Dear Bernd:
I try to simulate solidification of some Al alloys containing silicon. There is a problem on the simulation of the eutectic structure of (Al) and silicon, I couldn't get the eutectic silicon lamellae, like Fig 3. in your paper "Trans. IIM vol. 62 (4-5), pp. 299-304, 2009". The silicon phase can grow, but the shape is not like eutectic silicon lamellae. Could you give some suggestion on how to define the property of Si phase in the dri file shown below and the interaction parameters (including anisotropy parameters) between silicon / (Al) and silicon/liquid ? Can I set nuclei of silicon in the liquid bulk phase or must I set them on the interface of (Al) and liquid ?
# Data for phase 1:
# -----------------
# Is phase 1 anisotrop?
# Options: isotropic anisotropic faceted antifaceted
# Crystal symmetry of the phase?
# Options: none xyz_axis cubic hexagonal
#
Thank you
swh
eutectic silicon lamellae
Re: eutectic silicon lamellae
Hi swh,
In the publication you are referring to, the seeds were set on the fcc-liquid interface. Otherwise, you would not get an (irregular) eutectic structure.
For anisotropy, the facet model (look here) is used for the Si-liq and Si-fcc interface. The parameter which are given in this thread for the facet model should be reasonable start values for your trials. In this thread, also the meaning of the parameters is explained.
You should try to use a very small interface thickness (3.5-4 cells or 2.5-3 with fd_correction) in order to get a compact Si phase. With a bigger value, you would need a quite high resolution. Nevertheless, the lamellae perhaps will not always be completely "solid".
Furthermore, I typically use a value of 1E-4 or even higher for the surface energy of the the Si-liq and Si-fcc interface. This makes simulation easier becauses the lamellae are coarser (I do not know any experimental value...)
Good luck!
Bernd
In the publication you are referring to, the seeds were set on the fcc-liquid interface. Otherwise, you would not get an (irregular) eutectic structure.
For anisotropy, the facet model (look here) is used for the Si-liq and Si-fcc interface. The parameter which are given in this thread for the facet model should be reasonable start values for your trials. In this thread, also the meaning of the parameters is explained.
You should try to use a very small interface thickness (3.5-4 cells or 2.5-3 with fd_correction) in order to get a compact Si phase. With a bigger value, you would need a quite high resolution. Nevertheless, the lamellae perhaps will not always be completely "solid".
Furthermore, I typically use a value of 1E-4 or even higher for the surface energy of the the Si-liq and Si-fcc interface. This makes simulation easier becauses the lamellae are coarser (I do not know any experimental value...)
Good luck!
Bernd
Re: eutectic silicon lamellae
Dear Bernd:
As for the simulation of the eutectic structure of (Al) and silicon lamellae in later stage of solidification, I have used the facet model for the silicon phase. In fig1, the nuclei of silicon are put in the interface of (Al) and liquid, but they can't grow, and the simulaiton stops, or the (Al) phases grow to cover the silicon nuclei and the nuclei disappers. I changed the interface mobility of silicon phase and liquid phase to a higher value of 1E-5(cm**4/J/s, or change the interface thickness to smaller 3, there is no improvement.
The simulation is 2D. The input concerning the Si phase is in the following (0 for liquid, 1 for (Al), 4 for silicon):
# Data for phase 4:
# -----------------
# [identical phase number]
# Simulation of recrystallisation in phase 4?
# Options: recrystall no_recrystall
no_recrystall
# Is phase 4 anisotrop?
# Options: isotropic anisotropic faceted antifaceted
faceted
# Crystal symmetry of the phase?
# Options: none xyz_axis cubic hexagonal
none
# Number of type of facets in phase 4
1
# kin. anisotropy parameter Kappa?
# only one value for all facets/phases
# 0 < kappa <= 1
0.5000000
# Number of possible orientations of a facet 1
4
# 1 -th normal vector facet 1 ? 3*
1.000000
1.000000
1.000000
# 2 -th normal vector facet 1 ? 3*
1.000000
1.000000
-1.000000
# 3 -th normal vector facet 1 ? 3*
1.000000
-1.000000
1.000000
# 4 -th normal vector facet 1 ? 3*
-1.000000
1.000000
1.000000
# Should grains of phase 4 be reduced to categories?
# Options: categorize no_categorize
no_categorize
#
# Orientation
# -----------
# How shall grain orientations be defined?
# Options: angle_2d
# euler_zxz
# angle_axis
# miller_indices
angle_2d
#
#
# Input for seed type 4:
# ----------------------
# Type of 'position' of the seeds?
# Options: bulk region interface triple quadruple [restrictive]
interface
# Phase of new grains?
4
# 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 4?
50
# Grain radius [micrometers]?
0.500000
# Choice of growth mode:
# Options: stabilisation analytical_curvature
stabilisation
# min. undercooling [K] (>0)?
30.000
# Determination of nuclei orientations?
# Options: random fix range parent_relation
random
# Shield effect:
# Shield time [s] ?
100.00
# Shield distance [micrometers]?
30.000
# Nucleation range
# min. nucleation temperature for seed type 4 [K]
700.0000
# max. nucleation temperature for seed type 4 [K]
846.0000
# Time between checks for nucleation? [s]
0.50000
# Shall random noise be applied?
# Options: nucleation_noise no_nucleation_noise
nucleation_noise
# Factor for random noise?
# (applied as DeltaT -> (1+Factor*(RAND-1/2))*DeltaT)
1.000E-02
#
# Seed for random-number generator initialisation
# -----------------------------------------------
10
#
# 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
#
#
# Data for phase interaction 0 / 4:
# ---------------------------------
# Simulation of interaction between phase 0 and 4?
# 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 4?
# Options: constant temp_dependent
constant
# Surface energy between phases LIQUID and 4? [J/cm**2]
3.0E-05
# Type of mobility definition between phases LIQUID and 4?
# Options: constant temp_dependent dg_dependent
constant
# Kinetic coefficient mu between phases LIQUID and 4? [cm**4/(Js)]
1.00000E-06
# Is interaction isotropic?
# Options: isotropic anisotropic
anisotropic
# static anisotropy coefficient of facet 1 (< 1. <0.1>)
0.10000
# kinetic anisotropy coefficient of facet 1 (< 1. <0.1>)
0.10000
#
# Data for phase interaction 1 / 4:
# ---------------------------------
# Simulation of interaction between phase 1 and 4?
# 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 4?
# Options: constant temp_dependent
constant
# Surface energy between phases 1 and 4? [J/cm**2]
1.00000E-03
# Type of mobility definition between phases 1 and 4?
# Options: constant temp_dependent dg_dependent
constant
# Kinetic coefficient mu between phases 1 and 4? [cm**4/(Js)]
1.00000E-08
# Shall misorientation be considered?
# Optionen: misorientation no_misorientation
no_misorientation
# Is interaction isotropic?
# Options: isotropic anisotropic
anisotropic
# This anisotropic interaction is not yet implemented.
# Instead: isotropic-faceted
# static anisotropy coefficient of facet 1 (< 1. <0.1>)
0.10000
# kinetic anisotropy coefficient of facet 1 (< 1. <0.1>)
0.10000
#
# Other numerical parameters
# ==========================
# Phase minimum?
5.00E-04
# Interface thickness (in cells)?
4.00
#
Could you please check my input and give some suggestions?
Thanks
Sun
As for the simulation of the eutectic structure of (Al) and silicon lamellae in later stage of solidification, I have used the facet model for the silicon phase. In fig1, the nuclei of silicon are put in the interface of (Al) and liquid, but they can't grow, and the simulaiton stops, or the (Al) phases grow to cover the silicon nuclei and the nuclei disappers. I changed the interface mobility of silicon phase and liquid phase to a higher value of 1E-5(cm**4/J/s, or change the interface thickness to smaller 3, there is no improvement.
- fig1
- fig1.JPG (59.39 KiB) Viewed 4657 times
# Data for phase 4:
# -----------------
# [identical phase number]
# Simulation of recrystallisation in phase 4?
# Options: recrystall no_recrystall
no_recrystall
# Is phase 4 anisotrop?
# Options: isotropic anisotropic faceted antifaceted
faceted
# Crystal symmetry of the phase?
# Options: none xyz_axis cubic hexagonal
none
# Number of type of facets in phase 4
1
# kin. anisotropy parameter Kappa?
# only one value for all facets/phases
# 0 < kappa <= 1
0.5000000
# Number of possible orientations of a facet 1
4
# 1 -th normal vector facet 1 ? 3*
1.000000
1.000000
1.000000
# 2 -th normal vector facet 1 ? 3*
1.000000
1.000000
-1.000000
# 3 -th normal vector facet 1 ? 3*
1.000000
-1.000000
1.000000
# 4 -th normal vector facet 1 ? 3*
-1.000000
1.000000
1.000000
# Should grains of phase 4 be reduced to categories?
# Options: categorize no_categorize
no_categorize
#
# Orientation
# -----------
# How shall grain orientations be defined?
# Options: angle_2d
# euler_zxz
# angle_axis
# miller_indices
angle_2d
#
#
# Input for seed type 4:
# ----------------------
# Type of 'position' of the seeds?
# Options: bulk region interface triple quadruple [restrictive]
interface
# Phase of new grains?
4
# 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 4?
50
# Grain radius [micrometers]?
0.500000
# Choice of growth mode:
# Options: stabilisation analytical_curvature
stabilisation
# min. undercooling [K] (>0)?
30.000
# Determination of nuclei orientations?
# Options: random fix range parent_relation
random
# Shield effect:
# Shield time [s] ?
100.00
# Shield distance [micrometers]?
30.000
# Nucleation range
# min. nucleation temperature for seed type 4 [K]
700.0000
# max. nucleation temperature for seed type 4 [K]
846.0000
# Time between checks for nucleation? [s]
0.50000
# Shall random noise be applied?
# Options: nucleation_noise no_nucleation_noise
nucleation_noise
# Factor for random noise?
# (applied as DeltaT -> (1+Factor*(RAND-1/2))*DeltaT)
1.000E-02
#
# Seed for random-number generator initialisation
# -----------------------------------------------
10
#
# 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
#
#
# Data for phase interaction 0 / 4:
# ---------------------------------
# Simulation of interaction between phase 0 and 4?
# 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 4?
# Options: constant temp_dependent
constant
# Surface energy between phases LIQUID and 4? [J/cm**2]
3.0E-05
# Type of mobility definition between phases LIQUID and 4?
# Options: constant temp_dependent dg_dependent
constant
# Kinetic coefficient mu between phases LIQUID and 4? [cm**4/(Js)]
1.00000E-06
# Is interaction isotropic?
# Options: isotropic anisotropic
anisotropic
# static anisotropy coefficient of facet 1 (< 1. <0.1>)
0.10000
# kinetic anisotropy coefficient of facet 1 (< 1. <0.1>)
0.10000
#
# Data for phase interaction 1 / 4:
# ---------------------------------
# Simulation of interaction between phase 1 and 4?
# 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 4?
# Options: constant temp_dependent
constant
# Surface energy between phases 1 and 4? [J/cm**2]
1.00000E-03
# Type of mobility definition between phases 1 and 4?
# Options: constant temp_dependent dg_dependent
constant
# Kinetic coefficient mu between phases 1 and 4? [cm**4/(Js)]
1.00000E-08
# Shall misorientation be considered?
# Optionen: misorientation no_misorientation
no_misorientation
# Is interaction isotropic?
# Options: isotropic anisotropic
anisotropic
# This anisotropic interaction is not yet implemented.
# Instead: isotropic-faceted
# static anisotropy coefficient of facet 1 (< 1. <0.1>)
0.10000
# kinetic anisotropy coefficient of facet 1 (< 1. <0.1>)
0.10000
#
# Other numerical parameters
# ==========================
# Phase minimum?
5.00E-04
# Interface thickness (in cells)?
4.00
#
Could you please check my input and give some suggestions?
Thanks
Sun
Re: eutectic silicon lamellae
Dear shw,
unfortunately, I cannot directly see what could be the problem in this case. But I have some comments on your input data:
1.) You nucleate silicon with a radius of 0.5µm - but you should always start with a "small" grain! This is important because a "big" grain would be set with the "background" composition which is extremely wrong for pure Si. You automatically get "small" grains as nuclei if their initial radius is set to a value which is smaller than the grid resolution deltaX. I don´t know this value in your actual simulation but - to be sure - you should set the inital grain radius always to 0.
2.) There is large difference between the interfacial energies of the 0/4 and 1/4 interface! If one of the two values is too big and the grid size too small, then it could be that the seeds cannot overcome the size and curvature of one grid cell when the stabilisation of the seed ends. I would set the interface energy of 1/4 to the same value as 0/4!
3.) The mobility of 1/4 should be several orders of magnitude smaller than that of 0/4. I would make a try with 0 first, just to reduce complexity and to see whether it comes from that...
Apart from that, there are cases where divorced eutectic growth is observed (if the composition is outside the coupled-eutectic area). If this is the case, overgrowth of the seeds by the primary phase would be physical!
Do you observe any growth of the seeds, or are they just frozen from the beginning?
Please tell me whether my suggestions were successful!
Bernd
unfortunately, I cannot directly see what could be the problem in this case. But I have some comments on your input data:
1.) You nucleate silicon with a radius of 0.5µm - but you should always start with a "small" grain! This is important because a "big" grain would be set with the "background" composition which is extremely wrong for pure Si. You automatically get "small" grains as nuclei if their initial radius is set to a value which is smaller than the grid resolution deltaX. I don´t know this value in your actual simulation but - to be sure - you should set the inital grain radius always to 0.
2.) There is large difference between the interfacial energies of the 0/4 and 1/4 interface! If one of the two values is too big and the grid size too small, then it could be that the seeds cannot overcome the size and curvature of one grid cell when the stabilisation of the seed ends. I would set the interface energy of 1/4 to the same value as 0/4!
3.) The mobility of 1/4 should be several orders of magnitude smaller than that of 0/4. I would make a try with 0 first, just to reduce complexity and to see whether it comes from that...
Apart from that, there are cases where divorced eutectic growth is observed (if the composition is outside the coupled-eutectic area). If this is the case, overgrowth of the seeds by the primary phase would be physical!
Do you observe any growth of the seeds, or are they just frozen from the beginning?
Please tell me whether my suggestions were successful!
Bernd
Re: eutectic silicon lamellae
Hi, Bernd:
I have tried your suggestions. There is progress. The concentration of Si shows a little bit of growth as well as the phase field. But there are two problems: (1) It seems the phase field can not be solved properly. The Si phase looks like "interface" as indicated by the phase field. In addition, the Si phase is like a needle "without width", can it be a little wider? (2) The minimum and maximum concentration of Si become negative or above 100. I have checked the .log file ,it shows:
Error number 3 in Interface 7 61
time: 26.588628000000000 s
ERROR RETURN FROM solveCNewton BECAUSE THERE HAVE BEEN
Error number 3 in Interface 7 61
time: 26.609382000000000 s
ERROR RETURN FROM solveCNewton BECAUSE THERE HAVE BEEN
61 is a number of Si nuclei, 7 is fcc(Al) grain
Could you give some suggestions?
Thank you very much.
Sun
I have tried your suggestions. There is progress. The concentration of Si shows a little bit of growth as well as the phase field. But there are two problems: (1) It seems the phase field can not be solved properly. The Si phase looks like "interface" as indicated by the phase field. In addition, the Si phase is like a needle "without width", can it be a little wider? (2) The minimum and maximum concentration of Si become negative or above 100. I have checked the .log file ,it shows:
Error number 3 in Interface 7 61
time: 26.588628000000000 s
ERROR RETURN FROM solveCNewton BECAUSE THERE HAVE BEEN
Error number 3 in Interface 7 61
time: 26.609382000000000 s
ERROR RETURN FROM solveCNewton BECAUSE THERE HAVE BEEN
61 is a number of Si nuclei, 7 is fcc(Al) grain
Could you give some suggestions?
Thank you very much.
Sun
Re: eutectic silicon lamellae
Hi
it seems strange that you have problems with the 1/4 interface - can you please show the complete driving file?
Bernd
it seems strange that you have problems with the 1/4 interface - can you please show the complete driving file?
Bernd
Re: eutectic silicon lamellae
Dear swh2011,
Thanks for sending me the input file! Unfortunately I am in Montreal and will not be back at work before Nov 12. But after looking at the driving file I have a few comments:
- You are using a fixed time step for the simulation. This is dangerous because adding a new phase interaction or changing a mobility value can make the simulation instable! There will be no warning! If you use automatic time stepping instead and define a minimum value for the time steps, then any such instabilities will be removed by local reduction of the corresponding mobility value.
- The mobility value of 0.01 which you have chosen for the liquid-silicon interface appears to be too high!
- I would suggest to increase the interfacial energy of the liquid-silicon and liquid-fcc interfaces to at least 1E-4 J/cm2! This could improve the resolution of the Si lamellae. I do not know where you have the values from which you are using, and whether they are for the facets or for the edges...
- To be on the safe side, you should define also the silicon phase as completely stoichiometric (like you did for the intermetallics). MICRESS is able to automatically recognize stoichiometric elements if they have no solubility range at all, but the output comments in your input file (if they are actualized in your current driving file) indicate that element 4 (Si) was not recognized as not having any solubility range... This could cause a lot of trouble!
- Generally, it is quite difficult to correctly resolve the Si eutectics, if not a very high resolution is used. You could gain a little bit if you reduce the interface thickness from 4 to 3.5 cells and/or if you increase the interfacial energy!
- Apparently you are still using MICRESS version 5.501 - it would be much better if you could switch to a more recent version!
Best wishes and good luck!
Bernd
Thanks for sending me the input file! Unfortunately I am in Montreal and will not be back at work before Nov 12. But after looking at the driving file I have a few comments:
- You are using a fixed time step for the simulation. This is dangerous because adding a new phase interaction or changing a mobility value can make the simulation instable! There will be no warning! If you use automatic time stepping instead and define a minimum value for the time steps, then any such instabilities will be removed by local reduction of the corresponding mobility value.
- The mobility value of 0.01 which you have chosen for the liquid-silicon interface appears to be too high!
- I would suggest to increase the interfacial energy of the liquid-silicon and liquid-fcc interfaces to at least 1E-4 J/cm2! This could improve the resolution of the Si lamellae. I do not know where you have the values from which you are using, and whether they are for the facets or for the edges...
- To be on the safe side, you should define also the silicon phase as completely stoichiometric (like you did for the intermetallics). MICRESS is able to automatically recognize stoichiometric elements if they have no solubility range at all, but the output comments in your input file (if they are actualized in your current driving file) indicate that element 4 (Si) was not recognized as not having any solubility range... This could cause a lot of trouble!
- Generally, it is quite difficult to correctly resolve the Si eutectics, if not a very high resolution is used. You could gain a little bit if you reduce the interface thickness from 4 to 3.5 cells and/or if you increase the interfacial energy!
- Apparently you are still using MICRESS version 5.501 - it would be much better if you could switch to a more recent version!
Best wishes and good luck!
Bernd