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The Third International Workshop on DFT Applied to Metals and Alloys. Integrating Informatics with First Principle Calculations: Building a Materials Genome project. Krishna Rajan NSF International Materials Institute Combinatorial Sciences and Materials Informatics Collaboratory CoSMIC-IMI

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slide1

The Third International Workshop on DFT Applied to Metals and Alloys

Integrating Informatics with First Principle Calculations: Building a Materials Genome project

  • Krishna Rajan
    • NSF International Materials Institute
    • Combinatorial Sciences and Materials Informatics Collaboratory
    • CoSMIC-IMI
    • Department of Materials Science and Engineering
    • Iowa State University

May 3rd 2007

slide2

OVERVIEW

  • What is “materials informatics” ?
  • What is the link between first principle calculations and informatics?
      • Mining latent variables…eg. CASTEP
      • Establish virtual libraries
      • DFT a source of data for subsequent data mining
      • Clustering analysis of attributes….use DFT for final screening of stability ---suggesting crystal structures that yet need to be determined
  • Challenge for international collaboration
    • An virtual DFT toolkit combining data, DFT codes and informatics algorithms
    • CoSMIC infrastructure

Krishna Rajan

slide3

WHY MATERIALS INFORMATICS?

  • Potential of informatics:
  • Management of informational complexity
  • Accelerated discovery
  • Identifying new pathways
  • Building new learning communities through cyber-infrastructure
  • Realizing the potential:
  • Data mining and statistical learning
  • Cyber infrastructure
  • Research platforms
  • Impact on education – new paradigm for materials education

Krishna Rajan

slide4

DATA MINING and KNOWLEDGE DISCOVERY

Interpretation

Data Mining

& Visualization

Feature Extraction

Data

Warehousing

Knowledge

Patterns

Transformed

Data

  • Reducing the dimensionality of data offers
    • Identify the strongest patterns in the data
    • Capture most of the variability of the data by a small fraction of the total set of dimensions
    • Eliminate much of the noise in the data making it beneficial for both data mining and other data analysis algorithms

Original

Data

slide5

DATA DRIVEN MATERIALS SCIENCE

Data + Correlations + Theory =Knowledge Discovery

  • Combinatorial
  • experimentation
  • Digital libraries
  • & data bases
  • Atomistic based
  • calculations
  • Continuum based
  • theories
  • Materials discovery
  • Structure-property-processing
  • relationships
  • Hidden data trends
  • Data mining
  • Dimensionality
  • reduction

+

+

=

Information is multivariate, diverse , very large and access / expertise is globally distributed

slide6

INFORMATICS BASED DESIGN STRATEGIES

Ideker and Lauffenburger:(2003)

slide7

PRINCIPAL COMPONENT ANALYSIS: PCA

From a set of N correlated descriptors, we can derive a set of N uncorrelated descriptors (the principal components). Each principal component (PC) is a suitable linear combination of all the original descriptors. PCA reduces the information dimensionality that is often needed from the vast arrays of data in a way so that there is minimal loss of information

.

( from Nature Reviews Drug Discovery1, 882-894 (2002) : INTEGRATION OF VIRTUAL AND HIGH THROUGHPUT SCREENING Jürgen Bajorath   ; and Materials Today; MATERIALS INFORMATICS , K. Rajan , October 2005

slide8

Functionality 1 = F ( x1 , x2 , x3 , x4 , x5 , x6 , x7 , x8 ……)

Functionality 2 =F ( x1 , x2 , x3 , x4 , x5 , x6 , x7 , x8 ……)

I

…….

X1 = f ( x2)

X2 = g( x3)

X3= h(x4)

PC 1= A1 X1 + A2 X2 + A3 X3 + A4 X4 …….

PC 2 = B1 X1 + B2 X2 + B3 X3 +B4 X4 …….

PC 3 = C1 X1 + C2 X2 + C3 X3 + C4 X4…….

II

III

…….

slide9

Miedema map (’73)

Mooser-Pearson map (’59)

Villars map (’83)

Makino map (’94)

slide10

Stage 1

Stage 2

Mixing rules

Modeling & calculation

Elemental properties

Compound properties

(E.N.)A, (E.N.)B

(V.E.)A, (V.E.)B

(Rs+p)A, (Rs+p)B

E.N.

V.E.

Rs+p

Experimental database

AxBy Compounds

Compound properties

(structure descriptors)

For AB2, AB3, A2B3, A3B5

89 elements×88

= 7832 compounds

For AB compounds

½×(89 elements×88)

= 3916 compounds

slide11

HIGH DIMENSIONAL STRUCTURE MAPS : 3d

Unknown compound

Possible structure type

candidates

slide13

ASSOCIATION MINING:

Establishing association rules for crystal

chemistry

Krishna Rajan

slide14

TRACKING the PATHWAY for a CRYSTAL STRUCTURE

<

INPUT: AuBe2

elemental parameters

∆X = 0.85978

ΣVE = -0.30361

∆Rzs+p= 0.61403

∆nav = -1.61573

∆nws1/3 = -0.93887

2x∆X = -0.14441

∆Φ* = -1.68529

1

Structure decision route

2

Possible structure types of AuBe2

3

OUTPUT: Structure type

candidates list

1. MgCu2 (-3.65757 eV)

2. PbCl2(-3.60992 eV)

3. OsGe2 (-3.58157 eV)

4. CaF2 (-3.46498 eV)

5. AlB2 (-3.46430 eV)

First principles calculations

slide16

CRYSTAL CHEMISTRY DESIGN

Chinget.al J. Amer. Ceram.Soc. 85 75-80 (2002)

1. Assess influence of latent

variables ( i.e. electronic structure parameters) on properties of known data

2. Establish heuristic relationships on database of all input variables instead of phenomenological relationships in bivariate manner

3. Use statistical learning to

predict new materials behavior

on new multivariate input data

4. Inverse problem approach to formulate quantitative structure-property relationships

Krishna Rajan

slide17

Bond length

along body diagonal of unit cell, Wycoff notation) Lattice sites along the cubic unit cell body diagonal in the spinel, AB2X4

Polyhedral Volume

Interbond angle

A-X-B, X-A-X

B-X-B, X-B-X

A-X-A

slide18

Combinatorial selection of Spinel Nitride(AB2N4)

Bond length

Interbond angle

A-X-B, X-A-X

B-X-B, X-B-X

A-X-A

Polyhedral Volume

slide21

As distance from origin of PCA plot increases, the intensity of DOS peak is increased

Can quickly determine:1) Co-Al and Ni-Al alloys have DOS mostly below EF and Ti-Al alloys and Al have DOS mostly above EF.

2) DOS at EF highest for Co3Al and Ti-Al alloys.

All of these conclusions are correct

Demonstrate the usefulness of PCA in screening for these above points --- more useful as number of systems examined is increased

Co3Al

TiAl/ TiAl3

Al

CoAl/NiAl

Ni3Al

Blue: E < EF

Red: E > EF

slide22

Benefits of using PCA to examine entire DOS curves :

  • Accomplished:
  • 1) Remove energies that just provide background -- fewer energies to consider
  • 2) New way to visualize DOS curves, many figures converted to 1 figure -- once full interpretation is understood, much more convenient
  • 3) Classify alloy structures based on quantum structure
  • 4) Can quickly screen and visualize which DOS peaks are below or above EF, and can determine which alloys have the largest DOS value at EF
  • Longer term:
  • 1) Use plot to quickly visualize other effects, such as peak shifts, double peaks, etc.
  • 2) Compare to other properties to determine which DOS at a certain energy determine properties
  • 3) Understand many more features of the DOS curve
slide23

Normalize the DOS curves by shifting the curves so that EF of each alloy is at the same energy

Reason for doing this:

Two common things looked at in literature on DOS curves.

DOS relative to EF and DOS value at EF

We can quickly screen if an alloy’s DOS are primarily above or below EF.

Among a series of alloys, we can say which alloys have a high value of EF

EF

slide25

Computational Informatics

  • Searching for patterns of behavior among multivariate data sets
  • Can pattern recognition lead to predictions?
  • Establish new correlations
  • Identify outliers
  • Enlarge database / virtual libraries
  • Evaluate databases
  • Establish predictions
slide26

Objective / Rationale:

  • Accelerated discovery of new
  • materials, processes and mechanisms using
  • informatics / combinatorial methods
  • Global “E-science” virtual laboratory
  • and educational portal
  • International research / learning
  • community
  • International Materials Network:
  • Database and data mining network
  • Materials domain networks
  • IMI network
  • Network of NSF leveraged programs :
  • Intl. professional materials societies/ Intl. Agencies network
  • Int. Student exchange / research network / diversity
  • Approaches:
  • “Rational drug design” approach to
  • materials discovery (in-silicomaterials science)
    • combinatorial- high throughput
    • screening
    • informatics and data mining
  • Cyber infrastructure:
    • Ultra large scale databases
    • Data sharing and high performance computing
  • Research / Education Accomplishments:
  • Materials discovery:
    • Materials education:
    • Informatics for materials science

http://www.mse.iastate.edu/cosmic