Dear Bernd,

Thank you so much for the suggestion! We increased the spacing to be 0.07

m and the interface energy to be 1.62E-5 J/cm

^{2}, as shown below.

Code: Select all

```
# Phase interaction data
# ======================
#
# Data for phase interaction 0 / 1:
# ---------------------------------
# Simulation of interaction between phases 0 and 1?
# Options: phase_interaction no_phase_interaction
# [standard|particle_pinning[_temperature]|solute_drag]
# | [redistribution_control]
phase_interaction redistribution_control
# 'DeltaG' options: default
# avg ...[] max ...[J/cm^3] smooth ...[Deg] noise ...[J/cm^3] offset ...[J/cm^3]
avg 0.90 max 200.00 noise 0.10
# I.e.: avg +0.90 smooth +0.0 max +2.00000E+02
# Type of interfacial energy definition between phases 0 and 1?
# Options: constant temp_dependent
constant
# Interfacial energy between phases 0 and 1? [J/cm**2]
# [max. value for num. interface stabilisation [J/cm**2]]
1.62E-5
# Type of mobility definition between phases 0 and 1?
# Options: constant temp_dependent dg_dependent [fixed_minimum]
constant
# Kinetic coefficient mu between phases 0 and 1 [ min. value ] [cm**4/(Js)] ?
0.1
# Is interaction isotropic?
# Options: isotropic
# anisotropic [junction_force] [harmonic_expansion]
anisotropic
# Anisotropy of interfacial stiffness? (cubic)
# 1 - delta * cos(4*phi), (delta =delta_stiffness =15*delta_energy)
# Coefficient delta (<1.) ?
0.28800
# Anisotropy of interfacial mobility? (cubic)
# 1 + delta * cos(4*phi)
# Coefficient delta (<1.) ?
0.28800
#
# Data for phase interaction 1 / 1:
# ---------------------------------
# Simulation of interaction between phases 1 and 1?
# Options: phase_interaction no_phase_interaction identical phases nb
# [standard|particle_pinning[_temperature]|solute_drag]
# | [redistribution_control]
no_phase_interaction
```

Under the diffusion data, we chose the diagonal methods, as shown below.

Code: Select all

```
# Diffusion Data
# --------------
# ["Terse Mode": Each line starts with component number and phase number]
# Options: diagonal [x] multi [y(1..k)] multi_plus [y(1..k)]
# x: one of the characters "n", "d", "g", "l", "z", "i", "I", or "f"
# y: chain of "n", "d", "g", "l", "z", or "f" (for each component)
# default: "g" resp. "gggg..."
# Rem: "n":no diffusion, "d": input, "f": T-dep. from file
# "i":infinite, "I": infinite in each grain
# from database: "g": global, "l": local, "z" global z-segmented
# Extra line option: [+b] for grain-boundary diffusion
# Extra line option (prefactor on time step): cushion <0-1>
# Extra line option: infinite_limit [cm**2/s]
# Extra line option: maxfactor_local [real > 1.0] (default: 10.0)
# Extra line option: factor [real > 0.]
# Finish input of diffusion data with 'end_diffusion_data'.
#
# How shall diffusion of component 1 in phase 0 be solved?
diagonal l
# How shall diffusion of component 1 in phase 1 be solved?
diagonal g
# How shall diffusion of component 2 in phase 0 be solved?
diagonal l
# How shall diffusion of component 2 in phase 1 be solved?
diagonal g
#
# How shall the interval for updating diffusion coefficients
# data be set?
# Options: constant from_file
constant
# Interval for updating diffusion coefficients data? [s]
0.10000
#
```

We checked the exact diffusion coefficient in the output file "TabD.txt", as listed below. The diffusion coefficient of components 1 and 2 in phase 0 is ~10E-5 cm

^{2}/s, but another two are not. We are not sure if it can be a problem.

Code: Select all

```
# Simulation Temperature Diff. C. Diff. C. Diff. C. Diff. C.
# time [s] [K] P 0 C 1 P 0 C 2 P 1 C 1 P 1 C 2
0.000000 920.000 0.00E+00 0.00E+00 0.00E+00 0.00E+00
2.0000000E-04 917.097 8.30E-05 2.99E-05 2.47E-08 2.71E-08
4.0000000E-04 914.194 8.18E-05 2.98E-05 2.35E-08 2.58E-08
6.0000000E-04 911.291 8.05E-05 2.96E-05 2.23E-08 2.46E-08
8.0000000E-04 908.388 7.93E-05 2.95E-05 2.12E-08 2.34E-08
1.0000000E-03 905.485 7.81E-05 2.93E-05 2.01E-08 2.23E-08
1.2000000E-03 902.582 7.69E-05 2.91E-05 1.91E-08 2.12E-08
1.4000000E-03 899.679 7.57E-05 2.90E-05 1.81E-08 2.01E-08
1.6000000E-03 896.776 7.45E-05 2.90E-05 1.72E-08 1.91E-08
1.8000000E-03 893.873 7.32E-05 2.91E-05 1.63E-08 1.82E-08
2.0000000E-03 890.970 7.19E-05 2.93E-05 1.55E-08 1.72E-08
2.2000000E-03 888.067 7.06E-05 2.96E-05 1.47E-08 1.64E-08
2.4000000E-03 885.164 6.91E-05 3.01E-05 1.39E-08 1.55E-08
2.6000000E-03 882.261 6.75E-05 3.10E-05 1.32E-08 1.47E-08
2.8000000E-03 879.358 6.56E-05 3.29E-05 1.25E-08 1.40E-08
3.0000000E-03 876.455 6.22E-05 3.79E-05 1.18E-08 1.33E-08
3.2000000E-03 873.552 5.66E-05 4.88E-05 1.12E-08 1.26E-08
3.4000000E-03 870.649 5.51E-05 4.99E-05 1.06E-08 1.19E-08
3.6000000E-03 867.746 5.37E-05 5.08E-05 9.98E-09 1.13E-08
3.8000000E-03 864.843 5.23E-05 5.18E-05 9.44E-09 1.07E-08
4.0000000E-03 861.940 5.10E-05 5.27E-05 8.91E-09 1.01E-08
4.2000000E-03 859.037 4.98E-05 5.31E-05 8.42E-09 9.55E-09
4.4000000E-03 856.134 4.86E-05 5.39E-05 7.95E-09 9.03E-09
4.6000000E-03 853.231 4.73E-05 5.48E-05 7.50E-09 8.54E-09
4.8000000E-03 850.328 4.61E-05 5.55E-05 7.07E-09 8.07E-09
5.0000000E-03 847.425 4.49E-05 5.63E-05 6.67E-09 7.62E-09
5.2000000E-03 844.522 4.38E-05 5.68E-05 6.29E-09 7.19E-09
5.4000000E-03 841.619 4.26E-05 5.75E-05 5.92E-09 6.79E-09
5.6000000E-03 838.716 4.15E-05 5.82E-05 5.58E-09 6.41E-09
5.8000000E-03 835.813 4.04E-05 5.88E-05 5.25E-09 6.04E-09
6.0000000E-03 832.910 3.93E-05 5.95E-05 4.94E-09 5.69E-09
6.2000000E-03 830.007 3.84E-05 5.99E-05 4.65E-09 5.37E-09
6.4000000E-03 827.104 3.73E-05 6.05E-05 4.37E-09 5.05E-09
6.6000000E-03 824.201 3.63E-05 6.10E-05 4.11E-09 4.76E-09
6.8000000E-03 821.298 3.53E-05 6.16E-05 3.86E-09 4.48E-09
7.0000000E-03 818.395 3.44E-05 6.22E-05 3.62E-09 4.21E-09
7.2000000E-03 815.492 3.35E-05 6.25E-05 3.40E-09 3.96E-09
7.4000000E-03 812.589 3.26E-05 6.30E-05 3.19E-09 3.72E-09
7.6000000E-03 809.686 3.17E-05 6.34E-05 2.99E-09 3.50E-09
7.8000000E-03 806.783 3.08E-05 6.39E-05 2.80E-09 3.28E-09
8.0000000E-03 803.880 2.99E-05 6.44E-05 2.62E-09 3.08E-09
8.2000000E-03 800.977 2.91E-05 6.46E-05 2.46E-09 2.89E-09
8.4000000E-03 798.074 2.83E-05 6.50E-05 2.30E-09 2.71E-09
8.6000000E-03 795.171 2.75E-05 6.54E-05 2.15E-09 2.54E-09
8.8000000E-03 792.268 2.67E-05 6.58E-05 2.01E-09 2.38E-09
9.0000000E-03 789.365 2.60E-05 6.62E-05 1.88E-09 2.23E-09
9.2000000E-03 786.462 2.52E-05 6.63E-05 1.76E-09 2.09E-09
9.4000000E-03 783.559 2.45E-05 6.67E-05 1.64E-09 1.95E-09
9.6000000E-03 780.656 2.38E-05 6.70E-05 1.53E-09 1.82E-09
9.8000000E-03 777.753 2.31E-05 6.73E-05 1.43E-09 1.70E-09
1.0000000E-02 774.850 2.24E-05 6.76E-05 1.33E-09 1.59E-09
1.0200000E-02 771.947 2.18E-05 6.77E-05 1.24E-09 1.49E-09
1.0400000E-02 769.044 2.11E-05 6.80E-05 1.15E-09 1.39E-09
1.0600000E-02 766.141 2.05E-05 6.82E-05 1.07E-09 1.29E-09
1.0800000E-02 763.238 1.98E-05 6.84E-05 9.98E-10 1.21E-09
1.1000000E-02 760.335 1.92E-05 6.87E-05 9.28E-10 1.12E-09
1.1200000E-02 757.432 1.87E-05 6.87E-05 8.62E-10 1.05E-09
1.1400000E-02 754.529 1.81E-05 6.89E-05 8.01E-10 9.73E-10
1.1600000E-02 751.626 1.75E-05 6.91E-05 7.43E-10 9.05E-10
1.1800000E-02 748.723 1.70E-05 6.93E-05 6.89E-10 8.41E-10
1.2000000E-02 745.820 1.64E-05 6.94E-05 6.39E-10 7.82E-10
1.2200000E-02 742.917 1.59E-05 6.95E-05 5.92E-10 7.26E-10
1.2400000E-02 740.014 1.54E-05 6.96E-05 5.48E-10 6.73E-10
1.2600000E-02 737.111 1.49E-05 6.98E-05 5.07E-10 6.25E-10
1.2800000E-02 734.208 1.44E-05 6.99E-05 4.69E-10 5.79E-10
1.3000000E-02 731.305 1.39E-05 7.00E-05 4.33E-10 5.36E-10
1.3200000E-02 728.402 1.34E-05 7.00E-05 4.00E-10 4.96E-10
1.3400000E-02 725.499 1.30E-05 7.01E-05 3.69E-10 4.59E-10
1.3600000E-02 722.596 1.25E-05 7.02E-05 3.41E-10 4.25E-10
1.3800000E-02 719.693 1.21E-05 7.03E-05 3.14E-10 3.92E-10
1.4000000E-02 716.790 1.17E-05 7.03E-05 2.89E-10 3.62E-10
1.4200000E-02 713.887 1.13E-05 7.03E-05 2.66E-10 3.34E-10
1.4400000E-02 710.984 1.09E-05 7.04E-05 2.45E-10 3.08E-10
1.4600000E-02 708.081 1.05E-05 7.04E-05 2.25E-10 2.84E-10
1.4800000E-02 705.178 1.01E-05 7.05E-05 2.07E-10 2.62E-10
1.5000000E-02 702.275 9.71E-06 7.05E-05 1.90E-10 2.41E-10
```

After the simulation, We found the results still need to be improved because:

- The driving force of the dendrite tip varies a lot during the dendrite growth process. But I think it should stay relatively constant during the dendrite growing process.

- The small circular liquid phase formed between dendrites should not appear after solidification.

So my questions are,

- How should we improve it?

- Screenshot from 2020-12-21 13-33-44.png (238.35 KiB) Viewed 486 times

In case you may want to know other parameters, I post below all other parameters:

Code: Select all

```
# Flags and settings
# ==================
#
# Geometry
# --------
# Grid size?
# (for 2D calculations: CellsY=1, for 1D calculations: CellsX=1, CellsY=1)
# Cells in X-direction (CellsX):
285
# Cells in Y-direction (CellsY):
1
# Cells in Z-direction (CellsZ):
1000
# Cell dimension (grid spacing in micrometers):
# (optionally followed by rescaling factor for the output in the form of '3/4')
0.0700
#
# Flags
# -----
# Type of coupling?
# Options: phase concentration [volume_change] temperature temp_cyl_coord
# [stress] [stress_coupled] [flow] [flow_coarse] [dislocation]
concentration
# Type of potential?
# Options: double_obstacle multi_obstacle [fd_correction]
double_obstacle fd_correction
# Enable one dimensional far field approximation for diffusion?
# Options: 1d_far_field 1d_far_field_EW no_1d_far_field
1d_far_field
# Number of cells for the 1D external field?
100
# Shall an additional 1D field be defined in z direction
# for temperature coupling?
# Options: no_1d_temp 1d_temp 1d_temp_cylinder 1d_temp_polar [kin. Coeff]
# kin. Coeff: Kinetics of latent heat release (default is 0.01)
no_1d_temp
#
# Phase field data structure
# --------------------------
# Coefficient for initial dimension of field iFace
# [minimum usage] [target usage]
0.1
# Coefficient for initial dimension of field nTupel
# [minimum usage] [target usage]
0.1
# Phase data
# ==========
# Number of distinct solid phases?
1
#
# Data for phase 1:
# -----------------
# Simulation of recrystallisation in phase 1?
# Options: recrystall no_recrystall [verbose|no_verbose]
no_recrystall
# Is phase 1 anisotrop?
# Options: isotropic anisotropic faceted_a faceted_b antifaceted
anisotropic
# Crystal symmetry of the phase?
# Options: none cubic hexagonal tetragonal orthorhombic
cubic
# Should grains of phase 1 be reduced to categories?
# Options: categorize no_categorize
no_categorize
#
# Orientation
# -----------
# How shall grain orientations be defined?
# Options: angle_2d euler_zxz angle_axis miller_indices quaternion
angle_2d
#
#
# Grain input
# ===========
# Type of grain positioning?
# Options: deterministic random [deterministic_infile] from_file
deterministic
# NB: the origin of coordinate system is the bottom left-hand corner,
# all points within the simulation domain having positive coordinates.
# Number of grains at the beginning?
1
# Input data for grain number 1:
# Geometry?
# Options: round rectangular elliptic round_inverse
rectangular
# Center x,z coordinates [micrometers], grain number 1?
9.975
0.00000
# Length along x-axis [micrometers]
19.95
# Length along z-axis [micrometers]
1.5
# Should the Voronoi criterion be applied?
# Options: voronoi no_voronoi
no_voronoi
# Phase number? (integer)
1
# Rotation angle? [Degree]
0.000000000000000E+000
#
#
# Data for further nucleation
# ===========================
# Enable further nucleation?
# Options: nucleation nucleation_symm no_nucleation [verbose|no_verbose]
no_nucleation verbose
#
# Concentration data
# ==================
# Number of dissolved constituents? (int)
2
# Type of concentration?
# Options: atom_percent (at%)
# weight_percent (wt%)
weight_percent
#
#
# Phase diagram - input data
# ==========================
#
# List of phases and components which are stoichiometric:
# phase and component(s) numbers
# List of concentration limits (at%):
# <limits>, phase number and component number
# List for ternary extrapolation (2 elements + main comp.):
# <interaction>, component 1, component 2
# Switches: <stoich_enhanced_{on|off}> <solubility_{on|off}>
# List of relative criteria on phase composition
# <criterion_higher | criterion_lower>, phase No 1, phase No 2, component No
# List of source changes for diffusion data
# <switch_diff_data>, Phase-No., reference phase
# Switch: Add composition sets for calculation of diffusion/volume/enthalpy data
# <diff_comp_sets | vol_comp_sets | enth_comp_sets>, phase list
# End with 'no_more_stoichio' or 'no_stoichio'
no_more_stoichio
#
#
# Is a thermodynamic database to be used?
# Options: database database_verbose database_consistent no_database
database
#
# Name of Thermo-Calc *.GES5 file without extension?
GES_Files/AlSiMg
# Which global relinearisation mode shall be used?
# Options: manual from_file none
manual 1E-3
# Input of the phase diagram of phase 0 and phase 1:
# --------------------------------------------------
# Which phase diagram is to be used?
# Options: database [local|global[F]|globalG[F]] [start_value_{1|2}]
# linear linearTQ
database globalGF
# Relinearisation mode for interface 0 / 1
# Options: automatic manual from_file none
manual 1E-3
# Please specify the redistribution behaviour of each component:
# Format: forward [backward]
# Options: nple para paratq normal [mob_corr] atc [mob_corr] [verbose]
# Component 1:
atc mob_corr
# Component 2:
atc mob_corr
# Reading GES5 workspace ...
# Index relations between TC and MICRESS
# --------------------------------------
# The database contains the following components:
# 1: AL
# 2: MG
# 3: SI
# Specify relation between component indices Micress -> TC!
# The main component has in MICRESS the index 0
# Thermo-Calc index of (MICRESS) component 0?
1
# Thermo-Calc index of (MICRESS) component 1?
2
# Thermo-Calc index of (MICRESS) component 2?
3
# 0 -> AL
# 1 -> MG
# 2 -> SI
# The database contains 4 phases:
# 1: DIAMOND_A4
# 2: FCC_L12
# 3: LIQUID
# 4: MG2SI_C1
# Specify relation between phase indices Micress -> TC!
# The matrix phase has in MICRESS the index 0
# Thermo-Calc index of the (MICRESS) phase 0 [ name ('#'-->'$') ]?
3
# Thermo-Calc index of the (MICRESS) phase 1 [ name ('#'-->'$') ]?
2
# 0 -> LIQUID
# 1 -> FCC_L12
#
# Molar volume of phase 0 (LIQUID)? [cm**3/mol]
# Options: manual database [temp_extrapol] [conc_extrapol]
database
# Molar volume of phase 1 (FCC_L12)? [cm**3/mol]
# Options: manual database [temp_extrapol] [conc_extrapol]
database
# TQ update-interval for molar volumes [s] ?
1.0000
# Temperature at which the initial equilibrium
# will be calculated? [K]
920.0000
#
#
# Initial concentrations
# ======================
# How shall initial concentrations be set?
# Options: input equilibrium from_file [phase number]
equilibrium
# Initial concentration of component 1 (MG) in phase 0 (LIQUID) ? [wt%]
0.4100000000
# Initial concentration of component 2 (SI) in phase 0 (LIQUID) ? [wt%]
1.010000000
# 1D far-field diffusion approximation was set.
# From which distance from the front should the diffusion be
# solved as 1D? [micrometers]
10.0000000000000
# This distance is equivalent to 143 cells.
# How shall concentration of 1D extension for component 1 be set?
# Options: constant from_file
constant
# How shall concentration of 1D extension for component 2 be set?
# Options: constant from_file
constant
#
#
# 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]
920.0000
# Temperature gradient in z-direction? [K/cm]
727.00
# Cooling rate? [K/s]
-14515
# Moving-frame system in z-direction?
# Options: moving_frame no_moving_frame
no_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
ssii
#
# 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
sssf
# Fixed value for concentration field for component 1 in T-direction
0.41000
# Fixed value for concentration field for component 2 in T-direction
1.0100
# Unit-cell model symmetric with respect to the x/y diagonal plane?
# Options: unit_cell_symm no_unit_cell_symm
no_unit_cell_symm
#
#
# Other numerical parameters
# ==========================
# Phase minimum?
1.00E-04
# Interface thickness (in cells)?
3.00
```

Thanks in advance and best regards,

Yongliang Ou