Heat capacity, enthalpy and entropy of ternary bismuth tantalum oxides

Heat capacity and enthalpy increments of ternary bismuth tantalum oxides Bi₄Ta₂O₁₁, Bi₇Ta₃O₁₈ and Bi₃TaO₇ were measured by the relaxation time method (2-280 K), DSC (265-353 K) and drop calorimetry (622-1322 K). Temperature dependencies of the molar heat capacity in the form C_pm=445.8+0.005451T−7.489×10⁶/T² J K⁻¹ mol⁻¹, C_pm=699.0+0.05276T−9.956×10⁶/T² J K⁻¹ mol⁻¹ and C_pm=251.6+0.06705T−3.237×10⁶/T² J K⁻¹ mol⁻¹ for Bi₃TaO₇, Bi₄Ta₂O₁₁ and for Bi₇Ta₃O₁₈, respectively, were derived by the least-squares method from the experimental data. The molar entropies at 298.15 K, S°_m(298.15 K)=449.6±2.3 J K⁻¹ mol⁻¹ for Bi₄Ta₂O₁₁, S°_m(298.15 K)=743.0±3.8 J K⁻¹ mol⁻¹ for Bi₇Ta₃O₁₈ and S°_m(298.15 K)=304.3±1.6 J K⁻¹ mol⁻¹ for Bi₃TaO₇, were evaluated from the low-temperature heat capacity measurements.     

Heat capacity, enthalpy and entropy of bismuth niobate and bismuth tantalate

The heat capacity and the heat content of bismuth niobate BiNbO₄ and bismuth tantalate BiTaO₄ were measured by the relaxation method and Calvet-type heat flux calorimetry. The temperature dependencies of the heat capacities in the form C_pm=128.628+0.03340 T−1991055/T²+136273131/T³ (J K^-1 mol^-1) and 133.594+0.02539 T−2734386/T²+235597393/T³ (J K^-1 mol^-1) were derived for BiNbO₄ and BiTaO₄, respectively, by the least-squares method from the experimental data. Furthermore, the standard molar entropies at 298.15 K S_m(BiNbO₄)=147.86 J K^-1 mol^-1 and S_m(BiTaO₄)=149.11 J K^-1 mol^-1 were assessed from the low temperature heat capacity measurements. To complete a set of thermodynamic data of these mixed oxides an attempt was made to estimate the values of the heat of formation from the constituent binary oxides.     

Thermodynamic properties of BaCeO3 and BaZrO3 at low temperatures

Specific heat capacities (C_p) of polycrystalline samples of BaCeO₃ and BaZrO₃ have been measured from about 1.6 K up to room temperature by means of adiabatic calorimetry. We provide corrected experimental data for the heat capacity of BaCeO₃ in the range T < 10 K and, for the first time, contribute experimental data below 53 K for BaZrO₃. Applying Debye's T³-law for T → 0 K, thermodynamic functions as molar entropy and enthalpy are derived by integration. We obtain C_p = 114.8 (±1.0) J mol⁻¹ K⁻¹, S° = 145.8 (±0.7) J mol⁻¹ K⁻¹ for BaCeO₃ and C_p = 107.0 (±1.0) J mol⁻¹ K⁻¹, S° = 125.5 (±0.6) J mol⁻¹ K⁻¹ for BaZrO₃ at 298.15 K. These results are in overall agreement with previously reported studies but slightly deviating, in both cases. Evaluations of C_p(T) yield Debye temperatures and identify deviations from the simple Debye-theory due to extra vibrational modes as well as anharmonicity. The anharmonicity turns out to be more pronounced at elevated temperatures for BaCeO₃. The characteristic Debye temperatures determined at T = 0 K are Θ₀ = 365 (±6) K for BaCeO₃ and Θ₀ = 402 (±9) K for BaZrO₃.     

Thermal properties of the pyrochlore, Y2Ti2O7

The thermal conductivity and heat capacity of high-purity single crystals of yttrium titanate, Y₂Ti₂O_7, have been determined over the temperature range 2 K?T?300 K. The experimental heat capacity is in very good agreement with an analysis based on three acoustic modes per unit cell (with the Debye characteristic temperature, θ_D, of ca. 970 K) and an assignment of the remaining 63 optic modes, as well as a correction for C_p−C_v. From the integrated heat capacity data, the enthalpy and entropy relative to absolute zero, are, respectively, H(T=298.15 K)−H₀=34.69 kJ mol⁻¹ and S(T=298.15 K)−S₀=211.2 J K⁻¹ mol⁻¹. The thermal conductivity shows a peak at ca. θ_D/50, characteristic of a highly purified crystal in which the phonon mean free path is about 10 μm in the defect/boundary low-temperature limit. The room-temperature thermal conductivity of Y₂Ti₂O₇ is 2.8 W m⁻¹ K⁻¹, close to the calculated theoretical thermal conductivity, κ_min, for fully coupled phonons at high temperatures.     

Thermodynamic properties of lithium mica: Lepidolite

Calorimetric measurements were made on natural sample of lepidolite having the composition (K_0.80Na_0.05Ca_0.07Rb_0.16Cs_0.03)(Li_1.34Al_1.40Fe³⁺_0.01)[Si_3.25Al_0.75O₁₀]F_1.80(OH)_0.20 from Na-Li-type rare-element-rich pegmatites of East Sayany, Russia. High-temperature enthalpy increments were measured with a Tian-Calvet calorimeter at 444-972 K using the drop method. The resultant (T) equation in the interval T = 298.15-972 K was calculated:  = 316.10 + 228.12 × 10⁻³ T − 50.10 × 10⁵ T⁻² (J K⁻¹ mol⁻¹) [± 0.4%] and the value of (298.15 K) = 327.8 J K⁻¹ mol⁻¹ was obtained. The standard molar enthalpy of formation from the elements was determined by high-temperature drop solution calorimetry in molten lead borate at T = 973 K. The value of Δ_f(298.15 K) for lepidolite was found to be −6201 ± 18 kJ mol⁻¹. The thermodynamic properties of lepidolite of idealized composition KLi_1.5Al_1.5[Si₃AlO₁₀]F₂ were estimated based on the experimental data obtained.     

Thermophysical properties of SrHfO3 and SrRuO3

Polycrystalline samples of strontium series perovskite type oxides, SrHfO₃ and SrRuO₃ were prepared and the thermophysical properties were measured. The average linear thermal expansion coefficients are 1.13×10⁻⁵ K⁻¹ for SrHfO₃ and 1.03×10⁻⁵ K⁻¹ for SrRuO₃ in the temperature range between 423 and 1073 K. The melting temperatures T_m of SrHfO₃ and SrRuO₃ are 3200 and 2575 K, respectively. The longitudinal and shear sound velocities were measured by an ultrasonic pulse-echo method at room temperature in air, which enables to evaluate the elastic moduli and Debye temperature. The heat capacity was measured by using a differential scanning calorimeter, DSC in high-purity argon atmosphere. The thermal diffusivity was measured by a laser flash method in vacuum. The thermal conductivities of SrHfO₃ and SrRuO₃ at room temperature are 5.20 and 5.97 W m⁻¹ K⁻¹, respectively.     

Heat-capacity measurements and thermodynamic functions of crystalline adenine; revised thermodynamic properties of aqueous adenine

The standard molar heat capacity C^°_p,m of adenine(cr) has been measured using adiabatic calorimetry over the range 6<(T/K)<310 and the results used to derive thermodynamic functions for adenine(cr) at smoothed temperatures. At T=298.15 K, C^°_p,m=(142.67±0.29) J · K⁻¹ · mol⁻¹ and the third law entropy S^°_m=(145.62±0.29) J · K⁻¹ · mol⁻¹. The standard molar Gibbs free energy of formation Δ_fG^°_m at T=298.15 K for crystalline adenine was calculated, using the standard molar enthalpy of formation for the compound and entropies of the elements from the literature, and found to be Δ_fG^°_m=(301.4±1.0) kJ · mol⁻¹. The results were combined with solution calorimetry and solubility measurements from the literature to yield revised values for the standard molar thermodynamic properties of aqueous adenine at T=298.15 K: Δ_fG^°_m=(313.4±1.0) kJ · mol⁻¹, Δ_fH^°_m=(129.5±1.4) kJ · mol⁻¹, and S_m^°=(217.68±0.44) J · K⁻¹ · mol⁻¹.     

Thermodynamics of 2D polymerized tetragonal phase of fullerene C60 in the range from T→0 to 650 K at standard pressure

By dynamic calorimetry the temperature dependence of heat capacity for two-dimensional (2D) polymerized tetragonal phase of C₆₀ has been determined over the 300-650 K range at standard pressure mainly with an uncertainty ±1.5%. In the range 490-550 K, an irreversible endothermic transition of the phase, caused by the depolymerization of the polymer, has been found and characterized. Based on the experimental data obtained and literature information, the thermodynamic functions of 2D polymerized tetragonal phase of C₆₀, namely, the heat capacity C°_p(T), enthalpy H°(T)−H°(0), entropy S°(T), and Gibbs function G°(T)−H°(0), have been calculated over the range from T→0 to 490 K. From 150 to 330 K in an adiabatic vacuum calorimeter and between 330 and 650 K in a dynamic calorimeter the thermodynamic properties of the depolymerization products have been examined and compared with the corresponding data for the monomeric phase C₆₀.     

Crosslinking, thermal properties and relaxation behaviour of polyisoprene under high-pressure

The transient hot-wire method has been used to measure the thermal conductivity κ and heat capacity per unit volume ρc_p of untreated (virgin) and crosslinked cis-1,4-poly(isoprene) (PI) in the temperature range 160-513 K for pressures p up to 0.75 GPa. The results show that the crosslinking rate of the polymer chains becomes significant at ∼513 K on isobaric heating at 0.5 GPa changing PI into an elastomeric state within 4 h without the use of crosslinking agents. The crosslinked PI and untreated PI have about the same κ = 0.145 Wm⁻¹ K⁻¹ and c_p = 1.81 kJ kg⁻¹ K⁻¹ at 295 K and 20 MPa, but different relaxation behaviours. Two relaxation processes, corresponding to the segmental and normal modes, could be observed in both PI and crosslinked PI but these have a larger distribution of relaxation times and become arrested at higher temperatures (∼10 K) in the latter case. The arrest temperature for the segmental relaxation of untreated and crosslinked PI, for a relaxation time of ∼1 s, are described well by the empirical relations: T(p) = 209.4 (1 + 4.02 p)^0.31 and T(p) = 221.3 (1 + 2.33 p)^0.40 (p in GPa and T in K), respectively, which thus also reflects the pressure variations of the glass transition temperatures.     

Heat capacity and thermodynamic functions of LuPO4 in the range 0-320 K

The heat capacity of LuPO₄ was measured in the temperature range 6.51-318.03 K. Smoothed experimental values of the heat capacity were used to calculate the entropy, enthalpy and Gibbs free energy from 0 to 320 K. Under standard conditions these thermodynamic values are: (298.15 K) = 100.0 ± 0.1 J K⁻¹ mol⁻¹, S⁰(298.15 K) = 99.74 ± 0.32 J K⁻¹ mol⁻¹, H⁰(298.15 K) − H⁰(0) = 16.43 ± 0.02 kJ mol⁻¹, −[G⁰(298.15 K) − H⁰(0)]/T = 44.62 ± 0.33 J K⁻¹ mol⁻¹. The standard Gibbs free energy of formation of LuPO₄ from elements Δ_fG⁰(298.15 K) = −1835.4 ± 4.2 kJ mol⁻¹ was calculated based on obtained and literature data.     

Thermodynamics of linear polyurethanes on basis of 1,4-diisocyanatobutane with 1,4-butanediol and 1,6-hexanediol in the range from T → 0 to 490 K

The temperature dependence of heat capacity and characteristics of physical transformations of partially crystalline linear aliphatic polyurethanes based on 1,4-diisocyanatobutane with 1,4-butanediol and 1,6-hexanediol have been studied over the range 6.5-490 K by precision adiabatic vacuum and dynamic calorimetry. The calorimetric data were used to determine the thermodynamic quantities of devitrification and fusion and to calculate the standard thermodynamic functions , H⁰(T) − H⁰(0), S⁰(T) and G⁰(T) − H⁰(0) of linear polyurethanes in totally crystalline and amorphous states. The values of the fractal dimension D in the function of multifractal generalization of Debye's theory of the heat capacity of solids were estimated and the character of heterodynamics of their structures was detected. The energies of combustion of the substances were measured in a calorimeter with an isothermal shield and a static bomb. The enthalpies of combustion and the standard thermodynamic characteristics of formation of the polymers at T = 298.15 K were calculated too. The standard thermodynamic characteristics of polycondensation processes in bulk of 1,4-diisocyanatobutane with 1,4-butanediol and 1,6-hexanediol followed by the formation of linear polyurethanes were determined in the range from 0 to 350 K. A comparative analysis of the corresponding standard thermodynamic properties of the polymers under consideration and polyurethanes of isomeric structure was made and some dependences of their change on various conditions were found.     

Thermodynamics of dimethylene urethane and poly(dimethylene urethane) in the range from T → 0 to 490 K at standard pressure

By high-precision dynamic calorimetry the temperature dependences of heat capacity of dimethylene urethane (DMU) between 320 and 370 K and partially crystalline poly(dimethylene urethane) (PDMU) in the range 326-490 K at standard pressure have been determined within ±1.5%. The thermodynamic characteristics of fusion of the substances, namely the temperature interval of melting, temperature, enthalpy and entropy of fusion, as well as the characteristics of devitrification and glassy state for poly(dimethylene urethane) have been estimated. The first and the second cryoscopic constants have been calculated for dimethylene urethane. The experimental data obtained in the present work and literature findings on the heat capacity of the substances were used to calculate their thermodynamic functions: the heat capacity C°_p (T), enthalpy H°(T)−H°(0), entropy S°(T) and Gibbs function G°(T)−H°(0) over the range from T→0 to (370-480) K. Based on the data, the thermodynamic characteristics of polymerization process with five-membered ring opening Δ_polH°, Δ_polS° and Δ_polG° of dimethylene urethane with the formation of linear partially crystalline poly(dimethylene urethane) have been evaluated.     

Low-temperature heat capacity and thermodynamic properties of crystalline carboxin (C12H13NO2S)

Carboxin was synthesized and its heat capacities were measured with an automated adiabatic calorimeter over the temperature range from 79 to 380 K. The melting point, molar enthalpy (Δ_fusH_m) and entropy (Δ_fusS_m) of fusion of this compound were determined to be 365.29±0.06 K, 28.193±0.09 kJ mol⁻¹ and 77.180±0.02 J mol⁻¹ K⁻¹, respectively. The purity of the compound was determined to be 99.55 mol% by using the fractional melting technique. The thermodynamic functions relative to the reference temperature (298.15 K) were calculated based on the heat capacity measurements in the temperature range between 80 and 360 K. The thermal stability of the compound was further investigated by differential scanning calorimetry (DSC) and thermogravimetric (TG) analysis. The DSC curve indicates that the sample starts to decompose at ca. 290 °C with the peak temperature at 292.7 °C. The TG-DTG results demonstrate the maximum mass loss rate occurs at 293 °C corresponding to the maximum decomposition rate.     

Thermodynamic studies of monuron

Monuron (C₉H₁₁ClN₂O; N,N-dimethyl-N′-(4-chlorophenyl) urea, CAS 150-68-5) was synthesized and the heat capacities of the compound were measured in the temperature range from 79 to 385 K with a high precision automated adiabatic calorimeter. No phase transition or thermal anomaly was observed in this range. The enthalpy and entropy data of the compound relative to the reference temperature 298.15 K were derived based on the heat capacity data. The thermodynamic properties of the compound were further investigated through DSC and TG analysis. The melting point, the molar enthalpy, and entropy of fusion were determined to be 447.6±0.1 K, 29.3±0.2 kJ mol⁻¹, and 65.4 J K⁻¹ mol⁻¹, respectively.     

Isothermal crystallization of poly(3-hydroxybutyrate-co-3-hydroxyvalerate)

Isothermal crystallization behavior of poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) was investigated by means of differential scanning calorimetry and polarized optical microscopy (POM). The Avrami analysis can be used successfully to describe the isothermal crystallization kinetics of PHBV, which indicates that the Avrami exponent n=3 is good for all the temperatures investigated. The spherulitic growth rate, G, was determined by POM. The result shows that the G has a maximum value at about 353 K. Using the equilibrium melting temperature (448 K) determined by the Flory equation for melting point depression together with U∗=1500 cal mol⁻¹, T_∞=30 K and T_g=278 K, the nucleation parameter K_g was determined, which was found to be 3.14 ± 0.07 × 10⁵ (K²), lower than that for pure PHB. The surface-free energy σ=2.55×10⁻² J m⁻² and σ_e=2.70±0.06×10⁻² J m⁻² were estimated and the work of chain-folding (q=12.5±0.2 kJ mol⁻¹) was derived from σ_e, and found to be lower than that for PHB. This implies that the chains of PHBV are more flexible than that of PHB.     

Heat capacity and Raman spectra of Cr(C5H7O2)3 at low temperature

The heat capacity of Cr(C₅H₇O₂)₃ has been measured by the adiabatic method within the temperature range 5-320 K. An anomaly with a maximum at ∼60 K has been discovered which points to the phase transformation of the compound. Anomalous contributions to entropy and enthalpy have been revealed. The thermodynamic functions (entropy, enthalpy and reduced Gibbs energy) at 298.15 K have been calculated using the obtained experimental heat capacity data. The Raman spectra have been measured in the frequency range 60-400 cm⁻¹ and in the temperature range 5-220 K. It has been discovered that a new line (109 cm⁻¹) appears at ∼60 K. The nature of these peculiarities in heat capacity and in Raman spectra is discussed.     

Environmental assessment of CFC alternatives: Rate constants for the reactions of OH radicals with fluorinated compounds

The rate constants for the reactions of OH radicals with CF₃OCHFCF₃, and CF₃CHFCF₃ have been measured over the temperature range 250-430 K. Kinetic measurements have been carried out using the flash photolysis, and laser photolysis methods combined, respectively, with the laser induced fluorescence technique. The influence of impurities in the samples has been investigated by using gas chromatography. No sizable effect of impurities was found on the measured rate constants of these fluorinated compounds, if the purified samples were used in the measurements. The following Arrhenius expressions were determined: k(CF₃OCHFCF₃) = (4.39 ± 1.38) × 10⁻¹³ exp[−(1780 ± 100)/T] cm³ molecule⁻¹ s⁻¹, and k(CF₃CHFCF₃) = (6.19 ± 2.07) × 10⁻¹³ exp[−(1830 ± 100)/T] cm³ molecule⁻¹ s⁻¹.     

Heat capacity and thermodynamic properties of crystalline ornidazole (C7H10ClN3O3)

The molar heat capacities of 1-(2-hydroxy-3-chloropropyl)-2-methyl-5-nitroimidazole (Ornidazole) (C₇H₁₀ClN₃O₃) with purity of 99.72 mol% were measured with an adiabatic calorimeter in the temperature range between 79 and 380 K. The melting-point temperature, molar enthalpy, Δ_fusH_m, and entropy, Δ_fusS_m, of fusion of this compound were determined to be 358.59±0.04 K, 21.38±0.02 kJ mol⁻¹ and 59.61±0.05 J K⁻¹ mol⁻¹, respectively, from fractional melting experiments. The thermodynamic function data relative to the reference temperature (298.15 K) were calculated based on the heat capacities measurements in the temperature range from 80 to 380 K. The thermal stability of the compound was further investigated by DSC and TG. From the DSC curve an intensive exothermic peak assigned to the thermal decomposition of the compound was observed in the range of 445-590 K with the peak temperature of 505 K. Subsequently, a slow exothermic effect appears when the temperature is higher than 590 K, which is probably due to the further decomposition of the compound. The TG curve indicates the mass loss of the sample starts at about 440 K, which corresponds to the decomposition of the sample.     

Ab initio/DFT theory and multichannel RRKM study on the mechanisms and kinetics for the CH3S + CO reaction

The potential energy surface for the reaction of CH₃S with CO was calculated at the G3MP2//B3LYP/6-311++G(d,p) level. The rate constants for feasible channels leading to several products were calculated by TST and multichannel-RRKM theory. The results show that addition–elimination mechanism is dominant, while hydrogen abstraction mechanism is uncompetitive. The major channel is the addition of CO to CH₃S leading to an intermediate CH₃SCO which then decomposes to CH₃ + OCS. In the temperature range of 200–3000 K, the overall rate constants are positive temperature dependence and pressure independence, and it can be described by the expression as k = 1.10 × 10⁻¹⁶T^1.57exp(−3359/T) cm³ molecule⁻¹ s⁻¹. At temperature between 208 and 295 K, the calculated rate constants are in good agreement with the experimental upper limit data. At T = 1000 and 2000 K, the major product is CH₃ + OCS at lower pressure; while at higher pressure, the stabilization of IM1 is dominant channel.     

Design and construction of an adiabatic calorimeter for samples of less than 1 cm in the temperature range T = 15 K to T = 350 K

A small-scale adiabatic calorimeter has been constructed as part of a larger project to study the thermodynamics of nanomaterials and to facilitate heat capacity measurements on samples of insufficient quantity to run on our current large-scale adiabatic apparatus. This calorimeter is designed to measure the heat capacity of samples whose volume is less than 0.8 cm³ over a temperature range of T = 13 K to T = 350 K. Heat capacity results on copper, sapphire, and benzoic acid show the accuracy of the measurements to be better than ±0.4% for temperatures higher than T = 50 K. The reproducibility of these measurements is generally better than ±0.25%.