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Rocks Minerals and CrystalsPowerPoint Presentation

Rocks Minerals and Crystals

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Rocks are made of minerals

This pallasite meteorite rock came from the edge of the core of an unknown asteroid in our solar system. This thin slab is lit from both the front and back. Magnesium silicate olivine forms amber-colored crystal windows through iron crystals of kamacite and taenite ( the polished metal).

Minerals Are Crystalline

Geometrical crystal shapes suggest ordered structures.

Periodic 3D atomic order = crystals

External morphology in regular geometric shapes suggests internal periodic structure, such as for:

Layered silicate

chlorite

Ring silicate

beryl (gem=emerald)

How to Learn the Atomic Order?

- Put X-ray beams through crystals.
- X-rays are short electromagnetic waves of wavelength (l) between 0.1 and 10 Angstroms.
- If waves hit periodic array with spacing d l then COOPERATIVE SCATTERING occurs ( = DIFFRACTION ).
- This is NOT the same as taking an X-ray picture in a medical lab and magnifying it.

Cooperative Scattering

Waves on Pond with Array of Duck Decoys

Ripple train approaches line of ducks

d

d

d

l

Map View of Pond Surface

As the ripple train passes, each duck bobs up and down sending out new waves.

Those waves interfere with one another.

Both + & -

l

d

Condition for Scattering: l=d sina1

wave

)

d

no wave

a1

sin a1 = l/d

To keep parallel beams

at angle a1 in phase

must be l.

l

wave

Condition for Scattering: nl=d sina

1l =d sina1

wave

a1

)

no wave

d

wave

n = 1

a1

no wave

a2

2l =d sina2

n = 2

wave

For small a [ l >> d] get many beams. Large n resembles continuous scatter.

Wavelength must be shorter than d

n l = d sin a means sin a =n l /d

Maximum a is 90o – diffraction directly sideward - for which sin a 1

Giving n l /d 1 or n l d

Smallest n l when n = 1

The easiest to satisfy for n = 1

So l d to keep sin a 1

Otherwise no diffraction!

d

a = 90o

nl = d sina is satisfied both forward and backward from the array, as well as on either side.

n l = d sin a

n=2

n=2

n=1

n=1

l

d

a

a

a

a

n=1

n=1

n=2

- NOTICE for fixed l , smaller d gives bigger a
- Spots or wave beams spread as ducks become closer.
- Spots or wave beams spread as you move away from ducks.

n=2

XRD is not like medical X-ray imagery!

Spots spread as duck converge.

Spread grows with

distance from ducks.

Spots spread as fingers spread

Medical X-ray

XRD

Laser/grid diffraction demonstration

- Spots absent in nonperiodic fabric
- Spot symmetry same as that of grid
- Spots rotate with grid rotation but not XY
- Spots spread with grid tilt or smaller d
- Spot spacing s grows with S

s

)

a

S

d

Mineral Crystals Diffract X-rays

Therefore: X-rays are waves !

Crystals are periodic arrays !

l d !

This 1912 demonstration won Max von Laue the Nobel Prize in physics for 1914.

X-ray beam

For Mineralogists

- Symmetry of spots symmetry of array
- Spacing of spots array spacing of scattering atoms
- Intensity of spots atomic weight occupancy distribution.
This makes possible

crystal structure

analysis.

Library of patterns is reference resource of ‘fingerprints’ for mineral identification!

Chain

silicate

diopside

(along chains)

1915 Nobel Prize to the Braggs

Father and son team showed that XRD could be more easily used if diffraction spots treated as cooperative scattering “reflections” off planes in the crystal lattice.

Planes separated in perpendicular direction by dhkl

Angle of beam and reflection from lattice plane is

Braggs’ Law:n l = 2 dhkl sin

XRD Mineral identification done from tables of the characteristic Bragg dhkl which are

calculated from l and observations.

Powder XRD for mineral ID

d

2 = 90

d

d

d

dhkl

Powdered sample

2hkl

X-ray beam in

2 = 0

Make list of dhklfrom measured2hkl

using n l = 2 dhkl sin

Compare with standard tables <JCPDS>

LASER

Exercise- Measure screen to image distance (S).
- Measure distance from middle of pattern to first spot (s).
- Measure spacing of grid (d).

)

a

S

l = d sS

d

Compute wavelength l of laser light from n l = d sin a

Use l derived to measure the d of a larger or small grid spacing

Website References

- http://www.icdd.comCommercial library of the JCPDS powder patterns of over 60,000 crystal structures.
- http://www.ccp14.ac.ukXRD applications freeware and tutorials.
- http://webmineral.comFun resource for mineralogy, especially crystal shapes.
- http://ammin.minsocam.orgMineralogical Society of America’s site including “Ask A Mineralogist”.

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