Lecture 5

Lecture 5 Packing of atoms in

solids

Jayant Jain Assistant Professor,

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

Recap

Atomic packing in crystalline solids such as metals Crystal classes: FCC, BCC and HCP Key characteristics of these classes

Whenever we pack atoms no matter how densely we pack we ended up with open spaces/voids

Voids very imp: ceramics, second/third type of atom sits into that void

Formation of some special type of voids such as tetrahedral and octahedral voids are common when we pack atoms

Tetrahedral Octahedral OV TV

Voids in crystals

Courtesy: A. Subramaniam

FCC voids Position Voids / cell Voids / atom

Tetrahedral

¼ way from each vertex of the cube

along body diagonal <111>

((¼, ¼, ¼))

8 2

Octahedral • Body centre: 1 (½, ½, ½)

• Edge centre: (12/4 = 3) (½, 0, 0) 4 1

How many octahedral and tetrahedral voids per unit cell in FCC crystal

Octahedral void FCC

Ceramic Crystals

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

Technical ceramics off the hardest, most refractory materials of engineering

Structure of ceramics often have atoms arranged in a BCC, FCC, or HCP structure with a second and/or third type of atom inserted into the Interstitial sites of the first

Diamond Cubic (DC) Structure

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

Essentially an FCC lattice with an additional atom in each of its

tetrahedral interstices

Unit Cell of Diamond

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

Structure of silicon carbide; same DC structure as diamond with

different chemical composition

Silicon carbide (SiC) Structure

Oxides with the Rocksalt (Halite) Structure

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

Figure GL1.13

Have the formula MO, where M is a metal ion

The oxygen packs in an FCC structure and metal atoms

occupy the octahedral holes

Oxides with a Corundum Structure

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

Figure GL1.14

M2O3 formula with M being metal ions

Oxygen atoms close-packed in an HCP

structure with metal atoms occupying 2/3 of octahedral holes

Oxides with the Fluorite Structure

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

Formula of MO2, but unlike in earlier oxides, the metal atoms (M) are bigger than the oxygen atoms

The metal atoms form a close-packed FCC structure and the oxygen atoms

fill the tetrahedral insterstices

Problems