Principles of Mineral Behaviour (L7-13) Flashcards
What does a phase diagram show?
Which structure is stable at a given P, T
Which structure has lowest free energy = eq^m state
What causes a phase transition?
Change in P, T
Change in eq^m state
Phase transition
For SiO2, which phase transitions are displacive and which are reconstructive?
Displacive: α-β Qz, high-low crist, high-low trid
Reconstructive: Qz-trid, trid-crist, Qz-coesite
Where does β cristobalite occur?
Rarely
In volcanic ash
Where does high P tridymite occur?
Thermal aureoles around granite/gabbro intrusions
What form is Si in, in α quartz?
Si in tetrahedra
What form is Si in, in stishovite?
Si in octahedra
Where does coesite occur?
As inclusions in garnet in ultrahigh pressure metamorphic rocks
What can be said about the properties of an individual tetrahedron of SiO2?
Si-O bonds are strong
Rigid tetrahedron
How do tetrahedra link?
What can be said about the angle?
Sharing corner oxygen, forming chains, sheets, or frameworks
θ = 180 = purely ionic, θ = 109 = purely covalent
θ observed 140-180: partly covalent
What can be said about the variation of bond energy w.r.t Si-O bond length and Si-O-Si bond angle?
Si-O bond length has a narrow range
Changing θ doesn’t change energy by much, allowing variety in frameworks
High β quartz: Crystal system? Space group? When is it stable? What does a view down the c axis show?
Hexagonal
P6_2 22
Stable above 573°C
Spirals of tetrehedra around screw nodes
Low α quartz:
Crystal system?
Space group?
When is it stable?
Trigonal
P3_2 21
Stable below 573°C
How can the structures of tridymite and cristobalite be described?
Sheets of tetrahedra stacked in different ways
High tridymite:
Crystal system?
Space group?
Stacking of layers?
Hexagonal
P 6_3 /mmc
ABAB
High cristobalite:
Crystal system?
Space group?
Stacking of layers?
Cubic
Fd3m
ABCABC
Define polytypes
Different structure of identical layers
Coesite:
Crystal system?
Space group?
Framework?
Monoclinic
C2/c
3D, contains 4-fold rings of tetrahedra
Stishovite: Crystal system? Space group? Structure? When is it stable? Why so dense?
Tetragonal P4_2 /mnm Chains of edge sharing SiO6 octahedra Stable at v high P Dense as increased coordination of Si
Displacive transition of quartz from β to α:
How many orientations?
What happens to screw hexad?
What name is given to the product?
2
Becomes screw triad
Dauphiné twins
How can the SiO2 variants be told apart in thin section?
Quartz: uniaxial positive, dusty inclusions, undulose extinction
Tridymite: biaxial positive, arrow-head twinning
Cristobalite: uniaxial negative, fish scale texture
What happens in a displacive transition?
A high-symmetry structure transforms to a closely-related low-symmetry structure via small displacements of atoms
Displacements often described in terms of rotations of structural units
Displacive transitions:
Quenchable?
What happens if there’s a change in crystal system?
No, transition is too fast
Transformation twins appear
What happens in a reconstructive transition?
One polymorph transforms to another polymorph with an unrelated structure
Reconstructive transitions: Why is activation energy large? Quenchable? Any twins? Why does it cause seismic anomalies?
Bonds broken and reformed, diffusion of atoms, very slow process
Easily, because transformation is slow, metastability is possible
No since structures are unrelated
Because all physical properties change
What is the equation to determine free energy?
G = H_0 - TS + PV
Enthalpy:
What is it?
When does it dominate free energy?
What causes high enthalpy?
Bond energies + kinetic energy from atomic vibrations
When P and T are low
Electrostatic repulsion, unfavourable bond angles, strain, cation size mismatch, charge mismatch
Entropy:
What is it?
When does it dominate free energy?
What causes high entropy?
Measure of disorder in a crystal
When T is high
Large vibrational degree of freedom, configurational disorder
Volume:
What is it?
How is molar volume determined?
What does high P favour?
Efficiency with which atoms in structures fill space
Volume of unit cell and the number of formula units in it
Structures with small molar volume
Why is it unnecessary that H, S and V are a function of P, T?
ΔH, ΔS, ΔV are usually constant for solid-solid reactions
Temperature dependence of free energy:
Which phases are stable at low T and high T?
dG/dT = ?
Change at Ttr = ?
Low enthalpy phase stable at low T
High entropy phase stable at high T
dG/dT = -S
ΔS
Pressure dependence of free energy:
Which phases are stable at low P and high P?
dG/dP = ?
Change at Ptr = ?
Low enthalpy phase stable at low P
Low volume phase stable at high P
dG/dP = V
ΔV
How do first-order and second-order phase transitions differ?
First-order: discontinuous dG/dT at transition point
Second-order: continuous dG/dT, discontinuous d2G/dT2 at transition point
What kind of phase transition is Qz-trid?
Reconstructive
What determines the transition point in a phase transition?
ΔG = 0
Geological importance:
What is the SiO2 polymorph present indicative of?
What does the presence of transformation twins indicate?
How do reconstructive transitions relate to seismics?
How do displacive transitions relate to seismics?
PT conditions of formation
The cooling history
Reconstructive transitions -> Δρ -> Δv shear + body wave
Displacive transitions -> elastic property changes -> changes in v_s + v_p
Olivine:
General formula
Crystal system
Space group
R2SiO4
Orthorhombic
Pbnm
Where is olivine common?
Upper mantle
Basic igneous rocks
What is the structure of olivine?
Isolated SiO4 tetrahedra
Linked by cation sites (m1, m2) with 6 fold coordination
O(2-) arranged in close packed layers
What are the Goldschmidt rules for solid solution?
Cation differs in size by < 15%
Cations differ in charge by =< +/- 1
When is solid solution viable for olivine compositions, and when is it not?
Complete s.s. between Forsterite (Mg2SiO4) and Fayalite (Fe2SiO4)
No s.s. between Monticellite (CaMgSiO4) and Forsterite (Mg2SiO4)
