L03B: Chapter 3 (continued)

1
L03B Chapter 3 (continued)

• Note that an understanding of crystal structure
  is essential for doing well in the rest of this
  course.
• So you should be reading the text and doing
  example problems.
• Review the lectures and make certain you
  understand everything.
• If you don't, ask questions by email
  (wilcox_at_clarkson.edu).
• In this lecture we cover the following
• Closed-packed metal structures Face-centered
  cubic and hexagonal close packed.
• Methods to denote directions and planes in
  hexagonal structures. VERY DIFFERENT !
• Polymorphism in carbon diamond, graphite,
  graphene, buckeyballs, nano-fibers, amorphous,
  etc.

W.R. Wilcox, Clarkson University. Last revised
September 12, 2013
2
FCC Stacking Sequence
ABCABC... Stacking sequence of 111
close-packed planes.
3
Hexagonal Close-Packed Structure (HCP)
ABAB... Stacking Sequence for close-packed
planes in HCP
Hexagonal unit cell
6 atoms/unit cell
examples Cd, Mg, Ti, Zn
c/a 1.633
APF 0.74
The only difference between FCC and HCP is
second-nearest neighbors.
4
Crystallographic Directions in a Hexagonal
Structure

• Miller-Bravais lattice
• 4 axes a1, a2, a3, z
• Dimensions are a (for a1, a2, and a3 axes) and c
  (for z-axis)
• Direction uvtw
• Algorithm to draw vector.
• Remove brackets
• Divide by largest integer so all values are 1
• Multiply terms by appropriate unit cell dimension
  (a or c) to produce projections.
• Construct vector by stepping off these
  projections.

5
Example of Drawing a Direction in a Hexagonal
Lattice

• Draw the direction in a hexagonal
  unit cell.

4. Construct Vector
start at point o
proceed a/3 units along a1 axis to point p
2a/3 units parallel to a2 axis to point q
a/3 units parallel to a3 axis to point r
c units parallel to z axis to point s
6
Determination of Miller-Bravais Indices for
Direction
Algorithm
1. Vector repositioned (if necessary) to pass
through origin.2. Read off projections in
terms of three- axis (a1, a2, and z) unit
cell dimensions a and c 3. Adjust to
smallest integer values4. Enclose in square
brackets, no commas, for three-axis
coordinates 5. Convert to four-axis
Miller-Bravais lattice coordinates using
equations below 6. Adjust to smallest
integer values and enclose in brackets
uvtw
7
Example Determination of Indices for Direction
Determine indices for green vector
1. Reposition not needed
4. Brackets 110
6. Reduction Brackets
8
Denoting Crystallographic Planes in a Hexagonal
Lattice
9
Names of planes

• Three names are commonly used for
  crystallographic planes in the hexagonal system
  basal, prismatic and pyramidal.
• For example, in ice

• The basal plane is 0001.
• Three prismatic planes are 1000, 0100 and
  0010.
• The pyramidal planes intersect the c axis at an
  angle. Example of a hexagonal pyramid

10
Polymorphic Forms of Carbon

• Very strong covalent tetrahedral bonding.
• Consequently, very few free electrons and so is
  an electrical insulator.
• Single crystal diamond has many exceptional
  properties, e.g.
• Hardest material
• Highest thermal conductivity
• Diamond cubic structure.
• Can also be considered face-centered cubic, but
  not close packed.
• Each fcc lattice site has 2 atoms.

Diamond

• The group IV semiconductors, Si and Ge, also have
  the diamond structure.
• Integrated circuits are made from Si.
• Hexagonal diamond (Lonsdaleite) discovered in
  meteoriteshttp//en.wikipedia.org/wiki/Lonsdalei
  te

? VMSE
11
Diamond synthesis

• Diamond is thermodynamically stable only at high
  pressure.
• Created in the earth at high pressure.
• Graphite is the stable structure at atmospheric
  conditions.
• At room temperature, the rate of transformation
  to graphite is negligible.
• Crystals, powder and coatings are made
  synthetically
• High pressure
• Low pressure by forming H? and CH3? with high T
  or plasma.
• e.g. http//people.clarkson.edu/lregel/actaastr
  .pdf
• Many applications for lab-created diamond, e.g.
  hard coatings and abrasives.

12
Graphite

• Layers with hexagonal structures.
• Very strong covalent bonding within each
  hexagonal layer.
• Very weak van der Waals bonding between layers.
• Very anisotropic properties.
• Good electrical conductor within layers.
• Easy separation of the layers.
• Comes in various forms, including small crystals.
• Has many applications. For example, see
  https//en.wikipedia.org/wiki/Graphite
• Hexagonal BN has the same structure, with
  alternating B N atomshttp//en.wikipedia.org/w
  iki/Boron_nitride
• Polymorphism for elements is called allotropy
• Compounds can also show polymorphism.

? VMSE
13
Graphene

• A very hot two-dimensional material. See, for
  example, http//en.wikipedia.org/wiki/Graphene .
• Originally made by pulling adhesive tape from
  graphite crystals and dissolving the tape in a
  solvent.
• Very unusual thermal, mechanical, chemical, and
  electronic properties.
• Many potential applications have been
  demonstrated in the lab.
• The material of the future?

14
Carbon nanotubes

• Consists of a graphene sheet in the form of a
  seamless cylinder and closed by a cap on the end.
  A one-dimensional structure!
• May have a single wall (graphene layer) or
  multiple wall, and joined in different ways.
• Also very unusual properties and many potential
  applications.
• http//en.wikipedia.org/wiki/Carbon_nanotube

15
Buckminsterfullerene Molecule

• Buckey balls
• C60 molecule consisting of 20 hexagons and 12
  pentagons, similar to a soccer ball.
• Covalent bonding.
• Unusual chemical properties.
• Possible use for hydrogen storage.
• http//en.wikipedia.org/wiki/Buckminsterfullerene
  
• For 3D view, open the following in
  Chromehttp//www.3dchem.com/molecules.asp?ID217
  

• Three forms of amorphous carbon with commercial
  applications
• Glassy, or vitreous, carbon http//en.wikipedia.
  org/wiki/Glassy_carbon
• Carbon fibershttp//en.wikipedia.org/wiki/Carbon_
  (fiber)
• Diamond-like carbon (DLC)http//en.wikipedia.org
  /wiki/Diamond-like_carbon