Recent quantum mechanical calculations of the interaction energy of pairs of helium atoms are accurate and some include reliable estimates of their uncertainty. We combined these ab initio results with earlier published results to obtain a helium-helium interatomic potential that includes relativistic retardation effects over all ranges of interaction. From this potential, we calculated the thermophysical properties of helium, i.e., the second virial coefficients, the dilute-gas viscosities, and the dilute-gas thermal conductivities of 3He, 4He, and their equimolar mixture from 1 K to 104 K. We also calculated the diffusion and thermal diffusion coefficients of mixtures of 3He and 4He. For the pure fluids, the uncertainties of the calculated values are dominated by the uncertainties of the potential; for the mixtures, the uncertainties of the transport properties also include contributions from approximations in the transport theory. In all cases, the uncertainties are smaller than the corresponding experimental uncertainties; therefore, we recommend the ab initio results be used as standards for calibrating instruments relying on these thermophysical properties. We present the calculated thermophysical properties in easy-to-use tabular form.

Since 2000, atomic physicists have reduced the uncertainty of the helium-helium “ab initio” potential; for example, from approximately 0.6 % to 0.1 % at 4 bohr, and from 0.8 % to 0.1 % at 5.6 bohr. These results led us to: (1) construct a new inter-atomic potential ϕ07, (2) recalculate values of the second virial coefficient, the viscosity, and the thermal conductivity of 4He from 1 K to 10,000 K, and (3), analyze the uncertainties of the thermophysical properties that propagate from the uncertainty of ϕ07 and from the Born-Oppenheimer approximation of the electron-nucleon quantum mechanical system. We correct minor errors in a previous publication [J. J. Hurly and M. R. Moldover, J. Res. Nat. Inst. Standards Technol. 105, 667 (2000)] and compare our results with selected data published after 2000. The ab initio results tabulated here can serve as standards for the measurement of thermophysical properties.

We determined the zero-density viscosity η Ar 0,T and thermal conductivity λ Ar 0,T of argon with a standard uncertainty of 0.084% in the temperature range 200 K to 400 K. This uncertainty is dominated by the uncertainty of helium's viscosity η He 0,T , which we estimate to be 0.080% based upon the difference between ab initio and experimental values at 298.15 K. Our results may improve (1) the argon-argon interatomic potential, (2) calculated boundary-layer corrections for primary acoustic thermometry, and (3) calibrations of laminar flow meters as well as instruments for measuring transport properties. At 298.15 K, we determined the ratio η Ar 0,298 /η He 0,298 = 1.138 00 ± 0.000 13 from measurements of the flow rate of these gases through a quartz capillary while simultaneously measuring the pressures at the ends of the capillary. Between 200 K and 400 K, we used a two-capillary viscometer to determine η Ar 0,T /η He 0,T = 1.211 67 − 0.820 34 exp(−T /123.78 K) with an uncertainty of 0.024%. From η Ar 0,T /η He 0,T , we computed η Ar 0,T using the values of η He 0,T calculated ab initio. Finally, we computed the thermal conductivity of argon from η Ar 0,T and values of the Prandtl number that we computed from argon-argon interatomic potentials.

Second virial coefficient data and viscosity were used to evaluate effective isotropic intermolecular potential functions proposed in the literature for sulfur hexafluoride. It was found that none of the potentials could predict the properties simultaneously. We have constructed a Morse–Morse–Spline–van der Waals (MMSV) potential which satisfactorily correlates second virial coefficient and viscosity data at the same time.