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Pauling's Rules
part of Ch. 2
43
Chemistry
Undergraduate 4
01/14/2017

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Term
2 principal reasons that the types of bonds that occur in minerals are important
Definition
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
Term
the physical and chemical properties of all materials depend on...
Definition
the character of the bonds that hold them together
Term
weathering rxns and the stability of soil minerals are functions of...
Definition
the nature of the crystal chemical bonds
Term
the importance of the weakest bond type in a mineral
Definition
to a large extent, this dictates the mineral's physical and chemical properties
Term
the strongest bonds in soil minerals
Definition
the ones that are predominantly covalent in character
Term
the relative stability of a mineral in a weathering environment is determined by...
Definition
the ionic bonds that are inherent to the mineral
Term
the ion that dominates in soil minerals
Definition
the O2- anion
Term
some factors that must be considered when predicting the arrangement of atoms in a mineral
Definition
-geometric packing constraints
-electrostatic interactions between atoms
Term
the rules that describe the likely geometric arrangement of atoms in an ionic structure
Definition
Pauling's rules of crystal configuration
Term
Pauling's 1st rule of crystal configuration
Definition
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
Term
this determines the cation-anion distance
Definition
the sum of the radius of the cation and the radius of the anion (this is the radius sum)
Term
this determines the coordination number of the cation
Definition
the radius ratio
Term
coordination number (CN)
Definition
the number of anions that can pack around a single anion
Term
the coordination number of a cation is a function of...
Definition
cation size and anion size (radius)
Term
radius ratio
Definition
(cation radius)/(anion radius)
Term
limiting radius ratio
Definition
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
Term
the no rattle rule
Definition
if the central cation has room to move inside a given polyhedron, the configuration is unstable
Term
polyhedron type with coordination number of 2
Definition
linear
Term
polyhedron type with coordination number of 3
Definition
planar triangular or trigonal pyramidal
Term
polyhedron type with coordination number of 4
Definition
tetrahedral or planar square
Term
polyhedron type with coordination number of 6
Definition
octahedral
Term
polyhedron type with coordination number of 8
Definition
cubic
Term
polyhedron type with coordination number of 12
Definition
dodecahedral or cubooctahedral
Term
size of central metal atom vs. coordination number
Definition
as the size of the central metal atom increases, the coordination number increases
Term
Pauling's 2nd rule of crystal configuration (aka the electrostatic valence principle)
Definition
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
Term
how to calculate bond strength
Definition
bond strength = (cation valence) / (coordination number)
Term
coordination number for linear polyhedron
Definition
2
Term
coordination number for planar triangular or trigonal pyramidal polyhedron
Definition
3
Term
coordination number for tetrahedral or planar square polyhedron
Definition
4
Term
coordination number for octahedral polyhedron
Definition
6
Term
coordination number for cubic polyhedron
Definition
8
Term
coordination number for dodecahedral or cubooctahedral polyhedron
Definition
12
Term
Pauling's 3rd rule of crystal configuration
Definition
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)
Term
distance between cations vs. stability of the mineral structure
Definition
the greater the distance between the cations, the more stable the structure becomes; direct relationship
Term
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?
Definition
most stable: corner
least stable: face
Term
Pauling's 4th rule of crystal configuration
Definition
in a crystal containing different cations, those with large valence and small coordination number tend not to share polyhedron elements with each other
Term
how the electrostatic interaction of high valence cations is minimized in stable structures
Definition
thru the shielding provided by the coordinating anions
Term
size of cation vs. stability of structure
Definition
the larger the cation, the more stable the structure, pending everything else is equal; direct relationship
Term
charge density vs. stability of structure
Definition
the higher the charge density, the less stable the structure, pendine everything else is equal; inverse relationship
Term
Pauling's 5th rule of crystal configuration (the principal of parsimony)
Definition
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
Term
this dictates the presence of a cation in a given polyhedral configuration
Definition
the radius ratio
Term
the principal of parsimony
Definition
states that a stable structure will contain only a small number of essentially different kinds of atoms
Term
2 readily apparent reasons that support the validity of the principal of parsimony
Definition
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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