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Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
CHAPTER 5
Mineral Growth
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.1 The rock cycle, a mineralogist’s view. The rock cycle fundamentally involves mineralogic changes in response to different
temperature–pressure (T–P) conditions.
Mineral Stability
• A bulk composition of a rock must contain
components of a mineral for the mineral to
form.
• The same bulk composition may
conceivably lead to the formation of
hundreds of minerals
• Which particular mineral forms depends
on the stability and energy of formation of
the mineralIntroduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.2 Stability.
• State with lower energy is the stable state
• Stable: The book on the floor has lower
energy, in this case lower potential energy
• Unstable : will spontaneously move to a
lower energy position
• Metastable: The book on the shelf has
higher energy but it will not attain a lower
energy state unless it is nudged from it’s
position.
• The energy required to nudge the book is
the Activation Energy
• The stability of a mineral is judged with
Gibb’s Free Energy (G). It has units that of
energy (calories or joules = 0.2390 cal) per
mole
Stability
Gibb’s Free Energy• Free energy of formation from the elements ΔGf = energy difference
between the free energy of the element in standard state (298 K and 1A)
and the free energy of the element when it is bonded in a mineral structure
at the P,T condition of interest.• For two minerals with the same chemical composition (e.g. α-Quartz and β-
Quartz or calcite and aragonite – the one with lower free energy under the
specified P,T condition is the stable form.
• ΔGf of all minerals vary with P and T – so, for example, under certain P,t
condition calcite has lower free energy and under some other condition
aragonite has lower energy (hence more stable)
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
• New minerals form by chemical reactions. Let us consider
the reaction:
Muscovite + Quartz = K-feldspar+ Sillimanite + water
KAl2(AlSi3O10)(OH)2 + SiO2 = KAlSi3O8 + Al2SiO5+H2O
(Reactants) (Products)
ΔGf (reaction) = ΔGf (products) - ΔGf (reactants)
• If ΔGf (reaction) is <0 i.e., -ve, the reaction will proceed
towards right, If ΔGf (reaction) is +ve , i.e., >0 the reactants
are more stable. At equilibrium ΔGf (reaction) = 0,
• For a given P,T,X condition, the assemblage with the
lowest ΔGf is the stable assemblage
– In reality ΔGf of all the minerals in a rock is difficult to calculate
– Minerals commonly persist metastabily even though they are not in
the lowest free energy in a given P,T,X condition.
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Phase Diagram
• A phase can be a mineral, melt or gas.
• A phase diagram represents the stable
phases for a given composition under a
given P,T condition.
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.3 Aluminum silicate stability relations.
The metamorphic minerals: Kyanite,
andalusite and sillimanite are the polymorphs
of Al2Si2O5 (or Al2O3.SiO2)
• ΔGf of formation of these three polymorphs
vary with P,T as shown in the diagram.
• The lower figure shows the stability fields of
different polymorphs under changing P,T
condition.
• If Andalusite is heated Sillimanite forms. If
pressure is increased Kyanite will form at
the expense of Andalusite
• If metamorphic rock contains Andalusite,
we can infer that the rock was
metamorphosed under low P and low to
moderate temp – typical of contact
metamorphism.
• If a metamorphic rock contains all three
isomorphs, what is the P,T condition?
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.4 Crystallization in the system diopside (Di)–anorthite (An).
After Osborn (1942). See text for discussion
Binary (two component) Eutectic Phase Diagram
• Liquidus: composition
of liquids (or melt) in
equilibrium with solids
(crystals) at a particular
temperature
• Solidus: composition of
solids (or crystals) in
equilibrium with melts at
a particular temperature
• Eutectic: Where both
components crystallize
simultaneously. Eutectic
temperature is always
lower than the melting
temp of components A
or B
• The proportion of
solid:liquid at any temp
can be found by Lever
Rule
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.5 Lever rule.
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.6 Olivine crystallization at 1 atmosphere pressure. After Bowen and Schairer (1935). See text for discussion.
Binary (two component) with continuous solid solution Phase
Diagram
Introduction to Mineralogy,
Second edition
Figure 5.7 Alkali feldspar crystallization.
Binary (two component) with
solvus Phase Diagram
Solvus: curve that defines two
co-existing phases that unmixes
from a solid solution
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.8 Free energy of formation of crystal nuclei from a melt as a function of size.
Mineral Nucleation
Homogeneous Nucleation:
• Embryos have the chemical composition and mineral structure of a mineral and
forms by chance aggregation of component ions
• number of the embryos decrease exponentially with size: most consist of a few
atoms
• Embryos can only grow if the new mineral has a lower free energy than the melt.
• Crystals also contain surface energy due to disrupted chemical bonds at the
surface of embryos. Magnitude of the surface energy is proportional to the surface
area of the crystal
The free energy change in
forming a crystal of volume v
from a melt is:
ΔGv = (ΔGf(xl) – ΔGf(melt))*v +
ΔGs
Where ΔGs is the surface
energy of the crystal
ΔGs = ɣa (where ɣ = surface
energy per unit area and a is
the surface area of the
crystal
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
• The free energy change in forming a crystal of volume v from a melt is:
ΔGv = (ΔGf(xl) – ΔGf(melt))*v + ΔGs
• Where ΔGs is the surface energy of the crystal
• ΔGs = ɣa (where ɣ = surface energy per unit area and a is the surface area of the crystal)
• For a cubic crystal with edges of length c
ΔGv = (ΔGf(xl) – ΔGf(melt))*c3 + ɣ6c2
• For T0 (equilibrium temp) : ΔGv= 0 but ΔGs is positive for all embryo size ensuring
ΔGv is positive hence no crystal growth
• For T1 (slight undercooling) = for embryos smaller than critical growth radius rc
,ΔGv >0 but for larger embryo radius, ΔGv <0 : a few large crystals
• T2= rc smaller, more
stable crystals
• T3=strong undercooling,
ΔGv <0, rc even smaller,
many nuclei can be
stable
• Crystal growth requires super cooling to provide the
activation energy to overcome surface energy
• The required activation energy is low for slow cooling,
large for fast cooling
• Plutonic rocks cool slowly few, large crystals
• Volcanic rocks cool rapidly high undercooling, many
small crystals
• Metamorphic Rocks: rate of change of pressure/temp is
low hence early formed crystals are few and large
(porphyroblasts)
• Crystals grow as
– 1. temperature rises: increases the mobility of ions
– 2. smaller grains recrystallize to form larger grains as temp rises
– 3. Larger grains can become deformed and can recrystallize to
form smaller grains due to strong deformation.
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.9 Epitaxial growth. Hematite crystal (shaded) may nucleate and grow on the (111) face of magnetite.
• Epitaxial nucleation: new crystals grow on existing crystal face – requiring
less surface energy.
• example hematite growing on pre-existing magnetite
• Crystals can also grow on imperfections in preexisting crystals
Heterogeneous Nucleation
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.10 Growth on a crystal face.
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.11 Slow-growing faces become larger.
• The 111 faces on NaCl is all Na+ (attracts Cl-) or Cl-
(attracts Na+) – so this face grows fast
• The 100 face is made of equal number of Na+ and Cl-
so no net charge – no attraction. This face grows only
by chance encounter with bumbling ions
• So each new 111 layer will be thicker than 100 layer
which will make 111 progressively smaller
• The slowest growing face is the most prominent
in a crystal.
Face full of charged Na+ or Cl- has maximum surface
energy – so adding oppositely charged layers on that
face will lower the surface energy the most – hence
that faces grows fastest
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.12 Growth rates of
crystal faces are inversely
proportional to interplanar (d)
spacing.
Law of Bravais: Most
prominent face are those that
cuts the greatest density of
lattice nodes i.e., lattice nodes
are most closely spaced..
• Spacing d(100)>d(001)>d(102) planes
• So growth will be fastest normal to (102) face and
slowest normal to (100) face
• Lattice node spacing on (102)>(001)>(100)
• So, 102 will grow fastest and will be the smallest
• The growth rate of crystal face is, in
general, inversely proportional to the
interplanar spacing of that face
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.13 Photomicrograph of a thin section (see Chapter 7) showing zoned crystals of pyroxene (P) (crossed polarizers).
Zoned Crystals
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.14 Plagioclase phase diagram at 5 kbar water pressure. Adapted from Yoder and others (1957). (a) Equilibrium crystallization.
(b) Fractional crystallization.
Zoned plagioclase where
crystals are not allowed to
react with the melt
Structural Defects:• Point Defects
• Line Defects
• Edge Defects
Point Defectsa. Schottkey Defect: Vacanct cation balanced by vacant anion: no change in
formula
b. Frenkel Defect: Cation out of place: cations are smaller and move more easily
c. Interstitial Defect: Foreign ion push it’s way in. Charge is balanced by
elsewhere by substituting lower charge cation for higher charge cation
d. Substitution Defect: substitutes a normal ion: should we call it a defect?
More defects at higher temperature and also more diffusion
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.15 Point defects.
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.16 Slip system in a crystal lattice. Slip occurs on a crystal plane parallel to (001) and in a direction parallel to [010] (the b a xis),
so the slip system is { 001}[010].
Slip System = crystallographic plane (along
which slip is taking) and slip direction e.g.,
{001}[010] in the figure
Ductile deformation of rocks require deformation of constituent minerals
Deformation of minerals takes place by slip along favored crystallographic planes
• Dislocation line: edges of propagating
slip surface where bonds are being
broken
• Boundary between slipped and not yet
slipped domains
• Can be edge dislocation or screw
dislocation
Line Defects:
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.17 Dislocations.
Line Defects
• Buergers vector: Same as dislocation direction– Start at any point on lattice nodes and trace a circuit around the dislocation making sure to
move equal number of lattice nodes in opposite direction.
– The vector between the starting and finishing node is the Buergers vector
– Perpendicular to the dislocation line in Edge dislocation
– Parallel to dislocation line in screw dislocation
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.18 Unless terminated at the edge of a crystal, a dislocation line (DL) forms a continuous loop outlining a surface, equivalent to a
fault, with movement parallel to the Buergers vector.
Planar Defects:
Mismatch of crystal structure along a surface
• Grain Boundaries
• Stacking Faults: e.g., ABABCABAB – in a hexagonal
close packing structure
• Antiphase Boundaries: separates segments of crystal
known as Antiphase domains that are related to each
other by simple translation
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.20 Symmetry operations in twinning. (a) Twinning by reflection on {011} in rutile. (b) Twinning by rotation on [001] in K-feldspar
to produce a Carlsbad twin.
Twinning:
Symmetrical intergrowth of two or more crystal
segments of the same mineral
• Twin Operation: symmetry operation that relates
the two segment
• Reflection, Rotation, Inversion
• Twin Law: Twin operation + crystallographic plane
or operation associated with twinning.
• E.g., reflection on {hkl}
• Composition plane: surface along which the
two twin segments are joined
• Contact Twins: not intergrown joined along a plane
• Penetration Twins: Twin segments intergrown
• Simple Twins: Only two twin segments
• Multiple Twins
• Polysynthetic twins: successive parallel
composition planes
• Cyclic twins: composition planes are not
parallel
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.21 Contact twins. (a) Octahedron of spinel twinned by reflection on { 11T} (spinel law). (b) Gypsum twinned by reflection o n
{100}. ( c) Calcite twin with {001} composition plane.
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.22 Penetration twins. (a) Pyrite “Iron Cross” twin by 90o rotation on [001]. (b) Staurolite twin by reflection on { 231}.
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.23 Multiple twins. (a) Polysynthetic twinning in plagioclase by repeated reflection on {010}. These twins are known as albite
twins. (b) Cyclic twinning in rutile by repeated reflection on {011}.
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.24 Transformation twinning in leucite.
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.25 Deformation twinning in calcite can be produced by glide on {102} crystallographic planes.
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.26 Recrystallization.
Post Crystallization Processes:
• Ordering: in K-Feldspar polymorphs
• Twinning: often during polymorphic transition
• Recrystallization:
• Minerals tend to reduce their surface
area to reduce the surface energy
• Done by smoothening irregular outlines
• Increasing grain size
• Higher temperature facilitates movement
and diffusion of ions making
recrystallization effective
• At high enough temperature, defects are
healed.
• Exsolution
• Perthite (albite in K-feldspar) and anti-
perthite (K-Feldspar in Albite)
• Pseudomorphism: replacing mineral
maintains the form of the original mineral
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.27 Exsolution in alkali feldspar.
Introduction to Mineralogy,
Second edition
William D. Nesse Copyright © 2012, by Oxford University Press, Inc.
Figure 5.28 Photomicrograph of a thin section of mica schist showing dark pleochroic halos around radioactive zircon (Z) inclusions in
biotite (B).