Dibakar Datta

 Fall 2018: ME 618 – ST: Atomistic and Molecular Simulations Methods in   Mechanics and Materials Science (AMSM₃S)

Course Syllabus & Timeline

 * Week 1 *

Motivation for the Course

Why is this course very important? What will we learn? Examples of Molecular Simulations.

Review of the Fundamentals of Thermodynamics

Equilibrium and State Quantities - systems, phases, and state quantities; equilibrium and temperatures; pressure, work, and chemical potential; heat and heat capacity; The Laws of Thermodynamics – the zeroth law of thermodynamics, internal energy and the first law, entropy and the second law; Thermodynamic Potentials – free energy, enthalpy.

 * Week 2 *

Review of the Fundamentals of Thermodynamics (Contd.)

Thermodynamic Potentials – the principle of maximum entropy, entropy and energy as thermodynamic potentials, maxwell relations, thermodynamic stability; Phase Transitions and Chemical Reactions – gibbs’ phase rule, phase equilibrium

Review of the Fundamentals of Statistical Mechanics

Number of Microstates Ω and Entropy S - foundations, phase space, statistical definition of entropy, quantum mechanical counting of Ω; Ensemble Theory and Microcanonical Ensemble- the microcanonical ensemble, entropy as an ensemble average; The Canonical Ensemble – calculation of observable as ensemble averages, connection between microcanonical and canonical ensembles.

 * Week 3 *

Review of the Fundamentals of Statistical Mechanics (Contd.)

The Canonical Ensemble – virial theorem and equipartition theorem; Macrocanonical Ensemble – fluctuations in the macrocanonical ensemble

An Overview of Molecular Simulation - example of molecular simulations; fundamental components of molecular dynamics; newton’s equation of motion; a simple numerical integrator: verlet algorithm; Numerical Integrators - several versions of verlet algorithm; order of accuracy; other integrators; Perfect Crystal Structures – lattices and bases; miller indices

 * Week 4 *

Interatomic Interactions – why is it important? interatomic potential models; locality of interatomic interactions; computational cost of interatomic models; Energy minimization – why is it important? the steepest descent method; conjugate gradient relaxation; local and global minimization; Periodic Boundary Conditions – different boundary conditions; the importance of periodic boundary condition; Code – matlab code to make crystal structures; Application of MD in different fields – various problems in mechanics and materials science e.g. fracture, friction, nanofluidics, nanomedicine, environment, electronics, energy storage, etc.

 * Week 5 *

 Hands-on Session: MD software LAMMSP & visualization tool OVITO (Part I)

overview of LAMMPS; overview of OVITO visualization tool; shell-scripting; post-mortem of a simple LAMMPS script – MD for simple LJ (2D and 3D particles); coding to make 2D material graphene; analysis of LAMMPS script for graphene simulation

 * Week 6 *

 Hands-on Session: MD software LAMMPS & visualization tool OVITO (Part II) 

coding of bi- and multilayer graphene, LAMMPS script to compute bi- and multi-layer graphene (e.g. friction); coding of two-dimensional materials beyond graphene e.g. transition metal dichalcogenides (TMD); LAMMPS script for TMD; coding of graphene-TMD heterostructures; LAMMPS script of two-dimensional heterostructures

 * Week 7 *

 Hands-on Session: MD software LAMMPS & visualization tool OVITO (Part III)

computation of pressure, diffusivity, and thermal conductivity using LAMMPS; indentation using LAMMPS; indentation of 2D materials using LAMMPS

 * Week 8 *

Monte Carlo Methods in Statistical Mechanics – theoretical background, algorithm; coding of MC methods; Monte Carlo methods in LAMMPS. Introduction to the Kinetic Monte Carlo Method (Part - I) – motivation: the time-scale problem; infrequent-event systems, state-to-state dynamics, and the KMC concept

 * Week 9 *

Introduction to the Kinetic Monte Carlo Method (Part - II) -  The rate constant and first-order processes; The KMC procedure; determining the rates; the lattice assumption and the rate catalog; the low-barrier problem

 * Week 10 *

Hands-on Session: KMC Code in MATLAB

KMC code in MATLAB – Langmuir adsorption-desorption problem.

 * Week 11 *

A Brief Introduction to Density Functional Theory (DFT)

elementary quantum mechanics – the Schrodinger equation, the variational principle, the Hartree-Fock approximation; the Kohn-Sham equations; the exchange-correlation functionals; the basic machinery of DFT – basis sets; DFT applications for various problems

 * Week 12 *

Hands-on Session: DFT software VASP & Visualization tool VESTA (Part I)

overview of VASP; example on graphene – writing direct and cartesian coordinates, optimization of KPOINTS and ENCUT

 * Week 13 *

Hands-on Session: DFT software VASP (Part II)

chemo-mechanics problem with DFT – evaluation of mechanical properties of materials with DFT (e.g., stress-strain response, elastic modulus, etc.)

 * Week 14 *

Hands-on Session: DFT software VASP (Part III)

miscellaneous problems with DFT