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 σ 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).

中文翻译：

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硬环四聚物的2D晶体中的辅助，部分辅助和非辅助行为

硬的，环状四聚体的二维晶体的泊松比，还称为四聚体，由蒙特卡洛（MC）模拟调查。在等压-等温集成中研究了四聚体，这是一种非常简单的模型分子，由四个相同的直径σ的硬盘组成，其中心形成d角的正方形。发现，在相同的热力学参数下，但取决于各向异性参数$\alpha =d/\sigma$，四聚体自发形成结晶相，代表在2D空间中可能的五个Bravais晶格（BLs）。观察到以下BL：1）斜（单斜）1，2）矩形（斜方）1，3）居中的矩形（斜方）1，4）六边形1，和5）方形（四边形）1。在它们之中，发现了表现出拉力，部分拉力和非拉力行为的结构。这一事实使四聚体成为原型“分子”的一个有趣例子，根据其形状，它组装了所有与泊松比有关的可能行为的材料。值得注意的是$\alpha =1.7$ 在所考虑的热力学条件下，形成强膨胀相，其泊松比在-0.589（3）和-0.162（4）之间变化。