Title: Lecture 4: Chemistry of silicate melts and minerals: chemical thermodynamics, melting, mineralogy
1Lecture 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
2Chemical 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.
3Chemical 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!
4More 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.
5Chemical 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.
6Chemical 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.
7Chemical 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
8Chemical 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.
9Chemical 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.
10Chemical 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.
11Chemical 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)
12Chemical 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)
13Chemical 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.
14Chemical thermodynamics derivative properties
- More definitions
- coefficient of isobaric thermal expansion
- isothermal compressibility
- isentropic compressibility
- heat capacity at constant pressure
- heat capacity at constant volume
15Chemical 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.
16Chemical 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
17Chemical 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)
18Chemical 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.
19Chemical 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)
20Chemical 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.
21Chemical 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)
22Chemical 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.
23Chemical 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
24Phase 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.
25Phase diagrams one component
26Phase diagrams one component
27Phase 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.
28Phase 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.
29Phase 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
30Phase 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
31Phase 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.
32Phase 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.
33Phase 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)
34Phase 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.
35Phase diagrams two components, eutectic
36Phase 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).
37The 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
38Minerals
- 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).
39Minerals
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
40Classification 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).
41Classification of Minerals
Framework silicate (quartz, feldspars) all
corners shared no octahedral sites.
42Classification 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.
43Classification 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
44Classification 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
45Major 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
46Major 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.
47Major 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.
48Major 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.
49Synthesis 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.
50Synthesis 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...