INO-13

Coordination from radius ratio

CN jumps at the critical radius ratios. A hard-sphere snapshot.

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Crystal chemistryPauling CN

Governing equation

\mathrm{CN}=f(r_+/r_-)

where

r_+: Cation radius (Å)
r_-: Anion radius (Å)
CN: Coordination number (—)

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-13 — Coordination from radius ratio) is the form associated with Pauling CN. Working symbols: $r_+$ , $r_-$ $\rightarrow$ $CN$ . Cations sit in the largest hole they can rattle in: triangular, tetrahedral, octahedral, cubic.

Purpose

Purpose: compute

CN

from

r_+

r_-

in Inorganic chemistry via

\mathrm{CN}=f(r_+/r_-)

CN jumps at the critical radius ratios. A hard-sphere snapshot. 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

\mathrm{CN}=f(r_+/r_-)

yields

CN = 8\,\mathrm{—}

. Same radii as the radius-ratio sheet; output predicted CN. 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

Coordination number CN8 —

Reading speed

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Narration of this film

Same radii as the radius-ratio sheet; output predicted CN.

Cations sit in the largest hole they can rattle in: triangular, tetrahedral, octahedral, cubic.

Reading speed

Watch on YouTube