1. The Structure and Dynamics of Solids
The Muppet’s Guide to:
The Structure and Dynamics of Solids
6. Crystal Growth & Defects

2. Layer by Layer Growth For epitaxial growth we want the layer to stick:
Energy to remain on surface, Ea
Energy to diffuse on surface, Ed
Cohesive energy, Ec
Strain Energy, (U)

3. Pulsed Laser Deposition (PLD)
Laser produces a plasma of material which is then deposited on a substrate. Good for oxides and high melting point materials
Images Courtesy, Nessa Fereshteh Saniee, PhD Thesis, UoW 2014

4. inac.cea.fr/Images/astImg/479_1.png

5. Heterostructures
Dislocation/Disorder

6. Lattice Match through Rotations
aPt=3.9242Å
aFe=2.8665Å
45° Rotation of unit cells
Pt[100]//FeCo[110]

7. Disorder in crystalline materials
No such thing as a perfectly ordered material
Many materials are technologically of value because they are disordered/imperfect in some way:
silicon devices – controlled levels of deliberate impurity additions (ppb) p-type : B Si  B + h
n-type : P Si  P + e
steels – additions of 0.1 to 1 at.% other metals to improve mechanical properties and corrosion resistance

8. Types of Imperfections
• Vacancy atoms
• Interstitial atoms
• Substitutional atoms
Point defects
• Dislocations
Line defects
• Grain Boundaries
Area defects

9. Imperfections in Solids
Linear Defects (Dislocations)
Are one-dimensional defects around which atoms are misaligned
Edge dislocation:
extra half-plane of atoms inserted in a crystal structure
b  to dislocation line
Screw dislocation:
spiral planar ramp resulting from shear deformation
b  to dislocation line
Burger’s vector, b: measure of the magnitude and direction of lattice distortion.

10. Dislocations – linear defects
Source:
growth
stress
temperature
Evidence:
- metals more deformable than predicted (but can be strengthened by impurities)
- spiral growths on surface of some crystals
reactions occur at active surface sites
Types: edge, screw, intermediate
Transmission electron micrograph of Ti alloy – dark lines are dislocations
(Callister: Materials Science and Engineering)

11. Edge dislocation – partial plane of atoms
– lattice distorted where plane ends
Dislocations characterised by the Burgers vector, b
for metals, b points in a close-packed direction and equals the interatomic spacing
(Callister: Materials Science and Engineering)

12. Buffer Layers ┬ ┬ ┬

13. Screw dislocation partial slip of a crystal
Shear stress
partial slip of a crystal
on one side of dislocation line, crystal has undergone slip; on other side, crystal is normal
continued application of shear stress causes dislocation to move through crystal
(Callister: Materials Science and Engineering)

14. Edge, Screw, and Mixed Dislocations
(Callister: Materials Science and Engineering)

15. Interfacial (planar) defects
boundaries separating regions of different crystal structure or crystallographic orientation
External surfaces (see final section of module)
Internal boundaries
Layer Interfaces (2D)
Region Interfaces (3D)

16. Planar Defects in Solids
Freezing - result of casting of molten material
2 steps
Nuclei form
Nuclei grow to form crystals
Crystals grow until they meet each other
grain structure
nuclei
crystals growing
grain structure
liquid
(Callister: Materials Science and Engineering)

17. Polycrystalline Materials
Grain Boundaries
regions between crystals
transition from lattice of one region to that of the other
slightly disordered
low density in grain boundaries
high mobility
high diffusivity
high chemical reactivity
Adapted from Fig. 4.7, Callister 7e.

18. Grain boundaries
Internal surfaces of a single crystal where ideal domains (mosaic) meet with some misalignment: high-angle and small(low)-angle.
NB – in polycrystalline materials, grain boundaries are more extensive and may even separate different phases
D = b/ b
Small-angle grain boundary equivalent to linear array of edge dislocations
bonding not fully satisfied  region of higher energy, more reactive, impurities present.
(Callister: Materials Science and Engineering)

19. Planar Defects in Solids 2
Another case is a twin boundary (plane)
Essentially a reflection of atom positions across the twin plane.
Stacking faults
For FCC metals an error in ABCABC packing sequence
Ex: ABCABABC
(Callister: Materials Science and Engineering)

20. Point Defects small substitutional atom
vacancy
interstitial
small substitutional atom
large substitutional atom
Frenkel defect
Schottky defect
All of these defects disrupt the perfect arrangement of the surrounding atoms –relaxation effects
Schottky and Frenkel normally v low conc. since formation energy high

21. Schottky Defects Found in ionic crystals
Oppositely charged ions leave their lattice sites, creating vacancies
anion and cation vacancies balance such that charge neutrality is preserved

22. Frenkel Defect
Tend to be found in ionic solids with large size difference between the anion and cation
The defect forms when an atom or cation leaves its place in the lattice, creating a vacancy, and becomes an interstitial.
occur due to thermal vibrations
occurrence depends on
size of ion
charge on ion
electronegativity
temperature Ag Ag

23. Point Defects Vacancy self- interstitial
• Vacancies:
-vacant atomic sites in a structure.
Vacancy
distortion
of planes
• Self-Interstitials:
-"extra" atoms positioned between atomic sites.
self-
interstitial
distortion
of planes
(Callister: Materials Science and Engineering)

24. 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)
Substitutional solid soln.
(e.g., Cu in Ni)
Interstitial solid soln.
(e.g., C in Fe) OR
(Callister: Materials Science and Engineering)

25. Material Properties Dislocations & plastic deformation
Cubic & hexagonal metals - plastic deformation by plastic shear or slip where one plane of atoms slides over adjacent plane by defect motion (dislocations).
So we saw that above the yield stress plastic deformation occurs. But how? In a perfect single crystal for this to occur every bond connecting tow planes would have to break at once! Large energy requirement
Now rather than entire plane of bonds needing to be broken at once, only the bonds along dislocation line are broken at once.
If dislocations don't move, deformation doesn't occur!
Adapted from Fig. 7.1, Callister 7e.