Structural and calorimetric studies of order-disorder in CdMg(CO₃)₂

The disordering of CdMg(CO₃)₂ was studied near room temperature by powder X-ray diffraction and solution calorimetry using samples quenched from 600 to 850°C. The long-range order parameter changes from unity to zero in this range and the enthalpy of disordering is 13.7 ± 0.8 kJ/mole. The enthalpy of formation of ordered CdMg(CO₃)₂ from CdCO₃ and MgCO₃ is -5.6 ± 0.8 kJ/mole; that of the disordered phase is +8.1 ± 0.8 kJ/mole. These data support energetic models which assume positive interactions of Cd and Mg within cation layers and negative interactions (leading to ordering) between layers. A reasonable fit to the observed phase relations is achieved using either the point approximation (PA) of the generalized Bragg-Williams model or the tetrahedron approximation (TA) of the cluster variation method (CVM). These models however, do not give a quantitative fit to the variation of enthalpy and long-range order parameter with temperature. In particular, the observed order-disorder transition occurs more sharply over a smaller temperature range than predicted, perhaps because of more strongly cooperative behavior in which the carbonate groups as well as the divalent cations play a role.