Rocks Minerals and Rocks Minerals and CrystalsCrystals

By Guest ScientistDr. David WalkerLDEO-Columbia University

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 silicatechlorite

Ring silicateberyl (gem=emerald)

How to Learn the Atomic Order?

Put X-ray beams through crystals.X-rays are short electromagnetic waves of wavelength () between 0.1 and 10 Angstroms.If waves hit periodic array with spacing d 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

dd

Map View of Pond Surface

d

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

Those waves interfere with one another.

Both + & -

d

wave

wave

no wave

Condition for Scattering: =d sin

)

sin = /d

To keep parallel beams at angle 1 in phase must be

d

n = 1

n = 2

wave

wave

no wave

Condition for Scattering: n=d sin

For small [ >> dget many beams. Large n resembles continuous scatter.

1 =d sin

2 =d sin

)

waveno wave

n = d sin means sin =n /d

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

Giving n /d 1 or n d

Smallest n when n = 1

The easiest to satisfy for n = 1

So d to keep sin 1

Otherwise no diffraction!

d

= 90o

Wavelength must be shorter than d

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

d

n=2

n=2

n=2

n=2

n=1

n=1

n=1

n=1

NOTICE for fixed , smaller d gives bigger

•Spots or wave beams spread as ducks become closer.

•Spots or wave beams spread as you move away from ducks.

n = d sin

XRD is not like medical X-ray imagery!

Medical X-ray

XRD

Spots spread as fingers spread

Spots spread as duck converge.

Spread grows withdistance from ducks.

Laser/grid diffraction demonstration

)

dS

sLASER

•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

Mineral Crystals Diffract X-rays

Therefore: X-rays are waves !Crystals are periodic arrays !

d !This 1912 demonstration won Max von Laue the

Nobel Prize in physics for 1914.

X-ray beam

For Mineralogists

1. Symmetry of spots symmetry of array2. Spacing of spots array spacing of scattering atoms3. Intensity of spots atomic weight occupancy

distribution.This makes possible crystal structure

analysis.Library of patterns is reference resource of ‘fingerprints’ for

mineral identification!

Chainsilicate

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 dhklAngle of beam and reflection from lattice plane is

Braggs’ Law: n dhkl sin XRD Mineral identification done from tables of

the characteristic Bragg dhkl which arecalculated from and observations.

Powder XRD for mineral ID

2 = 0

2 = 90

X-ray beam in

Powdered sample2hkl

dhkl

Make list of dhkl from measured 2hkl

using n dhkl sin Compare with standard tables <JCPDS>

dddd

Exercise

1. Measure screen to image distance (S).2. Measure distance from middle of pattern to

first spot (s).3. Measure spacing of grid (d).

)

dS

sLASER

Compute wavelength of laser light from n = d sin

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

= d s S

Website References

http://www.icdd.com Commercial library of the JCPDS powder patterns of over 60,000 crystal structures.http://www.ccp14.ac.uk XRD applications freeware and tutorials.http://webmineral.com Fun resource for mineralogy, especially crystal shapes.http://ammin.minsocam.org Mineralogical Society of America’s site including “Ask A Mineralogist”.