PHYS 260 Lecture Notes - Lecture 4: Space Group, Sodium Chloride, Unit
25 May 2018
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Crystal structures
At the end of this chapter you should be able to
• Define Space lattice, Unit cell, Crystalographic axis and angles.
• Classify crystal systems
• Derive expression for SCC, BCCand FCC
• Understand Diamond, ZnCl, NaCl and CsCl structures.
CS1.SPACE LATTICE
A crystal is a three dimensional body. Crystals are made up of regular and periodic
three-dimensional patterns of atoms or molecules in space called the crystal structure.
The crystal structure may be described in terms of an idealized geometrical concept
called a space lattice. The space lattice may be defined as an array of points in space
such that the environment about each point is the same”. Similarly we can argue for
three-dimensional space. The three dimensional space lattice may be defined as an
infinite array of points in three dimensions in which every point has an identical
environment as any other point in the array.
Two –Dimensional lattice
Three – Dimensional lattice
CS2.UNIT CELL
Unit cell of a crystal is the smallest volume of a solid or geometric figure from which
the entire crystal is built up by translational repetition in three dimensions. Since the
unit cell reflects the structure and properties of the crystal it is enough to study the
unit cell alone to get the clear idea about the whole crystal.
Unit cell
CS3CRYSTALLOGRAPHIC AXES & ANGLES
The lines drawn parallel to the lines of intersection of any three faces of the unit cell
which do not lie in the same plane are called crystallographic axis X, Y, Z.
The angles between the three crystallographic axes represented by α, β, and γ are
called interfacial angles or interaxial angles
α
The intercepts a, b and c which define the dimensions of a unit cell on the respective
crystallographic axes are called primitives of the unit cell.
Thus the three primitives a,b and c and the three interfacial angles α, β and γ are the
lattice parameters.
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Z
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γ
β
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Document Summary
At the end of this chapter you should be able to: define space lattice, unit cell, crystalographic axis and angles, classify crystal systems, derive expression for scc, bccand fcc, understand diamond, zncl, nacl and cscl structures. Crystals are made up of regular and periodic three-dimensional patterns of atoms or molecules in space called the crystal structure. The crystal structure may be described in terms of an idealized geometrical concept called a space lattice. The space lattice may be defined as an array of points in space such that the environment about each point is the same . The three dimensional space lattice may be defined as an infinite array of points in three dimensions in which every point has an identical environment as any other point in the array. Unit cell of a crystal is the smallest volume of a solid or geometric figure from which the entire crystal is built up by translational repetition in three dimensions.
