Fast and Easy Background Modeling
For
Practical Quantitative Analysis
By John J. Donovan
University of Oregon, Department of Chemistry
MAN versus Off-peak
Background Measurements
• What Is It Good For?
Saving TIME!
t=$
How Much Time?
186 seconds
w/ Off-Peaks
94 seconds
w/ MAN
What Else is it Good For?
•
•
•
•
•
Avoiding Off-Peak Interferences
Spectrometer Reproducibility Issues
Beam Sensitive Samples
Quantitative Imaging
Avoiding Wear and Tear on Spectrometers
Avoiding Off-Peak Interferences
311.7
PC1 cps
By not measuring offpeak intensities in
samples of unknown
composition, one can
eliminate even
unforseen off-peak
interferences.
check off-peaks
O
KA1
O
KA2
Ti LB1
Cu LA1
Ti LB3
P
III
MA1
MA2KA1
LB4
W
III IIIIII
P KA1
KA24.9
IIIMBW Si
Si
KA2
III Ti Cu
PLB4KA1
KA2
32519.0
O (1) Spectrometer
II
CuNi
LB1
Cu
LA2MB
LG5IIIIII I
IV
WTi
LB4
II
44744.6
Spectrometer Reproducibility
Issues
By reserving a
spectrometer for a
single MAN
corrected element
x-ray line
(monochromator),
one can obtain:
• Handle spectrometer
re-positioning
problems for worn
instruments
• Ultra High Precision
Measurements
Sensitive Samples
Na/K Loss in glass (or Si/Al “grow-in”)
Un 6 test on std 308 ryholite
glass (w/ self volatile)
5.5
na Log (natural)
Intensity
Line 78
5.0
Line 79
4.5
Line 80
Line 81
4.0
0
5
10
Elapsed Time
15
• Everyone knows
about sodium loss
(and silica “gain”)
over time in some
glasses and
especially,
hydrous phasesbut did you know
that sodium can
also “grow-in”?
Sodium “grow-in” of
Calcium Silicate (cement “gel”)
Un 3 Mortar (steel fiber)
gr1-12b
7.5
na Log (natural)
Intensity
Line 288
7.0
Line 289
6.5
Line 290
6.0
Line 293
5.5
Line 294
Line 295
5.0
0
10
20
Elapsed Time
30
40
Quantitative Imaging
• Eliminate acquisition time for off-peak intensity
images and still obtain background corrected
quantitative images
(512 x 2048 pixels @ .5 sec equals 6 days!)
Equations for Calculation of Continuum Intensity
Ic (l) ~ iZmean[(l /l min) - 1]
Kramers (1923)
Ic (l) = (W/4p) fl Pl kl iZmean [(l /l min) - 1] Fiori et al. (1976)
where :
i
Zmean
W
fl
Pl
kl
is the absorbed electron current
is the average atomic number (Z-bar)
is the detector solid angle
is the absorption factor for the continuum
is the detector efficiency at wavelength l
is Kramers’ constant
But What Exactly Is The Average
Atomic Number?
Mass fraction weighting for continuum intensities in a
compound, (Z-bar), is given by (Goldstein et. al., 1992) :
n
Z ( ci Z i )   ci Z i
i 1
No difference in continuum
intensity due to mass
4
Continuum Measured at 12.1676 A
% deviation from average
% deviation from average
4
2
Ni
Cu
0
Mo
-2
Natural
Enriched
Continuum Measured at 8.5976 A
2
Ni
Cu
0
Mo
-2
Natural
Enriched
-4
-4
60
70
80
90
60
100
70
Continuum Measured at 3.8289 A
4
% deviation from average
% deviation from average
4
2
Ni
Cu
0
Mo
-2
80
90
100
atomic weight (A)
atomic weight (A)
Natural
Enriched
-4
Continuum Measured at 1.9776 A
2
Ni
Cu
0
Mo
-2
Natural
Enriched
-4
60
70
80
atomic weight (A)
90
100
60
70
80
atomic weight (A)
90
100
It should be something like this:
n
Z ( z( x)Z )   z Zi
i
Where,
i
z
( x)
i
( x)
i
i 1

ai Z
x
i
n
a Z
i 1
i
x
i
But the difference is generally small compared
to the uncertainty for continuum intensity
measurements
X-ray Intensity (cps per 100 nA)
Mass Fraction
Au
Au80-Ag20
Au60-Ag40
Au80-Cu20
Au40-Ag60
Au20-Ag80
Au60-Cu40
Ag
Au40-Cu60
200
150
SnO2
Au20-Cu80
100
Cu
Co
ZnO
V
NiO
SrTiO3
Ti
CoO
Cr2O3
50
V2O3
TiO2
Si
Al2O3
SiO2
Residual sum of squares = 808.356
MgO
Coef of determination, R-squared = 0.991718
0
0
20
40
z-bar (mass)
60
80
X-ray Intensity (cps per 100 nA)
250
250
Modified Electron Fraction
Au
Au80-Ag20
Au60-Ag40
Au80-Cu20
Au40-Ag60
Au20-Ag80
Au60-Cu40
Ag
Au40-Cu60
200
150
SnO2
Au20-Cu80
100
Cu
ZnOCo
NiO
SrTiO3
TiV
CoO
Cr2O3
V2O3
TiO2
Si
Al2O3
Residual sum of squares = 277.34
SiO2
MgO
50
Coef of determination, R-squared = 0.997159
0
0
20
40
60
z-bar ("modified" electron, x=0.7)
80
Therefore, let’s simply
assume (for now), that :
n
Z ( ci Z i )   ci Z i
i 1
FLOW DIAGRAM OF THE MEAN ATOMIC NUMBER CORRECTION
Correct the X-ray Counts
for deadtime, beam and
standard drift.
Calculate the concentration
of all elements in the unknown
and procede when ZAF
convergence is achieved.
Calculate the average atomic
number of the sample and
correct the peak intensities
using the MAN correction.
Test for MAN
convergence.
No
Yes
Output results.
So how does it actually work in
action?
Acquire on-peak intensity data as a function of the approximate
average atomic number range of the unknown samples.
Na K X-ray Intensity
(Uncorrected for continuum absorption)
10
Counts per second per 30nA
MgO synthetic
NiO synthetic
9
Cr2O3 (synthetic)
8
Magnetite U.C. #3380
MnO synthetic
7
TiO2 synthetic
6
SiO2 synthetic
5
8
12
16
20
Z-bar (average atomic number)
24
Correct the x-ray continuum (on-peak) intensities for absorption.
Na K X-ray Intensity
(Fit to 2nd order polynomial)
NiO synthetic
Counts per second per 30nA
40
30
Magnetite U.C. #3380
Cr2O3 (synthetic)
MnO synthetic
20
TiO2 synthetic
MgO synthetic
SiO2 synthetic
10
8
12
16
20
Z-bar (average atomic number)
24
Now fit the data to a 2nd order polynomial (or whatever).
Na K X-ray Intensity
(Obtain interpolated background)
NiO synthetic
Counts per second per 30nA
40
30
Magnetite U.C. #3380
Cr2O3 (synthetic)
MnO synthetic
Calculate Background Intensity
21 cps
20
TiO2 synthetic
MgO synthetic
From Unknown Composition
Z-bar = 18.2
SiO2 synthetic
10
8
12
16
20
Z-bar (average atomic number)
24
1. Next, DE-CORRECT the interpolated continuum for absorption!
21 cps divided by 1.8778* = 11.2 cps
to
2. Now, subtract the “raw” intensity from the “emitted” intensity!
313.5 cps minus 11.2 = 302.3 cps
3. Use this background corrected intensity in the matrix correction.
4. Iterate as necessary!
*Na Ka at 15 keV in unknown Na-Al silicate
Moderate Energy Region
Ca K X-ray Intensity
Counts per second per 30nA
28
NiO synthetic
MnO synthetic
24
Nepheline (partial anal.)
Cr2O3 (synthetic)
20
TiO2 synthetic
16
Orthoclase MAD-10
12
SiO2 synthetic
8
8
12
16
20
Z-bar (average atomic number)
24
“Moderate” energy region
Ca K X-ray Intensity
(without Nepheline)
Counts per second per 30nA
28
NiO synthetic
MnO synthetic
24
Rule of Thumb:
Cr2O3 (synthetic)
Background is
(generally) the
lowest thing one
can measure!
20
TiO2 synthetic
16
Orthoclase MAD-10
12
SiO2 synthetic
Delete the rest!
8
8
12
16
20
Z-bar (average atomic number)
24
“High” Energy Region
Fe K X-ray Intensity
Fe K X-ray Intensity
MnO synthetic
16
12
12
NiO synthetic
8
TiO2 synthetic
Cr2O3 (synthetic)
SiO2 synthetic
4
8
12
Counts per second per 30nA
Counts per second per 30nA
NiO synthetic
10
8
TiO2 synthetic
Cr2O3 (synthetic)
6
SiO2 synthetic
4
16
20
Z-bar (average atomic number)
24
8
12
16
20
Z-bar (average atomic number)
24
“Typical”
Silicate
Element
MAN
Background
Curves
Typical
“Sulfide”
Element MAN
Background
Curves
How Good Is It?
• Major Elements
• Minor Elements
• Trace Elements
• Comparison to Off-Peak Measurements
• Matrix Issues (Low Z-bar vs High Z-bar)
• Accuracy (reproducibility, drift, etc)
Comparison with Off-peak
20 kev, 20 nA, 5 um, 20 sec on, 20 sec off
Off-Peak
St 305 Set
2 Labradorite (Lake
ELEM:
Ca
K
Fe
AVER:
9.625
.102
.326
SDEV:
.036
.008
.018
%RSD:
.4
7.7
5.5
Co.)
Ti
.023
.014
61.8
Na
2.841
.039
1.4
Al
16.529
.032
.2
Mn
.008
.008
89.4
Ni
.003
.005
165.7
O
46.823
.000
.0
H
.000
.000
.0
Si
SUM
23.957 100.239
.000
.0
MAN
St 305 Set
2 Labradorite (Lake
ELEM:
Ca
K
Fe
AVER:
9.640
.100
.321
SDEV:
.034
.007
.017
%RSD:
.3
7.1
5.4
PUBL:
9.577
.100
.319
Co.)
Ti
.023
.012
51.9
n.a.
Na
2.864
.037
1.3
Al
16.543
.033
.2
Mn
.002
.003
140.3
2.841
16.359
.000
Ni
.004
.005
126.3
O
46.823
.000
.0
n.a.
46.823
H
.000
.000
.0
n.a.
Si
SUM
23.957 100.277
.000
.0
23.957
99.976
High Z-bar Off Peak Comparison
20 kev, 20 nA, 5 um, 20 sec on, 20 sec off
Off-Peak
St 396 Set
2 Chromite (UC # 523-9)
ELEM:
Ca
K
Fe
Ti
AVER:
.002
.004 20.392
.333
SDEV:
.003
.005
.109
.021
%RSD:
114.0
129.1
.5
6.5
Na
.006
.009
156.9
Al
8.004
.036
.5
Mn
.162
.013
8.0
Ni
.087
.014
15.9
O
33.042
.000
.0
H
.000
.000
.0
Cr
SUM
31.905 100.349
.000
.000
.0
.0
MAN
St 396 Set
2 Chromite (UC # 523-9)
ELEM:
Ca
K
Fe
Ti
AVER:
.001
.001 20.441
.346
SDEV:
.002
.002
.109
.016
%RSD:
316.2
223.9
.5
4.5
PUBL:
n.a.
n.a.
20.692
.300
Na
.007
.009
118.4
n.a.
Al
7.976
.036
.5
7.690
Mn
.155
.014
9.1
.225
Ni
.087
.008
9.0
n.a.
O
33.042
.000
.0
33.042
H
.000
.000
.0
n.a.
Cr
SUM
31.905 100.372
.000
.000
.0
.0
31.905 100.266
Drift Issues in MAN
Drift array background intensities for standards:
ELMXRY:
ca ka
k ka
fe ka
ti ka
na ka
al ka
mn ka
ni ka
MOTCRS: 2
PET 2
PET 4
LIF 3
LIF 1
TAP 1
TAP 3
LIF 4
LIF
STDASS:
358
374
395
22
305
374
25
28
19.3
20.0
15.7
15.6
33.0
33.0
20.3
21.2
9.3
9.9
28.5
28.9
25.1
25.8
46.8
47.5
Drift array standard intensities (background corrected):
ELMXRY:
ca ka
k ka
fe ka
ti ka
na ka
al ka
mn ka
ni ka
MOTCRS: 2
PET 2
PET 4
LIF 3
LIF 1
TAP 1
TAP 3
LIF 4
LIF
STDASS:
358
374
395
22
305
374
25
28
4564.9
4583.7
2741.4
2745.9
6926.4
6884.5
2341.0
2305.0
325.7
327.5
3296.5
3272.7
6976.5
6960.2
8176.6
8192.3
Note Fe drift in standard, but not background!
Typical Sequence of MAN Fit
Cr K-b interference removed
Trace Ni “contamination” removed
(natural chromite, 0.087 wt. % Ni)
Conclusions
1. Absorption correction critical for low/moderate energies
2. Save time and money (especially quant imaging)
3. Improves accuracy
4. You gotta’ try it to believe it!