Lecture 4

Lecture 4 Packing of atoms in

solids

Jayant Jain Assistant Professor,

Department of Applied Mechanics, IIT Delhi, Hauz Khas, 110016

Density Elastic modulus, stiffness of individual bonds Melting temperature, bond energy Coefficient of thermal expansion: deeper the energy well is stronger the bond and therefore lower the

Recap

Atomic packing in Engineering solids

Metals Ceramics Glasses Polymers

Packing in solids: broadly be divided into two categories

Courtesy: H Bhadhesia

Crystals: long range periodicity, Anisotropic Amorphous: Homogeneous, isotropic Examples of crystalline and amorphous solids

Crystalline material: periodic array Crystalline solids exhibit long range order in their atomic arrangement

Single crystal: periodic array over the entire extent of the material

Polycrystalline material: many small crystals or grains

1

2 3

4

5 6

7

Grain boundary

Crystalline solids

Materials: engineering, science, processing and design, 2nd edition Copyright (c)2010 Michael Ashby, Hugh Shercliff, David Cebon

Look at the atomic arrangement in an individual crystal

Atoms often behave as if they are

hard and spherical

Layer A represents the close-packed layer there is no way to pack the atoms

more closely than this

This close packed plane contains three close packed direction

Atomic Packing in Crystals

Many engineering solids are made of small crystals in which atoms are arranged in a regular repeating three dimensional pattern

Atomic Packing in Crystals

Now think about adding a second layer of atom to this close packed layer See depressions where atoms meet are ideal seats for next layer of atoms Likewise third, fourth and many layers can be added to make a sizeable piece of crystal This sounds simple--apparently there are two alternative and different sequences in which we can stack the close packed planes on top of one another


ABABAB stacking sequence: ABCABC stacking sequence: These two different stacking sequences give two different three dimensional packing structures

Close-packed structures

Close packed hexagonal

Face-centered cubic

Crystal Structures


Face-centered cubic (FCC)

Unit cell with one atom at each corner and one at each face

Atoms touch along the diagonals

of the cube faces

Close-packed planes stacked in an ABCABC sequence

17 metallic elements have this

structure

Engineering Materials with an FCC Structure

Very ductile when pure, work hardening rapidly, but softening again when annealed, allowing for various deformation processes

Generally tough high KIC Retain their ductility and toughness to absolute zero


Crystal Structures


Close-packed hexagonal (HCP)

Hexagonal unit cell with one atom at each corner, one at the center

of the hexagonal faces, and three in the middle

Close-packed planes stacked in an

ABABAB sequence

30 metallic elements have this structure

Engineering Materials with an HCP structure

Ductile enough for some deformation processes, but not as many as FCC materials

Plastic properties of HCP crystals is vastly different from FCC crystals

More anisotropic than FCC and BCC materials



Body-centered cubic (W, Cr, Fe and many important steels): ABABAB packing sequence Packing fraction = 0.68

Non Close-Packed Structures

Crystal Structures


Body-centered cubic (BCC)

Unit cell with one atom at each corner and one in the middle

Atoms touch along the internal

diagonal of the cube

21 metallic elements have this structure

Engineering Materials with a BCC Structure

Ductile, particularly when hot, allowing for various deformation processes

Generally tough - high KIC - at and above room temperature

Exhibits a transition from ductile to brittle behavior at low temperatures

Strength is temperature dependent

Can be hardened with interstitial solutes


Amorphous structure: Packing fraction 0.64

Non Close-Packed Structures

Documents

Lecture 4