Experimental study and thermodynamic calculation of Au–Bi–Sb system phase equilibria

Phase equilibria in the Au–Bi–Sb ternary system have been studied experimentally and calculated by the CALPHAD method. Three calculated isopleths with molar ratios Au:Bi=1, Bi:Sb=1 and Au:Sb=1 were compared with the DTA results from this work. The liquidus projection has been calculated. Two ternary invariant reactions were noted. Calculated phase diagram of isothermal section at 573 K was compared with the results of SEM/EDX analysis.     

Theoretical study on liquid crystal cyanobiphenyls: Phase stability and phase behavior

This article presents a theoretical study on liquid crystalline materials in homologous series of 4'-n-alkyl-4-cyanobiphenyl (nCB) with propyl (3CB), pentyl (5CB), and heptyl (7CB) groups. The atomic net charge and dipole moment components at each atomic center have been evaluated using the complete neglect differential overlap (CNDO/2) method. The modified Rayleigh–Schrodinger perturbation theory along with the multicentered-multipole expansion method has been employed to evaluate the long-range intermolecular interactions, while a ‘6-exp’ potential function has been assumed for short-range interactions. Further, these interaction energy values have been used as input to calculate the translational entropy, and free energy of nCB (n=3, 5, and 7) molecules during the stacking, and in-plane interactions. The observed results have been correlated with the mesogenic behavior and phase stability based on the thermodynamic parameters introduced in this article. Further, an attempt has been made to elucidate the flexibility of a configuration at a particular temperature, which has a direct relation with phase transition property of the molecules.     

Experimental constraints on the phase diagram of titanium metal

The phase transformations of titanium metal have been studied at temperatures and pressures up to 973 K and 8.7 GPa using synchrotron X-ray diffraction. The equilibrium phase boundary of the α-ω transition has a dT/dP slope of 345 K/GPa, and the transition pressure at room temperature is located at 5.7 GPa. The volume change across the α-ω transition is ΔV=0.197 cm³/mol, and the associated entropy change is ΔS=0.57 J/mol K. Except for ΔV, our results differ substantially from those of previous studies based on an equilibrium transition pressure of 2.0 GPa at room temperature. The α-ω-β triple point is estimated to be at 7.5 GPa and 913 K, which is comparable with previous results obtained from differential thermal analysis and resistometric measurements. An update, more accurate phase diagram is established for Ti metal based on the present observations and previous constraints on the α-β and ω-β phase boundaries.     

Immiscibility in the Fe3O4-FeCr2O4 spinel binary

A recent thermodynamic model of mixing in spinel binaries, based on changes in cation disordering (x) between tetrahedral and octahedral sites [Am. Mineral. 68 (1983) 18, 69 (1984) 733], is investigated for applicability to the Fe₃O₄-FeCr₂O₄ system under conditions where incomplete mixing occurs. Poor agreement with measured consolute solution temperature and solvus [N. Jb. Miner. Abh. 111 (1969) 184] is attributed to neglect of: (1) ordering of magnetic moments of cations in the tetrahedral sublattice antiparallel to the moments of those in the octahedral sublattice and (2) pair-wise electron hopping between octahedral site Fe³⁺ and Fe²⁺ ions. Disordering free energies (ΔG_D), from which free energies of mixing are calculated, are modeled by

     

Modeling the thermodynamic properties of bimetallic nanosolids

A model has been developed to account for size, shape, surface segregation, composition and dimension dependent cohesive energy of bimetallic nanosolids, and further been extended to predict the size dependent thermodynamic properties, such as melting temperature, Curie temperatures, ordering temperature and phase diagram. The cohesive energy, melting temperature, Curie temperatures and ordering temperature of bimetallic nanosolids decrease with decreasing the particle size. The depression is dramatic in the lower range of size, while it becomes smoothly in large size. For nano phase diagram, the solidus and liquidus curves drop and the two-phase zones become small, as the size of the nanosolids decreases. The two-phase zones of the nano phase are always lower than the regions indicated in the bulk Ag-Pd alloy phase diagram, and they may deteriorate into a curve at a critical size. It is also found that the thermodynamic properties of nanosolids not only depend on the compositions, the atomic diameter and the cohesive energy of each component, but also depend on the size and the shape. The model predictions are consistent with the corresponding simulation, semi-empirical model and experimental data.     

Thermodynamic modeling of Fe–Ni pentlandite

Gibbs energy modeling of iron–nickel pentlandite has been performed using experimental data of ternary phase equilibria. A three-sublattice approach in the framework of the Compound Energy Formalism is developed to refine a two-sublattice model of pentlandite recently applied within a complete assessment of the Fe–Ni–S system. Experimental data about the iron site fraction on the octahedral sublattice at 523.15 K for the composition Fe₅Ni₄S₈ as well as the enthalpy of formation at 298.15 K for the composition Fe_4.5Ni_4.5S₈ are predicted satisfactorily by the novel model. New possibilities to interpret experimental phase equilibrium data on complex phase relations with pentlandite are discussed together on the basis of the recent extension of a second high-temperature heazlewoodite phase to a ternary solution phase.     

Empirical correlation between melting temperature and cohesive energy of binary Laves phases

A list of 143 binary Laves phases with their melting temperature and melting type is collected, and used to study a correlation between melting temperature and cohesive energy. It is found that the melting temperature of Laves phases is roughly proportional to its cohesive energy calculated by Miedema's empirical model from their intrinsic atomic properties. The average predicted error of melting temperature of compounds is as low as 8.0%. This empirical rule is consistent with the result of the universal binding energy theory of solids.     

Molecular alloys as phase change materials (MAPCM) for energy storage and thermal protection at temperatures from 70 to 85 °C

Molecular alloys, that combine a relatively high heat of melting with a suitable melting temperature adapted to the application temperature, are excellent materials for thermal protection and for thermal energy storage. Of special interest is the fact that, by making alloys of molecular materials; the range of melting can be adjusted over a range of temperatures. The present paper reports on the design of MAPCMs to be used for energy storage and thermal protection at temperatures from 70 to 85 °C. The aim is to use these materials for thermal protection in the catering sector in order to avoid proliferation of micro organisms; the minimal temperature required is higher than 65 °C. The work illustrates how some fundamental studies are helpful in choosing the right composition that is able to work at the temperature required for an application. Several molecular alloys using the n-alkanes are elaborated and characterized. The preparation of mixed crystals, their crystallographic and thermodynamic properties and stability, phase change behaviour, and their use in practical applications are reported.     

Macroscale and microscale evolutions of mechanically alloyed FeZn systems

The present work aims to correlate, in time, macroscale and microscale phenomenological evolutions of the microstructure of Fe and FeZn alloys processed by mechanical milling (MM) and alloying (MA), respectively. Powders were characterized for particle size distribution (PSD), particle morphology (optical microscopy, OM, scanning electron microscopy, SEM), microhardness, crystallite size, differential scanning calometry (DSC) and transmission electron microscopy (TEM). Two macroscopic regimes of PSD behavior were distinguished: the first one dominated by the cold welding process; and, the other where both fracture and agglomeration play a significant role. Solid solubilization of Zn on bcc Fe was found to reduce the final microhardness as well as increase the lattice parameter and is very well predicted by Miedema's thermodynamical approach. Microhardness and solid solution formation kinetics were correlated in time and both could be precisely described by a logistic function. After 5 h of planetary milling, microhardness and the lattice parameter become stable as well as the PSD and particle morphology, indicating that the system has already reached steady state. Indeed, this condition can be monitored by both macroscopic and microscopic parameters. Prior to an homogeneous powder, DSC results suggest an endothermic solid-state amorphization reaction for samples processed for up to 1 h as a result of the formation of clean Fe/Zn interfaces during MA.     

First-principle study of phase stability,electronic structure and thermodynamic properties of cadmium sulfide under high pressure

By employing first principle and a quasi-harmonic Debye model, we study the phase stability, phase transition, electronic structure and thermodynamic properties of cadmium sulfide (CdS). The results indicate that CdS is a typical ionic crystal and that the zinc-blende phase in CdS is thermodynamically unstable. Moreover, the heat capacity of the wurtzite and rocksalt phases of CdS decreases with pressure and increases with temperature, obeying the rule of the Debye T³ law at low temperature and the Dulong–Petit limit at high temperature.     

The influence of the ideal mixing entropy on concentration profiles and diffusion paths in ternary systems

The diffusion profiles and the reaction paths in ternary solid solutions are determined by both thermodynamics and kinetics. The matrix of the diffusion coefficient can be described as the product of the Hessian matrix for the thermodynamic influences and the Onsager matrix for kinetic influences.In this paper the interest is focused on the influence of the ideal part of the Hessian matrix, i.e. the ideal mixing entropy on interdiffusion. The ideal diffusion profiles are calculated by a computer simulation and they are compared with experimental results from the literature. These comparisons reveal that in most cases the qualitative shape of the diffusion profiles and of the reaction paths can be considered as caused by the ideal mixing entropy. Surprisingly, the shape of the diffusion profiles turns out to depend on the component that was chosen as the so-called solvent of the ternary mixture. This means that the ideal reaction paths do not show the triangular symmetry expected for an ideal ternary system. Especially, reaction paths between starting positions showing the same concentration of one of the three components do not run along straight lines.     

The phase stability of Ca2TiO4 and related Ruddlesden–Popper phases

The Ruddlesden–Popper phases of the Ca–Ti–O system, Ca_n+1Ti_nO_3n+1, are investigated by means of atomistic simulations employing empirical pair potentials. The stability of the phases is examined in terms of various reaction schemes: the formation from the binary oxides, the addition of the perovskite oxide to a given phase, and the reaction between perovskite and rock-salt oxides. The energies of these reactions are compared with results previously obtained for the Ruddlesden–Popper phases of the Sr–Ti–O system. The importance of the disproportionation reaction of the various R–P phases in both Ca and Sr systems is also emphasized. The results obtained are in good agreement with experimental observations regarding both systems.     

Immiscibility in the nickel ferrite-zinc ferrite spinel binary

Immiscibility in the trevorite (NiFe₂O₄)-franklinite (ZnFe₂O₄) spinel binary is investigated by reacting 1:1:2 molar ratio mixtures of NiO, ZnO and Fe₂O₃ in a molten salt solvent at temperatures in the range 400-1000 °C. Single phase stability is demonstrated down to about 730 °C (the estimated consolute solution temperature, T_cs). A miscibility gap/solvus exists below T_cs. The solvus becomes increasingly asymmetric at lower temperatures and extrapolates to stoichiometric parameters = 0.15, 0.8 at 300 °C. A thermodynamic analysis, which accounts for changes in configurational and magnetic ordering entropies during cation mixing, predicts solvus phase compositions at room temperature in reasonable agreement with those determined by extrapolation of experimental results. The delay between disappearance of magnetic ordering above (for NiFe₂O₄) and disappearance of a miscibility gap at T_cs is explained by the persistence of long-range ordering correlations in a quasi-paramagnetic region above T_C.     

Thermochemical studies on RE2O2CO3 (RE=Gd, Nd) decomposition

Thermochemistry in the decomposition of gadolinium di-oxycarbonate, Gd₂O₂CO₃(s) and neodymium di-oxycarbonate, Nd₂O₂CO₃(s) was studied over the temperature region of 774-952 K and 775-1105 K, respectively. The equilibrium properties of the decomposition reactions were obtained by tensimetric measurement of the CO₂(g) pressure over the biphasic mixture of RE₂O₂CO₃(s) and RE₂O₃(s) at different temperatures (RE=Gd, Nd) and also by thermogravimetric analysis of the decomposition temperature at different CO₂ pressures. The temperature dependence of the equilibrium pressure of CO₂ thus measured could be given by

ln p_CO2/Pa (±0.13)=−22599.1/T+35.21 (774≤T (K)≤952) for Gd₂O₂CO₃ decomposition and

ln p_CO2/Pa (±0.19)=−23824.7/T+33.14 (775≤T (K)≤1105) for Nd₂O₂CO₃ decomposition.

From the above vapor pressure expressions, the median enthalpy and entropy of the decomposition of the oxycarbonates were calculated by the second law analysis and their thermodynamic stabilities were derived. The results are discussed in the light of available thermochemical data of the compounds.     

Immiscibility in the NiFe2O4-NiCr2O4 spinel binary

The solid solution behavior of the Ni(Fe_1−nCr_n)₂O₄ spinel binary is investigated in the temperature range 400-1200 °C. Non-ideal solution behavior, as exhibited by non-linear changes in lattice parameter with changes in n, is observed in a series of single-phase solids air-cooled from 1200 °C. Air-annealing for 1 year at 600 °C resulted in partial phase separation in a spinel binary having n=0.5. Spinel crystals grown from NiO, Fe₂O₃ and Cr₂O₃ reactants, mixed to give NiCrFeO₄, by Ostwald ripening in a molten salt solvent, exhibited single-phase stability down to about 750 °C (the estimated consolute solution temperature, T_cs). A solvus exists below T_cs. The solvus becomes increasingly asymmetric at lower temperatures and extrapolates to n values of 0.2 and 0.7 at 300 °C. The extrapolated solvus is shown to be consistent with that predicted using a primitive regular solution model in which free energies of mixing are determined entirely from changes in configurational entropy at room temperature.     

Investigation of thermodynamic properties of cerium dioxide by statistical moment method

The thermodynamic properties of the cerium dioxide (CeO₂) are studied using the statistical moment method, including the anharmonicity effects of thermal lattice vibrations. The free energy, linear thermal expansion coefficient, bulk modulus, specific heats at the constant volume and those at the constant pressure, C_V and C_P, are derived in closed analytic forms in terms of the power moments of the atomic displacements. The temperature dependence of the thermodynamic quantities of cerium dioxide is calculated using three different interatomic potentials. The influence of dipole polarization effects on the thermodynamic properties and thermodynamic stability of cerium dioxide have been studied in detail.     

Berezinsky-Kosterlitz-Thouless transition in phase fluctuating superconductors with inhomogeneous Gaussian distributed couplings

Within the framework of phase fluctuation picture for the pseudogap state of cuprate superconductors, we study the effects of both spatial inhomogeneity of coupling strength and thermal phase fluctuations on the superconducting transition temperature. Such a Berezinsky-Kosterlitz-Thouless (BKT) transition is characterized by a two-dimensional (2D) classical XY model, in which the bond coupling is assumed to be roughly proportional to the superconducting bond order parameter. In recent STM experiments with lattice-tracking spectroscopy technique, a Gaussian-like spatially distributed pairing strength is observed. Our Monte Carlo simulations using Wolff cluster update on such 2D classical XY model, in which the bond coupling obeys a similar spatial Gaussian distribution, indicate that the enhancement of the variance of Gaussian distribution may suppress the BKT transition temperature. In addition, we calculate the related physical quantities, including the spin stiffness, free energy, specific heat, magnetization and magnetic susceptibility, by changing the inhomogeneity variance.