Structures of Materials Crystal Structure Crystal Structure and Bravais lattice Atomic Packing Factor

1. Material Science and Metallurgy
Chapter 01:Structure of Materials
Presented By:
Dr.S.D.Patil
Associate Professor,
Department of Mechanical Engineering

2.  Crystal Structure
 Crystal Structure and Bravais lattice
 Atomic Packing Factor

5.  The crystal structures observed in solids are
described in terms of an idealized geometric
concept called a space lattice. Space lattice is
a three dimensional pattern of points in
space. This is also called point lattice and
shown in figure. The point in the space lattice
with identical surroundings are called lattice
points.

8.  Unit cells are described by three vectors a, b and c
drawn from one corner of the cell.
 These vectors define the cell and are called
crystallographic axes of the cell.
 They may also be described in terms of their lengths (a,
b,c) and the angles between them (α,β,γ).
 These lengths and angles are lattice constant or lattice
parameters of unit cell.

9.  Review (example with square lattice)
Lattice: square, with chosen primitive translation
vectors 𝑢1𝑎𝑥̂, 𝑢2𝑎𝑦̂ (u1 and u2 are integers); remember,
the lattice is a mathematical mesh of points on space
Basis: blue circle (located at (0,0)) + yellow oval
(located at (a/2,a/2)); basis coordinates are found by
identifying repeating unit cell, setting one corner of
the cell as (0,0), and finding the fractional coordinate
of the other atom(s) in the basis in terms of the
chosen primitive translation vectors
Unit cell=lattice+ basis; repeating unit in crystal Last
lecture we discussed the ‘primitive cell’ which is a
property of the lattice (mathematical construct). The
unit cell is a building block of a crystal

11.  Lattice point can be arranged in only 14
different arrangements (arrays) called as
Bravais lattices.
 The actual crystal structures will be similar to
these 14 bravais lattices and can be obtained
by assuming atoms or group of atoms at the
position of lattice points.