Lecture 10: Crystal Structures and Solid Solutions Read Chpt 2

Lecture 10:
Crystal Structures and Solid Solutions
How can we use symmetry to figure out what the internal structure of a
mineral looks like??
Example: Halite (NaCl(
NaCl)
External Morphology: cubes
Symmetry of these cubes: 4/mbar32/m = isometric crystal system
So, this suggests a unit cell with a=b=c, !="=#= = 90°
From XRD: a=5.64Å
From chemical measurements, Na:Cl
is 1:1
Molecular weight of NaCl: : 23g/mol (Na) + 35 g/mol (Cl)) = 58g/mol
Density measurements: 2.165 g/cm 3
Read Chpt 2

How can we use symmetry to figure out what the internal structure of a
mineral looks like??
How many Na and Cl atoms in a unit cell?
Unit cell volume = a 3 = (5.64Å) 3 = 179.4Å 3
Formula.units = mol
58g ! 2.165g ! 179.4Å3
23
6.023!10
!
cm 3 unitcell mol
cm 3
!
10 24 Å = 4 3
So, each unit cell should have 4 NaCl molecules (4 Na and 4 Cl ions)
These need to be arranged to keep the 4/mbar32/m symmetry

Many minerals share the same geometric structure, but built
from different atoms; this is called: ‘Isomorphism’ or
‘Isostructuralism’
Mineralogists often refer to ‘isostructural
groups’, , that is
groups of minerals that have the same coordination
geometry, , but are built out of different elements; ; usually
these groups have the same anion, but different cations,
an because of their structural similarity, it’s common to
have ‘substitution’ of one cation for another in these
minerals

Some Common Stucture Types
NaCl Structure:
Built from AX compounds; A = cation and X = anion
The anions are in ‘Cubic Closest Packing’ (CCP), also referred to as
‘ABCABC…’
packing, where A, B and C are layers of hexagonally closest
packed anions.
Hexagonal Packing (HP): each atom ‘sphere’ is surrounded by 6
others to form a hexagon pattern, the maximum ‘touching’
between spheres that can be achieved in 2D
ABC means that the layers are not directly on top of each other,
they are offset so that the spheres settle into ‘holes’ between
spheres in layers above and below, 6-fold coordination; edge
sharing octahedra result

Some Common Structure Types
CsCl Structure:
Built from AX compounds but with larger radius ratio than NaCl, , I.e.,
typically with larger cations
The anions are now in ‘Simple Cubic Packing’ (SCP),
8-fold cubic
polyhedra which share faces

Some Common Structure Types
Sphalerite (ZnS)) Structure:
Built from AX compounds but now with smaller radius ratio than NaCl, , I.e.,
typically with smaller cations
The anions are now in 4-fold coordination. This is the diamond structure --
you just replace half of the C by Zn and the other half of the C by S.

Some Common Structure Types
CaF 2 Structure:
Now consider an AX 2 compound
Each Ca +2 is surrounded by 8 F - and each F - is surrounded by 4 Ca +2
Looks just like the CsCl structure, except that half of the Cs + sites are vacant!!
The anions are now in ‘Simple Cubic Packing’ (SCP),
8-fold cubic polyhedra
which share faces

Structure Types
We will talk about the remaining crystal structures (especially for silicates!!)
as we talk about the various mineral groups.
Remember: isostructural groups may have “substitution” of cations from other
members of the group into the cation structure sites. This is a type of:
Solid Solution: a mineral structure in which specific atomic
sites are occupied in variable proportions by two or more
different chemical elements (or vacancies)
There are 3 different types of solid solution, the most important of which is
called “substitutional
solid solution’

Solid Solutions
1. Substitutional Solid Solution (based on ‘impurity’
defects); cations (usually) that aren’t t typically a part of
the mineral formula go into structural sites normally
occupied by other cations that are part of the mineral
formula
Complete binary solid solution series: substitution
of one element for another is possible over the entire
compositional range; ; that is, from one ‘endmember’ all
the way to the other endmember
Endmember: sites are all filled by one substituting ion
or the other

Solid Solutions: Substitutional Solid Solution
Example:
Olivine endmember minerals
Forsterite (Mg 2 SiO 4 ) and Fayalite (Fe 2 SiO 4 )
Mg +2 $% Fe +2 : all compositions from forsterite or
fayalite are possible and can occur in nature. Thus, we
write the general olivine formula as:
(Fe,Mg) 2 SiO 4

Solid Solutions: Substitutional Solid Solution
Olivine is an example of a:
Simple Substitution: trade ions of the same charge, , e.g.,
Fe +2 for Mg +2 or Al +3 for Fe +3
It is also possible to have:
Coupled Substitution: trade ions of different charges;
need to trade pairs to maintain electroneutrality
Example: Ca +2 + Al +3 = Na + + Si +4
This is common in feldspars.
NaAlSi 3 O 8 (albite)) to CaAl 2 Si 2 O 8 (anorthite)
But you can maintain neutrality another way, too:
Ex. Na + + Al +3 = Si +4 + EMPTY SITE

Solid Solutions:
This is an example of…
Ex. Na + + Al +3 = Si +4 + EMPTY SITE
2. Omission solid solution: highly charged cation replaces
two or more other cations, , leaving structural vacancies
Example: Pyrrhotite (Fe
(Fe 1-x S)
Note: if all sites were full, would be FeS, , instead, some Fe sites are
vacant and some have Fe +3 to compensate for the missing Fe +2

Solid Solutions:
Last type of solid solution:
3. Interstitial solid solution: ‘holes’ in the structure have extra
ions stuffed into them
Example: Zeolites

What determines the extent of solid solution?
1. Comparative sizes of atoms, ions or groups
substitution is no problem
>30% size difference --> substitution will not occur
2. Charges of ions: need to maintain electroneutrality
3. Temperature: more substitution at higher temperature
Why? Because increased thermal vibrations increase site sizes