How Many Molecules? Pyrite Cube weighs 778 g – how many molecules is that?? About 4,000,000,000,000,000,000,000,000 Are they ALL Iron and Sulfur?

Stoichiometry Some minerals contain varying amounts of 2+ elements which substitute for each other Solid solution – specific elements substitute for each other in the mineral structure, 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 that go into a particular place –Fe(OH) 3 – Fe bonded to 3 separate OH groups –(Mg, Fe)SiO 4 – Olivine group – mineral composed of % of Mg, 100-Mg% Fe

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

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 Goldschmidt’s rules of Substitution

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 (K,Na) 0-1 (Ca,Na,Fe,Mg) 2 (Mg,Fe,Al) 5 (Si,Al) 8 O 22 (OH) 2 - Hornblende Actinolite series minerals

Compositional diagrams FeO FeO wustite Fe 3 O 4 magnetite Fe 2 O 3 hematite A1B1C1A1B1C1 x A1B2C3A1B2C3 A CB x

Fe Mg Si fayaliteforsterite enstatite ferrosilite Pyroxene solid solution  MgSiO 3 – FeSiO 3 Olivine solid solution  Mg 2 SiO 4 – Fe 2 SiO 4 FeMg 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: Ca Mg Fe Mn Al Zn Cu Pb Si Se 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 ‘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