Lecture 4: Chemistry of silicate melts and minerals: chemical thermodynamics, melting, mineralogy

1
Lecture 4 Chemistry of silicate melts and
minerals chemical thermodynamics, melting,
mineralogy

• Questions
• What is Gibbs free energy and how do we use it to
  understand phase stability in chemical systems?
• What is a phase diagram and how do we use it to
  understand the melting of rocks?
• What minerals dominate igneous rocks in the
  Earths crust, and what does this have to do with
  their composition and structure?
• Tools
• Chemical thermodynamics (i.e., mostly calculus)
• Ionic radii

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Chemical thermodynamics

• Thermodynamics is the branch of science that
  predicts whether a state of some macroscopic
  system will remain unchanged or will
  spontaneously evolve to a new state.
• Kinetics is the branch of science that deals with
  how long it takes for a system to reach that new
  state. Mechanics is the branch of science that
  deals with the motions of small numbers of
  particles.
• Thermodynamics is most relevant to the
  understanding of processes on spatial scales
  large enough to neglect individual atoms and
  timescales long enough to neglect kinetics, so
  that the predictions of thermodynamics describe
  to good approximation the actual state of nature,
  rather than the expected state at infinite time.
• Often, geology and geochemistry deal with very
  long timescales or very large numbers of atoms,
  so we use a lot of thermodynamics!
• All kinetic processes go faster with increasing
  temperature, and hence the tools of
  thermodynamics are most useful for predicting the
  behavior of high-temperature geological phenomena
  like melting and metamorphism. But even for
  kinetically limited things (like life),
  thermodynamics tells which way it is favorable
  for processes to run.

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Chemical thermodynamics Definitions I

• System the region of interest, of sufficient
  size that average properties like temperature are
  well-defined to be distinguished from the
  environment (i.e., the rest of the universe)
• Isolated system exchanges neither matter nor
  energy across its boundaries
• Closed system may exchange energy across
  boundaries, but not matter
• Open system may exchange matter and energy
  across boundaries
• Phase a physically homogeneous and mechanically
  separable part of the system, e.g. a vapor,
  liquid, or mineral
• A system may be homogeneous (one phase) or
  heterogeneous (multiple phases).
• Component a chemical formula a basis vector for
  expressing compositional variations in
  thermodynamic systems e.g., H2O, SiO2, Fe, NaCl.
  Must be independently variable, but we choose the
  minimum set to span all phases.
• Avoid at all costs confusing phases (e.g., water
  or quartz) with components (e.g., H2O or SiO2),
  even though people often use the same name for
  both!

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More on Components

• Choice of components is often arbitrary but
  number of components is not.
• Example System Fe-O can also be described by
  FeO-Fe2O3.
• Example System H2O is a one-component system if
  the only phases of interest are pure water, ice,
  and vapor, and if we need not consider
  electrolysis (i.e. separation into H2 and O2) or
  acid-base chemistry (i.e. separation into H and
  OH).
• Example System Mg2SiO4-Fe2SiO4 is a
  two-component system if we are only concerned
  with olivine and coexisting liquid. But at very
  high pressure compositions in this system form
  MgSiO3 perovskite, and we need three components
  (e.g. MgO, FeO, SiO2) to describe the system
  under these conditions the line Mg2SiO4-Fe2SiO4
  is a pseudo-binary join.
• The number of independent compositional variables
  needed to specify the composition of a system
  (but not its total mass or size) is one less than
  the number of components.

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Chemical thermodynamics Definitions II

• Equilibrium a state in which macroscopic
  physical properties do not change during the
  period of observation.
• Microscopic processes are still occurring, but
  the rate of every process is exactly balanced by
  the rate of the reverse process.
• A stable equilibrium is a global minimum in
  potential energy. Subject to applied constraints,
  the system cannot achieve lower energy in any
  way. The system responds to small perturbations
  by returning to the stable equilibrium state.
• A metastable equilibrium is a local minimum in
  potential energy. The equilibrium is stable with
  respect to small perturbations and does not
  evolve spontaneously, but it might respond to a
  large perturbation by evolving away from the
  metastable equilibrium towards a lower energy
  state elsewhere.

An unstable equilibrium is a location where the
system may not spontaneously evolve, but any
small perturbation will cause it to move away
from the original state. This is a local maximum
in potential energy.
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Chemical thermodynamics Definitions III

• Volume (V) the size of a system in units of
  length3
• Temperature (T) a measure of the tendency of a
  body to exchange microscopic kinetic energy with
  neighboring bodies. At equilibrium, all parts of
  a system are at equal temperature.
• Heat (dq) that which is transferred from hot
  bodies to cold ones during equilibration.
  Convention heat transfer into the system from
  hot surroundings is positive heat transfer by
  the system to cold surroundings is negative.
• Pressure (P) a measure of the tendency of a body
  to exchange mechanical energy with neighboring
  bodies. At equilibrium, all parts of a system are
  at equal pressure (in the absence of
  gravitational fields, surface tensions, etc.).
• Work (dw) the transfer of mechanical energy
  between objects at different initial pressures.
  For our purposes work is always given by dw
  PdV. So by convention, work is positive when the
  system expands into low-pressure surroundings
  negative when high-pressure surroundings compress
  the system.

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Chemical thermodynamics Definitions IV

• Reversible an idealized process that proceeds
  through a sequence of equilibrium states as the
  parameters (P, V, T, etc.) are varied externally,
  without any finite deviation from equilibrium.
• Spontaneous a real process, where the internal
  state of a system changes in order to approach
  equilibrium from an initially disequilibrium state

Spontaneous
Reversible
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Chemical thermodynamics First Law

• It is empirically observed that for any path that
  brings a closed system from an initial state (P1,
  V1, T1) to a new state (P2, V2, T2), and back to
  (P1, V1, T1) that the sum of heat and work
  transferred across the boundaries of the system
  is zero.
• Neither heat nor work is a variable of state the
  quantities exchanged around closed paths of both
  heat and work can be non-zero only the sum is
  conserved.
• Hence it is inappropriate to speak of the amount
  of heat or work in a system these quantities are
  only used for transfers.
• We can, however, define a variable of state E,
  the internal energy, whose change for a closed
  system is given by

(4.1)

• This is the First Law of Thermodynamics. Note
  absolute values of E are arbitrary only its
  changes dE are significant.

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Chemical thermodynamics Second Law

• The thermodynamic temperature scale is defined so
  that during a reversible cycle among states that
  returns to the original state, the integral of
  dq/T is zero. Hence there exists another variable
  of state S, the entropy, whose change is given by
• If at any time our closed cycle deviates from
  reversibility and undergoes a spontaneous change,
  we find that the integral of dq/T is always
  positive. So we state another empirical rule

(4.2)
(4.3)

• This is the Second Law of Thermodynamics. If we
  expand our consideration to the system and its
  environment, which form an isolated system with
  dq0, the second law takes the more familiar form
  dStotal 0. In any spontaneous process, total
  entropy must increase. In a reversible process
  it is constant.

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Chemical thermodynamics Equilibrium

• Combining the first and second laws,

(4.4)

• This provides our first thermodynamic definition
  of equilibrium and the approach to equilibrium
  If in a closed system we fix constant S and
  constant V,

• That is, any spontaneous process that occurs at
  constant S and constant V is associated with a
  decrease in internal energy E.
• When E reaches a minimum no further spontaneous
  changes can occur and all state variables will be
  constant, so this is a condition for
  equilibriuma minimum in E.

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Chemical thermodynamics Open systems

• The form of (4.4) is only valid for a closed
  system (constant mass). If we have an open
  system that exchanges mass with the environment
  there are more variables.
• For a system of one chemical component (i.e., all
  phases are pure, equal, and constant in
  composition), we define a new quantity m, the
  chemical potential, such that for a change in the
  mass of the system dm,

(4.5)

• Likewise, for a system of n components
  (independently variable chemical species), each
  component has a chemical potential mi such that

(4.6)
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Chemical thermodynamics Partial Derivatives

• Fact from calculus the total differential of a
  function of j variables A(x1, x2, , xj) is
  related to the partial derivatives with respect
  to each variable as follows

• Comparing this form to (4.6), we see that for
  reversible changes

(4.7)
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Chemical thermodynamics E-S-V space
What is the curvature of the E-surface for a
stable phase?
Must be concave up! Otherwise at constant total
volume we lower E by unmixing into an
ever-shrinking low-V, low-P phase and an
ever-growing high-V, high-P phase. That is, only
a point on a concave-up E surface can be at
equilibrium.
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Chemical thermodynamics derivative properties

• More definitions
• coefficient of isobaric thermal expansion
• isothermal compressibility
• isentropic compressibility
• heat capacity at constant pressure
• heat capacity at constant volume

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Chemical thermodynamics derivative properties

• Note that bS and Cv are related to second
  derivatives of E, so their sign is fixed by the
  stability condition on concavity of the E-surface

• Actually, the E surface needs to be concave up
  along all directions, i.e. the Hessian Matrix of
  second derivatives must be positive definite. It
  can therefore be shown that that bT and Cp are
  also strictly positive for all stable phases.
• You cannot have a phase with negative
  compressibility or heat capacityit will
  spontaneously disintegrate!
• Note that ap can have either signit is perfectly
  acceptable to have a phase with negative thermal
  expansion.

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Chemical thermodynamics other potentials

• We have shown that internal energy E is minimized
  at equilibrium when the applied constraints are
  constant S and V.
• This is almost completely uselessthere are
  hardly any experimental or natural situations
  where S and V are the independent variables!
• Why? Because specific S and specific V (1/r) can
  differ between coexisting phases at equilibrium,
  unlike P and T, which must be equal among phases
  at equilibrium and so (1) are easy to control in
  the laboratory and (2) must be the independent
  variables at infinite time.
• We can get equivalents of 4.4, 4.5, and 4.6 with
  more useful independent variables that actually
  apply to natural and realizable experimental
  settings. We change variables using Legendre
  Transformations of the form

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Chemical thermodynamics other potentials

• First Legendre Transformation define enthalpy H

For a closed system, dE TdS PdV, so
(4.8)
For open system of one or many components,
respectively
(4.9)
(4.10)
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Chemical thermodynamics Equilibrium II

• This provides our second thermodynamic definition
  of equilibrium and the approach to equilibrium
  If in a closed system we fix constant S and
  constant P,

• Any spontaneous process that occurs at constant
  S and constant P is associated with a decrease in
  enthalpy H.
• When H reaches a minimum no further spontaneous
  changes can occur and all state variables will be
  constant, so this is a condition for
  equilibriuma minimum in H.
• This is no longer of strictly theoretical
  interest during adiabatic, reversible pressure
  changes (as in the atmosphere and the Earths
  mantle in both cases heat flow is negligible
  compared to advection), S and P are the
  independent variables, and equilibrium must be
  found by minimizing H.
• Note at constant P, dHdq, so enthalpy is a
  direct measure of heat transferred into or out of
  an isobaric system.

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Chemical thermodynamics other potentials

• 2nd Legendre Transformation define Helmholtz
  Free Energy F

For a closed system, dE TdS PdV, so
(4.11)
For open system of one or many components,
respectively
(4.12)
(4.13)
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Chemical thermodynamics Equilibrium III

• This provides our third thermodynamic definition
  of equilibrium and the approach to equilibrium
  If in a closed system we fix constant T and
  constant V,

• Any spontaneous process that occurs at constant
  T and constant V is associated with a decrease in
  Helmholtz free energy F.
• When F reaches a minimum no further spontaneous
  changes can occur and all state variables will be
  constant, so this is a condition for
  equilibriuma minimum in F.
• These constraints are obtainable during isochoric
  temperature changes, such as in a rigid container
  like a fluid inclusion in a mineral.
• Note at constant T, dFdw, so Helmholtz free
  energy is a direct measure of work done on or by
  an isothermal system.

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Chemical thermodynamics other potentials

• Finally, if we do both Legendre transformations,
  we obtain a definition of Gibbs Free Energy G

(Clearly G H TS F PV)
For closed system,
(4.14)
For open system of one or many components,
respectively
(4.15)
(4.16)
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Chemical thermodynamics Equilibrium IV

• Now we are getting somewhere If in a closed
  system we fix constant T and constant P,

• Any spontaneous process that occurs at constant
  T and constant P is associated with a decrease in
  Gibbs free energy G.
• When G reaches a minimum no further spontaneous
  changes can occur and all state variables will be
  constant, so this is a condition for
  equilibriuma minimum in G.
• These constraints are the easiest to understand,
  the most common in the laboratory, and the most
  common in geology. From here on we will consider
  T and P the independent variables and discuss
  equilibrium as a state of minimum G.

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Chemical thermodynamics more on G

• From the definition of dG, we find the partial
  derivatives of G

(4.17)

• Thus the second derivatives of G are

In G(P,T) space, then, the G surface is concave
down, but this does not imply instability.
Unmixing to phases at different T and P would
violate the conditions of equilibrium and the
applied constraints
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Phase diagrams

• A Phase diagram is 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 (or some subspace,
  section, or projection thereof).
• 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.
• Begin with a one-component system in which there
  are three phases solid, liquid, and vapor
• solid has the lowest specific entropy, liquid has
  intermediate specific entropy and vapor has the
  highest specific entropy (i.e., the entropies of
  fusion and boiling are positive).
• Liquid has the smallest specific volume (highest
  density, as in the case of H2O at low pressure),
  solid has intermediate specific volume, and vapor
  has the highest specific volume.

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Phase diagrams one component
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Phase diagrams one component
27
Phase diagrams two components

• In a one-component system there are two
  independent variables (e.g., P and T), so a
  complete phase diagram can be drawn in two
  dimensions, and stability relations visualized in
  three dimensions (e.g., G-P-T space).
• In a two-component system, there are three
  independent variables we add one compositional
  parameter, X, so now the space is
  four-dimensional.
• We therefore typically look at two-dimensional
  sections or projections through phase space to
  understand such systems. The most common is a map
  of minimum G assemblages as functions of (T, X)
  at constant P.
• We will seek here to understand how the two most
  common topologies in T-X space are derived by
  looking at sequences of G-X diagrams at constant
  P and T.

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Phase diagrams two components

• Condition of multicomponent equilibrium (a
  corollary to minimization of G, etc.) throughout
  the system at equilibrium, P, T, and mi of all
  components are equal.
• If P is larger in any one part of the system,
  work will be done until volumes adjust to reach
  constant P at equilibrium.
• If T is larger in any one part of the system,
  heat will flow until T is equalized.
• Likewise, if mi is larger in any one part of the
  system, mass will diffuse until mi is equalized.
• Consider a two-component system A-B with the mass
  of component A present in the system denoted mA
  and the mass of component B present mB. Total
  mass m mAmB. Define the mass fraction of
  component A, XA mA/m. Clearly XB mB/m 1
  XA.

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Phase diagrams two components

• For system A-B equation (4.16) reduces to

• It is useful to divide by mass to put this in
  intensive terms, where a bar over a quantity
  denotes per unit mass

• Now integrate over the whole system at
  equilibrium (constant T, constant P, and constant
  mA and mB)

So if we draw a plot of G vs. XA at constant T
and P, a stable phase is a concave-up curve,
otherwise it spontaneously breaks up into two
phases to lower G. The chemical potentials are
read from the tangent line to the phase at the
composition of interest. The intercepts give m of
each end-member
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Phase diagrams two components, solid solution

• Now let us postulate two phases, solid and
  liquid, each capable of dissolving the two
  components in any amount. This is intuitive for
  a liquid solution, perhaps less so for a solid
  solution (but think of metallic alloys!). At
  fixed P and T, the free energy curve of each
  phase as a function of composition is concave up
  and the diagram might look like this

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Phase diagrams two components, solid solution

• As we change T at constant P, how does this
  diagram evolve? Since (?G/?T)P S, with
  increasing T, both curves move downwards. The one
  with the higher entropy (liquid phase in this
  case) moves down faster, causing the equilibrium
  points to shift

• If we extract the stable, minimum G assemblage,
  either one phase or two phases, from this
  sequence of diagrams at each T and combine them,
  we can generate a T-X plot. This gives away
  information on the actual values of G, but
  usually all you need to know is what the minimum
  G state looks like.

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Phase diagrams two components, solid solution

• The resulting T-X diagram might look familiar

• This is a map of the stable assemblage for each
  choice of the three independent variables
  (P,T,XA), either one phase alone or a mixture of
  two phases. It is a projection of the minimum
  envelopes of the sequence of G-XA sections.
• The blue curve is the liquidus, the locus of
  minimum temperatures where each bulk composition
  XA is completely liquid. The green curve is the
  solidus, the locus of maximum temperatures where
  each bulk composition is completely solid. In
  between, the system is partially molten.

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Phase diagrams two components, solid solution

• Inside the two-phase region (where the red
  tie-lines are), the proportion of each phase is
  given by the lever rule, a statement of
  conservation of mass. For bulk composition XA

where fsolid is the mass fraction in the solid
phase, and the composition of the solid is a
point on the solidus XAsolid. Likewise for the
liquid. Given fsolid 1 - fliquid , we can state
the lever rule
(4.18)
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Phase diagrams two components, eutectic

• Next we consider a different two-component
  system, this time with two solid phases a and b
  that tend to have compositions of nearly pure
  component A and B, respectively.
• Do not confuse component A, a chemical formula
  such as SiO2, with phase a, a solid mineral with
  a definite crystal structure, such as quartz
  even though phase a may tend to be very close in
  composition to pure component A, they are not the
  same idea.
• We still have the liquid phase, which can
  continuously adopt any composition in A-B.
• Now we might generate a series of G-XA sections
  at constant P and a range of T like the following.

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Phase diagrams two components, eutectic
36
Phase diagrams two components, eutectic
If we assemble the stable sequences from each T
into a T-X section...
The red line represents a special equilibrium, a
eutectic, where the three phases a, b, and liquid
coexist (and liquid is intermediate between a and
b in composition). It is the lowest temperature
at which liquid can exist in this system at this
pressure. So this diagram has three kinds of
elements one-phase areas (where temperature and
phase composition vary freely), two-phase areas
(with a range of temperatures, but fixed phase
compositions), and three-phase lines (where
temperature and phase compositions are fixed).
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The Phase Rule

• The Gibbs phase rule is a fundamental relation
  between the number of components in a chemical
  system, the number of phases present, and the
  number of variables that can be independently
  varied while maintaining equilibrium (the
  variance, D).
• Consider a system of C components with f
  coexisting phases. How many free parameters are
  there?
• Total number of parameters P, T, and C1
  compositional parameters for each phase (C1)f
• Total number of constraints
• P must be equal in all phases f1 constraints
• T must be equal in all phases f1 constraints
• m for each component must be equal in all
  phases C(f1)
• in special cases (critical, singular points,
  etc.), other constraints
• Remaining degrees of freedom (C1)f
  (C2)(f1) C f 2

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Minerals

• Mineralogy is a whole course unto itself! We
  have time only for the briefest introduction.
• Definition A mineral is a naturally occurring,
  inorganic, solid crystalline material with a
  defined range of composition.
• Minerals can be essentially one-component phases
  (e.g., quartz, basically pure SiO2) or
  multi-component solid solutions (e.g. olivine,
  mostly Fe2SiO4-Mg2SiO4).
• Mineralogical and thermodynamic nomenclature are
  somewhat different
• Both mineral groups and specific components are
  assigned names, sometimes confusingly the same
  name.
• The mineral phase olivine is a solid solution
  between forsterite (Mg2SiO4), fayalite (Fe2SiO4),
  and some other components.
• The mineral phase spinel includes components
  magnetite (Fe3O4), chromite (MgCr2O4), and the
  component spinel (MgAl2O4).

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Minerals
Minerals are periodic structures constructed by
packing of ions (either single-atom ions like Na
or compound ions like carbonate CO32-) Ionic
radii and charge balance are the critical factors
determining mineral structure Anions ( ions) are
big, cations ( ions) are small, so volume is
usually dominated by anions, with cations in
interstitial spaces Radius determines whether a
cation is likely to be coordinated by 4
(tetrahedral), 6 (octahedral), 8, or 12 anions
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Classification of Minerals

• Minerals are usually organized by anionic groups
  silicates, carbonates, halides, sulfates,
  phosphates, oxides, etc.
• Within the silicates, which are all based on
  arrangements of SiO44- tetrahedra (below 10 GPa
  pressure), we classify minerals by the geometry
  of the network of tetrahedra
• Framework silicates all tetrahedra share four
  corners with other tetrahedra
• Layer silicates every tetrahedron shares three
  corners with other tetrahedra
• Double chain silicates half of the tetrahedra
  share three, half share two corners
• Single chain silicates every tetrahedron shares
  two corners with other tetrahedra
• Dimer silicates each tetrahedron shares one
  corner with another tetrahedron
• Isolated tetrahedra silicates every tetrahedron
  is isolated
• Mineral structure is a function of composition,
  expecially the ratio of octahedral to tetrahedral
  cations. The above list is in order of increasing
  fraction of octahedral cations (i.e. things
  bigger than Al3).

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Classification of Minerals
Framework silicate (quartz, feldspars) all
corners shared no octahedral sites.
42
Classification of Minerals

• Sheet silicate micas, most clay minerals.
• The unshared oxygens are all on one side of the
  layer these oxygens can help coordinate other
  cations. The layers are paired together around a
  layer of octahedrally coordinated cations

• There are two to six octahedral sites per 8
  tetrahedral sites.
• Example talc Mg6Si8O20(OH)4.

43
Classification of Minerals

• Chain silicate structures double chain in
  amphiboles, single chain in pyroxenes.
• Again, all the unshared oxygens are on one side
  of the chain, and these chains pair up around a
  chain of octahedral sites.

There are 7 octahedral sites per 8 tetrahedral
sites in amphibole, e.g. anthophyllite
Mg7Si8O22(OH)2 There are 8 octahedral sites for
each 8 tetrahedral sites in pyroxene. Example
enstatite MgSiO3
44
Classification of Minerals
Silicate dimer structure based on Si2O76-
groups Example epidote group Ca2Al3Si3O12(OH). Th
is structure allows about 5 octahedral sites per
3 tetrahedral sites.
Isolated tetrahedra no corner sharing This
structure allows 2 octahedral sites for every one
tetrahedral site. Example olivine group
(Mg,Fe,Ca,Mn,Ni)2SiO4
45
Major Minerals of Igneous Rocks
The relationship between mineral structure and
ratio of octahedral cations (mostly Fe, Mg, Ca)
and tetrahedral cations (mostly Si, Al) allows
you to readily understand the minerals that show
up in rocks as a function of composition
expressed as SiO2 content
46
Major Minerals of Igneous Rocks Ultramafic
The average composition of the Earths upper
mantle is SiO2 TiO2 Al2O3 FeO MgO CaO Na2O H2O Ot
hers 46 0.2 4 7.5 38 3.2 0.3 0.01 0.5 (MgFeCa
)/(SiAl) is between 1 and 2, so the upper mantle
is dominated by olivines (isolated tetrahedra
structure) and pyroxenes (chain
structure). olivine (Mg,Fe)2SiO4
Mg/(MgFe)0.9 orthopyroxene (Mg,Fe)2SiO6
clinopyroxene Ca(Mg,Fe)Si2O6 Plus an aluminous
mineral that depends on pressure 0-1 GPa,
feldspar (plagioclase) CaAl2Si2O8-NaAlSi3O8
Ca/(CaNa) 0.9 1-3 GPa, spinel MgAl2O4 gt3
GPa, garnet (Fe,Mg,Ca)3Al2Si3O12 A rock with
this mineralogy is a peridotite.
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Major Minerals of Igneous Rocks Mafic
The average composition of the Earths oceanic
crust is SiO2 TiO2 Al2O3 FeO MgO CaO Na2O K2O H2O
50.5 1.6 15 10.5 7.6 11.3 2.7 0.1 0.1 Large
enrichments over mantle in TiO2, Al2O3, CaO,
Na2O, K2O small enrichments in SiO2 and FeO
massive depletion of MgO. (FeMgCa)/(SiTiAl)
1, so basalts are dominated by pyroxenes, with
alkalis in feldspar Clinopyroxene Ca(Mg,Fe)Si2O
6 Feldspar (plagioclase) CaAl2Si2O8-NaAlSi3O8
Ca/(CaNa) 0.4-0.7 plus olivine,
orthopyroxene, and perhaps a bit of quartz. H2O
lives in Amphibole (hornblende) Ca2(Mg,Fe)4Al2Si7O
22(OH)2 A volcanic rock with this mineralogy is
a basalt. A plutonic rock with this mineralogy is
a gabbro.
48
Major Minerals of Igneous Rocks Felsic
The average composition of the Earths
continental crust is SiO2 TiO2 Al2O3 FeO MgO CaO
Na2O K2O H2O 57 0.9 16 9 5 7.4 3.1 1.0 1-3 Note
even larger enrichments over mantle in SiO2, K2O.
There are few octahedral cations, so lots of
framework silicates (quartz and feldspars to take
alkalis). H2O gives micas amphiboles before
alteration Feldspars (plagioclase) CaAl2Si2O8-NaA
lSi3O8 Ca/(CaNa) 0.1-0.6 Feldspar
(Alkali feldspar) NaAlSi3O8-KAlSi3O8 Quartz SiO
2 Mica biotite KMg3(AlSi3)O10(OH)2 Mica
Muscovite KAl2(AlSi3)O10(OH)2 Volcanic rocks
with this composition range from andesite to
rhyolite. Plutonic rocks range from diorite to
granite.
49
Synthesis Melting, mineralogy, and
differentiation

• Why does partial melting of mantle yield
  enrichment in partial melt (which goes to form
  crust) of SiO2, Al2O3, FeO, CaO, Na2O, K2O
  leaving a residue enriched in MgO?
• We can gain insight into this with a few
  essential phase diagrams.

The olivine binary phase loop an example of
continuous solid solution. Mg end-member has
higher melting point than Fe end-members. The
phase diagram shows that this translates into Mg
being more compatible than Fethe liquid is
always enriched in Fe/Mg relative to the residue.
50
Synthesis Melting, mineralogy, and
differentiation
The Mg2SiO4-SiO2 binary an example with
negligible solid solution and an intermediate
phase. The first liquid that appears on melting
of a rock consisting of forsterite (olivine) plus
enstatite (orthopyroxene) is more SiO2-rich than
enstatite. If we turn around and crystallize it,
it will make enstatite plus quartz (a model
basalt, not a peridotite!). Thus oceanic crust
is enriched in SiO2. We can make similar
arguments for CaO, Na2O, and K2O, but they
require ternary phase diagrams...