INO-12

Radius ratio

ρ = r+ / r−. Packing of a cation in an anion hole.

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Crystal chemistryRadius-ratio rule

Governing equation

\rho=r_+/r_-

where

r_+: Cation radius (Å)
r_-: Anion radius (Å)
\rho: Radius ratio (—)

Lecture brief

Historical brief

Pauling and Allred–Rochow electronegativity, Kapustinskii lattice energy, CFSE and Goldschmidt radii organise the periodic solid. The sheets predict bond character and crystal packing. This sheet (INO-12 — Radius ratio) is the form associated with Radius-ratio rule. Working symbols: $r_+$ , $r_-$ $\rightarrow$ $\rho$ . Critical ratios: 0.155 (3), 0.225 (4), 0.414 (6), 0.732 (8), 1 (12).

Purpose

Purpose: compute

\rho

from

r_+

r_-

in Inorganic chemistry via

\rho=r_+/r_-

ρ = r+ / r−. Packing of a cation in an anion hole. Use it when a real inorganic chemistry question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

r_+ = 0.950\,\mathrm{Å}

r_- = 1.810\,\mathrm{Å}

, the governing relation

\rho=r_+/r_-

yields

\rho = 0.525\,\mathrm{—}

. Hard-sphere ionic radii in Å. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Cation radius r_+0.95 ÅAnion radius r_-1.81 Å

Outputs

Radius ratio \rho0.525 —

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Narration of this film

Hard-sphere ionic radii in Å.

Critical ratios: 0.155 (3), 0.225 (4), 0.414 (6), 0.732 (8), 1 (12).

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