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Assist. Prof. Bilge Imer
MSN 504
Phase Transformations & Diffusion in Materials
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 UniversityInstitute 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 UniversityInstitute 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 UniversityInstitute of Materials Science and Nanotechnology
Materials
Bilkent UniversityInstitute of Materials Science and Nanotechnology
Nanomaterials
Types of Materials
Bilkent UniversityInstitute of Materials Science and Nanotechnology
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.
Periodic Table
Bilkent UniversityInstitute of Materials Science and Nanotechnology
5
• Valance electrons determine chemical, electrical, thermal and optical properties, and they are responsible for bonding
• Most elements: Electron configuration not stable.Element Hydrogen Helium Lithium Beryllium Boron Carbon ... Neon Sodium Magnesium Aluminum ... Argon ... Krypton
Atomic # 1 2 3 4 5 6
10 11 12 13
18 ... 36
Electron configuration 1s1 1s2 (stable) 1s22s1 1s22s2 1s22s22p1 1s22s22p2 ... 1s22s22p6 (stable) 1s22s22p63s1 1s22s22p63s2 1s22s22p63s23p1 ... 1s22s22p63s23p6 (stable) ... 1s22s22p63s23p63d104s246 (stable)
Adapted from Table 2.2, Callister 7e.
Atomic ConfigurationCourtesy of Prof. Erman Bengu, CHEM 201
He
Ne
Ar
Kr
Xe
Rn
inert
gase
s acc
ept
1e
acc
ept
2e
giv
e u
p 1e
giv
e u
p 2e
giv
e u
p 3e
F Li Be
Metal
Nonmetal
Intermediate
H
Na Cl
Br
I
At
O
S Mg
Ca
Sr
Ba
Ra
K
Rb
Cs
Fr
Sc
Y
Se
Te
Po
• Columns: Similar Valence Structure, Similar Properties
Electropositive elements:Readily give up electrons
to become + ions.
Electronegative elements:Readily acquire electrons
to become - ions.
THE PERIODIC TABLECourtesy of Prof. Erman Bengu, CHEM 201
Bonding types
Bilkent UniversityInstitute of Materials Science and Nanotechnology
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
Courtesy of Prof. Erman Bengu, CHEM 201
• Arises from a sea of donated valence electrons (1, 2, or 3 from each atom).
• Primary bond for metals and their alloys
+ + +
+ + +
+ + +Adapted from Fig. 2.11, Callister 6e.
METALLIC BONDING
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…
Courtesy of Prof. Erman Bengu, CHEM 201
Na (metal) unstable
Cl (nonmetal) unstable
electron
+ - Coulombic Attraction
Na (cation) stable
Cl (anion) stable
• Occurs between + and – ions (anion and cation).• Requires electron transfer.• Large difference in electronegativity required.• Example: Na+ Cl-
IONIC BONDINGCourtesy of Prof. Erman Bengu, CHEM 201
• Requires shared electrons• Example: CH4
C: has 4 valence e, needs 4 more
H: has 1 valence e, needs 1 more
Electronegativities are comparable.
shared electrons from carbon atom
shared electrons from hydrogen atoms
H
H
H
H
C
CH4
Adapted from Fig. 2.10, Callister 6e.
COVALENT BONDINGCourtesy of Prof. Erman Bengu, CHEM 201
Ceramics(Ionic & covalent bonding):
Metals(Metallic bonding):
Polymers(Covalent & Secondary):
Large bond energylarge Tm
large Esmall
Variable bond energymoderate Tm
moderate Emoderate
Directional PropertiesSecondary bonding dominates
small Tm
small E large
Summary: Primary Bonds
secondary bonding
Courtesy of Prof. Erman Bengu, CHEM 201
Arises from interaction between dipoles
• Permanent dipoles-molecule induced
• Fluctuating dipoles
-general case:
-ex: liquid HCl
-ex: polymer
Adapted from Fig. 2.13, Callister 7e.
Adapted from Fig. 2.14, Callister 7e.
SECONDARY BONDING
asymmetric electron clouds
+ - + -secondary
bonding
HH HH
H2 H2
secondary bonding
ex: liquid H2
H Cl H Clsecondary bonding
secondary bonding+ - + -
secondary bondingsecondary bonding
Courtesy of Prof. Erman Bengu, CHEM 201
Type
Ionic
Covalent
Metallic
Secondary
Bond Energy
Large!
Variablelarge-Diamondsmall-Bismuth
Variablelarge-Tungstensmall-Mercury
smallest
Comments
Nondirectional (ceramics)
Directional(semiconductors, ceramics
polymer chains)
Nondirectional (metals)
Directionalinter-chain (polymer)
inter-molecular
Summary: BondingCourtesy of Prof. Erman Bengu, CHEM 201
• Non dense, random packing
• Dense, ordered packing
Dense, ordered packed structures tend to have lower energies.
Energy and PackingEnergy
r
typical neighbor bond length
typical neighbor bond energy
Energy
r
typical neighbor bond length
typical neighbor bond energy
CO
OLI
NG
Courtesy of Prof. Erman Bengu, CHEM 201
• atoms pack in periodic, 3D arrays• typical of:
Crystalline materials...
-metals-many ceramics-some polymers
• atoms have no periodic packing• occurs for:
Noncrystalline materials...
-complex structures-rapid cooling
Si Oxygen
crystalline SiO2
noncrystalline SiO2"Amorphous" = NoncrystallineAdapted from Fig. 3.18(b),
Callister 6e.
Adapted from Fig. 3.18(a), Callister 6e.
MATERIALS AND PACKING
LONG RANGE ORDER
SHORT RANGE ORDER
Courtesy of Prof. Erman Bengu, CHEM 201
• Rare due to poor packing (only Po has this structure)• Close-packed directions are cube edges.
• Coordination # = 6 (# nearest neighbors)
(Courtesy P.M. Anderson)
SIMPLE CUBIC STRUCTURE (SC)
Closed packed direction is where the atoms touch each other
Courtesy of Prof. Erman Bengu, CHEM 201
• Coordination # = 8
(Courtesy P.M. Anderson)
• Close packed directions are cube diagonals.
--Note: All atoms are identical; the center atom is shaded differently only for ease of viewing.
BODY CENTERED CUBIC STRUCTURE (BCC)
ex: Cr, W, Fe (), Tantalum, Molybdenum
2 atoms/unit cell: 1 center + 8 corners x 1/8
Courtesy of Prof. Erman Bengu, CHEM 201
(Courtesy P.M. Anderson)
• Close packed directions are face diagonals.
--Note: All atoms are identical; the face-centered atoms are shaded differently only for ease of viewing.
FACE CENTERED CUBIC STRUCTURE (FCC)
• Coordination # = 12
Adapted from Fig. 3.1, Callister 7e.
ex: Al, Cu, Au, Pb, Ni, Pt, Ag
4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8
Courtesy of Prof. Erman Bengu, CHEM 201
• ABCABC... Stacking Sequence• 2D Projection
A sites
B sites
C sitesB B
B
BB
B BC C
CA
A
• FCC Unit CellA
BC
FCC STACKING SEQUENCECourtesy of Prof. Erman Bengu, CHEM 201
• ABAB... Stacking Sequence
• 3D Projection • 2D Projection
A sites
B sites
A sites Bottom layer
Middle layer
Top layer
Adapted from Fig. 3.3, Callister 6e.
HEXAGONAL CLOSE-PACKED STRUCTURE (HCP)
• Coordination # = 12
• APF = 0.74
6 atoms/unit cell
ex: Cd, Mg, Ti, Zn
• c/a = 1.633
Courtesy of Prof. Erman Bengu, CHEM 201
• Coordination # increases with
rcationranion
rcationranion
Coord #
< .155 .155-.225 .225-.414 .414-.732 .732-1.0
ZnS (zincblende)
NaCl (sodium chloride)
CsCl (cesium chloride)
2 3 4 6 8
Adapted from Table 12.2, Callister 6e.
Adapted from Fig. 12.2, Callister 6e.
Adapted from Fig. 12.3, Callister 6e.
Adapted from Fig. 12.4, Callister 6e.
COORDINATION # AND IONIC RADIICourtesy of Prof. Erman Bengu, CHEM 201
Imperfections in Solids
BONDING+
STRUCTURE+
DEFECTS
PROPERTIES
Is it enough to know bonding and structure of materials to estimate their
macro properties ?
Defects do have a significant impact on the properties of materials
Courtesy of Prof. Erman Bengu, CHEM 201
Imperfections in Solids
Defects in Solids0-D, Point defects
VacancyInterstitialSubstitutional
1-D, Line Defects / DislocationsEdgeScrew
2-D, Area Defects / Grain boundariesTiltTwist
3-D, Bulk or Volume defectsCrack, poreSecondary Phase
MA
TE
RIA
LS
P
RO
PE
RT
IES
Crystals in nature are never perfect, they have defects !
Atoms in irregular positions
Planes or groups of atoms in irregular
positions
Interfaces between homogeneous regions of
atoms
Courtesy of Prof. Erman Bengu, CHEM 201
Imperfections in SolidsAtomic Composition
Bonding
X’tal Structure
Microstructure:Materials properties
The
rmo-
Mec
hani
cal P
roce
ssin
g
Addition and manipulation of defects
Courtesy of Prof. Erman Bengu, CHEM 201
• Vacancies:
-vacant atomic/lattice sites in a structure.
Vacancydistortion of planes
• Self-Interstitials:
-"extra" atoms positioned between atomic sites.
self-interstitialdistortion
of planes
POINT DEFECTSCourtesy 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.
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
Courtesy of Prof. Erman Bengu, CHEM 201