Chapter 2: Atomic Structure and Interatomic Bondingmse125.cankaya.edu.tr/uploads/files/MSE...

Chapter 2 -

Chapter 2: Atomic Structure and Interatomic Bonding

•  Atomic Structure •  Electron Configuration •  Periodic Table •  Primary Bonding

–  Ionic –  Covalent –  Metallic

•  Secondary Bonding or van der Waals Bonding –  Three types of Dipole Bonding

•  Molecules

Chapter 2 -

Two Allotropes of CARBON

Graphite Diamond

-  Relatively soft -  Greasy feel to it -  Reasonably good

conductor of electricity

-  The hardest known material -  Poor conductor of electricity

The disparities in properties are attributed to a type of interatomic bonding found in graphite that does not exist in

diamond

Why Study Atomic Structure and Interatomic Bonding?

Chapter 2 - 3

Atomic Structure (Freshman Chem.) •  atom – electrons – 9.11 x 10-31 kg

protons neutrons

•  atomic number = # of protons in nucleus of atom = # of electrons of neutral species

•  A [=] atomic mass unit = amu = 1/12 mass of 12C Atomic wt = wt of 6.023 x 1023 molecules or atoms

1 amu/atom = 1g/mol

C 12.011 H 1.008 etc.

} 1.67 x 10-27 kg

Chapter 2 -

Atomic Models

Chapter 2 - 5

460 BC

Democritus’ atomos

Aristotle and Plato

360 BC

J.J. Thomson

1897

E. Rutherford

1909

N. Bohr

1913

Wave Mechanical

1923

Timeline of Atomic Theory

Dalton

1808

Chapter 2 -

~ 400 BC - Democritus

•  Ancient Greek philosopher •  Democritus coined the term átomos which

means "uncuttable" or "the smallest indivisible particle of matter".

Structure of Matter Physical world “VOID + BEING”

Chapter 2 -

•  Democritus postulated that atoms

were completely solid, hard and small particles with no internal structure and has an infinite variety of shapes and sizes.

•  This theory was ignored for more than 2000 years!

Democritus

7

Chapter 2 -

•  There can be no ultimately

indivisible particles. •  Believed that fire, earth, air and

water were the four main elements that world was made up of.

The Atomic Theory of Matter

Aristotle and Plato

8

Chapter 2 -

1803 – John Dalton

•  English instructor and natural philosopher

•  “Each element consists of atoms of single unique type and can join to form chemical compounds.”

•  Beginning the modern atomic theory

Chapter 2 -

1.  Elements are composed of

extremely small particles called atoms.

The Atomic Theory of Matter Dalton’s Atomic Theory Postulates

10

2.  All atoms of a given element are

identical, having the same size, mass and chemical properties. The atoms of different elements are different. Different elements have different atomic properties such as atomic mass.

Chapter 2 -

The Atomic Theory of Matter

11

4. Compounds are formed from the combination of atoms of more than one element. A compound always has the same relative number and kind of atoms.

Dalton’s Atomic Theory

3. Atoms of an element are neither created nor destroyed by any chemical reactions. Chemical reactions only involve the combination, rearrangement or separation of atoms.

Assist. Prof. Dr. İlkay KALAY

Chapter 2 -

1869 - Mendeleev

•  Building upon earlier discoveries by scientists, Mendeleev published the first functional PERIODIC TABLE.

•  Certain chemical properties of elements repeat periodically when arranged by atomic number.

•  The periodic table was first developed by Mendeleev and Meyer on the bases of similarity in chemical and physical properties exhibited on certain elements.

Chapter 2 -

Periodic Table

Draft of the first periodic table, Mendeleev, 1869

Chapter 2 -

1869…

Chapter 2 -

Today: Periodic Table of the Elements

Chapter 2 -

1897 – Sir J. J. Thomson

•  Although Dalton had postulated that atoms were indivisible, the studies have shown a more complex structure for an atom.

•  J. J. Thomson conducted a series of

experiments which showed that the atoms were not indivisible

•  Discovered the electron (1906 Nobel Prize

in Physics).

Chapter 2 - 17

J. J. Thomson proposed the atom consisted of a uniform positive sphere of matter in which the electrons were embedded.

J. J. Thomson's "plum-pudding" model of the atom

Atom is composed of even smaller particles but how the particles fit together?

Plum Pudding (1904): “The atom as being made up of electrons swarming in a sea of positive charge.

Chapter 2 -

•  Results: – Majority of a particles transmitted (pass through) or

deflected through small angles – Tiny fraction deflected through large angles

1909 – E. Rutherford •  Tested and disproved the Plum

Pudding Model.

Rutherford's experiment on the scattering of α particles by metal foil

Chapter 2 -

•  Conclusion: –  Disproved the Plum-Pudding Model –  Large amount of the atom's charge and mass is

concentrated into a small region –  Atom was mostly empty space

•  Objections to Rutherford model –  The laws of classical mechanics predict that the

electron will release electromagnetic radiation while orbiting a nucleus. Because the electron would lose energy, it would gradually spiral inwards, collapsing into the nucleus.

–  This atom model is unsuccessful, because it predicts that all atoms are unstable.

1909 – E. Rutherford

Chapter 2 - 20

The Modern View of Atomic Structure

The structure of an atom

Electron

Proton Neutron

Nucleus Particle Charge Mass (amu)

Electron Negative (-1) 5.486 x 10-4

Proton Positive (+1) 1.0073 Neutron Neutral (0) 1.0087

Particle Charge (C) Electron -1.6022 x 10-19

Proton 1.6022 x 10-19

Neutron 0

Chapter 2 - 21

The Modern View of Atomic Structure The structure of an atom

The atoms are small and the atomic dimensions are expressed in terms of Angstrom (Å) unit.

1 Å = 10-10 m

Schematic view of an atom

~ 10-4 Å 1-5 Å

Nucleus


Chapter 2 - Atomic number = Z

Mass number = A

22

The Modern View of Atomic Structure The structure of an atom

ü  All atoms of an element have the same number of protons in the nucleus.

ü  The number of protons in the nucleus of an atom is called atomic number (Z).

ü  Because the atoms have no net electrical charge, # of protons = # of electrons.

ü  The total number of protons and neutrons in a nucleus is called mass number (A).

612C


Chapter 2 - 23

The Modern View of Atomic Structure ü  All nuclei of the atoms of a particular element have the same

atomic number, but the the number of neutrons and so mass numbers may be different. Atoms of a given element with a different mass numbers are called isotopes.

ü  Most elements occur in nature as mixtures of isotopes. Symbol # of

electrons # of protons # of

neutrons 6 6 5 6 6 6 6 6 7 6 6 8

613C612C

614C

611C

An atom of a specific isotope is called a nuclide.


Chapter 2 - 24

The Periodic Table The periodic table, developed in 1869, shows the arrangement of elements with similar chemical and physical properties in order of increasing atomic number. Periodic table presents

atomic number, atomic symbol and atomic

weight for each element.

Zr91.224

40 Atomic number

Atomic weight Atomic symbol

Chapter 2 -

1912 – N. Bohr

•  Many phenomena involving electrons in solids could not be explained in terms of CLASSICAL MECHANICS.

•  We need QUANTUM MECHANICS…

Chapter 2 - 26

Line Spectra and The Bohr Model Bohr’s Model

Bohr proposed a model of the hydrogen atom that explains its line spectrum. Bohr’s postulates •  Rutherford atom is correct •  Classical EM theory not applicable to orbiting e- •  Newtonian mechanics applicable to orbiting e- •  Eelectron = Ekinetic + Epotential •  Only orbits of certain radii, corresponding to certain definite energies are

permitted for electrons in an atom. •  An electron in a permitted orbit has a specific energy and is in allowed

energy state. An electron in an allowed energy state will not radiate energy and therefore will not spiral into the nucleus.

•  During the transition of an electron from one allowed energy state to another, energy is only emitted or absorbed by an electron. This energy is emitted or absorbed as a photon, ΔE = Ef-Ei= hν = hc/λ where c = νλ

Chapter 2 - 27

Line Spectra and The Bohr Model

Energy levels in the hydrogen atom from the Bohr model. -‐  The arrows refer to the transi7ons of the

electron from one allowed energy state to another.

-‐  The states shown are those for which n = 1 through n = 6, and the state for n = ∞, for which the energy, E, equals zero.

Energy States of the Hydrogen Atom

Chapter 2 - 28

Bohr’s Model

The lower the value of n, the smaller the radius of the orbit, and the lower

the energy level.

n=1 ground state (lowest energy state) (orbit closest to the nucleus)

n=2, 3, or higher excited state

Energy levels in the hydrogen atom from the Bohr model.

The arrows refer to the transi7ons of the electron from one allowed energy state to another.

Chapter 2 -

Nucleus: Z = # protons

2

orbital electrons: n = principal quantum number

n=3 2 1

N = # neutrons

Atomic mass A ≈ Z + N

Adapted from Fig. 2.1, Callister 6e.

BOHR ATOM

Chapter 2 -

1913 - Sommerfeld

•  German theoretical physicist •  Modified the Bohr Model •  “suppose we have plurality of orbits” – a shell

containing multiple orbits: ORBITALS •  How to capture these new ideas quantitatively? •  We need new quantum numbers: n, l, m, s

n principal quantum number, distance of an electron from the nucleus l subshell, describes the shape of the subshell m number of energy states in a subshell s spin moment

Chapter 2 -

Wave mechanics to arrive at same place: E=E(n,l,m,s)

•  The Bohr model – significant limitations •  Resolution: Wave-mechanical model

(electron is considered to exhibit both wave-like and particle-like characteristics).

– De Broglie: “If a photon which has no mass, can behave as a particle, does an electron which has mass can behave as a wave (1920)?” λ = h/p = h/mv

– Heisenberg: Uncertainty Principle “I don’t know where any of one of electrons is, but I

can tell you an average where any of one of them is likely to be”

– Schrodinger

Chapter 2 -

Beyond Bohr’s Model De Broglie wavelength:

! =hm"

Heisenberg Uncertainty Principle: It is impossible to know simultaneously the exact posi7on and momentum of a par7cle. !x.!m! " h

4"

De Broglie wavelength states that electrons have wavelike mo7on

The more accurately we know the posi7on of the par7cle (smaller Δx), the less accurately we know its speed (larger Δu) and vice versa.

Wave mo>on of objects on the atomic scale

Schrödinger’s wave equaCon incorporates both the wave-‐like and par.cle-‐like behavior of the electron.

Wave function, ψ, Ψ2 provides information about an electron’s location when it s in an allowed energy state

Chapter 2 -

Quantum Mechanics and Atomic Orbitals

Electron-‐density diagram in the ground state of the hydrogen atom

Electron density: probability of the electron being at a point Higher density of dots region: larger values of Ψ2

Chapter 2 -

Bohr Model vs. Wave Mechanical Atom Model

Bohr WM

With WM model electron no longer treated as a particle moving in a discrete orbital,

rather position is described by a probability distribution

Chapter 2 -

Quantum Numbers

n…. The principal quantum number (K, L, M, N, O and so on that correspond to 1, 2, 3,4, 5…… As n increases: -  The orbital becomes larger -  The electron spends more time farther from the nucleus -  The electron has a higher energy and is therefore less tightly bound to the nucleus. l…. The second quantum number •  l can have integral values from 0 to n-1 for each value of n •  defines the shape of the orbital •  The value of l of a particular orbital is designated by s, p, d and f, corresponding l

values of 0, 1, 2 and 3 respectively s: sharp p:principal d:diffuse f: fundamental ml…. The magnetic quantum number •  Have integral values between l and –l including zero. •  Describes the orientation of the orbital in space

According to quantum mechanics, each electron in an atom is described by four different quantum numbers, three of which (n, l, ml) specify the wave function that gives the probability of finding the electron at various points in space.

Chapter 2 -

What is the filling sequence of electrons in orbitals by n, l, m, s is not adequate?

AUFBAU PRINCIPLE 3 principles:

1.  Pauli Exclusion Principle:only one electron can have a given set of four quantum numbers.

2.  Electrons -have discrete energy states -fill orbitals from lowest en. to highest en.

3. Hund’s rule

Chapter 2 - 37

Electron Configura>ons

Hund’s rule states that the lowest energy is attained by maximizing the number of electrons with the same electron spin. For example, for a carbon atom to achieve its lowest energy, the two 2p electrons will have the same spin.

Chapter 2 -

Quantum Numbers

ml l ms = ±½

Chapter 2 -

Quantum Numbers Electrons fill quantum levels in order of increasing energy ( only n and l make significant differences in energy configurations). 1s, 2s, 2p, 3s,3p,4s,3d,4p,5s,4d,5p,6s,4f,5d,…. When all electrons are at the lowest possible energy levels => ground state Excited states do exist such as in glow discharges etc…

Valence electrons occupy the outermost filled shell. Valence electrons are responsible for all bonding !

Chapter 2 - 40

Electronic Structure •  Electrons have wavelike and particulate

properties. –  This means that electrons are in orbitals defined by a

probability. –  Each orbital at discrete energy level determined by

quantum numbers. Quantum # Designation

n = principal (energy level-shell) K, L, M, N, O (1, 2, 3, etc.) l = subsidiary (orbitals) s, p, d, f (0, 1, 2, 3,…, n -1) ml = magnetic 1, 3, 5, 7 (-l to +l) ms = spin ½, -½

Chapter 2 - 41

Electron Energy States

1s

2s 2p

K-shell n = 1

L-shell n = 2

3s 3p M-shell n = 3

3d

4s

4p 4d

Energy

N-shell n = 4

• have discrete energy states • tend to occupy lowest available energy state.

Electrons...


Chapter 2 - 42

• Why? Valence (outer) shell usually not filled completely.

• Most elements: Electron configuration not stable. SURVEY OF ELEMENTS

Electron configuration

(stable)

...

... 1s 2 2s 2 2p 6 3s 2 3p 6 (stable) ... 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable)

Atomic #

18 ... 36

Element 1s 1 1 Hydrogen 1s 2 2 Helium 1s 2 2s 1 3 Lithium 1s 2 2s 2 4 Beryllium 1s 2 2s 2 2p 1 5 Boron 1s 2 2s 2 2p 2 6 Carbon

... 1s 2 2s 2 2p 6 (stable) 10 Neon 1s 2 2s 2 2p 6 3s 1 11 Sodium 1s 2 2s 2 2p 6 3s 2 12 Magnesium 1s 2 2s 2 2p 6 3s 2 3p 1 13 Aluminum

... Argon ... Krypton

Adapted from Table 2.2, Callister 7e.

Chapter 2 - 43

Electron Configura>ons


•  Elements in any given group in the periodic table have the same type of electron arrangements in their outermost shells.

•  The outer shell electrons those that lie outside the orbitals occupied in the next lowest noble gas element are called its valence electrons, whereas the electrons in the inner shells are called the core electrons.

Chapter 2 - 44

Electron Configurations •  Valence electrons – those in unfilled shells •  Filled shells more stable •  Valence electrons are most available for

bonding and tend to control the chemical properties

–  example: C (atomic number = 6)

1s2 2s2 2p2

valence electrons

Chapter 2 - 45

Electron Configura>ons and the Periodic Table


Chapter 2 - 46

Atomic Structure

•  Valence electrons determine all of the following properties

1)  Chemical 2)  Electrical 3)  Thermal 4)  Optical

Chapter 2 - 47

Electronic Configurations ex: Fe - atomic # = 26

valence electrons

1s

2s 2p

K-shell n = 1

L-shell n = 2

3s 3p M-shell n = 3

3d

4s

4p 4d

Energy

N-shell n = 4

1s2 2s2 2p6 3s2 3p6 3d 6 4s2

Chapter 2 - 48

The Periodic Table • Columns: Similar Valence Structure


Electropositive elements: Readily give up electrons to become + ions.

Electronegative elements: Readily acquire electrons to become - ions.

give

up

1e

give

up

2e

give

up

3e

iner

t gas

es

acce

pt 1

e ac

cept

2e

O

Se Te Po At

I Br

He Ne Ar Kr Xe Rn

F Cl S

Li Be H

Na Mg

Ba Cs Ra Fr

Ca K Sc Sr Rb Y

Chapter 2 - 49 Smaller electronegativity Larger electronegativity

Electronegativity - Tells us whether a given bond will be nonpolar covalent, polar covalent or ionic. - The ability of an atom in a molecule to attract electrons to itself. - Ranges from 0.7 to 4.0.

Chapter 2 -

REVIEW OF ATOMIC STRUCTURE (FRESHMAN CHEMISTRY)

•  Mass of an atom: –  Proton and Neutron: ~ 1.67 x 10-27 kg –  Electron: 9.11 x 10-31

kg •  Charge:

–  Electrons and protons: (±) 1.60 x 10-19 C

–  Neutrons are neutral The atomic mass (A): total mass of protons + total mass of neutrons Atomic weight ~ Atomic mass # of protons are used to identify elements (Z) # of neutron are used to identify isotopes ( e.g. 14C6 and 12C6 ) Isotopes are written as follows: AXZ , i.e. 1H1, 2H1, 3H1

ATOMS = (PROTONS+NEUTRONS) + ELECTRONS NUCLEUS BONDING

Chapter 2 -

Atomic bonding in solids

Things are made of atoms—little particles that move around, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence ... there is an enormous amount of information about the world. — Richard P. Feynman

Chapter 2 -

Two Allotropes of CARBON

Graphite Diamond

-  Relatively soft -  Greasy feel to it -  Reasonably good

conductor of electricity

-  The hardest known material -  Poor conductor of electricity

The disparities in properties are attributed to a type of interatomic bonding found in graphite that does not exist in

diamond

Why Study Atomic Structure and Interatomic Bonding?

Chapter 2 -

Atomic Bonding in Solids

•  Attractive component is due to type of the bonding (minimize energy thru electronic configuration)

•  Repulsive component is due to negatively charged electron clouds for two atoms and important only at small values of r

Interatomic separation, r

Interatomic forces that bind the atoms together are important to understand many properties of materials. •  Start with two atoms infinitely separated •  At large distances, interactions are negligible •  At small distances, each atom exerts forces on the other. •  Two types of forces: attractive, FA, and repulsive, FR

Chapter 2 - 54

Bonding Forces and Energies

FN=FA+FR At equilibrium FA+FR=0

EN= EA+ER

Chapter 2 -

Atomic Bonding

IONIC BONDING

COVALENT BONDING

METALLIC BONDING

Sulfur

Bromine Sucrose Magnesium

Gold

Copper

Magnesium oxide

Potassium dichromate

Nickel (II) oxide

Sharing of electrons between two atoms Bonding of metal atoms to

neighbor atoms

Electrostatic forces between ions

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 electrons

Chapter 2 - 56

• Occurs between + and – ions (anion and cation). • Requires electron transfer. • Large difference in electronegativity required. • Example: NaCl

Ionic Bonding

Na (metal) unstable

Cl (nonmetal) unstable

electron

+ - Coulombic Attraction

Na (cation) stable

Cl (anion) stable

Chapter 2 - 57

Ionic bond – metal + nonmetal

donates accepts electrons electrons

Dissimilar electronegativities

ex: MgO Mg 1s2 2s2 2p6 3s2 O 1s2 2s2 2p4 [Ne] 3s2

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6 [Ne] [Ne]

Chapter 2 - 8

IONIC BONDING

Oppositely charged ions attract, attractive force is coulombic. Ionic bond is non-directional, ions get attracted to one another in any direction. Bonding energies are high => 2 to 5 eV/atom,molecule,ion Hard materials, brittle, high melting temperature, electrically and thermally insulating

Chapter 2 - 59

Ionic Bonding •  Energy – minimum energy most stable

–  Energy balance of attractive and repulsive terms

Attractive energy EA

Net energy EN

Repulsive energy ER

Interatomic separation r

r A

n r B EN = EA + ER = - -

Adapted from Fig. 2.8(b), Callister 7e.

Chapter 2 - 60

• Predominant bonding in Ceramics

Adapted from Fig. 2.7, Callister 7e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.

Examples: Ionic Bonding

Give up electrons Acquire electrons

NaCl MgO CaF 2 CsCl

Chapter 2 - 61

C: has 4 valence e-, needs 4 more

H: has 1 valence e-, needs 1 more

Electronegativities are comparable.


Covalent Bonding •  Requires shared electrons •  Example: CH4

shared electrons from carbon atom

shared electrons from hydrogen atoms

H

H

H

H

C

CH 4

Chapter 2 - 10

COVALENT BONDING

Covalent bonds are formed by sharing of the valence electrons Covalent bonds are very directional Covalent bond model: an atom can have at most 8-N’ covalent bonds, where N’ = number of valence electrons Covalent bonds can be very strong, eg diamond, SiC, Si, etc, also can be very weak, eg Bismuth Polymeric materials do exhibit covalent type bonding.

Diamond, sp3

Chapter 2 - 11

• Molecules with nonmetals • Molecules with metals and nonmetals • Elemental solids (RHS of Periodic Table) • Compound solids (about column IVA)

He -

Ne -

Ar -

Kr -

Xe -

Rn -

F 4.0

Cl 3.0

Br 2.8

I 2.5

At 2.2

Li 1.0

Na 0.9

K 0.8

Rb 0.8

Cs 0.7

Fr 0.7

H 2.1

Be 1.5

Mg 1.2

Ca 1.0

Sr 1.0

Ba 0.9

Ra 0.9

Ti 1.5

Cr 1.6

Fe 1.8

Ni 1.8

Zn 1.8

As 2.0

SiC

C(diamond)

H2O

C 2.5

H2

Cl2

F2

Si 1.8

Ga 1.6

GaAs

Ge 1.8

O 2.0

co

lum

n IV

A

Sn 1.8Pb 1.8

Adapted from Fig. 2.7, Callister 6e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.

EXAMPLES: COVALENT BONDING

Chapter 2 - 64

Primary Bonding •  Ionic-Covalent Mixed Bonding

% ionic character =

where XA & XB are Pauling electronegativities of the

corresponding elements

%) 100 ( x

!

1"e" (XA"XB)2

4

#

$

% % %

&

'

( ( (

ionic 70.2% (100%) x e1 characterionic % 4)3.15.3( 2

=⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

−=

−−

Ex: MgO XMg = 1.3 XO = 3.5

Chapter 2 - 12

• Arises from a sea of donated valence electrons (1, 2, or 3 from each atom).

• Primary bond for metals and their alloys


METALLIC BONDING

Non valence and atomic nuclei form ion cores. 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…

Chapter 2 - 66

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

H H H H

H 2 H 2

secondary bonding

ex: liquid H 2

H Cl H Cl secondary bonding

secondary bonding + - + -

secondary bonding secondary bonding

Chapter 2 - 67

Type Ionic

Covalent

Metallic

Secondary

Bond Energy Large!

Variable large-Diamond small-Bismuth

Variable large-Tungsten small-Mercury

smallest

Comments Nondirectional (ceramics)

Directional (semiconductors, ceramics polymer chains)

Nondirectional (metals)

Directional inter-chain (polymer) inter-molecular

Summary: Bonding

Chapter 2 -

Bonding Energies

Chapter 2 - 69

Bonding in Solids

The physical properties of crystalline solids, such as melting point and hardness, depend both on the arrangements of particles and on the attractive forces between them.

Chapter 2 - 70

• Bond length, r

• Bond energy, Eo

• Melting Temperature, Tm

Tm is larger if Eo is larger.

Properties From Bonding: Tm

r o r

Energy r

larger Tm

smaller Tm

Eo = “bond energy”

Energy

r o r unstretched length

Chapter 2 - 16

• Elastic modulus, E

• E ~ curvature at ro

ΔL F Ao

= E Lo

Elastic modulus

r

larger Elastic Modulus

smaller Elastic Modulus

Energy

ro unstretched length

E is larger if Eo is larger.

PROPERTIES FROM BONDING: E

Chapter 2 - 72

Ceramics (Ionic & covalent bonding):

Metals (Metallic bonding):

Polymers (Covalent & Secondary):

Large bond energy large Tm large E small α

Variable bond energy moderate Tm moderate E moderate α

Directional Properties Secondary bonding dominates

small Tm small E large α

Summary: Primary Bonds

secondary bonding

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