Equation Of State For Nitrogen Research Articles

Molecular Dynamics Simulations and a Quintic Equation of State for Nitrogen in a Wide P–T Range, with Validation of a Reference Model up to Ultrahigh P–T Conditions

Molecular Dynamics Simulations and a Quintic Equation of State for Nitrogen in a Wide <i>P–T</i> Range, with Validation of a Reference Model up to Ultrahigh <i>P–T</i> Conditions

Phenomenological High-Pressure Equation of State for Nitrogen, Methane, Methanol, Carbon Dioxide, and Helium

Phenomenological High-Pressure Equation of State for Nitrogen, Methane, Methanol, Carbon Dioxide, and Helium

Solid molecular nitrogen (δ-N2) inclusions in Juina diamonds: Exsolution at the base of the transition zone

Diamonds originating from the transition zone or lower mantle were previously identified based on the chemistry of their silicate or oxide mineral inclusions. Here we present data for such a super-deep origin based on the internal pressure of nitrogen in sub-micrometer inclusions in diamonds from Juina, Brazil. Infrared spectroscopy of four diamonds, rich in such inclusions revealed high concentrations of fully aggregated nitrogen (average of 900 ppm, all in B centers) and almost no platelets. Raman spectroscopy indicated the presence of solid, cubic δ-N2 at 10.9±0.2 GPa (corresponding to a density of 1900 kg/m3). Transmission electron microscopy of two diamonds found two generations of octahedral inclusions: microinclusions (average size: 150 nm, average concentration: 100 ppm) and nanoinclusions (20–30 nm, 350 ppm). EELS detected nitrogen and a diffraction pattern of one nanoinclusion yielded a tetragonal phase, which resembles γ-N2 with a density of 1400 kg/m3 (internal pressure = 2.7 GPa). We also observed up-warping of small areas (∼150 nm in size) on the polished surface of one diamond. The ∼2 nm rise can be explained by a shallow subsurface microinclusion, pressurized internally to more than 10 GPa.Using available equations of state for nitrogen and diamond, we calculated the pressures and temperatures of mechanical equilibrium of the inclusions and their diamond host at the mantle geotherm. The inclusions originated at the deepest part of the transition zone at pressures of ∼22 GPa (630 km) and temperatures of ∼1640 °C. We suggest that both generations are the result of exsolution of nitrogen from B centers and that growth took a few million years in a subducting mantle current. The microinclusions nucleated first, followed by the nanoinclusions. Shortly after the exsolution events, the diamonds were trapped in a plume or an ascending melt and were transported to the base of the lithosphere and later to the surface.

Measurement of the (pressure, density, temperature) relation of two (methane + nitrogen) gas mixtures at temperatures between 240 and 400 K and pressures up to 20 MPa using an accurate single-sinker densimeter

Comprehensive ( p, ρ, T) measurements on two gas mixtures of (0.9CH 4 + 0.1N 2) and (0.8CH 4 + 0.2N 2) have been carried out at six temperatures between 240 and 400 K and at pressures up to 20 MPa. A total of 108 ( p, ρ, T) data for the first mixture and 134 for the second one are given. These measurements were performed using a compact single-sinker densimeter based on Archimedes’ buoyancy principle. The overall uncertainty in density ρ is estimated to be (1.5 · 10 −4 · ρ + 2 · 10 −3 kg · m −3) (coverage factor k = 2), the uncertainty in temperature T is estimated to be 0.006 K (coverage factor k = 2), and the uncertainty in pressure p is estimated to be 1 · 10 −4· p (coverage factor k = 2). The equipment has been previously checked with pure nitrogen over the whole temperature and pressure working ranges and experimental results (35 values) are given and a comparison with the reference equation of state for nitrogen is presented.

A Reference Quality Equation of State for Nitrogen

A new formulation describing the thermodynamic properties of nitrogen has been developed. New data sets which have been used to improve the representation of the p–ρ–T surface of gaseous, liquid and supercritical nitrogen, including the saturated states are now available. New measurements on the speed of sound from spherical resonators have been used to improve the accuracy of caloric properties in gaseous and supercritical nitrogen. State-of-the-art algorithms for the optimization of the mathematical structure of the equation and special functional forms for an improved description of the critical region were used to represent even the most accurate data within their experimental uncertainty. The uncertainty in density of the new reference equation of state ranges from ±0.01% between 270 and 350 K at pressures less than 12MPa, within ±0.02% over all other temperatures less than 550 K and pressures less than 12 MPa, and up to a maximum of ±0.6% at the highest pressures. The equation is valid from the triple point to temperatures of 1000 K and pressures up to 2200 MPa. The new formulation yields a reasonable extrapolation up to the limits of chemical stability of nitrogen as indicated by comparison to experimental shock tube data. Constraints regarding the structure of the equation ensure reasonable extrapolated properties up to temperatures and pressures of 5000 K and 25 GPa. For typical calibration applications, the new reference equation is supplemented by a simple but also highly accurate formulation, valid only for supercritical nitrogen between 270 and 350 K at pressures up to 30 MPa.

Vibrational spectroscopy of materials under extreme pressure and temperature

We have obtained vibrational spectra of molecular materials at simultaneous high pressure and high temperature using the combined techniques of shock wave compression and coherent Raman spectroscopy. The high pressure/high temperature states produced and investigated are similar to those found in the interior of planets and in detonating high explosives. The molecular structures of simple molecular fluids and fluid mixtures, such as of diatomic and triatomic molecules, are inferred from the spectral parameters — Raman frequencies, linewidths, and peak Raman susceptibilities — of the transitions, which are extracted from the spectral data using a standard semi-classical treatment. For a simple diatomic molecule such as N 2, CO or O 2, the measured vibrational frequencies increase with increasing shock pressure. In N 2, above 17 GPa single-shock pressure the vibrational frequency ceases to rise further and appears to begin to decrease. Observation of a further decrease at higher pressures is prevented by the onset of optical opacity. CO and O 2 become optically opaque at pressures insufficient to observe a similar maximum. The vibrational frequencies of CO and N 2 exhibit distinctly different shock pressure dependencies. The data show a factor of 5 smaller vibrational frequency versus pressure slope in CO as in N 2. Under shock compression, mixtures of CO and N 2 show a highly non linear dependence of their vibrational frequencies with mixture mole fraction, while at ambient pressure this dependence is linear. We have also estimated vibrational relaxation times for these simple molecules under shock-compression, using a simple population filling argument for the longitudinal relaxation time (T 1), and from the measured linewidth for the transverse relaxation time (T 2). T 2 shows a strong temperature dependence but little density (pressure) dependence. The intensities of the vibrational hot bands were those expected from a Boltzmann vibrational population distribution, and they were used to estimate vibrational temperatures. These temperatures have been also used to refine the equations of state for nitrogen and argon as well as to understand the effects of non-ideal mixing at these extreme conditions.

The prediction of high-density thermodynamic states using molecular shape factors

A new extended corresponding-states method for the prediction of high-density states for pure fluids is presented. The method incorporates the use of molecular shape factors. This approach requires accurate equations for the saturated-liquid density and the vapor pressure for the fluid in question. In addition, an equation of state for the vapor phase is also required. With this information, the molecular shape factors are calculated on the saturated-liquid line of the fluid being predicted, and they are assumed to be constant in the high-density, single-phase region along isotherms. This property prediction method is well suited for application to any fluid that has an equation of state valid in the vapor phase. Modern equations of state for nitrogen and oxygen were used to define properties of reference fluids in the development and testing of this new method. Experimental data for liquid ethylene were used to verify the accuracy of the new prediction method. Tests have shown that this approach predicts high-density data accurately to approximately six times the critical pressure and up to 85 % of the critical temperature. The results of these tests are presented and discussed.

Measurement and correlation of the (pressure, density, temperature) relation of nitrogen in the temperature range from 273.15 to 323.15 K at pressures up to 8 MPa

Comprehensive ( p, ϱ, T) measurements on pure nitrogen were carried out in the temperature range from 273.15 to 323.15 K at pressures up to 8 MPa. The precision of the density is better than ± 0.01 per cent or ± 0.001 kg·m −3, whichever is greater. Comparisons with experimental results of previous workers are presented. A truncated virial equation with four adjusted parameters has been established for the gas range investigated which represents the density of nitrogen with an uncertainty of less than ±0.01 per cent. The density under standard conditions (273.15 K, 0.101325 MPa) was calculated from this equation as ϱ s = (1.25039±0.00007) kg·m −3. The second and third virial coefficients were determined with an uncertainty of less than 0.17 cm 3·mol −1 or 75 (cm 3 · mol −1) 2, respectively. The truncated virial equation is compared with two current equations of state for nitrogen and with two equations of state for the determination of the compression factor of natural gas; the deviations are less than 0.03 per cent.

Theoretical equations of state for molecular fluids: nitrogen, oxygen, and carbon monoxide

Equations of state for nitrogen, oxygen, and carbon monoxide are derived and compared to experimental data. It is shown how to separate vibrational and rotational degrees of freedom from translational motion in computing statistical averages. Translational contributions can be computed by treating the molecules as spherical particles moving in a potential field which is averaged over the internal degrees of freedom. Agreement with experimental data is good.

An equation of state for dense nitrogen

An empirical equation of state for nitrogen at high pressure and density is considered. It is shown that for nitrogen at densities greater than 0.6 g/cm3, by using available data [1–3] on static compression of gaseous nitrogen and shock compression of liquid nitrogen, it is possible to construct a Mie-Gruneisen type equation of state which gives a pressuredensity relationship close to experiment along the shock adiabat of liquid nitrogen and agrees with the calculations of other authors for temperature values beyond the shock-wave front [2–3]. Heat capacity, entropy, and Gruneisen coefficient values beyond the shock-wave front in liquid nitrogen are calculated.

The determination of equations of state for nitrogen and oxygen

Methods of developing accurate thermodynamic equations of state for oxygen and nitrogen using least squares fitting to experimental data from the literature are presented and evaluated. A discussion of the critical evaluation and selection of experimental data is included. The selection of an appropriate functional form for the equation of state, weighting of the data points for least squares fitting, and the simultaneous fitting of various thermodynamic data including PVT data, isochoric heat capacity measurements, and saturation density values are presented. The resulting equation accurately represents all the data, and exhibits correct functional behaviour for the PVT surface and the derivatives used in the calculation of derived properties. Techniques of constraining the equation of state to be consistent with measured critical point parameters and with a vapour pressure equation determined from separate measurements of saturation properties are discussed. The equations developed in the work described here conform to the Maxwell criterion and may be used for the calculation of properties by continuous integration along isotherms through the two-phase region. Comparisons of the selected property values calculated from the equations of state with experimental PVT, C p, and C v data used in the development of equations are included. The calculations of the liquid properties by continuous integration along the isotherms and by use of the Clapeyron equation are compared.