The behavior of identical particles interacting through the harmonic-repulsive pair potential has been studied in 3D using molecular dynamics simulations at a number of different densities. We found that at many densities, as the temperature of the systems decreases, the particles crystallize into complex structures whose formation has not been anticipated in previous studies on the harmonic-repulsive pair potential. In particular, at certain densities, crystallization into the structure $Ia\overline{3}d$ (space group #230) with 16 particles in the unit cell occupying Wyckoff special positions (16b) was observed. This crystal structure has not been observed previously in experiments or in computer simulations of single component atomic or soft matter systems. At another density, we observed a liquid which is rather stable against crystallization. Yet, we observed crystallization of this liquid into the monoclinic C2/c (space group #15) structure with 32 particles in the unit cell occupying four different non-special Wyckoff (8f) sites. In this structure particles located at different Wyckoff sites have different energies. From the perspective of the local atomic environment, the organization of particles in this structure resembles the structure of some columnar quasicrystals. At a different value of the density, we did not observe crystallization at all despite rather long molecular dynamics runs. At two other densities, we observed the formation of the $\beta Sn$ distorted diamond structures instead of the expected diamond structure. Possibly, we also observed the formation of the $R\overline{3}c$ hexagonal lattice with 24 particles per unit cell occupying non-equivalent positions.

中文翻译：

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通过谐波排斥对电位相互作用的粒子的晶体结构

通过在许多不同密度下使用分子动力学模拟在3D中研究了通过谐波-排斥对电位相互作用的相同粒子的行为。我们发现，在许多密度下，随着系统温度的降低，颗粒会结晶成复杂的结构，而在以前的谐波排斥对电位研究中并未预料到这种结构的形成。特别是在某些密度下，结晶成结构$\mathrm{一世}\mathrm{一个}\overline{3}d$观察到（230号空间群）在晶胞中具有16个粒子占据了Wyckoff特殊位置（16b）。以前在单组分原子或软物质系统的实验或计算机模拟中尚未观察到这种晶体结构。在另一种密度下，我们观察到一种对结晶相当稳定的液体。但是，我们观察到该液体结晶为单斜晶C 2 / c（第15组空间）结构的晶胞中有32个粒子，占据四个不同的非特殊Wyckoff（8f）位点。在这种结构中，位于不同维克夫夫（Wyckoff）位置的粒子具有不同的能量。从局部原子环境的角度来看，这种结构中的粒子组织类似于某些柱状准晶体的结构。在不同的密度值下，尽管分子动力学相当长，但我们根本没有观察到结晶。在其他两种密度下，我们观察到了$\beta \mathrm{小号}ñ$扭曲的金刚石结构，而不是预期的金刚石结构。可能地，我们还观察到了$\mathrm{[R}\overline{3}C$ 单位格中有24个粒子的六边形晶格占据了不相等的位置。