**1. Introduction**

Microwave and millimetre-wave dielectric materials [1–6] have been investigated for a wide range of telecommunication applications, such as mobile and smartphones, wireless local area network (LAN) modules and intelligent transport system (ITS). Millimetre-wave dielectric materials with high quality factor *Q* and low dielectric constant *ε*r are required for the next 5G telecommunication applications used for noncondensed high data transfer on LAN/ personal area networks (PAN) and the higher frequency radar on autonomous cars.

In microwave dielectrics, there are three fundamental dielectric properties: quality factor (*Q )*, dielectric constant (*ε*r) and temperature coefficient of resonant frequency (*TCf/τ*f) [1, 2, 6]. Microwave dielectrics have been used as the critical constituents of wireless communications [7–10], such as resonators, filters and temperature-stable capacitors with a near zero ppm/°C *TCε*r (temperature

coefficient of the dielectric constant). Among the dielectric properties, the most essential property is *Q* , the inversion of the dielectric loss (tan*δ*); thus *Q* = 1/ tan*δ*. The dielectric losses of microwave dielectrics should be small. So, most of the microwave dielectrics are paraelectrics with inversion symmetry *i*, while most of the electronic materials are ferroelectrics with spontaneous polarity showing substantial dielectric losses [11–13]. The microwave dielectrics attract attention as a high potential material, which have an over-well-proportional rigid crystal structure with symmetry. That is, the structure should be without electric defects, nondistortion and without strain.

Under the influence of an electric field, four types of polarisation mechanisms can occur in dielectric ceramics, that is, interfacial, dipolar, ionic and electronic. In general, the microwave dielectric properties such as *ε*r and *Q* are mostly influenced by ionic or electronic polarisation. The dielectric polarisation generates the dielectric losses in the presence of an electromagnetic wave. When the frequency is increased to millimetre-wave values, the dielectric losses may be increased or decreased depending on the polarisation mechanism. There are two kinds of losses: those depending on crystal structure and losses due to external factors. It was believed that the intrinsic losses are due to the ordering/disordering, symmetry and phonon vibration, while extrinsic losses are due to factors such as grain size, defects, inclusions, density and distortion from stress.

In this chapter, the origins of high *Q* are discussed based on the intrinsic factors related to the crystal structure, such as symmetry, compositional ordering and compositional density. Although it has previously been believed that ordering based on the order-disorder phase transition brings high *Q* [14], the authors propose that it is primarily a high symmetry that leads to high *Q* [15]. The following focused studies relate to specific examples; indialite with high symmetry showing higher *Q* than cordierite with an ordered structure [16–18]; pseudo tungsten-bronze solid solutions without phase transition showing high *Q* based on the compositional ordering [19–21]; complex perovskite compounds with order-disorder transitions depending on density and grain size [22, 23] and complex perovskites with composition deviated from the stoichiometric depending on the compositional density showing a high *Q* [24–29].
