Characterization of the High-Pressure and High-Temperature Phase Diagram and Equation of State of Chromium

The high-pressure and high-temperature melting curve of chromium has been investigated both experimentally (in situ), using a laser-heated diamond-anvil cell technique coupled with synchrotron powder X-ray diffraction, and theoretically, using ab initio density-functional theory simulations. In the pressure–temperature range covered experimentally (up to 90 GPa and 4500 K, respectively) only the solid body-centred-cubic and liquid phases of chromium have been observed. Experiments and computer calculations give melting curves in agreement with each other, that can be described by a Simon–Glatzel equation Tm(P) = 2136K(1+P/25.9) 0.41. In addition, a quasi-hydrostatic equation of state at ambient temperature has been experimentally characterized up to 131 GPa and compared with the present simulations. Both methods give very similar third-order Birch-Murnaghan equations of state with a bulk modulus of 182-185 GPa and its pressure derivative of 4.74-5.15. According to the present calculations, the obtained melting curve and equation of state are valid at least up to 815 GPa, being the melting temperature at this pressure 9310 K. Finally, from the obtained results, it was possible to determine a thermal equation of state of chromium valid up to 65 GPa and 2100 K.

One-dimensional thermal equation modeled on a two-dimensional heat exchanger with variable solid-fluid interface

In this study, we are to present that a one-dimensional equation for vertically averaged temperature, modeled on a vertically thin, two-dimensional heat exchanger with variable top solid-fluid interface, recovers the two-dimensional thermal information, i.e. steady temperature and flux distribution on the top and temperature-fixed bottom faces. The relative error of these quantities is less than 5% with the maximum gradient of the height kept approximately below 0.5, while the computational time is reduced to 0.1–5%, when compared with direct two-dimensional computations, depending on the shape of the top face. The model equation, derived by the vertical averaging of the two-dimensional thermal conduction equation, is closed by an approximation that the heat exchanger is sufficiently thin in the sense that the second derivative of temperature with respect to the horizontal coordinate depends only on the coordinate. In this model equation, the fluid equation above the exchanger is decoupled by a conventional equation for the normal heat flux on the top surface. In principle, however, the coupling of the model and the fluid equation is possible through the temperature and heat flux on the top interface, recovered by the model equation. The type of mathematical modeling can be applicable to a wide variety of bodies with extremely small dimensions in some (coordinate-transformed) directions.

Ingeniería termodinámica. Ecuación de estado térmica de fluidos mediante experimentación / Engineering thermodynamics. Thermal equation of fluids by experimentation / Ingénierie thermodynamique. Équation d'etat thermique par l'expérimentation.

En muchas industrias se emplean fluidos en los procesos de producción. Estos fluidos, sean líquidos, gases o mezclas de ambos, se almacenan en depósitos y se transportan por conductos en las instalaciones industriales. El volumen que cada kilogramo de fluido ocupa en estas instalaciones puede variar si también lo hacen su presión y temperatura. Encontrar esta interdependencia entre presión, volumen y temperatura resulta crucial para dimensionar depósitos y conductos. Conocer la relación matemática que expresa la interdependencia física de estas tres propiedades es esencial en ingeniería. En este libro veremos de modo experimental la interdependencia que presentan las propiedades presión, volumen y temperatura en fluidos. Lo haremos a través un caso práctico. En este libro mostraremos: 1) la dependencia mutua de las variables de estado presión-volumen-temperatura (PVT) para el fluido contenido en un volumen variable al modificar la presión y la temperatura. 2 ) la distinción de las propiedades de un fluido en las diferentes zonas de operación. 3 ) la obtención de la curva de vaporización presión-temperatura (P-T) y el diagrama presión-volumen (P-V) de un fluido.

Delamination in Tibet: Deriving constraints from the density of eclogite

Tibet, which is characterized by collisional orogens, has undergone the process of delamination or convective removal. The lower crust and mantle lithosphere appear to have been removed through delamination during orogenic development. Numerical and analog experiments demonstrate that the metamorphic eclogitized oceanic subduction slab or lower crust may promote gravitational instability due to its increased density. The eclogitized oceanic subduction slab or crustal root is believed to be denser than the underlying mantle and tends to sink. However, the density of eclogite under high-pressure and high-temperature conditions and density differences from the surrounding mantle is not preciously constrained. Here, we offer new insights into the derivation of eclogite density with a single experiment to constrain delamination in Tibet. Using in situ synchrotron X-ray diffraction combined with diamond anvil cell, experiments focused on minerals (garnet, omphacite, and epidote) of eclogite are conducted under simultaneous high-pressure and high-temperature conditions, which avoids systematic errors. Fitting the pressure-temperature-volume data with the third-order Birch-Murnaghan equation of state, the thermal equation of state (EoS) parameters, including the bulk modulus (KT0), its pressure derivative (KT0′), the temperature derivative ((KT/T)P), and the thermal expansion coefficient (α0), are derived. The densities of rock-forming minerals and eclogite are modeled along with the geotherms of two types of delamination. The delamination processes of subduction slab breakoff and the removal of the eclogitized lower crust in Tibet are discussed. The Tibetan eclogite which containing 40–60 vol. % garnet and 37–64 % degrees of eclogitization can promote the delamination of slab break-off in Tibet. Our results indicate that eclogite is a major controlling factor in the initiation of delamination. A high abundance of garnet, a high Fe-content, and a high degree of eclogitization are more conducive to instigating the delamination.

DETERMINING THE THERMO PHYSICAL CHARACTERISTICS OF VIBRATION DRYING OBJECTS

Crop products require good moisture content for successful storage. The drying process is mainly used for this purpose. For its successful design and implementation it is necessary to have information about the physical and mechanical properties of the material, including thermo physical characteristics. It is for the successful implementation of the process of post-harvest processing of pumpkin seeds were planned and conducted experimental studies. Analysis of previous studies to determine the thermo physical characteristics of various materials, including plant products, showed that in most cases one series of experiments to determine three main indicators - heat capacity, thermal conductivity and thermal conductivity of products. Unfortunately, there is no universal method and installation for determining the required indicators, so in our research we used the original installation, the principle of which is based on the use of non-stationary heating patterns of two semi-bounded rods, where the source of heat is constant power. The theoretical basis of the implemented method is the solution and analysis of the thermal equation with the corresponding boundary conditions. Intermediate equations were obtained from which the values of thermal conductivity and thermal conductivity for each series of experiments were found by the graph-analytical method of solution. The value of heat capacity of the material was determined from the well-known formula of the ratio of these three indicators. As a result of research and processing of the obtained data, the dependences of the thermo physical properties of the material on its humidity were determined, which are presented in graphical and analytical form. The obtained dependences confirmed the results of researches of some authors on the presence of inflection in the graph of thermal conductivity which is explained by the transition of moisture from free to bound state.

Pressure dependence of the Grüneisen parameter and melting temperature of some metals

We have used a method for determining volume dependence of the Grüneisen parameter in the Lindemann law to study the pressure dependence of melting temperatures in case of 10 metals viz. Cu, Mg, Pb, Al, In, Cd, Zn, Au, Ag and Mn. The reciprocal gamma relationship has been used to estimate the values of Grüneisen parameters at different volumes. The results for melting temperatures of metals at high pressures obtained in this study using the Lindemann law of melting are compared with the available experimental data and also with the values calculated from the instability model based on a thermal equation of state. The analytical model used in this study is much simpler than the accurate DFT calculations and molecular dynamics.

P–V–T Equation of State of Iridium Up to 80 GPa and 3100 K

In the present study, the high-pressure high-temperature equation of the state of iridium has been determined through a combination of in situ synchrotron X-ray diffraction experiments using laser-heating diamond-anvil cells (up to 48 GPa and 3100 K) and density-functional theory calculations (up to 80 GPa and 3000 K). The melting temperature of iridium at 40 GPa was also determined experimentally as being 4260 (200) K. The results obtained with the two different methods are fully consistent and agree with previous thermal expansion studies performed at ambient pressure. The resulting thermal equation of state can be described using a third-order Birch–Murnaghan formalism with a Berman thermal-expansion model. The present equation of the state of iridium can be used as a reliable primary pressure standard for static experiments up to 80 GPa and 3100 K. A comparison with gold, copper, platinum, niobium, rhenium, tantalum, and osmium is also presented. On top of that, the radial-distribution function of liquid iridium has been determined from experiments and calculations.