xrf analysis: identifying and estimating errors jeddah... · – high voltage generator variations...

XRF Analysis: identifying and estimating errors

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Types of Error

Gross Error e.g. / Outlier Instrument failure Sample contamination Human errors

Random Error e.g. Counting statistics Sample preparation

Systematic Error e.g. Errors in calibration (model, constants) Dead time losses

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3

To evaluate the systematic error check the calibration against

well known standards

Accurate Precise and AccuratePrecise

Accuracy and precision

Typical sources of errors and their contribution in rel. %

Random Systematic

Sample taking or inhomogeneity 0 -50

Sample preparation 0 - 2 0 - 50

Spectrometer hardware 0.05-0.2 0.05-0.5

Counting statistics (time)

Absorption and enhancement effects 0 -50

Wrong regression parameters 0 - 200

Calibration standards (quality)

Operator mistakes4

Propagation of Random Errors

errorstatisticscountingCSEE

erroralinstrumentinstE

errornpreparatiosamplesmplE

222

++= CSEinstsmplRandom EEEE

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Distribution of Random Errors

Repeated measurement results are distributed around a mean N A measure of the error is the RMS

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Counting statistical error

C:\Documents and Settings\alexander.komelkov\Desktop\Count_rates.xlsx

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( )

tsmeasurementheofnumber

valueaverage

tmeasuremenpartuculartheofvalue

1

2

===

nxx

xxRMSRMSE n

xx

relrel

222CSEinstsmplRandom EEEE ++=

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Instrumental error

Instrumental error consist of: High voltage generator variations X-ray tube instability Sample positioning Other hardware issues

Usually Einst < 0.05 rel.% of the intensity (for WD XRF spectrometers)

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Counting Statistical Error (CSE)

Rp - gross peak count rate

Rb - background count rate at the peak wavelength

Net count rate = Rp - Rb

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r - count rate (counts per second, cps)

t - counting time (seconds)

N - total number of collected counts

trNCSE counts ==)(

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tr

ttr

tN

tCSE

CSE countscountrate ==== )()(

Relative Counting Statistical Error (RCSE)




CSErel decreases with increase of intensity or measurement time!

trNNNCSE countsrel

===

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Sample preparation errors

Due to errors of other equipment (scales, pipettes, press,)

Due to differences in batches of used chemicals (binders, fluxes, diluents,)

Not accurate handling of the samples

Etc.

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Evaluation of errors contribution

! softwarethebyreportedRMS

relrel RMSE =

222CSEinstsmplRandom EEEE ++=

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Statistic approach of the random error evaluation

1 bead 10 times

10 beads 1 time

Compound TiO2 Na2O TiO2 Na2OMeasure time (s) 8 36 8 36

Mean Raw kcps 7.93 1.03 7.96 1.03RMS rel. Raw kcps (%) 0.53 0.53 0.54 1.28

Mean Bg cor. kcps 7.17 0.84 7.20 0.84RMS rel. Bg cor. kcps (%) 0.60 0.58 0.63 1.53

CSE mean (kcps) 0.031 0.005 0.032 0.005CSE rel. (%) 0.397 0.517 0.396 0.518

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Typical sources of errors and their contribution in rel. %

Random Systematic

Sample taking or inhomogeneity 0 -50

Sample preparation 0 - 2 0 - 50

Spectrometer hardware 0.05-0.2 0.05-0.5

Counting statistics (time)

Absorption and enhancement effects 0 -50

Wrong regression parameters 0 - 200

Calibration standards (quality)

Operator mistakes20

Systematic errors due to the samples

Absorption effect -300%

Enhancement effect -25%

Particle size effect -100%

Chemical state / mineralogical / metallurgical effect -5-20 %

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Errors in chemical composition of standards

Best commercially available standards have a composition determination error up to 0.1% relative; but often worse.

e.g. SiO2 content 0.5% +/- 0.05% means:between 0.45% and 0.55%

(i.e. 10% relative !)

e.g. Ni content 10.2% +/- 0.05% means:

between 10.15% and 10.25%

(i.e. 0.5% relative !)

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Regression Analysis

Multi-linear Regression AnalysisCalculates by minimising errors:

A. slope & intercept of calibration line

B. inter-element correction factors

C. line overlap and background factors

using concentration & count rate data from standards

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Uncorrected Ni calibration

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Secondary fluorescence ; path indicated with AlphaSteel 40-50 %Geology

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Matrix corrections

Theoretical matrix corrections in SuperQ Classic alphas

Based on typical values from standards

Fundamental parameter Determined per standards

Better linearity over large calibration ranges

Sum of concentrations of standards must be close to 100%!

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Ni Corrected with as

Human Errors during calibration

Multi-linear Regression Analysis The regression software is very powerful but large errors in

the constants calculated are often caused by:

Too many correction constants calculated simultaneously

Poor data fitted with fictitious calculated correction constants

Deleting standards that contain valuable information such as interference from line overlap

Incomplete data on standards that must be used to correct for spectral interferences and matrix effects

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Typical expected errors in XRF

Concentration range Total relative error, %

2 -100 % 0.1 2

0.1 2 % 1-10

Traces (100 -1000 ppm) 5-20

< 50 -100 ppm 10-100

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Slide Number 1Types of ErrorAccuracy and precisionTypical sources of errors and their contribution in rel. %Propagation of Random ErrorsDistribution of Random ErrorsCounting statistical errorSlide Number 8Instrumental error Counting Statistical Error (CSE)Counting Statistical Error (CSE)Counting Statistical Error (CSE)Relative Counting Statistical Error (RCSE)Sample preparation errorsEvaluation of errors contributionSlide Number 16Slide Number 17Slide Number 18Statistic approach of the random error evaluationTypical sources of errors and their contribution in rel. %Systematic errors due to the samplesErrors in chemical composition of standardsRegression AnalysisUncorrected Ni calibrationWhat are matrix effects ?Matrix correctionsNi Corrected with asHuman Errors during calibrationTypical expected errors in XRF