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Arrangement of Carbon atoms can do wonders!

Carbon Nano Tube (CNT)=Rolled Graphene

BUCKMINISTER

FULLERINE (C60)

=Balled Graphene

Superconducting

DIAMOND

High thermal

conductivity,Insulating

GRAPHENE

Ultra high mobility

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GAS /LIQUID PHASE

coolingAMORPHOUS, NANO XTALLINE

POLY CRYSTALLINE

AND/OR

SINGLE CRYSTAL

Window glass isamorphous

Amorphous Solid

Supercooled Liquid

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Crystalline and amorphous structures illustrated schematically in 2D

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CRYSTALLINE SOLIDS : PERFECT PERIODICITY OF

ATOMIC STRUCTURE; BETTERUNDERSTOOD

AMORPHOUS SOLIDS: LITTLE OR NO PERIODCITY

SOLIDS - 2 VARIETIES

CRYSTALLINE AMORPHOUS

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(a) A simple square lattice. The unit cell is a square with a side a.

(b) Basis has two atoms.

(c) Crystal = Lattice + Basis. The unit cell is a simple square with two atoms.

(d) Placement of basis atoms in the crystal unit cell.

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Oblique Net

Square Net

Centered Rect. NetRectangular Net

Hexagonal Net

2D Bravais Lattice (Surface Crystallography)

http://upload.wikimedia.org/wikipedia/commons/e/ee/2d-bravais.svghttp://upload.wikimedia.org/wikipedia/commons/e/ee/2d-bravais.svghttp://upload.wikimedia.org/wikipedia/commons/e/ee/2d-bravais.svghttp://upload.wikimedia.org/wikipedia/commons/e/ee/2d-bravais.svghttp://upload.wikimedia.org/wikipedia/commons/e/ee/2d-bravais.svghttp://upload.wikimedia.org/wikipedia/commons/e/ee/2d-bravais.svghttp://upload.wikimedia.org/wikipedia/commons/e/ee/2d-bravais.svg

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BRAVAIS LATTICES (3-D)

1. Every lattice point in a 3-D lattice can be described by vectort(defined above)

2. 3-D space can be filled by repeating a smallest volume called

unit cell, defined by vectors a, b, c called lattice parametersand the angles , ,

3. The vectors a, b, c are primitive vectors if the parallelopiped

defined by them does not include any more lattice point.

integersare,,

&vector,naltranslatio

lkh

t

clbkaht

=++=r

r

r

rr

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6. There are 7 ways (obtained by giving different values to a, b,

c, , , and ) which can produce unit cells of variousshapes, and therefore various kinds ofpoint lattice. Theseare referred to as CRYSTAL SYSTEMS (points at corners)

7. As required by crystal symmetry, in 3D, there are 14 waysof arranging points in space lattices such that all the lattice

points have exactly the same surroundings. These are 14

BRAVAIS LATTICES (extra points at center of

cell/face/base)

4. The parallelopiped defined by

primitive vectors is called

primitive unit cell, and it hasthe smallest volume

5. Volume = a1.(a2a3) OR a. (bc)

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The seven crystal systems (unit cell geometries) and fourteen Bravais lattices.

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Contd..The 7 crystal systems (unit cell geometries) and 14 Bravais lattices.

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Q : Why not a new class Base-Centered Tetragonl (See Below) ?

Ans : It does not generate a new on.

It actually yields a Simple Tetragonal.

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Primitive Cell of a Face Centered Cell

Its a Rhombohedral, its axis angle is 60.,each axis is (1/2)times the length of the axes of the cubic unit cell (Volume=1/4)

It possess a cubic symmetry (it possess four 3-fold axes)

It does not belong to the usual Rhombohedral (

=

= 90),

which does not have cubic symmetry (as it only possesses

one 3-fold axis)

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(a) Copper -

face centered cubic (FCC). The atoms are positioned at

well defined sites arranged periodically and there is a long range

order in the crystal.

(b) An FCC unit cell with closed packed spheres.

(c) Reduced sphere representation of the unit cell. Examples: Ag,

Al, Au, Ca, Cu,

-Fe (>912 C), Ni, Pd, Pt, Rh.

Packing of atoms: Face Cenetered Cubic

Cu : Lattice Parameter a = 0.362 nm

Atomic Radius r = 0.128 nm

Face diagonal = 2 a = 4 r

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Examples: Alkali metals (Li, Na, K, Rb), Cr, Mo, W, Mn,

-Fe (< 912 C), -Ti (> 882 C)

Body diagonal = 3 a = 4 r

Body Centered Cubic crystal (BCC) crystal structure.

(a)

A BCC unit cell with closely packed hard spheres

representing the

Fe atoms.(b)A reduced-sphere unit cell.

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%68)3/4(

)3/4(2BCC,For

cellunitinatomsofNumberVolumeCellUnit

meAtomicVolu(APF)FractionPackingAtomic

3

3

=

=

=

r

rAPF

N

N

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(a) The Hexagonal

Close Packed (HCP)

Structure. A collectionof many Zn atoms.

Color difference

distinguishes layers

(stacks).

(b) The stacking

sequence of closely

packed layers isABAB

(c) A unit cell withreduced spheres

(d) The smallest unit cell

with reduced spheres.