3. atomic bonding

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CHAPTER 2

ATOMIC STRUCTURE AND BONDING INSOLIDS

Learning objectives:

After careful study of this chapter you should be able to do the following:

1. Name the two atomic models cited and note the difference between them2. Describe the important quantum-mechanical principle that relates to electron

energies3. a) schematically plot attractive, repulsive and net energies versus interatomic

separation for two atoms or ions( (b) note on this plot the equilibrium separation and the bonding energy

4. a) briefly describe ionic, covalent, metallic , hydrogen and van der Waals bondsb ) note with materials exhibit each of these bonding types

THE STRUCTURE OF MATERIAL: TECHNOLOGY RELEVANCE

In todays world, information technology (IT), biotechnology, energy technology,environmental technology and many other areas require smaller, lighter faster, portable,more efficient, reliable, durable and inexpensive devices. We want batteries that aresmaller, lighter and last longer. We need cars that are relatively affordable, light-weight,safe, highly fuel efficient, and loaded with many advanced features, ranging fromglobal positioning systems (GPS) to sophisticated sensors fro airbag deployment.

We will examine atomic structure in order to lay a foundation for understanding how itaffects the properties, behaviors, and resulting applications of engineering materials.The structure of atoms affects the types of bonds that hold materials together. Thesedifferent types of bonds directly affect suitability of materials for real world engineeringapplications.

Both the composition and the structure of a material have a profound influence on itsproperties and behavior. Engineers and scientist who study and develop materials mustunderstand their atomic structure. The properties of materials are controllable and canactually be tailored to the needs of a given application by controlling their structure andcomposition.

Structure of materials can be examine and describe at five different levels:

1. Macrostructure2. Microstructure3. Nanostructure4. Short and long range atomic arrangement5. Atomic structure


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Engineers and scientist concerned with development and practical applications ofadvanced materials need to understand the microstructure and macrostructure ofvarious materials and ways of controlling them.

Microstructure is the structure of material at a length-scale of ~10 to 1000 nm.Microstructure typically includes such features as average grain size, grain-sizedistribution, grain orientation and other features related to defects in material.

Macrostructure is the structure of a material at a macroscopic level where the length-scale is ~ 1000 100,000. Features that constitute macrostructure include porosity,surface coatings and such features as internal or external cracks.

Atomic structure it is also important to understand atomic structure and how theatomic bonds lead to different atomic or ionic arrangements in materials. The atomicstructure includes all atoms and their arrangements, which constitute the building ofblocks of matter.

It is from this building blocks that all the nano, micro and macrolevels of structuresemerge.

A close examination of atomic arrangement allows us to distinguish between materialsthat are amorphous or crystalline. Amorphous materials have only short range atomicarrangementwhile crystalline materials have short and long range arrangements.

In short range arrangement the atoms or ions shows a particular order only overrelatively short distances. For crystalline materials, the long range atomic order is in theform of atoms or ions arranged in a three dimensional pattern that repeats over muchlarger distances (from ~100 nm to few cm).

Properties and behavior of materials at micro levels can vary greatly when compared tothose in their macro or bulk state. As a result, understanding the structure at nano-scaleor nanostructure ( length-scale 1 100 nm) and microstructure are areas that havereceived considerable attention. The term nanotechnology is used to describe a set oftechnologies that are based on physical, chemical and biological phenomena occurringat nanoscale.

ATOMIC STRUCTURE

Atoms consist primarily of three basic subatomic particles: protons , neutrons andelectrons

The current simple model of an atom envisions a very small nucleus of about 10-14min diameter surrounded by a relatively thinly dispersed electron cloud of varying densityso that the diameter of the atom is of the order of 10 -10m.

The nucleus accounts for almost all the mass of the atom and contains protons andneutrons.


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Mass (gram) Charge ( C )

Proton 1.673 x 10-24 +1.602 x 10-19

Neutron 1.675 x 10-

0

Electron 9.109 x 10-

-1.602 x 10-

The electron charge cloud thus constitutes almost all the volume of the atoms butaccounts only for a very small part of its mass. The electrons, particularly the outerones, determine most of the electrical, mechanical, chemical and thermal properties ofthe atoms, thus a basic knowledge of atomic structure is important in the study ofengineering materials.

ATOMIC NUMBERS AND ATOMIC MASSES

ATOMIC NUMBERS

The atomic number of an atom indicates the number of protons (positively chargedparticles) that are in its nucleus, and in a neutral atom the atomic number is also equalto the number of electrons in its charge cloud. Each element has its own characteristicatomic number, and thus the atomic number identifies the element.

ATOMIC MASSES

The relative atomic mass of an element is the mass in grams of 6.023 x 10 23atoms (

Avogadros number NA ) of that element. The carbon atom with 6 protons and 6neutrons is the carbon 12 atom and is the reference mass for atomic masses.One atomic mass unit ( u ) is defined as exactly one-twelfth of the mass of the mass ofcarbon atom, which has a mass of 12u. One molar relative atomic mass of carbon 12has a mass of 12g on this scale.

H11.00794

Li36.941 Be

49.0121 C

612.011

Na1122.9898 Mg12

24.305 Al13

26.981

Atomic number

Atomic mass


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One gram-mole of mole (mol) of an element is defined as having the mass in grams ofthe relative molar atomic mass of that element. For example: 1 gram-mole of aluminumhas a mass of 26.98g and contains 6.023 x 1023atoms.

Mole and molecular (Relative) mass

Assume that the molecular mass of a substance/material is M and the mass is m gram.M gram of substance has a quantity of 1 mol

So m gram of substance has a quantity of n mol where n = molmxM

1

Mole and number of molecules

Assume that m gram of a gas has N number of molecules. The molecular mass of the

gas is M, that is one mole of gas has a mass of M gram.

M gram contains NAnumber of molecules. So:

A

A

N

Nnson

M

m

N

N

M

m

Where n = N/NA is the ratio of the number of molecules N with respect to Avogadros

number NAor alternatively n = m/M is the ratio of the mass of the gas m to the relative

molecular mass M.

Example

1. What is the mass in grams of one atom of copper?2. How many copper atoms are in 1g of copper

Solution:

1. the atomic mass of copper is 63.54 g/mol. Since in 63.54 g of copper there are6.022 x10

23atoms, the number of grams in one atom of copper is

gx

atomxmolatomsx

molg

atom

Cugx

molatomsx

Cumolg

N

Mm

A

22

23

23

1005.1

1/10022.6

/54.63

1/10022.6

/54.63

2. number of copper atoms in 1 g of copper


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atomsx

molg

molatomsxg

M

mNNatomscopperofnumber A

21

23

1048.9

/54.63

)/10022.6)(1(

ELECTRONS IN ATOMSAtomic models

An understanding and of the behavior of electrons in atoms and crystalline solidsnecessarily involves the discussion of quantum-mechanical concepts which will not bediscussed in this chapter.

Bohr atomic model, in which electrons are assumed to revolve around the atomicnucleus in discrete orbitals and the position of any particular electron is more or lesswell defined in terms of its orbital. This model of the atom is represented in Figure 1.

Electrons occupy discrete energy levels within the atom. Each electron possesses aparticular energy, with no more than two electrons in each atom having the sameenergy. This also implies that there is a discrete energy difference between any twoenergy levels

QUANTUM NUMBER

The energy level to which each electron belongs is determined by four quantumnumbers. The number of possible energy levels is determined by the first three quantumnumbers.

1. the principal quantum number n is assigned integral values 1,2,3,4, that referto the quantum shell to which the electron belongs ( figure). Quantum shells arealso assigned a letter: the shell for n = 1 is designated K, for n=2 is designated L,for n=3 is M and so on.


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Figure 1: Schematic representation of the Bohr atom

Maximum number of electrons for each principal atomic shell

Shell number, n(principal quantum

number)

Maximum number ofelectrons in each shell

(2n2)

Maximum number ofelectrons in orbitals

1 2(12) = 2 s2

2 2(22)=8 s2p6

3 2(32)=18 s2p6d10-

4 2(42)=32 s2p6d10f14

5 2(52)=50 s2p6d10f14

6 2(62)=72 s2..

7 2(72)=98 s2.

11 proton

12 neutrons

K shell ( n=1)

L shell ( n=2)

M shell ( n=3)


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2. the number of energy levels in each quantum shell is determined by theazimuthal quantum numberland the magnetic quantum number m l.

The azimuthal quantum numbers are also assigned numbers: l = 0. 1. 2, .n -1.

If n =2,then there are also two azimuthal quantum numbers, l = 0 and l = 1. Theazimuthal quantum numbers are designated by lowercase letters.

s for l = 0 d for l = 2

p for l = 1 f for l =3

The magnetic quantum numbers ml gives the number of energy levels, ororbitals, for each azimuthal quantum number. The total number of magneticquantum number for each l is 2l + 1. The values for m lare given by wholenumbers betweenl and +l. For l=2, there are 2(2) + 1 = 5 magnetic quantumnumbers, with values2, -1, 0, +1, +2

3. The Pauli exclusionprinciple specifies that no more than two electrons withopposing electronic spins, may be present in each orbital.

The shorthand notation frequently used to denote the electronic structure of anatom combines the numerical value of the principal quantum number, thelowercase letter notation for the azimuthal quantum number, and a superscriptshowing the number of electrons in each orbital. The shorthand notation forgermanium which has an atomic number of 32 is:

1s22s22p63s23p63d104s24p2

The pattern used to assign electrons to energy levelsl=0

(s)

l=1

(p)

l=2

(d)

l=3

(f)

l=4

(g)

l=5

(h)

n=1 (K) 2

n=2 (L) 2 6

n=3 (M) 2 6 10

n=4 (N) 2 6 10 14

n=5 (O) 2 6 10 14 18

n=6 (P) 2 6 10 14 18 22

Note: 2, 6, 10, 14, refer to the electrons inthe energy level


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INTERATOMIC FORCES FOR AN ION PAIR

Consider a pair of oppositely charged ions ( for example a Na++

Cl-ion pair) approaching

each other from a large distance of separation a.

As the ions comes closer together, they will be attracted to each other by coulombicforces. That is, the nucleus of one ion will attract the electrons charge cloud of the other,and vice versa. When the ions come still closer together, eventually their two electroncharge clouds will interact and repulsive forces will arise.

When the attractive forces equal the repulsive forces, there will be no net force betweenthe ions and they will remain at an equilibrium separation distance, the interionicdistance ao as shown in figure 2 below.

Figure 2:

F

A

B

ro

C

D

r

Fattractive

Frepulsive

Fresultant

r1

ao

Rr

r = cation

R = anion

ao= r + R


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The net force between a pair of oppositely charged ions is equal to the sum of theattractive and repulsive forces. Thus:

Fnet= Fattractive+ Frepulsive

2

2

21221

44

))((

a

eZZ

a

eZeZF

oo

att

where

Z1, Z2= number of electrons removed or added from the atoms during the ion formation

E = electron charge

a = interatomic separation distance

1

nrepul a

nbF

where

a = interatomic separation distance

b and n = are constants

12

2

21

4

n

o

neta

nb

a

eZZF

BINDING ENERGY AND INTERATOMIC SPACING

Interatomic spacingthe equilibrium distance between atoms is caused by a balancebetween repulsive and attractive forces. In the metallic bond, for example, the attractionbetween the electrons and the ion cores is balanced by the repulsion between iron core.Equilibrium separation occurs when the total interatomic energy (IAE) of the pair ofatoms is at a minimum, or when no net force is acting to either attract or repel theatoms (figure 3)


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Figure 3: Atoms or ions are separated by an equilibrium spacing that corresponds to theminimum interatomic energy for a pair of atoms or ions (or when zero force is acting torepel or attract the atoms or ions)

The interatomic spacing in a solid metal is approximately equal to the atomic diameter,or twice the atomic radius r. We cannot use this approach for ionically bonded materials,however, since the spacing is the sum of the two different ionic radii.

The minimum energy in figure is the binding energy , or the energy required to create orbreak the bond. Consequently, material having high binding energy also have a highstrength and a high melting temperature.

Ionically bonded materials have a particularly large binding energy because of the largedifference in electronegativities between the ions. Metals have lower binding energiesbecause the electronegativities of the atoms are similar.


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ATOMIC BONDING

TYPES OF ATOMIC AND MOLECULAR BONDS

Chemical bonding between atoms occurs since there is a net decrease in the potentialenergy of atoms in the bonded state. That is, atoms in the bonded state are in a morestable energy condition than when they are unbonded. In general, chemical bondsbetween atoms can be divided into two groups: PRIMARY (or strong bonds) andSECONDARY ( or weaker bonds).

PRIMARY ATOMIC BONDS

Primary atomic bonds in which relatively large interatomic forces develop can besubdivided into the following three classes:

1. Metallic bond2. Covalent bond

3. Ionic bondSECONDARY ATOMIC AND MOLECULAR BONDS

1. Permanent dipole bonds2. Fluctuating dipole bonds

PRIMARY BONDING:METALLIC BONDING:

Metallic bonding occurs in solid metals. In metals in the solid state, atoms are packedrelatively close together in a systematic pattern or crystal structure.

The metallic elements have more electropositive atoms that donate their valenceelectrons to form a sea of electrons surrounding the atoms (figure 4)


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Figure 4: The metallic bond forms when atoms give up their valence electrons, which

then form an electron sea. The positively charged atoms core are bonded by mutualattraction to the negatively charged electrons.

Aluminum for example gives up its three valence electrons, leaving behind a coreconsisting of the nucleus and inner electrons. Since three negatively charged electronsare missing from this core, it has a positive charge of three. The valence electronsmoves freely within the electron sea and become associated with several atom cores.The positively charges atom cores are held together by mutual attraction to the electron,thus producing a strong metallic bond.

COVALENT BOND

Materials with a covalent bond share electrons among two or more atoms. For example,a silicon atom, which has a valence of four, obtains eight electrons in its outer energyshell by sharing its electrons with four surrounding silicon atoms as shown in figure 5below. Each instance of sharing represents one covalent bond; thus each silicon atomis bonded to four neighboring atoms by four covalent bonds.


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Figure 5: a) covalent bonding requires that electrons be shared between atoms in sucha way that each atom has its outer sp orbital filled. (b) in silicon, with a valance of four,four covalent bonds must be formed

In order for the covalent bonds to be formed, the silicon atoms must be arrange so thebonds have a fixed directional relationship with one another. In the case of silicon, thisarrangement produces a tetrahedron, with angles of 109.5

obetween the covalent bonds

as shown in figure 6 below.

Figure 6: The tetrahedral structure ofsilica (Si2O3) which contains covalent bondsbetween silicon and oxygen atoms.

Although covalent bonds are very strong, materials bonded in this manner typically has

poor ductility and poor electrical and thermal conductivity.For an electron to move and carry a current, the covalent bond must be broken,requiring high temperatures and voltages. Many ceramic, semiconductor, and polymermaterials are fully or partly bonded by covalent bonds, explaining why glass shatterswhen dropped and why bricks are good insulating materials.


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IONIC BOND

The ionic bond arises from electrostatic attraction between the oppositely charged ions.These ions result from transfer of one or more electrons from an electropositive atom to

an electronegative atom, so that positive and negative ions are formed.

In chemical combination, atoms tend to attain the electronic configuration of an inertgas, or eight electrons in their outer shell. Thus the atoms of metallic elements that haveonly up to three valence electrons in their outer shell will lose their electrons andbecome positive ions, whereas electronegative elements tend to acquire additionalelectrons to complete their octet and become negative ions, or anions.

Figure 7: An ionic bond is created between two unlike atoms with differentelectronegativies. When sodium donates its valence electron to chlorine, each becomesanion; attraction occurs, and the ionic bond is formed.

SECONDARY BONDING ( VAN DER WAALS BONDING)

It has been discussed that primary bonding between atoms depends on the interactionof their valence electrons. The driving force for primary atomic bonding is the loweringof energy of the bonding electrons.

Secondary bonds are relatively weak in contrast to the primary bonds and haveenergies for only about 4 to 42 kJ/mol. The driving force for secondary bonding is theattraction of the electric dipoles contained in atoms or molecules.

The electric dipole moment is created when two equal and opposite charges areseparated, as shown in Figure 5a. Electric dipoles are created in atoms or moleculeswhen positive and negative charge centers exist (figure 8b).


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Figure 8: (a) An electric dipole. The dipole moment is qd (b) An electric dipole momentin a covalently bonded molecule. Note the separation of the positive and negativecharge centers.

Dipoles in atoms or molecules create dipole moments. A dipole moment is defined as,the charge value multiplied by the separation distance between positive and negativecharges, or

qd Unit: Coulomb-meter or Debye

Where:

= dipole moment

q = magnitude of electric charge

d = separation distance between the charge centers

In general, there are two main kinds of secondary bonds between atoms or molecules

involving electric dipoles; fluctuating dipoles and permanent dipoles. Collectively, thesesecondary dipole bonds are sometimes called van der Waals bond s.

FLUCTUATING DIPOLES:

Very weak secondary bonding forces can develop between atoms of noble-gaselements that have complete outer-valence-electron shells (s

2 for helium and s

2p

6 for

Ne, Ar, Kr, Xe and Rn).

These bonding forces arise because the asymmetrical distribution of electron charges inthese atoms creates electric dipoles. At any instant there is a high probability that there

will be more electron charge on one side of an atom than on the other (figure 9). Thus,in particular atom, the electron charge cloud will change with time, creating a fluctuatingdipoles.


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Figure 9: Electron charge cloud distribution in a noble-gas atom (a) idealizedsymmetrical electron charge cloud distribution (b) real case with asymmetrical electroncharge cloud distribution that changes with time, creating a fluctuating electric dipole.

PERMANENT DIPOLES

Weak bonding forces among covalently bonded molecules can be created if themolecules contain permanent dipoles. For example, the methane molecule, CH4, withits four C-H bonds arranged in a tetrahedral structure (Figure 10), has a zero dipolemoment because of its symmetrical arrangement of four C-H bonds.

Figure 10: Permanent dipole nature of water molecule

The bonding between molecules that have a permanent dipole moment, is known as theKeesom force, is often referred to as the hydrogen bond, where hydrogen atomsrepresent one of the polarized regions.

Note that van der Waals bonds are secondary bonds, but the atoms within themolecules or group of atoms are joined by strong covalent or ionic bonds. Heating water

to boiling point breaks the Van der Waals bonds and changes water to steam, but muchhigher temperature are required to break the covalent bonds joining oxygen andhydrogen atoms.

Van de Waals bonds can dramatically change the properties of materials. Sincepolymers normally have covalent bonds, we would expect polyvinyl chloride (PVCplastic) to be very brittle, but this material contains many long, chain-like molecules (asshown in figure 8). Within each chain, bonding is covalent, but individual chains are


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bonded to one another by Van der Waals bonds. Polyvinyl chloride can be deformed bybreaking the Van der Waals bonds, permitting the chains to slide past one another.

Figure 11: (a) In polyvinyl chloride (PVC) the chlorine atoms attached to the polymerchain have a negative charge and the hydrogen atoms are positively charged. Thechains are weakly bonded by van der Waals bond. This additional bonding makes PVCstiffer (b) when a force is applied to the polymer, the van der Waals bonds are brokenand the chains slide past one another.

MIXED BONDING

In most materials, bonding between atoms is a mixture of two or more types. Iron, forexample is bonded by a combination of metallic and covalent bonding which preventsatoms from packing as efficiently as we might expect.

Compounds formed from two or more metals (intermetallic compounds ) may bebonded by a mixture of metallic and ionic bonds, particularly when there is a largedifference in electronegativity between the elements. Because lithium has anelectronegativity of 1.0 and aluminum has an electronegativity of 1.5, we would expect

AlLi to have a combination of metallic and ionic bonding. On the other hand, becauseboth aluminum and vanadium have electronegativities of 1.5, we would expect Al3V to

be bonded primarily by metallic bonds.

Many ceramic and semiconducting compounds, which are combinations of metallic andnonmetallic elements, have mixture of covalent and ionic bonding. As theelectronegativity difference between the atoms increases, the bonding become moreionic.

3. atomic bonding

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