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Slide 1
X - Rays & Crystals Characterizing Mineral Chemistry &
Structure J.D. Price Characterizing Mineral Chemistry &
Structure J.D. Price
Slide 2
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.
Light - electromagnetic spectrum
Slide 3
Diffraction E.B. Watson
Slide 4
wave property Diffraction of light
Slide 5
Where intersections of the diffracted wave fronts occur, there
is constructive interference E.B. Watson
Slide 6
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. Scale
- grating and
Slide 7
Crystalline structure diffracts x-rays (XRD) Bragg equation: =
2d sin Crystal with unknown d spacing X-ray source with known
Crystal diffractometry
Slide 8
Modern diffractometer
Slide 9
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
Slide 10
The resulting information is structural! (100) 4.1341 (011)
=3.259 (110) 2.3868 This is the diffraction patter for quartz
(mindat.org). Peaks correspond to specific lattice planes. Their
relative intensity is diagnostic. Powder diffraction plot
Slide 11
This is great for polymorphs. Calcite (top) and aragonite
(bottom) have the same composition, but different structures as
evidenced from their diffraction patterns. Polymorphs
Slide 12
Most minerals are sized between 0.1 - 100s of mm. The rather
ordinary rock slab on the left is composed of small (1- 5mm) grains
of quartz and feldspar. The feldspar below is large (15 mm) but is
concentrically zoned. Chemical analysis
Slide 13
Feldspars are solid-solutions and exhibit a range of
compositions. How might we determine the composition of the
minerals in our rocks? What is unique about each element? M T
T
Slide 14
E photon = E H - E L = h f = h c / 1. To obtain composition, we
need a measurable characteristic for each element. Electron
structure is element specific. In other words, E photon is the
result of a specific jump in a specific element. Fluorescence:
electromagnetic radiation results from moving electrons closer to
the nucleus Photoelectric characteristic
Slide 15
Photo by Elizabeth Frank Fluorescence Visible light is produced
by energies in U.V. light.
Slide 16
Examples of transition levels in Barium K 37.44 keV L I 5.99
keV L II 5.63 keV L III 5.25 keV So L II to K (K 1 ) is 31.81 keV
Heavier atoms have many energy levels Energy levels
Slide 17
So L II to 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 m 2 kg/s c
= 3 10 8 m/s E = 31,810 eV 1.602 10 -19 J/ eV = 5.096 10 -15 J So =
3.900 10 -11 m Calculating the wavelength
Slide 18
2. To get analysis at micron scale, we need high energies (keV)
focused on small area Electrons are charged particles that can be
focused and redirected using a magnets Lower energy example: the
CRT Raymond Castaing formulated the technique for microanalysis and
built the first working unit by 1951. Focus!
Slide 19
3. Fluoresced x-rays need to be collected and counted. Recall
that crystalline structure diffracts x-rays (XRD) Bragg equation: =
2d sin Crystal with unknown d spacing X-ray source with known
Count
Slide 20
Castaings 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
Slide 21
The intensity of x-rays is much smaller relative to those
generated from a tube (as in XRD) The EMP wavelength spectrometer
uses crystals with curved lattices and ground curvature to reduce
lost x-rays The Rowland Circle Crystal Detector Inbound X-rays
Maximizing counts
Slide 22
Example of a modern EM probe Locate the following: Cathode and
anode Beam Magnets Sample Crystal Detector
Slide 23
The Cameca SX100 Five spectrometers Each with 2-4 crystals The
new RPI facility Cameca SX 100 EMP Rontec EDS detection Gatan mono
CL
Slide 24
Electron forces jump Char. photon produced Glancing background
ph n Produced photon adsorbed - may produce Auger e - Electron
bounces off atom (high E): backscattered Electron knocks out
another e - (low E): secondary Electron-sample interactions
Slide 25
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.
Analysis volume
Slide 26
Secondary electrons emitted from the first 50 nm Images surface
topography Backscattered electron intensity are a function of
atomic density Images relative composition Useful interactions
Slide 27
Ti Characteristic x-ray emission
Slide 28
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 E
0. Nonunique nature of emission volume
Slide 29
From the excitation volume behavior, it is clear atomic density
(Z) makes a difference in the emitted intensities. Some of the
x-rays are absorbed into atoms within and adjacent to the
excitation volume. Some of the x-rays promote electron jumps in
atoms within and adjacent to the excitation volume. Z A F 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
Sample effects
Slide 30
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. Quantification
requires comparison to a well-characterized standard. Standard
analyzed by other means Your sample with unknown composition
Standardization
Slide 31
Castaings 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 EDS
Slide 32
EDS spectrum for a 15kV beam on a gemmy crystal from the
Adirondacks (M. Lupulescu, NYSM). Al K & Si K & KKKK K K
Energy spectrum
Slide 33
Slide 34
EMPA traverses of spinel using WDS Formula for the spinel Nom:
Mg Al 2 O 4 Act: Mg 1-3x Al 2+2x O 4
Slide 35
Slide 36
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
Slide 37
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