MATERIALS SCIENCE &ENGINEERING Anandh Subramaniam & Kantesh Balani Materials Science and Engineering (MSE) Indian Institute of Technology, Kanpur URL: home.iitk.ac.in/~anandh AN INTRODUCTORY E-BOOK Part of A Learner’s Guide

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!

Geometrical Entity MOTIFS Physical Property or a combination Shapes, atoms, ions… Magnetization vector, field vortices, light intensity… Revision:  What is the role of the symmetry of the motif on the symmetry of the crystal?

General Motifs Atomic * Motifs  2D 3D Examples of Motifs * The term is used to include atom based entities like ions and molecules Virtually anything can be a motif! Ion + Atom Ar (in Ar crystal- molecular crystal) Group of ions +  Na + Cl  (in NaCl crystal) Cu +, Fe ++ (in Cu or Fe crystal) Group of atoms (Same atom) C in diamond Group of atoms (Different atoms) 1D In ideal mathematical and real crystals

 Viruses can be crystallized and the motif now is an individual virus (a entity much larger than the usual atomic motifs) Crystal of Tobacco Mosaic Virus [1] [1] Crystal Physics, G.S. Zhdanov, Oliver & Boyd, Ediburgh, 1965 A complete virus is sitting as a motif on each lattice position (instead of atoms or ions!)  We get a crystal of ‘virus’

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

 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 Sujatha Mahapatra (Unpublished)

Chip of the LED light sensing assembly of a mouse

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

 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 || [110] Ag, [001] lattice || [1  10] 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.finitediffracted Using Bragg’s equationBragg’s equation The laws of diffraction are identical to diffraction of X- rays from crystals with atomic entities (e.g. NaCl, Au, Si, Diamond etc.) 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 Things are little approximate in real life! Scale: ~cm

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

 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.