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1. Data from: Electrical transport in tunably-disordered metamaterials

   https://doi.org/10.5061/dryad.d2547d8bd  

   Obrero, Caitlyn; Tirfe, Mastawal; Lee, Carmen; Saptarshi, Sourabh; Rock, Christopher; Daniels, Karen; Newhall, Katherine (January 2025, Dryad)

   Naturally occurring materials are often disordered, with their bulk properties being challenging to predict from the structure, due to the lack of underlying crystalline axes. In this paper, we develop a digital pipeline from algorithmically-created configurations with tunable disorder to 3D printed materials, as a tool to aid in the study of such materials, using electrical resistance as a test case. The designed material begins with a random point cloud that is iteratively evolved using Lloyd's algorithm to approach uniformity, with the points being connected via a Delaunay triangulation to form a disordered network metamaterial. Utilizing laser powder bed fusion additive manufacturing with stainless steel 17-4 PH and titanium alloy Ti-6Al-4V, we are able to experimentally measure the bulk electrical resistivity of the disordered network. We found that the graph Laplacian accurately predicts the effective resistance of the structure, but is highly sensitive to anisotropy and global network topology, preventing a single network statistic or disorder characterization from predicting global resistivity. 

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2. An autonomous design algorithm to experimentally realize three-dimensionally isotropic auxetic network structures without compromising density

   https://doi.org/10.1038/s41524-024-01281-y  

   Shen, Meng; Reyes-Martinez, Marcos A; Powell, Louise Ahure; Iadicola, Mark A; Sharma, Abhishek; Byléhn, Fabian; Pashine, Nidhi; Chan, Edwin P; Soles, Christopher L; Jaeger, Heinrich M; et al (December 2024, npj Computational Materials)

   Abstract Auxetic materials have a negative Poisson’s ratio and are of significant interest in applications that include impact mitigation, membrane separations and biomedical engineering. While there are numerous examples of structured materials that exhibit auxetic behavior, the examples of engineered auxetic structures is largely limited to periodic lattice structures that are limited to directional or anisotropic auxetic response. Structures that exhibit a three-dimensionally isotropic auxetic response have been, unfortunately, slow to evolve. Here we introduce an inverse design algorithm based on global node optimization to design three-dimensional auxetic metamaterial structures from disordered networks. After specifying the target Poisson’s ratio for a structure, an inverse design algorithm is used to adjust the positions of all nodes in a disordered network structure until the desired mechanical response is achieved. The proposed algorithm allows independent control of shear and bulk moduli, while preserving the density and connectivity of the networks. When the angle bending stiffness in the network is kept low, it is possible to realize optimized structures with a Poisson’s ratios as low as −0.6. During the optimization, the bulk modulus of these networks decreases by almost two orders of magnitude, but the shear modulus remains largely unaltered. The materials designed in this manner are fabricated by dual-material 3D-printing, and are found to exhibit the mechanical responses that were originally encoded in the computational design engine. The approach proposed here provides a materials-by-design platform that could be extended for engineering of optical, acoustic, and electrical properties, beyond the design of auxetic metamaterials. 

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3. Order to disorder in quasiperiodic composites

   https://doi.org/10.1038/s42005-022-00898-z  

   Morison, David; Murphy, N. Benjamin; Cherkaev, Elena; Golden, Kenneth M. (December 2022, Communications Physics)

   Abstract From quasicrystalline alloys to twisted bilayer graphene, the study of material properties arising from quasiperiodic structure has driven advances in theory and applied science. Here we introduce a class of two-phase composites, structured by deterministic Moiré patterns, and we find that these composites display exotic behavior in their bulk electrical, magnetic, diffusive, thermal, and optical properties. With a slight change in the twist angle, the microstructure goes from periodic to quasiperiodic, and the transport properties switch from those of ordered to randomly disordered materials. This transition is apparent when we distill the relationship between classical transport coefficients and microgeometry into the spectral properties of an operator analogous to the Hamiltonian in quantum physics. We observe this order to disorder transition in terms of band gaps, field localization, and mobility edges analogous to Anderson transitions — even though there are no wave scattering or interference effects at play here. 

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4. Thermal and electronic transport properties of A Cr X ₂ superionic conductors (A=Cu, Ag and X=S, Se)

   https://doi.org/10.1088/2515-7655/addf7e  

   Rahman, Md_Towhidur; Ciesielski, Kamil; Pelkey, Joseph; Shawon, A_K_M_Ashiquzzaman; Toberer, Eric; Zevalkink, Alexandra (June 2025, Journal of Physics: Energy)

   Abstract Superionic conductors, includingACrX₂(A=Ag, Cu; X = S, Se) compounds, have attracted attention due to their low lattice thermal conductivity and high ionic conductivity. These properties are driven by structural characteristics such as anharmonicity, soft bonding, and disorder, which enhance both fast ion transport and thermal resistance. In the present study, we investigate the impact of various factors (e.g.A-site disorder, microstructure, speed of sound and chemical composition) on the thermal conductivity of the compounds CuCrS₂, CuCrSe₂, AgCrS₂and AgCrSe₂. The samples were synthesized using solid state reaction, ball milling and subsequent spark plasma sintering, and thermal diffusivity, electrical resistivity, Hall coefficients and Seebeck coefficients were measured as a function of temperature. The selenides were found to behave as degenerate semiconductors, with reasonable thermoelectric figure of merit (up to 0.79 in CuCrSe₂), while the sulfides behaved as non-degenerate semiconductors with high electrical resistivity. At room temperature, all samples are in the ordered phase and show low lattice thermal conductivity ranging from 0.60 W m⁻¹-K in AgCrSe₂to 1.1 W m⁻¹-K in CuCrSe₂. Little reduction in lattice thermal conductivity was observed in the high-temperature phase, despite the increased disorder on the cation site and the onset of superionic conductivity. This suggests that the low lattice thermal conductivity inACrX₂compounds is an inherent property of the crystal structure, caused by anharmonic bonding and diffuson dominated transport. 

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5. Small-world disordered lattices: spectral gaps and diffusive transport

   https://doi.org/10.1088/1367-2630/ac7db5  

   Rosa, Matheus I. N.; Ruzzene, Massimo (July 2022, New Journal of Physics)

   Abstract We investigate the dynamic behavior of lattices with disorder introduced through non-local network connections. Inspired by the Watts–Strogatz small-world model, we employ a single parameter to determine the probability of local connections being re-wired, and to induce transitions between regular and disordered lattices. These connections are added as non-local springs to underlying periodic one-dimensional (1D) and two-dimensional (2D) square, triangular and hexagonal lattices. Eigenmode computations illustrate the emergence of spectral gaps in various representative lattices for increasing degrees of disorder. These gaps manifest themselves as frequency ranges where the modal density goes to zero, or that are populated only by localized modes. In both cases, we observe low transmission levels of vibrations across the lattice. Overall, we find that these gaps are more pronounced for lattice topologies with lower connectivity, such as the 1D lattice or the 2D hexagonal lattice. We then illustrate that the disordered lattices undergo transitions from ballistic to super-diffusive or diffusive transport for increasing levels of disorder. These properties, illustrated through numerical simulations, unveil the potential for disorder in the form of non-local connections to enable additional functionalities for metamaterials. These include the occurrence of disorder-induced spectral gaps, which is relevant to frequency filtering devices, as well as the possibility to induce diffusive-type transport which does not occur in regular periodic materials, and that may find applications in dynamic stress mitigation. 

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