1. Another ‘picture’ of atom arrangement=

2. Nesosilicates – SiO44- Inosilicates (double) – Si4O116- Sorosilicates
Phyllosilicates
– Si2O52-
Cyclosilicates
– Si6O1812-
Picture of structure of 6 major types of silicates- Klein has one I think – not for painful detail at this point – in later section on silicate minerals we will get into this
Inosilicates
(single)
– Si2O64-
Tectosilicates
– SiO20

3. Pauling’s Rules for ionic structures
Radius Ratio Principle –
cation-anion distance can be calculated from their effective ionic radii
cation coordination depends on relative radii between cations and surrounding anions
Geometrical calculations reveal ideal Rc/Ra ratios for selected coordination numbers
Larger cation/anion ratio yields higher C.N.  as C.N. increases, space between anions increases and larger cations can fit
Stretching a polyhedra to fit a larger cation is possible
Discuss who Linus Pauling was… First to integrate quantum mechanics (wait to now to tell them the orbitals discussed earlier was quantum mechanics) and x-ray diffraction (study of how X-rays interact with repeating structures of minerals). Won 2 nobels – chemistry and peace!
For Radius ratio principle – just discussed ionic radii
Bigger cations – more room to put ions around it…
Thought exercise – stretching a polyhedra – space between cations and anions increases  larger cations will fit and C.N. would increase.
Oppose this to the other direction – can you compress the polyhedra? High P – would you expect the anions to get smaller and lower the Rc/Ra?  would metamorphic minerals then exhibit lower c.n.?
This would require that the anions themselves compress  difference between distorting the structure (easy with higher P) and making the ions themselves smaller (very difficult) and additionally making them change size at different rates relative to one another. Therefore, metamorphic minerals exhibit more distortion, which raises the C.N.!! Garnet a common example – dodecahedral mineral - bring one in for discussion!

4. Pauling’s Rules for ionic structures
2. Electrostatic Valency Principle
Bond strength = ion valence / C.N.
Sum of bonds to an ion = charge on that ion
Relative bond strengths in a mineral containing >2 different ions:
Isodesmic – all bonds have same relative strength
Anisodesmic – strength of one bond much stronger than others – simplify much stronger part to be an anionic entity (SO42-, NO3-, CO32-)
Mesodesmic – cation-anion bond strength = ½ charge, meaning identical bond strength available for further bonding to cation or other anion

5. Bond strength – Pauling’s 2nd Rule
Si4+
Bond Strength of Si = ½ the charge of O2-
O2- has strength (charge) to attract either another
Si or a different cation – if it attaches to another Si, the bonds between either Si will be identical
Bond Strength
= 4 (charge)/4(C.N.) = 1
O2-
Si4+
O2-

6. Mesodesmic subunit – SiO44-
Each Si-O bond has strength of 1
This is ½ the charge of O2-
O2- then can make an equivalent bond to cations or to another Si4+ (two Si4+ then share an O)
Reason silicate can easily polymerize to form a number of different structural configurations (and why silicates are hard)
SiO44- -piz orbitals – add picture of tetrahedra filled in (mesh?)
Discuss why they are hard – strong and equivalent bonds, no zone of weakness
Compare to a mineral like muscovite, which has very weak bonds

7. Pauling’s Rules for ionic structures
3. Sharing of edges or faces by coordinating polyhedra is inherently unstable
This puts cations closer together and they will repel each other
Need picture of a tetraheda to illustrate this sharing princliple – after figure 13.13

8. Pauling’s Rules for ionic structures
4. Cations of high charge do not share anions easily with other cations due to high degree of repulsion
5. Principle of Parsimony – Atomic structures tend to be composed of only a few distinct components – they are simple, with only a few types of ions and bonds.

9. Problem:
A melt or water solution that a mineral precipitates from contains ALL natural elements
Question: Do any of these ‘other’ ions get in?

10. Chemical ‘fingerprints’ of minerals
Major, minor, and trace constituents in a mineral
Stable isotopic signatures
Radioactive isotope signatures
Get this going towards normalization – how do we determine the exact chemical makeup and then how do we deal with classificartion - - interesting case here of how every mineral is essentially unique – African conflict diamonds example, how we ID moon and mars rocks, etc. Use as springboard to discuss in more detail?

11. 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

12. 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 Si0.0985Se0.002O4
One of the ions is a determined integer, the other numbers are all reported relative to that one.

13. 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
Fractionation discussion – go through mathematics of Rayleogh fractionation

14. 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

15. 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 % of Mg, 100-Mg% Fe
Go over this example in detail – maybe get a few others together

16. 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?

17. 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

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

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

20. 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) Hornblende
Actinolite series
minerals

21. 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

22. 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)

23. 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’ from Perkins Box 1.5, pg 22: 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