Mineral Structures From definition of a mineral: “…an ordered atomic arrangement…” How do Pauling’s rules control “ordered atomic arrangement?” How can crystal structure make one mineral different from another? Can mineral structures be used to group minerals (e.g. classify them)?

Illustrations of mineral structures 2-D representation of 3-D materials Ions represented as spheres – drawn to scale Stick and ball method Polyhedron method Hybrid: Stick and Ball, plus polyhedron Map view – unit cell dimensions

Olivine – view down a crystallographic axis Unit cell outline Olivine – view down a crystallographic axis Fig. 4-10

Structures Isostructural minerals Polymorphism – polymorphic minerals Same structure, different composition Polymorphism – polymorphic minerals Same composition, different structures

Isostructural Minerals Many minerals have identical structures, different compositions Example: halite (NaCl) and Galena (PbS) Differ in many physical properties - composition Identical symmetry, cleavage, and habit – elemental arrangement

Isostructural group Several isostructural minerals Have common anion group Much substitution between cations Example: calcite group

Polymorphism The ability for compounds with identical compositions to crystallize with more than one structure Polymorphs Polymorphic groups

P & T primary environmental variables Caused by balance of conflicting requirements and environmental factors: Attraction and repulsion of cations and anions (charge) Fit of cations in coordination site (size) Geometry of covalent bonds P & T primary environmental variables

Composition of environment unimportant P and T controls: High P favors tightly packed lattice, high density High T favors open lattice, low density, wide substitution Composition of environment unimportant All same elements in polymorphs Presence or absence of polymorphs provide information on P and T conditions

Four types of mechanisms to create polymorphs: Reconstructive – break bonds Order-disorder – cation placement Displacive – kink bonds Polytypism – stacking arrangement

1. Reconstructive polymorphism Requires breaking bonds – major reorganization Symmetry and/or structural elements may differ between polymorphs Symmetry and/or structural elements may be similar because identical composition Example: C

C = Diamond and Graphite Diamond – all 100% covalent bonds Graphite – covalent bonds within sheets, van der Waal bonds between sheets What conditions cause one mineral or the other to form?

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

What are temperatures at these depths? Found on a Phase Diagram – e.g. for single component Increasing Depth (linear) ~200 km depth ~100 km depth Where on (in) the earth would diamond form/be stable? Single component = C Increasing Depth (non-linear) Fig. 4-11

Diamond stability versus geothermal gradient Kimberlite Red line is geothermal gradient Diamond window Stability Boundary of Diamond and Graphite Lithosphere Asthenosphere Phase diagram Conceptual model of earth

Metastable minerals occur because of energy required for conversion Bonds must be broken to switch between polymorphs Cooling removes energy required to break bonds Rate of cooling often important for lack of conversion – e.g. fast cooling removes energy before reactions occur Quenching – “frozen”: e.g. K-feldspars Example of Order-disorder polymorphism

2. Order-disorder polymorphism The mineral structure remains same between polymorphs Difference is in the location of cations in structure Good examples are the K-feldspars One end-member of the alkali feldspars

Idealized feldspar structure Si or Al K (or Na, Ca) Si or Al K-feldspar has 4 tetrahedral sites called T1 and T2 (two each) Fig. 12-6

“K-spars” KAlSi3O8 – one Al3+ substitutes for one Si4+ High Sanidine (high T) – Al can substitute for any Si – completely disordered Low Microcline (low T) – Al restricted to one site – completely ordered Orthoclase (Intermediate T) – Intermediate number of sites with Al

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 Fig. 4-13

Degree of order depends on T High T favors disorder Low T favors order Sanidine formed in magmas found in volcanic rocks – quenched at disordered state: metastable Microcline found in plutonic rocks – slow cooling allows for ordering to take place Over time, sanidine will convert to microcline

3. Displacive Polymorphism No bonds broken a and b quartz are good examples b quartz (AKA high quartz) 1 atm P and > 573º C, SiO2 has 6-fold rotation axis. a quartz (AKA low quartz) 1 atm P and < 573º C, SiO2 distorted to 3-fold axis

Conversion can not be quenched, always happens View down c-axis b quartz a quartz 6-fold rotation axis 3-fold rotation axis Conversion can not be quenched, always happens Never find metastable b quartz Fig. 4-12

External crystal shape may be retained from conversion to low form Causes strain on internal lattice Strain may cause twinning or undulatory extinction Must have sufficient space for mineral to form Undulatory extinction

(4) Polytypism Stacking diffrences Common examples are micas and clays

Common Sheet silicates – like clay minerals Orthorhombic, two stacking vectors, not 90º Monoclinic, single stacking vector, not 90º Orthorhombic, single stacking vector, 90º Fig. 4-14

Eventually will get to controls on compositional variations First some “housekeeping” – necessary skills: Scheme for mineral classification Rules for chemical formulas A graphing technique – ternary diagrams

Mineral Classification Based on major anion or anionic group Consistent with chemical organization of inorganic compounds Families of minerals with common anions have similar structure and properties Cation contents commonly quite variable

Follows from Pauling’s rules 1, 3, and 4 (coordination polyhedron & sharing of polyhedral elements) - anions define basic structure 2: (electrostatic valency principle) anionic group separate minerals

Mineral group Anion or anion gp Native elements N/A Oxides O2- Hydroxides OH- Halides Cl-, Br-, F- Sulfides S2- Sulfates SO42- Carbonates CO32- Phosphates PO43- Silicates SiO44-

Mineral Formulas Rules Cations first, then anions or anionic group Charges must balance Cations of same sites grouped into parentheses Cations listed in decreasing coordination number Thus also decreasing ionic radius Also increasing valence state

Examples Diopside – a pyroxene: CaMgSi2O6 Charges balance Ca - 8 fold coordination: +2 valence Mg - 6 fold coordination: +2 valence Si – 4 fold coordination: +4 valence Anionic group is Si2O6

Substitution within sites indicated by parentheses: Ca(Fe,Mg)Si2O6 Intermediate of two end-members: Diopside CaMgSi2O6 – Hedenbergite CaFeSi2O6 complete solid solution series (more on “solid solution” in a moment)

Can explicitly describe substitution E.g. Olivine: (Mg2-x,Fex)SiO4 0 ≤ x ≤ 2 Alternatively: Can describe composition by relative amounts of end members: Forsterite = Fo Fayalite = Fa

General composition of olivine is (Mg,Fe)2SiO4 All of the following are the same exact composition: (Mg0.78Fe0.22)2SiO4 Mg1.56Fe0.44SiO4 Fo78Fa22 (here numbers are percentages of amount of each mineral) Fo78 (here implied that the remainder is Fa22) Fa22

How to calculate chemical formulas for solid solutions Eg. Plagioclase feldspars: Albite, Ab – NaAlSi3O8 Anorthite, An – CaAl2Si2O8 What is chemical composition of say Ab25An75?

Graphic representation Common to have three “end members” Ca2+, Mg2+ and Fe2+ common substitutions between silicate minerals Also K, Na, Ca – e.g. the Feldspars Ternary diagrams Used to describe distribution of each end member Total amount is 100%

See page 84

Fig. 4-17 Ca2Si2O6 8% Fs 50% Wo 42% En Composition is: En42Fs8Wo50 (Mg0.42Fe0.08Ca0.5)2Si2O6 Pyroxenes: (Mg,Fe,Ca)2Si2O6 Mg2Si2O6 Fe2Si2O6 Fig. 4-17

Compositional Variation Think of minerals as framework of anions Form various sites where cations reside Principle of parsimony Not all sites need to be filled Some sites can accommodate more than one type of ion (e.g. polymorphism in feldspar, solid solution in olivine)

Anions can substitute for each other, but this is rare Solid solution Occurs when different cations can occur in a particular site Three types: Substitution, omission, and interstitial Anions can substitute for each other, but this is rare

Tourmaline – an example of extreme amount of substitution Na(Mg,Fe,Li,Al)3Al6[Si6O18] (BO3)3(O,OH,F)4 W = 8-fold coordination, not cubic; usually Na, sometimes Ca or K X = Regular octahedral; usually Mg and Fe, sometimes Mn, Li, and Al Y = 6-fold coordination; usually Al, Less commonly Fe3+ or Mg, links columns B = trigonal; Borate ions, B is small, Fig. 15.9

Terms Substitution series or solid solution series: the complete range of composition of a mineral End members: the extremes in the range of compositions E.g. olivine: Forsterite and Fayelite

Terms Continuous or complete solid solution series: all intermediate compositions are possible E.g. Olivine Incomplete or discontinuous solid solution series: a restricted range of compositions E.g Calcite - magnesite

Substitutional Solid Solution Two requirements for substitution Size – substituting ions must be close in size Charge – electrical neutrality must be maintained

Size Comes from Pauling rule 1: coordination In general size of ions must be < 15% different for substitution Tetrahedral sites: Si4+ and Al3+ Octahedral sites: Mg2+, Fe2+, Fe3+, Al3+ Larger sites: Na+ and Ca2+

Temperature is important Example is K and Na substitution in alkali feldspar (Sanidine and Albite) Size difference is about 25% Complete solid solution at high T Limited solid solution at low T Results in exsolution

Types of substitution Substitutional solid solution Simple substitution Coupled substitution Omission substitution Interstitial substitution Different types have to do with where the substitution occurs in the crystal lattice

Simple Substitution Occurs with cations of about same size and same charge Example: Olivine

Olivine - (Fe.22Mg.78)2SiO4 View down a axis 22% Fe 78% Mg Fig. 4-15

Coupled Substitution Coupling two substitutions One that raises charge Linked one that decreases charge Example: Albite (NaAlSi3O8) and Anorthite (CaAl2Si2O8) Ca and Na occupy distorted 8-fold site Al and Si occupy tetrahedral sites

Coupled substitution: Coupled substitution in different sites Coupled substitution: Na+ + Si4+ = Ca2+ + Al3+ Fig. 4-15

Coupled substitution The substitution doesn’t always have to be different sites Corundum (Al203) Fe2+ and Ti4+ substitute for 2Al3+ (makes sapphire). Cr3+ makes Ruby Both elements are in octahedral sites Can couple cations and anions Hornblende: Fe2+ and OH- substitutes for Fe3+ and O2-

Omission substitution Charge balance maintained by leaving site vacant Pyrrhotite: variable amounts of Fe2+ and Fe3+ Formula: Fe(1-x)S where 0<X<0.13 General substitution: (n+1)Mn+ = nM(n+1)+ + □ where □ is vacant, n is the number of sites

14Fe2+ = 8 Fe2+ + 4 Fe3+ + 2□ 28+ = 28+ Fig. 4-15 14 sites = 14 sites

Interstitial substitution Type of omission substitution Difference is that regular lattice framework site is not location of substitution Example: Beryl, a ring silicate Al3+ substitution for Si in tetrahedral sites Balanced by K+, Rb+ and Cs+ substitution in open “channel” sites

Charge balance maintained by interstitial substitution Al, Be substition for Si Fig. 4-15

Structure of Beryl Be3Al2Si6O8 Silicate Rings Substitution important: Cr substition makes emerald, other substitutions make Aquamarine – blue green variety of emerald Al 6-fold coordination Fig. 15-6 Be 4-fold coordination