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

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

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.

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’ 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

Mineral assembly

• Most minerals will deal with ionic bonds between cations and anions (or anionic subunits which are themselves mostly covalent but do not dissociate)

• Assembly of minerals can be viewed as the assembly of individual ions/subunits into a repeatable framework

• This repeatable framework is a crystal or crystalline material

Mineral Assembly

• Isotropic – same properties in every direction

• Anisotropic- different properties in different directions most minerals are this type

• Assembly of ions from melts, water, or replacement reactions which form bonds

• The matrices the ions are in always contain many different ions – different conditions of formation for the same mineral creates differences…

Polymorphs• Two minerals with the same chemical formula but

different chemical structures• What can cause these transitions??

•sphalerite-wurtzite•pyrite-marcasite •calcite-aragonite•Quartz forms (10)•diamond-graphite

Complexes Minerals• Metals in solution are coordinated with ligands

(Such as H2O, Cl-, etc.)• Formation of a sulfide mineral requires direct

bonding between metals and sulfide – requires displacement of these ligands and

deprotonation of the sulfide

• Cluster development is the result of these requirements

Mineral growth

• Ions come together in a crystal – charge is balanced across the whole

• How do we get large crystals??– Different mechanisms for the growth of

particular minerals– All a balance of kinetics (how fast) and

thermodynamics (most stable)

Crystal Shapes

• Shape is determined by atomic arrangements

• Some directions grow faster than others

• Morphology can be distinct for the conditions and speed of mineral nucleation/growth (and growth along specific axes)

Ostwald Ripening

Larger crystals are more stable than smaller crystals – the energy of a system will naturally trend towards the formation of larger crystals at the expense of smaller ones

In a sense, the smaller crystals are ‘feeding’ the larger ones through a series of dissolution and precipitation reactions

Figure 3-17. “Ostwald ripening” in a monomineralic material. Grain boundaries with significant negative curvature (concave inward) migrate toward their center of curvature, thus eliminating smaller grains and establishing a uniformly coarse-grained equilibrium texture with 120o grain intersections (polygonal mosaic). © John Winter and Prentice Hall

Small crystals…

• In the absence of ripening, get a lot of very small crystals forming and no larger crystals.

• This results in a more massive arrangement

• Microcrystalline examples (Chert)

• Massive deposits (common in ore deposits)

Topotactic Alignment•Alignment of smaller grains in space – due to magnetic attraction, alignment due to biological activity (some microbes make a compass with certain minerals), or chemical/ structural alignment – aka oriented attachment