Mineral StructuresMineral Structures

From definition of a mineral:From definition of a mineral: “…“…an ordered atomic arrangement…”an ordered atomic arrangement…”

How do Pauling’s rules control How do Pauling’s rules control “ordered atomic arrangement?”“ordered atomic arrangement?”

How can crystal structure make one How can crystal structure make one mineral different from another?mineral different from another?

Can mineral structures be used to Can mineral structures be used to group minerals (e.g. classify them)?group minerals (e.g. classify them)?

Illustrations of mineral Illustrations of mineral structuresstructures

2-D representation of 3-D materials2-D representation of 3-D materials Ions represented as spheres – drawn to Ions represented as spheres – drawn to

scalescale Stick and ball methodStick and ball method Polyhedron methodPolyhedron method Hybrid: Stick and Ball, plus polyhedronHybrid: Stick and Ball, plus polyhedron Map view – unit cell dimensionsMap view – unit cell dimensions

Fig. 4-10Fig. 4-10

Olivine – view Olivine – view down a down a crystallographic crystallographic axisaxis

Unit cell outline

StructuresStructures

Isostructural mineralsIsostructural minerals Same structure, different compositionSame structure, different composition

Polymorphism – polymorphic Polymorphism – polymorphic mineralsminerals Same composition, different structuresSame composition, different structures

Isostructural MineralsIsostructural Minerals Many minerals have identical Many minerals have identical

structures, different compositionsstructures, different compositions Example: halite (NaCl) and Galena (PbS)Example: halite (NaCl) and Galena (PbS) Differ in many physical properties - Differ in many physical properties -

compositioncomposition Identical symmetry, cleavage, and habit Identical symmetry, cleavage, and habit

– elemental arrangement– elemental arrangement

Isostructural groupIsostructural group

Several isostructural mineralsSeveral isostructural minerals Have common anion groupHave common anion group Much substitution between cationsMuch substitution between cations Example: calcite groupExample: calcite group

PolymorphismPolymorphism

The ability for compounds with The ability for compounds with identical compositions to crystallize identical compositions to crystallize with more than one structurewith more than one structure PolymorphsPolymorphs Polymorphic groupsPolymorphic groups

Caused by balance of conflicting Caused by balance of conflicting requirements and environmental requirements and environmental factors:factors: Attraction and repulsion of cations and Attraction and repulsion of cations and

anions (charge)anions (charge) Fit of cations in coordination site (size)Fit of cations in coordination site (size) Geometry of covalent bondsGeometry of covalent bonds

P & T primary environmental variablesP & T primary environmental variables

P and T controls:P and T controls: High P favors tightly packed lattice, high densityHigh P favors tightly packed lattice, high density High T favors open lattice, low density, wide High T favors open lattice, low density, wide

substitutionsubstitution Composition of environment unimportantComposition of environment unimportant

All same elements in polymorphsAll same elements in polymorphs Presence or absence of polymorphs provide Presence or absence of polymorphs provide

information on P and T conditionsinformation on P and T conditions

Four types of mechanisms to create Four types of mechanisms to create polymorphs:polymorphs:1.1. Reconstructive – break bondsReconstructive – break bonds

2.2. Order-disorder – cation placementOrder-disorder – cation placement

3.3. Displacive – kink bondsDisplacive – kink bonds

4.4. Polytypism – stacking arrangementPolytypism – stacking arrangement

1. Reconstructive 1. Reconstructive polymorphismpolymorphism

Requires breaking bonds – major Requires breaking bonds – major reorganizationreorganization Symmetry and/or structural elements Symmetry and/or structural elements

may differ between polymorphsmay differ between polymorphs Symmetry and/or structural elements Symmetry and/or structural elements

may be similar because identical may be similar because identical compositioncomposition

Example: CExample: C

C = Diamond and GraphiteC = Diamond and Graphite

Diamond – all 100% covalent bondsDiamond – all 100% covalent bonds Graphite – covalent bonds within Graphite – covalent bonds within

sheets, van der Waal bonds between sheets, van der Waal bonds between sheetssheets

What conditions cause one mineral What conditions cause one mineral or the other to form?or the other to form?

Graphite – stable at earth surface T Graphite – stable at earth surface T and Pand P

Diamond stable only at high P and T Diamond stable only at high P and T – but found on earth surface– but found on earth surface Won’t spontaneously convert to graphiteWon’t spontaneously convert to graphite Minerals that exists outside of their Minerals that exists outside of their

stability fields are stability fields are metastablemetastable

Fig. 4-11Fig. 4-11

Found on a Phase Diagram – e.g. for single component

~200 km depth

~100 km depth

Where on (in) the earth would diamond form/be stable?

Single component = C

IncreasingDepth (linear)

What are temperatures at these depths?

IncreasingDepth (non-linear)

Red line is geothermal gradient

Kimberlite

Diamond stability versus geothermal gradient

Dia

mond w

indow

Phase diagram Conceptual model of earth

Stability Boundary of Diamond and Graphite

Asthenosphere

Lithosphere

MetastableMetastable minerals occur because of minerals occur because of energy required for conversionenergy required for conversion Bonds must be broken to switch between Bonds must be broken to switch between

polymorphspolymorphs Cooling removes energy required to break Cooling removes energy required to break

bondsbonds Rate of cooling often important for lack of Rate of cooling often important for lack of

conversion – e.g. fast cooling removes conversion – e.g. fast cooling removes energy before reactions occurenergy before reactions occur

Quenching – “frozen”: e.g. Quenching – “frozen”: e.g. K-feldsparsK-feldspars Example of Example of Order-disorder polymorphismOrder-disorder polymorphism

2. Order-disorder 2. Order-disorder polymorphismpolymorphism

The mineral structure remains same The mineral structure remains same between polymorphsbetween polymorphs

Difference is in the location of Difference is in the location of cations in structurecations in structure

Good examples are the K-feldsparsGood examples are the K-feldspars One end-member of the alkali feldsparsOne end-member of the alkali feldspars

K-feldspar has 4 tetrahedral sites called T1 and K-feldspar has 4 tetrahedral sites called T1 and T2 (two each)T2 (two each)

Idealized feldspar structure

Fig. 12-6

Si or Al

K (or Na, Ca)

Si or Al

““K-spars”K-spars”

KAlSiKAlSi33OO88 – one Al – one Al3+3+ substitutes for one substitutes for one SiSi4+4+

High Sanidine (high T) – Al can High Sanidine (high T) – Al can substitute for any Si – completely substitute for any Si – completely disordereddisordered

Low Microcline (low T) – Al restricted to Low Microcline (low T) – Al restricted to one site – completely orderedone site – completely ordered

Orthoclase (Intermediate T) – Orthoclase (Intermediate T) – Intermediate number of sites with AlIntermediate number of sites with Al

Fig. 4-13Fig. 4-13

Order-disorder in the K-feldspars

High Sanidine – Al3+

equally likely to be in any one of the four T sites

Microcline – Al3+ is restricted to one T1 site. Si4+ fills other three sites

Degree of order depends on TDegree of order depends on T High T favors disorderHigh T favors disorder Low T favors orderLow T favors order

Sanidine formed in magmas found in Sanidine formed in magmas found in volcanic rocks – quenched at disordered volcanic rocks – quenched at disordered state: state: metastablemetastable

Microcline found in plutonic rocks – slow Microcline found in plutonic rocks – slow cooling allows for ordering to take placecooling allows for ordering to take place

Over time, sanidine will convert to microclineOver time, sanidine will convert to microcline

3. Displacive Polymorphism3. Displacive Polymorphism

No bonds brokenNo bonds broken and and quartz are good examples quartz are good examples quartz quartz (AKA (AKA high quartzhigh quartz))

1 atm P and > 573º C, SiO1 atm P and > 573º C, SiO22 has 6-fold has 6-fold rotation axis.rotation axis.

quartz quartz (AKA (AKA low quartzlow quartz)) 1 atm P and < 573º C, SiO1 atm P and < 573º C, SiO22 distorted to distorted to

3-fold axis3-fold axis

Fig. 4-12Fig. 4-12

quartz quartzView View down c-down c-axisaxis

• Conversion can not be quenched, always Conversion can not be quenched, always happenshappens

• Never find metastable Never find metastable quartz quartz

6-fold 6-fold rotation rotation axisaxis

3-fold 3-fold rotation axisrotation axis

External crystal shape may be External crystal shape may be retained from conversion to low formretained from conversion to low form

Causes strain on internal latticeCauses strain on internal lattice Strain may cause Strain may cause twinningtwinning or or

undulatory extinctionundulatory extinction Must have sufficient space for mineral to Must have sufficient space for mineral to

formformUndulatory extinction

(4) Polytypism(4) Polytypism

Stacking diffrencesStacking diffrences Common examples are micas and claysCommon examples are micas and clays

Fig. 4-14Fig. 4-14

OrthorhombiOrthorhombic, single c, single stacking stacking vector, 90ºvector, 90º

Orthorhombic, Orthorhombic, two stacking two stacking vectors, not vectors, not 90º90º

Monoclinic, Monoclinic, single single stacking stacking vector, not vector, not 90º90º

Common Sheet silicates – like clay Common Sheet silicates – like clay mineralsminerals

Eventually will get to controls on Eventually will get to controls on compositional variations compositional variations

First some “housekeeping” – First some “housekeeping” – necessary skills:necessary skills: Scheme for mineral classificationScheme for mineral classification Rules for chemical formulasRules for chemical formulas A graphing technique – ternary A graphing technique – ternary

diagramsdiagrams

Mineral ClassificationMineral Classification

Based on major anion or anionic Based on major anion or anionic groupgroup Consistent with chemical organization of Consistent with chemical organization of

inorganic compoundsinorganic compounds Families of minerals with common Families of minerals with common

anions have similar structure and anions have similar structure and propertiesproperties

Cation contents commonly quite Cation contents commonly quite variablevariable

Follows from Pauling’s rulesFollows from Pauling’s rules 1, 3, and 4 (coordination polyhedron & 1, 3, and 4 (coordination polyhedron &

sharing of polyhedral elements) - anions sharing of polyhedral elements) - anions define basic structuredefine basic structure

2: (electrostatic valency principle) 2: (electrostatic valency principle) anionic group separate mineralsanionic group separate minerals

Mineral groupMineral group Anion or anion Anion or anion gpgp

Native Native elementselements

N/AN/A

OxidesOxides OO2-2-

HydroxidesHydroxides OHOH--

HalidesHalides ClCl--, Br, Br--, F, F--

SulfidesSulfides SS2-2-

SulfatesSulfates SOSO442-2-

CarbonatesCarbonates COCO332-2-

PhosphatesPhosphates POPO443-3-

SilicatesSilicates SiOSiO444-4-

Mineral FormulasMineral Formulas

RulesRules Cations first, then anions or anionic groupCations first, then anions or anionic group Charges must balanceCharges must balance Cations of same sites grouped into Cations of same sites grouped into

parentheses parentheses Cations listed in decreasing coordination Cations listed in decreasing coordination

numbernumber Thus also decreasing ionic radiusThus also decreasing ionic radius Also increasing valence stateAlso increasing valence state

ExamplesExamples

Diopside – a pyroxene: CaMgSiDiopside – a pyroxene: CaMgSi22OO66

Charges balanceCharges balance Ca - 8 fold coordination: +2 valenceCa - 8 fold coordination: +2 valence Mg - 6 fold coordination: +2 valenceMg - 6 fold coordination: +2 valence Si – 4 fold coordination: +4 valenceSi – 4 fold coordination: +4 valence Anionic group is SiAnionic group is Si22OO66

Substitution within sites indicated by Substitution within sites indicated by parentheses:parentheses: Ca(Fe,Mg)SiCa(Fe,Mg)Si22OO6 6

Intermediate of two end-members: Intermediate of two end-members: DiopsideDiopside CaMgSi CaMgSi22OO66 – – HedenbergiteHedenbergite CaFeSiCaFeSi22OO66 complete solid solution series complete solid solution series

(more on “solid solution” in a moment)(more on “solid solution” in a moment)

Can explicitly describe substitutionCan explicitly describe substitution E.g. Olivine: (MgE.g. Olivine: (Mg2-x2-x,Fe,Fexx)SiO)SiO44 0 ≤ 0 ≤

x ≤ 2x ≤ 2 Alternatively: Can describe Alternatively: Can describe

composition by relative amounts of composition by relative amounts of end members:end members: Forsterite = FoForsterite = Fo Fayalite = FaFayalite = Fa

General composition of olivine is (MgGeneral composition of olivine is (Mg,,Fe)Fe)22SiOSiO44

All of the following are the same All of the following are the same exactexact composition:composition:

(Mg(Mg0.780.78FeFe0.220.22))22SiOSiO44

MgMg1.561.56FeFe0.440.44SiOSiO44

FoFo7878FaFa2222 (here numbers are percentages of amount (here numbers are percentages of amount of each mineral)of each mineral)

FoFo78 78 (here implied that the remainder is Fa(here implied that the remainder is Fa2222)) FaFa2222

How to calculate chemical How to calculate chemical formulas for solid solutionsformulas for solid solutions

Eg. Plagioclase feldspars:Eg. Plagioclase feldspars: Albite, Ab – NaAlSiAlbite, Ab – NaAlSi33OO88

Anorthite, An – CaAlAnorthite, An – CaAl22SiSi22OO88

What is chemical composition of say What is chemical composition of say AbAb2525AnAn7575??

Graphic representationGraphic representation

Common to have three “end members”Common to have three “end members” CaCa2+2+, Mg, Mg2+2+ and Fe and Fe2+ 2+ common common

substitutions between silicate mineralssubstitutions between silicate minerals Also K, Na, Ca – e.g. the FeldsparsAlso K, Na, Ca – e.g. the Feldspars Ternary diagramsTernary diagrams

Used to describe distribution of each end Used to describe distribution of each end membermember

Total amount is 100%Total amount is 100%

See page 84

Fig. 4-17Fig. 4-17

Pyroxenes:(Mg,Fe,Ca)2Si2O6

8% Fs

50% Wo

42% En

Composition is:

En42Fs8Wo50

(Mg0.42Fe0.08Ca0.5)2Si2O6

Ca2Si2O6

Fe2Si2O6Mg2Si2O6

Compositional VariationCompositional Variation

Think of minerals as framework of Think of minerals as framework of anionsanions Form various sites where cations resideForm various sites where cations reside Principle of parsimonyPrinciple of parsimony Not all sites need to be filledNot all sites need to be filled Some sites can accommodate more Some sites can accommodate more

than one type of ion (e.g. polymorphism than one type of ion (e.g. polymorphism in feldspar, solid solution in olivine)in feldspar, solid solution in olivine)

Solid solutionSolid solution Occurs when different cations can occur Occurs when different cations can occur

in a particular sitein a particular site Three types: Substitution, omission, and Three types: Substitution, omission, and

interstitialinterstitial Anions can substitute for each other, Anions can substitute for each other,

but this is rarebut this is rare

Tourmaline – an Tourmaline – an example of extreme example of extreme amount of substitutionamount of substitution

Na(Mg,Fe,Li,Al)Na(Mg,Fe,Li,Al)33AlAl66[Si[Si66OO1818] (BO] (BO33))33(O,OH,F)(O,OH,F)44

W = 8-fold coordination, not cubic; usually Na, sometimes Ca or KW = 8-fold coordination, not cubic; usually Na, sometimes Ca or K

X = Regular octahedral; usually Mg and Fe, sometimes Mn, Li, and AlX = Regular octahedral; usually Mg and Fe, sometimes Mn, Li, and Al

Y = 6-fold coordination; usually Al, Less commonly FeY = 6-fold coordination; usually Al, Less commonly Fe3+3+ or Mg, links columns or Mg, links columns

B = trigonal; Borate ions, B is small, B = trigonal; Borate ions, B is small,

Fig. 15.9

TermsTerms

Substitution series Substitution series or or solid solution solid solution seriesseries: the complete range of : the complete range of composition of a mineralcomposition of a mineral

End membersEnd members: the extremes in the : the extremes in the range of compositionsrange of compositions E.g. olivine: Forsterite and FayeliteE.g. olivine: Forsterite and Fayelite

TermsTerms

ContinuousContinuous or or complete solid solution complete solid solution seriesseries: all intermediate compositions : all intermediate compositions are possibleare possible E.g. OlivineE.g. Olivine

IncompleteIncomplete or or discontinuous solid discontinuous solid solution series: solution series: a restricted range of a restricted range of compositionscompositions E.g Calcite - magnesiteE.g Calcite - magnesite

Substitutional Solid SolutionSubstitutional Solid Solution

Two requirements for substitutionTwo requirements for substitution Size – substituting ions must be close in Size – substituting ions must be close in

sizesize Charge – electrical neutrality must be Charge – electrical neutrality must be

maintainedmaintained

SizeSize

Comes from Pauling rule 1: Comes from Pauling rule 1: coordinationcoordination

In general size of ions must be < In general size of ions must be < 15% different for substitution15% different for substitution Tetrahedral sites: SiTetrahedral sites: Si4+4+ and Al and Al3+3+

Octahedral sites: MgOctahedral sites: Mg2+2+, Fe, Fe2+2+, Fe, Fe3+3+, Al, Al3+3+

Larger sites: NaLarger sites: Na++ and Ca and Ca2+2+

Temperature is importantTemperature is important Example is K and Na substitution in Example is K and Na substitution in

alkali feldspar (Sanidine and Albite)alkali feldspar (Sanidine and Albite) Size difference is about 25%Size difference is about 25% Complete solid solution at high TComplete solid solution at high T Limited solid solution at low TLimited solid solution at low T

Results in Results in exsolutionexsolution

Types of substitutionTypes of substitution

Substitutional solid solutionSubstitutional solid solution Simple substitutionSimple substitution Coupled substitutionCoupled substitution

Omission substitutionOmission substitution Interstitial substitutionInterstitial substitution Different types have to do with where Different types have to do with where

the substitution occurs in the crystal the substitution occurs in the crystal latticelattice

Simple SubstitutionSimple Substitution

Occurs with cations of about same Occurs with cations of about same size and same chargesize and same charge

Example: OlivineExample: Olivine

Fig. 4-15Fig. 4-15

View down a axis

Olivine - (Fe.22Mg.78)2SiO4

22% Fe78% Mg

Coupled SubstitutionCoupled Substitution

Coupling two substitutionsCoupling two substitutions One that raises chargeOne that raises charge Linked one that decreases chargeLinked one that decreases charge

Example: Albite (NaAlSiExample: Albite (NaAlSi33OO88) and ) and Anorthite (CaAlAnorthite (CaAl22SiSi22OO88)) Ca and Na occupy distorted 8-fold siteCa and Na occupy distorted 8-fold site Al and Si occupy tetrahedral sitesAl and Si occupy tetrahedral sites

Fig. 4-15Fig. 4-15

Coupled substitution:Coupled substitution:NaNa++ + Si + Si4+4+ = Ca = Ca2+2+ + Al + Al3+3+

Coupled substitution in different sitesCoupled substitution in different sites

Coupled substitutionCoupled substitution

The substitution doesn’t always have The substitution doesn’t always have to be different sitesto be different sites Corundum (AlCorundum (Al220033)) FeFe2+2+ and Ti and Ti4+4+ substitute for 2Al substitute for 2Al3+3+ (makes (makes

sapphire). Crsapphire). Cr3+3+ makes Ruby makes Ruby Both elements are in octahedral sitesBoth elements are in octahedral sites

Can couple cations and anionsCan couple cations and anions Hornblende: FeHornblende: Fe2+2+ and OH and OH-- substitutes for substitutes for

FeFe3+3+ and O and O2-2-

Omission substitutionOmission substitution

Charge balance maintained by leaving Charge balance maintained by leaving site vacantsite vacant

Pyrrhotite: variable amounts of FePyrrhotite: variable amounts of Fe2+2+ and Feand Fe3+3+

Formula: FeFormula: Fe(1-x)(1-x)S where 0<X<0.13S where 0<X<0.13 General substitution:General substitution: (n+1)M(n+1)Mn+n+ = nM = nM(n+1)+(n+1)+ + □ + □

where □ is vacant, n is the number of siteswhere □ is vacant, n is the number of sites

Fig. 4-15Fig. 4-15

14Fe2+ = 8 Fe2+ + 4 Fe3+ + 2□

28+ = 28+

14 sites = 14 sites

Interstitial substitutionInterstitial substitution

Type of omission substitutionType of omission substitution Difference is that regular lattice Difference is that regular lattice

framework site is not location of framework site is not location of substitutionsubstitution Example: Beryl, a ring silicateExample: Beryl, a ring silicate AlAl3+ 3+ substitution for Si in tetrahedral sitessubstitution for Si in tetrahedral sites Balanced by KBalanced by K++, Rb, Rb++ and Cs and Cs++ substitution substitution

in open “channel” sitesin open “channel” sites

Fig. 4-15Fig. 4-15

Al, Be substition for Si

Charge balance maintained by interstitial substitution

Fig. 15-6Fig. 15-6

Substitution important: Cr substition makes emerald, other substitutions make Aquamarine – blue green variety of emerald

Structure of BerylBe3Al2Si6O8

Silicate Rings

Al 6-fold coordination

Be 4-fold coordination