Канал: Phase Field Modelling

Grain growth: Fan-Chen model I

Grain growth: Fan-Chen model I

Grain growth: Fan-Chen model II

Grain growth: Fan-Chen model II

Grain boundary grooving I

Grain boundary grooving I

Overview of phase field modelling

Overview of phase field modelling

Grain boundary grooving II

Grain boundary grooving II

Precipitate growth II

Precipitate growth II

Precipitate growth I

Precipitate growth I

Grain growth

Grain growth

Gibbs Thomson effect

Gibbs Thomson effect

Order-disorder transformation

Order-disorder transformation

Spinodal decomposition in 2D

Spinodal decomposition in 2D

AC: numerical solution

AC: numerical solution

Order-disorder transition and Allen-Cahn equation

Order-disorder transition and Allen-Cahn equation

Interfacial energy: numerical versus analytical values

Interfacial energy: numerical versus analytical values

Interfacial energy in CH: analytical calculation

Interfacial energy in CH: analytical calculation

CH: analytical solution

CH: analytical solution

Interfacial energy in CH

Interfacial energy in CH

Free energy functional

Free energy functional

Derivation of Cahn-Hilliard (CH) equation I

Derivation of Cahn-Hilliard (CH) equation I

Free energy versus concentration curves

Free energy versus concentration curves

Derivation of Cahn-Hilliard (CH) equation II

Derivation of Cahn-Hilliard (CH) equation II

Numerical solution of CH: finite difference

Numerical solution of CH: finite difference

Diffusion equation versus CH

Diffusion equation versus CH

Numerical solution of CH: spectral method

Numerical solution of CH: spectral method

Variational derivative

Variational derivative

Optimization of functional II

Optimization of functional II

Optimization of functionals I

Optimization of functionals I

Variational calculus

Variational calculus

Representation quadric

Representation quadric

Understanding Neumann's principle

Understanding Neumann's principle

Crystal: symmetry elements II

Crystal: symmetry elements II

Crystal: symmetry elements I

Crystal: symmetry elements I

Spectral techniques I

Spectral techniques I

Spectral techniques II

Spectral techniques II

Scalars, vectors and tensors

Scalars, vectors and tensors

Implicit spectral method

Implicit spectral method

Coordinate transformation

Coordinate transformation

II rank tensors and Neumann principle

II rank tensors and Neumann principle

Transformation laws

Transformation laws

Group theory

Group theory

Diffusion equation : finite difference method

Diffusion equation : finite difference method

Diffusion equation : zero flux BC and explicit method

Diffusion equation : zero flux BC and explicit method

Diffusion equation : zero flux BC and implicit method

Diffusion equation : zero flux BC and implicit method

Diffusion equation : imposed concentration BC and explicit/implicit methods

Diffusion equation : imposed concentration BC and explicit/implicit methods

Periodic boundary conditions (PBC)

Periodic boundary conditions (PBC)

Expicit method with PBC

Expicit method with PBC

Diffusion equation : Analytical solution I

Diffusion equation : Analytical solution I

Diffusion equation : Analytical solution II

Diffusion equation : Analytical solution II

Diffusion equation : Error function solution I

Diffusion equation : Error function solution I

Diffusion equation: Error function solution II

Diffusion equation: Error function solution II

Regular solution using octave

Regular solution using octave

Ideal solution using octave

Ideal solution using octave

Constructing phase diagram

Constructing phase diagram

Non-dimensionalisation of diffusion equation

Non-dimensionalisation of diffusion equation

Plotting spinodal

Plotting spinodal

Diffusion and Fourier law of heat conduction

Diffusion and Fourier law of heat conduction

GNU Octave : script mode

GNU Octave : script mode

GNU Octave : interactive mode

GNU Octave : interactive mode

GNU Octave : Introduction

GNU Octave : Introduction

Non-classical diffusion equation

Non-classical diffusion equation

Failure of classical diffusion equation

Failure of classical diffusion equation

Diffusion and mobility II

Diffusion and mobility II

Diffusion and mobility I

Diffusion and mobility I

Solution to classical diffusion equation

Solution to classical diffusion equation

Tutorial 7

Tutorial 7

Understanding spinodal region

Understanding spinodal region

Regions of stability

Regions of stability

Thermodynamic property : composition dependence

Thermodynamic property : composition dependence

Stability

Stability

Spinodal decomposition

Spinodal decomposition

Spinodal decomposition - some history

Spinodal decomposition - some history

Some references

Some references

Failure of classical diffusion equation

Failure of classical diffusion equation

Fick's law

Fick's law

Diffusion and chemical potential

Diffusion and chemical potential

Tutorial 6

Tutorial 6

Tutorial 5

Tutorial 5

Tutorial 4

Tutorial 4

Tutorial 3

Tutorial 3

Tutorial 2

Tutorial 2

Tutorial 1

Tutorial 1

Solution models

Solution models

Summary of solution models

Summary of solution models

G vs X diagrams

G vs X diagrams

Phase diagrams

Phase diagrams

Chemical potential

Chemical potential

Bond breaking model

Bond breaking model

Course Intro-Phase field modelling-Prof. M.P. Gururajan

Course Intro-Phase field modelling-Prof. M.P. Gururajan