Download TYPES OF IMPERFECTIONS

TYPES OF IMPERFECTIONS
A perfect crystalline material usually does not exist rather a
various number of defects develop in the crystalline structure
mainly upon solidification. A molten metal is amorphous and
upon solidification it crystallizes but during the process some
defects happens.
• Vacancy atoms
• Interstitial atoms
• Substitutional atoms
Point defects
• Dislocations
Line defects
• Grain Boundaries
Area defects
1. Point Defects:
A. Vacancy defect: An atom missing from a normally occupied
lattice site.
-vacant atomic sites in a structure.
distortion
of planes
Vacancy
• Equilibrium number of vacancies Nv concentration
depends on and increase with temperature for a given
quantity of material
Where:
Nv = N exp ( -Qv / KT)
Nv: Equilibrium number of vacancies for a given quantity of material
(units usually is vacancies / m3)
N: total number of atomic sites
NA: Avagdro’s Number: 6.023 x 10 23 atoms/mole
ρ: density
A:atomic weight (g/mole)
K: Boltzmann’s constant =1.38x10-23 J/atom. K or 8.62x10-5 ev/atom K
T: Absolute temperature in kelvin (T k = T oC +273)
Qv : Energy required for the formation of a vacancy.
ESTIMATING VACANCY CONC.
• Find the equil. # of vacancies in 1m 3 of Cu at 1000C.
• Given:
ρ = 8.4 g/cm3
ACu = 63.5g/mol
QV = 0.9eV/atom NA = 6.02 x 1023 atoms/mole
Mass of Cu is: (ρ x v) = 8.4 g/cm3 x 106 (cm3/m3)x 1= 8.4x 106 g
63.5 g/mole ---------Æ 6.023 x1023 atoms
8.4x106 g
------Æ
N?
N : total number of atomic sites: 8.4x106 x 6.023x1023 / 63.5 =
8 x 1028 atoms/m3
Nv = 8 x1028 exp (-0.9 / 8.62x10-5 x 1273)= 2.2x1025 vacancies /m3
Remarks:
•As the temperature increase the number of vacancies
also increase.
•For most metals , just below melting temperature
Nv/N = 10-4 , which means that one lattice site out of
10000 site will be empty.
B. Self-Interstitials:
An atom from the crystal that is crowded in a small
void space that under normal conditions is not
occupied.
This type of defect introduces large distortions in the
surrounding lattice, consequently the formation of this
defect is not highly probable.
distortion
of planes
selfinterstitial
C. Impurities:
Either impurity atom or intentionally added atoms (alloying)
Find their way into the host crystal through two ways:
1. Producing solid solutions, 2. Producing new phases
Solid Solution: It take place when different atoms take part in building
a crystal lattice, solute atoms are added and no new phases are formed.
Phase: A homogeneous portion of a system that have uniform
physical and chemical characteristics
Types of solid solutions:
A. Substitutional Solid solution : Solute atoms replace a host
atom.
B. Interstitial Solid solution: Solute atoms fill the voids
among the host atoms.
Two outcomes if impurity (B) added to host (A):
• Solid solution of B in A (i.e., random dist. of point defects)
rCu=.128nm
rC=0.071 nm
OR
rFe=0.124 nm
rNi=0.125nm
Substitutional alloy
(e.g., Cu in Ni)
Interstitial alloy
(e.g., C in Fe)
• Solid solution of B in A plus particles of a new
phase (usually for a larger amount of B)
Second phase particle
--different composition
--often different structure.
Factors that affect the degree to which the solute atoms dissolves in the host
metal to form a substitutional solid solution:
1. Atomic size factor. Appreciable quantities of a solute may be
accommodated in this type of solid solution (substitutional ) only
when the difference in atomic radii between the two atom types is
less than about : 15% .Otherwise the solute atoms will create
substantial lattice distortions and a new phase will form.
∆r% =[ (r solute – r solvent) / r solvent ] x 100 ≤ ±15%
2. Crystal structure. For appreciable solid solubility the crystal
structures for metals of both atom types must be the same.
3. Electronegativity. The more electropositive one element and the
more elec- tronegative the other, the greater is the likelihood that
they will form an intrmetallic compound instead of a
substitutional solid solution. Similar electronegativity increases
solubility
4. Valences. Other factors being equal, a metal will have more of a
tendency to dissolve another metal of higher valency than one of
a lower valency. Similar valency increases solubility.
Remarks regarding interstitial solid solutions:
•The atomic radius of an interstitial atom must be substantially
smaller than that of the host atom.
•Metallic materials that have relatively high atomic packing factors
crystal structures, the interstitial positions are relatively small.
•Normally the maximum allowable concentrations of interstitial
atoms is low (less than 10%) due to the accompanied lattice
distortions.
4 In this problem we are asked to cite which of the
elements listed form with Cu the three possible solid
solution types. For complete substitutional solubility
the following criteria must be met: 1) the difference
in atomic radii between Cu and the other element
(∆R%) must be less than ±15%, 2) the crystal
structures
must
be
the
same,
3)
the
electronegativities must be similar, and 4) the
valences should be the same, or nearly the
same.
Below are tabulated, for the various
elements, these criteria.
El
Composition
how do you specify the composition of an alloy?
•Weight percent: (wt %)
, C2=
m2
x100 [4.3]
m1+m2
Weight ( or mass) of a particular element relative to the total alloy
weight.
C1+C2 =100
•Atom percent: (at%)
Number of moles of an element to the total number of the moles
of the elements in the alloy
nm1= m1’/A1 (4.4) , where: nm1: No. of moles of element 1
m1’ : mass in g of element 1
A1: Atomic weight (g/mole)
C1’=
nm1
x100
(4.5)
nm1+nm2
C2’=
nm2
nm1+nm2
C1’+C2’=100
x100
Composition Conversions:
4.6a
4.6b
4.7a
4.7b
Divide the numerator and denomenator by M’/100.
Multiply the numerator and denomenator by A1A2
To derive equation 4.7a
Since: nm1= m1’ (4.4)
A1
Since:
C1’= nm1
x100
(4.5)
nm1+nm2
C1=
[C1’ (nm1+nm2)/100] A1
[C1’ (nm1+nm2)/100]A1 + [C2’ (nm1+nm2)/100] A2
x 100
multiply the numerator and denominator by [100/ (nm1+nm2)]
LINE DEFECTS
Dislocations: They are introduced in the crystalline structure during
solidification (specially with rapid cooling) and during plastic
deformation.
• are line defects,
• cause slip between crystal plane when they move,
• produce permanent (plastic) deformation.
Edge dislocation: Extra ½ plane of atoms
Burgers vector: distance between
adjacent atoms that defines the
magnitude and the direction the
dislocation slip each unit step motion
LINE DEFECTS
Edge dislocation: Extra ½ plane of atoms
Dislocation line perpendicular
to burgers vector
Dislocation line motion
parallel to burgers vector
Lattice
Above dislocation line
distortions Compressive strain field
Dislocation line perpendicular
to the plane of the page
Lattice
distortions
Below dislocation line
Tensile strain field
Motion of
dislocation
line
Screw dislocation: A portion of the crystal is skewed one
atom spacing with respect to the other portion of the
crystal.
Dislocation line
motion is
perpendicular to
burgers vector
Dislocation
line motion
Dislocation
line
b
Dislocation line
parallel to
burgers vector
on
ne
m
oti
Li
b
Line motion
Edge
dislocation
Screw
dislocation
b
AREA DEFECTS: GRAIN BOUNDARIES
Grain boundaries:
•
•
•
•
are boundaries between crystals.
are produced by the solidification process, for example.
have a change in crystal orientation across them.
impede dislocation motion.
Solidification of metals:
liquid
nucleation
growth
Grain with different
lattice orientations
nucleation
Growth
Grains are formed
Angle of misalignment
grain
boundaries
Different grains have different orientations of atoms
Grain boundaries separate grains that have different lattice
orientations and impede dislocation motion.
When the orientation mismatch is
on the order of few degrees then a
small angle grain boundary is
generated .
Small angle boundary is formed
when edge dislocation are aligned
in the manner shown here.