1. TOPIC 2: SOLIDIFICATIONS, IMPERFECTIONS IN SOLIDS & DIFFUSIONS
ISSUES TO ADDRESS...
• What are the solidification mechanisms?
• 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?

2. Imperfections in Solids
Solidification- result of casting of molten material
2 steps
Nuclei form (nucleation : formation of stable nuclei)
Nuclei grow to form crystals – grain structure
(nuclei: small particles of a new phase formed by a phase change (i.e. solidification) which can grow until the phase change is complete).
Start with a molten material – all liquid
nuclei
crystals growing
grain structure
liquid
Adapted from Fig.4.14 (b), Callister 7e.
Crystals grow until they meet each other

3. Solidification: Nucleation Processes
Homogeneous nucleation
nuclei form in the bulk of liquid metal
Heterogeneous nucleation
much easier since stable “nucleus” is already present
The formation of very small regions of a new solid phase at the interfaces of solid impurities.
Could be wall of mold or impurities in the liquid phase

5. Homogeneous nucleation
Simplest case of nucleation
Occurs when the metal itself provide the atoms to form nuclei.
E.g. : The case of a pure metal solidifying. When a pure liquid metal is cooled below its equilibrium freezing temperature to a sufficient degree, numerous homogeneous nuclei are created by slow-moving atoms bonding together.
Requires a considerable amount of undercooling , ~ several hundreds degrees (Undercooling: Cooling a metal below the transformation temperature without obtaining the transformation). .
For a nucleus to be stable so that it can grow into a crystal and must reach a critical size**.
(the minimum radius which a particle of a new phase formed by nucleation must have to become a stable nucleus).

6. Heterogeneous nucleation
Nucleation that occurs in a liquid on the surfaces of its container, insoluble impurities or other structural material which lower the critical free energy required to form a stable nucleus.
Since large amounts of undercooling do not occur during industrial casting operations (usually only ~ oC), thus the nucleation must be heterogeneous and not homogeneous.
heterogeneous nucleation takes place more quickly since the foreign particles act as a scaffold for the crystal to grow on, thus eliminating the necessity of creating a new surface and the incipient surface energy requirements.

10. Cooling curve for pure metal (without impurities)
Liquid cools as specific heat is removed (A-B).
Undercooling (B-C).
Nucleation begins (C).
Homogeneous nucleation. Heat is released causing an increase in the temp of the liquid (C-D).
Solidification continue at constant temp. until complete at E.

12. Growth of crystals in liquid metal and formation of grain structure
After stable nuclei have been form in a solidifying metal, these nuclei will grow into crystals.
When, solidification of the metal is completed, the crystal join together in different orientations and form crystal boundaries.
Solidified metal containing many crystals is called polycrystalline.

13. 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.

14. Solidification
Grains can be - equiaxed (roughly same size in all directions)
- columnar (elongated grains)
~ 8 cm
heat
flow
Shell of equiaxed grains due to rapid cooling (greater T) near wall
Columnar in area with less undercooling
Adapted from Fig. 4.12, Callister 7e.
Grain Refiner - added to make smaller, more uniform, equiaxed grains.

15. Equiaxed grains: grains which are approximately equal in all directions and which have random crystallographic orientations. Commonly found adjacent to a cold mold wall
Columnar grains: long, thin grains in a solidified polycrystalline structure. These grains are formed in the interior of solidified metal ingots when heat flow is slow and uniaxial during solidification. The columnar grains have grown perpendicular to the mold faces since large thermal gradients were present in those directions.

17. increase

18. Dendrite – The treelike structure of the solid that grows as molten metal freezes (when an undercooled liquid solidifies).

19. Microstructure - dendrites
Cross section
sample

20. Effect of cooling rate (solidification rate)
Rapid cooling leads to greater nucleation and more smaller grains.
Slow cooling leads to slower nucleus formation and larger grains.
More grains means more grain boundary.

21. Solidification defects (casting)
Shrinkage: contraction of a casting during solidification
Gas porosity – bubbles of gas trapped within a casting during solidification, caused by the lower solubility of the gas in the solid compared with in the liquid.
Mold material defects – wrong mold material selection
Pouring metal defects – e.g. material freezing before it completely fills the mold cavity.
Metallurgical defects – hot tears and hot spots:
Hot tears are failures in the casting that occur as the casting cools, because the metal is weak when it is hot and the stresses in the material can cause the casting to fail as it cools. Solution, proper casting design is needed.
Hot spots: surface area of the casting that very hard because it chilled more quickly than surrounding. Can be avoided by proper cooling practises or by changing the chemical composition of the metal.

25. Continuous casting of steel ingots
(a) General setup; (b) closed up of the mold arrangement (After H. E. McGannon (ed.), “ The making, shaping and treating of steel” ,United States Steel Corp., 1971.

26. Defect in the crystalline structure & Diffusion of atom

27. Defect in the crystalline structure

28. Imperfections in Solids
There is no such thing as a perfect crystal.
What are these imperfections?
Why are they important?
Many of the important properties of materials are due to the presence of imperfections.

29. Defect in the crystalline structure can have an tremendous effect on a materials behavior.
We can modify and improve many of the physical, electrical, magnetic and optical properties of crystalline materials by controlling the imperfections in their lattice structure.

30. Types of Imperfections
• Vacancy atoms
• Interstitial atoms
• Substitutional atoms
Point defects
• Dislocations
Line defects
• Grain Boundaries
Area defects
Casting defect Volume defect

31. (1). Point defects Vacancies, Interstitial and substitutional …move by diffusion

32. Schottky and Frenkel defects in an ionic crystal
Schottky: a defect consisting of a cation and anion vacancies pair.
Frenkel : In an ionic solid, a cation-vacancy and cation interstitial pair.

33. 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

34. 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 solid soln.
(e.g., Cu in Ni)
Interstitial solid soln.
(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.

35. (2) Line Defects Dislocations: Schematic of Zinc (HCP): slip steps
• are line defects,
• slip between crystal planes result when dislocations move,
• produce permanent (plastic) deformation.
Schematic of Zinc (HCP):
• before deformation
• after tensile elongation
slip steps
Adapted from Fig. 7.8, Callister 7e.

36. 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 lattice distortion. Refer to magnitude and direction of lattice distortion associated with a dislocation.

37. Imperfections in Solids
Edge Dislocation
Fig. 4.3, Callister 7e.

39. Motion of Edge Dislocation
• 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.
(Courtesy P.M. Anderson)

40. Imperfections in Solids
Screw Dislocation
Screw Dislocation b
Dislocation
line
Burgers vector b
(b)
(a)
Adapted from Fig. 4.4, Callister 7e.

42. Edge, Screw, and Mixed Dislocations
Adapted from Fig. 4.5, Callister 7e.

43. (3) Surface defects (area defects) grain boundaries and material surface
The grain boundaries is a narrow zone where the atoms are not properly spaced

44. Grain boundaries are:
Boundaries between crystal
Produced by the solidification process (e.g.)
Have a change in crystal orientation across them
Impede dislocation motion.

45. Imperfections in Solids
Dislocations are visible in electron micrographs
Adapted from Fig. 4.6, Callister 7e.

46. Dislocations & Crystal Structures
• Structure: close-packed
planes & directions
are preferred.
view onto two
close-packed
planes.
close-packed directions
close-packed plane (bottom)
close-packed plane (top)
• Comparison among crystal structures: (more slip system: more ductile)
FCC: many close-packed planes/directions;
HCP: only one plane, 3 directions;
• Specimens that
were tensile
tested.
Mg (HCP)
tensile direction
Al (FCC)

47. Microscopic Examination
Crystallites (grains) and grain boundaries. Vary considerably in size. Can be quite large
ex: Large single crystal of quartz or diamond or Si
ex: Aluminum light post or garbage can - see the individual grains
Crystallites (grains) can be quite small (mm or less) – necessary to observe with a microscope.

48. Optical Microscopy • Useful up to 2000X magnification.
• Polishing removes surface features (e.g., scratches)
• Etching changes reflectance, depending on crystal
orientation.
0.75mm
crystallographic planes
Adapted from Fig. 4.13(b) and (c), Callister 7e. (Fig. 4.13(c) is courtesy
of J.E. Burke, General Electric Co.
Micrograph of
brass (a Cu-Zn alloy)

49. Optical Microscopy Grain boundaries... Fe-Cr alloy N = 2 n -1
• are imperfections,
• are more susceptible
to etching,
• may be revealed as
dark lines,
• change in crystal
orientation across
boundary.
Fe-Cr alloy
(b)
grain boundary
surface groove
polished surface
(a)
Adapted from Fig. 4.14(a) and (b), Callister 7e.
(Fig. 4.14(b) is courtesy
of L.C. Smith and C. Brady, the National Bureau of Standards, Washington, DC [now the National Institute of Standards and Technology, Gaithersburg, MD].)
ASTM grain
size number N
= 2 n -1
number of grains/in2
at 100x
magnification

50. Optical Microscopy Polarized light
metallographic scopes often use polarized light to increase contrast
Also used for transparent samples such as polymers

51. Microscopy Optical resolution ca. 10-7 m = 0.1 m = 100 nm
For higher resolution need higher frequency
X-Rays? Difficult to focus.
Electrons
wavelengths ca. 3 pm (0.003 nm)
(Magnification - 1,000,000X)
Atomic resolution possible
Electron beam focused by magnetic lenses.
Optical microscopy good to ca. wavelength of light
Higher frequencies
X-rays – good idea but difficult to focus
Electrons - wavelength proportional to velocity with high voltage (high acceleration) get wavelengths ca. 3pm (0.003nm) (x1,000,000)

53. Scanning Tunneling Microscopy (STM)
• Atoms can be arranged and imaged!
Photos produced from the work of C.P. Lutz, Zeppenfeld, and D.M. Eigler. Reprinted with permission from International Business Machines Corporation, copyright 1995.
Carbon monoxide molecules arranged on a platinum (111) surface.
Iron atoms arranged on a copper (111) surface. These Kanji characters represent the word “atom”.

54. Summary • Point, Line, Area and volume defects exist in solids.
• 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.)