Using the seed density model for heterogeneous nucleation

[jan]

Dear all,

I have been asked to give more details about the seed density model in MICRESS, here it is!

Unfortunately there is no detailed publication on this model, which we designed for the MICRESS software. The theoretical base is the heterogeneous nucleaton model of Lindsay Greer, which is referenced in our paper about equaxed solidification in technical alloys [1-3].

The model is describing nucleation from the melt, triggered by small seeding particles. In principle, the critical undercooling for nucleation of a given phase on this seeding particle depends essentially on the radius of this seeding particle and the surface energy of the new phase in the liquid. So, if a radius-density distribution of the seeding particles is specified, depending on the cooling conditions, the model can predict, how many nuclei will form.
If the different grains of the new phase are growing competitively, like in equiaxed solidification, the latent heat released by the growing particles has to be taken into account. In MICRESS this is most easily done, if the global volume heat extraction rate is specified as a temperature boundary condition, and the total amount of latent heat is released globally on all the simulation domain. To achieve this in MICRESS you need to do the following:

In the driving file:

#
# Automatic 'Driving File' written out by MICRESS.
#
#
# Type of input?
# ==============
shell input
#

... specify concentration coupling

#
# Flags
# -----
# Type of coupling?
# Options: phase concentration temperature temp_cyl_coord
# [stress] [stress_coupled] [flow]
concentration
# Type of potential?

... define the phase to be nucleated

#
#
# Phase data
# ==========
# Number of distinct solid phases?
2
#
# Data for phase 1:
# -----------------
# Simulation of recrystallisation in phase 2 ?
# Options: recrystall no_recrystall
no_recrystall
# Is phase 2 anisotrop?
# Options: isotropic anisotropic faceted
anisotropic
# Crystal symmetry of the phase?
# Options: none xyz_axis cubic hexagonal
cubic
# Should grains of phase 2 be reduced to categories?
# Options: categorize no_categorize
categorize
#
# Data for phase 2:
# -----------------

... swich on nucleation and specify a seed type for the heterogenious
nucleation of phase 1. You input the seed density distribution in the
form of concrete classes of seed particles with a given radius and density.

#
#
# Data for further nucleation
# ===========================
# Enable further nucleation?
# Options: nucleation no_nucleation
nucleation
# Additional output for nucleation?
# Options: out_nucleation no_out_nucleation
no_out_nucleation
#
# Data for further nucleation
# ---------------------------
# Number of types of seeds?
2
#
# Input for seed type 1:
# ----------------------
# Type of 'position' of the seeds?
# Options: bulk region interface triple quadruple [restrictive]
bulk
# Phase of new grains?
1
# Reference phase?
0
# Which nucleation model shall be used?
# Options: seed_undercooling seed_density
seed_density
# Integer for randomization?
77777
# How many classes shall be chosen for the critical radius?
12
# Specify radius [micrometers] and seed density [cm**-3] for class 1
1.4 2.E4
# Specify radius [micrometers] and seed density [cm**-3] for class 2
1.2 4.E4
# Specify radius [micrometers] and seed density [cm**-3] for class 3
1.0 1.E5
# Specify radius [micrometers] and seed density [cm**-3] for class 4
0.8 2.4E5
# Specify radius [micrometers] and seed density [cm**-3] for class 5
0.6 5.E5
# Specify radius [micrometers] and seed density [cm**-3] for class 6
0.5 7.5E5
# Specify radius [micrometers] and seed density [cm**-3] for class 7
0.42 1.1E6
# Specify radius [micrometers] and seed density [cm**-3] for class 8
0.35 1.5E6
# Specify radius [micrometers] and seed density [cm**-3] for class 9
0.3 2.E6
# Specify radius [micrometers] and seed density [cm**-3] for class 10
0.25 3.E6
# Specify radius [micrometers] and seed density [cm**-3] for class 11
0.20 5.E6
# Specify radius [micrometers] and seed density [cm**-3] for class 12
0.15 8.E6
# Determination of nuclei orientations?
# Options: random fix range parent_relation
random
# Shield effect:
# Shield time [s] ?
0.75000
# Shall categorization be applied to this seed type?
# Options: categorize {Number} no_categorize
categorize 36
# Nucleation range
# min. nucleation temperature for seed type 2 [K]
0.0000
# max. nucleation temperature for seed type 2 [K]
900.00
# Time between checks for nucleation? [s]
0.3
# 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)
0.10000
#
# Input for seed type 2:
# ----------------------

... finally, you specify, that latent heat is beeing taken into account (evtl. with 2D/3D-correction)

#
#
# Parameters for latent heat and 1D temperature field
# ===================================================
# Simulate release of latent heat?
# Options: lat_heat lat_heat_3d [matrix phase] no_lat_heat
lat_heat_3d
# Enthalpy of phase 0? ([J/cm^3])
0.0000000E+00
# Specific heat capacity (Cp) of phase 0? ([J/(cm^3*K)])
2.950000
# Enthalpy of phase 1? ([J/cm^3])
-1437.000
# Specific heat capacity (Cp) of phase 1? ([J/(cm^3*K)])
2.490000
# Enthalpy of phase 2? ([J/cm^3])
-1159.000
# Specific heat capacity (Cp) of phase 2? ([J/(cm^3*K)])

... and set the thermal boundary condition

#
# Boundary conditions
# ===================
# Type of heat flow trend?
# Options: linear sinus
linear
# Number of connecting points? (integer)
0
# Initial temperature at the bottom? (real) [K]
848.0000
# Temperature gradient in z-direction? [K/cm]
0.0000000E+00
# Heat flow? [J/s*cm^3]
-30.00000
#
# Boundary conditions for phase field in each direction


...


In the distribution examples, there is one which uses the seed density model (AlCu_Equiaxed_dri).

In principle, with this model it is possible to predict grain sizes for different thermal conditions, composition and seeding status, also if more phases are present. In practice, there are no seed density information available, so you will need calibration with experiments.



Literatur:

[1] B. Boettger et. al., Acta Mater 54 (2006) 2697.
[2] Quested TE, Greer AL, Acta Mater 52 (2004) 3859.
[3] Greer AL et. al., Adv Eng Mater 2003, 81.

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original message from Bernd

[jan]

Please suggest me some reading material about the seed undercooling model.

moreover,is it always necessary to consider release of latent heat when seed density model is used?

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original message from Deep

[jan]

Dear Deep,

the seed undercooling model is just our naming for a nucleation criterion based on an user-defined critical undercooling. Therefore there is no literature about this model avaliable.
In MICRESS we use this model whenever the seed density model is not applicable, e.g. for nucleation at interfaces. With additional parameters like the shield time and distance and the frequency of checking for nucleation one can design the nucleation conditions which are appropriate for the special requirements. But, in contrary to the seed density model, this is not a physical model.
For usage in MICRESS, you should refer to the MICRESS Manual and to the Contribution examples, or ask more specific questions to this forum.

In the seed density model, latent heat needs to be taken into account only if the thermal interaction of the early seeds is essential for their growth. If there are strong temperature gradients, or if the seeds are growing only to a very small phase fraction and thus latent heat is minimal, latent heat can be neglected.

Bernd

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original message from Bernd

[jan]

Thanks for the decent explanation..

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original message from Deep

[jan]

Dear Sir,

While using the above model for the solidification of Aluminum bronze(al=9 wt%),the grains of 1 phase (BCC_A2) first appear and then they grow.Due to the occupation of the domain by these grains the Alpha(FCC_A1) seeds doesn't get a chance to grow.I tried to keep them at the interface too,but it also failed.

Can you suggest some method (including solid state transformations,if required) to let the solidification work properly

Moreover , can you explain the significance of phase field no. -1.

Thanking You,

Deep

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original message from Deep

[jan]

Dear Deep,

I am not familiar with this alloy system, but from the phase diagram I would expect it to behave like a eutectic system in this concentration range. Therefore, as a first advice I would try to nucleate phase 2 at the interface of phase 1 and the liquid instead of using the seed density model like for the primary phase (as in the example file you sent me personally).
I am currently trying to run your problem with this variation:

#
# Input for seed type 1:
# ----------------------
# Type of 'position' of the seeds?
# Options: bulk region interface triple quadruple [restrictive]
interface
# Phase of new grains?
1
# Reference phase?
0
# maximum number of new nuclei 1?
10000
# Grain radius [micrometers]?
0.0000
# Choice of growth mode:
# Options: stabilisation analytical_curvature
stabilisation
# min. undercooling [K] (>0)?
2.0000
# Determination of nuclei orientations?
# Options: random fix range parent_relation
random
# Shield effect:
# Shield time [s] ?
0.20000
# Shield distance [micrometers]?
5.0000
# Nucleation range
# min. nucleation temperature for seed type 1
0.0000
# max. nucleation temperature for seed type 1
1350.0
# Time between checks for nucleation? [s]
0.01
# Shall random noise be applied?
# Options: nucleation_noise no_nucleation_noise
no_nucleation_noise
#

With this modification I get nucleation of the secondary phase after t=2.47 s.

If you nevertheless want to use still the seed density model for the secondary phase, because you believe that it nucleates from the melt, make shure that your seed density is high enough to create a sufficient number of possible seed positions. You can check this number in the .log file, where it is written in the place where the input data are mirorred. Otherwise it could happen, that they get hidden by the primary dendrites and you will not get nucleation.

According to your second question: In the .phas output the phase number of the particles is plotted. In the interface region we use -1 to mark the interface position. This has nothing to do with the phase-field parameter!

Bernd

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original message from Bernd

[jan]

Sir,
in this modification the phase of new grains appearing is phase 1,so where does the phase 2 comes into picture in this modification.I am a bit confused..

shall i have to apply the seed density model for the phase 2??

Moreover the results obtained from the file which I personally sent you show at some time steps the domain occupied by interfaces..is this possible?

Thanking you once again,
Deep

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original message from Deep

[jan]

Sorry about the confusion of the phase numbers! In your previous post you named the BCC primary phase "phase 1", while in the driving file you sent me it was phase 2. Therfore, the variation I proposed applies to phase 1, because this was FCC in your example!
So, to be clear, BCC should be nucleated using the seed density model, and FCC should be nucleated at the interface using seed_undercooling (which is default at interfaces at the moment).

Meanwhile, on my computer the variation of your example has gone further and is showing something which is a typical artefact, if resolution is too low or numerical parameters are wrong: The eutectic phases are growing together in a smeared way, showing only interface! In some cases, when it is impossible to resolve very fine structures, this may be considered as a pseudo phase for the eutectic phase mixture.
What you should check is:

1.) How fine is the eutectic structure in experiments? Do you have any chance to resolve it? The minimum size of your simulation would correspond to a quarter of a dendrite, if you put it to one corner (using initial grain setting or nucleation in a region) and you use symmetric boundary conditions. If not, let it grow as pseudo phase! You can still evaluate phase fractions.

2.) If it should be course enough, maybe the mobility for the fcc phase is just too high or the surface energies are wrong.

I hope that helps!

Bernd

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original message from Bernd

[jan]

Dear Deep,

I have run the same example with double as high resolution and smaller area and got the following after complete solidification:




This concentration output picture showes eutectic growth, which resolves the lamellae most oft the time, just at the end there are occuring some diffuse regions.
So, with an even somewhat higher resolution (=longer simulation time ) you would get it completely resolved.

After that some solid-solid transformation occurs, which transforms all bcc to fcc.

Best wishes

Bernd

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original message from Bernd

[jan]

Sir,


Thanks a lot for your detailed explanations with the result.


Sir,what resolution have you exactly taken for this simulation,because when I tried for half the resolution and lesser grid size ,no grains appeared and the simulation just passed its way.Moreover,I took a slightly higher resolution,then the results I got are different from what is shown here.some grains are always left even at time 15 secs in the .conc1 file.


Can you also tell the exact grid size so that I may rum the same simulation here.


Thanking You,


Sincerely,


Deep

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original message from Deep