MICRESS Forum

Dear Bernd:
I am simulating solidification of some technical Al based multi-component alloys by coupling to thermodynamic database via TQ interface. I have read your paper "simulation of microstructure formation in technical aluminum alloys using the multiphase-field method" and got some suggestion from it. However, I met a problem. In my simulation, the dimension is 200*200, grid spacing is 1 um, cooling rate is -2k/s. The process is fcc_A1(Al solution phase) dendrite formation from the liquid phase in the first. Then as the temperature is down, the alpha-AlMnSi stoichiometric phase is formed. I set the alpha-AlMnSi phase formation in the fcc_A1(Al)/liquid interface in the dri file. The problem is that it can not grow after nucleation. The calculation seems stopped at that time. I have calculated the phase diagram, the alpha-AlMnSi should form as temperature is down. I changed the numerical parameter "phase mini" to a very small value and also tested some parameters such as interface energy and interface mobility between fcc_Al/alpha-AlMnSi, liquid/alpha-AlMnSi. But it doesn't make sense. The following is some parts of the dri file where I think there may be some problem, could you please give some suggestions. In the dri file: liquid(phase 0), fcc_A1(Al)(phase 1), alpha-AlMnsi(phase 2)
-----------------------------------------------------------
# Data for further nucleation
# ===========================
# Enable further nucleation?
# Options: nucleation no_nucleation [verbose|no_verbose]
nucleation
# Additional output for nucleation?
# Options: out_nucleation no_out_nucleation
out_nucleation
#
# Number of types of seeds?
1
#
# Input for seed type 1:
# ----------------------
# Type of 'position' of the seeds?
# Options: bulk region interface triple quadruple [restrictive]
interface
# Phase of new grains?
2
# Reference phase?
0
# Substrat phase [2nd phase in interface]?
# (set to 0 to disable the effect of substrate curvature)
1
# maximum number of new nuclei 1?
5
# Grain radius [micrometers]?
1.00000
# Choice of growth mode:
# Options: stabilisation analytical_curvature
stabilisation
# min. undercooling [K] (>0)?
5.0000
# Shield effect:
# Shield time [s] ?
10.000
# Shield distance [micrometers]?
10.000
# Nucleation range
# min. nucleation temperature for seed type 1 [K]
173.0000
# max. nucleation temperature for seed type 1 [K]
880.0000
# Time between checks for nucleation? [s]
0.10000
# Shall random noise be applied?
# Options: nucleation_noise no_nucleation_noise
no_nucleation_noise
#
# Max. number of simultaneous nucleations?
# ----------------------------------------
# (set to 0 for automatic)
0
#
# Shall metastable small seeds be killed?
# ---------------------------------------
# Options: kill_metastable no_kill_metastable
no_kill_metastable
#
#
# Phase interaction data
# ======================
#
# Data for phase interaction 0 / 1:
# ---------------------------------
# Simulation of interaction between phase 0 and 1?
# Options: phase_interaction no_phase_interaction
# [standard|particle_pinning[_temperature]|solute_drag|redistribution_control]
phase_interaction
# 'DeltaG' options: default
# avg ... [] max ... [J/cm**3] smooth ... [degrees]
avg 1 max 2000
# I.e.: avg +1.00 smooth +45.0 max +2.00000E+03
# Type of surface energy definition between phases LIQUID and 1?
# Options: constant temp_dependent
constant
# Surface energy between phases LIQUID and 1? [J/cm**2]
9.30000E-06
# Type of mobility definition between phases LIQUID and 1?
# Options: constant temp_dependent dg_dependent
constant
# Kinetic coefficient mu between phases LIQUID and 1? [cm**4/(Js)]
2.00000E-03
# Is interaction isotropic?
# Options: isotropic anisotropic
anisotropic
# static anisotropy coefficient? (< 1.)
0.65000
# kinetic anisotropy coefficient? (< 1.)
0.45000
#
# Data for phase interaction 0 / 2:
# ---------------------------------
# Simulation of interaction between phase 0 and 2?
# Options: phase_interaction no_phase_interaction identical phases nb.
# [standard|particle_pinning[_temperature]|solute_drag|redistribution_control]
phase_interaction
# 'DeltaG' options: default
# avg ... [] max ... [J/cm**3] smooth ... [degrees]
avg 1 max 2000
# I.e.: avg +1.00 smooth +45.0 max +2.00000E+03
# Type of surface energy definition between phases LIQUID and 2?
# Options: constant temp_dependent
constant
# Surface energy between phases LIQUID and 2? [J/cm**2]
1.00000E-07
# Type of mobility definition between phases LIQUID and 2?
# Options: constant temp_dependent dg_dependent
constant
# Kinetic coefficient mu between phases LIQUID and 2? [cm**4/(Js)]
2.00000E-03
#
# Data for phase interaction 1 / 1:
# ---------------------------------
# Simulation of interaction between phase 1 and 1?
# Options: phase_interaction no_phase_interaction identical phases nb.
# [standard|particle_pinning[_temperature]|solute_drag|redistribution_control]
no_phase_interaction
#
# Data for phase interaction 1 / 2:
# ---------------------------------
# Simulation of interaction between phase 1 and 2?
# Options: phase_interaction no_phase_interaction identical phases nb.
# [standard|particle_pinning[_temperature]|solute_drag|redistribution_control]
phase_interaction
# 'DeltaG' options: default
# avg ... [] max ... [J/cm**3] smooth ... [degrees]
avg 1 max 2000
# I.e.: avg +1.00 smooth +45.0 max +2.00000E+03
# Type of surface energy definition between phases 1 and 2?
# Options: constant temp_dependent
constant
# Surface energy between phases 1 and 2? [J/cm**2]
1.00000E-06
# Type of mobility definition between phases 1 and 2?
# Options: constant temp_dependent dg_dependent
constant
# Kinetic coefficient mu between phases 1 and 2? [cm**4/(Js)]
1.00000E-06
# Is interaction isotropic?
# Options: isotropic anisotropic
isotropic
#
# Data for phase interaction 2 / 2:
# ---------------------------------
# Simulation of interaction between phase 2 and 2?
# Options: phase_interaction no_phase_interaction identical phases nb.
# [standard|particle_pinning[_temperature]|solute_drag|redistribution_control]
no_phase_interaction
#
#
-----------------------------------------------------------------------------------
# Phase diagram - input data
# ==========================
#
# List of phases and components which are stoichiometric:
# phase and component(s) numbers
# List of concentration limits:
# <Limits>, phase number and component number
# End with 'no_more_stoichio' or 'no_stoichio'
2 1 2 3 4
no_more_stoichio
# In phase 2 components 1, 2, 3 and 4 are stoichiometric.
#
------------------------------------------------------------------------------------
# Parameters for latent heat and 1D temperature field
# ===================================================
# Simulate release of latent heat?
# Options: lat_heat lat_heat_3d [matrix phase] no_lat_heat
no_lat_heat
#
#
# Boundary conditions
# ===================
# Type of temperature trend?
# Options: linear linear_from_file profiles_from_file
linear
# Number of connecting points? (integer)
0
# Initial temperature at the bottom? (real) [K]
880.0000
# Temperature gradient in z-direction? [K/cm]
0.0000
# Cooling rate? [K/s]
-2.0000
# Moving-frame system in z-direction?
# Options: moving_frame no_moving_frame
no_moving_frame
#
# Boundary conditions for phase field in each direction
# Options: i (insulation) s (symmetric) p (periodic/wrap-around) g (gradient) f (fixed)
# Sequence: E W (N S, if 3D) B T borders
ssss
#
# Boundary conditions for concentration field in each direction
# Options: i (insulation) s (symmetric) p (periodic/wrap-around) g (gradient) f (fixed)
# Sequence: E W (N S, if 3D) B T borders
ssss
# Unit-cell model symmetric with respect to the x/y diagonal plane?
# Options: unit_cell_symm no_unit_cell_symm
no_unit_cell_symm
#
#
# Other numerical parameters
# ==========================
# Phase minimum?
5.00E-04
# Interface thickness (in cells)?
5.00
#
#
Thank you very much for your suggestion.
swh

Dear swh,

if you say "the simulation seems stopped", I understand that the calculation gets such slow that you do not get any output anymore, right? Reasons for such behaviour could be:

- the simulation time step width is drastically decreased upon nucleation, e.g. due to a too high interface mobility of one of the new interfaces 0/2 or 1/2. The solution would be to correct the mobility or to use a minimum time step (which also effectively decreases the mobility in critical grid points, cf. here).

- there is a numerical problem with the new interfaces which creates huge simulation times, especially for TQ calculations. Typically, this is accompanied by a lot of error messages on screen...

From the excerpt of the driving file which you posted, I would say the mobility values for both, 0/2 and 1/2 are much too high. Please bear in mind that liquid/alpha-AlMnSi is growing much slower as fcc because it is segregating much more, and that the 1/2 interface depends on solid diffusion and thus is much slower!
You said that you changed the mobility values without success, but the question is in which range! I would estimate reasonable values to be around 1E-6 cm4/s for 0/1 and 1E-10 cm4/s for 1/2. To be sure, you should try even much smaller values and then increase them stepwise to see the effect.

If the interface mobilities are not the reason of the problem, more information is necessary to find out the point. Please check whether you got outputs in the .TabL, .TabP and .TabT files after nucleation of phase 2. If not, increase the output frequency for these "tablog" files such that you get them (at the end of output section of the driving file)! Then, the .TabL will tell you whether the timestep is strongly reduced and the .TabT why. The .TabP can tell you where the calculation time is going: whether it is used for TQ-coupling (in case of numerical instabilities, interface fluctuation or very high relinearisation rate for the new interfaces), for nucleation (if checking is done very often), for the phase-field solver (if the interface size is increased or the time-step is reduced drastically), of for diffusion (if e.g. diffusion in phase 2 were set to be extremely fast).

Please tell me which information you got from the tablog files!

Bernd

Dear Bernd:
I changed the interface mobility 0/2, 1/2 to a small value. After nucleation of alpha_AlMnSi in the interface of fcc_A1(Al solution) and liquid, the calculation can continue, but the problem is that the alpha_AlMnSi phase can not grow, only the fcc_A1(Al solution) is growing, and the fcc_A1(Al solution) can even grow to cover the nucleus of alpha_AlMnSi. I have calculated the equilibrium fraction of alpha_AlMnSi by Thermo-calc using the database as in the Micress TQ coupling, the result shows the mole_fraction of alpha_AlMnSi after nucleation is far from equilibrium fraction.
Thank you very much.
Best wishes.
swh

Dear shw,

In principle, this can be a physically correct effect: Sometimes, eutectic transformations have a divorced characteristic which means that particles of phase 2 are nucleating and growing a little, but then get overgrown by phase 1. Only successive nucleation can lead to the expected phase fraction.

But it is much more probable that phase 2 does not grow for numerical reasons. The simplest explanation is that now the mobility of 0/2 is too small, so that phase 2 cannot grow properly. You can check this in the driving force output (.driv) or just by stepwise increasing again this mobility value. If this is the reason, you should then get a stepwise bigger fraction/size of the precipitate. You should then increase the mobility further until the growth speed is not increasing anymore (if you assume diffusion controlled growth which is not necessarily the case!). This may imply a longer simulation time due to a smaller simulation time step (look here how to improve performance in this case).

A second candidate is curvature. If curvature undercooling is bigger than the driving force for growth, the particle cannot grow. I suppose you are using interface nucleation with stabilization mode. Then, curvature is neglected at the first stage, but continuously increased until the size of one grid cell is reached. Curvature at this stage is critical for successful growth.
When nucleation is checked for the first time, you get an output in the .log file of the minimum undercooling which is necessary to exceed this curvature. This value can be quite high if working with a very fine grid. Please check whether your nucleation undercooling is high enough for growth!

Please tell me whether you solved the problem!

Bernd

Dear Bernd:
I increased the interface mobility of alpha_AlMnSi and liquid phase step by step, but it seems that there is no improvement, the alpha_AlMnSi can nucleate on the interface of fcc_A1(Al solution) and liquid phases ,but it still can not grow(even a little growth is not observed), then the fcc_Al phase grow to cover the alpha_AlMnSi nucleus. I have checked the .driv file, it is strange that there is no driving force around alpha_AlMnSi nucleus. But I have tested another situation that the fcc_A1 is deleted (only liquid phase and alpha_AlMnSi phase are considered), and the alpha_AlMnSi nucleus is set in the liquid phase, then the alpha_AlMnSi can grow in the liquid phase as temperature is down. For the curvature, the undercooling (5K, set in the .dri file) can exceed the minimum undercooling indicated in the .log file.
Thank you very much for your help.
Best wishes
swh

Dear swh,

One effect which I could imagine is that nucleation of alpha_AlMnSi occurs at a too high temperature, where it is still not stable. This could be due to fluctuations of the 0/1 interface with the consequence that a sufficient nucleation undercooling occurs only intermittantly. You should check whether the temperature for stable growth of alpha_AlMnSi is already reached (e.g. by comparison to a Scheil simulation, by checking nucleation in the bulk liquid ("bulk restrictive"), or by forcing nucleation at a lower temperature by an appropriate choice of the temperature interval for nucleation).
If this is not helping, it is necessary to find out what exactly is happening directly after nucleation. Please put very dense outputs after nucleation, so that we get more information about this period before the seed is completely overgrown by the fcc phase. Then it is possible to monitore the exact growth speed (.TabF, .frac2), to see the local linearisation data for all pair-wise interfaces (.TabLin), which also give information about the driving force, and to check which restrictions the new interfaces impose on the time-step or local mobility value (.TabT, .mueS). Please note that, if the minimum allowed time step value is chosen too high, the local mobility value can be reduced to ensure stability. This could have lead to your observation that increasing the mobility has no effect...

Bernd

Dear Bernd:
I have tried some groups of interaction parameters between AlMnSi/(Al) and AlMnSi/Liquid, and currently, the AlMnSi can grow now. There are other two problems: (1) Previously, I set the intermetallics as isotropic. Currently, I try to adjust their shape because the experiment shows needle-like shape (or the length is much bigger than the width). Could you please give some suggestions on how to define the property of the intermetallics and anisotropy parameters with (Al) in the dri file to get the needle-like shape of the intermetallics, (2) The AlMnSi can grow to some extent, but later, the simulation is quite slow (almost stops), the TabL file shows the wallclock time jump from 140s per 0.1s(simulation time) to about 20000s per 0.1(simulation time) ? and I define "Tab_log 0.1" in the dri file, but in the TabL or TabP file, the output step is not 0.1, like 55.7, 55.8, 55.88712 ,55.88712 when the wallclock time jumps to a very high value ?
Thank you very much
Best wishes
swh

Hi swh,

needle-like growth is very complicated in MICRESS, because growth of a needle (plate) means that growth is only possible in exactly one direction (plane). Due to the effect of the numerical grid on the evaluation of the gradient direction, this is difficult to achieve.
In principle, needle growth can be done with the antifaceted model, but you would need a very high resolution to really achieve needles - typically, they can grow easily along the grid direcction, but it is very difficult to have them growing in other directions...
When you specify the output frequency for the TabL, TabP etc., you can define a maximum interval for the wallclock time in minutes as an optional second parameter, e.g.

tab_log 0.001 100

The purpose of this maximum interval is to get always some information from time to time how your job is doing. The default value for the second parameter is 360 min, this is the reasons why you get more outputs than expected if the wallclock time per output exceeds this value...

You should also check the .TabT file - probably the slow simulation is due to a very small time-step, and you could improve performance by e.g. defining a reasonable value for the minimum time step!

Bernd

Dear Bernd:
Could you please tell me which property of the intermetallics you define shown below in your simulation for KS1295, (fig 4b in Trans.IIM, vol.62, Issues 4-5, pp 299-305, 2009), it seems the shape of the intermetallics in my simulation is very similar to the intermetallics in Fig 4b.

# Is phase 1 anisotrop?
# Options: isotropic anisotropic faceted antifaceted

# Crystal symmetry of the phase?
# Options: none xyz_axis cubic hexagonal
#
Thank you for your help.
Best wishes.
swh

Hi swh,

There are many types of intermetallics you can see in figure 5b! I guess you mean the eutectic Si which forms the black/white structures (black is when they are not well-resolved). If I remember right, I assumed them to grow plate-like, and thus defined the phase in the following way (sorry that I have chosen the german language option):

# Daten fuer Phase 14:
# --------------------
# [identical Phasennummer]
# Soll Rekristallisation in Phase 14 beruecksichtigt werden?
# Optionen: recrystall no_recrystall
no_recrystall
# Ist Phase 14 anisotrop?
# Optionen: isotropic anisotropic faceted antifaceted
faceted
# Kristallsymmetrie der Phase?
# Optionen: none xyz_axis cubic hexagonal
none
# Anzahl Facetten Typen anzFacetten der Phase 14
1
# kin. Anisotropieparameter Kappa?
# bislang nur ein Kappa fuer alle Fac./Phasen
# 0 < kappa <= 1
0.8000000
# Anzahl Orientierungen der Facette (int anzOrient) 1
2
# 1 -ter Normalenvektor Facette 1 ? 3*(real)
1.000000
0.000000
0.000000
# 2 -ter Normalenvektor Facette 1 ? 3*(real)
0.000000
0.000000
1.000000
# Sollen Koerner der Phase 14 zu Kategorien zusammengefasst werden?
# Optionen: categorize no_categorize
categorize


Bernd