Improving acoustic determinations of the Boltzmann constant with mass spectrometer measurements of the molar mass of argon

Abstract

We determined accurate values of ratios among the average molar masses M Ar of 9 argon samples using two completely-independent techniques: (1) mass spectrometry and (2) measured ratios of acoustic resonance frequencies. The two techniques yielded mutually consistent ratios (RMS deviation of 0.16 × 10 −6 M Ar from the expected correlation) for the 9 samples of highly-purified, commercially-purchased argon with values of M Ar spanning a range of 2 × 10 −6 M Ar . Among the 9 argon samples, two were traceable to recent, accurate, argon-based measurements of the Boltzmann constant k B using primary acoustic gas thermometers (AGT). Additionally we determined our absolute values of M Ar traceable to two, completely-independent, isotopic-reference standards; one standard was prepared gravimetrically at KRISS in 2006; the other standard was isotopically-enriched 40 Ar that was used during NIST's 1988 measurement of k B and was sent to NIM for this research. The absolute values of M Ar determined using the KRISS standard have the relative standard uncertainty u r (M Ar ) = 0.70 × 10 −6 (Uncertainties here are one standard uncertainty.); they agree with values of M Ar determined at NIM using an AGT within the uncertainty of the comparison u r (M Ar ) = 0.93 × 10 −6 . If our measurements of M Ar are accepted, the difference between two, recent, argon-based, AGT measurements of k B decreases from (2.77 ± 1.43) × 10 −6 k B to (0.16 ± 1.28) × 10 −6 k B . This decrease enables the calculation of a meaningful, weighted average value of k B with a uncertainty u r (k B ) ≈ 0.6 × 10 −6 .

Determination of the molar mass of argon from high-precision acoustic comparisons

“…The samples for the comparison originated from very different sources. For the four samples listed in table 1, the averages of the molar masses span the fractional range of 1.3 × 10 −6 , which is comparable to the range (1.9 × 10 −6 ) spanned by the 15 samples reported in [8]. …”

“…Moreover, square speeds of sound derived from frequencies of different acoustic modes are spread by fractional differences of only (2 to 5) × 10 −7 , and so their ratio for two ideal gases can be obtained at a similar level of uncertainty. Such a level is comparable with that achieved using advanced mass spectrometry referenced to a standard reference gas mixture [8, 11, 12]. Thus, measurements using Method I can be compared to those using Method II and vice versa.…”

“…This is attributed to the different history of Samples C(1) and C(2) and the reproducibility of Method II. According to the analysis based on the intensive study in [8], M A(1) has to be decreased by 0.39 × 10 −6 from its value given in 2010 [14]. Thus, the fractional difference ( M A(1) − M A )/ M A is updated to 1.00 × 10 −6 .…”

“…Also shown are the data points from the 2014 study (circles) [8] and the atmospheric argon composition by Nier (triangle) [15] and Lee (square) [11]. Two lines in the figure represent mass fractionation lines that pass through the Lee measurement (solid) [11], and the KRISS 2014 measurements (dashed) [8]. The updated value is within the spread of measurements from the fractionation line that represents the data set from the 2014 measurements, but the old value was closer to the fractionation of the two atmospheric argon measurements by Nier or Lee.…”

“…To resolve the discrepancy, a collaborative study of the samples was performed using two methods: acoustic resonance frequency ratios (hereafter Method I) at the Laboratorie Commun de Metrologie—Conservatoire National des Arts et Métiers (LNE-CNAM) and National Institute of Metrology (NIM), and gravimetric mass spectrometry (Method II) at the Korea Research Institute of Standards and Science (KRISS). In a previous paper [8], a concise description of the work performed at NIM was given. Here, the experiment is described more thoroughly and the analysis is refined with the benefit of hindsight, and the work is presented in a broader context with an eye to future applications.…”