chapter 5 mineral growth - faculty.fiu.edu

Introduction to Mineralogy,

Second edition

William D. Nesse Copyright © 2012, by Oxford University Press, Inc.

CHAPTER 5

Mineral Growth


Second edition


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



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)


• 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.


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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.


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Second edition


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?


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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


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Figure 5.5 Lever rule.


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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


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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


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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


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• 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.


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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


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Figure 5.10 Growth on a crystal face.


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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


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Second edition


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


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Figure 5.13 Photomicrograph of a thin section (see Chapter 7) showing zoned crystals of pyroxene (P) (crossed polarizers).

Zoned Crystals


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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


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Figure 5.15 Point defects.


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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:


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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


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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


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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


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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.


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Figure 5.22 Penetration twins. (a) Pyrite “Iron Cross” twin by 90o rotation on [001]. (b) Staurolite twin by reflection on { 231}.


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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}.


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Figure 5.24 Transformation twinning in leucite.


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Figure 5.25 Deformation twinning in calcite can be produced by glide on {102} crystallographic planes.


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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


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Figure 5.27 Exsolution in alkali feldspar.


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Figure 5.28 Photomicrograph of a thin section of mica schist showing dark pleochroic halos around radioactive zircon (Z) inclusions in

biotite (B).

chapter 5 mineral growth - faculty.fiu.edu

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