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A CRITICAL EVALUATION OF LINE OVERLAP CORRECTIONS

IN X-RAY SPECTROMETRYLarry E. Creasy

Titanium Metals Corporation

900 Hemlock Road, Morgantown, PA 19543

ABSTRACT

While it is generally recognized that line overlaps in wavelength X-ray spectrometry may be

affected by factors such as variations in mass absorption, conventional line overlap correction

models define the correction function as a constant and assume that it does not vary down to zero

percent concentration of the interfering element. However, the overlap function is not a constant,

even within the scope of a normal calibration set, and it becomes zero before the concentration of

the interfering element reaches zero. By treating the overlap as a variable background and

measuring the background using the Lorentz model, the need to establish an overlap function is

removed and a more accurate calibration can be obtained.

INTRODUCTION

In X-ray spectrometry, the measured intensity (I) of the analyte peak is a composite of several

factors and may be represented by the following equation:

I = F[bkg] + F[conc.] + F[enh] F[abs] + F[ovr]

Where: F[bkg] is a function of background

F[conc.] is a function of concentration

F[enh] is a function of enhancement

F[abs] is a function of absorption, andF[ovr] is a function of line overlap

In the calibration equation, the background is assumed to be a constant or the background is

measured and subtracted from the measured peak intensity to give a net peak intensity. Intensity

due to concentration is a linear function of concentration. The absorption and enhancement

effects are not linear or constant. However, within narrow ranges, they may be approximated by

a single factor for each affecting element using such models as LaChance-Traill1, Rasberry-

Heinrich2, etc. These may be determined by regression or calculated using fundamental alpha

type equations3. In more complex calibrations, these factors may be calculated using

Fundamental Parameter models4. The line overlap function is always assumed to be constant

with a zero concentration/zero interference intercept. These constants are typically determined byone of a number of techniques. The three most common techniques are:

3

1. Measure the intensity at the analyte position on a sample of pure interfering element and ratiothat value to another peak of that element. For example, to determine the constant for the

overlap of Cr-K on the Mn-K peak, measure the intensity at the Mn-K location on a

sample of pure chromium and ratio this value to the intensity of the Cr-K or K peak. Thisrequires the use of very pure chromium.

Copyright(c)JCPDS-International Centre for Diffraction Data 2001,Advances in X-ray Analysis,Vol.44 3

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2. Using the same technique as above, but use a specimen that contains chromium, but nomanganese. It is not always easy to find such a specimen.

3. Determine the constant by regression in the calibration process.Procedures 1 and 2 assume that there are no major absorption edges between the analyte peak

and peak of the overlapping element that is used to make the correction. Even if there were nomajor absorption edges present, significant variations in the mass absorption coefficient could

affect this correction factor.

However, in dealing with the most common line overlaps where the analyte peak lies on the edge

of another overlapping peak, such as the overlap of the Cr-K on the Mn-K, the Ni-K on Cu-

K, or Fe-K on Co-K, etc., it will be shown that both of the assumptions, a zero/zero interceptand constancy, are not true.

In an effort to increase the accuracy of the line overlap correction, it proposed that the overlap be

treated as a variable background and measured for each sample, instead of assigning a single

constant that would be applied to all samples. The model for this measurement is the Lorentzmodel that is available in some software packages for background correction. With properly

selected locations around the analyte peak, the Lorentz equation models the shape of theshoulder of the overlapping peak very well. The equation for this model is as follows 5:

( )i

i

bxaa

aax

aI 54

3

2

2

1++

++

=

Where:Ib = Intensity of the background,xi = 2-Theta angle, anda1.a5 are coefficients.

Figure 1. Background Fit for Overlap Using Lorentz Equation

Intensity

62 62.4 62.8 63.2 63.6 64

Degrees 2-Theta

Mn-K

Cr-K


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An example of an overlap correction using the Lorentz equation to model the overlap

interference under the analyte is shown in Figure 1. A minimum of five points are selected andthe curve is generated, basically treating the overlap as a curved background. These five points

are measured for every specimen and the overlap is subtracted, resulting in a net peak intensity.

This study will deal only with the situations where the overlap is such that the analyte peak lies

on the tail of the overlapping element, such as the overlap of Cr-K on the Mn-K peak. It will

not address the situation where there is a complete overlap, such as the Mo-L1 on the P-K peak.

EXPERIMENTAL

Over 130 specimens were measured to determine overlap intensities. The measurements were

made on a Rigaku RIX-2000 scanning x-ray spectrometer. The matrices included aluminum,

iron, nickel, cobalt, copper (brasses), zirconium and titanium. The Mn-K, Cu-K, and Co-Klines were measured. The overlap intensities at the analyte locations were determined by direct

measurement of samples that had no analyte in them or by using a Lorentz fit. The Lorentz fit

was made using the standard software package for the instrument.

In addition, a calibration scheme was set up to compare the conventional treatment of line

overlap with a model that used the Lorentz equation to measure the overlap. In this test, about 25iron-based reference materials were used, generally of the type that would be considered

stainless steels. The accuracy of the Lorentz measured overlaps were compared to regression fits

using both the K and the K lines of the overlapping element.

RESULTS AND DISCUSSION

Below are example scans of the region surrounding the K- lines of Co and Cu withconcentrations of Fe and Ni at low levels.

Figure 2. Zero Overlap from Interfering Elements

In Figure 2, the overlap is shown to reach zero before the concentration or the intensity of the

overlapping element reaches zero. The intensity level at which the overlap reaches zero will

depend on the resolution of the spectrometer and the difference between the location of the twopeaks. The concentration level at which this occurs will also depend on the matrix, since mass

0

1

2

3

4

5

51.0 51.5 52.0 52.5 53.0

0

1

2

3

43.0 43.5 44.0 44.5 45.0 45.5 46.0

Intensity

(kcps)

Fe-K Ni-K

Cu-K Co-K

2-Theta 2-Theta

a b


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absorption affects the sensitivity of the peaks. In Figure 2a, the material is Ti with about 4.4%

Fe. In Figure 2b, the material is cast iron with about 2.3% Ni.

Having shown that the intercept of the overlap function is not zero-zero, the next question is Is

the overlap function a constant?. Over 130 specimens were measured as previously described.

The overlap ratios are shown plotted and described below.

Intensity of Cr-K (kcps) Intensity of Cr-K (kcps)

Figure 3. Overlap Ratio - Cr-K on the Mn-K peak

In the plot of all the data, Figure 3a, the ratios are fairly consistent as the intensity of the Cr-Kpeak decreases until the intensity reaches about 100 kcps, at which point, the ratio increases

significantly. Most of this rise is because the overlap values are at or near background and are

fairly constant, and these numbers are divided by increasingly smaller Cr-K peak intensities.When the plot of ratio values less than 0.01 are examined (Figure 3b where more detail is seen),

there is much scatter. Even in the region where the data is relatively flat, there is a range of ratios

from less than 0.001 to 0.004. If pure Cr were used to determine the overlap ratio, the ratiowould be found to be 0.0012, a value at the extreme low end.

Intensity of Fe-K (kcps) Intensity of Fe-K (kcps)

Figure 4. Overlap Ratio - Fe-K on the Co-K - Fe intensity less than 20 kcps (a) andratios less than 0.02 (b)

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0 200 400 600 800 1000 1200

OverlapRatio

a

0.000

0.002

0.004

0.006

0.008

0.010

0 200 400 600 800 1000 1200

0.0

0.4

0.8

1.2

1.6

2.0

0 4 8 12 16 20

0.000

0.004

0.008

0.012

0.016

0.020

0 50 100 150 200 250

OverlapRatio

b

ab


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The patterns for Fe-Co are similar to those for Cr-Mn. The range of the ratio values for Fe

intensities greater than 30kcps is 0.006 to 0.014. The values increase dramatically at the lowintensity levels. Again, the value for pure Fe is 0.0064, near the minimum.

Intensity of Ni-K (kcps) Intensity of Ni-K (kcps)

Figure 5. Overlap Ratio - Ni-K on Cu-K - Ni intensity less than 20 kcps (a) and ratiosless than 0.02 (b)

Exhibiting the same pattern as previously observed, the range of ratio values for Ni intensities

greater than 50 kcps is 0.002 to 0.009 and increases at the low intensity levels. In this case, thevalue for pure Ni is near the average at 0.0049.

It is apparent that the overlap ratio is not a precise constant and the function does not have azero-zero intercept. Having shown that the single factor function for line overlap is inadequate,

the question arises What is the practical implication? To determine this, a calibration was set

up for Mn, Co, and Cu in stainless steels. The Fe concentrations varied from 51 to 88%, the Cr

from 2 to 22% and the Ni from 0.2 to 28%. The three elements in question were calibrated using

regression to determine an overlap factor for the K line and the K line of the overlappingelements and using the Lorentz function to subtract the overlap. The sigma values for each fit

were examined. The data for each calibration is shown in the Appendix. A summary of the sigmavalues is shown in Table 1.

Table 1. Summary of Calibration Sigma Values

Mn Co Cu

K K Lorentz K K Lorentz K K Lorentz

Sigma 0.036 0.041 0.021 0.024 0.032 0.011 0.012 0.014 0.012

Using the Lorentz model, there was significant improvement over the conventional regression

fits for Co and Mn. The sigma value of the calibration using the Lorentz model to subtract the

overlap for Co improved to 0.011, as compared to 0.024 using the regression fit against the Fe-

0.0

0.5

1.0

1.5

2.0

2.5

0 4 8 12 16 20

0.000

0.004

0.008

0.012

0.016

0.020

0 100 200 300 400

OverlapRatio

a b


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K and 0.032 against the Fe-K. The improvements for Mn were 0.021 for the Lorentz model ascompared to 0.036 and 0.041 for the regression fits. There was no significant improvement in the

Cu calibrations, probably because the separation of Cu- K from the Ni- K is greater than forthe other two pairs. Therefore, the overlap interference is less.

CONCLUSION

It has been shown that the line overlap for the situation where the analyte peak lies on the tail of

another element is not best described by single factor function. The overlap does become zerobefore the concentration of the overlapping element becomes zero. There is considerable scatter

in the overlap ratios and the function is non-linear, especially near the low end. It was not the

intent to resolve the line overlap function, that is, to determine the best model to define the lineoverlap, but rather, to show that there is a better way to handle the overlap in these situations.

The Lorentz model, commonly used for curved background correction, is a very effective tool to

subtract this overlap and to calibrate using a net analyte intensity. This results in a more accurate

calibration, in some cases by a factor of more than two.

REFERENCES

1. LaChance, G.R. and Traill, R.J., A Practical Solution to the Matrix Problem in X-ray

Analysis, Can. Spectry., Vol. 11, 1966, p43.

2.Rasberry, S.D. and Heinrich, K.F.J., Calibration for Interelement Effects in X-RayFluorescence Analysis,Analytical Chemistry, Vol. 46, 1974, p81.

3.Standard Guide for Correction of Interelement Effects in X-ray Spectrometric Analysis

(E1361),Annual Book of ASTM Standards Vol. 0306.

4.A number of these are described in Jenkins, R, et al. Quantitative Spectrometry, SecondEdition, Marcel Dekker, Inc., NY 1995, Ch. 10.

5. Private discussion with Katsu Toda, Rigaku/USA


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APPENDIX CALIBRATION DATA FOR STAINLESS STEELS

Calibration Calculations for Mn Calibration Calculations for CuK

Correction

KCorrection

Lorentz KCorrection

KCorrection

Lorentz

Sample Cert.

Value

Calc Diff. Calc Diff. Calc Diff. Cert.

Value

Calc. Diff. Calc. Diff. Calc. Diff.

160 1.65 1.586 -0.064 1.647 -0.003 1.633 -0.017 0.172 0.168 -0.004 0.177 0.005 0.169 -0.003

1151 2.17 2.167 -0.003 2.141 -0.030 2.179 0.009 0.25 0.253 0.003 0.245 -0.005 0.250 0.000

1152 1.19 1.208 0.018 1.212 0.022 1.160 -0.030 0.50 0.516 0.016 0.504 0.004 0.490 -0.010

1154 1.74 1.731 -0.009 1.715 -0.025 1.748 0.008 0.56 0.560 0.000 0.544 -0.016 0.544 -0.016

1155 1.63 1.625 -0.005 1.607 -0.023 1.651 0.021 0.169 0.170 0.001 0.173 0.004 0.168 -0.001

1171 1.80 1.788 -0.012 1.875 0.075 1.795 -0.005 0.121 0.115 -0.006 0.121 0.000 0.121 0.000

1172 1.76 1.776 0.016 1.759 -0.001 1.764 0.004 0.105 0.111 0.006 0.110 0.005 0.114 0.009

1173 0.174 0.179 0.005 0.145 -0.029 0.175 0.001 0.204 0.204 0.000 0.199 -0.005 0.204 0.000

1184 1.04 0.997 -0.043 1.023 -0.017 1.022 -0.018 N.C. ------- ------- ------- ------- ------- -------

1185 1.22 1.243 0.023 1.224 0.004 1.236 0.016 0.067 0.063 -0.004 0.065 -0.002 0.065 -0.002

1193 0.65 0.615 -0.035 0.630 -0.020 0.653 0.003 0.103 0.139 0.036 0.153 0.050 0.141 0.038

1194 0.667 0.665 -0.002 0.652 -0.015 0.656 -0.011 0.047 0.061 0.014 0.064 0.017 0.052 0.0051223 1.08 1.170 0.090 1.153 0.073 1.140 0.060 0.081 0.067 -0.014 0.067 -0.014 0.083 0.002

1230 0.64 0.624 -0.016 0.639 -0.001 0.635 -0.005 0.14 0.138 -0.002 0.147 0.007 0.134 -0.006

1287 1.66 1.712 0.052 1.675 0.015 1.663 0.003 0.58 0.585 0.005 0.575 -0.005 0.571 -0.009

B474 1.70 1.660 -0.041 1.620 -0.080 1.702 0.002 0.35 0.355 0.005 0.340 -0.010 0.337 -0.013

C1154 1.42 1.450 0.030 1.499 0.079 1.433 0.013 0.40 0.394 -0.006 0.399 -0.002 0.388 -0.012

D845 0.77 0.782 0.012 0.762 -0.008 0.779 0.009 0.065 0.055 -0.010 0.056 -0.009 0.070 0.005

D846 0.53 0.511 -0.019 0.529 -0.001 0.505 -0.026 0.19 0.191 0.001 0.198 0.008 0.195 0.005

D848 2.13 2.083 -0.047 2.061 -0.069 2.096 -0.034 0.16 0.154 -0.006 0.148 -0.012 0.177 0.017

D849 1.63 1.672 0.042 1.664 0.034 1.650 0.020 0.21 0.210 0.000 0.203 -0.007 0.213 0.003

D850 N.C. ------- ------- ------- ------- ------- ------- 0.36 0.336 -0.024 0.353 -0.007 0.359 -0.001

Sigma 0.036 0.041 0.021 0.012 0.014 0.012

N.C. = Not Certified

Calibration Calculations for CoK

Correction

KCorrection

Lorentz

Sample Cert.

Value

Calc. Diff. Calc. Diff. Calc. Diff.

B474 0.019 0.017 -0.002 0.020 0.001 0.002 -0.017

1173 0.064 0.085 0.021 0.072 0.008 0.065 0.001

1171 0.10 0.084 -0.016 0.092 -0.008 0.088 -0.012

160 0.101 0.092 -0.009 0.098 -0.003 0.097 -0.004

1155 0.101 0.096 -0.005 0.098 -0.003 0.099 -0.002

1154 0.12 0.102 -0.018 0.100 -0.020 0.113 -0.0071172 0.12 0.111 -0.009 0.108 -0.012 0.117 -0.003

1230 0.15 0.147 -0.003 0.158 0.008 0.134 -0.016

1287 0.31 0.274 -0.036 0.227 -0.083 0.295 -0.015

C1154 0.38 0.326 -0.054 0.329 -0.051 0.382 0.002

1194 2.77 2.780 0.010 2.779 0.009 2.778 0.008

Sigma 0.024 0.032 0.011


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