Preparation of primary standard mixtures for atmospheric oxygen measurements with uncertainty less than 1 ppm for oxygen mole fractions

Primary standard mixtures with less than 1 ppm or 5 per meg standard uncertainty for O2 mole fractions or 10 for O2/N2 ratios were prepared to monitor changes, which occurred in atmospheric oxygen. These mixtures were crafted in 10 L high-pressure aluminum cylinders using a gravimetric method in which unknown uncertainty factors were identified and subsequently reduced. The mole fractions of the constituents, CO2, Ar, O2, and N2, were mainly determined using the masses of the respective source gases that had been filled into the cylinders. To precisely determine the masses of the source gases used in each case, the differences in the masses of the cylinders before and 15 after filling were calculated and compared to nearly identical reference cylinders. Although the mass of the cylinder with respect to the reference cylinder tended to vary in relation to temperature differences between both cylinders, the degree of change could be reduced by measuring both cylinders at the same temperature. The standard uncertainty for the cylinder mass was determined to be 0.82 mg. The standard uncertainties for the O2 mole fractions and O2/N2 ratios in the primary standard mixtures ranged from 0.7 ppm to 0.8 ppm and from 3.3 per meg to 4.0 per meg, respectively. 20 Based on the primary standard mixtures, the mole fractions of atmospheric O2 and Ar on Hateruma Island, Japan. In 2015, the O2 and Ar mole fractions were found to be 209339.1 ± 1.1 ppm and 9334.4 ± 0.7 ppm.

The mole fraction of atmospheric O2 is commonly expressed as a function of O2/N2 ratio relative to an arbitrary reference (Keeling and Shertz, 1992), according to Eq. (1).(1) In this equation, the subscripts "sample" and "standard" refer to a sample air and a standard air, respectively.As the O2 mole fraction of air is 20.946 %, a change of 4.8 per meg in δ(O2/N2) corresponds to a change of 1μmol mol −1 in 5 the O2 mole fraction.In this study, the unit of "μmol mol −1 " is abbreviated as "ppm." There are approved primary standard mixtures for use in these types of experiments for CO2, CH4, and N2O, which are prepared using either manometry (Zhao et al., 1997) or gravimetry (Tanaka et al., 1983;Matsueda et al., 2004;Dlugokencky et al., 2005;Hall et al., 2007).Tohjima et al. (2005) first prepared primary standard mixtures for observation of atmospheric O2 using a gravimetric method in which the standard uncertainties were noted at 15.5 per 10 meg for the O2/N2 ratio and 2.9 ppm for the O2 mole fraction.Since the 2.9 ppm standard uncertainty recorded by Tohjima et al. was much larger than the gravimetrically expected value of 1.6 ppm, it was suggested that there are unknown factors exerting influence on the mass readings of the cylinders.
Reported peak-to-peak amplitudes of seasonal cycles and trends for atmospheric δ(O2/N2) were within the range of 50 per meg to 150 per meg (from 10 ppm to 30 ppm for O2 mole fractions) and −20 per meg yr −1 (−4 ppm yr −1 for O2 15 mole fractions), respectively (Keeling et al., 1993;Battle et al., 2000;Van der Laan-Luijkx et al., 2013).To monitor these slight variations, it was recommended to develop primary standard mixtures with O2/N2 ratios that had standard uncertainty of less than 5 per meg or O2 mole fractions that had standard uncertainty of less than 1 ppm (Keeling et al., 1993;WMO, 2016).In this study, primary O2 standard mixtures with the recommended uncertainty of less than 5 per meg or 1 ppm is hereafter expressed as "a highly precise O2 standard mixture." 20 Since the variations in atmospheric O2 were less than 500 per meg (100 ppm) (Bender et al., 1994;Tohjima, 2000;Stephens et al., 2007;Goto et al., 2013), the highly precise O2 standard mixtures used to monitor atmospheric O2 required the use of a range of 500 per meg (100 ppm) upwards.The resultant standard uncertainty would be higher than the recommended uncertainty, which could interfere with its corresponding slope of calibration line in an analyzer used for the monitoring.For example, when two standard gases that had uncertainty values of 3 ppm (15 per meg) and 25 the difference in both O2 mole fractions of 100 ppm (500 per meg) were used for calibration of an analyzer, the slope of the calibration line calculated for the analyzer would reflect a 6 % deviation from the actual value if one cylinder would have O2 mole fraction which would be 3 ppm higher than the true level while the other cylinder would have a deviation that was 3 ppm lower than the true level.Given this, it is important to verify not only the scale but also its corresponding slope for each laboratory's standard gas mixtures using highly precise O2 standard mixtures.Because 30 the highly precise O2 standard mixtures have not been yet developed, there has been a need for their development.
Our laboratory has built upon a weighing system proposed by Matsumoto et al. (2004) in which gravimetry was used to prepare standard mixtures.This system allows accurate weight measurements in which the standard uncertainty is 2.6 mg.The integration of a new mass comparator with better repeatability have been made to the weighing system.
In this study, we developed a means of identifying and minimizing unknown uncertainty factors that contributed to 35 deviations in the mass readings of the cylinders during preparation of the highly precise O2 standard mixtures with the weighing system.The standard uncertainties for the mole fractions of various constituents in the highly precise O2 standard mixtures, which have been prepared using this improved weighing means, are discussed.Additionally, the constituents in the standard mixtures was validated by measuring the mole fractions of CO2 and O2, as well as both Ar/N2 and O2/N2 ratios.To validate the scale of O2/N2 ratio at National Institute of Advanced Industrial Science and Technology (AIST) determined using the highly precise O2 standard mixtures, the O2/N2 ratios for air samples collected at Hateruma Island, Japan obtained from our measurements were preliminary compared with the O2/N2 ratios 5 at Hateruma Island on the scale of National Institute for Environmental Studies (NIES) determined by Tohjima et al. (2005).Also, the mole fractions for Ar and O2 in air samples at Hateruma Island were determined and compared with previously reported values.

Weighing procedure for a high-pressure cylinder 10
The highly precise O2 standard mixtures were prepared in 10 L aluminum cylinders (Luxfer Gas Cylinders, UK), which had a diaphragm valve (G-55, Hamai Industries Limited, Japan) with poly(chlorotrifluoroethylene) (PCTFE) as sealant.The cylinder filled with highly precise O2 standard mixture was hereafter referred to as "gravimetric cylinder."The masses obtained for the gravimetric cylinders were determined using a weighing system which is the same as that reported by Matsumoto et al (2004) except a mass comparator.The mass comparator used in the research 15 of Matsumoto et al. was replaced with a new mass comparator (XP26003L, Mettler Toledo, Switzerland), which had a maximum capacity of 26.1 kg, a readability of 1 mg, and a linearity of 20 mg.The mass measurements for the gravimetric cylinders were performed in a weighing room in which temperature and humidity were controlled at 26 ± 0.5 ºC and 48 ± 1 %, respectively.The temperature, humidity, and atmospheric pressure surrounding the weighing system were measured using a USB connectable logger (TR-73, T & D Corporation, Japan).20 The mass measurement of each gravimetric cylinder was conducted with respect to a nearly identical reference cylinder aiming to reduce any influence exerted by zero-point drifts, sensitivity issue associated with the mass comparator, changes in buoyancy acting on the cylinder, and/or adsorption effects on the cylinder's surface as a result of the presence of water vapor (Alink et al., 2000;Milton et al., 2011).Each weighing cycle for both the gravimetric and reference cylinders consisted of several consecutive weighing operations in the ABBA order sequence, where "A" 25 and "B" denote the reference and gravimetric cylinder, respectively.The process of loading and unloading the cylinders was automated.One complete cycle of the ABBA sequence required five minutes.The mass reading recorded from the weighing system was given by the mass difference, which was computed by subtracting the reference cylinder reading from the gravimetric cylinder reading.
Generally, the outputs of mass comparators are known to be nonlinear, as such, there is a tendency to underestimate 30 or to overestimate the differences in the mass values obtained after each reading.This is because the calibration lines of the comparator tend to be different for various scale ranges.To reduce the influence of this nonlinearity, the cylinders were weighed only when the weight difference between the gravimetric and reference cylinders was less than 500 mg.This was achieved by placing standard weights in the weighing pan alongside each cylinder.Any mass differences obtained for our weighing system took into account the masses and the buoyancies of the standard weights.35 The masses of the standard weights were traced to International System of Units.The standard uncertainties of the masses were 0.25 mg, 0.045 mg, 0.028 mg, 0.022 mg, 0.018 mg, 0.014 mg, 0.011 mg, and 0.0090 mg for the 500 g, 100 g, 50 g, 20 g, 10 g, 5 g, 2 g, and 1 g, respectively.

Preparation of the highly precise O2 standard mixtures
Eleven highly precise O2 standard mixtures were prepared in accordance with ISO 6142-1:2015.Pure CO2 (>99.998%, Nippon Ekitan Corporation, Japan), pure Ar (G1-Grade, 99.9999 %, Japan Fine Products, Japan), pure O2 (G1-Grade, 5 99.9999 %, Japan Fine Products, Japan), and pure N2 (G1-Grade, 99.9999 %, Japan Fine Products, Japan) were used as soruce gases.The value of δ 13 C in pure CO2 (which was adjusted to the atmospheric level) was −8.92 ‰ relative to Vienna Pee Dee Belemnite (VPDB).Impurities in the source gases were identified and quantified using a gas chromatograph with a thermal conductivity detector for N2, O2, CH4 and H2 in pure CO2, a gas chromatograph with a mass spectrometer for O2 and Ar in pure N2 and N2 in pure O2, a Fourier transform infrared spectrometer for CO2, 10 CH4 and CO in pure N2, O2, and Ar, a galvanic cell-type O2 analyzer for O2 in pure Ar, a capacitance-type moisture meter for H2O in pure CO2, and a cavity ring-down-type moisture meter for H2O in pure N2, O2 and Ar.
First, standard mixtures of CO2 in Ar were prepared from pure CO2 and pure Ar using the gravimetric method.The molar ratios of CO2 to Ar were close to the atmospheric ratio of Ar (9340 ppm) to CO2 (400 ppm or 420 ppm).Next, the gravimetric cylinders were filled as follows with the mixtures of CO2 in Ar, pure O2 and pure N2 in a filling room 15 in which the temperature was controlled at 23 ± 1 ºC and humidity was not controlled.The gravimetric cylinder was evacuated using a turbomolecular pump before being weighed using the ABBA technique.Afterward, the evacuated cylinder was filled with the CO2 in Ar standard mixture and weighed again.The mass of the filled CO2 in Ar standard mixture was determined by the difference in mass before and after filling.The masses of filled pure O2 and N2 were also treated in the same manner.The final pressure in the cylinder was 12 MPa, and the masses of the individual gases 20 were approximately 8 g of the CO2 in Ar standard mixture, 300 g of pure O2, and 1000 g of pure N2.

Analytical methods
To validate the constituents in the highly precise O2 standard mixtures, the constituents were measured using a cavity ring-down spectrometer for measuring the mole fraction of CO2, a mass spectrometer for measuring the Ar/N2 and O2/N2 ratios, and a paramagnetic O2 analyzer for measuring the mole fraction of O2. 25

Measurement of CO2 mole fraction
The mole fractions of CO2 were measured using a cavity ring-down spectrometer (G2301, Picarro, USA), which was equipped with a multi-port valve (Valco Instruments Co. Inc., USA) for gas introduction and a mass flow controller (SEC-N112, 100SCCM, Horiba STEC, Japan).Mole fractions were determined using three primary standard gases (364.50 ± 0.14 ppm, 494.04 ± 0.14 ppm, and 500.32 ± 0.14 ppm) that had been prepared from pure CO2 and purified 30 Air (G1 grade, Japan Fine Products, Japan) in accordance with ISO 6142-1:2015, respectively.The value of δ 13 C in pure CO2 (which was adjusted to the atmosphere level) was −8.92 ‰ relative to VPDB.

Measurement of O2/N2 and Ar/N2 ratios
The O2/N2 and Ar/N2 ratios were measured using a mass spectrometer (Thermo Scientific Delta-V) (Ishidoya and Murayama, 2014).The O2/N2 ratio is expressed as δ(O 2 /N 2 ) according to Eq. (1).The Ar/N2 ratio, which is also 35 expressed as δ(Ar/N 2 ), is defined by (2) where the subscripts "sample" and "standard" refer to the sample air and standard air in the same way as δ(O 2 /N 2 ), respectively.In this study, natural air in 48 L aluminum cylinder (Cylinder No. CRC00045), equipped with a diaphragm valve (G-55, Hamai Industries Limited, Japan) was used as the standard air to determine the δ(O2/N2) and 5 δ(Ar/N2) values on the AIST scale (Ishidoya and Murayama, 2014).The mass spectrometer was adapted to simultaneously measure ion beam currents for masses 28 ( 14 N 14 N), 29 ( 15 N 14 N), 32 ( In the case of sample air, it was assumed that both the δ(O2/N2) and δ(Ar/N2) values were equal to those of δ( 16 O 16 O / 14 N 14 N) and δ( 40 Ar/ 14 N 14 N), since the ratios of Ar, O, and N isotopes present in the atmosphere tended to be spatiotemporally constant.On the other hand, the isotopic ratios of pure Ar, O2, and N2 used in this study were different from the atmospheric values listed in Table 1.Consequently, both the δ(O2/N2) and δ(Ar/N2) values in the highly precise O2 standard mixtures were computed using the measurements obtained for 15 N 14 N/ 14 N 14 N , 17   (4) The subscripts "STD" refer to the highly precise O2 standard mixtures that were prepared in this study.The values of 25 15 N 14 N/ 14 N 14 N, 17 O 16 O/ 16 O 16 O, and 18 O 16 O/ 16 O 16 O in both the O2 standard mixtures and standard air were calculated using the isotope abundances of O and N listed in Table 1.The 36 Ar/ 40 Ar ratio for the highly precise O2 standard mixtures was calculated from δ( 36 Ar/ 40 Ar) and ( 36 Ar/ 40 Ar)standard.The value of δ( 36 Ar/ 40 Ar) were determined using the mass spectrometer.The ( 36 Ar/ 40 Ar)standard was determined using the atmospheric value ( 36 Ar/ 40 Ar = 0.003349 ± 0.000004), because the ratio of Ar isotopes in standard air was equal to that of the atmospheric value.On the other 30 hand, the value of 38 Ar/ 40 Ar in the highly precise O2 standard mixtures was 38 Ar/ 40 Ar = 0.000631 ± 0.000004 which was atmospheric values.The atmospheric values of abundance for Ar isotopes were reported in an IUPAC technical report (Böhlk, 2014).A paramagnetic oxygen analyzer (POM-6E, Air Liquide Japan) was used to measure the mole fractions of O2 in the highly precise O2 standard mixtures.Details regarding the analyzer used have been reported by Aoki and Shimosaka (2017).Briefly, the analyzer was equipped with inlets for sample and reference gases (Kocache, 1986).Synthetic air with O2 mole fraction of 20.650 % was used as the reference gas, and the pressures of the reference gas and the sample gas were set at 300 kPa, and 180 kPa, respectively.5

Identifying and minimizing unknown factors of uncertainty
As mentioned before, there were several unknown factors that influenced the differences in mass obtained for the gravimetric and reference cylinders.These factors in uncertainty and the weighing procedure used to minimize them are discussed in this section.
Generally, the mass reading of a cylinder obtained from a mass comparator tends to vary as a result of numerous 10 factors.Buoyancy effects can be caused by changes in the density of the surrounding air due to the variations in ambient temperature, humidity, and pressure, whereas adsorption effects can greatly influence mass readings of the cylinder by the adsorption and desorption of water vapor in surrounding ambient air on the external surface of the cylinder (Alink et al., 2000;Mizushima, 2004Mizushima, , 2007;;Milton et al., 2011).Thermal effects are related to the temperature gradients between the cylinder and surrounding ambient air (Gläser, 1990(Gläser, , 1999;;Mana et al., 2002;Gläser and Borys, 15 2009;Schreiber et al., 2015).They change a weight force of the cylinder through friction forces exerted on the vertical surface of the cylinder and pressure forces on the horizontal surface.Both the friction and pressure forces are caused by the upward or downward flow of air, which was cooled or heated by the cylinder.Mass differences between the gravimetric and reference cylinders tend to deviate from true value when these effects are exerted independently and to varying degrees on the gravimetric and reference cylinders.20 When the ABBA technique is used to perform mass measurements, the deviations become negligible because they are equally exerted on both the gravimetric and reference cylinders under identical experimental conditions.Actually, any buoyancy effects could be canceled by adopting the ABBA technique in our mass measurements (see Section 4.3.1).
However, the temperature on the gravimetric cylinder's surface could change by adiabatic compression of the source gases and the work (evacuating and filling) in the filling room where is different from the weighing room in 25 temperature, whereas adsorption water amounts on the gravimetric cylinder's surface could change by the work in the filling room where is different from the weighing room in humidity.This non-uniformity was assumed to be the main contributor of uncertainties in the obtained mass values (Matsumoto et al., 2008).Therefore, we examined achievement of the equilibrium in both humidity and temperature for the gravimetric cylinder's surface, as well as the surrounding ambient air, before carrying out any measurement for identifying and minimizing the contribution of the 30 non-uniformity.

The time required for equilibration with ambient air
Achieving temperature and humidity equilibrium between the cylinder's surface and surrounding ambient air could be done by placing the cylinder on the weighing system for an appropriate time interval before mass readings.Here the equilibrium at the reference cylinders' surface always maintained because the reference cylinder had been left on 35 the weighing system, whereas the equilibrium of the gravimetric cylinder's surface had often been disturbed by processes of the cylinder evacuation and the gas filling.To quantify the time needed for equilibration after the disturbing, the mass differences between the gravimetric and reference cylinders recorded after evacuation of the gravimetric cylinder and subsequent filling of the source gases were monitored.The values were plotted against the time needed to achieve equilibrium (Figure 1).The equilibrium was considered to be achieved when the standard deviation of the values remained constant for two or more hours and were less than the repeatability value of 0.82 mg 5 (see in Section 4.3.1.).Interesting, the mass differences recorded after evacuating and filling with the CO2 in Ar mixture tended to decrease as time elapsed while those after filling with pure O2 and the N2 gases tended to increase.
The time needed for equilibration is defined as the time elapsed from cylinder evacuation or filling to the point of equilibrium.The equilibrium time was noted as 5 h after complete cylinder evacuation.The times needed to achieve the equilibrium after the cylinders were filled with the relevant gas were different between the filled gas species to 10 some extent.For the CO2 in Ar mixture, the equilibrium was achieved in 3 h to 5 h while 4 h to 5 h were required for O2 equilibration and 7 h to 9 h for N2.It is considered that each equilibrium time have some connection with the temperature of the gravimetric cylinder just after the evacuation and the gas filling, since the mass readings of the gravimetric cylinder decreases depending on increase in its surface temperature as for either thermal effect or adsorption effect.This is because the temperature differences between the gravimetric and reference cylinders was the 15 main factor contributing to the friction and pressure forces of thermal effect at room temperature.The mass difference decreases as the temperature of the gravimetric cylinder becomes higher than that of the reference cylinder.On the other hand, amount of adsorbed water on gravimetric cylinder's surface also decreases with increase of its temperature.
The mass difference decrease as the temperature of the gravimetric cylinder becomes higher than that of the reference cylinder.20 Actually, the deviations in the mass difference values shown in Figure 1 had some connection with the temperature of the gravimetric and reference cylinders, because the gravimetric cylinder's temperature recorded after the evacuation was 2 K lower while the temperatures recorded after filling with the standard CO2 in Ar mixture, pure O2, and pure N2 were −0.7 K, 1 K, and 6 K higher, respectively, than that of the reference cylinder.On the other hand, the temperature of the gravimetric cylinder after the evacuation and the filling depends on amounts of the source gases 25 and the conditions of the weighing room.Considering this, a reference parameter to clearly identify when equilibrium had been achieved was needed to determine more accurately the mass differences between the cylinders and to minimize associated factors of uncertainty.

Deviation of the mass difference by thermal effect
The relationship between the deviation values obtained in the recorded mass differences and the temperature 30 differences on the surface of the gravimetric and reference cylinders was investigated.The results of the closed squares shown in Figure 2 indicate that the deviation was proportional to the temperature differences and slope of the fitting line, which had been obtained by applying linear least square methods to the data.This deviation rate was determined to be −14.3mg K −1 .Although the results indicate that a temperature difference of 0.1 K caused a deviation of 1.4 mg, the deviation in the recorded mass differences ensures the repeatability value of 0.82 mg that is achieved by reducing 35 the temperature difference to below 0.06 K.By conducting measurements of the cylinder temperatures using a thermocouple-type thermometer with the resolution of 0.1 K (TX1001 digital thermometer, probe-90030, Yokogawa cycles (number 5 to 8) were conducted.In this experiment, the temperatures of the cooled or heated cylinder were 1 K to 3 K lower or 10 K to 20 K higher, respectively, than that of the reference cylinder.When the masses were recorded after the temperatures of both the gravimetric and reference cylinders were equivalent, no difference in the values recorded after the cooling and heating cycles was noticed.The reproducibility of the mass difference values was estimated to be 0.44 mg with regards to the standard deviation of the mass difference values shown in Figure 3. 10 The fact that the standard deviation was lower than the repeatability values confirmed the validity of the weighing procedure and indicated that the changes in the mass differences attributable to non-equilibrium conditions were negligible.It was confirmed that the proposed weighing procedure had a repeatability of 0.82 mg.
It is difficult to state whether changes in the mass differences recorded for the cylinders was caused by thermal or adsorption effects simply by analyzing these results.This is because both effects are related to temperature fluctuations.15 However, an important indication that the changes were caused by one factor or the other is related to the fact that thermal effects influenced the slope of the calibration line solely through temperature fluctuations, whereas the adsorption effects influenced the slope of the calibration line via a combination of both ambient temperature and humidity.This is due to the fact that the adsorbed or desorbed amounts of water on the surface of both cylinders is highly dependent on the cylinders' temperature, humidity of the surrounding ambient air, and condition of the 20 cylinder's surface.To determine which of these effects contributed the most to the changes in the mass readings, the relationship between the deviations and temperature differences was investigated under various conditions in the weighing room.Humidity was strictly controlled at 30 %, 50 %, 65 %, and 80 %, whereas the temperature levels were maintained at 22 ºC, 26 ºC, and 29 ºC.As shown in Figure 2, the results indicated that the deviation values did not depend on the humidity and temperature factors.These results indicated that the dominant factor of changes in the 25 mass difference values was temperature-related and not an effect of adsorption.Therefore, we focused on minimizing the impact of any thermal effects during the further experiments.

Preparation of the O2 Standard Mixtures
In this section, we discuss any uncertainty factors associated with the mole fractions of the constituents in the highly precise O2 standard mixtures.The gravimetric mole fraction (  ) of the constituent k (CO2, Ar, O2, and N2) was 30 calculated using the molar mass (  ) and a mole fraction ( , ) of the constituent i (CO2, Ar, O2, N2 and impurities) in the filled gas j (CO2 in Ar standard mixture, pure O2, and pure N2).Additionally, the mass (  ) of the gases filled with the cylinder were incorporated into the Eq. ( 5) in accordance with ISO 6142-1:2015.(5) In this equation, r and q represent the number of source gases j and constituents i, respectively while  , is the mole fraction of the constituent k in the source gas j.Uncertainties ((  )) associated with the gravimetric mole fraction were calculated according to the law of propagation.5 In this equation, () was the standard uncertainty for A. Gravimetric mole fractions of the constituents and their 10 associated uncertainties in the mole fractions for the highly precise O2 standard mixtures prepared in this study were calculated using Eq. ( 5) and Eq. ( 6) and they are listed in Table 2.As noted, the standard uncertainties for the constituents N2, O2, Ar, and CO2 were 0.8 ppm to 1.0 ppm, 0.7 ppm to 0.8 ppm, 0.6 ppm to 0.7 ppm, and 0.03 ppm, respectively.Table 3 lists the contribution of each uncertainty factor to the purity of the source gases, molar masses of the constituents, and masses of the source gases.These correspond to the square roots of the first, second, and third 15 terms found in Eq. ( 6), respectively.Uncertainty factors in the gravimetric mole fractions were mainly those of the masses obtained for the source gases.Contributions from other sources of uncertainty were negligible.The purity of the source gases and molar masses of the constituents i, as well as the masses of the source gases and their associated standard uncertainties are described in Sections 4.1, 4.2, and 4.3.

Purity of source gas 20
Pure O2, N2, Ar, and CO2 were used as source gases to prepare the standard O2 mixtures.The mole fractions of the impurities present in the source gases and their associated standard uncertainties were determined based on the primary standard gases prepared in accordance with ISO 6142-1:2015.When the mole fraction of impurity h was under detection limit (Lh), the mole fractions (xh) and standard uncertainty (u(xh, j)) in the gas j were calculated using the equations  ℎ, =  ℎ, 2 ⁄ and � ℎ, � =  ℎ, 2√3 ⁄ .The calculated values for the impurities and purities of source 25 gases are listed in Table 4.

Molar masses of constituents
The molar masses (  ) of the source gases were calculated using the most recent atomic masses and isotopic abundances reported by the IUPAC.However, IUPAC values for the atomic masses of O and N have large standard uncertainties because they reflect the variability present in the individual isotopic abundances of natural terrestrial 30 matter.Using IUPAC values, the standard uncertainties for the N2 and O2 mole fractions were calculated to be 4 ppm.
In addition, the atmospheric values of their isotopic abundances could not be used for calculating the molar masses of the source gases even though pure O2 and N2 were produced from air.This was because isotopically abundant O and N in the source gases tended to deviate from the corresponding atmospheric value during the production process.
Therefore, the isotopic abundances were precisely determined using mass spectrometry.
To prepare one highly precise O2 standard mixture, pure O2 of two 48 L cylinders were used, whereas pure N2 of three or four 48 L cylinders were used.The abundances of the respective isotopes of O and N were determined based on the ratios of 15 N/ 14 N, 18 O/ 16 O, and 17 O/ 16 O in each the highly precise O2 standard mixture.The ratios of 15 N/ 14 N, 18 O/ 16 O, 5 and 17 O/ 16 O were calculated using the corresponding atmospheric values (Junk and Svec, 1958;Baertschi, 1976;Li et al., 1988;Barkan and Luz, 2005)  The atomic masses of N and O in the source gases, the pure O2 and N2 were determined with the relative standard uncertainties of 0.000029 % and 0.000006 %, respectively.It was shown that the uncertainty in the molar masses is negligible (Table 3).Although the grade and supplier of the pure O2 and N2 used in this study were the same as those 15 of the source gases used by Tohjima et al. (2005), the atomic masses (15.999366(1) for O and 14.006717 (4) for N) obtained for each element were different from Tohjima's reported values (15.999481(8) for O and 14.006677(4) for N).These differences resulted in a deviation of 0.4 ppm and 1.2 ppm for O2 and N2, respectively.Since this results inferred that the ratios of O and N isotopes changed due to production time, the isotopic abundances of O and N in the source gases have to be precisely determined whenever the highly precise O2 standard mixtures is prepared.On the 20 other hand, the standard uncertainties in the atomic mass presented in an IUPAC technical report by De Laeter et al. (2003) were sufficient for further use in the case of Ar and CO2 as source gases.

Determining the masses of the filled gases
The mass of each gas that was filled into the gravimetric cylinders was calculated using the mass differences before and after filling.The standard uncertainty of the resultant mass was calculated by combining the standard uncertainties 25 in the mass differences obtained for each gas before and after filling.To determine the uncertainty in the mass difference, three factors were evaluated i.e., the repeatability, �  � of the mass difference values, permeation, �   � of the source gases during weighing, and buoyancy changes, �  � due to the expansion of the gravimetric cylinder.The standard uncertainties (�  �) were defined according to 30 These factors are discussed in detail in Sections 4.3.1,4.3.2, and 4.3.3.

Repeatability of the mass difference measurements
The repeatability of the weighing system was evaluated by continuously measuring the mass difference between the 35 gravimetric and reference cylinders using the ABBA technique over three days.This is because the preparation of one highly precise O2 standard mixture takes three days.The mass readings were taken after the gravimetric cylinder had been left on the weighing system for at least a week.Using our weighing system, we also obtained density values for the surrounding ambient air for three days by carefully monitoring temperature, humidity, and pressure changes in the surrounding ambient air (Figure 4).Our findings indicated that the obtained mass difference values remained stable during the three-day experiment.The standard deviation of the mass difference values (0.82 mg) are represented as repeatability, �  �.The fact that the mass difference values were not affected by changes in the air density also 5 indicated that buoyancy issues influencing the gravimetric cylinder were canceled out by changes simultaneously affecting the reference cylinder.

Permeation of source gases during weighing
The gravimetric and reference cylinders used in this study have diaphragm valves, which were joined to the cylinders via pipe fittings and sealed with Teflon tape.The seal of diaphragm valves was made from PCTFE, through which 10 gases tended to permeate quite slowly (Sturm, 2004).Since the permeation of the source gases during weighing the cylinders resulted in the evaluation error of the masses for source gases, we examined the permeability of purified air by monitoring the mass difference using the gravimetric cylinder filled with purified air at a pressure of 8 MPa.The changes in the mass difference values were measured over four months.From these results, it was determined that the permeability was 0.013 mg day −1 .This effect was considered to be negligible because it is much lower than the 15 repeatability.As such, the contribution of permeability (�   �) to the standard uncertainty calculations (�  �) was ignored.On the other hand, the permeation amount of the air from the cylinder over a year was calculated to be 4.7 mg.This may cause changes in the composition of the highly precise O2 standard mixture if the mixture is kept for longtime, since the gas permeability depends on the gas species (Sturm, 2004).

Buoyancy effect of cylinder expansion 20
Oh et al. ( 2013) reported that the volume in the 10 L aluminum cylinders linearly increases with changes in the internal pressure, and the volume expansion was determined to be 24 ± 2 ml when the pressure difference in the cylinder was 12 MPa.Tohjima et al. (2005) reported a volume expansion of 22 ± 4 ml when the pressure difference was 10 MPa.
In this study, we adopted that the volume expansion of the cylinders was 55 ± 5 ml, which was measured by a cylinder supplier, when the pressure difference was 25 MPa.Compared to the expansion rates to pressure variations reported 25 by Oh (2.0 ± 0.2 ml MPa −1 ) (2013) and Tohjima (2.2 ± 0.4 ml MPa −1 ) ( 2005), the rate of the cylinders was 2.2 ± 0.2 ml MPa −1 because the factors contributing to uncertainty within these rates tended to remain constant.The pressure differences recorded before and after filling were 0.12 MPa, 2.5 MPa, and 9.4 MPa for CO2 in Ar standard mixture, pure O2, and pure N2, respectively.These pressure differences were subsequently used to calculate buoyancy effects, which were reported as 0.3 mg, 6.4 mg, and 23.9 mg for CO2 in Ar standard mixture, pure O2, and pure N2, respectively.30 In turn, these caused changes in the gravimetric mole fraction of +0.5 ppm and −0.5 ppm for O2 and N2, respectively.
The final mass difference values were corrected to take these changes into account.The standard uncertainties �  � in linear expansion were considered to be negligible.

Validation of the Constituents in the Highly Precise O2 Standard Mixtures
The O2 mole fraction in the highly precise standard mixture would deviate from the gravimetric value if the mole 35 fractions of other constituents have the deviations from the gravimetric values.The gravimetric and measured values for the CO2 mole fractions, δ(Ar/N2), δ(O2/N2), and O2 mole fractions were compared to validate the mole fractions of the constituents in the O2 mole fractions in the highly precise O2 standard mixtures.The values of δ(O2/N2) and δ(Ar/N2) were the deviation from the corresponding values in the standard air on the AIST scale.Table 5 shows the measured δ(O2/N2) and δ(Ar/N2) values calculated using Eq.(3) and Eq.(4), as well as the values for δ( 15 N 14 N/ 14 N 14 N), 16 O / 14 N 14 N), δ( 36 Ar/ 40 Ar), and δ( 38 Ar/ 40 Ar). 5
On the AIST scale, these values corresponded to δ(O2/N2) = 0 and δ(Ar/N2) = 0. Associated standard uncertainties were determined with regards to the law of propagation of uncertainty.

CO2 mole fractions and Ar/N2 ratio
Three primary standard gases were used to measure the CO2 mole fractions in the highly precise O2 standard mixtures.15 Table 2 shows the gravimetric and measured values and associated standard uncertainties.The CO2 mole fractions in the cylinder labeled CPB28679, which had been prepared on 29 March 2017, were not measured.Differences between the gravimetric and measured values (obtained by subtracting the measured value from the gravimetric value) were found to range from −0.17 ppm to 0.03 ppm.The gravimetric values were in line with the measured values, both of which being within the accepted levels of uncertainty.20 From these results, the mass of the CO2 in Ar standard mixture was considered to be valid, since it was based on the mole fraction for the CO2 utilized in this calculation.Figure 5a shows the plot of the measured δ(Ar/N2) values versus the gravimetric δ(Ar/N2) values, as well as the residuals of the measured δ(Ar/N2) values that had been estimated using the line of best fit obtained using least squares method.The standard deviation of the residuals was 78 per meg.This standard deviation represents a scatter in the gravimetric Ar/N2 ratio mole fractions, since the measurement uncertainty 25 for δ(Ar/N2) was much smaller than the obtained standard deviation (Ishidoya and Murayama, 2014).The standard uncertainties for gravimetric δ(Ar/N2) values ranged from 74 per meg to 77 per meg.The standard uncertainties were comparable to the standard deviation values obtained for the residuals, thus supporting that the uncertainty calculations for the constituents, Ar and N2 were valid.

O2 mole fraction and O2/N2 ratio 30
Figure 5b illustrates a plot of the measured O2 mole fractions versus their gravimetric O2 counterparts in the highly precise O2 standard mixtures (Table 2), as well as the residual values, which had been determined from the fitting line obtained using least squares method.The standard deviation of the residuals shown in Figure 5b was determined to be 0.4 ppm, which was less than the standard uncertainties for the gravimetric O2 mole fractions (0.7 ppm to 0.8 ppm).
Figure 5a shows a plot of the measured δ(O2/N2) values listed in Table 5 against the gravimetric δ(O2/N2) values listed 35 in Table 2, as well as the residuals from the fitting line obtained using least squares method.The slope of the fitting line was determined to be 1.00162 ± 0.00029.The δ(O2/N2) values obtained were 0.16 % higher than those of indicate the variations existing on the NIES and AIST scales.They may also imply that the slope of Scripps Institution of Oceanography (SIO) scale was higher than the actual value, since accurate verification of slope was not performed without highly precise O2 standard mixtures.Additionally, other sources of error can exist.For this study, we were unable to directly compare the O2/N2 ratio or the O2 mole fraction between the AIST and NIES scales.If the direct comparison was possible, then the difference between both scales would become clear, and the slope of each scale 5 could be verified by using the highly precise O2 standard mixtures developed by our group.

Determination of atmospheric O2 and Ar mole fractions and comparison with previous data
The mole fractions for atmospheric O2 and Ar were determined based on the δ(O2/N2) and δ(Ar/N2) values for air samples taken at Hateruma Island in 2015.The δ(O2/N2) and δ(Ar/N2) values were −62.8 and −62.8 per meg, respectively.Regarding the (O2/N2)standard and (Ar/N2)standard ratios for the AIST scale, these values were used to 10 calculate the O2/N2 and Ar/N2 ratios using Eq. ( 1) and Eq. ( 2).In 2015, the calculated O2/N2 and Ar/N2 ratios for samples from Hateruma Island were 0.2680701 ± 0.0000013 and 0.011953665 ± 0.0000010, respectively.The mole fractions of O2 and Ar (  2 and   ) were calculated using the aforementioned O2/N2 and Ar/N2 ratios by using the equations below. 15 In these two equations, K is the sum of N2, O2, and Ar mole fractions in the air samples and was estimated to be 999567.8± 0.1 ppm.To calculate this value, the mole fractions of Ne (18.18 ppm), He (5.24 ppm), CH4 (1.82 ppm), 20 Kr (1.14 ppm), H2 (0.52 ppm), N2O (0.32 ppm), CO (0.15 ppm) and Xe (0.09 ppm) reported by Tohjima et al. (2005) and CO2 (404.7 ppm) in 2015 were used.The CO2 mole fraction was average CO2 mole fraction which was measured using a mass spectrometer.The calculated O2 and Ar mole fractions were 209339.1 ± 1.1 ppm and 9334.4 ± 0.7 ppm, respectively.The standard uncertainties were estimated in accordance with the law of propagation of uncertainties.
From 2000 to 2015, it was noted that the O2 mole fraction in the air samples taken at Hateruma decreased by 52.9 ppm 25 with a rate of 3.5 ppm yr −1 .In 2000, Tohjima reported an atmospheric Ar mole fraction of 9333.2 ± 2.1 ppm (2005), whereas the value reported for air samples collected on Korea's Anmyeon Island in 2002 and at Niwot Ridge in 2001 was 9332 ± 3 ppm (Park et al., 2004).Hence, our values for atmospheric Ar were in line with previously reported ones.

Conclusion 30
In this study, we demonstrated that the deviation of difference in mass between the gravimetric and reference cylinders is susceptible to temperature differences between these two cylinders.The contribution degree of the temperature difference was −14.3 mg K −1 .We also indicated that the variations of the mass difference values due to the temperature difference was able to be reduced to negligible levels by weighing both cylinders when the thermal equilibrium was reached.Since the variations mainly depended on temperature differences rather than factors relating to the adsorption 35 phenomena (e.g., the temperature of the gravimetric cylinder and/or the humidity of the ambient air), it was thus, concluded that the changes in the mass differences were influenced solely by thermal effects.
We have developed a preparation technique for the production of highly precise O2 standard mixtures with atmospheric levels of CO2, Ar, O2, and N2.To determine the O2 mole fractions with standard uncertainties of less than 1 ppm, repeatability in measuring the mass difference between the gravimetric and reference cylinders was determined.5 The impact of leakage or permeation of the source gases through the cylinders' valve, as well as change of buoyancy such as the expansion of the gravimetric cylinder as a factor of the cylinder's inner pressure were evaluated.
Additionally, the molar masses of the O2 and N2 source gases were determined based on the abundance of their isotopes.
The standard uncertainties gravimetrically calculated were in good agreement with the standard deviation for the corresponding measured values.This indicates that the uncertainty calculations of the gravimetric values for the 10 constituents performed in this study were accurate and valid.
On the basis of the highly precise O2 standard mixtures, we determined the mole fractions of atmospheric Ar and O2 at Hateruma Island in 2015.These values were 9334.4 ± 0.7 and 209339.1 ± 1.1 ppm, respectively.The atmospheric Ar mole fraction was in line with the values reported by Park (9332 ± 3 ppm) and Tohjima (9333.2 ± 2.1 ppm) (Park et al., 2004;Tohjima et al., 2005).Our research indicated that the atmospheric O2 mole fraction decreased by 52.9 15 ppm between 2000 and 2015 with a rate of 3.5 ppm yr −1 .Table 1.Isotopic composition and atomic masses of pure oxygen and nitrogen used to prepare a highly precise O2 standard mixture for the cylinder labeled CPB28912.

Isotope
Atomic mass  c The abundance of the isotope and the standard uncertainty as determined using calculations for the absolute 15 N/ 14 N ratio obtained by Junk and Svec (1958).d The abundance of the isotope and the standard uncertainty were calculated using 17 O/ 16 O = 12.08 ‰ and 18 O/ 16 O = 23.88 ‰ vs. the VSMOW as determined by Barkan and Luz (2005).The absolute isotope ratio for VSMOW and the 10 standard uncertainty were determined by Li et al. (1988) for 17 O/ 16 O and Baertschi (1976) for 18 O/ 16 O.
e The isotope ratio is defined as the difference in the corresponding atmospheric value (CRC00045) measured using a mass spectrometer.The numbers following the symbol ± denote the standard uncertainty.Table 3.Typical contribution of each source of uncertainty (including the mass of the source gas, molar mass, and purity) to the standard uncertainties obtained for the mole fractions of N2, O2, Ar, and CO2 in a highly precise O2 standard mixture.The numbers following the symbol ± denote the standard uncertainty.

Constituent
"-" represents the constituents which were not measured.

a
The numbers in the parentheses represent the standard uncertainty in the last digits.5 b The atomic mass and the standard uncertainty as determined by De Laeter et al. (2003).

Figure 4
Figure 4 Changes in the mass differences obtained for the gravimetric and reference cylinders and ambient air density for three days.The solid and dashed lines represent the mass differences and ambient air density, respectively.

Figure 5
Figure 5 a) The relationship between the measured and gravimetric values for δ(O2/N2) and δ(Ar/N2) as determined using the 5 AIST scale (upper).The residuals of the values for δ(O2/N2) and δ(Ar/N2) from the fitting line (lower).b) The relationship between the measured and gravimetric values for O2 mole fractions as measured in highly precise O2 standard mixtures (upper).The residuals of the measured O2 mole fraction from the fitting line (lower).

Table 4 .
Impurities in the source gases to prepare highly precise O2 standard mixtures

Table 5 .
Mole fractions and standard uncertainties as determined in highly precise O2 These values were calculated using the AIST scale and were given in per meg.The numbers following the symbol ± denote the standard uncertainty.