Measurement of the 30 Si mole fraction in the new Avogadro silicon material by Neutron Activation and high resolution spectrometry

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1 Measurement of the 30 Si mole fraction in the new Avogadro silicon material by Neutron Activation and high resolution spectrometry Marco Di Luzio 1,2, Attila Stopic 3, Giancarlo D Agostino 1, John W Bennett 3, Giovanni Mana 1, Massimo Oddone 2, Axel Pramann 4 1 Istituto Nazionale di Ricerca Metrologica (INRIM), Strada delle Cacce 91, Torino, Italy 2 Department of Chemistry, University of Pavia, via Taramelli 12, Pavia, Italy 3 Australian Nuclear Science and Technology Organisation (ANSTO), New Illawarra Road, Lucas Heights, New South Wales 2234, Australia 4 Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116, Braunschweig, Germany

2 Summary Avogadro constant and silicon x( 30 Si) investigation - State of the art - Si sample - Measurement - Result Conclusion

3 Redetermination of N A Use of silicon Choice of silicon Largely studied element Well defined crystalline structure Can be quite easily highly purified Measurement of Avogadro constant with uncertainty less than kg kg Atoms for unit cell M - Molar mass V - Volume a - Lattice parameter m -Mass M is strictly linked to isotopic composition while m to point defects vacancies impurities

4 x( 30 Si) State of the art Evaluation of M from less abundant isotopes of Si ( 29 Si and 30 Si) Discrepancy observed among mole fractions results obtained with the previous highly enriched 28 Si in Avogadro material using IDMS. Measurement of 29 Si and 30 Si mole fractions are performed with Isotope Dilution Mass Spectrometry (IDMS) in different National Metrology Institutes Vocke et al; Metrologia, 2014; 51,

5 x( 30 Si) INAA overview INAA analysis of an highly enriched silicon sample: reaction 28 Si n p 28 Al t 1/2 2.2 min mol mol 1 29 Si n p 29 Al t 1/2 6.6 min 10 6 mol mol 1 30 Si n 31 Si t 1/2 157 min 10 7 mol mol 1 Only 30 Si mole fraction measurement has been possible with INAA Relative method NAA was applied on the enriched sample in order to achieve the minimum possible uncertanty on x( 30 Si) measurement

6 x( 30 Si) Si sample Hyper pure, highly enriched 28 Si crystal and sample cut from main crystal Bartl et al; Metrologia, 2017; 54,

7 x( 30 Si) Si sample Highly enriched 28 Si sample cut from main crystal. (Part Q.4.1) In detail: New silicon batch (Si28-23Pr11). x( 28 Si) > mol mol -1. ø 20.0 mm, h 19.0 mm. m 14.0 g.

8 x( 30 Si) Measurement (Activation) 2 irradiations performed at OPAL reactor of ANSTO (20 MW power) Irradiation channel at OPAL reactor LE7 1C ( th = cm 2 s 1, f = 44.3) Irradiations: Sample [Si28 23Pr11 part Q.4.1] (3 h, Co wire monitor flux) Standard [Si V1382 part 8.1] (1 h, Co wire monitor flux)

9 x( 30 Si) Measurement (Counting) Emitted -rays ( kev) counted on a HPGe detector (65% relative efficiency, 1.87 kev FWHM at 1332 kev) Crystals placed at same position on the detector end-cap Acquisition sequences: Sample [Si28 23Pr11 part Q.4.1] Standard [Si V1382 part 8.1] 3 spectra (fixed t c = 7200 s) 7 spectra (fixed t c = 4000 s) min from end of irradiation min from end of irradiation 1.2% 2.6% uncertainties on -peak 0.4% 1.0% uncertainties on -peak detector dead time 17% detector dead time 18%

10 x( 30 Si) Measurement (Model) Si Si 1 s = 28 Si sample / n = natural standard C (td) = Count rate of kev gamma-rays at time td ti = Irradiation times td = Decay times R = Flux inhomogeneities = Detection efficiencies (positioning) ss = Neutron self-shielding sa = Gamma self-absorption g = Geometries x( 30 Si) = 30 Si mole fraction m = mass M = Molar mass

11 x( 30 Si) Measurement (Uncertainty) Combined uncertainty evaluated with quadratic propagation of relative standard uncertanties assuming absence of correlations among input parameters in eq. (1) C(td), 1,,,, 2 Count rate referred to starting time of acquisition sequence C(td) was calculated from the net count (n p ) values from all the acquired spectra of the sequence. A weighted average was then performed to reduce combined uncertainty. td, ti, R Correction factors for decay and irradiation times were calculated according to the experimental measured times. Decay constant,, of Si was redetermined to slighly decrease the literature uncertainty. Flux inhomogeneities were calculated with the ratio of specific activities measured from Co monitor wires. D Agostino et al; Metrologia, 2017; 54,

12 x( 30 Si) Measurement (Uncertainty) Combined uncertainty evaluated with quadratic propagation of relative standard uncertanties assuming absence of correlations among input parameters in eq. (1), ss, sa, g Correction factors (along with their respective uncertainties) were evaluated with considerations on shapes of the actual samples or knowledge deriving from previous analysis. These factors resulted in values very close to unity with low to negligible uncertainties. m, M Masses were measured on an analytical balance calibrated with standard traceble to SI. Molar masses (and x( 30 Si n ) consequently) were retrieved from literature and measurements performed by PTB.

13 x( 30 Si) Result Measured 30 Si mole fraction with uncertainty budget x u (x) ur (x) ur 2 (x) % ti % td % R % ε % kss % ksa % kg % C s (td s ) % C n (td n ) % x( 30 Si n ) % m % x( 30 Si s ) % Di Luzio et al; Analytical Chemistry, 2017; 89,

14 Conclusions INAA is an analyical technique providing bulk investigation with extremely high sensitivity without dissolution of the sample. It proved to be a independent source of information concerning the characterization of the silicon material used to determine the Avogadro constant. Valuable information on M (x( 30 Si) quantification) was obtained, corroborating the IDMS result. The 1.5% combined uncertainty achieved on x( 30 Si) reflected in a very small contribution on the combined uncertainty of N A determination.

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