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b. Diopside: CaMg [Si 2 O 6 ]. a sin . Where are the Si-O-Si-O chains??. Inosilicates: single chains- pyroxenes. Diopside (001) view blue = Si purple = M1 (Mg) yellow = M2 (Ca). b. a sin . Inosilicates: single chains- pyroxenes.

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inosilicates single chains pyroxenes

b

Diopside: CaMg [Si2O6]

a sin

Where are the Si-O-Si-O chains??

Inosilicates: single chains- pyroxenes

Diopside (001) view blue = Si purple = M1 (Mg) yellow = M2 (Ca)

inosilicates single chains pyroxenes1

b

a sin

Inosilicates: single chains- pyroxenes

Diopside (001) view blue = Si purple = M1 (Mg) yellow = M2 (Ca)

inosilicates single chains pyroxenes2

b

a sin

Inosilicates: single chains- pyroxenes

Diopside (001) view blue = Si purple = M1 (Mg) yellow = M2 (Ca)

inosilicates single chains pyroxenes3

b

a sin

Inosilicates: single chains- pyroxenes

Diopside (001) view blue = Si purple = M1 (Mg) yellow = M2 (Ca)

inosilicates single chains pyroxenes4

b

a sin

Inosilicates: single chains- pyroxenes

Diopside (001) view blue = Si purple = M1 (Mg) yellow = M2 (Ca)

inosilicates single chains pyroxenes5

b

a sin

Inosilicates: single chains- pyroxenes

Diopside (001) view blue = Si purple = M1 (Mg) yellow = M2 (Ca)

inosilicates single chains pyroxenes6

Perspective view

Inosilicates: single chains- pyroxenes

Diopside (001) view blue = Si purple = M1 (Mg) yellow = M2 (Ca)

inosilicates single chains pyroxenes7

SiO4 as polygons

(and larger area)

IV slab

VI slab

IV slab

a sin

VI slab

Inosilicates: single chains- pyroxenes

IV slab

VI slab

IV slab

b

Diopside (001) view blue = Si purple = M1 (Mg) yellow = M2 (Ca)

inosilicates single chains pyroxenes8

M1 octahedron

Inosilicates: single chains- pyroxenes

inosilicates single chains pyroxenes9

M1 octahedron

Inosilicates: single chains- pyroxenes

inosilicates single chains pyroxenes10

(+)

M1 octahedron

(+) type by convention

Inosilicates: single chains- pyroxenes

inosilicates single chains pyroxenes11

M1 octahedron

This is a (-) type

(-)

Inosilicates: single chains- pyroxenes

inosilicates single chains pyroxenes12

T

M1

T

Creates an “I-beam” like unit in the structure.

Inosilicates: single chains- pyroxenes

inosilicates single chains pyroxenes13

(+)

T

M1

T

Creates an “I-beam” like unit in the structure

Inosilicates: single chains- pyroxenes

slide15

(+)

(+)

(+)

(+)

(+)

Inosilicates: single chains- pyroxenes

The pyroxene structure is then composed of alternating I-beams

Clinopyroxenes have all I-beams oriented the same: all are (+) in this orientation

Note that M1 sites are smaller than M2 sites, since they are at the apices of the tetrahedral chains

slide16

(+)

(+)

(+)

(+)

(+)

Inosilicates: single chains- pyroxenes

The pyroxene structure is then composed of alternation I-beams

Clinopyroxenes have all I-beams oriented the same: all are (+) in this orientation

slide17

Inosilicates: single chains- pyroxenes

Tetrehedra and M1 octahedra share tetrahedral apical oxygen atoms

slide18

Inosilicates: single chains- pyroxenes

The tetrahedral chain above the M1s is thus offset from that below

The M2 slabs have a similar effect

The result is a monoclinic unit cell, hence clinopyroxenes

(+) M2

c

a

(+) M1

(+) M2

slide19

Inosilicates: single chains- pyroxenes

Orthopyroxenes have alternating (+) and (-) I-beams

the offsets thus compensate and result in an orthorhombic unit cell

This also explains the double a cell dimension and why orthopyroxenes have {210} cleavages instead of {110) as in clinopyroxenes (although both are at 90o)

c

(-) M1

(+) M2

a

(+) M1

(-) M2

slide20

Clinpyroxene vs. orthopyroxene structures

C2/c

e.g. diopside CaMgSi2O6

Pbca

e.g. enstatite Mg2Si2O6

slide21

Alternative clinopyroxene structure (P21/c)

The C2/c and P21/c structures differ in the way the tetrahedral chains are kinked.

In the C2/c structure the chains are relatively straight and are all symmetry-related to each other.

In the P21/c structure, chains in the same (100) layer are kinked in opposite senses, so they are no longer symmetry-related.

174°

149°

170°

slide25

M1

M2

Low temperature

Mg

Fe2+

Intermediate temperature

Mg1-xFe2+x

MgxFe2+1-x

“Infinite” temperature

Mg0.5Fe2+0.5

Mg0.5Fe2+0.5

Non-convergent cation ordering in orthopyroxenes

Fe2+ is slightly larger than Mg and prefers to sit on the larger M2 site (i.e. the crystal has a lower enthalpy when Fe2+ is sitting on M2).

Example: For a composition (Mg0.5Fe2+0.5)SiO3

We can measure “x” experimentally and use it to determine what the cooling rate and effective equilibration rate of the mineral was (geospeedometry).

slide27

Pigeonite and augite solid solutions

Hypersthene transforms to the pigeonite (C2/c) structure at high temperatures. Pigeonite has an expanded M2 site, and can accept larger amounts of Ca substituting for (Mg, Fe2+).

The endmembers diopside (CaMgSi2O6) and hedenbergite (CaFeSi2O6) are both clinopyroxenes (C2/c). Ca occupies M2 and there is complete solid solution between Mg and Fe2+ on M1. The term augite is used to describe the Ca-rich clinopyroxene solid solution.

Pigeonite and augite are separated by a large miscibility gap because of the large difference between the radius of (Mg, Fe) and Ca

slide29

Phase diagram for the pigeonite-diopside “binary”

At high temperature, both pigeonite and augite are monoclinic with the same C2/c structure. Miscibility between these two endmembers is limited due to the large difference in the ionic radii of (Mg, Fe) and Ca.

The eutectic melting loops are typical features of the solidification of a solid solution with limited miscibility.

Mg

0.86 Å

32%

Ca

1.14 Å

slide30

Reconstructive phase transition and low-T eutectoid point

In low-Ca pigeonite, the M2 site is too large for the small Mg and Fe cations.

The mismatch is tolerated at high temperature because thermal vibration of the Mg and Fe atoms prevents the structure from collapsing.

At low temperature there is a reconstructive phase transition to the orthopyroxene (hypersthene structure, which has a much smaller M2 site.

The reconstructuve phase transition leads to the development of a eutectoid point.

slide31

Crystallographic and optical axes align

C crystallographic axis at 32 to 42º angle to the Z optical axis

Pigeonite – CPX - Monoclinic

OPX - Orthorhombic

slide32

Reconstructive phase transition and low-T eutectoid point

The reconstructuve phase transition from monoclinic pigeonite to orthorhombic hypersthene is very slow, and will only occur in very slowly-cooled rocks.

If the transition doesn’t take place, the structure needs another way of coping with the small Mg and Fe cations in M2.

Displacive phase transition to the low pigeonite structure (P21/c) occurs instead.

Transition temperature decreases with increasing Ca content, as the larger Ca atoms hold the structure apart.

slide33

Exsolution phenomena in pyroxenes

(Mg, Fe)-Ca diffusion can occur, therefore augite exsolution lamellae develop on entering the miscibility gap. Lamellae are parallel to (001) of monoclinic host.

No time for reconstructive phase transition. Displacive phase transition occurs below Tc in the pigeonite component of the intergrowth

(Mg, Fe)-Ca diffusion can occur. Augite lamellae develop parallel to (001) of monoclinic host.

Reconstructive phase transition occurs in pigeonite component of the intergrowth.

Further exsolution of augite occurs // (100) of orthorhombic host.

No time for (Mg, Fe)-Ca diffusion, therefore no exsolution.

No time for reconstructive phase transition.

Displacive phase transition from high to low pigeonite occurs below Tc

slide34

Microstructures of exsolved pyroxenes

The exsolving phase forms as lamellae (thin slabs). The orientation of the lamellae is determined by the plane of best fit between the two phases.

Augite in pigeonite (and vice versa) has best fit close to (001)

Augite in hypersthene (and vice versa) has best fit close to (100)

coherence at interfaces
Coherence at interfaces
  • Coherent/semi-coherent/incoherent interfaces: these terms are based on the degree of atomic matching across the interface.
  • Coherent interface means an interface in which the atoms match up on a 1-to-1 basis (even if some elastic strain is present).
  • Incoherent interface means an interface in which the atomic structure is disordered.
  • Semi-coherent interface means an interface in which the atoms match up, but only on a local basis, with defects (dislocations) in between.
slide36

Coherent interface

Incoherent interface

Semi-coherent interface

homophase vs heterophase
Homophase vs. Heterophase
  • There is a useful comparison that can be made between grain boundaries (homophase) and interphase boundaries (heterophase).Structure              Grain Boundary       Interface

atoms no boundary coherentmatch (or, S3 coherent twin in fcc) interface

dislocations low angle g.b. semi- coherent

disordered high angle g.b. incoherent

  • Remember: for a grain boundary to exist, there must be a difference in the lattice position (rotationally) between the two grains. An interface can exist even when the lattices are the same structure and in the same (rotational) position because of the chemical difference.
lagb to hagb transition
LAGB to HAGB Transition
  • LAGB: steep risewith angle.HAGB: plateau

Disordered Structure

Dislocation Structure

read shockley model

b

Read-Shockley model
  • Start with a symmetric tilt boundary composed of a wall of infinitely straight, parallel edge dislocations (e.g. based on a 100, 111 or 110 rotation axis with the planes symmetrically disposed).
  • Dislocation density (L-1) given by:1/D = 2sin(q/2)/b  q/b for small angles.

D

Phase Transformation

read shockley contd
Read-Shockley, contd.
  • For an infinite array of edge dislocations the long-range stress field depends on the spacing. Therefore given the dislocation density and the core energy of the dislocations, the energy of the wall (boundary) is estimated (r0 sets the core energy of the dislocation):ggb = E0 q(A0 - lnq), whereE0 = µb/4π(1-n); A0 = 1 + ln(b/2πr0)

Phase Transformation

high angle g b structure
High angle g.b. structure
  • High angle boundaries have a disordered structure.
  • Bubble rafts provide a useful example.
  • Disordered structure results in a high energy.

Low angle boundarywith dislocation structure

Phase Transformation

slide44

Microstructures of exsolved pyroxenes

Exact orientation depends on lattice parameters of the two phases. The orientation varies systmatically with temperature. This can be used to constrain the temperature at which a particular generation of lamellae grew.

slide45

Microstructures of exsolved pyroxenes

The thickness and spacing of lamellae depends on temperature and the time available for them to grow.

By performing annealing experiments and measuring the wavelength of exsolution features using transmission electron microscopy, we are able to calibrate the changes in wavelength as a function of isothermal annealing time.

For a process determined by volume diffusion, we observe that the spacing of lamellae is proportional to (time)1/3.

slide46

Example: Cooling rate of chondrules in the Allende carbonaceous chondrite

Chondrules are a major component of chondritic meteorites. It is believed that chondrules formed in the solar nebula prior to accretion of the meteorite parent bodies.

Chondrules are thought to have formed by crystallisation of melt droplets.

Pyroxene textures from granular olivine-pyroxene chondrules (GOP’s) provide constraints on their cooling history and therefore provide information about the conditions in the solar nebula.

Wavelengths between 25 and 33 nm are observed, translating to cooling rates between 25 and 0.4 °C/hour over the temperature range 1350-1200 °C.

No orthopyroxene suggests more rapid cooling (>104 °C/hour) below 1000 °C.

pyroxene chemistry
Pyroxene Chemistry

Jadeite

Aegirine

NaAlSi2O6

“Non-quad” pyroxenes

NaFe3+Si2O6

0.8

Omphacite

aegirine- augite

Spodumene: LiAlSi2O6

Ca / (Ca + Na)

Ca-Tschermack’s molecule

0.2

CaAl2SiO6

Augite

Diopside-Hedenbergite

Ca(Mg,Fe)Si2O6

slide51

Sodic Pyroxenes

Jadeite (NaAlSi2O6) is a high-pressure pyroxene, formed by reactions such as:

nepheline (NaAlSiO4) + albite (NaAlSi3O8) -> 2 jadeite (NaAlSi2O6)

and

albite (NaAlSi3O8) -> jadeite (NaAlSi2O6) + quartz (SiO2)

Because it contains a mixture of a monovalent and a trivalent cations, it forms coupled substitution solid solutionswith the (Ca, Mg, Fe) pyroxenes.

slide52

Jadeite-diposide solid solution

In the solid solution between NaAlSi2O6 and CaMgSi2O6, Na and Ca mix on M2 and Al and Mg mix on M1.

Differently-charged cations prefer to order at low temperatures (this lowers the Coulomb energy of the crystal). Omphacite is an ordered phase with intermediate composition.

pyroxene chemistry1
Pyroxene Chemistry

The general pyroxene formula:

W1-P (X,Y)1+P Z2O6

Where

  • W = Ca Na
  • X = Mg Fe2+ Mn Ni Li
  • Y = Al Fe3+ Cr Ti
  • Z = Si Al

Anhydrous so high-temperature or dry conditions favor pyroxenes over amphiboles

pyroxene chemistry2
Pyroxene Chemistry

The pyroxene quadrilateral and opx-cpx solvus

Coexisting opx + cpx in many rocks (pigeonite only in volcanics)

Wollastonite

pigeonite

1200oC

orthopyroxenes

clinopyroxenes

1000oC

Diopside

Hedenbergite

clinopyroxenes

Solvus

800oC

pigeonite

(Mg,Fe)2Si2O6

Ca(Mg,Fe)Si2O6

orthopyroxenes

Ferrosilite

Enstatite

slide55

17.4 A

12.5 A

7.1 A

5.2 A

Pyroxenoids

“Ideal” pyroxene chains with 5.2 A repeat (2 tetrahedra) become distorted as other cations occupy VI sites

Pyroxene

2-tet repeat

Wollastonite

(Ca  M1)

 3-tet repeat

Rhodonite

MnSiO3

 5-tet repeat

Pyroxmangite

(Mn, Fe)SiO3

 7-tet repeat

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