GOLDSCHMIDT’S RULES
1. The ions of one element can extensively replace
those of another in ionic crystals if their radii differ
by less than approximately 15%.
2. Ions whose charges differ by one unit substitute
readily for one another provided electrical neutrality
of the crystal is maintained. If the charges differ by
more than one unit, substitution is generally slight.
3. When two different ions can occupy a particular
position in a crystal lattice, the ion with the higher
ionic potential forms a stronger bond with the
anions surrounding the site.
RINGWOOD’S MODIFICATION OF
GOLDSCHMIDT’S RULES
4. Substitutions may be limited, even when the size
and charge criteria are satisfied, when the
competing ions have different electronegativities
and form bonds of different ionic character.
This rule was proposed in 1955 to explain
discrepancies with respect to the first three
Goldschmidt rules.
For example, Na+ and Cu+ have the same radius
and charge, but do not substitute for one
another.
INCOMPATIBLE VS. COMPATIBLE
TRACE ELEMENTS
Incompatible elements: Elements that are too large
and/or too highly charged to fit easily into common
rock-forming minerals that crystallize from melts.
These elements become concentrated in melts.
Large-ion lithophile elements (LIL’s): Incompatible owing to
large size, e.g., Rb+, Cs+, Sr2+, Ba2+, (K+).
High-field strength elements (HFSE’s): Incompatible owing to
high charge, e.g., Zr4+, Hf 4+, Ta4+, Nb5+, Th4+, U4+, Mo6+, W6+,
etc.
Compatible elements: Elements that fit easily into rockforming minerals, and may in fact be preferred, e.g.,
Cr, V, Ni, Co, Ti, etc.
Partition Coefficients
• How can we quantify the distribution of trace
elements into minerals/rocks?
• Henry’s Law describes equilibrium distribution of
a component (we usedit for thinking about gases
dissolved in water recently):
– aimin = kiminXimin
– aimelt = kimeltXimelt
– All simplifies to:
 ppmimin   X imin 
D






K
i
melt 
melt 

 ppmi   X i 
• Often termed KD, values tabulated…
http://www.earthref.org/databases/index.html?main.htm
Changes in element concentration in the magma
during crystal fractionation of the Skaergaard
intrusion: Divalent cations
Changes in element concentration in the magma
during crystal fractionation of the Skaergaard
intrusion: Trivalent cations
THREE TYPES OF TRACEELEMENT SUBSTITUTION
1) CAMOUFLAGE
2) CAPTURE
3) ADMISSION
CAMOUFLAGE
• Occurs when the minor element has the
same charge and similar ionic radius as
the major element (same ionic potential;
no preference.
• Zr4+ (0.80 Å); Hf4+ (0.79 Å)
• Hf usually does not form its own mineral; it
is camouflaged in zircon (ZrSiO4)
CAPTURE
• Occurs when a minor element enters a
crystal preferentially to the major
element because it has a higher ionic
potential than the major element.
• For example, K-feldspar captures Ba2+
(1.44 Å; Z/r = 1.39) or Sr2+ (1.21 Å; Z/r =
1.65) in place of K+ (1.46 Å, Z/r = 0.68).
• Requires coupled substitution to
balance charge: K+ + Si4+  Sr2+ (Ba2+)
+ Al3+
ADMISSION
• Involves entry of a foreign ion with an ionic
potential less than that of the major ion.
• Example Rb+ (1.57 Å; Z/r = 0.637) for K+
(1.46 Å, Z/r = 0.68) in K-feldspar.
• The major ion is preferred.
Melt composition, evolution
• Lots of different igneous rock types…
• Where do all these different magma
compositions come from?
Melts
• Liquid composed of predominantly silica and
oxygen. Like water, other ions impart greater
conductivity to the solution
• Si and O is polymerized in the liquid to differing
degrees – how ‘rigid’ this network may be is
uncertain…
• Viscosity of the liquid  increases with increased
silica content, i.e. it has less resistance to flow with
more SiO2… related to polymerization??
• There is H2O is magma  2-6% typically – H2O
decreases the overall melting T of a magma, what
does that mean for mineral crystallization?
• Minerals which form are
thus a function of melt
composition and how fast it
cools (re-equilibration?) 
governed by the stability of
those minerals and how
quickly they may or may not
react with the melt during
crystallization
Ca2+
O2Si4+
O2-
Mg2+
Na+
Fe2+
Liquid hot O2MAGMA
2O
O2- Si4+ O2- O2O2- O2- Si4+
Mg2+
O2-
cooling
rock
Mg2+
Fe2+
Processes of chemical differentiation
• Partial Melting: Melting of a different solid
material into a hotter liquid
• Fractional Crystallization: Separation of
initial precipitates which selectively
differentiate certain elements…
• Equilibrium is KEY --? Hotter temperatures
mean kinetics is fast…
Melting
• First bit to melt from a solid rock is generally more
silica-rich
• At depth in the crust or mantle, melting/precipitation
is a P-T process, governed by the ClausiusClapeyron Equation – Slope is a function of entropy
and volume changes!
• But with water… when minerals precipitate they
typically do not pull in the water, melt left is ‘diluted’
 develop a negative P-T slope
Melting and Crystallization
• Considering how trace elements incorporate the
melt or solid:
Cimelt
1
 D
0
Ci (rock ) K i (1  F )  F
• Where KD(rock)=SKD(j minerals)Xj
• For consideration of trace elements into a solid,
use Rayleigh fractionation equation:
melt
i
C
C
0
i ( rock )

K
F

D
i 1
• Where F is the fraction of melt remaining
Thermodynamic definitions
• Gi(solid) = Gi(melt)
• Ultimately the relationships between these is related to the
entropy of fusion (DS0fus), which is the entropy change
associated with the change in state from liquid to crystal
 dT  RT fus

 
0
dX
D
S
fus
 i
• These entropies are the basis for the order associated with
Bowen’s reaction series  greater bonding changes in
networks, greater entropy change  lower T equilibrium
SOLID SOLUTION
• Occurs when, in a crystalline solid, one
element substitutes for another.
• For example, a garnet may have the
composition:
(Mg1.7Fe0.9Mn0.2Ca0.2)Al2Si3O12.
• The garnet is a solid solution of the following
end member components:
Pyrope - Mg3Al2Si3O12; Spessartine Mn3Al2Si3O12;
Almandine - Fe3Al2Si3O12; and Grossular -
Melt-crystal equilibrium 1b
• Precipitated crystals
react with cooling
liquid, eventually will
re-equilibrate back,
totally cooled magma
xstals show same
composition
• UNLESS it cools so
quickly the xstal
becomes zoned or the
early precipitates are
segregated and
removed from contact
with the bulk of the
melt
Why aren’t all feldspars
zoned?
• Kinetics, segregation
• IF there is sufficient time, the crystals will
re-equilibrate with the magma they are in
– and reflect the total Na-Ca content of
the magma
• IF not, then different minerals of different
composition will be present in zoned
plagioclase or segregated from each other
physically
• What about minerals that do not
coexist well – do not form a solid
solution – are immiscible??
• More than 1 crystal can precipitate from a melt –
different crystals, different stabilities…
– 2+ minerals that do not share equilibrium in a melt are
immiscible (opposite of a solid solution)
– Liquidus  Line describing equilibrium between melt and
one mineral at equilibrium
– Solidus  Line describing equilibrium with melt and solid
– Eutectic  point of composition where melt and solid can
coexist at equilibrium
Diopside is a pyroxene
Anorthite is a feldspar
Eutectic
Solidus
Liquidus
• Melt at composition X cools to point Y where anorthite
(NOT diopside at all) crystallizes, the melt becomes more
diopside rich to point C, precipitating more anorthite with
the melt becoming more diopside-rich
• This continues and the melt continues to cool and shift
composition until it reaches the eutectic when diopside
can start forming
At eutectic, diopside
AND anorhtite crystals
precipitate
Lever Rule 
diopside/anorthite
(42%/58%) crystallize
until last of melt
precipitates and the rock
composition is Z
A
B
C
S1
S2
Z
• Melting  when heated to eutectic, the
rock would melt such that all the heat goes
towards heat of fusion of diopside and
anorthite, melts so that 42% diopside /
58% anorthite…
• When diopside gone, temperature can
increase and rest of anorthite can melt
(along liquidus)
Constructing immiscibility diagrams
Melt-crystal equilibrium 2 miscibility
monalbite
anorthoclase
1100
Temperature (ºC)
• 2 component mixing
and separation 
chicken soup
analogy, cools and
separates
• Fat and liquid can
crystallize separately
if cooled slowly
• Miscibility Gap – no
single mineral is
stable in a
composition range
for x temperature
high albite
900
700
500
sanidine
intermediate albite
orthoclase
low albite
microcline
Miscibility Gap
300
10
Orthoclase
KAlSi3O8
30
50
% NaAlSi3O8
70
90
Albite
NaAlSi3O8
Homework
• Chapter 8
• Problems 2, 6