Bernal-Fowler rules

Fig. 10.1. Fragment of ice lattice. Open circles, oxygen atoms solid circles, protons. The proton distribution satisfies the Bernal-Fowler rules.

Notwithstanding the fact that motion of ionic defects is connected with the motion of protons, it does not imply a real proton transfer. Actually there occur only successive local displacements of protons along the bonds. Due to the memory of the protonic system, after a certain amount of current has passed, all the bonds appear to be blocked, and further passage of current is impossible. It should be remembered however, that there are also defects of the second type in the system, namely, D and L defects, shown in Fig. 10.2, which represent violations of the first Bernal-Fowler rule. A D defect moving in the same direction as an defect, polarizes the bonds in the opposite direction, that is, it unblocks them as seen in Fig. 10.2. In an analogous way the motions of OH and L defects are related. So, by a combined motion of all the defects (or of only an D pair) a current may pass through ice indefinitely. D and... 

One of the more relevant questions related to amorphous ices is probably how to quantify the number of known amorphous states. From the structural point of view, one can identify three amorphous ices, namely LDA, HDA, and VHDA. Both experiments and computer simulations indicate that the structure of these amorphous ices is characterized by the absence of long-range order beyond 10-20 A and by local tetrahedral coordination, in agreement with the Walrafen pentamer geometry. Thus, in all these amorphous ices, the arrangement of a water molecule and its four nearest neighbors is not different from ice and the Bernal-Fowler rules... 

The first thing to do is to count the number of H-bonds and their types for each molecule. We define a donor bond as a bond created by a hydrogen atom of a given molecule and an acceptor bond as the one created by an oxygen atom of the molecule. We use a modification of the venerable Bernal-Fowler ice rules [44] and require that... 

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