Why the Allen-Cahn equation can not be used to characterize the time evolution of a conserved order parameter?

Why not to use Allen-Cahn equation plus a Lagrange multiplier term (to the free energy to apply the conservation) to characterize the time evolution of a conserved order parameter?

There is an answer at Page 38, last paragraph of the book "Phase-field methods in materials science and engineering"

Timetable for “Phase-field methods in materials science and engineering”

Timetable for the study of the book “Phase-field methods in materials science and engineering”

Progress will be recorded in this post. I hope I could finish the whole book in two months, that is, before 01 July. Then I will have enough time to try to parallel my own code following the example of the book. The dead line for the whole studying and code parallelization is before 01 September.

Chapter 1 Introduction

finished at 29/04/11

Chapter 2 Mean field theory of phase transformations

begin at 04/05/11

finished at 06/05/11

This chapter introduces the lattice model and Landau order parameter theory. The later one discussed the form of the free energy for several simple systems, and how to determine the coefficients.

Chapter 3 Spatial variations and interfaces

begin at 06/05/11

finished at 06/05/11

This chapter derived the Cahn-Hilliard free energy functional form at first. The surface tension is further derived at second part.

Chapter 4 Noequilibrium dynamics

begin at 06/05/11

finished at 09/05/11

This chapter introduced the Cahn-Hilliard and Allen-Cahn equations and how to numerically implement them into fortran codes. Structure factor is discussed at Page 41.

Chapter 5 Introduction to phase field modeling: Solidification of pure materials

Chapter 6 Phase field modeling of solidification in binary alloys

Just quick through these two chapters and the accompany codes at 09/05/11

Need more time to gasp the physics behind the codes

Chapter 5 has been understood mostly at 09/05/11

How to visualize 3D results of phase field simulation?

Following is a matlab script I used to visualize 3D result of phase field simulation. If someone has better choice, please let me know.

##########################

figure

data = timekk;

data = smooth3(data,'box',5);

isoval = 0.0;

h = patch(isosurface(data,isoval),...

'FaceColor','blue',...

'EdgeColor','none',...

'AmbientStrength',.2,...

'SpecularStrength',.7,...

'DiffuseStrength',.4);

isonormals(data,h)

patch(isocaps(data,isoval),...

'FaceColor','interp',...

'EdgeColor','none')

colormap winter

colorbar

daspect([1,1,1])

axis tight

view(3)

camlight right

camlight left

set(gcf,'Renderer','zbuffer');

lighting phong

saveas(gcf,f3d,'jpg')

#############################

Precipitates will dissolve under compress loading?

I do phase field simulation of multiparticle precipitates rafting under a uniaxial a stress and find that precipitates will dissolve under compress stress, but will show rafting behavior under tensile stress. This is interesting. I don't know this is possible in reality or just a mistake of my code. Some one can give me some hints? I should discuss this with others and do a literature search. If this phenomena is true, I could test the critical grain size and critical stress with my code maybe.

book: phase-field methods in materials science and engineering

Got this book today. Should read it ASAP and try the sample codes. The MPI implementation in the sample is a good example. I will revise my own code into parallelization accordingly.

Phase field simulation of phase change materials. How to perform?

Phase change materials (PCMs) can be categorized into nucleation-dominated and growth-dominated materials. For nucleation-dominated materials, many nuclei are formed in a unit volume; these nuclei grow relatively slowly. Critical nuclei formation also occurs continuously during the growth process so that crystals of different sizes are formed (31). For growth-dominated materials, very few critical nuclei are formed after an often relatively long incubation time, but then crystallization occurs by rapid growth. For these materials, the crystals have similar sizes (31).

Depending on the temperature, sometimes the same materials can behave as either nucleation

dominated or growth dominated.

I wander if there is way to simulate this phenomena with phase field method. Keep this for another day.

Codes for phase field simulation, updated at 04/05/11

1. simple code

http://sites.google.com/site/gururajanmp/phase-field

lCH-muSE

Phase field modelling of microstructural evolution using the Cahn-Hilliard equation: A report to accompany CH-muSE

lCA-muSE

Phase field modelling of microstructural evolution using the Allen-Cahn equation

Comments: Simple but with a detailed description file, suitable for the beginners. FFTW is used so that it could be easy to parallelize

2. lFiPy

http://www.ctcms.nist.gov/py/

lDaniel Wheeler，Jonathan E. Guyer，James A. Warren

lPython language

lCurrently implemented models include phase eld treatments of polycrystalline, dendritic, and electrochemical phase transformations as well as a level set treatment of the electrodeposition process

Comments: Need python. Very good for checking your ideas with several lines of coding. Afraid not suitable for large system and 3D, for the limitation of computational efficiency of the python.

3. lExamples in the book:

Provatas, Nikolas / Elder, Ken

Phase-Field Methods in Materials Science and Engineering

This comprehensive and self-contained source discusses the topic in a fundamental way, such that readers can carry out their own code developments. Please find additional codes on

www.wiley-vch.de/publish/en/books/bySubjectEE00/ISBN3-527-40747-2

Comments: In Fortran 90, modulated. Easy to extend. Including phase field crystal method. Very good to begin with

4. lDigital Material

lhttp://www.lassp.cornell.edu/sethna/DM/

lmultiscale materials simulation

lPhase Fields

The phase field code defines field types and operators on them, currently with applications using fourier transforms (FFTW) and explicit time-stepping. Projects using this code include surface deposition and simulation of crack growth.

Comments: No experience yet

5. lRheoPlast:

Marrying Phase Field and Fluid-Structure Interactions

lRheoPlast is a code framework for phase field solidification modeling with fluid flow and elastic solid behavior using a fluid-structure interactions formulation. It is designed to be modular and flexible, such that one can select on the command line between various phase field energy functions, transport coupling terms, initial and boundary conditions, in addition to the various parameters of the model.

Comments: Not developed.