Stoichiometry is the calculation of reactants and products in chemical reactions. Stoichiometry is founded on the law of conservation of mass where the total mass of the reactants equals the total mass of the products, leading to the insight that the relations among quantities of reactants and products form a ratio of positive integers; this means that if the amounts of the separate reactants are known the amount of the product can be calculated. Conversely, if one reactant has a known quantity and the quantity of the products can be empirically determined the amount of the other reactants can be calculated; this is illustrated in the image here, where the balanced equation is: CH4 + 2 O2 → CO2 + 2 H2O. Here, one molecule of methane reacts with two molecules of oxygen gas to yield one molecule of carbon dioxide and two molecules of water; this particular chemical equation is an example of complete combustion. Stoichiometry measures these quantitative relationships, is used to determine the amount of products and reactants that are produced or needed in a given reaction.
Describing the quantitative relationships among substances as they participate in chemical reactions is known as reaction stoichiometry. In the example above, reaction stoichiometry measures the relationship between the methane and oxygen as they react to form carbon dioxide and water; because of the well known relationship of moles to atomic weights, the ratios that are arrived at by stoichiometry can be used to determine quantities by weight in a reaction described by a balanced equation. This is called composition stoichiometry. Gas stoichiometry deals with reactions involving gases, where the gases are at a known temperature and volume and can be assumed to be ideal gases. For gases, the volume ratio is ideally the same by the ideal gas law, but the mass ratio of a single reaction has to be calculated from the molecular masses of the reactants and products. In practice, due to the existence of isotopes, molar masses are used instead when calculating the mass ratio; the term stoichiometry was first used by Jeremias Benjamin Richter in 1792 when the first volume of Richter's Stoichiometry or the Art of Measuring the Chemical Elements was published.
The term is derived from the Ancient Greek words στοιχεῖον stoicheion "element" and μέτρον metron "measure". In patristic Greek, the word Stoichiometria was used by Nicephorus to refer to the number of line counts of the canonical New Testament and some of the Apocrypha. A stoichiometric amount or stoichiometric ratio of a reagent is the optimum amount or ratio where, assuming that the reaction proceeds to completion: All of the reagent is consumed There is no deficiency of the reagent There is no excess of the reagent. Stoichiometry rests upon the basic laws that help to understand it better, i.e. law of conservation of mass, the law of definite proportions, the law of multiple proportions and the law of reciprocal proportions. In general, chemical reactions combine in definite ratios of chemicals. Since chemical reactions can neither create nor destroy matter, nor transmute one element into another, the amount of each element must be the same throughout the overall reaction. For example, the number of atoms of a given element X on the reactant side must equal the number of atoms of that element on the product side, whether or not all of those atoms are involved in a reaction.
Chemical reactions, as macroscopic unit operations, consist of a large number of elementary reactions, where a single molecule reacts with another molecule. As the reacting molecules consist of a definite set of atoms in an integer ratio, the ratio between reactants in a complete reaction is in integer ratio. A reaction may consume more than one molecule, the stoichiometric number counts this number, defined as positive for products and negative for reactants. Different elements have a different atomic mass, as collections of single atoms, molecules have a definite molar mass, measured with the unit mole. By definition, carbon-12 has a molar mass of 12 g/mol. Thus, to calculate the stoichiometry by mass, the number of molecules required for each reactant is expressed in moles and multiplied by the molar mass of each to give the mass of each reactant per mole of reaction; the mass ratios can be calculated by dividing each by the total in the whole reaction. Elements in their natural state are mixtures of isotopes of differing mass, thus atomic masses and thus molar masses are not integers.
For instance, instead of an exact 14:3 proportion, 17.04 kg of ammonia consists of 14.01 kg of nitrogen and 3 × 1.01 kg of hydrogen, because natural nitrogen includes a small amount of nitrogen-15, natural hydrogen includes hydrogen-2. A stoichiometric reactant is a reactant, consumed in a reaction, as opposed to a catalytic reactant, not consumed in the overall reaction because it reacts in one step and is regenerated in another step. Stoichiometry is not only used to balance chemical equations but used in conversions, i.e. converting from grams to moles using molar mass as the conversion factor, or from grams to milliliters using density. For example, to find the amount of NaCl in 2.00 g, one would do the following: 2.00 g NaCl 58.44 g NaCl mol − 1 = 0.034 mol In the above example, when written out in fraction form, the units of grams form a multiplicative identity, equivalent to one, wit
Crystalline solids exhibit a periodic crystal structure. The positions of atoms or molecules occur on repeating fixed distances, determined by the unit cell parameters. However, the arrangement of atoms or molecules in most crystalline materials is not perfect; the regular patterns are interrupted by crystallographic defects. Point defects are defects that occur only around a single lattice point, they are not extended in space in any dimension. Strict limits for how small a point defect is are not defined explicitly. However, these defects involve at most a few extra or missing atoms. Larger defects in an ordered structure are considered dislocation loops. For historical reasons, many point defects in ionic crystals, are called centers: for example a vacancy in many ionic solids is called a luminescence center, a color center, or F-center; these dislocations permit ionic transport through crystals leading to electrochemical reactions. These are specified using Kröger–Vink notation. Vacancy defects are lattice sites which are vacant.
If a neighboring atom moves to occupy the vacant site, the vacancy moves in the opposite direction to the site which used to be occupied by the moving atom. The stability of the surrounding crystal structure guarantees that the neighboring atoms will not collapse around the vacancy. In some materials, neighboring atoms move away from a vacancy, because they experience attraction from atoms in the surroundings. A vacancy is sometimes called a Schottky defect. Interstitial defects are atoms that occupy a site in the crystal structure at which there is not an atom, they are high energy configurations. Small atoms in some crystals can occupy interstices without high energy, such as hydrogen in palladium. A nearby pair of a vacancy and an interstitial is called a Frenkel defect or Frenkel pair; this is caused when an ion creates a vacancy. Due to fundamental limitations of material purification methods, materials are never 100% pure, which by definition induces defects in crystal structure. In the case of an impurity, the atom is incorporated at a regular atomic site in the crystal structure.
This is neither a vacant site nor is the atom on an interstitial site and it is called a substitutional defect. The atom is not supposed to be anywhere in the crystal, is thus an impurity. In some cases where the radius of the substitutional atom is smaller than that of the atom it is replacing, its equilibrium position can be shifted away from the lattice site; these types of substitutional defects are referred to as off-center ions. There are two different types of substitutional defects: Isovalent substitution and aliovalent substitution. Isovalent substitution is where the ion, substituting the original ion is of the same oxidation state as the ion it is replacing. Aliovalent substitution is where the ion, substituting the original ion is of a different oxidation state than the ion it is replacing. Aliovalent substitutions change the overall charge within the ionic compound, but the ionic compound must be neutral. Therefore, a charge compensation mechanism is required. Hence either one of the metals is or oxidised or reduced, or ion vacancies are created.
Antisite defects occur in an ordered alloy or compound when atoms of different type exchange positions. For example, some alloys have a regular structure. If one cube has an A atom at its center, the atom is on a site occupied by a B atom, is thus an antisite defect; this an impurity. Topological defects are regions in a crystal where the normal chemical bonding environment is topologically different from the surroundings. For instance, in a perfect sheet of graphite all atoms are in rings containing six atoms. If the sheet contains regions where the number of atoms in a ring is different from six, while the total number of atoms remains the same, a topological defect has formed. An example is the Stone Wales defect in nanotubes, which consists of two adjacent 5-membered and two 7-membered atom rings. Amorphous solids may contain defects; these are somewhat hard to define, but sometimes their nature can be quite understood. For instance, in ideally bonded amorphous silica all Si atoms have 4 bonds to O atoms and all O atoms have 2 bonds to Si atom.
Thus e.g. an O atom with only one Si bond can be considered a defect in silica. Moreover, defects can be defined in amorphous solids based on empty or densely packed local atomic neighbourhoods, the properties of such'defects' can be shown to be similar to normal vacancies and interstitials in crystals. Complexes can form between different kinds of point defects. For example, if a vacancy encounters an impurity, the two may bind together if the impurity is too large for the lattice. Interstitials can form'split interstitial' or'dumbbell' structures where two atoms share an atomic site, resulting in neither atom occupying the site. Line defects can be described by gauge theories. Dislocations are linear defects. There are two basic types of the edge dislocation and the screw dislocation. "Mixed" dislocations, combining aspects of both types, are common. Edge dislocations are caused by the termination of a plane of atoms in the middle of a crystal. In such a case, the adjacent planes are not straig
Third law of thermodynamics
The third law of thermodynamics is sometimes stated as follows, regarding the properties of closed systems in thermodynamic equilibrium: The entropy of a system approaches a constant value as its temperature approaches absolute zero. This constant value cannot depend on any other parameters characterizing the closed system, such as pressure or applied magnetic field. At absolute zero the system must be in a state with the minimum possible energy. Entropy is related to the number of accessible microstates, there is one unique state with minimum energy. In such a case, the entropy at absolute zero will be zero. If the system does not have a well-defined order there may remain some finite entropy as the system is brought to low temperatures, either because the system becomes locked into a configuration with non-minimal energy or because the minimum energy state is non-unique; the constant value is called the residual entropy of the system. The entropy is a state-function meaning the inherent value of different atoms and other configurations of particles including subatomic or atomic material is defined by entropy, which can be discovered near 0 K.
The Nernst–Simon statement of the third law of thermodynamics concerns thermodynamic processes at a fixed, low temperature: The entropy change associated with any condensed system undergoing a reversible isothermal process approaches zero as the temperature at which it is performed approaches 0 K. Here a condensed system refers to solids. A classical formulation by Nernst is: It is impossible for any process, no matter how idealized, to reduce the entropy of a system to its absolute-zero value in a finite number of operations. There exists a formulation of the Third Law which approaches the subject by postulating a specific energy behavior: If the composite of two thermodynamic systems constitutes an isolated system any energy exchange in any form between those two systems is bounded; the third law was developed by chemist Walther Nernst during the years 1906–12, is therefore referred to as Nernst's theorem or Nernst's postulate. The third law of thermodynamics states that the entropy of a system at absolute zero is a well-defined constant.
This is because a system at zero temperature exists in its ground state, so that its entropy is determined only by the degeneracy of the ground state. In 1912 Nernst stated the law thus: "It is impossible for any procedure to lead to the isotherm T = 0 in a finite number of steps."An alternative version of the third law of thermodynamics as stated by Gilbert N. Lewis and Merle Randall in 1923: If the entropy of each element in some crystalline state be taken as zero at the absolute zero of temperature, every substance has a finite positive entropy; this version states not only ΔS will reach zero at 0 K, but S itself will reach zero as long as the crystal has a ground state with only one configuration. Some crystals form defects; this residual entropy disappears when the kinetic barriers to transitioning to one ground state are overcome. With the development of statistical mechanics, the third law of thermodynamics changed from a fundamental law to a derived law; the basic law from which it is derived is the statistical-mechanics definition of entropy for a large system: S − S 0 = k B ln Ω where S is entropy, kB is the Boltzmann constant, Ω is the number of microstates consistent with the macroscopic configuration.
The counting of states is from the reference state of absolute zero, which corresponds to the entropy of S0. In simple terms, the third law states that the entropy of a perfect crystal of a pure substance approaches zero as the temperature approaches zero; the alignment of a perfect crystal leaves no ambiguity as to the location and orientation of each part of the crystal. As the energy of the crystal is reduced, the vibrations of the individual atoms are reduced to nothing, the crystal becomes the same everywhere; the third law provides an absolute reference point for the determination of entropy at any other temperature. The entropy of a closed system, determined relative to this zero point, is the absolute entropy of that system. Mathematically, the absolute entropy of any system at zero temperature is the natural log of the number of ground states times Boltzmann's constant kB = 1.38×10−23 J K−1. The entropy of a perfect crystal lattice as defined by Nernst's theorem is zero provided that its ground state is unique, because ln = 0.
If the system is composed of one-billion atoms, all alike, lie within the matrix of a perfect crystal, the number of combinations of one-billion identical things taken one-billion at a time is Ω = 1. Hence: S − S 0 = k B ln Ω = k B ln 1 = 0 The difference is zero, hence the initial entropy S0 can be any selected value so long as all other such calculations include that as the initial entropy; as a result, the initial entropy value of zero is selected S0 = 0 is used for convenience. S − S 0 = S
In chemistry, a salt is an ionic compound that can be formed by the neutralization reaction of an acid and a base. Salts are composed of related numbers of cations and anions so that the product is electrically neutral; these component ions can be inorganic, such as organic, such as acetate. Salts can be classified in a variety of ways. Salts that produce hydroxide ions when dissolved in water are called alkali salts. Salts that produce acidic solutions are acidic salts. Neutral salts are those salts that are neither basic. Zwitterions contain an anionic and a cationic centres in the same molecule, but are not considered to be salts. Examples of zwitterions include amino acids, many metabolites and proteins. Solid salts tend to be transparent. In many cases, the apparent opacity or transparency are only related to the difference in size of the individual monocrystals. Since light reflects from the grain boundaries, larger crystals tend to be transparent, while the polycrystalline aggregates look like white powders.
Salts exist in many different colors, which arise either from the cations. For example: sodium chromate is yellow by virtue of the chromate ion potassium dichromate is orange by virtue of the dichromate ion cobalt nitrate is red owing to the chromophore of hydrated cobalt. copper sulfate is blue because of the copper chromophore potassium permanganate has the violet color of permanganate anion. Nickel chloride is green of sodium chloride, magnesium sulfate heptahydrate are colorless or white because the constituent cations and anions do not absorb in the visible part of the spectrumFew minerals are salts because they would be solubilized by water. Inorganic pigments tend not to be salts, because insolubility is required for fastness; some organic dyes are salts, but they are insoluble in water. Different salts can elicit all five basic tastes, e.g. salty, sour and umami or savory. Salts of strong acids and strong bases are non-volatile and odorless, whereas salts of either weak acids or weak bases may smell like the conjugate acid or the conjugate base of the component ions.
That slow, partial decomposition is accelerated by the presence of water, since hydrolysis is the other half of the reversible reaction equation of formation of weak salts. Many ionic compounds exhibit significant solubility in water or other polar solvents. Unlike molecular compounds, salts dissociate in solution into cationic components; the lattice energy, the cohesive forces between these ions within a solid, determines the solubility. The solubility is dependent on how well each ion interacts with the solvent, so certain patterns become apparent. For example, salts of sodium and ammonium are soluble in water. Notable exceptions include potassium cobaltinitrite. Most nitrates and many sulfates are water-soluble. Exceptions include barium sulfate, calcium sulfate, lead sulfate, where the 2+/2− pairing leads to high lattice energies. For similar reasons, most alkali metal carbonates are not soluble in water; some soluble carbonate salts are: potassium carbonate and ammonium carbonate. Salts are characteristically insulators.
Molten salts or solutions of salts conduct electricity. For this reason, liquified salts and solutions containing dissolved salts are called electrolytes. Salts characteristically have high melting points. For example, sodium chloride melts at 801 °C; some salts with low lattice energies are liquid near room temperature. These include molten salts, which are mixtures of salts, ionic liquids, which contain organic cations; these liquids exhibit unusual properties as solvents. The name of a salt starts with the name of the cation followed by the name of the anion. Salts are referred to only by the name of the cation or by the name of the anion. Common salt-forming cations include: Ammonium NH+4 Calcium Ca2+ Iron Fe2+ and Fe3+ Magnesium Mg2+ Potassium K+ Pyridinium C5H5NH+ Quaternary ammonium NR+4, R being an alkyl group or an aryl group Sodium Na+ Copper Cu2+Common salt-forming anions include: Acetate CH3COO− Carbonate CO2−3 Chloride Cl− Citrate HOC2 Cyanide C≡N− Fluoride F− Nitrate NO−3 Nitrite NO−2 Oxide O2− Phosphate PO3−4 Sulfate SO2−4 Salts with varying number of hydrogen atoms, with respect to the parent acid, replaced by cations can be referred to as monobasic, dibasic or tribasic salts: Sodium phosphate monobasic Sodium phosphate dibasic Sodium phosphate tribasic Salts are formed by a chemical reaction between: A base and an acid, e.g. NH3 + HCl → NH4Cl A metal and an acid, e.g. Mg + H2SO4 → MgSO4 + H2 A metal and a non-metal, e.g. Ca + Cl2 → CaCl2 A base and an a
Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. The word "crystallography" derives from the Greek words crystallon "cold drop, frozen drop", with its meaning extending to all solids with some degree of transparency, graphein "to write". In July 2012, the United Nations recognised the importance of the science of crystallography by proclaiming that 2014 would be the International Year of Crystallography. X-ray crystallography is used to determine the structure of large biomolecules such as proteins. Before the development of X-ray diffraction crystallography, the study of crystals was based on physical measurements of their geometry; this involved measuring the angles of crystal faces relative to each other and to theoretical reference axes, establishing the symmetry of the crystal in question. This physical measurement is carried out using a goniometer; the position in 3D space of each crystal face is plotted on a stereographic net such as a Wulff net or Lambert net.
The pole to each face is plotted on the net. Each point is labelled with its Miller index; the final plot allows the symmetry of the crystal to be established. Crystallographic methods now depend on analysis of the diffraction patterns of a sample targeted by a beam of some type. X-rays are most used; this is facilitated by the wave properties of the particles. Crystallographers explicitly state the type of beam used, as in the terms X-ray crystallography, neutron diffraction and electron diffraction; these three types of radiation interact with the specimen in different ways. X-rays interact with the spatial distribution of electrons in the sample. Electrons are charged particles and therefore interact with the total charge distribution of both the atomic nuclei and the electrons of the sample. Neutrons are scattered by the atomic nuclei through the strong nuclear forces, but in addition, the magnetic moment of neutrons is non-zero, they are therefore scattered by magnetic fields. When neutrons are scattered from hydrogen-containing materials, they produce diffraction patterns with high noise levels.
However, the material can sometimes be treated to substitute deuterium for hydrogen. Because of these different forms of interaction, the three types of radiation are suitable for different crystallographic studies. An image of a small object is made using a lens to focus the beam, similar to a lens in a microscope. However, the wavelength of visible light is three orders of magnitude longer than the length of typical atomic bonds and atoms themselves. Therefore, obtaining information about the spatial arrangement of atoms requires the use of radiation with shorter wavelengths, such as X-ray or neutron beams. Employing shorter wavelengths implied abandoning microscopy and true imaging, because there exists no material from which a lens capable of focusing this type of radiation can be created. Scientists have had some success focusing X-rays with microscopic Fresnel zone plates made from gold, by critical-angle reflection inside long tapered capillaries. Diffracted X-ray or neutron beams cannot be focused to produce images, so the sample structure must be reconstructed from the diffraction pattern.
Sharp features in the diffraction pattern arise from periodic, repeating structure in the sample, which are very strong due to coherent reflection of many photons from many spaced instances of similar structure, while non-periodic components of the structure result in diffuse diffraction features - areas with a higher density and repetition of atom order tend to reflect more light toward one point in space when compared to those areas with fewer atoms and less repetition. Because of their ordered and repetitive structure, crystals give diffraction patterns of sharp Bragg reflection spots, are ideal for analyzing the structure of solids. Coordinates in square brackets such as denote a direction vector. Coordinates in angle brackets or chevrons such as <100> denote a family of directions which are related by symmetry operations. In the cubic crystal system for example, <100> would mean, or the negative of any of those directions. Miller indices in parentheses such as denote a plane of the crystal structure, regular repetitions of that plane with a particular spacing.
In the cubic system, the normal to the plane is the direction, but in lower-symmetry cases, the normal to is not parallel to. Indices in curly brackets or braces such as denote a family of planes and their normals which are equivalent in cubic materials due to symmetry operations, much the way angle brackets denote a family of directions. In non-cubic materials, <hkl> is not perpendicular to. Some materials that have been analyzed crystallographically, such as proteins, do not occur as crystals; such molecules are placed in solution and allowed to crystallize through vapor diffusion. A drop of solution containing the molecule and precipitants is sealed in a container with a reservoir containing a hygroscopic solution. Water in the drop diffuses to the reservoir increasing the concentration and allowing a crystal to form. If the concentration were to rise more the molecule would precipitate out of solution, resulting in disorderly granules rather than an orderly and hence usable crystal. Once a crystal is obtained, data can be collected using a beam of radiation.
Although many universities that engage in crystallographic research have their own X-ray producing equipment, synchrotrons are used as X-ray sources, bec
An alloy is a combination of metals and of a metal or another element. Alloys are defined by a metallic bonding character. An alloy may be a mixture of metallic phases. Intermetallic compounds are alloys with a defined crystal structure. Zintl phases are sometimes considered alloys depending on bond types. Alloys are used in a wide variety of applications. In some cases, a combination of metals may reduce the overall cost of the material while preserving important properties. In other cases, the combination of metals imparts synergistic properties to the constituent metal elements such as corrosion resistance or mechanical strength. Examples of alloys are steel, brass, duralumin and amalgams; the alloy constituents are measured by mass percentage for practical applications, in atomic fraction for basic science studies. Alloys are classified as substitutional or interstitial alloys, depending on the atomic arrangement that forms the alloy, they can be heterogeneous or intermetallic. An alloy is a mixture of chemical elements, which forms an impure substance that retains the characteristics of a metal.
An alloy is distinct from an impure metal in that, with an alloy, the added elements are well controlled to produce desirable properties, while impure metals such as wrought iron are less controlled, but are considered useful. Alloys are made by mixing two or more elements, at least one of, a metal; this is called the primary metal or the base metal, the name of this metal may be the name of the alloy. The other constituents may or may not be metals but, when mixed with the molten base, they will be soluble and dissolve into the mixture; the mechanical properties of alloys will be quite different from those of its individual constituents. A metal, very soft, such as aluminium, can be altered by alloying it with another soft metal, such as copper. Although both metals are soft and ductile, the resulting aluminium alloy will have much greater strength. Adding a small amount of non-metallic carbon to iron trades its great ductility for the greater strength of an alloy called steel. Due to its very-high strength, but still substantial toughness, its ability to be altered by heat treatment, steel is one of the most useful and common alloys in modern use.
By adding chromium to steel, its resistance to corrosion can be enhanced, creating stainless steel, while adding silicon will alter its electrical characteristics, producing silicon steel. Like oil and water, a molten metal may not always mix with another element. For example, pure iron is completely insoluble with copper; when the constituents are soluble, each will have a saturation point, beyond which no more of the constituent can be added. Iron, for example, can hold a maximum of 6.67% carbon. Although the elements of an alloy must be soluble in the liquid state, they may not always be soluble in the solid state. If the metals remain soluble when solid, the alloy forms a solid solution, becoming a homogeneous structure consisting of identical crystals, called a phase. If as the mixture cools the constituents become insoluble, they may separate to form two or more different types of crystals, creating a heterogeneous microstructure of different phases, some with more of one constituent than the other phase has.
However, in other alloys, the insoluble elements may not separate until after crystallization occurs. If cooled quickly, they first crystallize as a homogeneous phase, but they are supersaturated with the secondary constituents; as time passes, the atoms of these supersaturated alloys can separate from the crystal lattice, becoming more stable, form a second phase that serve to reinforce the crystals internally. Some alloys, such as electrum, an alloy consisting of silver and gold, occur naturally. Meteorites are sometimes made of occurring alloys of iron and nickel, but are not native to the Earth. One of the first alloys made by humans was bronze, a mixture of the metals tin and copper. Bronze was an useful alloy to the ancients, because it is much stronger and harder than either of its components. Steel was another common alloy. However, in ancient times, it could only be created as an accidental byproduct from the heating of iron ore in fires during the manufacture of iron. Other ancient alloys include pewter and pig iron.
In the modern age, steel can be created in many forms. Carbon steel can be made by varying only the carbon content, producing soft alloys like mild steel or hard alloys like spring steel. Alloy steels can be made by adding other elements, such as chromium, vanadium or nickel, resulting in alloys such as high-speed steel or tool steel. Small amounts of manganese are alloyed with most modern steels because of its ability to remove unwanted impurities, like phosphorus and oxygen, which can have detrimental effects on the alloy. However, most alloys were not created until the 1900s, such as various aluminium, titanium and magnesium alloys; some modern superalloys, such as incoloy and hastelloy, may consist of a multitude of different elements. As a noun, the term alloy is used to describe a mixture of atoms in which the primary constituent is a metal; when used as a verb, the term refers to the act of mixing a metal with other elements. The primary metal is called the matrix, or the solvent; the secondary constituents are called s
A crystal or crystalline solid is a solid material whose constituents are arranged in a ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals are 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, meaning both "ice" and "rock crystal", from κρύος, "icy cold, frost". Examples of large crystals include snowflakes and table salt. Most inorganic solids are not crystals but polycrystals, i.e. many microscopic crystals fused together into a single solid. Examples of polycrystals include most metals, rocks and ice. A third category of solids is amorphous solids, where the atoms have no periodic structure whatsoever.
Examples of amorphous solids include glass and many plastics. Despite the name, lead crystal, crystal glass, related products are not crystals, but rather types of glass, i.e. amorphous solids. Crystals are used in pseudoscientific practices such as crystal therapy, along with gemstones, are sometimes associated with spellwork in Wiccan beliefs and related religious movements; the scientific definition of a "crystal" is based on the microscopic arrangement of atoms inside it, called the crystal structure. A crystal is a solid where the atoms form a periodic arrangement.. Not all solids are crystals. For example, when liquid water starts freezing, the phase change begins with small ice crystals that grow until they fuse, forming a polycrystalline structure. In the final block of ice, each of the small crystals is a true crystal with a periodic arrangement of atoms, but the whole polycrystal does not have a periodic arrangement of atoms, because the periodic pattern is broken at the grain boundaries.
Most macroscopic inorganic solids are polycrystalline, including all metals, ice, etc. Solids that are neither crystalline nor polycrystalline, such as glass, are called amorphous solids called glassy, vitreous, or noncrystalline; these have no periodic order microscopically. There are distinct differences between crystalline solids and amorphous solids: most notably, the process of forming a glass does not release the latent heat of fusion, but forming a crystal does. A crystal structure is characterized by its unit cell, a small imaginary box containing one or more atoms in a specific spatial arrangement; the unit cells are stacked in three-dimensional space to form the crystal. The symmetry of a crystal is constrained by the requirement that the unit cells stack with no gaps. There are 219 possible crystal symmetries, called crystallographic space groups; these are grouped into 7 crystal systems, such as hexagonal crystal system. Crystals are recognized by their shape, consisting of flat faces with sharp angles.
These shape characteristics are not necessary for a crystal—a crystal is scientifically defined by its microscopic atomic arrangement, not its macroscopic shape—but the characteristic macroscopic shape is present and easy to see. Euhedral crystals are those with well-formed flat faces. Anhedral crystals do not because the crystal is one grain in a polycrystalline solid; the flat faces of a euhedral crystal are oriented in a specific way relative to the underlying atomic arrangement of the crystal: they are planes of low Miller index. This occurs; as a crystal grows, new atoms attach to the rougher and less stable parts of the surface, but less to the flat, stable surfaces. Therefore, the flat surfaces tend to grow larger and smoother, until the whole crystal surface consists of these plane surfaces. One of the oldest techniques in the science of crystallography consists of measuring the three-dimensional orientations of the faces of a crystal, using them to infer the underlying crystal symmetry.
A crystal's habit is its visible external shape. This is determined by the crystal structure, the specific crystal chemistry and bonding, the conditions under which the crystal formed. By volume and weight, the largest concentrations of crystals in the Earth are part of its solid bedrock. Crystals found in rocks range in size from a fraction of a millimetre to several centimetres across, although exceptionally large crystals are found; as of 1999, the world's largest known occurring crystal is a crystal of beryl from Malakialina, Madagascar, 18 m long and 3.5 m in diameter, weighing 380,000 kg. Some crystals have formed by magmatic and metamorphic processes, giving origin to large masses of crystalline rock; the vast majority of igneous rocks are formed from molten magma and the degree of crystallization depends on the conditions under which they solidified. Such rocks as granite, which have cooled slowly and under great pressures, have crystallized.