crystal structure ppt

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UNIT - II Structure and imperfections in crystals: crystal structure crystal geometry,

structure of solids, methods of determining structures. Imperfections in crystals

!ypes of imperfections. "oint imperfection, diffusion in solids self diffusion fic#$s

la%, self diffusion. applications of diffusion.



CONTENTS

&rystal Structure

'hy do you study the structure of crystalline solids(

&rystalline Solids

)on crystalline solids or *morphous crystals

"olycrystalline Solid

+undamental terms of crystallography

!ypes of crystals

ra-ais attices

&rystal structure of material12/01/15 07:31 2



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Crystal Structure

&rystallography deals %ith the study of all possi le types of crystals and determinationof the actual structure of the crystalline solids y ay iffraction method, )eutron

eams or lectron eams etc.

In all the materials, the atoms or molecules or ions are arranged in three dimensional

structure.!he atomic arrangements in crystals is termed as crystal structure

!he solid are classified into t%o categories ased on the arrangement of atoms or

molecules in the solid.

&rystalline solids*morphous solids 4)on metallic &rystals



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Why do you study the structure of crystalline solids?

!he properties of some materials are directly related to their crystal structures.

+or e6ample. "ure and undeformed magnesium and eryllium ha-ing one crystal

structure

!hese are much more rittle i.e. fracture at lo%er degrees of deformation than that of gold

and sil-er 4ha-ing another crystal structure

Significant property differences e6ist et%een crystalline and noncrystalline materials

ha-ing same composition.

+or e6ample, non crystalline ceramics and polymers normally are optically transparent

the same materials in crystalline 4or semi crystalline form tend to e opa8ue or at est

translucent



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Crystalline Solids!he solids in %hich the atoms are arranged in some regular manner in all three directions

of crystals are called crystalline solids

!he crystalline solids ha-e different periodic arrangement in all the three directions andthe physical properties are -ary %ith directions are called anisotropic su stances.

!he structure may e made up of metallic crystals or non metallic crystals.

!he metallic crystals are mainly used in engineering application ecause of their strength,

conducti-ity and reflection

g. &opper, sil-er, aluminium and tungsten etc.

crystalline SiO 2

Si Oxygen



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Non crystalline solids or Amorphous crystals!he atoms or molecules are arranged in irregular manner in all directions are called

amorphous crystals or non crystalline solids.

*morphous solids ha-e irregular structure and ha-e same physical properties in all

directions are called isotropic su stances. Such materials ha-e no specific electrical

property, ut ha-e only plasticity

g. 9lass, plastics and ru er



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"olycrystalline Solid"olycrystal is a material made up of an aggregate of many small single crystals 4also

called crystallites or grains .!he grains are usually 100 nm 100 microns in diameter. "olycrystals %ith grains that are

;10 nm in diameter are called nanocrystalline

Polycrystal

PolycrystallinePyrite form

(Grain)

http://www.alaskanessences.com/gembig/Pyrite.jpg



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Fundamental terms of crystallo raphy !attice

* lattice is a regular and periodic arrangement of points in three dimensions.

It can e e6pressed in another %ay.In an arrangement of points, if the surrounding en-ironment loo#s li#e same %hen

the arrangement -ie%ed from the different lattice points, then that arrangement is

said to e lattice.



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"asis

!o construct the crystal structure, some asic arrangement is to e fi6ed at each and e-ery

lattice point.

!he asic arrangement is said to e asis or motif

Crystal structure

* crystal structure is o tained y arranging the asis in each and e-ery lattice point. It can

e %ritten as

&rystal structure < lattice = asis

!his is used to e6plain the formation of crystal structure



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Unit cell

>nit cell is defined as a fundamental uilding loc# of a crystal structure

Its geometry and atomic positions define the crystal structure.



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#rimiti$es

et a, , c are the length along the a6es 6,y,? in cu ic

cell is called primiti-es

!attice parameter

!o represent a unit cell, the interfacial angles and intercept in a6es are important.

!hese parameters are called lattice parameters

Intera%ial an les or interfacial an les

In the crystal, the angles et%een 6, y and ? a6es are called interfacial angles it is

represented y @, A and B

a

b

c



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#rimiti$e cell

It is the smallest unit cell in -olume constructed y primiti-es. It consists of only one full

atom.

If a unit cell consists of more than one atom, then it is not primiti-e cell

* simple cu ic cell is said to e primiti-e cell, %here as a ody centered cu ic unit cell is

not a primiti-e cell

a 1

a 3

a 2

Primitive Cell:

• Smallest building blockfor

the crystal structure

!e"etition of the "rimitive cell

crystal structure



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Important )ote:

attice points are a purely mathematical concept,

%hereas atoms are physical o Cects.

attice "oints do not necessarily lie at the center of atoms.

+or e6ample, the only element e6hi iting Simple &u ic structure is "o &#olonium'(

In +igure 4a is the 3 periodic arrangement of "o atoms, and

+igure 4 is the corresponding space lattice.

In this case, atoms lie at the same point as the space lattice.



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Types of crystals&rystallographers ha-e classified crystalline su stances into systems and classes

according to the e6ternal symmetry of indi-idual %ell informed crystals.

!here is a total of 230 possi le crystal forms or space groups.

Dn the asis of their symmetry, these forms may e grouped into 32 crystal classes or

point groups.

!hese 32 crystal classes are grouped into se-en crystal system on the asis of the unit

cell.

!hese are classified in terms of length of unit cells and the angle of inclination et%een

them. &u ic

!riclinic

!etragonal!rigonal

Ee6agonal

Drthorhom ic

Fonoclinic



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#ossi)le Crystal Classes



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#ossi)le Crystal Classes

$



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ra$a s a cesIn 1GH , ra-ais sho%ed that there are 1H ra-ais lattices in three dimensional space .

!hese are o tained y com ining one of the se-en lattice systems 4or a6ial systems %ith

one of the se-en lattice types 4or lattice centerings .

In general, the lattice systems can e characteri?ed y their shapes according to the

relati-e lengths of the cell edges 4 a , b, c and the angles et%een them 4 α, β , γ .

!he lattice types identify the locations of the lattice points in the unit cell as follo%s:

"rimiti-e 4" : lattice points on the cell corners only 4sometimes called simple

ody &entered 4I : lattice points on the cell corners %ith one additional point at the center

of the cell

+ace &entered 4+ : lattice points on the cell corners %ith one additional point at the center

of each of the faces of the cell

ase &entered 4*, , or & : lattice points on the cell corners %ith one additional point at

the center of each face of one pair of parallel faces of the cell 4sometimes called end centered

hom ohedral 4 : lattice points on the cell corners only %here a < b < c and α < β < γ J

G0K 4special case for the rhom ohedral lattice system

https://en.wikipedia.org/wiki/Lattice_system

https://en.wikipedia.org/wiki/Rhombohedral_lattice_system

https://en.wikipedia.org/wiki/Rhombohedral_lattice_system

https://en.wikipedia.org/wiki/Lattice_system



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Crystal structure of material Some of the important parameters %hich are used to descri e the crystal structure of

materials.

*tomic radius

&oordination num er

ensity of pac#ing

Atomic *adius

It is the half the distance et%een the any t%o successi-e atoms.

+or e6ample cu ic system,

r < a / 2

%here a is the interatomic distance

Coordination Num)er

It is the num er of nearest neigh oring atoms to a particular atom.

e.g.. Simple cu ic unit cell, the coordination num er is L



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+ensity of #ac,in

It is the ratio et%een the total -olume occupied y the atoms or molecules in a unit cell

and the -olume of unit cell. i.e.

!otal -olume occupied y atoms in a unit cell

ensity of pac#ing <

Molume of the unit cell

)um er of atoms present in a unit cell 6 -olume of one atom

ensity of pac#ing <

Molume of the unit cell



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&rystal symmetry

!he atom or ions in a natural crystal are arranged in a regular and periodic manner in

three dimensions.

!he property, %hich ma#es the unit cells of the crystals are indistinguisha le et%een

their original position and the ne% position o tained after performing any one or

more operations li#e rotation, reflection etc. is #no%n as symmetry.

!hree different types of symmetry

*6is symmetry

"lane symmetry

&entre of symmetry



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A%is of symmetry

* unit cell is said to possess a6is of symmetry if its ne% position, o tained after

performing a symmetrical operation li#e rotation, reflection, remains in-ariant from its

initial position.

In general, the unit cell of a crystal is said to posses n fold a6is of symmetry, if it

remains in-ariant from initial position and the ne% position o tained after performing

rotation through 43L0 / n 0 .

+i-e different types of a6is of symmetry

Dne fold a6is of symmetry or identity

!%o fold a6is of symmetry or diad a6is

!hree fold a6is of symmetry or triad a6is

+our fold a6is of symmetry or tetrad a6is

Si6 fold a6is of symmetry or he6ad a6is



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#lane of symmetry

!he symmetrical operations, li#e mirror image or reflection, performed in a unit cell

y ta#ing a plane, is #no%n as plane of symmetry.

* cu ic unit cell has nine planes of symmetries

Dthers are three direct planes and si6 diagonal plane

Centre of symmetry

It is a symmetrical operation performed y ta#ing a centre point.

If a line is dra%n through the centre of a unit cell, it %ill pass through the centre of the

opposite faces and the line is at e8uidistance from the edges of the unit cell.

* unit cell has only one centre of symmetry.

!he total num er of symmetries present in a cu ic unit cell is 23



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Countin !attice #oints Atoms in .+ !attices>nit cell is Primitive (1 lattice point) ut contains TWO atoms in the Fotif

*toms at the corner of the 2 unit cell contri ute only 1/4 to unit cell count

*toms at the edge of the 2 unit cell contri ute only 1/2 to unit cell count

*toms within the 2 unit cell contri ute 1 4i.e. uni8uely to that unit cell



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Countin Atoms in /+ Cells*toms in different positions in a cell are shared y differing num ers of unit cells Merte6

atom shared y 8 cells N 1/8 atom per cell

dge atom shared y 4 cells N 1/4 atom per cell

+ace atom shared y 2 cells N 1/2 atom per cell

ody uni8ue to 1 cell N 1 atom per cell

crystal structure ppt

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