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Novel low temperature firing microwave dielectric ceramic LiCa3MgV3O12 (LCMV) with garnet structure was fabricated by the conventional solid‐state reaction method. The phase purity, microstructure, and microwave dielectric properties were investigated. The densification temperature for the LCMV ceramic is 900°C. LCMV ceramic possessed εr = 10.5, Qu × f = 74 700 GHz, and τf = −61 ppm/°C. Furthermore, 0.90LiCa3MgV3O12–0.10CaTiO3 ceramic sintered at 925°C for 4 h exhibited good properties of εr = 12.4, Qu × f = 57 600 GHz, and τf = 2.7 ppm/°C. The LCMV ceramic could be compatible with Ag electrode, which makes it a promising ceramic for LTCC technology application.

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A Ginzburg–Landau type theory of interaction of randomly distributed local dipoles in a paraelectric crystal is developed. The interaction is caused by the polarization of the host lattice generated by these dipoles. The obtained effective Hamiltonian of the dipole–dipole interaction is employed for the Monte Carlo simulation of ferroelectric properties of a system with off-center dopant ions producing local dipoles. The computer simulation shows that at low dopant ion concentration the paraelectric state transforms into a macroscopically paraelectric state consisting of randomly oriented polar clusters. These clusters amplify the effective dipole moment and dramatically increase the dielectric constant. The interaction between the clusters results in a spectrum of relaxation time and transition to the relaxor state. The real and imaginary parts of the susceptibility of this state are calculated. At intermediate dopant concentration, the material undergoes a diffuse phase transition into a ferroelectric state smeared within a temperature range. A further increase in the dopant concentration makes the transition sharper and closer to the conventional ferroelectric transition. The results obtained are compared with the behavior of the K1−xLixTaO3 relaxor ferroelectric.