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

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

Goldschmidt’s rules of Substitution

FeS2• What ions would

substitute nicely

into pyrite??

• S- radius=219

pm

• Fe2+ radius=70

pm

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

• (K,Na)0-1(Ca,Na,Fe,Mg)2(Mg,Fe,Al)5(Si,Al)8O22(OH)2

- Hornblende

Actinolite series

minerals

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)4O8

oxide

Atomic

weight

of oxide

(g/mol)

# cations in

oxide

# of O2-

in oxide

Oxide wt %

in the

mineral

(determined

by analysis)

# of moles

of oxide in

the

mineral

mole % of

oxides in

the mineral Cation

moles of

cations

in

sample

moles of O2-

contributed

by each

cation

Number of

moles of

ion in the

mineral

SiO2 60.08 1 2 65.90 1.09687 73.83 Si4+

73.83 147.66 2.95

Al2O3 101.96 2 3 19.45 0.19076 12.84 Al3+

25.68 38.52 1.03

Fe2O3 159.68 2 3 1.03 0.00645 0.43 Fe3+ 0.87 1.30 0.03

CaO 56.08 1 1 0.61 0.01088 0.73 Ca2+ 0.73 0.73 0.03

Na2O 61.96 2 1 7.12 0.11491 7.73 Na+ 15.47 7.73 0.62

K2O 94.20 2 1 6.20 0.06582 4.43 K+ 8.86 4.43 0.35

SUM 1.48569 100 125.44 200.38

# of moles Oxygen choosen: 8

Ca0.73Na15.47K8.86Fe0.87Al25.68Si73.83O200.38

Ca0.03Na0.62K0.35Fe0.03Al1.03Si2.95O8

to get here from formula above, adjust by 8 / 200.38

Compositional diagrams

Fe O

FeO

wustite

Fe3O4

magnetiteFe2O3

hematite

A1B1C1

xA1B2C3

A

CB

x

Fe Mg

Si

fayalite forsterite

enstatite ferrosilite

Pyroxene solid solution MgSiO3 – FeSiO3

Olivine solid solution Mg2SiO4 – Fe2SiO4

Fe Mg

forsteritefayalite