Today we test the clickers

again

We now venture into the world of

Metals

Metallic xl Structures

1) Face-Centered Cubic (FCC)

2) Body-Centered Cubic (BCC)

3) Hexagonal Close-Packed (HCP)

FCCAtoms at 8 corners & 6 faces

Equivalent of ? whole atoms.

Atomic Packing Factor (APF)= .74

Fig. 3.1

FCC Cubic structure

STM of PlatinumDept. Kings.edu/chemlab, Property of IBM

A scanning tunneling microscope (STM) is an instrument for imaging surfaces at the atomic level.

What’s an STM image?

Atoms….

You are under our control!

• 1990: IBM scientist Don Eigler used an STM to move single xenon atoms on a nickel surface

•The engineers moved 35 atoms to spell out "IBM" in a 10 micrometer logo.

FCC examples

Lab-grown copper (SEM)0.3 mm

Etched Aluminum (SEM)

GoldGalena (Pb ore)

A scanning electron microscope (SEM) produces images by scanning a sample with a focused beam of electrons. Yields topography and composition.

What’s an SEM image?

BCC

Atoms at 8 corners & 1 in center of

cube

Equivalent of ? whole atoms

APF = .68Fig. 3.2

BCC Cubic structure

STM of Aluminum (100) surface

https://wiki.fysik.dtu.dk/dacapo/Examples

BCC examples

Molybdenum Iron

HexagonalSystem

a1 = a2 = a3 ≠ z

º

º

Fig. 3.7

HCP

Atoms at 12 corners, 3 in interior, 2 centered on basal planes

Equivalent of ? whole atoms

(APF)= .74Fig. 3.3

Hexagonal structure

STM of Nickel surface structure.

Dept. Kings.edu/chemlab, Property of IBM

Zinc hand sample

Hexagonal structure

SEM of Fine Cadmium powder

http://www.sciencephoto.com/media/8998/enlarge

SEM of ZnO nanowireshttp://www.lac.tu-clausthal.de/en/arbeitsgruppen/angewandte-photonik-

lac/projekte/zinc-oxide-nanowires-for-photonic-applications/

Hexagonal structure

HCP Examples

Titanium crystals

Cadmium crystal bar

Magnesium (SEM)

Atomic Packing Factors

BCC = 0.68 FCC = 0.74 HCP = 0.74

Metallic xl Structures

Body-Centered Cubic (BCC) APF = 0.68

Na, Fe, Cr, Mo, W

Face-Centered Cubic (FCC) APF = 0.74

Cu, Al, Ag, Au, Pb, Ni, Pt

Hexagonal Close-Packed (HCP) APF = 0.74

Ti, Zn, Cd, Co, Mg

Crystallographic Directions

Section 3.9

Crystallographic direction

A vector between two points in a crystal.

Example:y

x

z

Unit cube

And I should know this because….

Helps us communicate about crystals no matter where we

are in the world…

A systematic study of symmetric tilt-boundaries in hard-sphere f.c.c. crystals

Abstract

A new method is developed for the search of mechanically stable

configurations of symmetric tilt boundaries in hard sphere f.c.c.

crystals. The problem of finding out relative displacements which

minimize the total volume of two crystal blocks forming a boundary, is

simplified to a problem of positioning a single atom sphere relative to a

block which consists of real and “image” atoms; the latter are placed in

such a way to reflect the arrangement in the other crystal block. The

method (the image atom method) has been applied to the analysis of

symmetric coincidence boundaries with [100], [110] and [111] tilt axes

with ∑-values 3–103. For the [100] (013)∑5 boundary, the procedure of

the analysis is described in detail; the derived structures are compared

with those by computer simulation. Numerical data are given in

tabulated forms for some boundaries.

Steps for finding

Crystallographic

Directions

Examples

yx

z

Unit cube

x

z

y

y

x

z

y

x

z

1 2

3 4

Family of Directions

In the same family:

Vector 1

Vector 2

y

x

z

Unit cube

Family of Directions: <1 1 0>

y

x

z

Unit cube

1= [1 1 0]

2 = 3= [1 1 0]

4 = [1 1 0]

5 = [1 1 0]

4 3

12

5

• Structurally equivalent

• Atomic packing is equivalent

Family of Directions: <1 1 0>

• Structurally equivalent

• Atomic packing is equivalent

Family of Directions: <1 1 0>

[a1 a2 a3 z]

Vector:[1 0 0 1]

HexagonalCrystallographic directions

Other Directions[ 1 1 0] [ 1 0 2]

[ 1 1 1] [ 2 1 1] [ 2 1 1] [ 0 0 1]

[ 1 0 1]

Wednesday:

Clicker Questions will include finding

Crystallographic Planes and Crystallographic

Directions

Solved Examples posted on Canvas

Section 3.10

Crystallographic

Planes:

Miller Indices

Steps for finding

Crystallographic

Planes

Examples1

2

3

z

x

y

Families of Planes

(100) (010) (001)

{100} {010} {001}

Family of Planes MI: (X Y Z)

Structurally equivalent planes: {X Y Z}

Hexagonal

Crystallographic planes:The basal plane

Other Planes:

( 1 2 3)

(0 0 1) (0 1 1) (1 1 2)

(2 0 1) (1 0 1)

Notation Summary

Solved Examples posted on Canvas:

Files>Assignments, Homework, Extra Credit