** Last Update :: June 15, ****2020**

**Email : dibakar _ datta [@] alumni . brown . edu ; dibakar . datta [@] njit . edu**

**Phone : 973 596 3647 (Office) **

** Fall 2018: ME 618 – ST: Atomistic and Molecular Simulations Methods in Mechanics and Materials Science (AMSM _{3}S)**

**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