lecture on materials

Lecture 8Structure of Solids

Outline

Packing of atoms in crystals: FCC, HCP and BCC crystals, stacking sequence

Close packed planes and directions, Packing fraction

Voids in solids: tetrahedral and octahedral voids

Implications of voids

3

Solids

Crystalline Noncrystalline

Gives sharp diffraction patterns

Does not give sharp diffraction patterns

Long-range periodicity No long-range periodicity

Has sharp melting point Does not have a sharp melting point

Has higher density Has a lower density

4

Peak Broadening

Actual bonding in material need not to be of one kind, it can be of mixed nature

Classification of crystals based on bonding

COVALENT IONIC

METALLIC

Molecular crystals: molecules are held by primary covalentbonds, while intermolecular bonding are of weak Van der wall/hydrogen type.

Non-molecular crystals: Metallic, covalent, ionic type of bond

Metallic crystals

Positive ions in a free electron cloud

Metallic bonds are non-directional

Each atoms tends to surround itself with as many

neighbours as possible!

Usually high temperature→ BCC (Open structure)

The partial covalent character of transition metals is a

possible reason for many of them having the BCC

structure at low temperatures

FCC → Al, Fe (910 - 1410ºC), Cu, Ag, Au, Ni, Pd, Pt

BCC → Li, Na, K , Ti, Zr, Hf, Nb, Ta, Cr, Mo, W, Fe

(below 910ºC),

HCP → Be, Mg, Ti, Zr, Hf, Zn, Cd

Cubic close packed (CCP) crystal: FCC lattice monoatomically decorated with a single atom/ion motif

Body centred crystal (BCC) crystal: BCC lattice monoatomically decorated with a single atom/ion motif

Hexagonal close packed (HCP) crystal: hexagonal lattice decorated with a two atom/ion motif

We will understand about structure and position of voidsin above structures.

How these voids can be occupied by alloying elements to give us interstitial alloys

CCP and HCP crystals are close packed crystals (packing fraction of 0.74): They have close packed planes and directions

The voids observed in CCP and HCP crystals are regular tetrahedron and regular Octahedron

Coordination number for above two: 12

BCC crystal is not a close packed structure. It does not have close packed plane, but have <111> direction is a close packed direction

The voids in BCC are non-regular tetrahedron and non regular Octahedron

Some facts

Close packing of equal hard spheres

A close packed row of atoms in 1D

A 2D close packed hexagonal layer of atoms (A layer)Close-packed plane of atoms

Close-packed directions? 3

10

Close packing of equal hard spheres

3-D packing

A A A

AA AA

AA

A

A

A AA

A

A

B BB

B B B

B B B

CC C

C

C

C C

C C

First layer A

Second layer B

Third layer A or C

Close packed crystals:

…ABABAB… Hexagonal close packed (HCP)…ABCABC… Cubic close packed (CCP)

11

Geometrical properties of ABCABC stacking

A A A

AA AA

AA

A

A

A AA

A

A

B BB

B B B

B B B

CC C

C

C

C C

C C

A

A

A

A AA

12

Geometrical properties of ABCABC stacking

B

A

C

B

A

C

ABCABC stacking = CCP crystal

= FCC lattice + single atom motif 000

3 a

All atoms are equivalent and their centres form a lattice

Motif: single atom 000

What is the Bravais lattice?

13

A

C

A

Body diagonal

B

Close packed planes in the FCC unit cell of cubic close packed crystal

Close packed planes: {1 1 1}

B

14

Stacking sequence?

15

Stacking sequence?

AB

+

HCP

=

A

+

Note: Atoms are coloured differently but are the same

HCP

Unit cell of HCP (Rhombic prism)

Courtesy: A. Subramanium

Hexagonal Lattice

Two atom Motif

=

+

HCP crystal

Motif

As we have seen that HCP crystal is constructed starting with a hexgonal close packed layer,

with ABABAB.. packing.

The 6-fold axis (present in a single layer) is lost on ABABAB.. packing and only a 3-fold remains.

Though 3 unit cells are often shown in diagrams- the rhombic prism (blue outline) is the unit cell.


Atoms: (0,0,0), (⅔, ⅓,½)


Geometrical properties of ABAB stacking

A A A

AA AA

AA

A

A

A AA

A

A

BB

B B B

B B B

C C C

C

C

C C

C C

B

A and B do not have identical neighbours

Either A or B as lattice points, not both

a

b = a

=120

Unit cell: a rhombus based prism with a=bc; ==90, =120

A

A

B

Bc

The unit cell contains only one lattice point (simple) but two atoms (motif)

ABAB stacking = HCP crystal = Hexagonal P lattice + 2 atom motif 000

2/3 1/3 1/2

½

½ ½

½

Lattice: Simple hexagonal

hcp lattice hcp crystal

Hexagonal close-packed (HCP) crystal

x

y

z

Corner and inside atoms do not have the same neighbourhood

Motif: Two atoms: 000; 2/3 1/3 1/2

If the HCP crystal has only a 3-fold axis why does it comeunder the ‘Hexagonal class of crystals?


The rotation is degrees.The translation is units along the screw axis.

Screw Axes are a combination of rotation axes and translations.

The symbols are:21 31 32 41 42 43

61 62 63 64 65

The symbols are of the form xy

lecture on materials

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