Another ‘picture’ of atom arrangement

=

Nesosilicates – SiO4

4-

Sorosilicates– Si2O7

6-

Cyclosilicates – Si6O18

12-

Inosilicates (single) – Si2O6

4-

Inosilicates (double) – Si4O11

6-

Phyllosilicates – Si2O5

2-

Tectosilicates – SiO2

0

Pauling’s Rules for ionic structures

1. Radius Ratio Principle – • cation-anion distance can be calculated from

their effective ionic radii• cation coordination depends on relative radii

between cations and surrounding anions• Geometrical calculations reveal ideal Rc/Ra ratios

for selected coordination numbers• Larger cation/anion ratio yields higher C.N. as

C.N. increases, space between anions increases and larger cations can fit

• Stretching a polyhedra to fit a larger cation is possible

Pauling’s Rules for ionic structures2. Electrostatic Valency Principle

– Bond strength = ion valence / C.N.– Sum of bonds to an ion = charge on that ion– Relative bond strengths in a mineral containing

>2 different ions:• Isodesmic – all bonds have same relative strength• Anisodesmic – strength of one bond much stronger

than others – simplify much stronger part to be an anionic entity (SO4

2-, NO3-, CO3

2-)• Mesodesmic – cation-anion bond strength =

½ charge, meaning identical bond strength available for further bonding to cation or other anion

Bond strength – Pauling’s 2nd Rule

Si4+

Bond Strength = 4 (charge)/4(C.N.) = 1

Bond Strength of Si = ½ the charge of O2-

O2- has strength (charge) to attract either anotherSi or a different cation – if it attaches to another Si, the bonds between either Si will be identical

O2-Si4+ Si4+O2-

Mesodesmic subunit – SiO44-

• Each Si-O bond has strength of 1

• This is ½ the charge of O2-

• O2- then can make an equivalent bond to cations or to another Si4+ (two Si4+ then share an O)

• Reason silicate can easily polymerize to form a number of different structural configurations (and why silicates are hard)

Pauling’s Rules for ionic structures

3. Sharing of edges or faces by coordinating polyhedra is inherently unstable– This puts cations closer together and they will

repel each other

Pauling’s Rules for ionic structures

4. Cations of high charge do not share anions easily with other cations due to high degree of repulsion

5. Principle of Parsimony – Atomic structures tend to be composed of only a few distinct components – they are simple, with only a few types of ions and bonds.

Problem:

• A melt or water solution that a mineral precipitates from contains ALL natural elements

• Question: Do any of these ‘other’ ions get in?

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

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:

• Ca0.004Mg1.859Fe0.158Mn0.003Al0.006Zn0.002Cu0.001Pb0.000

01Si0.0985Se0.002O4

• One of the ions is a determined integer, the other numbers are all reported relative to that one.

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 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

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 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

Compositional diagrams

Fe O

FeOwustite

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

• 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

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

• ‘Fudge factor’ from Perkins Box 1.5, pg 22: 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 0.03CaO 56.08 1 1 0.61 0.01088 0.73 Ca2+ 0.73 0.73 0.03Na2O 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