Materials Modeling

Notes of modeling materials; from first principals, on.

Lecture 1: Introduction to Material Science

Multiscale Modeling is touched on in Fluid Mechanics but here, will traverse the scale through the lectures.

Ab Inito Methods derive materials properties from first principals or wave equation

  • Pros

    • electronic and structural behavior and properties

    • bond breaking and formation in chemical reaction

    • can systematically improve results to prove quality

    • in principal, can obtain exact properties

  • Cons

    • very small systems, ~O(10E2) atoms

    • very small timescales, ~O(10E-12) or pico seconds

    • numerically expensive on even super computers of ~O(10E15) flops

Atomistic Methods is the range of semi classical statistical mechanics for thermodynamic and transport properties

  • Pros

    • Systems larger on scale of ~O(10E4) and ~O(10E6) atoms

    • Larger timescales of ~O(10E-9) to O(10E-6) second

  • Cons

    • results depend on force field used

    • Transport properties dependent on macroscale conditions which affect physical processes

Mesoscale methods is a level of simplification treating clusters of atoms as blobs of matter. An abstraction which allows for some computational savings by calculation as entities moving through a potential field.

  • Pros

    • Study structural features of complex systems on size ~O(10E8) or more

    • Dynamic processes on the order of a second

  • Cons

    • Mostly only qualitative tendencies, with quality difficult to ascertain

    • Approximations limit insight

Continuum Methods: assume matter can be treated as field quantity which changes continuously. Solve balance equations, per FEM and CFD.

  • Pro: rest of the time lengthscale diagram is accessible

  • Con Require viscosity, diffusion coefficients, and other transport properties

Upscaling is the using a lower lengthscale information to inform the properties of higher length scales in a deductive approach

Downscaling is using higher scale, often experimental information, to inform lower order parameters. More difficult due to non-uniqueness.

Lecture 2: Ab Inito Principals, Fundamentals

Lecture 3: Ab Inito and Density Functional Theory, Part 1

Lecture 4: Ab Inito and DFT, Part 2

Lecture 5: Linux

Lecture 6: Ab Inito and DFT, Part 3

Lecture 7: Molecular Dynamics (MD), Introduction

Lecture 8: MD Introduction to Integrators

Lecture 9: MD Force Fields and Ensembles

Lecture 10: MD Static Properties

Lecture 11: MD Dynamic Properties

Lecture 12: MD Tricks of the Trade

Lecture 13: Project Guidelines

Lecture 14: Introduction to Monte Carlo Methods

Lecture 15: Ising Model

Lecture 16: Kinetic and Reverse Monte Carlo

Lecture 17: Brownian Dynamics

Lecture 18: Dissipative Particle Dynamics

Lecture 19: Continuum Methods and Beyond

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