Lectures 15-20 Flashcards
How much of the earth is the core?
roughly 1/3
What is the main composition of the core?
Fe-Ni alloy
- some other siderophile elements (iron loving)
- 10% of a lighter material—>unknown but most likely O, S, Si
Crust composition
75% = Si and O
8 elements make up 99%
What is a mineral?
An element or chemical compound that is normally crystalline and that has been formed as a result geological processes
What does crystalline mean?
Regular repeating pattern of atoms
What are the 7 most common mineral types?
1) Silicates (SiO4 4-)
2) Oxides/hydroxides (O2-/OH-)
3) Sulfides (S2-)
4) Halides (Cl-, F-)
5) Carbonates (CO3 2-)
6) Phosphates (PO4 3-)
7) Sulphates (SO4 2-)
What is the chemical formula of olivine?
(Mg, Fe)2 SiO4
What is the chemical composition of Pyroxene?
Ca(Mg, Fe) Si2O6
What is the chemical composition of Garnet?
(Mg, Fe, Ca)3 Al2Si3O12
What is the chemical formula of Quartz?
SiO2
What is the chemical formula of Alkali Feldspar?
NaAlSi3O8-KAlSi3O8
Chemical formula of plagioclase Feldspar
NaAlSi3-CaAl2Si2O8
Chemical formula of calcite
CaCO3
What is a solid solution
A series formed when there are intermediary minerals
- so 2 possible forms so 1 rock has mix
- fully one = endmember
What are the endmembers of Olivine?
Forsterite (Mg2)
Fayalite (Fe2)
What does the ability of a cation to be substituted by another depend on?
1) Ionic radius
2) Ionic charge (lesser extent)
Size within 15%
Charge within 1
What is the basic unit of silicate structure?
SiO4 4- tetrahedron
- so angles of 109.5 degrees
- sp3 hybrid orbitals of Si4+ atoms form a mixed ionic covalent bond with oxygens
What are the types of oxygens in a SiO4 tetrahedra structure?
bridging oxygens and non-bridging oxygens
- non count 1 towards total number of oxygens
- bridging count 1/2
What allows a lot of different structural topologies to be created ion SiO4 tetrahedron?
Si-O-Si bond is relatively flexible
What are orthosilicates?
Isolated tetrahedra closely packed in regularly-spaced array and linked by metal cations
MOST IMPORTANT IS OLIVINE
- [SiO4]4-
What is the most important orthosilicate?
Olivine
- Mg and/or Fe cations occupy 6-fold coordinated octahedral sites between the tetrahedra
- simple substitution between the two as same size (roughly) and same charge
What are two examples of isolated tetrahedra SiO4 other than olivine?
1) Garnet
2) Ringwoodite (high pressure form of olivine)
What are single chain silicates?
Give example
[Si2O6]4-
- silica tetrahedra linked into chains
- each group shares 2 oxygens with neighbours
-PYROXENES
What are the two main types of pyroxenes?
1) Clinopyroxene (monoclinic)
- Ca(Mg, Fe) Si2O6
2) Orthopyroxene (orthorhombic)
- (Mg, Fe) Si2O6
How to the single chain silicates form large crystals?
Cations cross link chains together
How are the pair of chains in single chain silicates joined?
held by Mg octohedra form a tightly-bonded unit = I-beam
What gives pyroxenes their 90 degree cleavage plane?
The fact it is easier to break bonds between I beams
What are the essential constituents of basalt?
1) pyroxenes
2) Plagioclase feldspar
What are double chain silicates
two single chains joined together, side by side
= AMPHIBOLES
= [Si8O22]12-
- chains linked by cations to make up charge deficit and make stable
What gives amphiboles the distinctive 56 degree cleavage?
double width of I-beams
What are the difference between tremolite and hornblende
- what can they tell us about the magma that cooled?
What are sheet silicates?
[SiO10]4-
- tetrahedra groups linked into sheets
- each one shares 3 oxygens with neighbours
- stacked sheets
- MICAS
What are the two types of micas and their chemical formulas?
How often is one of the tetrahedra occupied by aluminium in muscovite and biotite?
every 4
How are sheet silicates held together?
Weakly bonded by large K+ or Na+ ions
- perfect basal cleavage
What are tectosilicates?
Framework silicates = [Si4O8]
- all 4 oxygens are bonded
- like quartz = SiO2
- charge neutral so no other ions
Which framework silicates (tectosilicates) need ions?
Alumnosilicates
- like feldspars
- Al3+ in places of Si4+ (only 1 or 2)
- so accomodate K+, Al+ or Ca2+
What are the three endmembers of Feldspars?- chemical formula?
1) orthoclase = KAlSi3O8
2) Albite = NaAlSi3O8
3) Anorthite = CaAl2Si2O8
What is the name of the feldspars that are a solid solution of orthoclase and albite?
Alkali feldspars
What is the name of the solid solution feldspars between albite and anorthite?
Plagioclase feldspars
Why is ionic radii extremely useful in deciding suitability of cation given structural site?
- cation must not rattle around in polyhedron
- must touch all
LIMITING CASE=
Ra/Rb = 0.414 for squares (4 anions)
- a is anion and b is cation
Ra/Rb = 0.732 fro 8 anions
What are the common coordination numbers for the common cations?
GRAPH
What is the type of structure for Ra/Ro of 1
12=coordination number
- cuboctohedral
- like Fe in core
Ra/Ro of 1-0.732
8 = cubic
- garnet [FeO8]
Ra/Ro = 0.732-0.414
6 = octahedral
[MgO6] in olivine
Ra/Ro =0.414-0.225
4 = tetrahedral
[SiO4] in feldspar
Ra/Ro = 0.225-0.155
3 = triangular
[CO3] in calcite
Is the earth’s core isotropic or anisotropic?
The solid inner core is anisotropic
What is the most efficient way of packing identical spheres in two dimensions?
packed layer with 6 contacts with neighbouring atoms - in a hexagon
- layers can then be stacked on top
- various packing structure
- HCP and CCP
What is HCP packing?
HEXAGONAL CLOSE PACKING
- so in 3D each atom has 12 neighbouring = 12 coordination number - 3 above and 3 below and 6 in own layer
- typical if packing same size atoms
- ABABABA layers
What is CCP?
CUBIC CLOSE PACKING - ABCABCABC layering 12 fold coordination - similar to but not identical to hcp structures - same packing but different symmetry - fcc is the face centred cubic - bcc is the body centred cubic
What is FCC?
FACE CENTRED CUBIC
- cubic with 12 coord
What is BCC?
BODY CENTRED CUBIC
- 8 coord
- lower density than hcp or fcc structures
What is the most suitable packing for iron?
- dont know as not completely pure iron in core
- using high pressure phase diagram GRAPH
- most stable at certain temp and pressure
- good at low temp
- and high pressures low temp
- harder after
What is the packing efficiency of HCP, fcc and bcc?
- HCP = 74%
- FCC = 74%
- BCC = 68%
- extremely hot so vibrate more - higher entropy vs efficient packing
- only know that if pure Fe then hcp under core conditions
How hot is the core?
From phse diagram, know it is 330GPa at boundary
- so if pure Fe then 6300K
- but not pure - presence of light elements reduces temperature
- 5400-5700K
Do we know the mineral composition of the mantle?
Yes
- easier to do pressure and temperature experiments
GRAPH
What 2 minerals make up the lower mantle?
Perovskite
Ferropericlase
What makes up the transition zone?
ringwoodite (γ)
wadsleyite
majorite garnet
What is the upper mantle made of?
Olivine
Orthopyroxene
clinopyroxene
pyrope garnet
What silicate coordination is favoured in the upper mantle?
tetrahedral in all phases
What characterises a crystalline material
regular atomic structure
- repeats itself in 3 dimensions
- translation symmetry
What is a lattice
- generated from any repeating pattern
- each point which can be superimposed is a lattice point
- not all atoms sit on lattice points
What is the unit cell?
The repeating unit of the lattice
- in two dimensions it is a parallelogram with lattice points at the corners
- primitive unit cell has no lattice points contained
- non-primitive if they do
- IN 3D = parallelepiped
Diagram of primitive unit cell and angles
DIAGRAM
What are lattice parameters
- defining the 3 dimension
- choose axes x,y,z
- point along edges of unit cell
- The lattice parameters are the lengths along the axes and then the angles between them
Body centred vs face centred vs primitive lattice
Body centred = I = one lattice point also in the centre
Face centred = F = lattice points on corners and also centre of each face
- c face centred - only two on opposite faces
Rhombohedral
- a = b = c
α = β = γ not equal to 90 degrees
What is a lattice vector?
vector joining lattice points
- written =
t = Ua + Vb + Wc
t written as [UVW]
- negative values have bar on top
Rotational symmetry
An n fold rotational symmetry operation
- rotates by 360/n
- only 1,2,3,4,6 in periodic structure
Mirror symmetry
reflection of the object in a plane = itself
What are crystal systems?
the rotational symmetry of a crystal constrains the shape of the conventional unit cell we describe the structure with
- 7 possible
Lattice parameters of crystal systems - table
TABLE
What is a lattice plane?
plane which passes through any three lattice points
- not in a straight line
What is a set of parallel lattice planes?
Miller indices indicate
(hkl)
- define where first plane away from origin intersects the x,y,z crystallographic axes
- if parallel to axis then zero
INTERSECTIONS
- at a/h along x axis and then b/k on y and c/l on z
What does form mean?
set of related planes or faces in a crystal
- denoted {hkl}
- related to (hkl) by symmetry
What does habit mean?
Described overall shape of crystal (or group of crystal)
- depends on relative development of faces in the various forms present
- a substance can take on more than one habit depending on the growth conditions - not always diagnostic feature
What is twinning?
a twinned crystal consists of two or more adjacent parts in which the crystal structure is differently oriented
- separated by twin boundary - related by a symmetry element like mirror plane or rotation axis
How might twinning arise?
mistakes during crystal growth
1. mechanical deformation
What type of microscope is used to examine thin rock slices?
Petrographic
What are the properties of light?
Transverse electromagnetic wave
- perpendicular electric (E) and magnetic field (B)
- vibration always taken as parallel to E and perpendicular to travel direction of the wave
Unpolarised light vibrates in all directions perpendicular to the travel direction
- polarised means only in one vibration direction
What is the speed of light
c = C0/n
C0 is speed of light in a vacuum
- The higher the refractive index, the slower the light travels
What is an isotropic material
Same refractive index in all directions
What is an anisotropic material?
Different directions have different refractive indexes
What is the habit/shape of the thin section?
The order/shape of the minerals
What is the microstructure of thin section?
The cleavage, twinning, zoning
- how the mineral differs across the crystal
What is the relief of a mineral?
term used to describe how clearly the edge of a grain/crystal can be seen
- depends between the RIs of grain and bedding medium = 1.54
- if same then invisible
Low relief = RI close to mounting
- little refraction by surface topography
High relief = RI very different from medium
- large surface topography
What is the Becke line test
Test to see if RI is greater than or less than RI of medium
- Lower stage = raise focal plane
- Line moves into higher RI medium
What does anisotropy in plane polarised light?
In petrographic microscope electic field vibrates E-W
- Variation in Relief
- relief changes as rotate - Pleochroism
- Colour variation as rotate
- specific, diagnostic in many cases
What are the slow and fast directions?
The directions where
- Small n = fast
- large n = slow
What is double refraction
Through anisotropic material - two separate rays, one fast and other slow, perpendicular directions
- called double refraction
Ordinary = unrefracted
Extraordinary = Slight angle to ordinary ray
What is it meant when ‘crossed polars’
Crossed polarisers
- in this isotropic materials always dark (no light through)
- In anisotropic - extinction positions at 90 degrees from one another and colours at other points
Why do isotropic materials appear black in crossed polars?
In these materials, every direction is a permitted vibration direction
- so straight through without changing polarisation state
- absorbed by analyser so appears black
identify isotropic materials like cubic minerals or glass
Why do anisotropic materials go extinct every 90 degrees?
If one of the permitted vibration directions of an anisotropic material is parallel to polariser
- then same as isotropic
- in extinction position
Straight and inclined extinction
What is the difference between straight extinction or inclined extinction?
Crystals have distinct microstructure
- straight extinction is when vibration length slow
How to measure extinction angle?
- rotate the stage so feature of interest is oriented N-S
- note angular position of the graduated stage - Rotate crystal clockwise to extinction position
- note angle of stage - Repeat 1 and 2 but rotate anticlockwise to another extinction position
- Calculate angle between feature of interest and which vibration direction was the closest
What happens if we try and send light through crystal vibrating in a non-permitted direction
- light resolved into two components vibrating in one of the permitted vibration directions
- The two components then travel at different speeds
- causing optical path difference/retardation
What is the birefringence of a material?
difference in refractive indices of two vibration directions
How to work out retardation (Δ)?
t (n1-n2)
t = thickness of crystal
n1 = refractive index of slow direction n2 = RI of fast direction
Phase difference between fast and slow components
the difference between the components when they recombine when leave crystal
if in phase then does not pass through analyser
- if out of phase does pass
Fringe spacing of red vs green
Red larger spacing than green as t increases uniformally
White light in quartz of varying lengths?
no dark as in single wavelength
- violet instead at each order
- called sensitive tint
What is the Michel-Levy chart?
Shows colours superimposed on a plot of thickness against retardation
GRAPH
What is the optical indicatrix?
A 3D ellipsoid which describes how the RI varies in all directions in a crystal
What is the optical axis?
The point that if we look down then an anisotropic material looks isotropic
Uniaxial vs Biaxial
Uniaxial = one optic axis
Biaxial = 2
What minerals have uniaxial indicatrix?
- Tetragonal
- Hexagonal
- Trigonal
Optical indicatrix of cubic crystals
Perfect sphere
- so isotropic
What are the two types of uniaxial indicatrix?
- Positive uniaxial ε > ω
- Like quartz, like a rugby ball - Negative ω > ε
- like calcite = burger
Which minerals have a biaxial indicatrix?
- Orthorhombic
- Monoclinic
- Triclinic
Orientation of the biaxial indicatrix
Constrained by symmetry
- Orthorhombic = principle axes along x, y, z
- Monoclinic = principle axes, one must be on y axis of crystal
- Triclinic have no symmetry so no constraint on indicatrix orientation
