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The mass fraction of element B at the liquidus is given by w B l (represented as w l in this diagram) and the mass fraction of element B at the solidus is given by w B s (represented as w s in this diagram). The mass fraction of solid and liquid can then be calculated using the following lever rule equations: [1]
Mass fraction can also be expressed, with a denominator of 100, as percentage by mass (in commercial contexts often called percentage by weight, abbreviated wt.% or % w/w; see mass versus weight). It is one way of expressing the composition of a mixture in a dimensionless size ; mole fraction (percentage by moles , mol%) and volume fraction ...
When expressed in percent, it is known as the mole percent or molar percentage (unit symbol %, sometimes "mol%", equivalent to cmol/mol for 10-2). The mole fraction is called amount fraction by the International Union of Pure and Applied Chemistry (IUPAC) [1] and amount-of-substance fraction by the U.S. National Institute of Standards and ...
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).
Here, a A (1-x) B x is the lattice parameter of the solid solution, a A and a B are the lattice parameters of the pure constituents, and x 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. [3]
A closely related concept is the atomic percent (or at.%), which gives the percentage of one kind of atom relative to the total number of atoms. [1] The molecular equivalents of these concepts are the molar fraction , or molar percent .
Pell's equation, also called the Pell–Fermat equation, is any Diophantine equation of the form =, where n is a given positive nonsquare integer, and integer solutions are sought for x and y. In Cartesian coordinates , the equation is represented by a hyperbola ; solutions occur wherever the curve passes through a point whose x and y ...
In thermodynamics, vapor quality is the mass fraction in a saturated mixture that is vapor; [1] in other words, saturated vapor has a "quality" of 100%, and saturated liquid has a "quality" of 0%. Vapor quality is an intensive property which can be used in conjunction with other independent intensive properties to specify the thermodynamic ...