Md. Kamrul Hasan Reza
Department of Physics
Khulna University of Engineering & Technology Khulna-9203, Bangladesh
Tel.: +880-41-769468~75 Ext. 587(O), 588 (R)
e-mail: [email protected], [email protected] Website : www.kuet.ac.bd/phy/reza/
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Welcome to my Class
Physics Ph 1101
11:45 AM
October 14, 2020
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Try to stay at home
The branch of science that deals with discerning the arrangement and bonding of atoms in crystalline solids and with the geometric structure of crystal lattices.
What is Crystallography?
A space lattice is an array of points showing how particles (atoms, ions or molecules) are arranged at different sites in three dimensional spaces.
space lattice
A lattice is in general defined as a discrete but infinite regular arrangement of points in a vector space.
Bravais Lattice
In solid state physics one usually encounters lattices which exhibit a discrete translational symmetry. If one considers for instance the vector space R this means that a translation of the whole lattice by any translation vector given by
leaves the lattice unchanged.
Crystal Lattice and Unit Cell
Unit Cell
Unit Cell
Space Lattice
Space Lattice & Unit Cell
Crystal is a homogeneous portion of a crystalline substance, composed of a regular pattern of structural units (ions, atoms or molecules) by plane surfaces making definite angles with each other giving a regular geometric form.
A regular array of points (showing atoms/ions) in three dimensions is commonly called as a space lattice, or lattice.
Each point in a space lattice represents an atom or a group of atoms.
Each point in a space lattice has identical surroundings throughout.
A three dimensional group of lattice points which when repeated in space generates the crystal called unit cell.
The unit cell is described by the lengths of its edges, a, b, c (which are related to the spacing between layers) and the angles between the edges,
α ,
β and ϒ.The Seven Crystal System
By joining of these points we get the geometry (or shape) of the crystal
Characteristics of Crystal Lattice
The fourteen Bravais Lattices show some similar characteristics. These are:
Every one of the fourteen lattices has such a unique geometry.
These lattice points of a crystal are joined together by straight lines.
Each point on the lattice represents one particle of the crystal. This is a lattice point.
This particular particle may be an atom, a molecule or even ions
Symmetry Elements of a Crystalline Solids
The main symmetry elements of a crystalline solid are a) axes of symmetry, b) planes of symmetry and center of symmetry
axes of symmetry
Plane of symmetry
Centre of symmetry
Density of Packing
The relative density of packing is defined as the fraction of volume occupied by the spherical atoms as compared to the available volume of the structure
Imperfections in Crystalline Solids
a) Theoretical yield strength, Point defects and Line defects or Dislocations
b) Interfacial defects, Bulk or Volume defects and Atomic vibrations
Ideal solids are made of atoms arranged in orderly way.
Theoretical yield strength
Point defects
Point defects are of zero-dimensional i.e. atomic disorder is restricted to point-like regions.
Thermodynamically stable compared with other kind of defects.
In ionic crystals, defects can form on the condition of charge neutrality. Two possibilities are:
Line defects
Line defects or Dislocations are abrupt change in atomic order along a line.
They occur if an incomplete plane inserted between perfect planes of atoms or when vacancies are aligned in a line.
A dislocation is the defect responsible for the phenomenon of slip, by which most metals deform plastically.
Dislocation form during plastic deformation, solidification or due to thermal stresses arising from rapid cooling.
Line defects – Screw dislocation
It is also called as Burger’s dislocation
It will have regions of shear stress around the dislocation line
For positive screw dislocation, dislocation line direction is parallel to Burger’s vector, and vice versa.
