# Data for phase interaction 1 / 1:
# ---------------------------------
# Simulation of interaction between phase 1 and 2 ?
# Options: phase_interaction no_phase_interaction
# [standard|particle_pinning|solute_drag]
phase_interaction particle_pinning
To implement the “particle_pinning” model presented in MICRESS, two parameters should be defined (“critical pinning force” and “minimal mobility”).
What is the physical meaning of these parameters?
How does this model consider the particle pinning?
What is the equation relating mobility to these two factors?
Particle pinning
Re: Particle pinning
Dear mtoloui,
the particle pinning model is a mesoscale model which takes into account the microscopic particle pinning effect without explicitely treating the individual particles. According to the Zener model a critical pinning force
P* ~ 3 sigma c / r
is defined, where sigma is the surface energy of the particles, c the particle "concentration" and r the particle radius.
In earlier times, we performed a microscale simulation of this pinning force using MICRESS.
From this simulation, we could get the velocity as a function of the driving force for different values of the critical drag force p*:
The velocity curves can be described by an effective mobility
which afterwards has been implemented as mesoscopic particle pinning model in MICRESS. The values the user has to provide is the critical pinning force p* in units of a critical curvature (1/µm) and a minimal mobility. The latter parameter, according to the theory above, would be zero. But in many cases, even after pinning a very slow movement of the grain boundaries is observed, e.g. due to particle ripening. MICRESS gives the user the possibiliy to account for that by specifying a minimal mobility >0.
One can also use a hidden option for reading temperature dependent values for the critical pinning force and the minimal mobility from file:
# Data for phase interaction 1 / 1:
# ---------------------------------
# Simulation of interaction between phase 1 and 2 ?
# Options: phase_interaction no_phase_interaction
# [standard|particle_pinning|solute_drag]
phase_interaction particle_pinning_temperature
Bernd
the particle pinning model is a mesoscale model which takes into account the microscopic particle pinning effect without explicitely treating the individual particles. According to the Zener model a critical pinning force
P* ~ 3 sigma c / r
is defined, where sigma is the surface energy of the particles, c the particle "concentration" and r the particle radius.
In earlier times, we performed a microscale simulation of this pinning force using MICRESS.
From this simulation, we could get the velocity as a function of the driving force for different values of the critical drag force p*:
The velocity curves can be described by an effective mobility
which afterwards has been implemented as mesoscopic particle pinning model in MICRESS. The values the user has to provide is the critical pinning force p* in units of a critical curvature (1/µm) and a minimal mobility. The latter parameter, according to the theory above, would be zero. But in many cases, even after pinning a very slow movement of the grain boundaries is observed, e.g. due to particle ripening. MICRESS gives the user the possibiliy to account for that by specifying a minimal mobility >0.
One can also use a hidden option for reading temperature dependent values for the critical pinning force and the minimal mobility from file:
# Data for phase interaction 1 / 1:
# ---------------------------------
# Simulation of interaction between phase 1 and 2 ?
# Options: phase_interaction no_phase_interaction
# [standard|particle_pinning|solute_drag]
phase_interaction particle_pinning_temperature
Bernd
Re: Particle pinning
How does MICRESS calculate P?
Is there any relationship between P and the average grain size (used in MICRESS)?
Is there any relationship between P and the average grain size (used in MICRESS)?
Re: Particle pinning
Dear mtoloui,
p is calculated by the phase-field equation:
If there is no chemical driving force like in your case, only the first term is important. For grain growth it consists of curvature and the force balance at the triple junction. Especially the latter is not directly linked to the grain size. Therefore, with the particle pinnng model, anormalous grain growth can be observed, i.e. one huge grain goes on growing while the other smaller ones are already pinned. But in general, p is decreasing with the average grain size.
Bernd
p is calculated by the phase-field equation:
- PF-Gleichung1.gif (3.22 KiB) Viewed 11241 times
- PF-Gleichung2.gif (2.27 KiB) Viewed 11217 times
Bernd
Re: Particle pinning
In the particle_pinning model, “critical pinning force [1/micrometer]” is needed.
Is this f/r or (3/2)(f/r)?
Is this f/r or (3/2)(f/r)?
Re: Particle pinning
Dear mtoloui,
if your question is whether the critical driving force, corresponding to a critical radius, in a 2D calculation is corrected for dimensionality, the answer is "no"!
Bernd
if your question is whether the critical driving force, corresponding to a critical radius, in a 2D calculation is corrected for dimensionality, the answer is "no"!
Bernd
Re: Particle pinning
Dear Bernd,
As you know, there are different suggestions for the relationship of limiting grain size and fraction (f) and radius (r) of pinning particles.
The question is, when you calculate f and r, what should be entered as the critical pinning force [1/micrometer]?
As you know, there are different suggestions for the relationship of limiting grain size and fraction (f) and radius (r) of pinning particles.
The question is, when you calculate f and r, what should be entered as the critical pinning force [1/micrometer]?
Re: Particle pinning
Dear mtoloui,
The critical pinning force which has to be input in the MICRESS driving file is the driving force which is needed to overcome pinning. In the case of pure grain growth, the only source of driving force is the curvature of the grain boundary. This is the reason why we defined the critical pinning force in units of curvature.
The question how this critical pinning force is related to the size, shape and density of the pinning particles is not part of our mesoscopic pinning model. The user may apply analytical approaches like the Zener model in order to obtain a value for the critical pinning force, alternatively one may apply microscopic simulations like the one shown above in this thread. I personally cannot give you any suggestions...
Bernd
The critical pinning force which has to be input in the MICRESS driving file is the driving force which is needed to overcome pinning. In the case of pure grain growth, the only source of driving force is the curvature of the grain boundary. This is the reason why we defined the critical pinning force in units of curvature.
The question how this critical pinning force is related to the size, shape and density of the pinning particles is not part of our mesoscopic pinning model. The user may apply analytical approaches like the Zener model in order to obtain a value for the critical pinning force, alternatively one may apply microscopic simulations like the one shown above in this thread. I personally cannot give you any suggestions...
Bernd
Re: Particle pinning
Dear Bernd,
Thank you for your consideration,
I am a bit confused about how you calculate P (driving force stemming from the curvature).
In the paper ISIJ Int. 49, 2009, 1024 you have mentioned that “Beside the thermodynamic driving force the curvature pressure is calculated separately and the sum of both values enter the mobility function.”
Do you find driving force from the geometry of the boundary and not from the distribution of the phase field parameter (K term as you shown in this webpage)?
It is obvious that you cannot use the K term as it is potential gradient with the dimensionality of [1/length^2] while curvature has a dimensionality of [1/length].
On the other hand. How do you subtract critical pinning force with the dimensionality of [1/length] from driving force with the dimensinality of [energy/length^3]?
Thank you for your consideration,
I am a bit confused about how you calculate P (driving force stemming from the curvature).
In the paper ISIJ Int. 49, 2009, 1024 you have mentioned that “Beside the thermodynamic driving force the curvature pressure is calculated separately and the sum of both values enter the mobility function.”
Do you find driving force from the geometry of the boundary and not from the distribution of the phase field parameter (K term as you shown in this webpage)?
It is obvious that you cannot use the K term as it is potential gradient with the dimensionality of [1/length^2] while curvature has a dimensionality of [1/length].
On the other hand. How do you subtract critical pinning force with the dimensionality of [1/length] from driving force with the dimensinality of [energy/length^3]?
Re: Particle pinning
Dear mtoloui,
For particle pinning, curvature is calculated independently from the K term by using the differences of the normal vectors for neighbouring cells. This is what you also find in the curvature output.
By multiplying this curvature (1/µm) with the interface stiffness sigma* and correcting for the different length units, we get the same units as the chemical driving force (J/cm3), and hence the values can be added.
Bernd
For particle pinning, curvature is calculated independently from the K term by using the differences of the normal vectors for neighbouring cells. This is what you also find in the curvature output.
By multiplying this curvature (1/µm) with the interface stiffness sigma* and correcting for the different length units, we get the same units as the chemical driving force (J/cm3), and hence the values can be added.
Bernd