Imperfections in Solids

All solids contain large number of imperfections or deviations from crystalline perfection.

Only single crystals have a near perfect crystalline structure.

Presence of imperfections has a profound influence on the material properties (eg. optical, electrical, thermal, chemical, mechanical, etc.)

Point Defects Vacancies

Vacant lattice sites which increase the entropy or randomness of a crystal.

A vacancy is formed when an atom is missing from a normal site during solidification from high temperatures or radiation damage.

The equilibrium number of vacancies (Nv) increases with temperature (T):

)exp(kTQ

NN vv =N = total number of atomic sitesQv = energy required to form a vacancy

k = Boltzmanns constant (1.38x10-23 J/atom-K)

Example ProblemCalculate the equilibrium number of vacancies/m3 for copper at 1000C. The energy for vacancy formation is 0.9 eV/atom; the atomic weight and density (at 1000C) for copper are 63.5 g/mol and 8.4 g/cm3, respectively.

= 8.0 1028 atoms/m3

At 1000C (1273 K)

= 2.2 1025 vacancies/m3

Cu

A

ANN =

molgmcmcmgmolatoms

/5.63)/10)(/4.8)(/10023.6( 336323=

)exp(kTQ

NN vv =

= )1273)(/1062.8(

9.0exp)/100.8( 5328

KKeVeVmatoms

Self- Interstitials Host atoms that occupy

interstitial sites and their presence can cause large distortions in the surrounding lattice.

Self-interstitial and vacancy.

Impurities /Additives

Foreign atoms that occupy the lattice or interstitial sites of metals to form alloys.

Presence of impurity atoms can lead to formation of a solid solution and/or a new second phase.

Solid Solutions

A solid solution is formed when foreign atoms are added to the host material.

The crystal structure of the host material is maintained and no new structures or phases are formed.

Substitutional solid solution Foreign atoms substitute

for the host atoms. The degree of substitution

depends on (a) the atomic size, (b) crystal structure, (c) electronegativity and (d) valency of the foreign atoms.

Get complete solubility if the foreign atom has a similar size (R 15%), crystal structure, and electronegativity but higher valency.

eg. Copper/Nickel large substitutional atom

small substitutional atom

Characteristics of copper and nickel.

Cu Ni

Atomic size (nm)

0.128 0.125

Crystal structure FCC FCC

Electronegativity 1.9 1.8

Valency +1 +2

Interstitial solid solution Small foreign atoms (eg.

C, N, H) fill the voids or interstitials among the host atoms.

eg. carbon (2%)-Iron (Steel)

RFe = 0.124 nm RC = 0.071 nm

Line Defects

Dislocations Line defects around which some of the atoms

are misaligned. Movement of dislocations leads to deformation

in metals and ceramics. The direction and distance that a dislocation

moves in each step is known as the Burgers vector (b).

Edge Dislocation () A dislocation

introduced into the lattice by adding an extra half plane of atoms.

The Burgers vector and the dislocation are perpendicular to each other.

Slip system of an edge dislocation.

Screw Dislocation (3)A dislocation produced by shearing a crystal so that one atomic plane produces a spiral ramp about the dislocation.

The Burgers vector and the dislocation are parallel to each other.

Mixed Dislocation (,3)A dislocation that contains partly edge components and partly screw components.

Electron Micorgraphs of Dislocations

Dislocation loops. Dislocation network.

Example ProblemCalculate the length of the Burgers vector in copper (nm).

36151.0=a

The close-packed directions are or along the face diagonals.

Face diagonal:

4R = (0.36151) = 0.51125 nm=2a 2

b= 2R = 0.25563 nm=)51125.0(21

Interfacial Defects

Boundaries that have two dimensions which separate regions of the materials that have different crystal structures or crystallographic orientations.

External surfaces

Boundaries where the crystal structure terminates.

Due to incomplete bonding, surface atoms have higher energy and more reactive than the bulk of the material.

Grain Boundaries

Low-angle and high-angle grain boundaries.

Boundaries between two grains having a different orientations in a polycrystalline material.

There is lack of regular bonding and some atomic mismatch or disorder within the grain boundary.

Hence grain boundaries have a higher energy state and are more chemical reactive than the grains.

Bamboo (x-section)

Bamboo (longitudinal section)

Diffraction Patterns of Bamboo with Fibre Bundles Aligned: (a) Parallel and (b) Perpendicular to the Surface.

Tooth Enamel x-section

Tooth Enamel axial section

Nano and Microstructure of CeO2/CuO Nano/Molecular Level Composite Powder

Layer-by-Layer Lattice Composite in Li1+x-y Nb1-x-3yTix-4yO3

FerroelectricLN cells

PhaseBoundary

A small angle grain boundary is produced by an array of dislocations causing a small misorientation of the lattice across the surface of the imperfection.

Formation of a tilt boundary from edge dislocations.

Tilt boundary formed by edge dislocations

Twist boundary formed by screw dislocations.

Twin BoundariesBoundaries across the twins where there is a mirror image mis-orientation of the lattice.

Twins are formed from atomic displacements due to mechanical shear forces (mechanical twins) or annealing heat treatments following deformation (annealing twins).

Mechanical twins are found in BCC and HCP metals.

Annealing twins are found in FCC metals.

Stacking FaultsSurface defects in FCC metals caused by the improper stacking sequence of close-packed planes.eg. FCC lattice ABCABCABCABC..

Stacking fault ABCABABCBACA.

Surface Energy (J.m-210-3)

Surface Defect

Al Cu Pt Fe

Grain boundary

625 645 1000 780

Twin boundary

120 45 195 190

Stacking fault

200 75 95 -

Volume Defects

Cracks, pores, foreign inclusions and other phases.

Imperfections in SolidsImpurities /AdditivesSolid SolutionsCharacteristics of copper and nickel.Line DefectsSlip system of an edge dislocation.Screw Dislocation ()Mixed Dislocation (,)Electron Micorgraphs of DislocationsInterfacial DefectsBamboo (x-section)Bamboo (longitudinal section)Diffraction Patterns of Bamboo with Fibre Bundles Aligned: (a) Parallel and (b) Perpendicular to the Surface.Tooth Enamel x-sectionTooth Enamel axial sectionNano and Microstructure of CeO2/CuO Nano/Molecular Level Composite PowderLayer-by-Layer Lattice Composite in Li1+x-y Nb1-x-3yTix-4yO3