Heat capacities,third-law entropies and thermodynamic functions of the geometrically frustrated antiferromagnetic spinels GeCo2O4 and GeNi2O4 from T=(0 to 400) K

The molar heat capacities of GeCo₂O₄ and GeNi₂O₄, two geometrically frustrated spinels, have been measured in the temperature range from T=(0.5 to 400) K. Anomalies associated with magnetic ordering occur in the heat capacities of both compounds. The transition in GeCo₂O₄ occurs at T=20.6 K while two peaks are found in the heat capacity of GeNi₂O₄, both within the narrow temperature range between 11.4<(T/K)<12.2. Thermodynamic functions have been generated from smoothed fits of the experimental results. At T=298.15 K the standard molar heat capacities are (143.44 ± 0.14) J · K⁻¹ · mol⁻¹ for GeCo₂O₄ and (130.76 ± 0.13) J · K⁻¹ · mol⁻¹ for GeNi₂O₄. The standard molar entropies at T=298.15 K for GeCo₂O₄ and GeNi₂O₄ are (149.20 ± 0.60) J · K⁻¹ · mol⁻¹ and (131.80 ± 0.53) J · K⁻¹ · mol⁻¹ respectively. Above 100 K, the heat capacity of the cobalt compound is significantly higher than that of the nickel compound. The excess heat capacity can be reasonably modeled by the assumption of a Schottky contribution arising from the thermal excitation of electronic states associated with the CO²⁺ ion in a cubic crystal field. The splittings obtained, 230 cm⁻¹ for the four-fold-degenerate first excited state and 610 cm⁻¹ for the six-fold degenerate second excited state, are significantly lower than those observed in pure CoO.     

Structural,magnetic and Mössbauer spectroscopic investigations of the magnetoelectric relaxor Pb(Fe0.6W0.2Nb0.2)O3

The complex perovskite lead iron tungsten niobium oxide, Pb(Fe_0.6W_0.2Nb_0.2)O₃ (PFWN) which belongs to the class of disordered magnetoelectrics, has been studied by X-ray and neutron powder diffraction, magnetic and Mössbauer spectroscopic measurements. Structural, dielectric and magnetic properties of PFWN are presented and reviewed. Magnetic measurements indicate that the most important interactions are of antiferromagnetic nature yielding T_N = 300 K, however, with indications of a reentrant spin glass behaviour below 20 K. The parameters of Mössbauer spectra also support the existence of the magnetic order and are consistent with the presence of high-spin Fe³⁺ cations located in the octahedral B-site. Rietveld refinements of diffraction data at different temperatures between 10 and 700 K have been carried out. The long-range structure of PFWN is cubic (space group Pm−3m) over the whole temperature interval. The Fe, W and Nb cations were found to be disordered over the perovskite B-sites. The Pb cations show a position disorder along the 〈111〉 direction shifting from their high-symmetry position. At the temperatures below T_N, an antiferromagnetic arrangement of the magnetic moments of Fe³⁺ cations in the B-site is proposed in accordance with the antiferromagnetic properties of PFWN. The factors governing the observed nuclear and magnetic structures of PFWN are discussed and compared with those of pure Pb(Fe_0.67W_0.33)O₃, Pb(Fe_0.5Nb_0.5)O₃ and other quaternary Pb-based perovskites containing iron.     

Study on the valence fluctuation and the magnetism of an iron mixed-valence complex, (n-C4H9)4N[FeIIFeIII(mto)3](mto = C2O3S)

In the case of iron mixed-valence complexes whose spin states are situated in the spin-crossover region, conjugated phenomena coupled with spin and charge are expected. In general, the Fe site coordinated by six S atoms is in the low-spin state, while the Fe site coordinated by six O atoms is in the high-spin state. From this viewpoint, we have synthesized and investigated physical properties for an monothiooxalato-bridged (mto = C₂O₃S) iron mixed-valence complex, (n-C₄H₉)₄N[Fe^IIFe^III(mto)₃], consisting of Fe^IIIO₃S₃ and Fe^IIO₆ octahedra, which behaves as a ferrimagnet with its magnetic transition temperature of T_N = 38 K and Weiss temperature of θ = ?93 K. From the analysis of ⁵⁷Fe Mössbauer spectra of ⁵⁷Fe enriched complexes, (n-C₄H₉)₄N[⁵⁷Fe^IIFe^III(mto)₃] and (n-C₄H₉)₄N[Fe^II57Fe^III(mto)₃], the charge transfer between Fe^II and Fe^III exists in the paramagnetic phase. Considering the time window of ⁵⁷Fe Mössbauer spectroscopy, the time scale of the valence fluctuation is at least slower than 10^?7 s. In order to confirm the valence fluctuation between Fe^II and Fe^III, we investigated the dielectric constant and found an anomalous enhancement attributed to the Fe valence fluctuation between 170 and 250 K.     

Thermodynamics of Cr2O3, FeCr2O4, ZnCr2O4, and CoCr2O4

High-temperature heat capacity measurements were obtained for Cr₂O₃, FeCr₂O₄, ZnCr₂O₄, and CoCr₂O₄ using a differential scanning calorimeter. These data were combined with previously available, overlapping heat capacity data at temperatures up to 400 K and fitted to 5-parameter Maier–Kelley C_p(T) equations. Expressions for molar entropy were then derived by suitable integration of the Maier–Kelley equations in combination with recent S^∘(298) evaluations. Finally, a database of high-temperature equilibrium measurements on the formation of these oxides was constructed and critically evaluated. Gibbs free energies of Cr₂O₃, FeCr₂O₄, and CoCr₂O₄ were referenced by averaging the most reliable results at reference temperatures of (1100, 1400, and 1373) K, respectively, while Gibbs free energies for ZnCr₂O₄ were referenced to the results of Jacob [K.T. Jacob, Thermochim. Acta 15 (1976) 79–87] at T = 1100 K. Thermodynamic extrapolations from the high-temperature reference points to T = 298.15 K by application of the heat capacity correlations gave Δ_fG^∘(298) = (−1049.96, −1339.40, −1428.35, and −1326.75) kJ · mol⁻¹ for Cr₂O₃, FeCr₂O₄, ZnCr₂O₄, and CoCr₂O₄, respectively.     

Magnetic dilution effect on the charge transfer phase transition and the ferromagnetic transition for an iron mixed-valence complex, (n-C3H7)4N[FeII1−xZnIIxFeIII(dto)3] (dto = C2O2S2)

Iron mixed-valence complex, (n-C₃H₇)₄N[Fe^IIFe^III(dto)₃] (dto = C₂O₂S₂) shows a new-type of phase transition coupled with spin and charge around 120 K, where the charge transfer between the Fe^II and Fe^III sites occurs reversibly, and shows the ferromagnetic transition at 7 K. To investigate the magnetic structure and its dimensionality of (n-C₃H₇)₄N[Fe^IIFe^III(dto)₃], we have synthesized a mixed crystal system, (n-C₃H₇)₄N[Fe^II_1?xZn^II_xFe^III(dto)₃], and measured its magnetic properties. In this system, the magnetic moment is reduced with increasing of Zn ratio. Moreover, the ferromagnetic interaction changes to the antiferromagnetic one and the remnant magnetization disappears between x = 0.48 and 0.96, while the charge transfer between the Fe^II and Fe^III sites disappears above x = 0.26. In this paper, we present the magnetic dilution effect on the charge transfer phase transition and the ferromagnetic transition by means of magnetic susceptibility measurement and ⁵⁷Fe Mössbauer spectroscopy.     

Magnetoelectric perovskite (Bi0.5Pb0.5)(Fe0.5Zr0.5)O3: Preparation,structural and magnetic properties

The perovskite (Bi_0.5Pb_0.5)(Fe_0.5Zr_0.5)O₃ was synthesized by solid-state reaction in an attempt to find magnetoelectric materials, in which ferroelectricity and ferromagnetism coexist. This complex perovskite has been studied by X-ray and neutron powder diffraction in combination with magnetic measurements. The compound crystallizes in the orthorhombic space group Pbam with a ～ √2a_p, b ～ 2√2a_p and c ～ 2a_p (with a_p ～ 4.057 Å). The field and temperature dependence of the magnetization combined with neutron diffraction data showed antiferromagnetic behavior with the Neel temperature, T_N ～ 450 K. Rietveld refinements of neutron powder diffraction data collected at different temperatures, between 10 and 700 K, have been carried out in order to extract information about the thermal evolution of the nuclear and magnetic structures. A distorted orthorhombic perovskite structure was found within the whole temperature interval. The Bi/Pb and Fe/Zr ions were found to be partially ordered over the perovskite A-site and disordered over the B-site. The neutron diffraction patterns of the (Bi_0.5Pb_0.5)(Fe_0.5Zr_0.5)O₃ sample showed evidence of a long-range magnetic ordering below T_N with a propagation vector k = (0,0,0) and an antiferromagnetic arrangement of the magnetic moments of the Fe³⁺ cations in the B-site. This is consistent with an A_y-type magnetic structure. The factors governing the structural and magnetic properties of (1 ? x)BiFeO₃–xPbZrO₃ solid solutions are discussed and compared with those of pure BiFeO₃ and PbZrO₃. A solid solution strategy for developing magnetoelectric properties in BiFeO₃-based compounds is described, with the aim of realizing both a spontaneous polarization and magnetization at room temperature.     

Size-dependence of the heat capacity and thermodynamic properties of hematite (α-Fe2O3)

The heat capacity of a 13 nm hematite (α-Fe₂O₃) sample was measured from T = (1.5 to 350) K using a combination of semi-adiabatic and adiabatic calorimetry. The heat capacity was higher than that of the bulk which can be attributed to the presence of water on the surface of the nanoparticles. No anomaly was observed in the heat capacity due to the Morin transition and theoretical fits of the heat capacity below T = 15 K show a small T³ dependence (due to lattice contributions) with no T^3/2 dependence. This suggests that there are no magnetic spin-wave contributions to the heat capacity of 13 nm hematite. The use of a large linear term to fit the heat capacity below T = 15 K is most likely due to superparamagnetic contributions. A small anomaly within the temperature range (4 to 8) K was attributed to the presence of uncompensated surface spins.     

Mössbauer spectroscopic study of photo-sensitive organic–inorganic hybrid system, (SP)[Fe(II)Fe(III)(dto)3](dto = C2O2S2, SP = spiropyran)

A photo-sensitive organic–inorganic hybrid system (SP)[Fe^IIFe^III(dto)₃] (SP = spiropyran, dto = C₂O₂S₂), has recently been developed, where the photo-isomerization of the intercalated spiropyran in solid state triggers the change of the magnetic properties, including the ferromagnetic transition temperature from 5 to 22 K. We performed ⁵⁷Fe Mössbauer measurement in order to probe the microscopic states of iron ions in (SP)[Fe^IIFe^III(dto)₃] and have investigated the photo-induced effect on them. The sample without UV-irradiation shows the charge transfer phase transition between 200 and 70 K and the higher and lower temperature phases coexist below 70 K, whereas the UV-irradiated sample does not undergo the charge transfer phase transition and the higher temperature phase is stable between 200 and 6 K.     

Low-temperature thermodynamic properties of Ir(C5H7O2)3: Connection of entropy with the molecule volume for tris-acetylacetonates of metals

The heat capacity of Ir(C₅H₇O₂)₃ has been measured by the adiabatic method within the temperature range (5 to 305) K. The thermodynamic functions (entropy, enthalpy, and reduced Gibbs free energy) at 298.15 K have been calculated using the obtained experimental heat capacity data. A connection has been found between the entropy and the volume of the elementary crystalline cell for β-acetylacetonates of some metals. The reasons for this interdependence are discussed. The values of entropies at T = 298.15 K have been calculated for all the metal acetylacetonates on which there are structural data.     

Thermal properties of [Cr(NH3)6](BF4)3 studied by adiabatic and relaxation calorimetry

Four (solid–solid) phase transitions were detected in the temperature range of (9 to 300) K in polycrystalline [Cr(NH₃)₆](BF₄)₃ at T_C1 = 240.7 K, T_C2 = 108.0 K, T_C3 = 91.9 K, and T_C4 = 61.3 K by adiabatic calorimetry. The measurements by relaxation calorimetry were followed on lowering temperature from 20 K down to 0.35 K under six different external magnetic field values (9, 7, 5, 3, 1 and 0) T. For non-zero values of applied magnetic field well-defined Schottky anomaly appears. Magnetic heat capacity was calculated assuming the zero-field splitting for the decoupled Cr(III) ions. There is no discrepancy between the observed and calculated values. Isothermal magnetization curve recorded up to 5 T was measured at temperature of 1.8 K.     

Thermodynamic properties of calcium titanates: CaTiO3, Ca4Ti3O10, and Ca3Ti2O7

The chemical potentials of CaO in two-phase fields (TiO₂ + CaTiO₃), (CaTiO₃ + Ca₄Ti₃O₁₀), and (Ca₄Ti₃O₁₀ + Ca₃Ti₂O₇) of the pseudo-binary system (CaO + TiO₂) have been measured in the temperature range (900 to 1250) K, relative to pure CaO as the reference state, using solid-state galvanic cells incorporating single crystal CaF₂ as the solid electrolyte. The cells were operated under pure oxygen at ambient pressure. The standard Gibbs free energies of formation of calcium titanates, CaTiO₃, Ca₄Ti₃O₁₀, and Ca₃Ti₂O₇, from their component binary oxides were derived from the reversible e.m.f.s. The results can be summarised by the following equations: CaO(solid) + TiO₂(solid) → CaTiO₃(solid), ΔG° ± 85/(J · mol^?1) = ?80,140 ? 6.302(T/K); 4CaO(solid) + 3TiO₂(solid) → Ca₄Ti₃O₁₀(solid), ΔG° ± 275/(J · mol^?1) = ?243,473 ? 25.758(T/K); 3CaO(solid) + 2TiO₂(solid) → Ca₃Ti₂O₇(solid), ΔG° ± 185/(J · mol^?1) = ?164,217 ? 16.838(T/K).The reference state for solid TiO₂ is the rutile form. The results of this study are in good agreement with thermodynamic data for CaTiO₃ reported in the literature. For Ca₄Ti₃O₁₀ Gibbs free energy of formation obtained in this study differs significantly from that reported by Taylor and Schmalzried at T = 873 K. For Ca₃Ti₂O₇ experimental measurements are not available in the literature for direct comparison with the results obtained in this study. Nevertheless, the standard entropy for Ca₃Ti₂O₇ at T = 298.15 K estimated from the results of this study using the Neumann–Koop rule is in fair agreement with the value obtained from low-temperature heat capacity measurements.     

Thermodynamic properties of Na2Ti6O13 and Na2Ti3O7: electrochemical and calorimetric determination

Standard values of Gibbs free energy, entropy, and enthalpy of Na₂Ti₆O₁₃ and Na₂Ti₃O₇ were determined by evaluating emf-measurements of thermodynamically defined solid state electrochemical cells based on a Na–β″-alumina electrolyte. The central part of the anodic half cell consisted of Na₂CO₃, while two appropriate coexisting phases of the ternary system Na–Ti–O are used as cathodic materials. The cell was placed in an atmosphere containing CO₂ and O₂. By combining the results of emf-measurements in the temperature range of 573⩽T/K⩽1023 and of adiabatic calorimetric measurements of the heat capacities in the low-temperature region 15⩽T/K⩽300, the thermodynamic data were determined for a wide temperature range of 15⩽T/K⩽1100. The standard molar enthalpy of formation and standard molar entropy at T=298.15 K as determined by emf-measurements are Δ_fH_m⁰=(−6277.9±6.5) kJ · mol⁻¹ and S_m⁰=(404.6±5.3) J · mol⁻¹ · K⁻¹ for Na₂Ti₆O₁₃ and Δ_fH_m⁰=(−3459.2±3.8) kJ · mol⁻¹ and S_m⁰=(227.8±3.7) J · mol⁻¹ · K⁻¹ for Na₂Ti₃O₇. The standard molar entropy at T=298.15 K obtained from low-temperature calorimetry is S_m⁰=399.7 J · mol⁻¹ · K⁻¹ and S_m⁰=229.4 J · mol⁻¹ · K⁻¹ for Na₂Ti₆O₁₃ and Na₂Ti₃O₇, respectively. The phase widths with respect to Na₂O content were studied by using a Na₂O-titration technique.     

An experimental setup for isobaric heat capacities for viscous fluids at high pressure: Squalane,bis(2-ethylhexyl) sebacate and bis(2-ethylhexyl) phthalate

A high-pressure flow calorimeter has been used to determine highly accurate isobaric heat capacities for different viscous fluids, squalane (SQN), bis(2-ethylhexyl) sebacate (DEHS) and bis(2-ethylhexyl) phthalate (DEHP) from T = (293.15 to 353.15) K and up to 30 MPa. The experimental device was adapted for viscous liquids at high pressure and it can measure heat capacities with an estimated total uncertainty better than 1%. The isobaric heat capacity values were analysed together with their temperature and pressure dependences. In addition, a fitting equation of the experimental molar isobaric heat capacity for these viscous fluids as a function of temperature and pressure was proposed.     

A simple synthesis and room temperature magnetic properties of new binary Mn0.5Fe0.5(H2PO4)2·xH2O obtained from a rapid co-precipitation at ambient temperature

A new binary Mn_0.5Fe_0.5(H₂PO₄)₂·xH₂O powder was synthesized by simple and cost-effective method using phosphoric acid, manganese and iron metals as starting chemicals. The synthesized solid shows the complex thermal transformations and the final decomposition product is a new binary manganese iron cyclo-tetraphosphate, MnFeP₄O₁₂. The X-ray diffraction and FTIR results indicate that the synthesized new binary Mn_0.5Fe_0.5(H₂PO₄)₂·xH₂O and the decomposition MnFeP₄O₁₂ powders are a pure monoclinic phase with space group P2₁/n (Z = 2) and C2/c (Z = 4), respectively. The particle morphologies of Mn_0.5Fe_0.5(H₂PO₄)₂·xH₂O and MnFeP₄O₁₂ powders appear as the rod-like tetragonal shape and show a high agglomeration of small particles, which are similar to the case of Mn(H₂PO₄)₂·2H₂O and Fe₂P₄O₁₂, respectively. Room temperature magnetization results show a ferromagnetic behavior of the Mn_0.5Fe_0.5(H₂PO₄)₂·xH₂O and MnFeP₄O₁₂ powders, having the hysteresis loops in the range of ?10,000 Oe < H < +10,000 Oe with the specific magnetization values of 25.63 and 13.14 emu/g at 10 kOe, respectively. The lower magnetizations of Mn_0.5Fe_0.5(H₂PO₄)₂·xH₂O and MnFeP₄O₁₂ than those of Fe(H₂PO₄)₂·2H₂O and Fe₂P₄O₁₂ powders indicate the presence of Mn ions in substitution position of Fe ions.     

Effects of Fe doping on the electrochemical performance of LiCoPO4/C composites for high power-density cathode materials

LiCo_1?xFe_xPO₄/C composites with various amounts of Fe (x = 0, 0.05 and 0.1) were synthesized by vibrant type ball-milling coupled with microwave heating to investigate the role of doped Fe²⁺ in LiCo_1?xFe_xPO₄/C composites. The initial charge–discharge curves and cyclic voltammetry profiles of LiCo_1?xFe_xPO₄/C composites apparently featured an improved kinetic property compared to LiCoPO₄. It was observed that the initial discharge capacity (120 mA hg^?1) of LiCo_0.95Fe_0.05PO₄ is higher than that (108 mA hg^?1) of LiCoPO₄ and the difference between the oxidation–reduction peaks is getting smaller with the increase of Fe doping. The electrochemical improvement in LiCo_1?xFe_xPO₄/C composites could be attributed to the enhanced Li⁺ diffusivity induced by the enlargement of 1D channel in polyanion structure of LiCoPO₄.     

The heat capacities and thermodynamic properties of NiAl2O4 and CoAl2O4 measured by adiabatic calorimetry from T = (4 to 400) K

The low-temperature heat capacity of NiAl₂O₄ and CoAl₂O₄ was measured between T = (4 and 400) K and thermodynamic functions were derived from the results. The measured heat-capacity curves show sharp anomalies peaking at around T = 7.5 K for NiAl₂O₄ and at T = 9 K for CoAl₂O₄. The exact cause of these anomalies is unknown. From our results, we suggest a standard entropy for NiAl₂O₄ at T = 298.15 K of (97.1 ± 0.2) J · mol^?1 · K^?1 and for CoAl₂O₄ of (100.3 ± 0.2) J · mol^?1 · K^?1.     

(Liquid + solid) metastable equilibria in quinary system Li2CO3 + Na2CO3 + K2CO3 + Li2B4O7 + Na2B4O7 + K2B4O7 + H2O at T=288 K for Zhabuye salt lake

An experimental study on metastable equilibria at T=288 K in the quinary system Li₂CO₃ + Na₂CO₃ + K₂CO₃ + Li₂B₄O₇ + Na₂B₄O₇ + K₂B₄O₇ + H₂O was done by isothermal evaporation method. Metastable equilibrium solubilities and densities of the solution were determined experimentally. According to the experimental data, the metastable equilibrium phase diagram under the condition saturated with Li₂CO₃ was plotted, in which there are four invariant points; nine univariant curves; six fields of crystallization: K₂CO₃ · 3/2H₂O, K₂B₄O₇ · 5H₂O, Li₂B₂O₄ · 16H₂O, Na₂B₂O₄ · 8H₂O, Na₂CO₃ · 10H₂O, NaKCO₃ · 6H₂O. Some differences were found between the stable phase diagram at T=298 K and the metastable one at T=288 K.     

Phase transitions and thermodynamic properties of (NH4)3VO2F4 cryolite

Calorimetric measurements performed in a wide temperature range on (NH₄)₃VO₂F₄ have shown the presence of four heat capacity anomalies at T₁ = 438 K, T₂ = 244 K, T₃ = 210.2 K, T₄ = 205.1 K associated with the first order phase transitions. In accordance with the permittivity behavior, the structural transformations are of nonferroelectric nature. Pressure dependence of the phase transition temperatures has been studied by DTA under pressure. The entropy of phase transitions is analyzed mainly in the framework of the orientational disordering of NH₄⁺ and VO₂F₄^3? ions in a cubic phase.     

Mesoporous Fe2O3 nanoparticles as high performance anode materials for lithium-ion batteries

This work introduces an effective, inexpensive, and large-scale production approach to the synthesis of Fe₂O₃ nanoparticles with a favorable configuration that 5 nm iron oxide domains in diameter assembled into a mesoporous network. The phase structure, morphology, and pore nature were characterized systematically. When used as anode materials for lithium-ion batteries, the mesoporous Fe₂O₃ nanoparticles exhibit excellent cycling performance (1009 mA h g^− 1 at 100 mA g^− 1 up to 230 cycles) and rate capability (reversible charging capacity of 420 mA h g^− 1 at 1000 mA g^− 1 during 230 cycles). This research suggests that the mesoporous Fe₂O₃ nanoparticles could be suitable as a high rate performance anode material for lithium-ion batteries.