Transcript ppt

X - Rays & Crystals
Characterizing Mineral Chemistry &
Structure
J.D. Price
Light - electromagnetic spectrum
Wave behavior vs. particle behavior
If atoms are on the 10-10 m scale, we need to use sufficiently small
wavelengths to explore this realm if we want to learn something
about atoms and lattices.
Diffraction
E.B. Watson
Diffraction of light
wave property
E.B. Watson
E.B. Watson
Where intersections of the diffracted
wave fronts occur, there is
constructive interference
Scale - grating and 
The difference is only of scale. We can use optical
wavelengths for the grid on the left, because they are
appropriately spaced for those wavelengths. With
small wavelengths, lattices diffract.
Crystal diffractometry
X-ray source with
known 
Crystalline structure
diffracts x-rays
(XRD)
Crystal with unknown d
spacing
Bragg equation: = 2d sin 
Modern diffractometer
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Diffraction lines are generated by any
plane within the crystal geometry.
That of course means the root planes
to the unit cell, but it also includes all
of the possible diagonals.
Miller indices are used to label to the
lines resulting from the planes (you
know all about indexing).
In a powdered sample, grains
typically orient in a myriad of
directions*, such that many diffraction
lines are simultaneously generated
*exception - sheet silicates
Powder diffraction plot
The resulting information is structural!
(011) =3.259Å
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(100) 4.1341Å
(110) 2.3868Å
This is the diffraction patter for quartz (mindat.org).
Peaks correspond to specific lattice planes. Their
relative intensity is diagnostic.
Polymorphs
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This is great for
polymorphs.
Calcite (top) and
aragonite
(bottom) have the
same
composition, but
different
structures as
evidenced from
their diffraction
patterns.
Chemical analysis
Most minerals are sized
between 0.1 - 100’s of mm.
The rather ordinary rock slab on
the left is composed of small (15mm) grains of quartz and feldspar.
The feldspar below is large (15
mm) but is concentrically zoned.
Feldspars are solid-solutions
and exhibit a range of
compositions.
How might we determine the
composition of the minerals in
our rocks?
M
What is unique about each
element?
T
T
Photoelectric characteristic
1. To obtain composition, we need a measurable
characteristic for each element.
Fluorescence: electromagnetic
radiation results from moving
electrons closer to the nucleus
Ephoton = EH - EL = h f = h c / 
Electron structure is element specific. In other words,
Ephoton is the result of a specific jump in a specific element.
Fluorescence
Visible light is produced by
energies in U.V. light.
Photo by Elizabeth Frank
Energy levels
Examples of transition
levels in Barium
K 37.44 keV
LI
5.99 keV
LII
5.63 keV
LIII
5.25 keV
So LII to K (K 1) is…
31.81 keV
Heavier atoms have many energy levels
Calculating the wavelength
So LIIto K is 31.81 keV or 31,810 eV
The wavelength of the photon produced by this jump is
 h c / E
h = 6.626 × 10-34 m2 kg/s
c = 3 × 108 m/s
E = 31,810 eV × 1.602 × 10-19 J/ eV = 5.096 × 10-15 J
So  = 3.900 × 10-11 m
Focus!
2. To get analysis at micron scale, we need high energies
(keV) focused on small area
Raymond Castaing
formulated the technique for
microanalysis and built the
first working unit by 1951.
Electrons are charged particles
that can be focused and
redirected using a magnets
Lower energy example: the
CRT
Count
3. Fluoresced x-rays need to be collected and counted.
X-ray source with
known 
Recall that crystalline structure
diffracts x-rays (XRD)
Crystal with unknown d
spacing
Bragg equation:  = 2d sin 
Castaing’s machine: focused electron beam that produces x-rays in
an unknown, that may be counted at known diffraction angles.
Wavelength dispersive spectrometry (WDS)
Bragg equation:  = 2d sin 
Maximizing counts
Crystal
The intensity of x-rays is
much smaller relative to
those generated from a
tube (as in XRD)
The Rowland Circle
Detector
Inbound
X-rays
The EMP wavelength spectrometer uses crystals with curved
lattices and ground curvature to reduce lost x-rays
Example of a
modern EM probe
Locate the following:
Cathode and
anode
Beam
Magnets
Sample
Crystal
Detector
The Cameca SX100
• Five spectrometers
• Each with 2-4 crystals
The new RPI facility
Cameca SX 100 EMP
Rontec EDS detection
Gatan mono CL
Electron-sample interactions
Electron forces jump
Char. photon produced
Glancing background phn
Produced photon adsorbed - may produce Auger e-
Electron bounces off atom
(high E): backscattered
Electron knocks out another e- (low
E): secondary
Analysis volume
EMPA does not analyze surfaces (thin film), but penetrates a
small volume of the sample.
The collectable products of electron collision origin originate from
specific volumes under the surface.
Useful interactions
Secondary electrons emitted from
the first 50 nm
Backscattered electron intensity are
a function of atomic density
Images surface topography
Images relative composition
Characteristic x-ray emission
Ti
Nonunique nature of emission volume
The x-ray volume changes
as a function of a number
variables.
A sample with higher
average atomic density will
have a shallower but wider
volume than one with a
lower density.
A beam with higher energy
(keV) will produce a larger
volume than one with a
lower E0.
Sample effects
Z
From the excitation volume behavior, it is clear atomic
density (Z) makes a difference in the emitted intensities.
A
Some of the x-rays are absorbed into atoms within and
adjacent to the excitation volume.
F
Some of the x-rays promote electron jumps in atoms within
and adjacent to the excitation volume.
Raw data are corrected for ZAF influences. The
total correction produces a rather long equation
that may be satisfied only through iteration.
The microprobe advanced as a tool because of the
microprocessor
Standardization
The number of x-rays counted at the appropriate diffraction angle is
proportional to the concentration of the fluorescing element. But the
excitation volume is not unique.
Standard analyzed by
other means
Your sample with
unknown composition
Quantification requires comparison to a well-characterized standard.
EDS
Castaing’s micro WDS machine was a breakthrough. By
1960, advances in semiconduction permitted the construction
of a new detector that could collect all of the emitted x-ray
energies (pulses and background) within a few seconds.
Energy Dispersive Spectrometry (EDS)
•Measures charges in semiconductor [Si(Li)]
•Makes histogram of measured charges
•Extremely fast
•Very inexpensive
•Lower accuracy relative to WDS
Energy spectrum
Si K& 
Al K& 
K
K
K K
EDS spectrum for a 15kV beam on a gemmy crystal from the
Adirondacks (M. Lupulescu, NYSM).
EMPA traverses of spinel using WDS
Formula for the spinel
Nom: Mg Al2O4
Act: Mg1-3x Al2+2x O4
EMPA is a powerful tool for compositional analysis at the
micrometer scale
High voltage electron beam can be focused on one
micrometer area
Composition is determined by characteristic x-rays from
excited atoms
WDS
•Characteristic x-rays are focused through diffraction
•Permits better resolution
EDS
•All x-rays are counted simultaneously
•Permits faster analysis / identification
Limitations
•Good standards are essential
•Quantification is dependant on accurate correction
for ZAF effects
•User needs to be aware of excitation volume
Results
•Accurate assessment of mineral stoichiometry
•WDS provides trace element compositions
•May assess inhomogeneity at small scales