Transcript Document 7378416

UofO- Geology 619
Electron Beam MicroAnalysisTheory and Application
Electron Probe MicroAnalysis (EPMA)
X-ray Production:
Ionization and Absorption
Schrödinger Model:
EM Spectrum Lines Produced by Electron Shell Ionization
Inner-shell ionization:
Production of X-ray or Auger eTime
K shell
(=photoelectron)
1
2
3
L shell
Blue Lines indicate
subsequent times: 1
to 2, then 3 where
there are 2 alternate
outcomes
Incident 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).
(Goldstein et al, 1992, p 120)
X-ray Lines - K, L, M
Ka X-ray is produced due to
removal of K shell electron,
with L shell electron taking
its place. Kb occurs in the
case where K shell electron
is replaced by electron from
the M shell.
La X-ray is produced due to
removal of L shell electron,
replaced by M shell electron.
Ma X-ray is produced due to
removal of M shell electron,
replaced by N shell electron.
Ionization of Electron Shells
(Originally Woldseth, 1973,
reprinted in Goldstein et al,
1992, p 125)
X-ray Lines with
initial + final levels
(Reed, 1993)
Nomenclature of X-rays
•X-rays are described,
from the traditional
Siegbahn notation
(e.g. Ka1) to the the
IUPAC (K-L3).
• (International Union
of Pure and Applied
Chemistry).
•This table is from
their 1991
recommendation.
(Reed, 1993)
One slide Schrödinger Model of the Atom
n = principal quantum number and indicates the electron shell or orbit (n=1=K, n=2=L, n=3=M, n=4=N) of the
Bohr model. Number of electrons per shell = 2n2
l = orbital quantum number of each shell, or orbital angular momentum, values from 0 to n –1
Electrons have spin denoted by the letter s, angular momentum axis spin, restricted to +/- ½ due to magnetic
coupling between spin and orbital angular momentum, the total angular momentum is described by j = l + s
In a magnetic field the angular momentum takes on specific directions denoted by the quantum number m <= ABS(j)
or m = -l… -2, -1, 0, 1, 2 … +l
Rules for Allowable Combinations of Quantum Numbers:
The three quantum numbers (n, l, and m) that describe an orbital must be integers.
"n" cannot be zero. "n" = 1, 2, 3, 4...
"l" can be any integer between zero and (n-1), e.g. If n = 4, l can be 0, 1, 2, or 3.
"m" can be any integer between -l and +l. e.g. If l = 2, m can be -2, -1, 0, 1, or 2.
"s" is arbitrarily assigned as +1/2 or –1/2, but for any one subshell (n, l, m combination), there can only
be one of each. (1 photon = 1 unit of angular momentum and must be conserved, that is no ½ units,
hence “forbidden transitions)
n
l
s
m
j
number of
Sub shell
X-ray
electrons
No two electrons in an atom can have
the same exact set of quantum
numbers and therefore the same
energy. (Of course if they did, we
couldn’t observably differentiate them
but that’s how the model works.)
notation
1
0
½
0
½
2
1s
K
2
2
2
0
1
1
½
0
2
2s
½
-1, 0, 1
½
½
½
½
6
2p
LI
LII
LIII
3
3
3
0
1
1
½
½
0
-1, 0, 1
2
6
3s
3p
MI
MII
MIII
3
3
2
2
½
-2, -1, 0,
1, 2
½
½
½
½
½
½
½
½
½
10
3d
MIV
MV
Fluorescence yield
Fluorescence yield (w) is fraction of ionizations that
yield characteristic X-ray versus Auger yield (a)
within a particular family of X-rays. w + a =1
Absorption Edge Energy
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) Xray energy; the characteristic
energy is value measured by our
X-ray detector.
Example: Pt (Z=78)
X-ray line energies and
associated critical excitation
(absorption edge) energies,
in keV
Ka1
Lb3
Lb1
La1
K-L3
L1-M3
L2-M4
L3-M5
M1-N3
M M2-N4
M1 M3-N5
Mb1 M4-N6
Ma1 M5-N7
Line
66.83
11.23
11.07
9.442
2.780
2.695
2.331
2.127
2.051
Edge
78.38
13.88
13.27
11.56
3.296
3.026
2.645
2.202
2.133
Overvoltage
Example: Pt (Z=78)
X-ray line energies and
associated critical excitation
(absorption edge) energies,
in keV
Ka1
Lb3
Lb1
La1
K-L3
L1-M3
L2-M4
L3-M5
M1-N3
M M2-N4
M1 M3-N5
Mb1 M4-N6
Ma1 M5-N7
Line
66.83
11.23
11.07
9.442
2.780
2.695
2.331
2.127
2.051
Edge
78.38
13.88
13.27
11.56
3.296
3.026
2.645
2.202
2.133
Overvoltage 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
* recall: E0=gun accelerating voltage; Ec=critical excitation energy
Continuum X-rays
HV 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
EDS spectrum showing absorption edge
Continuum and Atomic Number
At a given energy (or l), 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”).
Continuum intensity around the Si Ka peak,
varying with Z: Mo (42), Ti (22), B (5). X
axis is sin theta position units.
MAN plot
(Z-bar = average Z =
MAN)
General observations
•Above atomic number 10, the K family splits into Ka and Kb pairs
•Above atomic number 20, the L family becomes generally observable at
about 0.2 keV
•Above atomic number 50, the M family of lines begin to appear
When an electron beam has sufficient energy to excite the shell edge
(absorption edge), all lines of lower energy for that element will also be
excited.
This is an important fact to consider when trying to positively identify the
presence of an element in a spectra. Therefore if K lines are present, then L and
M lines must also be present at their appropriate energies.
X-ray units: A, keV, sin q, mm
l = hc/E0 where h=Plancks constant, c=speed of light
l = 12.398/E0 where is l is in Å and E0 in keV
also, the 2 main EMPs plot up X-ray positions thusly:
Cameca: n l = 2d sin q so for n=1 and a given 2d, an Xray line can be given as a sin value (or 105 times sin q)
JEOL: distance (L, in mm) between the sample (beam
spot) and the diffracting crystal, i.e. L= l R/d, where R is
Rowland circle radius (X-ray focusing locus of points) and
d is interlayer spacing of crystal.
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.
(Goldstein et al, 1992, p 80)
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 Ranges
Several 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)/(r Z0.89)
X-ray range. Anderson and Hasler (1966) give the depth of Xray production as:
RAH=(0.064)(E01.68 - Ec1.68)/ r
where Ec is the absorption edge (critical excitation) energy.
Incident keV & Penetration
5 kV
25 kV
Ranges and
Interaction
Volumes
Contact Lens simulation using a 5 um
beam on carbon coated (20 nm) silicon
rubber of nominal composition.
5 keV, 5 um beam diameter:
Electron energy is color coded and
red indicated electrons that were
backscattered out of the sample.
10 keV, 5 um beam diameter:
Secondary electrons
~100A-10nm
Backscatter
electrons 1-2µm
Characteristic
X-rays 2-5um
20 keV, 5 um beam diameter:
14um
Ionization cross section (in units of ionizations/e-/(atom/cm2)
- Bethe (1930)
Q  6.5110
 20
ns bs
log e (csU )
2
UEC
where: ns is the number of electron in a shell of subshell (e.g., 2 for K shell)
bs and cs are constants for a particular shell
Ec is the critical excitation energy
U is the overvoltage
E
U
EC
To calculate the number photons generated we need to modify
the previous expression to units of photons/e- or nx
1
n x  Qw N O r t
A
where: Q is the ionization cross section from above
w is the florescent yield (explain later)
NO is the Avogadro’s number
A is atomic weight
r is density
t is thickness of the thin foil (which experimentally) minimizes the
effect of elastic scattering
For thick targets the thickness is replaced by the infinitesimal path increment ds
and so the bulk x-ray yield, Ic, is calculated by the integration along the
Bethe range (RB) to the point where the electron energy falls below the
critical excitation energy for the x-ray of interest
Ic  
RB
0
QiwN O r
wN O r
ds 
A
A

EC
EO
where: dE/ds is the rate of energy
loss from inelastic scattering (the
Bethe range expression we discussed
last week)
Qi
dE
dE / ds
“Harper’s Index” of EPMA
1 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.
From Lehigh Microscopy Summer School
Phi-Rho-z Distribution:
Fig 1: from Bastin and Heijligers, 1992, Present and future of
light element analysis with electron beam instruments.
Microbeam Analysis, 1, 61-73.
X-ray Absorption
I
 e ( t )
I0
Mass absorption coefficients
I
 e (  / r )( rt )
I0
i
i


    j   C j
 r  spec
 r j
Emitter
Absorber Henke
Ebisu
Henke et
al.
Bastin
Pouchou
Heijligers Pichoir
B ka
B
3353
3350
3500
3471
B ka
C
6456
6350
6500
6750
B ka
N
10570
11200
11200
11000
B ka
O
B ka
Al
65170
64000
64000
64000
B ka
Si
74180
84000
84000
80000
B ka
Ti
15280
15300
14700
15000
B ka
V
16710
16700
17700
18000
B ka
Cr
20670
20700
20200
20700
B ka
Fe
25780
27600
27300
27800
B ka
Co
28340
30900
33400
32000
B ka
Ni
33090
35700
42000
37000
B ka
Zr
384101
8270
4000
4400
B ka
Nb
4417
6560
4600
4500
B ka
Mo
4717
5610
4550
4600
B ka
La
3826
3730
2500
2500
B ka
Ta
20820
20800
22500
23000
B ka
W
19660
19700
21400
21000
B ka
U
2247
9020
8200
7400
16500