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A lattice model of terephthalic acid (TPA) and iron ordering on the Cu(100) surface is proposed and investigated using Monte Carlo simulation in a grand canonical ensemble. We have an evidence that the emergence of all the experimentally observed metal–organic structures cannot be explained in terms of short-ranged interactions such as hydrogen bonding and metal–carboxylate coordination proposed and discussed in earlier papers. The self-assembly of the “cloverleaf” and “interlocked” structures requires the presence of long-ranged TPA–Fe interaction. The unidentate carboxylate–Fe interaction is demonstrated to be 0.6–0.7 times weaker as compared to the bidentate bond. The phase diagram with all the experimentally observed structures is obtained. It has been established that one type of the ladder structures distinguished on scanning tunneling microscopy images is a metastable state and not a phase …