Crystal Structure

  • June 2020
  • PDF

This document was uploaded by user and they confirmed that they have the permission to share it. If you are author or own the copyright of this book, please report to us by using this DMCA report form. Report DMCA


Overview

Download & View Crystal Structure as PDF for free.

More details

  • Words: 1,425
  • Pages: 9
Structure of Crystalline Solids • surface of gold - (111) plane

Phenomenon • electron diffraction pattern of a single crystal GaAs (gallium arsenide)

• Atoms are periodically arranged in a crystalline solid 436-101 Unit 2: Engineering Materials

Dr. K. Xia

Structure of Crystalline Solids (2) Structure of a solid

Structure of crystals

• 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

• Approximation – atoms ~ hard spheres of a certain radius • Unit cell: the repeating unit

Reading: 3.1-3.6 (6th ed) 436-101 Unit 2: Engineering Materials

Dr. K. Xia

1

Structure of Crystalline Solids (3) • 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

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

IMSE: FCC Structure

436-101 Unit 2: Engineering Materials

Dr. K. Xia

Structure of Crystalline Solids (4) Face-Centered Cubic (FCC) • geometric relationships a = 2 2R

• total volume of atoms in a unit cell 4 16 FCC = 4 × πR 3 = πR 3 V atoms 3 3

• volume of the unit cell

• atomic packing factor (APF) V FCC APF FCC = atoms FCC = 0.74 VUC

FCC UC

V

= a = 16 2R 3

3

FCC is one of the closest packed structures. It is still only 3 quarters filled by atoms.

a

Materials with FCC: Al, Cu, Ni

Self Study: Density calculationExample 3.3

436-101 Unit 2: Engineering Materials

Dr. K. Xia

2

Structure of Crystalline Solids (5) 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

436-101 Unit 2: Engineering Materials

Dr. K. Xia

Structure of Crystalline Solids (6) Body-Centered Cubic (BCC) • geometric relationships 4R a= 3 • volume of the unit cell 64 R 3 BCC VUC = a3 = 3 3

• total volume of atoms in a unit cell 4 8 BCC = 2 × πR 3 = πR 3 V atoms 3 3 • atomic packing factor (APF) V BCC APF BCC = atoms BCC = 0.68 VUC BCC is not as densely packed as FCC Materials with BCC: α–Fe, Cr, W

a 4R 4R

? 436-101 Unit 2: Engineering Materials

Self Study: Density calculationtutorial question

Dr. K. Xia

3

Structure of Crystalline Solids (7) 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, α-Ti, Zn

436-101 Unit 2: Engineering Materials

Dr. K. Xia

Structure of Crystalline Solids (8) • coordinates Cubic crystal systems • way of describing unit cells – general α " β " γ; a " b " c – Cubic α = β = γ = 90° a=b=c

– right hand system: x, y, z – use a as one unit

011 001 111 101

111 222

000 100

010 110

Reading: 3.7-3.10 (excluding hexagonal)

436-101 Unit 2: Engineering Materials

Dr. K. Xia

4

Structure of Crystalline Solids (9) Indexing crystallographic directions • a system of describing directions in crystals - Miller indices

[111]

B

A

1/2

[021] [100]

[110]

• 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 = [00 1 ]

436-101 Unit 2: Engineering Materials

Dr. K. Xia

Structure of Crystalline Solids (10) • family of directions – <100> includes [100], [010] and [001] as well as [1 00 ] [0 1 0 ] [00 1 ] – <110> includes [110], [101], [011], [1 1 0 ] [1 10 ] ……

– <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 directions

[1 10 ] [110]

[111]

[1 1 1 ]

436-101 Unit 2: Engineering Materials

Dr. K. Xia

5

Structure of Crystalline Solids (11) Indexing crystallographic planes • a system of describing planes in crystals - Miller indices the intercept on z is "

(111)

(110)

2/3

1/2

A

(010)

• convention and procedure – the indices, hkl, of a plane are the reciprocals of the intercepts of the plane with x, y and z – make hklsmallest 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)

the intercepts on x & z are "

436-101 Unit 2: Engineering Materials

Dr. K. Xia

Structure of Crystalline Solids (12) • family of planes – {100} includes (100), (010) and (001) – {110} includes (110), (101), (011), (1 1 0 ) (10 1 ) …… (001)

(010)

– {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 (00 1 ) (001)

(100)

(00 1 ) 436-101 Unit 2: Engineering Materials

Dr. K. Xia

6

Structure of Crystalline Solids (13) 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

C A

The third layer can be either C or A, but not both on the same layer!

Reading: 3.12 (6th ed)

436-101 Unit 2: Engineering Materials

Dr. K. Xia

Structure of Crystalline Solids (14) • ABC packing = FCC

Viewing direction

6 1

1

1 5

2

3

4

3

6

2

1 1

5 1 3

2 2

3

4

Projection along the viewing direction Video - Open Uni. T201/VC1:1

436-101 Unit 2: Engineering Materials

Dr. K. Xia

7

Structure of Crystalline Solids (15) • AB packing = HCP

436-101 Unit 2: Engineering Materials

Dr. K. Xia

Structure of Crystalline Solids (16) Noncrystalline solids

Some questions

• amorphous packing of atoms is random

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 912°C – Why? Again, to lower the potential energy corresponding to conditions (e.g. temperature)

Si

O

Crystalline (2D)

SiO2 Glass (2D) Cristobalite

Reading: 3.17 (6th ed)

436-101 Unit 2: Engineering Materials

Dr. K. Xia

8

Structure of Crystalline Solids - Summary Phenomenon

Quantitative description

• Periodic diffraction patterns by Xray or electrons • Atomic images showing periodic patterns

• Miller indices for directions and planes – indexing directions or planes – plotting directions or planes from indices

Basic structures • FCC & BCC • Unit cells – geometric relationships – density – packing factor

436-101 Unit 2: Engineering Materials

Physical understanding • Structures are determined by atomic structure and bonding – minimum potential energy for the solid – structural changes

Dr. K. Xia

9

Related Documents

Crystal Structure
June 2020 7
Crystal
June 2020 26
Crystal
November 2019 47