Ab Initio Calculation of Fluid Properties for Precision Metrology

Abstract

Recent advances regarding the interplay between ab initio calculations and metrology are reviewed, with particular emphasis on gas-based techniques used for temperature and pressure measurements. Since roughly 2010, several thermophysical quantities – in particular, virial and transport coefficients – can be computed from first principles without uncontrolled approximations and with rigorously propagated uncertainties. In the case of helium, computational results have accuracies that exceed the best experimental data by at least one order of magnitude and are suitable to be used in primary metrology. The availability of ab initio virial and transport coefficients contributed to the recent SI definition of temperature by facilitating measurements of the Boltzmann constant with unprecedented accuracy. Presently, they enable the development of primary standards of thermodynamic temperature in the range 2.5–552 K and pressure up to 7 MPa using acoustic gas thermometry, dielectric constant gas thermometry, and refractive index gas thermometry. These approaches will be reviewed, highlighting the effect of first-principles data on their accuracy. The recent advances in electronic structure calculations that enabled highly accurate solutions for the many-body interaction potentials and polarizabilities of atoms – particularly helium – will be described, together with the subsequent computational methods, most often based on quantum statistical mechanics and its path-integral formulation, that provide thermophysical properties and their uncertainties. Similar approaches for molecular systems, and their applications, are briefly discussed. Current limitations and expected future lines of research are assessed.

Four-Body Nonadditive Potential Energy Surface and the Fourth Virial Coefficient of Helium

“…In eq , the average ⟨·⟩ is performed over the configuration of ring polymers sampled according to the path-integral prescription, and r i is the position of the first bead of the ring polymer associated with particle i . The overbar represents the average interaction potential among the ring polymers, as specified by the path-integral approach . We performed the integration over the coordinates r i using the VEGAS Monte Carlo algorithm as implemented in the Cuba library, using 10 6 evaluations.…”

“…The propagation of the uncertainty of the potentials to the uncertainty in D ( T ) was performed using the functional-differentiation approach . In particular, we have δ D 32 false( T false) = β N normal A ∫ true| ⟨ δ u 3 ̅ false( 4 normale − β V̅ 4 − 4 normale − β V̅ 3 + 12 normale − β V̅ 3 ( e − β V̅ 2 − 1 ) false) ⟩ true| ∏ i = 1 4 d r i / V δ D 43 false( T false) = β N normal A ∫ false⟨ δ u 4 ̅ exp false( − β V̅…”

“…The propagation of the uncertainty of the potentials to the uncertainty in D(T) was performed using the functionaldifferentiation approach. 1 In particular, we have…”

“…Standards for high-accuracy temperature and pressure metrology increasingly rely on acoustic, dielectric, or refractive measurements of gases. In recent years, the accuracy of these temperature and pressure determinations has been greatly improved by the ability to compute properties of noble gases, particularly helium, at low and moderate pressures based on ab initio quantum calculations . Example applications include a primary gas-pressure standard with relative uncertainties as small as 5 ppm (1 ppm = 10 –6 ) at pressures up to 7 MPa, , dielectric-constant gas thermometry in relation to determination of the Boltzmann constant, and refractive-index gas thermometry at temperatures below 25 K that is able to measure the thermodynamic temperature with uncertainties on the order of 0.1 mK …”

Small corrections to 1989 NIST constant-volume gas thermometry data

“…The ability to determine thermodynamic temperature continues to improve due to advances in gas-based metrology based on acoustic, dielectric, and refractivity techniques, enabled in part by the ability to calculate thermophysical properties of helium gas from first principles [7]. Improved values of (T − T 90 ) were recently presented by a CCT working group [8], but this recommendation was limited to temperatures below 335 K where most of the new data have been measured.…”