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X-RAY DIFFRACTIONX-RAY DIFFRACTION

X- Ray Sources Diffraction: Bragg’s Law Crystal Structure Determination

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For electromagnetic radiation to be diffracted the spacing in the grating should be of the same order as the wavelength

In crystals the typical interatomic spacing ~ 2-3 Å so the suitable radiation is X-rays

Hence, X-rays can be used for the study of crystal structures

Beam of electrons Target X-rays

An accelerating (/decelerating) charge radiates electromagnetic radiation

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A beam of X-rays directed at a crystal interacts with the electrons of the atoms in the crystal

The electrons oscillate under the influence of the incoming X-Rays and become secondary sources of EM radiation

The secondary radiation is in all directions

The waves emitted by the electrons have the same frequency as the incoming X-rays coherent

The emission will undergo constructive or destructive interference with waves scattered from other atoms

Incoming X-raysSecondaryemission

The Diffraction Phenomenon Diffraction occurs when a wave encounters a series of

regularly spaced obstacles that (1) are capable of scattering the wave, and (2) have spacings that are comparable in magnitude to the wavelength.

Furthermore, diffraction is a consequence of specific phase relationships established between two or more waves that have been scattered by the obstacles.

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BRAGG’s EQUATION

d

dSin

The path difference between ray 1 and ray 2 = 2d Sin

For constructive interference: n = 2d Sin

Ray 1

Ray 2

Deviation = 2

Imperfections in Solids

The properties of some materials are profoundly influenced by the presence of imperfections.

It is important to have knowledge about the types of imperfections that exist and the roles they play in affecting the behavior of materials.

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.

1. There are no perfect crystals.2. Many material properties are improved by the presence of

imperfections and deliberately modified (alloying and doping). 6

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• Vacancy atoms• Interstitial atoms• Substitutional atoms

Point defects1-2 atoms

Types of Imperfections

• Dislocations Line defects1-dimensional

• Grain Boundaries Area defects2-dimensional

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• Vacancies:

-vacant atomic sites in a structure.

• Self-Interstitials:

-"extra" atoms positioned between atomic sites.

Point Defects in Metals

Vacancydistortion of planes

self-interstitial

distortion of planes

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In metals, a self interstitial introduces relatively large distortions (strain) in the surrounding lattice since the atom is substantially larger than the interstitial site.

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Boltzmann's constant

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

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

NvN

exp Qv

kT

No. of defects, or equilibrium number of vacancies

No. of potential defect sites

Activation energy – energy required for formation of vacancy

Temperature

Each lattice site is a potential vacancy site

• Equilibrium concentration varies with temperature.

Equilibrium Concentration:Point Defects

Line DefectsLine defects or Dislocations are abrupt change in atomic

order along a line.They occur if an incomplete plane inserted between perfect planes of atoms or when vacancies are aligned in a line. A dislocation is the defect responsible for the phenomenon of slip, by which most metals deform plastically.Dislocations occur in high densities, intimately connected

to almost all mechanical properties which are in fact structure-sensitive.

Dislocation form during plastic deformation, solidification or due to thermal stresses arising from rapid cooling.

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Line defects – Burger’s vector

The magnitude and direction of the lattice distortion associated with a dislocation is expressed in terms of a Burgers vector, denoted by a b.

It is unique to a dislocation, and usually have the direction of close packed lattice direction. It is also the slip direction of a dislocation.

It represents the magnitude and direction of distortion associated with that particular dislocation.

Two limiting cases of dislocations, edge and screw, are characterized by Burger’s vector perpendicular to the dislocation line (t) and Burger’s vector parallel to the dislocation line respectively. Ordinary dislocation is of mixed character of edge and screw type.

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Line defects – Edge dislocation

It is also called as Taylor-Orowan dislocation. It will have regions of compressive and tensile stresses on

either side of the plane containing dislocation.

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Burger’s vector, b: measure of lattice distortion

Edge dislocation: extra half-plane of atoms

inserted in a crystal structure; the edge of the plane terminates within the crystal.

Around the dislocation line there is some localized distortion.

b perpendicular () to dislocation line

Line defects – Screw dislocation

It is also called as Burger’s dislocation.It will have regions of shear stress around the dislocation lineFor positive screw dislocation, dislocation line direction is

parallel to Burger’s vector, and vice versa.

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Line defects – Dislocation motion

Dislocations move under applied stresses, and thus causes plastic deformation in solids.

Dislocations can move in three ways – glide/slip, cross-slip and climb - depending on their character. Slip is conservative in nature, while the climb is non- conservative, and is diffusion-controlled.

Any dislocation can slip, but in the direction of its burger’s vector.

Edge dislocation moves by slip and climb.Screw dislocation moves by slip / cross-slip. Possibility for

cross-slip arises as screw dislocation does not have a preferred slip plane as edge dislocation have.

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Interfacial defects

An interfacial defect is a 2-D imperfection in crystalline solids, and have different crystallographic orientations on either side of it.

Region of distortion is about few atomic distances.They usually arise from clustering of line defects into a

plane. These imperfections are not thermodynamically stable, but

meta-stable in nature.E.g.: External surface, Grain boundaries, Stacking faults,

Twin boundaries, Phase boundaries.

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Bulk or Volume defects

Volume defects are three-dimensional in nature. These defects are introduced, usually, during

processing and fabrication operations like casting, forming etc.

E.g.: Pores, Cracks, Foreign particlesThese defects act like stress raisers, thus deleterious to

mechanical properties of parent solids. In some instances, foreign particles are added to

strengthen the solid – dispersion hardening..

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