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Plan of the talk

Systematic, multisite,short-range-order corrections to the electronic structure of disordered alloys from first-principles: the KKR-nonlocal CPA Subhradip Ghosh Department of Physics,IIT Guwahati Collaborators D.D.Johnson & D.Biava, UIUC W.A.Shelton, ORNL. Plan of the talk. Motivation Our aim

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Plan of the talk

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  1. Systematic, multisite,short-range-order corrections to the electronic structure of disordered alloys from first-principles: the KKR-nonlocal CPASubhradip GhoshDepartment of Physics,IIT GuwahatiCollaboratorsD.D.Johnson & D.Biava, UIUCW.A.Shelton, ORNL

  2. Plan of the talk • Motivation • Our aim • Existing methods • The Non-local CPA • First-principles KKR-NLCPA • Results • Future directions

  3. Motivation • Technologically important alloys are size-mismatched multi-component alloys displaying a variety of complex behavior all tied to various underlying electronic effects. Example: Metallic alloys, ferroelectric & superconducting oxides. • In multi-component alloys at high T Atoms move aboutthermodynamic equilibrium “big” atoms replace “small” ones & vice versa environment of the site responds Strain, concentration, magnetic fluctuations Example: CrW, NiPt • Material characterization experiments usually cannot uniquely determine the electronic “driving force” responsible for ordering behavior.

  4. Our Aim Construct a first-principles based thermodynamic theory of static correlations (atomic, magnetic and displacive correlations) for size-mismatched multi-component alloys with multi-sublattice disorder Pinpoint the electronic origin for ordering behavior in these systems. Tailoring of material properties.

  5. Green function based formalism • Hamiltonian • Dyson Equation Equation for a random alloy Configuration of Self-Energy (Describes the effective medium)

  6. Coherent potential approximation Coherent potential medium Random alloy Coherent potential medium A/B CPA Condition:

  7. Embedded cluster method (ECM) CPA medium No new “effective medium” • Molecular CPA (MCPA) MCPA “effective medium” Site translational invariance is broken.

  8. Non local CPA (NLCPA) 2 site impurity cluster 2 site cavity Cavity Impurity Effective medium Medium G.F. Impurity G.F. NLCPA condition

  9. Coarse graining in reciprocal space • depend only on (I – J). • Sample the Brillouin zone accordingly. For cluster having N sites, surround them with a tile having the symmetry of the lattice and can be periodically repeated to fill out all space. Periodicity of the real – space tiles define a reciprocal lattice. Lattice cluster

  10. a Real space tiling • 1-D Example for N = 4 Reciprocal space tilling 0 Set of is determined by Lattice Mapping cluster Coarse grained self-energy I. II.

  11. Effective medium • Lattice Green’s function

  12. NLCPA within first-principles KKR Effective medium Scattering path operator for the impurity cluster All scattering outside the cluster that started and finished inside Translational invariance demands

  13. Representation of Coarse graining of effective medium NLCPA condition Density of states is obtained from

  14. Applications : fcc Cu50Au50, bcc Ni50Al50 • Calculation Details • Starting potentials are KKR-CPA ones. • CPA equilibrium lattice constant is used. • 20x20x20 Monkhorst-Pack special point mesh is used.

  15. FCC Cu Au Ordered L10

  16. BCC Ni Al Ordered B2

  17. Effect of SRO on electronic structure: Ni Al B2

  18. Towards DFT based first principles NLCPA a. leads to DFT total energy b. Thermodynamics can be studied via variation of with respect to various fluctuation [Ref:-Gyorffy and Stocks, PRL 50, 374(1983)] • Construction of electronic Grand potential because Electronic grand potential

  19. An analytic expression for : Lloyd’s formula: • Utilities : • a. A stationary leads to a variational total energy. • b. Fermi level can be estimated accurately avoiding basis-set truncation error. • Critical for systems with band gap

  20. KKR-NLCPA Lloyd’s formula Effective medium Cluster term Ref:- Ghosh et.al. PRB 73, 085106(2006)

  21. Validation of Lloyd’s formula: Ni Al

  22. Work In Progress • DFT-KKR-NLCPA is formulated. • Variational Grand potential obtained. • Application on bcc Cu50Zn50 at finite T is in progress.

  23. Summary • NLCPA provides us with a cluster generalization of single-site CPA that takes care of site translational invariance. • Coarse-graining the reciprocal space is key to achieve this. • First-principles KKR-NLCPA is a mathematically simple & numerically tractable method to deal with off-diagonal disorder in alloys. • DFT based total energy formulation of KKR-NLCPA is underway which will pave the way for construction of a first-principles based linear-response theory to study alloy thermodynamics that includes all kinds of relevent correlations.

  24. Effect of SRO • Normalized pair correlation for M component alloy: Occupation variable No. of independent variables

  25. Example : Binary bcc for • Independent variable : For Possible values of

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