‘’IMPERFECTIONS IN SOLIDS’’

IE-114 Materials Science and General Chemistry

Lecture-4

1) Imperfect crystal

2) Types of Imperfections (Point, Linear, Area)

3) Microscopic Examination of defects and

the structure of materials

Outline

Perfectly ordered

crystalline structure

Imperfection

Such an idealized solid generally does not exist

All solids contain large number of various

defects or imperfections

Defects may exist:

1) In impure metals or alloys (Substitutional or interstitial foreign

atoms)

2) During solidification (e.g. Grain boundaries, dislocations, vacancies) 3) During deformation (e.g. Dislocations)

The properties (mechanical, optical, electrical, etc.) of the materials are profoundly influenced by the presence of imperfections (defects)

The influence is not always adverse, often specific characteristics are enhanced.

EXAMPLE 1: Mechanical property

Materials are stronger when they have defects

Pure iron & Fe-C alloy

Pure iron : soft and ductile

Fe-C alloy (steel) : strong and tough

EXAMPLE 2: Electrical conductivity

Electrical conductivity decreases when materials have defects

Electrical conductivity of pure copper is higher than that of impure copper Impure Copper: Copper containing impurity (unwanted) elements

Why study Imperfections in Solids?

O-Dimensional (point) defects

(associated with one or two atomic positions)

Vacancies

Impurities

a) Interstitial atoms

b) Substitutional atoms

1-Dimensional (line) defects

Dislocations (edge, screw and mixed dislocations)

2-Dimensional (area) defects

Stacking Faults

External Surfaces

Grain Boundaries (High angle and small angle grain boundaries)

3-Dimensional (volume) defects

Cracks, pores, foreign inclusions

Types of Imperfections:

Vacancies

Self interstitials

Impurities (seen in solid-solution alloys)

vacant atomic sites in a structure.

Vacancydistortion of planes

O-Dimensional (point) defects

A lattice vacancy is equivalent to missing atom or ions (in case of ionic crystal).

Formed during solidification or as a result of atomic vibration (atomic vibration increases by temperature)

1) Vacancy

Equilibrium concentrations of

vacancies

* As T increases the number of vacancies increases exponentially.

For most of the metals just below melting point, the fraction of vacancies (N/Nv) is

on the order of 10-4. This means one lattice site out of 10.000 is empty.

Example:

Find the equilibrium # of vacancies in 1m3 of Cu at 1000oC.

• Given:

Solution:

"extra" atoms positioned between atomic sites.

self-interstitialdistortion

of planes

Atoms of same type accomodate into interstitial sites,

which are not occupied under ordinary circumstances.

Self interstitial defects produce large lattice distortion.

Because self-interstitial atoms usually larger than the void

space (interstitial sites).

2) Self-Interstitials:

A pure metal consisting of only one type of atom just isn’t

possible; impurity or foreign atoms will always be present, and

some will exist as crystalline point defects.

The addition of impurity atoms to a metal will result in the formation of SOLID SOLUTION or a new second phase (, ,

)

Solvent: Represents the element or compound that is

present in the greatest amount (host atoms)

Solute : An element or compound present in a minor

concentration (e.g. Impurity atoms)

3) Impurities in solids

A foreign atom (the solute), whether it be an impurity atom or deliberate

alloying addition, can occupy one of two distinct positions in a crystal,

(1) Substitutional alloy

(e.g., Cu in Ni)

(2)Interstitial alloy

(e.g., C in Fe)

Solid Solutions

Solute atoms substitute for solvent atoms in a

crystalline lattice Solute atoms( C, H, O, N) fit into spaces

between solvent atoms in a crystalline lattice.

Some important features for

substitutional solid solution

1) Atomic size difference should be less than 15%. Otherwise the solute

atoms will create substantial lattice distortions and a new phase will form.

2) Crystal structure should be the same.

3) Electronegativities should be similar to prevent the ionic bonding.

4) Valances:Other factors being equal, a metal has a higher tendency to dissolve another metal of higher valency.

EXAMPLE: Cu-Ni solid solution. The type is substitutional. WHY?

Because: a) Radii for Cu and Ni are 0.128 and 0.125 nm respectively.

b) They both have FCC structure.

c) Their electronegativities are 1.9 and 1.8 for Cu and Ni respectively.

d) The most common valence is +1 for Cu and +2 for Ni.

Impurity atoms fill the voids or interstices among the host atoms.

Interstitial atoms introduce lattice strains since most of the interstitial atoms have atomic radii higher than interstitial site’s radius

For metals with a high APF, the interstitial positions are small in size and therefore the diameter of the impurity atoms should be smaller than that of the host atoms.

The concentration of impurity atoms is low (<10 %).

(For example, in Fe-C alloys in which carbon is an interstitial atom, max. Carbon solubility is 2%)

Some important features for

interstitial solid solutions

Summary of point defects

Specification of Composition

Weight percent

100x %BA

A

mm

mAcomponentofwt

mA = mass of component A

Atomic percent

nA = number of moles of component A= mA/ MWA

Consider an alloy system containing components A and B;

100x %BA

A

nn

nAcomponentofat

MWA = molecular weight of A, gr/mol

Composition Conversions

Assume that you have an A-B alloy;

at. % A + at. % B =100 % wt. % A + wt. % B =100 % or

at.% A = (wt.%A / MWA) / [(wt.%A / MWA) + (wt.%B / MWB)]

at.% B = (wt.%B / MWB) / [(wt.%A / MWA) + (wt.%B / MWB)]

Where MW is molecular weight of each component, gr/mol

wt.% A = (at.%A x MWA) / [(wt.%A x MWA) + (wt.%B x MWB)]

wt.% B = (at.%B x MWB) / [(wt.%A x MWA) + (wt.%B x MWB)]

Convertion from wt% to at%

Convertion from at% to wt%

• cause slip between crystal plane when they move,

• produce permanent (plastic) deformation.

Dislocation: It is a group of point defects forming a linear one

dimensional defect in the structure of the material.

Edge Dislocation

Screw Dislocation

Mixed Type of Dislocation

Types of Dislocations

Dislocations (edge, screw and mixed dislocations)

Dislocations are introduced;

during solidification of crystalline solids

by the permanent deformation of crystalline solids

1-Dimensional (line) defects

1)Edge dislocation:

Edge dislocation is shown by symbol ‘’ ’’

Extra plane of atoms causes localized lattice distortion.

The magnitude and direction of lattice distortion is expressed in terms

of a Burgers vector, b, which is perpendicular to edge dislocation line.

(Perpendicular to the plane of

page)

Atoms squeezed together

Atoms pulled

apart

is created in a crystal by insertion of an extra half plane of atoms

Edge Dislocation Motion

Dislocation line is linear.

Burgers vector is parallel to dislocation line.

2) Screw Dislocation: can be formed in a perfect crystal by applying upward and

downward shear stresses to regions of a perfect crystal

Dislocation line

Edge dislocation

Screw dislocation

3) Mixed dislocations: very common

Mixed dislocation has both edge and screw character

Nature of dislocation is defined by relative orientations of dislocation

line and Burgers vector

Dislocation line and Burger’s vector (b)

Relation

Edge Screw Mixed

Relative

orientation

Perpendicular Parallel Neither parallel

nor

perpendicular

Direction and magnitude of Burger’s vector;

Direction : In the close packed crystallographic direction

Magnitude: One interatomic distance

2-Dimensional (area) defects

Interfacial (area) defects are boundaries that have two dimensions and

separate regions of different crystal structures or crystallographic

orientations.

External Area Defects Internal Area Defects

Grain Boundaries

Twin Boundaries

Stacking Fault

Phase boundaries

External Surface

1)External surface: is the boundary of material at which the

structure terminates.

e.g. Solid-gas, solid-liquid

Surface atoms are not bonded (surface have higher energy state than the atoms at

the inner parts of the structure). This energy is called surface energy (J/m2 or

erg/cm2). To minimize this energy, materials minimizes the surface area.

2) Grain boundary:

Grain boundary may be defined as the interface between crystals that

differ in crystallographic orientation, composition or dimension of the crystal

lattice (in some cases in two or all of these).

A) High Angle Grain Boundary

B) Small Angle Grain boundary

Tilt boundary

Twist boundary

grain boundaries

t=t1 t=t2

t=t3 t=t3

Structure of the

material seen under

microscope

Completely solid. Material

contains many

grains(polycrystalline material)

Liquid and small

crystals

Liquid and relatively larger

crystals

2.1. High-angle grain boundary

Formed during solidification

Fracture surface of a steel

a.1. Tilt boundary

Orientation mismatch is slight, on the order of

a few degrees. Tilt boundary is formed when

dislocations are aligned, Angle represents

angle of misorientation.

a.2. Twist boundary

Results from arrays of screw dislocations

2.1. Small-angle grain boundary

3)Twin Boundary: is a special type of grain boundary across which

there is a mirror lattice symmetry.

observed due to atomic displacements produced as a result of shear force

application and during annealing heat treatments following deformation.

Annealing twin is commonly observed in materials with FCC structures.

Mechanical twins are observed in BCC and HCP metals.

Twinning plane

Energies of Boundaries

External Surface

High Angle Grain Boundary

Low Angle grain Boundary

Energy is related to number of unbonded atoms through the interface

Increasing energy

Chemical reactivity increases as the energy of the boundary increases

Observation of Crystal Defects

Macroscopic Examination

Microscopic Examination (optical and electron microscopes (SEM,

TEM))

Sample Preparation Steps for Microscopic Examination

Surfaces of metals are prepared before examination

1) Cutting

2) Grinding (with emery papers)

3) Polishing (water+Al2O3 solution or diamond paste)

4) Etching (acid solutions)

More reaction is observed in defects having higher energies

• Useful up to 2000X magnification.

Optical Microscopy

Examination of Grain Boundaries by optical microscope

are more susceptible to etching

may be revealed as dark lines

Polished Surface Grain Boundary Phases

Electron Microscopy

Beam of electrons of shorter

wave-length (0.003nm) (when

accelerated across large voltage

drop)

High resolutions and

magnification (up to 50,000x

SEM); (TEM up to 1,000,000x)

Dislocation are observed using

TEM(transmission electron

microscope)