Transcript Bonding and the Structures of Minerals

Fundamentals of crystal
chemistry
Mineralogy
Carleton College
Crystal Chemistry
• As we have been discussing for the last
week, crystals, and thus minerals, are made
up of a 3-dimensional array of atoms
arranged in an orderly fashion.
Crystal Chemistry
• Now we will explore what these atoms are
and how they interact with one another to
determine the physical and structural
properties of crystals.
Crystal chemistry
• We can better understand the wide variety
of different mineral species and the
variations exhibited by individual mineral
species by recognizing the gross chemical
features of the Earth and especially of the
crust.
Composition of the crust
Element
O
Si
Al
Fe
Ca
Na
K
Mg
Composition of the crust
Element
O
Si
Al
Fe
Ca
Na
K
Mg
Weight %
Composition of the crust
Element
O
Si
Al
Fe
Ca
Na
K
Mg
Weight %
46
Composition of the crust
Element
O
Si
Al
Fe
Ca
Na
K
Mg
Weight %
46
28
Composition of the crust
Element
O
Si
Al
Fe
Ca
Na
K
Mg
Weight %
46
28
8
Composition of the crust
Element
O
Si
Al
Fe
Ca
Na
K
Mg
Weight %
46
28
8
5
4
Composition of the crust
Element
O
Si
Al
Fe
Ca
Na
K
Mg
Weight %
46
28
8
5
4
3
3
Composition of the crust
Element
O
Si
Al
Fe
Ca
Na
K
Mg
Total
Weight %
46
28
8
5
4
3
3
2
99
Composition of the crust
Element
O
Si
Al
Fe
Ca
Na
K
Mg
Total
Weight %
46
28
8
5
4
3
3
2
99
Atom %
63
21
7
2
2
3
1
2
100
Composition of the crust
Element
O
Si
Al
Fe
Ca
Na
K
Mg
Total
Weight %
46
28
8
5
4
3
3
2
99
Atom %
63
21
7
2
2
3
1
2
100
Ionic Radius Å
1.4
0.42
0.51
0.74
0.99
0.97
1.33
0.66
Composition of the crust
Element
O
Si
Al
Fe
Ca
Na
K
Mg
Total
Weight %
46
28
8
5
4
3
3
2
99
Atom %
63
21
7
2
2
3
1
2
100
Ionic Radius Å
1.4
0.42
0.51
0.74
0.99
0.97
1.33
0.66
Volume %
94
1
1
2
2
100
Crystal chemistry
• While Oxygen comprises almost half of the
crust by weight, it occupies almost 94% by
volume!
Crystal chemistry
• This is directly reflected in minerals as well.
• Oxygen is the most dominant anion in
crustal minerals, and as you would predict
from the numbers, the silicate minerals
make up the bulk of the crustal rocks.
Crystal chemistry
• The Earth's crust, on an atomic scale
consists essentially of a close packing of
oxygen anions with interstitial metal
cations, chiefly Silicon.
Crystal chemistry
• In addition to the silicate minerals, the crust
also contains significant amounts of other
oxygen compounds such as the oxide and
carbonate minerals.
Chemical Bonding
• The chemical and physical properties
of crystals depend almost entirely on
the forces that bind the atoms together
in a crystal structure. Forces known
collectively as chemical bonds.
Chemical Bonding
• Chemical bonding depends on the
electronic structure of the atoms
involved, in particular the valence
electrons in the outermost shells, and
on the size of the ion or atom.
Chemical Bonding
• In general we recognize 4 different
types of chemical bonds, although as
we will see, all bond types are
transitional from one type to another.
Types of Chemical Bonds
•
•
•
•
•
Ionic
Covalent
Metallic
Van der Waals
Hydrogen Bond
Ionic Bonds
• Ionic Bonds
– There is a tendency for atoms to lose or gain
electrons and become ions in order to achieve
the stable electronic configuration with
completely filled outer electron shells.
Ionic Bonds
• Ionic Bonds
– Positively charged ions are called cations and
negatively charged ions are called anions.
Ionic Bonds
• Ionic Bonds
– These ions can achieve various values of
electronic charge depending on the number of
electrons gained or lost.
Ionic Bonds
• Electron charges







+1
+2
+3
+4
+5
-1
-2
monovalent cations
divalent cations
trivalent cations
tetravalent cations
pentavalent cations
monovalent anions
divalent anions
Ionic Bonds
• For example, Na has one electron in its
outermost shell. It will tend to give up this
electron to become Na+1 ion.
Ionic Bonds
• Similarly, Cl has 7 electrons in its outermost
shell and would like to gain an electron to
become Cl -1ion.
Ionic Bonds
• Once these atoms become Na +1 and Cl-1,
the force of attraction between the
oppositely charged ions results in an ionic
bond.
Ionic Bonds
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Ionic Bonds
• Formed between atoms of very different
electronegativity
• The less electronnegativity atom completely
donates one or more electron to the more
elctronegative atom. The resulatin ions are held
together by electronstatic attaraction
Ionic Bonds
• Most important for bonding between oxygen and
Mg, Si, Al, Na, K
• Hence, the primary bonding type in silicate and
oxide minerals
Ionic Bonds
• Ionic bonds are non-directional
in nature, that is the attractive
forces occur form all directions.
Ionic Bonds
• Crystals made of ionically
bonded atoms tend to have the
following properties:
Ionic Bonds
• Dissolve easily in polar solvents like water (H2O
is a polar solvent because the hydrogen ions occur
on one side the water molecule and give it a slight
positive charge while the other side of the water
molecule has a slight negative charge).
Ionic Bonds
•
•
•
•
Tend to form crystals with high symmetry.
Moderate hardness and density.
High melting temperatures.
Generally poor conductors of heat and electricity
(they are good materials for thermal and electrical
insulation).
Covalent Bonds
• Elements near the right hand side of the periodic
table tend to bond to each other by covalent bonds
to form molecules that are found in crystal
structures.
• For example Si and O form an SiO4-4 molecule
that can bind to other atoms or molecules either
covalently or ionically.
Covalent Bonds
• Carbon has four electrons in its outer shell and
needs 4 more to achieve the stable electronic
configuration.
• So a Carbon atom can share electrons with 4 other
Carbon atoms to form covalent bonds. This
results in compounds like diamond or graphite that
are held together by strong covalent bonds
between Carbon atoms.
Covalent Bonds
• In reality, bonding between atoms usually does
not take place as pure covalent or pure ionic
bonds, but rather as a mixture of bond types. The
amount of each type is determined by the
electronegativity difference between the atoms
involved.
Covalent Bonds
• Covalent bonds can also be thought of as
shared electron bonds. Covalent bonds
develop when atoms can achieve the a
stable outer shell electron configuration by
sharing electrons with another atom. This
results in each of the atoms having a stable
electronic configuration part of the time.
Covalent Bonds
• Formed between atoms of similar
electronegativity
• Atoms are held together by “Sharing
electrons”
• Sulfide minerals
• Most organic compounds
Covalent Bonds
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Covalent Bonds
• Covalent bonds are very strong directional bonds,
that is they occur along the zone where they
electrons are shared.
Covalent Bonds
• Covalently bonded crystals have the following
properties:
–
–
–
–
–
Relatively insoluble in polar solvents like water.
High melting temperatures.
Generally form crystals structures of low symmetry.
Tend to have high hardness.
Generally poor conductors of heat and electricity.
Covalent Bonds
• In reality, bonding between atoms
usually does not take place as pure
covalent or pure ionic bonds, but rather
as a mixture of bond types. The
amount of each type is determined by
the electronegativity difference
between the atoms involved.
Covalent Bonds
• For example, consultation of electronegativity
chart above shows Cl with a value of 3.16 and Na
with a value of 0.93. The electronegativity
difference is 2.3, suggesting that only 80% of the
bonding in NaCl is ionic.
• Even looking a larger electronegativity difference like for
NaF, the bonding would by only about 90% ionic.
Bonding between Oxygen atoms or between Carbon
atoms, where the electronegativity difference is 0, would
result in pure covalent bonds.
Electronegativity
Covalent Bonds
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Chemical Bonds in Minerals
Very ionic
Partially Covalent Very Covaletn
Mg-O
Al-O
C-O (as in CO3)-2
Ca-O
Si-O
S-O (as in SO4)-2
Na-O
Fe-S
S-S (as in S2)-2
K-O
Ti-O
Metallic Bonds
• None of the bond types discussed so
far result in materials that can easily
conduct electricity. Pure metals
however, do conduct electricity easily
and therefore must be bonded in a
different way.
Metallic Bonds
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Metallic Bonds
• This is the metallic bond, where positively
charge atomic nuclei share electrons in their
electron clouds freely. In a sense, each
atom is sharing electrons freely with other
atoms, and some of the electrons are free to
move from atom to atom.
Metallic Bonds
• Since some of the electrons are free to
move, metallically bonded materials have
high electrical conductivity.
Metallic Bonds
• Pure metals appear to bind in this way.
• When crystals are formed with metallic bonds
they have the following properties:
Metallic Bonds
•
Low to Moderate hardness.
•
Usually very malleable and ductile.
•
Good thermal and electrical conductors.
•
Soluble only in acids.
•
Crystals with high symmetry.
Residual Bonds
• Residual bonds are weak bonds that
involve the attraction of partially
charged atoms or molecules. These
partial charges are created when
electrons become concentrated on one
side of an atom or molecule to satisfy
ionic or covalent bonds.
Residual Bonds
• This sometimes creates a polar atom or
molecule which has a concentration of
negative charges on one side and a
concentration of positive charges on
the other side.
Residual Bonds
• When residual bonds occur in a crystal
structure, they generally form planes or
zones of easy cleavage because of the
weakness of the residual bond.
Residual Bonds
• Two special cases are discussed here.
– Hydrogen Bonds
–van der Waals
Residual Bonds
• Hydrogen Bonds - These occur in the
special case of hydrogen, because H has
only one electron. When Hydrogen gives
up this electron to become H+1 ion or shares
its single electron with another atom in a
covalent bond, the positively charged
nucleus of the hydrogen atom is exposed,
giving that end of the H ion a residual +1
charge.
Residual Bonds
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Residual Bonds
• This is what causes the H2O molecule to be a polar
molecule seen here.
Residual Bonds
• Similarly, an OH-1 molecule, common in sheet
silicate minerals like micas and clay minerals,
although possessing a -1 charge will have exposed
H nuclei that can bond to other negative residual
charges forming a weak hydrogen bond.
• Layers of OH-1 molecules in the sheet silicates
result in the easy cleavage along the {001} planes.
Residual Bonds
• van der Waals Bonds are also residual bonds that
result from polarization of atoms or molecules.
• In the mineral graphite, the C atoms are held
together by strong covalent bonds, that result in
concentrations of positive and negative charges at
either end of the C atoms. Bonding between
sheets takes place as a result of the slight attraction
between these residual charges from one sheet to
another.
Residual Bonds
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Residual Bonds
• Mixture of Bonds in Crystals
• Since most crystals are complex mixtures of
atoms, there will likely be more than one
bond type in complex crystals. Thus,
except in very simple compounds properties
such as hardness, cleavage, solution rate,
and growth rate may be directional, as
discussed in a previous lecture.
Stable Ionic Structure
• Between an pair of oppositely charged ions
there is an attractive force, that is
proportional to the products of their charges
and inversely proportional to the square of
the distance between their centers.
(Coulomb’s Law)
Stable Ionic Structure
• F = K qi, qj/r2
• Where F = Coulomb force (bond strength)
K
=
proportionality
constant
•
• Q = point charges of ions I and j
R
=
distance
between
ion
I
and
j
•
Coordination
• Coordination Principles - As ions bond to
each other, they gather in an arrangement
such that they are symmetrically clustered.
Coordination
• The convention is chosen such that cations
lie at the center of coordination, with anions
residing as nearest neighbors. The number
of anions that form this polyhedron around
thecation is known as the coordination
number (C.N.).
Coordination
• C.N. = 4
• C.N. = 6 (octahedral)
Coordination
• The geometry of the first coordination shell
(nearest neighbors) is related to the relative
size of the atomic radii. Relative sizes can
be expressed as the Radius Ratio.
• R = RA / RB
• Where: RA = Radius of cations
• RB = Radius of anions
Coordination
•
•
•
•
Example: Potassium and oxygen
RA = 1.33Å ,
RB =1.40Å ,
RA / RB
• KO = 0.95
Coordination
•
•
•
•
•
Example: Silica and oxygen
RA = 0.42Å ,
RA =1.40Å ,
RA / RB
SiO = 0.30
Coordination
• When coordinating identically sized spheres
there are several possible ways of packing
so as to create contact between the spheres.
• 1. C.N. =12
– a. Hexagonal Closest Packing (HCP)
– b. Cubic Closest Packing (CCP)
Coordination
• 2. Cubic Packing where the C.N. = 8 (cubic
coordination)
Coordination
• 3. For relative R values less than 0.732, the
6 C.N. (or octahedral coordination) is the
preferred packing arrangement. The limiting
value for the interior of octahedrally
coordinated anions (relative size of 1) is in
the range of R = 0.732 - 0.414.
Coordination
• 4. Tetrahedral coordination is the next
smallest interior space with R = 0.414 0.225
• 5. Triangular coordination is next smallest
space with R = 0.225 - 0.155
• 6. Linear coordination is smallest where
R< 0.155
Ionic Radii
Radius Ratio
• RA/RB
• Where A is radius of Cation and B is radius
of anion.
Pauling’s Rules for Ionic Structures
Rule 1: The coordination number of a cation A by an anion B will be determined
by the radius ration of the ions A and B
R /R < 0.16
3-fold coordination
0.16>R /R < 0.41
4-fold coordination
0.41>R /R < 0.73
6-fold coordination
0.73>R /R < 1.00
8-fold coordination
1.00>R /R
12-fold coordination
A
B
A
A
A
A
B
B
B
B
Basis for Rule 1 (Octahedral example)
Basis for Rule 1 (Octahedral example)
• Cos 30o = 0.5 / (0.5 + 0.5 x)
• 0.5 + 0.5 x = 0.5 / Cos 30o
 = 0.5 / 0.8660
 =0.5774
 0.5 x = 0.5774-0.5
 x= 0.155
Basis for Rule 1 (Octahedral example)
Basis for Rule 1 (Octahedral example)
Basis for Rule 1 (Octahedral example)
• (1 + x) 2 = 12 + 12
• 1+ x = √2 = 1.414
• X = 0.414
Pauling’s Rules for Ionic Structures (cont.)
• Rule 2:
An ionic structure will be stable to the extent that the sum of
the strengths* of the electrostatic bonds that reach an anion from its
coordinatio of cations will equal the charges on the anion. This is the
electrostatic valency principle.
•
(* The strength of a bond from each cation is its charge/coordination
number)
Pauling’s Rule for Ionic Structures
• Rule 3:
The sharing of edges and faces by coordination
polyhedra decreases the stablity of a structure.
Pauling’s Rules for Ionic Structures
• Rule 4: In Structures
with more than one
cation, those of high
valency and small
coordination number
tend not share
polyhedron elements
with each other.
Pauling’s Rules for Ionic Structures
• Rule 5: The number of different kinds of
sites in a stable structure tends to be
small.
• Hornblende
• NaCa2(Mg,Fe,Al)5[(Al,Si)4O11](OH) 2