Pyroxene Mineral Formula

Sheet1

Oxide Mineral Calculation

Clinopyroxene 91145

Col 1Col 2Col 3Col 4Col 5

Wt% OxMol WtMol OxAt Ox# anionsCationsIVVI

50.5260.090.84071.68153.8301.911.91

0.2879.90.00350.00700.0160.010.01

2.77101.940.02720.08150.1860.120.080.05

159.70.00000.00000.0000.000.00

FeO10.9471.850.15230.15230.3470.350.35

MnO0.2370.940.00320.00320.0070.010.01

MgO12.6340.320.31320.31320.7130.710.71

CaO21.7556.080.38780.38780.8830.880.88

0.4861.980.00770.00770.0180.040.04

94.20.00000.00000.0000.000.00

99.602.63432.001.99

# O's =6WoEnFs

0.880.710.35

E17/E16 =2.2776453718

Orthopyroxene 91145

Col 1Col 2Col 3Col 4Col 5

Wt% OxMol WtMol OxAt Ox# anionsCationsIVVI

52.0960.090.86691.73373.9191.961.96

0.1279.90.00150.00300.0070.000.00

1.63101.940.01600.04800.1090.070.040.04

159.70.00000.00000.0000.000.00

FeO27.0671.850.37660.37660.8580.860.86

MnO0.6670.940.00930.00930.0210.020.02

MgO19.1140.320.47400.47401.0791.081.08

CaO0.5156.080.00910.00910.0210.020.02

0.0561.980.00080.00080.0020.000.00

94.20.00000.00000.0000.000.00

101.232.65452.001.98

# O's =6WoEnFs

0.021.080.86

E37/E36 =2.260315644

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Paulings Rulesfor Ionic CrystalsDeal with the energy state of the crystal structure

1st RuleThe cation-anion distance = radii

Can use RC/RA to determine the coordination number of the cation

This is our previous discussion on coordination polyhedra

Paulings Rulesfor Ionic Crystals2nd RuleFirst note that the strength of an electrostatic bond = valence / CN

Na+ in NaCl is in VI coordination

For Na+ the strength = +1 divided by 6 = + 1/6ClClClClNa

Paulings Rulesfor Ionic Crystals2nd Rule: the electrostatic valence principle+ 1/6+ 1/6+ 1/6+ 1/6NaNaNaNaCl-An ionic structure will be stable to the extent that the sum of the strengths of electrostatic bonds that reach an anion from adjacent cations = the charge of that anion

6 ( + 1/6 ) = +1 (sum from Nas)charge of Cl = -1

These charges are equal in magnitude so the structure is stable

Paulings Rules3rd Rule:The sharing of edges, and particularly of faces, of adjacent polyhedra tend to decrease the stability of an ionic structureFig 9-18 of Bloss, Crystallography and Crystal Chemistry. MSA

Paulings Rules4th Rule:In a crystal with different cations, those of high valence and small CN tend not to share polyhedral elements

An extension of Rule 3Si4+ in IV coordination is very unlikely to share edges or faces

Paulings Rules5th Rule:The number of different kinds of constituents in a crystal tends to be small

Using the analogy of CP oxygens this rule states that the number of types of interstitial sites that are filled in a regular and periodic array tends to be small

4 common types of cation sites in such an array:XII (large cations replace O positions)VI VIII is not CPIVIII (small and uncommon cations)

Paulings Rules5th Rule:Cant fill both (share face)HCPIV sitesVI sitesVI and IV sites in HCP array of oxygen anions(not all will be occupied due to charge balance)

Paulings Rules5th Rule:CCPIV sitesVI sitesVI and IV sites in CCP array of oxygen anions(not all will be occupied due to charge balance)

Paulings Rules5th Rule:The spinel structure at various angles

NoteCCP abcabc layers of OxygensWhite VI sitesBlue IV sites

Paulings Rules5th Rule:The spinel structure at various anglesPolyhedral modelWhite VI sitesBlue IV sites

Paulings Rules5th Rule:The spinel structure at various anglesNow see lines of VI and IV sitesNot all are occupied 1/8 of IV sites 1/2 of VI sites

Paulings Rules5th Rule:The spinel structure at various anglesRotating to where cation sites almost line up

Paulings Rules5th Rule:The spinel structure at various anglesThis orientation is looking down (010)It makes an excellent projection, since atoms all stack up on top of one another toward you The order becomes apparentBut you lose the third dimension

Two miscellaneous structural conceptsIsostructuralismMinerals with the same structure, but different compositionsCaF2 - BaCl2

AntistructuralismMinerals with the same struture, but one has cations where the other has anions and vice-versaCaF2 - Na2O

PolymorphismDifferent structural forms for compounds of the same composition different mineralsThe compound SiO2 has several different structural forms, or polymorphsThe common form is - or low-quartz, but there are others that become stable under different conditions, including - or high-quartz, tridymite, cristobalite, coesite, and stishoviteThe SiO2 phase diagram After Swamy and Saxena (1994) J. Geophys. Res., 99, 11,787-11,794.

Polymorphism

1. Displacive polymorphism quartz at 573oC at atmospheric pressure

Polymorphism

1. Displacive polymorphismNote: higher T higher symmetry due to more thermal energy (may twin as lower T)Transition involves small adjustments and no breaking of bondsEasily reversed and non-quenchable (low E barrier)HighLowP6222P3221

Polymorphism

2. Reconstructive polymorphsMore common: other quartz polymorphs, graphite-diamond, calcite-aragonite, sillimanite-kyanite-andalusiteTransition involves extensive adjustments, including breaking and reformation of bondsHigh E barrier, so quenchable and not easily reversed (still find Precambrian tridymite)StableUnstableMetastable

Pseudorphism

May be confused with polymorphsA completely different thingComplete replacement of one mineral by one or more other minerals such that the new minerals retain the external shape of the original oneLimonite after pyriteChlorite after garnetetc.Can use the shape to infer the original mineralVery useful in petrogenetic interpretations

Solid Solutions

Substitution (mixing, solution) of ions on specific sitesForsterite: Mg2SiO4Mg occupies the VI sites in the olivine structureCan substitute Fe for Mg and create Fayalite: Fe2SiO4In olivine the substitution is very readily accomplished and any intermediate composition is possibleOlivine: (Mg, Fe)2SiO4This means that olivine is a solid-solution series in which any ratio of Mg/Fe is possible as long as they sum to two ions per formula unit (required for electric neutrality)

Solid Solutions

Intermediate compositions can be expressed as:1. A chemical analysis (in weight % oxides)SiO238.5FeO22.9MgO38.6Total 100.0Such an analysis is very difficult to interpret in terms of the mineral that it represents

Solid Solutions

Intermediate compositions can be expressed as:1. A chemical analysis (in weight % oxides)SiO238.5FeO22.9MgO38.6Total 100.02. This can be converted to a mineral formulaMg1.5 Fe0.5 SiO4Such an analysis is very difficult to interpret in terms of the mineral that it represents

Solid Solutions

Intermediate compositions can be expressed as:1. A chemical analysis (in weight % oxides)SiO238.5FeO22.9MgO38.6Total 100.02. This can be converted to a mineral formulaMg1.5 Fe0.5 SiO43. This can then be expressed in terms of end-membersXMg = Mg / (Mg + Fe) on an atomic basis = 1.5 / 2 = 0.75orFo75 where the sum of the end-members = 1(Fo75 implies Fa25)Such an analysis is very difficult to interpret in terms of the mineral that it represents

Solid Solutions

Solid solutions are most extensive if the valence and radius of the substituting ions are similarGood if radii differ by < 15%Fe 2+ = 0.80 A Mg 2+ = 0.74 A (7.5%)Mn 2+ = 0.91 A (14% - Fe and 21% - Mg)Limited or rare if differ by 15-30 %Never if > 30 %

Solid Solutions

Solid solutions are most extensive if the valence and radius of the substituting ions are similarIf valence differs will not substitute or requires coupled substitutionNaAlSi3O8 - CaAl2Si2O8 in plagioclaseNa+ + Si4+ exchange for Ca2+ + Al3+ to maintain 5+ total

Jadeite NaAlSi2O6 - diopside CaMgSi2O6

ExsolutionLower TLimits impurityStructure may reject excessExsolutionOriented lamellae, orEntirely rejected from the crystalNon-coherent masses

As temperature drops, the decreasing thermal energy in the lattice, the tolerance of one end-member for the complementary ion becomes lessIn some solid solutions this may result in only limited admittance for the smaller (or larger) ionAs a result the structure may reject the excess that it tolerated at higher temperatures The process is exsolution and the product may be oriented lamellae of the lesser complementary phase in the greater hostAlternatively the exsolved material may be entirely rejected from the crystal, or form as non-coherent masses

ExsolutionThe process is exsolution and the product may be oriented lamellae of the lesser complementary phase in the greater host

Alternatively the exsolved material may be entirely rejected from the crystal, or form as non-coherent masseswhispy perthite lamellae as albite is exsolved from orthoclaseBlebby cpx exsolved from opx host, Skaergaard Intrusion Opx with lamellae of exsolved plagioclase, Nain anorthosite Opx with 2 lamellae of exsolved cpx, Bushveld Intrusion From Deer et al Rock-Forming Minerals vol 1A. WIley

Order - Disorder

Random vs. ordered atoms 1. Random 2. Perfect OrderAlternating A and B- Lower TNote larger unit cell!Each atom is statistically identical (chance of being A is the same for each position) Higher T

At 0 K entropy drops to zero and all solutions become perfectly ordered at equilibriumAt higher temperatures solutions (even in solids) become progressively disordered until they eventually become completely disorderedThe degree of disorder is a function of temperature, such that there is some equilibrium degree of disorder for a given solution at a given temperature

Order - Disorder

Triclinic monoclinic in KAlSi3O8 requires mirror symmetry

Must disorder at high temperature before monoclinicpotential mirror

This is not a trivial concept that merely concerns sub-microscopic propertiesThe triclinic monoclinic transition in feldspar KAlSi3O8 requires that there is mirror symmetryIf Al and Si are ordered on the IV sites (Al is grey in this picture, while Si is blue), then no mirror is possibleMust disorder at high temperature before can become monoclinicSome feldspars, if they are heated rather slowly, may remain partially ordered, and thus will not invert to the monoclinic form at the temperature predicted (based on disordered feldspars)!

Crystal DefectsDefects can affectStrengthConductivityDeformation styleColor

All of our previous discussion is based on perfect crystalsNew techniques of XRD and HRTEM have shown that defects are common in crystalline substances

Crystal DefectsSteel spheres:a) Regular packed array with 3 point defectsb) Point and line defectsc) Mosaic (or domains) separated by defect boundariesThese are not twins!Fig 3.50 of Klein and Hurlbut, Manual of Mineralogy, John Wiley and Sons

Crystal Defects1. Point Defectsa) Schottky (vacancy) - seen with steel balls in last frame

b) ImpurityForeign ion replaces normal one (solid solution)

Not considered a defectForeign ion is added (interstitial)Both combined

Crystal Defects1. Point Defects

c) Frenkel (cation hops from lattice site to interstitial)= a + b combination

Crystal Defects2. Line Defectsd) Edge dislocation

Migration aids ductile deformationFig 10-4 of Bloss, Crystallography and Crystal Chemistry. MSA

Crystal Defects2. Line Defectse) Screw dislocation (aids mineral growth)Fig 10-5 of Bloss, Crystallography and Crystal Chemistry. MSA

Crystal Defects3. Plane Defectsf) Lineage structure or mosaic crystalBoundary of slightly mis-oriented volumes within a single crystalLattices are close enough to provide continuity (so not separate crystals)Has short-range order, but not long-range (V4)Fig 10-1 of Bloss, Crystallography and Crystal Chemistry. MSA

Crystal Defects3. Plane Defectsg) Domain structure (antiphase domains) Also has short-range but not long-range orderFig 10-2 of Bloss, Crystallography and Crystal Chemistry. MSA

Crystal Defects3. Plane Defects

h) Stacking faultsCommon in clays and low-T disequilibriumA - B - C layers may be various clay types (illite, smectite, etc.)

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As temperature drops, the decreasing thermal energy in the lattice, the tolerance of one end-member for the complementary ion becomes lessIn some solid solutions this may result in only limited admittance for the smaller (or larger) ionAs a result the structure may reject the excess that it tolerated at higher temperatures The process is exsolution and the product may be oriented lamellae of the lesser complementary phase in the greater hostAlternatively the exsolved material may be entirely rejected from the crystal, or form as non-coherent masses

At 0 K entropy drops to zero and all solutions become perfectly ordered at equilibriumAt higher temperatures solutions (even in solids) become progressively disordered until they eventually become completely disorderedThe degree of disorder is a function of temperature, such that there is some equilibrium degree of disorder for a given solution at a given temperature

This is not a trivial concept that merely concerns sub-microscopic propertiesThe triclinic monoclinic transition in feldspar KAlSi3O8 requires that there is mirror symmetryIf Al and Si are ordered on the IV sites (Al is grey in this picture, while Si is blue), then no mirror is possibleMust disorder at high temperature before can become monoclinicSome feldspars, if they are heated rather slowly, may remain partially ordered, and thus will not invert to the monoclinic form at the temperature predicted (based on disordered feldspars)!

All of our previous discussion is based on perfect crystalsNew techniques of XRD and HRTEM have shown that defects are common in crystalline substances