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Critical Radius Ratio. This diagram is for octahedral interstices (coordination number six): 4 anions in the plane shown, 1 above the plane and 1 below. The stability limit is at r C /r A = 0.414. The radius ratio rule defines a critical radius ratio for different crystal structures, based on their coordination geometry. [1]
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. [5]
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 .
Under some definitions, the value of the radius may depend on the atom's state and context. [1] Atomic radii vary in a predictable and explicable manner across the periodic table. For instance, the radii generally decrease rightward along each period (row) of the table, from the alkali metals to the noble gases; and increase down each group ...
The following table shows empirically measured covalent radii for the elements, as published by J. C. Slater in 1964. [17] The values are in picometers (pm or 1×10 −12 m), with an accuracy of about 5 pm. The shade of the box ranges from red to yellow as the radius increases; gray indicates lack of data.
Toggle the table of contents. ... is a dimensionless number that is calculated from the ratio of the ionic radii: [1] ... r A is the radius of the A cation.
The van der Waals radius, r w, of an atom is the radius of an imaginary hard sphere representing the distance of closest approach for another atom. It is named after Johannes Diderik van der Waals, winner of the 1910 Nobel Prize in Physics, as he was the first to recognise that atoms were not simply points and to demonstrate the physical consequences of their size through the van der Waals ...
Toggle the table of contents. ... Thin circular loop of radius r and mass m. ... where t = (r 2 − r 1)/r 2 is a normalized thickness ratio;