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The Na+-Mg2+-NO3--SO42--H2O quaternary reciprocal systemis an important subsystem of several natural brine types associated with nitrate deposits on earth (e.g. in the Atacama Desert), in atmospheric aerosols, in natural stone or building stones subjected to atmospheric pollution and in cave nitrates. We report on an ion interaction (Pitzer) model that is used to calculate activities and solubilities in this reciprocal system. Model parameterization is based on binary and ternary experimental data. New parameters are reported for Mg(NO3)(2)-H2O and the ternary systems Na+-Mg2+-NO3--H2O and Mg2+-NO3--SO42--H2O. We also report on the details of the model parameterization of the NaNO3-H2O binary. Calculated solubility diagrams of the full reciprocal system are compared to experimental data. In most cases the calculations are within the experimental uncertainty. Several important invariant points of the reciprocal system are calculated and the stability ranges of the various solids are discussed in detail. It is shown that both darapskite, Na3NO3SO4 center dot H2O, and bloedite, Na2Mg(SO4)(2)center dot 4H(2)O, have large stability fields in the reciprocal system at near ambient temperatures. This is in agreement with their common occurrence in nitrate deposits. (C) 2016 Elsevier B.V. All rights reserved.