ab initio crystal structure prediction: high-throughput and data mining dane morgan massachusetts...
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Ab Initio Crystal Structure Prediction:High-throughput and Data Mining
Dane Morgan
Massachusetts Institute of Technology
NSF Division of Materials Research
ITR Computational Workshop
June 17-19, 2004
Why Does Structure Matter? Essential for Rational Materials Design
Structure key to understand properties and performance
Key input for property computational modeling
Performance
Properties
Structure and
Composition
Processing
Why Do We Need Structure Predictions?Structural Information is Often Lacking
Binary alloys incomplete
Multi-component systems largely unknown
Massalski, Binary Alloy Phase Diagrams ‘90
The Structure Prediction Problem
Given elements A, B, C, … predict the stable low-temperature phases
Crystalline phasesAb initio methods
Present focus
Why is Structure Prediction Hard?
Ene
rgy
Atomic positions
Local minima
Global minimumTrue structure
Infinite structural space Rough energy surface – many local minima
Ab initio methods give accurate energies, but …
Two New Tools
Data MiningCalculated/Experimental
Databases
High-Throughput Ab Initio
High-Throughput Ab Initio
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1965 1975 1985 1995 2005
Lo
g(#
ca
lcu
lati
on
s)
Cheilokowsky and Cohen, ‘74
Si
Metals Database
~14,000 EnergiesCurtarolo, et al., Submitted ‘04
Robust methods/codesAutomated tasksParallel computation
Ab Initio Structure Prediction
Directly optimize ab initio Hamiltonian with Monte Carlo, genetic algorithms, etc. (too slow)
Simplified Hamiltonians – potentials, cluster expansion (fitting challenges, limited transferability/accuracy)
Intelligent guess at good candidates
Obtain a manageable list of likely candidate structures for high-throughput calculation
How good can this be?
“Usual Suspects” Structure List
80 binary intermetallic alloys176 “usual suspects” structures(“usual suspects” = Most frequent in CRYSTMET, hcp, bcc, fcc superstructures)
Metals Database
~14,000 Energies
Calculate energiesConstruct convex hullsCompare to experiment
High-Throughput Predictions
Metals Database
~14,000 Energies
95 predictions of new compounds
21 predictions for unidentified compounds
110 agreements
3 unambiguous errorsCurtarolo, et al., Submitted ‘04
But far too many structures + alloys to explore!! Need smart way to choose “sensible” structures!!
Data Mining
New alloy system A,B,C,…
Predicted crystal structure
DatabaseData Miningto choose
“sensible” structures
Data Mining with Correlations
Atomic positions
Ene
rgy
E( ) = E( )
E( ) = [E( ) + E( )]2
1
Linear correlations between energies
Faster to find low energies
All energies do not need to be calculated
Do linear correlations exist between structural energies across alloys?
Structural Energy Correlations Exist!
Principal Component Analysis identifies correlations
0
0.05
0.1
0.15
0.2
0.25
0 20 40 60 80 100% Total Degrees of Freedom
RM
S E
rro
r (e
V/a
tom
)
N structural energies from N/3 independent variables
True data
Randomized data
Using Correlations for Structure Prediction
Databasecalculated energies(AC, BC, etc.) + AB
New alloy system: AB
Predicted crystal structure
Correlations Predict likely stable structure i for alloy AB
Calculate Ei
Accurate convex hull?No
Yes
Data Mining Example: AgCd
Compound Forming Vs. Phase Separating
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60
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95 96 97 98 99 100Accuracy (%)
# C
alcu
lati
on
s
~2-8x speedup from Data Mining
No DM
With DM
Ground State Prediction
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20
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60
80
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50 60 70 80 90 100Accuracy (%)
# C
alcu
lati
on
s
No DM
With DM
~4x speedup from Data Mining
Conclusions
Future workMore experimental/computed dataMore data mining tools Web interface
Practical tool to predict crystal structure
High-throughput ab initio approaches are a powerful tool for crystal structure prediction.
Data Mining of previous calculations can create significant speedup when studying new systems.
Web Access to Database
Easy Interface Analysis: Convex hull, Ground States
Structural and Computational Data, Visualization
Collaborators/Acknowledgements
Collaborators Mohan Akula (MIT) Stefano Curtarolo (Duke) Chris Fischer (MIT) Kristin Persson (MIT) John Rodgers (NRC Canada, Toth, Inc.) Kevin Tibbetts (MIT)
FundingNational Science Foundation Information Technology Research (NSF-ITR) Grant No. DMR-0312537
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