Gibbs Energy Of Formation Research Articles

Vaporisation studies on Sn-Te-O system by Knudsen effusion mass spectrometry: Thermodynamic properties over (SnO2+SnTe3O8) biphasic region

Vaporisation studies along the pseudo binary line of SnO2–TeO2 (SnTe3O8 + SnO2) in the Sn-Te-O system were conducted by using Knudsen effusion mass spectrometry in the temperature range 843–968 K. SnTe3O8 vaporises incongruently and TeO2(g), TeO(g), Te2(g) and O2(g) were the neutral species observed over the equilibrium vapour. Partial pressure – temperature (p-T) relations of TeO2(g), TeO(g), Te2(g) over (SnTe3O8 + SnO2) “two phase” region were determined in the temperature range 843–968 K. Partial pressures of O2(g) were calculated by considering gas phase equilibrium reactions involving this species and TeO2(g), TeO(g), Te2(g). Using the p-T relations, enthalpy changes of the following reactions were evaluated: SnTe3O8(s) ⇌ SnO2(s) + 3TeO2(g); SnTe3O8(s) + 2TeO(g) ⇌ 4TeO2(g) + 0.5 Te2(g) + SnO2(s) and 0.5Te2(g) + TeO2(g) ⇌ 2TeO(g). Subsequently, the enthalpy and Gibbs energy of formation of SnTe3O8 phase at 298.15 K were deduced as ΔfHm° = −1613.7 ± 67.8 kJ mol−1 and ΔfGm° = −1386.7 ± 67.8 kJ mol−1. Knudsen effusion mass spectrometric studies on this system are being reported for the first time.

A review on dissimilar metals’ welding methods and mechanisms with interlayer

The study of dissimilar metals’ welding is an important issue due to their increasing applications in many industrial fields. Welding of dissimilar metals is challenging because of the formation of large residual stress and brittle intermetallic compounds (IMCs). In order to solve this problem, intermediate interlayers were used to eliminate or inhibit the formation of brittle intermetallic reaction layers in many welding techniques, such as diffusion bonding, laser welding, electron beam welding, and other welding techniques. The aim of this paper is to review the recent progress of dissimilar metals’ welding methods and mechanisms with interlayer to offer a basis for the following research. The work discussed several criteria for the selection of interlayer, such as physical properties, metallurgical compatibility, mode, and thickness of the interlayer. Then, formation enthalpy, Gibbs energy of formation (ΔG), and brittleness of the IMCs, as well as welding parameters, were also discussed. Simultaneously, the present work had proposed a design guideline for the selection of interlayer in dissimilar metals’ welding to acquire a welded joint with good quality.

DFT Quantum-Chemical Calculation of the Molecular Structures of (5665)Macrotetracyclic Chelates in the M(II)—4,5-Diaminoacridone—2-[(2-Formylphenyl)amino]benzenecarbaldehyde Systems (M = Mn, Fe, Co, Ni, Cu, Zn)

The geometries of (5665)macrotetracyclic Mn(II), Fe(II), Co(II), Ni(II), Cu(II), and Zn(II) complexes with the NNNN-coordination of the chelant donor sites and the MN4 chelate core, which can be formed through template processes in the M(n)-2-[(2-formylphenyl)amino]benzenecarbaldehyde-4,5-diaminoacridone have been calculated by the hybrid DFT OPBE/TZVP method with the Gaussian 09 program package. The bond lengths, bond angles, and selected nonbonded angles in these complexes have been determined. It has been demonstrated that none of the chelate rings is strictly planar although these rings in all complexes, except the Co(II) complex, are pairwise identical. The six-membered rings are more noncoplanar than the five-membered rings. The standard enthalpies, entropies, and Gibbs energies of formation of these compounds have been calculated.

A Modified Neumann–Kopp Treatment of the Heat Capacity of Stoichiometric Phases for Use in Computational Thermodynamics

Since the early days of phase diagram calculation, the CALPHAD community has accepted a method of data assessment that is based on using Gibbs energy expressions for stoichiometric compounds that consist of a part that represents the contributions of the reference components, the so-called Neumann–Kopp sum, and a part that represents the Gibbs energy of formation. Usually, the latter consists only of a simple A + B * T term, which implies on the one hand that enthalpy and entropy of formation of a compound are temperature independent, and on the other, that the heat capacity of the respective compound is given by the Neumann–Kopp sum of the Cps of the constituents. In most cases this method yields acceptable results, also for the heat capacity. However, if certain elementary components are involved, this is not so. The paper highlights the problem outlining a remedial treatment that can be applied to problematic heat capacity functions present in pre-existing assessments, and thus giving a suggestion of how to prevent the problem in the future.

Determination of Thermodynamic Properties of Si-B Alloys

This study establishes the thermodynamic properties of the Si-B binary alloy system. The electromotive force (emf) as a function of temperature (823 K to 923 K) was measured using solid-state electrochemical cells, represented as $$(-)\,{\text{Pt}},{\text{Ar}}/\{\text{Si}\|{\text{CaF}}_{2}\|\;\{{\text{Si}} - {\text{B}}({\text{alloy}})\}/{\text{Ar}},{\text{Pt}}( + )$$ Using the experimental emf data obtained from the solid-state heterogeneous phase equilibrium, the activities of Si and B in Si-B alloys were calculated. The integral Gibbs energy of mixing \( (\Delta G^{\text{M}} ) \) of alloys were calculated from the activity of Si and B. A large negative deviation from ideality was found for the integral Gibbs energy of mixing \( (\Delta G^{\text{M}} ) \) of the binary Si-B system. From the activities of Si and B, the Gibbs energies of formation \( \left( {\Delta G_f^{0 } } \right) \) of phases present were calculated. The \( \Delta G_{f}^{ 0 } \) of SiB3, the most thermodynamically stable phase, was calculated as − 13.13 ± 0.19 kJ/mole-atoms at 923 K. The heterogeneous phases and microstructure after the equilibrium study of the electrode were characterized using XRD, SEM, and EDS analyses.

Stability of the pyrochlore Tm2Ru2O7(s) & comparison of its stability with other heavy rare earth ruthenium pyrochlores

The Gibbs energy of formation of Tm2Ru2O7(s) has been determined employing a solid-state electrochemical cell incorporating an oxide ion conducting electrolyte. The reversible electromotive force (e.m.f.) of the following cell was measured:Cell : (−)Pt/{Tm2O3(s) + Tm2Ru2O7(s) + Ru(s)}//CSZ//O2(p(O2) = 21.21kPa)/Pt(+)The standard molar Gibbs energy of formation of Tm2Ru2O7(s) from elements in their standard state, calculated by the least squares regression analysis of the data obtained in the present study, can be given by:{ΔfG°(Tm2Ru2O7,s)/(kJ · mol−1) ± 1.9} = − 2511.9 + 0.625 ⋅ (T/K); (977 ≤ T/K ≤ 1265).Standard molar heat capacity Cop,m(T) of Tm2Ru2O7(s), was measured using a heat flux type differential scanning calorimeter (DSC) in two different temperature ranges, from 128 K to 276 K and 307 K to 686 K. The heat capacity in the higher temperature range was fitted into a mathematical expression and can be represented by:C°p,mTm2Ru2O7sT)(J⋅K−1·mol−1=297.8+2.0⋅10−3TK−62.1⋅105/T2K.307≤TK≤686The standard molar heat capacity data of Tm2Ru2O7(s), along with the data obtained from the oxide electrochemical cell were used to calculate the standard enthalpy of formation and absolute molar entropy of the compound. The standard Gibbs energy of formation obtained earlier for other heavy rare earth ruthenium pyrochlores were compared with the present results.

Thermodynamic stability of CaThF6(cr) by transpiration and e.m.f. techniques

In the present paper, we report the standard molar Gibbs energy of formation for CaThF6 measured by gas equilibration and e.m.f. methods. The HF(g) vapour pressure over the equilibrium reaction: $${\text{CaThF}}_{6} \left( {\text{cr}} \right) + 2 {\text{H}}_{ 2} {\text{O}}\left( {\text{g}} \right) = {\text{CaF}}_{2} \left( {\text{cr}} \right) + {\text{ThO}}_{2} \left( {\text{cr}} \right) + 4{\text{HF}}\left( {\text{g}} \right)$$ has been measured using transpiration technique. The above reaction mechanism has been established employing TG and XRD techniques. A fluoride e.m.f. cell: (−)Pt, CaF2(cr) + ThOF2(cr) + CaThF6(cr) |CaF2(cr)| NiO(cr) + NiF2(cr), Pt(+) has been constructed to measure Gibbs energy of formation of CaThF6 (cr) using CaF2 (cr) as a solid electrolyte. The isobaric heat capacity $${\text{Cp}}_{\text{m}}^{{\circ }} \left( T \right)$$ of the compound has been measured using differential scanning calorimetric technique. Based on the experimental results, thermodynamic functions for CaThF6 have been generated.

Thermodynamics of tetraphenylantimony benzoate Ph4SbOC(O)Ph

In the present research, the temperature dependence of the heat capacity Cp,mo = f(T) of tetraphenylantimony benzoate Ph4SbOC(O)Ph has been measured in the range T = (5 and 480) K in the precision adiabatic vacuum and differential scanning calorimeters and reported for the first time. In the studied temperature region the melting of the compound has been revealed and its standard thermodynamic characteristics were analyzed. The standard thermodynamic functions (p° = 0.1 MPa) of Ph4SbOC(O)Ph in crystalline and liquid states were calculated with the obtained experimental data: Cp,mo/R, Δ0THmo/RT, Δ0TSmo/R and Φmo = Δ0TSmo – Δ0THmo/T (where R is the universal gas constant) from T → 0 to 480 K. The energy of combustion of Ph4SbOC(O)Ph was measured. The standard enthalpy of combustion, formation enthalpy, formation entropy, Gibbs energy of formation of the substance in the crystalline state at T = 298.15 K were calculated. Comparison of thermodynamic properties was made for the derivatives of antimony studied in the present work, Ph5Sb and other of type Ph3SbX2.

Influence of Hydroxyl Functional Group on the Structure and Stability of Xanthone: A Computational Approach.

The present work addresses computational research focused on the energetic and structural properties of four isomers monohydroxyxanthone, using the G3(MP2)//B3LYP method, in order to evaluate the influence of the hydroxyl (—OH moiety) functional group on the xanthone molecule. The combination of these computational results with previous experimental data of these compounds enabled the determination of their enthalpies, entropies and Gibbs energies of formation, in the gaseous phase, and consequently to infer about the relative thermodynamic stability of the four isomers. Other issues were also addressed for the hydroxyxanthone isomers, namely the conformational and the tautomeric equilibrium analysis of the optimized molecular structures, the frontier orbitals, and the electrostatic potential energy maps. Complementarily, an energetic study of the intramolecular hydrogen bond for 1-hydroxanthone was also performed.

Study of temperature effect on carbide layer formation behaviour of dual elements thermal reactive deposition on SUJ2 steel substrate

In this research, the formation of carbide layer coating on SUJ2 steel by pack Thermal Reactive Deposition method was studied. Mixture of 35/65 weight percent of ferrochromium/ferrovanadium (FeCr/FeV) powder was applied as coating elements. The process was carried out at temperatures of 900, 950, and 1000 °C for 6 hours for each temperature. The effects of temperature on layer thickness, microstructures, homogeneity, hardness, and wear resistance were analyzed. The result showed that the higher the temperature, the thicker the layer formed on substrate surface. The higher percentage of vanadium in the coating layer compared to chromium found by EDS Linescan results indicate that vanadium has higher affinity to carbon than chromium. This result also means the possibility of vanadium carbide formation will be higher than chromium carbides, due to the lower Gibbs energy for vanadium carbide formation. XRD results showed that the layer formed in this process consists of vanadium carbide (V8C7 and V6C5), chromium carbide (Cr23C6 and Cr7C3), and complex carbides. The average micro hardness and wear rate of all coatings with three different temperature variations were 2100 HV, and 3 × 10−4 mm3/m respectively. This hardness was close to FeV hardness as single carbide former at approximately 2400 HV.

Differential scanning calorimetric measurements and thermodynamic functions of YbRhO3(s)

Abstract

Determination of the thermodynamic properties of the Li2CaThF8 in Li-Ca-Th-F system by the solid-state electrochemical cell method

In the present paper, we have reported the standard molar Gibbs energy of formation for Li2CaThF8(s) measured by solid electrolyte galvanic cell technique with CaF2 as solid electrolyte. The heat capacity, Cp, of the compound has been measured using the differential scanning calorimetric technique. Based on the experimentally obtained thermodynamic parameters, thermodynamic functions for Li2CaThF8(s) have been generated.

Thermodynamic investigations on BaNd2O4 compound

The MLn2O4 (M = Ba, Sr and Ln = lanthanides) are being studied recently as a class of frustrated magnetic materials. Solid-state reaction route was used to prepare BaNd2O4 compound. The Gibbs energy of formation of BaNd2O4 was evaluated by measuring the partial pressures of CO2 over the equilibrium phase mixture of BaCO3 and Nd2O3. Gibbs energy formation of the compound as a function of temperature is given as: $$\Delta_{\text{f}} G_{\text{m}}^{\text{o}} ({\text{BaNd}}_{2} {\text{O}}_{4} ,\,{\text{s}},\;{\text{kJ}}\,{\text{mol}}^{ - 1} )\left( { \pm \,7} \right) = - 2400 + 0.362 \times (T /K)\quad (690 \le T /K \le 870)$$ The molar heat capacity of the compound was measured using differential scanning calorimeter as a function of temperature and is given as: $$C_{{{\text{p}},{\text{m}}}}^{\text{o}} ({\text{BaNd}}_{2} {\text{O}}_{4} ,\,{\text{s}},\,{\text{J}}\,{\text{mol}}^{ - 1} \,{\text{K}}^{ - 1} ) = 164.5 + 0.04078 \times (T /K) - 174{,}3853/ \times (T /K)^{2} \quad (350 \le T /K \le 1000)$$ Based on these experimental data, thermodynamic functions of this compound were also generated.

A Calorimetric and Thermodynamic Investigation of the Synthetic Analogue of Mandarinoite, Fe2(SeO3)3·5H2O

Thermophysical and thermochemical calorimetric investigations were carried out on the synthetic analogue of mandarinoite. The low-temperature heat capacity of Fe 2 ( SeO 3 ) 3 · 5 H 2 O ( cr ) was measured using adiabatic calorimetry between 5.3 and 324.8 K, and the third-law entropy was determined. Using these C p , m o ( T ) data, the third law entropy at T = 298.15 K, S m o , is calculated as 520.1 ± 1.1 J∙K−1∙mol−1. Smoothed C p , m o ( T ) values between T → 0 K and 320 K are presented, along with values for S m o and the functions [ H m o ( T ) − H m o ( 0 ) ] and [ Φ m o ( T ) − Φ m o ( 0 ) ] . The enthalpy of formation of Fe 2 ( SeO 3 ) 3 · 5 H 2 O ( cr ) was determined by solution calorimetry with HF solution as the solvent, giving Δ f H m o ( 298 K , Fe 2 ( SeO 3 ) 3 · 5 H 2 O , cr ) = −3124.6 ± 5.3 kJ/mol. The standard Gibbs energy of formation for Fe 2 ( SeO 3 ) 3 · 5 H 2 O ( cr ) at T = 298 K can be calculated on the basis on Δ f H m o ( 298 K ) and Δ f S m o ( 298 K ) : Δ f G m o ( 298 K , Fe 2 ( SeO 3 ) 3 · 5 H 2 O , cr ) = −2600.8 ± 5.4 kJ/mol. The value of ΔfGm for Fe2(SeO3)3·5H2O(cr) was used to calculate the Eh–pH diagram of the Fe–Se–H2O system. This diagram has been constructed for the average contents of these elements in acidic waters of the oxidation zones of sulfide deposits. The behaviors of selenium and iron in the surface environment have been quantitatively explained by variations of the redox potential and the acidity-basicity of the mineral-forming medium. These parameters precisely determine the migration ability of selenium compounds and its precipitation in the form of solid phases.

Understanding the Stability of Salt-Inclusion Phases for Nuclear Waste-forms through Volume-based Thermodynamics

Formation enthalpies and Gibbs energies of actinide and rare-earth containing SIMs with silicate and germanate frameworks are reported. Volume-based thermodynamics (VBT) techniques complemented by density functional theory (DFT) were adapted and applied to these complex structures. VBT and DFT results were in closest agreement for the smaller framework silicate structure, whereas DFT in general predicts less negative enthalpies across all SIMs, regardless of framework type. Both methods predict the rare-earth silicates to be the most stable of the comparable structures calculated, with VBT results being in good agreement with the limited experimental values available from drop solution calorimetry.

Thermodynamic properties of MgGa2O4 and phase relations in the system Mg-Ga-O

Materials based on MgGa2O4 find use in microwave dielectrics, optoelectronics, spintronics and solid electrolytes for high-temperature fuel cells. For designing optimum processing conditions and evaluating interactions with other materials and environments, thermodynamic data and appropriate phase diagrams are required. As part of a larger systematic study on spinels with functional applications, thermodynamic properties of MgGa2O4 are determined in the temperature range from 875 to 1325 K using an electrochemical cell incorporating yttria-stabilized zirconia as the solid electrolyte. The Gibbs energy of formation of MgGa2O4 from its constituent binary oxides MgO with halite structure and β-Ga2O3 with monoclinic structure is obtained: ΔGf(ox)o (±135)/J mol−1 = –39868–8.742 (T/K). The heat capacity of MgGa2O4 in the temperature range from 310 to 1200 K is measured by DSC. Both positive and negative deviations from Neumann-Kopp rule are seen in different temperature ranges. Derived from these measurements are the standard enthalpy of formation and standard entropy of MgGa2O4 at 298.15 K. The isothermal section of the phase diagram of the system Mg-Ga-O and oxygen potential-composition diagram at 1200 K are computed from thermodynamic data.

The Dependence of Gibbs Energy of Formation of Niobium Mononitride on its Composition and Temperature in the Range of 1773-2023 K

The article demonstrates the applicability of the interaction parameter method for describing the thermodynamic properties of non-stoichiometric niobium nitrides at temperatures of 1773 ± 2023 K. The authors obtained the equation of dependence of the nitride dissociation elasticity on its composition and temperature. They derived the expression for calculating Gibbs energy of formation of nitrides with a set composition, including stoichiometric, in the range of 1773 - 2023 K.

Thermodynamic Assessment of the Ag-Se System Aided by First-Principles Calculations

The substitution of Ag for Cu in CuInxGa1−xSe2-based photovoltaic absorber layers can be used to adjust the bandgap energy to better optimize the overall cell efficiency. Based on available thermochemical, equilibrium, and structural data, the Ag-Se system has been assessed and modeled. Given the order-disorder structure transition Ag2Se, the 2- and 3-sublattice models were used to represent the low- and high-temperature phases of the intermetallic compound respectively. Density functional theory based first-principles calculations were used to calculate the Gibbs energy of formation of the end-member compounds. A set of modeling parameters was obtained by the CALculation of PHAse Diagram approach and reasonable agreement was obtained between the experimental thermodynamic properties of the stable phases and the phase relationships in the Ag-Se system.

Thermodynamics on the Bi-Fe-Ti System and the Gibbs Energy of Bi9Ti8

Partial isothermal sections of the Bi-Fe-Ti system at 700 °C and 900 °C were constructed to investigate the reactivity of Fe with Bi-Ti liquid alloy. In the ternary system, three-phase equilibria such as liquid-Fe-Fe2Ti, liquid-Fe2Ti-Bi2FeTi4, and liquid-Bi9Ti8-Bi2FeTi4 were confirmed at both temperatures. The solubility of Fe in liquid Bi at these temperatures is negligibly small. On the other hand, it is notable that the solubility of Fe in liquid Bi containing Ti at 900 °C is much larger and reaches 2.3 mol pct. Then, we measured the electromotive force (emf) between Bi-20 mol pct Ti alloy and pure Ti at 700 °C in equimolar NaCl-KCl where 1 mol pct TiCl2 was added. From the result, the interaction parameter of the liquid phase in the Bi-Ti system and the standard molar Gibbs energies of formation of Bi9Ti8 and Bi2FeTi4 at 700 °C were estimated.

Vapour pressures and thermodynamic stability of the three aminophenol isomers

The Knudsen mass-loss effusion method was used to determine the sublimation vapour pressures, at different temperatures, of ortho and para aminophenols in the temperature intervals T = (321.1 to 343.3) K and T = (337.2 to 359.2) K, respectively. The vapour pressures of crystalline meta-aminophenol were measured using the referred to above technique, between (321.4 and 343.3) K, and a static method, based on capacitance diaphragm manometers, between (354.4 and 391.8) K. The latter technique was also used to measure the liquid vapour pressures of this isomer over the temperature range T = (370.0 to 423.3) K. The experimental results enabled the determination of the standard (po = 0.1 MPa) molar enthalpies, entropies and Gibbs energies of sublimation, at T = 298.15 K, of the three compounds, and of vaporization of the meta isomer. The standard enthalpies of formation in the gaseous phase were calculated using quantum chemical calculations and also by combining literature results of enthalpies of formation in the crystalline phase with the sublimation enthalpies results determined in this work. Gas-phase absolute entropies and heat capacities of the three compounds studied were also calculated using theoretical methods. The standard Gibbs energies of formation in crystalline and gaseous phases were determined and used to evaluate the thermodynamic stability of the three isomers in standard conditions. DSC analysis enabled the determination of the temperature and molar enthalpies of fusion of the compounds studied.