Entropy Of Fusion Research Articles

Thermodynamic properties of N, N-dimethylformamide and N, N-dimethylacetamide

The heat capacity of N, N-dimethylformamide and N, N-dimethylacetamide in both crystalline and liquid state was determined between T = (7 to 305) K and T = (7 to 340) K, respectively, by adiabatic vacuum calorimetry, generally with an uncertainty of ±0.2%. The melting temperatures and the enthalpies of fusion were measured and the entropies of fusion were estimated. The experimental data were used to calculate the standard ( p ∘ = 0.1 MPa) thermodynamic functions of the examined amides C p ,m ∘ / R , Δ o T H m ∘ / R , Δ o T S m ∘ / R , and Φ m ∘ = Δ o T S m ∘ - Δ o T H m ∘ / T (where R is the universal gas constant) in the range from T → 0 to T = 305 (340) K.

Thermodynamic investigation of the Cu–Zr system

High temperature heat contents of the Cu–Zr system alloys were measured over temperature range from 880 to 1470 K using a drop calorimeter. The enthalpies of fusion of some solid compounds were determined by the heat content—temperature plots and the entropies of fusion were calculated. Enthalpies of mixing in the liquid Cu–Zr system were measured by high temperature reaction calorimetry in the concentration range of x Zr = 0.182–0.667 at 1443 K. This system has negative enthalpies of mixing over the measured concentration range. The standard enthalpies of formation at 298.15 K of Cu 9Zr 2, Cu 51Zr 14, Cu 8Zr 3, Cu 10Zr 7 and CuZr 2 compounds were determined from the obtained data for the heat contents and enthalpies of mixing. Based on the experimental data, published thermodynamic and phase diagram data, the Cu–Zr binary system was analyzed using Redlich–Kister polynomial equation. The thermodynamic properties and the phase diagram calculated from the optimized parameters agree well with the experimental data.

Interaction between single grain solidification and macrosegregation: Application of a cellular automaton—Finite element model

A two-dimensional (2D) cellular automaton (CA)—finite element (FE) model developed for the prediction of grain structure formation during solidification processes is presented. While the FE method solves the macroscopic conservation equations for heat and mass transfers, the CA method is used at a mesoscopic scale to simulate the growth of a mushy zone domain. The limit between this mushy zone domain and the undercooled liquid melt in which it develops defines the envelope of a single grain. A verification is first performed to check that the CAFE model retrieves the solution of a purely FE simulation for a vanishing undercooling of the growth front. Since the present 2D CAFE model is relevant with respect to the solidification experiment developed by Yin and Koster [H. Yin, J. N. Koster, J. Crystal Growth 205 (1999) 590; H. Yin, J. N. Koster, J. Alloy Compd. 352 (2003) 197], comparison is then performed. In particular, the position of the growth front is considered as a time sequence. The effect of the growth undercooling is clearly revealed. The kinetics of the growth front used in the model assumes the development of a rough interfacial dendrite-like morphology. This assumption is discussed considering the value of the normalized entropy of fusion of gallium.

The density and compressibility of KAlSi3O8 liquid to 6.5 GPa

The thermodynamic properties of crystalline and liquid KAlSi 3 O 8 are used to calculate the fusion curve of sanidine to 6.5 GPa. New values for the enthalpy and entropy of fusion of sanidine at one bar and 1200 °C (ΔH Tf = 63.0 kJ/mol, ΔS Tf = 42.8 J/mol-K) are recommended on the basis of improved heat-capacity equations for KAlSi 3 O 8 crystal, glass, and liquid. On the basis of phase-equilibrium experiments on the congruent melting reaction between 2 and 6.5 GPa, the pressure dependence of the liquid compressibility (K 0 ’ = dK 0 /dP, where K 0 = 1/β 0 ) is constrained to be 12.2 ± 1.0 in a thirdorder Birch-Murnaghan equation of state (EOS). The metastable, one-bar melting temperature (T f ) is additionally constrained to be 1203 ± 26 °C. Determination of the liquid K0’ allows the density and compressibility of KAlSi 3 O 8 liquid to be calculated to 6.5 GPa (2.709 ± 0.014 g/cm 3 at 1600 °C). The uncertainty in K 0 ’ of ±1.0 leads to an error in melt density at 6.5 GPa of ±0.52%. With a K 0 ’ = 12.2, the relatively high compressibility of KAlSi 3 O 8 liquid at 1600 °C (K 0 = 15.8 GPa) drops rapidly with increasing pressure. The dominant mechanism of compression for KAlSi 3 O 8 liquid between 0 and 6.5 GPa most likely involves topological changes and increases in network connectivity with pressure. It is probable that highly compressible liquids, such as hydrous, silica-rich liquids formed by partial melting of a subducted slab, may have K 0 ’ values that exceed 12 (at pressures ≤6.5 GPa).

Thermal Stability and Kinetics of Thermal Decomposition for Protionamide

The thermal stability and the kinetics of thermal decomposition of protionamide were studied by thermogravimetry. activation energy e-a of thermal decomposition of this substance was obtained to be 54.65 kj center dot mol(-1) by kissinger method and ozawa-flynn-wall method. kinetics model function and frequency factor a of protionamide were predicted with the malek method, which were f(alpha)=alpha(0.391)(1-alpha)(0.145) and ina=13.12, respectively. moreover, melting point, molar enthalpy and entropy of fusion of this compound were determined to be 414.09 k, 23.21 kj center dot mol(-1), and 56.06 j center dot mol(-1) center dot k-1, respectively.

Lanthanide(III) halides: Thermodynamic properties and their correlation with crystal structure

Temperatures and enthalpies of phase transitions of 17 lanthanide(III) halides determined experimentally are reported. Correlations were made between temperature of fusion of lanthanide(III) halides, on the one hand, and enthalpy of fusion, on the other, versus atomic number of lanthanide. According to this classification, the lanthanide(III) halides split into groups, as also do the corresponding crystal structures. A correlation between the crystal structure of lanthanide(III) halides and their respective entropy of fusion (or entropy of fusion + entropy of solid–solid phase transition) was inferred from the aforementioned features. Fusion in those halides with hexagonal, UCl 3-type and orthorhombic, PuBr 3-type, structures entails an entropy of fusion change (or entropy of fusion + entropy of solid–solid phase transition change) by 50 ± 4 J mol −1 K −1. The homologous entropy change within the group of halides having the rhomboedric, FeCl 3-type, structure, is smaller and equals 40 ± 4 J mol −1 K −1. Halides with monoclinic, AlCl 3-type, crystal structure constitute a third group associated to an even smaller entropy change upon fusion, only 31 ± 4 J mol −1 K −1. The halides with lower entropies of fusion also have a lower S 1300 K − S 298 K indicating either a higher degree of order in the liquid or a higher entropy in the solid at room temperatures.

Thermodynamic analysis of the Pt–Sn system

A consistent thermodynamic description of the Pt–Sn system is generated using the Calphad method. Serious artifacts in a previous thermodynamic assessment of this system are pointed out. The thorough reassessment is based on all published original experimental data on phase equilibria and thermodynamic alloy properties, which have been critically evaluated. The associate solution model was used for the liquid phase with a strongly forming associate “PtSn” and the relevance for possible short-range order or cluster formation is discussed. The (Pt) solution phase is modeled as substitutional solution and the intermediate phases Pt3Sn, PtSn, Pt2Sn3, PtSn2, PtSn4 are considered as stoichiometric phases. The assignment of reasonable values of thermodynamic parameters is further demonstrated by the consideration of absolute entropies and entropies of fusion of all the intermetallic compounds.

Molecular symmetry depresses the entropy of fusion of organic molecules with regard to their expected values when comparing structural isomers

Using published data, the symmetry effect on the entropy of fusion, Δ S f, of rigid organic molecules has been investigated by comparing structural isomers. Because Δ S f is dependent on the enthalpy of fusion, Δ H f, [A.S. Gilbert, Thermochim. Acta 339 (1999) 131–142] this dependence must be allowed for as Δ H f values can vary quite widely. When this is done, it is found that more symmetric isomers usually have lower than expected values of Δ S f, in relation to Δ H f, than their less symmetric counterparts. This is the reason that more symmetric isomers generally melt at higher temperatures, a fact noted by many workers over the years.

Thermochemical studies on five N-thenoylthiocarbamic- O- n-alkylesters

The standard ( p ∘ = 0.1 MPa) molar enthalpies of combustion in oxygen of five N-thenoylthiocarbamic- O- n-alkylesters, C 4H 3SCONHCSOR, R = Et (Httee), n-Pr (Httpe), n-Bu (Httbe), n-Pen (Httpene), and n-Hex (Htthe), were measured, at T = 298.15 K, by rotating-bomb calorimetry. The standard molar enthalpies of sublimation of these compounds were determined using Calvet microcalorimetry. These values were used to derive the standard molar enthalpies of formation of the title compounds, in their crystalline and gaseous phases, respectively. Furthermore, differential scanning calorimetry was applied in order to measure the temperatures and enthalpies of fusion for all compounds. Entropies of fusion were derived from the experimental results and the odd and even effect was found. - Δ c U m ∘ (cr) kJ · mol - 1 - Δ f H m ∘ (cr) kJ · mol - 1 Δ cr g H m ∘ kJ · mol - 1 N-thenoylthiocarbamic- O-ethylester (Httee) 5303.5 ± 3.1 325.5 ± 3.3 143.2 ± 3.1 N-thenoylthiocarbamic- O- n-propylester (Httpe) 5980.3 ± 2.5 326.8 ± 2.8 136.5 ± 1.8 N-thenoylthiocarbamic- O- n-butylester (Httbe) 6636.8 ± 2.5 348.5 ± 2.9 147.5 ± 1.9 N-thenoylthiocarbamic- O- n-pentylester (Httpene) 7284.5 ± 3.8 378.7 ± 4.0 165.6 ± 2.1 N-thenoylthiocarbamic- O- n-hexylester (Htthe) 7937.6 ± 3.8 403.7 ± 4.2 180.1 ± 3.0

Shear rate dependence of viscosity and configurational entropy of the Zr 41.2Ti 13.8Cu 12.5Ni 10.0Be 22.5 metallic glass forming liquid

In this study the viscosity of Zr 41.2Ti 13.8Cu 12.5Ni 10.0Be 22.5 (Vit 1) has been measured as a function of temperature and shear rate above the liquidus temperature, T liq = 1026 K, using a high temperature Couette Rheometer. It has been discovered that there exists a pronounced decrease in viscosity with increasing shear rate. This is contrary to the general belief that metallic systems above the liquidus temperature should show Newtonian behavior. It has also been discovered that this shear rate dependence of the viscosity decreases with increasing temperature and approaches the Newtonian behavior and viscosities of simple monatomic liquids or binary alloys at approximately 1300 K. These results are discussed in terms of configurational entropy, S c, by using the Adam–Gibbs entropy model for viscous flow. It is suggested that a large amount of short-range order still exists above the liquidus temperature. At high shear rates this order is destroyed causing the configurational entropy to increase by a magnitude that is on the order of the entropy of fusion.

Glass transition in the stable crystalline state of 2,5-dichlorothiophene

Heat capacities of 2,5-dichlorothiophene were measured between 13 and 300K using an adiabatic calorimeter. Fusion temperature at the triple point was found to be 232.72K and the enthalpy and entropy of fusion were determined to be 11.87kJmol−1 and 51.0JK−1mol−1, respectively. The glass transition temperature and the associated heat capacity jump in the stable crystalline phase were determined to be 138K and 0.53JK−1mol−1, respectively. The activation energy was estimated to be 45kJmol−1, and a linear relation between the activation energy and the glass transition temperature was confirmed to hold.

Novel criterion for formation of metastable phase from undercooled melt

Undercooling a melt facilitates the preferential nucleation of a metastable phase. In the present study, the formation of metastable phases from undercooled melts was considered from the viewpoint of the competitive nucleation criterion. The classical nucleation theory shows us that the most critical factor for forming a critical nucleus is the interface free energy σ. Furthermore, Spaepen's negentropic model on σ generated the role of the scaling factor α that depends on the polyhedral order in the liquid and solid phases prominent in simple liquids such as the melt of monoatomic metals. In ionic materials such as oxides, however, in which oxygen polyhedrons including a cation at their center are the structural units both in the solid and liquid phases, the entropy of fusion, rather than α, can be expected to become dominant in the determination of σ. In accordance with this idea, using REFeO 3 as the model material (where RE denotes rare-earth elements) the entropy-undercooling regime criterion was proposed and verified.

Molar Heat Capacities, Thermodynamic Properties, and Thermal Stability of the Synthetic Complex [Er(Pro)2(H2O)5]Cl3

The molar heat capacity, Cp,m, of a complex of erbium chloride coordinated with l-proline, [Er(Pro)2(H2O)5]Cl3, was measured from T = 80 K to T = 400 K with an automated adiabatic calorimeter. The temperature, the molar enthalpy, and the entropy of fusion and decomposition were calculated using equations and diagrammatic area integration. The thermodynamic functions [HT−H298.15] and [ST−S298.15] were derived from T = 80 K to T = 360 K with a temperature interval of 5 K. The thermal stability of the compound was investigated by differential scanning calorimetry and the thermogravimetric techniques.

Low-Temperature Heat Capacity of Room-Temperature Ionic Liquid, 1-Hexyl-3-methylimidazolium Bis(trifluoromethylsulfonyl)imide

Heat capacities of liquid, stable crystal, and liquid-quenched glass of a room-temperature ionic liquid (RTIL), 1-hexyl-3-methylimidazolium bis(trifluromethylsulfonyl)imide were measured between 5 and 310 K by adiabatic calorimetry. Heat capacity of the liquid at 298.15 K was determined for an IUPAC project as (631.6 +/- 0.5) J K(-1) mol(-1). Fusion was observed at T(fus) = 272.10 K for the stable crystalline phase, with enthalpy and entropy of fusion of 28.34 kJ mol(-1) and 104.2 J K(-1) mol(-1), respectively. The purity of the sample was estimated as 99.83 mol % by the fractional melting method. The liquid could be supercooled easily and the glass transition was observed around T(g) approximately 183 K, which was in agreement with the empirical relation, T(g) approximately ((2)/(3)) T(fus). The heat capacity of the liquid-quenched glass was larger than that of the crystal as a whole. In the lowest temperature region, however, the difference between the two showed a maximum around 6 K and a minimum around 15 K, at which the heat capacity of the glass was a little smaller than that of crystal.

Odd–even effect in melting properties of 12 alkane-α,ω-diamides

Fusion and solid-to-solid transitions of a homologous series of 12 linear alkane-α,ω-diamides H 2NCO–(CH 2) ( n−2) –CONH 2, where n = (2 to 12 and 14), were investigated by differential scanning calorimetry (d.s.c.). The temperatures of fusion of even terms decreased from T fus ≈ 572 K to about 460 K, whereas those of odd terms remained substantially constant at about 450 K. Solid-to-solid transitions were also detected for oxamide, malonamide, succinamide, adipamide, suberamide, and dodecanediamide. Regular odd–even alternation was displayed by the temperature, enthalpy, and entropy of fusion values, terms with even number of carbon atoms showing higher values than odd terms. This behaviour was attributed to different crystal packing allowing consonance between hydrogen bonding and dispersive interaction in even terms, which are characterised by multilayer structure, whereas in odd terms a strained three-dimensional network results in looser packing. Parallel alternation of densities in solid alkane-α,ω-diamides supports this interpretation. Comparison was made with literature values for temperatures, enthalpies, and entropies of fusion of isoelectronic linear alkanes, dicarboxylic acids, and alkyldiamines.

Evaluation of entropies of fusion of polychlorinated naphthalenes by model congeners: A DSC study

Thirteen congeners of polychlorinated naphthalenes (PCN) were synthesized and studied by differential scanning calorimetry (DSC). Melting points ( T m) were obtained for all thirteen, and enthalpies of fusion (Δ H f) were obtained for nine congeners. Melting points of other PCNs, except for five, were found in literature. In addition, experimental Δ H f values determined by DSC were found only for 1- and 2-mono-chloronaphthalenes in the literature. The missing or uncertain values of the eight melting points and 64 enthalpies of fusion were estimated by multiple linear regressions using a set of thirteen molecular descriptors as candidates for independent variables. The stepwise model of regression (SMLR) appeared to be most effective. The perfect linearity for melting points was reached with three variables: solubility parameter (DB), ionization potential (IP) and dipole moment ( μ). Similarly, SMLR produced linear result for Δ H f values with descriptors μ, S (polarizability), and L (the logarithm of the gas–hexadecane partition coefficient). The individual entropy of fusion values (Δ S f) were calculated for all 75 PCNs as ratio of Δ H f and melting point (in Kelvin).

Conformational Characteristics of Poly(trimethylene sulfide) and Structure−Property Relationships of Representative Polysulfides and Polyethers

Conformational characteristics of poly(trimethylene sulfide) (PTMS) have been investigated by a rotational isomeric state analysis of ab initio molecular orbital calculations and 1H and 13C NMR experiments for a monomeric model compound, 1,3-bis(methylthio)propane, and the characteristic ratio and dipole moment ratio of the unperturbed PTMS chain. Both C−S (the first-order interaction energy, −0.30 kcal mol-1) and C−C (−0.58 kcal mol-1) bonds prefer the gauche conformation. For comparison, conformational analysis of the corresponding polyether, poly(trimethylene oxide), has also been carried out. The C−O (+0.97 kcal mol-1) and C−C (−0.47 kcal mol-1) bonds show trans and gauche preferences, respectively. These results are consistent with the conformational stabilities predicted by the natural bond orbital analysis on model compounds of poly(ethylene sulfide) (PES) and poly(ethylene oxide). Without the strong S···S repulsion, therefore, the C−C bond adjacent to the C−S bond exhibits its inherent gauche preference. Without the (C−H)···O attraction, the ethereal C−C bond is subject to the attractive gauche effect. For representative polysulfides and polyethers, relationships between conformations in the ϑ and crystalline states and thermal properties have been investigated. Even in the ϑ and crystalline states, the polymers mostly keep the conformational preferences found for their small model compounds; as an exception, poly(propylene sulfide) and poly(propylene oxide), having a methyl side chain, crystallize to adopt the metastable all-trans conformation. On average, the configurational entropy of the polymers amounts to 80−90% of entropy of fusion, and the configurational energy change between crystalline and molten states accounts for ca. 30% of enthalpy of fusion. Of the polymers investigated here, PES has an exceptionally high melting point; the dipole−dipole interaction in the PES crystal was evaluated to be −1.0 kcal mol-1 (ca. 30% of the enthalpy of fusion), thus being the source of the thermostability.

Thermophysical properties of sulfur heterocycles: Thiane and thiophene derivatives

The present study reports a DSC study of the sulfur heterocyclic compounds: 2,2’-bithiophene [492-97-7]; 2,5-thiophenedicarboxylic acid [4282-31-9]; 3-acetylthiophene [1468-83-3]; 2-thiopheneacetic acid [1918-77-0]; 3-thiopheneacetic acid [6964-21-2]; 1,4-dithiane sulfone [139408-38-1]; 1,3-oxathiane-3,3-dioxide (1,3-oxathiane sulfone) [109577-03-9] and 1,4-oxathiane-4,4-dioxide (1,4-oxathiane sulfone) [107-61-9] in the temperature interval T = 268 K and the melting temperatures. Temperatures, enthalpies and entropies of fusion are reported. 1,4-Oxathiane sulfone presents solid–solid phase transitions near to fusion. No additional solid–solid phase transitions were observed for the other solid compounds. For the compounds that are solids over the temperature interval, the heat capacity of the condensed phase was measured. Heat capacities at T = 298.15 K for the liquids 2-acetylthiophene [88-15-3]; methyl, 2-thiopheneacetate [19432-68-9]; methyl, 3-thiopheneacetate [58414-52-1] and thiazole [288-47-1] were also measured. The C p,m (298.15 K) values obtained in this work were compared with the available experimental data and with values estimated with group contribution schemes.

Fragility of metallic glass-forming liquids: A simple thermodynamic connection

Fragility measures the degree by which the viscosity or relaxation time of a glass-forming liquid deviates from the Arrhenius behavior. We will demonstrate that kinetic fragility of a glass-forming liquid is quantitatively related to ΔSf/(Tm−TK), where ΔSf is the entropy of fusion, Tm the melting point, and TK the Kauzmann temperature of a glass-forming liquid. A positive correlation between ΔSf/(Tm−TK) and the kinetic fragility was found to hold in metallic glass-forming liquids, where both thermodynamic and kinetic data are available. It will be demonstrated that such correlation is consistent with the energy landscape model of the glass transition. Furthermore, the thermodynamic fragility index ΔSf/(Tm−TK) was reduced to ΔSf/Tm assuming TK≈Tm/2, and the correlation between ΔSf/Tm and kinetic fragility was discussed within the context of recently proposed cluster model of the glass transition.

The low-temperature heat capacity and ideal gas thermodynamic properties of isobutyl tert-butyl ether

The heat capacities of isobutyl tert-butyl ether in crystalline, liquid, supercooled liquid, and glassy states were measured by vacuum adiabatic calorimetry over the temperature range from (7.68 to 353.42) K. The purity of the substance, the glass-transition temperature, the triple point and fusion temperatures, and the enthalpy and entropy of fusion were determined. Based on the experimental data, the thermodynamic functions (absolute entropy and changes of the enthalpy and Gibbs free energy) were calculated for the solid and liquid states over the temperature range studied and for the ideal gas state at T = 298.15 K. The ideal gas heat capacity and other thermodynamic functions in wide temperature range were calculated by statistical thermodynamics method using molecular parameters determined from density-functional theory. Empirical correction for coupling of rotating groups was used to calculate the internal rotational contributions to thermodynamic functions. This correction was found by fitting to the calorimetric entropy values.