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 Iintroduced binary diagrams before, use a ternary example – feldspar, get figure in here… Go over several examples in class – make sure students understand this – many mneral subclasses differ only in one or the other elemental substitution – garnet as an example may be good – isostructural, two sets of 3 with a ternary substitution Work into functional difference of solid solution – differentiate between minerals of solid solution and ones in which substitution is less interchangable – why the difference – is this a chemical or environmental reason?

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 Go over this example in detail – maybe get a few others together

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 Fe3O4 magnetite FeO wustite Fe2O3 hematite A Fe O A1B2C3 C=50%, B=35%, C=15% A1B1C1 x A1B2C3 x B C

Fe Mg Si fayalite forsterite enstatite ferrosilite Fe Mg forsterite fayalite Pyroxene solid solution  MgSiO3 – FeSiO3 Olivine solid solution  Mg2SiO4 – Fe2SiO4

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: Ca0.004Mg1.859Fe0.158Mn0.003Al0.006Zn0.002Cu0.001Pb0.00001Si0.0985Se0.002O4 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 ‘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