A first-principles thermodynamics characterization of the stabilities and structures of SrHfO3 (110) polar terminations has been performed using density functional theory simulations and the surface grand potential technique. The investigated terminations include the SrHfO-, O-2-, HfO-, Sr-, and O-terminated (110) surfaces. Based on the computed surface relaxations (reconstructions), charge redistribution, and electronic structures, the polarity compensation mechanisms of the terminations, i.e., how the polarity compensation criterion is fulfilled, are discussed in detail. To account for the effect of the chemical environment and make a reasonable comparison, the (001) surface and the precipitation of small mono metal oxide crystals on the grown surfaces are considered in the construction of the stability diagram. Based on the constructed stability phase diagram, the stability regions of the (110) and (001) terminations are determined. Additionally, a comparison of the stability behaviors with several analogues is further drawn. (C) 2016 Elsevier B.V. All rights reserved.