GA Tech: S.R. Kalidindi, D.M. Turner, LANL: S.R. Niezgoda, Drexel: A. Cecan, C. Kumbur, Teledyne: B. Cox, LLNL: H. Bale, ISU: O. Wodo,

Basker G., Dartmouth: U. Wegst, OSU: H. Fraser, P. Collins

Novel and Enhanced Structure-Property-Processing Relationships with Microstructure Informatics

Tony Fast

University of California Santa Barbara

Materials Department

PSED seminar at Northwestern, November 8, 2012

U. Wegst, Dartmouth

H. Bale, LLNL

From Materials Selection

Materials selection relies on effective material descriptors.

From Materials Selection to Microstructure (μS) Informatics…

Advances in characterization and computational materials science are contributing to the materials data deluge.

H. Fraser, OSU.

Each module is self-contained

μInformatics workflow is a systemA robust paradigm to address dimensionality challenges in materials science

μInformatics is material and hierarchy independent statistical framework aimed to distill rich physical data into tractable forms that facilitate structural taxonomies and bi-direction

structure-property-processing homogenization and localization relationships.

Future Work

Image Segmenting identifies important features of the μSA necessary evil in data-driven materials science

Hough transform Methods

Raw Segmented(EM/MPM) @ bluequartz.net

Segmentation

Modules

Image Segmentation uses DSP methods to minimize the human interaction necessary to analyze digital images. Most problems problems are subjective and ill-posed.

Ceramic Matrix Composite

Virtual Metallic

Kalidindi, S.R., S.R. Niezgoda, and A.A. Salem, Microstructure informatics using higher-order statistics and efficient data-mining protocols. JOM, 2011. 63(4): p. 34-41.

First-Order Higher-Order

Discrete

Continuous

H

hs

hhs vm

1

10,11

hs

H

h

hs mmPrimitive Basis

Function

nsm

nm1nm3

nm5

nm6

nm2

poreblack

solidwhitem

s

shs /1

/0

N

N

hts

hts

hs

hs mmmm 1

1

0~~

Gradients contain local conformation

Local conformation of pixels

ssss ,,~

210~~ h

shs

hs

hs mmmm

shs fm 1 sh

s fm 2

Segmentation

Modules

The primitive basis converts any μS to a digital signalInformatics benefit from a generalized higher-order microstructure description

Extensible to any number of discrete phases

Other Basis Functions: Legendre, Generalized Spherical Harmonics, Chebyshev

𝑓 𝑟hh′= 1

𝑆∑𝑠=1

𝑆

𝑚𝑠h𝑚𝑠+𝑟

h′

A. 2-pt Correlation Function – Statistical correlation between random points in space/time and reveals systematic patterns in the microstructure

B. Chord Length Distribution – length and orientation of chords in a heterogeneous medium

C. Interfacial Surface Distribution - The principal curvatures of surfaces in the μS.

A.

B. C.

Statistical distributions are the crux of μInformaticsDistributions capture traditional effective statistical measures

Chen et al., Morphological and topological analysis of coarsened nanoporous gold by x-ray nanotomography, Advanced Physics Letters 2010.

The rich internal structure of the material is the microstructure. However, the μSprovides statistical, not deterministic material information.

Statistical

Modules

The Microstructure as a stochastic processDistributions provide a framework to effectively compare microstructures

Mic

rost

ruct

ure

Aut

ocor

rela

tion

-

- =

=

HT1.1 HT1.2 Difference

The direct comparison of the μS is useless due to the lack of origin.

(+) Provide a ground truth and metric space for comparison, or there is a natural origin(+) Autocorrelation contains all of the information in its respective μS.

(+) Amenable to homogenization and localization relationships (-) Very large dimensionality

Statistical

Modules

Data-mining modules are the vehicle for linkagesDimensionality reduction, classification, and regression

Regression methods allow the salient microstructure features to be connected with homogenized and localized materials static and evolving properties. (Structure-Property and Structure-Processing)

Dimension reduction converts large dimensional data (D) to a reduced

space (d) based upon specfic characteristics of the data

Clustering and classification provide methods to automatically identify microstructures with certain performance or structural criterion. Ideal for searching the intrinsically large space of microstructures.

Data-Mining

Modules

Maaten, et al., Dimension Reduction: A Comparative Review, Tilburg centre for Creative Computing, Tilburg University, 2009.

Linear dimension reduction with PCADimension reduction to deal with the scale of data

Principal Component Analysis, Wikipedia

Data-Mining

Modules

Principal Component Analysis: Reduced embedding of linearly independent variables that correspond to decreasing levels of variance starting with the highest (Dd)

PCA (most DR methods) require a natural origin for the data-points

PCA is typical for linear systems and exploratory data analysis.

Many nonlinear techniques exist.

Sensitivity – metric for accurate classification

Specificity – metric for accurate nonclassification

Range between 0 and 1

k-Means Clustering: A data-mining approach that creates cluster partitions based on the means of clusters to automatically classify datapoints.

k-Means clustering for automatic feature recognitionQuantitative data-mining techniques

Classification cases - compare training classes to predicted classes

TP – Correct classificationTN – Correct nonclassificationFP – Incorrect classificationFN – Incorrect nonclassification

Data-Mining

Modules

K-means Clustering, Wikipedia

W Improved homogenization relationships for diffusivity in porous media (sProp)

Localization meta-model for the evolution of a binary alloy (sProc)

Localization meta-model for medium contrast dual phase composites (sProp)

μS Taxonomy of α-β Ti (s-s)

μS Taxonomy of Organic Blends in Solar Cells (s-s)Data-MiningPCAAutocorrelationFirst-Order Signal130 Experiments

K-meansPCAAutocorrelationFirst-Order SignalN-pt StatisticsHigher-Order Signal1100 Simulations

RegressionPCAAutocorrelationFirst-Order SignalExperiments

RegressionN/AFirst-Order SignalSimulation

RegressionN/AHigher-Order Signal400 Simulation

μS informatics is a versatile framework that relies on workflowsPlug-n-play operations with modules provide solutions for diverse problems

μInformatics is a growing suite of modular functions that when combined into a workflow system provide solutions to traditional empirical relationships and

emerging big data in materials science. μInformatics can be seamlessly applied to 1-D, 2-D,3-D, and 4-D datasets generated empirically or computationally.

ORKFLOW OUTLINE

Data-driven structural diffusion coefficients in fuel cellsRegressionN/AFirst-Order SignalSimulation RegressionPCAAutocorrelationFirst-Order SignalExperiments

XCTFIB-SEM

MPL

GDL

RVE’s from the experimental data are input into a Fickian diffusion model to evaluate the diffusivity.

Each point is one RVE~1e6 variables

Data-driven fitting outperforms traditional fitting methods and extends the reach of the fit to both the GDL and MPL layers.

The Materials Knowledge SystemExtracting compact knowledge from boat loads of information

microstructure signal local response

Stress, strain, evolution

How can information about new structures be extracted?What knowledge is gained?

Many Inputs and Many Outputs Repetitive simulation is demanding

Simulation produces a lot of data, but what is determined about the system?

The Materials Knowledge SystemExtracting compact knowledge from boat loads of information

DSP representation of local structure-local response Localization relationship and its influence coefficients

Influence coefficients capture the combined point effects of the MS configuration on the local response

Strong implications on multi-scale modeling

microstructure signal local response influence coefficients

𝔍 (𝜀𝑠 )𝑘=∑𝑖=1

𝐼

𝐴❑𝑖𝑘𝑀

𝑖𝑘❑𝔍

An evolutionary meta-model for phase separation

A Materials Knowledge System for structure-processing relationships

Phase separation guided by a negative energy gradient Cahn Hilliard Relationship evolved by way of Euler forward

Double well potential free energy curve Simulated using Phase Field Model (PFM)

Concentration is continuous between spinodal points [.15, .23]- Bounds of microstructure

Interested in structure evolution of spinodal structure

a

a

aaa cK

dc

cdfcDc 22

Cahn JW. On spinodal decomposition. Acta Metallurgica 1961;9:795.

RegressionN/AFirst-Order SignalSimulation

Iterations of PFM used to calibrate coefficients Discretization contains 125 discrete points on a 20x20

spatial domain

Time derivative of concentration is captured extremely accurately by MKS method

IC provide accurate simulation resultsRegressionN/AFirst-Order SignalSimulation

• From an initial starting structure, ONE set of influence coefficients can be used to evolve the material structure

Time Derivative

MSE Error

IC are amenable to numerical integrationRegressionN/AFirst-Order SignalSimulation

Attenuated Error

Magnitude of influence coefficients decay rapidly with distance Influence coefficients can be easily extended to larger domains by

zero-padding with complexity

RegressionN/AFirst-Order SignalSimulation

Influence coefficients can be used to scale the simulation

63ta

Ø Padding

Original

63ta

Scaled

20x20:

100x100:

RegressionN/AFirst-Order SignalSimulation

Scaled linkages are provide accurate predictions

complexity vs. complexity

Time Derivative

MSE Error

RegressionN/AFirst-Order SignalSimulation

Scaled IC allow for scaled evolution simulations

Meta-modeling of moderate contrast strain fields in composites

A Materials Knowledge System for Structure-Property relationships

2

1

E

E

FEMε=5e-4

MICROSTRUCTURE

RESPONSE

Contrast (nonlinearity) – Young’s modulus ratio First-order microstructure descriptors are ineffective for high contrast

Results are presented for uniaxial 1-1 strain Calibrating coefficients for other modes is trivial

Random distribution of phases in 21x21x21 microstructure

RegressionN/AHigher-Order Signal400 Simulation

52

1 E

E10

2

1 E

E

Case 1: First Order Case 2 – 7: Second Order Case 8-9: Seventh Order

Influence coefficients accurately capture the response fieldsRegressionN/AHigher-Order Signal400 Simulation

HOIC of increasing order captures local information better Drastic improvement of linkages of FOIC

Accuracy has a strong dependence on nonlinearity

52

1 E

E10

2

1 E

E

Case 1: First Order Case 2 – 7: Second Order Case 8-9: Seventh Order

Different HOICs calibrated from 400 FEM simulations Training (calibration) set vs. Validation set describes how well

knowledge is captured

Accurate agreement between calibration and validationRegressionN/AHigher-Order Signal400 Simulation

Case 9: Seventh-Order to First Neighborhood and Second-Order to Sixth Neighborhoods

153 influences coefficients have finite memory and decay to zero at larger distances

FEM required 45 min on supercomputer MKS required 15 seconds on a desktop computer

MKS – NlogN(N)

Scalability of the influence coefficientsRegressionN/AHigher-Order Signal400 Simulation

Data-MiningPCAAutocorrelationFirst-Order Signal130 ExperimentsMicrostructure taxonomy of α-βTitanium

Kalidindi, S.R., S.R. Niezgoda, and A.A. Salem, Microstructure informatics using higher-order statistics and efficient data-mining protocols. JOM, 2011. 63(4): p. 34-41.

Each point in the PCA indicate ONE μS, or ~6e6 variables. Microstructures generated by similar heat treatments naturally

cluster together in the reduced embedding.

PCA EmbeddingH., Fraser, OSU

μS Taxonomy of Continuous Material States An Application to Organic Blends in Solar Cells

10% FAST PHASE SEPARATION 90% SLOW GRAIN COARSENING

FINAL STRUCTURES

11 Distinct TopologiesMany Topologies

Olga Wodo and Baskar Ganapathysubramanian at ISU.

Isosurfaces of atomic fraction1100 Datasets

Use data driven techniques to classify the final topology before the simulation is complete. i.e. Reduce Redundancy, Time Savings

End Goal

Develop Microstructure Taxonomies of the Final Structuresi.e. Build Utilities for Continuous Materials Features

First Goal

K-meansPCAAutocorrelationFirst-Order SignalN-pt StatisticsHigher-Order Signal1100 Simulations

Microstructure taxonomy of binary organic blendsK-meansPCAAutocorrelationFirst-Order Signal1100 Simulations

Each point describes 21^3 variables and each color is a different topology Binning and microstructure features effect the clustering quality

Hard clustering in the PCA space allows the final topologies to be classified qualitatively

Microstructure taxonomy of binary organic blendsK-meansPCAN-pt StatisticsHigher-Order Signal1100 Simulations

Different choices of local state descriptions lead to different levels of clustering

AF

FG

SGAF

FG

SG

AF – Atomic FractionFG – First GradientSG – Second Gradient

ClockwiseFG,SGAF,SGAF,FGAF,FG,SG

Quantitative Measures of Clustering

Sensitivity and specificity analysis of PCA embeddingK-meansPCAN-pt StatisticsHigher-Order Signal1100 Simulations

Class A

Class B

Class C

Good Identification Poo

r Ide

ntific

atio

n

PCA embedding can be used to visualize 3-D processing historyμInformatics collectively can visualize SPP linkages

Each path is defined by the spinodal decomposition and grain coarsening simulation. The paths are created by a reduced

embedding of the N-pt statistics of 21x21x21 periodic microstructures.

Structure-Processing MKSProcessing History

Structure-PropertyHomogenization

PCA embedding can be used to visualize 3-D processing historyμInformatics can collectively visualize bidirectional SPP linkages

Structure-PropertyLocalization