CRYSTAL

DEFECTS (Cacat Kristal)

BY GROUP 2

PHYSICAL METALLURGY 1 - TMT614207 A

3334131364 ACTUR S. NUGROHO

3334130675 DESY AKMALIA

3334132631 EBEN U. SANTOSO

3334130779 GINANJAR SAPUTRA

3334130181 ISMI P. PERMATASARI

Crystals are like people, it is the defects in

them which tend to make them interesting.

Colin Humphreys

If we assume a perfect crystal structure containing pure elements, then anything that deviated from this concept or intruded in this uniform homogeneity would be an imperfection, or a defect.

On an atomic scale, all crystalline materials contain large numbers of various defects or imperfections.

As a matter of fact, many of the properties of materials are profoundly sensitive to deviations from crystalline perfection.

Classification of crystalline imperfections is frequently made according to geometry or dimensionality of the defect.

CLASSIFICATIONS

Crystal Defects

Point Defects

Vacancy

Self-interstitial

Substitutional

Linear Defects (Dislocations)

Edge dislocations

Screw Dislocations

Surface Defects

Grain Boundaries

Twinning

1. POINT DEFECTS

Figure 1. Disruptions of the perfect arrangement of the surrounding atoms: (a) vacancy, (b) interstitial atom, (c) small substitutional atom, (d) large substitutional atom, (e) Frenkel defect, (f) Schottky defect.

1.1 VACANCIES Vacancy

distortion

of planes

Boltzmann's constant

N v

N = exp

Qv k T

# vacancy

# vacant sites

Activation energy energy required to form

vacancy

Temperature

in kelvins 1.381023 J/atom-K;

8.6210-5 eV/atom-K

Vacancy: lattice site which is normally occupied becomes

vacant because an atom or an

ion is missing.

The equilibrium number of vacancies Nv for a given quantity of material depends on and increases with temperature according to:

The number of vacancies increases exponentially with temperature.

Figure 2

1.2 SELF-INTERSTITIALS

A self-interstitial is an atom from the crystal that is crowded into an interstitial site, a small void space that

under ordinary circumstances is not occupied.

Figure 3

In metals, a self-interstitial introduces relatively large distortions (strain) in the surrounding lattice because

the atom is substantially larger than the interstitial

position in which it is situated.

self-

interstitial distortion of planes

1.3 POINT DEFECTS in ionic compounds (e.g. ceramics)

Vacancies exist in ceramics for both cations and anions

Interstitials exist for cations.

Interstitials are not normally observed for anions because anions are relatively large to the interstitial sites.

Cation

Interstitial

Cation

Vacancy

Anion

Vacancy Figure 4

1.3 POINT DEFECTS in ionic compounds (e.g. ceramics)

Frenkel defects: involves

a cationvacancy and a

cationinterstitial pair.

A cation leaves its normal

position and moves into an

interstitial site.

Schottky

Defect

Frenkel

Defect

Reminder: When atomic defects in ceramics occur, conditions of

electroneutrality (equal numbers of + and - charges from the ions)

must be maintained.

Schottky defects:

a cation vacancyanion vacancy pair. One cation and one

anion are removed from the interior of the crystal and

then placed at an external surface.

Figure 5

1.4 IMPURITIES

Figure 6

The addition of impurity atoms to a metal results in the formation of a solid solution.

The impurity defects in the solid solution are either substitutional or interstitial.

Substitutional defects occur when an atom is removed from a regular lattice point and replaced with a

different atom, usually of a different size.

Substitutional solid solution.

(e.g., Cu in Ni)

Interstitial solid solution.

(e.g., C in Fe)

Figure 7

HUME-ROTHERY RULES

To form a substitutional solid solutions, the solute and solvent must follow the following rules:

1. r < 15%

2. Similar electronegativities

3. Same crystal structure

4. Same valence

To form a interstitial solid solutions:

1. Solute atoms must be smaller than the pores in the solvent lattice.

2. Solute and solvent have similar electronegativity.

Solute: present in minor concentration

Solvent: host atoms; element that is present in the greatest amount

2. LINEAR DEFECTS (DISLOCATIONS)

A dislocation is a linear (one-dimensional) defect around which some of the atoms are misaligned.

Virtually, all crystalline materials contain some dislocations that were introduced during

solidification, during plastic deformation, and as a

consequence of thermal stresses that result from

rapid cooling.

2.1 EDGE DISLOCATION

There is some localized distortion around the

dislocation line.

b is perpendicular () to dislocation line.

An extra portion or a half-plane of atoms inserted in a crystal structure; the edge of the plane terminates

within the crystal.

b is the Burgers vector: magnitude and direction of the lattice distortion associated with a dislocation.

Figure 8

Dislocation motion requires the successive bumping of a half plane of atoms (from left

to right).

Bonds across the slipping planes are broken and remade in succession.

The (plastic) permanent deformation of most crystalline materials is caused by

dislocation movement

Figure 9

Figure 10

2.2 SCREW DISLOCATION

Formed by a shear stress that is applied to produce

the distortion.

Screw dislocation derives its name from the spiral

or helical path or ramp

that is traced around the

dislocation line by the

atomic planes of atoms.

The spiral stacking of crystal planes leads to the Burgers vector b being parallel () to the dislocation line.

Figure 11

Most dislocations found in crystalline materials are

probably neither pure edge

nor pure screw, but exhibit

components of both types;

these are termed mixed

dislocations.

Dislocations can be observed in crystalline materials using electron-microscopic

techniques.

Picture on the left shows a transmission electron micrograph of a titanium alloy in

which the dark lines are dislocations

(51.450)

Figure 12

Figure 13

2.3 SCHMIDS LAW

=

=

0

=

0

= =0

=

=

0

Schmids

factor

= total stress that works on the slip plane; = tensile force; 0= specimens area; = slip planes area

Plastic deformation by slip (dislocation) is due to shear stresses.

Even if tensile force on is applied the specimen the shear stress resolved onto the slip plane is responsible for slip.

When the Resolved Shear Stress (RSS) reaches a critical value Critical Resolved Shear Stress (CRSS) plastic deformation starts

(The actual Schmids law)

Figure 14

3. SURFACE DEFECTS

Surface / interfacial defects:

Boundaries that have two dimensions and normally separate regions of the materials that

have different crystal structures and/or

crystallographic orientations.

These defects include grain boundaries, twin

boundaries, stacking faults, and phase boundaries.

3.1 GRAIN BOUNDARIES

Grain boundary: a surface defect that

separates regions of different crystalline orientation (such as

grains) within a polycrystalline solid.

Grain boundaries are usually the result of

uneven growth when the solid is

crystallizing.

Grain boundaries tend to decrease the electrical and thermal conductivity of the material.

Figure 15

Grain boundaries have two types, as per their

orientation:

Low-angle grain boundaries: orientation mismatch is less than about 11 degrees.

High-angle grain boundaries: orientation mismatch is greater than about 11 degrees.

Most grain boundaries are preferred sites for the

onset of corrosion and for the precipitation of new

phases from the solid.

They are also important to many of the mechanisms of

creep. On the other hand, grain boundaries disrupt

the motion of dislocations through a material.

3.2 TWIN BOUNDARIES

A twin boundary is a special type

of grain

boundary across

which there is a

specific mirror

lattice symmetry.

Atoms on one side of the boundary are located in mirror image positions of the atoms on the other side.

The region of material between these boundaries is appropriately termed a twin.

Figure 16

3.2 TWIN BOUNDARIES

Mechanical twins:

Result from atomic displacements that are produced from applied mechanical shear forces.

Observed in BCC and HCP metals.

Annealing twins:

Result during annealing heat treatments following deformation.

Typically found in metals that have the FCC crystal structure.

3.3 MISCELLANEOUS

SURFACE DEFECTS

Stacking faults:

Found in FCC metals when there is an interruption in the ABCABCABC. stacking sequence of close-packed planes

Phase boundaries:

If more than one phase is present in a given system, each will have its own distinct properties, and a boundary separating the phases will exist across which there will be a discontinuous and abrupt change in physical and/or chemical characteristics.

4. THE IMPORTANCE OF

DEFECTS

It depends upon the material, type of defect, and properties, which are being considered.

The term defect carries the connotation of undesirable qualities, BUT defects are responsible for many of the important properties of materials.

Some properties (e.g. density and elastic constants), are proportional to the concentration of defects. A small defect concentration will have a very small effect on these.

The color of an insulating crystal or the conductivity of a semiconductor crystal, may be much more sensitive to the presence of small number of defects.

Much of material science involves the study and engineering of defects so that solids will have desired properties.

A defect free, i.e. ideal silicon crystal would be of little use in modern electronics. Its use is dependent upon small concentrations of chemical impurities such as phosphorus and arsenic which give it desired properties.

REFERENCES

Callister, William D. 2001. Fundamentals of Materials

Science and Engineering, An Interactive, 5th Edition.

New York: John Wiley & Sons.

Callister, William D. 2007. Materials Science and

Engineering, An Introduction, 7th Edition. New York:

John Wiley & Sons.