Defects Engineering

ABDUL SAMIPhD Student

Department of Chemical Engineering

Outline of Presentation:

Defects with classifications

Case study Graphene & Perovskite

Crystal: IDEAL vs. Reality

Ideal Crystal: An ideal crystal can be described in terms a three-dimensionally periodic arrangement of points called lattice and an atom or group of atoms associated with each lattice point called motif:

Crystal = Lattice + Motif (basis)

Real Crystal: Deviations from this ideality.

These deviations are known as crystal defects.

Therefore, defects engineering is major field of novel research.

Diffused atoms Vacancy

Extrinsic Defects Intrinsic Defects

0D(Point defects)

CLASSIFICATION OF DEFECTS BASED ON DIMENSIONALITY

1D(Line defects)

2D(Surface / Interface)

3D(Volume defects)

Vacancy

Impurity

Frenkeldefect

Schottkydefect

Dislocation Surface

Interphaseboundary

Grainboundary

Twinboundary

Twins

Precipitate

Faultedregion

Voids / Cracks

Stackingfaults

Disclination

Dispiration

Thermalvibration

Guess: There may be some vacant sites in a crystal

Surprising Fact

There must be a certain fraction of vacant sites in a crystal in equilibrium.

Equilibrium means Minimum Gibbs free energy G at constant T and P

A crystal with vacancies has a lower free energy G than a perfect crystal

What is the equilibrium concentration of vacancies?

Point Defects: Vacancy

Gibbs Free Energy G

G = H – T S

1. Enthalpy H=E+PV

2. Entropy S=k ln W

T Absolute temperature

E internal energyP pressureV volume

k Boltzmann constantW number of microstates

Vacancy increases H of the crystal due to energy required to break bonds

Enthalpy H=E+PV

D H = n D Hf

Vacancy increases S of the crystal due to configurational entropy

Entropy S=k ln W

Number of atoms: N

Increase in entropy S due to vacancies:

WkS lnD

Number of vacancies: n

Total number of sites: N+n

The number of microstates:

n

nN CW!!)!(

NnnN

!!)!(ln

NnnNk

]!ln!ln)![ln( NnnNk

Vacancy increases S of the crystal due to configurational entropy

DG = DH TDS

neq

G of a perfect crystal

n

DG

DHfHnH DD

TDS]lnln)ln()[( NNnnnNnNkS D

Change in G of a crystal due to vacancy

fHnH DD

]lnln)ln()[( NNnnnNnNTkHnG f DD

0D

eqnnnG

With neq<<N

D

kTH

Nn feq exp

]lnln)ln()[( NNnnnNnNkS D

9

Equilibrium concentration of vacancy

Contribution of vacancy to thermal expansion

Increase in vacancy concentration increases the volume of a crystal

A vacancy adds a volume equal to the volume associated with an atom to the volume of the crystal.

Thus vacancy makes a small contribution to the thermal expansion of a crystal

Thermal expansion =

lattice parameter expansion + Increase in volume due to vacancy

NvV

NVvNV DDD

NN

vv

VV D

D

D

V=volume of crystalv= volume associated with one atomN=no. of sites (atoms+vacancy)

Total expansio

n

Lattice parameter increase

vacancy

Contribution of vacancy to thermal expansion

Increase in vacancy concentration increases the volume of a crystal

vacancy Interstitialimpurity

Substitutionalimpurity

Point Defects

Frenkel defect

Schottky defect

Cation vacancy+

cation interstitial

Cation vacancy+

anion vacancy 13

Defects in ionic solids

Line Defects:Also called EDGE DISLOCATION

Defect

An extra half plane…

…or a missing half plane16

An extra half plane…

…or a missing half plane

Edge Dislocation

17

1 2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8 9

slip no slipSlip planeb

Burgers vector

t

Line vector

Relationship between the directions of b and t?

b t

Edge dislocation

In general, there can be any angle between the Burgers vector b (magnitude and the direction of slip) and the line vector t (unit vector tangent to the dislocation line)

b t Edge dislocation

b t Screw dislocation

b t , b t Mixed dislocation

Screw Dislo

cation Line

b

t

12

3

Screw Dislocation

Slip plane

slipped

unslipped

20

b t

b is a lattice translation

b

If b is not a complete lattice translation then a surface defect will be created along with the line defect.

Surface defect

N+1 planes

N planes

Compression

Above the slip plane

TensionBelow the slip plane

Elastic strain field associated with an edge dislocation

Elastic energy per unit length of a dislocation line

Shear modulus of the crystalb Length of the Burgers vectorUnit: J m1

2

21 bE

A dislocation line cannot end abruptly inside a crystal

Slip plane

slip no slip

slip no slip

disl

ocat

ion

b

Dislocation: slip/no slip boundary

Slip plane

A

P

Q

A dislocation line cannot end abruptly inside a crystal

It can end on a free surface

A

B

C

D

Q

P

Dislocation Line AB Dislocation Line APQ

Grain 1 Grain 2

Grain Boundary

Dislocation can end on a grain boundary

It can end on Free surfaces or Grain boundaries

A nice diagram showing a variety of crystal defects

a) Interstitial impurity atom, b) Edge dislocation, c) Self interstitial atom, d) Vacancy, e) Precipitate of impurity atoms, f) Vacancy type dislocation loop, g) Interstitial type dislocation loop, h) Substitutional impurity atom

Graphene gets designer defects An extended one-dimensional defect that has the potential to act as a conducting wire has been embedded in another perfect graphene sheet.

One-dimensional defects in graphene have a strong influence on its physical properties, suchas electrical charge transport and mechanical strength.

Detect can tune the properties of Graphene. Atomic layer deposition allows us to deposit Pt predominantly on graphene’s grain boundaries, folds and cracks due to the enhanced chemical reactivity of these line defects, which is directly confirmed by transmission electron microscopy imaging.

Application: Sensing

Defect structure and superimposed defect model

Graphene require the ability to tune its electronic structure at the nanoscale.

The approach is ‘self-doping, in which extended defects are introduced into the graphene lattice.

The controlled engineering of these defects represents a viable approach to creation and nanoscale control of one-dimensional charge distributions with widths of several atoms.

Here, the realization of a one-dimensional topological defect in graphene, containing octagonal and pentagonal sp2-hybridized carbon rings embedded in a perfect graphene sheet.

By doping the surrounding graphene lattice, the defect acts as a quasi-one-dimensional metallic wire. Such wires may form building blocks for atomic-scale, all-carbon electronics.

The DFT relaxed geometry of the defect structure,

including bond lengths (in Å) and bond angles

Defect structure and superimposed defect model

New Generation of Solar Cells: 2012~2014

Perovskite Materials. PUBLISHED ONLINE: 31 AUGUST 2014 | DOI: 10.1038/NNANO.2014.181

Defects Engineering

ABDUL SAMIPhD Student

Department of Chemical Engineering