Thermodynamic properties of compounds with kosnarite-type structure

350-356<span style="font-size: 9.0pt;mso-bidi-font-size:10.0pt;mso-bidi-font-weight:bold" lang="EN-US">Synthesis and thermodynamic properties of the<span style="font-size:9.0pt; mso-bidi-font-size:10.0pt" lang="EN-US"> crystalline kosnarite-type structure compounds, viz., A<i style="mso-bidi-font-style: normal">xMe2.25-0.25x(PO4)3 (A = Na, Cs; Me = Ti, Zr, Hf; x = 0, 1 and 5) are reported. The heat capacities of the phosphates have been measured between 6 and 650 K. Investigations on the isostructural solid-to-solid phase transitions of Na5Zr(PO4)3 and Na5Hf(PO4)3 show centering of the off-centered Me atoms in octahedral sites and Na+ occupation transfer between sodium sites. The transition temperatures (T<span style="mso-bidi-font-style: italic">0trs), enthalpy of transition (ΔtrsH0), entropy of transition (ΔtrsS0), molar heat capacities (C0p,m), enthalpy (H0(<i style="mso-bidi-font-style: normal">T) – H0(0)), entropy (S0(T)) and Gibbs) energy (G0(<i style="mso-bidi-font-style: normal">T) H0(0)) are calculated from the experimental data. Standard enthalpies of formation at T = 298.15 K for the phosphates Zr3(PO4)4, NaZr2(PO4)3, CsZr2(PO4)3 and Na5Zr(PO4)3 are estimated by solution reaction calorimetry. By combining the data obtained by the two techniques, their Gibbs energies of formation at 298.15 K have been obtained. Thermodynamic functions of the reactions for solid-state synthesis of the compounds of kosnarite-type structure are calculated. </span

Polyanionic Lattice Modifications Leading to High‐Entropy Sodium Ion Conductors: Mathematical Solution of Accessible Compositions

Sodium zirconium double phosphate NaZr2(PO4)3 can be used as a starting point for investigations of high‐entropy materials. Apart from the frequently used approach of partial substitution with four or more different transition metal cations, this class of materials also allows multiple substitutions of the phosphate groups. Herein modifications of the polyanionic lattice are considered and high‐entropy compositions are numerically determined with up to eight elements on the central tetrahedral lattice site of the so‐called NaSICON structure. For this study, the chemical formula was fixed as Na3Zr2(EO4)3 with E=B, Al, Si, P, As, Sb, S, Se and Te. The number of compositions increases exponentially with the increasing number of elements involved and with decreasing equal step size for each element. The maximum number of 237258 compositions is found for Na3Zr2([B,Al,Si,P,As,Sb,S,Se]O4)3 with a step size of 0.1 mol/formula unit. Of this compositional landscape, 143744 compositions fulfil the definitions of high‐entropy materials. The highest entropy factor of ΔSconfig/R=‐2.0405 is attributed to the compositions Na3Zr2(B0.5Al0.6Si0.4P0.3As0.3Sb0.3S0.3Se0.3)O12 and Na3Zr2(B0.6Al0.5Si0.4P0.3As0.3Sb0.3S0.3Se0.3)O12