Specific Heat of an Ising Linear-Chain Crystal

The specific heat of a single crystal of ludlamite [${\mathrm{Fe}}_3$ ${\left(\mathrm{P}{\mathrm{O}}_4\right)}_2$·4 ${\mathrm{H}}_2$O] has been measured in the temperature range 2.4-68°K, indicating a $\lambda$ peak at (15.0±0.4)°K, thus suggesting the existence of a magnetically ordered state below that temperature. By subtracting the lattice contribution, which was obtained by measuring the specific heat of the isomorphic crystal hopeite [${\mathrm{Zn}}_3$ ${\left(\mathrm{P}{\mathrm{O}}_4\right)}_2$·4 ${\mathrm{H}}_2$O], a broad peak was observed above 15.0°K, suggesting linear-chain coupling. A calculation was made, based on a linear-chain Ising model, and the most satisfactory fit yielded $\frac{J}{k}=10.0\mathrm{}°$K for the intrachain exchange coupling. A sublattice-magnetization calculation has also been made and compared with the molecular-field approximation.