PAULING’S RULE III
Date: 09/22/25
Cole, Clint Ryner J.
Magsayo, Jeanelle
Department of Material and Resources Engineering and
Technology, College of Engineering
Introduction
Pauling's Rules are five heuristic
principles established by Linus Pauling to
describe and predict the structures of ionic
crystal compounds, especially minerals.
In 1929, Linus Pauling formulated five
rules
that
provide
some
broad
generalizations about the structure of
solids, especially for those with ionic
bonding.
Source:
https://en.wikipedia.org/wiki/Linus_Pau
ling
Pauling’s 3rd Rule
Cole & Magsayo | Page 2
Introduction
1. Radius Ratio Rule
2. Electrostatic Valency Principle
3. Sharing Polyhedra Edges/Faces
4. Cations with High Valence and Small Coordination Avoid
Sharing
5. Principle of Parsimony
Pauling’s 3rd Rule
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Rule 3: The Sharing of Edges and Faces
“The presence of shared edges, and particularly of
shared faces, in a coordinated structure decreases
its stability.”
Pauling’s 3rd Rule
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Rule 3: The Sharing of Edges and Faces
Crystal structures become less stable when:
✓ coordinating polyhedra share edges
✓ become even more unstable when they share faces.
When polyhedra share edges, or faces, the central cations
in the polyhedra come closer together and tend to repel
each other on account of their positive charges.
✓ larger effects for cations with a high valence and a low
coordination number.
Pauling’s 3rd Rule
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Rule 3: The Sharing of Edges and Faces
Figure 1: Change in the relative distance between two cations (each centered in a tetrahedron) when the
geometry is changed from linking across an apex, an edge, and a face. The distances shown reflect the
relative
decrease
in
cation-cation
distance
due
to
sharing
(Source:
https://www.academia.edu/34283833/Earth_Materials_INTRODUCTION_TO_MINERALOGY_AND_PETRO
LOGY)
Pauling’s 3rd Rule
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Rule 3: The Sharing of Edges and Faces
In silicate structures, silica
tetrahedra typically share only
their oxygen vertices (corners) to
maximize stability and avoid
cation repulsion.
✓ Bridging oxygens provide
link between two tetrahedra.
Example: Quartz
tectosilicates
Pauling’s 3rd Rule
and
Source:
https://opentextbc.ca/physicalgeologyh5p/chapter/silicate-mi
nerals/
other
Source: https://byjus.com/chemistry/silicate/
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Rule 3: The Sharing of Edges and Faces
✓ Tetrahedra are (a)
rarely
joined
across edges and
never share faces.
Special case: Periclase (MgO)
has octahedra sharing all their
edges.
(b)
Source (a)(b):
https://pmc.ncbi.nlm.nih.gov/articles/PMC7217010/
Pauling’s 3rd Rule
Source:
https://www.sciencedirect.com/to
pics/earth-and-planetary-science
s/periclase
https://www.researchgate.net/figure/r
ight-The-crystal-structure-of-periclas
e-MgO-The-structure-is-the-same-as
-that-of_fig2_299038200
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Rule 3: The Sharing of Edges and Faces
• Analysis of connected
pairs of polyhedra
• Exceptions (examples)
BaTiO₃, Barium Titanate
(a polycrystalline material)
Source: https://pmc.ncbi.nlm.nih.gov/articles/PMC7217010/
Pauling’s 3rd Rule
Al₂O₃, Aluminum Oxide
(alumina)
Source: https://pmc.ncbi.nlm.nih.gov/articles/PMC7217010/
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References:
George J, Waroquiers D, Di Stefano D, Petretto G, Rignanese GM, Hautier G. (2020). The limited predictive
power of the Pauling rules. Angewandte Chemie International Edition, 59(19), 7569–7575.
https://doi.org/10.1002/anie.202000829
Klein
and
Philpotts
(2013).
Earth
Materials
INTRODUCTION
TO
MINERALOGY
AND
PETROLOGY.https://www.academia.edu/34283833/Earth_Materials_INTRODUCTION_TO_MINERALO
GY_AND_PETROLOGY
Perkins
(2022).
13.4.3:
Pauling’s
third
rule.
Geosciences
LibreTexts.
https://geo.libretexts.org/Bookshelves/Geology/Mineralogy_(Perkins_et_al.)/13%3A_Crystal_Structures/
13.04%3A_Paulings_Rules/13.4.03%3A_Paulings_Third_Rule
Pauling’s 3rd Rule
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