Related Thermodynamic Functions Research Articles

Study of the solid-phase equilibria in the GeTe-Bi2Te3-Te system and thermodynamic properties of GeTe-rich germanium bismuth tellurides

A set of self-consistent thermodynamic parameters of the GeTe-rich germanium-bismuth tellurides were determined using an electromotive force (EMF) method with a glycerol electrolyte in a temperature range from 300 to 450 K. The solid-phase equilibrium diagram of the GeTe-Bi2Te3-Te system at 400 K was constructed using X-ray diffraction (XRD) and scanning electron miscroscope (SEM) techniques of synthesized electrode alloys, as well as available literature data. It is found that all telluride phases in GeTe-Bi2Te3 pseudo-binary section have a tie-line connection with elemental tellurium. The relative partial thermodynamic functions of GeTe in alloys were calculated using data from EMF measurements of concentration cells relative to the GeTe electrode. These findings together with the corresponding thermodynamic functions of GeTe and Bi2Te3 were used to calculate the relative partial molar functions of germanium in alloys, and also the standard thermodynamic functions of formation and standard entropies of the ternary compounds, namely Ge2Bi2Te5, Ge3Bi2Te6 and Ge4Bi2Te7.

Design and construction of a refrigerator-cooled adiabatic calorimeter for heat capacity measurement in liquid helium temperature region.

Heat capacity is a fundamental thermodynamic property of a substance. Although heat capacity values and related thermodynamic functions are available for many materials, low-temperature heat capacity measurements, especially for novel materials, can still provide valuable insights for research in physics, chemistry, thermodynamics, and other fields. Reliable low-temperature heat capacity data are typically measured using classical adiabatic calorimeters, which use liquid helium as the refrigerant to provide a cryogenic environment for heat capacity measurements. However, liquid helium is not only expensive but also not easy to obtain, which greatly limits the application of adiabatic calorimetry. In this work, an accurate adiabatic calorimeter equipped with a Gifford-MacMahon refrigerator was designed and constructed for measuring the heat capacity of condensed matter in the temperature range from 4 to 100K. The Gifford-MacMahon refrigerator was utilized to provide a stable liquid helium-free cryogenic environment. A simple mechanical thermal switch assembly was designed to facilitate switching between the refrigeration mode and the adiabatic measurement mode of the calorimeter. Based on the measurement results of standard reference materials, the optimized repeatability and accuracy of heat capacity measurements were determined to be within 0.8% and 1.5%, respectively. The heat capacity of α-Fe2O3 nanoparticles was also investigated with this device. Furthermore, this adiabatic calorimeter only requires electricity to operate in the liquid helium temperature range, which may significantly advance the research on low-temperature heat capacity based on adiabatic calorimetry.

Low-temperature heat capacity and the thermodynamic functions of a novel ether-based ionic liquid 1-(2-ethoxyethyl)-3-ethylimidazolium thiocyanate.

A novel ionic liquid (IL) modified by ether was prepared by a two-step synthesis method for the first time in this paper. The structure of 1-(2-ethoxyethyl)-3-ethylimidazolium thiocyanate ([C22O2Im][SCN]) was characterized and analyzed by hydrogen nuclear magnetic resonance (1H-NMR), carbon nuclear magnetic resonance (13C-NMR), Fourier transform infrared spectroscopy (FT-IR), electrospray ionization-mass spectrometry (ESI-MS), elemental analysis and thermal gravity analysis (TG). Within a specific temperature range from 79 to 393 K, the low temperature heat capacity of [C22O2Im][SCN] was determined, using a high precision low temperature adiabatic calorimeter. Then, the related thermodynamic functions, such as (H T - H 298.15), (S T - S 298.15) and (G T - G 298.15), were calculated, which can provide a theoretical basis for the application of ether-based ILs in the future.

Thermodynamic properties of substrate-induced graphene superlattice in homogeneous magnetic field

In this article we study the thermodynamic properties of a substrate-induced graphene superlattice in the presence of uniform magnetic field B. We derive an expression for the partition function of the system with uniform magnetic field B using the zeta function approach and find all related thermodynamic functions such as Helmholtz free energy, total energy, specific heat capacity and entropy for three cases related to the sublattice potential. We also show that the Dulong-Petit law is verified for all cases in the high-temperature limit. These results may shed light on the study of graphene superlattices in the developement of thermo-electric devices.

Computing thermodynamic properties of some diatomic molecules using a q-deformed Scarf-like potential

This paper computes the vibrational partition function of some diatomic molecules using an improved energy spectrum obtained recently with the q-deformed hyperbolic Scarf-like potential. Compared to the experimental energy curves, this potential proved to represent well the interaction between the atoms in the studied molecules. The related thermodynamic functions are derived for the , ScI and molecules. Results demonstrated that the computed molecular entropy is in very good agreement with the experimental data for a large range of temperature values. In addition, results are given for the ScI molecule for which no experimental entropy values exist. Our results can serve as a reference to experimental studies in chemical physics.

Studies on synthesis, volume and conductivity behaviors of three novel pharmaceutical salts [CnPy][AceSA] (n = 8, 10, 12)

In the present work, three new pharmaceutical salts based on N-alkyl-pyridinium ([CnPy]+, n = 8, 10, 12) as the cations and acetyl-sulfacetamide ([AceSA]-) as an anion were synthesized. The thermal stability was measured by synchronous thermal analyzer. The solvation and micellization behaviors in aqueous solution were investigated by experimental density and conductivity data at different temperatures. These data were used to calculate the apparent molar volume at infinite dilution, V2,φ0, the apparent molar expansibility at infinite dilution, Eφ0, limiting molar conductivity, Ʌ0, critical micelle concentration, cmc, and the relative thermodynamic functions for the micellization of [CnPy][AceSA] in aqueous solution. The effect of the aliphatic chain length of N-alkyl-pyridinium cation and temperature on the estimated properties was examined. The obtained results confirmed that [CnPy]+(n = 8, 10, 12) cations with longer alkyl chain exhibit higher decomposition temperature, large V2,φ0, low cmc and Ʌ0 values. The results were discussed in terms of solute–solvent interactions and structural changes of [CnPy][AceSA] in water.

Thermodynamic study of the thallium-thulium tellurides by EMF method

In this study the phase equilibria in the Tl2Te–Tl2Te3–TlTmTe2compositions area of the Tl–Tm–Te ternary system were studied by powder X-ray diffraction (PXRD) analysis. Based on PXRD data, the solid-phase equi-libria diagram was plotted. The thermodynamic functions of the Tl9TmTe6and TlTmTe2ternary compounds were calculated by the electromotive forces method. The electrochemical cells of the following type (−) TmТе (s.) | glycerol + KCl + TmCl3 | (Tm in alloys of Tl–Tm–Te system) (s.) (+) were assembled and their EMF were measured in the 300-450 Ktemperature range. Based on obtained EMF data for the Tl2Te3–TlTe–TlTmTe2and TlTe–TlTmTe2–Tl9TmTe6three-phase regions, the relative partial thermodynamic functions of TmTe in alloys were calculated. The combination of these functions with the partial molar functions of thulium in TmTe allowed calculating the corresponding partial functions of thulium in the above phase regions. The potential-forming reactions responsible for the indicated partial molar values were obtained based on con-structed solid-phase equilibria diagram. Using indicated potential-forming reactions, for the first time, the standard thermodynamic functions of formation and standard entropies of the Tl9TmTe6and TlTmTe2 compounds were calculated.

Thermodynamic insights into n-alkanes phase change materials for thermal energy storage

n-Alkanes have been widely used as phase change materials (PCMs) for thermal energy storage applications because of their exceptional phase transition performance, high chemical stability, long term cyclic stability and non-toxicity. However, the thermodynamic properties, especially heat capacity, of n-alkanes have rarely been comprehensively investigated in a wide temperature range, which would be insufficient for design and utilization of n-alkanes-based thermal energy storage techniques. In this study, the thermal properties of n-alkanes (C18H38-C22H46), such as thermal stability, thermal conductivity, phase transition temperature and enthalpy were systematically studied by different thermal analysis and calorimetry methods, and compared with previous results. Thermodynamic property of these n-alkanes was studied in a wide temperature range from 1.9 K to 370 K using a combined relaxation (Physical Property Measurement System, PPMS), differential scanning and adiabatic calorimetry method, and the corresponding thermodynamic functions, such as entropy and enthalpy, were calculated based on the heat capacity curve fitting. Most importantly, the heat capacities and related thermodynamic functions of n-heneicosane and n-docosane were reported for the first time in this work, as far as we know. This research work would provide accurate and reliable thermodynamic properties for further study of n-alkanes-based PCMs for thermal energy storage applications.

Solid-phase Relationships in the Tl2Te-Tl2Te3-TlTbTe2 System and Thermodynamic Properties of Thallium–Terbium Tellurides

This work presents new data on the solid-phase equilibria of the Tl-Tb-Te ternary system in the Tl2Te-Tl2Te3-TlTbTe2 composition region and the thermodynamic functions of the TlTbTe2, and Tl9TbTe6 ternary compounds. Studies were carried out by using the electromotive forces method (EFM) and the powder x-ray diffraction technique. From the EMF measurements of the concentration cells of the type (−) TbTe (s) | glycerol + KCl + TbCl3 | (Tb in Tl-Tb-Te alloys) (s) (+) in the 300-450 K temperature interval, the relative partial thermodynamic functions of TbTe and Tb in alloys of the Tl2Te3-TlTe-TlTbTe2, and TlTe-TlTbTe2-Tl9TbTe6 three-phase regions were determined. Based on the solid-phase equilibria diagram, the potential-forming reactions responsible for the indicated partial molar quantities were determined and the standard thermodynamic functions of formation and standard entropies of the TlTbTe2 and Tl9TbTe6 ternary compounds were calculated.

Thermodynamic study of a synthetic analog of the famatinite mineral - Cu3SbS4

Fundamental thermodynamic properties of the synthetic analog of the famatinite mineral - Cu3SbS4 were studied on the basis of electromotive force (EMF) measurements. The EMF of the concentration chains relative to the Cu electrode with a solid electrolyte was measured for the alloys from the Cu3SbS4 + Sb2S3 + S phase region at 300-380K temperature interval. Based on measurement data, the relative partial thermodynamic functions of copper in alloys, the standard thermodynamic functions of formation, as well as, the standard entropy of the Cu3SbS4 ternary compound were calculated for the first time.

Thermal kinetic analysis of a complex process from a solid-state reaction by deconvolution procedure from a new calculation method and related thermodynamic functions of Mn0.90Co0.05Mg0.05HPO4·3H2O

Abstract Three individual peaks of thermal solid-state reaction processes of the synthesized Mn0.90Co0.05Mg0.05HPO4·3H2O were observed corresponding to dehydration I, dehydration II and polycondensation processes. An alternative method for the calculation of the extent of conversion was proposed from the peak area of the individual DTG peak after applying the best fitting deconvolution function (Frazer-Suzuki function). An iterative integral isoconversional equation was used to compute the values of the apparent activation energy Eα and they were found to be 65.87, 78.16 and 119.32 kJ/mol for three peaks, respectively. Each individual peak was guaranteed to be a single-step kinetic system with its unique kinetic parameters. The reaction mechanism functions were selected by the comparison between experimental and model plots. The results show that the first, second and final individual peaks were two-dimensional diffusion of spherical symmetry (D2), three-dimensional diffusion of spherical symmetry (D3) and contracting cylinder (cylindrical symmetry, R2) mechanisms. Pre-exponential factor values of 3.91×106, 1.35×107 and 2.15×107 s−1 were calculated from the Eα values and reaction mechanisms. The corresponded standard thermodynamic functions of the transition-state (activated) complexes were determined and found to agree well with the experimental data.

The statistical properties of q-deformed Morse potential for some diatomic molecules via Euler–MacLaurin method in one dimension

In this paper, we present a closed-form expression of the vibrational partition function for the one-dimensional q-deformed Morse potential energy model. Through this function, the related thermodynamic functions are derived and studied in terms of the parameters of the model. Especially, we plotted the q-deformed vibrational partition function and vibrational specific heat for some diatomic molecule systems such as \(\text {H}_{2}\), HCl, LiH, and CO. The idea of a critical temperature \(T_{C}\) is introduced in relation to the specific heat.

Critical assessment of three kinds of activity coefficients of carbon and related mixing thermodynamic functions of Fe–C binary melts based on atom–molecule coexistence theory

Raoultian activity coefficients $${\gamma}_{\text{C}}^{0}$$ of C in infinitely dilute Fe–C binary melts at temperatures of 1833, 1873, 1923, and 1973 K have been determined from the converted mass action concentrations $$N_{\text{C}}^{\prime}$$ of C in Fe–C binary melts by the developed AMCT-N i model based on the atom–molecule coexistence theory (AMCT). The obtained expression of $$\gamma_{\text{C}}^{0}$$ by the developed AMCT-N i model has been evaluated to be accurate based on the reported ones from the literature. Meanwhile, three activity coefficients $$\gamma_{\text{C}}$$ , $$f_{{\%,{\text{ C}}}}$$ , and $$f_{\text{H, C}}$$ of C coupled with activity $$a_{\text{R, C}}$$ or $$a_{{\%,{\text{ C}}}}$$ or $$a_{\text{H, C}}$$ have been obtained by the developed AMCT-N i model and assessed through comparing with the predicted ones by other models from the literature. The first-order activity interaction coefficients $$\varepsilon_{\text{C}}^{\text{C}}$$ , $$e_{\text{C}}^{\text{C}}$$ , and $$h_{\text{C}}^{\text{C}}$$ related to $$\gamma_{\text{C}}$$ , $$f_{{\%,{\text{ C}}}}$$ , and $$f_{\text{H, C}}$$ are also determined and assessed in comparison with the reported ones from the literature. Furthermore, the integral molar mixing thermodynamic functions such as $$\Delta_{\text{mix}} H_{{{\text{m, Fe}} - {\text{C}}}}$$ , $$\Delta_{\text{mix}} S_{{{\text{m, Fe}} - {\text{C}}}}$$ , and $$\Delta_{\text{mix}} G_{{{\text{m, Fe}} - {\text{C}}}}$$ of Fe–C binary melts over a temperature range from 1833 to 1973 K have been determined and evaluated to be valid based on the determined ones from the literature.

Thermodynamic Properties of AgIn2Te3I and AgIn2Te3Br, Determined by EMF Method

Differential thermal analysis (DTA), X-ray diffraction (XRD), and electromotive force (EMF) are used to triangulate Ag–In–Te–I(Br) systems in the vicinity of compounds AgIn2Te3I and AgIn2Te3Br. The three-dimensional position of the AgIn2Te3I–InTe–Ag2Te–AgI and AgIn2Te3Br–InTe–Ag3TeBr phase areas with respect to the figurative points of silver is used to create equations of potential-determining chemical reactions. The potential-determining reactions are conducted in (−)C|Ag|Ag3GeS3I(Br) glass|D|C(+) electrochemical cells (ECCs), where C stands for inert (graphite) electrodes, Ag and D are ECC electrodes (D denotes alloys of one-, three-, and four-phase areas), and Ag3GeS3I and Ag3GeS3Br glasses are membranes with purely ionic Ag+ conductivity. Linear parts of the temperature dependences of the cell EMFs are used to calculate the standard integral thermodynamic functions of saturated solid solutions based on AgIn2Te3I and AgIn2Te3Br, and the relative partial thermodynamic functions of silver in the stoichiometric quaternary compounds.

Deconvolution technique for the kinetic analysis of a complex reaction and the related thermodynamic functions of the formation of LiMn0.90Co0.05Mg0.05PO4

Four separated peaks of the thermal reaction of the mixture between NH4Mn0.90Co0.05Mg0.05PO4⋅H2O and Li2CO3 were considered to be dehydration, deammoniation, polycondensation and decarbonization. Alternative technique for the conversion calculation was proposed by using the deconvoluted DTG peak after the Fraser–Suzuki equation was used. Iteration was used to estimate the activation energy Eα. Each peak was confirmed as a single-step kinetic. Dual-plots were compared to choose the mechanisms. Mechanisms were found to be contracting cylinder, contracting sphere, assumed random nucleation and 2D diffusion. Pre-exponential factor was obtained from Eα and mechanisms. Thermodynamic data were found to agree with the experimental data.

Quantum Mechanics Approach to Hydration Energies and Structures of Alanine and Dialanine.

A systematic approach to the phenomena related to hydration of biomolecules is reported at the state of the art of electronic-structure methods. Large-scale CCSD(T), MP4-SDQ, MP2, and DFT(M06-2X) calculations for some hydrated complexes of alanine and dialanine (Ala⋅13 H2 O, Ala2 H+ ⋅18 H2 O, and Ala2 ⋅18 H2 O) are compared with experimental data and other elaborate modeling to assess the reliability of a simple bottom-up approach. The inclusion of a minimal number of water molecules for microhydration of the polar groups together with the polarizable continuum model is sufficient to reproduce the relative bulk thermodynamic functions of the considered biomolecules. These quantities depend on the adopted electronic-structure method, which should be chosen with great care. Nevertheless, the computationally feasible MP2 and M06-2X functionals with the aug-cc-pVTZ basis set satisfactorily reproduce values derived by high-level CCSD(T) and MP4-SDQ methods, and thus they are suitable for future developments of more elaborate and hence more biochemically significant peptides.

The Tl–I phase diagram revisited and the thermodynamic properties of thallium iodides

The Tl–I system has been studied using differential thermal analysis, X-ray diffraction, and emf measurements on TlI concentration cells. A more accurate Tl–I phase diagram is presented, according to which the compounds existing in the Tl–I system are TlI, Tl2I3, and TlI3. Thallium monoiodide melts congruently at 715 K and undergoes a polymorphic transformation at 440 K. The other iodides melt peritectically at 535 and 404 K, respectively. In contrast to what was reported previously, no compound of composition Tl3I4 has been obtained. Using experimental emf data, we evaluated relative partial molar thermodynamic functions of the TlI in alloys of the TlI–I system and the standard Gibbs free energy, enthalpy of formation, and standard entropies of TlI3 (−ΔG 298 0 = 142.79 ± 0.73 kJ/mol, −ΔH 298 0 = 135.37 ± 2.85 kJ/mol, and S 298 0 = 263.3 ± 7.4 J/(mol K)) and Tl2I3 (271.39 ± 1.47, 262.40 ± 5.34, and 322.8 ± 13.2).

Double function method for the confirmation of the reaction mechanism of LiCoPO4 nanoparticle formation, reliable activation energy, and related thermodynamic functions

In this study, dehydration I and II, polycondensation, and decarbonization processes of the thermal solid-state reaction between CoHPO4⋅3H2O and Li2CO3 were observed and the LiCoPO4 nanoparticles were obtained. For the sample characterization, the TG/DTG/DTA, FTIR, and AAS/AES techniques were applied. Structures and morphologies were investigated by the XRD and SEM techniques, respectively. To calculate the variable activation energy (\(E_{\alpha }\)) value, various isoconversional equations were used. In addition, the iterative isoconversional equations were also used to obtain the more reliable \(E_{\alpha }\) values of 64.04 ± 3.20, 78.54 ± 3.23, 100.41 ± 6.00, and 140.07 ± 5.02 kJ mol−1 for the first (regions I and II), second, and final steps, respectively. The first (regions I and II) as well as the second and final steps were confirmed to be a single-step kinetic process with the unique kinetic parameters. The double function \(y(\alpha )\) and \(z(\alpha )\) method was used to confirm the reaction mechanisms and found to be \(R_{2}\), \(R_{3}\), \(A_{3}\), and \(P_{3}\) corresponding to contracting cylinder, contracting sphere, assumed random nucleation (and its subsequent growth), and nucleation processes, respectively. The studied processes lead to the formation of the final nanoparticle product LiCoPO4. The four pre-exponential factors calculated using \(E_{\alpha }\) and mechanism functions were found to be 1.01 (±0.016) × 107, 7.80 (±0.009) × 107, 4.52 (±0.010) × 105, and 1.03 (±0.003) × 106 s−1, respectively. The related standard thermodynamic functions of the transition-state complexes were evaluated by using the calculated kinetic parameters.

Thermodynamic Study of Tl6SBr4 Compound and Some Regularities in Thermodynamic Properties of Thallium Chalcohalides

The solid-phase diagram of the Tl-TlBr-S system was clarified and the fundamental thermodynamic properties of Tl6SBr4 compound were studied on the basis of electromotive force (EMF) measurements of concentration cells relative to a thallium electrode. The EMF results were used to calculate the relative partial thermodynamic functions of thallium in alloys and the standard integral thermodynamic functions (-ΔfG0, -ΔfH0, and S0298) of Tl6SBr4 compound. All data regarding thermodynamic properties of thallium chalcogen-halides are generalized and comparatively analyzed. Consequently, certain regularities between thermodynamic functions of thallium chalcogen-halides and their binary constituents as well as degree of ionization (DI) of chemical bonding were revealed.

On the generalization of statistical thermodynamic functions by a Riccati differential equation.

In this work, we propose a non-linear differential equation of Riccati-type, where the standard partition function Z(T) is taken as its particular solution leading to their generalization Zg(T); from there, other related statistical thermodynamic functions are generalized. As an useful application of our proposal, other thermodynamic functions, namely, the internal energy, heat capacity, Helmholtz free energy and entropy, associated to the model of the ideal monatomic gas in D-dimensions are generalized. According to our results, thermodynamic properties derived from the standard partition functions by means of ordinary statistical mechanics are incomplete. In fact, although asymptotically with the increasing of temperature the generalized statistical thermodynamic functions reduce to the standard ones, these contain an extra term which is dominant at very low temperature indicating that standard findings should be corrected.