Lecture 4: Chemistry of silicate melts and minerals

Report
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 Earth’s
crust, and what does this have to do with their
composition and structure?
• Tools
– Chemical thermodynamics (i.e., mostly calculus)
– Ionic radii
1
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.
2
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!
3
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.
4
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.
unstable
not at equilibrium
metastable
– 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.
stable
5
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.
6
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
7
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
dE  dq  dw  dq  PdV
(4.1)
• This is the First Law of Thermodynamics. Note: absolute
values of E are arbitrary; only its changes dE are significant.
8
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
dS  dqrev / T
(4.2)
• 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:
(4.3)
dS  dq / T
• This is the Second Law of Thermodynamics. If we expand our
consideration to the system and its environment, which form
an isolated system with dq=0, 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.
9
Chemical thermodynamics: Equilibrium
• Combining the first and second laws,
dE  TdS  PdV
(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,
dS  0, dV  0  dE  0
• 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 equilibrium…a minimum in E.
10
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,
dE  TdS  PdV  mdm
(4.5)
• Likewise, for a system of n components (independently
variable chemical species), each component has a chemical
potential mi such that
n
dE  TdS – PdV +  mi dmi
i=1
(4.6)
11
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:
A 
 A 
dA   
dx1   
dx2 
x1 x , ,x
x2 x ,x , ,x
2
j
1 3
j
A 
  
dx j
xj x , ,x
1
j 1
• Comparing this form to (4.6), we see that for reversible
changes
n
dE  TdS – PdV +  mi dmi
i=1
E 
T
S V,m
i
 E 
E 
 P  
V S,m
mi S,V,m
i
 mi
(4.7)
ji
12
Chemical thermodynamics: E-S-V space
E
 E 
 P
 V S
S
 E 
T
 S  V
V
What is the curvature of the E-surface for a stable phase?
E
2

 E
2 
 V S
V
E
2

 E
2 
 V S
V
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 evergrowing high-V, high-P phase. That
is, only a point on a concave-up E
surface can be at equilibrium.
13
Chemical thermodynamics: derivative properties
• More definitions:
1 V 
• coefficient of isobaric thermal expansion  P 
V T P
1 V 



• isothermal compressibility
T
V P T
1 V 
• isentropic compressibility S  
V P S
Q
S
• heat capacity at constant pressure CP   rev   T  
 T P
T P
Q
S
• heat capacity at constant volume CV   rev   T  
 T V
T V
14
Chemical thermodynamics: derivative properties
• Note that S and Cv are related to second derivatives of E, so their
sign is fixed by the stability condition on concavity of the Esurface
 2 E 
1
P 
 E 

 V
V
 V  2   0
V S
S
V V S
V S
1 1 T 
1  E 
1  2 E 


  2   0
Cv T S V T S S V T S V
• 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 T and Cp are
also strictly positive for all stable phases.
• You cannot have a phase with negative compressibility or heat
capacity…it will spontaneously disintegrate!
• Note that p can have either sign…it is perfectly acceptable to
have a phase with negative thermal expansion.
15
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 useless…there 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
df
df
g( )  f (x)  x
dx
dx
16
Chemical thermodynamics: other potentials
• First Legendre Transformation: define enthalpy H
E 

H(P,S, mi )  E(V, S, mi )  V
 E  PV
V S,m
i
H(P)=E+PV
 E 
 P
V S
E(V)
V
dH  dE  PdV  VdP
For a closed system,
dE≤ TdS – PdV, so
dH  TdS  PdV  PdV  VdP
dH  TdS  VdP
For open system of one or many components, respectively:
dH  TdS + VdP + mdm
(4.9)
n
dH  TdS + VdP +  mi dmi
i=1
(4.10)
17
(4.8)
Chemical thermodynamics: Equilibrium II
dH  TdS  VdP
• 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,
dS  0, dP  0  dH  0
• 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 equilibrium…a
minimum in H.
• This is no longer of strictly theoretical interest: during adiabatic, reversible
pressure changes (as in the atmosphere and the Earth’s 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, dH=dq, so enthalpy is a direct measure of heat transferred
into or out of an isobaric system.
18
Chemical thermodynamics: other potentials
• 2nd Legendre Transformation: define Helmholtz Free Energy F
E 

F(V,T,mi )  E(V,S, mi )  S
 E  TS
S V,m
i
dF  dE  TdS  SdT
E(S)
F(T)=E–TS
 E 
T
  S V
S
For a closed system,
dE≤ TdS – PdV, so
dF  TdS  PdV  TdS  SdT
dF  SdT  PdV
(4.11)
For open system of one or many components, respectively:
dF  SdT  PdV + mdm (4.12)
n
dF  SdT  PdV +  mi dmi (4.13)
i=1
19
Chemical thermodynamics: Equilibrium III
dF  SdT  PdV
• 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,
dT  0,dV  0  dF  0
• 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 equilibrium…a 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, dF=dw, so Helmholtz free energy is a direct
measure of work done on or by an isothermal system.
20
Chemical thermodynamics: other potentials
• Finally, if we do both Legendre transformations, we obtain a
definition of Gibbs Free Energy G
E 
E 


G(P,T, mi )  E(V, S, mi )  S
V
 E  TS  PV
S V,m
V S,m
i
i
(Clearly G = H – TS = F + PV)
dG  dE  TdS  SdT  PdV  VdP
For closed system,
dG  TdS  PdV  TdS  SdT  PdV  VdP
dG  SdT  VdP
(4.14)
For open system of one or many components, respectively:
dG  SdT  VdP + mdm (4.15)
n
dG  SdT  VdP +  mi dmi (4.16)
i=1
21
Chemical thermodynamics: Equilibrium IV
dG  SdT  VdP
• Now we are getting somewhere: If in a closed system we fix
constant T and constant P,
dT  0,dP  0  dG  0
• 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 equilibrium…a 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.
22
Chemical thermodynamics: more on G
• From the definition of dG, we find the partial derivatives of G:
G 
G 

G 
 S
 V 
(4.17)
 mi
 
T P,m
P T,m
mi 
i
i
P,T,m j i
• Thus the second derivatives of G are
Cp
 2 G 
S 


0
 2 


T P,mi
T
T P,m
i
G
 G 
 S
 T P
T
 2 G 
V 

 VT  0
 2 


P T,mi
P T,m
i
 G 
V
 P  T
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
P
23
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.
24
Phase diagrams: one component
vapor
G
T=To
P=Po
solid
G
G 
V
P T,m
i
liquid
G 
 S
T P,m
solid
liquid
vapor
vapor
To
i
solid liquid
P2 P1 Po
P
T
P=P1
G
P=P2
G
solid
vapor
To
T
solid
vapor
To
T
25
Phase diagrams: one component
T
P
melting/freezing curve
SOLID
LIQUID
boiling/condensation
curve
G
VAPOR
liquid
P
solid
triple point
vapor
sublimation curve
P
SOLID
LIQUID
VAPOR
T
T
26
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 GX diagrams at constant P and T.
27
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 = mA+mB. Define the mass
fraction of component A, XA = mA/m. Clearly XB = mB/m = 1 – XA.
28
Phase diagrams: two components
• For system A-B equation (4.16) reduces to
dG  SdT  VdP + mAdmA + mBdmB
• It is useful to divide by mass to put this in intensive terms, where
a bar over a quantity denotes per unit mass:
dG  S dT  V dP + m AdXA + mBdXB
• Now integrate over the whole system at equilibrium (constant T,
constant P, and constant mA and mB):
G  m A XA  mB XB  mA XA  m B 1  XA   mB  m A  m B XA
G(XA) for a phase
(concave-up = stable)
G
mB(XA)
slope=( m A-mB)
B
XA
m A(XA)
A
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
29
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:
T=T1,P=constant
G
mB (XA)
SOLID
LIQUID
SOLID
stable
B
SOLID+LIQU ID
stable
XA
LIQUID
stable
mA(XA)
A
• The sequence of stable, minimum G assemblages across the diagram is found
by locating the common tangent line, which gives the compositions of solid and
liquid where they have equal mB and equal mA – they are in equilibrium!
Between these points, a mixture of the two phases gives G along the common
tangent line, lower than either of the one-phase curves. Outside these points,
since a mixture of phases must have positive amounts of each, the lowest G is
achieved with one phase alone.
30
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:
T3>T2,P=constant
T2>T1,P=constant
T0<T1,P=constant
SOLID
SOLID
LIQUID
G
LIQUID
LIQUID
LIQUID stable
XA
S S+L
SOLID
LIQUID
stable
XA
SOLID stable
XA
• 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.
31
Phase diagrams: two components, solid solution
• The resulting T-X diagram might look familiar:
T3
LIQUID
T2
TT
1
SOLID
SO
stable
LID
+L
IQ
UID
s
ta b
le
stable
T0
P=constant
B
XA
A
• 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.
32
Phase diagrams: two components, solid solution
T3
LIQUID
T2
TT
1
SOLID
SO
stable
LID
+L
IQ
UID
s
ta b
le
stable
T0
P=constant
B
XA
A
• 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
XA  f
solid
X
solid
A
f
li qui d
X
li qui d
A
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
solid
X

X
A
A
f li qui d  li qui
d
solid
XA  XA
(4.18)
33
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.
34
Phase diagrams: two components, eutectic
T3,P=constant
a
T2,P=constant
b
b
a
LIQUID stable
A
a+LIQUID
B
XA
TE,P=constant
A
B
XA
T1,P=constant
a
b
a
LIQUID stable
b+LIQUID
LIQUID
a stable
LIQUID
b stable
G
b
LIQUID
G
XA
B
a stable
A
a+b stable
b stable
A
a+b+LIQUID
b stable
a stable
LIQUID
XA
B
35
Phase diagrams: two components, eutectic
If we assemble the stable sequences from each T into a T-X section...
T3
P=constant
LIQUID
T
T2
a
a+LIQUID
b+
LIQUID
TE
b
a+b
T1
A
XA
B
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).
36
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 C–1 compositional
parameters for each phase = (C+1)f
• Total number of constraints:
• P must be equal in all phases: f–1 constraints
• T must be equal in all phases: f–1 constraints
• m for each component must be equal in all phases: C(f–1)
• in special cases (critical, singular points, etc.), other constraints
• Remaining degrees of freedom: (C+1)f – (C+2)(f–1) = C – f + 2
D  C  f  2  other
37
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).
38
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
39
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 SiO44tetrahedra (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+).
40
Classification of Minerals
Framework silicate (quartz, feldspars): all corners shared; no
octahedral sites.
41
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.
42
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
43
Classification of Minerals
Silicate dimer structure: based on Si2O76- groups
Example: epidote group Ca2Al3Si3O12(OH).
This 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
44
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:
45
Major Minerals of Igneous Rocks: Ultramafic
The average composition of the Earth’s upper mantle is:
SiO2 TiO2 Al2O3 FeO MgO CaO Na2O H2O
46% 0.2
4
7.5
38
3.2
0.3
0.01
Others
≤0.5
(Mg+Fe+Ca)/(Si+Al) 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/(Mg+Fe)~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/(Ca+Na) ~0.9]
1-3 GPa, spinel
MgAl2O4
>3 GPa, garnet
(Fe,Mg,Ca)3Al2Si3O12
A rock with this mineralogy is a peridotite.
46
Major Minerals of Igneous Rocks: Mafic
The average composition of the Earth’s oceanic crust is:
SiO2 TiO2 Al2O3 FeO MgO CaO Na2O K2O
50.5 1.6
15
10.5 7.6
11.3 2.7
0.1
H2O
0.1
Large enrichments over mantle in TiO2, Al2O3, CaO, Na2O, & K2O;
small enrichments in SiO2 and FeO; massive depletion of MgO.
(Fe+Mg+Ca)/(Si+Ti+Al) ~ 1, so basalts are dominated by
pyroxenes, with alkalis in feldspar
Clinopyroxene
Feldspar (plagioclase)
Ca(Mg,Fe)Si2O6
CaAl2Si2O8-NaAlSi3O8
[Ca/(Ca+Na) ~0.4-0.7]
plus olivine, orthopyroxene, and perhaps a bit of quartz. H2O lives in
Amphibole (hornblende)
Ca2(Mg,Fe)4Al2Si7O22(OH)2
A volcanic rock with this mineralogy is a basalt.
A plutonic rock with this mineralogy is a gabbro.
47
Major Minerals of Igneous Rocks: Felsic
The average composition of the Earth’s 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)
Feldspar (Alkali feldspar)
Quartz
Mica: biotite
Mica: Muscovite
CaAl2Si2O8-NaAlSi3O8
[Ca/(Ca+Na) ~0.1-0.6]
NaAlSi3O8-KAlSi3O8
SiO2
KMg3(AlSi3)O10(OH)2
KAl2(AlSi3)O10(OH)2
Volcanic rocks with this composition range from andesite to rhyolite.
Plutonic rocks range from diorite to granite.
48
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 endmembers. The phase diagram
shows that this translates into
Mg being more compatible
than Fe…the liquid is always
enriched in Fe/Mg relative to
the residue.
49
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 SiO2rich 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...
50

similar documents