Chapter 2-

ISSUES TO ADDRESS...

• What promotes bonding?

• What types of bonds are there?

• What properties are inferred from bonding?

1

CHAPTER 2:Atomic Structure and Interatomic Bonding

Chapter 2-

Ch 2 Callister – Atomic Structure and Bonding in Solids

• Before we get started …– This should be a review of what you saw in general

chemistry

• Basic idea … many properties of materials are a consequence of– Identity of the atoms that comprise them– Spatial arrangement of the atoms that comprise them– Interactions between the atoms that comprise them

• So, we need to talk about atomic structure/bonding!

Chapter 2-

Atomic Structure and Bonding in Solids

• So what do I mean by atomic structure?– Atomic number– Number of electrons/electronic configuration

• e.g. you might expect electronic properties to depend on the number of electrons an atom has (i.e. open v closed shells)

– Type of bonding (ionic versus covalent)

• And how these things change as you move around the periodic table!

• Last chance … have any of you not taken general chemistry?

Chapter 2-

Nucleus: Z = # protons

2

orbital electrons: n = principal quantum number

n=3 2 1

= 1 for hydrogen to 94 for plutoniumN = # neutrons

Atomic mass A ≈ Z + N

Adapted from Fig. 2.1, Callister 6e.

BOHR ATOM

Chapter 2-

Atomic Structure and Bonding in Solids

• Basic concepts– Atoms are made of protons, neutrons and electrons

• me = 9.11 x 10-31 kg, mp = mn = 1.67 x 10-27 kg• Charge of a proton and electron is the same: 1.60 x 10-19 C

– Atomic number (Z) describes the number of protons in the nucleus

– Atomic mass (A) of an element is approximately equal to the number of neutrons and protons the element has (why do I say approximately)

• Remember elements have isotopes – elements can have different numbers of neutrons (e.g. 12C, 13C, 14C)

– Atomic weight is the weighted average of the element based on the relative amounts of its isotopes (e.g. 1 mol/carbon = 12.011 g/mol, NOT 12 g/mol!)

• pp 11,12 – definition of atomic mass unit (amu), mole

Chapter 2-

Atomic Structure and Bonding in Solids

• Electrons in atoms– Why do we care about electrons?– Turns out to understand properties of materials need to have at

least a basic appreciation for electrons!– A rigorous description – quantum mechanics!– An early outgrowth of quantum mechanics was the Bohr atomic

model• Basic idea – electrons revolve around the nucleus

Nucleus

Orbital electrons

Adapted from Fig 2.1 Callister

Chapter 2-

Atomic Structure and Bonding in Solids

• Electrons in atoms– Turns out the Bohr model has some significant shortcomings!– That’s ok though … it is a useful starting point– Few other implications of quantum mechanics

• Energies are quantized – electrons are only permitted to have specific values of energy

• Adjacent energy states are separated by finite energy (i.e. the energy states are not continuous)

– 1kT, 2kT, …

– Bohr model was an early attempt to describe electrons in terms of position and energy

– Turns out electrons have both particle and wave properties (wave-mechanical model)

• Position is described by probability distribution (Figure 2.3; you’ll learn more about this in quantum mechanics)

Chapter 2-

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

3

Incr

easi

ng e

nerg

y

n=1

n=2

n=3

n=4

1s2s

3s2p

3p

4s4p

3d

Electrons...

Adapted from Fig. 2.5, Callister 6e.

ELECTRON ENERGY STATES

Chapter 2-

Atomic Structure and Bonding in Solids

• Quantum numbers– Using wave mechanics the electrons in atoms can be

characterized using quantum numbers– Principal quantum number n – refers to shells (distance of an

electron from the nucleus) n = 1, 2, 3, 4, 5 … or K, L, M, N– Second quantum number l – signifies the subshell s, p, d, f

– Third quantum number ml – denotes number of energy states in the s, p, d, f subshells

• s subshell (orbital) – 1 state

• p subshell – 3 states

• d subshell – 5 states

• f subshell – 7 states

– Spin moment – fourth quantum number• Spin up or spin down

Table 2.1, Figure 2.4 summarize all this!

Chapter 2-

Atomic Structure and Bonding in Solids

• Electronic configurations– That is all well and good, but how are the various states filled?

• Where do the electrons actually go?

– Pauli exclusion principle – Each electron state can hold no more than 2 electrons, and they must have opposite spins

• Take home – s, p, d, f subshells can hold 2, 6, 10, and 14 electrons respectively (does this make sense based on what I said before?)

• But there is more … not all possible states are always filled!– Electrons fill the lowest energy states in the shells/subshells first

(makes sense) and do not violate the Pauli exclusion principle!• This is said to be the ground state of the atom

– Electron configuration describes this – hydrogen (1s1), helium (1s2), sodium (1s2, 2s2, 2p6,3s1)

Chapter 2-

Atomic Structure and Bonding in Solids

• Okay, hopefully no surprises so far.

• Key points regarding electronic configuration– Valence electrons are extremely important

• Valence electrons are those that occupy the outermost shell

• These participate in chemical bonding

– “Stable electron configurations” - states where the outermost electron shell is filled

• These were probably referred to as “closed shell” in your chemistry course

• Typically means s and p shells are full– Explains inertness of Ar, Kr (noble gases)

• This also has implications for bonding/coordination/oxidation states of metals

Chapter 2-

Atomic Structure and Bonding in Solids

• Periodic table (pp 18 – 19)– Read it!– I know you have seen this before– Note trends in electronegativity as one moves across the periodic

table– Which elements are metals, intermediate, and non-metals and

where are they in the periodic table?

Chapter 2-4

• have complete s and p subshells• tend to be unreactive.

Stable electron configurations...

Z Element Configuration

2 He 1s2

10 Ne 1s22s22p6

18 Ar 1s22s22p63s23p6

36 Kr 1s22s22p63s23p63d104s24p6

Adapted from Table 2.2, Callister 6e.

STABLE ELECTRON CONFIGURATIONS

Chapter 2-5

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

• 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 6e.

SURVEY OF ELEMENTS

Chapter 2-6

• Columns: Similar Valence Structure

Electropositive elements:Readily give up electronsto become + ions.

Electronegative elements:Readily acquire electronsto become - ions.

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

Adapted from Fig. 2.6, Callister 6e.

THE PERIODIC TABLE

Chapter 2-7

• Ranges from 0.7 to 4.0,

Smaller electronegativity Larger electronegativity

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

• Large values: tendency to acquire electrons.

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 CornellUniversity.

ELECTRONEGATIVITY

Chapter 2-

Bonding in Solids • Bonding forces and energies

– Start with simple picture … forces and energies experienced by two atoms as a function of their separation distance

(Remember: Energy is the integral of the force over the length)

Chapter 2-

Bonding in Solids

• Bonding forces and energies– Explain in words/equations what I just showed pictorially

– Far apart: atoms don’t know about each other– As they approach one another, start to exert force on one another

• In general terms two types of forces– Attractive (FA) – can vary with distance

– Repulsive (FR) – typically short-range

– Net force is the sum of these

FN = FA + FR

– At some point the net force is zero; at that position a state of equilibrium exists (who has taken thermo? Ever hear of equilibrium before?)

Chapter 2-

Bonding in Solids

• Bonding forces and energies– We are more accustomed to thinking in terms of potential energy

instead of forces – in that case

RAN

RAN

EEE

drFdrFE

FdrE

00

or

• The point where the forces are zero also corresponds to the minimum potential energy for the two atoms (i.e. the trough in Figure 2.8), which makes sense because dE/dr = F =0 at a minimum.

• The interatomic separation at that point (ro) corresponds to the potential energy at that minimum (Eo, it is also the bonding energy)• The physical interpretation is that it is the energy needed to separate the

atoms infinitely far apart

Chapter 2-

Bonding in Solids

• Bonding forces and energies– Ok, things are more complicated in real solids– But the picture above is extremely insightful

• Why? Can describe interactions between atoms/molecules using pair interatomic potentials (e.g. Lennard-Jones potential, etc..)

• Many material properties will depend on the shape of the potential energy surface

– Position of ro, depth of potential well, etc.– Why is that? Can you give me a simple example of how a physical

property might be related to the bonding energy?

Chapter 2-

Bonding in Solids

• Types of chemical bonds found in solids– Ionic– Covalent– Metallic

• As you might imagine, the type of bonding influences properties – why?

• Bonding involves the valence electrons!!!

Chapter 2-

Na (metal) unstable

Cl (nonmetal) unstable

electron

+ - Coulombic Attraction

Na (cation) stable

Cl (anion) stable

8

• Occurs between + and - ions.• Requires electron transfer.• Large difference in electronegativity required.• Example: NaCl

IONIC BONDING

Chapter 2-

Bonding in Solids

• Ionic bonding– Prototype example – sodium chloride (NaCl)

• Sodium gives up one its electrons to chlorine – sodium becomes positively charged, chlorine becomes negatively charged

– The attraction energy is electrostatic in nature in ionic solids (opposite charges attract)

– The attractive component of the potential energy (for 2 point charges) is given by

r

eZeZE

oA

1

421

– The repulsive term is given by

8~ , nr

BE

nR

Chapter 2-

Bonding in Solids

• Ionic bonding – few other points– Ionic bonding is non-directional – magnitude of the bond is equal in

all directions around the ion– Many ceramics have an ionic bonding characteristic– Bonding energies typically in the range of 600 – 1500 kJ/mol– Often hard, brittle materials, and generally insulators

Chapter 2-9

• Predominant bonding in Ceramics

Give up electrons Acquire electrons

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

CsCl

MgO

CaF2

NaCl

O 3.5

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 CornellUniversity.

EXAMPLES: IONIC BONDING

Chapter 2-10

• 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 BONDING

Chapter 2-

Bonding in Solids

• Covalent bonding– Saw this in general chemistry (Molecular orbital theory)– Sharing of electrons between adjacent atoms– Most nonmetallic elements and molecules containing dissimilar

elements have covalent bonds– Polymers!– Here bonding is highly directional!– Number of covalent bonds possible is determined by the number of

valence electrons• Typically is 8 – N, where N is the number of valence electrons• Work? Carbon has 4 valence e’s – 4 bonds (ok!)

– Read p 24 – I am assuming you are already very familiar with covalent bonds

Chapter 2-

Bonding in Solids

• But one more point– Many materials will have bonding that is both ionic and covalent in

nature (very few materials actually exhibit pure ionic or covalent bonding)

– Easy way to estimate % of ionic bonding character:

XA, XB are the electronegativities of atoms A and B involved

100x))(25.0(exp1character ionic % 2BA XX

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

colu

mn IVA

Sn 1.8Pb 1.8

Adapted from Fig. 2.7, Callister 6e. (Fig. 2.7 isadapted 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 2-12

• 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

Chapter 2-

Bonding in Solids

• Metallic bonding– You can guess which type of matter exhibits this type of bonding– Simple idea: most metals have one, two, or at most three valence

electrons– These electrons are highly delocalized from a specific atom – have

a “sea of valence electrons”

– Free electrons shield positive core of ions from one another (reduce ER)

– Metallic bonding is also non-directional

– Free electrons also act to hold structure together

– Wide range of bonding energies, typically good conductors (why?)

Chapter 2-13

Arises from interaction between dipoles

• Permanent dipoles-molecule induced

• Fluctuating dipoles

+ - secondary bonding + -

H Cl H Clsecondary bonding

secondary bonding

HH HH

H2 H2

secondary bonding

ex: liquid H2asymmetric electron clouds

+ - + -secondary bonding

-general case:

-ex: liquid HCl

-ex: polymer

Adapted from Fig. 2.13, Callister 6e.

Adapted from Fig. 2.14, Callister 6e.

Adapted from Fig. 2.14, Callister 6e.

SECONDARY BONDING

Chapter 2-

Bonding in Solids

• Secondary (van der Waals), physical bonding

– Hallmark of this: interactions are much weaker (~10 kJ/mol) as compared to chemical bonds (> 100 kJ/mol)

– Secondary bonding is almost always present– Secondary bonding is a consequence of

atomic/molecular dipoles• What is a dipole?• Electric dipole exists whenever there is a separation of positive

and negative charges• These dipoles can interact with one another

– Hydrogen bonding is another type of secondary bonding

Chapter 2-

Bonding in Solids

• Dipoles– Fluctuation induced dipoles

• Even molecules/atoms that symmetrically charged can have dipoles– Why? Displacements of electron cloud can lead to short-lived asymmetries– Very weak interaction (liquefaction of inerts, diatomics)

Chapter 2-

Bonding in Solids

• Dipoles– Polar molecule induced dipoles

• Many molecules do not have a symmetric distribution/arrangement of positive and negative charges (e.g. H2O, HCl)

• These molecules can induce dipoles in adjacent, non-polar molecules– Interaction stronger than fluctuating dipoles

Chapter 2-

Bonding in Solids

• Permanent dipoles (hydrogen bonds)– Van der Waals interactions between polar molecules– Best known example – hydrogen bonding

• See picture below• These interactions are fairly strong, very complex, and surprisingly not

well understood!

Chapter 2-14

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large!

Variablelarge-Diamondsmall-Bismuth

Variablelarge-Tungstensmall-Mercury

smallest

Comments

Nondirectional (ceramics)

Directionalsemiconductors, ceramics

polymer chains)

Nondirectional (metals)

Directionalinter-chain (polymer)

inter-molecular

SUMMARY: BONDING

Chapter 2-15

• Bond length, r

• Bond energy, Eo

F F

r

• Melting Temperature, Tm

Eo=

“bond energy”

Energy (r)

ro r

unstretched length

r

larger Tm

smaller Tm

Energy (r)

ro

Tm is larger if Eo is larger.

PROPERTIES FROM BONDING: TM

Chapter 2-16

• Elastic modulus, Ecross sectional area Ao

L

length, Lo

F

undeformed

deformed

L F Ao

= E Lo

Elastic modulus

PROPERTIES FROM BONDING: E

E ~ dF/dr|ro elastic modulus

Chapter 2-17

• Coefficient of thermal expansion,

• ~ symmetry at ro

is larger if Eo is smaller.

L

length, Lo

unheated, T1

heated, T2

= (T2-T1) L Lo

coeff. thermal expansion

r

smaller

larger

Energy

ro

PROPERTIES FROM BONDING:

Chapter 2-18

Ceramics(Ionic & covalent bonding):

Metals(Metallic bonding):

Polymers(Covalent & Secondary):

secondary bonding

Large bond energylarge Tm

large Esmall

Variable bond energymoderate Tm

moderate Emoderate

Directional PropertiesSecondary bonding dominates

small Tsmall Elarge

SUMMARY: PRIMARY BONDS

Chapter 2-

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