Pauling’s Rules

2 principal reasons that the types of bonds that occur in minerals are important
1: the physical and chemical properties of all materials depend on the character of the bonds that hold them together
2: weathering rxns and the stability of soil minerals are functions of the nature of the crystal chemical bonds
the physical and chemical properties of all materials depend on…
the character of the bonds that hold them together
weathering rxns and the stability of soil minerals are functions of…
the nature of the crystal chemical bonds
the importance of the weakest bond type in a mineral
to a large extent, this dictates the mineral’s physical and chemical properties
the strongest bonds in soil minerals
the ones that are predominantly covalent in character
the relative stability of a mineral in a weathering environment is determined by…
the ionic bonds that are inherent to the mineral
the ion that dominates in soil minerals
the O2 anion
some factors that must be considered when predicting the arrangement of atoms in a mineral
-geometric packing constraints
-electrostatic interactions between atoms
the rules that describe the likely geometric arrangement of atoms in an ionic structure
Pauling’s rules of crystal configuration
Pauling’s 1st rule of crystal configuration
a coordinated polyhedron of anions is formed about each cation, the cation-anion distance being determined by the radius sum and the coordination number of the cation by the radius ratio
this determines the cation-anion distance
the sum of the radius of the cation and the radius of the anion (this is the radius sum)
this determines the coordination number of the cation
the radius ratio
coordination number (CN)
the number of anions that can pack around a single anion
the coordination number of a cation is a function of…
cation size and anion size (radius)
radius ratio
(cation radius)/(anion radius)
limiting radius ratio
the radius ratio at which the coordinating anions just touch; if the cation was any smaller, the anions would overlap and repel each other, making the structure unstable and making a lower coordination number necessary
the no rattle rule
if the central cation has room to move inside a given polyhedron, the configuration is unstable
polyhedron type with coordination number of 2
linear
polyhedron type with coordination number of 3
planar triangular or trigonal pyramidal
polyhedron type with coordination number of 4
tetrahedral or planar square
polyhedron type with coordination number of 6
octahedral
polyhedron type with coordination number of 8
cubic
polyhedron type with coordination number of 12
dodecahedral or cubooctahedral
size of central metal atom vs. coordination number
as the size of the central metal atom increases, the coordination number increases
Pauling’s 2nd rule of crystal configuration (aka the electrostatic valence principle)
in a stable structure, the valence of each anion, with changed sign, is equal or nearly equal to the sum of the strengths of the electrostatic bonds to it from adjacent cations
how to calculate bond strength
bond strength = (cation valence) / (coordination number)
coordination number for linear polyhedron
2
coordination number for planar triangular or trigonal pyramidal polyhedron
3
coordination number for tetrahedral or planar square polyhedron
4
coordination number for octahedral polyhedron
6
coordination number for cubic polyhedron
8
coordination number for dodecahedral or cubooctahedral polyhedron
12
Pauling’s 3rd rule of crystal configuration
the presence of shared edges and especially shared faces in a coordinated structure decreases its stability; the effect is larger for cations with large valence and small coordination number (lignancy)
distance between cations vs. stability of the mineral structure
the greater the distance between the cations, the more stable the structure becomes; direct relationship
out ofg anions that are shared by polyhedrons at the face, corner, and edge, which is the most stable and which is the least stable?
most stable: corner
least stable: face
Pauling’s 4th rule of crystal configuration
in a crystal containing different cations, those with large valence and small coordination number tend not to share polyhedron elements with each other
how the electrostatic interaction of high valence cations is minimized in stable structures
thru the shielding provided by the coordinating anions
size of cation vs. stability of structure
the larger the cation, the more stable the structure, pending everything else is equal; direct relationship
charge density vs. stability of structure
the higher the charge density, the less stable the structure, pendine everything else is equal; inverse relationship
Pauling’s 5th rule of crystal configuration (the principal of parsimony)
the number of essentially different kinds of atoms or coordinated polyhedron in a crystal tends to be small; this is a natural consequence of the other 4 rules
this dictates the presence of a cation in a given polyhedral configuration
the radius ratio
the principal of parsimony
states that a stable structure will contain only a small number of essentially different kinds of atoms
2 readily apparent reasons that support the validity of the principal of parsimony
1: although several different cations can reside in a particular coordination, generally only 1 particular cation fits best in the structure (is best suited for the location); other cations, which are not as well suited for that location, cause stress and instability
2: a +4 or +6 cation residing in a location normally occupied by a +2 cation will result in electrostatic imbalances, destabilizing the structure
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