analysis in capillary preparation. In despite of, to 100 mg 20 g in reliability of the the the drop first and weighing readings used in third drop

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1 Uncertainty evaluation of a modified elimination weighing for source preparation F L Cacais 1,, J U Delgado 1 V M Loayza 1 Laboratório Nacional de Metrologia das Radiações Ionizantes / Instituto de Radioproteção e Dosimetria LNMRI/IRD Brasil Instituto Nacional de Metrologia, Qualidade e Tecnologia Inmetro Brasil Abstract: Some modifications in elimination weighing method for radioactive source allowed correcting weighing results without non-linearity problems assign a uncertainty contribution for correction of same order of masss of drop uncertainty check weighing variability in series source preparation. This analysis has focused in knowing achievable weighingg accuracy uncertainty estimated by Monte Carlo method for a mass of a 0 mg drop was at maximum of 0.06%. Keywords: radionuclide metrology, source preparation; elimination weighingg method; uncertainty evaluation. 1. INTRODUCTION In radionuclide metrology, radioactive sources preparation encompasses a weighing procedure able to achieve stard uncertainties below than 0 in range from 10 mg to 100 mg [1]. The Elimination Weighing method meets this requirement for micro-drops deposition or dilution of a master solution using a plastic pycnometer []. In this weighingg procedure three weighingg steps are performed per source: pycnometer is weighed before after dispensing drop of solution, by knowing mass of drop (by weighing difference), one or several stard weights [3] are added on balance load receptor third weighing reading is recorded. The mass of drop is obtained from difference between first third weighing thus avoiding non- in linearity errors problems. To avoid correlations series sources preparation this method suggests to weigh pycnometer before each drop deposition The absence of systematic errors between weighing (evaporation, drying of a drop in capillary stem, zero drift of balance) is checked by criterion that difference between third second weighing readings should be in agreement with conventional mass [4] of stards within twice uncertainty. In despite of, by elimination weighingg it is not possible to correct systematic errors without take into account non-linearity errors on third second weighingg its uncertainty contribution. Furrmore, this method does not provide any estimate to check variability in seriess sources preparation. Thus, in order to improve reliability of eliminationn method, this work proposes a modification that allows: correcting weighing resultss without non-linearity problems, assign a uncertainty contribution for correction of same order of masss of drop uncertainty check weighing variability in series source preparation. The modification consists in performer second weighingg in elimination method also with same or different stard weights used in third weighing. In original elimination method [5] second weighing was performed 1

2 by this way it relies on previously planned procedure. For an experienced staff diameter of stem tip of a laboratory-made pycnometer [6] is adjusted such masss per drop is previously known with mg of difference from true value. This approximation could be improved by performing weighing of some drops before to execute weighing procedure. Thus, suitable amount of mass stardss can be available close to balance at moment of weighing. By this way, stard weights pycnometer are placed toger on balance receptor at second weighing its mass is adjusted until difference to first reading is less than 3 mg (for mg resolution balance) limiting non-linearity error [7]. By this proposal, one can obtain two weighing differences to form a restrained underdetermined equation system which can be solved including a restrain, mass of stardd weights. This solution provides a mass value of stard weights in addition to mass of drop. The mass of stards could be used to estimate errors difference in weighing on some assumptions about linear error structure (constant, increasing different in one weighingg from two equal ors). The values for masss stards obtained from weighing of a series source preparing could be used to set a long-runn stard deviation [8] to check weighingg variability in source preparation serie, so providing information to variability studies [9]. In this study measurement models for mass measurement are showed an estimate of correction to linear errors in weighing is presented. A routinely assumed error structure on weighingg is defined to evaluate applicability of correction its uncertainty. The uncertainty to correction mass values corrected are calculated by Monte Carlo method [10] to a simulated weighing condition in order to evaluate achievable accuracy for this modified method in order to implement it.. MEASUREM MENT MODEL On assumption of balance has been adjusted beforee weighing, difference I 1i between first weighing, that includes conventional mass of drop mc d, i th ( nd or 3 rd ) weighing with stard weights of conventional mass mc pi can be written: Here difference I 1i includes balance readings for 1 st weighing R 1 i th R i, sensitivity error S buoyancy correction [11] which take in account air density a, conventional air density 0 (1. kg m -3 ), density of master solution S, density of balance reference stards R density of stards weighed toger with solution i : 1 1 From two weighing differences equation system in matrix form can be mounted: The solution of this system, on assumption of one stard reference with conventional mass mc p1 provides measurement model for conventional mass mc d1r (1R means obtained by one reference), mc p : 1 1

3 When both stards are set as referencee just one solution for conventional mass of drop mc dr is possible: 1 In se equations, terms e 1, e e 3 are sum of readability repeatability errors (zero mean with uncertainty) it is not considered non-linearity error (avoided by method) evaporation errorr (because it is corrected by this approach). If one performs weighingg with two references three equations can be used. However if second weighing is carried out with same stard of first, only two first equations should be used. A conversion factor F should be multiplied to conventional mass of drop to obtain its mass value. This factor takes in account conventional air density 0, density of master solution S conventional stard weight density c (8000 kg m -3 ): 3. ERRORS STRUCTURE The errors in weighing ( 1,, 3 ) were considered as additional linear terms in equations of conventional mass values because for two weighing differences it is not possible to take any conclude about additional higher order systematic errorr as in mass comparisons [1]. The redefined values for mc d1r, mc p mc dr are: For two references errors difference ( 3 - ) should be estimated from difference between mc p calibration result mc pc, however if only one reference was used ( 3 - ) is (mcp - mc p1 ) because mc p1 is determinedd from its calibration result. It is emphasized that underlying hyposis for this approach is no stard weights mass drift. This way, estimate ( 3 - )* can be written by: ( references) (1 reference) Five assumptions about difference of systematic errors in weighingg were studied: a) Constant ( 1 = = 3 ), in this case value ( 3 - ) = 0 ( 1 - ) = 0, so no correction should be applied to mc d1r or mc dr. This case could occur in practice for zeroing balance before each weighing evaporation balance drift are constant but not necessarily negligible. b) Linear increasing ( = 1 + k 3 = + k), thus ( 3 - ) = k ( 1 - ) = -k. Heree ( 3 - )* should be add with changed signal to mc d1r to mc dr added as 1.5( 3 - )*. The linear increasing shows commonly for linear evaporation / /or balance drift when balance is left to drift. c) ( 1 = 3 ) implies ( 3 - ) = ( 1 - ), by this way estimate -( 3 -,)* should be summed to mc d1r -0.5( 3 - )* to mc dr. When balance is zeroing before weighing, this case will most likely occur in drying of a drop in capillary stem or improper hling of 3

4 stardd weights or pycnometer in put m on balance receptor. d) ( = 1 3 ), in this case ( 1 - ) = 0 estimated value for ( 3 - )* shows a value which should not correct mc d1r. This case should be true for improper hling of weights or pycnometer in third weighing. e) ( = 3 1 ), here ( 3 - ) = 0 implying that no correction should be applied when it should be. This case is most likely to occur if care previously to weighing as suggested by Lourenço Bobin was not taken. From se assumptions, some conclusions can be taken about applicability of estimate ( 3 - )* its uncertainty u( 3 - )*: 1. ( 3 3- )* < u( 3 3- )*: Casess a ( 1 = =3=0), b ( 1 =0 k= 0) c (( 3 - ) = ( 1 - ) =0) are fundamental hyposis to a carefully weighingg practice, for a trained staff, so ( 3 - )* < u( 3 - )* accomplishes it no correction should be applied but uncertainty should be applied. If re some evidence that had occurred case e, uncertainty should be taken in same way.. ( 3 3- )* > u( 3 - )*: Case b can occur even for a carefully weighing so ( 3 - )* uncertainty should be applied to mass of drop. Case c d relies on technician judgment. For case c applies correction uncertainty, however for case d no correction is applied but uncertainty will be. Due to errors structure, ( 3 - )* is correlated with mc d1r mc dr thus, in according to multiplicative term for ( 3 - )* to correct mass, correlation effect could be higher or lower. 4. UNCERTAINTY EVALUATION In order to evaluate if uncertainty of mass achievable by this method weighingg requirements, complies uncertainty with for estimate ( 3 - )*, mass corrected m d1r, mass corrected m dr conventional mass mc p were calculated to a 0 mg weight for a simulated weighingg conditionn close to real. The uncertainty was calculated by Monte Carlo method to trials. The environmental conditions taken in se calculations are: temperature variation within 1.5 C T.5 C, pressure variation is 995 hpa p 1005 hpa, relative humidity variation within 40% h 60%. By se values, air density value is (Euramet, 015) 1,1811 (1) kg m 3. The assumed density of master solution is (3) kg m 3, density of balance reference weights is 8000 (00) kg m 3 density of stard weights 8000 (15) kg m 3. The balance was adjusted before weighing loads are centred carefully. The Table 1 shows uncertainty components, probability distribution parameters to be used in Monte Carlo simulation for uncertainty of ( 3 - )* mass corrected md 1R R, mc p md R. Table 1: Uncertainty components for mass. Uncertainty component Parametersa a Readability (zero) Readability (load) Repeatability Distribution N(, ) Unit a= 1 a= 1 = 0 = 4 Sensitivity tolerancee a= Temperature sensitivity 10-7 Air density N(, ) kg m -3 = = 0.01 Solution density 1000 N(, ) kg m -3 = = 3 Balance stard density Stard weights 1 density 8000 N(, ) kg m -3 kg m -3 a= 00 = = 15 Masss instability of weight 1 Masss weights 1 0 mg E 10 3 N(, ) a= 6 = 0 = 1.5 Stard weights density 8000 N(, ) kg m -3 = = 15 Masss instability of weight Masss weights 0 mg E 10 3 N(, ) a= 6 = 0 = 1.5 Additional parameters R1= R= R3 = Value Unit mg kg m -3 3 a= 5.8 4

5 0 c Table shows uncertainty for ( 3 - )* of mass corrected md 1R, mc p md R. Additionally, non-corrected mass uncertainty, relative stard uncertainties errors are presented. Table : Errors uncertainties (). Error values u r (%) 1 =0 3 =0 1 = 10 = 0 3 = 30 1 = 10 = 0 3 = 10 No Error ( 3 - )* m u By Table, relative uncertainty to 0 mg is always lower than limit for relative stardd uncertainty, i.e., 0.1%. The higher than 6.5 uncertainty of md 1R md R for cases with error zero means correlation effect which arises from sum of ( 3 3- )* to mass. As previously, higher uncertainty in error linearly increasing means correlation effect from added corrections ( 3 -)* for md 1R 1.5( 3 - )* for md R. Orwise, for errors just in second weighingg correlation in md 1R md R is reduced due to correction, respectively, - ( 3 - )* -0.5( 3 - )*. If it was not regard error, lowest uncertainty for mass is obtained. Just in this case usage of two mass stards would be justified. 5. CONCLUSIONSS md 1R mc p md R u u r (%) u u r (%) u kg m -3 kg m The uncertainty calculation achievable for a modification in elimination weighing method was performed. This modification, in contrast to stardd eliminationn weighing, allows correcting common errors in weighing of radioactive source provide informationn for variability studies, thus improving reliability of elimination weighing. By results, relative stard uncertainty complies with limit for relative stard uncertainty of drop mass usage of additional stard weights is not fundamental. ACKNOWLEDGEMENTS One of authors wishes to thank IRD/CNEN Pronametro/Inmetro for financial scholarship sponsor. REFERENCES [1] Campion P. J., Procedures for Accurately Diluting Dispensing Radioactive Solutions (Sèvres: Monographie BIPM-1). [] Lourenço, V., Bobin, C., 015. Weighing uncertainties in quantitative source preparation for radionuclide metrology. Metrologia, vol. 5, p. S18 S9. [3] OIML R111-1, Weights of classes E 1, E, F 1, F, M 1, M 1-, M, M -3 M 3, Part 1: Metrological technical requirements, Edition 004 (E). [4] OIML D 8. Conventional value of result of weighing in air: OIML, Edition 004. [5] Gallic, Y.L., Problems in microweighing. Nucl. Instr. Meth., vol. 11, p [6] Sibbens, G. Altzitzoglou, T., 007. Preparation of radioactive sources for radionuclide metrology. Metrologia 44, S71 S78. [7] Kochsiek, M. Gläser, M., 000. Comprehensive Mass Metrology. WILEY-VCH Verlag Berlin GmbH, Berlin (Federal Republic of Germany). [8]Croarkin C., An Extended Error Model for Comparison Calibration, Metrologia, vol. 6, pp [9] Fitzgerald R., Bailat C., Bobin C., Keightley J. D., 015. Uncertainties in 4πβ-γ coincidence counting. Metrologia, vol. 5, p. S86 S96. EURAMET, 015. cg-18 Guidelines on calibration of nonauromatic weighing instruments Version 4.0 (11/015). [10] JCGM 101:008. Evaluation of Measurement Data Supplement 1 to Guide 5

6 to Expression of Uncertainty in Measurement Propagation of Distributions using a Monte Carlo Method, BIPM, Sevres. [11] Malengo, A., 014. Buoyancy effects correlations in calibration use of electronic balances. Metrologia 51, [1] Sutton, C. M. Clarkson, M. T., 1993/1994. A General Approach to Comparisons in Presencee of Drift. Metrologia, 30,