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Lever Rule
In chemistry, the lever rule is a formula used to determine the mole fraction (''xi'') or the mass fraction (''wi'') of each phase of a binary equilibrium phase diagram. It can be used to determine the fraction of liquid and solid phases for a given binary composition and temperature that is between the liquidus and solidus line. In an alloy An alloy is a mixture of chemical elements of which at least one is a metal. Unlike chemical compounds with metallic bases, an alloy will retain all the properties of a metal in the resulting material, such as electrical conductivity, ductilit ... or a mixture with two phases, α and β, which themselves contain two elements, A and B, the lever rule states that the mass fraction of the α phase is :w^\alpha = \frac where * w_^\alpha is the mass fraction of element B in the α phase * w_^\beta is the mass fraction of element B in the β phase * w_ is the mass fraction of element B in the entire alloy or mixture all at some fixed t ...
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Chemistry
Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo during a Chemical reaction, reaction with other Chemical substance, substances. Chemistry also addresses the nature of chemical bonds in chemical compounds. In the scope of its subject, chemistry occupies an intermediate position between physics and biology. It is sometimes called the central science because it provides a foundation for understanding both Basic research, basic and Applied science, applied scientific disciplines at a fundamental level. For example, chemistry explains aspects of plant growth (botany), the formation of igneous rocks (geology), how atmospheric ozone is formed and how environmental pollutants are degraded (ecology), the properties ...
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Mixture
In chemistry, a mixture is a material made up of two or more different chemical substances which are not chemically bonded. A mixture is the physical combination of two or more substances in which the identities are retained and are mixed in the form of Solution (chemistry), solutions, Suspension (chemistry), suspensions and colloids. Mixtures are one product of mechanically blending or mixing chemical substances such as chemical element, elements and Compound (chemistry), compounds, without chemical bonding or other chemical change, so that each ingredient substance retains its own chemical properties and makeup. Despite the fact that there are no chemical changes to its constituents, the physical properties of a mixture, such as its melting point, may differ from those of the components. Some mixtures can be separation process, separated into their components by using physical (mechanical or thermal) means. Azeotropes are one kind of mixture that usually poses considerable diffi ...
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Phase Transitions
In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure. This can be a discontinuous change; for example, a liquid may become gas upon heating to its boiling point, resulting in an abrupt change in volume. The identification of the external conditions at which a transformation occurs defines the phase transition point. Types of phase transition At the phase transition point for a substance, for instance the boiling point, the two phases involved - liquid and vapor, have identic ...
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Metallurgy
Metallurgy is a domain of materials science and engineering that studies the physical and chemical behavior of metallic elements, their inter-metallic compounds, and their mixtures, which are known as alloys. Metallurgy encompasses both the science and the technology of metals; that is, the way in which science is applied to the production of metals, and the engineering of metal components used in products for both consumers and manufacturers. Metallurgy is distinct from the craft of metalworking. Metalworking relies on metallurgy in a similar manner to how medicine relies on medical science for technical advancement. A specialist practitioner of metallurgy is known as a metallurgist. The science of metallurgy is further subdivided into two broad categories: chemical metallurgy and physical metallurgy. Chemical metallurgy is chiefly concerned with the reduction and oxidation of metals, and the chemical performance of metals. Subjects of study in chemical metallurgy include mi ...
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Line Segment
In geometry, a line segment is a part of a straight line that is bounded by two distinct end points, and contains every point on the line that is between its endpoints. The length of a line segment is given by the Euclidean distance between its endpoints. A closed line segment includes both endpoints, while an open line segment excludes both endpoints; a half-open line segment includes exactly one of the endpoints. In geometry, a line segment is often denoted using a line above the symbols for the two endpoints (such as \overline). Examples of line segments include the sides of a triangle or square. More generally, when both of the segment's end points are vertices of a polygon or polyhedron, the line segment is either an edge (geometry), edge (of that polygon or polyhedron) if they are adjacent vertices, or a diagonal. When the end points both lie on a curve (such as a circle), a line segment is called a chord (geometry), chord (of that curve). In real or complex vector spa ...
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Lever Rule
In chemistry, the lever rule is a formula used to determine the mole fraction (''xi'') or the mass fraction (''wi'') of each phase of a binary equilibrium phase diagram. It can be used to determine the fraction of liquid and solid phases for a given binary composition and temperature that is between the liquidus and solidus line. In an alloy An alloy is a mixture of chemical elements of which at least one is a metal. Unlike chemical compounds with metallic bases, an alloy will retain all the properties of a metal in the resulting material, such as electrical conductivity, ductilit ... or a mixture with two phases, α and β, which themselves contain two elements, A and B, the lever rule states that the mass fraction of the α phase is :w^\alpha = \frac where * w_^\alpha is the mass fraction of element B in the α phase * w_^\beta is the mass fraction of element B in the β phase * w_ is the mass fraction of element B in the entire alloy or mixture all at some fixed t ...
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Chemical Element
A chemical element is a species of atoms that have a given number of protons in their nuclei, including the pure substance consisting only of that species. Unlike chemical compounds, chemical elements cannot be broken down into simpler substances by any chemical reaction. The number of protons in the nucleus is the defining property of an element, and is referred to as its atomic number (represented by the symbol ''Z'') – all atoms with the same atomic number are atoms of the same element. Almost all of the baryonic matter of the universe is composed of chemical elements (among rare exceptions are neutron stars). When different elements undergo chemical reactions, atoms are rearranged into new compounds held together by chemical bonds. Only a minority of elements, such as silver and gold, are found uncombined as relatively pure native element minerals. Nearly all other naturally occurring elements occur in the Earth as compounds or mixtures. Air is primarily a mixture o ...
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Alloy
An alloy is a mixture of chemical elements of which at least one is a metal. Unlike chemical compounds with metallic bases, an alloy will retain all the properties of a metal in the resulting material, such as electrical conductivity, ductility, opacity (optics), opacity, and lustre (mineralogy), luster, but may have properties that differ from those of the pure metals, such as increased strength or hardness. In some cases, an alloy may reduce the overall cost of the material while preserving important properties. In other cases, the mixture imparts synergistic properties to the constituent metal elements such as corrosion resistance or mechanical strength. Alloys are defined by a metallic bonding character. The alloy constituents are usually measured by mass percentage for practical applications, and in Atomic ratio, atomic fraction for basic science studies. Alloys are usually classified as substitutional or interstitial alloys, depending on the atomic arrangement that forms the ...
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Mole Fraction
In chemistry, the mole fraction or molar fraction (''xi'' or ) is defined as unit of the amount of a constituent (expressed in moles), ''ni'', divided by the total amount of all constituents in a mixture (also expressed in moles), ''n''tot. This expression is given below: :x_i = \frac The sum of all the mole fractions is equal to 1: :\sum_^ n_i = n_\mathrm ; \ \sum_^ x_i = 1. The same concept expressed with a denominator of 100 is the mole percent, molar percentage or molar proportion (mol%). The mole fraction is also called the amount fraction. It is identical to the number fraction, which is defined as the number of molecules of a constituent ''Ni'' divided by the total number of all molecules ''N''tot. The mole fraction is sometimes denoted by the lowercase Greek letter (chi) instead of a Roman ''x''. For mixtures of gases, IUPAC recommends the letter ''y''. The National Institute of Standards and Technology of the United States prefers the term amount-of-substance fraction o ...
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Solidus (chemistry)
In chemistry, materials science, and physics, the solidus is the locus of temperatures (a curve on a phase diagram) below which a given substance is completely solid (crystallized). The solidus temperature, TS or Tsol, specifies the temperature below which a material is completely solid, and the minimum temperature at which a melt can co-exist with crystals in thermodynamic equilibrium. The solidus is applied, among other materials, to metal alloys, ceramics, and natural rocks and minerals. The solidus quantifies the temperature at which melting of a substance ''begins'', but the substance is not necessarily melted ''completely'', i.e., the solidus is not necessarily a melting point. For this distinction, the solidus may be contrasted to the liquidus. The solidus is always less than or equal to the liquidus, but they need not coincide. If a gap exists between the solidus and liquidus it is called the freezing range, and within that gap, the substance consists of a mixture of so ...
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