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28-697: The main product of Peñoles is refined silver in the form of ingots and granulated silver which are 99.99% pure silver, this product is made in Torreón ( northern Mexico ) and from this location is exported all over the world. In 2012, the company was awarded with the Fray International Sustainability Award for its initiatives in sustainable development. They approach sustainability by achieving three dimensions: Economics, Ecology, and Ethics, and by consistently measuring and analyzing their environmental impact. Peñoles' history begins in 1887, with

56-431: A {\displaystyle a} is the magnitude of the noise and χ {\displaystyle \chi } is a random number distributed uniformly on [ − 0.5 , 0.5 ] {\displaystyle [-0.5,0.5]} . An application of dendritic growth in directional solidification is gas turbine engine blades which are used at high temperatures and must handle high stresses along

84-1006: A currency reserve, as with gold bars . Ingots are generally made of metal, either pure or alloy, heated past its melting point and cast into a bar or block using a mold chill method. A special case are polycrystalline or single crystal ingots made by pulling from a molten melt. Single crystal ingots (called boules ) of materials are grown (crystal growth) using methods such as the Czochralski process or Bridgeman technique . The boules may be either semiconductor (e.g. electronic chip wafers , photovoltaic cells ) or non-conducting inorganic compounds for industrial and jewelry use (e.g., synthetic ruby, sapphire). Single crystal ingots of metal are produced in similar fashion to that used to produce high purity semiconductor ingots, i.e. by vacuum induction refining. Single crystal ingots of engineering metals are of interest due to their very high strength due to lack of grain boundaries . The method of production

112-426: A larger contact area. Molds may be either solid "massive" design, sand cast (e.g. for pig iron), or water-cooled shells, depending upon heat transfer requirements. Ingot molds are tapered to prevent the formation of cracks due to uneven cooling. A crack or void formation occurs as the liquid to solid transition has an associated volume change for a constant mass of material. The formation of these ingot defects may render

140-464: A polished specimen. As dendrites develop further into the liquid metal, they get hotter because they continue to extract heat. If they get too hot, they will remelt. This remelting of the dendrites is called recalescence. Dendrites usually form under non-equilibrium conditions. The first computational model of dendritic solidification was published by Kobayashi, who used a phase-field model to solve two coupled partial differential equations describing

168-451: A rapid cooling cycle with a large undercooling will increase the number of nuclei and thus reduce the size of the resulting dendrites (and often lead to small grains). Smaller dendrites generally lead to higher ductility of the product. One application where dendritic growth and resulting material properties can be seen is the process of welding . The dendrites are also common in cast products, where they may become visible by etching of

196-407: A shape-preserving manner at constant velocity. Nucleation and growth determine the grain size in equiaxed solidification while the competition between adjacent dendrites decides the primary spacing in columnar growth. Generally, if the melt is cooled slowly, nucleation of new crystals will be less than at large undercooling . The dendritic growth will result in dendrites of a large size. Conversely,

224-584: Is a piece of relatively pure material, usually metal , that is cast into a shape suitable for further processing. In steelmaking , it is the first step among semi-finished casting products . Ingots usually require a second procedure of shaping, such as cold/hot working, cutting, or milling to produce a useful final product. Non-metallic and semiconductor materials prepared in bulk form may also be referred to as ingots, particularly when cast by mold based methods. Precious metal ingots can be used as currency (with or without being processed into other shapes), or as

252-525: Is an Allen-Cahn equation with an anisotropic gradient energy coefficient: where ϵ ¯ {\displaystyle {\bar {\epsilon }}} is an average value of ϵ {\displaystyle \epsilon } , θ {\displaystyle \theta } is the angle between the interface normal and the x-axis, and δ {\displaystyle \delta } and j {\displaystyle j} are constants representing

280-413: Is that the liquid (the molten material) be undercooled, aka supercooled , below the freezing point of the solid. Initially, a spherical solid nucleus grows in the undercooled melt. As the sphere grows, the spherical morphology becomes unstable and its shape becomes perturbed. The solid shape begins to express the preferred growth directions of the crystal. This growth direction may be due to anisotropy in

308-400: Is the dimensionless equilibrium temperature. The temperature has been non-dimensionalized such that the equilibrium temperature is T e = 1 {\displaystyle T_{e}=1} and the initial temperature of the undercooled melt is T = 0 {\displaystyle T=0} . The evolution equation for the temperature field is given by and is simply

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336-644: Is via single crystal dendrite and not via simple casting. Possible uses include turbine blades . In the United States, the brass and bronze ingot making industry started in the early 19th century. The US brass industry grew to be the number one producer by the 1850s. During colonial times the brass and bronze industries were almost non-existent because the British demanded all copper ore be sent to Britain for processing. Copper based alloy ingots weighed approximately 20 pounds (9.1 kg). Ingots are manufactured by

364-440: The heat equation with a source term due to the evolution of latent heat upon solidification, where K {\displaystyle K} is a constant representing the latent heat normalized by the strength of the cooling. When this system is numerically evolved, random noise representing thermal fluctuations is introduced to the interface via the a χ {\displaystyle a\chi } term, where

392-537: The United Kingdom, United States and Germany. During the decade of 1960 to 1970 the Mexican mining industry was "mexicanized" and therefore Mr. Raúl Bailleres acquired the majority of the company shares, after that the company received the name of Industrias Peñoles. Peñoles has three mining related divisions and a branch created for other business. They are located mainly in northern México. Ingot An ingot

420-426: The cast ingot useless and may need to be re-melted, recycled, or discarded. The physical structure of a crystalline material is largely determined by the method of cooling and precipitation of the molten metal. During the pouring process, metal in contact with the ingot walls rapidly cools and forms either a columnar structure or possibly a "chill zone" of equiaxed dendrites , depending upon the liquid being cooled and

448-461: The cooling of a molten liquid (known as the melt) in a mold. The manufacture of ingots has several aims. Firstly, the mold is designed to completely solidify and form an appropriate grain structure required for later processing, as the structure formed by the cooling of the melt controls the physical properties of the material. Secondly, the shape and size of the mold is designed to allow for ease of ingot handling and downstream processing. Finally,

476-429: The cooling rate of the mold. For a top-poured ingot, as the liquid cools within the mold, differential volume effects cause the top of the liquid to recede leaving a curved surface at the mold top which may eventually be required to be machined from the ingot. The mold cooling effect creates an advancing solidification front, which has several associated zones, closer to the wall there is a solid zone that draws heat from

504-403: The evolution of the phase-field, ϕ {\displaystyle \phi } (with ϕ = 0 {\displaystyle \phi =0} in the liquid phase and ϕ = 1 {\displaystyle \phi =1} in the solid phase), and the temperature field, T {\displaystyle T} , for a pure material in two dimensions: which

532-477: The highest surface energy. The dendrite thus exhibits a sharper and sharper tip as it grows. If the anisotropy is large enough, the dendrite may present a faceted morphology. The microstructural length scale is determined by the interplay or balance between the surface energy and the temperature gradient (which drives the heat/solute diffusion) in the liquid at the interface. As solidification proceeds, an increasing number of atoms lose their kinetic energy, making

560-456: The history of metallurgy . Dendrite (metal) A dendrite in metallurgy is a characteristic tree-like structure of crystals growing as molten metal solidifies, the shape produced by faster growth along energetically favourable crystallographic directions. This dendritic growth has large consequences in regard to material properties. Dendrites form in unary (one-component) systems as well as multi-component systems. The requirement

588-621: The liquid melt alloy compositions. Continuous casting methods for ingot processing also exist, whereby a stationary front of solidification is formed by the continual take-off of cooled solid material, and the addition of a molten liquid to the casting process. Approximately 70 percent of aluminium ingots in the U.S. are cast using the direct chill casting process, which reduces cracking. A total of 5 percent of ingots must be scrapped because of stress induced cracks and butt deformation. Plano-convex ingots are widely distributed archaeological artifacts which are studied to provide information on

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616-422: The major axes. At high temperatures, grain boundaries are weaker than grains. In order to minimize the effect on properties, grain boundaries are aligned parallel to the dendrites. The first alloy used in this application was a nickel-based alloy (MAR M-200) with 12.5% tungsten, which accumulated in the dendrites during solidification. This resulted in blades with high strength and creep resistance extending along

644-509: The mining concession of certain mines located within the Sierra de Peñoles in the state of Durango and the foundation of the Compañía Minera de Peñoles under the regime of President Porfirio Díaz . From 1890 to 1960 the company suffered several mergers, fusions and acquisitions with others mining companies. During this time the company was owned by different shareholders, among them some from

672-452: The mold is designed to minimize melt wastage and aid ejection of the ingot, as losing either melt or ingot increases manufacturing costs of finished products. A variety of designs exist for the mold, which may be selected to suit the physical properties of the liquid melt and the solidification process. Molds may exist in the top, horizontal or bottom-up pouring and may be fluted or flat walled. The fluted design increases heat transfer owing to

700-414: The process exothermic. For a pure material, latent heat is released at the solid–liquid interface so that the temperature remains constant until the melt has completely solidified. The growth rate of the resultant crystalline substance will depend on how fast this latent heat can be conducted away. A dendrite growing in an undercooled melt can be approximated as a parabolic needle-like crystal that grows in

728-411: The solidifying melt, for alloys there may exist a "mushy" zone, which is the result of solid-liquid equilibrium regions in the alloy's phase diagram , and a liquid region. The rate of front advancement controls the time that dendrites or nuclei have to form in the solidification region. The width of the mushy zone in an alloy may be controlled by tuning the heat transfer properties of the mold or adjusting

756-467: The strength and mode of anisotropy, respectively. The parameter m {\displaystyle m} describes the thermodynamic driving force for solidification, which Kobayashi defines for a supercooled melt as: where α {\displaystyle \alpha } is a constant between 0 and 1, γ {\displaystyle \gamma } is a positive constant, and T e {\displaystyle T_{e}}

784-401: The surface energy of the solid–liquid interface, or to the ease of attachment of atoms to the interface on different crystallographic planes, or both (for an example of the latter, see hopper crystal ). In metallic systems, interface attachment kinetics is usually negligible (for non-negligible cases, see dendrite (crystal) ). The solid then attempts to minimize the area of those surfaces with

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