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Alloy Electronic Structure and Structural Formation Energies and the CE
Duane D. Johnson
MatSE
University of Illinois at Urbana-Champaign
Phone: (217) 256-0319
Email: duanej ---> uiuc.edu
Nikolai Zarkevich
MatSE
University of Illinois at Urbana-Champaign
Email: zarkevich --->uiuc.edu
Lectures
- Electronic Structure Effects and Energies of Alloy Transformations (PDF, 5.3 MB)
- Basics of Cluster Expansions and Getting a Optimal Cluster Expansion (PDF, 3.1MB)
- Improving Accuracy of Thermodynamics predicted from Multi-scale methods by Global Data integration (PDF, 2.11MB), (N. Zarkevich)
Computer Lab
Download the test files:
And the tutorial notes:
References
(* key references for lectures. **recent useful review for CE )
- *Connolly, J.W.D., and Williams, A.R., “Density-functional theory applied to phase transformations in transition-metal alloys,” Phys. Rev. B 27, 5169 (1983).
- Sanchez J M, Ducastelle F and Gratias D., Physica A 128, 334 (1984).
- Johnson, D.D., Smirnov, A.V., et al., "Temperature-induced configurational excitations for predicting thermodynamic and mechanical properties of alloys," Phys. Rev. B 62, RC11917-20 (2000).
- **Mueller, S., “Bulk and surface ordering phenomena in binary metal alloys,” J. Phys.: Condens. Matter 15, R1429–R1500 (2003). PDF, 3.4 MB Review Typ
e Article.
- *Nikolai Zarkevich and D.D. Johnson, "Reliable Alloy Thermodynamics from Truncated Cluster Expansions," Phys. Rev. Lett. 92, 255702 (2004). (pdf, 213Kb)
- N.A. Zarkevich and D.D. Johnson, "Energy Scaling and Surface Patterning of Halogen-Terminated Si(001) Surfaces", Submitted to Elsevier Science, April 2005 (pdf, 1.6 MB)
Details for Lectures and Computer Labs
Lecture will be introduction to energetics of alloy order/disorder and defect energies, electronic mechanism for mixing and ordering, and structural formation energies -- how you get them and what they tell you. Rudiments of the Cluster Expansion (CE)
for representing alloy structural formation energies will be presented. Lecture will utilize (un)published results and concepts to help guide intuition and understanding.
Nikolai Zarkevich, MatSE, UIUC, Email: zarkevich --->uiuc.edu
A developing automated CE toolkit that performs ground-state search and Monte Carlo thermodynamics based on a structural energy databases will be briefly presented for use in day 1 labs.
Lab activities: (taught jointly with Gus Hart)
(i) Learn how to calculate and converge formation enthalpies.
(ii) Use data from (i) to do a simple CE fit
(iii) Make ground state search (direct enumeration) using that fit.
(iv) Show how one refines the fit/input database iteratively
Lectures
Presented by Professor Johnson and his research group member, Dr. Nikolai Zarkevich
Electronic Structure Effects and Energies of Alloy Transformations | PDF (5.3 MB)
- 1 WEEK2: Ab Initio Thermodynamics via Cluster Expansions and DFT-based Energy Databases
- 2 Week 2 Lecturers for Cluster Expansions
- Explaining Characterization Experiments from Cluster Expansions
- 3 Coming Topics / Connecting to Experiment
- Cluster Expansion Free Energies and Experiment
- 4 Part 1: Electronic Structure Effects and Energies of Alloy Transformations
- 5 My background (briefly)
- Part 1: Electronic Structure Effects and Energies of Alloy Transformations
- 6 Where do atoms go and why?
- Formation Enthalpy or Structural Formation Energies
- 7 Structural Formation Energies and Ground States
- Mixing vs Ordering Energies
- 8 Short-Range Order: a high-temperature state
- SRO and Diffuse Scattering (e.g., binary alloy)
- 9 Measured SRO: Free Energy (high-T case)
- Formation Enthalpies and Phase Diagrams
- 10 Gibbs Free Energy and Configurational Entropy
- Generic Phase Diagram Types
- 11 Miscibility Gap in fcc Pd-Rh
- Vibrational Entropy (example)
- 12 Generic Classification of Ordering Types
- Strain Energy (e.g., surface misfit strain)
- 13 Generic Phase Diagram: favorable mixing and ordering
- DFT Energies for Structural Transformations: considerations
- 14 DFT-based Formation Energies
- FCC Cu: Is Pseudo-Potential Energy Cutoff Converged?
- 15 FCC Cu: Total Energy vs. k-point Convergence
- Total Energy vs. k-point Convergence
- 16 k-point convergence: bcc W (B2 two-atom cubic cell)
- Example: fcc Cu-Au Formation Energies
- 17 Bands and Density of States
- 18 Types of Orbitals Dictate Bands and How They "Run"
- Estimating Density of States
- 19 Band-Width Dictated by Size (lattice constant)
- H on Square Lattice: Band Widths and Nodes
- 20 DOS, Band-filling, and magnetism: fcc Ni-Fe
- Density of States of fcc Ni-Fe: KKR-CPA
- 21 Fermi-Surface Nesting: Kohn Anomalies
- Hybridization: far, far away from the Fermi Surface
- Pt
- 22 Coupling States Near the Fermi Surface: fcc CuPt
- Summary
Basics of Cluster Expansions and Getting a Optimal Cluster Expansion | (PDF, 3.1MB)
- 1 What is the "coarse-graining" Cluster Expansion concept?
- 2 Some "older" References on Cluster Expansion
- Cluster Expansion Procedure
- 3 Cluster Expansion by Direct Inversion (Connolly-Williams)
- Connolly-Williams: fcc Cu-Au
- 4 Correlation Fct. for L1
- Completing the Connolly-Williams: fcc Cu-Au
- 5 Direct Inversions: a few thoughts
- Cross Validation Score (CV): LS Remove-n Estimator
- 6 CV0 = LS is not helpful for predictive power
- Uniqueness of CE fit can to be problem: e.g., fcc Ni3V
- 7 DFT and SRO Diffuse Scattering Data
- Consider the Effects of Partial Order (like in real systems)
- 8 KKR-CPA: direct calculation of partially-ordered state
- KKR-CPA: electronic DOS vs ? (LRO parameter)
- 9 KKR-CPA: electronic DOS vs ? (LRO parameter)
- Optimal Truncated Cluster Expansion: fcc Ni
- 10 Optimal CE Gives Thermodynamic Predictions that converge to Experimental Data within given CV1-score (accuracy)
- CE-Predicted Ni3V Structural Energies (meV)
- 11 (001) antiphase boundary (APB) within the D022 phase
- CE not always good: (001) APB from metastable L12
- 12 Optimal Truncated CE results are Robust and Agree with Experiment.
- Cluster Expansions: Synopsis
- 13 Addendum: Correlation Fct. for L1
- Addendum: Connolly-Williams for fcc Cu-Au
- 14 Addendum: fcc Cu-Au with Occupation Variable
Improving Accuracy of Thermodynamics predicted from Multi-scale methods by Global Data integration | (PDF, 2.11MB), (N. Zarkevich)
- Multi-scaling: cost of predicted ThermodynamicsThermodynamics
- The Structural Database
- Design of The Structural Database: ER diagram
- The Structural Database Attributes
- The Structural Database Relational Schema
- Implementation:
- The Structural Database is implemented:
- The Structural Database
- Thermodynamic Toolkit: Potentials and Capabilities
- Ab initio Thermodynamics from Structural Data
- Cluster Expansion Methodology
- Cluster Expansion
- Optimal Truncated Cluster Expansion
- Where the Rules come from?
- Rules for the optimal CE truncation come from Physics
- Tc and for metallic binaries alloys
- Ordering Energies and Transition Temperatures
- Thermodynamics Predicted with Desired Accuracy
- Reliability of CE Error Estimate:
- Cluster Expansion on Surface: halogenated Si(001)
- Halogen Repulsion Energy Scales as n2
- New Vacancy Line Defect for I on Si(001)
- VLD
- Conclusions
Computer Lab
Taught with Drs. Nikolai Zarkevich and Dan Finkenstadt and RA Teck Leong
ABINIT will be used to obtain structural energies for an alloy, including addressing structural optimization and k-point convergence issues, and then utilize these results for a fixed-composition and composition-dependent CE.
Download the test files:
And the tutorial notes:
- Part 1: Reliable Formation Energies for Alloy Thermodynamics. ABINIT is used to explore k-points convergence and structural relaxation effects in alloys. Formation energies are then used in analytic cluster expan
sion to better understand pitfalls. Johnson-Part1-ABINIT-CE.doc (76Kb) |
Johnson-Part1-ABINIT-CE.pdf (204Kb)
- Part 2: Reliable and Not-So Reliable Cluster Expansions.Cluster expansions and CV1-score are explored for optimality, then and Monte Carlo simulation is done via ThermoToolKit. Simple estimates are shown to help validate results. Johnson-Part2-CE-Ni3V.doc (100Kb) | Johnson-Part2-CE-Ni3V.pdf (244 Kb)