Chapter 2 - 1

Chapter 2: Atomic Structure and Interatomic Bonding (updated)

These notes have been prepared by Jorge Seminario from the textbook material

Chapter 2 - 2

ISSUES TO ADDRESS...• What promotes bonding?

• What types of bonds are there?

• What properties are inferred from bonding?

Chapter 2-

– Atoms are made of protons, neutrons and electrons• me=0.00091094x10-27= 9.1094x10-31kg = 0.511MeV• mp = 1.6726 x 10-27 kg = 938.272 MeV

• mn = 1.6749 x 10-27 kg = 939.566 MeV = • mn = mp + 1.293 MeV

• proton & electron charge 1.6022 x 10-19 C• However p are +’ve and e are –’ve – 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

• 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 = 12.0107 g/mol, NOT 12 g/mol!)

Basic concepts

Chapter 2-

2.2 Fundamental Concept

Atomic Weight Weighted average of the atomic masses of an atom's

naturally occurring isotopes Atomic Mass Unit (amu)

Measure of atomic mass 1/12 the mass of C12 atom

Mole Quantity of a substance corresponding to 6.022X1023 atoms

or molecules 1 amu/ atom (or molecule) = 1g/mol

Chapter 2-

How many grams are there in one amu of a material?

The two major isotopes of carbon:

98.93% of 12C with an atomic weight of 12.00000 amu, and

1.07% of 13C with an atomic weight of 13.00335 amu.

Confirm that the average atomic weight of C is 12.011 amu.

Sum the product of the isotope atomic weight and the percent abundance.

(12 amu)*(.9893)+(13.00335 amu)*(.0107) = 12.011 amu

Examples

Chapter 2-

2.3 Electrons In AtomsBohr Atomic Model (old view)

Early outgrowth of quantum mechanics

Electrons revolve around nucleus in discrete orbitals

Electrons closer to nucleus travel faster then outer orbitals

Principal quantum number (n); 1st shell, n=1; 2nd shell, n=2; 3rd shell, n=3

Chapter 2-c02f02

Quantum Numbers—Hydrogen atom

Chapter 2-

c02f03

Bohr AtomWave-mechanical atom

Chapter 2-

Atomic Models

Wave-Mechanical Model

Electron exhibits both wave-like and particle-like characteristics

Position is now considered to be the probability of an electron being at various locations around the nucleus, forming an electron cloud

Chapter 2-

Atomic ModelsQuantum numbers

Principal quantum number n, represents a shell

K, L, M, N, O correspond to n=1, 2, 3, 4, 5....

Quantum number l, signifies the subshell Lowercase italics letter s, p, d, f; related to

the shape of the subshell

Quantum number ml , represents the

number of energy state s, p, d, f have 1, 3, 5, 7 states respectively

Quantum number ms, is the spin moment

Each electron is a spin moment (+1/2) and (-1/2)

Chapter 2-

Electron Configuration

Electron configuration represents the manner in which the states are occupied

Valence electrons Occupy the outermost

shell Available for bonding Tend to control chemical

properties Ex. Silicon (Si)

Chapter 2-

Energy

Chapter 2-

c02tf02

When some elements covalently bond, they form sp hybrid bonds, e.g., C, Si, Ge

Chapter 2-

ExamplesGive the electron configurations for the following:C 1s2 2s2 2p2

Br 1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p5

Mn+2

1s2 2s2 2p6 3s2 3p6 3d5

F-

1s2 2s2 2p6

Cr1s2 2s2 2p6 3s2 3p6 4s1 3d5

Chapter 2 - 15

Electronic Structure• Electrons have wave-like and particle-like (old view) properties. • We can better say that the wave-particle nature is the real thing;

individual wave and particle states are limiting cases; usually observed in measurements (collapse of the wave function)

• To better understand electronic structure, we assume– Electrons “reside” in orbitals.– Each orbital at discrete energy level is determined by quantum

numbers.c

Quantum # Designation n = principal (energy level-shell) K, L, M, N, O (1, 2, 3, etc.)

l = angular (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 - 16

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 - 17

Electronic Configurationsex: Fe - atomic # = 26

valence electrons

Adapted from Fig. 2.4, Callister & Rethwisch 3e.

1s

2s2p

K-shell n = 1

L-shell n = 2

3s3p M-shell n = 3

3d

4s

4p4d

Energy

N-shell n = 4

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

Chapter 2-

2.4 Periodic Table

Elements classified according to electron configuration Elements in a given column or group have similar valence electron

structures as well as chemical and physical properties Group 0 – inert gases, filled shells and stable Group VIIA – halogen Group IA and IIA - alkali and alkaline earth metals Groups IIIB and IIB – transition metals Groups IIIA, IVA and VA – characteristics between the metals and

nonmetals

Chapter 2-

2.4

Chapter 2 - 20

Atomic Bonding

• Valence electrons determine all of the following properties

1) Chemical

2) Electrical

3) Thermal

4) Optical

5) Deteriorative

6) etc.

Chapter 2-

Atomic Bonding in Solids

Chapter 2-

2.5 Bonding Forces and Energies

FN = FA + FR

EN = EA + ER

When 0 = FA + FR, equilibrium exists. The centers of the atoms will remain separated by the

equilibrium spacing ro.

This spacing also corresponds to the

minimum of the potential energy

curve. The energy that would be

required to separate two

atoms to an infinite separation is Eo

Figure 2.8

Chapter 2-

2.5 Bonding Forces and Energies

• A number of material properties depend on Eo, the curve shape, and bonding type– Material with large Eo typically have higher melting

points

– Mechanical stiffness is dependent on the shape of its force vs. interatomic separation curve

– A material’s linear coefficient of thermal expansion is related to the shapeof its Eo vs. ro curve

Chapter 2-

Bonding in Solids

• 2.5 Bonding forces and energies

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

• Forces are– Attractive (FA) – slowly changing 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

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

r

R

r

AN

EEE

drFdrFE

• 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

FdrESetting our ZERO ENERGY reference at infinite

Chapter 2-

ExamplesCalculate the force of attraction between ions X+ and an Y-, the centers of which are separated by a distance of 2.01 nm.

&

Chapter 2-

• 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!!!

2.6 Primary Interatomic Bonds

Chapter 2-

2.6 Primary Interatomic Bonds• Ionic Bonding

– Compounds composed of metallic and nonmetallic elements

– Coulombic Attractive Forces: positive and negative ions, by virtue of their net electrical charge, attract one another

• EA = -A/r• ER = -B/rn

– Bonding is nondirectional: the magnitude of the bond is equal in all directions around an ion

– Properties: generally large bonding energies (600-1500 kJ/mol) and thus high melting temperatures, hard, brittle, and electrically and thermally insulative

A, B, and n are constants

Na+ Cl-Coulombic bonding Force

Chapter 2-c02f09

2.6 Primary Interatomic Bonds

Chapter 2-

2.6 Primary Interatomic Bonds

• 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

128~ , nr

BE

nR

Chapter 2-

IONIC BONDING– 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 - 32

Ionic bond: metal + nonmetal

donates accepts electrons electrons

 

Dissimilar electronegativities  

ex: MgOMg 1s2 2s2 2p6 3s2 O 1s2 2s2 2p4

[Ne] 3s2 

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

Chapter 2 - 33

• Occurs between + and - ions.

• 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 - 34

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

rA

nrBEN = EA + ER =

Adapted from Fig. 2.8(b), Callister & Rethwisch 3e.

Chapter 2 - 35

• Predominant bonding in Ceramics

Adapted from Fig. 2.7, Callister & Rethwisch 3e. (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

NaClMgO

CaF2CsCl

Chapter 2-

2.6 Primary Interatomic Bonds• Covalent Bonding

– Stable electron configurations are assumed by the sharing of electrons between adjacent atoms

– Bonding is directional: between specific atoms and may exist only in the direction between one atom and another that participates in electron sharing

– Number of covalent bonds for a particular molecule is determined by the number of valence electrons

– Bond strength ranges from strong to weak

• Rarely are compounds purely ionic or covalent but are a percentage of both.

Sharing 4 electrons

Sharing 2 electrons

%ionic character = {1 – exp[-(0.25)(XA-XB)2]} x 100

XA and XB are electronegatives

Chapter 2-

Covalent bonding

– Sharing of electrons between adjacent atoms

– Most nonmetallic elements and molecules containing dissimilar elements have covalent bonds

– Polymers!

– Bonding is highly directional!

– Number of covalent bonds possible is guessed by the number of valence electrons

• Typically is 8 – N, where N is the number of valence electrons

• Carbon has 4 valence e’s – 4 bonds (ok!)

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 - 39

C: has 4 valence e-, needs 4 more

H: has 1 valence e-, needs 1 more

Electronegativities are comparable.

Adapted from Fig. 2.10, Callister & Rethwisch 3e.

Covalent Bonding• similar electronegativity share electrons• bonds determined by valence – s & p orbitals

dominate bonding

• Example: CH4 shared electrons from carbon atom

shared electrons from hydrogen atoms

H

H

H

H

C

CH4

Chapter 2-

Bonding in Solids

• Many materials have bonding that is both ionic and covalent in nature (very few materials actually exhibit pure ionic or covalent bonding)

• Easy (empirical) way to estimate % of ionic bonding character:

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

Notice: this is a very very very empirical formula

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

Chapter 2 - 41

Primary Bonding

• Ionic-Covalent Mixed Bonding

% ionic character =  

where XA & XB are Pauling electronegativities

%)100( x

1 e

(XA XB )2

4

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

2

Ex: MgO XMg = 1.3XO = 3.5

Chapter 2-

2.6 Primary Interatomic Bonds• Metallic Bonding

– Found in metals and their alloys– 1 to 3 valence electrons that form a

“sea of electrons” or an “electron cloud” because they are more or less free to drift through the entire metal

– Nonvalence electrons and atomic nuclei form ion cores

– Bonding energies range from weak to strong

– Good conductor of both electricity and heat

– Most metals and their alloys fail in a ductile manner

Ion Cores

Sea of Valence Electrons

+

+

+

+

+

+

+

+

+

- -

- -

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– 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 -

2.7 Secondary Bonding or van der Walls Bonding

• Also known as physical bonds

• Weak in comparison to primary or chemical bonds

• Exist between virtually all atoms and molecules

• Arise from atomic or molecular dipoles– bonding that results from the coulombic attraction

between the positive end of one dipole and the negative region of an adjacent one

– a dipole may be created or induced in an atom or molecule that is normally electrically symmetric

Chapter 2 -

2.7 Secondary Bonding or van der Waals Bonding

• Fluctuating Induced Dipole Bonds– A dipole (whether induced or instantaneous)

produces a displacement of the electron distribution of an adjacent molecule or atom and continues as a chain effect

– Liquefaction and solidification of inert gases

– Weakest Bonds

– Extremely low boiling and melting pointAtomic nucleus

Atomic nucleus

Electron

cloud

Electron

cloudInstantaneous

Fluctuation

Chapter 2 -

2.7 Secondary Bonding or van der Waals Bonding

• Polar Molecule-Induced Dipole Bonds– Permanent dipole moments exist by virtue of an

asymmetrical arrangement of positively and negatively charged regions

– Polar molecules can induce dipoles in adjacent nonpolar molecules

– Magnitude of bond greater than for fluctuating induced dipoles

+ -

Polar Molecule

Induced Dipole

Atomic nucleusElectron Cloud

Chapter 2 -

2.7 Secondary Bonding or van der Waals Bonding

• Permanent Dipole Bonds– Stronger than any secondary bonding with induced

dipoles

– A special case of this is hydrogen bonding: exists between molecules that have hydrogen as one of the constituents

H Cl H Cl

Hydrogen Bond

Chapter 2-

Bonding in Solids• Permanent dipoles (hydrogen

bonds)– Van der Waals interactions between

polar molecules– Best known example – hydrogen

bonding• These interactions are fairly strong,

very complex, and surprisingly not well understood!

Chapter 2-

c02tf03

Chapter 2-

c02f16

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

MATERIAL OF IMPORTANCEWater

Chapter 2-c02uf01

Chapter 2 - 53

• Bond length, r

• Bond energy, Eo

• Melting Temperature, Tm

Tm is larger if Eo is larger.

Properties From Bonding: Tm

r o r

Energyr

larger Tm

smaller Tm

Eo =

“bond energy”

Energy

r o r

unstretched length

Chapter 2 - 54

• Coefficient of thermal expansion,

• ~ symmetric at ro

is larger if Eo is smaller.

Properties From Bonding :

= (T2 -T1) LLo

coeff. thermal expansion

L

length, Lo

unheated, T1

heated, T2

r or

smaller

larger

Energy

unstretched length

Eo

Eo

Chapter 2-16

• Elastic modulus, E cross 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 - 56

Ceramics(Ionic & covalent bonding):

Large bond energylarge Tm

large Esmall

Metals(Metallic bonding):

Variable bond energymoderate Tm

moderate Emoderate

Summary: Primary Bonds

Polymers(Covalent & Secondary):

Directional PropertiesSecondary bonding dominates

small Tm

small E large

secondary bonding

Chapter 2 - 57

Type

Ionic

Covalent

Metallic

Secondary

Bond Energy

Large!

Variablelarge-Diamondsmall-Bismuth

Variablelarge-Tungstensmall-Mercury

smallest

Comments

Nondirectional (ceramics)

Directional(semiconductors, ceramicspolymer chains)

Nondirectional (metals)

Directionalinter-chain (polymer)inter-molecular

Summary: Bonding