How many molecules?Goldschmidt’s rules of SubstitutionSlide 3FeS2Slide 5Problem:Chemical ‘fingerprints’ of mineralsMajor, minor, and trace constituents in a mineralStable IsotopesRadioactive IsotopesChemical heterogeneityStoichiometryChemical FormulasSlide 14Minor, trace elementsNormalizationSlide 17Normalization exampleSlide 19Compositional diagramsSlide 21How many molecules?•Pyrite – FeS2•Would there be any other elements in there???Goldschmidt’s rules of Substitution1. 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 minimal3. 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 site4. Substitution may be limited when the electronegativities of competing ions are different, forming bonds of different ionic characterGoldschmidt’s rules of SubstitutionFeS2•What ions would substitute nicely into pyrite??•S- radius=219 pm•Fe2+ radius=70 pmProblem:•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 signaturesMajor, 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 historyStable 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 processesRadioactive 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 processesChemical 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 structureStoichiometry•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 elementsChemical 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 - HornblendeActinolite series mineralsMinor, 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:•Ca0.004Mg1.859Fe0.158Mn0.003Al0.006Zn0.002Cu0.001Pb0.00001Si0.0985Se0.002O4•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 normalizationNormalization•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 anotherFeldspar analysis(Ca, Na, K)1(Fe, Al, Si)4O8oxideAtomic weight of oxide (g/mol)# cations in oxide# of O2- in oxideOxide wt % in the mineral (determined by analysis)# of moles