Experimental research on mass determination of non-metal weights ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 23 ACTA IMEKO ISSN: 2221-870X December 2020, Volume 9, Number 5, 23 - 26 EXPERIMENTAL RESEARCH ON MASS DETERMINATION OF NON-METAL WEIGHTS M. Hu, J. Wang, C. Cai, R. Zhong, K. Jiao, D. Wu, P. Cheng National Institute of Metrology, Beijing, China, hmh@nim.ac.cn Abstract: With the revision of the definition of the kilogram, more and more weights made of non-metal material, such as silicon spheres and PM 2.5 film, need to be determined with high accuracy. As conventional mass is commonly used in mass metrology, this paper discusses the mass-measuring process for silicon and PM 2.5 film. Electrostatic eliminators are used to eliminate the electrostatic effects of non-metal material to improve the stability of mass measurement. Due to the big difference of weights’ densities, the air buoyancy correction and its uncertainty evaluation are also conducted. Keywords: mass determination; non-metal weights; uncertainty evaluation; silicon sphere 1. INTRODUCTION There are more and more demands in mass metrology for mass measurement of non-metal material [1-4]. As conventional mass is commonly used in mass dissemination of mass metrology, according to OIML R111 [5], altitude and corresponding changes in air density can affect the measurement process when using the conventional mass of weights. The mass of test weight, 𝑚t, can be expressed by equation (1): 𝑚t = 𝑚r + (𝑉t − 𝑉r) × 𝜌a + ∆𝐼 × 𝑚cs ∆𝐼s⁄ . (1) in which 𝑚t and 𝑚r are the mass of test weight and reference weight; 𝑉t and 𝑉r are the volume of test weight and reference weight; 𝜌a is density of moist air; ∆𝐼 is indication difference of the balance; 𝑚cs is the conventional mass of the sensitivity weight; and ∆𝐼s is the indication difference of the balance when the sensitivity weight is put on the weighing pan. Thus electrostatic effects and air buoyancy correction become the two most important aspects for the determination of mass object of non-metal material. To evaluate electrostatic effects and air buoyancy correction to the stability of weighing process of non-metal weights, a silicon sphere of 1 kg and PM 2.5 film are used to experimentally evaluate the standard deviation of weighing process. The PM 2.5 film is tested for its common use and need to be weighed with high accuracy in determination of air pollution. The air buoyancy correction is also investigated and the uncertainty evaluation is also conducted. 2. DESCRIPTION OF THE WORK M-one mass comparator is used for mass determination below 1 kg. With 6 weighing positions, the electronic weighing range is (0 ~ 1.5) g and readability is 0.1 µg. According to air density calculation formula of CIPM 2007, the density of moist air 𝜌a can be expressed as: 𝜌a = (𝑝𝑀a 𝑍𝑅𝑇⁄ ) × [1 − 𝑥v(1 − 𝑀v 𝑀a⁄ )] . (2) where: 𝑝 is the air pressure; 𝑀a is the molar mass of dry air; 𝑍 is the compressibility; 𝑅 is the molar gas constant; 𝑇 is the dynamic temperature using ITS-90; 𝑥v is the mole fraction of water vapour; and 𝑀v is the molar mass of water. Figure 1: Picture of new M-one prototype mass standard comparator The air density measuring system, developed by NIM, China, can measure the pressure, temperature, relative humidity, and carbon dioxide content, as shown in Figure 2. The mass comparator and PM 2.5 film are shown in Figure 3. Figure 2: Pictures of air density measurement system http://www.imeko.org/ mailto:hmh@nim.ac.cn ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 24 Table 1: Uncertainty budget for the density of moist air Source Xi Standard uncertainty value u(Xi) Sensitivity coefficient ci Uncertainty contribution ui(ρa) Pressure, 𝑝 1.2 Pa 1 × 10-5 kg·m-3·Pa-1 1.2 × 10-5 kg·m-3 Temperature, 𝑡 0.007 K -4 × 10-3 kg·m-3·K-1 2.8 × 10-5 kg·m-3 Relative humidity, ℎ𝑟 0.008 -9 × 10-3 kg·m-3 7.2 × 10-5 kg·m-3 Carbon dioxide content, 𝑥CO2 0.000 003 4 0.4 kg·m -3 1.3 × 10-6 kg·m-3 CIPM 2007 formula, 𝑢F 22 × 10 -6 kg·m-3 Combined uncertainty of air density u(ρa) 8.3 × 10-5 kg·m-3 U(ρa) (k = 2) 1.7 × 10 -4 kg·m-3 Figure 3: Pictures of mass comparator, stainless steel standard weights and PM 2.5 polypropylene film 3. RESULTS AND DISCUSSION According to equation (2), the uncertainty of air density, 𝑢𝜌a , can be expressed as: 𝑢𝜌𝑎 = √ 𝑢F 2 + ( 𝜕𝜌a 𝜕𝑝 𝑢𝑝) 2 + ( 𝜕𝜌a 𝜕𝑡 𝑢𝑡 ) 2 +( 𝜕𝜌a 𝜕ℎ𝑟 𝑢ℎ𝑟 ) 2 + ( 𝜕𝜌a 𝜕𝑥CO2 𝑢𝑥CO2 ) 2 (3) in which: 𝑢F = 22 × 10 −6𝜌a , 𝜕𝜌a 𝜕𝑝 = 10−5𝜌a Pa −1 𝜕𝜌a 𝜕𝑡 = −4 × 10−3𝜌a K −1 𝜕𝜌a 𝜕ℎ𝑟 = −9 × 10−3𝜌a , 𝜕𝜌a 𝜕 2CO x = 0.4𝜌a The uncertainty budget for the density of moist air is shown in Table 1. The density of stainless steel weights is around 7950 kg·m-3. The density of PM 2.5 film made of Teflon is 2300 kg·m-3. According to equation (4), for the difference density and volume, the true mass of PM 2.5 film due to air buoyancy correction is around 59 μg, when comparing with stainless steel weights with density around 7950 kg·m-3. 𝑚ct = 𝑚cr + (𝑉t − 𝑉r) × (𝜌a − 𝜌0) ± ∆𝐼 × 𝑚cs ∆𝐼cs (4) in which 𝑚ct and 𝑚cr are the conventional mass values of the test and reference weights respectively, 𝜌0 is the reference air density value of 1.2 kg·m -3, and ∆𝐼cs is the change in indication of the balance due to the sensitivity weight. Figure 4: Volume difference of stainless steel weights and Teflon PTFE film (PALL) of 160 mg When the air density is around 1.1834 kg·m-3, the air buoyancy correction is around 0.8 μg. However, due to the air buoyancy effect, when measuring the mass of the non-metal material such as Teflon film, the mass deviation of 6 μg is observed between the ABBA weighing cycles, which can be seen in Figure 5. When measuring the mass of silicon sphere using stainless steel weights, same mass deviation is also be observed. For the 1 kg silicon sphere, the density of silicon is (2320 ~ 2340) kg·m-3, the air buoyancy for the true mass is around 370.795 mg. while measuring in air with density of 1.1834 kg·m-3, the air buoyancy correction for the conventional mass can be 5.1 mg, which means that the air density including the air temperature, relative humidity, air pressure and contents of CO2 need to be determined with high accuracy for the air buoyancy correction. Stainless steel sheet weights Teflon membrane Stainless steel weights PM 2.5 film XPR comparator http://www.imeko.org/ ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 25 Table 2: Uncertainty budget for PM 2.5 Teflon membrane Source of uncertainty Standard uncertainty Sensitivity coefficient Uncertainty contribution / mg Standard uncertainty of average (�̅�) 0.001 mg 1 0.001 Standard uncertainty of 160 mg standard 0.001 mg 1 0.001 Volume of stainless steel weights 0.000 2 cm3 1.1834 mg·cm-3 0.000 237 Volume of Teflon 0.000 2 cm3 1.1834 mg·cm-3 0.000 237 Air density 0.000 083 mg·cm-3 0.0494 cm3 0.000 004 1 Balance linearity 0.000 000 7 mg 1 0.000 000 7 Combined standard uncertainty 0.001 5 Expanded uncertainty (k = 2) 0.003 0 Figure 5: Mass difference of Teflon material between ABBA weighing cycles due to the air buoyancy correction As shown in Figure 6, the electrostatic eliminator is used to decrease the influence of electrostatic effects. 11 ABBA weighing cycles are carried out between stainless steel weights and silicon sphere. Figure 6: Volume difference of different weights between stainless steel weights and silicon sphere weights Figure 7: Mass difference of silicon sphere between ABBA weighing cycles due to the air buoyancy correction As shown in Figure 7, the mass difference between different weight cycles can be up to 13.5 μg which were carried out over a period of 48 hours in the laboratory. The uncertainty of air buoyancy correction due to volume difference between stainless steel weights and the non-metal material of PM 2.5 Teflon film are listed in Table 2. Due to the high accuracy determination and relative small nominal mass value and volume difference between Teflon membrane and stainless steel weights, the uncertainty contribution of air buoyancy correction is only 0.004 μg. The expanded uncertainty (k = 2) for the conventional mass of PM 2.5 Teflon film is 3 μg. 4. CONCLUSION For mass determination of non-metal weights, it is important to ensure the limitation of electrostatic effects. For that conventional mass is commonly used in mass metrology, this paper discusses about mass measuring process for silicon and PM 2.5 membrane. Electrostatic eliminators are used to eliminate the electrostatic effects of non-metal material to improve the stability of mass measurement. Due to the big difference of density of weights, the air density including the air temperature, relative humidity, air pressure and contents of CO2 need to be determined with high accuracy for the air buoyancy correction, the air buoyancy correction and its uncertainty evaluation are also conducted. 5. ACKNOWLEDGEMENT This research is supported by National Key Research and Development Program for National Quality Infrastructure under Grant 2017YFF0205006. 6. REFERENCES [1] M. Gläser, M. Borys, “Precision mass measurements”, Rep. Prog. Phys., vol. 72, no. 12, 126101, 2009. [2] M. Borys, M. Glaser, M. Mecke, “Mass determination of silicon spheres used for the Avogadro project”, Measurement, vol. 40, pp. 785-790, 2007. -25 -20 -15 -10 -5 0 5 10 15 20 25 1 2 3 4 5 6 Mass difference between two ABBA weighing cycles μg 14.818 14.820 14.822 14.824 14.826 14.828 14.830 14.832 14.834 14.836 0 1 2 3 4 5 6 7 8 9 10 11 silicon sphere vs stainless steel mg Electrostatic eliminator http://www.imeko.org/ ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 26 [3] P. Fuchs, K. Marti, S. Russi, “New instrument for the study of ‘the kg, mise en pratique’: first results on the correlation between the change in mass and surface chemical state”, Metrologia, vol. 49, pp. 607-614, 2012. [4] K. Lehrmann, D. Knopf, F. Härtig, “Status of the realization and dissemination of the kilogram via silicon spheres”, CPEM, 2018. [5] OIML R111-1, “Weights of classes E1, E2, F1, F2, M1, M1-2, M2, M2-3, and M3”, 2004. http://www.imeko.org/