The morphologies, self-assembly structures, and stability of cobalt-phthalocyanines (CoPc) molecules adsorbed on Cu(001) with coverage ranging from 0.2 monolayer (ML) to 1.6 ML are investigated by ultrahigh-vacuum low-temperature scanning tunneling microscopy (UHV LT-STM) at liquid nitrogen temperature. Upon increasing the deposition of CoPc molecules various structures, such as isolated adsorption, quasi-hexagonal structure, square root(29) x square root(29) structure, are well characterized by the corresponding high-resolution STM images. The CoPc-CoPc intermolecular interaction and CoPc-substrate interfacial interaction dominate the structural evolutions. For the coverage higher than 1 ML, CoPc molecules preferentially locate on top of the molecules underneath and organize into square root(58) x square root(58) structure. As more and more CoPc molecules adsorb on the first layer, in some square root(58) x square root(58) regions molecular insertion leads to the formation of the square root(29) x square root(29) domain to effectively decrease the energy of the whole system.

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