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Quasibinary solid solutions of calcite-structure carbonate minerals play an important role in rock formation. We have investigated solid solutions with cations Ca 2+ , Cd 2+ , Mg 2+ and Zn 2+ by performing first-principles phase diagram calculations for Ca 1-x Zn x CO 3 , Cd 1x Zn x CO 3 , Ca 1-x Cd x CO 3 and Mg 1-x Zn x CO 3 (0 ≤ x ≤ 1) with density functional theory, cluster expansion and Monte Carlo simulations. The end members and the dolomite structures were individually studied to analyze their structural parameters and bonding characteristics. Consolute temperatures and continuous order-disorder transition temperatures are 1450 K for Ca 1-x Zn x CO 3 and 1000 K for Cd 1-x Zn x CO 3 , but below 100 K for Ca 1-x Cd x CO 3 and Mg 1-x Zn x CO 3. In agreement with existing literature, consolute temperatures increase with increasing differences in cation radii. If the dolomite structures are assumed to be stable, the phase diagram calculations predict that they persist to 1150 K for Ca 1-x Zn x CO 3 , and 900 K for Cd 1-x Zn x CO 3 before decomposition at peritectoid points. This confirms the conjectured phase diagram for Ca 1-x Zn x CO 3 in (Goldsmith, 1983. Rev. Mineral. Geochemistry 11). In addition, formation energies of the dolomite structures were decomposed into two parts: first a volume change, then chemical exchange and relaxation. They were compared with the corresponding random solid solutions at the same bulk compositions. (Meta)stability of the dolomite structures was demonstrated by this analysis, and was also studied by examining the bond lengths and cation octahedral distortions.