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The Scherrer equation, in X-ray diffraction and crystallography, is a formula that relates the size of sub-micrometre crystallites in a solid to the broadening of a peak in a diffraction pattern. It is often referred to, incorrectly, as a formula for particle size measurement or analysis.
It is the mean diameter, which is directly obtained in particle size measurements, where the measured signal is proportional to the volume of the particles. The most prominent examples are laser diffraction [3] and acoustic spectroscopy (Coulter counter). The De Brouckere mean is defined in terms of the moment-ratio system as,
Within the branch of materials science known as material failure theory, the Goodman relation (also called a Goodman diagram, a Goodman-Haigh diagram, a Haigh diagram or a Haigh-Soderberg diagram) is an equation used to quantify the interaction of mean and alternating stresses on the fatigue life of a material. [1]
The Van 't Hoff equation relates the change in the equilibrium constant, K eq, of a chemical reaction to the change in temperature, T, given the standard enthalpy change, Δ r H ⊖, for the process. The subscript r {\displaystyle r} means "reaction" and the superscript ⊖ {\displaystyle \ominus } means "standard".
Pitzer equations [1] are important for the understanding of the behaviour of ions dissolved in natural waters such as rivers, lakes and sea-water. [ 2 ] [ 3 ] [ 4 ] They were first described by physical chemist Kenneth Pitzer . [ 5 ]
Furthermore, a surface which evolves under the mean curvature of the surface , is said to obey a heat-type equation called the mean curvature flow equation. The sphere is the only embedded surface of constant positive mean curvature without boundary or singularities. However, the result is not true when the condition "embedded surface" is ...
In chemistry, the mass fraction of a substance within a mixture is the ratio (alternatively denoted ) of the mass of that substance to the total mass of the mixture. [1] Expressed as a formula, the mass fraction is:
The equation is named after Edward Wight Washburn; [1] also known as Lucas–Washburn equation, considering that Richard Lucas [2] wrote a similar paper three years earlier, or the Bell-Cameron-Lucas-Washburn equation, considering J.M. Bell and F.K. Cameron's discovery of the form of the equation in 1906.