صفحه 1:
~ Rocks Minerals and
Crystals
By Guest Scientist
Dr. David Walker
LDEO-Columbia University
صفحه 2:
ocks are made o
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).
صفحه 3:
Minerals Are Crystalline
Geometrical crystal shapes suggest
t
صفحه 4:
riodic 3D atomic order
= crystals
External morphology in regular geometric sha
suggests internal periodic structure, such as f
Layered silicate Ring silicate
chlorite bery! (gem=emerald)
صفحه 5:
X-ray beams through crystals. بط
X-rays are short electromagnetic waves of
wavelength (4) between 0.1 and 10
Angstroms.
elf waves hit periodic array with spacing d 1
2 then COOPERATIVE SCATTERING occurs
( = DIFFRACTION ).
&This is NOT the same as taking an X-ray
picture in a medical lab and magnifying it.
صفحه 6:
Waves on Pond with Array of عير
5لادعع] كع هما لم م 76
approaches
line of ducks
og a
صفحه 7:
As the ripple
train passes,
each duck
bobs up and
down sending
out new
waves.
Those waves
interfere with
one another.
Both + & -
صفحه 8:
no wave
20 keep parallel bea
at angle a, in phase wave
must be i.
صفحه 9:
wave
__no wave
no wave
ae
: wave
For small a [4% >> d] get Sg
many beams. Large n
resembles continuous scatter.
صفحه 10:
na=dsina means sina
=na/d
Maximum a. is 90°-
diffraction directly
sideward - for which — sin
a <1
Giving ۱7/۵ 51 0۲۳ 2 >
d
Smallest na when n=1
The < easiest to satisfy for
n=1
صفحه 11:
95 0۲۱ 6۱۱۵۲ 6
BF sin «
۳ a
C7
NOTICE for fixed % , smaller d gives bigger »
*Spots or wave beams spread as ducks become n=2
closer.
ی نی
صفحه 12:
Spots spread Spots spread
as fingers as duck
Medical ‘i converge.
4 Spread grows
Swan
اااا ۲ با
صفحه 13:
*Spots absent in nonperiodic
fabric
*Spot symmetry same as that of
grid
*Spots rotate with grid rotation
but not XY
map [}\_+Spots spreaabuith aig)
smaller &
Hd *Spot spacing s grows | “with
صفحه 14:
X-ray beam
Therefore: X-rays are waves !
Crystals are periodic arrays !
2> 0 !
This 1912 demonstration won Max von
Laue the Nobel Prize in physics for
1914.
صفحه 15:
۳
or Mineralogists
1. Symmetry of spots = symmetry of array
2. Spacing of spots = array spacing of scattering
atoms
3. Intensity of spots = atomic weight occupancy
distribution. 2 Chain
This makes possibl@ silicate
crystal structuré® * diopside
analysis. & along chains)
Library of patterns is réierénce resource of
‘fingerprints’ for mineral identification!
صفحه 16:
Father and son team showed that XRD
could be more easily used if diffraction
spots treated as cooperative scattering
0۷ ماع 0 و8و عم زو مق
Angle’? and reflection from lattice plane is 6
Braggs’ Law: ۱ < 2 م0 sin @
XRD Mineral identification done
from tables of the characteristic
Bragg d,,, which are
calculated from xX and ©
صفحه 17:
20 < 90] Yer
Powdered sam bee nk
260
me
X- ray beamin + beam in
و - و2 عم
Make list of مر ۲۲۵۲۳۸ ۲۸6۵5۷۲۵ 0
15189 5 < م20 sin @
Compare with standard tables <JCPDS>
صفحه 18:
1. Measure screen to image distance (S).
2. Measure distance from middle of
pattern to first spot (s).
3. Measure spacing of grid (d). .
In >
Il
la.
Compute wavelength 2 of laser light fromn v= ¢
dsina
بر ی eee شا سس را ار ate ae
صفحه 19:
@http://www.icdd.com
Commercial library of the JCPDS powder
patterns of over 60,000 crystal structures.
/www.ccp14.ac.uk
XRD applications freeware and tutorials.
Whttp://webmineral.com
Fun resource for mineralogy, especially
crystal shapes.
@http://ammin.minsocam.org
Mineralogical Society of America’s site
including “Ask A Mineralogist”.