Crystal Growth Mineral Formation & Stability Gibbs Free Energy ...

Crystal Growth 

Chapter 5 

Gibbs Free Energy 

E. Goeke, Fall 2006 

• 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 (ΔG f) = difference between 

the elements that comprise the mineral at standard state 

and the mineral at the P & T of interest 

– Lowest ΔG f = stable mineral 

– ΔG f varies with T & P 

ΔG f 

T 

Kinetics 


• From the Gibbs free energy, we can determine what 

phase(s) should be stable, but it doesn’t give us any idea 

about what is actually in the rock or how quickly a reaction 

will 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 others 

remain metastable 


Mineral Formation & Stability 

• For a given mineral to form: 

– Chemical components must 

be available 

– Appropriate pressure (P) and 

temperature (T) conditions 

must exist 

• Three possible conditions for a 

mineral: 

– Stable 

– Metastable 

– Unstable 

• Activation energy = amount of 

energy required to transform 

from a metastable to a stable 

state 

metastable 

Mineral Reactions 

• Written out reactions must be chemically balanced!!! 

Pyrophyllite = aluminosilicate + quartz + fluid 

Al 2Si 4O 10(OH) 2 = Al 2SiO 5 + 3SiO 2 + H 2O 

activation energy 


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

stable 

• ΔGreaction is used to determine the change in energy for a 

reaction as well as which side of the equation will be stable 

at a given P & T 

– ΔGproduct = minerals produced by the reaction 

– ΔGreactants = minerals that react to cause the reaction 

ΔGreaction = ΔGproduct - ΔGreactant ΔGreaction = (ΔGaluminosilicates + ΔGquartz + ΔGfluid) - ΔGpyrophyllite ΔGreaction < 0, products more stable 

ΔGreaction > 0, reactants more stable 

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

Phase Diagrams 

• System = section of the universe under consideration; 

determined by the scientist, so it can vary from the size of 

a 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 travel 

coffee mug) 

– Closed system = no exchange of mass, but energy can 

cross the boundary between the surroundings and the 

system (e.g. coffee is now in a closed coke bottle) 

– Open system = both energy and mass can exchange 

freely between the system and the surroundings (e.g. 

coffee is now in an uncovered paper cup & you’re 

adding cream and sugar) 


E. Goeke, Fall 2006

• Phase = physically separable portion of the system that is 

chemically and physically distinct from everything else in 

the system (e.g. one phase is present when sugar & milk is 

dissolved in the coffee, but two phases exist when the 

sugar is sitting on the bottom of the cup instead of 

dissolved in the coffee) 

• Components = each phase is composed of 1+ components; 

chosen by scientist, but you try to choose as few 

components as possible that describe your entire system 

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

1 

3 

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

2 

A 

B 

AB 

BC 

BCA 




Phase Rule 

• Phase rule = used to determine how many variables & 

equations are required to describe a system that’s in 

equilibrium 

• 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 

2 Component Eutectic Systems 




• Liquidus = line 

that separates all 

melt and melt + 

xtal 

• Solidus = line that 

separates melt + 

xtal and all xtal 

• Eutectic = point at 

which melt + A + 

B exists 



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

EQ Melting 


Lever rule = how 

much L vs. xtal 

is present 

%xtals of A = 

b/(a+b)(100) 

%liquid = 

a/(a+b)(100) 


Fractional Melting 


Binary Complete Solid Solution 

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



We can also use 

the Lever rule 

for binary solid 

solution 

diagrams 

% solid = 

[x/(x+y)][100] 

%liquid = 

[y/(x+y)][100] 

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

http://www.tulane.edu/~sanelson/eens211/2compphasdiag.html E. Goeke, Fall 2006 


http://www.brocku.ca/earthsciences/people/gfinn/petrology/ab-an2.gif 

Nucleation 

EQ xtalization -> 

final xtal comp = 

starting L comp 


• 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 mineral 

will 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 length 

V = (side length) 3 

http://www.tulane.edu/~sanelson/eens212/metamorphreact.htm 

S.A. = 6 * 2 * 5 

V = 5 3 

S.A./V = 60/125 

S.A. = 6 * 2 * 1 

V = 1 3 

S.A./V = 12/1 



http://www.brocku.ca/earthsciences/people/gfinn/petrology/ab-an3.gif 

– T d = melt has an equal 

ΔG to the xtal, so if 

nuclei form, the high 

surface energy causes the 

xtals to simply dissolve 

back into the melt 

– T a = xtals have a slightly 

lower ΔG than the melt, 

but nuclei must be above 

a critical size in order to 

avoid being resorbed; 

only a small number of 

nuclei are present & grow 

– T b = xtals have a 

significantly lower ΔG 

than the melt, so many 

nuclei form & grow 

fractional 

xtalization -> 

final xtal comp ≠ 

starting L comp 


Winter, 2001, An Introduction to Igneous & Metamorphic Geology 

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 was 

higher for the original xtal but the new nucleation 

lowers the surface energy 


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

T d 

E. Goeke, Fall 2006

Crystal Growth 

• Still have to worry about surface 

energy 

– Less when new growth is 

along a pre-existing row or at 

flaw in the xtal 

– Screw dislocations cause 

growth that continually has an 

edge available 

– New growth will try and 

reduce the surface energy of 

the pre-existing xtal 

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) 2Si 3O 12, olivine 

(Fe,Mg) 2SiO 4, plagioclase (Na,Ca)Al(Al,Si)Si 2O 8), which 

means that the xtal could change compositions as it grows 

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

zoning 


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 more 

prominent 

– Faces with higher surface energy 

will grow faster 

– Xtal growth tries to minimize 

surface energy, so the slow 

growing faces will tend to 

dominate in the end 


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


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

http://www.jwave.vt.edu/crcd/farkas/lectures/dislocations/tsld007.htm 


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 & in 

preferred directions (slip system) 

– Edge dislocation = at right angles to the main stress 

– Screw dislocation = movement is parallel to the main 

stress 

• Planar defects = mismatch of the xtal structure along a 

surface 

– 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 



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 in 

P/T conditions 

– Always adds symmetry, so it doesn’t occur along 

existing 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 lattice 

points are shared by the twins 


Origin of Twinning 

• Three ways to get twins: 

1. Growh twins 

– Due to accidents during xtal growth that cause the a 

new xtal to be added to the face of a pre-existing xtal 

– 2 xtals share lattice points, but have different 

crystallographic orientations 

– Either contact or penetration twins 

2. Transformation twins 

– Pre-existing xtal changes form due to a change in 

pressure 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, different 

portions of the xtal arrange themselves in different 

• Contact twins = planar composition surface 

separates 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 composition 

surfaces = cyclical twins 

• Penetration twins = irregular composition 

surface 

– Due to a twin center or twin axis 

– Two xtals appear intergrown 

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


orientations E. Goeke, Fall 2006 


Common Twin Laws 

• Twin law = describes the twin operation 

& the orientation of the plane/axis along 

which the symmetry operation occurs 

– {hkl} = along a plane 

– [hkl] = axis of rotation 

• Triclinic 

– Mainly feldspars 

– Albite law = {010} polysynthetic 

twins ⊥ to b axis; diagnostic property 

of plagioclase 

– Pericline law = [010]; normally occurs 

during the transformation of 

orthoclase/sanidine to microcline & is 

present with albite twinning to form 

tartan twinning 

http://www.geolab.unc.edu/Petunia/ 

IgMetAtlas/minerals/plagtwins.X.html 


– Tartan twinning in 

microcline is due to the 

combination of albite & 

pericline twinning that occur 

when 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) 

• Monoclinic 

– Orthoclase & sanidine mainly 

– Manebach law = {001} in 

orthoclase; diagnostic when it 

occurs 

– Carlsbad law = [001], penetration 

twin in orthoclase; two xtals 180° 

from each other; most common type 

of twinning in orthoclase, so very 

diagnostic 

– Braveno law = {021}, contact twin 

in orthoclase 

– Swallow tail twins = {100}, 

commonly found in gypsum 

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

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




• Orthorhombic 

– Commonly twin on planes // to 

a prsim face 

– {110} cyclical twins = 

aragonite, chrysoberyl, 

cerrusite all have these twins; 

cyclical twins can cause the 

mineral to appear hexagonal 

– Staurolite law = staurolite is 

really monoclinic, but the β ~ 

90°, so it appears orthorhombic 

• {031} forms right-angled 

cross 

• {231} form cross at ~60° 

• Isometric 

– Spinel law = {⎺⎺1⎺11} 

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; twinning 

causes an apparent 4-fold symmetry 


http://www.ged.rwth-aachen.de/Ww/projects/rexx/Urai+86Recrystallization/Urai+86Recrystallization5.htm 





• Tetragonal 

– {011} cyclical contact twins = 

common in rutile & cassiterite 

• Hexagonal 

– Calcilte twins = two types of 

contact twins 

• {0001} 

• {01⎺12} can also occur as 

polysynthetic twins due to 

deformation 

– In quartz: 

• Brazil law = {11⎺20} penetration 

twins due to transformation 

• Dauphiné law = [0001] 

penetration twin due to 

transformation 

• Japanese law = {11⎺22} contact 

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

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 a 

change in bulk composition 

• Several processes may occur to change the metastable 

minerals 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 by 

removing structure defects, mineral grains change 

shape and/or size 

– Exsolution -> occurs in minerals that have complete 

solid solution at high T, but only partial solid solution 

at low T’s 

http://tesla.jcu.edu.au/Schools/Earth/EA1001/Mineralogy/Minerals/Feldspars.html 


At high T’s, we will have 1 feldspar, 

but at lower T’s 2 feldspars will be 

present (proportion with Lever rule) 

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



K-feldspar w/ 

blebs of 

plagioclase 

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 

Opx w/ 

blebs of cpx 

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

Radioactivity & Minerals 

• Radioactive decay can also cause post-crystallization 

alteration 

• 40 K and 14 C 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. 40 K -> 40 Ar or 40 Ca, where neither daughter 

element is the same size or charge as the parent) 

• Decay can also cause structural damage to the mineral 

grain as the released alpha particle disrupts the normal 

structure (cause of metamict minerals) 

• Released alpha particles may also leave the original 

grain that contained the parent mineral & enter a 

neighboring grain, which can cause a pleochroic halo to 

form around the primary mineral 


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


Pseudomorphism 

• Pseudomorphism = replacement of 

a mineral grain by another mineral, 

but the 2nd mineral retains the 

characteristic grain outline of the 1st 

mineral 

– Three types: 

1. Substitution = direct 

replacement of one mineral by a 

second (e.g. chlorite after 

garnet) 

2. Encrustation = thin crust of a 

new mineral forms on the 

surface of a preexisting mineral, 

which is followed by the 

removal of the 1st grain 

3. Alteration = partial removal of 

original mineral & only partial 

replacement by the new mineral http://www.ucl.ac.uk/~ucfbrxs/PLM/opx.html

Crystal Growth Mineral Formation & Stability Gibbs Free Energy ...

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