Motifs

1
(No Transcript)
2
Motifs

• Basis is a synonym for Motif
• Any entity which is associated with each lattice
  point is a motif
• This entity could be a geometrical object or a
  physical property (or a combination)
• This could be a shape like a pentagon (in 2D),
  cube (in 3D) or something more complicated
• Typically in atomic crystals an ? atom (or
  group of atoms) ? ions (or groups of ions) ?
  molecules (or group of Molecules) associated
  with each lattice point constitutes a motif
• The motif should be positioned identically at
  each lattice point (i.e. should not be rotated or
  distorted from point to point) Note If the atom
  has spherical symmetry rotations would not matter!

3
Revision
MOTIFS
Geometrical Entity
Physical Property
or a combination
Shapes, atoms, ions
Magnetization vector, field vortices, light
intensity

• What is the role of the symmetry of the motif on
  the symmetry of the crystal?

4
Examples of Motifs
In ideal mathematical and real crystals
Atomic Motifs
General Motifs
1D
Atom
2D
Ar(in Ar crystal- molecular crystal)
Group of atoms(Different atoms)
Cu, Fe(in Cu or Fe crystal)
3D
?
Group of ions

NaCl? (in NaCl crystal)
Virtually anything can be a motif!
The term is used to include atom based entities
like ions and molecules
5

• Viruses can be crystallized and the motif now is
  an individual virus (a entity much larger than
  the usual atomic motifs)

A complete virus is sitting as a motif on each
lattice position (instead of atoms or ions!) ?
We get a crystal of virus
Crystal of Tobacco Mosaic Virus 1
1 Crystal Physics, G.S. Zhdanov, Oliver Boyd,
Ediburgh, 1965
6

• In the 2D finite crystal as below, the motif is a
  triangular pillar which is obtained by focused
  ion beam lithography of a thermally evaporated
  Gold film 200nm in thickness (on glass
  substrate).
• The size of the motif is 200nm.

Scale 200nm
Unit cell
Micrograph courtesy Prof. S.A. Ramakrishna Dr.
Jeyadheepan, Department of Physics, I.I.T. Kanpur
7

• 2D finite crystal.
• Crystalline regions in nano-porous alumina ? this
  is like a honeycomb
• Sample produced by anodizing Al.

Scale 200nm
Pore
Photo Courtesy- Dr. Sujatha Mahapatra
(Unpublished)
8
Chip of the LED light sensing assembly of a mouse
9

• 3D Finite crystal of metallic balls ? motif is
  one brown metallic ball and one metallic ball
  (uncolored) lattice is FCC.

Scale mm
10

• Crystals have been synthesized with silver
  nanocrystals as the motif in an FCC lattice. Each
  lattice point is occupied by a silver nanocrystal
  having the shape of a truncated octahedron- a
  tetrakaidecahedron (with orientational and
  positional order).
• The orientation relation between the particles
  and the lattice is as follows 110lattice
  110Ag, 001lattice 1?10Ag

Ag nanocrystal as the motif
11

• Why do we need to consider such arbitrary
  motifs?
• Arent motifs always made of atomic entities?

• It is true that the normal crystal we consider in
  materials science (e.g. Cu, NaCl, Fullerene
  crystal etc.) are made out of atomic entities,
  but the definition has general application and
  utilities

• Consider an array of metallic balls (ball bearing
  balls) in a truncated (finite) 3D crystal.
  Microwaves can be diffracted from this array.

The laws of diffraction are identical to
diffraction of X-rays from crystals with atomic
entities (e.g. NaCl, Au, Si, Diamond etc.)
Using Braggs equation
Crystal made of metal balls and not atomic
entities!
12

• Example of complicated motifs include? Opaque
  and transparent regions in a photo-resist
  material which acts like an element in
  opto-electronics

• A physical property can also be a motif
  decorating a lattice point
• Experiments have been carried out wherein matter
  beams (which behave like waves) have been
  diffracted from LASER Crystals! ? Matter being
  diffracted from electromagnetic radiation!

Motif
Lattice
Scale cm
Is now a physical property (electromagnetic flux
density)
An actual LASER crystal created by making LASER
beams visible by smoke
Things are little approximate in real life!
13

• The motif could be a combination of a geometrical
  entity with a physical property
• E.g.? Fe atoms with a magnetic moment (below
  Curie temperature).
• Fe at Room Temperature (RT) is a BCC crystal ?
  based on atomic position only.
• At RT Fe is ferromagnetic (if the specimen is
  not magnetized then the magnetic domains are
  randomly oriented? with magnetic moments aligned
  parallel within the domain).
• The direction of easy magnetization in Fe is
  along 001 direction.
• The motif can be taken to be the Fe atom along
  with the magnetic moment vector (a combination of
  a geometrical entity along with a physical
  property).
• Below Curie temperature , the symmetry of the
  structure is lowered (becomes tetragonal) ? if
  we consider this combination of the magnetic
  moment with the atom.
• Above Curie temperature the magnetic spins are
  randomly oriented? If we ignore the magnetic
  moments the crystal can be considered a BCC
  crystal? If we take into account the magnetic
  moment vectors the structures is amorphous!!!

CRYSTALLINE
AMORPHOUS
combination of the magnetic moment with the Fe
atom
Mono-atomic decoration of the BCC lattice
14

• Wigner crystal
• Electrons repel each other and can get ordered to
  this repusive interaction. This is a Wigner
  crystal! (here we ignore the atomic enetites).

15

• Ordering of Nuclear spins
• We had seen that electron spin (magnetic moment
  arising from the spin) can get ordered (e.g.
  ferromagnetic ordering of spins in solid Fe at
  room temperature)
• Similarly nuclear spin can also get ordered.