What's The Earth Made Of? (Lectures 9-14) Flashcards
What are the 8 most abundant elements in the crust?
Oxygen Silicon Aluminium Iron Calcium Sodium Potassium Magnesium
Define a mineral
An element or chemical compound that is normally crystalline and that has been formed as a result of geological processes
What are the main silicate minerals?
Olivine Pyroxene Garnet Quartz Alkali/plagioclase feldspar Biotie/muscovite mica Amphibole
What is the general rule of thumb for when a wide range of substitution is possible for the ions in a mineral?
The size difference between ions is less than 15%
For some mineral groups, the extent of ion substitution depends on what and why?
Temperature
Higher T gives greater flexibility in the lattice
How are SiO4 tetrahedra joined and why?
Join by the corners using bridging oxygens
Minimises repulsion between Si(4+) ions
What are the different frameworks for silica tetrahedra?
Isolated tetrahedra
Single chains all pointing in one direction
Double chains
Continuous sheet
A 3D framework where each shares 4 corners
How are suitable cations chosen to balance the -ve charge from the oxygens in tetrahedra?
(4 points)
Ionic radii
Cation must touch all co-ordinating anions
Lowest is radius of anion x sqrt(2) for 2D
Lowest is radius of anion x sqrt(3) for 3D
What are the possible forms of cation coordination structure?
Cuboctohedral: 12 fold Cubic: 8 fold Octahedral: 6 fold Tetrahedral: 4 fold Triangular: 3 fold
How are isolated silica tetrahedra linked together in olivine?
By Mg2+ and/or Fe2+ cations
Octahedral 6-fold coordinates sites between silica 4- tetrahedra
How are single-chain silicates balanced in charge?
Silica tetrahedra share two oxygens so repeating group [Si2O6]4-
Two chains linked together by Mg2+/Ca2+/Fe2+ in octahedral form
What cleavage is seen in single-chain silicates like pyroxenes in the basal section? Why?
90-degree cleavage
Bonds are easily broken between I-beams
How are double-chain silicates balanced in charge?
Repeating group of [Si8O22]12-
2+ cations join two chains in octahedral sites
What cleavage is seen in double-chain silicates like amphiboles in the basal section? Why is this different to that of single-chain silicates?
60-degree and 120-degree cleavage
I-beam is twice the size of that of pyroxene’s
How is charge balanced for sheet silicates?
Tetrahedra linked into sheets, each tetrahedron shares 3 oxygens
Repeating group of [Si4O10]4-
1/4 of tetrahedra occupied by aluminium
2 hydroxyl groups associated with the group
[AlSi3O10(OH)2]7- balanced by 2 Al3+/3 Mg2+ and a K+
What cleavage is seen in sheet silicates and why?
Perfect basal cleavage seen
Sheets weakly bonded together by large K+ or Na+
What is quartz?
SiO4 tetrahedra linked at all four corners
Gives neutral SiO2 repeating group
What is the difference between plagioclase and alkali feldspar?
Alkali involve the substitution of Na+ for K+
Plagioclase require the substitution of (CaAl)5+ for (NaSi)5+
What is translational symmetry?
A periodic arrangement such that a copy can be moved in a certain way for there to be overlap
What is the unit cell?
The repeating unit of the lattice
What is the difference between a primitive and non-primitive unit cell?
Primitive: lattice points at corners only
Non-primitive: lattice points at corners and inside the unit cell
If x, y and z axes are defined by the unit vectors a, b and c respectively, what are the lattice parameters?
α = b ^ c (angle between b and c) β = a ^ c (angle between a and c) γ = a ^ b (angle between a and b)
What is a lattice vector?
A vector joining any two lattice points
Written as a combination of the unit cell vectors
What is the shorthand for a lattice vector if it was: t = U x a + V x b + W x c?
How are negative values written?
t = [UVW]
Bar over the top
What are the 5 lattice types?
Primitive - all points at corners
Body centred - lattice point in the centre
Face centred - lattice points in the centres of each face
C face centred - only two opposite faces have lattice points in the centre
Rhombohedral - a=b=c and α=β=γ=/=90
What are the forms of mirror symmetry?
2 fold = diad
3 fold = triad
4 fold = tetrad
6 fold = hexad
What are the 7 crystal systems?
Cubic Tetragonal Hexagonal Trigonal Orthorhombic Monoclinic Triclinic
What symmetry is seen for each crystal system?
Cubic: 4 triads Hexagonal: 1 hexad Trigonal: 1 triad Tetragonal: 1 tetrad Orthorhombic: 3 diads Monoclinic: 1 diad Triclinic: no symmetry
Define a lattice plane
A plane which passes through any three lattice points which are not in a straight line
A set of parallel lattice planes are characterised by what?
Miller indices (hkl)
If a plane is parallel to an axis, what is the corresponding miller index?
Zero
Define form
Sets of related planes or faces in a crystal
Why are curly brackets used?
To distinguish forms from individual planes
Define the habit of a crystal
Describes the overall shape of the crystal
What is twinning in a crystal?
Two or more adjacent parts in which the crystal structure is differently oriented
How does twinning arise?
Mistakes during crystal growth from:
mechanical deformation
crystal structure changing on cooling to a more stable, lower T structure
Define an isotropic material
Define an anisotropic material
The same refractive index in all directions
Refractive index is not the same for all directions
What are the four things that can be seen in a thin section?
Habit
Microstructure (twinning, cleavage, zoning)
Colour
Relief
Define relief
How clearly the edge of a grain or crystal can be seen
What does relief depend on?
The difference in refractive indices of the grain and the embedding medium
Outline the Becke Line Test
Becke Line is a bright fringe often observed just outside/inside the crystal outline
Raising the focal plane moves the Becke Line into the medium of higher RI
What is pleochroism?
How does it work?
Colour change with orientation
Anisotropic minerals absorb different wavelengths of light in different vibration directions
Polarised light in an anisotropic medium is only permitted to vibrate along two perpendicular what?
Permitted vibration directions
What constrains the permitted vibration directions?
Crystal’s symmetry
Why are the two permitted vibration directions different?
One interacts with fewer atoms and so has a lower RI and is called “fast”
Other interacts with more atoms and so has a higher RI and is called “slow”
What is double refraction?
Light travels through an anisotropic material as two separate rays, vibrating in perpendicular directions
Define birefringence
The difference between the RIs of the two rays brought about by double refraction
What are the observations under crossed polars?
3 points
Isotropic materials let no light through and appear black
Anisotropic materials let light of a specific colour through
Rotating an anisotropic material such that one of its permitted vibration directions is parallel to the polariser, no light gets through (extinction position)
How often do extinction positions occur?
Every 90 degrees
Why are isotropic materials black under crossed polars?
Every direction is a permitted vibration direction
So all light is absorbed by the E-W and N-S polariser/analyser
What causes straight extinction?
Permitted vibration direction with the larger RI is parallel to the length of the crystal (length slow)
What happens if light is sent through a crystal vibrating in a non-permitted direction?
(3 points)
Light resolved into two components along the permitted vibration directions
Component along the direction of smaller RI travels faster than component along the direction of larger RI
When slower component exits material, the fast component has travelled an extra distance called optical path difference
What is the equation to figure out the optical path difference?
Δ = t(n1 - n2)
What happens if the two components of light exit in phase or out of phase?
In phase: resulting light vibrates in same direction as the incident light
Out of phase: resulting light vibrates at 90 degrees to the incident light
When does the light pass through the analyser, in or out of phase?
In phase does not
Out of phase does
What is the optical indicatrix?
A radius vector parallel to each vibration direction with length proportional to the RI for the crystal with that VD
Always forms an ellipsoid
What is the significance of an isotopic section?
A circular cross-section through the indicatrix
Normal to the optic axis
Why do cubic crystal systems give a spherical optical indicatrix?
3-fold symmetry means the RI is always the same
Which crystal systems give a uniaxial indicatrix?
What is the difference between the two forms of a uniaxial indicatrix?
Tetragonal, hexagonal and trigonal
Indicatrix contains one isotropic section and one optic axis, isotropic section always parallel to (001) or z
Positive uniaxial ε > ω (rugby ball shape)
Negative uniaxial ε < ω (burger shape)
What are ε and ω with respect to the optical indicatrix?
ε is the value of RI parallel to the z-axis
ω is the value of RI within the plane perpendicular to z
When a mineral is cut in the thin section, when is the anisotropy at a maximum and zero?
Maximum: cut parallel to the optic axis
Zero: cut perpendicular to the optic axis
Which crystal systems have a biaxial indicatrix?
Orthorhombic, monoclinic and triclinic
What is a biaxial indicatrix?
Two isotropic sections and two optic axes
How is the biaxial indicatrix different for the crystal systems that can have it?
Orthorhombic: diad symmetry along x, y and z axes so principle axes must lie along x, y and z
Monoclinic: diad symmetry along the y-axis so one of the principle axes lies along the axis
Triclinic: no symmetry so indicatrix can adopt any orientation
Close packed layers of identical spheres can be stacked to form which two structure types?
Hexagonal close-packed (hcp)
Cubic close-packed (ccp)
What is the difference between hcp and ccp structures?
What is the similarity?
hcp has two kinds of atoms, A and B, and stacks ABABAB
ccp has three kinds of atoms, A, B and C, and stacks ABCABC
Both have a coordination number 12
What is the body centred cubic structure (bcc)?
A cubic unit cell with atoms at the corners and one at the centre of the unit cell
Coordination number 8
What are the packing efficiencies for hcp, ccp and bcc?
hcp and ccp 74%
bcc 68%
Which minerals are there in the lower mantle?
Perovskite
Ferropericlase
Which minerals are there in the transition zone?
Ringwoodite
Wadsleyite
Majorite garnet
Which minerals are there in the upper mantle?
Olivine
Orthopyroxene
Clinopyroxene
Pyrope garnet
What shows that perovskite is under very high pressure?
Mg has 12-fold coordination and normally has 6
Si is in 6-fold octahedral coordination
What is a feature of majorite garnet that shows it is under high pressure?
Si is in both tetrahedral and octahedral sites
