Lecture 15: XRD and Other Analytical Techniques X-Ray Diffraction ...

Lecture 15:
XRD and Other Analytical Techniques
Read Chpt 7
X-Ray Diffraction in the Lab:
1. Assume n=1 (can’t distinguish between n=1 and n=2 separated by twice
the distance)
2. Use X-ray of fixed !
3. Strike at many angles (vary ")
4. Some d values will satisfy Bragg’s law ! diffraction occurs at angle of 2"
relative to incident beam and hits detector with high intensity
5. Many planes of atoms in a mineral, therefore diffraction may occur at
many 2" values (can check by moving sample, or by moving the detector!)

We can write {hkl} for any planes, does that mean that there will be
infinitely many solutions to Bragg’s Law?
NO! We only get diffraction along planes of high atomic
density that aren’t effect by EXTINCTIONS
Example:
a
d 210
d 010
d 020
d 100
d 200
b
b=5Å
a = 3Å
Which d hkl spacings will give intense diffraction peaks??

d 010 = 6Å ?
lots of atoms => intense diffraction
peaks
d 010
d 020
d 020 = 3Å ?
No atoms on every other => peak occurs though,
because n=2 with d 020 is just like d 010 (less
intense than d 010 peak)

d 200 = 2Å ?
lots of atoms => intense diffraction
peaks
d 200
d 100 = 4Å ?
no diffraction (EXTINCTION)
d 100

Extinctions: due to destructive interference, one plane of atoms
‘cancels’ diffraction from another plane
Note: End-centered, Body-centered unit cells will result in extinctions

Higher symmetry minerals
will have fewer, but more
intense diffraction peaks

2 Types of XRD:
(1) Single Crystal:
Laue Technique: orient crystal with axes perp. or parallel to X-ray beam,
put film behind crystal, record spots
Modern single crystal: rotate crystal and/or detector
Crystal structure determination: chemical composition and single
crystal diffraction patterns allows complete structure to be
determined

2 Types of XRD:
(2) Powder Diffraction: X-ray finely powdered samples; random
orientation ensure that all {hkl} planes will satisfy Bragg’s Law
Ex. d 111 = 5Å {111} has high density
n=1; d 111 = 5Å; CuK# = 1.54Å
Then:
n ! = 2d sin "
(1) (1.54Å)/(2)(5Å) = sin "
" = 17.74°
Therefore, grains oriented at " = 17.74° will give strong diffraction peak
In practice: measure " and intensity
Calculate d hkl

Peak intensity reflects:
1. density of atoms on {hkl} planes
2. types of atoms on {hkl} planes
X-Ray Powder Diffraction File:
1. Assign most intense peak 100%
2. Index peaks (assign d-values)
3. Look up d values/relative intensities
A Pain!!! Intensities depend on sample prep, purity (solid solution)…

(1) X Ray Fluorescence Spectroscopy
“bulk technique”
sample prep = grind sample to powder, make pressed pellet
Method:
• irradiate sample with high energy X-rays
• some electrons knock out inner shell electrons; outer shell electrons fall and
emit characteristic wavelength secondary X-rays
• intensity of characteristic spectrum relates to quantity; samples with many
elements will result in many spectral line emissions

(2) Electron Microscope
"! use electrons rather than visible light
"! Why? Better resolution; theoretical limit = ~1/2 ! radiation (e.g., 3000Å
for light microscope)
"! Concept: collimate and focus an electron beam using magnetic coils
(analogous to optical lens in a light microscope); resolving power
now:

a. Electron Microprobe (EM)
•! electrons excite inner electrons to produce secondary X-rays, measure just like
in XRF
•! spot size: ~1micron (10000 Å)
•! sample prep: polished thin section
•! Advantage: quantitative chemical analyses can be made over very small areas
(e.g., study exsolution lamellae); relatively nondestructive, quick

. Scanning Electron Microscope (SEM)
•! bombard specifment with rastering electron beam
•! secondary electrons (emitted from speciment) + backscattered electrons (interact
with specimen and reflect out) result
•! collect emitted current, amplify and display as trace on cathode tube (fluorescent
screen)
•! result: very high magnification topography (like light microscope) with either
secondary or backscattered electrons (heavy atoms = more scattering = darker
image); emitted secondary x-rays can also be collected and used for chemical
analysis

c. Transmission Electron Microscope
! much like SEM, but now can get resolution ~1.5Å!!; not quite
individual atoms
n" = 2d hkl sin#
!

(3) Atomic Force Microscopy
"! mount a very small tip (usually triangle 100-200micron long,
5 micron thick) at the end of a cantilever
"! drag it back and forth over sample, measure deflection with a
laser, yields topography at Å resolution in air or water,
on insulators or conductors (some tip artifacts)
"! used to study adsorbed atoms, mineral dissolution and growth
processes

Scanning Tunnelling Microscopy (STM)
!
* look at electronic structure of surface
* position tip over point, ramp voltage
* negative sample bias: electrons tunnel from sample to tip
* measure tunneling current
* can’t be used on insulators