Ab initio Berechungen für Datenbanken

Transcription

1 J

2 Ab initio Berechungen für Datenbanken Jörg Neugebauer University of Paderborn Lehrstuhl Computational Materials Science Computational Materials Science Group CMS Group

3 Scaling Problem in Modeling length (m) dislocations interfaces point defects chemical bonds Phenomenological approaches: FEM materials properties Phase fields crystal growth : growth mechanism microstructure formation time (s)

4 Scaling Problem in Modeling length (m) dislocations interfaces point defects chemical bonds Free energy: growth mechanism microstructure formation 2 F = ε φ + f φ, T, cα, σ, V Phenomenological approaches: FEM materials properties Phase fields crystal growth : ( ) dv 1 empirical, fitted parameters/functions 10 3 time (s)

5 Atomistic picture: Ab initio Description r 1,e r 2,e Rr 1, Z 1 R r 2, Z 2 Hamiltonian: H = T el + T ion I r I, i R I Z r i i, j i j 1 r r i j i, j i j 1 r r R I R J e-ion e-e Ion-Ion Solve Schrödinger equation: HΨ = EΨ r r r ( ) Ultimate information: E Ψ R, KR, r, r, K,, 1 M 1 2 r N Advantage: Free of adjustable/empirical parameters (ab initio) r r

6 Scaling Problem in Modeling length (m) 1 Phenomenological approaches: FEM materials properties Phase fields crystal growth : 10 Density-Functional Al (111) -3 Theory: microstructure 2 h r 2 ext r H r xc r formation r r + v ( ;{ RI, Z I }) + v [ n( )] + v [ n( )] ϕ i ( ) = ε iϕi ( ) me dislocations interfaces growth material point defects mechanism universal 10-9 r functional DFT chemical bonds ({ R Z }) E, tot I I Energy barrier Phase II -3 Phase I 1 x int 10 3 time (s)

7 Scaling Problem in Modeling length (m) DFT dislocations interfaces point defects ~2050 ~2020 growth mechanism microstructure formation materials properties crystal growth time (s)

8 Scaling Problem in Modeling length (m) DFT dislocations interfaces point defects Phenomenological approaches: FEM materials properties Phase fields crystal growth : microstructure formation How to growth bridge mechanism length and time scales? time (s)

9 Ab initio based Multiscale Simulations Continuum models Thermodyn. Kinetics Strain Electr. struct. DFT: E tot ({R I }), ε i, φ i DFT code library: SFHIngX (

10 Potential Energy Surfaces Example: Crystal Structure of Aluminum reaction coordinates: angle length

11 Potential Energy Surfaces Example: Aluminum bcc fcc Energy [H] lattice constant [Bohr] Angle between lattice vectors

12 Potential Energy Surfaces Example: Aluminum Angle between lattice vectors fcc barrier bcc Angle between lattice vectors

13 Application: Phonon Dispersion Example: Aluminum

14 Ab initio based Multiscale Simulations Continuum models Thermodyn. Kinetics Strain Electr. struct. DFT: E tot ({R I }), ε i, φ i DFT code library: SFHIngX (

15 Method: Ab initio Thermodynamics Key: Calculate partition function DFT = r BO E RI Z( V, T) e r R { } I V ({ } ) V / k Experiment B T Z Phase ( V, T) = N deg e E tot r Phase { } vib R I V / kbt E { R } I e r { R } I V r Phase V / k B T F(V,T) = k B T ln G ( p, T ) = F V, T + n G(A ) µ A = n { Z(V,T) } ( ) pv T,p equil. config. D I, J E = tot u ({ r } ) Phase R I I u V vibronic config. J

16 Diluted Alloys Example: Mg in GaN Solubility/ Miscibility: Mg 3 N 2 Mg bulk µ Mg µ Ga Incorporation on other sites: Mg Ga Mg N Mg i

17 Intrinsic Solubility/Doping Efficiency Formation Energy (ev) Formation Energies: V N Mg Ga Fermi Energy (ev) Concentration (log 10 cm -3 ) Defect Concentrations: Mg Ga V N Temperature (K) Strong compensation at characteristic growth temperatures! very limited doping efficiency J. Neugebauer and C. Van de Walle, Appl. Phys. Lett. 68, 1829 (1996)

18 Co-Doping Example: Co-doping with hydrogen Formation Energy (ev) Formation Energies: V N H + Mg Ga Fermi Energy (ev) Concentration (log 10 cm -3 ) Defect Concentrations: 22 H free case 20 H-rich conditions Mg Ga H V N Temperature (K) Co-Doping: significantly increases dopant concentration significantly suppresses defect formation But: fully compensated material J. Neugebauer and C. Van de Walle, Appl. Phys. Lett. 68, 1829 (1996)

19

20

21

22

23

24

25

26

27

28

29 Example: Dislocations

30 Example: Dislocations continuum elastic theory emp. pot. DFT Main Main challenge: How How to to connect zones zones at at boundaries? New New approach: Projection method without explicit boundaries!

31 Comparison with Experiment Theory Experiment L. Lymperakis, J. Neugebauer, M. Albrecht, H. Strunk, PRL in print. EC-TMR Project: IPAM

32

33

34 J