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Microstructure and Materials Informatics

University of Florida - May 20th 2013

Krishna Rajan

Microstructural Data and Information Role of informatics and microstructure Microscopy and informatics - SEM - TEM - APT Summary

Outline

Krishna Rajan: Iowa State University

1. “Crystallographic Evolution in Directionally Solidified Microstructures” J. Trogolo and

K.Rajan in Microstructure Evolution: Characterization and Modeling, pp.39-47 eds. J. Dantzig and S. Marsh, TMS ,Warrendale (1998)

2. Microtexture and Anisotropy in Wire Drawn Copper”, R.Petkie and K.Rajan Materials Science and Engineering A 257 185-197 ( 1998).

3. Rodrigues-Frank Representations of Crystallographic Texture in Electron Backscatter Diffraction in Materials Science Eds. Schwartz, A.J.; Kumar, M.; Adams, B.L pp. 39-50 Kluwer Academic NY (2000).

4. Refining Spatial Distribution Maps for Atom Probe Tomography via Data Dimensionality Reduction Methods". S.K.Suram and K.Rajan ; Journal of Microscopy and Microanalysis 18 , 941-952 (2012)

5. "A Graph-Theoretic Approach for Characterization of Precipitates in Alloys from Atom Probe Tomography data S. Samudrala, O. Wodo, S. K. Suram, S. Broderick, K. Rajan, B. Ganapathysubramanian, " Computational Material Science, vol. , (in press-2013)

6. Data Mining for Isotope Discrimination in Atom Probe Tomography: S.R. Broderick, A. Bryden, S.K. Suram and K. Rajan : Ultramicroscopy (in press - , http://dx.doi.org/10.1016/j.ultramic.2013.02.001 -2013)

References

Krishna Rajan: Iowa State University

Multidimensional

Microstructural characteristics

Features controlling microstructure –property relationships

Challenge:

To construct Robust Correlations

between microstructure, chemistry, processing and properties

Methods:

Data analysis

•Statistical learning

Materials modeling

•Electronic structure

•Microstructure

•Continuum property

Informatics

Materials functionality= F ( x1 , x2 , x3 , x4 , x5 , x6 , x7 , x8 ……)

Krishna Rajan: Iowa State University

Signal and Spatial Domains

Krishna Rajan: Iowa State University

Signal and Spatial Domains

Krishna Rajan: Iowa State University

N. Bonnet J. Microscopy 190 2-18 (1997)

G. Mobus, R. Schweinfest, T. Gemming, T. Wagner and M. Ruhle J. Microscopy vol 190 , pts 1 / 2 April / May 1998 , pp. 109-130

Data Cube

Krishna Rajan: Iowa State University

Krishna Rajan: Iowa State University

Mechanical property- microstructure data cube

Mechanical property- microstructure data cube

Krishna Rajan: Iowa State University

Mechanical property- microstructure data cube- outlier detection

Krishna Rajan: Iowa State University

Mechanical property- microstructure data cube- outlier detection

Krishna Rajan: Iowa State University

Mechanical property- microstructure data cube- outlier detection

Krishna Rajan: Iowa State University

Krishna Rajan: Iowa State University

Informatics guided imaging: where to look

“Crystallographic Evolution in Directionally Solidified Microstructures” J.

Trogolo and K.Rajan in Microstructure Evolution: Characterization and Modeling, pp.39-47 eds. J. Dantzig and S. Marsh, TMS ,Warrendale (1998

N data channels

Energy loss

DE

E

DE

Extracted image spectrum

K.Kelton, X.Li and K. Rajan J. Non-Crystalline Solids (2005)

Al-RE-Ni Glass

x

y

Krishna Rajan

Chemistry- microstructure data cube- correlation imaging

Krishna Rajan: Iowa State University

Atom Probe : imaging modalities

Krishna Rajan: Iowa State University

Atom Probe : a multidimensional problem

Krishna Rajan: Iowa State University

Chemical Noise Chemical Noise f(Crystal structure, pulse energy, pulse fraction, surface diffusion, specimen geometry …) .

APT

Spatial Noise in APT

Spatial Noise f(Crystal structure, dhkl , missing data, local magnification effects, reconstruction errors, pulse energy, pulse fraction, surface diffusion …)

Phenomenological relationships between most of these parameters and their effect on spatial/chemical noise are unknown. Thus, data driven treatment is necessary for analysis of noise in APT data.

Signal/ Noise enhancement

Krishna Rajan: Iowa State University

PCA

NLDR

Geometric

Distance

Euclidian Geodesic

(eg. IsoMap)

Other

(eg. KPCA)

Topology

PDL

(eg. SOM)

DDL (eg. LLE)

Other

AA NN

Data dimensionality reduction

Krishna Rajan: Iowa State University

Spatial –Signal Domain noise

Krishna Rajan: Iowa State University

Plane A Plane B

Anti-correlation

d110

A B A B A B A B A

Ideal Material

APT data

z-SDMs d0

11

Crystal structure can be observed

and anti-correlation in the

structure between adjacent planes is

observed

Does this slice have any crystallographic information. Can we salvage this information?

Spatial –Signal Domain noise

Krishna Rajan: Iowa State University

(40000*200)

Right Singular Vectors capturing correlations in the SDM data

Projection of SDM data onto right singular vectors

Spatial –Signal Domain noise : quantification

Krishna Rajan: Iowa State University

Noise Reduction achieved consists of two aspects: Noise reduction based on data reconstruction using only the Structural Relevant Singular

Vectors. Noise reduction by identifying xy-SDMs that contribute to noise within the SRSVs.

EVSUX T

SRSVSRSVSRSV

(40000x200)

Structure Signal Noise alienated in the error term.

Spatial –Signal Domain noise : quantification

Krishna Rajan: Iowa State University

Sectioning of Data set

Eigenvalue Decomposition

(PCA)

TOF

Load

ings

Co

un

t

TOF

Raw TOF Spectra: No obvious patterns

Eigenspectra: “Hiddn” patterns

Spatial –Signal Domain noise : uncovering “hidden” patterns

Krishna Rajan: Iowa State University

Data Mining for Isotope Discrimination in Atom Probe Tomography: S.R. Broderick, A. Bryden, S.K. Suram and K. Rajan : Ultramicroscopy (in press - , http://dx.doi.org/10.1016/j.ultramic.2013.02.001 -2013)

24Mg2+

25Mg2+ 26Mg2+

27Al2+

Mg2+ Al2+

Before After

TOF TOF

Spatial –Signal Domain noise : uncovering “hidden” patterns

Krishna Rajan: Iowa State University

Data Mining for Isotope Discrimination in Atom Probe Tomography: S.R. Broderick, A. Bryden, S.K. Suram and K. Rajan : Ultramicroscopy (in press - , http://dx.doi.org/10.1016/j.ultramic.2013.02.001 -2013)

What data do we need?

Krishna Rajan: Iowa State University

Extracting information beyond models and experiment 3D imaging Quantification of uncertainty and noise Stereology: back to basics

Summary

Krishna Rajan: Iowa State University