11 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Chapter 3: Fundamentals of Crystallography

ISSUES TO ADDRESS...

22 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Energy, Materials, and Packing

Non dense, random packing

Dense, ordered packing

Dense, ordered packed structurestend to have lower energies.

Crystalline materials

Noncrystalline materials

"Amorphous" = Noncrystalline

33 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Fundamentals Concepts and Unit Cells

3.2 Fundamental ConceptsCrystalline materials

Noncrystalline or amorphous materials

3.3 Unit Cells

44 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

3.4 Crystal Systems

The unit cell geometry is completely defined in terms of the lattice parameters

55 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

3.5 Point Coordinates

Three point coordinate indices: q, r, and s

Ex. 3.1 & Ex. 3.2

Point coordinates for unit cell center are a/2, b/2, c/2: ½½½Point coordinates for unit cell corner are 111.Translation: integer multiple of lattice constants identical position inanother unit cell.

66 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

3.6 Crystallographic Directions

A crystallographic direction: A line directed between two points or a vector.

Family of Crystallographic Directions: <uvw>

Practice with Examples 3.3 & 3.4.

czz

byy

axx 121212

czzn w

byyn v

axxnu 121212 ,,

77 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

3.6 Crystallographic Directions (HCP)

Miller Bravais coordinate system (four axes)

Algorithm

WwvutVUvVUuuvtwUVW ),(),2(31),2(

31:][][

WwvutVUvVUu ),(),2(31),2(

31

][UVW

88 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

3.7 Crystallographic Planes

Miller Indices

Algorithm

Family of Crystallographic Planes: {hkl}

99 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

3.7 Crystallographic Planes

Example 1

Example 2

Example 3

z

x

ya b

c

z

x

ya b

c

z

x

ya b

c

110 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

3.7 Crystallographic Planes (HCP)

Miller Bravais system (four axes)

Crystallographic Planes (HCP)

Example Problem 3.8

111 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Crystallographic Point, Direction, & Planar Indices

112 SCHOOL OF MECHANICAL ENGINEERINGLECTURER: PROF. SEUNGTAE CHOI

Crystalline and Noncrystalline Materials

Single Crystals

Polycrystalline Materials

Anisotropy

Noncrystalline (Amorphous) Solids