Fast and Easy Background ModelingFor

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

By not measuring off-peak intensities in samples of unknown composition, one can eliminate even unforseen off-peak interferences.

check off-peaks

PC

1 c

ps

O (1) Spectrometer

4.9

311.7

32519.0 44744.6 P KA1 III P KA2 III W MB III W MA1 III W MA2 III Si KA1 III Si KA2 III

O KA2

O KA1

Ti LB3 Ti LB4

Cu LB4 II P KA1 IV P KA2 IV Cu LB1 II Ni LB4 II Cu LA2 II

Cu LA1 II

W MB IV Ti LG5

Ti LB1

Spectrometer Reproducibility Issues

• Handle spectrometer re-positioning problems for worn instruments

• Ultra High Precision Measurements

By reserving a spectrometer for a

single MAN corrected element

x-ray line (monochromator),

one can obtain:

Sensitive Samples

• Everyone knows about sodium loss (and silica “gain”) over time in some glasses and especially, hydrous phases- but did you know that sodium can also “grow-in”?

Un 6 test on std 308 ryholiteglass (w/ self volatile)

Line 78

Line 79

Line 80

Line 81

na L

og (

natu

ral)

Inte

nsity

Elapsed Time

4.0

4.5

5.0

5.5

0 5 10 15

Na/K Loss in glass (or Si/Al “grow-in”)

Un 3 Mortar (steel fiber)gr1-12b

Line 288

Line 289

Line 290

Line 293

Line 294

Line 295

na L

og (

natu

ral)

Inte

nsity

Elapsed Time

5.0

5.5

6.0

6.5

7.0

7.5

0 10 20 30 40

Sodium “grow-in” of Calcium Silicate (cement “gel”)

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!)

Ic (~ iZmean[( / min) - 1] Kramers (1923)

Ic (= (/4) f P k iZmean [( / min) - 1] Fiori et al. (1976)

where :i is the absorbed electron current

Zmean is the average atomic number (Z-bar) is the detector solid angle

fis the absorption factor for the continuumP is the detector efficiency at wavelength k is Kramers’ constant

Equations for Calculation of Continuum Intensity

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

iiiZc ZcZ

ii1

)(

No difference in continuum intensity due to mass

6 0 7 0 8 0 9 0 1 0 0atom ic w eight (A)

- 4

- 2

0

2

4%

dev

iatio

n fr

om a

vera

ge

N atura lEnriched

C ontinuum M easured at 12.1676 A

Ni Cu

M o

6 0 7 0 8 0 9 0 1 0 0

atom ic w eight (A)

- 4

- 2

0

2

4

% d

evia

tion

from

ave

rage

N atura lEnriched

C ontinuum M easured a t 8 .5976 A

Ni Cu

M o

6 0 7 0 8 0 9 0 1 0 0atom ic w eight (A)

- 4

- 2

0

2

4

% d

evia

tion

from

ave

rage

N atura lEnriched

C ontinuum M easured at 3 .8289 A

Ni Cu

M o

6 0 7 0 8 0 9 0 1 0 0

atom ic w eight (A)

- 4

- 2

0

2

4

% d

evia

tion

from

ave

rage

N atura lEnriched

C ontinuum M easured at 1 .9776 A

N i C u

M o

It should be something like this:

n

ii

xiZzZzZ

ixi

1

)(

)( )(

Where,

n

i

xii

xiix

i

Za

Zaz

1

)(

But the difference is generally small compared to the uncertainty for continuum intensity

measurements

0 20 40 60 80z-ba r (m ass)

0

50

100

150

200

250

X-r

ay

Inte

nsi

ty (

cps

pe

r 1

00

nA

)

M gOAl2O 3SiO 2

TiO 2V2O 3Cr2O 3C oO

N iOZnO

SrT iO 3

SnO 2

S i

T iVC o

C u

Ag

Au

Au80-C u20

Au60-C u40

Au40-C u60

Au20-C u80

Au80-Ag20

Au60-Ag40

Au40-Ag60Au20-Ag80

R esidual sum of squares = 808.356C oef o f determ ination, R -squared = 0.991718

M ass Fraction

0 20 40 60 80z-ba r ("m od ified " e lectron , x=0 .7 )

0

50

100

150

200

250

X-r

ay

Inte

nsi

ty (

cps

pe

r 1

00

nA

)

M gOAl2O 3S iO 2

TiO 2V2O 3Cr2O 3CoO

N iOZnO

SrT iO 3

SnO 2

S i

T iVC o

C u

Ag

Au

Au80-C u20

Au60-C u40

Au40-C u60

Au20-C u80

Au80-Ag20

Au60-Ag40

Au40-Ag60Au20-Ag80

R esidual sum of squares = 277.34C oef o f determ ination, R -squared = 0.997159

M odified E lectron Fraction

Therefore, let’s simply assume (for now), that :

n

iiiZc ZcZ

ii1

)(

FLOW DIAGRAM OF THE MEAN ATOMIC NUMBER CORRECTION

Correct the X-ray Countsfor deadtime, beam and

standard drift.

Calculate the concentrationof all elements in the unknown

and procede when ZAFconvergence is achieved.

correct the peak intensitiesusing the MAN correction.

Calculate the average atomicnumber of the sample and

Test for MANconvergence.

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.

8 12 16 20 24Z-bar (average atom ic num ber)

5

6

7

8

9

10C

ount

s pe

r se

cond

per

30n

A

M gO synthetic

S iO 2 synthetic

T iO 2 synthetic

C r2O 3 (synthetic)

M nO synthetic

N iO synthetic

M agnetite U .C . #3380

N a KX-ray In tensity(U ncorrected for continuum absorption)

Correct the x-ray continuum (on-peak) intensities for absorption.

8 12 16 20 24Z-bar (average atom ic num ber)

1 0

2 0

3 0

4 0C

ount

s pe

r se

cond

per

30n

A

M gO syntheticS iO 2 synthetic

T iO 2 synthetic

C r2O 3 (synthetic)

M nO synthetic

N iO synthetic

M agnetite U .C . #3380

N a KX-ray Intensity(F it to 2nd order po lynom ial)

Now fit the data to a 2nd order polynomial (or whatever).

8 12 16 20 24Z-bar (average atom ic num ber)

1 0

2 0

3 0

4 0C

ount

s pe

r se

cond

per

30n

A

M gO synthetic

S iO 2 synthetic

T iO 2 synthetic

C r2O 3 (synthetic)

M nO synthetic

N iO synthetic

M agnetite U .C . #3380

N a KX-ray In tensity(O bta in in terpolated background)

From Unknown Com positionZ-bar = 18.2

Calculate Background Intensity21 cps

1. Next, DE-CORRECT the interpolated continuum for absorption!

21 cps divided by 1.8778* = 11.2 cps

*Na Ka at 15 keV in unknown Na-Al silicate

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!

to

Moderate Energy Region

8 12 16 20 24Z-bar (average atom ic num ber)

8

12

16

20

24

28

Cou

nts

per

seco

nd p

er 3

0nA

SiO 2 synthetic

T iO 2 synthetic

C r2O 3 (synthetic)

M nO syntheticN iO syntheticNepheline (partia l anal.)

O rthoclase M AD -10

C a KX-ray In tensity

“Moderate” energy region

8 12 16 20 24Z-bar (average atom ic num ber)

8

12

16

20

24

28

Cou

nts

per

seco

nd p

er 3

0nA

SiO 2 synthetic

T iO 2 synthetic

C r2O 3 (synthetic)

M nO syntheticN iO synthetic

O rthoclase M AD -10

C a KX-ray In tensity(w ithout N epheline)

Rule of Thumb:

Background is (generally) the lowest thing one can measure!

Delete the rest!

“High” Energy Region

8 12 16 20 24Z-bar (average atom ic num ber)

4

8

12

16

Cou

nts

per

seco

nd p

er 3

0nA

SiO 2 synthetic

T iO 2 syntheticC r2O 3 (synthetic)

M nO synthetic

N iO synthetic

Fe KX-ray In tensity

8 12 16 20 24Z-bar (average atom ic num ber)

4

6

8

10

12

Cou

nts

per

seco

nd p

er 3

0nA

SiO 2 synthetic

T iO 2 syntheticC r2O 3 (synthetic)

N iO synthetic

Fe KX-ray In tensity

“Typical” SilicateElement 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

St 305 Set 2 Labradorite (Lake Co.) ELEM: Ca K Fe Ti Na Al Mn Ni O H Si SUM AVER: 9.625 .102 .326 .023 2.841 16.529 .008 .003 46.823 .000 23.957 100.239SDEV: .036 .008 .018 .014 .039 .032 .008 .005 .000 .000 .000%RSD: .4 7.7 5.5 61.8 1.4 .2 89.4 165.7 .0 .0 .0

Off-Peak

MANSt 305 Set 2 Labradorite (Lake Co.)ELEM: Ca K Fe Ti Na Al Mn Ni O H Si SUM AVER: 9.640 .100 .321 .023 2.864 16.543 .002 .004 46.823 .000 23.957 100.277SDEV: .034 .007 .017 .012 .037 .033 .003 .005 .000 .000 .000%RSD: .3 7.1 5.4 51.9 1.3 .2 140.3 126.3 .0 .0 .0

20 kev, 20 nA, 5 um, 20 sec on, 20 sec off

PUBL: 9.577 .100 .319 n.a. 2.841 16.359 .000 n.a. 46.823 n.a. 23.957 99.976

High Z-bar Off Peak Comparison

St 396 Set 2 Chromite (UC # 523-9)ELEM: Ca K Fe Ti Na Al Mn Ni O H Cr SUM AVER: .002 .004 20.392 .333 .006 8.004 .162 .087 33.042 .000 31.905 100.349SDEV: .003 .005 .109 .021 .009 .036 .013 .014 .000 .000 .000 .000%RSD: 114.0 129.1 .5 6.5 156.9 .5 8.0 15.9 .0 .0 .0 .0

Off-Peak

MANSt 396 Set 2 Chromite (UC # 523-9)ELEM: Ca K Fe Ti Na Al Mn Ni O H Cr SUM AVER: .001 .001 20.441 .346 .007 7.976 .155 .087 33.042 .000 31.905 100.372SDEV: .002 .002 .109 .016 .009 .036 .014 .008 .000 .000 .000 .000%RSD: 316.2 223.9 .5 4.5 118.4 .5 9.1 9.0 .0 .0 .0 .0

20 kev, 20 nA, 5 um, 20 sec on, 20 sec off

PUBL: n.a. n.a. 20.692 .300 n.a. 7.690 .225 n.a. 33.042 n.a. 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 kaMOTCRS: 2 PET 2 PET 4 LIF 3 LIF 1 TAP 1 TAP 3 LIF 4 LIFSTDASS: 358 374 395 22 305 374 25 28

19.3 15.7 33.0 20.3 9.3 28.5 25.1 46.8 20.0 15.6 33.0 21.2 9.9 28.9 25.8 47.5

Drift array standard intensities (background corrected):ELMXRY: ca ka k ka fe ka ti ka na ka al ka mn ka ni kaMOTCRS: 2 PET 2 PET 4 LIF 3 LIF 1 TAP 1 TAP 3 LIF 4 LIFSTDASS: 358 374 395 22 305 374 25 28

4564.9 2741.4 6926.4 2341.0 325.7 3296.5 6976.5 8176.6 4583.7 2745.9 6884.5 2305.0 327.5 3272.7 6960.2 8192.3

Note Fe drift in standard, but not background!

Typical Sequence of MAN Fit

Cr K- 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!