1. Durham, 6th-13th December 2001 CASTEP Developers’ Group with support from the ESF  k Network The Nuts and Bolts of First-Principles Simulation 20: Surfaces and Interfaces

2. Surfaces and Interfaces Lecture 20: surfaces and interfaces 2 Outline  What would be interesting to calculate?  What is feasible to calculate today?  Definitions of surface and interface related quantities  Practical procedures  How to include temperature and environment (example: oxidation of NiAl)

3. Surfaces and Interfaces Lecture 20: surfaces and interfaces 3 Reference for interfaces: Sutton, A. P. and R. W. Balluffi (1995). Interfaces in Crystalline Materials. Oxford, Clarendon. For specific applications, eg. to NiAl (described in this lecture, or alumina, visit the recent publications page on our website: http://titus.phy.qub.ac.uk

4. Surfaces and Interfaces Lecture 20: surfaces and interfaces 4 Wish list  Structure (including stoichiometry) and energy  Mechanical strength  Dependence on preparation conditions and environment (p,T)  Effect of composition and impurities  Electrical and other transport properties

5. Surfaces and Interfaces Lecture 20: surfaces and interfaces 5 Work of separation and work of adhesion         Unit area separate W sep is the increase in free energy with no diffusion or segregation W ad is the increase in free energy under equilibrium conditions; e.g. oxygen or other contaminants may adhere to the fresh surfaces. W ad =       But we can directly calculate only W sep

6. Surfaces and Interfaces Lecture 20: surfaces and interfaces 6 Real clean surfaces… + planned and unplanned components

7. Surfaces and Interfaces Lecture 20: surfaces and interfaces 7 Thermodynamics Definition of surface energy 

8. Surfaces and Interfaces Lecture 20: surfaces and interfaces 8 Contributions to free energy We calculate directly zero K internal energy. To correct for finite temperature we can incorporate quasi-harmonic phonon free energies. In addition, we can incorporate the configurational entropy within simple models (eg. regular solution model). Still not a complete and tested approach for surfaces and interfaces.

9. Surfaces and Interfaces Lecture 20: surfaces and interfaces 9 Excesses  Simple example: grain boundary in a binary compound Grain boundary Grain Interfacial excess of component 2 with respect to component 1:

10. Surfaces and Interfaces Lecture 20: surfaces and interfaces 10 Segregation thermodynamics For the simple two component grain boundary: This is a Gibbs adsorption equation..

11. Surfaces and Interfaces Lecture 20: surfaces and interfaces 11 Surface stress = surface tension Surface stress and energy are the same for fluids. For crystalline surfaces or interfaces the surface stress may be anisotropic; it is a tensor. Crystallite in compression

12. Surfaces and Interfaces Lecture 20: surfaces and interfaces 12 The Coincident Site Lattice 1. (CSL)

13. Surfaces and Interfaces Lecture 20: surfaces and interfaces 13 The Coincident Site Lattice 2. (CSL) Grain boundaries, surfaces Small tilt or rotation -> large unit cell. Heterogeneous interfaces Small difference in lattice parameters -> large unit cell. May need to strain one of the lattices to make a smaller unit cell.

14. Surfaces and Interfaces Lecture 20: surfaces and interfaces 14 Example: Early stage of oxidation of NiAl

15. Surfaces and Interfaces Lecture 20: surfaces and interfaces 15 NiAl oxidation: Background and Questions  Al 2 O 3 forms a coherent film ca. 0.5nm thick, then oxidation rate drops by 2 orders of magnitude.  Al 2 O 3 /NiAl interface is atomically sharp, Ni does not participate.  At low T it is amorphous (locally ordered), at high T (ca. 1300K) get  Al 2 O 3. Layer sequence NiAl-Al-O-Al-O.  What determines the growth mode?  What is the atomic mechanism?  How does oxygen initiate Al segregation?  Are vacancies injected or absorbed at the surface?

16. Surfaces and Interfaces Lecture 20: surfaces and interfaces 16 Growth mode? Island growthLayer-by-layer growth How can we predict growth mode? - Calculate nanoscale thermodynamic driving forces

17. Surfaces and Interfaces Lecture 20: surfaces and interfaces 17 Energy balance Island is favoured over monolayer if: or in terms of the surface excess of oxygen:

18. Surfaces and Interfaces Lecture 20: surfaces and interfaces 18 Definition of surface energy Periodic Boundary Conditions A/2 For NiAl:

19. Surfaces and Interfaces Lecture 20: surfaces and interfaces 19 Chemical potentials of Ni and Al

20. Surfaces and Interfaces Lecture 20: surfaces and interfaces 20 Scheme for  calculation

21. Surfaces and Interfaces Lecture 20: surfaces and interfaces 21 NiAl structure

22. Surfaces and Interfaces Lecture 20: surfaces and interfaces 22 NiAl (100)

23. Surfaces and Interfaces Lecture 20: surfaces and interfaces 23 Method:Plane-waves, pseudopotentials, FEMD (Troullier-Martins PP for Al, M.-H. Lee PP for Ni and O) Supercell:4 layers of 4 atoms + 4 layers vacuum (2 bottom layers fixed) Structural relaxation:starting with 300-500 MD steps at 1000K k-point mesh:16 special k-points Cutoff energy:50Ry Details of Calculation

24. Surfaces and Interfaces Lecture 20: surfaces and interfaces 24 Results For 1, 3 and 6 O atoms per surface cell. Use many starting configurations. Include point defects in the starting configurations.

25. Surfaces and Interfaces Lecture 20: surfaces and interfaces 25 Without defects - ‘normal’ behaviour With defects - ‘inverted’ behaviour Oxide layer or islands?

26. Surfaces and Interfaces Lecture 20: surfaces and interfaces 26 Oxidised surfaces