Polycrystals vs. Single Crystal
Single crystal
Specimen with perfect
arrangement of unit cells
Polycrystal
Crystalline solids composed of grains
Grain
Region of consistent
crystallographic orientation
http://www.tf.uni-kiel.de/matwis/amat/def_en/metamod/preface.html Feb 2016
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Number of vacancies
Thermodynamics
Reaction occurs spontaneously if it results in a
reduction in total energy of the state
⇢Structure determined by energy minimization
From energy minimization follows:
Qv
Nv = N exp (
)
kT
Nv: equilibrium number of vacancies (/m3)
N: total number of atomic sites (/m3)
Qv: activation energy required to form a vacancy
(J/mol or eV/atom)
k: Boltzmann’s constant (1.38x10-23 J/(atom K)
or 8.62x10-5 eV/(atom K))
T: absolute Temperature (K)
Callister Textbook, Fig: 4.1, 4.2
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Imperfections in Solids - Summary
•
•
Imperfections are unavoidable
Imperfections are often desired
0D
Point Defects
Vacancies
Substitutional atoms
Interstitial atoms (self, impurity)
1D
Line Defects
Dislocations
2D
Area/Interfacial Defects
External Surface
Grain Boundary
Twins
Stacking Faults
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Linear defect - thought experiment
21
Linear defect - thought experiment
21
Linear defect - thought experiment
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Linear defect - thought experiment
atoms have been dislocated!
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Dislocations
linear defect separating regions of
Dislocation identical perfect atomic arrangement
due to atomic motion
screw dislocation
edge dislocation
b k dislocation line
b ? dislocation line
t
b
t
t
23
Dislocations
Dislocations can be made visible with a
Transmission Electron Microscope (TEM)
Callister Textbook: Fig. 4.7
24
Area Defects
Interfacial Defects
•
•
•
external surface
internal surfaces
• grain boundaries
• phase boundaries
• twin boundaries
stacking faults
http://www.tf.uni-kiel.de/matwis/amat/def_en/metamod/preface.html Feb 2016
26
grain boundaries and phase boundaries
from Callister Textbook: Fig. 4.15
http://www.tms.org/pubs/journals/JOM/9801/Felkins-9801.fig.3.lg.gif
http://www.metallographic.com/Images/Al-anodized-IA.jpg
27
grain boundaries and phase boundaries
If not only the orientation of the atomic arrangement changes
but also the types of elements involved
➜phase boundary
from Callister Textbook: Fig. 4.15
http://www.tms.org/pubs/journals/JOM/9801/Felkins-9801.fig.3.lg.gif
http://www.metallographic.com/Images/Al-anodized-IA.jpg
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Twin boundary - TWIP Steel
3 twists @ room temperature
mirror
Callister Textbook: Fig. 4.10
U. Brüx, G. Frommeyer, D. Steinmetz, MPIE Düsseldorf
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Twin boundary - TWIP Steel
3 twists @ room temperature
mirror
Callister Textbook: Fig. 4.10
U. Brüx, G. Frommeyer, D. Steinmetz, MPIE Düsseldorf
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Stacking faults
FCC ABCABC
HCP ABAB
Stacking faults occur
•
•
•
during crystal growth
other defects agglomerate (vacancies)
as part of dislocations
http://www.tf.uni-kiel.de/matwis/amat/iss/kap_5/backbone/r5_3_3.html
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Copper
Smallest scale
−10
(~10 m):
Atoms ordered!
250μm
https://www.copper.org/resources/
properties/microstructure/coppers.html
https://www.researchgate.net/figure/226744772_fig1_Figure-1-a-TEM-micrograph-of-ahttp://www.nature.com/nmat/journal/v10/n8/fig_tab/nmat3055_F5.html
dislocation-cell-structure-in-copper-after-plastic
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Substitutional Solid Solution - formation rules
Hume-Rothery-Rules
Substitutional solid solution in metals
Callister Textbook, Fig: 4.2
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