Lattice evolution, ordering transformation and microwave dielectric properties of rock-salt Li_3+xMg_2–2xNb_1-xTi_2xO₆ solid-solution system: A newly developed pseudo ternary phase diagram

Abstract

New types of multi-component Li_3+xMg_2–2xNb_1-xTi_2xO₆ (0 ≤ x ≤ 1) solid-solution ceramics were designed based on the Li₂TiO₃−Li₃NbO₄−MgO pseudo ternary phase diagram and studied for microwave dielectric applications. As the substitution amount (x) increased, we detected the phase transitions among the orthorhombic, cubic, and monoclinic phase driven by the compositional changes, as well as accompanied by an order-disorder-order transformation. A full range of solid solutions was formed between the Li₃Mg₂NbO₆ and Li₂TiO₃ endmembers, with no trace of other impurities. In the sample with the low substitution concentration (x = 0.2 mol), a coherent phase interface (CPI) between the cubic and orthorhombic lattices was formed with no obvious misfit dislocation or stacking fault, indicating the small differences in crystal configuration, chemical bonding properties, and subcell lattice parameters between the two phases. Besides, there were observed diverse reconstructed superlattices, one kind is that possessed a “transition form” of the two phases and was formed nearby the CPI, and the other kind was formed based on the cubic or orthorhombic lattices independently and was observed on a larger scale nearby the CPI. The preferential substitutions of the non-equivalent cations, which were determined by ionic radius, electronegativity, and local electroneutrality, and the interfacial strains would together act on the formation of these superlattices. The Q × f values measured in the microwave range increased considerably around the compositional range where the superlattices were formed, indicating that the effect of reconstructed superlattices on the intrinsic loss should not be overlooked. As proven by the dielectric response in the high-frequency range (0.5 − 1 THz), the x = 0.2 sample indeed showed extremely higher Q × f values than other ones, which illustrated that the sample with the reconstructed superlattices was related to a small lattice vibrational anharmonicity that is favorable for the low dielectric loss.

Introduction

The ever-growing traffic explosion in mobile communications has recently drawn increasing interest in the designs of new microwave dielectric components for high data rates. Certain frequency range near the bottom of the millimeter-wave spectrum (30−80 GHz) is being used in the 5th generation cellular networks because of the enhanced spectrum bandwidth, which enables high-speed signal transmission [1]. Because the relative permittivity is inversely proportional to the signal propagation velocity through the medium, materials with low permittivities (ε_r≤25) are considered fitting for the millimeter-wave applications [2]. Besides, a high quality factor (Q) and a near-zero temperature coefficient of the resonant frequency (τ_f) are essential factors for the practical usage of dielectric ceramics [3,4].

In recent years, numerous ceramics with the rock-salt structure were explored with properties well-suited for millimeter-wave applications because of their low relative permittivities and low dielectric losses, such as Li₂TiO₃, Li₃NbO₄, Li₃Mg₂NbO₆, and Li₂Mg₃TiO₆, etc. [5], [6], [7], [8]. Among these matrix ceramics, the Li₂TiO₃ ceramic attracted much attention because of its unique positive τ_f (τ_f=30−36 ppm/ °C) within the group of low-permittivity dielectric ceramics. According to the mixing rule of dielectrics, Li₂TiO₃ was a useful dopant to composite with another phase with a negative τ_f to get a near-zero τ_f value [9], [10], [11]. The dielectric loss will be inevitably increased if the impurity phase is introduced into the matrix, but this effect can be avoided by forming a solid solution in the Li₂TiO₃-based ceramic system, where a high Q together with a near-zero τ_f value can be jointly achieved. For instance, Bian et al. utilized Mg²⁺ ions to co-substitute Li⁺/Ti⁴⁺ions to form the (1-x)Li₂TiO₃-xMgO solid solutions, where the replacement mechanism is 3Mg²⁺⇄2Li⁺+Ti⁴⁺, and the excellent microwave dielectric properties were achieved in the x = 0.24 sample with ε_r=19.2, Q × f = 106,226 GHz, and τ_f=3.56 ppm/ °C [12]. Interestingly, a continuous monoclinic-cubic phase transition accompanied by an order-disorder transformation occurred in the Li₂TiO₃-rich end of the Li₂TiO₃−MgO solid-solution system, and the transformed phase corresponded to the symmetry of the MgO cubic structure with Fm$\overline{3}$m space group (S.G.). The Li₂Mg₃TiO₆ ceramic adopted a disordered cubic structure and exhibited ultra-high Q × f values (ε_r=15.2, Q × f = 152,000 GHz, and τ_f=−39 ppm/ °C), and it belongs to the Li₂TiO₃−MgO solid-solution system [8]. Besides, phase-transition phenomena appeared to be common in the solid solutions formed by the endmembers with a rock-salt crystal configuration but different symmetries. For other examples of the two-endmember systems, an ordered cubic (S.G. I-43 m)-disordered cubic (S.G. Fm$\overline{3}$m)-monoclinic (S.G. C2/c) phase transition was reported in the Li₂TiO₃−Li₃NbO₄ system, and an orthorhombic (S.G. Fddd)-cubic (S.G. Fm$\overline{3}$m) phase transition was found in the Li₃NbO₄−MgO pseudo-binary system [13,14]. Among these solid solution systems, a wide range of desired properties was tunable by compositional modifications. On the whole, the above-mentioned studies indicated that the Li₂TiO₃, Li₃NbO₄, and MgO could form solid solutions in pairs. We supposed that the three-endmember solid solution systems would offer more degrees of freedom to obtain promising properties that cannot be achieved in the two-endmember systems. As we have preliminarily studied in our earlier work, the compound of the central section of the Li₂TiO₃−Li₃NbO₄−MgO phase diagram, Li₅MgTiNbO₈, adopted a pure cubic phase and exhibited excellent properties of ε_r=17.55, Q × f = 109,700 GHz, and τ_f=−32.5 ppm/ °C, which has shown great potential for the development of the materials with excellent performance in the Li₂TiO₃−Li₃NbO₄−MgO pseudo ternary system [15]. To make it easier to be comprehended the structural evolutions among the Li₂TiO₃, Li₃NbO₄, and MgO ceramics, we plotted the pseudo ternary phase diagram of the Li₂TiO₃−Li₃NbO₄−MgO system according to the data from the abovementioned literature and the other studies concerning the Li₂MgTiO₄, Li₃Mg₂NbO₆, and Li₄Mg₃Ti₂O₉ compounds [7,16,17], as shown in Fig. 1.

Apart from the solid solutions in the Li₂TiO₃−Li₃NbO₄−MgO pseudo ternary system, there were many other two-endmember systems with large solid solubilities and excellent microwave dielectric properties, such as the Li₂SnO₃−MgO [18], Li₂ZrO₃−MgO [19], and Li₂ZrO₃−Li₃NbO₄ [20] systems. The universal large solid solubilities in the rock-salt solid solutions may be attributed to the loose constraint of the ion radius for the rock salt structure, where the radii of the cations (R_A) and the radii of the anions (R_X) should meet the scope of 0.42≤R_A/R_X≤0.72 [21]. A large solid solubility of a rock-salt system represents that there is a broad compositional range that can be adjusted to seek desired properties without worsening them due to impurities. On the other hand, it appeared that the composition-driven phase transitions in the abovementioned solid solutions were induced by the complex substitutions of the non-equivalent ions, and what could be determined was that the change of cation ordering and crystal symmetry would inevitably affect the intrinsic loss of the dielectrics [22,23]. But the studies concerning the mechanisms of the phase transitions and the origins of the ultra-low loss of these rock-salt systems were limited until now. It is noticeable that there has been a phenomenological correlation between the high ordering degree and high Q value widely studied in complex perovskites [24,25]. Besides, the high Q values were also found in the complex perovskites that were substituted by the non-equivalent ions, and the extremely low losses were owed to the formation of the ordering-induced domains in the samples with the low dopant or substituent concentration [26]. It is vital and necessary to understand the intrinsic loss affected by structural changes and the most promising approach is to study the high-frequency response of materials, including the whole submillimeter (0.3 − 3 THz) and part of the far-infrared (1.5 − 36 THz) range. The intrinsic dielectric properties of materials are overwhelmingly stronger than the extrinsic ones in the dielectric response at tremendously high frequency due to the proximity of phonon eigenfrequencies (generally in the order of 10¹¹−10¹² Hz) [27,28]. The classic damped oscillator model which fits the far-infrared reflectivity data were widely used to extrapolate the dielectric properties from far-infrared down to the microwave range, but it is not accurate for materials with permittivities below 20 [28]. Direct extrapolation of dielectric properties from submillimetre to microwave range is valid because the proportionality ε’’ (imaginary part of dielectric function) ∝ f (frequency) is roughly obeyed in the whole range from the microwave to submillimeter wave [27], [28], [29].

In this paper, we are aiming to clarify the relationship among the structural changes, phonon vibrations, and microwave dielectric properties of the Li_3+xMg_2–2xNb_1-xTi_2xO₆ (0 ≤ x ≤ 1) ceramics in the Li₂TiO₃−Li₃NbO₄−MgO pseudo ternary system. The Li₃Mg₂NbO₆ endmember was chosen due to its promising properties (ε_r=16.8, Q × f = 79,600 GHz and τ_f=−27.2 ppm/ °C), and several studies have proved that the properties could be effectively improved by the non-equivalent ion substitutions [7,[30], [31], [32]]. The Li₂TiO₃ endmember was selected because the temperature-stable sample was expected in the Li₂TiO₃-rich end of the phase diagram.