X – Rays & Crystals

Characterizing Mineral Chemistry &Structure

J.D. Price

Wave behavior vs. particle behavior

If atoms are on the 10-10 m scale, we need to use sufficientlysmall wavelengths to explore this realm if we want to learnsomething about atoms and lattices.

Light - electromagnetic spectrum

Dif

fra

cti

on

E.B. Watson

E.B. Watson

wave property

Diffraction of light

Where intersections of the diffracted

wave fronts occur, there is

constructive interference

E.B. Watson

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 !

Crystalline structurediffracts x-rays(XRD)

Bragg equation: ! = 2d sin "

Crystal with unknownd spacing

X-ray source withknown !

Crystal diffractometry

Modern diffractometer

Diffraction lines are generated byany plane within the crystalgeometry. That of course meansthe root planes to the unit cell, but italso includes all of the possiblediagonals.

Miller indices are used to label tothe lines resulting from the planes(you know all about indexing).

In a powdered sample, grainstypically orient in a myriad ofdirections*, such that manydiffraction lines are simultaneouslygenerated

*exception – sheet silicates

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 latticeplanes. Their relative intensity is diagnostic.

Powder diffraction plot

This is great forpolymorphs.Calcite (top)and aragonite(bottom) havethe samecomposition,but differentstructures asevidenced fromtheir diffractionpatterns.

Polymorphs

Most minerals are sizedbetween 0.1 – 100’s of mm.

The rather ordinary rock slab onthe left is composed of small (1-5mm) grains of quartz andfeldspar.

The feldspar below is large (15mm) but is concentrically zoned.

Chemical analysis

Feldspars are solid-solutions and exhibit arange of compositions.

How might we determinethe composition of theminerals in our rocks?

What is unique about eachelement?

MM

TT

TT

Ephoton = EH – EL = h f = h c / !

1. To obtain composition, we need a measurablecharacteristic for each element.

Electron structure is element specific. In other words,Ephoton is the result of a specific jump in a specific element.

Fluorescence: electromagneticradiation results from movingelectrons closer to the nucleus

Photoelectric characteristic

Photo by Elizabeth Frank

Fluorescence Visible light is produced byenergies in U.V. light.

Examples of transitionlevels 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

Energy levels

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

Calculating the wavelength

2. To get analysis at micron scale, we need highenergies (keV) focused on small area

Electrons are chargedparticles that can be focusedand redirected using amagnets

Lower energy example: theCRT

Raymond Castaingformulated the techniquefor microanalysis andbuilt the first working unitby 1951.

Focus!

3. Fluoresced x-rays need to be collected and counted.

Recall that crystalline structurediffracts x-rays (XRD)

Bragg equation: ! = 2d sin "

Crystal with unknownd spacing

X-ray source withknown !

Count

Castaing’s machine: focused electron beam that produces x-raysin an unknown, that may be counted at known diffraction angles.

Wavelength dispersive spectrometry (WDS)

Bragg equation: ! = 2d sin "

The intensity of x-rays ismuch smaller relative tothose generated from atube (as in XRD)

The EMP wavelength spectrometer uses crystals with curvedlattices and ground curvature to reduce lost x-rays

The Rowland Circle

Crystal

Detector

InboundX-rays

Maximizing counts

Example of amodern EM probe

Locate the following:Cathode and

anodeBeamMagnetsSampleCrystalDetector

The Cameca SX100• Five spectrometers• Each with 2–4 crystals

The new RPI facility

Cameca SX 100 EMPRontec EDS detectionGatan mono CL

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

Electron-sample interactions

EMPA does not analyze surfaces (thin film), but penetrates asmall volume of the sample.

The collectable products of electron collision origin originatefrom specific volumes under the surface.

Analysis volume

Secondary electrons emittedfrom the first 50 nm

Images surface topography

Backscattered electron intensityare a function of atomic density

Images relative composition

Useful interactions

Ti

Characteristic x-ray emission

The x-ray volumechanges as a function of anumber variables.

A sample with higheraverage atomic densitywill have a shallower butwider volume than onewith a lower density.

A beam with higherenergy (keV) will producea larger volume than onewith a lower E0.

Nonunique nature of emission volume

From the excitation volume behavior, it is clear atomicdensity (Z) makes a difference in the emitted intensities.

Some of the x-rays are absorbed into atoms within andadjacent to the excitation volume.

Some of the x-rays promote electron jumps in atomswithin and adjacent to the excitation volume.

Z

A

F

Raw data are corrected for ZAF influences. Thetotal correction produces a rather long equationthat may be satisfied only through iteration.

The microprobe advanced as a tool because of

the microprocessor

Sample effects

The number of x-rays counted at the appropriate diffractionangle is proportional to the concentration of the fluorescingelement. But the excitation volume is not unique.

Quantification requires comparison to a well-characterizedstandard.

Standard analyzed by

other meansYour sample with

unknown composition

Standardization

Castaing’s micro WDS machine was a breakthrough. By1960, advances in semiconduction permitted theconstruction of a new detector that could collect all of theemitted x-ray energies (pulses and background) within afew 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

EDS spectrum for a 15kV beam on a gemmy crystal from theAdirondacks (M. Lupulescu, NYSM).

Al K# & $

Si K# & $

K K#

K K$

Energy spectrum

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 atthe micrometer scale

High voltage electron beam can be focused on onemicrometer area

Composition is determined by characteristic x-raysfrom excited atoms

WDS

•Characteristic x-rays are focused throughdiffraction

•Permits better resolution

EDS

•All x-rays are counted simultaneously

•Permits faster analysis / identification

Limitations

•Good standards are essential

•Quantification is dependant on accuratecorrection 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