Thermodynamic properties of NaZr<Subscript>2</Subscript>(AsO<Subscript>4</Subscript>)<Subscript>3</Subscript>

The heat capacity C _p ⁰ of crystalline NaZr₂(AsO₄)₃ has been measured in the range 7–650 K using precision adiabatic calorimetry and differential scanning calorimetry. The experimental data have been used to calculate the standard thermodynamic functions of the arsenate: C _p ⁰, enthalpy H ⁰(T) − H ⁰(0), entropy S ⁰(T), and Gibbs function G ⁰(T) − H ⁰(0) from T → 0 to 650 K. The standard entropy of its formation from elements is Δ_f S ⁰(NaZr₂(AsO₄)₃, cr, 298.15 K) = −1087 ± 1 J/(mol K).     

Thermodynamic properties of NaZr2(PO4)3

The heat capacity of crystalline NaZr₂(PO₄)₃ was measured between 7 and 340 K by adiabatic calorimetry. The results were used to calculate the thermodynamic functionsC _p ⁰ ,H ⁰(T) -H ⁰(0),S ⁰(T), andG ⁰(T) -H ⁰(0) in the range 0-340 K. The absolute entropy was found to be S⁰NaZr₂(PO₄)₃, cr, 298.15 K) = 327.1 ±1.0 J/(mol K), and the standard entropy of formation Δ_fS⁰(NaZr₂(PO₄)₃, cr, 298.15 K) = -1101±1 J/(mol K). Solution calorimetry was used to determine the standard enthalpy of formation, Δ_f H ⁰(NaZr₂(PO₄)₃, cr, 298.15 K) = -5236 ±5 kJ/mol. By combining the data obtained by the two techniques, the standard Gibbs energy of formation was determined to be Δ_fG⁰(NaZr₂(PO₄)₃, cr, 298.15 K) = -4908 ±5 kJ/mol.     

Heat capacity of In2Cu2O5 in the range 364–984 K

The heat capacity of In₂Cu₂O₅ has been determined by differential scanning calorimetry in the temperature range 364–984 K. The C _p (T) data have been used to evaluate the thermodynamic functions of indium cuprate: enthalpy increment H ⁰(T) — H ⁰(364 K) and entropy change S ⁰(T) ? S ⁰(364 K).     

Heat capacity and thermodynamic functions of LaVO<Subscript>4</Subscript> and LuVO<Subscript>4</Subscript> from 7 to 345 K

The heat capacities of lanthanum and lutetium orthovanadates have been measured at temperatures from 7 to 345 K using an adiabatic calorimeter. No anomalies have been detected in the heat capacity data. The thermodynamic functions (C _p ⁰(T), S ⁰(T), and H ⁰(T) − H ⁰(0)) of the two compounds have been calculated in the temperature range studied, and their Debye characteristic temperatures have been estimated.     

Heat Capacity and Thermodynamic Functions of NdMeFe2O5 (Me is Li, Na, K, Cs) Ferrites

The values of heat capacity of NdMeFe₂O₅ (Me is Li, Na, K, Cs) ferrites in the temperature range from 298 to 673 K are experimentally determined. Equations of the temperature dependence of heat capacity are derived and used to calculate the thermodynamic functions C _p ⁰(T), S ⁰(T), H ⁰(T) - H ⁰ (298.15 K), and **(T) of ferrites in the range identified above.     

Synthesis of Pr2CuO4 and its heat capacity in the range 364–1064 K

The heat capacity of Pr₂CuO₄ has been determined by differential scanning calorimetry in the temperature range 364–1064 K. The experimental C _p (T) data have been used to evaluate the thermodynamic functions of praseodymium cuprate: enthalpy increment H ⁰(T)–H ⁰(364 K) and entropy change S ⁰(T)–S ⁰(364 K).     

Thermodynamic properties of TeO2-ZnO glasses in the range 0–650 K

The heat capacity C _p ⁰ of (TeO₂)_n(ZnO)_{1 ? n} (n = 0.65, 0.70, 0.80) tellurite glasses has been determined by precision adiabatic (6–350 K) and dynamic scanning (320–650 K) calorimetry. The thermodynamic characteristics of their devitrification and glassy state have been determined. The experimental data have been used to calculate the standard thermodynamic functions of samples in the glassy and “supercooled liquid” states (0–650 K): heat capacity C _p ⁰ (T), enthalpy H ⁰(T) ? H ⁰(0), entropy S ⁰(T) ? S ⁰(0), and Gibbs function G ⁰(T) ? H ⁰(0). Multifractal processing of the low-temperature heat capacity data has been used to assess the character of structural heterodynamicity of the tellurite glasses. The heat capacity of the glasses has been analyzed in comparison with that of their constituent oxides. The composition dependences of the glass transition temperature, crystallization onset temperature, and thermodynamic functions at 298.15 and 600 K have been obtained.     

Thermodynamic properties of Cu<Subscript>5</Subscript>SmSe<Subscript>4</Subscript>

The heat capacity of Cu₅SmSe₄ has been measured from 80 to 300 K. The results have been used to assess the main thermodynamic functions of Cu₅SmSe₄: entropy (S ⁰(T) − S ⁰(0)), enthalpy increment (H ⁰(T) − H ⁰(0)), and reduced Gibbs energy (Φ⁰(T)).     

Revised heat capacity and thermodynamic functions of GdVO<Subscript>4</Subscript>

The heat capacity of GdVO₄ has been determined by adiabatic calorimetry in the range 5–345 K. The present experimental data and earlier results have been used to evaluate the thermodynamic functions of gadolinium orthovanadate (C _p ⁰(T), S ⁰(T), H ⁰(T) − H ⁰(0), and Φ⁰(T)) as functions of temperature (5–350 K). Its Gibbs energy of formation is determined to be Δ_f G ⁰(GdVO₄, 298.15 K) = −1684.5 ± 1.6 kJ/mol.     

Cesium dizirconium phosphate: Synthesis and thermal properties

Crystalline CsZr₂(PO₄)₃ with the NZP [NaZr₂(PO₄)₃] structure was prepared by a sol gel procedure. The purity and composition of the sample were determined by scanning electron microscopy with energy-dispersive X-ray analysis as well as by X-ray phase analysis and IR spectroscopy. CsZr₂(PO₄)₃ is thermally stable in the range 7 K < T < 1553 K. Temperature dependences of the heat capacity C _p ⁰ = f(T) and thermal conductivity λ = f(T) of the phosphate in the range 320–650 K corresponding to thermal conditions of a nuclear waste repository were studied. The standard thermodynamic functions C _p ⁰ (T), H ⁰(T)–H ⁰(0), S ⁰(T), and G ⁰(T)–H ⁰(0) were calculated. The thermodynamic functions of formation of CsZr₂(PO₄)₃ were calculated. The possibility of decreasing the temperature of the synthesis-immobilization to 1000 K was experimentally confirmed.     

Thermodynamic properties of (TeO2) n (WO3)1 − n glasses in the range 0–650 K

The heat capacity of (TeO₂) _n (WO₃)_{1 ? n} tellurite glasses with n = 0.75, 0.78, 0.85, and 0.90 has been determined using precision adiabatic calorimetry (6–350 K) and dynamic scanning calorimetry (320–650 K), and the thermodynamic characteristics of their glassy state and devitrification have been evaluated. The experimental heat capacity data have been used to calculate the standard thermodynamic functions of the glassy and supercooled liquid states at temperatures from T → 0 to 650 K: heat capacity C _p ⁰ (T), enthalpy H ⁰(T) — H ⁰(0), entropy S ⁰(T), and Gibbs function G ⁰(T) — H ⁰(0). The character of structural heterodynamicity of the tellurite glasses has been assessed by processing the low-temperature heat capacity data using the multifractal formulation of the Debye theory of heat capacity of solids. The composition dependences of the devitrification temperature and 298.15-K thermodynamic functions have been obtained, and the 298.15-K C _p ⁰ of tellurium dioxide has been estimated. The thermal and thermodynamic properties of the (TeO₂) _n (WO₃)_{1 ? n} tellurite glasses have been compared with those of (TeO₂) _n (ZnO)_{1 ? n} glasses.     

Temperature Dependence of the Volumetric Properties of Binary Mixtures Containing Polyethers and 1-Propanol

Excess molar volumes (V ^E _m ) were measured at 288.15, 298.15, and 308.15 K and atmospheric pressure as a function of composition with a continuous dilution dilatometer for the binary mixtures of 1-propanol [CH₃CH₂CH₂OH] with glymes [CH₃O(CH₂CH₂O) _m CH₃, m=1,2,3, and 4]. With these results and other thermodynamic data from the literature, the following mixing quantities have been reported over the complete range of concentration or at equimolar concentration: , volume expansivity; ^E , excess volume expansivity; (V ^E _m /T) _P , and (H ^E /P) _T at 298.15 K. The Prigogine–Flory–Patterson theory (PFP) of liquid mixtures has been applied to estimate interaction, free-volume, and internal-pressure contributions to V ^E _m and to estimate the different mixing quantities for the mixtures. The calculated values using the PFP theory were then compared at 298.15 K with the experimentally obtained results. The PFP theory predicts excess volume V ^E _m values rather well, while the calculated value of (V ^E _m /T) _P and (H ^E /P) _T by using the Flory theory show general variation with the chain length of the glyme. The (V ^E _m /T) _P and (H ^E /P) _T show deviations between theoretical and experimental values that are slightly larger in systems with lower glyme.     

Ideal Gas Thermodynamic Properties of Propyl tert-Butyl Ethers from Density Functional Theory Results Combined with Experimental Data

Ideal gas thermodynamic properties, S°(T), C _p°(, T), H°(T)–H°(0), _f H°(T), and _f G°(T), are obtained on the basis of density functional B3LYP/6-31G(d,p) and B3LYP/6-311 + G(3df,2p) calculations for two propyl tert-butyl ethers. All torsional motions about C–C and C–O bonds were treated as hindered internal rotations using the independent-rotor model. An empirical approximation was assumed to account for the effect of the coupling of rotor potentials. The correction for rotor–rotor coupling was found by fitting to entropy values determined from calorimetric measurements. Enthalpies of formation were calculated using isodesmic reactions.     

Thermodynamic Properties and Decomposition of Lithium Hexafluoroarsenate, LiAsF6

The heat capacity of lithium hexafluoroarsenate is determined in the temperature range 50–750 K by adiabatic and differential scanning calorimetry techniques. The thermodynamic properties of LiAsF₆ under standard conditions are evaluated: C _p ⁰(298.15 K) = 162.5 ± 0.3 J/(K mol), S ⁰(298.15 K) = 173.4 ± 0.4 J/(K mol), ⁰(298.15 K) = 81.69 ± 0.20 J/(K mol), and H ⁰(298.15 K) – H ⁰(0) = 27340 ± 60 J/mol. The C _p(T) curve is found to contain a lambda-type anomaly with a peak at 535.0 ± 0.5 K, which is due to the structural transformation from the low-temperature, rhombohedral phase to the high-temperature, cubic phase. The enthalpy and entropy of this transformation are 5.29 ± 0.27 kJ/mol and 10.30 ± 0.53 J/(K mol), respectively. The thermal decomposition of LiAsF₆ is studied. It is found that LiAsF₆ decomposes in the range 715–820 K. The heat of decomposition, determined in the range 765–820 K using a sealed crucible and equal to the internal energy change U _r(T), is 31.64 ± 0.08 kJ/mol.     

Thermodynamics of the Superconducting State in Calcium at 200 GPa

The thermodynamic parameters of the superconducting state in Calcium under the pressure at 200 GPa were calculated. The Coulomb pseudopotential values (μ ^⋆) from 0.1 to 0.3 were taken into consideration. It has been shown that the specific heat’s jump at the critical temperature and the thermodynamic critical field near zero Kelvin strongly decrease with μ ^⋆. The dimensionless ratios r ₁≡ΔC(T _C)/C ^N (T _C) and r₂ o T_CC^N(T_C)/H²_C(0)r_{2}\equiv T_{\mathrm{C}}C^{N}(T_{\mathrm{C}})/H^{2}_{\mathrm{C}}(0) significantly differ from the predictions based on the BCS model. In particular, r ₁ decreases from 2.64 to 1.97 with the Coulomb pseudopotential; whereas r ₂ increases from 0.140 to 0.157. The numerical results have been supplemented by the analytical approach.     

Speeds of Sound and Isentropic Compressibilities of n-Alkoxyethanols and Polyethers with Propylamine at 298.15 K

The speeds of sound (u) have been measured at 298.15 K and atmospheric pressure, as a function of composition for seven binary liquid mixtures of propylamine (CH₃CH₂CH₂NH₂, PA) + ethylene glycol monomethyl ether (2-methoxyethenol, CH₃(OC₂H₄)OH, EGMME); + diethylene glycol monomethyl ether [{2-(2-methoxyethoxy)ethanol}, CH₃(OC₂H₄)₂OH, Di-EGMME]; + triethylene glycol monomethyl ether [{2-(2-(2-methoxyethoxy)ethoxy) ethanol}, CH₃(OC₂H₄)₃OH, Tri-EGMME]; + diethylene glycol monoethyl ether [{2-(2-ethoxyethoxy)ethanol}, C₂H₅(OC₂H₄)₂OH, Di-EGMEE]; + diethylene glycol monobutyl ether [{2-(2-butoxyethoxy) ethanol}, C₄H₉(OC₂H₄)₂OH, Di-EGMBE]; + diethylene glycol diethyl ether [bis(2-ethoxyethyl)ether, C₂H₅ (OC₂H₄)₂ OC₂H₅, DEGDEE]; and + diethylene glycol dibutyl ether [bis(2-butoxyethyl) ether, C₄H₉(OC₂H₄)₂OC₄ H₉; DEGDBE] using a Nusonic velocimeter based on the sing–around technique. These values have been combined with densities derived from excess molar volumes to obtain estimates of the molar isentropic compressibility K _S,m, and their excess values . The values are shown to be negative for all mixtures over the entire composition range. The deviations u ^D of the speeds of sound from the values calculated for ideal mixtures have been obtained for all estimated values of mole fraction x₁. The change of and u ^D with composition and the number of –OC₂H₄ – units in the alkoxyethanol are discussed with a view to understand some of the molecular interactions present in alkoxyethanol – propylamine mixtures.Also, theoretical values of the molar isentropic compressibility of K _S,m and of the speed of sound u ^D have been calculated using the Prigogine-Flory-Patterson (PFP) theory with the van der Waals (vdW) potential energy model, and the results have been compared with experimental values.     

Heat Capacity and thermodynamic functions of DyMe<Superscript>II</Superscript>Cr<Subscript>2</Subscript>O<Subscript>5.5</Subscript>(Me<Superscript>II</Superscript>-Mg,Ca) in the range from 298.15 to 673 K

The calorimetric method is used to investigate the heat capacity of DyMe^IICr₂O_5.5(Me^II-Mg, Ca) chromites in the range from 298.15 to 673 K. The C _p ⁰ ～ f(T) curves exhibit λ-like effects at 348 and 548 K for DyMgCr₂O_5.5 and at 473 K for DyCaCr₂O_5.5, which apparently relate to second-order phase transitions. The temperature dependences are calculated for thermodynamic functions C _p ⁰ (T), H ⁰(T)-H ⁰(298.15), S ⁰(T), and Φ**(T).     

High-temperature heat capacity and thermodynamic properties of Tb<Subscript>2</Subscript>Sn<Subscript>2</Subscript>O<Subscript>7</Subscript>

Tb₂Sn₂O₇ has been prepared by solid-state reaction in air at 1473 K over a period of 200 h and its isobaric heat capacity has been studied experimentally in the range 350–1073 K. The C _p(T) data for this compound have no extrema and are well represented by the classic Maier–Kelley equation. The experimental C _p(T) data have been used to evaluate the thermodynamic properties of terbium stannate (pyrochlore structure): enthalpy increment H°(T)–H°(350 K), entropy change S°(T)–S°(350 K), and reduced Gibbs energy Ф°(Т).     

Synthesis and high-temperature heat capacity of Gd<Subscript>2</Subscript>Sn<Subscript>2</Subscript>O<Subscript>7</Subscript>

Gd₂Sn₂O₇ gadolinium stannate with the pyrochlore structure has been prepared by solid-state reaction and its high-temperature heat capacity has been determined by differential scanning calorimetry in the temperature range 350–1020 K. The C_p(T) data are shown to be well represented by the classic Maier–Kelley equation. The experimental C_p(T) data have been used to evaluate the thermodynamic functions of gadolinium stannate: enthalpy increment H°(T)–H°(339 K), entropy change S°(T)–S°(339 K), and reduced Gibbs energy Ф°(Т).     

Thermal Dissociation of RMnO<Subscript>3</Subscript> (R = Dy,Yb, Lu)

The phase equilibria involved in the thermal dissociation of RMnO₃ (R = Dy, Yb, Lu) were studied in the range 973–1173 K by a static method in a vacuum circulation unit and by x-ray diffraction analysis of quenched solid phases. The RMnO₃ manganites were shown to dissociate by the reaction RMnO₃ = 1/2R₂O₃ + MnO + 1/4O₂. The temperature dependences of the equilibrium oxygen pressure and Gibbs energy change in this reaction were determined for the three compounds. The experimental data were used to evaluate the standard thermodynamic functions of formation of RMnO₃ from R₂O₃ and Mn₂O₃: ΔH⁰(T) = ?88.93 kJ/mol, Δ S⁰(T) = 46.56 J/(mol K) for DyMnO₃; ΔH⁰(T) = ?130.95 kJ/mol, Δ S⁰(T) = 86.25 J/(mol K) for YbMnO₃; ΔH⁰(T) = ?142.94 kJ/mol, Δ S⁰(T) = 102.87 J/(mol K) for LuMnO₃.