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

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.


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.


Materials


Nanomaterials

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.

Periodic Table


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


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…


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


Arises from interaction between dipoles

• Permanent dipoles-molecule induced

• Fluctuating dipoles

-general case:

-ex: liquid HCl

-ex: polymer



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


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


• 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


• 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


• Coordination # = 8


• 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



• 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)



ex: Al, Cu, Au, Pb, Ni, Pt, Ag

4 atoms/unit cell: 6 face x 1/2 + 8 corners x 1/8


• 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


HEXAGONAL CLOSE-PACKED STRUCTURE (HCP)


• APF = 0.74

6 atoms/unit cell

ex: Cd, Mg, Ti, Zn

• c/a = 1.633


• 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.




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


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


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


• 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.


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


Documents

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