Grain boundary structure initialization from atomic-resolution HAADF STEM imaging [wiki] [paper]
Getting started
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HAADF–STEM Image
This is an example of an atomic–resolution HAADF STEM image of a CdTe (100)-(110) grain boundary with tilt. In many optimization approaches, a solver might benefit from a good initial guess on where to start; That is what this code provides. It is assumed that the orientation and the chemical composition of each constituent crystal is known.
image credit: Guo, Jinglong,
Example Usage
Input chemistry & orientation information for each grain.
# Import main ingrained package modules
from ingrained.structure import Bicrystal
from ingrained.optimize import CongruityBuilder
# For top grain
grain_1 = {}
grain_1["chemical_formula"] = "CdTe"
grain_1["space_group"] = "F-43m"
# screen to viewer
grain_1["uvw_project"] = [1,1,0]
# upward on screen
grain_1["uvw_upward"] = [-1,1,0]
# CCW around "uvw_project"
grain_1["tilt_angle"] = 8
# maximum width (Å)
grain_1["max_dimension"] = 40
# For bottom grain
grain_2 = {}
grain_2["chemical_formula"] = "CdTe"
grain_2["space_group"] = "F-43m"
# screen to viewer
grain_2["uvw_project"] = [1,1,0]
# upward on screen
grain_2["uvw_upward"] = [0,0,1]
# CCW around "uvw_project"
grain_2["tilt_angle"] = 0
# maximum width (Å)
grain_2["max_dimension"] = 40
Initialize Bicrystal from grain information and setup optimization.
bicrystal = Bicrystal([grain_1,grain_2], \
minmax_width=(10,40), \
minmax_depth=(8,20))
# Use pixel scaling (dm3) to constrain size
if dm3lib.DM3(dm3_path).pxsize[1].decode('UTF-8') == 'nm':
pixsz = dm3lib.DM3(dm3_path).pxsize[0]*10
# Constraints
iw = [-1,2.5] # interface widths (Å)
df = [0.75,1.75] # defocus values (Å)
px = [0.85*pixsz,1.15*pixsz] # allowable pixel sizes (Å)
bx = [0.0,0.15] # x-border red. ratio (vert)
by = [0.0,0.15] # y-border red. ratio (horiz)
# Initialize ConguityBuilder to optimize fit
congruity = CongruityBuilder(bicrystal=bicrystal,dm3=dm3_path)
# Define a starting point for optimization
# | iw | df | bx | by | px |
x0 = [-0.1, 1.3, 0, 0.1, pixsz]
Perform constrained minimization using a COBYLA solver.
res1 = congruity.find_correspondence(optimizer='COBYLA', \
initial_solution=x0, constraint_list=[iw,df,bx,by,px])
⋮
Final Solution:
>>> IW : -0.6078157487413525
>>> DF : 1.4319874724494737
>>> PX : 0.163556437666011
>>> BX : 0.1542803492239945
>>> BY : 0.11378092964375788
🌀 FOM : 0.7996850224295375
Optimization terminated successfully.
Current function value: 0.799685
Iterations: 4
Function evaluations: 805
Example Output
The final parameterization provides an optimal correspondence solution between the experimental image and the proposed initial structure. Notice the high degree of similarity between the simulation and experiment!