Shi Wenlong, Keeney David, Chen Duyu, Jiao Yang, Torquato Salvatore
Materials Science and Engineering, Arizona State University, Tempe, Arizona 85287, USA.
Materials Research Laboratory, University of California, Santa Barbara, California 93106, USA.
Phys Rev E. 2023 Oct;108(4-2):045306. doi: 10.1103/PhysRevE.108.045306.
Disordered hyperuniform materials are an emerging class of exotic amorphous states of matter that endow them with singular physical properties, including large isotropic photonic band gaps, superior resistance to fracture, and nearly optimal electrical and thermal transport properties, to name but a few. Here we generalize the Fourier-space-based numerical construction procedure for designing and generating digital realizations of isotropic disordered hyperuniform two-phase heterogeneous materials (i.e., composites) developed by Chen and Torquato [Acta Mater. 142, 152 (2018)1359-645410.1016/j.actamat.2017.09.053] to anisotropic microstructures with targeted spectral densities. Our generalized construction procedure explicitly incorporates the vector-dependent spectral density function χ[over ̃]{{V}}(k) of arbitrary form that is realizable. We demonstrate the utility of the procedure by generating a wide spectrum of anisotropic stealthy hyperuniform microstructures with χ[over ̃]{{V}}(k)=0 for k∈Ω, i.e., complete suppression of scattering in an "exclusion" region Ω around the origin in Fourier space. We show how different exclusion-region shapes with various discrete symmetries, including circular-disk, elliptical-disk, square, rectangular, butterfly-shaped, and lemniscate-shaped regions of varying size, affect the resulting statistically anisotropic microstructures as a function of the phase volume fraction. The latter two cases of Ω lead to directionally hyperuniform composites, which are stealthy hyperuniform only along certain directions and are nonhyperuniform along others. We find that while the circular-disk exclusion regions give rise to isotropic hyperuniform composite microstructures, the directional hyperuniform behaviors imposed by the shape asymmetry (or anisotropy) of certain exclusion regions give rise to distinct anisotropic structures and degree of uniformity in the distribution of the phases on intermediate and large length scales along different directions. Moreover, while the anisotropic exclusion regions impose strong constraints on the global symmetry of the resulting media, they can still possess structures at a local level that are nearly isotropic. Both the isotropic and anisotropic hyperuniform microstructures associated with the elliptical-disk, square, and rectangular Ω possess phase-inversion symmetry over certain range of volume fractions and a percolation threshold ϕ_{c}≈0.5. On the other hand, the directionally hyperuniform microstructures associated with the butterfly-shaped and lemniscate-shaped Ω do not possess phase-inversion symmetry and percolate along certain directions at much lower volume fractions. We also apply our general procedure to construct stealthy nonhyperuniform systems. Our construction algorithm enables one to control the statistical anisotropy of composite microstructures via the shape, size, and symmetries of Ω, which is crucial to engineering directional optical, transport, and mechanical properties of two-phase composite media.
无序超均匀材料是一类新兴的奇异非晶态物质，具有独特的物理性质，包括大的各向同性光子带隙、优异的抗断裂性以及近乎最优的电和热输运性质等等。在此，我们推广了基于傅里叶空间的数值构建方法，用于设计和生成由Chen和Torquato [《材料学报》142, 152 (2018)1359 - 645410.1016/j.actamat.2017.09.053] 开发的各向同性无序超均匀两相异质材料（即复合材料）的数字实现，以适用于具有目标谱密度的各向异性微结构。我们的广义构建方法明确纳入了可实现的任意形式的与矢量相关的谱密度函数χ̃_{V}(k)。我们通过生成一系列各向异性的隐身超均匀微结构来证明该方法的实用性，对于k∈Ω，χ̃_{V}(k)=0，即在傅里叶空间中围绕原点的“排除”区域Ω内完全抑制散射。我们展示了具有各种离散对称性的不同排除区域形状，包括不同大小的圆盘形、椭圆形、方形、矩形、蝴蝶形和双纽线形区域，如何作为相体积分数的函数影响所得的统计各向异性微结构。Ω的后两种情况导致定向超均匀复合材料，它们仅在某些方向上是隐身超均匀的，而在其他方向上是非超均匀的。我们发现，虽然圆盘形排除区域产生各向同性超均匀复合微结构，但某些排除区域的形状不对称（或各向异性）所施加的定向超均匀行为在不同方向的中长尺度上产生了不同的各向异性结构和相分布的均匀程度。此外，虽然各向异性排除区域对所得介质的全局对称性施加了强约束，但它们在局部层面上仍可具有近乎各向同性的结构。与椭圆形、方形和矩形Ω相关的各向同性和各向异性超均匀微结构在一定体积分数范围内都具有相反转对称性和渗流阈值ϕ_{c}≈0.5。另一方面，与蝴蝶形和双纽线形Ω相关的定向超均匀微结构不具有相反转对称性，并且在低得多的体积分数下沿某些方向渗流。我们还应用我们的通用方法来构建隐身非超均匀系统。我们的构建算法使人们能够通过Ω的形状、大小和对称性来控制复合微结构的统计各向异性，这对于设计两相复合介质的定向光学性质、输运性质和力学性质至关重要。
