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Register a new userUncertainty Quantification in Atomistic Modeling of Metals and its Effect on Mesoscale and Continuum Modeling A Review
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The design of next-generation alloys through the Integrated Computational Materials Engineering (ICME) approach relies on multi-scale computer simulations to provide thermodynamic properties when experiments are difficult to conduct. Atomistic methods such as Density Functional Theory (DFT) and Molecular Dynamics (MD) have been successful in predicting properties of never before studied compounds or phases. However, uncertainty quantification (UQ) of DFT and MD results is rarely reported due to computational and UQ methodology challenges. Over the past decade, studies have emerged that mitigate this gap. These advances are reviewed in the context of thermodynamic modeling and information exchange with mesoscale methods such as Phase Field Method (PFM) and Calculation of Phase Diagrams (CALPHAD). The importance of UQ is illustrated using properties of metals, with aluminum as an example, and highlighting deterministic, frequentist and Bayesian methodologies. Challenges facing routine uncertainty quantification and an outlook on addressing them are also presented.
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FLAME is a software package to perform a wide range of atomistic simulations for exploring the potential energy surfaces (PES) of complex condensed matter systems. The range of methods include molecular dynamics simulations to sample free energy landscapes, saddle point searches to identify transition states, and gradient relaxations to find dynamically stable geometries. In addition to such common tasks, FLAME implements a structure prediction algorithm based on the minima hopping method (MHM) to identify the ground state structure of any system given solely the chemical composition, and a framework to train a neural network potential to reproduce the PES from $textit{ab initio}$ calculations. The combination of neural network potentials with the MHM in FLAME allows a highly efficient and reliable identification of the ground state as well as metastable structures of molecules and crystals, as well as of nano structures, including surfaces, interfaces, and two-dimensional materials. In this manuscript, we provide detailed descriptions of the methods implemented in the FLAME code and its capabilities, together with several illustrative examples.
The Nernst effect is the transverse electric field produced by a longitudinal thermal gradient in presence of magnetic field. In the beginning of this century, Nernst experiments on cuprates were analyzed assuming that: i) The contribution of quasi-particles to the Nernst signal is negligible; and ii) Gaussian superconducting fluctuations cannot produce a Nernst signal well above the critical temperature. Both these assumptions were contradicted by subsequent experiments. This paper reviews experiments documenting multiple sources of a Nernst signal, which, according to the Brigman relation, measures the flow of transverse entropy caused by a longitudinal particle flow. Along the lines of Landauers approach to transport phenomena, the magnitude of the transverse magneto-thermoelectric response is linked to the quantum of thermoelectric conductance and a number of material-dependent length scales: the mean-free-path, the Fermi wavelength, the de Broglie thermal wavelength and the superconducting coherence length. Extremely mobile quasi-particles in dilute metals generate a widely-documented Nernst signal. Fluctuating Cooper pairs in the normal state of superconductors have been found to produce a detectable Nernst signal with an amplitude conform to the Gaussian theory, first conceived by Ussishkin, Sondhi and Huse. In addition to these microscopic sources, mobile Abrikosov vortices, mesoscopic objects carrying simultaneously entropy and magnetic flux, can produce a sizeable Nernst response. Finally, in metals subject to a magnetic field strong enough to truncate the Fermi surface to a few Landau tubes, each exiting tube generates a peak in the Nernst response. The survey of these well-established sources of the Nernst signal is a helpful guide to identify the origin of the Nernst signal in other controversial cases.
Parameterization of interatomic forcefields is a necessary first step in performing molecular dynamics simulations. This is a non-trivial global optimization problem involving quantification of multiple empirical variables against one or more properties. We present EZFF, a lightweight Python library for parameterization of several types of interatomic forcefields implemented in several molecular dynamics engines against multiple objectives using genetic-algorithm-based global optimization methods. The EZFF scheme provides unique functionality such as the parameterization of hybrid forcefields composed of multiple forcefield interactions as well as built-in quantification of uncertainty in forcefield parameters and can be easily extended to other forcefield functional forms as well as MD engines.
Using the dynamics of information propagation on a network as our illustrative example, we present and discuss a systematic approach to quantifying heterogeneity and its propagation that borrows established tools from Uncertainty Quantification. The crucial assumption underlying this mathematical and computational technology transfer is that the evolving states of the nodes in a network quickly become correlated with the corresponding node identities: features of the nodes imparted by the network structure (e.g. the node degree, the node clustering coefficient). The node dynamics thus depend on heterogeneous (rather than uncertain) parameters, whose distribution over the network results from the network structure. Knowing these distributions allows us to obtain an efficient coarse-grained representation of the network state in terms of the expansion coefficients in suitable orthogonal polynomials. This representation is closely related to mathematical/computational tools for uncertainty quantification (the Polynomial Chaos approach and its associated numerical techniques). The Polynomial Chaos coefficients provide a set of good collective variables for the observation of dynamics on a network, and subsequently, for the implementation of reduced dynamic models of it. We demonstrate this idea by performing coarse-grained computations of the nonlinear dynamics of information propagation on our illustrative network model using the Equation-Free approach
We calculate quantum transport for metal-graphene nanoribbon heterojunctions within the atomistic self-consistent Schrodinger/Poisson scheme. Attention is paid on both the chemical aspects of the interface bonding as well the one-dimensional electrostatics along the ribbon length. Band-bending and doping effects strongly influence the transport properties, giving rise to conductance asymmetries and a selective suppression of the subband formation. Junction electrostatics and p-type characteristics drive the conduction mechanism in the case of high work function Au, Pd and Pt electrodes, while contact resistance becomes dominant in the case of Al.
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