# Browsing by Subject "Inverse design"

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Item Inverse design methods for targeted self-assembly(2014-12) Jain, Avni; Truskett, Thomas Michael, 1973-Show more In this thesis, we study the problem of what microscopic thermodynamic driving forces can stabilize target macroscopic structures. First, we demonstrate that inverse statistical mechanical optimization can be used to rationally design inter-particle interactions that display target open structures as ground states over a wide range of thermodynamic conditions. We focus on designing simple interactions (e.g., isotropic, convex-repulsive) that drive the spontaneous assembly of material constituents to low-coordinated ground states of diamond and simple cubic lattices. This is significant because these types of phases are typically accessible given more complex systems (e.g., particles with orientation-dependent attractive interactions) and for a narrow range of conditions. We subject the optimal interactions to stringent stability tests and also observe assembly of the target structures from disordered fluid states. We then use extensive free energy based Monte Carlo simulation techniques to construct the equilibrium phase diagrams for the model materials with interactions designed to feature diamond and simple cubic ground states, i.e., at zero temperatures. We find that both model materials, despite the largely featureless interaction form, display rich polymorphic phase behavior featuring not only thermally stable target ground state structures, but also a variety of other crystalline (e.g., hexagonal and body-centered cubic) phases. Next, we investigate whether isotropic interactions designed to stabilize given two-dimensional (2D) lattices (e.g., honeycomb or square) will favor their analogous three-dimensional (3D) structures (e.g., diamond or simple cubic), and vice versa. We find a remarkable transferability of isotropic potentials designed to stabilize analogous morphologies in 2D and 3D, irrespective of the exact interaction form, and we discuss the basis of this cross-dimensional behavior. Our results suggest that computationally inexpensive 2D material optimizations can assist in isolating rare isotropic interactions that drive the assembly of materials into 3D open lattice structures.Show more Item Inverse design of metamaterials for wave control(2020-05-11) Goh, Heedong; Kallivokas, Loukas F.; Alù, Andrea; Cox, Brady; Haberman, Michael R.; Hamilton , Mark F.; Manuel, LanceShow more Metamaterials are engineered materials, whose spatially periodic arrangement of their constituent materials endows the composite assembly with rather unconventional properties, when macroscopically observed. In the context of the three wave-supporting physics regimes -elastodynamics, acoustics, and electromagnetics- metamaterials present unique opportunities for previously unimaginable user control over the resulting wave behavior. To date, the design of metamaterials is mostly done on an ad hoc basis, relying mostly on one-of-a-kind or incremental physical experiments and forward computational modeling. This dissertation introduces a systematic methodology, rooted in inverse problem theory, for engineering the dispersive properties of periodic media to meet a priori, user-defined, wave control objectives. Both scalar and vector waves are considered. In the developed methodology, the material properties and geometry parameters of the unit cell of the periodic medium become the inversion variables. The inversion is driven by the user-defined wave control objective, constrained by the dispersive characteristics of the unit cell. Though the methodology is flexible enough and can accommodate fairly broad dispersion engineering objectives, here the focus is on band-gaping propagating waves at user-defined frequency ranges. Numerical results in the frequency domain demonstrate that the inversion process yields unit cells that indeed attain the user-defined dispersive behavior. The inverted-for unit cells are then used to build metamaterial assemblies of not only finite periodicity, as opposed to infinite, but of fairly narrow periodicity, and are tested in the time domain against broadband excitations: it is shown that it is possible to attain the desired wave control with sub-wavelength size metamaterial assemblies.Show more Item Novel inverse methods for crystal self-assembly(2018-06-15) Piñeros Gonzalez, William D.; Truskett, Thomas Michael, 1973-; Makarov, Dmitrii E.; Elber, Ron; Henkelman, Graeme; Jones, Richard AShow more Inverse design methods are a promising new strategy to aid the discovery of materials with targeted properties. In this thesis, we employ two novel inverse design methods and apply it to the study of crystal self-assembly in two dimensions. In particular, we introduce a novel zero temperature (ground state -GS) analytical method and find effective interactions that stabilize targeted lattices by means of a constrained non-linear optimization. We demonstrate advantages of this new formulation by designing a square lattice to display increasing energetic differences over relevant lattice competitors and show that such constraints correlate with crystal thermal stability. However, these constraints also reduce density range representation of the target lattice in its phase diagram and suggests an inherent tradeoff in the constrained strategy. Having established a link between crystal property and constraint type, we design the snubsquare lattice by means of energetic constraints over close competitors and show this is in contrast to the design of the kagome lattice which required no such constraints. We then test the limits of the GS method and design the open and challenging truncated square (TS) and truncated hexagonal lattices (TH). Unlike the previous targets, these lattices require the inclusion of a large pool of competitor micro-phases that greatly complicate optimization. Nevertheless, we show the system is still solvable by judicious use of constraints and decision variables. Next, we use a novel relative entropy minimization approach (RE) and the GS method to explore the design space of particles interacting via a potential featuring a single attractive well. Specifically, we design a square, honeycomb and kagome lattice and show that we are able to infer a set of `design rules' from generalities of the resulting interactions in both methods. We validate these rules by designing the challenging TS and TH lattices and show that optimized interactions readily promote target assembly from the fluid state. Finally, we expand the RE method to accommodate multi-component systems and inverse design a variety of crystal binary mixtures featuring triangular, square as well as other intricate and open motifs. We demonstrate how binary systems can help achieve equivalent single component structures but with simpler underlying interactions. Further, we analyze the binary assembly process and find that self interactions act as a `primer' that place particles in the correct local positions while cross interactions, through system coupling, act as the `binder' that lock particles into the correct binary structure.Show more