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Part Part ⅠⅠ

STRUCTURE AND PROPERTIES OF STRUCTURE AND PROPERTIES OF MATERIALSMATERIALS

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Chapter 2Chapter 2

Atomic Scale StructureAtomic Scale Structure ：：Interatomic BondingInteratomic Bonding

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I. Materials, Properties, Applications and Synthesis

Materials Applications

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I. Materials, Properties, Applications and Synthesis

Materials Applications

Properties

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I. Materials, Properties, Applications and Synthesis

Materials Applicationsreactants

Properties

Synthesis ，

(operation

Processing

Conditions)

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II. Structure and Properties ： Synthesis and Applications

Materials Applicationsreactants

Properties

Synthesis ，

operation

Structurestructure

Processing

conditions

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Structure ：atomic

crystalline

Nano

microscopic

macroscopic

scale structure (~0.1nm)

(scale) structure (>~0.1µm) ：SEM structure (>~0.1cm)

III. Structure of Materials

raw materials

synthesisshape

forming sintering fabrication material products

Processing techniques and

operation conditions

Structure (結構 )

Properties (性質 )

F 4.11

F 4.12

structure (>~10nm)

scale structure(>~10nm)

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※ Many materials properties are determined by the atomic scale structure alone

IV. Atomic Scale StructureIV. Atomic Scale Structure

˙Different types of atoms (different chemical formula) different materials

(1) the types of atoms present,

(2) the types of bonding between the atoms,

˙Different types of bonding different materials

(3) the way the atoms are packed together：( coordination and coordination number )

˙same type of atoms and same type of bonding

˙same type of atoms (same chemical formula)

different materialsDifferent coordination or different crystal structure

Different coordination or different crystal structure different materials

F 12.15

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◎ the energy of the electrons in the atom

◎ the ease of adding or removing one or more electrons from the atom to create a charged ion ： Electropositive elements /Electronegative elements

Electronegativity, EN(or x) , of an element ： relative tendency of that element to gain, or attract, an electron (obtained by arbitrarily fixing the value of H at 2.1)

◎ Spatial distribution and bond angles.

◎ valence electrons ： the electrons that occupy the outmost filled shell.

→ stable electron configurations: normally, outmost

V. Atomic Bonding in SolidsV. Atomic Bonding in SolidsA. Atomic properties related to (Primary) bonding

S+P=8(except He) chemical bonding

F 2.7

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B. Bonding Forces and Energies

FN = FA + FR (2-2)

FN: net force; FA: attractive force; FR: repulsive force

at equilibrium: FA+ FR = 0 (2-3)

r = r0 (≒3Å) (equilibrium spacing ： bond length)

E =∫Fdr (W = F · L , W = E ) (2.4)

EN = ∫ FN dr = ∫ FA dr +∫ FR dr = EA+ ER (2.5-7)

F = - dE / dr

E0: bonding energy

r

∞ ∞

r

∞

r

F 2.8

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C-1. PRIMARY BONDS

◎ Three types of primary bonds ： ionic, covalent, and metallic

◎ Factors determining the type of bonding:

(1) electronegativity of each atom

(2) electronegativity difference between the atoms (Δ EN, or Δx )

C. Types of Bonding

˙ primary (or chemical) bonds˙ secondary (or van der Waals,or physical) bonds

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◎ This bond involves electron transfer from the

electropositive atom.

A high Δ EN between the atoms favors the formation of

ionic bonds.

◎ The attractive bonding forces are coulombic: positive and

negative ions.

C-1-1. Ionic Bonding

F 2.4-1

F 2.9

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◎ The bond-force curve and the bond energy curve

◎ Equilibrium separation distance, r ° , occurs at the

value of r for which

FN(r) = FA ( r ) + FR ( r ) = 0

FA ( r) = |z1 z2| e2 /4Π ε0 r2 FR(r ) = –k/rm

r ° : bond length

(FA(r ) ≡ Fa ( x ), FR

(r ) ≡ Fr ( x ), FN(r )≡ Ft ( x ) )

F 2.4-2

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Electron affinity, e.g., 4.02 eV for C1 + e- C1-

E ( r ) = Ui — [|Z1Z2|e2/ (4 0 r)] + (B/ rn )

Ui = 5.14 – 4.02 = 1.12 eV

n = m–1, B = k/n (E(r) = U(r) )

◎ The relationship between E and r and will be referred to as

either the bond-energy curve or the bond-energy well.

◎ The depth of the energy well (at r0 ) is the strength of the

bond, i.e., bond energy. The equilibrium separation distance, r0, corresponds to the bond length.

◎ Ionization potential, e.g., 5.14 eV for Na Na+ +e-

F 2.4-2

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◎ Covalent bonds form in compounds composed of electronegative elements, especially those with four or more valence electrons.

Since there are no electropositive atoms present, the “ex-tra” electrons required to fill the valence shell of the electronegative atoms must be obtained by sharing electrons.

◎ r 0 can be found using a similar equation:

FA(r ) + FR

(r ) = 0 = A' / χ p– B' / χ q

C-1-3. Covalent Bonding

F 12.15

F 12.17

F 2.10

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◎ Solids composed primarily of electropositive elements

containing three or fewer valence electrons are generally

held together by metallic bonds.

◎ The valence electrons form a “cloud” or “sea” of electrons

that surrounds the ion cores. The electrons are shared,

but they are not spatially localized.

◎ Metallic bonding may be weak or strong; energies range

from 68 kJ/ mol (0.7 eV/ atom; m.p., –390C ) for mercury to

850 kJ/ mol (0.8 eV/ atom; m.p., 34100C ) for tungsten.

C-1-3. Metallic Bonding (metals)

F 2.11

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C-1-4. Mixed bonding

◎ Many Compounds (ceramics) display a bond with mixed

ionic / covalent characteristics. ◎ A bond is considered predominantly ionic when Δx > 1.7

and predominantly covalent if Δx <1.7

C-1-4-1 。 Mixed bonding

between primary bonds

◎The bondings of most ceramics have a certain degree of

ionic in nature , and ceramics are usually considered as

ionic solids , i-e-, being composed of ions (cations and

anions).

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◎ Many ceramics contain primary bonds with mixed

ionic/covalent characteristics, e.g., SiO2 : Si atom,

EN (XB ) = 1.9 ; O atom, EN (X

A )= 3.44, ΔEN(Δ X)=

1.54, the Si-O bond is ~45% ionic and ~55% covalent.

The percent ionic character of a bond between elements

A and B ( A being the most electronegative ) may be

approximated by the expression % ionic character =

( 1-e –(0.25)(XA

-XB

)2 ) 100

where xA and xB are the electronegativities for the

respective elements. T 12.1

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◎ In the Group IA metals, moving from left to right in the periodic table, bonds begin to take on some covalent characteristics. The increase in covalent characteristic is part of the reason the density of metals generally decreases as one moves to the right

in the periodic table in a given row.

◎ Intermetallics, e.g., AlLi, Ni3Al, Al3V, AlSb, CuZn, Ti3Al, and

Mg2S, exhibit either mixed metallic/covalent or mixed metallic / ionic bond characteristics.

They are more brittle than metals because of possessing ceramic properties.

These materials often have good high-temperature resistance

and a high strength-to weight ratio. As a result, Ni3Al and Ti3Al

are finding usage in the aerospace industry)

F 2.7

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C-1-4-2 Mixed bonding between primary and secondary bonds

◎ Another type of “mixed” bonding occurs in materials having both primary and secondary bonds.

F 2.9-1 F 13.19 F 3.14 F 12.17

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C-2. SECONDARY BONDS(or van der Waals, or physical bonds)

◎ bonding energies are typically on the order of 10 Kj/mol ( 0.1 ev/ atom).

◎ Secondary bonds are fundamentally different from primary bonds in that they involve neither electron transfer nor electron sharing.

Instead, attractive forces are produced when the center of positive charge is different from the location of the center of negative charge.

The resulting electric dipole can be either temporary, induced, or permanent and can occur in atoms or molecules

F 2.12 F 2.14 F 2.27 F 2.13

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◎ Two major types of secondary bonds • dipoles (or van der Waals bonding) • hydrogen bonding

(A) Bonding by dipoles

(a) Temporary dipole (or van der waals bonding, <4KJ/mol)

Fuctuating induced (temporary) dipole bonds

˙Temporary dipole is responsible for the condensation of noble gases at low temperatures

˙The strength of the van der waals bond generally increases as the number of atoms in the compound increases. This phenomenon explains why the melting temperatures and also b.p. of the hydrocarbons with chemical formulas CnH2n+2 increase as n increases.

F 2.13

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(b) Permanent dipoles ： formed between polar molecules, generally stronger than van der waals bonds.

(c) Polar molecule — induced dipole bonds.

(B) Hydrogen bond (8-40 KJ/mol) ˙occurs whenever a hydrogen atom can be shared between two strongly electronegative atoms such as N, O, F, or C1. ˙Hydrogenbonds hold the wood fibers in a sheet of paper together.

◎ Secondary bonds control properties such as melting point and elastic modulus in solids where primary bonds do not form a three-dimensional (3-D) network.

F 2.13

F 2.14

F 2.15

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◎ Classification of Crystals (solids) according to bonding

3-D network of

Primary Boding

existingProperties (e.g., melting point, strength) are determined by primary bonding

covalent bonding - Covalent crystals (solids)

ionic bonding - ionic crystals (solids)

metallic bonding - metallic crystals (solids)

non existing Properties are determined by secondary bonding molecular crystals (solids)

hydrogen bonding–hydrogen bonded crystals

(solids): e.g., ice.

van der Waals forces–van der Waals crystals (solids)

F 12.15

F 2.9-2

F 13.2

F 2.11

F 2.9-1

F 13.17

F 13.18

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VI. Influence of Bonding on Material Properties

Some of the mechanical and electrical properties of

solids are a function of bond type.

A-1.Metallic Bonded Materials

◎ Atoms in the metal can slip and slide past one another

with regard to applied force and thus absorb the

impact without breaking. This phenomenon is called

ductile.(A large extent of deformation can occur.)

◎ Examples ： most metals.

A. Ductility and Brittleness

F 2.4-5

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◎ In an ionic solid, each ion is surrounded by oppositely

charged ions. Ionic slip may lead to like charges moving

adjacent positions, causing Coulombic repulsion.

This makes slipping much more difficult to achieve and

the material responds by breaking. Such behavior is

known as brittle.(Little deformation can occur.)

◎ Examples ： most ceramics.

A-2. Ionic Bonded Materials

F 2.4-5

A-3. Covalent Bonded Materials

◎ Covalent bonds are directional bondings, thus are not flexible.

Such materials are therefore brittle.(Little deformation can occur.)

◎ Example ： diamond.

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B. Electrical Conductivity

◎ Electrical conductivity of materials depends

(1) the type of charge carrier in the materials (electrons or ions),

(2) the spatial density of charge carriers

(3) the charge carrier mobility.

→ determined by type of bonding

◎ Metallic bonded materials

The combination of high mobility and high concentration of charge carriers leads to high electrical conductivities for most metals.

◎ Ionic and covalent bonded materials

electrical insulators

F 2.11

F 2.10

F 2.9

F 13.17

F 13.18

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C. Stiffness and Elastic Modulus

◎ The slope of the bond force curve, ( F/ χ ), at χ 。 is a

measure of the force required to displace atoms from their equilibrium positions. Usually

F or F aE (χ≡r ，≡ r) (2.5-1)

Where a is a geometric factor and E is a materials property known As Young’s modulus. Young’s modulus is a measure of the resistance of the material to relative atomic separation (stiffness).

The steeper the slope (I.e., the higher the value of E), the greater the force required to move the atoms from their equilibrium positions.

Materials with large values of E are stiff.

F 2.8 F 2.5-1 F 6.7＃70 ＃71 ＃72 ＃73 ＃74

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Several important macroscopic materials properties directly

from the bond-energy curve, e.g., bond energy, average

bond length, elastic modulus and coefficient of thermal

expansion.

◎ Bond Energy and Bond Length

The depth of the energy well (at r0) is the strength of the bond,

i.e., bond energy. The equilibrium separation distance, r ° ,

corresponds to the bond length.

D. Bond Energy and Bond Length

◎The bond-energy curve

F 2.8

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◎ Elastic (young’s) Modulus

As discussed previously

U F and 2U 2 F (2.5-2)

U a (2.5-3)

property) ic(macroscop

E /

E

curve) force (bond

bonding) mic(interatio

property) ic(microscop

aEx / F

xF

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E. Coefficient of thermal expansion, αth

Over a limited temperature range,

(χ - χ0) / χ0 = αth ( T –T0) (2.5-4)

Where χ is the equilibrium spacing at temperature T,

χ0 is the equilibrium spacing at reference temperature

T0 and αth is the coefficient of linear expansion.

(L - L0) / L0 = αth(T-T0)

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◎ As temperature increases, the atoms gain energy and

are able to “ move up “ the sides of the energy well , i.e.,

the average atomic-separation distance increases as

the temperature increases.

◎ The magnitude of α th increases as the bond-energy curve

becomes more asymmetric. Deeper energy wells tend to be

more symmetric, materials with high bond energies- those

with deep and symmetric wells-- should have low α th

values .

F 2.5-1 F 2.5-2 F 13.17F 2.5-3

Thermal expansion coefficient

αth

L↑ T↑

(macroscopic property)

Atomic scale structure

(interatomic bonding)

(bond energy curve)

Bond length↑ potential energy↑ T↑

(microscopic property)

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F. Others

Latent heat of fusion( H△ f)

Melting temperature (mp)

Coefficient of thermal expansion

Bonding Energy

T 2.3 T 2.5-1

△Hf↑ higher bond energy mp↑ deeper energy well αth↓

(stronger bonding) &

steeper bond energy curve

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Thermal Shock Resistant Materials ：(Thermal Shock Resistance)low thermal expansion coefficient material

symmetric energy well ： strong bonding

low density ： low CN

F 2.5-2

F 12.15 F 12.10

T 2.5-1 T 4.3 T 4.3-1 F 4.4

strong covalent bonded materials

Thermal shock resistant material

A material, which does not crack under a thermal shock

low thermal expansion coefficient material

strong

covalent

bonded

materials

Thermal shock : very quick change of themperature

uneven thermal expansion (or contraction) within the material

cracking

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◎ The relationships between the bond-energy curve and

macroscopic properties developed in this section show

general trends. The constants in the corresponding

equations are not known with sufficient accuracy to

facilitate calculation of the absolute values of bond

length , bond energy, modulus of elasticity, and

coefficient of thermal expansion. The values of these

properties for engineering materials are usually directly

measured in the laboratory.

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(A) Tension

◎ For most metals at relatively low levels, stress and strain are proportional to each other

Hooke’s law; the constant of proportionality E (GPa or psi):

Modulus of elasticity or Young’s modulus.

For most typical metals, E=45 GPa (6.5 x 106 psi) for Mg to 407 MPa (59 x 106 psi) for W.

E

B. ELASTIC DEFORMATION (B. ELASTIC DEFORMATION ( 彈性變形彈性變形 ))

B-1. Stress-Strain BehaviorB-1. Stress-Strain Behavior

(6.5)

T 6.1

F 6.11

＃ 27

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◎ Engineering stress

F： the instantaneous load applied newtons (N) or pounds force (lbf) ；

A0 ： original cross-sectional area (m2 or in.2) ； ：

engineering stress, MPa (SI) (where 1 MPa = 106 N/m2), and pounds force per square inch, psi (Customary U.S.).2

0A

F

(6.1)

＃ 27

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◎ Engineering strain

l0 ： the original length ；

li ： the instantaneous length ；

Δl＝ li - l0Engineering strain, ： unitless (meters per meter or inches per inch ; or a percentage)

00

0

l

l

l

lli

(6.2)

＃ 27

74

＃ 27

75

＃ 27