How can you tell if a mug is ceramic?

Ceramic material is an inorganic, non-metallic oxide, nitride, or carbide material. Some elements, such as carbon or silicon, may be considered ceramics. Ceramic materials are brittle, hard, strong in compression, and weak in shearing and tension. They withstand chemical erosion that occurs in other materials subjected to acidic or caustic environments. Ceramics generally can withstand very high temperatures, ranging from 1,000 °C to 1,600 °C (1,800 °F to 3,000 °F).
The crystallinity of ceramic materials varies widely. Most often, fired ceramics are either vitrified or semi-vitrified as is the case with earthenware, stoneware, and porcelain. Varying crystallinity and electron composition in the ionic and covalent bonds cause most ceramic materials to be good thermal and electrical insulators (researched in ceramic engineering). With such a large range of possible options for the composition/structure of a ceramic (nearly all of the elements, nearly all types of bonding, and all levels of crystallinity), the breadth of the subject is vast, and identifiable attributes (hardness, toughness, electrical conductivity) are difficult to specify for the group as a whole. General properties such as high melting temperature, high hardness, poor conductivity, high moduli of elasticity, chemical resistance and low ductility are the norm, with known exceptions to each of these rules (piezoelectric ceramics, glass transition temperature, superconductive ceramics). Many composites, such as fiberglass and carbon fiber, while containing ceramic materials are not considered to be part of the ceramic family.
Highly oriented crystalline ceramic materials are not amenable to a great range of processing. Methods for dealing with them tend to fall into one of two categories – either make the ceramic in the desired shape, by reaction in situ, or by "forming" powders into the desired shape, and then sintering to form a solid body. Ceramic forming techniques include shaping by hand (sometimes including a rotation process called "throwing"), slip casting, tape casting (used for making very thin ceramic capacitors), injection molding, dry pressing, and other variations.
Many ceramics experts do not consider materials with amorphous (noncrystalline) character (i.e., glass) to be ceramics even though glassmaking involves several steps of the ceramic process and its mechanical properties are similar to ceramic materials. However, heat treatments can convert glass into a semi-crystalline material known as glass-ceramic.
Traditional ceramic raw materials include clay minerals such as kaolinite, whereas more recent materials include aluminum oxide, more commonly known as alumina. The modern ceramic materials, which are classified as advanced ceramics, include silicon carbide and tungsten carbide. Both are valued for their abrasion resistance and hence find use in applications such as the wear plates of crushing equipment in mining operations. Advanced ceramics are also used in the medicine, electrical, electronics industries, and body armor.