another ‘picture’ of atom arrangement =. nesosilicates – sio 4 4- sorosilicates – si 2 o 7...
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Another ‘picture’ of atom arrangement
=
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Nesosilicates – SiO4
4-
Sorosilicates– Si2O7
6-
Cyclosilicates – Si6O18
12-
Inosilicates (single) – Si2O6
4-
Inosilicates (double) – Si4O11
6-
Phyllosilicates – Si2O5
2-
Tectosilicates – SiO2
0
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Pauling’s Rules for ionic structures
1. 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
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Pauling’s Rules for ionic structures2. 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 (SO4
2-, NO3-, CO3
2-)• Mesodesmic – cation-anion bond strength =
½ charge, meaning identical bond strength available for further bonding to cation or other anion
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Bond strength – Pauling’s 2nd Rule
Si4+
Bond Strength = 4 (charge)/4(C.N.) = 1
Bond Strength of Si = ½ the charge of O2-
O2- has strength (charge) to attract either anotherSi or a different cation – if it attaches to another Si, the bonds between either Si will be identical
O2-Si4+ Si4+O2-
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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)
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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
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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.
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Problem:
• A melt or water solution that a mineral precipitates from contains ALL natural elements
• Question: Do any of these ‘other’ ions get in?
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Chemical ‘fingerprints’ of minerals
• Major, minor, and trace constituents in a mineral
• Stable isotopic signatures
• Radioactive isotope signatures
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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
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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:
• Ca0.004Mg1.859Fe0.158Mn0.003Al0.006Zn0.002Cu0.001Pb0.000
01Si0.0985Se0.002O4
• One of the ions is a determined integer, the other numbers are all reported relative to that one.
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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
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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
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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
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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
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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
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Compositional diagrams
Fe O
FeOwustite
Fe3O4
magnetiteFe2O3
hematite
A1B1C1
xA1B2C3
A
CB
x
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Fe Mg
Si
fayalite forsterite
enstatite ferrosilite
Pyroxene solid solution MgSiO3 – FeSiO3
Olivine solid solution Mg2SiO4 – Fe2SiO4
Fe Mg
forsteritefayalite
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• 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
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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
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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)
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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
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Feldspar analysis(Ca, Na, K)1(Fe, Al, Si)4O8
oxide
Atomic weight
of oxide (g/mol)
# cations in oxide
# of O2-
in oxide
Oxide wt % in the
mineral (determined by analysis)
# of moles of oxide in
the mineral
mole % of oxides in
the mineral Cation
moles of cations
in sample
moles of O2-
contributed by each cation
Number of moles of ion in the mineral
SiO2 60.08 1 2 65.90 1.09687 73.83 Si4+73.83 147.66 2.95
Al2O3 101.96 2 3 19.45 0.19076 12.84 Al3+25.68 38.52 1.03
Fe2O3 159.68 2 3 1.03 0.00645 0.43 Fe3+ 0.87 1.30 0.03CaO 56.08 1 1 0.61 0.01088 0.73 Ca2+ 0.73 0.73 0.03Na2O 61.96 2 1 7.12 0.11491 7.73 Na+ 15.47 7.73 0.62
K2O 94.20 2 1 6.20 0.06582 4.43 K+ 8.86 4.43 0.35
SUM 1.48569 100 125.44 200.38
# of moles Oxygen choosen: 8
Ca0.73Na15.47K8.86Fe0.87Al25.68Si73.83O200.38
Ca0.03Na0.62K0.35Fe0.03Al1.03Si2.95O8
to get here from formula above, adjust by 8 / 200.38