IN IMPERFECTIONS SOLIDS
ISSUES TO ADDRESS...
What types of defects arise in solids? Can the number and type of defects be varied and controlled? How do defects affect material properties? Are defects undesirable?
CHAPTER 4:
1
Imperfections in Solids (Defects): Introduction
Real crystals are never perfect, there are always defects
Defects have a profound impact on the macroscopic properties of materials
The processing determines the defect type and defect concenration:
TYPES OF IMPERFECTIONS
Vacancy atoms Interstitial atoms Substitutional atoms Dislocations Grain Boundaries Point defects
Line defects Area defects
POINT DEFECTS
Vacancies:
-vacant atomic sites in a structure.
Vacancy
distortion of planes
Self-Interstitials:
-"extra" atoms positioned between atomic sites.
distortion of planes
selfinterstitial
3
Schematic representation of different point defects:
(1) (2) (3) Vacancy; Self-interstitial; Interstitial impurity;
(4,5) Substitutional impurities
EQUIL. CONCENTRATION: POINT DEFECTS
Equilibrium concentration varies with temperature!
No. of defects Activation energy
No. of potential defect sites.
Q ND = D exp kT N
Temperature Boltzmann's constant (1.38 x 10 -23 J/atom K) (8.62 x 10 -5 eV/at om K)
Each lattice site is a potential vacancy site
ESTIMATING VACANCY CONC.
Find the equil. # of vacancies in 1m of Cu at 1000C. Given: = 8.4 g /cm 3 ACu = 63.5g/mol N A = 6.02 x 10 23 atoms/mole Q V = 0.9eV/atom
NV D = exp N
For 1m 3 , N = Answer:
1273K 8.62 x 10 -5 eV/atom-K NA x 1m 3 = 8.0 x 10 28 sites x ACu
Q V D = 2.7 10 -4 kT
0.9eV/atom
N D = 2.7 10 -4 8.0 x 10 28 sites = 2.2x 10 25 vacancies V
POINT DEFECTS IN ALLOYS
Two outcomes if impurity (B) added to host (A):
Solid solution of B in A (i.e., random dist. of point defects)
OR
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.
COMPOSITION
Definition: Relative amount of constituents (A and B) in an (A-B) Alloy. Two descriptions:
Weight % Atom %
mass of B x 100 CB = total mass
C' B AB C' AAA + C' B AB
C' B =
# atoms of B x 100 total # atoms
Conversion between wt % and at% in an A-B alloy:
CB =
x 100
C' B = C A/AA + C B /AB
C B /AB
Basis for conversion:
mass of B = moles of B
x AB
atomic weight of B atomic weight of A
mass of A = moles of A x AA
Line defects: Dislocations
Dislocations: are line defects, Schematic of a Zinc (HCP):
before deformation cause slip between crystal plane when they move, produce permanent (plastic) deformation. after tensile elongation
slip steps
Number of dislocations and their interaction with the applied and load forces determine the deformation behavior of metals. (CHAPTER 7)
Edge Dislocations
Edge Dislocations
Atomic rearrangements that accompany the motion of an edge dislocation as it moves in response to an applied shear stress.
BOND BREAKING AND REMAKING
Dislocation motion requires the successive bumping of a half plane of atoms (from left to right here). Bonds across the slipping planes are broken and remade in succession.
Atomic view of edge dislocation motion from left to right as a crystal is sheared.
INCREMENTAL SLIP
Dislocations slip planes incrementally... The dislocation line (the moving red dot)...
...separates slipped material on the left from unslipped material on the right.
Simulation of dislocation motion from left to right as a crystal is sheared.
Screw Dislocations
Mixed Dislocations
DISLOCATIONS & CRYSTAL STRUCTURE
Structure: close-packed planes & directions are preferred.
close-packed plane (bottom)
view onto two close-packed planes.
close-packed directions close-packed plane (top)
Comparison among crystal structures:
FCC: many close-packed planes/directions; HCP: only one plane, 3 directions; BCC: none
Results of tensile testing.
tensile direction
Mg (HCP)
Al (FCC)
14
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. Metal Ingot
~ 8cm
Schematic
grain boundaries
heat flow
Pure Pb
OPTICAL MICROSCOPY (1)
Useful up to 2000X magnification. Polishing removes surface features (e.g., scratches) Etching changes reflectance, depending on crystal orientation. Micrograph of
Light Brass (Cu and Zn)
microscope
0.75mm
OPTICAL MICROSCOPY (2)
microscope
Grain boundaries...
are imperfections, are more susceptible to etching, may be revealed as dark lines, change direction in a polycrystal.
polished surface surface groove grain boundary
Fe-Cr alloy
OTHER AREA DEFECTS
! Twin Boundaries (Mirror lattice image) ! Stacking Faults (in FCC distortion in ABCABC stacking) ! Phase Boundaries (Boundaries between two chemically different grains) ! Domain Walls (in Ferromagnetic and Ferrimagnetic materials, boundaries
between regions with different direction of magnetization)
Summary
TYPES OF IMPERFECTIONS Vacancy atoms Interstitial atoms Substitutional atoms Dislocations Grain Boundaries Point defects Line defects Area defects
The number and type of defects can be varied and controlled (e.g., T controls vacancy conc.) Defects affect material properties (e.g., grain boundaries control crystal slip). Defects may be desirable or undesirable (e.g., dislocations may be good or bad, depending on whether plastic deformation is desirable or not.)