Energy of Formation of NiTi and NiZr intermetallics using DFT

Transcript

1. 1/20 Introduction DFT Softwares Experiment Results Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12 National Institute of Technology, Karnataka June 16, 2020 Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
2. 2/20 Introduction DFT Softwares Experiment Results Contents 1 Introduction 2 DFT 3 Softwares 4 Experiment 5 Results Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
3. 3/20 Introduction DFT Softwares Experiment Results Objective • To study the crystallographic information of NiTi and NiZr system. • To optimize the cut-off energy and k-points for NiTi and NiZr system using single point energy calculation. • To determine the ground state energy of Ni-FCC, Ti and Zr in HCP, NiTi-B2 and NiZr-orthorhombic crystal structure using geometric optimization. • To determine the energy of formation of NiTi and NiZr and compare with literature data. Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
4. 4/20 Introduction DFT Softwares Experiment Results Why add Zr to Nitinol? Back Scattering Electron Images [2] Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
5. 4/20 Introduction DFT Softwares Experiment Results Why add Zr to Nitinol? Back Scattering Electron Images [2] Property Ni(50)Ti(50) Ni(50)Ti(45)Zr(5) Ni(40)Ti(50)Zr(10) Hardness (VPN) 194 359 535 Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
6. 4/20 Introduction DFT Softwares Experiment Results Why add Zr to Nitinol? Back Scattering Electron Images [2] Property Ni(50)Ti(50) Ni(50)Ti(45)Zr(5) Ni(40)Ti(50)Zr(10) Hardness (VPN) 194 359 535 Corrosion rate (mpy) 1.3391 0.7469 0.7218 Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
7. 4/20 Introduction DFT Softwares Experiment Results Why add Zr to Nitinol? Back Scattering Electron Images [2] Property Ni(50)Ti(50) Ni(50)Ti(45)Zr(5) Ni(40)Ti(50)Zr(10) Hardness (VPN) 194 359 535 Corrosion rate (mpy) 1.3391 0.7469 0.7218 % Shape memory effect 75% 31% 25% Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
8. 5/20 Introduction DFT Softwares Experiment Results Density Functional Theory Time Independent Schrodinger Equation: ˆ Hψ(RI , ri ) = Eψ(RI , ri ) Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
9. 5/20 Introduction DFT Softwares Experiment Results Density Functional Theory Time Independent Schrodinger Equation: ˆ Hψ(RI , ri ) = Eψ(RI , ri ) Many-body hamiltonian: ˆ H = ˆ TN + ˆ Te + ˆ Ve−N + ˆ Ve−e + ˆ VN−N Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
10. 5/20 Introduction DFT Softwares Experiment Results Density Functional Theory Time Independent Schrodinger Equation: ˆ Hψ(RI , ri ) = Eψ(RI , ri ) Many-body hamiltonian: ˆ H = ˆ TN + ˆ Te + ˆ Ve−N + ˆ Ve−e + ˆ VN−N Very difficult to solve even for small systems
11. 5/20 Introduction DFT Softwares Experiment Results Density Functional Theory Time Independent Schrodinger Equation: ˆ Hψ(RI , ri ) = Eψ(RI , ri ) Many-body hamiltonian: ˆ H = ˆ TN + ˆ Te + ˆ Ve−N + ˆ Ve−e + ˆ VN−N Very difficult to solve even for small systems Approximations! Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
12. 6/20 Introduction DFT Softwares Experiment Results Density Functional Theory Born-Oppenheimer or adiabatic approximation! Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
13. 6/20 Introduction DFT Softwares Experiment Results Density Functional Theory Born-Oppenheimer or adiabatic approximation! Mproton ≈ 1800 . Melectron
14. 6/20 Introduction DFT Softwares Experiment Results Density Functional Theory Born-Oppenheimer or adiabatic approximation! Mproton ≈ 1800 . Melectron Electronic motion = 103 Nuclear motion Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
15. 6/20 Introduction DFT Softwares Experiment Results Density Functional Theory Born-Oppenheimer or adiabatic approximation! Mproton ≈ 1800 . Melectron Electronic motion = 103 Nuclear motion ˆ H = ˆ TN + ˆ Te + ˆ Ve−N + ˆ Ve−e + ˆ VN−N Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
16. 6/20 Introduction DFT Softwares Experiment Results Density Functional Theory Born-Oppenheimer or adiabatic approximation! Mproton ≈ 1800 . Melectron Electronic motion = 103 Nuclear motion ˆ H = ˆ TN + ˆ Te + ˆ Ve−N + ˆ Ve−e + ˆ VN−N Electronic Hamiltonian: ˆ H = ˆ Te + ˆ Ve−N + ˆ Ve−e Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
17. 7/20 Introduction DFT Softwares Experiment Results Density Functional Theory ˆ Hψ(RI , ri ) = Eψ(RI , ri ) Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
18. 7/20 Introduction DFT Softwares Experiment Results Density Functional Theory ˆ Hψ(RI , ri ) = Eψ(RI , ri ) Wave-function ψ depends on 3 spatial coordinates. Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
19. 7/20 Introduction DFT Softwares Experiment Results Density Functional Theory ˆ Hψ(RI , ri ) = Eψ(RI , ri ) Wave-function ψ depends on 3 spatial coordinates. Scales upto 3n coordinates for n electrons. Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
20. 7/20 Introduction DFT Softwares Experiment Results Density Functional Theory ˆ Hψ(RI , ri ) = Eψ(RI , ri ) Wave-function ψ depends on 3 spatial coordinates. Scales upto 3n coordinates for n electrons. Focus shifted from wave-function to electron density Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
21. 7/20 Introduction DFT Softwares Experiment Results Density Functional Theory ˆ Hψ(RI , ri ) = Eψ(RI , ri ) Wave-function ψ depends on 3 spatial coordinates. Scales upto 3n coordinates for n electrons. Focus shifted from wave-function to electron density Energy represented as a functional of electron density. Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
22. 8/20 Introduction DFT Softwares Experiment Results Density Functional Theory Hohenberg-Kohn Theorems: Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
23. 8/20 Introduction DFT Softwares Experiment Results Density Functional Theory Hohenberg-Kohn Theorems: Treats density as the basic variable: the external potential determines uniquely the charge density, and the charge density determines uniquely the external potential E[ρ(r)]. Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
24. 8/20 Introduction DFT Softwares Experiment Results Density Functional Theory Hohenberg-Kohn Theorems: Treats density as the basic variable: the external potential determines uniquely the charge density, and the charge density determines uniquely the external potential E[ρ(r)]. A universal functional for the energy E[ρ(r)] can be defined in terms of the density. The exact ground state is the global minimum value of this functional. E[ρ(r)] ≥ E[ρ0(r)] Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
25. 9/20 Introduction DFT Softwares Experiment Results Density Functional Theory Most difficult task: Modeling electron-electron repulsion [1] Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
26. 9/20 Introduction DFT Softwares Experiment Results Density Functional Theory Most difficult task: Modeling electron-electron repulsion [1] Introduced a correlation function EXC [ρ(r)] Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
27. 9/20 Introduction DFT Softwares Experiment Results Density Functional Theory Most difficult task: Modeling electron-electron repulsion [1] Introduced a correlation function EXC [ρ(r)] • Local Density Approximation (LDA) Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
28. 9/20 Introduction DFT Softwares Experiment Results Density Functional Theory Most difficult task: Modeling electron-electron repulsion [1] Introduced a correlation function EXC [ρ(r)] • Local Density Approximation (LDA) • Generalized Gradient approximation (GGA) Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
29. 9/20 Introduction DFT Softwares Experiment Results Density Functional Theory Most difficult task: Modeling electron-electron repulsion [1] Introduced a correlation function EXC [ρ(r)] • Local Density Approximation (LDA) • Generalized Gradient approximation (GGA) Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
30. 10/20 Introduction DFT Softwares Experiment Results Density Functional Theory Pseudopotentials make calculations easier! Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
31. 10/20 Introduction DFT Softwares Experiment Results Density Functional Theory Pseudopotentials make calculations easier! Replacing the complicated effects of the motion of core electrons and nucleus with an effective potential or pseudopotential. Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
32. 10/20 Introduction DFT Softwares Experiment Results Density Functional Theory Pseudopotentials make calculations easier! Replacing the complicated effects of the motion of core electrons and nucleus with an effective potential or pseudopotential. Pseudopotential Approach Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
33. 11/20 Introduction DFT Softwares Experiment Results Softwares involved • Quantum ESPRESSO: Open-Source software for electronic-structure calculations and materials modeling based on density-functional theory, plane waves, and pseudopotentials. • BURAI: A GUI for Quantum ESPRESSO Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
34. 12/20 Introduction DFT Softwares Experiment Results Experimental Calculations • Download the particular CIF. • Perform fixed cell calculation for optimization of Ecut an k-points. 1 2 |k + G|2 ≤ Ecut • Perform vc-relax calculation for optimization of the geometric cell. • Calculate the energy of formation for NiTi and NiZr. Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
35. 13/20 Introduction DFT Softwares Experiment Results Experimental Calculations Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
36. 14/20 Introduction DFT Softwares Experiment Results Total Energy Calculation Results Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
37. 15/20 Introduction DFT Softwares Experiment Results Total Energy Calculation Results • Ni (FCC) = -426.5321 Ry • Ti (HCP) = -181.7691 Ry • Zr (HCP) = -303.0994 Ry • NiTi (B2) = -608.4033 Ry • NiZr (Orthorhombic) = -729.75205 Ry Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
38. 16/20 Introduction DFT Softwares Experiment Results Energy of Formation Calculation Results ∆EApBq = 1 p + q EApBq − p p + q EA − q p + q EB • ∆ ENiTi = -34.1971 kJ/mol • ∆ ENiZr = -46.3072 kJ/mol Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
39. 17/20 Introduction DFT Softwares Experiment Results Comparison with Previous Literature Data 1,950 1,970 1,990 2,010 2,030 30 32 34 36 38 40 This Year Energy of formation (in kJ/mol) Data for NiTi 1,975 1,985 1,995 2,005 2,015 2,025 42 44 46 48 50 52 This Year Energy of formation (in kJ/mol) Data for NiZr Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
40. 18/20 Introduction DFT Softwares Experiment Results Conclusions • The binary compound NiTi is in B2 crystal structure with 2 atoms in the primitive cell and NiZr in orthorhombic crystal structure with 4 atoms in the primitive cell. Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
41. 18/20 Introduction DFT Softwares Experiment Results Conclusions • The binary compound NiTi is in B2 crystal structure with 2 atoms in the primitive cell and NiZr in orthorhombic crystal structure with 4 atoms in the primitive cell. • The required cut-off energy and k-point for geometric optimisation are calculated by series of single point energy calculation. Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
42. 18/20 Introduction DFT Softwares Experiment Results Conclusions • The binary compound NiTi is in B2 crystal structure with 2 atoms in the primitive cell and NiZr in orthorhombic crystal structure with 4 atoms in the primitive cell. • The required cut-off energy and k-point for geometric optimisation are calculated by series of single point energy calculation. • The calculated energy of formation of standard reference state structure of NiTi and NiZr at 0K are comparable with literature data. Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
43. 19/20 Introduction DFT Softwares Experiment Results References Hammes-Schiffer, S. A conundrum for density functional theory. Science 355, 6320 (2017), 28–29. Khan, A. N., Muhyuddin, M., and Wadood, A. Development and characterization of nickel–titanium–zirconium shape memory alloy for engineering applications. Russian Journal of Non-Ferrous Metals 58, 5 (2017), 509–515. Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12
44. 20/20 Introduction DFT Softwares Experiment Results Thank you for your time. Questions? Study on Energy of Formation of NiTi and NiZr Intermetallic compounds using DFT Deepnika Jain 16MT12