Directional Solidification of Ni-Based Alloy

[parimalmaity]

Hello,
I am very new to MICRESS. I have started the example problem CMSX4.
The MICRESS & ThermoCalc version I am running are 6.300 and 2016b respective. I am having thermodynamic and mobility databases for FE and NI based alloy system.
I have couple of questions regarding the example problem CMSX4.
1. In the "time input data", limits data are given below. How to get those data?
# Limits: (real) min./s, [max./s], [phase-field factor], [segregation factor]
1.E-3 0.1
2. In the "Grain input", in this particular example 14 initial grains are defined in the beginning. In the eight occasion rotation angle is defined as 75 degree and six occasions orientation angle is defined as 105. Why? can we have any angle? Is all the grains should have initially different angle or same? Is there any reason to have 14 initial grains? or it is user choice? What is the best practice?
# Rotation angle? [Degree]
75.0000000000000
# Rotation angle? [Degree]
105.000000000000
3. In the "Data for further nucleation", number of types of seeds is used as 3. Is the default number is (bulk, region, interface, triple and quadruple)3 or 5? Can you please help me in understanding "Reference phase (integer)", "Substrate phase" and "Phase of new grains (integer)"?
# Number of types of seeds?
3
4. In the "Phase interaction data", How to get those values? and what is best practice?
# 'DeltaG' options: default
# avg ... [] max ... [J/cm**3] smooth ... [degrees] noise ... [J/cm**3]
avg 0.80 max 100 smooth 45.0
5. In the "Phase interaction data", How to get interfacial energy between phases? why two values?
# Interfacial energy between phases LIQUID and 1? [J/cm**2]
# [max. value for num. interface stabilisation [J/cm**2]]
5.00000E-06 2.E-5
6. In the "Phase interaction data", How to get temperature dependent mobility between phases?
# Type of mobility definition between phases LIQUID and 1?
# Options: constant temp_dependent dg_dependent [fixed_minimum]
temp_dependent
# File for kinetic coefficient between phases LIQUID and 1? [ min. value ] [cm**4/(Js)]
CMSX4_mueVonT0_1
7. In the "Phase interaction data", what is 0.2? Is delta is same in both the expression? How to get it?
# Anisotropy of interfacial stiffness? (cubic)
# 1 - delta * cos(4*phi), (delta =delta_stiffness =15*delta_energy)
# Coefficient delta (<1.) ?
0.20000
# Anisotropy of interfacial mobility? (cubic)
# 1 + delta * cos(4*phi)
# Coefficient delta (<1.) ?
0.20000

Regards
Parimal

[Bernd]

Dear parimalmaity,

Welcome to the MICRESS user forum!

Maybe, starting as a very beginner with the CMSX4 example is not a good idea given that this shows a quite advanced use of the MICRESS software.

Nevertheless, of course, I will try to answer your questions as far as possible:

1.) These two values give the range of the allowed numerical time step value for the phase-field solver. The main reason for their specification is simulation performance. They are very case-dependent, and choosing such values belongs to the advanced skills of a MICRESS user.

2.) The reason why 14 grains with two distinct orientations have been chosen was to represent a grain boundary between two grains in a directional solidification (isothermal cross section). Thus, in this 2D-simulation, the dendrites are modeled as if they would grow out of the simulation plane, in form of a quite regular cubic grid for each grain. Building up the initial setup for a simulation lies full in the responsibility of the user. Any configuration could have been chosen, given it makes sense for the user.

3.) The number of seed types is determined by the different phases, locations, and conditions under which nucleation should occur. There is no default value. If no new grains or phases should appear in the simulation, no nucleation is needed at all.

4.) The driving force options are mostly numerical parameters which allow fine tuning how the driving force is used to describe the movement of the corresponding interfaces. While the averaging parameter "avg" is used to prevent spreading of the interfaces in case of strong gradients of the driving force and typically used with intermediate values (e.g. 0.5), the others are expert settings: "max" sets a numerical limit and "smooth" introduces a directional noise which reduces numerical grid anisotropy. Furthermore, since version 6.3, "offset" can be used to add a constant value to the driving force.

5.) The interface energy can be either taken from experiments (literature) or be estimated. The second (optional) expert input introduces an additional stabilisation term which helps to prevent spreading of the interface.

6.) In this case, the temperature-dependent mobility data have been calibrated. Alternatively, an automatic mode for diffusion-limited interface kinetics is available (mob_corr) which was still not functional when the example was designed.

7.) The two values describe anisotropy of the interface stiffness and interface mobility. They are sometimes available from experiments or atomistic simulations or need to be estimated. 0.2 is a reasonable estimation in case of cubic metallic phases.

I know that my short answers are far from being fully conclusive, as each point would be subject of a longer discussion. As a beginner, of course you cannot and need not understand all details of such a complicated setup. The typical way to proceed is to start from a (simple!) example which is close to your targeted application and adapt it to your needs. Ideally, you should start with a MICRESS training. The next one here in Aachen/Germany will be March 29-31.

Best wishes

Bernd

[parimalmaity]

Hello Bernd,
Thank you for answering the questions and really appreciated. Actually, we are focused on particularly NI-based alloy and hence I took as starting example. I have already registered for workshop. I am eager to meet you and counting the days . Please bear with me I have many doubts. But, before I meet you I would like to run some simulations and need your help for clearing by doubts.

Question:

1. What is meaning of orientation of grain in below definition?
is it plane in which a user would like to orient the grain?
# Orientation
# -----------
# How shall grain orientations be defined?
# Options: angle_2d euler_zxz angle_axis miller_indices quaternion

regards
Parimal

[Bernd]

Hi Parimal,

I like the idea to try out MICRESS already before you come to our workshop. It certainly will increase your awareness and help you to get out as much as possible from the training.

I also understand that your topic of interest is Ni-based alloys, and that you prefer starting directly in that topic. For sure, I will help you as much as possible and hope that you won't be frustrated with the relatively complex example. For historical reasons, most of our simple standard examples are from the field of steel.

Orientation of grains is important as soon as anisotropy of interface energy and mobility or misorientation is involved. In 3D-simulations, orientations always have to be given in 3D, which can either be accomplished by Euler angles, Miller indices, quaternions, or by specifying an angle and an axis.
In 2D simulations, mostly, a single angle value is used for definition of a grain orientation, assuming that all orientations lie within the simulation plane (xz-plane). This is specified by the keyword "angle_2d" like in the CMSX4-example. However, for example if grain orientations from a 2D-simulation shall be used for 3D-analysis with an external tool, it makes sense to use 3D-orientations in 2D as well. This can be accomplished by using the keywords " euler_zxz", "angle_axis", "miller_indices", or "quaternion".
Depending on the choice of the keyword, different units of orientation will be requested during the further parameter input like in grain input or nucleation input.

Bernd

[parimalmaity]

Hello Bernd,
Thank you for your reply.
I have few other doubts. Looking you help.
In this particular Ni-based supper alloy system (CMSX4), 3 types of seeds are defined
Below are the input
Seed type#1
# min. nucleation temperature for seed type 1 [K]
0.000000
# max. nucleation temperature for seed type 1 [K]
1585.000
Seed type#2
# min. nucleation temperature for seed type 2 [K]
0.000000
# max. nucleation temperature for seed type 2 [K]
1500.000
Seed type#3
# min. nucleation temperature for seed type 3 [K]
0.000000
# max. nucleation temperature for seed type 3 [K]
1400.000

Question:
1. How to get the maximum temperatures for different seed type?


# Molar volume of (MICRESS) phase 0 (LIQUID)? [cm**3/mol]
8.0000
# Molar volume of (MICRESS) phase 1 (FCC_A1)? [cm**3/mol]
8.0000
# Molar volume of (MICRESS) phase 2 (FCC_L12)? [cm**3/mol]
8.0000
# Temperature at which the initial equilibrium
# will be calculated? [K]
1652.000

Question:
1. At what temperature molar volume of liquid phase as phase 0 and solid phases as Phase 1 and phase 2 are calculated?
2. Is the initial equilibrium temperature is liquidus temperature?
3. Can we have any temperature as initial equilibrium temperature?
4. If we calculate above molar volume at temperature 1652K, thermo-calc results showing phase 0 (79% volume fraction) and phase 1 (21% volume fraction) only.


Thermo-calc Results @ liquidus temperature:

Conditions:
P=1E5, N=1., W(CR)=6.5E-2, W(CO)=6E-2, W(MO)=6E-3, W(W)=6E-2, W(TA)=6.5E-2,
W(AL)=5.6E-2, W(TI)=1E-2, W(RE)=3E-2, W(HF)=1E-3
FIXED PHASES
LIQUID=1
DEGREES OF FREEDOM 0

Temperature 1660.51 K ( 1387.36 C), Pressure 1.000000E+05
Number of moles of components 1.00000E+00, Mass in grams 6.06378E+01
Total Gibbs energy -1.24651E+05, Enthalpy 3.98198E+04, Volume 7.88308E-06

Component Moles W-Fraction Activity Potential Ref.stat
AL 1.2585E-01 5.6000E-02 3.5739E-07 -2.0495E+05 SER
CO 6.1736E-02 6.0000E-02 7.6630E-05 -1.3084E+05 SER
CR 7.5803E-02 6.5000E-02 3.9963E-04 -1.0803E+05 SER
HF 3.3973E-04 1.0000E-03 1.3320E-11 -3.4573E+05 SER
MO 3.7922E-03 6.0000E-03 3.6394E-05 -1.4112E+05 SER
NI 6.6847E-01 6.4700E-01 4.8435E-04 -1.0538E+05 SER
RE 9.7693E-03 3.0000E-02 9.7699E-05 -1.2748E+05 SER
TA 2.1782E-02 6.5000E-02 3.9794E-08 -2.3525E+05 SER
TI 1.2665E-02 1.0000E-02 4.0876E-08 -2.3488E+05 SER
W 1.9789E-02 6.0000E-02 3.8105E-04 -1.0869E+05 SER

LIQUID Status FIXED Driving force 0.0000E+00
Moles 1.0000E+00, Mass 6.0638E+01, Volume fraction 1.0000E+00 Mass fractions:
NI 6.47000E-01 CO 6.00000E-02 RE 3.00000E-02 HF 1.00000E-03
CR 6.50000E-02 W 6.00000E-02 TI 1.00000E-02
TA 6.50000E-02 AL 5.60000E-02 MO 6.00000E-03

FCC_L12 DISORD Status ENTERED Driving force 0.0000E+00
Moles 0.0000E+00, Mass 0.0000E+00, Volume fraction 0.0000E+00 Mass fractions:
NI 6.53785E-01 CR 6.09187E-02 TA 3.96522E-02 HF 4.09349E-05
W 7.02703E-02 AL 4.91414E-02 TI 4.81868E-03
CO 7.02474E-02 RE 4.64990E-02 MO 4.62670E-03

[Bernd]

Hi Parimal,

There are several reason why to restrict checking for nucleation to a temperature range (though in principle no such restriction is required, i.e. the nuclei would just not appear when checked for them at too high temperature):

1.) The most common purpose is not to lose calculation time, because checking for nucleation requires calls to TQ-subroutines which are slow. It makes no sense to check for nucleation at temperatures where we are sure the phase can't be stable. This in the CMSX-4-example holds for seed type 2 where nucleation of secondary (eutectic) FCC_A1 is checked which should not appear during primary FCC_A1 growth.

2.) Phases which constitute composition sets or order-disorder pairs of the same phase description like FCC_A1 and FCC_L12 can easily switch to the "wrong" composition. This is especially the case if on of them (FCC_L12) is only stable at lower temperatures. Checking for FCC_L12 at high temperatures would result in effective switching of FCC_L12 to FCC_A1. Thus this should be avoided (seed type 1).

3.) Finally, nucleation in MICRESS can adopt special functionalities: Use of "add_to_grain" allows redefining properties of already existing grains. With seed type 3, very small rests of the liquid grain 0 are redefined to phase 1 (FCC_A1) - a very specific trick to avoid numerical issues with those. In that specific case, the upper limit for nucleation checking defines the temperature where this happens.

Comments to your further questions follow soon...

[Bernd]

Here my further comments to questions 1-4 of the post before last:

1.) Molar volumes here are just given as constant values. In this setting, they just serve for translating driving forces per mole (as obtained from the database) to driving force per cm2. Thus the values only affect the competence between curvature and chemical driving force. Given the fact that interface energies are typically not very precise or need to be calibrated anyway, there is no need to determine molar volumes very exactly (this is different in case of latent heat or stress coupling!).

2.), 3.) The temperature for calculation of the initial equilibrium may be chosen to be liquidus temperature in case of solidification. However, the most important issue is that the initial equilibrium (the result of which are given in the .log output) should not fail, otherwise everything which comes after is rubbish. Therefore, the possibility of choosing other temperatures is given.

4.) I guess that you mean "molar fraction" instead of "molar volume" here. In our case, the initial temperature is chosen below liquidus temperature because there is a considerable dendrite tip undercooling in directional solidification. At this temperature, therefore there would exist already about 20% fcc if there was global equilibrium.
However, the value of this initial undercooling is not well defined in such a simulation because the 2D-approximation used here is especially wrong for the dendrite tip. That means, there is no valid argument why I have chosen exactly that undercooling.

Best wishes

Bernd