Dear Bernd,
I am doing the eutectic solidification simulation of Mg-32Al alloy now. I want to get the lamellar microstructure of the α-Mg and β-M17Al12 directly nucleation and growth form the liquid. Could you please tell me how can I set the input file for this simulation? How Can I get the phases α-Mg and β-M17Al12 grow simultaneous with a lamellar microstructure?
Thank you very much!
Yi Chen
eutectic solidification simulation in Mg-32Al alloy
Re: eutectic solidification simulation in Mg-32Al alloy
Dear Yichen,
Thank you very much for discussing this question in the MICRESS forum! So, other users can also profit from our discussion and learn about simulation of eutectic systems.
As I understand, you want to start with a binary Mg-Al system which forms an invariant two-phase eutectic consisting of α-Mg and β-M17Al12. During steady state growth in a temperature gradient, such a system can either form lamellar or rod-like structures. The latter typically appear when the amounts (volumes) of the two phases are very different. In our case, we rather expect lamellar structures.
Lamellar eutectics can be simulated in 2D without problems. The only fundamental restriction of simulating in 2D is that splitting of lamellae which can happen of course in 3D, is not possible without a nucleation event in 2D. Therefore, if stationary lamellar spacing is to be simulated, one should start either with a too small spacing (selection of spacing by vanishing of lamellae) or allow nucleation of both phases at the solid-liquid interfaces. 3D simulations would remove this restriction, but at the cost of huge simulation times. Thus, 2D simulation is a good choice here.
The simplest approach would be to start with already existing lamellae in a temperature gradient. To set up a simulation of this type do the following:
- use an already existing input file with similar characteristics (directional solidification, binary system, e.g. AlCu_dri.txt from the Examples folder). Then, you just need to change the driving file according to the specific needs.
- define a rectangular simulation domain with e.g. 100x200 grid cells in x and z direction. The grid resolution should be chosen such that at least 10-20 grid cells correspond to the expected lamellar spacing. It is always wise to start with a rather small domain size. The size can be increased afterwards when the numerical parameters are properly set and the simulation is running correctly. Resolution should be increased if it turns out not to be sufficient for the given conditions.
- set the initial temperature at the bottom slightly below the eutectic temperature, and apply a constant cooling rate.
- use periodic boundary conditions in east/west direction, isolation at the bottom. At the top, a fixed boundary condition (at nominal alloy composition) should be used for the concentration field which assures that the far-field liquid composition cannot change. If long diffusion fields ahead of the eutectic front are expected (in case of an off-eutectic initial composition or in ternary systems), a one-dimensional extension of the domain at the top can be used (1d_far_field option). In this case, the top boundary condition is automatically shifted to the top of this extension. For phase-field, isolation can be used at the top (the solid phases anyway will not touch the top boundary...).
- define two solid phases. Specify the thermodynamic data either by using coupling to a thermodynamic database or by defining a linear phase diagram around the eutictic point.
- create an initial lamellar structure by defining initial grains of alternating phases at the bottom of the domain which overlap. It is most convenient to use a quadratic shape for these grains. The initial spacing should be smaller than the expected stationary spacing, otherwise oscillating structures will be obtained.
- use the moving frame option in order to track the solidification front. As tracking criterion use distance. The tracking distance should be at least 2-3 lamellar spacings.
- start the simulation and wait until stationary growth is obtained.
An alternative approach is the use of nucleation for creating new lamellae. This is important when the simlation is not started at the eutectic point of when the temperature boundary conditions (temperature gradient, cooling rate) are changing during the simulation. As managing nucleation in MICRESS is a bit more complex, this should not be the first try.
Please tell me if you encounter any problems with this suggested approach or if you plan to to something different to what I proposed!
Bernd
Thank you very much for discussing this question in the MICRESS forum! So, other users can also profit from our discussion and learn about simulation of eutectic systems.
As I understand, you want to start with a binary Mg-Al system which forms an invariant two-phase eutectic consisting of α-Mg and β-M17Al12. During steady state growth in a temperature gradient, such a system can either form lamellar or rod-like structures. The latter typically appear when the amounts (volumes) of the two phases are very different. In our case, we rather expect lamellar structures.
Lamellar eutectics can be simulated in 2D without problems. The only fundamental restriction of simulating in 2D is that splitting of lamellae which can happen of course in 3D, is not possible without a nucleation event in 2D. Therefore, if stationary lamellar spacing is to be simulated, one should start either with a too small spacing (selection of spacing by vanishing of lamellae) or allow nucleation of both phases at the solid-liquid interfaces. 3D simulations would remove this restriction, but at the cost of huge simulation times. Thus, 2D simulation is a good choice here.
The simplest approach would be to start with already existing lamellae in a temperature gradient. To set up a simulation of this type do the following:
- use an already existing input file with similar characteristics (directional solidification, binary system, e.g. AlCu_dri.txt from the Examples folder). Then, you just need to change the driving file according to the specific needs.
- define a rectangular simulation domain with e.g. 100x200 grid cells in x and z direction. The grid resolution should be chosen such that at least 10-20 grid cells correspond to the expected lamellar spacing. It is always wise to start with a rather small domain size. The size can be increased afterwards when the numerical parameters are properly set and the simulation is running correctly. Resolution should be increased if it turns out not to be sufficient for the given conditions.
- set the initial temperature at the bottom slightly below the eutectic temperature, and apply a constant cooling rate.
- use periodic boundary conditions in east/west direction, isolation at the bottom. At the top, a fixed boundary condition (at nominal alloy composition) should be used for the concentration field which assures that the far-field liquid composition cannot change. If long diffusion fields ahead of the eutectic front are expected (in case of an off-eutectic initial composition or in ternary systems), a one-dimensional extension of the domain at the top can be used (1d_far_field option). In this case, the top boundary condition is automatically shifted to the top of this extension. For phase-field, isolation can be used at the top (the solid phases anyway will not touch the top boundary...).
- define two solid phases. Specify the thermodynamic data either by using coupling to a thermodynamic database or by defining a linear phase diagram around the eutictic point.
- create an initial lamellar structure by defining initial grains of alternating phases at the bottom of the domain which overlap. It is most convenient to use a quadratic shape for these grains. The initial spacing should be smaller than the expected stationary spacing, otherwise oscillating structures will be obtained.
- use the moving frame option in order to track the solidification front. As tracking criterion use distance. The tracking distance should be at least 2-3 lamellar spacings.
- start the simulation and wait until stationary growth is obtained.
An alternative approach is the use of nucleation for creating new lamellae. This is important when the simlation is not started at the eutectic point of when the temperature boundary conditions (temperature gradient, cooling rate) are changing during the simulation. As managing nucleation in MICRESS is a bit more complex, this should not be the first try.
Please tell me if you encounter any problems with this suggested approach or if you plan to to something different to what I proposed!
Bernd
Re: eutectic solidification simulation in Mg-32Al alloy
Dear Bernd,
Thank you for your detailed reply. I am silmulate the eutectic solidification of Mg-32Al following your advises these days. However, I can not get the lamellar microstructure of the α-Mg and β-M17Al12. Only β-M17Al12 can be nucleated and growth along the Z direction, while the growth of α-Mg had been inhibited. Could you please give some suggestion about adjusting the parameters in the input file? Which parameters are important in the determination of eutectic growth?
Thank you very much!
Best regards!
Thank you for your detailed reply. I am silmulate the eutectic solidification of Mg-32Al following your advises these days. However, I can not get the lamellar microstructure of the α-Mg and β-M17Al12. Only β-M17Al12 can be nucleated and growth along the Z direction, while the growth of α-Mg had been inhibited. Could you please give some suggestion about adjusting the parameters in the input file? Which parameters are important in the determination of eutectic growth?
Thank you very much!
Best regards!
Re: eutectic solidification simulation in Mg-32Al alloy
Hi Yichen,
you say that a-Mg cannot "nucleate" and that its growth is "inhibited". These are two different things!
If a-Mg does not nucleate, it can e.g. be due to the following errors:
- Errors in checking for nucleation. Use "nucleation verbose" to be informed when and where nucleation is checked
- Nucleation is checked, but at the wrong place. You should check for nucleation at the Mg-32Al/liquid interface
- Nucleation is checked correctly, but there is no driving force/undercooling for nucleation: Perhaps the initial temperature is wrong. It should be slighly below the eutectic temperature as defined by the database/linearized phase diagran description used.
At the beginning, it would be more easy to already set a sufficiently large initial grain of a-Mg in order to check whether it is growing or not. If the phase is nucleated or set at the beginning, but growth is not possible, it could be due to the following:
- The phase melts away because the temperature is too high or because the inital composition is outside the eutectic composition range
- The composition of the melt is inside the eutectic range, but the corresponding eutectic phase fraction of a-Mg is so small that it is overgrown immediately (divorced eutectic mode). Check whether you perhaps confused at% and wt%...
- Numerical parameters for the interface a-Mg/liquid or a-Mg/Mg-32Al are bad. If e.g. the interface mobility of a-Mg/liquid is too high, fluctuations may remove the seed, if too low, it gets overgrown rapidly.
If you can tell us more exactly how it is going wrong, I could give you more specific advice!
Bernd
you say that a-Mg cannot "nucleate" and that its growth is "inhibited". These are two different things!
If a-Mg does not nucleate, it can e.g. be due to the following errors:
- Errors in checking for nucleation. Use "nucleation verbose" to be informed when and where nucleation is checked
- Nucleation is checked, but at the wrong place. You should check for nucleation at the Mg-32Al/liquid interface
- Nucleation is checked correctly, but there is no driving force/undercooling for nucleation: Perhaps the initial temperature is wrong. It should be slighly below the eutectic temperature as defined by the database/linearized phase diagran description used.
At the beginning, it would be more easy to already set a sufficiently large initial grain of a-Mg in order to check whether it is growing or not. If the phase is nucleated or set at the beginning, but growth is not possible, it could be due to the following:
- The phase melts away because the temperature is too high or because the inital composition is outside the eutectic composition range
- The composition of the melt is inside the eutectic range, but the corresponding eutectic phase fraction of a-Mg is so small that it is overgrown immediately (divorced eutectic mode). Check whether you perhaps confused at% and wt%...
- Numerical parameters for the interface a-Mg/liquid or a-Mg/Mg-32Al are bad. If e.g. the interface mobility of a-Mg/liquid is too high, fluctuations may remove the seed, if too low, it gets overgrown rapidly.
If you can tell us more exactly how it is going wrong, I could give you more specific advice!
Bernd
Re: eutectic solidification simulation in Mg-32Al alloy
Dear Bernd,
I have checked the simulation process. I fould the temperature go down first and then go up, such as follows:
# Simulation Temperature Fraction Fraction Fraction
# time [s] [K] Liquid Phase 1 Phase 2
0.00000 700.00000 0.98348977 0.00832788 0.00818235
0.100000 699.00000 0.74635356 0.07147908 0.18216736
0.200000 698.00000 0.49628438 0.14072012 0.36299550
0.300000 697.44000 0.32897179 0.21148014 0.45954806
0.400000 700.46000 0.50476741 0.49523259 0.00000000
0.500000 702.18000 0.40843265 0.59156735 0.00000000
0.600000 703.90000 0.39599989 0.60400011 0.00000000
0.700000 705.58000 0.39442058 0.60557942 0.00000000
0.800000 707.24000 0.39423993 0.60576007 0.00000000
The Boundary conditions I set are as follows:
# 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]
700.0000
# Temperature gradient in z-direction? [K/cm]
200.00
# Cooling rate? [K/s]
-10.000
# Moving-frame system in z-direction?
# Options: moving_frame no_moving_frame
moving_frame
# Should the distance or the bottom temperature be
# used as criterion for moving frame?
# Options: distance [matrix phase (negative: special phase)] temperature
distance
# At which distance from the upper boundary should the frame
# be moved? (real) [micrometers]
60.00000
#
# Store data shifted out of moving-frame system?
# Options: out_moving_frame no_out_moving_frame
out_moving_frame
#
# Boundary conditions for phase field in each direction
# Options: i (insulation) s (symmetric) p (periodic/wrap-around)
# g (gradient) f (fixed) w (wetting)
# Sequence: W E (S N, if 3D) B T borders
ppii
#
# Boundary conditions for concentration field in each direction
# Options: i (insulation) s (symmetric) p (periodic/wrap-around) g (gradient) f (fixed)
# Sequence: W E (S N, if 3D) B T borders
ppif
# Fixed value for concentration field for component 1 in T-direction
3.0000
# Unit-cell model symmetric with respect to the x/y diagonal plane?
# Options: unit_cell_symm no_unit_cell_symm
no_unit_cell_symm
#
Could you please tell me how to solve this problem?
Thank you very much!
I have checked the simulation process. I fould the temperature go down first and then go up, such as follows:
# Simulation Temperature Fraction Fraction Fraction
# time [s] [K] Liquid Phase 1 Phase 2
0.00000 700.00000 0.98348977 0.00832788 0.00818235
0.100000 699.00000 0.74635356 0.07147908 0.18216736
0.200000 698.00000 0.49628438 0.14072012 0.36299550
0.300000 697.44000 0.32897179 0.21148014 0.45954806
0.400000 700.46000 0.50476741 0.49523259 0.00000000
0.500000 702.18000 0.40843265 0.59156735 0.00000000
0.600000 703.90000 0.39599989 0.60400011 0.00000000
0.700000 705.58000 0.39442058 0.60557942 0.00000000
0.800000 707.24000 0.39423993 0.60576007 0.00000000
The Boundary conditions I set are as follows:
# 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]
700.0000
# Temperature gradient in z-direction? [K/cm]
200.00
# Cooling rate? [K/s]
-10.000
# Moving-frame system in z-direction?
# Options: moving_frame no_moving_frame
moving_frame
# Should the distance or the bottom temperature be
# used as criterion for moving frame?
# Options: distance [matrix phase (negative: special phase)] temperature
distance
# At which distance from the upper boundary should the frame
# be moved? (real) [micrometers]
60.00000
#
# Store data shifted out of moving-frame system?
# Options: out_moving_frame no_out_moving_frame
out_moving_frame
#
# Boundary conditions for phase field in each direction
# Options: i (insulation) s (symmetric) p (periodic/wrap-around)
# g (gradient) f (fixed) w (wetting)
# Sequence: W E (S N, if 3D) B T borders
ppii
#
# Boundary conditions for concentration field in each direction
# Options: i (insulation) s (symmetric) p (periodic/wrap-around) g (gradient) f (fixed)
# Sequence: W E (S N, if 3D) B T borders
ppif
# Fixed value for concentration field for component 1 in T-direction
3.0000
# Unit-cell model symmetric with respect to the x/y diagonal plane?
# Options: unit_cell_symm no_unit_cell_symm
no_unit_cell_symm
#
Could you please tell me how to solve this problem?
Thank you very much!
Re: eutectic solidification simulation in Mg-32Al alloy
Hi yichen,
I interpret your information in the following way:
Simulation starts with two solid phases, and up to 0.3 s both of them are growing simultaneously, like expected for eutectic growth. Then, suddenly, phase 1 is shooting ahead, leading to overgrowth (or moving out) of phase 2 and a strong increase of the bottom temperature (as a consequence of moving frame action).
So, from the given information, it seems to be probably a problem of the boundary conditions.
My first guess: Are you sure that the fixed condition for concentration at the top boundary is correct? 3% seems to me not like eutectic...
This would easily explain the behaviour: The fixed concentration condition should (in almost all cases) correspond to the far-field composition, i.e. the nominal melt composition!
Could that be the problem?
Bernd
I interpret your information in the following way:
Simulation starts with two solid phases, and up to 0.3 s both of them are growing simultaneously, like expected for eutectic growth. Then, suddenly, phase 1 is shooting ahead, leading to overgrowth (or moving out) of phase 2 and a strong increase of the bottom temperature (as a consequence of moving frame action).
So, from the given information, it seems to be probably a problem of the boundary conditions.
My first guess: Are you sure that the fixed condition for concentration at the top boundary is correct? 3% seems to me not like eutectic...
This would easily explain the behaviour: The fixed concentration condition should (in almost all cases) correspond to the far-field composition, i.e. the nominal melt composition!
Could that be the problem?
Bernd
Re: eutectic solidification simulation in Mg-32Al alloy
Dear Bernd,
Thank you for your reply. I changed the fixed concentration condition to the eutcetic concentration which is 32%. However, the condition now changed as follows:
0.00000 700.00000 0.98348977 0.00832788 0.00818235
0.100000 699.00000 0.74636884 0.07160806 0.18202310
0.200000 698.00000 0.49290164 0.14170947 0.36538889
0.300000 697.32000 0.32403831 0.18621457 0.48974712
0.400000 697.36000 0.32572496 0.18608359 0.48819145
0.500000 697.40000 0.33018954 0.18492869 0.48488177
0.600000 697.44000 0.33101649 0.18461931 0.48436420
0.700000 697.46000 0.33004691 0.18505904 0.48489404
0.800000 697.48000 0.32905613 0.18527651 0.48566736
0.900000 697.52000 0.33621212 0.18330655 0.48048133
1.00000 697.52000 0.33009432 0.18491200 0.48499368
The temperature seems changeless. Is these still the problem of the boundary conditions?
Thank you for your reply. I changed the fixed concentration condition to the eutcetic concentration which is 32%. However, the condition now changed as follows:
0.00000 700.00000 0.98348977 0.00832788 0.00818235
0.100000 699.00000 0.74636884 0.07160806 0.18202310
0.200000 698.00000 0.49290164 0.14170947 0.36538889
0.300000 697.32000 0.32403831 0.18621457 0.48974712
0.400000 697.36000 0.32572496 0.18608359 0.48819145
0.500000 697.40000 0.33018954 0.18492869 0.48488177
0.600000 697.44000 0.33101649 0.18461931 0.48436420
0.700000 697.46000 0.33004691 0.18505904 0.48489404
0.800000 697.48000 0.32905613 0.18527651 0.48566736
0.900000 697.52000 0.33621212 0.18330655 0.48048133
1.00000 697.52000 0.33009432 0.18491200 0.48499368
The temperature seems changeless. Is these still the problem of the boundary conditions?
Re: eutectic solidification simulation in Mg-32Al alloy
Dear yichen,
this appears to be perfect! The temperature reaches a stationary value because the moving frame is working at constant velocity!
How does the microstructure look like? Do you get nice lamellae?
Bernd
this appears to be perfect! The temperature reaches a stationary value because the moving frame is working at constant velocity!
How does the microstructure look like? Do you get nice lamellae?
Bernd
Re: eutectic solidification simulation in Mg-32Al alloy
Dear Bernd,
Also the microstructure get from the .korn file seems like the lamellae. However, when I check the .phas file, it seems that the α-Mg and β-M17Al12 phase do not grow as a lamellae structure.
Also the microstructure get from the .korn file seems like the lamellae. However, when I check the .phas file, it seems that the α-Mg and β-M17Al12 phase do not grow as a lamellae structure.
Re: eutectic solidification simulation in Mg-32Al alloy
Hi yichen,
this is a typical example of spreading interfaces: Interfaces may get instable and get much broader than the numerical interface thickness, if:
- the resolution is so low that the concentration fields are poorly resolved
- the interface mobility is very high
- the interface energy is very low
- averaging of the driving force is not used
- the temperature is far below the eutectic temperature, so that extremely fine lamellae would form in the initial transient
- the numerical interface thickness is higher than necessary
Thus, it is all about setting up suitable numerical conditions. For this it is important to look at the .driv output (see here).
But first of all, you should make sure that the lenth scale of your simulation setup corresponds to that at which you expect the microstructure to form!
Bernd
this is a typical example of spreading interfaces: Interfaces may get instable and get much broader than the numerical interface thickness, if:
- the resolution is so low that the concentration fields are poorly resolved
- the interface mobility is very high
- the interface energy is very low
- averaging of the driving force is not used
- the temperature is far below the eutectic temperature, so that extremely fine lamellae would form in the initial transient
- the numerical interface thickness is higher than necessary
Thus, it is all about setting up suitable numerical conditions. For this it is important to look at the .driv output (see here).
But first of all, you should make sure that the lenth scale of your simulation setup corresponds to that at which you expect the microstructure to form!
Bernd