Introduction to Mineralogy
Dr. Tark Hamilton
Chapter 4: Lecture 12
The Chemical Basis of Minerals
(Pauling’s Rules)
Camosun College GEOS 250
Lectures: 9:30-10:20 M T Th F300
Lab: 9:30-12:20 W F300
Pauling’s Rules
• 1: Coordination Principle: all ions in polyhedra
• 2: Electrostatic Valency Principle: Σ bonds = charge
• 3: Sharing of Polyhedral Elements decreases
stability (e.g. corners OK, edges rare or faces
empty)
• 4: Hi valence & Low C.N. Cations don’t share
• 5: Principle of Parsimony (few geometries, common
environments, high symmetry)
Pauling Rule 2: Electrostatic Valency
Principle ("Bond Strength")
• "In a stable ionic structure the charge on an ion
is balanced by the sum of electrostatic bond
strengths to the ions in its coordination
polyhedron"
• i.e. A stable ionic structure must be arranged to
preserve Local Electroneutrality
• (Ions in a crystal are surrounded by ions of opposite
charge so as not to produce large volumes of
similar charge in the crystal - this maximizes
Madelung potential!)
• Ion-ion or ion-radical all the same or unstable
2: Bond Strength (e.v.) = Z+ / C.N.
Na+ or F- in NaCl
C.N. = 6, e.v. = 1
Octahedral
e.b.s. = 1/6
Ca+2 in CaF2
C.N. = 8, e.v. = 2
Cubic
e.b.s. = 2/8 = ¼
F- in CaF2
C.N. = 4, e.v. = 1
Tetrahedral
e.b.s. = ¼
Only 1 Bond Strength
• Uniform Bond Strength – Isodesmic crystals
• NaCl Chloride all bonds = 1 (ordinary ionic crystal implied,
but preference for C.N.=6 due to Cl- ‘s 3 normal p-orbitals.)
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MgAl2O4 Aluminate, FeCr2O4 Chromrate (mol. radicals?)
Spinels: AB2O4 Radicals or Isodesmic?
Mg+2 or Fe2+ , tetrahedral, 2/4 = ½
Al+3 or Cr+3 , octahedral, 3/6 = ½
So isodesmic and no radicals!
Different I.R. & valence made up for by varying C.N.
1 bond strength = 1 uniform energy level throughout
Unequal Bond Strengths
• Small highly charged cations form radicals with
larger low valence anions, Anisodesmic
• (CO3)-2 , (NO3)- , (PO4)-3 , (SO4)-2 , (WO4)-2
• C+4 in Carbonate is 3 C.N. so bond is 4/3 = 1.33
• N+5 in Nitrate is 3 C.N. so bond is 5/3 = 1.67
• S+6 in Sulphate is 4 C.N. so bond is 6/4 = 1.5
• These are more than half of O-2 valence, so O in
these groups is more tightly bonded than to Cations
• Oxygens much more tightly bonded to core atom
(C,N,S,P, W, V, Cr…) than to surrounding cations
• These molecular radicals usually persist through
melting, decrepitation or mineral-chemical reactions
• Carbonatite melts, Apatite-Magnetite melts
Tightly Bonded Radicals (Viva Che!)
2 Lone Pairs
(-2)
3 Isomers in solutions
1 radical in solid minerals
3 Lone Pairs
4 isomers in solutions
1 radical in solid minerals
Pauling Rule 3: Polyhedral
Linking
• "The stability of structures with different types of
polyhedral linking is vertex-sharing > edge-sharing >
face-sharing"
• effect is largest for cations with high charge and low
coordination number
• especially large when r+/r- approaches the lower
limit of the polyhedral stability
• Why? Sharing edges/faces brings ions at the centre of
each polyhedron closer together, hence increasing
electrostatic repulsions
• i.e. disposition of ions of similar charge will be such as
to minimize the Electrostatic Energy between them
• Linked polyhedra act as a single ionic structural unit
2+- 4+: Sharing Polyhedral Elements
Rare
Tetrahedra
+4 cations
not +3, 1.5 e.v.
OK
Edge contracts
+2 cations
Octahedra
Empty
+sites,
too much
cation
repulsion
Pauling’s Rules 1-4 all:
• Tend to maximize cation-anion
interactions due to attraction
• Tend to minimize cation-cation
or anion-anion interactions due
to repulsion
#5 - Principle of Parsimony
• # of contrasting elements are small because
there are few anion or cation sites
• Complex compositions tend toward several
constituents (cations) in the same kind of site
• This is termed solid solution: Fe for Mg, Si
for Al, Ca for Na (definite not exact compositions)
• Goldschmidt’s rules say ions have to be
similar size +/-15% and +/- 1 charge unit
Limited Types of Coordination
Halite
Fluorite
Sphalerite
Octahedral – Na & Cl
Cubic – Ca
Tetrahedral – F
Octahedral – empty
Tetrahedral - S