How many molecules Pyrite FeS2 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 S radius 219 pm Fe2 radius 70 pm FeS2 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 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 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 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 Actinolite series minerals K Na 0 1 Ca Na Fe Mg 2 Mg Fe Al 5 Si Al 8O22 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 Ca0 004Mg1 859Fe0 158Mn0 003Al0 006Zn0 002Cu0 001Pb 0 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 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 4O8 Oxide wt in the of moles mineral of oxide in mole of 2 cations in of O determined the oxides in oxide in oxide by analysis mineral the mineral 2 oxide Atomic weight of oxide g mol SiO2 60 08 1 2 65 90 1 09687 73 83 Si Al2O3 Fe 2O3 CaO Na2 O K2O 101 96 159 68 56 08 61 96 94 20 2 2 1 2 2 3 3 1 1 1 19 45 1 03 0 61 7 12 6 20 0 19076 0 00645 0 01088 0 11491 0 06582 12 84 0 43 0 73 7 73 4 43 Al 1 48569 100 SUM Cation 4 3 Fe3 Ca2 Na K moles of moles of O Number of cations contributed moles of in by each ion in the sample cation mineral 73 83 147 66 2 95 25 68 0 87 0 73 15 47 8 86 38 52 1 30 0 73 7 73 4 43 1 03 0 03 0 03 0 62 0 35 125 44 200 38 of moles Oxygen choosen 8 Ca0 73 Na15 47 K8 86 Fe 0 87 Al25 68 Si73 83 O200 38 Ca0 03 Na0 62 K0 35 Fe 0 03 Al1 03 Si2 95 O8 to get here from formula above adjust by 8 200 38 Compositional