Part of

MATERIALS SCIENCE &

A Learner’s Guide

ENGINEERING AN INTRODUCTORY E-BOOK

Anandh Subramaniam & Kantesh Balani

Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur- 208016

Email: [email protected], URL: home.iitk.ac.in/~anandh http://home.iitk.ac.in/~anandh/E-book.htm

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

MOTIFS

 Typically in atomic crystals an 

atom

( or

group of atoms)

Geometrical Entity

Shapes, atoms, ions…



ions (or groups of ions)



molecules (or group of Molecules)

or a combination

associated with each lattice point constitutes a motif Physical Property

Magnetization vector, field vortices, light intensity…

 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!

Revision:

MOTIFS

Geometrical Entity

Shapes, atoms, ions… or a combination

Physical Property

Magnetization vector, field vortices, light intensity…

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

Examples of Motifs

In ideal mathematical and real crystals

Atomic

*

Motifs

General Motifs

1D  2D Atom Ar (in Ar crystal- molecular crystal)

+

Ion Cu + , Fe ++

(in Cu or Fe crystal)

Group of atoms

(Different atoms)

3D

+

 Group of ions Na + Cl  (in NaCl crystal) Group of atoms

(Same atom)

C in diamond

Virtually anything can be a motif!

* The term is used to include atom based entities like ions and molecules

 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

  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 Micrograph courtesy: Prof. S.A. Ramakrishna & Dr. Jeyadheepan, Department of Physics, I.I.T. Kanpur Unit cell

   2D finite crystal.

Crystalline regions in nano-porous alumina → this is like a honeycomb Sample produced by anodizing Al.

Pore Scale: ~200nm Photo Courtesy- Dr. Sujatha Mahapatra (Unpublished)

Chip of the LED light sensing assembly of a mouse

 3D Finite crystal of metallic balls → motif is one brown metallic ball and one metallic ball (uncolored) [lattice is FCC].

Scale: ~mm

  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: [110] lattice [001] lattice || [1  10] Ag || [110] Ag , Ag nanocrystal as the motif

 Why do we need to consider such arbitrary motifs?

 Aren’t 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 Bragg’s equation

n

  2

d Sin

 1(3)  2(4.5)

Sin

 1 2(3) 3(3)   2(4.5)

Sin

 2 2 (4.5)

Sin

 3  1 19.47

   2   3  41.81

 Crystal made of metal balls and not atomic entities!

 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!

Lattice

+ =

Motif

Is now a physical property (electromagnetic flux density)

An actual LASER crystal created by making LASER beams visible by smoke Scale: ~cm

Things are little approximate in real life!

   

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!!!

combination of the magnetic moment with the Fe ‘atom’ * Mono-atomic decoration of the BCC lattice

 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).

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.