: Atomic Systems and Bonding :

R. R. Lindeke, Ph.D.Engr 2110 – Lecture 2

ISSUES TO ADDRESS...

The Structure of Matter A Quick Review

What Promotes Bonding? What type of Bonding is Possible? What Properties are Inferred from

Bonding?

Just as before:

How the atoms are arranged & how they bond

GREATLY AFFECTS

Their FINAL PROPERTIES& therefore use

ATOMIC StructureElectron configurations

Primary & secondary BONDING

Structure of Matter: Atoms are the smallest particle in Nature that exhibits

the characteristics of a substance The radius of a typical atom is on the order of

0.00000000001 meter and cannot be studied without very powerful microscopes

Pictured here is an “Electron

Microscope” It can greatly magnify

materials but can’t resolve individual atom – we need a

TEM or STP for that

Structure of Matter: A molecule consists of 2 or more atoms bound together

In a common glass of water “upon closer examination” we would find a huge number of Water “Molecules” consisting of 1 atom of Oxygen and 2 atoms of hydrogen

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 12.011H 1.008 etc.

} 1.67 x 10-27 kg

Atomic Weight is rarely a whole number – it is a weighted average of all of the natural isotopes of an “Element”

What is this in weight or mass in “Real Terms”

Example 1:

What is this in weight or mass in “Real Terms”

Ex. 2:

Structure of Matter – an Element Any material that is composed of only one type of

atom is called a chemical element, a basic element, or just an element.

Every element has a unique atomic structure. Scientists know of only about 109 basic elements at

this time. (This number has a habit of changing!) All matter is composed of combinations of one or

more of these elements. Ninety-one of these basic elements occur naturally on

or in the Earth. These elements are pictured in the “Periodic Table”

The Periodic Table of the Elements

Structure of Matter Each of the “boxes” in the

periodic table help us to understand the details of a given elements

Here we see atomic Number (# of Electrons or Protons) and Atomic Weight

Some tables provide information about an elements “Valance State” or the ability to gain or shed their outermost electrons when they form molecules or “Compounds”

Structure of Matter

These outermost or Valence electrons determine all of the following properties concerning an element:

1) Chemical2) Electrical 3) Thermal4) Optical

Electronic Structure

Electrons have wavelike and particulate properties. This means that electrons exist in orbitals defined by a

probability. – Boer coupled w/ Schrödinger models Each orbital is located at a 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

Electron Energy States

1s

2s2p

K-shell n = 1

L-shell n = 2

3s3p M-shell n = 3

3d

4s

4p4d

Energy

N-shell n = 4

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

Adapted from Fig. 2.4, Callister 7e.

Can hold up to 2 electrons

Can hold up to 8 electrons

Can hold up to 18 Electrons

Can hold up to 32 electrons

More exhaustively:

• Why? Valence (outer) shell usually not filled completely so the electrons can ‘move out’!

• For Most elements: This Electron configuration not stable.

SURVEY OF ELEMENTS

Electron configuration

(stable)

...

...

1s22s 22p 63s23p 6 (stable)... 1s22s 22p 63s23p 63d 10 4s 24p 6 (stable)

Atomic #

18...36

Element1s1 1Hydrogen1s22Helium1s22s 1 3Lithium1s22s24Beryllium1s22s 22p 15Boron1s22s 22p 26Carbon

...

1s22s 22p 6 (stable)10Neon1s22s 22p 63s111Sodium1s22s 22p 63s2 12Magnesium1s22s 22p 63s23p 113Aluminum

...

Argon...Krypton

Adapted from Table 2.2, Callister 7e.

Electron Configurations

Valence electrons – those in unfilled shells Filled shells are 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

Lets Try one: How about Fe (iron w/ Atomic Number 26)

ex: Fe - atomic # =

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

Schematic Image of Atoms:

Atomic number

is 29

Considering Copper: It valance electrons are far from the nucleus and thus are not too

tightly bound (making it easier to ‘move out’) Notice that in the copper atom pictured above that the outside

shell had only one electron When the valence electron in any atom gains sufficient energy

from some outside force, it can break away from the parent atom and become what is called a free electron

Atoms with few electrons in their valence shell tend to have more free electrons since these valence electrons are more loosely bound to the nucleus. In some materials like copper, the electrons are so loosely held by the atom and so close to the neighboring atoms that it is difficult to determine which electron belongs to which atom!

Under normal conditions the movement of the electrons is truly random, meaning they are moving in all directions by the same amount.

However, if some outside force acts upon the material, this flow of electrons can be directed through materials and this flow is called electrical current in a conductor.

We measure this directed flow of Freed Valence Electrons as “Amperage”

AMPERAGEIt is very important to have a way to measure and quantify the flow of electrical current. When current flow is controlled it can be used to do useful work. Electricity can be very dangerous and it is important to know something about it in order to work with it safely. The flow of electrons is measured in units called amperes. The term amps is often used for short. An amp is the amount of electrical current that exists when a number of electrons, having one coulomb (ku`-lum) of charge, move past a given point in one second. A coulomb is the charge carried by 6.25 x 1018 electrons. 6.25 x 1018 is scientific notation for 6,250,000,000,000,000,000 -- a lot of electrons moving past a given point in one second!

Matter (or elements) Bond as a result of their Valance states

give

up

1egi

ve u

p 2e

give

up

3e iner

t ga

ses

acce

pt 1

eac

cept

2e

O

Se

Te

Po At

I

Br

He

Ne

Ar

Kr

Xe

Rn

F

ClS

Li Be

H

Na Mg

BaCs

RaFr

CaK Sc

SrRb Y

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

Electronegative elements:Readily acquire electronsto become - ions.

Molecular/Elemental Bonding Bonding is the result of the balance of the

force of attraction and the force of repulsion of the electric nature of atoms (ions)

Net Force between atoms: FN = FA + FR and at some equilibrium (stable) bond location of separation, FN = 0 or FA = FR

From Physics we like to talk about bonding energy where: r

E Fdr Fdr

Bonding Energy

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 7e.

n is 7-9 for most ionic pairs

Equilibrium separation (r0) is about .3 nm for many atoms

Bonding Energy, the Curve Shape, and Bonding Type Properties depend on shape, bonding type and values

of curves: they vary for different materials. Bonding energy (minimum on curve) is the energy

that would be required to separate these two atoms to an infinite separation.

Modulus of elasticity depends on force versus distance curve: the slope at r = r0 position on the curve will be quite steep for very stiff materials, slopes are shallower for more flexible materials.

Coefficient of thermal expansion depends on E0 versus r0 curve: a deep and narrow trough correlates with a low coefficient of thermal expansion

Here: A, B and n are “material constants”

rA

nrBEN = EA + ER =

1 20

120

:

1 -- Coulomb's Law

4

is valence number of the species,

e is electronic charge,

is the permittivity of a vacuum (8.85x10 / )

r r

N N A R

r

A A

i

E F dr F F dr

AE F dr r

here

A Z e Z e

Z

F m

Bonding Types of Interest: Ionic Bonding: Based on donation and acceptance of

valance electrons between elements to create strong “ions” – CaIONs and AnIONs due to large electro-negativity differences

Covalent Bonding: Based on the ‘sharing’ of valance electrons due to small electro negativity differences

Metallic Bonding: All free electrons act as a moving ‘cloud’ or ‘sea’ to keep charged ion cores from flying apart in their ‘stable’ structure

secondary bonding: van der wahl’s attractive forces between molecules (with + to – ‘ends’) This system of attraction takes place without valance

electron participation in the whole Valence Electrons participate in the bonding to build

the molecules not in ‘gluing’ the molecules together

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]

Note: after exchange we have a stable (albeit ionic) electron structure for both Mg & O!

• 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

CaF2CsCl

Ionic Bonding – a Closely held Structure of +Ions and –Ions (after this Valence exchange) These structure a held together

by Coulombic Bonding forces after the Atoms exchange Valance Electrons to form the stable ionic cores:

It the solid state these ionic cores will sit at highly structured “Crystallographic Sites”

We can compute the coulombic forces holding the ions together – it is a balance between attraction force (energy) of due to the ionic charge and repulsion force (energy) due to the nuclear cores of the ions

These forces of attraction and repulsion compete and will achieve a energy minimum at some inter-ion spacing

Example: Using these energy issues

Here, ‘r0’ equals the sum of the ionic radii of each and represents the r in

the energy balance equations!

Another Example (working backward with Coulomb’s Law):

Covalent Bonding

similar electronegativity share electrons bonds determined by valence – s & p orbitals dominate

bonding Example: CH4

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 7e.

shared electrons from carbon atom

shared electrons from hydrogen atoms

H

H

H

H

C

CH4

Primary BondingIonic-Covalent Mixed Bonding

% ionic character =  

where XA & XB are Pauling electronegativities

%)100( x

1 e

(XA XB )2

4

Ex: MgO XMg = 1.2XO = 3.5

23.5 1.2

4%IonicCharacter 1 100% 73.4%e

Metallic Bonding:

In a metallic bonded material, the valence electrons are “shared” among all of the ionic cores in the structure not just with nearest neighbors!

Arises from interaction between “electric” dipoles

• Permanent dipoles-molecule induced

SECONDARY BONDING

• Fluctuating dipoles

Adapted from Fig. 2.13, Callister 7e.

asymmetric electron clouds

+ - + -secondary

bonding

HH HH

H2 H2

secondary bonding

ex: liquid H2

-general case:

-ex: liquid HCl

-ex: polymer

Adapted from Fig. 2.14, Callister 7e.

H Cl H Clsecondary bonding

secondary bonding+ - + -

secondary bondingsecondary bonding

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

• 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

• Coefficient of thermal expansion,

• ~ symmetry 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

larger

smaller

Energy

unstretched length

Eo

Eo

Ceramics(Ionic & covalent bonding):

Metals(Metallic bonding):

Polymers(Covalent & Secondary):

Variable bond energymoderate Tm

moderate Emoderate

Directional PropertiesSecondary bonding dominates

small Tm

small E large

Summary: Primary Bonds

secondary bonding

Large bond energylarge Tm

large Esmall