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The radius ratio rule defines a critical radius ratio for different crystal structures, based on their coordination geometry. [1] The idea is that the anions and cations can be treated as incompressible spheres, meaning the crystal structure can be seen as a kind of unequal sphere packing .
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.
[citation needed] In a close-packed structure there are 4 atoms per unit cell and it will have 4 octahedral voids (1:1 ratio) and 8 tetrahedral voids (1:2 ratio) per unit cell. [1] The tetrahedral void is smaller in size and could fit an atom with a radius 0.225 times the size of the atoms making up the lattice. An octahedral void could fit an ...
where is the void ratio, is the porosity, V V is the volume of void-space (gases and liquids), V S is the volume of solids, and V T is the total (or bulk) volume. This figure is relevant in composites , in mining (particular with regard to the properties of tailings ), and in soil science .
A dense packing of spheres with a radius ratio of 0.64799 and a density of 0.74786 [22] Many problems in the chemical and physical sciences can be related to packing problems where more than one size of sphere is available.
Void content in composites is represented as a ratio, also called void ratio, where the volume of voids, solid material, and bulk volume are taken into account.Void ratio can be calculated by the formula below where e is the void ratio of the composite, V v is the volume of the voids, and V t is the volume of the bulk material.
Fiber volume ratio is an important mathematical element in composite engineering. Fiber volume ratio, or fiber volume fraction, is the percentage of fiber volume in the entire volume of a fiber-reinforced composite material. [1] When manufacturing polymer composites, fibers are impregnated with resin.
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 .