Equation Of State For Helium Research Articles

Accurate quantum-corrected cubic equations of state for helium, neon, hydrogen, deuterium and their mixtures

Cubic equations of state have thus far yielded poor predictions of the thermodynamic properties of quantum fluids such as hydrogen, helium and deuterium at low temperatures. Furthermore, the shape of the optimal α functions of helium and hydrogen have been shown to not decay monotonically as for other fluids. In this work, we derive temperature-dependent quantum corrections for the covolume parameter of cubic equations of state by mapping them onto the excluded volumes predicted by quantum-corrected Mie potentials. Subsequent regression of the Twu α function recovers a near classical behavior with a monotonic decay for most of the temperature range. The quantum corrections result in a significantly better accuracy, especially for caloric properties. While the average deviation of the isochoric heat capacity of liquid hydrogen at saturation exceeds 80% with the present state-of-the-art, the average deviation is 4% with quantum corrections. Average deviations for the saturation pressure are well below 1% for all four fluids. Using Péneloux volume shifts gives average errors in saturation densities that are below 2% for helium and about 1% for hydrogen, deuterium and neon. Parameters are presented for two cubic equations of state: Peng–Robinson and Soave–Redlich–Kwong. The quantum-corrected cubic equations of state are also able to reproduce the vapor-liquid equilibrium of binary mixtures of quantum fluids, and they are the first cubic equations of state that are able to accurately model the vapor-liquid equilibrium of the helium–neon mixture. Similar to the quantum-corrected Mie potentials that were used to develop the covolume corrections, an interaction parameter for the covolume is needed to represent the helium–hydrogen mixture to a high accuracy. The quantum-corrected cubic equation of state paves the way for technological applications of quantum fluids that require models with both high accuracy and computational speed.

Molecular dynamics modeling of helium bubbles in austenitic steels

Abstract The austenitic steel devices from pressurized water reactors are continuously subjected to neutron irradiation that produces crystalline point defects and helium atoms in the steel matrix. These species evolve into large defects such as dislocation loops and helium filled bubbles. This paper analyzes, through molecular dynamics simulations with recently developed interatomic potentials, the impact of the helium/steel interface on the helium behavior in nanosize bubbles trapped in an austenitic steel matrix. It is shown that the repulsive helium-steel interactions induce higher pressures in the bubble compared to bulk helium at the same temperature and average density. A new equation of state for helium is proposed in order to take into account these interface effects.

Modification of the Peng–Robinson equation of state for helium in low temperature regions

ABSTRACTHelium shows the nearest behaviour to ideal gas in the room conditions. In contrast, thermodynamic behaviour of helium in the critical region, in which its liquefaction is possible, is extremely complicated. The equation of state (EOS), which is in common use for helium, is the modified Benedict–Webb–Rubin (MBWR) EOS developed by McCarty and Arp which is a 13th-order equation with 32 substance-dependent parameters. MBWR is a complicated EOS and its use is time consuming. In this work, the modified Peng–Robinson EOS introduced by Feyzi et al. is customised with 10 adjustable parameters for helium in the temperature range of 2.20–15.20 K and pressures up to 16 bar. The proposed EOS is able to predict the properties of helium in the vapour–liquid equilibrium (VLE) conditions and in the single gas-phase region. In addition, a temperature-dependent correlation for constant pressure heat capacity of helium from very low up to normal temperatures is proposed. The liquefaction process of helium, which is being done by cooling it to very low temperatures by passing through a Joule–Thomson valve, is predicted by the proposed EOS. Very accurate results are observed.

Schrödinger-Poisson model for very-high-pressure cold helium

An alternative numerical solution of the Hartree-Fock integro-differential equations is reported that consists of reformulating the self-consistent ansatz as a nonlinear set of coupled Schr\odinger and Poisson equations. In the simple case of helium, this yields an amazingly simple dynamical system whose statistical properties are constrained by the virial theorem. This approach leads to an equation of state for helium at zero temperature and very high densities, covering the whole range of astrophysical interest, up to the pressure ionization phase transition that is predicted around 44 Mbar by the present model.

Equations of state for helium, hydrogen, deuterium, nitrogen, oxygen, carbon monoxide, carbon dioxide, and methane at high temperatures and pressures

Equations of state are constructed for He, Ar, H2, D2, N2,O2, CO, CO2, and CH4 in the temperature range of (1–20) × 103 K and at pressures up to 40 GPa on the basis of the model of canonical equation of state previously proposed by us.

The study of bubble formation in 316L stainless steel irradiated with helium ions at 873 K

Samples of solution annealed (SA) and 20% cold worked (CW) 316L austenitic stainless steel were irradiated with 2.5 MeV helium ions at 873 K. The ion fluence is 2.0 × 10 17 ions/cm 2 and flux is 2.11 × 10 12 ions/cm 2s. The bubble morphology and distribution along ion penetrating depth were observed with transmission electron microscope (TEM). Bubbles are faceted and the mechanism underlying bubble nucleation seems to be in the transition regime of di-atomic nucleation and multi-atomic nucleation in the SA sample. Helium depth distribution was deduced from the measured bubble size and density with the help of high density equation of state for helium. At the same irradiation condition, dislocations introduced in the CW sample before irradiation can increase bubble nucleation rate and decrease bubble growth rate. The swelling produced by bubbles is smaller in CW sample.

The role of gas pressure and lateral stress on blistering

Both gas pressure in bubbles and lateral stress have been suggested as primary causes of blistering. An analysis of both mechanisms is presented, and the conditions for blistering are examined. To realistically predict the gas pressure in bubbles, a recently derived high-density equation of state for helium is utilized. It is shown that the formation of overpressurized gas bubbles leads to a state of stress in the surface layer which is a superposition of a tensile microstress surrounding the bubbles and a lateral compressive macrostress across the bombarded layer. When the microstress reaches a value of 0.003 μ for fcc metals or 0.009 μ for bcc metals, interbubble fracture occurs. These critical values are reached for an implanted helium concentration between 20 to 40%. The exact value depends to some degree on the bubble density, the temperature, and the helium to vacancy ratio. The lateral stress is shown to saturate prior to the onset of blistering, but it remains the driving force for blister dome formation once a sufficiently large area of the bombarded layer is detached.

A method of calculating the numerical equation of state for helium below 6 absolute, and of estimating the relative importance of gas degeneracy and inter-atomic forces

Gas (the effect of non-Maxwellian distribution of molecular velocities) is distinguished from gas (the effect of intermolecular forces), and it is shown that specific heat measurements cannot be used to verify theories of the former, unless account is taken of the very rapid increase of the latter at the lowest temperatures and highest pressures. Accordingly a thermodynamic method is used to calculate the sum of degeneracy and imperfection at 4° and 5° Abs. for helium. Theories of degeneracy can then be roughly tested by the extent to which they allow a residual value of the imperfection to be calculated, and determine a consistent extension of the course taken by isothermals down to 15°. The method is applied to Fermi's expressions for degeneracy, and also to Berthelot's equation of state. One of the equations alone satisfies the required condition; it is shown that on this basis degeneracy would comprise 15 per cent. of the total departure of helium from the ideal gas laws at 4° and 5°, the remainder being due to true imperfection or intermolecular forces.