Spatially Resolved Pair Correlation Functions
for Structure-Processing Taxonomies
DATASOURCES
Chandler Becker
Al Molecular...
μInformatics is material AGNOSTIC statistical framework aimed to distill
rich physical data into tractable forms that faci...
Hey, I don’t
know what
direction to
hold this
microscope
image so I’m
going home!
MATERIAL / population RVE / sample
Mater...
reveal
Statistical correlations between random points in space/time which reveal systematic patterns
in the microstructure...
Evenly Gridded
Spatial Domain
& Outside Cell
Inside Cell
k-d tree range to
find point indices in
each partition
8
47
22
An...
ot make dumb coding mistakes I will not make dumb coding mistakes I will not
ot make dumb coding mistakes I will not make ...
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...
POLYMER SIMULATIONSXin Dong, Karl Jacobs,GA Tech
Each point indicates
the statistics, or a
structure, in a simulation.
Eac...
Al Molecular Dynamics
Chandler Becker, NIST
Liquid
Crystalline
SOLIDIFICATION
OF AL-CU ALLOYS20% Vf
15% Vf
Peter Voorhees, John Gibbs
Northwestern University
Interfacial curvatures betw...
Chandler Becker
Al Molecular Dynamics
Peter Voorhees, John Gibbs
X-CT Al-Cu Solidification
Karl Jacobs, Xin Dong
Polymer M...
Spatially resolved pair correlation functions for structure processing taxonomies - ICME 2013
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Spatially resolved pair correlation functions for structure processing taxonomies - ICME 2013

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Presentation given at the Integrated Computational Materials Engineering conference 2013. This presentation provides a brief survey of what spatial correlation functions can provide for point cloud microstructure datasets. This method is applicable to very large (~1,000,000 datapoints) both experimental and computational microstructure datasets. It is applied to Aluminum molecular dynamics simulations provided by Chandler Becker at NIST, molecular dynamics simulations of mechanical deformation of polymer materials provided by Karl Jacobs and Xin Dong at Georgia Tech, and lastly experimental datasets of the solidfication of Al-Cu alloys generated from X-ray Computed Tomography as provided by Peter Voorhees and John Gibbs at Northwestern University.

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

  1. 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. 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. 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. 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. 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. 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,…
  7. 7. Correlation Function Visualization
  8. 8. Correlation Function Visualization
  9. 9. Correlation Function Visualization
  10. 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. 11. 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
  12. 12. Al Molecular Dynamics Chandler Becker, NIST Liquid Crystalline
  13. 13. 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
  14. 14. 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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