Goldschmidtʼs rules"

Fosterite Fayalite

Goldschmidt’s Rule 1"

ü  Ions of one element can extensively replace those of another if they have the same charge and their radii differ by less than about 15%"•  e.g., Fe2+ replacing Mg2+ in many silicate

structures, or Cl- replacing F-."

Goldschmidt’s Rule 2"

ü  Ions whose charges differ by one unit substitute readily for another provide electrical neutrality of the crystal is maintained. This requires coupled substitution. "ü  Ca2+ can replace Na+ in feldspars as long as

Al3+ replaces Si4+ at the same time to maintain local charge balance. For charge difference greater than one, substitution is quite limited."

Goldschmidt’s Rule 3"

ü  When two different ions can occupy a position in a crystal lattice, the ion with the higher ionic potential forms a stronger bond with surrounding anions (ionic potential = charge/radius). Therefore, these elements are concentrated in “early” formed minerals. "

ü  Mg-rich olivines form at a higher temperature than more Fe-rich olivines."

Goldschmidt’s Rule 4"

ü  Even if size and charge are the same, substitution may be limited if two ions have different electronegativities and thus form bonds of different ionic character."

•  Na+ and Cu+ have similar ratios and same charge but very different electronegativities; they rarely substitute to one another"

Growth of minerals"

ü Rule of mineral stability"ü Crystal nucleation"ü Crystal growth"

Just a little bit of thermodynamics"

A thermodynamics system:"

Some portion of the universe that you wish to study"

Changes in a system are associated with the transfer of energy"

Natural systems tend toward states of minimum energy"

Thermodynamics"

a Phase: a mechanically separable portion of a system"ü Mineral"ü Liquid"ü Vapor"

a Reaction: some change in the nature or types of phases in a system"

reactions are written in the form:"" " "reactants = products"

Energy States"

ü  Unstable: falling or rolling"

ü Stable: at rest in lowest energy state"

ü Metastable: in low-energy perch"

Figure 5-1. Stability states. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.

Gibbs Free Energy"

Gibbs free energy is a measure of chemical energy"

All chemical systems tend naturally toward states of minimum Gibbs free energy"

G = H - TS"Where:"

G = Gibbs Free Energy (in Joules)"H = Enthalpy (heat content; in Joules; H=U-PV, with U as the

internal energy, P is pressure, and V is volume)"T = Temperature in K"S = Entropy (~ randomness; Joules/K)"

Relations between two chemically equivalent minerals or mineral assemblages can be expressed as a

chemical reaction between reactants and products:

e.g., Al2SiO5 = Al2SiO5 (kyanite = sillimanite)

KAl3Si3O10(OH)2 + SiO2 = KAlSi3O8 + Al2SiO5 + H2O (muscovite + quartz = K-feldspar + sillimanite + water)

note that reactions must be stochiometrically balanced,

# atoms reactants = # atoms products

Mineral Stability

Given two chemically equivalent mineral assemblages,

(reactants = products) which is stable at a given P, T?

the assemblage with the lowest G is always more stable

evaluate ΔGreaction = Gproducts – Greactants

(or ΔGreaction = ΔGf products – ΔGf reactants) at specified P, T

if ΔGreaction < 0

ΔGreaction > 0

ΔGreaction = 0

products stable (forward reaction favoured)

reactants stable (reverse reaction favoured)

equilibrium (no reaction)

Stability

Thermodynamics - Summary"ü G is a measure of relative chemical stability for a phase or an assemblage"

ü We can determine G for any phase-assemblage by measuring H and S for the reaction creating the phase(s) from the elements"

ü We can then determine G at any T and P mathematically"ü Computer programs that provides the stable mineral

assemblage for given conditions"

Use?"If we know G for various phases, we can determine which

is most stable"ü Why is melt more stable than solids at high T?"ü Is diamond or graphite stable at 150 km depth?"ü What will be the effect of increased P on melting?"

Once a mineral is stable, …"

1.  It needs to nucleate"2.  It needs to grow"3.  It can be modified by post-

crystallization processes"

Crystallization takes place by…"

ü  Crystallization from a melt ü  Igneous minerals

ü  Solid - Solid reactions ü  Metamorphic minerals

ü  Precipitation from a fluid like H2O or CO2 ü  Hydrothermal area, diagenesis, evaporation

ü  Sublimation from a vapor ü  Volcanic vent

Ø Need phase diagrams

Phase diagrams"

Definition"

ü Phase diagram: graphical representation of chemical equilibrium

ü  A map of the phase or assemblage of phases that are stable in a chemical system at each point in the space of independent parameters (mostly T and P for a given composition)

ü  If P and T are the independent variables, this means a phase diagram divides the volume of available conditions into regions where the minimum G is obtained with different phases or assemblages of phases

Phase diagram Water"

the assemblage with the lowest G is always more stable

reactions driven by need to reduce G

Phase diagram aluminosilicates

Nesse, Fig. 5.3a

ΔG in Al2SiO5 system

as a function of P and T

Phase diagram Olivines"

Nucleation

Homogeneous: spontaneous, random nucleation in a

homogeneous medium (e.g., crystallization from a silicate melt)

Heterogeneous:

nucleation facilitated by pre-existing nucleii or structural heterogeneities (e.g.,

metamorphic growth of crystals)

Nucleation

Heterogeneous: à many small crystals: mica grains in matrix

Homogeneous à few large crystals: andalusite porphyroblasts

OM-14: andalusite porphyroblast in schist (6.5 mm, XN) ERTH 2001 collection

Growth"

Crystal growth is limited by: Need to diffuse material towards edge of crystal Grow by adding atoms/ions at the surface of the mineral

Energetically difficult on flat surfaces Ø  Uses structural defects and/or tips http://www.classzone.com/books/earth_science/terc/

content/investigations/es0506/es0506page04.cfm

Structural defects"

ü Point defects"ü Line defects"ü Planar defects"ü Bulk defects"

Shapes

ideal stable shape à sphere but for crystals some faces are more stable

Different shapes depend on:

1.  Mineral structure

2.  Growth rate

3.  Environment

Postcrystallization processes"

ü Ordering"ü Twinning"ü Recrystallization (Pseudomorphism)"ü Exsolution"

Remember these… More in following lectures