Lecture 1 – Introduction to Mineralogy

Minerals are:1) naturally occuring 2) homogenous 3) solids (exception is Mercury which is liquid at room temperature)4) definite chemical composition (though not fixed, substitutions may occur)5) highly ordered atomic arrangement (mineraloids lack this, metaminct minerals lack it due to the

degradation of it's internal structure by radioactive decay of it's constituents)6) formed by inorganic processes (when organic, known as biogenic minerals)

Unit cell: basic building block, contains all of the symmetry and chemical information for a mineral, if you were to repeat it regularly you'd get a mineral. Cannot be broken into smaller parts. Smallest unit.

Development of crystal faces depends on: 1) cooling time (slow cooling means more crystal faces, rapid means fewer)2) pressure (in high pressure environments more faces will form)3) space (more spaces will grow if there is more space)

Euhedral: completely bound by crystal facesSubhedral: partially bound by crystal facesAnhedral: no crystal faces

Reflection: symmetry with respect to a planeRotation: symmetry with respect to an axisInversion: symmetry with respect to a point

Lecture 2 – Point Groups and Crystal Systems

Sides AnglesTriclinic a ≠ b ≠ c α ≠ β ≠ γ ≠ 90º

Monoclinic a ≠ b ≠ c α=γ=90º, β>90ºOrthorhombic a ≠ b ≠ c α = β = γ = 90º

Tetragonal α = β = γ = 90ºHexagonalIsometric α = β = γ = 90º

a1= a2 ≠ ca1=a2=a3≠ c a,b,c = 120º

a1=a2=a3

ba b ccc

4 diagonals 6 edges

1st 2nd 3rd

a1,a2 45º from a1,a2

a1,a2,a3 30º from a1,a2,a3

a1,a2,a3

No Centre Centre Summary1 1 No symmetry

2/m One 2x, or m222, 2mm 2/m 2/m 2/m Three 2x Axes

One 4x AxisOne 6x or 3xFour 3x Axes

2, 2

4, 4, 422, 4mm, 42m 4/m, 4/m 2/m 2/m3, 32, 3m, 6, 6, 622, 6mm, 62m 3, 3 2/m, 6/m, 6/m 2/m 2/m

23, 432, 43m 2/m 3, 4/m 3 2/m

Lecture 3 – Crystallization

Crystal growth is related to:1. Nucleation2. Transport3. Crystal face growth

Nucleation: occurs as a result of a decrease in free energy in a system, nucleation will only occur if a nucleated or solid state is more stable than the state of the melt. For this to occur, there are barriers to overcome: the thermal energy barrier and the surface forming energy barrier. High temperatures do not favour nucleation (high temperatures means lots of ionic energy which means less likelihood of stability as a nucleus). Forming faces requires a lot of energy, when they're small the surface energy contributions are small, but obviously larger crystals will have greater energy barriers to overcome as they increase in size. Therefore to promote nucleation we must: decrease temperatures, increase pressure, and introduce impurities (nucleation substrates).

1. Homogenous nucleation: formation of a stable critical nucleus (embryo) in a melt due to undercooling.

Δ Gv = (Δ Gformation of a crystal + Δ Gformation of a melt) v

For the formation of a nucleus to be favourable, Δ G<0 (solid has a lower energy configuration than the same atoms in a melt. If Δ G=0, the melt and solid have the same energy configuration and if ΔG>0, the melt has a lower energy configuration than the solid state.

Δ Gs = γ a = γ 4π 2

Where γ is the surface energy per unit area, and a (or 4π 2) is the surface area of the cyrstal or nucleus.

Undercooling: lowering the temperature of a phase below the point or range at which a phase change would occur at equilibrium. Slows ionic motion, generates supersaturation, and creates an all-aroud unstable melt which makes rapid nucleation and crystal growth favourable.

2. Heterogenous nucleation: the formation of a nucleus by taking advantage of a previously existing mineral structure, avoids the energy requirements to form your own free-floating embryo.

Transport: things we need to transport include heat (we need to get rid of it to promote clumping, no one is clumping in a high energy atomic shitshow), and new materials for rock building into the nucleation area, and garbage products away (you need to feed your mineral).

1) Transfer heat: radiation, conduction or convection, anything to get rid of it. Latent heat is seriously detrimental to making your rock.

2) Increasing concentration: if you give your nucleus more to work with, it's more likely to grow.

3) Changing composition: mixing some other stuff in for kicks. Try it.

More importantly: the rate determining step is always the slowest. You might have gotten rid of your heat, but if there's no Calcium and you really need it, your nucleus baby will die.

Removal of heat: not uniform, there's a larger surface area for heat exchange at the corners, so you lose it faster there. Since the heat is lost faster at the corners, your mineral's corners will also form faster, followed by the edges, and lastly by the faces. Dendrites form because of the whole heat lost at corners effect, tree-like branchings of crystals from rapid crystallization and undercooling – the heat really had to go and it really wanted to keep growing.

• When growth is slow, neither heat dissipation nor diffusion are significant in crystal growth, those only reall dominate when there's a high ammount of undercooling.

Midterm Question (crystals will be bigger in this condition rather than that, because?):

High is preferred over low density of nucleii: lots of nucleii return to the melt, better chances if there are more.Slow cooling is favoured to rapid cooling: more time to crystallize, more time to growCalm environments are favoured to turbulent: less energy in the system means more nucleationSmall degrees of undercooling are preferred to large: promotes crystal growth, but way too quickly if there's a lot of it, would be dendritic bullshit.

Law of Bravais: the most prominent faces of a crystal are those that are parallel to internal planes having the greatest density of lattice points. Lattice points can be thought of as the connections in a fishing net. The connections representing either atoms or atomic groups in a mineral.Each lattice point represents an atom or atomic group. Unit cells will more frequently attach to crystal faces having the smallest interplanar spacings.

Lecture 4: Twinning and Intergrowths

Intergrowths

1. Aggregate: intergrowth of randomly oriented crystals.2. Parallel Growths: aggregate of identical cyrstals with parallel crystallographic faces and axes,

they're technically one mineral though because their structure remains unchanged throughout the specimen.

3. Epitaxis: Intergrowth of 2 different minerals. Overgrowth occurs along crystallographic planes along which there is a good fit between the 2 interal structures.

Twinning

• Symmetrical intergrowth of 2 or more crystals of the same mineral. Minerals are related by a symmetry element that was absent in the original minerals. Twins inrease the apparent symmetry of a mineral. Minerals can twin because sometimes it's energetically favourable.

Symmetry operators: twin plane, twin axis, twin centre. A twin law is the nature of the symmetry element between the two individuals twinned. Composition plane is the plane on which the twins are joined. Twin planes are never parallel to existing mirror planes.

1. Contact: well-defined composition plane between two minerals.2. Penetration: irregular, interpenetrating, twin law defined by twin axis.3. Polysynthetic: two or more parallel composition planes.4. Cyclic: two or more non-parallel composition planes.

Causes of twinning:1) Growth – Something grew in irregular spot due to an accident during crystallization or

nucleation and the mineral just kept growing around it. Primary twinning.2) Transformation – Result of a change to pressure and temperature in pre-existing crystals. At

higher temperatures particles can vibrate around and find new spots. Secondary twinning. 3) Glide – Result of shear stress causes atom slippage. Secondary twinning.

Polymorph: same chemical formula, different structure.Isostructural: same structure, different chemical formula.

Polymorphism: ability of a chemical substance to crystallize with more than 1 type of structure (or polymorphs).

Types of polymorphism:

1) Reconstructive: internal rearrangement which involves breaking atomic bonds and reassembling a new strucutral unit in a new arrangement

2) Displacive: no bonds are broken and only slight displacement of ions is needed with readjustment in going from one form to the other, you only need to kink the structure.

3) Order-Disorder: temperature changes cause natural change (more vibration and molecular shifting at higher temperatures)

• Sanidine(hi T) – Totally disordered – (25% chance of Al and 75% chance Si in T1 and T2)• Orthoclase (med T)- Partially ordered (50% Si/Al in T1 sites, 100% Si in T2)• Microcline (lo T) – Totally ordered (100% Al in the T1o site, 100% Si in T2 and T1m)

Lecture 5 – Bonding and Pauling

Abundant minerals: O, Si, Al, Fe, Ca, Na, K, Mg

Atomic Radius: radius in covalent molecules, since there's equal sharing, it only really applies for diatomic molecules or covalent molecules.

Ionic Radius: in ionic compounds there's uneven sharing of electrons and ions have different shapes based on their charges (due to electron hugging and stuff). So if you want to know the size of an atom in an ionic compound, you sue the ionic radius. Ionic radius increases DOWN a group and to the LEFT of a period. There are exceptions due to orbitals (d orbitals hug super tight so when they're introduced the atoms get smaller for a second, eventually that effect cancels out though).

Valence State: depends on temperature, composition, and redox potnential. Increasing the positive charge makes ions smaller.

Ionization Potential: the energy required to remove the weakest held atom from an atom. Easier to remove from large, low charge density atoms. Very hard to remove from tiny, high charge density atoms.

Electron Affinity: the amount of energy released when you give an atom an electron. Easy to force your electrons on smaller atoms who's nucleus still has some effect, but huge atoms don't need that extra electron baggage, and certain elements with full orbitals might also reject an extra electron.

Electronegativity: ability to attract electrons within a molecule.

Types of bonding:1. Ionic: high electronegativity differences, full transfer of electrons. No sharing, non-directional

bond. Poor conductors, moderate hardness and specific gravity. High melting point, high symmetry.

Ionic Character = 1-e1/4(Xa-Xb). Where Xa and Xb are electronegativities of ions.

2. Covalent: similar electronegativities, highly directional bonds with orbital overlap. Insoluble, high melting point, non-conductors with low symmetry.

3. Metallic: outer electrons are loosely held and can float around and mingle with other atoms. Like an electron sharing orgy. Common in native elements, and you know, metals. Good conductors that are ductile and malleable.

4. Hydrogen: electrostatic attraction between positive Hydrogen atom and negatively charged ion. Common in clays and micas. Weak bonds, not as weak as VDW

5. Van der Waal: Super weak bonds that link neutral polar molecules together as a result of the formation of an electric dipole, resulting in a dipole-dipole interaction. Uncommon in crystalline solids but exists in micas and stuff.

Diamond: isometric holohedral, covalent sp3 hybrid, 4 bonding electrons, hardness of 10, adamantine lustre, poor conductors. Stable at pressures greater than 50Kb.Graphite: hexagonal holohedral, covalent sp2 hybrid with VDW, 3 bonding electrons, hardness of 1-2, dull or metallic lustre, good conductors. Stable at pressures less than 50Kb.

Coordination number: how many anions a cation can surround itself with, or however many cations an anion can surround itself with.Coordination polyhedra: the shape those bonds make!

Pauling's Rule 1 : cation/anion distances are determined by the radius sum and the coordination number by the radius ratio.

Radius Ratio = Radius of Cation/ Radius of AnionRadius Ratio Coordination Number Polyhedra

<0.155 2 Linear

0.155<RR<0.225 3 Triangular

<0.225<RR<0.414 4 Tetrahedral

0.414<RR<0.732 6 Octahedral

0.732<RR<1.00 8 Cubic

1 12 Cation and anion are the same size.

Pauling's Rule 2: Electrostatic Valency Principle. Rule that explains bonding in and between polyhedra. Charge of an atom is distributed amongst the bond it makes.

Bond Strength = Charge/Coordination Number Bond strength can qualify a mineral as Isodesmic (all bonds of equal strength scation<½), Anisodesmic (scation>½ ,tight bonds, small tight cations with less dense anions), or Mesodesmic (bond strenght= ½, can polymerize or form dimers and stuff).

Pauling's Rule 3: Sharing of Polyhedra Elements 1. Rule that explains bonding in and between polyhedra. Sharing corners is more stable. Sharing edges is less, and sharing faces is just stupid.Pauling's Rule 4: Sharing of Polyhedra Elements 2. If you have high valency cations with small radii, they will probably only share corners.Pauling's Rule 5: Parsimony. Though it looks complicated, it's not.

Lecture 6 – Substitutions and Defects

• There are relatively few sites in a mineral for cations and anions, we get species due to substitution. Substitutions occur in isostructural minerals.

Solid Solution: a prominent substitution. Can be represented by a solid solution series, with end members.

Substitutions depend on:1) Ion size – If the difference is more than 15%, the substitution is unlikely.2) Charges Involved – If the valency varies by more than 1, it's unlikely.3) Ionization Potential – If the ionization potential differs by more than 25%, it's unlikely4) Temperature – temperatures favour substitution because molecules can hover around (Debye-

Waller temperature factor).

Exsolution: Homogenous solid separates into 2 distinct crystalline phases without the addition or subtraction of starting materials. The product is oriented lamellae of the lesser complementary phase in a greater host. Exsolved material may be entirely rejected or form as a non-coherent mass.

Types of Solid Solution:1) Substitutional: an element replaces another, may be partial(limit to degree at which solid

solution can occur) or extensive(100%)2) Interstitial: atoms or ions sit in voids or channels or pores. 3) Omission: one highlly charged ion replaces two or more cations for charge balance purposes,

occurs in one site, leaving the other vacant.• Shottky Defect: Absence of a cation or anion from it's proper site and it's relocation to an

interstitial site.• Frenkel Defect: Complete absence.

Zeolites: molecular sieves, porous aluminosilicates of aluminium and silicon tetrahedra, low temperature minerals which form in basalt cavities. Aluminium gives the interal structure a negatively charged framework, which is counter-balanced by a positively charged cation which results in a strong electrostatic field on internal surface, cations can be exchanged to adjust the size of the pore.

Lecture 7: Tectosilicates

• Silicates are 25% of the Earth's minerals.• Plagioclase feldspar, Alkali feldspar, Quartz, Pyroxenes, Amphiboles, Micas, Clays, Other

Silicates, Other Non-Silicates

Silicates: silicon tetrahedra are main building block. Si4+ coordinated by 4O2-, which is a mesodesmic compound (can polymerize).

Subclasses of Silicates:1) Nesosilicates (4:1)– isolated tetrahedra, (SiO4)4-

2) Sorosilicates (3.5:1)– SiO4 dimers, (Si2O7)6-

3) Cyclosilicates (3:1)– SiO4 rings, (Si6O18)12-

4) Inosilicates (3:1/2.75:1)– SiO4 chains, single pyroxenes (Si2O6)4-, amphiboles double (Si4O11)6- 5) Phyllosilicates (2.5:1) – sheets of tetrahedra, (Si4O11)4-

6) Tectosilicates (2:1)– 3D framework of tetrahedra (Si2O)0

Feldspars: framework silicates linked by corner sharing, large cations filling voids for charge balancing. Four-membered rings of tetrahedra are linked into slightly offset chains like a double-crankshaft, expressed outwardly as 90 degree cleavage. Silicon and Al distributed amongst T sites. [9]coordinated Na, Ca, and K fill voids in alrge interstices.

AT4O8

T= [9]-[13], large monovalent or divalent cationsA= [4] T1 and T2 sites

Alkali Feldspars: NaAlSi2O8 – Albite, KAlSi3O8 - Orthoclase, SanidinePlagioclase Feldspars:NaAlSi3O8 – MicroclineCaAl2Si3O8 – Anorthite Complete solid solution between albite and anorthite.

Sanidine - 2/m (hi T) – Totally disordered – (25% chance of Al and 75% chance Si in T1 and T2)Orthoclase - 2/m (med T)- Partially ordered (50% Si/Al in T1 sites, 100% Si in T2)

Microcline Triclinic - (lo T) – Totally ordered (100% Al in the T1o site, 100% Si in T2 and T1m)

Lecture 8 – Phyllosilicates

• 3 bonding oxygens, one non-bonding, flaky or platy habit, soft, low hardness, low specific gravity, good basal cleavage, generally hydrated with OH or H2O, flexible or elastic cleavage. 2D sheets of silicon tetrahedra.

• [Si2O5]2-

T-Sheet: Tetrahedral sheet, it has a net negative charge which allows it to bond to cations.O-Sheet: Total 6+ charge, can be dioctahedral or trioctahedral. Base of O-sheets are made of 2 oxygens and 1 OH- which needs to be charge balanced. Must bond to another O-sheet, a T-sheet, or add some OH- groups.Trioctahedral Sheet: divalent in cations in all 3 octahedral sites. No solid solution with dioctahedral, phlogopite, biotite, annite, lepidolite.Dioctahedral Sheet: trivalent cations in 2-3 octahedral sites. No solid solution with trioctahedral, muscovite, paragonite, glauconite.

1:1 Phyllosilicates: TO TO TO, hydrogen bonds holding TO's together, with VDW, serpentine2:1 Phyllosilicates: TOT TOT TOT, VDW forcesTrue Micas: TOT MONOVALENT TOT MONOVALENT TOT, we bend – TOT-1 + K, NaBrittle Micas: TOT DIVALENT TOT DIVALENT TOT, we break - TOT-2 + Ca, Ba2:1:1 Phyllosilicates: TOT O TOT O TOT, chlorite

Polytype: same layer structure, different stacking sequence.

Mica General Formula:W1Y2-3Z4O10(OH, F, Cl)2

W: [12] interlayerY: O-sheetZ: T-sheet

Lecture 9 – Inosilicates (Pyroxenes and amphiboles)

Pyroxenes: tetrahedra linked to form a single linear chain, all pointing the same direction and share corners. 3:1. (Si2O6)4-. Two opposing chains linked by a chain of octahedra, makes a nice I-beam.Pyroxene General Formula:

XYZ2O6

X: [6]-[8] distorted M2 siteY: [6] M1 site

Z: [4] tetrahedra

Clinopyroxenes: monoclinic unit cells, larger cations in M2 – Diopside(CaMgSi2O6), Augite, Hedenbergite (CaFeSi2O6)Orthopyroxenes: orthorhombic unit cells, smaller cations in M2 – Enstatite (MgSiO3), Pigeonite, Ferrosilite (FeSiO3)

Pyroxenoids: kink and twist the chains, reaction to cations in M1 and M2 sites. Ideal would be 2 tet-repeat pattern. Pyroxenoids have more than 2.

Amphiboles: double chain silicates, bases in a common plane all pointing in the same direction, half of the tetrahedra share 2 corners, the other half share 3. 3:1. (Si4O11)6-. I-beams are double the width of the pyroxenes. General formula:

W0-1X2Y5Z8O22(OH)2

W: [10]-[13] A siteX: [6]-[8] M4 siteY: [6]M1, M2, M3

Z: [4] Si or Al tetrahedra

• Variable amount of substitution of Fe2+ for Mg2+ in oxidizing environments, and Fe3+ for Al3+ in octahedral sits.

• More Al3+ substitutes in the octahedral sites in high pressure rocks.• Weak M2 site bonds give amphiboles a 60-120 cleavage.

Biopyriboles: disordered structures with 4+ chain-widths, biotite, pyroxene, amphiboles

Pyroxenes and Amphiboles:• Very similar,• Both SiO4 chained inosilicates,• Both connected by M octahedra to make I-beams,• High Ca monoclinic forms have T-O-T offsets in the same directions• Low Ca orthorhombic forms have alternating (+) (-) offsets.

Lecture 10 – Nesosilicates

• Isolated silica tetrahedra, (SiO4)4-, bonded to one another via ionic bonds with interstitial cations. High density, crystal habits are equidimensional and lack pronounced cleavage. Al3+ substitution in T site is generally low. No polymerization.

Garnets: cubic minerals. A2+3B3+

2(SiO4)3

A: [8]B: [6]

Ugrandite: Ca in A site Grossular - Ca3Al2(SiO4)3

Andradite – Ca3Fe2(SiO4)3

Uvarovite – Ca3Cr2(SiO4)3

Pyralspite: Pyrope - Mg3Al2(SiO4)3

Almandine - Fe3Al2(SiO4)3

Spessartine – Mn3Al2(SiO4)3

• Solid solution within groups common, and between groups only when it's above 700 degrees.• Silicon tetrahedra held together by oxygens, pure garnet endmembers are rare, most are

intemediate, exchange between Mg, Fe, Ca, and Mn are favourable due to similar size and charge.

Olivine: M2SiO4

M: M1 and M2• M1 is slightly more distorted relative to M2, Octahedral sites may be occupied by Mg2+ or Fe2+

,

similar size, interchangeable. Orthorhombic, euhedral crystams, 1st mineral to crystallize from melt.

Al2SiO5: aluminium tetrahedra, also some silica tetrahedra, considered subsatuates, not enough oxygens, naive. All are straight chains sharing eldges of AlO6 octahedra along c, chains contain ½ the aluminium in the structural formula.Kyanite: remaining Al are [6], densest, high pressure, low temperatures, subduction zonesAndalusite: remaining Al are [5], least dense, low pressures, high temperatures, contact metamorphismSillimanite: remaining Al are [4], high pressure and temperature, regional metamorphism