How many molecules?
• Pyrite – FeS2
• Would there be any other elements in
there???
Goldschmidt’s rules of Substitution
1. The ions of one element can extensively
replace those of another in ionic crystals
if their radii differ by less than about 15%
2. Ions whose charges differ by one may
substitute readily if electrical neutrality is
maintained – if charge differs by more
than one, substitution is minimal
Goldschmidt’s rules of Substitution
3. When 2 ions can occupy a particular
position in a lattice, the ion with the
higher charge density forms a stronger
bond with the anions surrounding the site
4. Substitution may be limited when the
electronegativities of competing ions are
different, forming bonds of different ionic
character
• What ions would
substitute nicely
into pyrite??
• S- radius=219
pm
• Fe2+ radius=70
pm
FeS2
Problem:
• A melt or water solution that a mineral
precipitates from contains ALL natural
elements
• Question: Do any of these ‘other’ ions get
into a particular mineral?
Chemical ‘fingerprints’ of minerals
• Major, minor, and trace constituents in a
mineral
• Stable isotopic signatures
• Radioactive isotope signatures
Major, minor, and trace constituents
in a mineral
• A handsample-size rock or mineral has around 5*1024
atoms in it – theoretically almost every known element is
somewhere in that rock, most in concentrations too small
to measure…
• Specific chemical composition of any mineral is a record
of the melt or solution it precipitated from. Exact chemical
composition of any mineral is a fingerprint, or a genetic
record, much like your own DNA
• This composition may be further affected by other
processes
• Can indicate provenance (origin), and from looking at
changes in chemistry across adjacant/similar units - rate
of precipitation/ crystallization, melt history, fluid history
Stable Isotopes
• A number of elements have more than one naturally
occuring stable isotope.
– Why atomic mass numbers are not whole  they
represent the relative fractions of naturally occurring
stable isotopes
• Any reaction involving one of these isotopes can
have a fractionation – where one isotope is favored
over another
• Studying this fractionation yields information about
the interaction of water and a mineral/rock, the
origin of O in minerals, rates of weathering, climate
history, and details of magma evolution, among
other processes
Radioactive Isotopes
• Many elements also have 1+ radioactive isotopes
• A radioactive isotope is inherently unstable and
through radiactive decay, turns into other isotopes
(a string of these reactions is a decay chain)
• The rates of each decay are variable – some are
extremely slow
• If a system is closed (no elements escape) then the
proportion of parent (original) and daughter
(product of a radioactive decay reaction) can yield a
date.
• Radioactive isotopes are also used to study
petrogenesis, weathering rates, water/rock
interaction, among other processes
Chemical heterogeneity
• Matrix containing ions a mineral forms in
contains many different ions/elements –
sometimes they get into the mineral
• Ease with which they do this:
– Solid solution: ions which substitute easily form
a series of minerals with varying compositions
(olivine series  how easily Mg (forsterite) and
Fe (fayalite) swap…)
– Impurity defect: ions of lower quantity or that
have a harder time swapping get into the
structure
Stoichiometry
• Some minerals contain varying amounts of
2+ elements which substitute for each
other
• Solid solution – elements substitute in the
mineral structure on a sliding scale,
defined in terms of the end members –
species which contain 100% of one of the
elements
Chemical Formulas
• Subscripts represent relative numbers of
elements present
• (Parentheses) separate complexes or
substituted elements
– Fe(OH)3 – Fe bonded to 3 separate OH
groups
– (Mg, Fe)SiO4 – Olivine group – mineral
composed of 0-100 % of Mg, 100-Mg% Fe
• KMg3(AlSi3O10)(OH)2 - phlogopite
• K(Li,Al)2-3(AlSi3O10)(OH)2 – lepidolite
• KAl2(AlSi3O10)(OH)2 – muscovite
• Amphiboles:
• Ca2Mg5Si8O22(OH)2 – tremolite
• Ca2(Mg,Fe)5Si8O22(OH)2 –actinolite
Actinolite series
minerals
• (K,Na)0-1(Ca,Na,Fe,Mg)2(Mg,Fe,Al)5(Si,Al)8O22(OH)2
- Hornblende
Minor, trace elements
• Because a lot of different ions get into any
mineral’s structure as minor or trace
impurities, strictly speaking, a formula
could look like:
• Ca0.004Mg1.859Fe0.158Mn0.003Al0.006Zn0.002Cu0.001Pb
0.00001Si0.0985Se0.002O4
• One of the ions is a determined integer, the
other numbers are all reported relative to that
one.
Normalization
• Analyses of a mineral or rock can be reported in
different ways:
– Element weight %- Analysis yields x grams element in
100 grams sample
– Oxide weight % because most analyses of minerals and
rocks do not include oxygen, and because oxygen is
usually the dominant anion - assume that charge
imbalance from all known cations is balanced by some %
of oxygen
– Number of atoms – need to establish in order to get to a
mineral’s chemical formula
• Technique of relating all ions to one (often Oxygen)
is called normalization
Normalization
• Be able to convert between element weight
%, oxide weight %, and # of atoms
• What do you need to know in order convert
these?
– Element’s weight  atomic mass (Si=28.09
g/mol; O=15.99 g/mol; SiO2=60.08 g/mol)
– Original analysis
– Convention for relative oxides (SiO2, Al2O3,
Fe2O3 etc)  based on charge neutrality of
complex with oxygen (using dominant redox
species)
Normalization example
• Start with data from quantitative analysis: weight
percent of oxide in the mineral
• Convert this to moles of oxide per 100 g of
sample by dividing oxide weight percent by the
oxide’s molecular weight
• ‘O factor’ from page 204: is process called
normalization – where we divide the number of
moles of one thing by the total moles  all
species/oxides then are presented relative to
one another
Feldspar analysis
(Ca, Na, K)1 (Fe, Al, Si)4 O8
Oxide wt %
in the
# of moles
mineral of oxide in mole % of
2# cations in # of O (determined
the
oxides in
oxide
in oxide by analysis) mineral the mineral
2-
oxide
Atomic
weight
of oxide
(g/mol)
SiO2
60.08
1
2
65.90
1.09687
73.83
Cation
4+
Si
Al2 O3
Fe 2 O3
CaO
Na2 O
K2 O
101.96
159.68
56.08
61.96
94.20
2
2
1
2
2
3
3
1
1
1
19.45
1.03
0.61
7.12
6.20
0.19076
0.00645
0.01088
0.11491
0.06582
12.84
0.43
0.73
7.73
4.43
Al3+
Fe3+
Ca2+
Na+
K+
1.48569
100
SUM
moles of moles of O Number of
cations contributed moles of
in
by each ion in the
sample
cation
mineral
73.83
147.66
2.95
25.68
0.87
0.73
15.47
8.86
38.52
1.30
0.73
7.73
4.43
1.03
0.03
0.03
0.62
0.35
125.44
200.38
# of moles Oxygen choosen:
8
Ca0.73 Na15.47 K8.86 Fe 0.87 Al25.68 Si73.83 O200.38
Ca0.03 Na0.62 K0.35 Fe 0.03 Al1.03 Si2.95 O8
to get here from formula above, adjust by 8 / 200.38
Compositional diagrams
FeO
wustite
Fe3O4
magnetite
Fe2O3
hematite
A
Fe
O
A1B1C1
A1B2C3
x
x
B
C
Si
fayalite
forsterite
enstatite
Fe
ferrosilite
Mg
fayalite
Fe
forsterite
Mg
Pyroxene solid solution  MgSiO3 – FeSiO3
Olivine solid solution  Mg2SiO4 – Fe2SiO4