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Structure of Crystalline Solids

- Phenomenon
- electron diffraction pattern of a single crystal

GaAs (gallium arsenide)

- surface of gold - (111) plane
- Atoms are periodically arranged in a crystalline

solid

Structure of Crystalline Solids

- Structure of a solid
- Structure of a building
- building blocks e. g. bricks
- how bricks are laid and bound
- Building blocks for a solid atoms
- How atoms are laid and bound
- Types of possible structures
- amorphous random packing of atoms
- e.g. glasses
- crystalline periodic packing of atoms (repeating

patterns) - e.g. most engineering metals and ceramics
- very important

- Structure of crystals
- Approximation
- atoms hard spheres of a certain radius
- Unit cell the repeating unit

Reading 3.1-3.6 (6th ed)

Structure of Crystalline Solids

- Basic types of crystal structures
- Face-Centered Cubic (FCC)
- one atom at each corner of the cubic unit cell
- one atom at each face certer
- lattice 3D array of center positions of atoms

- 4 (equivalent) atoms are completely contained in

a FCC unit cell - each corner atom 1/8
- 8 x 1/8 1
- each face center atom 1/2
- 6 x 1/2 3

IMSE FCC Structure

Structure of Crystalline Solids

- Face-Centered Cubic (FCC)
- geometric relationships
- volume of the unit cell

- total volume of atoms in a unit cell
- atomic packing factor (APF)

FCC is one of the closest packed structures. It

is still only 3 quarters filled by atoms.

Materials with FCC Al, Cu, Ni

a

Self Study Density calculation- Example 3.3

Structure of Crystalline Solids

- Body-Centered Cubic (BCC)
- one atom at each corner of the cubic unit cell
- one atom at the body center

- 2 (equivalent) atoms are completely contained in

a BCC unit cell - each corner atom 1/8
- 8 x 1/8 1
- the body center atom 1

IMSE BCC Structure

Structure of Crystalline Solids

- Body-Centered Cubic (BCC)
- geometric relationships
- volume of the unit cell

- total volume of atoms in a unit cell
- atomic packing factor (APF)

BCC is not as densely packed as FCC

Materials with BCC aFe, Cr, W

a

4R

Self Study Density calculation- tutorial question

?

Structure of Crystalline Solids

- Hexagonal Close-Packed (HCP)
- unit cell is a hexagon
- c/a 1.633 (ideal value)

- 6 (equivalent) atoms are contained in a unit cell
- as close packed as FCC (APF 0.74)

IMSE HCP Structure

Materials with HCP Mg, a-Ti, Zn

Structure of Crystalline Solids

- coordinates
- right hand system x, y, z
- use a as one unit

- Cubic crystal systems
- way of describing unit cells
- general
- a ? b ? g a ? b ? c
- Cubic
- a b g 90
- a b c

Reading 3.7-3.10 (excluding hexagonal)

Structure of Crystalline Solids

- convention and procedure
- the indices, uvw, of a direction are simply the

components of the equivalent vector (projected

lengths of the direction on x, y and z) - make uvw smallest integers
- put any minus sign on top
- use uvw to indicate a particular direction
- direction A
- components of vector 0, 1, 1/2
- smallest integers 0, 2, 1 (x 2, i.e. double the

length) - direction A 021
- direction B

- Indexing crystallographic directions
- a system of describing directions in crystals -

Miller indices

111

B

1/2

A

021

100

110

Structure of Crystalline Solids

- lt111gt includes
- homework fill in the rest of the lt110gt and lt111gt

family members - members of a family have the same arrangement of

atoms (for a cubic system) although they are

different directions

- family of directions
- lt100gt includes 100, 010 and 001 as well as
- lt110gt includes 110, 101, 011,

110

111

Structure of Crystalline Solids

- convention and procedure
- the indices, hkl, of a plane are the reciprocals

of the intercepts of the plane with x, y and z - make hkl smallest integers
- put any minus sign on top
- use (hkl) to indicate a particular plane
- plane A
- intercepts x 1, y 1/2 and z 2/3
- reciprocals of intercepts 1, 2, 3/2
- smallest integers (reciprocals x 2) 2, 4, 3
- plane A (243)

- Indexing crystallographic planes
- a system of describing planes in crystals -

Miller indices

the intercept on z is 8

(110)

(111)

2/3

A

1/2

(010)

the intercepts on x z are 8

Structure of Crystalline Solids

- 111 includes
- homework fill in the rest of the 110 and 111

family members - members of a family have the same arrangement of

atoms (for a cubic system) although they are

different planes - equivalent planes (they are exactly the same),

e.g. (001) and

- family of planes
- 100 includes (100), (010) and (001)
- 110 includes (110), (101), (011),

(001)

(010)

(001)

(100)

Structure of Crystalline Solids

- Packing of atoms in FCC and HCP
- close-packed plane (e.g. layer A)
- interstitial sites
- B e.g. the up right triangles
- C e.g. the upside down triangles
- stacking of close-packed planes
- first layer A
- second layer B
- third layer
- C ABCABC ... packing
- A ABAB packing

The third layer can be either C or A, but not

both on the same layer!

Reading 3.12 (6th ed)

Structure of Crystalline Solids

- ABC packing FCC

Viewing direction

Projection along the viewing direction

Video - Open Uni. T201/VC11

Structure of Crystalline Solids

- AB packing HCP

Structure of Crystalline Solids

- Some questions
- Why a material takes a certain structure, e.g. Al

is FCC? - So that the lowest potential energy is achieved
- Can a material takes more than one structure?
- For some materials, yes
- e.g. Fe is BCC (ferrite) at room temperature, but

transforms to FCC (austenite) at 912C - Why?
- Again, to lower the potential energy

corresponding to conditions (e.g. temperature)

- Noncrystalline solids
- amorphous
- packing of atoms is random

Si

O

Crystalline (2D)

SiO2

Glass (2D)

Cristobalite

Reading 3.17 (6th ed)

Structure of Crystalline Solids - Summary

- Phenomenon
- Periodic diffraction patterns by X-ray or

electrons - Atomic images showing periodic patterns
- Basic structures
- FCC BCC
- Unit cells
- geometric relationships
- density
- packing factor

- Quantitative description
- Miller indices for directions and planes
- indexing directions or planes
- plotting directions or planes from indices
- Physical understanding
- Structures are determined by atomic structure and

bonding - minimum potential energy for the solid
- structural changes

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