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Spatially Resolved Pair Correlation Functions
for Structure-Processing Taxonomies
DATASOURCES
Chandler Becker
Al Molecular Dynamics
Peter Voorhees, John Gibbs
X-CT Al-Cu Solidification
Karl Jacobs, Xin Dong
Polymer MD
MAT
SCI
DATA
SCI
Tony Fast
Materials Data Analyst
μInformatics is material AGNOSTIC statistical framework aimed to distill
rich physical data into tractable forms that facilitate structural
taxonomies and bi-directional structure-property/processing
homogenization and localization relationships. It provides a foundation
for rigorous microstructure sensitive materials design.
3 Statistical Modules
5 Value Assessment
4
Data-Mining Modules
2
μS Signal Processing Modules
Experiment &
Simulation
Objective &
Subjective μS
metrics
DSP and image
segmentation
“HUGE influence on μI”
1
Physical Models
DSP
Spatial
Statistics
MKS Dimension
Reduction
MICROSTRUCTURE
INFORMATICS (μI)
Hey, I don’t
know what
direction to
hold this
microscope
image so I’m
going home!
MATERIAL / population RVE / sample
Materials science Statistics
?
? ?
Difference Between
Direct comparison of microstructures is most often
impractical which demands novel statistical interpretations.
Statistically speaking,
you probably never
will, so stay here and
use some statistics!
reveal
Statistical correlations between random points in space/time which reveal systematic patterns
in the microstructure. Contains the original μS within a translation & inversion.
Difference
Between
MaterialInformation
SpatialCorrelation Objective
Comparison
𝑚 𝑠
ℎ A digital signal of the microstructure at a position maybe voxel in the volume, s,
of S total positions for a channel, h, of H total channels. The channels describe
material features (e.g. phase, angle, curvature) using a prescribed basis function.
𝑓𝑟
ℎℎ′
=
1
𝑆
𝑚 𝑠
ℎ 𝑚 𝑠+𝑟
ℎ′
𝑆
𝑠=1
Evenly Gridded
Spatial Domain
& Outside Cell
Inside Cell
k-d tree range to
find point indices in
each partition
8
47
22
An Algorithm for Point
Cloud Spatial Statistics
Provides a look-up table
for material features
Build a kd-tree & partition the spatial domain
Build: O(N) & Search: O(log(N))
ot make dumb coding mistakes I will not make dumb coding mistakes I will not
ot make dumb coding mistakes I will not make dumb coding mistakes I will not
ot make dumb coding mistakes I will not make dumb coding mistakes I will not
ot make dumb coding mistakes I will not make dumb coding mistakes I will not
ot make dumb coding mistakes I will not make dumb coding mistakes I will not
ot make dumb coding mistakes I will not make dumb coding mistakes I will not
t make dumb coding mistakes I will not make dumb coding mistakes I will not
t make dumb coding mistakes I will not make dumb coding mistakes I will not
t make dumb coding mistakes I will not make dumb coding mistakes I will not
t make dumb coding mistakes I will not make dumb coding mistakes I will not
t make dumb coding mistakes I will not make dumb coding mistakes I will not
t make dumb coding mistakes I will not make dumb coding mistakes I will not
t make dumb coding mistakes I will not make dumb coding mistakes I will not
t make dumb coding mistakes I will not make dumb coding mistakes I will not
t make dumb coding mistakes I will not make dumb coding mistakes I will not
t make dumb coding mistakes I will not make dumb coding mistakes I will not
t make dumb coding mistakes I will not make dumb coding mistakes I will not
Combining Domains - The μS Function
𝑚 𝑠′
ℎ is the average of the weighted average of Legendre Polynomials of the
processed digital signal in each partition.
8
47
22
𝑚 𝑠′
ℎ =
𝐴𝑖 𝑚𝑖
ℎ
𝑖∈𝑃
𝐴𝑖𝑖∈𝑃
Position of the Partition(𝑠′
)
𝑑𝑥
Material Features: Orientation, Phase, Category, Curvature, Volume Fraction,…
Correlation Function
Visualization
Correlation Function
Visualization
Correlation Function
Visualization
HEAT TREATED α-β TITANIUMMicrostructure Taxonomies
Albeit these datasets are sampled from different
processing routes, the taxonomy is a structure-structure relationship that doesn’t
track processing history because the images are sampled after heat treatment.
Principal Components Analysis
Reduces D variables to d variables. Each axis corresponds to the
i-th greatest direction of variance.
Kalidindi, Surya R.; Niezgoda, Stephen R.; Salem, Ayman A
,"Microstructure informatics using higher-order statistics and efficient data-mining protocols", "JOM" , 2011
POLYMER SIMULATIONSXin Dong, Karl Jacobs,GA Tech
Each point indicates
the statistics, or a
structure, in a simulation.
Each color is a different
initial structure & lines
track history.
Initial
Stages
★Final
Structure
Al Molecular Dynamics
Chandler Becker, NIST
Liquid
Crystalline
SOLIDIFICATION
OF AL-CU ALLOYS20% Vf
15% Vf
Peter Voorhees, John Gibbs
Northwestern University
Interfacial curvatures between Al & Cu
during solidification rendered from X-CT
2 different volume fractions
Chandler Becker
Al Molecular Dynamics
Peter Voorhees, John Gibbs
X-CT Al-Cu Solidification
Karl Jacobs, Xin Dong
Polymer MD
Le Fin

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Spatially resolved pair correlation functions for structure processing taxonomies - ICME 2013

  • 1. Spatially Resolved Pair Correlation Functions for Structure-Processing Taxonomies DATASOURCES Chandler Becker Al Molecular Dynamics Peter Voorhees, John Gibbs X-CT Al-Cu Solidification Karl Jacobs, Xin Dong Polymer MD MAT SCI DATA SCI Tony Fast Materials Data Analyst
  • 2. μInformatics is material AGNOSTIC statistical framework aimed to distill rich physical data into tractable forms that facilitate structural taxonomies and bi-directional structure-property/processing homogenization and localization relationships. It provides a foundation for rigorous microstructure sensitive materials design. 3 Statistical Modules 5 Value Assessment 4 Data-Mining Modules 2 μS Signal Processing Modules Experiment & Simulation Objective & Subjective μS metrics DSP and image segmentation “HUGE influence on μI” 1 Physical Models DSP Spatial Statistics MKS Dimension Reduction MICROSTRUCTURE INFORMATICS (μI)
  • 3. Hey, I don’t know what direction to hold this microscope image so I’m going home! MATERIAL / population RVE / sample Materials science Statistics ? ? ? Difference Between Direct comparison of microstructures is most often impractical which demands novel statistical interpretations. Statistically speaking, you probably never will, so stay here and use some statistics!
  • 4. reveal Statistical correlations between random points in space/time which reveal systematic patterns in the microstructure. Contains the original μS within a translation & inversion. Difference Between MaterialInformation SpatialCorrelation Objective Comparison 𝑚 𝑠 ℎ A digital signal of the microstructure at a position maybe voxel in the volume, s, of S total positions for a channel, h, of H total channels. The channels describe material features (e.g. phase, angle, curvature) using a prescribed basis function. 𝑓𝑟 ℎℎ′ = 1 𝑆 𝑚 𝑠 ℎ 𝑚 𝑠+𝑟 ℎ′ 𝑆 𝑠=1
  • 5. Evenly Gridded Spatial Domain & Outside Cell Inside Cell k-d tree range to find point indices in each partition 8 47 22 An Algorithm for Point Cloud Spatial Statistics Provides a look-up table for material features Build a kd-tree & partition the spatial domain Build: O(N) & Search: O(log(N))
  • 6. ot make dumb coding mistakes I will not make dumb coding mistakes I will not ot make dumb coding mistakes I will not make dumb coding mistakes I will not ot make dumb coding mistakes I will not make dumb coding mistakes I will not ot make dumb coding mistakes I will not make dumb coding mistakes I will not ot make dumb coding mistakes I will not make dumb coding mistakes I will not ot make dumb coding mistakes I will not make dumb coding mistakes I will not t make dumb coding mistakes I will not make dumb coding mistakes I will not t make dumb coding mistakes I will not make dumb coding mistakes I will not t make dumb coding mistakes I will not make dumb coding mistakes I will not t make dumb coding mistakes I will not make dumb coding mistakes I will not t make dumb coding mistakes I will not make dumb coding mistakes I will not t make dumb coding mistakes I will not make dumb coding mistakes I will not t make dumb coding mistakes I will not make dumb coding mistakes I will not t make dumb coding mistakes I will not make dumb coding mistakes I will not t make dumb coding mistakes I will not make dumb coding mistakes I will not t make dumb coding mistakes I will not make dumb coding mistakes I will not t make dumb coding mistakes I will not make dumb coding mistakes I will not Combining Domains - The μS Function 𝑚 𝑠′ ℎ is the average of the weighted average of Legendre Polynomials of the processed digital signal in each partition. 8 47 22 𝑚 𝑠′ ℎ = 𝐴𝑖 𝑚𝑖 ℎ 𝑖∈𝑃 𝐴𝑖𝑖∈𝑃 Position of the Partition(𝑠′ ) 𝑑𝑥 Material Features: Orientation, Phase, Category, Curvature, Volume Fraction,…
  • 10. HEAT TREATED α-β TITANIUMMicrostructure Taxonomies Albeit these datasets are sampled from different processing routes, the taxonomy is a structure-structure relationship that doesn’t track processing history because the images are sampled after heat treatment. Principal Components Analysis Reduces D variables to d variables. Each axis corresponds to the i-th greatest direction of variance. Kalidindi, Surya R.; Niezgoda, Stephen R.; Salem, Ayman A ,"Microstructure informatics using higher-order statistics and efficient data-mining protocols", "JOM" , 2011
  • 11.
  • 12. POLYMER SIMULATIONSXin Dong, Karl Jacobs,GA Tech Each point indicates the statistics, or a structure, in a simulation. Each color is a different initial structure & lines track history. Initial Stages ★Final Structure
  • 13. Al Molecular Dynamics Chandler Becker, NIST Liquid Crystalline
  • 14. SOLIDIFICATION OF AL-CU ALLOYS20% Vf 15% Vf Peter Voorhees, John Gibbs Northwestern University Interfacial curvatures between Al & Cu during solidification rendered from X-CT 2 different volume fractions
  • 15. Chandler Becker Al Molecular Dynamics Peter Voorhees, John Gibbs X-CT Al-Cu Solidification Karl Jacobs, Xin Dong Polymer MD Le Fin