How many molecules? Pyrite FeS 2 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?? FeS 2 S - radius=219 pm Fe 2+ 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*10 24 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)SiO 4 Olivine group mineral composed of 0-100 % of Mg, 100-Mg% Fe
KMg 3 (AlSi 3 O 10 )(OH) 2 - phlogopite K(Li,Al) 2-3 (AlSi 3 O 10 )(OH) 2 lepidolite KAl 2 (AlSi 3 O 10 )(OH) 2 muscovite Amphiboles: Ca 2 Mg 5 Si 8 O 22 (OH) 2 tremolite Ca 2 (Mg,Fe) 5 Si 8 O 22 (OH) 2 actinolite Actinolite series minerals (K,Na) 0-1 (Ca,Na,Fe,Mg) 2 (Mg,Fe,Al) 5 (Si,Al) 8 O 22 (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: Ca 0.004 Mg 1.859 Fe 0.158 Mn 0.003 Al 0.006 Zn 0.002 Cu 0.001 Pb 0.00001Si 0.0985 Se 0.002 O 4 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; SiO 2 =60.08 g/mol) Original analysis Convention for relative oxides (SiO 2, Al 2 O 3, Fe 2 O 3 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 O 8 oxide Atomic weight of oxide (g/mol) # cations in oxide # of O 2- 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 O 2- contributed by each cation Number of moles of ion in the mineral SiO 2 60.08 1 2 65.90 1.09687 73.83 Si 4+ 73.83 147.66 2.95 Al 2 O 3 101.96 2 3 19.45 0.19076 12.84 Al 3+ 25.68 38.52 1.03 Fe 2 O 3 159.68 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 Na 2 O 61.96 2 1 7.12 0.11491 7.73 Na+ 15.47 7.73 0.62 K 2 O 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 Ca 0.73 Na 15.47 K 8.86 Fe 0.87 Al 25.68 Si 73.83 O 200.38 Ca 0.03 Na 0.62 K 0.35 Fe 0.03 Al 1.03 Si 2.95 O 8 to get here from formula above, adjust by 8 / 200.38
Compositional diagrams FeO wustite Fe 3 O 4 magnetite Fe 2 O 3 hematite A Fe O A 1 B 1 C 1 A 1 B 2 C 3 x x B C
Si fayalite forsterite Fe Mg enstatite fayalite ferrosilite forsterite Fe Mg Pyroxene solid solution MgSiO 3 FeSiO 3 Olivine solid solution Mg 2 SiO 4 Fe 2 SiO 4