Allotropes of phosphorusElemental phosphorus can exist in several allotropes, the most common of which are white and red solids. Solid violet and black allotropes are also known. Gaseous phosphorus exists as diphosphorus and atomic phosphorus. White phosphorus, yellow phosphorus or simply tetraphosphorus () exists as molecules made up of four atoms in a tetrahedral structure. The tetrahedral arrangement results in ring strain and instability. The molecule is described as consisting of six single P–P bonds. Two crystalline forms are known.
Rare-earth elementThe rare-earth elements (REE), also called the rare-earth metals or rare earths or, in context, rare-earth oxides, and sometimes the lanthanides (although yttrium and scandium, which do not belong to this series, are usually included as rare earths), are a set of 17 nearly indistinguishable lustrous silvery-white soft heavy metals. Compounds containing rare earths have diverse applications in electrical and electronic components, lasers, glass, magnetic materials, and industrial processes.
Calcium oxideCalcium oxide (formula: CaO), commonly known as quicklime or burnt lime, is a widely used chemical compound. It is a white, caustic, alkaline, crystalline solid at room temperature. The broadly used term lime connotes calcium-containing inorganic compounds, in which carbonates, oxides, and hydroxides of calcium, silicon, magnesium, aluminium, and iron predominate. By contrast, quicklime specifically applies to the single compound calcium oxide. Calcium oxide that survives processing without reacting in building products, such as cement, is called free lime.
MarshA marsh is - according to ecological definitions - a wetland that is dominated by herbaceous rather than woody plant species. More in general, the word can be used for any low-lying and seasonally waterlogged terrain. In Europe and in agricultural literature low-lying meadows that require draining and embanked polderlands are also referred to as marshes or marshland. Marshes can often be found at the edges of lakes and streams, where they form a transition between the aquatic and terrestrial ecosystems.
ApatiteApatite is a group of phosphate minerals, usually hydroxyapatite, fluorapatite and chlorapatite, with high concentrations of OH−, F− and Cl− ion, respectively, in the crystal. The formula of the admixture of the three most common endmembers is written as Ca10(PO4)6(OH,F,Cl)2, and the crystal unit cell formulae of the individual minerals are written as Ca10(PO4)6(OH)2, Ca10(PO4)6F2 and Ca10(PO4)6Cl2.
Infinite productIn mathematics, for a sequence of complex numbers a1, a2, a3, ... the infinite product is defined to be the limit of the partial products a1a2...an as n increases without bound. The product is said to converge when the limit exists and is not zero. Otherwise the product is said to diverge. A limit of zero is treated specially in order to obtain results analogous to those for infinite sums. Some sources allow convergence to 0 if there are only a finite number of zero factors and the product of the non-zero factors is non-zero, but for simplicity we will not allow that here.
Wallis productIn mathematics, the Wallis product for pi, published in 1656 by John Wallis, states that Wallis derived this infinite product using interpolation, though his method is not regarded as rigorous. A modern derivation can be found by examining for even and odd values of , and noting that for large , increasing by 1 results in a change that becomes ever smaller as increases. Let (This is a form of Wallis' integrals.) Integrate by parts: Now, we make two variable substitutions for convenience to obtain: We obtain values for and for later use.
TailingsIn mining, tailings or tails are the materials left over after the process of separating the valuable fraction from the uneconomic fraction (gangue) of an ore. Tailings are different from overburden, which is the waste rock or other material that overlies an ore or mineral body and is displaced during mining without being processed. The extraction of minerals from ore can be done two ways: placer mining, which uses water and gravity to concentrate the valuable minerals, or hard rock mining, which pulverizes the rock containing the ore and then relies on chemical reactions to concentrate the sought-after material.
PhosphoritePhosphorite, phosphate rock or rock phosphate is a non-detrital sedimentary rock that contains high amounts of phosphate minerals. The phosphate content of phosphorite (or grade of phosphate rock) varies greatly, from 4% to 20% phosphorus pentoxide (P2O5). Marketed phosphate rock is enriched ("beneficiated") to at least 28%, often more than 30% P2O5. This occurs through washing, screening, de-liming, magnetic separation or flotation. By comparison, the average phosphorus content of sedimentary rocks is less than 0.
