inosilicates: single chains- pyroxenes diopside (001) view blue = si purple = m1 (mg) yellow = m2...

Inosilicates: single chains- Inosilicates: single chains- pyroxenespyroxenes

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

Diopside: CaMg [SiDiopside: CaMg [Si22OO66]]

bb

a si

na

sin

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

Inosilicates: single chains- pyroxenes Inosilicates: single chains- pyroxenes


bb

a si

na

sin



Perspective viewPerspective view



SiOSiO44 as polygons as polygons

(and larger area)(and larger area)IV slabIV slab

IV slabIV slab

IV slabIV slab

IV slabIV slab

VI slabVI slab

VI slabVI slab

VI slabVI slab

bb

a si

na

sin


M1 octahedronM1 octahedron



(+) type by convention(+) type by convention

(+)



This is a (-) typeThis is a (-) type

(-)


TT

M1M1

TT

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

structure.structure.


TT

M1M1

TT

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

structurestructure

(+)(+)

The pyroxene The pyroxene structure is then structure is then

composed of composed of alternating I-beamsalternating I-beams

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

(+)(+)

(+)(+)(+)(+)

(+)(+)(+)(+)


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

tetrahedral chainstetrahedral chains

The pyroxene The pyroxene structure is then structure is then

composed of composed of alternation I-beamsalternation I-beams

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

(+)(+)

(+)(+)(+)(+)


(+)(+)(+)(+)

Tetrehedra and M1 Tetrehedra and M1 octahedra share octahedra share

tetrahedral apical tetrahedral apical oxygen atoms oxygen atoms


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

The M2 slabs have a The M2 slabs have a similar effectsimilar effect

The result is a The result is a monoclinicmonoclinic unit cell, unit cell, hence hence clinopyroxenesclinopyroxenes


cc

aa

(+) M1(+) M1

(+) M2(+) M2

(+) M2(+) M2

OrthopyroxenesOrthopyroxenes have have alternating (+) and (-) alternating (+) and (-)

I-beams I-beams

the offsets thus the offsets thus compensate and result compensate and result in an in an orthorhombicorthorhombic

unit cellunit cell

This also explains the This also explains the double double aa cell dimension cell dimension and why orthopyroxenes and why orthopyroxenes

have have {210}{210} cleavages cleavages instead of {110) as in instead of {110) as in

clinopyroxenes (although clinopyroxenes (although both are at 90both are at 90oo))


cc

aa

(+) M1(+) M1

(-) M1(-) M1

(-) M2(-) M2

(+) M2(+) M2

Clinpyroxene vs. orthopyroxene structures

C2/c

e.g. diopside CaMgSi2O6

Pbca

e.g. enstatite Mg2Si2O6

Alternative clinopyroxene structure (P21/c)

174° 149° 170°

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.

Table 1 C2/c Pbca P21/c

Size andcoordination

Small[6]

Small[6]

Small[6]

Shape Regular Regular RegularM1

CationsSmall cations such

asMg, Fe2+, Al

Small cations suchas

Mg, Fe2+, Al

Small cations suchas

Mg, Fe2+, Al

SizeLarge

[8]Small[6]-[7]

Small[7]

Shape Irregular Irregular IrregularM2

CationsLarge cations such

asNa, Ca

Only small cationssuch as Mg and Fe2+

Very little Ca!

Small amount ofCa is tolerated.Mainly Mg and

Fe2+

Crystal chemistry of the pyroxene polymorphs

The pyroxene quadrilateral

The orthopyroxene solid solution : Enstatite (MgSiO3) to ferrosilite (FeSiO3)

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

M1 M2Low temperature Mg Fe2+

Intermediate temperature

“Infinite” temperature

Mg1-xFe2+x MgxFe2+

1-x

Mg0.5Fe2+0.5 Mg0.5Fe2+

0.5

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

(geospeedometry).

Non-convergent cation ordering in orthopyroxenes

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

Phase diagram for the pigeonite-diopside “binary”

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

Ca

1.14 Å

32%

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.

OPX - Orthorhombic Pigeonite – CPX - Monoclinic

Crystallographic and optical axes align

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

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.

Exsolution phenomena in pyroxenes

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

(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.

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)

35

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.

Coherent interface Incoherent interface

Semi-coherent interface

37

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, 3 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.

39

LAGB to HAGB Transition

• LAGB: steep risewith angle.HAGB: plateau

Dislocation Structure

Disordered Structure

Phase Transformation 40

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(/2)/b /b for small angles.

b

D


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):

gb = E0 ln, where

µb/4π(1-); A0 = 1 + ln(b/2πr0)


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

Mechanism of eutectoidal decompostion of pigeonite to augite and orthopyroxene


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.


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.

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.

Example: Cooling rate of chondrules in the Allende carbonaceous chondrite

Inverted Pigeonite


Pyroxene ChemistryPyroxene Chemistry

““Non-quad” pyroxenesNon-quad” pyroxenesJadeiteJadeite

NaAlSiNaAlSi22OO66

Ca(Mg,Fe)SiCa(Mg,Fe)Si22OO66

AegirineAegirine

NaFeNaFe3+3+SiSi22OO66

Diopside-HedenbergiteDiopside-Hedenbergite

Ca-Tschermack’s Ca-Tschermack’s moleculemolecule CaAl2SiOCaAl2SiO66

Ca / (Ca + Na)Ca / (Ca + Na)

0.20.2

0.80.8

Omphaciteaegirine- augite

AugiteAugite

Spodumene: Spodumene: LiAlSiLiAlSi22OO66

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 solutions with the (Ca, Mg, Fe) pyroxenes.

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.


The general pyroxene formula: The general pyroxene formula:

WW1-P1-P (X,Y) (X,Y)1+P1+P Z Z22OO66

WhereWhere W = W = CaCa Na Na X = X = Mg FeMg Fe2+2+ Mn Ni Li Mn Ni Li Y = Al FeY = Al Fe3+3+ Cr Ti Cr Ti Z = Z = SiSi Al Al

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


The pyroxene quadrilateral and opx-cpx solvusThe pyroxene quadrilateral and opx-cpx solvusCoexisting opx + cpx in many rocks (pigeonite only in volcanics)Coexisting opx + cpx in many rocks (pigeonite only in volcanics)

DiopsideDiopside HedenbergiteHedenbergite

WollastoniteWollastonite

EnstatiteEnstatite FerrosiliteFerrosiliteorthopyroxenes

clinopyroxenes

pigeonite (Mg,Fe)(Mg,Fe)22SiSi22OO66 Ca(Mg,Fe)SiCa(Mg,Fe)Si22OO66

pigeonite clinopyroxenes

orthopyroxenes

SolvusSolvus

12001200ooCC

10001000ooCC

800800ooCC

PyroxenoidsPyroxenoids““Ideal” pyroxene chains with Ideal” pyroxene chains with

5.2 A repeat (2 tetrahedra) 5.2 A repeat (2 tetrahedra) become distorted as other become distorted as other cations occupy VI sitescations occupy VI sites

WollastoniteWollastonite (Ca (Ca M1) M1) 3-tet repeat3-tet repeat

RhodoniteRhodoniteMnSiOMnSiO33

5-tet repeat5-tet repeat

PyroxmangitePyroxmangite (Mn, Fe)SiO(Mn, Fe)SiO33

7-tet repeat7-tet repeat

PyroxenePyroxene2-tet repeat2-tet repeat

7.1 A12.5 A

17.4 A

5.2 A

inosilicates: single chains- pyroxenes diopside (001) view blue = si purple = m1 (mg) yellow = m2...

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