Study of thermodynamic properties of substitutional mixture of Co(II)- and Fe(II)-based octacyanoniobates
A comprehensive study of thermodynamic properties of three samples of bimetallic molecular magnets [Co$^{\mathrm{II}}$(pyrazole)$_{4}$]$_{2x}$[Fe$^{\mathrm{II}}$(pyrazole)$_{4}$]$_{2(1-x)}$[Nb$^{\mathrm{IV}}$(CN)$_{8}$]$\cdot$4H$_{2}$O with $x$=0 (Co$_{2}$Nb), 0.5 (CoFeNb), and 1 (Fe$_{2}$Nb) is reported. The three samples display the same crystallographic structure crystallizing in the tetragonal system with space group $I4_1/a$. Their heat capacities are measured in the temperature range 0.36-100 K without applied field as well as in the field of $μ_0 H$ = 0.1, 0.2, 0.5, 1, 2, 5, and 9 T. The results imply the presence of the second-order phase transitions to magnetically ordered phases at 4.87(8) K, 7.1(2) K, and 8.44(3) K for $x$=0, 0.5, and 1, respectively. The corresponding thermodynamic functions are analyzed to discuss the stability of the mixed compound and the magnetocaloric effect (MCE). The Gibbs energy of mixing is found to be positive but smaller in magnitude than the energy of thermal fluctuations indicating that the mixed sample is marginally stable in the full detected temperature range. The enthalpy of mixing is negative, which points to an ordered arrangement of the Co(II) and Fe(II) ions in the solid solution CoFeNb. The negative values of the entropy of mixing are explained by considering the enhanced rigidity of the crystal lattice of the solid solution sample. To extract the magnetic contribution to the heat capacity an approach based on a reasonable frequency spectrum is adopted. Taking advantage of the in-field heat capacity measurements MCE was described in terms of the isothermal entropy change $ΔS_\mathrm{M}$ and the adiabatic temperature change $ΔT_\mathrm{ad}$. The magnitudes of these quantities are typical for the class of molecular magnets.