Crystallography in the context of X-ray diffraction

Plagioclase (/ˈplædʒ(i)əˌkleɪs, ˈpleɪdʒ-, -ˌkleɪz/ PLAJ-(ee)-ə-klayss, PLAYJ-, -⁠klayz) is a series of tectosilicate (framework silicate) minerals within the feldspar group. Rather than referring to a particular mineral with a specific chemical composition, plagioclase is a continuous solid solution series, more properly known as the plagioclase feldspar series. This was first shown by the German mineralogist Johann Friedrich Christian Hessel (1796–1872) in 1826. The series ranges from albite to anorthite endmembers (with respective compositions NaAlSi₃O₈ to CaAl₂Si₂O₈), where sodium and calcium atoms can substitute for each other in the mineral's crystal lattice structure. Plagioclase in hand samples is often identified by its polysynthetic crystal twinning or "record-groove" effect.

Plagioclase is a major constituent mineral in Earth's crust and is consequently an important diagnostic tool in petrology for identifying the composition, origin and evolution of igneous rocks. Plagioclase is also a major constituent of rock in the highlands of the Moon. Analysis of thermal emission spectra from the surface of Mars suggests that plagioclase is the most abundant mineral in the crust of Mars.

A 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. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification.

The word crystal derives from the Ancient Greek word κρύσταλλος (krustallos), meaning both "ice" and "rock crystal", from κρύος (kruos), "icy cold, frost".

Solid-state chemistry, also sometimes referred as materials chemistry, is the study of the synthesis, structure, and properties of solid phase materials. It therefore has a strong overlap with solid-state physics, mineralogy, crystallography, ceramics, metallurgy, thermodynamics, materials science and electronics with a focus on the synthesis of novel materials and their characterization. A diverse range of synthetic techniques, such as the ceramic method and chemical vapour depostion, make solid-state materials. Solids can be classified as crystalline or amorphous on basis of the nature of order present in the arrangement of their constituent particles. Their elemental compositions, microstructures, and physical properties can be characterized through a variety of analytical methods.

The Necker cube is an optical illusion that was first published as a rhomboid in 1832 by Swiss crystallographer Louis Albert Necker. It is a simple wire-frame, two dimensional drawing of a cube with no visual cues as to its orientation, so it can be interpreted to have either the lower-left or the upper-right square as its front side.

In academia and librarianship, conference proceedings are a collection of academic papers published in the context of an academic conference or workshop. Conference proceedings typically contain the contributions made by researchers at the conference. They are the written record of the work that is presented to fellow researchers. In many fields, they are published as supplements to academic journals; in some, they are considered the main dissemination route; in others they may be considered grey literature. They are usually distributed in printed or electronic volumes, either before the conference opens or after it has closed.

A less common, broader meaning of proceedings are the acts and happenings of an academic field, a learned society. For example, the title of the Acta Crystallographica journals is Neo-Latin for "Proceedings in Crystallography"; the Proceedings of the National Academy of Sciences of the United States of America is the main journal of that academy. Scientific journals whose ISO 4 title abbreviations start with Proc, Acta, or Trans are journals of the proceedings (transactions) of a field or of an organization concerned with it, in that secondary meaning of the word.

Crystal twinning occurs when two or more adjacent crystals of the same mineral are oriented so that they share some of the same crystal lattice points in a symmetrical manner. The result is an intergrowth of two separate crystals that are tightly bonded to each other. The surface along which the lattice points are shared in twinned crystals is called a composition surface or twin plane.

In crystallography twinned crystals are described by a number of twin laws, which are specific to the crystal structure. The type of twinning can be a diagnostic tool in mineral identification. There are three main types of twinning. The first is growth twinning which can occur both in very large and very small particles. The second is transformation twinning, where there is a change in the crystal structure. The third is deformation twinning, in which twinning develops in a crystal in response to a shear stress, and is an important mechanism for permanent shape changes in a crystal.

In crystallography, the hexagonal crystal family is one of the six crystal families, which includes two crystal systems (hexagonal and trigonal) and two lattice systems (hexagonal and rhombohedral). While commonly confused, the trigonal crystal system and the rhombohedral lattice system are not equivalent (see section crystal systems below). In particular, there are crystals that have trigonal symmetry but belong to the hexagonal lattice (such as α-quartz).

The hexagonal crystal family consists of the 12 point groups such that at least one of their space groups has the hexagonal lattice as underlying lattice, and is the union of the hexagonal crystal system and the trigonal crystal system. There are 52 space groups associated with it, which are exactly those whose Bravais lattice is either hexagonal or rhombohedral.

In crystallography, crystal structure is a description of the ordered arrangement of atoms, ions, or molecules in a crystalline material. Ordered structures occur from the intrinsic nature of constituent particles to form symmetric patterns that repeat along the principal directions of three-dimensional space in matter.

The smallest group of particles in a material that constitutes this repeating pattern is the unit cell of the structure. The unit cell completely reflects the symmetry and structure of the entire crystal, which is built up by repetitive translation of the unit cell along its principal axes. The translation vectors define the nodes of the Bravais lattice.

In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals.

There are three main varieties of these crystals:

In crystallography, a crystal system is a set of point groups (a group of geometric symmetries with at least one fixed point). A lattice system is a set of Bravais lattices (an infinite array of discrete points). Space groups (symmetry groups of a configuration in space) are classified into crystal systems according to their point groups, and into lattice systems according to their Bravais lattices. Crystal systems that have space groups assigned to a common lattice system are combined into a crystal family.

The seven crystal systems are triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic. Informally, two crystals are in the same crystal system if they have similar symmetries (though there are many exceptions).

In crystallography, the tetragonal crystal system is one of the seven crystal systems. Tetragonal crystal lattices result from stretching a cubic lattice along one of its lattice vectors, so that the cube becomes a rectangular prism with a square base (a by a) and height (c, which is different from a).

In crystallography, the orthorhombic crystal system is one of the seven crystal systems. Orthorhombic lattices result from stretching a cubic lattice along two of its orthogonal pairs by two different factors, resulting in a rectangular prism with a rectangular base (a by b) and height (c), such that a, b, and c are distinct. All three bases intersect at 90° angles, so the three lattice vectors remain mutually orthogonal.

Cleavage, in mineralogy and materials science, is the tendency of crystalline materials to split along definite crystallographic structural planes. These planes of relative weakness are a result of the regular locations of atoms and ions in the crystal, which create smooth repeating surfaces that are visible both in the microscope and to the naked eye. If bonds in certain directions are weaker than others, the crystal will tend to split along the weakly bonded planes. These flat breaks are termed "cleavage". The classic example of cleavage is mica, which cleaves in a single direction along the basal pinacoid, making the layers seem like pages in a book. In fact, mineralogists often refer to "books of mica".

Diamond and graphite provide examples of cleavage. Each is composed solely of a single element, carbon. In diamond, each carbon atom is bonded to four others in a tetrahedral pattern with short covalent bonds. The planes of weakness (cleavage planes) in a diamond are in four directions, following the faces of the octahedron. In graphite, carbon atoms are contained in layers in a hexagonal pattern where the covalent bonds are shorter (and thus even stronger) than those of diamond. However, each layer is connected to the other with a longer and much weaker van der Waals bond. This gives graphite a single direction of cleavage, parallel to the basal pinacoid. So weak is this bond that it is broken with little force, giving graphite a slippery feel as layers shear apart. As a result, graphite makes an excellent dry lubricant.

In materials science, a single crystal (or single-crystal solid or monocrystalline solid) is a material in which the crystal lattice of the entire sample is continuous and unbroken to the edges of the sample, with no grain boundaries. The absence of the defects associated with grain boundaries can give monocrystals unique properties, particularly mechanical, optical and electrical, which can also be anisotropic, depending on the type of crystallographic structure. These properties, in addition to making some gems precious, are industrially used in technological applications, especially in optics and electronics.

Because entropic effects favor the presence of some imperfections in the microstructure of solids, such as impurities, inhomogeneous strain and crystallographic defects such as dislocations, perfect single crystals of meaningful size are exceedingly rare in nature. The necessary laboratory conditions often add to the cost of production. On the other hand, imperfect single crystals can reach enormous sizes in nature: several mineral species such as beryl, gypsum and feldspars are known to have produced crystals several meters across.

Igneous petrology is the study of igneous rocks—those that are formed from magma. As a branch of geology, igneous petrology is closely related to volcanology, tectonophysics, and petrology in general. The modern study of igneous rocks uses a number of techniques, some of them developed in the fields of chemistry, physics, or other earth sciences. Petrography, crystallography, and isotopic studies are common methods used in igneous petrology.