IMPERFECTIONS INIMPERFECTIONS INCRYSTALSCRYSTALS

BY, MAYUR BAGALE AND SUSHANT MODI.

IMPERFECTIONS IN CRYSTALS

ISSUES TO ADDRESS...

• How do defects affect material properties?• What types of defects arise in solids?• Are defects undesirable?

Crystalline Imperfections There is no such thing as a perfect crystal! • Thermodynamically “impossible”

• “defects” lower the energy of a crystal & make it more stable

• always have vacancies and impurities, to some extent

Defect does not necessarily imply a bad thing • addition of C to Fe to make steel

• addition of Cu to Ni to make thermocouple wires

• addition of Ge to Si to make thermoelectric materials

• addition of Cr to Fe for corrosion resistance

• introduction of grain boundaries to strengthen materials

…… and so on

“Defect” (in this context) can be either desirable or undesirable.

In general, a defect simply refers to a disruption in the crystalline

order of an otherwise periodic material.

CRYSTALLINE CRYSTALLINE IMPERFECTIONS IMPERFECTIONS areare frequently frequently classified according to geometry or classified according to geometry or dimensionality of the defect.dimensionality of the defect.

Point defectsPoint defects Line defectsLine defects Interfacial defects Interfacial defects Bulk or volume defects Bulk or volume defects

Point Defects Atoms in solid possess vibrational energy, some

atoms have sufficient energy to break the bonds which hold them in eqbm position. Hence once the atoms are free they give rise to Point Defects.

Classes of point defects:Intrinsic defects.1.Vacancy2.InterstitialExtrinsic defects 1.Substitution2.Interstitial

VacanciesA lattice position that is vacant because the

atom is missingThere are naturally occurring vacancies in

all crystalsThe concentrations of vacancies increase

with:increasing temperaturedecreasing activation energy

Vacancies -vacant atomic sites in a structure.

Vacancy

distortion

of planes

Self-Interstitial

If the matrix atom occupies its own interstitial site, the defect is called Self Interstitial.

Self-interstitials in metals introduce large distortions in the surrounding lattice.

self-interstitial

distortion of planes

For Ionic Solids, Frenkel and Schottky defects are likely to form.

Schottky Defects When cation vacancy is associated with anion

vacancy, the defect is called Schottky Defect.Frenkel Defects When an atom leaves its regular site and

occupy nearby interstitial site it gives rise to two defects i.e. one vacancy and other self interstitial these two defects are called as Frenkel Defects.

8

• Frenkel Defect

--a cation is out of place.

• Shottky Defect

--a paired set of cation and anion vacancies.

Shottky Defect:

Frenkel Defect

• Equilibrium concentration of defects ~e QD /kT

Adapted from Fig. 13.20, Callister 5e. (Fig. 13.20 is from W.G. Moffatt, G.W. Pearsall, and J. Wulff, The Structure and Properties of Materials, Vol. 1, Structure, John Wiley and Sons, Inc., p. 78.) See Fig. 12.21, Callister 6e.

DEFECTS IN CERAMICDEFECTS IN CERAMIC STRUCTURESSTRUCTURES

11

Boltzmann's constant

(1.38 x 10 -23 J/atom-K)

(8.62 x 10 -5 eV/atom-K)

Nv

Nexp

Qv

kT

No. of defects

No. of potential

defect sites.

Activation energy

Temperature

Each lattice site

is a potential

vacancy site

• Equilibrium concentration varies with temperature!

Equilibrium Concentration:Equilibrium Concentration:Point DefectsPoint Defects

12

Measuring Activation EnergyMeasuring Activation Energy• We can get Qv from an experiment.

Nv

N= exp

Q v

kT

• Measure this...

N v

N

T

exponential dependence!

defect concentration

• Replot it...

1/ T

N

N vln

-Q v /k

slope

Line Defects

Line defects are imperfections in a crystal structure for which a row of atoms have a local structure that differs from the surrounding crystal.

1. Edge dislocations

2. Screw dislocations

Linear Defect (Dislocations)

Are one-dimensional defects around which atoms are misaligned

Edge dislocation:◦extra half-plane of atoms inserted in a crystal

structure◦Burger vector to dislocation line

Screw dislocation:◦spiral planar ramp resulting from shear

deformation◦Berger vector to dislocation line

Edge DislocationEdge Dislocation

Screw Dislocation

Interfacial Defects Are boundaries that have two dimensions

and normally separate regions of the materials that have different crystal structures.

1. External surface2. Grain boundary3. Twin boundary

External Surfaces

Surface atoms have unsatisfied atomic bonds, and higher surface energies, γ (J/m2 or, erg/cm2) than the bulk atoms.

To reduce surface free energy, material tends to minimize its surface areas against the surface tension (e.g. liquid drop).

Grain Boundaries

Polycrystalline material comprised of many small crystals or grains having different crystallographic orientations.

Atomic mismatch occurs within the regions where grains meet. These regions are called grain boundaries.

Segregation of impurities occurs at grain boundary.Grains tend to grow in size at the expense of smaller grains

to minimize surface energy. This occurs by diffusion, which is accelerated at high temperatures.

Dislocations can usually not cross the grain boundary.

Twin Boundaries

Special type of grain boundaries with twin directions mirrored atomic positions across the boundary.

May be produced by shear deformation of BCC/HCP materials (mechanical twin), or during annealing following deformation (annealing twin) of FCC materials

Bulk or Volume DefectsPores

affect optical, thermal, and mechanical properties

Cracks

affect mechanical propertiesForeign inclusions

affect electrical, mechanical, optical properties

22

• Point, Line, and Area defects exist in solids.

• The number and type of defects can be varied and controlled (e.g., T controls vacancy conc.)

• Defects affect material properties (e.g., grain boundaries control crystal slip).

• Defects may be desirable or undesirable (e.g., dislocations may be good or bad, depending on whether plastic deformation is desirable or not.)

SummarySummary

THE END