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Pyroxene Mineral Formula. Pauling’s Rules for Ionic Crystals Deal with the energy state of the crystal structure 1 st Rule The cation-anion distance =

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Presentation on theme: "Pyroxene Mineral Formula. Pauling’s Rules for Ionic Crystals Deal with the energy state of the crystal structure 1 st Rule The cation-anion distance ="— Presentation transcript:

1 Pyroxene Mineral Formula

2 Pauling’s Rules for Ionic Crystals Deal with the energy state of the crystal structure 1 st Rule The cation-anion distance =  radii Can use R C /R A to determine the coordination number of the cation This is our previous discussion on coordination polyhedra

3 Pauling’s Rules for Ionic Crystals 2 nd Rule First 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 / 6 Cl Cl Cl Cl Na

4 Pauling’s Rules for Ionic Crystals 2 nd Rule: “the electrostatic valence principle” + 1/6+ 1/6+ 1/6+ 1/6 + 1/6+ 1/6+ 1/6+ 1/6 + 1/6+ 1/6+ 1/6+ 1/6 + 1/6+ 1/6+ 1/6+ 1/6 Na Na Na Na Cl - 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 Na’s) charge of Cl = -1 These charges are equal in magnitude so the structure is stable

5 Pauling’s Rules 3 rd Rule: The sharing of edges, and particularly of faces, of adjacent polyhedra tend to decrease the stability of an ionic structure Fig 9-18 of Bloss, Crystallography and Crystal Chemistry. © MSA

6 Pauling’s Rules 4 th Rule: In a crystal with different cations, those of high valence and small CN tend not to share polyhedral elements An extension of Rule 3 Si 4+ in IV coordination is very unlikely to share edges or faces

7 Pauling’s Rules 5 th 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: s XII (large cations replace O positions) s VI VIII is not CP s IV s III (small and uncommon cations)

8 Pauling’s Rules Can’t fill both (share face) HCP IV sites VI sites 5 th Rule: VI and IV sites in HCP array of oxygen anions (not all will be occupied due to charge balance)

9 Pauling’s Rules CCP IV sites VI sites 5 th Rule: VI and IV sites in CCP array of oxygen anions (not all will be occupied due to charge balance)

10 Pauling’s Rules 5 th Rule: The spinel structure at various angles ()()ABO IVVI  Note CCP abcabc layers of Oxygens White VI sites Blue IV sites

11 Pauling’s Rules 5 th Rule: The spinel structure at various angles Polyhedral model White VI sites Blue IV sites ()()ABO IVVI 

12 Pauling’s Rules 5 th Rule: The spinel structure at various angles Now see lines of VI and IV sites Not all are occupied 1/8 of IV sites 1/8 of IV sites 1/2 of VI sites 1/2 of VI sites ()()ABO IVVI 

13 Pauling’s Rules 5 th Rule: The spinel structure at various angles Rotating to where cation sites almost line up ()()ABO IVVI 

14 Pauling’s Rules 5 th Rule: The spinel structure at various angles This 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 apparent But you lose the third dimension ()()ABO IVVI 

15 Two miscellaneous structural concepts Isostructuralism Minerals with the same structure, but different compositions CaF 2 - BaCl 2 Antistructuralism Minerals with the same struture, but one has cations where the other has anions and vice-versa CaF 2 - Na 2 O

16 Polymorphism Different structural forms for compounds of the same composition  different minerals The compound SiO 2 has several different structural forms, or polymorphs The common form is  - or low- quartz, but there are others that become stable under different conditions, including  - or high-quartz, tridymite, cristobalite, coesite, and stishovite The SiO 2 phase diagram  After Swamy and Saxena (1994) J. Geophys. Res., 99, 11,787-11,794.

17 Polymorphism 1. Displacive polymorphism    quartz at 573 o C at atmospheric pressure High-Quartz Low-Quartz 500 Temperature 0 Coesite Pressure (GPa)

18 Polymorphism 1. Displacive polymorphism Note: higher T  higher symmetry due to more thermal energy (may twin as lower T) Transition involves small adjustments and no breaking of bonds Easily reversed and non- quenchable (low E barrier) High Low P P3 2 21

19 Polymorphism 2. Reconstructive polymorphs More common: other quartz polymorphs, graphite-diamond, calcite-aragonite, sillimanite-kyanite-andalusite Transition involves extensive adjustments, including breaking and reformation of bonds High E barrier, so quenchable and not easily reversed (still find Precambrian tridymite) StableUnstableMetastable

20 Pseudorphism May be confused with polymorphs A completely different thing Complete replacement of one mineral by one or more other minerals such that the new minerals retain the external shape of the original one Limonite after pyrite Chlorite after garnet etc. Can use the shape to infer the original mineral Very useful in petrogenetic interpretations

21 Solid Solutions Substitution (mixing, solution) of ions on specific sites Forsterite: Mg 2 SiO 4 Mg occupies the VI sites in the olivine structure Can substitute Fe for Mg and create Fayalite: Fe 2 SiO 4 In olivine the substitution is very readily accomplished and any intermediate composition is possible Olivine: (Mg, Fe) 2 SiO 4 This 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)

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

23 Solid Solutions Intermediate compositions can be expressed as: 1. A chemical analysis (in weight % oxides) SiO FeO22.9 MgO38.6 Total This can be converted to a mineral formula Mg 1.5 Fe 0.5 SiO 4 Such an analysis is very difficult to interpret in terms of the mineral that it represents

24 Solid Solutions Intermediate compositions can be expressed as: 1. A chemical analysis (in weight % oxides) SiO FeO22.9 MgO38.6 Total This can be converted to a mineral formula Mg 1.5 Fe 0.5 SiO 4 3. This can then be expressed in terms of end-members X Mg = Mg / (Mg + Fe) on an atomic basis = 1.5 / 2 = 0.75 or Fo 75 where the sum of the end-members = 1 (Fo 75 implies Fa 25 ) Such an analysis is very difficult to interpret in terms of the mineral that it represents

25 Solid Solutions Solid solutions are most extensive if the valence and radius of the substituting ions are similar Good 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 % Never if > 30 %

26 Solid Solutions Solid solutions are most extensive if the valence and radius of the substituting ions are similar If valence differs will not substitute or requires coupled substitution NaAlSi 3 O 8 - CaAl 2 Si 2 O 8 in plagioclase Na + + Si 4+ exchange for Ca 2+ + Al 3+ to maintain 5+ total Jadeite NaAlSi 2 O 6 - diopside CaMgSi 2 O 6

27 Exsolution l Lower T l Limits impurity l Structure may reject excess l Exsolution F Oriented lamellae, or F Entirely rejected from the crystal F Non-coherent masses

28 Exsolution The 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 masses whispy perthite lamellae as albite is exsolved from orthoclase Blebby 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

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

30 Order - Disorder Triclinic  monoclinic in KAlSi 3 O 8 requires mirror symmetry Must disorder at high temperature before  monoclinic  monoclinic potential mirror

31 Crystal Defects Defects can affect F Strength F Conductivity F Deformation style F Color

32 Crystal Defects Steel spheres: a) Regular packed array with 3 point defects b) Point and line defects c) Mosaic (or domains) separated by defect boundaries These are not twins! Fig 3.50 of Klein and Hurlbut, Manual of Mineralogy, © John Wiley and Sons

33 Crystal Defects 1. Point Defects a) Schottky (vacancy) - seen with steel balls in last frame b) Impurity s Foreign ion replaces normal one (solid solution) Not considered a defect s Foreign ion is added (interstitial) s Both combined a. Schottky defect b. Interstitial (impurity) defect

34 Crystal Defects 1. Point Defects c) Frenkel (cation hops from lattice site to interstitial) = a + b combination b. Frenkel defect

35 Crystal Defects 2. Line Defects d) Edge dislocation Migration aids ductile deformation Fig 10-4 of Bloss, Crystallography and Crystal Chemistry.© MSA

36 Crystal Defects 2. Line Defects e) Screw dislocation (aids mineral growth) Fig 10-5 of Bloss, Crystallography and Crystal Chemistry. © MSA

37 Crystal Defects 3. Plane Defects f) Lineage structure or mosaic crystal Boundary of slightly mis-oriented volumes within a single crystal Lattices are close enough to provide continuity (so not separate crystals) Has short-range order, but not long-range (V 4 ) Fig 10-1 of Bloss, Crystallography and Crystal Chemistry. © MSA

38 Crystal Defects 3. Plane Defects g) Domain structure (antiphase domains) Also has short-range but not long-range order Also has short-range but not long-range order Fig 10-2 of Bloss, Crystallography and Crystal Chemistry. © MSA

39 Crystal Defects 3. Plane Defects h) Stacking faults Common in clays and low-T disequilibrium A - B - C layers may be various clay types (illite, smectite, etc.) ABCABCABCABABCABC AAAAAABAAAAAAA ABABABABABCABABAB


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