The Uncertainty Sources Taken Into Account Within Preparation of Samples and Standards

Electronic Supplementary Material

Evaluation of uncertainty budget

The uncertainty budget takes into account all possible sources of uncertainty starting from sampling up to measurements. Recognition of the biggest contribution define the most sensitive step in the elaborated procedure, and can initiate appropriate procedure corrections. In the case of highly accurate RNAA methods, estimation of expanded uncertainty should prove the significance of these methods from metrological point of view.

For radiochemical neutron activation analysis, the sources of uncertainty (u) are divided into four groups [1]:

§  preparation of samples, standards and monitors to the irradiation in the reactor u1 ;

§  irradiation in the neutron flux in nuclear reactor u2;

§  radiochemical separations u3;

§  gamma-ray spectrometric measurements u4.

The standard uncertainties within particular categories connected with individual sources of uncertainty can all be quantitatively evaluated and expressed in SI units [2,3].

In RNAA, when the samples are irradiated together with the standards, CRMs and blank in one package in the neutron flux, measurements are carried out under the same geometric conditions using the same HPGe detector, mass fraction wx of the element to be determined (x) is given by the equation [1]:

wx = (1)

where symbols Ax, Dx, Cx, mx, Yx are for the sample, and Ast, Dst, Cst, mst for standard respectively; and

-  D is the decay factor (D = exp(-λtd)), where td is the decay time;

-  C is the measurement factor (C = (1-exp(-λtm)/ λtm), where tm is the measurement time).

-  Ax is the count rate of analytical gamma-ray of indicator nuclide (s-1, Ax = Np tc-1, where Np is net number of counts in peak corrected for pulse losses and tc is the live counting time);

-  mx is the sample mass (g);

-  Yx is the chemical yield of the separation.

The uncertainty sources taken into account within preparation of samples and standards to the irradiation were: sample and standard mass determination, standard purity, sample mass changing during weighing, determination of moisture content. The uncertainty in sample and standard weighing was estimated according to the producer specification to be at maximum 0.1%. In the case of moisture determination, uncertainty has been estimated from measurements of water content of the several samples (not used for analysis) accordingly to CRMs producer recommendation. The relative uncertainty associated with moisture determination, calculated from rectangular distribution () is almost negligible. Similarly, in the case of standard purity; arsenic standard solution was prepared from high-purity As2O3 thus uncertainty associated with it is negligible. Also the uncertainties associated with the other sources of uncertainty in the stage of preparation of the sample and standard i.e. change of sample mass during weighing, stoichiometry, variation of isotopic abundance and residual blank can be neglected.

Sources of uncertainty associated with the irradiation step are: differences in irradiation geometry and neutron spectrum in space and time including neutron self-shielding and scattering, differences in irradiation time, nuclear reaction interferences and volatilization losses during irradiation. Differences of the neutron flux caused by the flux gradient in space are determined and corrected for by use of sandwich elemental standards. The standard uncertainty attached to this correction has been calculated from triangular distribution () and is equal to 0.1%. The standard uncertainty related to thermal neutron self-shielding and scattering is significant in the case of high density samples or for elements with very high cross-section. For typical biological samples this component is usually negligible and was evaluated to be less than 0.2% [1]).

In arsenic determination by NAA, interfering nuclear reactions should be taken into account: 76Se(n, p)76As, 79Br(n, a)76As and 74Ge(n, g)75Ge75As(n, g)76As [4]. The possibility of appearance of these reactions was checked, no corrections were needed. The uncertainty connected with differences in irradiation time is zero due to simultaneous irradiation of samples, standards, CRMs and blank. Uncertainty associated with the analyte losses during irradiation was negligible. Irradiation of arsenic was done with using various irradiation vessels: polyethylene capsules and sealed quarts ampoules; independently on the container used, the recovery of irradiated arsenic was the same and quantitative.

Sources of uncertainty related to radiochemical separation are: quantitative separation of determined element and standard, isotope exchange between analysed radionuclide and stable carrier (or radioindicator). In the elaborated procedure, the chemical yield was evaluated by several analyses of various biological materials spiked with 73As radiotracer. The yield was determined as 100% ± 1%. The uncertainty estimated from the rectangular distribution is equal to 0.6% for both sample and standard. Uncertainty related to the isotope exchange between isolated radionuclide 76As and stable carrier 75As is negligible, when carrier is added before sample decomposition.

Sources of uncertainty associated with gamma-ray spectrometric measurement are: counting statistics, blank correction, differences in counting geometry and time, pulse-up losses, cascade summing, effects of dead-time and decay time, gamma-ray interferences, self-shielding and peak integration.

The uncertainty resulting from counting statistics of the samples and the standards is calculated from the Poisson’s distribution, according to the equation: u=100(Np+2B)1/2/Np, where B-background, Np-net peak area. For the elaborated method standard uncertainty for sample is equal 1%, for standard-0.6%. Differences in these values results from differences in number of counts for standard and for sample; this is connected with relatively short half-life time of 76As (26.3 h). In the case of long time measurements of several samples, counting statistics for first samples are much better than for the last one. Uncertainty from the counting geometry was evaluated using triangular distribution and was calculated to be 0.4%. In the case of peak area evaluation, higher uncertainties are to be expected for small peaks (close to detection limit) and for multiplets. In the case of the present method, the purity of isolated 76As is very high-only energy peak of 559 keV is visible in the spectra. Increased background the low energy region originated from beta-emitter 32PO43- does not influence the count rate and peak shape of arsenic. Also, the high cross section of 75As(n, g)76As reaction results in relatively high number of counts. Uncertainty associated with peak integration was calculated to be 0.3%. The uncertainty related to other sources attached to this step is neglected.

The combined standard uncertainty calculated according to uncertainty propagation law amounted to 1.7%.

The uncertainty budget for the arsenic determination in Oriental Tobacco Leaves CTA-OTL-1 is presented in Table 4. Obtained value for As determination in CTA-OTL-1 is 543 ng g-1, combined standard uncertainty: 9.2 ng g-1, expanded uncertainty for coverage factor k=2 (a level of confidence of approximately 95 %): 18.5 ng g-1. The final results with expanded uncertainty is equal (543 ± 19) ng g-1, where the certified value is (539 ± 59) ng g-1.

1.  Kucera J, Bode P, Stepanek V (2004) Uncertainty evaluation in instrumental and radio-chemical neutron activation analysis in quantifying uncertainty in nuclear analytical measurements. IAEA-TECDOC1401, IAEA Vienna

2.  Tian W, Ni B, Wang P, Cao L, Zhang Y (2001) Metrological role of neutron activation analysis. IA. Inherent characteristics of relative INAA as a primary ratio method of measurement. Accred Qual Assur 6:488-492. doi 10.1007/s00769-001-0407-1

3.  Tian W, Ni B, Wang P, Cao L, Zhang Y (2002) Metrological role of neutron activation analysis, IB Inherent characteristics of relative INAA as a primary ratio method of measurement. Accred Qual Assur 7:7-12. doi 10.1007/s00769-001-0408-0

4.  Koch RC (1960) Activation Analysis, Handbook, Academic Press

Table. The uncertainty budget for the arsenic determination in Oriental Tobacco Leaves CTA-OTL-1 by highly accurate RNAA method.

Source of uncertainty / term / value / Relative standard uncertainty (%)
Mass of sample
Mass of standard
Residue blank
Neutron flux gradient
Neutron self-shielding/scattering
Sample counting statiscics
Standard counting statistics
Counting geometry of sample
Counting geometry of standard
Pulse pile-up losses of sample
Pulse pile-up losses of standard
Peak integration method for sample
Peak integration method for standard
Radiochemical separation of sample
Radiochemical separation of standard / Ws
Wst
Wb
DF
DF
Ns
Nst
Ns
Nst
Ns
Nst
Ns
Nst
Ys
Yst / 200 mg
5 mg
0 mg
1.00 ± 0.002
1.00
30000 counts
50000 counts
1.00
1.00
0 (%)
0 (%)
1.00
1.00
1.00 ± 0.1
1.00 ± 0.1 / 0.1
0.1
0.1
0.1
0.2
1.0
0.6
0.4
0.4
0.3
0.3
0.3
0.3
0.6
0.6