At the limit of stability of a supercooled tetrahedral liquid modeled by monatomic (mW) water potential, it was recently shown that relaxation occurs across a unique value of per particle potential energy (ϕmid), which corresponds to a dynamical (non-stationary) condition of Gibbs free energy function G(T, P, N, ϕ): [2(G/N)/∂ϕ2 = 0] and [(G/N)/∂ϕ ≠ 0]. In this work, we explore the inherent structures responsible for the formation of the amorphous states through such a mechanism of relaxation of mW liquid. We first identify 6-member boat and chair shaped rings using a criterion based on the internal dihedral angles. We then consider the stacking of the cubic diamond (10-atom cluster with 4 chair shaped rings) and hexagonal wurtzite (12-atom cluster with 3 boat and 2 chair shaped rings) units through a shared chair ring. We find that the local crystalline (tetrahedral) order is exhibited by the eclipsed bond particles of the laterally connected wurtzite units which are stacked from both sides with the diamond units (DWD stacking). Increasingly longer range crystalline order is obtained as the number of stacked wurtzite layers increases: the particles shared by the stacked (laterally connected) wurtzite layers in DWWD show a longer range crystalline order. An even longer range crystalline order is exhibited by the eclipsed bond particles of the middle (laterally connected) wurtzite layer of DWWWD stacking. We find that cubic-hexagonal stacking occurs primarily in the form of DWD layers across the limit of stability. The local tetrahedral order of the purely cubic (diamond) network particles (which are not shared with wurtzite units) deviates significantly from that of the hexagonal crystal. Nonetheless, the average length of the bonds in the purely cubic network approaches that in the hexagonal crystal very closely. Thus a large increase in the purely cubic ice across the instability also leads to an increase in the local crystalline order in the form of bond-lengths. Our results are consistent with previous experimental and simulation studies which find a significant fraction of cubic ice along with cubic-hexagonal stacking layers in deeply supercooled water.

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