1. LINEAR DENSITY  When planes slip over each other, slip takes place in the direction of closest packing of atoms on the planes.  The linear density of a crystal direction [h k l] is determined as: δ [h k l] = length # of atoms

2. 2 ex: linear density of Al in [110] direction a = 0.405 nm FCC: Linear Density Linear Density of Atoms  LD = a [110] Unit length of direction vector Number of atoms # atoms length 1 3.5 nm a2 2 LD   Adapted from Fig. 3.1(a), Callister & Rethwisch 8e.

3. BCC: Linear Density Calculate the linear density for the following directions in terms of R: a.[100] b.[110] c.[111]

4. PLANAR DENSITY  When slip occurs under stress, it takes place on the planes on which the atoms are most densely packed. δ (hkl) = area # of atoms in a plane Example: FCC unit cell a2a2 (100) z y x δ (100) = 4*1/4+1 a2a2 = a2a2 2 a= 1 r 2 4 δ (100) = 4r 2

5. Quasicrystal  A quasiperiodic crystal, or, in short, quasicrystal, is a structure that is ordered but not periodic. A quasicrystalline pattern can continuously fill all available space, but it lacks translational symmetry. quasiperiodiccrystalstructureorderedperiodictranslational symmetry  A material with sharp diffraction peaks with a forbidden symmetry by crystallography.  They have long-range positional order without periodic translational symmetry.  Shechtman was awarded the Nobel Prize in Chemistry in 2011 for his work on quasicrystals. “His discovery of quasicrystals revealed a new principle for packing of atoms and molecules.” Nobel Prize in Chemistry HOW IS A QUASICRYSTAL DIFFERENT FROM A CRYSTAL? ORDEREDPERIODIC QC ARE ORDERED STRUCTUR ES WHICH ARE NOT PERIODIC CRYSTAL S QC  AMORPH OUS 

6. UNIVERSE PARTICLES ENERGY SPACE FIELDS GAS BAND STRUCTURE AMORPHOUS ATOMIC NON-ATOMIC STATE / VISCOSITY SOLIDLIQUID LIQUID CRYSTALS QUASICRYSTALS CRYSTALS RATIONAL APPROXIMANTS STRUCTURE NANO-QUASICRYSTALSNANOCRYSTALS SIZE Where are quasicrystals in the scheme of things?

7. Quasicrystals x ( ) 1 0 1 1 4 5 1 2 3 x Al 6 Mn 1  m

8. Types of Quasicrystals  Two types:  Quasiperiodic in Two Dimensions: This is also referred to as polygonal or dihedral quasicrystals. It has sub elements namely octagonal, decagonal and dodecagonal. This has one periodic direction which lies perpendicular to the quasiperodic layers.  Quasiperiodic in Three Dimensions: This type has no periodic direction and icosahedral quasicrystals fall under this type.  New type: Icosahedral quasicrystals with broken symmetry fall in this category.

9. Characteristics hard and brittle low surface energy (non-stick) high electrical resistivity high thermal resistivity high thermoelectric power … Quasicrystalline coating method shows promise for cookware and prosthetic devices.

10. APPLICATIONS OF QUASICRYSTALS WEAR RESISTANT COATING (Al-Cu-Fe-(Cr)) NON-STICK COATING (Al-Cu-Fe) NON-STICK COATING (Al-Cu-Fe) THERMAL BARRIER COATING (Al-Co-Fe-Cr) THERMAL BARRIER COATING (Al-Co-Fe-Cr) HIGH THERMOPOWER (Al-Pd-Mn) HIGH THERMOPOWER (Al-Pd-Mn) IN POLYMER MATRIX COMPOSITES (Al-Cu- Fe) IN POLYMER MATRIX COMPOSITES (Al-Cu- Fe) SELECTIVE SOLAR ABSORBERS (Al-Cu-Fe- (Cr)) SELECTIVE SOLAR ABSORBERS (Al-Cu-Fe- (Cr)) HYDROGEN STORAGE (Ti-Zr-Ni) HYDROGEN STORAGE (Ti-Zr-Ni)

11. Application  Quasicrystals have been used in surgical instruments, LED lights and non stick frying pans. They have poor heat conductivity, which makes them good insulators.  Quasicrystals vary depending on their direction.  One direction might conduct electricity easily - another direction might not conduct electricity at all.  Quasicrystalline cylinder liners and piston coatings in motor-car engines would undoubtedly result in reduced air pollution and increased engine lifetimes.

12. Assignment 1

13. Chapter 2. Reciprocal Lattice Issues that are addressed in this chapter include:  Bragg law  Scattered wave amplitude  Brillouin Zones  Fourier analysis of the basis

14. The set of all waves vectors k that yield plane wave with the periodicity of a given Bravais lattice. Reciprocal lattice A diffraction pattern is not a direct representation of the crystal lattice The diffraction pattern is a representation of the reciprocal lattice

15. Reciprocal Lattice/Unit Cells We will use a monoclinic unit cell to avoid orthogonal axes We define a plane and consider some lattice planes (001) (100) (002) (101) (102)