1. Phase Transformations & Diffusion in Materials
MSN 504
Phase Transformations & Diffusion in Materials
Assist. Prof. Bilge Imer

2. Institute of Materials Science and Nanotechnology
Phase
A phase is a physically distinct, homogeneous portion of a thermodynamic system delineated in space by a bounding surface, the interphase interface, and distinguished by its state of aggregation (solid, liquid or gas), its crystal structure, composition and/or degree of order. Each phase generally exhibits a characteristic set of physical, mechanical and chemical properties and is conceivably mechanically separable from the whole.
Bilkent University
Institute of Materials Science and Nanotechnology

3. Institute of Materials Science and Nanotechnology
Phase Transformation
A Phase transformation is a change in the state of an assembly of interacting particles (atoms, molecules, electrons, etc.) as indicated by qualitative changes in the physical, mechanical and chemical properties induced by small quantitative changes in the thermodynamic variables such as T, P, E (electric field), H (magnetic field), etc. The rearrangement of the constituent particles carries the system from one configuration to another of lower free energy which can be described generally by one or several so-called order parameters which define the particular state of the system.
Bilkent University
Institute of Materials Science and Nanotechnology

4. Institute of Materials Science and Nanotechnology
Diffusion
It is a form of mass transport. In liquids and gases mass transport occurs in the form of convection and diffusion while in solids it only occurs with diffusion.
It can be said that diffusion is the movement of particles/atoms/electrons/defects in a matter from high to low concentration in the presence of gradient until equilibrium is reached.
Bilkent University
Institute of Materials Science and Nanotechnology

5. Institute of Materials Science and Nanotechnology
Nanomaterials
Bilkent University
Institute of Materials Science and Nanotechnology

6. Institute of Materials Science and Nanotechnology
Types of Materials
Materials can be classified according to structural, physical, electrical, optical and magnetic properties, area of use, etc. All these properties are closely related with bonding type and energies between atoms.
However if a group of material shows close resemblance in all properties we can classify them in one category. So according to this: Metals, Polymers, Ceramics and Composites can be the general classification of materials.
Materials
Metals
Polymers
Ceramics
Composites
Bilkent University
Institute of Materials Science and Nanotechnology

7. Institute of Materials Science and Nanotechnology
Periodic Table
Bilkent University
Institute of Materials Science and Nanotechnology

8. Courtesy of Prof. Erman Bengu, CHEM 201
Atomic Configuration
• Most elements: Electron configuration not stable.
Adapted from Table 2.2, Callister 7e.
• Valance electrons determine chemical, electrical, thermal
and optical properties, and they are responsible for bonding 5

9. Courtesy of Prof. Erman Bengu, CHEM 201
THE PERIODIC TABLE
• Columns: Similar Valence Structure, Similar Properties
Electropositive elements:
Readily give up electrons
to become + ions.
Electronegative elements:
Readily acquire electrons
to become - ions.

10. Institute of Materials Science and Nanotechnology
Bonding types
BONDS
PRIMARY
METALLIC
IONIC
COVALENT
SECONDARY (van der waals)
Fluctuating induced dipole, polar molecule induced dipole, permanent dipole (hydrogen bond)
Bilkent University
Institute of Materials Science and Nanotechnology

11. Atomic Bonding in Solids
Courtesy of Prof. Erman Bengu, CHEM 201
Atomic Bonding in Solids
Start with two atoms infinitely separated
Attractive component is due to nature of the bonding (minimize energy thru electronic configuration)
Repulsive component is due to Pauli exclusion principle; electron clouds tend to overlap
Essentially atoms either want to give up (transfer) or acquire (share) electrons to complete electron configurations; minimize their energy
Transfer of electrons => ionic bond
Sharing of electrons => covalent
Metallic bond => sea of electons r

12. Courtesy of Prof. Erman Bengu, CHEM 201
METALLIC BONDING
• Arises from a sea of donated valence electrons
(1, 2, or 3 from each atom).
Ion cores in the “sea of electrons”.
Valance electrons belong no one particular atom but drift throughout the entire metal.
“Free electrons” shield +’ly charged ions from repelling each other…
Adapted from Fig. 2.11, Callister 6e.
• Primary bond for metals and their alloys

13. Courtesy of Prof. Erman Bengu, CHEM 201
IONIC BONDING
• Occurs between + and – ions (anion and cation).
• Requires electron transfer.
• Large difference in electronegativity required.
• Example: Na+ Cl-

14. Courtesy of Prof. Erman Bengu, CHEM 201
COVALENT BONDING
• Requires shared electrons
• Example: CH4
C: has 4 valence e,
needs 4 more
H: has 1 valence e,
needs 1 more
Electronegativities
are comparable.
Adapted from Fig. 2.10, Callister 6e.

15. Summary: Primary Bonds
Courtesy of Prof. Erman Bengu, CHEM 201
Summary: Primary Bonds
Ceramics
Large bond energy
large Tm
large E
small a
(Ionic & covalent bonding):
Metals
Variable bond energy
moderate Tm
moderate E
moderate a
(Metallic bonding):
Polymers
Directional Properties
Secondary bonding dominates
small Tm
small E
large a
(Covalent & Secondary):
secondary bonding

16. Courtesy of Prof. Erman Bengu, CHEM 201
SECONDARY BONDING
Arises from interaction between dipoles
• Fluctuating dipoles
asymmetric electron
clouds + -
secondary
bonding H 2
ex: liquid H
Adapted from Fig. 2.13, Callister 7e.
• Permanent dipoles-molecule induced + -
-general case:
secondary
bonding
Adapted from Fig. 2.14,
Callister 7e. Cl Cl
-ex: liquid HCl
secondary H H
bonding
secondary bonding
-ex: polymer
secondary bonding

17. Courtesy of Prof. Erman Bengu, CHEM 201
Summary: Bonding
Type
Bond Energy
Comments
Ionic
Large!
Nondirectional (ceramics)
Covalent
Variable
Directional
(semiconductors, ceramics
polymer chains)
large-Diamond
small-Bismuth
Metallic
Variable
large-Tungsten
Nondirectional (metals)
small-Mercury
Secondary
smallest
Directional
inter-chain (polymer)
inter-molecular

18. Courtesy of Prof. Erman Bengu, CHEM 201
Energy and Packing
• Non dense, random packing
Energy r
typical neighbor
bond length
bond energy
COOLING
• Dense, ordered packing
Energy r
typical neighbor
bond length
bond energy
Dense, ordered packed structures tend to have
lower energies.

19. Courtesy of Prof. Erman Bengu, CHEM 201
MATERIALS AND PACKING
Crystalline materials...
• atoms pack in periodic, 3D arrays
• typical of:
-metals
-many ceramics
-some polymers
crystalline SiO2
Adapted from Fig. 3.18(a),
Callister 6e.
LONG RANGE ORDER
Noncrystalline materials...
• atoms have no periodic packing
• occurs for:
-complex structures
-rapid cooling
"Amorphous" = Noncrystalline
noncrystalline SiO2
Adapted from Fig. 3.18(b),
Callister 6e.
SHORT RANGE ORDER

20. SIMPLE CUBIC STRUCTURE (SC)
Courtesy of Prof. Erman Bengu, CHEM 201
SIMPLE CUBIC STRUCTURE (SC)
• Rare due to poor packing (only Po has this structure)
• Close-packed directions are cube edges.
Closed packed direction is where the atoms touch each other
• Coordination # = 6
(# nearest neighbors)
(Courtesy P.M. Anderson)

21. BODY CENTERED CUBIC STRUCTURE (BCC)
Courtesy of Prof. Erman Bengu, CHEM 201
BODY CENTERED CUBIC STRUCTURE (BCC)
• Close packed directions are cube diagonals.
--Note: All atoms are identical; the center atom is shaded
differently only for ease of viewing.
ex: Cr, W, Fe (), Tantalum, Molybdenum
• Coordination # = 8
2 atoms/unit cell: 1 center + 8 corners x 1/8
(Courtesy P.M. Anderson)

22. FACE CENTERED CUBIC STRUCTURE (FCC)
Courtesy of Prof. Erman Bengu, CHEM 201
FACE CENTERED CUBIC STRUCTURE (FCC)
• Close packed directions are face diagonals.
--Note: All atoms are identical; the face-centered atoms are shaded
differently only for ease of viewing.
ex: Al, Cu, Au, Pb, Ni, Pt, Ag
• Coordination # = 12
Adapted from Fig. 3.1, Callister 7e.
4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8
(Courtesy P.M. Anderson)

23. Courtesy of Prof. Erman Bengu, CHEM 201
FCC STACKING SEQUENCE
• ABCABC... Stacking Sequence
• 2D Projection
• FCC Unit Cell

24. HEXAGONAL CLOSE-PACKED STRUCTURE (HCP)
Courtesy of Prof. Erman Bengu, CHEM 201
HEXAGONAL CLOSE-PACKED STRUCTURE (HCP)
• ABAB... Stacking Sequence
• 3D Projection
• 2D Projection
Adapted from Fig. 3.3,
Callister 6e.
• Coordination # = 12
6 atoms/unit cell
• APF = 0.74
ex: Cd, Mg, Ti, Zn
• c/a = 1.633

25. COORDINATION # AND IONIC RADII
Courtesy of Prof. Erman Bengu, CHEM 201
COORDINATION # AND IONIC RADII
• Coordination # increases with
Adapted from Fig. 12.4, Callister 6e.
Adapted from Fig. 12.2, Callister 6e.
Adapted from Fig. 12.3, Callister 6e.
Adapted from Table 12.2, Callister 6e.

26. Imperfections in Solids
Courtesy of Prof. Erman Bengu, CHEM 201
Imperfections in Solids
Is it enough to know bonding and structure of materials to estimate their macro properties ?
BONDING +
STRUCTURE
DEFECTS
PROPERTIES
Defects do have a significant impact on the properties of materials

27. Imperfections in Solids
Courtesy of Prof. Erman Bengu, CHEM 201
Imperfections in Solids
Defects in Solids
0-D, Point defects
Vacancy
Interstitial
Substitutional
1-D, Line Defects / Dislocations
Edge
Screw
2-D, Area Defects / Grain boundaries
Tilt
Twist
3-D, Bulk or Volume defects
Crack, pore
Secondary Phase
Crystals in nature are never perfect, they have defects !
Atoms in irregular positions
MATERIALS PROPERTIES
Planes or groups of atoms in irregular positions
Interfaces between homogeneous regions of atoms

28. Imperfections in Solids
Courtesy of Prof. Erman Bengu, CHEM 201
Imperfections in Solids
Atomic Composition
Bonding
Microstructure:
Materials properties
Thermo-Mechanical Processing
X’tal Structure
Addition and manipulation of defects

29. Courtesy of Prof. Erman Bengu, CHEM 201
POINT DEFECTS
• Vacancies:
-vacant atomic/lattice sites in a structure.
• Self-Interstitials:
-"extra" atoms positioned between atomic sites.

30. Point Defects: Vacancies & Interstitials
Courtesy of Prof. Erman Bengu, CHEM 201
Point Defects: Vacancies & Interstitials
Most common defects in crystalline solids are point defects.
At high temperatures, atoms frequently and randomly change their positions leaving behind empty lattice sites.
In general, diffusion (mass transport by atomic motion) - can only occur because of vacancies.

31. Point Defects: Vacancies & Interstitials
Courtesy of Prof. Erman Bengu, CHEM 201
Point Defects: Vacancies & Interstitials
Schematic representation of a variety of point defects:
(1) vacancy;
(2) self-interstitial;
(3) interstitial impurity;
(4,5) substitutional impurities
The arrows represent the local stresses introduced by the point defects.
less distortion caused