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Glass Batch Calculation
Glass batch calculation or glass batching is used to determine the correct mix of raw materials (batch) for a glass melt. Principle The raw materials mixture for glass melting is termed "batch". The batch must be measured properly to achieve a given, desired glass formulation. This batch calculation is based on the common linear regression equation: N_B = (B^T\cdot B)^\cdot B^T \cdot N_G with NB and NG being the molarities 1-column matrices of the batch and glass components respectively, and B being the batching matrix. The symbol "T" stands for the matrix transpose operation, "−1" indicates matrix inversion, and the sign "·" means the scalar product. From the molarities matrices N, percentages by weight (wt%) can easily be derived using the appropriate molar masses. Example calculation An example batch calculation may be demonstrated here. The desired glass composition in wt% is: 67 SiO2, 12 Na2O, 10 CaO, 5 Al2O3, 1 K2O, 2 MgO, 3 B2O3, and as raw materials are used ...
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Glass
Glass is a non- crystalline, often transparent, amorphous solid that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by rapid cooling (quenching) of the molten form; some glasses such as volcanic glass are naturally occurring. The most familiar, and historically the oldest, types of manufactured glass are "silicate glasses" based on the chemical compound silica (silicon dioxide, or quartz), the primary constituent of sand. Soda–lime glass, containing around 70% silica, accounts for around 90% of manufactured glass. The term ''glass'', in popular usage, is often used to refer only to this type of material, although silica-free glasses often have desirable properties for applications in modern communications technology. Some objects, such as drinking glasses and eyeglasses, are so commonly made of silicate-based glass that they are simply called by the name of the material. De ...
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Limestone
Limestone ( calcium carbonate ) is a type of carbonate sedimentary rock which is the main source of the material lime. It is composed mostly of the minerals calcite and aragonite, which are different crystal forms of . Limestone forms when these minerals precipitate out of water containing dissolved calcium. This can take place through both biological and nonbiological processes, though biological processes, such as the accumulation of corals and shells in the sea, have likely been more important for the last 540 million years. Limestone often contains fossils which provide scientists with information on ancient environments and on the evolution of life. About 20% to 25% of sedimentary rock is carbonate rock, and most of this is limestone. The remaining carbonate rock is mostly dolomite, a closely related rock, which contains a high percentage of the mineral dolomite, . ''Magnesian limestone'' is an obsolete and poorly-defined term used variously for dolomite, for lim ...
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Optimization (mathematics)
Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems of sorts arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries. In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. The generalization of optimization theory and techniques to other formulations constitutes a large area of applied mathematics. More generally, optimization includes finding "best available" values of some objective function given a defi ...
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Linearly Dependent
In the theory of vector spaces, a set of vectors is said to be if there is a nontrivial linear combination of the vectors that equals the zero vector. If no such linear combination exists, then the vectors are said to be . These concepts are central to the definition of dimension. A vector space can be of finite dimension or infinite dimension depending on the maximum number of linearly independent vectors. The definition of linear dependence and the ability to determine whether a subset of vectors in a vector space is linearly dependent are central to determining the dimension of a vector space. Definition A sequence of vectors \mathbf_1, \mathbf_2, \dots, \mathbf_k from a vector space is said to be ''linearly dependent'', if there exist scalars a_1, a_2, \dots, a_k, not all zero, such that :a_1\mathbf_1 + a_2\mathbf_2 + \cdots + a_k\mathbf_k = \mathbf, where \mathbf denotes the zero vector. This implies that at least one of the scalars is nonzero, say a_1\ne 0, and ...
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Water
Water (chemical formula ) is an inorganic, transparent, tasteless, odorless, and nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living organisms (in which it acts as a solvent). It is vital for all known forms of life, despite not providing food, energy or organic micronutrients. Its chemical formula, H2O, indicates that each of its molecules contains one oxygen and two hydrogen atoms, connected by covalent bonds. The hydrogen atoms are attached to the oxygen atom at an angle of 104.45°. "Water" is also the name of the liquid state of H2O at standard temperature and pressure. A number of natural states of water exist. It forms precipitation in the form of rain and aerosols in the form of fog. Clouds consist of suspended droplets of water and ice, its solid state. When finely divided, crystalline ice may precipitate in the form of snow. The gaseous state of water is steam or water vap ...
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Carbon Dioxide
Carbon dioxide ( chemical formula ) is a chemical compound made up of molecules that each have one carbon atom covalently double bonded to two oxygen atoms. It is found in the gas state at room temperature. In the air, carbon dioxide is transparent to visible light but absorbs infrared radiation, acting as a greenhouse gas. It is a trace gas in Earth's atmosphere at 421  parts per million (ppm), or about 0.04% by volume (as of May 2022), having risen from pre-industrial levels of 280 ppm. Burning fossil fuels is the primary cause of these increased CO2 concentrations and also the primary cause of climate change.IPCC (2022Summary for policy makersiClimate Change 2022: Mitigation of Climate Change. Contribution of Working Group III to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change Cambridge University Press, Cambridge, United Kingdom and New York, NY, USA Carbon dioxide is soluble in water and is found in groundwater, lakes, ...
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Borax
Borax is a salt (ionic compound), a hydrated borate of sodium, with chemical formula often written . It is a colorless crystalline solid, that dissolves in water to make a basic solution. It is commonly available in powder or granular form, and has many industrial and household uses, including as a pesticide, as a metal soldering flux, as a component of glass, enamel, and pottery glazes, for tanning of skins and hides, for artificial aging of wood, as a preservative against wood fungus, and as a pharmaceutic alkalizer. In chemical laboratories, it is used as a buffering agent. The compound is often called sodium tetraborate decahydrate, but that name is not consistent with its structure. The anion is not tetraborate but tetrahydroxy tetraborate , so the more correct formula should be . Informally, the product is often called sodium borate decahydrate or just sodium borate. The terms tincal "tinkle" and tincar "tinker" refer to native borax, historically mined f ...
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Dolomite (mineral)
Dolomite () is an anhydrous carbonate mineral composed of calcium magnesium carbonate, ideally The term is also used for a sedimentary carbonate rock composed mostly of the mineral dolomite. An alternative name sometimes used for the dolomitic rock type is dolostone. History As stated by Nicolas-Théodore de Saussure the mineral dolomite was probably first described by Carl Linnaeus in 1768. In 1791, it was described as a rock by the French naturalist and geologist Déodat Gratet de Dolomieu (1750–1801), first in buildings of the old city of Rome, and later as samples collected in the mountains now known as the Dolomite Alps of northern Italy. Nicolas-Théodore de Saussure first named the mineral (after Dolomieu) in March 1792. Properties The mineral dolomite crystallizes in the trigonal-rhombohedral system. It forms white, tan, gray, or pink crystals. Dolomite is a double carbonate, having an alternating structural arrangement of calcium and magnesium ions. Unle ...
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Orthoclase
Orthoclase, or orthoclase feldspar ( endmember formula K Al Si3 O8), is an important tectosilicate mineral which forms igneous rock. The name is from the Ancient Greek for "straight fracture," because its two cleavage planes are at right angles to each other. It is a type of potassium feldspar, also known as K-feldspar. The gem known as moonstone (see below) is largely composed of orthoclase. Formation and subtypes Orthoclase is a common constituent of most granites and other felsic igneous rocks and often forms huge crystals and masses in pegmatite. Typically, the pure potassium endmember of orthoclase forms a solid solution with albite, the sodium endmember (NaAlSi3O8), of plagioclase. While slowly cooling within the earth, sodium-rich albite lamellae form by exsolution, enriching the remaining orthoclase with potassium. The resulting intergrowth of the two feldspars is called perthite. The higher-temperature polymorph of KAlSi3O8 is sanidine. Sanidine is common in ra ...
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Albite
Albite is a plagioclase feldspar mineral. It is the sodium endmember of the plagioclase solid solution series. It represents a plagioclase with less than 10% anorthite content. The pure albite endmember has the formula . It is a tectosilicate. Its color is usually pure white, hence its name from Latin, . It is a common constituent in felsic rocks. Properties Albite crystallizes with triclinic pinacoidal forms. Its specific gravity is about 2.62 and it has a Mohs hardness of 6–6.5. Albite almost always exhibits crystal twinning often as minute parallel striations on the crystal face. Albite often occurs as fine parallel segregations alternating with pink microcline in perthite as a result of exolution on cooling. There are two variants of albite, which are referred to as 'low albite' and 'high albite'; the latter is also known as 'analbite'. Although both variants are triclinic, they differ in the volume of their unit cell, which is slightly larger for the 'high' form. ...
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Trona
Trona (trisodium hydrogendicarbonate dihydrate, also sodium sesquicarbonate dihydrate, Na2CO3•2NaHCO3•3H2O) is a non- marine evaporite mineral. It is mined as the primary source of sodium carbonate in the United States, where it has replaced the Solvay process used in most of the rest of the world for sodium carbonate production. Etymology The word entered English by way of either Swedish () or Spanish (), with both possible sources having the same meaning as in English. Both of these derive from the Arabic ''trōn'', which in turn derives from the Arabic '' natron'', and Hebrew (''natruna''), which comes from ancient Greek (''nitron''), derived ultimately from ancient Egyptian ''ntry'' (or ''nitry'’). Natural deposits Trona is found at Owens Lake and Searles Lake, California; the Green River Formation of Wyoming and Utah; the Makgadikgadi Pans in Botswana and in the Nile Valley in Egypt. The trona near Green River, Wyoming, is the largest known deposit in t ...
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Borax
Borax is a salt (ionic compound), a hydrated borate of sodium, with chemical formula often written . It is a colorless crystalline solid, that dissolves in water to make a basic solution. It is commonly available in powder or granular form, and has many industrial and household uses, including as a pesticide, as a metal soldering flux, as a component of glass, enamel, and pottery glazes, for tanning of skins and hides, for artificial aging of wood, as a preservative against wood fungus, and as a pharmaceutic alkalizer. In chemical laboratories, it is used as a buffering agent. The compound is often called sodium tetraborate decahydrate, but that name is not consistent with its structure. The anion is not tetraborate but tetrahydroxy tetraborate , so the more correct formula should be . Informally, the product is often called sodium borate decahydrate or just sodium borate. The terms tincal "tinkle" and tincar "tinker" refer to native borax, historically mined f ...
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