Atomic structure, bonding

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Atomic structure, bonding

Chapter 2: Atomic Structure & Interatomic Bonding

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

1


• Basic idea … properties of materials are a

consequence of

– Identity of the atoms

– Spatial arrangement of the atoms

– Interactions between the atoms

• Thus, we need to study atomic structure/bonding!


Chapter 2: Atomic Structure &

Interatomic Bonding

ISSUES TO ADDRESS...

• What promotes bonding?

• What types of bonds are there?

• What properties are inferred from bonding?


2.2 Atomic Structure (Freshman Chem.)

• atom – electrons – 9.11 x 10 -31 kg

protons

} neutrons 1.67 x 10 -27 kg

• atomic number = # of protons in nucleus of atom

= # of electrons of neutral species

• A [=] atomic mass unit = amu = 1/12 mass of 12 C

Atomic wt = wt of 6.022 x 10 23 molecules or atoms

C 12.011

H 1.008 etc.

1 amu/atom = 1g/mol

4


Atomic Structure

• Some of the following properties

1) Chemical

2) Electrical

3) Thermal

4) Optical

are determined by electronic structure


2.2 Fundamental Concepts

• Atoms consist of a small nucleus

containing

• Protons

+1.60 x 10 -19 C = e

1.67 x 10 -27 kg

• Neutrons

0 C (neutral)

1.67 x 10 -27 kg

• Electrons (which circle the

nucleus)

-1.60 x 10 -19 C = -e

9.11 x 10 -31 kg


2.2 Fundamental Concepts

Atomic Number (Z)

• Number of protons in the nucleus

• Electrically neutral or complete

atom: Z = # electrons

Atomic Mass (A)

• Sum of the masses of protons and

neutrons; atomic mass unit = amu =

1/12 mass of 12 C

• Isotopes

• Atoms of the same element with

different atomic masses due to varying

number of neutrons (e.g. 12 C, 13 C, 14 C


Basic concepts

– Atoms are made of protons, neutrons and electrons

• m e = 0.00091094x10 -27 = 9.1094x10 -31 kg = 0.511 MeV

• m p = 1.6726 x 10 -27 kg = 938.272 MeV

• m n = 1.6749 x 10 -27 kg = 939.566 MeV = m p + 1.293 MeV

– Charge of a proton and electron are the same: 1.6022x10 -19 C

– However p are +’ve and e are –’ve

– Since J = C x V (1 joule = 1 coulomb x 1 volt),

1 eV = 1.6022x10 -19 J

– mass is related to energy by E = mc 2


2.3 Electrons In Atoms

Bohr Atomic Model

• 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); 1 st shell,

n=1; 2 nd shell, n=2;

3 rd shell, n=3


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Quantum Numbers

For the H atom

Scaled for

hydrogen-like

atoms

Degenerate states

Same energy


Bohr Atom

Wave-mechanical atom

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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


Electron Configuration

• Pauli Exclusion Principle

• Stipulates that electron states (orbital or shell) can have no

more than two electrons, must have opposite spins

• Ground state

• All electrons occupy the lowest energies

• Electrons can move to higher states

• Filled shells are more stable


Electronic Structure

• Electrons have wave-like and particle-like properties (old view)

• We can better say that the wave-particle nature is the real

thing; individual wave and particle states are limiting cases,

observed in measurements (collapse of the wave function)

• To better understand electronic structure, we assume

– Electrons “reside” in orbitals.

– Each orbital, at a discrete energy level, is determined by

quantum numbers.

c

Quantum numbers

n = principal (energy level-shell)

Designation

K, L, M, N, O (1, 2, 3, etc.)

l = angular (orbitals) s, p, d, f (0, 1, 2, 3,…, n -1)

m l = magnetic

m s = spin ½, -½

1, 3, 5, 7 (-l to +l)

14


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Quantum Numbers

Relative electrons

energies (E) for shells

and subshells

if n↓ then E↓

Within each shell E↑

with quantum number

Overlapping in energy

of a state in one shell

with states in adjacent

shells, true of d and f

states


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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)

1s 2 2s 2 2p 2

valence electrons

17


Atomic Models

Quantum 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 m l

, represents the

number of energy states

• s, p, d, f have 1, 3, 5, 7 states respectively

• Quantum number m s

, is the spin moment

• Each electron is a spin moment

• (+1/2) and (-1/2)


Electron Configuration

Silicon (Si)

• 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


Electron Configurations - Pauli Exclusion Principle

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Na Atom

Z = 11


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When some elements covalently

bond, they form sp hybrid bonds,

e.g., C, Si, Ge


Examples

Give the electron configurations for the following:

C

1s 2 2s 2 2p 2

Br

1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 10 4p 5

Mn +2

1s 2 2s 2 2p 6 3s 2 3p 6 3d 5

F - 1s 2 2s 2 2p 6

Cr

1s 2 2s 2 2p 6 3s 2 3p 6 4s 1 3d 5


Electronic Configurations

ex: Fe - atomic # = 26

1s 2 2s 2 2p 6 3s 2 3p 6 3d 6 4s 2

4d

4p

3d

4s

N-shell n = 4

valence

electrons

Energy

3p M-shell n = 3

3s

2p

2s

Adapted from Fig. 2.4,

Callister & Rethwisch 3e.

L-shell n = 2

1s

K-shell n = 1

Notice that 2s and 2p do not have the same energy

23


Electron Configuration

• “Stable electron configurations”

• States within the outermost or valence electron shell are

completely filled

• Some atoms of elements with unfilled shells assume

stable electron configurations by gaining or losing

electrons to form charged ions

• Sometimes s and p orbitals form hybrid sp n orbitals

• 3A, 4A, and 5A group elements typically

• Lower energy state for the valence electrons


SURVEY OF ELEMENTS

• 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

1s 1

1s 2

(stable)

1s 2 2s 1

1s 2 2s 2

1s 2 2s 2 2p 1

1s 2 2s 2 2p 2

...

1s 2 2s 2 2p 6 (stable)

1s 2 2s 2 2p 6 3s 1

1s 2 2s 2 2p 6 3s 2

1s 2 2s 2 2p 6 3s 2 3p 1

...

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)

Adapted from Table 2.2,

Callister & Rethwisch 3e.

25


STABLE ELECTRON CONFIGURATIONS

Stable electron configurations...

• have complete s and p subshells

• tend to be unreactive.

Adapted from Table 2.2,

Callister 6e.

4


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---IIB – transition metals

• Groups IIIA, IVA and VA – characteristics between the metals and

nonmetals


2.4


Electronegativity Values

• Electropositive:

• Capable of giving up their

valence electrons to become

positively charged

• Electronegative:

• Readily accept electrons to form

negatively charged ions

• Sometimes share electrons with

other atoms


Atomic Bonding

• Valence electrons determine all of the

following properties

1) Chemical

2) Electrical

3) Thermal

4) Optical

5) Deteriorative

6) etc.

30


Atomic Bonding in Solids


When 0 = F A + F R ,

equilibrium exists.

The centers of the

atoms will remain

separated by the

equilibrium spacing

r o .

2.5 Bonding Forces and

Energies

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 E o

F N = F A + F R

Figure 2.8

E N = E A + E R


2.5 Bonding Forces and Energies

• A number of material properties depend on E o ,

the curve shape, and bonding type

– Material with large E o typically have higher melting

points

– Mechanical stiffness is dependent on the shape of its

force vs. interatomic separation curve (F vs r)

– A material’s linear coefficient of thermal expansion

is related to the shape of its E vs. r curve


Bonding in Solids

• 2.5 Bonding forces and energies

– Far apart: atoms don’t know about each other

– As they approach one another, start to exert force on one

another

• two types of forces

– Attractive (F A ) – slowly changing with distance

– Repulsive (F R ) – typically short-range

– Net force is the sum of these

F N = F A + F R

– At some point the net force is zero; at that position a state of

equilibrium exists


Bonding forces and energies

F

E

E

dE

F

dr

F A

F R

N

N



r



E

F

A

A


dr

E


R

r



F

R

Bonding in Solids

dr

E


The interatomic separation at that point (r o ) corresponds

to the potential energy at that minimum

E o , it is also the bonding energy

E o is the energy needed to separate the atoms


Fdr



r


Fdr

& setting our ZERO ENERGY reference at ∞



r


Fdr

The point where the forces

are zero also corresponds

to the minimum potential

energy for the two atoms,

which makes sense because

-dE/dr = F = 0 at a minimum.


Examples

(book wrong sign of the F)

Calculate the force of attraction between ions X + and an Y - , the

centers of which are separated by a distance of 2.01 nm.

&


2.6 Primary Interatomic Bonds

• 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

• 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

• E A = -A/r

• E R = B/r n

Coulombic bonding Force

A, B, n are

Cl

Na

constants -

+

– 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


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2.6 Primary Interatomic Bonds


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

– The repulsive term is given by

E

E

A

R




B

n

r

Z eZ

e

1 2


4

o

1

r

, n ~ 8 12


Ionic bond: metal + nonmetal

donates

electrons

accepts

electrons

Dissimilar electronegativities

ex: MgO Mg 1s 2 2s 2 2p 6 3s 2 O 1s 2 2s 2 2p 4

[Ne] 3s 2

Mg 2+ 1s 2 2s 2 2p 6 O 2- 1s 2 2s 2 2p 6

[Ne]

[Ne]

41


Ionic Bonding

• Occurs between + and - ions.

• Requires electron transfer.

• Large difference in electronegativity required.

• Example: NaCl

Na (metal)

unstable

electron

Cl (nonmetal)

unstable

Na (cation)

stable

+ -

Coulombic

Attraction

Cl (anion)

stable

42


Ionic Bonding

• Energy – minimum energy most stable

– Energy balance of attractive and repulsive terms

E N = E A + E R =


A

r


B

r n

Repulsive energy E R

Interatomic separation r

Net energy E N

Adapted from Fig. 2.8(b),

Callister & Rethwisch 3e.

Attractive energy E A

43


Examples: Ionic Bonding

• Predominant bonding in Ceramics

NaCl

MgO

CaF 2

CsCl

Give up electrons

Acquire electrons

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.

44


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 2

electrons

Sharing

4

electrons

%ionic character = {1 – exp[-(0.25)(X A -X B ) 2 ]} x 100

X A and X B are electronegatives


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!)


H

2.1

Li

1.0

Na

0.9

K

0.8

Rb

0.8

Cs

0.7

Fr

0.7

EXAMPLES: COVALENT BONDING

Be

1.5

Mg

1.2

Ca

1.0

Sr

1.0

Ba

0.9

Ra

0.9

H2

Ti

1.5

Cr

1.6

Fe

1.8

H2O

C(diamond)

SiC

Ni

1.8

Zn

1.8

Ga

1.6

column IVA

C

2.5

Si

1.8

As

2.0

GaAs

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.

Ge

1.8

Sn

1.8

Pb

1.8

O

2.0

F

4.0

Cl

3.0

Br

2.8

I

2.5

At

2.2

He

-

Ne

-

Ar

-

Kr

-

Xe

-

Rn

-

F2

Cl2

• Molecules with nonmetals

• Molecules with metals and nonmetals

• Elemental solids (RHS of Periodic Table)

• Compound solids (about column IVA)

11


Covalent Bonding

• similar electronegativity share electrons

• bonds determined by valence – s & p orbitals

dominate bonding

• Example: CH 4

shared electrons

C: has 4 valence e - ,

needs 4 more

CH 4

H

from carbon atom

H: has 1 valence e - ,

needs 1 more

Electronegativities

are comparable.

H

C

H

H

shared electrons

from hydrogen

atoms

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

48


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:

%ionic character




2

1exp

(0.25)(

X ) x

100

A

X B

X A , X B are the electronegativities of atoms A and B involved

Notice: this is a very very very empirical formula


Primary Bonding

• Ionic-Covalent Mixed Bonding

% ionic character =

x ( 100 %)

where X A & X B are Pauling electronegativities


Ex: MgO X Mg = 1.3

X O = 3.5


1 e (X AX B ) 2



4







(3.5


% ionic character 1

e 4



1.3)

2






x (100%)

70.2%ionic

50


Example

Compute the percentage ionic character of the interatomic bond for

zinc oxide (ZnO). Refer to the periodic Table for electronegativity

values. Note: Electronegativity values in slides differ slightly from

those in book.

% ionic character = {1-exp[-(0.25)*(X Zn -X O ) 2 ]}*100

= {1-exp[-(0.25)*(1.7-3.5) 2 ]}*100

= 55.51%


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

+

+

+


METALLIC BONDING

• Arises from a sea of donated valence electrons

(1, 2, or 3 from each atom).

Adapted from Fig. 2.11, Callister 6e.

• Primary bond for metals and their alloys

12


• Metallic bonding

Bonding in Solids

– 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 E R )

– Metallic bonding is also nondirectional

– Free electrons also act to hold

structure together

– Wide range of bonding energies,

typically good conductors (why?)


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


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 point

Atomic nucleus

Electron

cloud

Instantaneous

Fluctuation

Atomic nucleus

Electron

cloud


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

+ -

Atomic nucleus

Electron Cloud

Polar

Molecule

Induced

Dipole


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

Hydrogen Bond

H Cl H Cl


Permanent dipoles

Hydrogen-bonds

These interactions are fairly strong, very

complex, and surprisingly not well understood!

van der Waals

interactions between

polar molecules

2.82 Å

109.47°

Best known example

hydrogen bonding


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MATERIAL OF IMPORTANCE

Water

Many molecules do not have a

symmetric distribution/arrangement

of positive and negative charges

(e.g. H 2 O, HCl)

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