SapphireSapphire is a precious gemstone, a variety of the mineral corundum, consisting of aluminium oxide () with trace amounts of elements such as iron, titanium, cobalt, lead, chromium, vanadium, magnesium, boron, and silicon. The name sapphire is derived via the Latin from the Greek sappheiros (), which referred to lapis lazuli. It is typically blue, but natural "fancy" sapphires also occur in yellow, purple, orange, and green colors; "parti sapphires" show two or more colors.
Mill (grinding)A mill is a device, often a structure, machine or kitchen appliance, that breaks solid materials into smaller pieces by grinding, crushing, or cutting. Such comminution is an important unit operation in many processes. There are many different types of mills and many types of materials processed in them. Historically mills were powered by hand or by animals (e.g., via a hand crank), working animal (e.g., horse mill), wind (windmill) or water (watermill). In modern era, they are usually powered by electricity.
CrystalA crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals are usually identifiable by their geometrical shape, consisting of flat faces with specific, characteristic orientations. The scientific study of crystals and crystal formation is known as crystallography.
Verneuil methodThe Verneuil method (or Verneuil process or Verneuil technique), also called flame fusion, was the first commercially successful method of manufacturing synthetic gemstones, developed in the late 1883 by the French chemist Auguste Verneuil. It is primarily used to produce the ruby, sapphire and padparadscha varieties of corundum, as well as the diamond simulants rutile, strontium titanate and spinel. The principle of the process involves melting a finely powdered substance using an oxyhydrogen flame, and crystallising the melted droplets into a boule.
Scattering parametersScattering parameters or S-parameters (the elements of a scattering matrix or S-matrix) describe the electrical behavior of linear electrical networks when undergoing various steady state stimuli by electrical signals. The parameters are useful for several branches of electrical engineering, including electronics, communication systems design, and especially for microwave engineering. The S-parameters are members of a family of similar parameters, other examples being: Y-parameters, Z-parameters, H-parameters, T-parameters or ABCD-parameters.
Set theorySet theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory.
Set (mathematics)A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements. Sets are ubiquitous in modern mathematics.
Crystallographic databaseA crystallographic database is a database specifically designed to store information about the structure of molecules and crystals. Crystals are solids having, in all three dimensions of space, a regularly repeating arrangement of atoms, ions, or molecules. They are characterized by symmetry, morphology, and directionally dependent physical properties. A crystal structure describes the arrangement of atoms, ions, or molecules in a crystal.
Empty setIn mathematics, the empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero. Some axiomatic set theories ensure that the empty set exists by including an axiom of empty set, while in other theories, its existence can be deduced. Many possible properties of sets are vacuously true for the empty set. Any set other than the empty set is called non-empty. In some textbooks and popularizations, the empty set is referred to as the "null set".
Zone axisZone axis, a term sometimes used to refer to "high-symmetry" orientations in a crystal, most generally refers to any direction referenced to the direct lattice (as distinct from the reciprocal lattice) of a crystal in three dimensions. It is therefore indexed with direct lattice indices, instead of with Miller indices. High-symmetry zone axes through a crystal lattice, in particular, often lie in the direction of tunnels through the crystal between planes of atoms.
