Lecture by Prof Rajendra Singh on material science fundamentals.

Lecture by Prof Rajendra Singh on material science fundamentals.

1. PYL 701
Physical Foundations of Materials Science
Instructor:Prof. Rajendra Singh
Department of Physics
Lecture 03

2. Imperfections/Defects in Solids
• Vacancy
• Interstitial atoms
• Substitutional atoms
• Dislocations
• Grain Boundaries
Point defects (0D)
Line defects (1D)
Area defects (2D)
TYPES OF IMPERFECTIONS
Defect characterization: TEM, PAS, DLTS, PL, Raman, RBS, EPR, SIMS
• Cavities/precipitates
Volume defects (3D)

3. Point Defects: Vacancies and Self-Interstitials
➢The simplest of the point defects is a vacancy, or vacant
lattice site, one normally occupied from which an atom is
missing.
➢All crystalline solids contain vacancies and, in fact, it is not
possible to create such a material that is free of these
defects.
➢A self-interstitial is an atom from the crystal that is
crowded into an interstitial site, a small void space that
under ordinary circumstances is not occupied.
➢A self-interstitial introduces relatively large distortions in
the surrounding lattice because the atom is substantially
larger than the interstitial position in which it is situated.

4. Point Defects: Vacancies and Self-Interstitials

5. Point Defects: VacanciesBoltzmann's constant
(1.38 x 10
-23
J/atom K)
(8.62 x 10
-5
eV/atom K)
 
N
D
N
=
exp
−Q
D
kT






No. of defects
No. of potential
defect sites.
Activation energy
Temperature
Each lattice site
is a potential
vacancy site
• Equilibrium concentration varies with temperature!
❖The number of vacancies increases exponentially with
temperature.
❖For most metals, the fraction of vacancies just below the
melting temperature is on the order of 10
−4
; that is, one
lattice site out of 10,000 will be empty.

6. •Number of Vacancies Computation at a Specified Temperature
Point Defects: Vacancies
Solution:
The number of vacancies per unit volume at 1000
o
C is:

7. Point Defects: Impurities in solids
➢A pure metal consisting of only one type of atom just isn’t
possible; impurity or foreign atoms will always be present,
and some will exist as point defects.
➢Even with relatively sophisticated techniques, it is difficult to
refine metals to a purity in excess of 99.9999% (6N purity).
➢The addition of impurity atoms to a metal will result in the
formation of a solid solution and/or a new second phase,
depending on the kinds of impurity, their concentrations, and
the temperature of the alloy.
➢The present discussion is concerned with the notion of a solid
solution.

8. ❖A solid solution forms when, as the solute atoms are added to
the host material, the crystal structure is maintained, and no
new structures are formed.
Point Defects: Impurities in solids
Interstitial &
Substitutional
impurity atoms

9. Point Defects: Impurities in solids
❑If two liquids, soluble in each other (such as water and
alcohol) are combined, a liquid solution is produced as the
molecules intermix, and its composition is homogeneous
throughout.
❑A solid solution is also compositionally homogeneous; the
impurity atoms are randomly and uniformly dispersed
within the solid.
❑Impurity point defects are found in solid solutions, of which
there are two types: substitutional and interstitial. For
the substitutional type, solute or impurity atoms replace or
substitute for the host atoms

10. The schematic diagram of point defects in semiconductor: (a) vacancy, (b) interstitial atom,
(c) small substitutional atom, (d) large substitutional atom, (e) Frenkel defect, (f) Schottky defect.

11. The schematic diagram of point defects in compound semiconductors

12. Schematic diagram of point defects and complex defects in materials