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In condensed matter physics and inorganic chemistry, the cation-anion radius ratio can be used to predict the crystal structure of an ionic compound based on the relative size of its atoms. It is defined as the ratio of the ionic radius of the positively charged cation to the ionic radius of the negatively charged anion in a cation-anion compound.
An octahedron may then form with a radius ratio greater than or equal to 0.414, but as the ratio rises above 0.732, a cubic geometry becomes more stable. This explains why Na + in NaCl with a radius ratio of 0.55 has octahedral coordination, whereas Cs + in CsCl with a radius ratio of 0.93 has cubic coordination.
Body roundness index (BRI) is a calculated geometric index used to quantify an aspect of a person's individual body shape.Based on the principle of body eccentricity, it provides a rapid visual and anthropometric tool for health evaluation.
r B is the radius of the B cation. r O is the radius of the anion (usually oxygen). In an ideal cubic perovskite structure, the lattice parameter (i.e., length) of the unit cell (a) can be calculated using the following equation: [ 1 ]
Ionic radius, r ion, is the radius of a monatomic ion in an ionic crystal structure. Although neither atoms nor ions have sharp boundaries, they are treated as if they were hard spheres with radii such that the sum of ionic radii of the cation and anion gives the distance between the ions in a crystal lattice .
[1] [4] That is, if a given munitions design has a CEP of 100 m, when 100 munitions are targeted at the same point, an average of 50 will fall within a circle with a radius of 100 m about that point. There are associated concepts, such as the DRMS (distance root mean square), which is the square root of the average squared distance error, a ...
These first Heisler–Gröber charts were based upon the first term of the exact Fourier series solution for an infinite plane wall: (,) = = [ + ], [1]where T i is the initial uniform temperature of the slab, T ∞ is the constant environmental temperature imposed at the boundary, x is the location in the plane wall, λ is the root of λ * tan λ = Bi, and α is thermal diffusivity.
In all of the following nose cone shape equations, L is the overall length of the nose cone and R is the radius of the base of the nose cone. y is the radius at any point x, as x varies from 0, at the tip of the nose cone, to L. The equations define the two-dimensional profile of the nose shape.