E. Goeke, Fall 2006, 12:041 Mineralogy 1

E. Goeke, Fall 2006

Crystal Growth

Chapter 5

E. Goeke, Fall 2006

Mineral Formation & Stability• For a given mineral to form:

– Chemical components mustbe available

– Appropriate pressure (P) andtemperature (T) conditionsmust exist

• Three possible conditions for amineral:– Stable– Metastable– Unstable

• Activation energy = amount ofenergy required to transformfrom a metastable to a stablestate

stable

metastable

activation energy

E. Goeke, Fall 2006

Gibbs Free Energy• Gibbs free energy = G = measure of energy to judge the

stability of a phase– Measured in Joules– Relative measure to a standard state (1 atm, 298.15 K)

• Gibbs free energy of formation (ΔGf) = difference betweenthe elements that comprise the mineral at standard stateand the mineral at the P & T of interest– Lowest ΔGf = stable mineral– ΔGf varies with T & P

ΔGf

T E. Goeke, Fall 2006

Mineral Reactions• Written out reactions must be chemically balanced!!!

• ΔGreaction is used to determine the change in energy for areaction as well as which side of the equation will be stableat a given P & T– ΔGproduct = minerals produced by the reaction– ΔGreactants = minerals that react to cause the reaction

Pyrophyllite = aluminosilicate + quartz + fluidAl2Si4O10(OH)2 = Al2SiO5 + 3SiO2 + H2O

ΔGreaction = ΔGproduct - ΔGreactantΔGreaction = (ΔGaluminosilicates + ΔGquartz + ΔGfluid) - ΔGpyrophyllite

ΔGreaction < 0, products more stableΔGreaction > 0, reactants more stable

ΔGreaction = 0, reaction at equilibrium and both sides are equally stable

E. Goeke, Fall 2006

Kinetics• From the Gibbs free energy, we can determine what

phase(s) should be stable, but it doesn’t give us any ideaabout what is actually in the rock or how quickly a reactionwill occur!!!

• Kinetics = study of reaction rates– Depend on T, P, composition of the system– Reactions tend to occur more quickly at higher T’s– Different elements will diffuse at different rates, which

can cause some minerals to become stable while othersremain metastable

E. Goeke, Fall 2006

Phase Diagrams• System = section of the universe under consideration;

determined by the scientist, so it can vary from the size ofa single unit cell all the way up to the Himalayas– Isolated system = no exchange of mass or energy with

the surroundings outside the system (e.g. closed travelcoffee mug)

– Closed system = no exchange of mass, but energy cancross the boundary between the surroundings and thesystem (e.g. coffee is now in a closed coke bottle)

– Open system = both energy and mass can exchangefreely between the system and the surroundings (e.g.coffee is now in an uncovered paper cup & you’readding cream and sugar)

E. Goeke, Fall 2006, 12:041 Mineralogy 2

E. Goeke, Fall 2006

• Phase = physically separable portion of the system that ischemically and physically distinct from everything else inthe system (e.g. one phase is present when sugar & milk isdissolved in the coffee, but two phases exist when thesugar is sitting on the bottom of the cup instead ofdissolved in the coffee)

• Components = each phase is composed of 1+ components;chosen by scientist, but you try to choose as fewcomponents as possible that describe your entire system

AB

AB

BC

BCAE. Goeke, Fall 2006

Phase Rule• Phase rule = used to determine how many variables &

equations are required to describe a system that’s inequilibrium

• Variables:– Number of chemical components– Extensive variables (pressure & temperature)

• F = C + 2 - P– F = degrees of freedom or variance of the system– C = number of components (as defined on the last slide)– P = number of phases in equilibrium– 2 comes from P & T

E. Goeke, Fall 2006http://www.tulane.edu/~sanelson/eens211/mineral_stability.htm

12

3

E. Goeke, Fall 2006

2 Component Eutectic Systems

http://csmres.jmu.edu/geollab/Fichter/IgnRx/BinryEu.html

• Liquidus = linethat separates allmelt and melt +xtal

• Solidus = line thatseparates melt +xtal and all xtal

• Eutectic = point atwhich melt + A +B exists

E. Goeke, Fall 2006

http://csmres.jmu.edu/geollab/Fichter/IgnRx/BinryEu.html

E. Goeke, Fall 2006

http://csmres.jmu.edu/geollab/Fichter/IgnRx/BinryEu.html

E. Goeke, Fall 2006, 12:041 Mineralogy 3

E. Goeke, Fall 2006

EQ Melting

E. Goeke, Fall 2006http://csmres.jmu.edu/geollab/Fichter/IgnRx/BinryEu.html

Fractional Melting

E. Goeke, Fall 2006

Lever rule = howmuch L vs. xtalis present

%xtals of A =b/(a+b)(100)%liquid =a/(a+b)(100)

E. Goeke, Fall 2006http://csmres.jmu.edu/geollab/Fichter/IgnRx/SolidSol.html

Binary Complete Solid Solution

E. Goeke, Fall 2006http://csmres.jmu.edu/geollab/Fichter/IgnRx/SolidSol.html E. Goeke, Fall 2006http://www.tulane.edu/~sanelson/eens211/2compphasdiag.html

We can also usethe Lever rulefor binary solidsolutiondiagrams

% solid =[x/(x+y)][100]%liquid =[y/(x+y)][100]

E. Goeke, Fall 2006, 12:041 Mineralogy 4

E. Goeke, Fall 2006http://www.brocku.ca/earthsciences/people/gfinn/petrology/ab-an2.gif

EQ xtalization ->final xtal comp =starting L comp

E. Goeke, Fall 2006http://www.brocku.ca/earthsciences/people/gfinn/petrology/ab-an3.gif

fractionalxtalization ->final xtal comp ≠starting L comp

E. Goeke, Fall 2006

Nucleation• For minerals to nucleate, the new cluster of atoms/ions

must have a lower ΔG then the other phases in the system(e.g. melt, aqueous solution, other minerals)

• Whether or not a mineral will nucleate will depend on P, T,and chemical composition of the system

• Size of nucleus will determine whether the new mineralwill grow in size or dissolve– Greater surface energy = less stable– Small xtals have a high surface area to volume ratio

S.A. = 6 * 2 * side lengthV = (side length)3 S.A. = 6 * 2 * 5

V = 53

S.A./V = 60/125

S.A. = 6 * 2 * 1V = 13

S.A./V = 12/1E. Goeke, Fall 2006

– Td = melt has an equalΔG to the xtal, so ifnuclei form, the highsurface energy causes thextals to simply dissolveback into the melt

– Ta = xtals have a slightlylower ΔG than the melt,but nuclei must be abovea critical size in order toavoid being resorbed;only a small number ofnuclei are present & grow

– Tb = xtals have asignificantly lower ΔGthan the melt, so manynuclei form & grow

Winter, 2001, An Introduction to Igneous & Metamorphic Geology

Td

E. Goeke, Fall 2006http://www.tulane.edu/~sanelson/eens212/metamorphreact.htm

E. Goeke, Fall 2006

Heterogeneous Nucleation• Heterogeneous nucleation occurs by a new xtal taking

advantage of a pre-existing surface or flaw to nucleate– Largely eliminates the need for seed nuclei– Reduces surface energy problems

• Can occur on:– Specific crystallographic faces of a pre-existing xtal =

epitaxial nucleation– On a structural defect such as as grain boundary or

another imperfection, where the surface energy washigher for the original xtal but the new nucleationlowers the surface energy

E. Goeke, Fall 2006, 12:041 Mineralogy 5

E. Goeke, Fall 2006

Crystal Growth• Still have to worry about surface

energy– Less when new growth is

along a pre-existing row or atflaw in the xtal

– Screw dislocations causegrowth that continually has anedge available

– New growth will try andreduce the surface energy ofthe pre-existing xtal

E. Goeke, Fall 2006

Rate of Growth• Xtals will grow fastest usually along

longer dimensions of the unit cell (e.g.halite will grow fastest along the{111} faces & slower along the {100}faces)

• Slow growing faces tend to be moreprominent– Faces with higher surface energy

will grow faster– Xtal growth tries to minimize

surface energy, so the slowgrowing faces will tend todominate in the end

E. Goeke, Fall 2006

Zoned Crystals• As a xtal grows, it changes the composition of the

melt/rock that its growing from• Some minerals can have a variation in their composition

(e.g. garnet (Fe,Mg,Ca,Mn)3(Al,Fe)2Si3O12, olivine(Fe,Mg)2SiO4, plagioclase (Na,Ca)Al(Al,Si)Si2O8), whichmeans that the xtal could change compositions as it grows

• Changes in P, T, and bulk composition can all causezoning

http://www.mtholyoke.edu/acad/geo/faculty/sd/zoned.html E. Goeke, Fall 2006

Structural Defects• Point defects = xtal imperfections dealing with single

locations in the structure– Vacant sites = Schottky defects– Atoms in the improper position = Frenkel defects– Extra atoms/ions = Interstitial defects– Atoms/ions substituted into the structure =

Substitutional defects• Line defects = due to deformation at high temperatures;

xtals deform along specific crystallographic planes & inpreferred directions (slip system)– Edge dislocation = at right angles to the main stress– Screw dislocation = movement is parallel to the main

stress

E. Goeke, Fall 2006

http://www.engr.ku.edu/~rhale/ae510/lecture2/sld027.htm

http://www.jwave.vt.edu/crcd/farkas/lectures/dislocations/tsld007.htmE. Goeke, Fall 2006

• Planar defects = mismatch of the xtal structure along asurface– Grain boundaries– Stacking faults = layers are either out of position or

sequence (e.g. ABABAABABA)– Antiphase boundaries = separate two+ sections of a xtal

that are related by a simple translation• Both have the same crystallographic orientation

http://wwwuser.gwdg.de/~upmp/neu/Arbeitsgruppen/Jooss/vizinal.html

E. Goeke, Fall 2006, 12:041 Mineralogy 6

E. Goeke, Fall 2006

Twinning• Twinning = symmetrical intergrowth of 2+ crystals of the

same mineral– Can occur during growth, due to the application of

stress to a pre-existing xtal, or because of a change inP/T conditions

– Always adds symmetry, so it doesn’t occur alongexisting symmetry of the xtal

• Operations that can cause twins:– Twin plane = reflection across a mirror plane– Twin axis = rotation around a line; always ⊥ to a lattice

plane– Twin center = inversion through a point

• Composition surface = plane/line along which latticepoints are shared by the twins

E. Goeke, Fall 2006

• Contact twins = planar composition surfaceseparates the 2+ xtals– Normally defined by a twin plane– No intergrowth of xtals– In 3+ xtals, if the composition surfaces are

parallel to each other = polysnthetic twins(e.g. plagioclase)

– If 3+ xtals have non-parallel compositionsurfaces = cyclical twins

• Penetration twins = irregular compositionsurface– Due to a twin center or twin axis– Two xtals appear intergrown

http://www.tulane.edu/~sanelson/eens211/twinning.htm

E. Goeke, Fall 2006

Origin of Twinning• Three ways to get twins:1. Growh twins

– Due to accidents during xtal growth that cause the anew xtal to be added to the face of a pre-existing xtal

– 2 xtals share lattice points, but have differentcrystallographic orientations

– Either contact or penetration twins2. Transformation twins

– Pre-existing xtal changes form due to a change inpressure and/or temperature

– Common in minerals that have different xtal structures& symmetry at different P’s & T’s (e.g. K-feldspars,pyroxenes)

– As the xtal transforms into its new structure, differentportions of the xtal arrange themselves in differentorientations E. Goeke, Fall 2006

– Tartan twinning inmicrocline is due to thecombination of albite &pericline twinning that occurwhen sanidine (high T)transforms to microcline(low T)

3. Deformation twins– Atoms are pushed out of

alignment due to stress– Commonly forms

polysynthetic twins (e.g.plagioclase, calcile)

http://www.geolab.unc.edu/Petunia/IgMetAtlas/minerals/microcline.X.html

http://www.ucl.ac.uk/~ucfbrxs/PLM/calcite.html

E. Goeke, Fall 2006

Common Twin Laws• Twin law = describes the twin operation

& the orientation of the plane/axis alongwhich the symmetry operation occurs– {hkl} = along a plane– [hkl] = axis of rotation

• Triclinic– Mainly feldspars– Albite law = {010} polysynthetic

twins ⊥ to b axis; diagnostic propertyof plagioclase

– Pericline law = [010]; normally occursduring the transformation oforthoclase/sanidine to microcline & ispresent with albite twinning to formtartan twinning

http://www.geolab.unc.edu/Petunia/IgMetAtlas/minerals/plagtwins.X.html

E. Goeke, Fall 2006

• Monoclinic– Orthoclase & sanidine mainly– Manebach law = {001} in

orthoclase; diagnostic when itoccurs

– Carlsbad law = [001], penetrationtwin in orthoclase; two xtals 180°from each other; most common typeof twinning in orthoclase, so verydiagnostic

– Braveno law = {021}, contact twinin orthoclase

– Swallow tail twins = {100},commonly found in gypsum

http://www.tulane.edu/~sanelson/eens211/twinning.htm

E. Goeke, Fall 2006, 12:041 Mineralogy 7

E. Goeke, Fall 2006

• Orthorhombic– Commonly twin on planes // to

a prsim face– {110} cyclical twins =

aragonite, chrysoberyl,cerrusite all have these twins;cyclical twins can cause themineral to appear hexagonal

– Staurolite law = staurolite isreally monoclinic, but the β ~90°, so it appears orthorhombic

• {031} forms right-angledcross

• {231} form cross at ~60°

http://www.tulane.edu/~sanelson/eens211/twinning.htm

E. Goeke, Fall 2006

• Tetragonal– {011} cyclical contact twins =

common in rutile & cassiterite• Hexagonal

– Calcilte twins = two types ofcontact twins

• {0001}• {01 12} can also occur as

polysynthetic twins due todeformation

– In quartz:• Brazil law = {11 20} penetration

twins due to transformation• Dauphiné law = [0001]

penetration twin due totransformation

• Japanese law = {11 22} contacttwin during growth http://www.tulane.edu/~sanelson/eens211/twinning.htm

E. Goeke, Fall 2006

• Isometric– Spinel law = { 111} parallel to octahedron;

common in spinel– [111] = twin axis ⊥ to octahedral face that

adds a 3-fold rotational symmetry– Iron cross = [001], interpenetration of two

pyritohedrons; occurs in pyrite; twinningcauses an apparent 4-fold symmetry

http://www.tulane.edu/~sanelson/eens211/twinning.htm

E. Goeke, Fall 2006

Postcrystallization Processes• Once a mineral has xtalized, it may become unstable due to

a change in P and/or T, the addition of a fluid phase, or achange in bulk composition

• Several processes may occur to change the metastableminerals into more stable phases:– Ordering -> may cause changes in the unit cell

dimensions and/or the symmetry (e.g. pyroxenes,amphiboles, K-feldspars)

– Twinning -> transformation twinning (e.g. K-feldspar,leucite)

– Recrystallization -> to reduce the surface energy byremoving structure defects, mineral grains changeshape and/or size

– Exsolution -> occurs in minerals that have completesolid solution at high T, but only partial solid solutionat low T’s

E. Goeke, Fall 2006http://www.ged.rwth-aachen.de/Ww/projects/rexx/Urai+86Recrystallization/Urai+86Recrystallization5.htm

E. Goeke, Fall 2006http://tesla.jcu.edu.au/Schools/Earth/EA1001/Mineralogy/Minerals/Feldspars.html

http://www.tulane.edu/~sanelson/eens211/2compphasdiag.html

At high T’s, we will have 1 feldspar,but at lower T’s 2 feldspars will bepresent (proportion with Lever rule)

E. Goeke, Fall 2006, 12:041 Mineralogy 8

E. Goeke, Fall 2006

http://www.geolab.unc.edu/Petunia/IgMetAtlas/plutonic-micro%7F/perthite1.X.html http://www.geolab.unc.edu/Petunia/IgMetAtlas/plutonic-micro%7F/perthite2.X.html

http://www.ucl.ac.uk/~ucfbrxs/PLM/opx.html

K-feldspar w/blebs ofplagioclase

Opx w/blebs of cpx

E. Goeke, Fall 2006

Pseudomorphism• Pseudomorphism = replacement ofa mineral grain by another mineral,but the 2nd mineral retains thecharacteristic grain outline of the 1stmineral– Three types:1. Substitution = direct

replacement of one mineral by asecond (e.g. chlorite aftergarnet)

2. Encrustation = thin crust of anew mineral forms on thesurface of a preexisting mineral,which is followed by theremoval of the 1st grain

3. Alteration = partial removal oforiginal mineral & only partialreplacement by the new mineral http://www.ucl.ac.uk/~ucfbrxs/PLM/opx.html

E. Goeke, Fall 2006

Radioactivity & Minerals• Radioactive decay can also cause post-crystallization

alteration• 40K and 14C are two common radioactive constituents in

minerals• U & Th may also be found in various minerals, but

usually not as a major component• The decay of one element to another can cause space

issues (e.g. 40K -> 40Ar or 40Ca, where neither daughterelement is the same size or charge as the parent)

• Decay can also cause structural damage to the mineralgrain as the released alpha particle disrupts the normalstructure (cause of metamict minerals)

• Released alpha particles may also leave the originalgrain that contained the parent mineral & enter aneighboring grain, which can cause a pleochroic halo toform around the primary mineral

http://ww

w.ucl.ac.uk/~ucfbrxs/PLM

/zircon.html