Thermodynamic properties of tin: Part I Experimental investigation,ab-initio modelling of α-, β-phase and a thermodynamic description for pure metal in solid and liquid state from 0 K

Thermodynamic data for crystalline white and grey tin were assessed using an extended Einstein model from 0 K. Ab-initio simulations in the framework of density functional theory (DFT) with the quasiharmonic approximation (QHA) were carried out to define the heat capacities for both phases of tin from 0 K up to room temperatures. Good agreement was observed between theoretical and experimental heat capacities, which makes it possible to combine theoretical and experimental data to determine the standard entropies. Data for the liquid phase were described using a two state model. During the assessment, careful analysis of the experimental data was carried out. In order to fulfil the need for a precise evaluation of S^o₂₉₈ we needed to use an additional technique using multiple Einstein functions, which allows the experimental heat capacity and enthalpy data for the solid phase to be approximated accurately from 0 K up to the melting point and to estimate solid phase transition entropy and enthalpy which are difficult to measure due to a high activation barrier. Additional measurements of heat capacity were carried out where existing data were scarce.     

Thermodynamic assessment of the Bi-alkali metal (Li,Na, K,Rb) systems using the modified quasichemical model for the liquid phase

Bi-alkali metal (Li, Na, K, Rb) binary systems have been systematically assessed based on the available phase diagrams and thermodynamic data. The modified quasichemical model, which takes short-range ordering into account, is used to describe the liquid phase. All intermetallic phases are treated as stoichiometric compounds. A set of self-consistent model parameters is obtained and the experimental data are reproduced well within experimental error limits. The enthalpy of mixing, entropy of mixing, and activity of element are calculated, showing the liquid phase exhibits maximum short-range ordering at 75 at% X (X=Li, Na, K, Rb). Some systematic variations and regularities are presented, indicating the enthalpy and entropy of mixing for the liquid phase at the maximum short-range ordering along with the enthalpy of formation and melting temperature of intermediate compound BiX₃ change with the atomic radius of alkali metals regularly.     

Use of third generation data for the elements to model the thermodynamics of binary alloy systems: Part 1 – The critical assessment of data for the Al-Zn system

Over the last four years there has been a renewed interest in the development of new critically assessed data using physically based models. Nearly all work so far has been concerned with the critical assessment of data for the elements. This has involved the selection of Einstein or Debye temperatures for the stable crystalline phases and the liquid phase and associated parameters. However, until now, these data have not been extended in a comprehensive way to model the thermodynamic properties of binary, ternary and multicomponent systems. In this paper the way in which the parameters underlying these physical models vary with composition is explored. This includes a method to define the Einstein temperature for metastable phases of the elements and its relation to the so-called lattice stabilities used in the past, and the variation of the Einstein temperature with composition to account for the composition dependence of the excess entropy. This approach is demonstrated for the Al-Zn system which shows extensive regions of solid solution and complete miscibility in the liquid phase. Here Einstein temperatures are derived for Al in the HCP_ZN phase and Zn in the FCC_A1 phase together with parameters describing the variation of the Einstein temperature with composition for the HCP_ZN, FCC_A1 and liquid phases.     

Thermodynamic assessment of the cesium–oxygen system by coupling density functional theory and CALPHAD approaches

The thermodynamic properties of cesium oxides were calculated by combining ab initio calculations at 0 K and a quasi-harmonic statistical thermodynamic model to determine the temperature dependency of the thermodynamic properties. In a second approach, the CALPHAD method was used to derive a model describing the Gibbs energy for all the cesium oxide compounds and the liquid phase of the cesium–oxygen system. For this approach, available experimental data in the literature was reviewed and it was concluded that only experimental thermodynamic data for Cs₂O are reliable. All these data together with the thermodynamic data calculated by combining ab initio and the statistical model were used to assess the Gibbs energy of all the phases of the cesium–oxygen system. A consistent thermodynamic model was obtained. The variation of the relative stability of the different oxides is discussed using structural and bond data for the oxides investigated by ab initio calculations. This work suggests that the melting point for Cs₂O₂ reported in the literature (863 K) is probably overestimated and should be re-measured.     

The Cd–Te phase diagram

The properties of the liquid phase in the Cd–Te system are fit using thermodynamic properties of CdTe(c) recently optimized by the author. These include a high temperature heat capacity significantly lower than commonly used such that the enthalpy of formation of CdTe(c) at its melting point is about 10 kJ/mol less negative than previously thought. An associated solution model with Cd, CdTe, and Te species is used. Seven adjustable parameters are sufficient to quantitatively fit the liquidus and partial pressures of Te₂ and Cd. Additional partial pressures for Te rich CdTe(c) near its melting point are extracted from an earlier study and tabulated. The parameters giving good fits to the liquidus and partial pressures give only a fair fit to the enthalpy of mixing of the liquid phase. Moreover, the parameters giving a good fit to the enthalpy give poor fits to the other data. The sensitivity of the different data types to changes in the interaction parameters of the associated solution model is established. A variation of ±160 J/g atom in the enthalpy parameter determining the CdTe–Te interaction is sufficient to double the fractional standard deviation between experimental and calculated partial pressures of Te₂ over Te rich CdTe(c) from 0.034 to 0.07. Because the degree of association is near its maximum, the measures of fit to the data are insensitive to changes in the parameters determining the Cd–Te interaction.     

The B-rich side of the B–C phase diagram

The melting behavior of ß-boron at the boron-rich side of the B–C binary phase diagram is a long standing question whether eutectic or peritectic. Floating zone experiments have been employed to determine the melting type on a series of C-containing feed-rods prepared by powder metallurgy and sinter techniques. Melting point data as a function of carbon-content clearly yielded a peritectic reaction isotherm: L+B_4+δC=(ßB). The partition coefficient of carbon is ~2.6. The experimental melting point data were used to improve the existing thermodynamic modeling of the system B–C. Relative to the thermodynamically accepted melting point of pure ßB (T_M=2075 °C), the calculated reaction isotherm is determined at 2100.6 °C, a peritectic point at 0.75 at% C and a maximum solid solubility of 1.43 at% C in (ßB) at reaction temperature. With the new melting data the refractory system Hf–B–C has been recalculated and the liquidus surface is presented. The influence of the melting behavior of (ßB) on the phase reactions in the B-rich corner of M–B–C diagrams will be discussed and demonstrated in case of the Ti–B–C system.     

Thermodynamic assessment of the Ga-Sn-Zn system

The integral molar mixing enthalpy of liquid ternary Ga-Sn-Zn alloys has been investigated using drop calorimetry method along five intersections as follows: X_Ga/X_Zn = 3/1 at 720 K, x_Ga/x_Zn = 1/1 at 718 K and 720 K, x_Ga/x_Zn = 1/3 at 718 K, x_Ga/x_Sn = 3/17 at 718 K and for x_Ga/x_Sn = 1/3 at 720 K. Based on obtained thermodynamic results and those available in the literature the thermodynamic optimization was done using Thermo-Calc software. Next, the phase equilibria in the binary and ternary systems were calculated and the results were compared with those obtained using different experimental techniques.     

Ab initio-assisted assessment of the CaO-SiO2 system under pressure

We present the results of an ab initio-assisted assessment of melting and subsolidus phase relations in the system CaO-SiO₂ up to high pressure conditions. All solid compounds known to nucleate in the system have been treated as purely stoichiometric and the liquid resolved in the framework of a simple polymeric model. Mixing properties of the binary liquid phase are fully described by a single-parameter purely enthalpic chemical interaction plus a strain energy contribution. The latter is required to predict liquid immiscibility of SiO₂-rich liquid compositions at ambient conditions and becomes irrelevant at P > 2 GPa. A detailed survey of thermodynamic properties of silica polymorphs and calcium oxide and silicates in a broad range of P-T conditions reveals quite controversial stability relations and melting behavior. First-principles calculations on CaO and SiO₂ pure liquid components and solid phases (lime and stishovite) have been used, along with a sound assessment of first- and second-order phase transitions, to reconcile thermochemical data with topological details of the observed phase diagrams. A physically-consistent coupling between thermodynamic and thermoelastic properties (viz. compressibility and thermal expansion) turns out to be of fundamental importance to infer reliable stability relations both at subsolidus and melting conditions. Pressure effects shift the composition of the main invariant points in the CaO-SiO₂ system and also change the melting behavior of the CaSiO₃ metasilicate in a complex manner.     

Calorimetric measurement of the standard enthalpy of formation of ZnSb at 298 K

After a critical review of the literature data on the standard enthalpy of formation of ZnSb, discrepancies between various experimental studies are highlighted. Moreover, experimental values disagree with values calculated by ab initio methods. As many of the experimental methods used suffer from some serious drawbacks, a new determination of the standard enthalpy of formation of ZnSb by an alternative calorimetric method, drop solution calorimetry in liquid tin, has been performed. Two different synthesis methods have been used to obtain a pure ZnSb phase and drop solution experiments were performed at 665 and at 974 K. The standard enthalpy of formation values derived from these experiments are − 6.1±2.5 kJ mol of atoms⁻¹ for the ZnSb sample prepared by ball milling and − 7.9±0.4 kJ mol of atoms⁻¹ for the ZnSb sample prepared by melting. These results are discussed and compared to literature data.     

Novel design of ferronickel smelting slag by utilizing red mud as a fluxing agent: Thermochemical computations and experimental confirmation

The effect of red mud on the melting behavior of ferronickel slag was investigated in a laboratory-scale horizontal tube furnace. Melting and softening of slag samples fluxed with different amounts of red mud were examined by an in-situ visualization technique in the temperature ranges from 1673 K to 1823 K. FactSage™ 7.0 was used to perform thermodynamic calculations of the multi-component system of ferronickel slag and red mud. The liquid phase area was extended to lower temperatures by adding red mud, and this implied that red mud was an excellent flux. The primary solid phase field was confirmed to be dependent on the red mud content from X-ray diffraction measurements. Microscopic observations using a scanning electron microscope (SEM-EDX) confirmed that the primary solid phase changed from olivine to spinel with the addition of red mud.     

Thermodynamic modeling of the Ca(NO3)2-MNO3 (M: alkali metal) systems

This work presents a thermodynamic evaluation of the Ca(NO₃)₂-MNO₃ (M: Li, Na, K, Rb, Cs) binary systems using the CALPHAD approach. The required Gibbs energy of liquid Ca(NO₃)₂ is missing in the literature and has been successfully evaluated in the present work with a fusion enthalpy of 23849 J mol⁻¹. The substitutional solution model can thus be employed to describe the Ca(NO₃)₂-base liquid phase. All the intermediate compounds are treated to be stoichiometric and their Gibbs energies comply with the Neumann-Kopp rule. Empirical functions relating mixing enthalpies to ionic parameters are employed to predict the corresponding values of binary melts which are used as input data to assist in parameters optimization for the liquid phases. The final calculated results show good agreement with most of the experimental and predicted data.     

Phase change materials in the ternary system NH4Cl+CaCl2+H2O

Solubility isotherms of the ternary system (NH₄Cl+CaCl₂+H₂O) were elaborately determined at T= (273.15 and 298.15) K by using the isothermal method. In the equilibrium phase diagram, there are two solubility branches corresponding to the solid phases CaCl₂⋅6H₂O and NH₄Cl. Invariant point compositions are 36.32 wt% CaCl₂ and 3.4 wt% NH₄Cl at 273.15 K, and 45.86 wt% CaCl₂ and 5.22 wt% NH₄Cl at 298.15 K. A Pitzer-Simonson-Clegg thermodynamic model was applied to represent the thermodynamic properties of this ternary system and to construct a partial phase diagram of the ternary system at temperatures between (273.15 and 323.15) K. It was found in the predicted solubility phase diagram that the double salt 2NH₄Cl⋅CaCl₂⋅3H₂O, found by other authors at (323.1 and 348.1) K, will disappear at temperatures below 298.15 K. Besides, it was found that there are two peritectic points in the ternary system with peritectic temperatures at 299.65 K and 298.15 K, and the former peritectic point falls just on the line between the composition points of NH₄Cl and CaCl₂⋅6H₂O. According to phase rule, a solution made of this point will begin to crystallize at 299.65 K and end at 298 K and therefore can be acted as a “pseudo eutectic” phase change material (PCM). A heat storing and releasing experiment of 50 grams of the PCM was carried out, obtaining a satisfying result.     

Thermodynamics of Fe–S at ultra-high pressure

Earth's core is believed to consist of a solid inner core and an outer liquid core. Since the inner core is mostly solid iron, most geophysical work has focused on melting of pure iron at core conditions. The inner core density is well matched with seismological data if some S is added to iron. The available phase equilibrium experimental data in the binary Fe–S system to pressures as high as ~200 GPa is used to create a thermodynamic database extending to core pressures that can be used to calculate the inner core density if S were the only other constituent. Such a calculation gives the maximum temperature of the solid inner core as 4428 (±500) K (363.85 GPa, density=13.09 g/cm³) with a sulfur content of ~15 wt%. To be consistent with the seismically determined density, the outer liquid core requires mixing of yet another light element or elements; both oxygen and carbon are suitable.