20: surfaces and interfaces - durham university

Durham, 6 th- 13th December 2001CASTEP Developers ’ Groupwith support from the ESF ψk Network

The Nuts and Bolts of First-Principles Simulation

20: Surfaces and Interfaces

Surfaces and Interfaces Lecture 20: surfaces and interfaces 2

Outline

r What would be interest ing to calculate?

r What is feasible to calculate today?

r Definit ions of surface and interface related quantit ies

r Pract ical procedures

r How to inc lude temperature and environment (example : oxidat ion of NiAl )


Reference for interfaces:

Sutton, A. P. and R. W. Balluff i (1995). Interfaces in Crystalline Materials. Oxford, Clarendon.

For specific applications, eg. to N iA l (described in this lecture, or alumina, visit the recent publications page on our website:

http://titus.phy.qub.ac.uk


Wish list

q Structure (including stoichiometry) and energy

q Mechanical strength

q Dependence on preparation conditions and environment (p,T)

q Effect of composition and impurities

q Electrical and other transport properties


Work of separationand work of adhesion

α β α β

γαβ γα γβ

Uni

t ar

ea

separate

W sep is the increase in free energy with no diffusion or segregation

Wad is the increase in free energy under equilibrium conditions;e.g. oxygen or other contaminants may adhere to the fresh surfaces.

Wad = γα + γβ − γαβ But we can directly calculate only Wsep


Real clean surfaces…

S t e p

P i t

K in k

Is l a n d

V a c a nc y

A da t o m

T e rr a c e

+ planned and unplanned components


Thermodynamics

α βA

A+dAα β

dE = TdS − PdV + µii

∑ dNi +γdA

E = TS − PV + µii

∑ Ni +γA

γ = 1/ A( ) E − TS + PV − µii

∑ Ni

Definition of surface energy γ


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.


Excesses

Γ2 = [N2]− [N1]N2

α

N1α

α α

Simple example: grain boundary

in a binary compound

Grain boundary

Grain Grain

Interfacial excess of component 2 with respect to component 1:

Surfaces and Interfaces Lecture 20: surfaces and interfaces 1 0

Segregation thermodynamics

∂γ∂µ2 T,p

= −Γ2

For the simple two component grain boundary:

This is a Gibbs adsorption equation.

.


Surface stress

dW = d(γA) = σdA

σ = γ + AdγdA

= 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


The Coincident Site Lattice 1. (CSL)


The Coincident Site Lattice 2. (CSL)

Grain boundaries, surfacesSmall tilt or rotation -> large unit cell.

Heterogeneous interfacesSmall difference in lattice parameters -> large unit cell.May need to strain one of the lattices to make a smaller

unit cell.


Example: Early stage of oxidation of NiAl


NiAl oxidation:Background and Questions

q Al2 O3 forms a coherent film ca. 0.5nm thick, then

oxidation rate drops by 2 orders of magnitude.

q Al2 O3/ NiAl interface is atomically sharp, Ni does not participate.

q At low T it is amorphous (locally ordered), at high T

(ca. 1300K) get γ−Al2 O3. Layer sequence NiAl-Al-O-Al-O.

q What determines the growth mode?

q What is the atomic mechanism?

q How does oxygen initiate Al segregation?

q Are vacancies injected or absorbed at the surface?


Growth mode?

Island growth Layer-by-layer growth

How can we predict growth mode?

- Calculate nanoscale thermodynamic driving forces


Energy balance

xσn + (1− x)σ0

xnx

nxσ1 + (1− nx)σ0

Island is favoured over monolayer if:

σn − σ0 < n(σ1 −σ0 )

σn − σ0

ΓO(n) <

(σ1 − σ0 )ΓO

(1)

or in terms of the surface excess of oxygen:


Definition of surface energyPeriodic Boundary Condit ions

A/2

σ(x,T, pO2) = (Gs − NNi gNiAl ) / A − µAl (x,T)ΓAl − µO( pO2

,T)ΓO

For NiAl:


Chemical potentials of Ni and Al


Scheme for σ calculation


NiAl structure


NiAl (100)


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


Results

• For 1, 3 and 6 O atoms per surface cell.

• Use many starting configurations.

• Include point defects in the starting configurations.


Without defects

- ‘normal’ behaviourWith defects- ‘inverted’ behaviour

Oxide layer or islands?

σn − σ0

ΓO(n) <

(σ1 − σ0 )ΓO

(1)

σn − σ0

ΓO(n) >

(σ1 − σ0 )ΓO

(1)

σ0 σ0


Oxidised surfaces

20: surfaces and interfaces - durham university

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