Lecture 4 (9/18/2006)
Crystal Chemistry
Part 3:
Coordination of Ions
Pauling’s Rules
Crystal Structures
Coordination of Ions
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For minerals formed largely by ionic bonding,
the ion geometry can be simply considered to be
spherical
Spherical ions will geometrically pack
(coordinate) oppositely charged ions around
them as tightly as possible while maintaining
charge neutrality
For a particular ion, the surrounding
coordination ions define the apices of a
polyhedron
The number of surrounding ions is the
Coordination Number
Coordination
Number and
Radius Ratio
See Mineralogy CD: Crystal
and Mineral Chemistry Coordination of Ions
Coordination
with O-2
Anions
When
Ra(cation)/Rx(anion)
~1
Closest
Packed
Array
See Mineralogy
CD: Crystal and
Mineral Chemistry
– Closest Packing
Pauling’s Rules of Mineral Structure
Rule 1: A coordination polyhedron
of anions is formed around each
cation, wherein:
- the cation-anion distance is
determined by the sum of the
ionic radii, and
- the coordination number of the
polyhedron is determined by the
cation/anion radius ratio (Ra:Rx)
Linus Pauling
Pauling’s Rules of Mineral Structure
Rule 2: The electrostatic valency principle
The strength of an ionic (electrostatic)
bond (e.v.) between a cation and an anion
is equal to the charge of the anion (z)
divided by its coordination number (n):
e.v. = z/n
In a stable (neutral) structure, a charge
balance results between the cation and its
polyhedral anions with which it is bonded.
Charge Balance
of Ionic Bonds
Formation of Anionic Groups
Results from high valence cations with electrostatic
valencies greater than half the valency of the
polyhedral anions; other bonds with those anions will
be relatively weaker.
Carbonate
Sulfate
Pauling’s Rules of Mineral Structure
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Rule 3: Anion polyhedra that share edges or
faces decrease their stability due to bringing
cations closer together; especially significant for
high valency cations
Rule 4: In structures with different types of
cations, those cations with high valency and
small CN tend not to share polyhedra with each
other; when they do, polyhedra are deformed to
accommodate cation repulsion
Pauling’s Rules of Mineral Structure
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Rule 5: The principle of parsimony
Because the number and types of different structural
sites tends to be limited, even in complex minerals,
different ionic elements are forced to occupy the same
structural positions – leads to solid solution.
See amphibole structure for example (See Mineralogy CD:
Crystal and Mineral Chemistry – Pauling’s Rules - #5)
Visualizing Crystal Structure
Beryl - Be3Al2(Si6O18)
Ball and Stick Model
Polyhedra Model
Portraying Crystal Structure in Two
Dimensions
Isostructural Types
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AX Compounds – Halite (NaCl) structure
Anions – in CCP packing
Cations – in octahedral sites
Ra/Rx=.73-.41
Examples:
Halides: +1 cations (Li, Na, K, Rb) w/ -1
anions (F, Cl, Br, I)
Oxides: +2 cations (Mg, Ca, Sr, Ba, Ni) w/ O-2
Sulfides: +2 cations w/ S-2
(See Mineralogy CD: Crystal and Mineral Chemistry –
Illustrations of Crystal Structures – Halite)
Isostructural Types
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AX Compounds – Sphalerite (ZnS) structure
RZn/RS=0.60/1.84=0.32 (tetrahedral)
Isostructural Types
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AX2 Compounds – Flourite (CaF2) structure
RCa/RF=1.12/1.31=0.75 (cubic)
Examples: Halides (CaF2, BaCl2...); Oxides (ZrO2...)
Isostructural Types
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ABO4 Compounds – Spinel (MgAl2O4)structure
- Oxygen anions in CCP array
- Two different cations (or same cation with two different valences) in
tetrahedral (A) sites (e.g. Mg2+, Fe2+, Mn2+, Zn2+) or octahedral (B) sites
(e.g. Al3+, Cr3+, Fe3+)
Nesosilicates
Inosilicates
(double chain)
Sorosilicates
Cyclosilicates
Phyllosilicates
Inosilicates
(single chain)
Tectosilicates
Next Lecture
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Crystal Chemistry IV
Compositional Variation of Minerals
Solid Solution
Mineral Formula Calculations
Graphical Representation of Mineral
Compositions
Read p. 90 - 103