Dear Dr. Bernd,
Thank you again for your earlier guidance on MICRESS modeling. Building on our previous discussion, I would like to humbly seek your professional opinion on whether the current version of MICRESS could help address the specific challenges in our Cu-Cr-Ti alloy research.
We observed 108° and 54° dislocation bending angles when dislocations interact with spherical vs. cuboidal precipitates，with the morphological differences stemming from the competitive relationship between the interfacial energy and elastic strain energy between precipitates and the copper matrix.
Our research objectives are:
1.Use computational methods (e.g., phase field) to clarify the atomic-scale mechanisms behind the specific bending angles observed in TEM.
2. Investigate the relationship between precipitate morphology, dislocation behavior, and mechanical properties.
We greatly value your expertise and would appreciate your thoughts on whether MICRESS is suitable for this study. Thank you for your time and guidance.
Best regards,
yimi_rui
Follow-up Inquiry on MICRESS Capabilities for Dislocation-Precipitate Studies
Re: Follow-up Inquiry on MICRESS Capabilities for Dislocation-Precipitate Studies
Dear yimi_rui,
The phase-field method is a mean-field approach and as such not useful for studying mechanisms at the atomistic level. Thus, it will certainly not be possible to clarify specific bending angles of dislocations at the phase boundary. However, sometimes, atomistic problems can be reformulated within a mean-field approach. So I cannot fully exclude that there might be some useful approach with MICRESS with respect to the bending angles.
What MICRESS definitively can provide is to reveal the transition of the particle morphology between cubic and spherical. As you said, this is due to the interaction of surface energy and elastic strain energy, an effect which is well included in the current MICRESS Version 7.3 model with elastic stress coupling. The main challenges here are that knowledge of the eigenstrains, of the elastic constants of the individual phases, and of the interface energy, which are required input parameters.
Regarding the effects of dislocations, the capabilities of MICRESS 7.3 are limited. As I explained, there is a still experimental version of a plasticity model which considers the formation of dislocations as function of the average stresses in the matrix by a simple law, and describes the formation of interface dislocation networks in terms of a change of eigenstrains. This simple approach has proven to be quite efficient in describing plasticity effects during γ'-rafting in Ni-based superalloys (within an industry project, unpublished). The effects of interface dislocation networks - in the frame of this simple model - on morphology is automatically included. Other effects, like the formation of thermal dislocations, which during long heat treatments would slowly transform the cubical precipitates to spherical ones, could be easily included, if a corresponding mean-field model is formulated. We as MICRESS developers are no experts in dislocation science, and would appreciate proposals and help from experts with formulating such models in future.
When it comes to mechanical properties, it is important to note that those cannot be directly obtained by phase-field methods. Phase-field primarily provides morphological information, which must be handed over to other methods which make the link to mechanical properties. These can be empirical laws (like Orowan equation), or e.g. homogenization models like our HOMAT package, which can calculate average properties using the properties of the pure phase and their distribution (=microstructure).
Best wishes
Bernd
The phase-field method is a mean-field approach and as such not useful for studying mechanisms at the atomistic level. Thus, it will certainly not be possible to clarify specific bending angles of dislocations at the phase boundary. However, sometimes, atomistic problems can be reformulated within a mean-field approach. So I cannot fully exclude that there might be some useful approach with MICRESS with respect to the bending angles.
What MICRESS definitively can provide is to reveal the transition of the particle morphology between cubic and spherical. As you said, this is due to the interaction of surface energy and elastic strain energy, an effect which is well included in the current MICRESS Version 7.3 model with elastic stress coupling. The main challenges here are that knowledge of the eigenstrains, of the elastic constants of the individual phases, and of the interface energy, which are required input parameters.
Regarding the effects of dislocations, the capabilities of MICRESS 7.3 are limited. As I explained, there is a still experimental version of a plasticity model which considers the formation of dislocations as function of the average stresses in the matrix by a simple law, and describes the formation of interface dislocation networks in terms of a change of eigenstrains. This simple approach has proven to be quite efficient in describing plasticity effects during γ'-rafting in Ni-based superalloys (within an industry project, unpublished). The effects of interface dislocation networks - in the frame of this simple model - on morphology is automatically included. Other effects, like the formation of thermal dislocations, which during long heat treatments would slowly transform the cubical precipitates to spherical ones, could be easily included, if a corresponding mean-field model is formulated. We as MICRESS developers are no experts in dislocation science, and would appreciate proposals and help from experts with formulating such models in future.
When it comes to mechanical properties, it is important to note that those cannot be directly obtained by phase-field methods. Phase-field primarily provides morphological information, which must be handed over to other methods which make the link to mechanical properties. These can be empirical laws (like Orowan equation), or e.g. homogenization models like our HOMAT package, which can calculate average properties using the properties of the pure phase and their distribution (=microstructure).
Best wishes
Bernd
Re: Follow-up Inquiry on MICRESS Capabilities for Dislocation-Precipitate Studies
Hi, Bernd. Thank you again for your detailed reply, which is very useful for my future studies! I'm sorry, but I have another rather novice question. Currently, there is version 6.4 of MICRESS installed on our research group's computers. If we want to update to version 7.3 of MICRESS, besides downloading it from the downloads section, do we need to pay for any functions?
Re: Follow-up Inquiry on MICRESS Capabilities for Dislocation-Precipitate Studies
Hi yimi_rui,
If your research group regularly payed for maintenance & support, then you should have got all version updates automatically. Otherwise, your group needs to pay for the update depending on the version you have bought (6.4 in your case). Please ask your local dealer for a quote:
https://www.micress.de/contact.html#partners
Bernd
If your research group regularly payed for maintenance & support, then you should have got all version updates automatically. Otherwise, your group needs to pay for the update depending on the version you have bought (6.4 in your case). Please ask your local dealer for a quote:
https://www.micress.de/contact.html#partners
Bernd
Re: Follow-up Inquiry on MICRESS Capabilities for Dislocation-Precipitate Studies
Hi, Bernd. Sorry to bother you again! Today's question is about the driving file for Micress version 6.402. (Why not update the software to version 7 or above? Because my supervisor wants me to use the old version to explore the software's logical rules and update it after initially completing the simulation.)
As a beginner, my first goal is to use Micress to simulate the precipitation and growth process of Cr-rich precipitates in a Cu-Cr binary alloy. The current confusion during the simulation relates to the setting of the phase diagram. Version 6.402 of Micress has two temperature settings for the phase diagram, and with my current temperature settings, I cannot simulate the growth process of precipitates:
1、Temperature of reference point
Assuming I do not rely on a thermodynamic database and manually input relevant parameters based on the Cu-Cr binary phase diagram, can the "Temperature of reference point" be taken as any point on the solid solubility line (the line where Cr precipitates out of the Cu matrix)
Let me take my simulation parameters as an example：
# Temperature of reference point? [K]
1149
# Entropy of fusion between phase 1 and 2? [J/(cm**3 K)]
1
# Input of the concentrations at reference points
# Reference point 1: Concentration of component 1 in phase 1? [wt%]
0.246 (See Fig. 1: Point a)
# Reference point 2: Concentration of component 1 in phase 2? [wt%]
99.995 (See Fig. 2: Point b)
# Input of the slopes at reference points
# Slope m = dT/dC at reference point 1, component 1? [K/wt%]
1000 (Estimated slope of the tangent to the solidus line at Reference point 1 in Fig. 1)
# Slope m = dT/dC at reference point 2, component 1? [K/wt%]
-10000 (Estimated slope of the tangent to the solidus line at Reference point 2 in Fig. 2)
2、#Initial temperature at the bottom? (real) [K]
1100.000
#Corresponding to this is # Initial concentration of component 1 in phase 0 ? [wt%]
0
This indicates that there is no liquid phase at 1100K.
When I see # Initial concentration of component 1 in phase 0 ? [wt%], where phase 0 is the liquid phase, should I set the initial temperature higher, into the temperature range of the liquid phase, so that I can obtain the concentration of component 1 (Cr) in phase 0?
In my simulation results:
(1) The concentration of component 0 (Cu) in phase 1 (Cu matrix), such as c0pha1, shows no trend of change, and some concentration values exceed 100%. Is this related to the settings of the phase diagram, initial temperature, and initial concentration?
(2) No precipitates are formed. Is this related to the phase diagram, initial temperature, and initial concentration settings? Or is it related to the degree of undercooling?
Look forward to your reply.
As a beginner, my first goal is to use Micress to simulate the precipitation and growth process of Cr-rich precipitates in a Cu-Cr binary alloy. The current confusion during the simulation relates to the setting of the phase diagram. Version 6.402 of Micress has two temperature settings for the phase diagram, and with my current temperature settings, I cannot simulate the growth process of precipitates:
1、Temperature of reference point
Assuming I do not rely on a thermodynamic database and manually input relevant parameters based on the Cu-Cr binary phase diagram, can the "Temperature of reference point" be taken as any point on the solid solubility line (the line where Cr precipitates out of the Cu matrix)
Let me take my simulation parameters as an example：
# Temperature of reference point? [K]
1149
# Entropy of fusion between phase 1 and 2? [J/(cm**3 K)]
1
# Input of the concentrations at reference points
# Reference point 1: Concentration of component 1 in phase 1? [wt%]
0.246 (See Fig. 1: Point a)
# Reference point 2: Concentration of component 1 in phase 2? [wt%]
99.995 (See Fig. 2: Point b)
# Input of the slopes at reference points
# Slope m = dT/dC at reference point 1, component 1? [K/wt%]
1000 (Estimated slope of the tangent to the solidus line at Reference point 1 in Fig. 1)
# Slope m = dT/dC at reference point 2, component 1? [K/wt%]
-10000 (Estimated slope of the tangent to the solidus line at Reference point 2 in Fig. 2)
2、#Initial temperature at the bottom? (real) [K]
1100.000
#Corresponding to this is # Initial concentration of component 1 in phase 0 ? [wt%]
0
This indicates that there is no liquid phase at 1100K.
When I see # Initial concentration of component 1 in phase 0 ? [wt%], where phase 0 is the liquid phase, should I set the initial temperature higher, into the temperature range of the liquid phase, so that I can obtain the concentration of component 1 (Cr) in phase 0?
In my simulation results:
(1) The concentration of component 0 (Cu) in phase 1 (Cu matrix), such as c0pha1, shows no trend of change, and some concentration values exceed 100%. Is this related to the settings of the phase diagram, initial temperature, and initial concentration?
(2) No precipitates are formed. Is this related to the phase diagram, initial temperature, and initial concentration settings? Or is it related to the degree of undercooling?
Look forward to your reply.
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Re: Follow-up Inquiry on MICRESS Capabilities for Dislocation-Precipitate Studies
Dear yimi_rui,
As I understand, you want to simulate a solid-state precipitation. According to the literature phase diagram, the slopes are quite steep, and they have opposite slopes. If you use a simple linearized phase diagram description for that in MICRESS, this cannot work, because it would be demixing (you got a warning about that in the MICRESS Screen-output)! The reason is that no redistribution of solute is possible for any given phase fractions, so that the simulation must fail.
However, the system is not really demixing - because ΔS for both sides, i.e. the change of driving force with temperature on both sides, have also opposite sign:
{dGαβ/dT}cα=const * {dGαβ/dT}cb=const < 0
For doing such a simulation in MICRESS without a thermodynamic database (which would do it automatically correct), you need to use the "linearTQ" option instead of the "linear" option. Then, you have the possibility to define the 2 values for ΔS with opposite sign (e.g. dSf+=1.0 and dSf-=-1,0), so that the phase-diagram formulation in ΔG (instead of T) is non-demixing.
"linearTQ" format is identical to the way how MICRESS uses thermodynamic data from databases. It requests further parameters on the dependency of c0 on temperature which you can simply set to 0, and for enthalpy. The latter is only a dummy and can be set arbitrarily (it just is included there for convenience so that users can copy the whole block of linearization data in one singe chunk from the log-file of a TQ-coupled simulation).
I can't really understand your second point about the liquid phase. This phase does not exist at this temperature, and also not in your simulation. There is no need to worry about this phase.
I hope this information solves your problems.
Bernd
As I understand, you want to simulate a solid-state precipitation. According to the literature phase diagram, the slopes are quite steep, and they have opposite slopes. If you use a simple linearized phase diagram description for that in MICRESS, this cannot work, because it would be demixing (you got a warning about that in the MICRESS Screen-output)! The reason is that no redistribution of solute is possible for any given phase fractions, so that the simulation must fail.
However, the system is not really demixing - because ΔS for both sides, i.e. the change of driving force with temperature on both sides, have also opposite sign:
{dGαβ/dT}cα=const * {dGαβ/dT}cb=const < 0
For doing such a simulation in MICRESS without a thermodynamic database (which would do it automatically correct), you need to use the "linearTQ" option instead of the "linear" option. Then, you have the possibility to define the 2 values for ΔS with opposite sign (e.g. dSf+=1.0 and dSf-=-1,0), so that the phase-diagram formulation in ΔG (instead of T) is non-demixing.
"linearTQ" format is identical to the way how MICRESS uses thermodynamic data from databases. It requests further parameters on the dependency of c0 on temperature which you can simply set to 0, and for enthalpy. The latter is only a dummy and can be set arbitrarily (it just is included there for convenience so that users can copy the whole block of linearization data in one singe chunk from the log-file of a TQ-coupled simulation).
I can't really understand your second point about the liquid phase. This phase does not exist at this temperature, and also not in your simulation. There is no need to worry about this phase.
I hope this information solves your problems.
Bernd
Re: Follow-up Inquiry on MICRESS Capabilities for Dislocation-Precipitate Studies
Hi，Bernd! I'm glad you were able to reply promptly! Thank you so much! As a beginner, I still need to further understand the deeper meaning of your suggestions on using the LineTQ phase diagram settings, but I couldn't help but try them right away! Here are the statements in the following driving file:
# Input of the phase diagram of phase 1 and phase 2:
# --------------------------------------------------
# Which phase diagram is to be used?
# Options: linear linearTQ
linearTQ
# Please input linearisation data in the TQ format!
# T0 [K] ?
1149
# dG [J/cm**3] ?
20
# dSf+ [J/cm**3K] ?
1
# dSf- [J/cm**3K] ?
-1
# dH [J/cm**3] (dummy)?
10
# c0 of component 1 in phase 1 ? [wt%]
0
# c0 of component 1 in phase 2 ? [wt%]
0
# m of component 1 in phase 1 ? [K/wt%]
1000
# m of component 1 in phase 2 ? [K/wt%]
-10000
# dcdT of component 1 in phase 1 ? [wt%/K]
0
# dcdT of component 1 in phase 2 ? [wt%/K]
0
My confusion here is about the specific meaning of c0—is it the concentration parameter in the phase? When I tried setting c0 of component 1 in phase 1? [wt%] = 0 and c0 of component 1 in phase 2 ? [wt%] = 0 (as you suggested), the MICRESS Screen-output finally indicated that seeds formed! But they would DISAPPEAR immediately. Why is that?
Additionally, in the display interface, a c1pha1 display window appears even though I only set one solute element. Why is this happening? I look forward to your reply!
# Input of the phase diagram of phase 1 and phase 2:
# --------------------------------------------------
# Which phase diagram is to be used?
# Options: linear linearTQ
linearTQ
# Please input linearisation data in the TQ format!
# T0 [K] ?
1149
# dG [J/cm**3] ?
20
# dSf+ [J/cm**3K] ?
1
# dSf- [J/cm**3K] ?
-1
# dH [J/cm**3] (dummy)?
10
# c0 of component 1 in phase 1 ? [wt%]
0
# c0 of component 1 in phase 2 ? [wt%]
0
# m of component 1 in phase 1 ? [K/wt%]
1000
# m of component 1 in phase 2 ? [K/wt%]
-10000
# dcdT of component 1 in phase 1 ? [wt%/K]
0
# dcdT of component 1 in phase 2 ? [wt%/K]
0
My confusion here is about the specific meaning of c0—is it the concentration parameter in the phase? When I tried setting c0 of component 1 in phase 1? [wt%] = 0 and c0 of component 1 in phase 2 ? [wt%] = 0 (as you suggested), the MICRESS Screen-output finally indicated that seeds formed! But they would DISAPPEAR immediately. Why is that?
Additionally, in the display interface, a c1pha1 display window appears even though I only set one solute element. Why is this happening? I look forward to your reply!
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Re: Follow-up Inquiry on MICRESS Capabilities for Dislocation-Precipitate Studies
Hi yimi_rui,
The c0-values are the equilibrium compositions of the two phases at T0=1149 K. Just use those you had before. What I meant what you should set to 0 were the dcdT-values (what you already have done).
There is another parameter I forgot to tell, which is dG. This should also be set to 0 (as your phase diagram is an equilibrium phase diagram).
Bernd
The c0-values are the equilibrium compositions of the two phases at T0=1149 K. Just use those you had before. What I meant what you should set to 0 were the dcdT-values (what you already have done).
There is another parameter I forgot to tell, which is dG. This should also be set to 0 (as your phase diagram is an equilibrium phase diagram).
Bernd
Re: Follow-up Inquiry on MICRESS Capabilities for Dislocation-Precipitate Studies
Hi, Bernd. I'm sorry to disturb you again! I have modified the parameters of dG and c0 as your suggestion, but unfortunately, the precipitation phase still hasn't been simulated. I want to paste the complete code after the phase diagram to you. I suspect there may be errors in the settings of Initial temperature at the bottom or Initial concentrations.
Question 1:Is the value of “Initial concentration of component 1 in phase 0” the value under the condition corresponding to “Initial temperature at the bottom”?
Question 2: Should I set the initial temperature at the position marked in Figure 1, or is it acceptable as long as the temperature is above the solvus line in principle? Additionally, the initial concentration of component 1 in phase 0 (liquid phase) is set to 0.
# Input of the phase diagram of phase 1 and phase 2:
# --------------------------------------------------
# Which phase diagram is to be used?
# Options: linear linearTQ
linearTQ
# Please input linearisation data in the TQ format!
# T0 [K] ?
1149
# dG [J/cm**3] ?
0
# dSf+ [J/cm**3K] ?
1
# dSf- [J/cm**3K] ?
-1
# dH [J/cm**3] (dummy)?
10
# c0 of component 1 in phase 1 ? [wt%]
0.246
# c0 of component 1 in phase 2 ? [wt%]
99.995
# m of component 1 in phase 1 ? [K/wt%]
1000
# m of component 1 in phase 2 ? [K/wt%]
-10000
# dcdT of component 1 in phase 1 ? [wt%/K]
0
# dcdT of component 1 in phase 2 ? [wt%/K]
0
# Initial concentrations
# ======================
# How shall initial concentrations be set?
# Options: input equilibrium from_file [phase number]
equilibrium
# Initial concentration of component 1 in phase 0 ? [wt%]
0.000000000
# License check
# =============
# 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_dsc
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]
1100.000
# Temperature gradient in z-direction? [K/cm]
0.0000
# Cooling rate? [K/s]
-10.000
# Moving-frame system in z-direction?
# Options: moving_frame no_moving_frame
no_moving_frame
#
Question 1:Is the value of “Initial concentration of component 1 in phase 0” the value under the condition corresponding to “Initial temperature at the bottom”?
Question 2: Should I set the initial temperature at the position marked in Figure 1, or is it acceptable as long as the temperature is above the solvus line in principle? Additionally, the initial concentration of component 1 in phase 0 (liquid phase) is set to 0.
# Input of the phase diagram of phase 1 and phase 2:
# --------------------------------------------------
# Which phase diagram is to be used?
# Options: linear linearTQ
linearTQ
# Please input linearisation data in the TQ format!
# T0 [K] ?
1149
# dG [J/cm**3] ?
0
# dSf+ [J/cm**3K] ?
1
# dSf- [J/cm**3K] ?
-1
# dH [J/cm**3] (dummy)?
10
# c0 of component 1 in phase 1 ? [wt%]
0.246
# c0 of component 1 in phase 2 ? [wt%]
99.995
# m of component 1 in phase 1 ? [K/wt%]
1000
# m of component 1 in phase 2 ? [K/wt%]
-10000
# dcdT of component 1 in phase 1 ? [wt%/K]
0
# dcdT of component 1 in phase 2 ? [wt%/K]
0
# Initial concentrations
# ======================
# How shall initial concentrations be set?
# Options: input equilibrium from_file [phase number]
equilibrium
# Initial concentration of component 1 in phase 0 ? [wt%]
0.000000000
# License check
# =============
# 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_dsc
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]
1100.000
# Temperature gradient in z-direction? [K/cm]
0.0000
# Cooling rate? [K/s]
-10.000
# Moving-frame system in z-direction?
# Options: moving_frame no_moving_frame
no_moving_frame
#
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Re: Follow-up Inquiry on MICRESS Capabilities for Dislocation-Precipitate Studies
Dear yimi_rui,
When using "equilibrium" for the definition of the initial compositions, you cannot specify the composition of phase 0, because it does not exist. You must chose phase 1 which is existing at the beginning:
# Initial concentrations
# ======================
# How shall initial concentrations be set?
# Options: input equilibrium from_file [phase number]
equilibrium 1
# Initial concentration of component 1 in phase 1 ? [wt%]
x.xxxxxxxx
Then you input the composition of your alloy as x.xxxxxxxx, which should be >0.
To get precipitation during cooling, the initial temperature should be chosen above the solvus line of phase 2 (for the given initial composition), otherwise you get precipitation right away at the initial temperature.
By the way, the averaging parameter in the dG-options in Phase Interaction Data should be between 0 and 1 (0.5 is recommended).
Bernd
When using "equilibrium" for the definition of the initial compositions, you cannot specify the composition of phase 0, because it does not exist. You must chose phase 1 which is existing at the beginning:
# Initial concentrations
# ======================
# How shall initial concentrations be set?
# Options: input equilibrium from_file [phase number]
equilibrium 1
# Initial concentration of component 1 in phase 1 ? [wt%]
x.xxxxxxxx
Then you input the composition of your alloy as x.xxxxxxxx, which should be >0.
To get precipitation during cooling, the initial temperature should be chosen above the solvus line of phase 2 (for the given initial composition), otherwise you get precipitation right away at the initial temperature.
By the way, the averaging parameter in the dG-options in Phase Interaction Data should be between 0 and 1 (0.5 is recommended).
Bernd