This method involves the use of the fundamental equation, without using any standard for the deteimination of elemental concentrations. Equation 3.7 is the fundamental equation used for thick homogeneous sample
f
<^ÂE)TXE)dE At
S(E)and the X-ray attenuation
(3.8) c o iû ls { E )
where I (x) = intensity per unit concentration per steradian per unit beam charge for a particular matiix
Aw = atomic weight of the element S(E) = proton stopping power
bx = fraction of the series X-ray intensity Na = Avogadro’s number
Wx = fluorescence yield
p = mass attenuation coefficient
q = angle of the incoming beam with respect to the target surface noimal Q, = angle of the outgoing X-ray with respect to the target surface normal
As we can see from the equation 3.7 and 3.8 the method is highly reliant on an accurate database of cross section, fluorescence, stopping power and attenuation coefficient as well as the geometrical parameters of the system.
The GUPIX package in Dan 32 used in this thesis employs a database for X- ray production cross-section that is based almost entirely upon theoretical calculation of the necessary atomic quantities K, L and M sub-shell ionisation cross-sections are based upon those computed in the ECPSSR model by Chen and Crasemann
using Dirach-Harti'ee-Slater (DHS) wave functions for the bound electron. The fluorescence and Coster-Kroning transition probabilities for L and M sub shells are also derived from the DHS wave frmction
Accuracy and precision of the absolute method
Duplicate samples of NIST standaid reference materials Peach Leaves (SRM 1547), Polish certified reference material Tobacco Leaves (CTA-OTL-1) and IAEA reference material Animal Blood (IAEA-A-13), each of mass 50mg were compressed into pellets of diameter 5 mm. The samples were stuck to 3 mm thick aluminium plates using double-sided adhesive tape and were carbon coated to ensure good electiical conductivity. A proton beam of size 3 x 4 pm^, cuirent 200 pA and energy 2.5 MeV was used to iiTadiate for 10 minutes an area of 1.5 x 1.5 mm^ of sample pellets. The characteristic X-ray spectra were collected by an 80 mm^ Si(Li) detector (with a Be filter of thickness 130 pm) placed at 135° to the beam and 25 cm fr om the samples. The RBS spectra were collected using a Si(Li) detector placed at 160° and 30 mm from the samples.
The RBS and PIXE spectra were fitted and the elemental concentrations calculated by GUPIX of Dan32 which utilises the absolute method of analysis.
However, the experimental concentrations of the elements in all tluee analysed reference materials did not match with the certified values. The experimental concentrations were found to be 20% - 60% higher than that of the certified values.
Plots of certified against experimental values were straight lines with similai"
slopes, which indicated a systematic eiTor in the experimental set up. This might probably be due to poor characterisation of the system as the absolute method depends on the accuracy of essential parameters of the set up, such as solid angle, H values, which is an instrumental value equal to detector solid angle modified by a calibration factor mvolved in a beam charge measuiements, and the detection efficiency. Poor characterisation of the ion beam system of the University of Surrey has been reported previously by Admans (2004) who used H value method to validate the system. In order to reduce the error. Admans suggested inputs to the Dan32 package that would improve the system. However, results from this thesis
demonstrate no improvement. Therefore, re-characterisation of the University of Surrey ion beam for PIXE is recommended.
As an illustration. Fig 3.8 is a plot of certified concentiations against experimental concentiations for Peach Leaves (SRM 1547). Similar slopes were obtained in the gi'aphs for Tobacco Leaves (0.77) and Blood Reference Material (0.65) with 6% standard deviation between the materials (fig III and IV of Appendix 2). Hence, average value of the tliree slopes were calculated and found to be 0.70±0.04 which was taken as a correcting factor. After normalisation with the correcting factor, the experimented values were lowered and hence improved by 6%
to 30%.
y = 0.6922X -16.647
= 0 . 9 ^
3000 n
r 2000 -1000
-1000 2000
Experimental values (ppm)
3000 4000
Fig 3.8: The graph of certified values against the experimental values of Peach Leaves (SRM 1547),
R~ is a statistic that gives information about the goodness offit o f a model
The deviation from the certified values of the elements in the tlnee reference materials varied between elements depending on the certified amount and uncertainty of the element in the sample. However, most of the corrected experimental values fi'om the tloi'ee reference materials improved to an accuiacy of 15% for peach leaves, 18% for the animal blood and 20% for tobacco leaves. The high percentage deviation fi'om the certified value for Cu in the thi'ee reference materials and Sr in peach leaves were probably because these element are cei'tified to have concenti ations which were near to the MDL obtained in this study hence, they needed more time of counting in order to have had more precise statistics. For instance, the MDL for Cu and Sr in
Peach leaves were 3.1jig/g and 34|ig/g respectively compared to the values of 3.7pg/g and 53pg/g respectively certified to be in the sample. These elements had also the highest uncertainties of all the elements in the sample.
Fig.3,9 shows the ratio of the certified over experimental concentrations for Peach and Tobacco Leaves as a function of atomic number Z of the elements. As could be seen, the plots of the two reference materials followed the same trend and their ratios were comparable witli less than 10% difference for Z higher than 19. Fig 3.9 (b) shows 6% to 30% improvements on the ratios for both materials after the experimental concentrations were normalised by the correcting factor.The eiror bars represent the error of the resulting ratio, which is the root mean square combination of certified uncertainties of the elements in the standai'd and the uncertainty in the experimental value.
1.2 1
Fig 3.9: The graph of the ratio of certified over experimental values for Peach Leaves (SRM 1547) and Tobacco Leaves (CTA-OTL-1): (a) uncorrected data (b) experimental values normalised by the correcting factor.