Modeling of liquid internal energy and heat capacity over a wide pressure–temperature range from first principles

Recently, there have been significant theoretical advances in our understanding of liquids and dense supercritical fluids based on their ability to support high frequency transverse (shear) waves. Here, we have constructed a new computer model using these recent theoretical findings (the phonon theory of liquid thermodynamics) to model liquid internal energy across a wide pressure–temperature range. We have applied it to a number of real liquids in both the subcritical regime and the supercritical regime, in which the liquid state is demarcated by the Frenkel line. Our fitting to experimental data in a wide pressure–temperature range has allowed us to test the new theoretical model with hitherto unprecedented rigor. We have quantified the degree to which the prediction of internal energy and heat capacity is constrained by the different input parameters: the liquid relaxation time (initially obtained from the viscosity), the Debye wavenumber, and the infinite-frequency shear modulus. The model is successfully applied to output the internal energy and heat capacity data for several different fluids (Ar, Ne, N2, and Kr) over a range of densities and temperatures. We find that the predicted heat capacities are extremely sensitive to the values used for the liquid relaxation time. If these are calculated directly from the viscosity data, then, in some cases, changes within the margins of the experimental error in the viscosity data can cause the heat capacity to exhibit a completely different trend as a function of temperature. Our code is computationally inexpensive, and it is available for other researchers to use

Raman spectroscopy of ethane (C 2 H 6 ) to 120 GPa at 300 K

We have conducted a Raman study of solid ethane (C2H6) at pressures up to 120 GPa at 300 K. We observe changes within the ν3 and ν11 Raman‐active vibrational modes providing evidence for several previously unobserved phase transitions at room temperature. These are located from 16 to 20 GPa, ~35 GPa, and ~60 GPa. We also could no longer measure the ν3 and ν11 modes from 75 GPa onward. We did not, however, observe any signs of the ethane molecule undergoing decomposition, up to the highest pressures measured. We also recorded spectra of the (2ν8, 2ν11), ν1, and ν10 modes but observed more limited changes in the behaviour of these modes

Electric discharge machine for preparation of diamond anvil cell sample chambers

We have designed and constructed a novel electric discharge machine designed primarily for the preparation of sample chambers in rhenium and stainless steel gaskets for diamond anvil cell experiments. Our design combines automatic stage movement with relatively low voltage (100 V) operation and routinely achieves a drilling/erosion speed of approximately 0.4 μms−1. The machine is used for preparing 100 μm diameter sample chambers for diamond anvil cell experiments with 250 μm culets and has also been used to prepare 50 μm diameter sample chambers for diamond anvil cell experiments with 100 μm culets to access a pressure of 165 GPa

Observation of liquid–liquid phase transitions in ethane at 300 K

We have conducted Raman spectroscopy experiments on liquid ethane (C2H6) at 300 K, obtaining a large amount of data at very high resolution. This has enabled the observation of Raman peaks expected but not previously observed in liquid ethane and a detailed experimental study of the liquid that was not previously possible. We have observed a transition between rigid and nonrigid liquid states in liquid ethane at ca. 250 MPa corresponding to the recently proposed Frenkel line, a dynamic transition between rigid liquid (liquidlike) and nonrigid liquid (gaslike) states beginning in the subcritical region and extending to arbitrarily high pressure and temperature. The observation of this transition in liquid (subcritical) ethane allows a clear differentiation to be made between the Frenkel line (beginning in the subcritical region at higher density than the boiling line) and the Widom lines (emanating from the critical point and not existing in the subcritical region). Furthermore, we observe a narrow transition at ca. 1000 MPa to a second rigid liquid state. We propose that this corresponds to a state in which orientational order must exist to achieve the expected density and can view the transition in analogy to the transition in the solid state away from the orientationally disordered phase I to the orientationally ordered phases II and III

Derivation of the field due to a magnetic dipole without use of the vector potential

The mathematical form of the magnetic field due to a current loop, and the fact that it is identical to the electric field due to an electric dipole in the far field, are fundamental to our understanding of electromagnetism. While undergraduate level electromagnetism textbooks usually derive the electric field from an electric dipole, few derive the magnetic field from a current loop. Most simply state it without proof, or perform the derivation for simpler cases such as the on-axis field. Those that perform the derivation use the magnetic vector potential, a relatively advanced concept that most undergraduate students would not encounter until their final year of study, if at all. Here, a simple derivation to obtain the magnetic field due to a current loop in the far-field approximation is presented. The derivation begins from the Biot–Savart law and does not require the vector potential. The problem is set up so that only a single integration is necessary (from angle α = 0 to α = 2π around the current loop), and the result is compared with that for the electric field surrounding an electric dipole

High pressure Raman, optical absorption, and resistivity study of SrCrO4

We studied the electronic and vibrational properties of monazite-type SrCrO4 under compression. The study extended the pressure range of previous studies from 26 to 58 GPa. The existence of two previously reported phase transitions was confirmed at 9 and 14 GPa, and two new phase transitions were found at 35 and 48 GPa. These transitions involve several changes in the vibrational and transport properties with the new high-pressure phases having a conductivity lower than that of the previously known phases. No evidence of chemical decomposition or metallization of SrCrO4 was detected. A tentative explanation for the reported observations is discussed

Melting curve and phase diagram of vanadium under high-pressure and high-temperature conditions

We report a combined experimental and theoretical study of the melting curve and the structural behavior of vanadium under extreme pressure and temperature. We performed powder x-ray diffraction experiments up to 120 GPa and 4000 K, determining the phase boundary of the bcc-to-rhombohedral transition and melting temperatures at different pressures. Melting temperatures have also been established from the observation of temperature plateaus during laser heating, and the results from the density-functional theory calculations. Results obtained from our experiments and calculations are fully consistent and lead to an accurate determination of the melting curve of vanadium. These results are discussed in comparison with previous studies. The melting temperatures determined in this study are higher than those previously obtained using the speckle method, but also considerably lower than those obtained from shock-wave experiments and linear muffin-tin orbital calculations. Finally, a high-pressure high-temperature equation of state up to 120 GPa and 2800 K has also been determined

Krypton and the fundamental flaw of the Lennard-Jones Potential

We have performed a series of neutron scattering experiments on supercritical krypton. Our data and analysis allow us to characterize the Frenkel line crossover in this model monatomic fluid. The data from our measurements was analyzed using Empirical Potential Structure Refinement to determine the short- and medium-range structure of the fluids. We find evidence for several shells of neighbors which form approximately concentric rings of density about each atom. The ratio of second to first shell radius is significantly larger than in any crystal structure. Modeling krypton using a Lennard-Jones potential is shown to give significant errors, notably that the liquid is overstructured. The true potential appears to be longer ranged and with a softer core than the 6–12 powerlaws permit

Transition from gas-like to liquid-like behavior in supercritical N2

We have studied in detail the transition from gas-like to rigid liquidlike behavior in supercritical N2 at 300 K (2.4 TC). Our study combines neutron diffraction and Raman spectroscopy with ab initio molecular dynamics simulations. We observe a narrow transition from gas-like to rigid liquid-like behavior at ca. 150 MPa, which we associate with the Frenkel line. Our findings allow us to reliably characterize the Frenkel line using both diffraction and spectroscopy methods, backed up by simulation, for the same substance. We clearly lay out what parameters change, and what parameters do not change, when the Frenkel line is crossed

High pressure photoluminescence of bismuth-doped yttria-alumina-silica glass

We report the effects of high pressure, up to 10.45 GPa, on the photoluminescence of Bi-doped yttria-alumina-silica (Bi:YAlSi) glass under 532 nm excitation. We identify three emission bands attributed to Bi3+, Bi+ and the controversial NIR emitting Bi centre, BiNIR. As the pressure is increased up to ~6 GPa, an irreversible discontinuity in the trend for emission band energies indicates that an irreversible structural modification occurs. This irreversible discontinuity results in the peak energy of emission bands attributed to Bi+ and BiNIR shifting from those typical of Bi-doped oxide glasses to those observed in Bi-doped gallium-lanthanum-sulfide (Bi:GaLaS) glass. The Bi3+ emission band can be almost eliminated at ~6 GPa, but its intensity increases rapidly as the pressure in further increased. The ability we report here to irreversibly modify the emission of Bi-doped glass using pressure treatment adds an extra degree of freedom in the processing parameters available to researchers looking to optimize the emission from Bi-doped glasses