Spatially Resolved Pair Correlation Functions

for Structure-Processing Taxonomies

DATA

SO

UR

CES

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

Mate

rial In

form

atio

n

Sp

atia

l Co

rrela

tion

Objective

Comparison

𝑚𝑠ℎ 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.

𝑓𝑟ℎℎ′ =

1

𝑆 𝑚𝑠

ℎ𝑚𝑠+𝑟ℎ′

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))

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

I will not make dumb coding mistakes I will not make dumb coding mistakes I will not make dumb coding mistakes

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 =

𝐴𝑖𝑚𝑖ℎ

𝑖∈𝑃 𝐴𝑖 𝑖∈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 TITANIUM

Microstructure 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 SIMULATIONS Xin 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 ALLOYS 20% 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