Mineral Structures

From definition of a mineral:




“…an ordered atomic arrangement…”
How do Pauling’s rules control “ordered
atomic arrangement?”
How can crystal structure make one
mineral different from another?
Can mineral structures be used to group
minerals (e.g. classify them)?
Illustrations of mineral structures






2-D representation of 3-D materials
Ions represented as spheres – drawn to
scale
Stick and ball method
Polyhedron method
Hybrid: Stick and Ball, plus polyhedron
Map view – unit cell dimensions
Unit cell outline
Olivine – view down
a crystallographic
axis
Fig. 4-10
Structures

Isostructural minerals


Same structure, different composition
Polymorphism – polymorphic minerals

Same composition, different structures
Isostructural Minerals

Many minerals have identical structures,
different compositions



Example: halite (NaCl) and Galena (PbS)
Differ in many physical properties composition
Identical symmetry, cleavage, and habit –
elemental arrangement
Isostructural group




Several isostructural minerals
Have common anion group
Much substitution between cations
Example: calcite group
Polymorphism

The ability for compounds with identical
compositions to crystallize with more than
one structure


Polymorphs
Polymorphic groups

Caused by balance of conflicting
requirements and environmental factors:




Attraction and repulsion of cations and anions
(charge)
Fit of cations in coordination site (size)
Geometry of covalent bonds
P & T primary environmental variables

P and T controls:



Composition of environment unimportant


High P favors tightly packed lattice, high
density
High T favors open lattice, low density, wide
substitution
All same elements in polymorphs
Presence or absence of polymorphs
provide information on P and T conditions

Four types of mechanisms to create
polymorphs:
1.
2.
3.
4.
Reconstructive – break bonds
Order-disorder – cation placement
Displacive – kink bonds
Polytypism – stacking arrangement
1. Reconstructive polymorphism

Requires breaking bonds – major
reorganization



Symmetry and/or structural elements may
differ between polymorphs
Symmetry and/or structural elements may be
similar because identical composition
Example: C
C = Diamond and Graphite



Diamond – all 100% covalent bonds
Graphite – covalent bonds within sheets,
van der Waal bonds between sheets
What conditions cause one mineral or the
other to form?


Graphite – stable at earth surface T and P
Diamond stable only at high P and T – but
found on earth surface


Won’t spontaneously convert to graphite
Minerals that exists outside of their stability
fields are metastable
What are temperatures at these depths?
Found on a Phase Diagram – e.g. for single component
Increasing
Depth
(linear)
~200 km depth
~100 km depth
Single component = C
Increasing
Depth (non-linear)
Where on (in) the earth would diamond form/be stable?
Fig. 4-11
Diamond stability versus geothermal gradient
Kimberlite
Stability
Boundary of
Diamond
and
Graphite
Diamond window
Red line is
geothermal
gradient
Lithosphere
Asthenosphere
Phase diagram
Conceptual model of earth

Metastable minerals occur because of
energy required for conversion




Bonds must be broken to switch between
polymorphs
Cooling removes energy required to break
bonds
Rate of cooling often important for lack of
conversion – e.g. fast cooling removes energy
before reactions occur
Quenching – “frozen”: e.g. K-feldspars

Example of Order-disorder polymorphism
2. Order-disorder polymorphism



The mineral structure remains same
between polymorphs
Difference is in the location of cations in
structure
Good examples are the K-feldspars

One end-member of the alkali feldspars
Idealized feldspar structure
Si or Al
K (or Na, Ca)
Si or Al

K-feldspar has 4 tetrahedral sites called T1 and
T2 (two each)
Fig. 12-6
“K-spars”

KAlSi3O8 – one Al3+ substitutes for one Si4+



High Sanidine (high T) – Al can substitute for
any Si – completely disordered
Low Microcline (low T) – Al restricted to one
site – completely ordered
Orthoclase (Intermediate T) – Intermediate
number of sites with Al
Order-disorder in the K-feldspars
High Sanidine – Al3+ equally
likely to be in any one of
the four T sites
Microcline – Al3+ is restricted
to one T1 site. Si4+ fills other
three sites
Fig. 4-13

Degree of order depends on T





High T favors disorder
Low T favors order
Sanidine formed in magmas found in
volcanic rocks – quenched at disordered
state: metastable
Microcline found in plutonic rocks – slow
cooling allows for ordering to take place
Over time, sanidine will convert to
microcline
3. Displacive Polymorphism



No bonds broken
a and b quartz are good examples
b quartz (AKA high quartz)


1 atm P and > 573º C, SiO2 has 6-fold
rotation axis.
a quartz (AKA low quartz)

1 atm P and < 573º C, SiO2 distorted to 3-fold
axis
View down
c-axis
b quartz
a quartz
6-fold
rotation
axis
3-fold rotation
axis
• Conversion can not be quenched, always happens
• Never find metastable b quartz
Fig. 4-12



External crystal shape may be retained
from conversion to low form
Causes strain on internal lattice
Strain may cause twinning or undulatory
extinction

Must have sufficient space for mineral to form
Undulatory extinction
(4) Polytypism

Stacking diffrences

Common examples are micas and clays
Common Sheet silicates – like clay minerals
Orthorhombic,
single stacking
vector, 90º
Orthorhombic,
two stacking
vectors, not 90º
Monoclinic,
single stacking
vector, not 90º
Fig. 4-14


Eventually will get to controls on
compositional variations
First some “housekeeping” – necessary
skills:



Scheme for mineral classification
Rules for chemical formulas
A graphing technique – ternary diagrams
Mineral Classification

Based on major anion or anionic group



Consistent with chemical organization of
inorganic compounds
Families of minerals with common anions
have similar structure and properties
Cation contents commonly quite variable

Follows from Pauling’s rules


1, 3, and 4 (coordination polyhedron &
sharing of polyhedral elements) - anions
define basic structure
2: (electrostatic valency principle) anionic
group separate minerals
Mineral group
Native elements
Oxides
Hydroxides
Halides
Sulfides
Sulfates
Carbonates
Phosphates
Silicates
Anion or anion gp
N/A
O2OHCl-, Br-, FS2SO42CO32PO43SiO44-
Mineral Formulas

Rules




Cations first, then anions or anionic group
Charges must balance
Cations of same sites grouped into
parentheses
Cations listed in decreasing coordination
number
Thus also decreasing ionic radius
 Also increasing valence state

Examples

Diopside – a pyroxene: CaMgSi2O6





Charges balance
Ca - 8 fold coordination: +2 valence
Mg - 6 fold coordination: +2 valence
Si – 4 fold coordination: +4 valence
Anionic group is Si2O6

Substitution within sites indicated by
parentheses:
Ca(Fe,Mg)Si2O6
 Intermediate of two end-members: Diopside
CaMgSi2O6 – Hedenbergite CaFeSi2O6
complete solid solution series
(more on “solid solution” in a moment)


Can explicitly describe substitution


E.g. Olivine: (Mg2-x,Fex)SiO4
0≤x≤2
Alternatively: Can describe composition by
relative amounts of end members:


Forsterite = Fo
Fayalite = Fa


General composition of olivine is
(Mg,Fe)2SiO4
All of the following are the same exact
composition:





(Mg0.78Fe0.22)2SiO4
Mg1.56Fe0.44SiO4
Fo78Fa22 (here numbers are percentages of
amount of each mineral)
Fo78 (here implied that the remainder is Fa22)
Fa22
How to calculate chemical
formulas for solid solutions

Eg. Plagioclase feldspars:



Albite, Ab – NaAlSi3O8
Anorthite, An – CaAl2Si2O8
What is chemical composition of say
Ab25An75?
Graphic representation




Common to have three “end members”
Ca2+, Mg2+ and Fe2+ common substitutions
between silicate minerals
Also K, Na, Ca – e.g. the Feldspars
Ternary diagrams


Used to describe distribution of each end
member
Total amount is 100%
See page 84
Ca2Si2O6
8% Fs
Pyroxenes:
(Mg,Fe,Ca)2Si2O6
50% Wo
Composition is:
En42Fs8Wo50
(Mg0.42Fe0.08Ca0.5)2Si2O6
Mg2Si2O6
42% En
Fe2Si2O6
Fig. 4-17
Compositional Variation

Think of minerals as framework of anions




Form various sites where cations reside
Principle of parsimony
Not all sites need to be filled
Some sites can accommodate more than one
type of ion (e.g. polymorphism in feldspar,
solid solution in olivine)

Solid solution



Occurs when different cations can occur in a
particular site
Three types: Substitution, omission, and
interstitial
Anions can substitute for each other, but
this is rare
Tourmaline – an example
of extreme amount of
substitution
Na(Mg,Fe,Li,Al)3Al6[Si6O18] (BO3)3(O,OH,F)4
W = 8-fold coordination, not cubic; usually
Na, sometimes Ca or K
X = Regular octahedral; usually Mg and Fe,
sometimes Mn, Li, and Al
Y = 6-fold coordination; usually Al, Less
commonly Fe3+ or Mg, links columns
B = trigonal; Borate ions, B is small,
Fig. 15.9
Terms


Substitution series or solid solution series:
the complete range of composition of a
mineral
End members: the extremes in the range
of compositions

E.g. olivine: Forsterite and Fayelite
Terms

Continuous or complete solid solution
series: all intermediate compositions are
possible


E.g. Olivine
Incomplete or discontinuous solid solution
series: a restricted range of compositions

E.g Calcite - magnesite
Substitutional Solid Solution

Two requirements for substitution


Size – substituting ions must be close in size
Charge – electrical neutrality must be
maintained
Size


Comes from Pauling rule 1: coordination
In general size of ions must be < 15%
different for substitution



Tetrahedral sites: Si4+ and Al3+
Octahedral sites: Mg2+, Fe2+, Fe3+, Al3+
Larger sites: Na+ and Ca2+

Temperature is important




Example is K and Na substitution in alkali
feldspar (Sanidine and Albite)
Size difference is about 25%
Complete solid solution at high T
Limited solid solution at low T

Results in exsolution
Types of substitution

Substitutional solid solution





Simple substitution
Coupled substitution
Omission substitution
Interstitial substitution
Different types have to do with where the
substitution occurs in the crystal lattice
Simple Substitution


Occurs with cations of about same size
and same charge
Example: Olivine
Olivine - (Fe.22Mg.78)2SiO4
View down a axis
22% Fe
78% Mg
Fig. 4-15
Coupled Substitution

Coupling two substitutions



One that raises charge
Linked one that decreases charge
Example: Albite (NaAlSi3O8) and Anorthite
(CaAl2Si2O8)


Ca and Na occupy distorted 8-fold site
Al and Si occupy tetrahedral sites
Coupled substitution in different sites
Coupled substitution:
Na+ + Si4+ = Ca2+ + Al3+
Fig. 4-15
Coupled substitution

The substitution doesn’t always have to be
different sites




Corundum (Al203)
Fe2+ and Ti4+ substitute for 2Al3+ (makes
sapphire). Cr3+ makes Ruby
Both elements are in octahedral sites
Can couple cations and anions

Hornblende: Fe2+ and OH- substitutes for Fe3+
and O2-
Omission substitution





Charge balance maintained by leaving site
vacant
Pyrrhotite: variable amounts of Fe2+ and
Fe3+
Formula: Fe(1-x)S where 0<X<0.13
General substitution:
(n+1)Mn+ = nM(n+1)+ + □

where □ is vacant, n is the number of sites
14Fe2+ = 8 Fe2+ + 4 Fe3+ + 2□
28+ = 28+
14 sites = 14 sites
Fig. 4-15
Interstitial substitution


Type of omission substitution
Difference is that regular lattice
framework site is not location of
substitution



Example: Beryl, a ring silicate
Al3+ substitution for Si in tetrahedral sites
Balanced by K+, Rb+ and Cs+ substitution in
open “channel” sites
Charge balance
maintained by interstitial
substitution
Al, Be substition for Si
Fig. 4-15
Structure of Beryl
Be3Al2Si6O8
Silicate Rings
Substitution important: Cr
substition makes emerald,
other substitutions make
Aquamarine – blue green
variety of emerald
Al 6-fold coordination
Be 4-fold coordination
Fig. 15-6