systems, for example, in the Li_2_TiO_3_–Li_2_WO_4_ system [18]. However, it has also been reported that Li_2_WO_4_ reacts with Ag electrodes, raising potential limitations in its direct use as a sintering aid in LTCC systems containing internal Ag conductors [18].

In our laboratory, we found that Li_2_WO_4_ reacts with Ba-containing compounds such as Ba_3_(VO_4_)2, BaV_2_O_6_, or Ba_5_Nb_4_O_15_ to produce BaWO_4_ and Li-containing vanadates or niobates such as Li_3_VO_4_, LiVO_3_, and LiNbO_3_. In particular, when Li_2_WO_4_ reacts with Ba_3_(VO_4_)2, BaWO_4_ and Li_3_VO_4_ phases are formed and Li_2_WO_4_ eventually disappears, while a certain amount of Ba_3_(VO_4_)2 can remain as a residual phase depending on the initial Li_2_WO_4_ content. Unlike conventional glass additives that primarily act as inert fluxes, Li_2_WO_4_ functions as a reactive liquid-phase sintering additive that forms a low-temperature incipient liquid and chemically interacts with Ba_3_(VO_4_)2 during sintering. Through this reaction pathway, crystalline BaWO_4_ and Li_3_VO_4_ phases are generated in situ instead of forming an amorphous glass. This reactive liquid-phase sintering mechanism enables efficient densification at 850 °C while maintaining a fully glass-free microstructure, which is highly advantageous for LTCC processing. From the dielectric perspective, the in situ formation of BaWO_4_ and Li_3_VO_4_ is particularly important because both phases possess negative $[eqn]$ values and lower intrinsic permittivities relative to Ba_3_(VO_4_)2. Consequently, the overall dielectric response can be systematically tuned by controlling the initial Li_2_WO_4_ content, which directly determines the final phase fractions through the stoichiometric reaction pathway.

Ba_3_(VO_4_)2 sintered at 1600 °C exhibits $[eqn]$ ≈ 11, Q × f ≈ 40,000 GHz, and $[eqn]$ ≈ +60 ppm/°C [6]. BaWO_4_ sintered at 1100 °C shows $[eqn]$ ≈ 8, Q × f ≈ 57,500 GHz, and $[eqn]$ ≈ −78 ppm/°C [7]. The Li_3_VO_4_ phase, which was characterized in our laboratory, exhibits $[eqn]$ ≈ 8, Q × f ≈ 22,000 GHz, and $[eqn]$ ≈ −38 ppm/°C when sintered at 900 °C. Although each individual phase shows a relatively large $[eqn]$ and requires a relatively high sintering temperature, an appropriate combination of the positive $[eqn]$ (Ba_3_(VO_4_)2) and the negative $[eqn]$ (BaWO_4_ and Li_3_VO_4_) phases suggests that a composite with near-zero $[eqn]$ can be achieved.

For LTCC applications, most microwave dielectric composites reported so far have been designed by physically mixing crystalline phases with opposite $[eqn]$ values (a positive $[eqn]$ component and a negative $[eqn]$ component), together with a small amount of a low-melting glass or oxide, such as V_2_O_5_, CuO-V_2_O_5_, or LiF, to reduce the sintering temperature [22,23,24]. In such systems, the glassy or liquid additive acts essentially as an inert sintering aid, while the overall $[eqn]$ is tuned by adjusting the volume ratio between the positive and negative $[eqn]$ phases. Although this approach is effective in lowering the firing temperature, the incorporation of low-melting additives can adversely affect the microwave dielectric properties because the liquid phase introduced during sintering may increase dielectric loss or disrupt the intrinsic performance of the crystalline phases.

In contrast, the present work adopts a different strategy. Instead of using an inert glassy sintering aid, we introduce Li_2_WO_4_ as a low-melting, reactive liquid-phase sintering additive into a Ba_3_(VO_4_)2 matrix with positive $[eqn]$ . During low-temperature sintering, Li_2_WO_4_ reacts in situ with Ba_3_(VO_4_)2 to form BaWO_4_ and Li_3_VO_4_, both of which possess negative $[eqn]$ values, while simultaneously providing a transient liquid phase that promotes densification. Consequently, the overall $[eqn]$ of the resulting Ba_3_(VO_4_)2–BaWO_4_–Li_3_VO_4_ composite can be tuned by controlling the initial Li_2_WO_4_ content, without introducing any glassy phase. To the best of our knowledge, this reactive liquid-phase sintering route—in which a low-temperature sintering additive is intentionally used to generate in situ negative $[eqn]$ phases and achieve $[eqn]$ compensation in a glass-free LTCC-compatible composite—represents a novel and distinct strategy for LTCC-compatible microwave dielectric design and has not been explicitly reported. This work therefore focuses specifically on the Li_2_WO_4_–Ba_3_(VO_4_)2 reaction, which represents a complete reactive pathway leading to BaWO_4_ and Li_3_VO_4_ and enables $[eqn]$ tuning via a fully glass-free approach. Through this approach, a glass-free LTCC-compatible composite strategy is established in which a stoichiometrically constrained reactive liquid-phase pathway is intentionally employed to achieve systematic $[eqn]$ compensation. Accordingly, in this study, we demonstrate this concept by preparing (1–x)Ba_3_(VO_4_)2–xLi_2_WO_4_ mixtures (x = 0.3–0.7), clarifying the reaction pathway between Ba_3_(VO_4_)2 and Li_2_WO_4_, and systematically investigating the densification behavior, microstructure, phase assemblage, and microwave dielectric properties of the resulting Ba_3_(VO_4_)2–BaWO_4_–Li_3_VO_4_ ceramics.

2. Materials and Methods

The starting materials used were high-purity (99.9%) powders of BaCO_3_, V_2_O_5_, Li_2_CO_3_, and WO_3_ (Sigma Aldrich, St. Louis, MO, USA). Ba_3_(VO_4_)2 and Li_2_WO_4_ powders were separately synthesized via a conventional mixed-oxide route by calcining mixtures of BaCO_3_–V_2_O_5_ and Li_2_CO_3_–WO_3_ of stoichiometric compositions at 800 and 550 °C, respectively, for 5 h with a heating rate of 10 °C/min. These calcination temperatures were selected with reference to previously reported synthesis conditions [6,20] and were slightly adjusted to ensure complete phase formation for the precursors used in this study. Phase purity of both calcined powders was confirmed by XRD. Prior to calcination, oxide/carbonate mixtures (25 g total) were wet-milled in 100 mL of ethanol for 12 h at 20 rpm using a Teflon jar containing zirconia balls of two sizes (10 mm, 400 g; and 6 mm, 200 g), corresponding to a ball-to-powder ratio of 24:1, to achieve homogeneous mixing. After calcination, the resulting Ba_3_(VO_4_)2 and Li_2_WO_4_ powders were lightly milled and passed through a 150-mesh sieve.

The (1–x)Ba_3_(VO_4_)2–xLi_2_WO_4_ mixtures (x = 0.3–0.7) were prepared by mixing the synthesized Ba_3_(VO_4_)2 and Li_2_WO_4_ powders with desired molar ratios. The composition range (x = 0.3–0.7) was selected to ensure complete reaction between Ba_3_(VO_4_)2 and Li_2_WO_4_, effective low-temperature densification via reaction-assisted liquid-phase sintering, and stable three-phase formation without excessive dominance of either the residual Ba_3_(VO_4_)2 phase or the reaction-derived BaWO_4_–Li_3_VO_4_ phase assemblage. Compositions with lower Li_2_WO_4_ contents resulted in insufficient densification at 850 °C, whereas excessively high Li_2_WO_4_ contents led to phase assemblages dominated by BaWO_4_ and Li_3_VO_4_, which are less favorable for temperature-stable LTCC applications. The mixtures were then ball-milled under the same conditions as described above. For granulation, the milled powder was mixed with 1 wt.% polyvinyl alcohol (PVA) as a binder in a 3-roll mill (EXAKT 50I, EXAKT, Norderstedt, Germany); the resulting granules were then dried at 90 °C and sieved through a 60-mesh sieve.

The granulated powders were uniaxially pressed into cylindrical pellets with a height of 5 mm and a diameter of 10 mm under a pressure of 150 MPa for the measurement of density, microstructure, and microwave dielectric properties. Rectangular bars with dimensions of 5 mm (width) × 3 mm (thickness) × 10 mm (length) were also prepared for shrinkage-curve measurements. Linear shrinkage ( $[eqn]$ ) as a function of temperature was monitored using a dilatometer (DIL 402PC, Netzsch-Gerätebau GmbH, Selb, Germany) at a heating rate of 10 °C/min. The onset temperature of net shrinkage, $[eqn]$ , was defined as the intersection point of the linear extrapolations of the thermal expansion region and the subsequent shrinkage region in the shrinkage curve. The maximum shrinkage rate temperature, $[eqn]$ , was taken as the temperature at which the shrinkage rate curve $[eqn]$ reached its most negative, corresponding to the peak shrinkage rate ( $[eqn]$ ).

For sintering, the green pellets were first heated to 600 °C at a rate of 2 °C/min and held for 4 h to burn out the organic binder. Subsequently, the temperature was raised to 850 °C at a heating rate of 10 °C/min, and the pellets were sintered at 850 °C for 1 h in air, followed by furnace cooling at 10 °C/min. The dwell time and sintering temperature were selected based on the dilatometric shrinkage behavior. To evaluate chemical compatibility with Ag, mixed powders containing 20 wt.% Ag were cofired at 850 °C for 1 h under the same conditions.

The crystalline phases formed in the sintered samples were identified by X-ray diffraction (XRD) using an Empyrean diffractometer (PANalytical, Almelo, The Netherlands), with Cu $[eqn]$ radiation over a 2 $[eqn]$ range of 10–70°. For phase identification, diffraction patterns were collected with a step size of 0.02° (2 $[eqn]$ ) and a counting time of 1 s per step. For Rietveld refinement, high-statistics scans were recorded with a reduced step size of 0.01° (2θ) and a counting time of 4 s per step to ensure reliable quantitative analysis. A representative sample (x = 0.6) was selected for Rietveld refinement, which was performed using the FullProf Suite (May 2021 release, Institut Laue–Langevin, Grenoble, France). The bulk densities ( $[eqn]$ ) of the sintered specimens were measured by Archimedes’ method, and the relative densities were calculated from the bulk densities and the theoretical densities ( $[eqn]$ ). The theoretical density ( $[eqn]$ ) of the composites was calculated using Equation (1) [18]:

$$[eqn]$$

where $[eqn]$ , $[eqn]$ , and $[eqn]$ are the theoretical densities of Ba_3_(VO_4_)2, BaWO_4_, and Li_3_VO_4_ (5.18, 6.38, and 2.64 g/cm^3^, respectively), and $[eqn]$ , $[eqn]$ , and $[eqn]$ are the corresponding mass fractions of Ba_3_(VO_4_)2, BaWO_4_, and Li_3_VO_4_ in the composite. The mass fractions were calculated based on the molar amounts predicted by the stoichiometric reaction pathway described in Equation (3), using the molar masses and theoretical densities of the individual phases.

The microstructures of the polished and thermally etched (800 °C for 10 min) surfaces were observed using a scanning electron microscope (SEM, Coxem SNE-3000M, Daejeon, Republic of Korea). Energy-dispersive X-ray spectroscopy (EDS) was employed to qualitatively analyze the local chemical compositions of grains with different contrast. Grain sizes were quantitatively evaluated from thermally etched SEM micrographs using ImageJ image-analysis software (version 1.54g, NIH, Bethesda, MD, USA). For grain size measurement, SEM micrographs were acquired from multiple randomly selected areas for each composition to ensure statistical representativeness. Grain size was defined as the maximum grain length measured along a fixed in-plane reference direction (x-direction) from two-dimensional SEM images. This fixed-direction intercept length was used consistently for all samples, and the grains did not exhibit pronounced in-plane anisotropy, making this metric appropriate for compositional comparison. For each composition, more than 200 grains were analyzed to obtain statistically reliable grain size distributions.

Microwave dielectric properties were measured in the frequency range of approximately 7–11 GHz using a vector network analyzer (HP 8720ES, Agilent Technologies, Santa Clara, CA, USA). The $[eqn]$ was determined according to the Hakki–Coleman resonator method using the TE_011_ resonant mode at ~11 GHz, while the unloaded Q × f was measured by the cavity method using the TE_01δ_ resonant mode at ~7 GHz [25,26]. The temperature coefficient of resonant frequency ( $[eqn]$ ) was calculated using Equation (2) by measuring the resonant frequencies $[eqn]$ and $[eqn]$ at $[eqn]$ = 25 °C and $[eqn]$ = 85 °C, respectively [27]:

$$[eqn]$$

This temperature interval (25–85 °C) follows a standard range commonly adopted for $[eqn]$ evaluation in microwave dielectric measurements.

The detailed experimental procedure is schematically summarized in Figure S1 of the Supplementary Materials.

3. Results and Discussion

3.1. Phase Formation and Reaction Pathway in the Ba3(VO4)2–Li2WO4 System

X-ray diffraction (XRD) patterns of the (1–x)Ba_3_(VO_4_)2–xLi_2_WO_4_ ceramics (x = 0.3–0.7) sintered at 850 °C for 1 h are presented in Figure 1. The rationale for selecting the sintering temperature (850 °C) and dwell time (1 h), based on the dilatometric shrinkage behavior, is described in detail in Section 3.2. All compositions exhibit three crystalline phases—Ba_3_(VO_4_)2 (rhombohedral, $[eqn]$ ), BaWO_4_ (tetragonal, $[eqn]$ ), and Li_3_VO_4_ (orthorhombic, $[eqn]$ )—and no residual Li_2_WO_4_ (rhombohedral, $[eqn]$ ) is detectable within the XRD detection limit. With increasing Li_2_WO_4_ content, the intensities of BaWO_4_ ( $[eqn]$ ) and Li_3_VO_4_ ( $[eqn]$ ) peaks increase systematically, whereas those of Ba_3_(VO_4_)2 ( $[eqn]$ ) decrease, indicating progressive consumption of the Ba_3_(VO_4_)2 phase.

In addition, SEM–EDS analysis reveals V–O-rich grains without detectable Ba or W, which is consistent with the formation of Li_3_VO_4_ inferred from XRD. These complementary structural and microchemical observations consistently indicate that sintering proceeds through a well-defined reaction pathway leading to a Ba_3_(VO_4_)2–BaWO_4_–Li_3_VO_4_ three-phase assemblage. Although the precise reaction pathway cannot be conclusively determined from the present data, the shrinkage behavior suggests that Li_2_WO_4_ undergoes partial and localized melting as the temperature approaches its melting point. The resulting transient liquid enhances cation mobility at the Ba_3_(VO_4_)2/Li_2_WO_4_ interfaces. Such liquid-assisted reactions may proceed either through partial dissolution of Ba_3_(VO_4_)2 followed by precipitation of BaWO_4_ and Li_3_VO_4_, or through liquid infiltration into Ba_3_(VO_4_)2 grains, which facilitates cation exchange and structural rearrangement. Increasing the Li_2_WO_4_ content likely increases the extent of such localized liquid formation, consistent with the earlier shrinkage onset ( $[eqn]$ ) and higher maximum shrinkage rates ( $[eqn]$ ) observed in in the shrinkage analysis.

Based on these considerations and XRD evidence, Li_2_WO_4_ is found to be fully consumed during sintering, forming BaWO_4_ and Li_3_VO_4_ as reaction products. Accordingly, the overall mass-balanced reaction for the (1–x)Ba_3_(VO_4_)2–xLi_2_WO_4_ mixtures can be expressed as:

$$[eqn]$$

Because this reaction pathway is uniquely constrained by stoichiometry, the final phase fractions are determined solely by the initial Li_2_WO_4_ content. To experimentally validate Equation (3), Rietveld quantitative phase analysis was performed for a representative composition (x = 0.6), and a typical refined pattern is shown in Figure 2. The composition x = 0.6 was selected because the reaction produces Ba_3_(VO_4_)2, BaWO_4_, and Li_3_VO_4_ in well-balanced proportions, avoiding cases in which one phase becomes excessively dominant or too minor for reliable refinement. Such a balanced phase assemblage provides the most stable conditions for quantitative analysis and therefore offers the most appropriate basis for validating the stoichiometric reaction in Equation (3). The refined weight fractions of the three phases show excellent agreement with the theoretical values predicted by Equation (3), with deviations below 2% in mean absolute percentage error (MAPE). The refinement quality indicators (R_wp_ = 9.67%, Bragg R–factors of approximately 7–8%, and RF–factors of approximately 6–7%) further support the stability of the refinement and the reliability of the phase-fraction estimates. Collectively, these results provide strong experimental evidence supporting the validity of the proposed reaction pathway. Accordingly, in the subsequent analyses, quantities such as the theoretical density and the phase volume fractions were calculated using the phase amounts derived directly from the stoichiometric reaction pathway described in Equation (3).

3.2. Sintering Behavior and Microstructural Evolution of the Ba3(VO4)2–BaWO4–Li3VO4 Composites

To clarify how Li_2_WO_4_ influences the densification of the (1–x)Ba_3_(VO_4_)2–xLi_2_WO_4_ ceramics, dilatometric shrinkage measurements were carried out as a function of Li_2_WO_4_ content. Figure 3 shows the shrinkage ( $[eqn]$ ) and shrinkage rate [ $[eqn]$ ] curves for the (1–x)Ba_3_(VO_4_)2–xLi_2_WO_4_ compacts (x = 0.3–0.7), together with those of the pure Ba_3_(VO_4_)2, BaWO_4_, Li_3_VO_4_, and Li_2_WO_4_ ceramics for comparison.

All (1–x)Ba_3_(VO_4_)2–xLi_2_WO_4_ compositions exhibit a similar shrinkage onset temperature, $[eqn]$ , of approximately 690 °C. However, the magnitude and rate of shrinkage change systematically with x. As the Li_2_WO_4_ content increases from x = 0.3 to 0.7, the maximum shrinkage rate ( $[eqn]$ ) increases from ~0.083 to ~0.207%/°C, while the temperature of the maximum shrinkage rate ( $[eqn]$ ) shifts from ~773 °C down to ~740 °C. This quantitative trend indicates that higher Li_2_WO_4_ contents promote earlier and more rapid densification through reaction-assisted transient liquid-phase formation. In contrast, compositions with lower Li_2_WO_4_ contents retain a larger fraction of Ba_3_(VO_4_)2, which exhibits relatively poor sinterability and therefore requires higher temperatures for effective densification. These results demonstrate that both the sintering behavior and the resulting phase assemblage can be optimized by controlling the initial Li_2_WO_4_ content.

These variations in $[eqn]$ , $[eqn]$ , and $[eqn]$ cannot be reproduced solely by a linear combination of the shrinkage behaviors of the individual end-member phases Ba_3_(VO_4_)2, BaWO_4_, and Li_3_VO_4_. This behavior indicates that Li_2_WO_4_ is not a passive component but actively participates in the densification process of the (1–x)Ba_3_(VO_4_)2–xLi_2_WO_4_ ceramics before it is completely consumed according to Equation (3).

To further examine the role of Li_2_WO_4_, two different specimens were prepared with the same final overall composition, namely 0.3Ba_3_(VO_4_)2–0.7Li_2_WO_4_ and 0.067Ba_3_(VO_4_)2–0.7BaWO_4_–0.47Li_3_VO_4_, according to the reaction in Equation (3), and their shrinkage behaviors are compared in Figure 4. Although both compositions are expected to yield the same Ba_3_(VO_4_)2–BaWO_4_–Li_3_VO_4_ phase assemblage after complete reaction, the two compacts exhibit markedly different densification behaviors. The 0.067Ba_3_(VO_4_)2–0.7BaWO_4_–0.47Li_3_VO_4_ compact, in which Li_2_WO_4_ is absent from the beginning, shows a higher shrinkage onset temperature ( $[eqn]$ ≈ 786 °C), a higher temperature of the maximum shrinkage rate ( $[eqn]$ ≈ 831 °C), and a smaller maximum shrinkage rate ( $[eqn]$ ≈ 0.129%/°C) than the 0.3Ba_3_(VO_4_)2–0.7Li_2_WO_4_ compact ( $[eqn]$ ≈ 698 °C, $[eqn]$ ≈ 740 °C, $[eqn]$ ≈ 0.207%/°C). In other words, when the mixture is pre-reacted so that Ba_3_(VO_4_)2, BaWO_4_, and Li_3_VO_4_ are present before shrinkage starts, densification becomes slower and requires a higher temperature, suggesting that efficient densification is difficult to achieve without Li_2_WO_4_ during the early sintering stage.

The melting temperature of Li_2_WO_4_ (~741 °C) is higher than the shrinkage onset temperature of the 0.3Ba_3_(VO_4_)2–0.7Li_2_WO_4_ compact, so the enhanced densification cannot be attributed to simple bulk melting of Li_2_WO_4_. Instead, these results suggest that a transient liquid—likely eutectic or reactive in nature—forms at the interfaces between Li_2_WO_4_ and Ba_3_(VO_4_)2 at relatively low temperatures, promotes particle rearrangement and rapid densification, and then disappears as Li_2_WO_4_ is fully consumed by the reaction in Equation (3). Thus, Li_2_WO_4_ acts as a temporary but very effective liquid-phase sintering aid that plays its role before vanishing from the final microstructure. Taken together, the earlier-than-expected shrinkage onset, complete consumption of Li_2_WO_4_, and concurrent formation of BaWO_4_ and Li_3_VO_4_ provide consistent indirect evidence for reaction-assisted liquid-phase sintering in the present system.

When developing new dielectric materials for LTCC applications, reactions with conductive electrodes must be carefully considered. To minimize interdiffusion between the dielectric and the Ag electrode, the sintering temperature should generally not exceed 850 °C. As shown in Figure 3, the linear shrinkage of the composites, particularly for compositions with low initial Li_2_WO_4_ contents (x = 0.3–0.4), is approximately 11.6–13% at 850 °C. To assess whether this level of shrinkage is sufficient to achieve practical densification under LTCC-compatible conditions, the final density can be roughly estimated from the green density assuming isotropic shrinkage using the following relation [28]:

$$[eqn]$$

where $[eqn]$ and $[eqn]$ are the calculated and pressed (green) densities, respectively, and $[eqn]$ is the shrinkage value at 850 °C. The green density ( $[eqn]$ ) was determined from the measured mass of the pellet and its geometrically calculated volume. Using a green density of approximately 58.2% of the theoretical density, Equation (4) indicates that the estimated density remains below full densification, suggesting that additional holding time at 850 °C is necessary to achieve sufficient densification.

The effect of Li_2_WO_4_ content and dwelling time on the densification behavior is further illustrated in Figure 5. The relative density values shown in Figure 5 were determined from the ratio of the bulk density ( $[eqn]$ ), measured by the Archimedes’ method, to the theoretical density ( $[eqn]$ ) calculated using Equation (1). As shown in Figure 5a, the relative density of the (1–4x/3)Ba_3_(VO_4_)2–xBaWO_4_–(2x/3)Li_3_VO_4_ ceramics obtained from the (1–x)Ba_3_(VO_4_)2–xLi_2_WO_4_ mixtures at 850 °C varies with both the Li_2_WO_4_ content and the sintering time. Compositions with higher initial Li_2_WO_4_ contents (x ≥ 0.5) exhibit rapid densification during the first 20–40 min, which is consistent with the formation of a transient liquid phase, which promotes particle rearrangement and mass transport. In contrast, the x = 0.3 and 0.4 samples show comparatively slower densification because they contain a larger fraction of Ba_3_(VO_4_)2, which shrinks at higher temperatures and with a lower shrinkage rate than BaWO_4_ and Li_3_VO_4_ (see Figure 3), consistent with its relatively poor sinterability [6]. Even so, all compositions eventually reach high relative densities. As summarized in Figure 5b, the relative density increases monotonically with x, and all samples achieve ≈ 94–98% of the theoretical density after sintering at 850 °C for 1 h. These results demonstrate the important role of Li_2_WO_4_ prior to its complete reaction with Ba_3_(VO_4_)2 in enhancing the densification of the Ba_3_(VO_4_)2–BaWO_4_–Li_3_VO_4_ composite system.

The microstructural evolution of the Ba_3_(VO_4_)2–BaWO_4_–Li_3_VO_4_ composites was investigated using SEM observation, quantitative grain size analysis, and EDS characterization, as summarized in Figure 6, Figure 7 and Figure 8.

Representative SEM micrographs of the polished and thermally etched samples are shown in Figure 6. Three distinct grain types can be observed: small bright grains corresponding to the Ba_3_(VO_4_)2 phase, larger bright grains corresponding to the BaWO_4_ phase, and darker grains corresponding to the Li_3_VO_4_ phase. These phase assignments are consistent with the XRD results and with the EDS observations (Figure 8), in which V–O-rich grains without detectable Ba or W are observed, consistent with the Li_3_VO_4_ phase identified by XRD. As the initial Li_2_WO_4_ content increases, the microstructure evolves from one dominated by fine Ba_3_(VO_4_)2 grains to one containing an increasing fraction of larger BaWO_4_ and Li_3_VO_4_ grains. This trend reflects the progressive consumption of Ba_3_(VO_4_)2 and the concurrent formation of BaWO_4_ and Li_3_VO_4_ as predicted by the reaction pathway in Equation (3). In addition, pronounced grain growth is observed for the BaWO_4_ and Li_3_VO_4_ phases at higher x values, whereas the Ba_3_(VO_4_)2 grains remain relatively small, which is consistent with the much higher optimum sintering temperature and relatively poorer sinterability of Ba_3_(VO_4_)2 [6].

Quantitative grain size analysis was carried out based on the thermally etched SEM micrographs, and the resulting grain size distributions are presented in Figure 7. The average grain size increases markedly with increasing x, from approximately 1.04 μm at x = 0.3 to 2.48 μm at x = 0.7, indicating systematic grain growth as the Li_2_WO_4_ content increases. This quantitative trend provides a strong indication for enhanced mass transport and particle rearrangement at higher Li_2_WO_4_ contents, which is consistent with reaction-assisted transient liquid-phase sintering inferred from the dilatometric shrinkage behavior.

Figure 8 presents representative EDS spectra acquired from grains with different contrast in the SEM micrographs. Grains assigned to the Ba_3_(VO_4_)2 phase exhibit dominant Ba and V signals, whereas BaWO_4_ grains are characterized by strong Ba and W peaks. In contrast, V–O–rich grains without significant Ba or W are observed, consistent with the formation of the Li_3_VO_4_ phase identified by XRD.

BaWO_4_, Ba_3_(VO_4_)2, and Li_3_VO_4_ possess distinct crystal structures, which prevent the formation of solid solutions among them. BaWO_4_ crystallizes in the scheelite-type tetragonal structure ( $[eqn]$ ), in which W^6+^ is tetrahedrally coordinated, and the [WO_4_] units are linked through eight-fold coordinated Ba^2+^ ions [29]. Ba_3_(VO_4_)2 adopts a rhombohedral structure ( $[eqn]$ ), where V^5+^ occupies tetrahedral [VO_4_] sites connected through six- and ten-fold coordinated Ba^2+^ ions [30]. Li_3_VO_4_ crystallizes in the orthorhombic $[eqn]$ structure, which can be regarded as an ordered wurtzite derivative, with both V^5+^ and Li^+^ in tetrahedral coordination. The [VO_4_] tetrahedra remain close to the ideal geometry (107.6–111.2°), whereas the [LiO_4_] tetrahedra deviate more significantly (105.5–121.9°) [31].

Because these three phases differ substantially in both cation coordination environments and in the connectivity of their tetrahedral units, the formation of BaWO_4_–Ba_3_(VO_4_)2–Li_3_VO_4_ solid solutions is not favored due to their distinct crystal chemistries. As a result, the three phases coexist in the sintered ceramics without forming additional reaction products, in full agreement with the XRD patterns shown in Figure 1.

3.3. Microwave Dielectric Properties of the Ba3(VO4)2–BaWO4–Li3VO4 Composites

The microwave dielectric properties of the (1–4x/3)Ba_3_(VO_4_)2–xBaWO_4_–(2x/3)Li_3_VO_4_ ceramics with maximal densities are shown in Figure 9. The dielectric properties of the end-member phases obtained in this study— $[eqn]$ = 10.82, Q × f = 43,200 GHz, and $[eqn]$ = +63.34 ppm/°C for Ba_3_(VO_4_)2 and $[eqn]$ = 8.25, Q × f = 58,900 GHz, and $[eqn]$ = −76.82 ppm/°C for BaWO_4_—are in good agreement with previously reported values [6,7]. The Li_3_VO_4_ synthesized in this study exhibited $[eqn]$ = 7.62, $[eqn]$ = −37.59 ppm/°C, and Q × f = 22,300 GHz under the present synthesis conditions. Because the dielectric properties of Li_3_VO_4_ are known to be highly sensitive to synthesis conditions and microstructural features, the values reported in the literature vary widely [32,33]. In this study, the dielectric behavior of the composite ceramics was analyzed using the dielectric properties of the constituent phases synthesized and characterized in this work. The composition-dependent trends in $[eqn]$ , Q × f, and $[eqn]$ are presented in Figure 9 and are discussed in detail below.

As x increased from 0.3 to 0.7, the $[eqn]$ values decreased from 9.95 to 8.23, whereas the $[eqn]$ values shifted from +23.97 to −45.48 ppm/°C. In contrast, the Q × f values increased from 44,300 to 47,400 GHz over the same composition range, as shown in Figure 9.

As shown in Figure 9a, this monotonic decrease in $[eqn]$ with increasing x is primarily attributed to the increasing volume fractions of BaWO_4_ ( $[eqn]$ = 8.25) and Li_3_VO_4_ ( $[eqn]$ = 7.62), both of which possess significantly lower intrinsic permittivities than Ba_3_(VO_4_)2 ( $[eqn]$ = 10.82). It should also be noted that, for compositions with x = 0.3–0.4, the measured $[eqn]$ values are noticeably lower than the corresponding porosity-corrected values, which is consistent with the relatively higher porosity observed for these compositions, as shown in Figure 5b.

The corrected dielectric permittivity $[eqn]$ , eliminating the influence of porosity, was calculated using the empirical relation [34,35]:

$$[eqn]$$

where $[eqn]$ is the porosity and $[eqn]$ is the measured permittivity. Here, the porosity $[eqn]$ was determined from the bulk density measurements presented in Section 3.2 (Figure 5b), where $[eqn]$ . In the following discussion, $[eqn]$ refers to the porosity corrected value $[eqn]$ .

To provide a quantitative description of the compositional dependence of $[eqn]$ based on the phase assemblage, an empirical multiphase mixing model was employed [36]. The effective permittivity $[eqn]$ was simulated using the generalized mixing law:

$$[eqn]$$

where $[eqn]$ , $[eqn]$ , and $[eqn]$ are the volume fractions of Ba_3_(VO_4_)2, BaWO_4_ and Li_3_VO_4_, respectively, and $[eqn]$ , $[eqn]$ , and $[eqn]$ are their intrinsic permittivities. The phase volume fractions ( $[eqn]$ – $[eqn]$ ) were calculated from the reaction stoichiometry given in Equation (3), based on the predicted molar amounts of Ba_3_(VO_4_)2, BaWO_4_, and Li_3_VO_4_ for a given composition x, and then converted to pore-free volume fractions using the theoretical densities of the individual phases. The phase volumes were normalized such that $[eqn]$ + $[eqn]$ + $[eqn]$ = 1, excluding porosity. The parameter $[eqn]$ determines the mixing behavior: $[eqn]$ = 1, −1, and 0 correspond to the parallel, series, and logarithmic (Lichtenecker) models, respectively. The case $[eqn]$ = 0 does not represent a simple mathematical exponent of zero. Instead, the logarithmic mixing rule is obtained as the limiting form of Equation (6) as $[eqn]$ →0, yielding the Lichtenecker relation [37]:

$$[eqn]$$

In Figure 9a, the $[eqn]$ = 0 logarithmic mixing model provides a reasonable description of the composition-dependent variation of the corrected permittivity $[eqn]$ in the present system. This logarithmic model is commonly used for randomly intermixed multiphase microstructures [37,38]. The smooth, composition-dependent variation of $[eqn]$ further indicates good interfacial compatibility between the Ba_3_(VO_4_)2, BaWO_4_ and Li_3_VO_4_ phases and suggests negligible Maxwell–Wagner interfacial polarization within the measured microwave frequency range [39].

The $[eqn]$ was simulated using the linear volume-fraction-weighted rule:

$$[eqn]$$

where $[eqn]$ , $[eqn]$ , and $[eqn]$ are the $[eqn]$ values of Ba_3_(VO_4_)2, BaWO_4_ and Li_3_VO_4_, respectively. Here, $[eqn]$ – $[eqn]$ denote the pore-free phase volume fractions, consistent with those used in the permittivity analysis. The linear relationship can be derived by substituting the permittivity-mixing relation (Equation (9)) into the general identity for $[eqn]$ (Equation (10)):

$$[eqn]$$ $$[eqn]$$

where $[eqn]$ denotes the temperature coefficients of permittivity; subscripts 1, 2, and 3 refer to the Ba_3_(VO_4_)2, BaWO_4_ and Li_3_VO_4_ phases; and $[eqn]$ is the effective linear thermal-expansion coefficient of the composite, approximated by a volume-fraction average ( $[eqn]$ ). It should be emphasized that the linear volume-fraction-weighted relation for $[eqn]$ is a direct consequence of the logarithmic mixing behavior of $[eqn]$ and the thermodynamic definition of $[eqn]$ as the temperature derivative of ln $[eqn]$ , together with the thermal-expansion contribution. Therefore, the use of different apparent mixing rules for $[eqn]$ and $[eqn]$ is mathematically consistent and does not imply an incoherent modeling framework.

Figure 9b shows that Equation (8) captures the compositional trend of $[eqn]$ , which shifts from positive to negative with increasing x due to the increasing contributions of the negative $[eqn]$ phases BaWO_4_ and Li_3_VO_4_. A straight line computed from Equation (8) using the $[eqn]$ values of end-member phases reproduces the overall slope, although the experimental data points are slightly offset. This modest, composition-independent offset is expected, since residual porosity and microstructural features—such as closed pores and boundary cavities, or thin intergranular films—can still influence the temperature dependence of permittivity, $[eqn]$ , even after standard porosity correction, and consequently cause a small shift in $[eqn]$ [34,35]. In addition, Equation (10) indicates that the thermal-expansion term can contribute a constant offset: minor variations in the effective linear expansion coefficient ( $[eqn]$ )—arising from CTE mismatch, mechanical constraint between the phases, or residual thermal-expansion stresses at their interfaces—may further shift $[eqn]$ .

Figure 9c shows the Q × f values of the (1–4x/3) Ba_3_(VO_4_)2–xBaWO_4_–(2x/3)Li_3_VO_4_ ceramics as a function of x. Although both Q × f and density increase with x, the difference in their compositional trends indicates that porosity alone is insufficient to account for the observed evolution of Q × f. At first glance, the increase in Q × f with increasing x appears to follow the same trend as the increase in relative density, as shown in Figure 5b. The influence of porosity on microwave dielectric loss has been widely reported [34,35]. However, although both density and Q × f increase with x in the present system, the differences in relative density (94–98%) are too small to account for the full variation in Q × f. Thus, porosity alone cannot explain the observed Q × f evolution.

According to Tamura, lattice anharmonicity and defect-related scattering—particularly those associated with disordered charge distributions—play an important role in determining the intrinsic microwave loss of dielectric ceramics rather than porosity alone [40]. Therefore, changes in defect concentration and lattice dynamics with composition may also contribute to the Q × f behavior. Nevertheless, in the present composite system, the main factor governing the Q × f values is the intrinsic loss behavior of the constituent phases and their relative fractions determined by the reaction in Equation (3). BaWO_4_ possesses a significantly higher intrinsic Q × f (~58,900 GHz) than Ba_3_(VO_4_)2 (~40,000–43,000 GHz) and Li_3_VO_4_ (~22,300 GHz). As x increases, the progressive formation and accumulation of BaWO_4_ enhance the overall Q × f of the composite. At the same time, the increasing fraction of Li_3_VO_4_—which has the lowest intrinsic Q × f among the three phases—partially offsets this beneficial effect. This competition between the enhancement driven by BaWO_4_ and the reduction associated with Li_3_VO_4_ results in the moderate, nearly linear increase in the Q × f values observed in Figure 9c. Consequently, the evolution of Q × f in the (1–4x/3)Ba_3_(VO_4_)2–xBaWO_4_–(2x/3)Li_3_VO_4_ composites is controlled primarily by the intrinsic Q × f values and volume fractions of Ba_3_(VO_4_)2, BaWO_4_, and Li_3_VO_4_, rather than by small differences in porosity among samples. This behavior reflects the significant influence of intrinsic lattice vibrational characteristics on microwave dielectric loss in heterogeneous composite systems. It should be noted that, in the present composition series, grain size and phase fractions change simultaneously with the initial Li_2_WO_4_ content; therefore, the isolated effect of grain size on the dielectric properties cannot be rigorously separated. Moreover, because the intrinsic dielectric properties ( $[eqn]$ , Q × f, and $[eqn]$ ) of Ba_3_(VO_4_)2, BaWO_4_, and Li_3_VO_4_ differ far more significantly than any grain-size-related contributions, the observed dielectric trends are dominated by phase-fraction effects, with grain-size effects considered secondary.

At x = 0.5, the composite exhibits $[eqn]$ = 9.19, Q × f = 45,900 GHz, and $[eqn]$ = −1.15 ppm/°C, representing a temperature-stable, low-permittivity LTCC material obtained via the reactive sintering of 0.5Ba_3_(VO_4_)2–0.5Li_2_WO_4_ at 850 °C/1 h.

3.4. Chemical Compatibility with Ag Electrodes

To assess the suitability of the (1–4x/3)Ba_3_(VO_4_)2–xBaWO_4_–(2x/3)Li_3_VO_4_ composites for LTCC applications, their chemical compatibility with Ag electrodes was examined. The composition 0.5Ba_3_(VO_4_)2–0.5Li_2_WO_4_ was selected for this test because it exhibited the most favorable microwave dielectric properties among the investigated compositions. Figure 10 shows the XRD pattern of a mixture of 0.5 Ba_3_(VO_4_)2–0.5Li_2_WO_4_ powders containing 20 wt.% Ag (D_50_ ≈ 5 μm) that was cofired at 850 °C for 1 h. After cofiring, only the peaks corresponding to Ba_3_(VO_4_)2, BaWO_4_, Li_3_VO_4_, and metallic Ag are observed, and no detectable reaction phases are detected. This result indicates that the reaction between Ba_3_(VO_4_)2 and Li_2_WO_4_ proceeds normally in the presence of Ag and that no reaction products are detectable within the XRD detection limit between the dielectric phases and Ag during the cofiring process. Therefore, the present composite system is chemically compatible with Ag under the present cofiring conditions.

It is worth placing these results in the context of previously reported LTCC-related microwave dielectrics. Many low-temperature sintering systems, such as Bi_2_W_2_O_9_-, BiNbO_4_-, and Zn_2_Te_3_O_8_-based materials, can be densified below 900 °C but often require glass additives or exhibit poor compatibility with Ag electrodes, which limits their applicability in multilayer structures. In contrast, the present Ba_3_(VO_4_)2–BaWO_4_–Li_3_VO_4_ composites achieve densification at 850 °C without any glassy phase and show good compatibility with Ag. The dielectric properties obtained for x = 0.5 ( $[eqn]$ = 9.19, Q × f = 45,900 GHz, and $[eqn]$ = −1.15 ppm/°C) lie within a practically useful regime for LTCC substrates, offering a balanced combination of low relative permittivity, reasonably high Q × f values, and near-zero thermal drift.

This performance is achieved through a reactive liquid-phase sintering mechanism, in which Li_2_WO_4_ simultaneously promotes densification and generates in situ negative $[eqn]$ phases (BaWO_4_ and Li_3_VO_4_). The dual function of Li_2_WO_4_ distinguishes the present approach from many conventional LTCC strategies that rely on inert glass additives and physical mixing of positive and negative $[eqn]$ phases. Therefore, the proposed method provides an alternative route to obtaining temperature-stable, glass-free LTCC dielectrics with controllable thermal behavior and reliable electrode compatibility.

4. Conclusions

Ceramic composites with the Ba_3_(VO_4_)2–BaWO_4_–Li_3_VO_4_ phase assemblage were successfully obtained by reactive sintering of Ba_3_(VO_4_)2 and Li_2_WO_4_ mixtures at 850 °C for 1 h. During sintering, Li_2_WO_4_ reacts completely with Ba_3_(VO_4_)2 to form BaWO_4_ and Li_3_VO_4_ while providing a transient liquid phase that promotes densification. The onset and peak temperatures of shrinkage for the composite consisting only of Ba_3_(VO_4_)2–BaWO_4_–Li_3_VO_4_ ( $[eqn]$ = 785.8 °C, $[eqn]$ = 830.5 °C) occur at significantly higher temperatures than those of the corresponding Ba_3_(VO_4_)2–Li_2_WO_4_ mixture ( $[eqn]$ = 698.3 °C, $[eqn]$ = 739.5 °C), confirming that Li_2_WO_4_ acts as an effective reactive liquid-phase sintering aid.

Among the compositions studied, the 0.33Ba_3_(VO_4_)2–0.5BaWO_4_–0.33Li_3_VO_4_ ceramic obtained by sintering the 0.5Ba_3_(VO_4_)2–0.5Li_2_WO_4_ mixture at 850 °C for 1 h exhibits attractive microwave dielectric properties, with $[eqn]$ = 9.19, Q × f = 45,900 GHz, and $[eqn]$ = −1.15 ppm/°C, together with a high relative density of approximately 97% of the theoretical value. Chemical compatibility tests further demonstrated that this ceramic is stable in contact with Ag electrodes during cofiring at 850 °C. The present approach demonstrates that reactive liquid-phase sintering can be effectively used in this system not only to lower the sintering temperature but also to generate in situ functional phases for precise control of microwave dielectric properties.

In summary, sintering the 0.5Ba_3_(VO_4_)2–0.5Li_2_WO_4_ mixture at 850 °C for 1 h provides a practical processing window that meets the key dielectric requirements for LTCC applications, such as sub-900 °C firing, low $[eqn]$ , reasonably high Q × f, near-zero $[eqn]$ , and good compatibility with Ag electrodes. These results establish the Ba_3_(VO_4_)2–BaWO_4_–Li_3_VO_4_ composites developed in this work as promising glass-free, temperature-stable, low-loss LTCC materials for advanced microwave applications, including 5G-advanced and future 6G systems.