Nucleation is the first step in the formation of either a new thermodynamic phase or a new structure via self-assembly or self-organization. Nucleation is defined to be the process that determines how long an observer has to wait before the new phase or self-organized structure appears. For example, if a volume of water is cooled below 0° C, it will tend to freeze into ice. Volumes of water cooled only a few degrees below 0° C stay free of ice for long periods. At these conditions, nucleation of ice does not occur at all. However, at lower temperatures ice crystals appear after no delay. At these conditions ice nucleation is fast. Nucleation is how first-order phase transitions start, it is the start of the process of forming a new thermodynamic phase. By contrast, new phases at continuous phase transitions start to form immediately. Nucleation is found to be sensitive to impurities in the system; these impurities may be too small to be seen by the naked eye, but still can control the rate of nucleation.
Because of this, it is important to distinguish between heterogeneous nucleation and homogeneous nucleation. Heterogeneous nucleation occurs at nucleation sites on surfaces in the system. Homogeneous nucleation occurs away from a surface. Nucleation is a stochastic process, so in two identical systems nucleation will occur at different times; this behaviour is similar to radioactive decay. A common mechanism is illustrated in the animation to the right; this shows nucleation of a new phase in an existing phase. In the existing phase microscopic fluctuations of the red phase appear and decay continuously, until an unusually large fluctuation of the new red phase is so large it is more favourable for it to grow than to shrink back to nothing; this nucleus of the red phase grows and converts the system to this phase. The standard theory that describes this behaviour for the nucleation of a new thermodynamic phase is called classical nucleation theory. However, the CNT fails in describing experimental results of vapour to liquid nucleation for model substances like Argon by several orders of magnitude.
For nucleation of a new thermodynamic phase, such as the formation of ice in water below 0° C, if the system is not evolving with time and nucleation occurs in one step the probability that nucleation has not occurred should undergo exponential decay as seen in radioactive decay. This is seen for example in the nucleation of ice in supercooled small water droplets; the decay rate of the exponential gives the nucleation rate. Classical nucleation theory is a used approximate theory for estimating these rates, how they vary with variables such as temperature, it predicts that the time you have to wait for nucleation decreases rapidly when supersaturated. It is not just new phases such as crystals that form via nucleation followed by growth; the self-assembly process that forms objects like the amyloid aggregates associated with Alzheimer's disease starts with nucleation. Energy consuming self-organising systems such as the microtubules in cells show nucleation and growth. Heterogeneous nucleation, nucleation with the nucleus at a surface, is much more common than homogeneous nucleation.
For example, in the nucleation of ice from supercooled water droplets, purifying the water to remove all or all impurities results in water droplets that freeze below around - 35 C, whereas water that contains impurities may freeze at - 5 C or warmer. Thus here, we have direct evidence that nucleation of ice on impurities can occur at much higher temperatures than without impurities; this observation that heterogeneous nucleation can occur when the rate of homogeneous nucleation is zero, is understood using classical nucleation theory. This predicts that the nucleation slows exponentially with the height of a free energy barrier ΔG*; this barrier comes from the free energy penalty of forming the surface of the growing nucleus. For homogeneous nucleation the nucleus is approximated by a sphere, but as we can see in the schematic of macroscopic droplets to the right, droplets on surfaces are not complete spheres and so the area of the interface between the droplet and the surrounding fluid is less than a sphere's 4 π r 2.
This reduction in surface area of the nucleus reduces the height of the barrier to nucleation and so speeds nucleation up exponentially. Nucleation can start at the surface of a liquid. For example, computer simulations of gold nanoparticles show that the crystal phase nucleates at the liquid-gold surface. Classical nucleation theory makes a number of assumptions, for example it treats a microscopic nucleus as if it is a macroscopic droplet with a well-defined surface whose free energy is estimated using an equilibrium property: the interfacial tension σ. For a nucleus that may be only of order ten molecules across it is not always clear that we can treat something so small as a volume plus a surface. Nucleation is an inherently out of thermodynamic equilibrium phenomenon so it is not always obvious that its rate can be estimated using equilibrium properties. However, modern computers are powerful enough to calculate exact nucleation rates for simple models; these have been compared with the classical theory, for example for the case of nucleation of the crystal phase in the model of hard spheres.
This is a model of hard spheres in thermal motion, is a simple model of some colloids. For the crystallization of hard spheres the classical theory is a reasonable approximate theory. So for the simple models w
A crystal dendrite is a crystal that develops with a typical multi-branching tree-like form. Dendritic crystal growth is common and illustrated by snowflake formation and frost patterns on a window. Dendritic crystallization forms a natural fractal pattern. Dendritic crystals can grow into a supercooled pure liquid or form from growth instabilities that occur when the growth rate is limited by the rate of diffusion of solute atoms to the interface. In the latter case, there must be a concentration gradient from the supersaturated value in the solution to the concentration in equilibrium with the crystal at the surface. Any protuberance that develops is accompanied by a steeper concentration gradients at its tip; this increases the diffusion rate to the tip. In opposition to this is the action of the surface tension tending to flatten the protuberance and setting up a flux of solute atoms from the protuberance out to the sides. However, the protuberance becomes amplified; this process occurs again until a dendrite is produced.
The term "dendrite" comes from the Greek word dendron, which means "tree". In paleontology, dendritic mineral crystal forms are mistaken for fossils; these pseudofossils form as occurring fissures in the rock are filled by percolating mineral solutions. They form when water rich in manganese and iron flows along fractures and bedding planes between layers of limestone and other rock types, depositing dendritic crystals as the solution flows through. A variety of manganese oxides and hydroxides are involved, including: birnessite coronadite cryptomelane hollandite romanechite todorokite and others. A three-dimensional form of dendrite develops in fissures in quartz. In chemistry, a dendrite is a crystal; the Isothermal Dendritic Growth Experiment is a materials science solidification experiment that researchers use on Space Shuttle missions to investigate dendritic growth in an environment where the effect of gravity can be excluded. Dendritic solidification is one of the most common forms of solidifying alloys.
When materials crystallize or solidify under certain conditions, they freeze unstably, resulting in dendritic forms. Scientists are interested in dendrite size and how the branches of the dendrites interact with each other; these characteristics determine the properties of the material. Monocrystalline whisker Whisker Brownian tree Patterns in nature STS-87 - Space Shuttle mission Mindat Manganese Dendrites What is a dendrite? http://minerals.gps.caltech.edu/FILES/DENDRITE/Index.html The Isothermal Dendritic Growth Experiment Snow crystals Dendritic Solidification Dendritic growth in Local-Nonequilibrium Solidification Model
Zone melting is a group of similar methods of purifying crystals, in which a narrow region of a crystal is melted, this molten zone is moved along the crystal. The molten region melts impure solid at its forward edge and leaves a wake of purer material solidified behind it as it moves through the ingot; the impurities concentrate in the melt, are moved to one end of the ingot. Zone refining was invented by John Desmond Bernal and further developed by William Gardner Pfann in Bell Labs as a method to prepare high purity materials semiconductors, for manufacturing transistors, its early use was on germanium for this purpose, but it can be extended to any solute-solvent system having an appreciable concentration difference between solid and liquid phases at equilibrium. This process is known as the float zone process in semiconductor materials processing; the principle is that the segregation coefficient k is less than one. Therefore, at the solid/liquid boundary, the impurity atoms will diffuse to the liquid region.
Thus, by passing a crystal boule through a thin section of furnace slowly, such that only a small region of the boule is molten at any time, the impurities will be segregated at the end of the crystal. Because of the lack of impurities in the leftover regions which solidify, the boule can grow as a perfect single crystal if a seed crystal is placed at the base to initiate a chosen direction of crystal growth; when high purity is required, such as in semiconductor industry, the impure end of the boule is cut off, the refining is repeated. In zone refining, solutes are segregated at one end of the ingot in order to purify the remainder, or to concentrate the impurities. In zone leveling, the objective is to distribute solute evenly throughout the purified material, which may be sought in the form of a single crystal. For example, in the preparation of a transistor or diode semiconductor, an ingot of germanium is first purified by zone refining. A small amount of antimony is placed in the molten zone, passed through the pure germanium.
With the proper choice of rate of heating and other variables, the antimony can be spread evenly through the germanium. This technique is used for the preparation of silicon for use in computer chips. A variety of heaters can be used for zone melting, with their most important characteristic being the ability to form short molten zones that move and uniformly through the ingot. Induction coils, ring-wound resistance heaters, or gas flames are common methods. Another method is to pass an electric current directly through the ingot while it is in a magnetic field, with the resulting magnetomotive force set to be just equal to the weight in order to hold the liquid suspended. Optical heaters using high powered halogen or xenon lamps are used extensively in research facilities for the production of insulators, but their use in industry is limited by the low power of the lamps, which limits the size of crystals produced by this method. Zone melting can be done as a batch process, or it can be done continuously, with fresh impure material being continually added at one end and purer material being removed from the other, with impure zone melt being removed at whatever rate is dictated by the impurity of the feed stock.
Indirect-heating floating zone methods use an induction-heated tungsten ring to heat the ingot radiatively, are useful when the ingot is of a high-resistivity semiconductor on which classical induction heating is ineffective. When the liquid zone moves by a distance d x, the number of impurities in the liquid change. Impurities are incorporated in freezing solid. K O: Segregation coefficient L: Zone length C O: Initial uniform impurity concentration of the rod C L: Concentration of impurities in the liquid I: Number of impurities in the liquid I O: Number of impurities in zone when first formed at bottomThe number of impurities in the liquid changes in accordance with the expression below during the movement d x of the molten zone d I = d x C L = I / L ∫ 0 x d x = ∫ I O I d I C O − k O I L I O = C O L C S = k O I / L C S = C O ( 1 − e − k O x
The Kyropoulos process is a method of bulk crystal growth used to obtain single crystals. The process is named for Spyro Kyropoulos, who proposed the technique in 1926 as a method to grow brittle alkali halide and alkali earth metal crystals for precision optics; the largest application of the Kyropoulos process is to grow large boules of single crystal sapphire used to produce substrates for the manufacture gallium nitride-based LEDs, as a durable optical material. The Kyropoulos process for sapphire crystal growth was developed in the 1970s in the Soviet Union, it is used by several companies around the world to produce sapphire for the electronics and optics industries. High-purity, aluminum oxide is melted in a crucible at over 2100 °C; the crucible is made of tungsten or molybdenum. A oriented seed crystal is dipped into the molten alumina; the seed crystal is pulled upwards and may be rotated simultaneously. By controlling the temperature gradients, rate of pulling and rate of temperature decrease, it is possible to produce a large, single-crystal cylindrical ingot from the melt.
In contrast with the Czochralski process, the Kyropoulos process crystallizes the entire feedstock volume into the boule. The size and aspect ratio of the crucible is close to that of the final crystal, the crystal grows downward into the crucible, rather than being pulled up and out of the crucible as in the Czochralski method; the upward pulling of the seed is at a much slower rate than the downward growth of the crystal, serves to shape the meniscus of the solid-liquid interface via surface tension. The growth rate is controlled by decreasing the temperature of the furnace until the entire melt has solidified. Hanging the seed from a weight sensor can provide feedback to determine the growth rate, although precise measurements are complicated by the changing and imperfect shape of the crystal diameter, the unknown convex shape of the solid-liquid interface, these features' interaction with buoyant forces and convection within the melt; the Kyropoulos method is characterized by smaller temperature gradients at the crystallization front than the Czochralski method.
Like the Czochralski method, the crystal grows free of any external mechanical shaping forces, thus has few lattice defects and low internal stress. This process can be performed under high vacuum; the sizes of sapphire crystals grown by the Kyropoulos process have increased since the 1980s. In the mid-2000s sapphire crystals up to 30 kg were developed which could yield 150 mm diameter substrates. By 2017, the largest reported sapphire grown by the Kyropoulos method was 350 kg, could produce 300 mm diameter substrates; because of sapphire's anisotropic crystal structure, the orientation of the cylindrical axis of the boules grown by the Kyropoulos process is perpendicular to the orientation required for deposition of GaN on the LED substrates. This means that cores must be drilled through the sides of the boule before being sliced into wafers; this means the as-grown boules have a larger diameter than the resulting wafers. As of 2017 the leading manufacturers of blue and white LEDs use 150 mm diameter sapphire substrates, with some manufacturers still using 100 mm, 2 inch substrates.
Czochralski process Monocrystalline silicon Bridgman–Stockbarger technique Float-zone silicon Laser-heated pedestal growth Micro-pulling-down Verneuil process Kyropoulos Process on YouTube Crystal growth technique summaries
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.
Crystallization is the process by which a solid forms, where the atoms or molecules are organized into a structure known as a crystal. Some of the ways by which crystals form are precipitating from a solution, freezing, or more deposition directly from a gas. Attributes of the resulting crystal depend on factors such as temperature, air pressure, in the case of liquid crystals, time of fluid evaporation. Crystallization occurs in two major steps; the first is nucleation, the appearance of a crystalline phase from either a supercooled liquid or a supersaturated solvent. The second step is known as crystal growth, the increase in the size of particles and leads to a crystal state. An important feature of this step is that loose particles form layers at the crystal's surface lodge themselves into open inconsistencies such as pores, etc; the majority of minerals and organic molecules crystallize and the resulting crystals are of good quality, i.e. without visible defects. However, larger biochemical particles, like proteins, are difficult to crystallize.
The ease with which molecules will crystallize depends on the intensity of either atomic forces, intermolecular forces or intramolecular forces. Crystallization is a chemical solid–liquid separation technique, in which mass transfer of a solute from the liquid solution to a pure solid crystalline phase occurs. In chemical engineering, crystallization occurs in a crystallizer. Crystallization is therefore related to precipitation, although the result is not amorphous or disordered, but a crystal; the crystallization process consists of two major events and crystal growth which are driven by thermodynamic properties as well as chemical properties. In crystallization Nucleation is the step where the solute molecules or atoms dispersed in the solvent start to gather into clusters, on the microscopic scale, that become stable under the current operating conditions; these stable clusters constitute the nuclei. Therefore, the clusters need to reach a critical size; such critical size is dictated by many different factors.
It is at the stage of nucleation that the atoms or molecules arrange in a defined and periodic manner that defines the crystal structure — note that "crystal structure" is a special term that refers to the relative arrangement of the atoms or molecules, not the macroscopic properties of the crystal, although those are a result of the internal crystal structure. The crystal growth is the subsequent size increase of the nuclei that succeed in achieving the critical cluster size. Crystal growth is a dynamic process occurring in equilibrium where solute molecules or atoms precipitate out of solution, dissolve back into solution. Supersaturation is one of the driving forces of crystallization, as the solubility of a species is an equilibrium process quantified by Ksp. Depending upon the conditions, either nucleation or growth may be predominant over the other, dictating crystal size. Many compounds have the ability to crystallize with some having different crystal structures, a phenomenon called polymorphism.
Each polymorph is in fact a different thermodynamic solid state and crystal polymorphs of the same compound exhibit different physical properties, such as dissolution rate, melting point, etc. For this reason, polymorphism is of major importance in industrial manufacture of crystalline products. Additionally, crystal phases can sometimes be interconverted by varying factors such as temperature. There are many examples of natural process. Geological time scale process examples include: Natural crystal formation. Human time scale process examples include: Snow flakes formation. Crystal formation can be divided into two types, where the first type of crystals are composed of a cation and anion known as a salt, such as sodium acetate; the second type of crystals are composed for example menthol. Crystal formation can be achieved by various methods, such as: cooling, addition of a second solvent to reduce the solubility of the solute, solvent layering, changing the cation or anion, as well as other methods.
The formation of a supersaturated solution does not guarantee crystal formation, a seed crystal or scratching the glass is required to form nucleation sites. A typical laboratory technique for crystal formation is to dissolve the solid in a solution in which it is soluble at high temperatures to obtain supersaturation; the hot mixture is filtered to remove any insoluble impurities. The filtrate is allowed to cool. Crystals that form are filtered and washed with a solvent in which they are not soluble, but is miscible with the mother liquor; the process is repeated to increase the purity in a technique known as recrystallization. For biological molecules in which the solvent channels continue to be present to retain the three dimensional structure intact, microbatch crystallization under oil and vapor diffusion methods have been the common methods. Equipment for the main industrial processes for crystallization. Tank crystallizers. Tank crystallization is an old method still used in some specialized cases.
Saturated solutions, in tank crystallization, are allowed to cool in open tanks. After a period of time the mother liquo
Citric acid is a weak organic acid that has the chemical formula C6H8O7. It occurs in citrus fruits. In biochemistry, it is an intermediate in the citric acid cycle, which occurs in the metabolism of all aerobic organisms. More than a million tons of citric acid are manufactured every year, it is used as an acidifier, as a flavoring and chelating agent. A citrate is a derivative of citric acid. An example of the former, a salt is trisodium citrate; when part of a salt, the formula of the citrate ion is written as C6H5O3−7 or C3H5O3−3. Citric acid exists in greater than trace amounts in a variety of fruits and vegetables, most notably citrus fruits. Lemons and limes have high concentrations of the acid; the concentrations of citric acid in citrus fruits range from 0.005 mol/L for oranges and grapefruits to 0.30 mol/L in lemons and limes. Within species, these values vary depending on the cultivar and the circumstances in which the fruit was grown. Industrial-scale citric acid production first began in 1890 based on the Italian citrus fruit industry, where the juice was treated with hydrated lime to precipitate calcium citrate, isolated and converted back to the acid using diluted sulfuric acid.
In 1893, C. Wehmer discovered. However, microbial production of citric acid did not become industrially important until World War I disrupted Italian citrus exports. In 1917, American food chemist James Currie discovered certain strains of the mold Aspergillus niger could be efficient citric acid producers, the pharmaceutical company Pfizer began industrial-level production using this technique two years followed by Citrique Belge in 1929. In this production technique, still the major industrial route to citric acid used today, cultures of A. niger are fed on a sucrose or glucose-containing medium to produce citric acid. The source of sugar is corn steep liquor, hydrolyzed corn starch or other inexpensive sugary solutions. After the mold is filtered out of the resulting solution, citric acid is isolated by precipitating it with calcium hydroxide to yield calcium citrate salt, from which citric acid is regenerated by treatment with sulfuric acid, as in the direct extraction from citrus fruit juice.
In 1977, a patent was granted to Lever Brothers for the chemical synthesis of citric acid starting either from aconitic or isocitrate/alloisocitrate calcium salts under high pressure conditions. This produced citric acid in near quantitative conversion under what appeared to be a reverse non-enzymatic Krebs cycle reaction. In 2007, worldwide annual production stood at 1,600,000 tons. More than 50% of this volume was produced in China. More than 50% was used as an acidity regulator in beverages, some 20% in other food applications, 20% for detergent applications and 10% for related applications other than food, such as cosmetics, pharmaceutics and in the chemical industry. Citric acid was first isolated in 1784 by the chemist Carl Wilhelm Scheele, who crystallized it from lemon juice, it can exist either as a monohydrate. The anhydrous form crystallizes from hot water, while the monohydrate forms when citric acid is crystallized from cold water; the monohydrate can be converted to the anhydrous form at about 78 °C.
Citric acid dissolves in absolute ethanol at 15 °C. It decomposes with loss of carbon dioxide above about 175 °C. Citric acid is considered to be a tribasic acid, with pKa values, extrapolated to zero ionic strength, of 5.21, 4.28 and 2.92 at 25 °C. The pKa of the hydroxyl group has been found, by means of 13C NMR spectroscopy, to be 14.4. The speciation diagram shows that solutions of citric acid are buffer solutions between about pH 2 and pH 8. In biological systems around pH 7, the two species present are the citrate ion and mono-hydrogen citrate ion; the SSC 20X hybridization buffer is an example in common use. Tables compiled for biochemical studies are available. On the other hand, the pH of a 1 mM solution of citric acid will be about 3.2. The pH of fruit juices from citrus fruits like oranges and lemons depends on the citric acid concentration, being lower for higher acid concentration and conversely. Acid salts of citric acid can be prepared by careful adjustment of the pH before crystallizing the compound.
See, for example, sodium citrate. The citrate ion forms complexes with metallic cations; the stability constants for the formation of these complexes are quite large because of the chelate effect. It forms complexes with alkali metal cations. However, when a chelate complex is formed using all three carboxylate groups, the chelate rings have 7 and 8 members, which are less stable thermodynamically than smaller chelate rings. In consequence, the hydroxyl group can be deprotonated, forming part of a more stable 5-membered ring, as in ammonium ferric citrate, 5Fe2·2H2O. Citric acid can be esterified at one or more of the carboxylic acid functional groups on the molecule, to form any of a variety of mono-, di-, tri-, mixed esters. Citrate is an intermediate in the TCA cycle, a central metabolic pathway for animals and bacteria. Citrate synthase catalyzes the condensation of oxaloacetate with acetyl CoA to form citrate. Citrate acts as the substrate for aconitase and is converted into aconitic acid.
The cycle ends with regeneration of oxaloacetate. This series