electron probe microanalysis electron - specimen interaction revised 1/19/13 uw- madison geoscience...

Electron probe microanalysis

Electron - Specimen

Interaction

Revised 1/19/13

UW- Madison Geoscience 777

What’s the point?Electrons from a source

interact with electrons in specimen

yielding a variety of photons and electrons

via elastic and inelastic scattering processes.

These are the “signals” that we use to make images and measure to characterize the

composition of our specimens.

UW- Madison Geology 777

Overview•Elastic and inelastic processes

•Characteristic and continuum X-rays

•K,L,M etc: families of X-rays

•Energy versus wavelength

•Moseley’s relation

•Absorption or critical excitation energy

•Interaction volume and ranges

•Monte Carlo models

•Odds of X-ray production

•Distinction between X-rays and electrons


Elastic and inelastic scattering of HV electron by sample

Elastic (a): incident electron’s direction altered by Coulombic field of nucleus (Rutherford scattering), screened by orbital electrons. Direction may be changed by 0-180° (ave 2-5°) but velocity remains virtually constant. <1 eV of beam energy transferred.

Inelastic (b): incident electron transfers some energy (up to all, E0) to tightly bound inner-shell electrons and loosely bound outer-shell electrons. Direction barely changes (<0.1°)

(Goldstein et al, 1992, p.72)

E0 = accelerating voltage (of electrons emitted from gun); usually 15-20 keV


Elastic and inelastic scattering of HV electron by sample

(Goldstein et al, 1992, p.72)

This Monte Carlo program output represents 1000 electron trajectories (idealized), in a cross-section--both elastic and inelastic scattering. Twenty years ago this took a fair amount of computing power….


Monte Carlo simulations are very useful

Gopon et al, 2013

Today, you can simulate the “interaction volume” of scattered electrons for whatever kV and whatever composition material you may be interested in, in seconds. (above: using “Casino”)


Scattering lexicon

Cross section: a measure of the probability that an event of a certain kind will occur, e.g. K-shell cross section. Defined as Q = N/nint, where N=events of certain type/vol (sites/cm3), ni=number incident particles/unit area (particles/cm2), and nt=number target sites/vol (sites/cm3). Q has units of cm2 and is thought of as an effective ‘size’ which the atom presents as a target to incident particle. The Q for elastic scattering is ~10-

17 cm2 and for K-shell ionization is ~10-20 cm2.

Mean free path: average distance an electron travels within a specimen between events of a specific type. MFP=A/(NAQ) where A is atomic wt (g/mol), NA is Avogadro’s number, is density (g/cm3).


Elastic and inelastic scattering Elastic :

Backscattering of electrons (~high energy)

Inelastic :

Plasmon excitation (in metals, loosely bound outer-shell electrons are excited)

Phonon excitation (lattice oscillations: heating)

Secondary electron excitation

Inner-shell ionization (Auger electrons, X-rays)

Bremsstrahlung (continuum) X-ray generation

Cathodoluminescence radiation (non-metal valence shell phenomenon)


Backscattered ElectronsHigh energy beam electrons may suffer single or multiple elastic scattering events in the solid, escaping from the material.

The fraction of beam electrons that scatter back () was found experimentally to vary directly as a function of composition (atomic number Z). This provides a valuable imaging tool: a rapid means to discriminate phases that have different mean Z values.

Intensity (grey level) varies from black (voids/epoxy), to plagioclase, olivine, basaltic glass, with Ti-magnetite the brightest phase.


Secondary ElectronsInelastic scattering of HV beam electron can promote loosely bound electrons from valence to conduction band in semiconductor or insulator with enough energy to move thru the solid (in metals, promotion from conduction-band directly). Backscattered electrons can also produce secondary electrons.

a) Complete energy distribution of electrons emitted from target. Region I and II are BSE, Region III secondary. b) Secondary electron energy distribution, measured (points) and modeled (lines)

By definition, these secondary electrons are <50 eV, with most <10 eV.

(Goldstein et al, 1992, p. 107)


SE imagesSecondary electrons are generated throughout the interaction volume, but only secondary electrons produced near the surface are able to escape (~5 nm in metals, ~50 nm in insulators). For this reason, secondary electron imaging (SEI) yields high resolution images of surface features.These have grey-scales, though pseudo-coloring is sometimes done.

Pollen, cat flea, and Si nanowires on alumina sphere.

20 m


SE and BSE coefficients


Coefficients for backscattered-electron () and secondary electron () as function of Z. Tilt of specimen from 90° beam incidence () is 0. E0=30 keV. Data from 1966; more recent views suggest the flat SE curve may be due to carbon contamination on specimen hindering SE escape.


Inner-shell ionization:Production of X-ray or Auger e-

(Goldstein et al, 1992, p 120)

HV electron knocks inner shell (K here) electron out of its orbit (time=1). This is an unstable configuration, and an electron from a higher energy orbital (L here) ‘falls in’ to fill the void (time=2). There is an excess of energy present and this is released internally as a photon. The photon has 2 ways to exit the atom (time=3), either by ejecting another outer shell electron as an Auger electron (L here, thus a KLL transition), or as X-ray (KL transition).

K shell

L shell

(=photoelectron)

Blue Lines indicate subsequent times: 1 to 2, then 3 where there are 2 alternate outcomes

Time

1

2

3


X-ray Lines - K, L, M


K X-ray is produced due to removal of K shell electron, with L shell electron taking its place. K occurs in the case where K shell electron is replaced by electron from the M shell.

L X-ray is produced due to removal of L shell electron, replaced by M shell electron.

M X-ray is produced due to removal of M shell electron, replaced by N shell electron.


All possible K, L, M X-ray Lines

(Originally Woldseth, 1973, reprinted in Goldstein et al, 1992, p 125)


X-ray Lines with initial + final levels

(Reed, 1993)


L LL N

NB:not Greek!

Nomenclature of X-rays

(Reed, 1993)

There is some movement now to change the way X-rays are described, from the traditional Siegbahn notation (e.g. K1) to the the IUPAC (K-L3). (International Union of Pure and Applied Chemistry). This table is from their 1991 recommendation.


X-ray energies, Cu for example

Where do the values for characteristic x-rays come from: here are the numbers for Cu K x-rays:

Subtract the energy of the L shell (binding) energy from that of the K shell (binding) energy, and you have the characteristic value.


L3 2p3/2 933 ev

L2 2p1/2 952 ev

L1 2s 1097 ev

K1 K2

K 1s 8979 ev

8979 - 933 = 8046 ev (book says 8048)

8979 - 952 = 8027 ev (book says 8028)

Or… Fe L linesUW- Madison Geology 777

Ll = M1-L3 = 615.2 eVLα= M5-L3 = 705.0 eVLβ= M3-L2 = 718.5 eV (Gopon et al., 2013)

Absorption Edge Energy

Example: Pt (Z=78) X-ray line energies and

associated critical excitation (absorption edge) energies,

in keV

Edge or Critical ionization energy: minimum energy required to remove an electron from a particular shell. Also known as critical excitation energy, X-ray absorption energy, or absorption edge energy. It is higher than the associated characteristic (line) X-ray energy; the characteristic energy is value measured by our X-ray detector.


OvervoltageOvervoltage is the ratio of accelerating (gun) voltage to critical excitation energy for particular line*. U = E0/Ec

Maximum efficiency (cross-section) is at 2-3x critical excitation energy.

Example of Overvoltage for Pt: for efficient excitation of this line, would be (minimally) thisß accelerating voltage

• La -- 23 keV

• Ma -- 4 keV

Example: Pt (Z=78) X-ray line energies and

associated critical excitation (absorption edge) energies,

in keV

* recall: E0=gun accelerating voltage; Ec=critical excitation energy


Fluorescence yield

(Goldstein et al, 1992)

Fluorescence yield () is fraction of ionizations that yield characteristic X-ray versus Auger yield () within a particular family of X-rays. + =1


Fluorescence yield …can cause misunderstanding

2. Measured characteristic x-rays by WDS will additionally be a function of (a) the crystal diffraction efficiency, (b) the gas absorption efficiency, and c) the spectrometer sin theta position (distance between detector and sample).

For example, from the above chart, you cannot predict whether Hf La or Hf Ma will have higher count rates.


1. These are fractions, so each one is normalized to one. You cannot say anything about absolute detected x-ray intensities.

Continuum X-raysHV beam electrons can decelerate in the Coulombic field of the atom (+ field of nucleus screened by surrounding e-). The loss in energy as the electron brakes is emitted as a photon, the bremsstrahlung (“braking radiation”). The energy emitted in this random process varies up from 0 eV to the maximum, E0.

On an EDS plot of X-ray intensity vs energy, the continuum intensity decreases as energy increases. The high energy value where the continuum goes to zero is known as the Duane-Hunt limit.

Duane-Hunt Limit


The Duane-Hunt limit is very important to remember -- and utilize continuously!

Kramer’s Law

Kramer’s Law (or Relation) is a mathematical description (formula) for the background or continuum shape and intensity:

I = constant x Z (E0 - E) / E

Where I is the intensity of the continuum at any energy E, Z is atomic number and E0 is the accelerating voltage


Duane-Hunt Limit

Continuum and Atomic NumberAt a given energy (or ), the intensity of the continuum increases directly with Z (atomic number) of the material. This is of critical importance for minor or trace element analysis, and also lends itself to a timesaving technique (Mean Atomic Number,“MAN”).


X-ray units: A, keV, sin , mm

= hc/E0 where h=Plancks constant, c=speed of light

= 12.398/E0 where is is in Å and E0 in keV

also, the 2 main EMPs plot up X-ray positions thusly:

Cameca: n = 2d sin so for n=1 and a given 2d, an X-ray line can be given as a sin value (or 105 times sin )

JEOL: distance (L, in mm) between the sample (beam spot) and the diffracting crystal, i.e. L= R/d, where R is Rowland circle radius (X-ray focusing locus of points) and d is interlayer spacing of crystal.


Moseley’s Relation


Moseley (1913, 1914) found that there is a regular relationship between the atomic number of a material and its characteristic X-ray wavelength.

=B/(Z-C)2,

where B and C are constants for each family of X-rays.


Cathodoluminesce

When insulators and semiconductors are hit by HV electrons, long photons (UV, visible, IR light) may be emitted. The light may be bright enough to be seen in the reflected light image (examples are benitoite, scheelite, zircon, corundum, diamond, wollastonite, YAG, GaAlAs).

Incident electrons may promote valence shell electrons across the band gap to the empty conduction band, creating electron-hole pairs. With no bias to sweep the electron away, it will recombine with the hole. The excess energy (= gap energy) will be emitted as a long photon.

CL ImagesImpurity atoms as well as dislocations increase the possibilities for additional gap energies, yielding different wavelengths of emitted light.These may be valuable for production of diagnostic images. CL is a cheap way to view overgrowths (inherited cores) and healed fractures in quartz and zircons.

CL image of zircon from Yellowstone tephra (Lava Creek Tuff). Note faint oscillatory zoning surrounding sector-zoned core, and healed fractures. These are not visible in the BSE image. ~50 um grain. (courtesy Ilya Bindeman)


Electron interaction volumes


Effect of beam interaction (damage) in plastic (polymethylmethacrylate), from Everhart et al., 1972. All specimens received same beam dosage, but were etched for progressively longer times, showing in (a) strongest electron energies, to (g) the region of least energetic electrons. Note teardrop shape in (g). Same scale for all.

Ranges and interaction volumes

It is useful to have an understanding of the distance traveled by the beam electrons, or the depth of X-ray generation, i.e. specific ranges. For example: If you had a 1 um thick layer of compound AB atop substrate BC, is EPMA of AB possible?


Electron and X-ray RangesSeveral researchers have developed physical/mathematical expressions to approximate electron and X-ray ranges. Two common ones are given below.

Electron range. Kanaya and Okayama (1972) developed an expression for the depth of electron penetration:

RKO=(0.0276 A E01.67)/( Z0.89)

X-ray range. Anderson and Hasler (1966) give the depth of X-ray production as:

RAH=(0.064)(E01.68 - Ec

1.68)/

where Ec is the absorption edge (critical excitation) energy.

There are nomograms for these ranges, given on the next slides.

Ranges

From Will Bigelow, now emeritus U MI (Ann Arbor)


Monte Carlo simulationsWith the development of PCs, Monte Carlo simulations of electron-beam interactions have been very easy to perform. You can input your specific sample composition and run various “what if” scenarios, e.g. what is the maximum penetration of the electron beam through a thin film, or what is the smallest size crystal in a glass matrix that can be analyzed.

You will be performing some of these MC simulations in a take home exercise.

Each MC run has distinct conditions: specific E0, specific composition (Atomic wt and average Z), density, and potentially different tilt angle.


Specimen HeatingCastaing (1951) derived the maximum temperature rise in a solid impacted by electrons of E0 energy and i current (in A) and beam diameter d (m):

T = 4.8 E0 i /kd

where k is thermal conductivity (W/cmK).

For E0=20 keV and 20 nA, d=1 um, in a metal (k=1), T is 2 K. In a typical mineral (k=0.1), T is 20 K. And in organic material, (k=0.002), T is 1000 K! (e.g. epoxy)

Difficult materials: carbonates, hydrated materials, halides, phosphates, glasses, feldspars.

(Reed 1993, p 158)


“Harper’s Index” of EPMA1 nA of beam electrons = 10-9 coulomb/sec

1 electron’s charge = 1.6x 10-19 coulomb

ergo, 1 nA = 1010 electrons/sec

Probability that an electron will cause an ionization: 1 in 1000 to 1 in 10,000

ergo, 1 nA of electrons in one second will yield 106 ionizations/sec

Probability that ionization will yield characteristic X-ray (not Auger electron):

1 in 10 to 4 in 10.

ergo, our 1 nA of electrons in 1 second will yield 105 xrays.

Probability of detection: for EDS, solid angle < 0.01 (1 in 100). WDS, <.001

ergo 103 X-rays/sec detected by EDS, and 102 by WDS. These are for pure

elements. For EDS, 10 wt%, 102 X-rays; 1 wt% 10 X-rays; 0.1 wt % 1 X-ray/sec.

ergo, counting statistics are very important, and we need to get as high count rates

as possible within good operating practices.


Acknowledgement: I first encountered this treatment at the Lehigh Microscopy Summer School

Sources of X-ray data• J.A. Bearden, 1964 (NBS; AEC)

• White et al (“Penn State” 1965) tables

• main lines in tables in Goldstein et al, and Reed texts

• Probe for EPMA database (includes higher order lines for WDS), also online at <epmalab.uoregon.edu/UCB_EPMA/xray>

• NIST database: click on “X-ray Database” at bottom of page: www.cstl.nist.gov/div837/Division/outputs/DTSA/DTSA.htm

• Lawrence Berkeley National Lab online at xdb.lbl.gov for data


Electrons and X-rays … don’t get them confused !

• X-rays have no mass, no charge; electrons have charge (key!) and a small mass• X-rays can be produced by accelerating HV electrons in a vacuum and colliding them with a target.• The resulting electron-generated X-ray spectra contains (1) continuum or continuous background (Bremsstrahlung), (2) occurrence of sharp lines (characteristic X-rays), and (3) a cutoff of continuum at a short wavelength/high keV.• X-rays can also generate other x-rays, but unlike the above process, NO Bremsstrahlung is produced!

electron probe microanalysis electron - specimen interaction revised 1/19/13 uw- madison geoscience...

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