Transcript Document 7365556

Crystal Chemistry
Nesse, Chapter 3
Klein & Hurlbut, Chapter 4
EPSC210 Introductory Mineralogy
2nd Mineral identification test this Friday.
Make sure you show up for the right session.
People who filled the 2nd session last time have
first pick if they wish to register for the 1st
session this time.
No wooden model this time... Only straight
mineral identification (mineral name and
formula).
Sulfur (Z=16): 1s2 2s2 2p6 3s2 3p4
In minerals, the common valence states of S are:
S+6: 1s2 2s2 2p6 [3s 3p]emptied as in neon
S-2: 1s2 2s2 2p6 [3s2 3p6]filled as in argon
The difference in electronegativity between S (2.5)
and O (3.5) gives the bond S-O a fairly covalent
character.
In SO42- the 3s and 3p orbitals of sulfur are
hybridized into a tetrahedral arrangement sp3. This
enables electron sharing among 4 identical bonds with
a tetrahedron of four oxygen ions.
Less common: sulfite SO3-2, S+4: 1s2 2s2 2p6 3s2;
hyposulfite (S O -2), S+3: 1s2 2s2 2p6 3s2 3p1.
The bonding of ions with similar
electronegativity values have hardly any ionic
character.
If their electronegativity values are both high,
the bonding will be dominantly covalent.
If their electronegativiy values are both low,
the bonding will be dominantly metallic. Valence
electrons will travel freely throughout the
crystal structure rather than being held by a
single atom or a pair of atoms.
The degree of ionic character for a chemical
bond depends mostly on the difference in
electronegativity between chemical elements.
Pauling’s scale of ionic character:
% = 1 –e0.25 (Xa-Xc)squared
<- Si-O bond
Structures determined by X-ray diffraction
suggest that hybridized orbitals (sp2, sp3, sp3d2)
occur in crystalline structures. Tetrahedral and
octahedral coordinations are particularly common.
sp3 hybridization -- and tetrahedral
coordination with angles of 109.5 degrees-are common:
C-C (diamond)
Si-O (silicate minerals)
S-O (SO4 2- in sulfate minerals)
C (Z=6 1s 2s22p2can form four (4) identical bonds
to other carbon atoms if it promotes one electron
from its 2s orbital to a 2p orbital... and mixes s
and p orbitals into four hybridized sp3 orbitals.
Recognize a fcc cell?
The coordination (no
of nearest neighbors)
is 4. Very hard
(H=10) but cleavable
along (111).
The pair of electron not
used in sp2 forms “pi”
bonding... Electrons can
move among C atoms
parallel to the sheets...
Some metallic character.
The C sheets are electrically neutral... and
held together by the much weaker forces of
Van der Waals bonding.
The 8 most abundant elements in the Earth’s crust
Element Weight% Atom% Volume% Weight%
in crust
total Earth
0
Si
Al
Fe
Ca
Na
K
Mg
46.6
27.7
8.1
5.0
3.6
2.8
2.6
2.1
62.5
21.2
6.5
1.9
1.9
2.6
1.4
1.8
91.7
0.2
0.5
0.5
1.5
2.2
3.1
0.4
29.5
15.2
1.1
34.6
1.1
0.6
0.1
12.7
The bonding character of most mineral
structures can be described as nearly
ionic.
We can use the valence state of anions
and cations to calculate how many
neighbours each ion should have in a
structure, and compare bond strenths
among the different anions by considering
their valence and the distances between
their nuclei.
Given the predominance of oxygen and its
high electronegativity (3.5), it is the main
anion in the Earth’s crust.
As a result, most minerals consist of Si-O
and Me-O bonds (Me = metal, i.e. element
with electronegativity < 2.5) , and are
dominantly ionic in character.
Properties of ionic solids:
- ionic bonds are more soluble in water
- the ions tend to pack as hard spheres
- packing tends to be highly symmetrical
- brittle when deformed (sliding one part of
the crystal over another would bring cations
against cations and anions against anions)
- good cleavage
halite NaCl
fluorite CaF2
Both structures have a face-centered cell.
The ions are “shrunk” for visibility: their nearly
spherical electronic cloud actually occupies all
the available space.
halite, NaCl: a = 5.64, Z = 4, H = 2.5
cubic cleavage
fluorite, CaF2: a = 5.46, Z = 4, H = 4
octahedral cleavage
How are
the ionic radii
(values in
angstroms)
affected by
increasing
atomic number
within a single
family of the
periodic table?
Ion Radius Radius
C.N. = 4 C.N. = 8
+
Li 0.74
0.92
+
Na 1.02
+
K
1.18
1.38
1.51
+
Rb 1.52
1.61
+
1.74
Cs 1.67
Relative sizes of 1s and 2s orbitals in lithium.
The n value of the last shell occupied is an indicator
of the relative size of the electronic cloud.
The ionic character
decreases with
increasing size of either
the cation or the anion.
Large ions are
polarizable, i.e. their
electronic cloud is
deformed. Solids with
the same structure may
show a transition
between ionic character
to slightly metallic
character.
Replace Na+ by Ag+... what do you get?
halite
NaCl
galena
Same structure,
PbS
cubic cleavage
but metallic luster,
opaque streak,
less brittle
and nearly insoluble
Each chemical formula must be electrically
neutral. Some ions can substitute for each
other in a crystalline structure, but they
must be a good “match” for each other in
term of size and charge.
Some minerals are always nearly pure
(diamond, quartz)... Others are members of
compositional series called “solid solutions”.
In others, substitution among ions can occur
but is quite limited (happens only in small
amounts).
Pauling’s Rule 1:
Around every cation, a coordination
polyhedron of anions forms, in which the
cation-anion distance is determined by the
radius sums and the coordination number
(C.N.) is determined by the radius ratio.
Radius ratio: Rx/Rz
where Rx = radius of cation
Rz = radius of anion
C.N.: no of nearest neighbours
C.N.= 4
How are ionic
radii affected
by increasing
atomic number
along a row of
the periodic
table?
NOTE: Most
ions occur in
more than one
C.N.
Ion
Na+
Mg
2+
Radius Radius
C.N. = 4 C.N. = 6
0.99
1.02
0.57
0.72
3+
0.39
0.48
4+
Si
0.26
0.40
P5+
0.17
0.38
S6+
0.12
0.29
2-
1.84
Al
S
-
Cl
1.81
Are these ionic radii physically realistic?
Well, not necessarily.
Look at the values of ionic radii compiled for C+4
and N+5. Do you notice anything odd?
The radii are the space left between oxygen
anions, whose precise position was determined by
X-rays. The size of oxygen anions is calculated
from quantum mechanics.
When they form covalent bonds, oxygens are
drawn closer to the cation than predicted by
ionic radii… because covalent bonding requires
that some orbitals from cation and anion
overlap.
For C-O and NO bonds, the
overlap of
oxygen ions is
counted as a
negative space
left for the
cation radius.
2 ways of packing spheres of equal
size:
I) hexagonal close packing
layer A has B and C voids
layer B… covers B voids
layer A… aligned with 1st layer
layer B… aligned with 2nd layer
II) cubic closest packing
layer A has B and C voids
layer B… covers B voids in layer A
layer C… covers B voids in layer B
Why is this first type of closest packing
called “hexagonal close packing?”
When seen
from above,
the spheres are
in a pattern
with a 6-fold
rotation axis
perpendicular
to each layer.
Each sphere has
exactly 12
neighbours.
Why is this second type of closest packing
called “cubic close packing?”
When seen
from a
different angle,
the spheres are
packed within a
cube.
Each sphere has
exactly 12
neighbours.
Many metals crystallize with hcp or ccp structures...
…but very few of them are minerals. Why?

Structures based on CCP are often isometric, F-cell.
In some minerals, like fluorite and
halite, the large anions are cubic
close-packed, in a face-centered
cell.
In fluorite, the smaller Ca2+
cations occupy the B voids left
between these large anions.
In hcp, the cationic sites could be:
- B voids surrounded by 4 anions
(3 from layer A, 3 from layer B)
-C voids surrounded by 6 anions (3
from layer A, 3 from layer b)
NOTE: a void is a “hole”...
One can prove geometrically
that the smallest ion that
could sit in that hole
without “rattling” must have
a radius of 0.732 or more, if
the ions around have a
radius of 1.0 (units are
unspecified).
A cation surrounded by six
larger anions of radius “1”,
must have a radius between
0.414 (to avoid rattling) and
0.732 (or the anions will be
too far apart to shield it.)
Rx:
usually
the
smaller
cation
Rz: usually
the larger
anion
Rx/Rz
C.N.
Type
1.0
12
hcp or ccp
1.0 - 0.732
8
cubic
0.732 - 0.414 6
octahedral
0.414 - 0.225 4
tetrahedral
0.225 - 0.155 3
trigonal
<0.155
linear
2
The radius ratio rule is a generalization, rather
than a firm prediction. Its usefulness lies in the
fact that exceptions, in specific crystal
structures, are a sign of structures stable at
unusually high temperature or pressure
conditions.
In Al2SiO5
polymorphs, Al
occurs as either
AlO4, (Rx/Rz=0.27)
AlO5 (Rx/Rz=0.34)
AlO6 (Rx/Rz=0.39)
polyhedra.
viAl
2SiO5
ivAlviAlSiO
vAlviAlSiO
5
5
The effect of pressure is to favour higherthan-usual coordination around small cations.
It is as if pressure reduced the size of anions
(here the O2- ions) faster than the size of
the cations (already smaller, less
compressible electronic cloud).
Therefore, more anions than usual can be
packed around a small cation.
Among the aluminosilicates, this is kyanite,
viAl SiO , with Al in 6-fold coordination.
2
5
Rule 3
The sharing of edges, and particularly the
sharing of faces of two anion polyhedra in a
crystal structure decreases its stability.
Sharing of only the corners of
polyhedra places the positively charged
cations at the greatest distance from
each other. This minimizes the repulsive
forces among the cations.
Example of Rule 4
In a crystal structure containing several
cations, those of high valency and small
coordination number tend not to share
polyhedral elements.
In kyanite, Al2SiO5,
SiO4 polyhedra do not
share corners with
similar polyhedra. AlO6
tetrahedra share edges
with each other, and
corners with SiO4.
Could carbonate ions ever
share oxygen anions and
form layered structures?
e.v. strength of
a C4+-O2- bond is calculated
by taking
“charge on cation / C.N.”
= 4/3
An oxygen anion, shared by two C4+ ions, would
receive twice 4/3 valence units = 8/3 (or 2.67),
which far exceeds its need (2)… This is never
observed.
Higher temperatures favour crystal structures
of lower density.
Chemical bonds stretch only slightly at higher
temperatures. Another way to decrease density
without stretching bonds, is to modify the
linkage among polyhedra.
Polyhedra with smaller C.N. tend to share less
edges and more corners. This leads to less
efficient packing. Among polymorphs, higher
temperature favours structures built of
smaller-than-usual coordination polyhedra.
Andalusite, Alvi Alv SiO5
G = 3.2, low pressure
Sillimanite, Alvi Aliv SiO5,
G = 3.23, opposite effects of
pressure and temperature.
Kyanite, Alvi Alvi SiO5
G = 3.6, high pressure
Rule 2, The Electrostatic Valency Principle
An ionic structure will be stable to the
extent that the sum of the strengths of the
electrostatic bonds that reach an ion equal
the charge on that ion.
There are many polymorphs of SiO2, stable at
different ranges of temperature and pressure.
Most of them are built of SiO4 tetrahedra.
We
must first define
electrostatic valency, e.v.
e.v = Charge on the ion / C.N.
C.N. = coordination number
(number of nearest neighbours)
Si+4 (valence: 4), by bonding to four oxygen ions (4
Si-O bonds), satisfies exactly half of the valence
need of O2- (valence:2). This Si-O bonding is said to
be mesodesmic.
Isodesmic structures: all bonds of same e.v. strength
Rule 5, The Principle of Parsimony.
The number of different kinds of
constituents in a crystal tends to be
small.
A typical
hornblende
may include 14
metallic
elements but
they occupy no
more than 5
types of sites.
Throughout the rest of this course we
will see how these principles apply to
minerals, particularly the silicate
minerals.