XRF PEAK DECONVOLUTION

USING PEAK RATIOS

REFINED BY FUNDAMENTAL

PARAMETERS

Shinichi Terada

X-Bridge Technologies Co., Ltd.

Hiroki Yamashita and Yoshie Araki

X-tec. Co., Ltd.

This presentation was for an oral presentation at Denver

X-ray Conference 2011 held in Colorado Springs CO, USA

• Every quantification method calculates

concentrations based on XRF peak

intensity extracted from a spectrum

• Accuracy in peak intensity extraction is as

important as accuracy in quantification

calculation

All quantification calculations in XRF analysis such as

fundamental parameter method or calibration curve method

are based on XRF peak intensities of elements that are

extracted from spectra using sorts of peak deconvolution

methods.

3

For extracting XRF peak intensity of each element,

peak deconvolution is very important.

8 9 10 11 12 13 14 15 16

Inte

nsi

ty (c

ts)

Energy (keV)

Accuracy of peak deconvolution is highly important because

errors in peak deconvolution results errors in composition

and/or thickness values.

Fixed intra-element peak intensity

ratio Gaussian fitting

• G(E, W) Gaussian function

• Ez,l Peak energy

• W(E) FWHM at energy E

• Pz Height of the main peak

(fitting parameter)

• Rz,l Intra-element peak height ratios

Model

Function

We highly recommend use of fixed intra-element peak ratio

Gaussian fitting for most of applications since it is stable for

small peaks near the detection limits.

How should we determine

intra-element peak intensity ratios?

• Dependent on..

– Composition / Thickness

• Absorption of XRF

• Secondary excitations (L & M L lines)

• Absorption of irradiating X-ray (L & M lines)

– Energy distribution of primary X-rays

• Very important for L lines

However, determinations of intra-element peak ratios are

not easy because they are dependent of composition of a

sample and excitation conditions.

In cases of K-lines, the ratios of generation of K-alfa and

K-beta are always constants. However, after generation

deep in the sample, some part of fluorescence X-rays are

absorbed by sample. K-alfa and K-beta have different

absorption probability. Therefore, ratios are dependent on

the composition.

In cases of L-lines, the situations are much more

complicated because of multiple L absorption edges. In the

extreme case, a characteristics X-ray that has the energy

between L-III and L-II does not excite L-beta but L-alfa.

7 7.5 8 8.5 9 9.5 10

Inte

nsi

ty

Energy (keV)

Profile

Cu-Kα

Zn-Kα

Cu-Kβ

Zn-Kβ

Are ratios determined for pure metal

good for alloys?

7 7.5 8 8.5 9 9.5 10

Inte

nsi

ty

Energy (keV)

Profile

Cu

Cu-Kα

Cu-Kβ

6

7 7.5 8 8.5 9 9.5 10

Inte

nsi

ty

Energy (keV)

Profile

Zn

Zn-Kα

Zn-Kβ

Cu

-K吸収端

7 7.5 8 8.5 9 9.5 10

Inte

nsi

ty

Energy (keV)

Profile

Zn

Cu

Cu-Ka

Cu-Kb

Zn-Ka

Zn-Kb

Cu-Zn Alloy Spectrum(Cu:３８％ Zn:62%)

Cu – K

Absorption

edgeZn-Kb fit is bad

because of heavy

absorption by Cu

atoms in the alloy

This is well known simple example of Cu-Zn alloy case. If we

try to make fixed intra-element ratio peak deconvolution

based on peak ratios obtained from Cu and Zn pure metal

samples, the fitting is not good. The error mainly appear as

bad fitting of Zn-Kb because only Zn-Kb among those four

peaks is above Cu-K absorption edge and strongly

absorbed by the sample.

Practical solutions in the past

• For trace analysis, a table is prepared for

each main matrix (e.g. steel, Al alloy, Cu

alloy, plastic, etc.)

• For composition analysis of the main

matrix, change in the ratios are ignored

Some XRF users and manufacturers used multiple sets of

intra-element peak ratio tables in order to solve the problem.

Others just have been ignored.

Refinement of ratios by FP

• After the initial calculation of XRF peak

intensity based on the default ratio table,

we can calculate approximate composition

• Once composition is known, theoretical

intensity of each line is calculated and

ratio table for the particular sample is

produced

Our new approach is refining the intra-element peak ratios

using fundamental parameter method. For the calculation,

we need the composition of the sample.

Iterative refinement of peak ratios

Peak Fitting using Rz,l,i

Spectrum => Pz,i

Quantification by FP

Pz,i => Cz,i

Cz,i ~ Cz,i-1?

END

Calculation Rz,l,i+1 by FP

i = i+1

Therefore, we do iterative refinement of peak ratios as well

as compositions.

After peak-ratio refinement

10

7 7.5 8 8.5 9 9.5 10

Inte

nsi

ty

Energy (keV)

Profile

Cu-Kα

Cu-Kβ

Zn-Kα

Zn-Kβ

Fittings for both

Zn-Kb and Cu-Kb

become better

7 7.5 8 8.5 9 9.5 10

Inte

nsi

ty

Energy (keV)

Profile

Cu

Cu-Kα

Cu-Kβ

7 7.5 8 8.5 9 9.5 10

Inte

nsi

ty

Energy (keV)

Profile

Zn

Zn-Kα

Zn-Kβ

7 7.5 8 8.5 9 9.5 10

Inte

nsi

ty

Energy (keV)

Profile

Zn

Cu

Cu-Ka

Zn-Ka

Zn-Kb

Cu-Kb

Cu-Zn Alloy Spectrum

(Cu:38％ Zn:62%)

After doing the refinement, the fitting of the example

spectrum becomes much closer.

20 21 22 23 24 25 26

Inte

nsi

ty

Energy (keV)

Profile

Pd-Kα

Pd-Kβ

Ag-Kα

Ag-Kβ

20 21 22 23 24 25 26

Inte

nsi

ty

Energy (keV)

Profile

Ag

Ag-Kα

Ag-Kβ

20 21 22 23 24 25 26

Inte

nsi

ty

Energy (keV)

Profile

Pd

Ag

Pd-Kb

Ag-Ka

Ag-Kb

Pd-Ka

20 21 22 23 24 25 26

Inte

nsi

ty

Energy (keV)

Profile

Pd-Kα

Pd-Kβ

Ag-Kα

Ag-Kβ

20 21 22 23 24 25 26

Inte

nsi

ty

Energy (keV)

Profile

Ag

Ag-Kα

Ag-Kβ

20 21 22 23 24 25 26

Inte

nsi

ty

Energy (keV)

Profile

Pd

Ag

Pd-Kb

Ag-Ka

Ag-Kb

Pd-Ka

Ag – Pd Alloy

11

Based on Pure

metal Ratios

FP Refinement

Ag:25%,Pd75%

Pd

-K A

bs.

Ed

ge

This is similar example Ag-Pd alloy.

Au base alloy

12

8 10 12 14

Inte

nsity

Energy (keV)

Ｋ９

Ｋ１４

Ｋ２４

K24 Au100％K14 Au58.5% Pd41.5％K9 Au37.5％ Cu62％ Ag0.5%

Normalized for Au-La

Au-Lα Au-Lβ

Au-Lγ

This is L-line example. Three different gold alloys that have

different composition have different intra-element peak

ratios as shown in these spectra.

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Inte

nsi

ty

Energy (keV)

Profile

Pd-Kα

Pd-Kβ

7 9 11 13 15 17 19 21 23 25

Inte

nsi

ty

Energy (keV)

Profile

Au

7 9 11 13 15 17 19 21 23 25

Inte

nsi

ty

Energy (keV)

Profile

Pd

Au

Pd-Kα

Pd-Kβ

7 8 9 10 11 12 13 14 15

Inte

nsi

ty

Energy (keV)

Profile

Cu-Kα

7 8 9 10 11 12 13 14 15

Inte

nsi

ty

Energy (keV)

Profile

Au

Au Alloy

Peak ratio refinements

13

7 8 9 10 11 12 13 14 15

Inte

nsi

ty

Energy (keV)

Profile

Cu

Au

Cu-Kα

Au-LγAu-Lｌ

Au-LβAu-Lα

K18(Au-Pd)Au75% Pd25％

K18(Au-Cu)Au75% Cu25％

Au-LγAu-Lｌ

Au-LαAu-Lβ

The ratio refinement solves the issues in fittings.

7 10 13 16 19 22 25 28

Inte

nsi

ty

Eergy (keV)

Sn Alloy (Trace Impurity)

Sn Alloy SpectrumPb0.174％, Bi0.196％,As0.064％,

Cu2.99％,Ag0.55％,Sb1.06％, 14

Sn-Ka

Sn-Kb

8 10 12 14

Inte

nsi

ty

Eergy (keV)C

u-K

b

Pb-L

a,A

s-K

aB

i-L

a

Pb-L

b

Bi-

Lb

Cu-Ka

This is trace impurity example in Tin alloy.

8 9 10 11 12 13 14 15

Inte

nsi

ty

Energy (keV)

Profile

8 9 10 11 12 13 14 15

Inte

nsi

ty

Energy (keV)

Profile

Sn Alloy (Cont.)

Because of Errors in peak ratios of Pb and Bi, As intensity is calculated as 0

Cu

-Kβ

Pb

-Lα,As-Kα

Bi-Lα

Pb

-Lβ

Bi-Lβ

Cu

-Kβ

Pb

-Lα,As-Kα

Bi-Lα

Pb

-Lβ

Bi-Lβ

Based on Pure

metal ratios

Refined by FP

8 9 10 11 12 13 14 15

Inte

nsi

ty

Energy (keV)

Profile

Cu

Pb

As

Bi

Pb

-La

Bi-

La

Pb

-Lb

Bi-

Lb

Cu

-Kb

8 9 10 11 12 13 14 15

Inte

nsi

ty

Energy (keV)

Profile

Cu

Pb

As

Bi

Cu

-Kb

Pb

-La,A

s-K

a

Bi-

La

Pb

-Lb

Bi-

Lb

If we make fitting based on ratios obtained from pure

element, Cu, Pb and Bi are detected. However, if we refine

the ratios, As appears in the fitting result as shown.

This is serious known issue in trace impurity detections.

Conclusion

• Peak deconvolution software that uses

intra-element peak ratios refined by FP is

produced

• Improvements of the accuracy in peak

fittings for both main matrix analysis and

trace analysis were achieved

Note: International Patent Application has been

made for this invention. Applicants plans to

license the pending patent and one of the

authors is ready to provide consulting service to

those who want to implement the function into

their own software.

Please feel free to write to st@xbrt.net