Synthesis,structure and NMR characterization of a new monomeric aluminophosphate [dl-Co(en)3]2[Al(HPO4)2(H1.5PO4)2(H2PO4)2](H3PO4)4 containing four different types of monophosphates

A new zero-dimensional (0D) aluminophosphate monomer [dl-Co(en)₃]₂[Al(HPO₄)₂(H_1.5PO₄)₂(H₂PO₄)₂](H₃PO₄)₄ (designated AlPO-CJ38) with Al/P ratio of 1/6 has been solvothermally prepared by using racemic cobalt complex dl-Co(en)₃Cl₃ as the template. The Al atom is octahedrally linked to six P atoms via bridging oxygen atoms, forming a unique [Al(HPO₄)₂(H_1.5PO₄)₂(H₂PO₄)₂]^6? monomer. Notably, there exists intramolecular symmetrical O?H?O bonds, which results in pseudo-4-rings stabilized by the strong H-bonding interactions. The structure is also featured by the existence of four different types of monophosphates that have been confirmed by ³¹P NMR and ¹H NMR spectra. The crystal data are as follows: AlPO-CJ38, [dl-Co(en)₃]₂[Al(HPO₄)₂(H_1.5PO₄)₂(H₂PO₄)₂](H₃PO₄)₄, M = 1476.33, monoclinic, C2/c (No. 15), a = 36.028(7) Å, b = 8.9877(18) Å, c = 16.006(3) Å, β = 100.68(3)°, U = 5093.2(18) Å³_, Z = 4, R₁ = 0.0509 (I > 2σ(I)) and wR₂ = 0.1074 (all data). CCDC number 689491.     

Crystal structures of Th(OH)PO4, U(OH)PO4 and Th2O(PO4)2. Condensation mechanism of MIV(OH)PO4 (M = Th,U) into M2O(PO4)2

Three new crystal structures, isotypic with β-Zr₂O(PO₄)₂, have been resolved by the Rietveld method. All crystallize with an orthorhombic cell (S.G.: Cmca) with a = 7.1393(2) Å, b = 9.2641(2) Å, c = 12.5262(4) Å, V = 828.46(4) Å³ and Z = 8 for Th(OH)PO₄; a = 7.0100(2) Å, b = 9.1200(2) Å, c = 12.3665(3) Å, V = 790.60(4) Å³ and Z = 8 for U(OH)PO₄; a = 7.1691(3) Å, b = 9.2388(4) Å, c = 12.8204(7) Å, V = 849.15(7) Å³ and Z = 4 for Th₂O(PO₄)₂. By heating, the M(OH)PO₄ (M = Th, U) compounds condense topotactically into M₂O(PO₄)₂, with a change of the environment of the tetravalent cation that lowers from 8 to 7 oxygen atoms. The lower stability of Th₂O(PO₄)₂ compared to that of U₂O(PO₄)₂ seems to result from this unusual environment for tetravalent thorium.     

Synthesis,crystal structure,and magnetic properties of K4Mn3(HPO4)4(H2PO4)2

A new layered compound, K₄Mn₃(HPO₄)₄(H₂PO₄)₂ (1), has been synthesized under hydrothermal conditions. It crystallizes in the monoclinic space group P2₁/n with a = 8.874(2) Å, b = 6.554(1) Å, c = 18.075(4) Å, and β = 93.39(3)°. The structure consists of zigzag [Mn₃O₁₄]_n chains of edge-sharing MnO₆ octahedrons and MnO₇ pentagonal bi-pyramids, which form layers of formula [Mn₃(HPO₄)₄(H₂PO₄)₂]^4? in the ab plane via H₂PO₄ and HPO₄ units with vertex-sharing. Potassium ions lie between these layers. Magnetic measurements indicate Curie–Weiss behavior above 6 K for 1. A Heisenberg model, with alternating exchange interactions J₁J₁J₂… within the chain and exchange interactions J₃J₃… between the chains, is proposed to describe the magnetic behavior.     

Crystal structure and ionic conductivity of AgCr2(PO4)(P2O7)

Single crystals of a new phosphate AgCr₂(PO₄)(P₂O₇) have been prepared by the flux method and its structural and the infrared spectrum have been investigated. This compound crystallizes in the monoclinic system with the space group C2/c and the parameters are, a = 11.493 (3) Å, b = 8.486 (3) Å, c = 8.791 (2) Å, β = 114.56 (2)°, V = 779.8 (3) ųand Z = 4. Its structure consists of CrO₆ octahedra sharing corners with P₂O₇ units to form undulating chains extending infinitely along the [110] direction. These chains are connected by the phosphate tetrahedra giving rise to a 3D framework with six-sided tunnels parallel to the [101] direction, where the Ag⁺ ions are located. The infrared spectrum of this compound was interpreted on the basis of P₂O₇^4? and PO₄^3? vibrations. The appearance of ν_sP–O–P in the spectrum suggests a bent P–O–P bridge for the P₂O₇^4? ions in the compound, which is in agreement with the X-ray data. The electrical measurements allow us to obtain the activation energy of (1.36 eV) and the conductivity measurements suggest that the charge carriers through the structure are the silver captions.     

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.     

Raman spectra of Sr3(PO4)2 and Ba3(PO4)2 orthophosphates at various temperatures

The Raman spectra for Sr₃(PO₄)₂ and Ba₃(PO₄)₂ were investigated in the temperature range from 80 to 1623 K at atmospheric pressure. An unexpected melting of each sample was observed around 1573–1583 K in this study. In the temperature range from 80 to 1323 K, the Raman wavenumbers of all observed bands for Sr₃(PO₄)₂ and Ba₃(PO₄)₂ continuously decrease with increasing temperature. A quantitative analysis on the wavenumbers of Raman bands for both samples reveals that the ν₃ antisymmetric stretching vibrations show the strongest temperature dependence and the ν₂ symmetric bending vibration displays the weakest temperature dependence. The effects of cations on Raman bands are discussed. The reason for the unexpected melting of both samples is mainly attributed to the significant contribution from excess surface energy and the grain-boundary energy that has apparently lowered the melting points of the small samples, i.e., Gibbs–Thomson effect.     

Comparison of the spin exchange interactions in PbCu2(PO4)2 and SrCu2(PO4)2 on the basis of spin dimer analysis

The spin exchange interactions of PbCu₂(PO₄)₂ were examined by performing the spin dimer analysis based on the extended Hückel tight-binding method, and were compared with those of SrCu₂(PO₄)₂. The two strongest Cu–O⋯O–Cu super–superexchange interactions, J₁ (with Cu⋯Cu = 5.868 Å) and J₂ (with Cu⋯Cu = 5.184 Å), are strong and lead to a linear-four-spin-cluster model for both PbCu₂(PO₄)₂ and SrCu₂(PO₄)₂. Adjacent linear-four-spin-clusters interact substantially in SrCu₂(PO₄)₂, but weakly in PbCu₂(PO₄)₂. The difference in the magnetization behaviors of the two compounds was examined by calculating the magnetic excitation energies of the linear-four-spin-cluster model.     

A calorimetric and thermodynamic investigation of A2[(UO2)2(MoO4)O2] compounds with A = K and Rb and calculated phase relations in the system (K2MoO4 + UO3 + H2O)

A calorimetric and thermodynamic investigation of two alkali-metal uranyl molybdates with general composition A₂[(UO₂)₂(MoO₄)O₂], where A = K and Rb, was performed. Both phases were synthesized by solid-state sintering of a mixture of potassium or rubidium nitrate, molybdenum (VI) oxide and gamma-uranium (VI) oxide at high temperatures. The synthetic products were characterised by X-ray powder diffraction and X-ray fluorescence methods. The enthalpy of formation of K₂[(UO₂)₂(MoO₄)O₂] was determined using HF-solution calorimetry giving Δ_fH° (T = 298 K, K₂[(UO₂)₂(MoO₄)O₂], cr) = −(4018 ± 8) kJ · mol⁻¹. The low-temperature heat capacity, С_р°, was measured using adiabatic calorimetry from T = (7 to 335) K for K₂[(UO₂)₂(MoO₄)O₂] and from T = (7 to 326) K for Rb₂[(UO₂)₂(MoO₄)O₂]. Using these С_р° values, the third law entropy at T = 298.15 K, S°, is calculated as (374 ± 1) J · K⁻¹ · mol⁻¹ for K₂[(UO₂)₂(MoO₄)O₂] and (390 ± 1) J · K⁻¹ · mol⁻¹ for Rb₂[(UO₂)₂(MoO₄)O₂]. These new experimental results, together with literature data, are used to calculate the Gibbs energy of formation, Δ_fG°, for both phases giving: Δ_fG° (T = 298 K, K₂[(UO₂)₂(MoO₄)O₂], cr) = (−3747 ± 8) kJ · mol⁻¹ and Δ_fG° (T = 298 K, Rb₂[(UO₂)₂(MoO₄)], cr) = −3736 ± 5 kJ · mol⁻¹. Smoothed С_р°(Т) values between 0 K and 320 K are presented, along with values for S° and the functions [H°(T) − H°(0)] and [G°(T) − H°(0)], for both phases. The stability behaviour of various solid phases and solution complexes in the (K₂MoO₄ + UO₃ + H₂O) system with and without CO₂ at T = 298 K was investigated by thermodynamic model calculations using the Gibbs energy minimisation approach.     

Nano-structured Li3V2(PO4)3/carbon composite for high-rate lithium-ion batteries

Nano-structured Li₃V₂(PO₄)₃/carbon composite (Li₃V₂(PO₄)₃/C) has been successfully prepared by incorporating the precursor solution into a highly mesoporous carbon with an expanded pore structure. X-ray diffraction analysis, scanning electron microscopy, and transmission electron microscopy were used to characterize the structure of the composites. Li₃V₂(PO₄)₃ had particle sizes of < 50 nm and was well dispersed in the carbon matrix. When cycled within a voltage range of 3 to 4.3 V, a Li₃V₂(PO₄)₃/C composite delivered a reversible capacity of 122 mA h g^? 1 at a 1C rate and maintained a specific discharge capacity of 83 mA h g^? 1 at a 32C rate. These results demonstrate that cathodes made from a nano-structured Li₃V₂(PO₄)₃ and mesoporous carbon composite material have great potential for use in high-power Li-ion batteries.     

Low temperature heat capacity Study of Fe(PO3)3 and Fe2P2O7

The heat capacities of two iron phosphates, Fe(PO₃)₃ and Fe₂P₂O₇, have been measured over the temperature range from (2 to 300) K using the heat capacity option of a Quantum Design Physical Property Measurement System (PPMS). A phase transition related to magnetic ordering has been found in the heat capacity at T = 8.76 K for Fe(PO₃)₃ and T = 18.96 K for Fe₂P₂O₇, which are comparable with literature values from magnetic measurements. By fitting the experimental heat capacity values, the thermodynamic functions, magnetic heat capacities, and magnetic entropies have been determined. Additionally, theoretical fits at low temperatures suggest that Fe₂P₂O₇ has an anisotropic antiferromagnetic contribution to the heat capacity and a large linear term likely caused by oxygen vacancies. Further data fitting in a series over widened temperature regions found that this linear term exists only below 15 K and disappears gradually from (15 to 17) K.     

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.     

Syntheses and crystal structures of new vanadium(IV) oxyphosphates M(VO)2(PO4)2 with M = Co,Ni

We have extended our research interest on titanium oxyphosphates (M^II(TiO)₂(PO₄)₂, with M^II = Mg, Fe, Co, Ni, Cu, Zn) to vanadium oxyphosphates M^II(V^IVO)₂(PO₄)₂ (M^II = Co, Ni). For each compound two phases, named α and β according to synthesis conditions, have been stabilized at room temperature, then characterized. The four crystal structures M(VO)₂(PO₄)₂ (α and β for M = Co, Ni) have been determined in monoclinic P2₁/c space group using X-ray single crystals diffraction data. Structure of the α phase is derived from the Li(TiO)(PO₄) (orthorhombic Pnma) and LiNi_0.50(TiO)₂(PO₄)₂ (monoclinic P2₁/c) types, with cell parameters: a = 6.310(1) Å, b = 7.273(1) Å, c = 7.432(1) Å, β = 90.43(1)° for M = Co, and a = 6.297(2) Å, b = 7.230(2) Å, c = 7.421(2) Å, β = 90.36(2)° for M = Ni. Structure of the β phase is derived from the Ni(TiO)₂(PO₄)₂-type (monoclinic P2₁/c) with cell parameters: a = 7.2742(2) Å, b = 7.2802(2) Å, c = 7.4550(2) Å, β = 120.171(2)° for M = Co, and a = 7.2691(2) Å, b = 7.2366(2) Å, c = 7.4453(2) Å, β = 120.231(2)° for M = Ni. All these structures consist of a three dimensional (3D) framework built up of infinite chains of tilted corner-sharing [VO₆] octahedra, cross-linked by corner-sharing [PO₄] tetrahedra. The M²⁺ ion (M = Co, Ni) is located in a triangular based antiprism which shares faces with two [VO₆] octahedra. Structural filiation is discussed based on a common structural unit, a sheet where divalent cations M²⁺ (M = Co, Ni) are inserted. A thermal study of the α ? β transition is also presented.     

High-temperature calorimetry of (La1−xLnx)PO4 solid solutions

The enthalpy increment of the monazite-type solid solutions of LaPO₄ with NdPO₄, EuPO₄ and GdPO₄ has been measured by drop calorimetry at T = 1000 K. The results show deviations (excess enthalpy) from ideal behaviour that have been interpreted in terms of lattice strains resulting from the ion size effects of substitution of La³⁺ by Ln³⁺. For (La_0.5Gd)_0.5PO₄ also the temperature dependence has been determined for T = (515 to 1565) K, indicating that the excess enthalpy decreases with increasing temperature.     

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.     

Apparent molar heat capacities and apparent molar volumes ofY2(SO4)3(aq),La2(SO4)3(aq),Pr2(SO4)3(aq),Nd2(SO4)3(aq),Eu2(SO4)3(aq),Dy2(SO4)3(aq),Ho2(SO4)3(aq), andLu2(SO4)3(aq)atT = 298.15 K andp = 0.1 MPa

The apparent molar heat capacities C_{p, φ} ^∘ and apparent molar volumes V_φ ^∘ of Y₂(SO₄)₃(aq), La₂(SO₄)₃(aq), Pr₂(SO₄)₃(aq), Nd₂(SO₄)₃(aq), Eu₂(SO₄)₃(aq), Dy₂(SO₄)₃(aq), Ho₂(SO₄)₃(aq), and Lu₂(SO₄)₃(aq) were measured at T =  298.15 K and p =  0.1 MPa with a Sodev (Picker) flow microcalorimeter and a Sodev vibrating-tube densimeter, respectively. These measurements extend from lower molalities of m =  (0.005 to 0.018) mol ·kg ^− 1to m =  (0.025 to 0.434) mol ·kg ^− 1, where the upper molality limits are slightly below those of the saturated solutions. There are no previously published apparent molar heat capacities for these systems, and only limited apparent molar volume information. Considerable amounts of the R SO₄ ⁺ (aq) and R(SO₄)₂ ⁻ (aq) complexes are present, where R denotes a rare-earth, which complicates the interpretation of these thermodynamic quantities. Values of the ionic molar heat capacities and ionic molar volumes of these complexes at infinite dilution are derived from the experimental information, but the calculations are necessarily quite approximate because of the need to estimate ionic activity coefficients and other thermodynamic quantities. Nevertheless, the derived standard ionic molar properties for the various R SO₄ ⁺ (aq) and R(SO₄)₂ ⁻ (aq) complexes are probably realistic approximations to the actual values. Comparisons indicate that V_φ ^∘ {RSO₄ ⁺ , aq, 298.15K}  =  − (6  ±  4)cm³· mol ^− 1and V_φ ^∘ {R(SO₄)₂ ⁻ , aq, 298.15K}  =  (35  ±  3)cm³· mol ^− 1, with no significant variation with rare-earth. In contrast, values of C_{p, φ} ^∘ { RSO₄ ⁺ , aq, 298.15K } generally increase with the atomic number of the rare-earth, whereas C_{p, φ} ^∘ { R(SO₄)₂ ⁻ , aq, 298.15K } shows a less regular trend, although its values are always positive and tend to be larger for the heavier than for the light rare earths.     

Piperazinium dihydrogen phosphate,C4H12N2(H2PO4)2: Synthesis, 31P CP/MAS NMR,structural and thermal investigations

A new piperazinium dihydrogen orthophosphate, C₄H₁₂N₂(H₂PO₄)₂ was discovered and characterized by combining information from X-ray diffraction, ³¹P CP/MAS NMR and thermal analysis (TG/DTA). The compound C₄H₁₂N₂(HPO₄)·H₂O, was also studied in order to compare these two similar materials. The hydrothermal stability is investigated for the system: 1.0 C₄H₁₀N₂: n H₃PO₄: 55–60 H₂O, 0.5 < n < 3. The reaction mixtures with pH in the range 1.6–8.4 were placed at a fixed temperature in the range 20–180 °C for ca. 5 days. C₄H₁₂N₂(H₂PO₄)₂ was obtained when n > ca. 2. A crystal of piperazinium dihydrogen phosphate, C₄H₁₂N₂(H₂PO₄)₂ was structurally investigated using X-ray diffraction: triclinic, space group $P\overline{1}$, a = 7.023(2), b = 7.750(3), c = 12.203(4) Å, α = 84.668(7), β = 81.532(7) and γ = 63.174(6)°, V = 586.0(4) Å³ and Z = 2. The reactivity of C₄H₁₂N₂(H₂PO₄)₂ was investigated by systematic solvothermal syntheses.     

Synthesis and crystal structure of sodium copper tetrametaphosphimate heptahydrate Na2Cu(PO2NH)4·7H2O and sodium potassium copper tetrametaphosphimate heptahydrate KxNa2−xCu(PO2NH)4·7H2O

Na₂Cu(PO₂NH)₄·7H₂O and K_xNa_2−xCu(PO₂NH)₄·7H₂O (x ≈ 0.5) were synthesized by gel crystallization in sodium silicate gels. The crystal structures were solved by single-crystal X-ray methods and found to be isotypic (Pnma, Z = 4; Na₂Cu(PO₂NH)₄·7H₂O: a = 627.5(2) pm, b = 1456.0(3) pm, c = 1900.5(4) pm, R1 = 0.0352; K_0.47Na_1.53Cu(PO₂NH)₄·7H₂O: a = 632.2(2) pm, b = 1460.0(3) pm, c = 1936.4(4) pm, R1 = 0.0345). The P₄N₄ rings of the tetrametaphosphimate anion exhibit a distorted chair-2 conformation with admixtures of saddle and crown conformation. The M⁺ ions are six- and sevenfold coordinated by oxygen atoms, the Cu²⁺ ions are fivefold coordinated, respectively. The MO₇ and the CuO₅ units form pairs of face-sharing polyhedra, which are connected by common corners forming chains and are further interconnected by tetrametaphosphimate anions, forming a three-dimensional network structure with channels along [100] and [010]. The MO₆ units form chains of face-sharing polyhedra, which are situated in the channels along [100]. Extended hydrogen bonding reinforces the three-dimensional framework structure of the compounds. ²³Na-MAS NMR experiments were conducted to verify the K/Na distribution on the M sites derived from the X-ray crystal structure refinement.     

Na4Co2.4Mn0.3Ni0.3(PO4)2P2O7: High potential and high capacity electrode material for sodium-ion batteries

Na₄Co_2.4Mn_0.3Ni_0.3(PO₄)₂P₂O₇ has been evaluated as a positive electrode for sodium-ion batteries. The novel material has two redox couples around 4.2 V and 4.6 V and can deliver the high capacity of ca. 103 mAh g^− 1 at the high current density of 850 mA g^− 1 (5 C). X-ray absorption spectroscopy (XAS) results show that the redox reactions of Co, Mn and Ni ions proceed simultaneously in the charge process and it is indicated the novel material provide high mixed potential by the redox reactions of Co, Mn and Ni ions. These findings suggest that the derivatives of Na₄Co₃(PO₄)₂P₂O₇ should be employed as high potential and high capacity electrode materials.     

Magnetic properties of hybrid organo-inorganic copper(II) oxovanadate(V) phosphate and phosphonate bridged systems

The hybrid organo-inorganic compounds [Cu₄(bipy)₄V₄O₁₁(PO₄)₂]nH₂O (n ∼ 5) (1), [Cu₂(phen)₂(PO₄)(H₂PO₄)₂(VO₂) · 2H₂O] (2) and [Cu₂(phen)₂(O₃PCH₂PO₃)(V₂O₅) (H₂O)]H₂O (3) which present different bridging forms of the phosphate/phosphonate group, show different bulk magnetic properties. We herein analyze the magnetic behaviour of these compounds in terms of their structural parameters. We also report a theoretical study for compound (1) assuming four different magnetic exchange pathways between the copper centres present in the tetranuclear unit. For compound (1) the following J values were obtained J₁ = +3.29; J₂ = −0.63; J₃ = −2.23; J₄ = −46.14 cm⁻¹. Compound (2) presents a Curie–Weiss behaviour in the whole range of temperature (3–300 K), and compound (3) shows a maximum for the magnetic susceptibility at 64 K, typical for antiferromagnetic interactions. These data where fitted using a model previously reported in the literature, assuming two different magnetic exchange pathways between the four copper(II) centres, with J₁ = −30.0 and J₂ = −8.5 cm⁻¹.     

Determination of thermodynamic properties of Na2S using solid-state EMF measurements

To obtain reliable thermodynamic data for Na₂S(s), solid-state EMF measurements of the cell Pd(s)|O₂(g)|Na₂S(s), Na₂SO₄(s)|YSZ| Fe(s), FeO(s)|O₂(g)_ref| Pd(s) were carried out in the temperature range 870 < T/K < 1000 with yttria stabilized zirconia as the solid electrolyte. The measured EMF values were fitted according to the equation E_fit/V (±0.00047) = 0.63650 − 0.00584732(T/K) + 0.00073190(T/K) ln (T/K). From the experimental results and the available literature data on Na₂SO₄(s), the equilibrium constant of formation for Na₂S(s) was determined to be lg K_f(Na₂S(s)) (±0.05) = 216.28 − 4750(T/K)⁻¹ − 28.28878 ln (T/K). Gibbs energy of formation for Na₂S(s) was obtained as Δ_fG^∘(Na₂S(s))/(kJ · mol⁻¹) (±1.0) = 90.9 − 4.1407(T/K) + 0.5415849(T/K) ln (T/K). By applying third law analysis of the experimental data, the standard enthalpy of formation of Na₂S(s) was evaluated to be Δ_fH^∘(Na₂S(s), 298.15 K)/(kJ · mol⁻¹) (±1.0) = −369.0. Using the literature data for C_p and the calculated Δ_fH^∘, the standard entropy was evaluated to S^∘(Na₂S(s), 298.15 K)/(J · mol⁻¹ · K⁻¹) (±2.0) = 97.0.