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Vegard's Law
In crystallography, materials science and metallurgy, Vegard's law is an empirical finding (heuristic approach) resembling the rule of mixtures. In 1921, Lars Vegard discovered that the lattice parameter of a solid solution of two constituents is approximately a weighted mean of the two constituents' lattice parameters at the same temperature: :a_ = (1-x)\ a_\mathrm + x\ a_\mathrm e.g., in the case of a mixed oxide of uranium and plutonium as used in the fabrication of MOX nuclear fuel: :a_\mathrm = 0.93\ a_\mathrm + 0.07\ a_\mathrm Vegard's law assumes that both components A and B in their pure form (i.e. before mixing) have the same crystal structure. Here, is the lattice parameter of the solid solution, and are the lattice parameters of the pure constituents, and is the molar fraction of B in the solid solution. Vegard's law is seldom perfectly obeyed; often deviations from the linear behavior are observed. A detailed study of such deviations was conducted by King. Howe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystallography
Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The word "crystallography" is derived from the Greek word κρύσταλλος (''krystallos'') "clear ice, rock-crystal", with its meaning extending to all solids with some degree of transparency, and γράφειν (''graphein'') "to write". In July 2012, the United Nations recognised the importance of the science of crystallography by proclaiming that 2014 would be the International Year of Crystallography. denote a direction vector (in real space). * Coordinates in ''angle brackets'' or ''chevrons'' such as <100> denote a ''family'' of directions which are related by symmetry operations. In the cubic crystal system for example, would mean 00 10 01/nowiki> or the negative of any of those directions. * Miller indices in ''parentheses'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semiconductor
A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glass. Its electrical resistivity and conductivity, resistivity falls as its temperature rises; metals behave in the opposite way. Its conducting properties may be altered in useful ways by introducing impurities ("doping (semiconductor), doping") into the crystal structure. When two differently doped regions exist in the same crystal, a semiconductor junction is created. The behavior of charge carriers, which include electrons, ions, and electron holes, at these junctions is the basis of diodes, transistors, and most modern electronics. Some examples of semiconductors are silicon, germanium, gallium arsenide, and elements near the so-called "metalloid staircase" on the periodic table. After silicon, gallium arsenide is the second-most common s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kopp's Law
Kopp's law can refer to either of two relationships discovered by the German chemist Hermann Franz Moritz Kopp (1817–1892). #Kopp found "that the molecular heat capacity of a solid compound is the sum of the atomic heat capacities of the elements composing it; the elements having atomic heat capacities lower than those required by the Dulong–Petit law retain these lower values in their compounds." #In studying organic compounds, Kopp found a regular relationship between boiling points and the number of CH2 groups present.See page 942 of Kopp–Neumann law The Kopp–Neumann law, named for Kopp and Franz Ernst Neumann, is a common approach for determining the specific heat ''C'' (in J·kg−1·K−1) of compounds using the following equation: C = \sum_^N C_i f_i, where ''N'' is the total number of compound constituents, and ''Ci'' and ''fi'' denote the specific heat and mass fraction of the ''i''-th constituent. This law works surprisingly well at room-temperature conditi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermal Expansion
Thermal expansion is the tendency of matter to change its shape, area, volume, and density in response to a change in temperature, usually not including phase transitions. Temperature is a monotonic function of the average molecular kinetic energy of a substance. When a substance is heated, molecules begin to vibrate and move more, usually creating more distance between themselves. Substances which contract with increasing temperature are unusual, and only occur within limited temperature ranges (see examples below). The relative expansion (also called strain) divided by the change in temperature is called the material's coefficient of linear thermal expansion and generally varies with temperature. As energy in particles increases, they start moving faster and faster weakening the intermolecular forces between them, therefore expanding the substance. Overview Predicting expansion If an equation of state is available, it can be used to predict the values of the thermal expan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volume Fraction
In chemistry and fluid mechanics, the volume fraction φ''i'' is defined as the volume of a constituent ''V''''i'' divided by the volume of all constituents of the mixture ''V'' prior to mixing: :\phi_i = \frac Being dimensionless, its unit is 1; it is expressed as a number, e.g., 0.18. It is the same concept as volume percent (vol%) except that the latter is expressed with a denominator of 100, e.g., 18%. The volume fraction coincides with the volume concentration in ideal solutions where the volumes of the constituents are additive (the volume of the solution is equal to the sum of the volumes of its ingredients). The sum of all volume fractions of a mixture is equal to 1: :\sum_^ V_i = V ; \qquad \sum_^ \phi_i = 1 The volume fraction (percentage by volume, vol%) is one way of expressing the composition of a mixture with a dimensionless quantity; mass fraction (percentage by weight, wt%) and mole fraction (percentage by moles, mol%) are others. Volume concentration and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molar Volume
In chemistry and related fields, the molar volume, symbol ''V''m, or \tilde V of a substance is the ratio of the volume occupied by a substance to the amount of substance, usually given at a given temperature and pressure. It is equal to the molar mass (''M'') divided by the mass density (''ρ''): V_ = \frac . The molar volume has the SI unit of cubic metres per mole (m3/mol), although it is more typical to use the units cubic decimetres per mole (dm3/mol) for gases, and cubic centimetres per mole (cm3/mol) for liquids and solids. Definition The molar volume of a substance ''i'' is defined as its molar mass divided by its density ''ρ''''i''0: V_ = . For an ideal mixture containing ''N'' components, the molar volume of the mixture is the weighted sum of the molar volumes of its individual components. For a real mixture the molar volume cannot be calculated without knowing the density: V_ = \frac. There are many liquid–liquid mixtures, for instance mixing pure ethanol and pure w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isotropic
Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe situations where properties vary systematically, dependent on direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. Mathematics Within mathematics, ''isotropy'' has a few different meanings: ; Isotropic manifolds: A manifold is isotropic if the geometry on the manifold is the same regardless of direction. A similar concept is homogeneity. ; Isotropic quadratic form: A quadratic form ''q'' is said to be isotropic if there is a non-zero vector ''v'' such that ; such a ''v'' is an isotropic vector or null vector. In complex geometry, a line through the origin in the direction of an isotropic vector is a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Refractive Index
In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or refracted, when entering a material. This is described by Snell's law of refraction, , where ''θ''1 and ''θ''2 are the angle of incidence and angle of refraction, respectively, of a ray crossing the interface between two media with refractive indices ''n''1 and ''n''2. The refractive indices also determine the amount of light that is reflected when reaching the interface, as well as the critical angle for total internal reflection, their intensity ( Fresnel's equations) and Brewster's angle. The refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is , and similarly the wavelength in that medium is , where '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compressibility
In thermodynamics and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal compressibility) is a measure of the instantaneous relative volume change of a fluid or solid as a response to a pressure (or mean stress) change. In its simple form, the compressibility \kappa (denoted in some fields) may be expressed as :\beta =-\frac\frac, where is volume and is pressure. The choice to define compressibility as the negative of the fraction makes compressibility positive in the (usual) case that an increase in pressure induces a reduction in volume. The reciprocal of compressibility at fixed temperature is called the isothermal bulk modulus. Definition The specification above is incomplete, because for any object or system the magnitude of the compressibility depends strongly on whether the process is isentropic or isothermal. Accordingly, isothermal compressibility is defined: :\beta_T=-\frac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermal Expansion
Thermal expansion is the tendency of matter to change its shape, area, volume, and density in response to a change in temperature, usually not including phase transitions. Temperature is a monotonic function of the average molecular kinetic energy of a substance. When a substance is heated, molecules begin to vibrate and move more, usually creating more distance between themselves. Substances which contract with increasing temperature are unusual, and only occur within limited temperature ranges (see examples below). The relative expansion (also called strain) divided by the change in temperature is called the material's coefficient of linear thermal expansion and generally varies with temperature. As energy in particles increases, they start moving faster and faster weakening the intermolecular forces between them, therefore expanding the substance. Overview Predicting expansion If an equation of state is available, it can be used to predict the values of the thermal expan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Correlation
In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are ''linearly'' related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve. Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example, there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling. However ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gladstone–Dale Relation
The Gladstone–Dale relation is a mathematical relation used for optical analysis of liquids, the determination of composition from optical measurements. It can also be used to calculate the density of a liquid for use in fluid dynamics (e.g., flow visualization). The relation has also been used to calculate refractive index of glass and minerals in optical mineralogy. Uses In the Gladstone–Dale relation, (n-1)/\rho = \sum km, the index of refraction (n) or the density (ρ in g/cm3) of miscible liquids that are mixed in mass fraction (m) can be calculated from characteristic optical constants (the molar refractivity k in cm3/g) of pure molecular end-members. For example, for any mass (m) of ethanol added to a mass of water, the alcohol content is determined by measuring density or index of refraction (Brix refractometer). Mass (m) per unit volume (V) is the density m/V. Mass is conserved on mixing, but the volume of 1 cm3 of ethanol mixed with 1 cm3 of water is reduc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
