Evaluation Of Phase Equilibria Research Articles

Free-Volume Theory Coupled with Soft-SAFT for Viscosity Calculations: Comparison with Molecular Simulation and Experimental Data

The evaluation of phase equilibria and solubility properties through theoretical approaches is a well-known field, where a significant amount of models are able to describe them with a good degree of accuracy. However, the simultaneous calculation of transport properties together with thermodynamic phase properties still remains a challenge, due to the difficulties in describing the behavior of properties like the viscosity of fluids with the same approach. In this work, the free-volume theory (FVT) has been coupled with the soft-SAFT equation for the first time to extend the capabilities of the equation to the calculation of transport properties. The theory has been first tested using simulation data of the viscosity of the Lennard-Jones (LJ) fluid and LJ chains over a wide range of temperature and pressure. Good agreement has been found at all chain lengths, except for some deviations at near-zero density values. Several trends of the viscosity parameters with the length of the chain are identified, allowing the prediction of other chain fluids. Finally, the new equation has been applied to the n-alkanes family, where viscosity is a key property, and results are compared with experimental data. The three viscosity parameters were fitted to viscosity data of the pure fluid at several isotherms or isobars, whereas the density and pressure (or temperature) were taken from the soft-SAFT output. Again, the effect of these parameters on the viscosity has been investigated and compared with results obtained for the LJ chains and with previous work of other authors. The new equation performs very well in all cases, with a global average absolute deviation of 2.12% and shows predictive capabilities for heavier compounds. This empowers soft-SAFT with new capabilities, allowing the equation to calculate phase, interfacial, and transport properties with the same model and degree of accuracy.

An improved thermodynamic modeling of the Fe–Cr system down to zero kelvin coupled with key experiments

A thermodynamic modeling of the Fe–Cr system down to 0 K is performed on the basis of our recent comprehensive review of this binary system [W. Xiong, M. Selleby, Q. Chen, J. Odqvist, Y. Du, Evaluation of phase equilibria and thermochemical properties in the Fe–Cr system, Crit. Rev. Solid State Mater. Sci. 35 (2010) 125–152]. The model predicts a sign change for the magnetic ordering energy of mixing rather than the enthalpy of mixing in the bcc phase at 0 K. Designed key experiments are performed not only to check the validity of the present modeling but also to assist in understanding the mechanism for spinodal decomposition of the Fe–Cr alloy. Heat capacities and Curie temperatures of several Fe-rich alloys are determined between 320 and 1093 K by employing differential scanning calorimetry. The measured heat capacities are found to be in remarkable agreement with the prediction based on the present modeling. Microstructural patterns and frequency distribution diagrams of Cr are studied in alloys containing 26.65, 31.95, and 37.76 at.% Cr by using atom probe tomography. The observed phase separation results correspond well with our model-predicted boundary for the spinodal decomposition. Interestingly, a horn on the Cr-rich spinodal boundary is predicted below 200 K for the first time. This work demonstrates a way to bridge the ab initio calculations and CALPHAD approach.

Evaluation of phase equilibria in the Nb-rich portion of Nb–B system

The phase equilibria in the Nb-rich portion of Nb–B system have been evaluated experimentally using metallographic analysis, differential thermal analysis (DTA) and X-ray diffraction. It showed that Nb ss (solid solution) and NbB are the only two primary phases in the 0–40 at.% B composition range, and the eutectic reaction L ↔ Nb ss + NbB exists, instead of the generally accepted reaction L ↔ Nb ss + Nb 3 B 2 , as indicated in the Nb–B phase diagram. The Nb 3B 2 phase, however, forms by the peritectoid reaction Nb ss + NbB ↔ Nb 3 B 2 . DTA tests were conducted on annealed Nb–14B, Nb–16B, Nb–18B and Nb-40B alloys, and temperature and heat of phase transition were determined. The eutectic reaction ( L ↔ Nb ss + NbB ) temperature was determined to be 2104 ± 5 °C, and the heat of phase transition was estimated as 22–30 kJ/mol, depending on the method of calibration used. The thermal event associated with peritectoid reactions was not observed in DTA curves due to sluggish solid state transformation, but the thermal annealing experiments show that peritectoid temperature is above 1900 °C.

Constituent phase diagrams of the Al–Cu–Fe–Mg–Ni–Si system and their application to the analysis of aluminium piston alloys

The evaluation of phase equilibria in quinary systems that constitute the commercially important Al–Cu–Fe–Mg–Ni–Si alloying system is performed in the compositional range of casting alloys by means of metallography, electron probe microanalysis, X-ray diffractometry, differential scanning calorimetry, and by the analysis of phase equilibria in the constituent systems of lesser dimensionality. Suggested phase equilibria are illustrated by bi-, mono- and invariant solidification reactions, polythermal diagrams of solidification, distributions of phase fields in the solid state, and isothermal and polythermal sections. Phase composition of as-cast alloys is analyzed in terms of non-equilibrium solidification. It is shown that the increase in copper concentration in piston Al–Si alloys results in the decrease in the equilibrium solidus from 540 to 505°C. Under non-equilibrium solidification conditions, piston alloys finish solidification at ∼505°C. Iron is bound in the quaternary Al8FeMg3Si6 phase in low-iron alloys and in the ternary Al9FeNi and Al5FeSi phases in high-iron alloys.

Coupled optimization and evaluation of phase equilibria and thermodynamic properties of the benzene‐cyclohexane system

AbstractAn extensive review of reported vapour‐liquid equilibrium, solid‐liquid equilibrium, excess enthalpy, excess heat capacity and other phase equilibrium and thermodynamic data for the system benzene‐cyclohexane is presented. Selected phase equilibrium and thermodynamic data have been simultaneously optimized and fitted to a single polynomial series expression in composition and temperature for the excess Gibbs energy of the liquid. This expression has been used to evaluate all the diverse types of data known for this system. This single expression gives a self‐consistent description of all known data in the very wide temperature interval 232–500 K.