Auxetic, Partially Auxetic, and Nonauxetic Behaviour in 2D Crystals of Hard Cyclic Tetramers

Poisson's ratios of 2D crystals of hard, cyclic tetramers, further referred to as tetramers, are investigated by Monte Carlo (MC) simulations. The tetramers, very simple model molecules, which are composed of four identical hard disks of diameter sigma with centers forming a square of side d, are studied in the isobaric-isothermal ensemble. It is found that, at the same thermodynamical parameters, but depending on the anisotropy parameter alpha=d/sigma, the tetramers spontaneously form crystalline phases, representing each of the five Bravais lattices (BLs) which are possible in the 2D space. The following BLs are observed: 1) the oblique (monoclinic) one, 2) the rectangular (orthorhombic) one, 3) the centered rectangular (orthorhombic) one, 4) the hexagonal one, and 5) the square (tetragonal) one. Among them, structures showing auxetic, partially auxetic, and nonauxetic behaviour are found. This fact makes the tetramer an interesting example of a prototype "molecule," which, depending on its shape, assembles materials of all possible behaviors regarding Poisson's ratio. It is worth noting that tetramers with alpha=1.7 form a strongly auxetic phase that, at the considered thermodynamic conditions, reaches Poisson's ratios varying in the range between -0.589(3) and -0.162(4).