Ground state of localized deuterons

The internal geometry of all layers is identical but they can be divided into two types - L0 and L1/2 in respect of their position in lattice. As from Fig. 1 (1) the layers of different types are alternated, (2) the nearest-neighboring layers L0 (as well as Li/2) are matched by the c-translations, and (3) each L0 layer is matched with its two L1/2 neighbors by the simultaneous shifts by b/2 and cj2. 

All of structures (3) relate to antiferroelectric phase that is in an agreement with the available measurements evidencing just the same character of low-temperature phase in the M3D(A04)2 crystals [6], It is also evident that the doubling of b-parameter of the paraelectric A2/a cell under transition to the low-temperature D-ordered phase directly follows from proposed scheme (3). Recently, such fe-doubling is observed experimentally in [7]. This scheme is also consistent with the doubling of c-parameter of A2/a cell found in the cited paper. In particular, such fe-doubling takes place when the layer sequence (3) takes the form  

It should be noted, however, that we do not discuss many different structural changes in crystals accompanying the low-temperature D-ordering transition (displacements of metal cations, rotations of the A04-terahedra, etc.). Therefore, our analysis is limited by specific changes in H-bond network only and does not claim on the exhaustive treatment of all crystallographic problems. 

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