3-1

C H A P T E R 3

A T O M I C S T R U C T U R E

3.1 THE ATOM

3.2 THE ELECTRONIC STRUCTURE OF ATOMS

3.3 THE PERIODIC TABLE

3.4 PRIMARY BONDS 3.4.1 Ionic Bonding 3.4.2 Covalent Bonding 3.4.3 Meta l l ic Bonding

3.5 SECONDARY BONDS 3.5.1 Van der Waals Bonding 3.5.2 Hydrogen Bonding

3.6 BONDING CHARACTER OF MATERIALS

3.7 BONDING FORCES AND ENERGIES

3.8 BONDING TYPE AND PROPERTIES 3.8.1 Thermal Expans ion 3.8.2 Melt ing Point 3.8.3 E last ic Modulus 3.8.4 Hardness , Duct i l i ty and Toughness

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• The mechanical and physical properties of a material are,

at the most fundamental level, determined by the

composition and structure of the material.

• Composition refers to the types of elements that make up

the material and the proportions in which they exist.

• The constituent elements will govern the nature of

bonding and forces holding atoms together (Chp. 3), as well

as the ways in which atoms/molecules pack together (Chp 4).

3.1 THE ATOM

• The atom is the smallest unit building block of all matter; it

is the smallest quantity of an element that can take part in

a chemical reaction.

• An atom may be thought of as a very small, dense nucleus

surrounded by moving electrons (Fig. 3.1-1).

Fig. 3.1-1 Schematic representation

of an atom.

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3.2 THE ELECTRONIC STRUCTURE OF ATOMS

• The electronic structure (arrangement of electrons) of

atoms dictates the nature of bonds and chemical reactions

between atoms, as well as electrical, thermal, magnetic

and optical properties of materials.

• Electrons are held to the nucleus by electrostatic (positive-

negative) attraction, the force of which decreases with

distance from the nucleus. Electrons may be thought of as

being arranged in ‘shells’ of increasing discrete energy

levels with increasing distances from the nucleus. Shells

are designated K, L, M, N, …, (K being the closest to the

nucleus) (Fig. 3.2-1).

(a) (b)

Fig. 3.2-1 Schematic representation of (a) the electron configuration; and (b) the filled energy states for a sodium (Na) atom.

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• Each shell may be further divided into subshells s, p, d, f,

…, each differing slightly in their energy levels (Fig. 3.2-2 and

Table 3.2-1).

Fig. 3.2-2 Schematic representation of the

relative energies of the electrons for the various

shells and subshells.

• Electrons tend towards the lowest energy states (i.e.

greater stability). The electronic structure of an atom of

atomic number Z can be specified by putting one electron

in each of the Z lowest energy states.

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• The most stable (lowest energy) electron configuration is

that in which the electron states within the outermost shell

are completely filled; e.g., He, Ne, Ar (inert gases). Fully-

filled shells are considered ‘closed’; electrons in closed

shells do not readily enter into reactions.

• Electrons occupying partially-filled outermost shells, known

as the valence electrons, are most likely to enter into

chemical reactions because their distance away from the

nucleus reduces their binding energy to the nucleus. In

addition, the closed inner shells ‘shield’ the outermost

shells from the positive nuclear charge.

3.3 THE PERIODIC TABLE

• Each element is identified by its atomic number, Z, which

is equal to the number of protons in the nucleus. Elements

are arranged in ascending atomic numbers (horizontal

rows) in chemically similar groups (vertical columns) in the

Periodic Table (Fig. 3.3-1).

• Elements in the same column (i.e. with similar chemical

behaviour) in the Periodic Table have similar electronic

configurations in the outermost shells of their atoms.

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3-7

3.4 PRIMARY BONDS

• Atoms bond because there is a reduction in the overall

energy (i.e. greater stability) when the electrons amongst

the bonding atoms rearrange to achieve the stable

configuration of fully-filled outermost shells.

• There are 3 types of primary bonds between atoms: ionic,

covalent and metallic.

3.4.1 Ionic Bonding

• Ionic bonding involves the transfer of electrons from the

nearly-empty outermost shell of one element to the nearly-

full outermost shell of another element, resulting in

complete outermost shells in both (Fig. 3.4-1).

• Ionic bonds form between elements located at the

horizontal extremities of the Periodic Table; e.g. between

Group I (metal) and Group VII elements (non-metal); e.g.

NaCl (Fig. 3.4-1).

• The bond arises from electrostatic (Coulombic) attraction

between the positive and negative ions (Fig. 3.4-1).

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Fig. 3.4-1 Ionic bonding in sodium chloride (NaCl).

• Since electrostatic attraction is omnidirectional and long-

ranged, ionic bonds are non-directional. The (usually)

smaller positive ions are surrounded by as many negative

ions as possible and vice versa (Fig. 3.4-2).

Fig. 3.4-2 Ionic bonding is non-directional.

• Ionic bonding is found in many ceramics; e.g. alumina

(Al2O3), titanium carbide (TiC), and zirconia (ZrO2).

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3.4.2 Covalent Bonding

• Atoms with difficulty in gaining or losing electrons in their

outermost shells tend towards sharing of electrons in

pairs to complete their outermost shells; e.g. C, Si (Fig. 3.4-3).

Fig. 3.4-3 Covalent bonding in silicon.

• Each pair of shared electrons orbit about both atomic

cores, mainly traversing the space between the two atomic

cores (Fig. 3.4-4).

Fig. 3.4-4 Electron orbital penetrating two atomic cores.

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• The bond arises from the electrostatic attraction between

the negatively-charged pair of shared electrons and the

two positively-charged atomic cores (Fig. 3.4-4).

• Due to strong mutual repulsion, each negatively-charged

valence electron cloud assumes equilibrium positions as far

from one another as possible. Covalent bonds therefore

have a fixed directional relationship with one another (Fig.

3.4-5).

Fig. 3.4-5 Directional covalent bonding in diamond.

• Materials with covalent bonding include: semiconductors

(Si, Ge, GaAs), some ceramics (SiC, Si3N4), and diamond.

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3.4.3 Metall ic Bonding

• Metallic bonding is confined to metals and near-metals

with few valence electrons in their outermost shells; e.g. in

Groups I, II and III of the Periodic Table.

• Valence electrons, which are weakly-bound to the nucleus,

become easily detached and move freely around the ion

cores. These electrons are delocalized from their nucleus,

forming a randomly-moving ‘sea’ of electrons surrounding

the ion cores.

• The electrostatic attraction between the negatively-

charged electron ‘sea’ and the positive ion cores acts as a

‘glue’ that bonds the metallic structure. (Fig. 3.4-6).

Fig. 3.4-6 Schematic

illustration of metallic bonding showing positive ion cores immersed in a randomly-moving ‘sea’ of negative

electrons.

• Metallic bonds are non-directional.

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3.5 SECONDARY BONDS

• Secondary bonds are formed between molecules; no

change in the electronic structure is involved.

• Secondary bonds are weaker than primary bonds.

3.5.1 Van der Waals Bonding • Van der Waals bonding involves the attraction between

atomic or molecular dipoles.

• A dipole arises when the centres of positive and negative

charge in an atom or molecule do not coincide.

• Due to the constant motion of

electrons, the negative charge is

sometimes not symmetric with

respect to the positive nucleus,

forming a temporary dipole.

• A dipole may induce a similar dipole in an adjacent atom

or molecule. The bond arises from weak electrostatic

attraction between the positive end of one dipole to the

negative end of the other dipole (Fig. 3.5-2).

Fig. 3.5-2 Van der Waals bonding between two temporary dipoles.

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3.5.2 Hydrogen Bonding

• Hydrogen bonding is a special type of van der Waals

bonding that involves the attraction between molecular

dipoles with hydrogen as a constituent.

• Covalent bonding between hydrogen and an element with

a nearly-full outermost shell concentrates the electron

away from the hydrogen nucleus, leaving a positive charge

at the hydrogen end of molecule; this forms a permanent

dipole (Fig. 3.5-3).

• The bond arises from electrostatic attraction between the

positive and negative ends of permanent dipoles (Fig. 3.5-3).

Fig. 3.5-3 Hydrogen

bonding between water molecules.

• Hydrogen bonds are stronger than van der Waals bonds

between fluctuating induced dipoles because the dipoles

involved in the bonding are permanent.

• Hydrogen bonds are important in polymers and biological

molecules; e.g. cellulose, DNA.

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• Van der Waals bonding may be found between the layers

of covalently-bonded C atoms in graphite (Fig. 3.5-4), and

between chains of thermoplastic polymers; e.g.

polyethylene (PE), polyvinyl chloride (PVC) (Fig. 3.5-5),

polystyrene, and nylon.

Fig. 3.5-4 Structure of graphite showing covalent bonding between carbon atoms in each layer, and van der Waals bonding between the layers.

Fig. 3.5-5 Atoms within each chain of polyvinyl chloride (PVC) are covalently bonded, while van der Waals (hydrogen) bonding exists between the chains.

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3.6 BONDING CHARACTER OF MATERIALS

• Bonding between atoms may involve more than one type

of primary bond and can also involve secondary bonds.

• The transition from pure ionic to pure covalent bonding is

gradual and many ceramics display mixed ionic/covalent

bonding.

• The transition metals (e.g. Fe, Cr, Mo, W, Pt) display mixed

metallic/covalent bonding because partially-filled inner

shells result in some covalent bonding.

Fig. 3.6-1 Tetrahedron representing the relative contribution of different bond types to the four

fundamental categories of engineering materials.

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3.7 BONDING FORCES AND ENERGIES

• When two atoms are brought close together, an attractive force, FA, is set up, which increases with decreasing atomic separation (Fig. 3.7-1a).

• At short separations, a repulsive force, FR, arises due to the resistance of the closed inner shells to mutual penetration (Fig. 3.7-1a).

Fig. 3.7-1 The variation of (a) forces and (b) energies with

interatomic separations. C and K in FA and FR are constants,

and m < n.

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• Equilibrium spacing (bond-length), ro, occurs when

FN = FA + FR = 0

• Potential energy due to the interaction between the atoms,

UN, is such that:

!

FN =dUNdr

or

!

UN = FN dr"

r#

• When r = r0, potential energy is a minimum (Fig. 3.7-1b):

!

FN =dU

Ndr

"

#

$ $ $

%

&

' ' ' r=r0

= 0

• Mechanical model of a solid: a solid may be envisaged as

an array of particles (atoms) with each particle linked to its

neighbours by springs (bonds) (Fig. 3.7-2).

( a ) ( b ) Fig. 3.7-2 Mechanical model of a solid showing (a) atoms linked by atomic bonds that behave like springs, and (b) the variation in forces and energies with atomic separation.

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• The energy-separation curve is also known as the potential

well; it represents the potential energy of an atom due to

the influence of its neighbouring atom. The bottom of the

well (minimum of the curve) corresponds to the total

energy of the atom at absolute zero (0 Kelvin). At this

temperature, the atom has potential energy only, without

any kinetic energy.

• Above 0 K, the atom also possesses kinetic energy, which

must be added above the potential energy curve (Fig. 3.7-3a).

As the temperature increases, the atom may be seen as

moving up the potential well (Fig.3.7-3b), vibrating back and

forth the distance dictated by the width of the well at any

particular temperature.

(a) (b)

Fig. 3.7-3 (a) Potential and kinetic energy components of the total energy of an atom. (b) The atom moves up the potential well as temperature increases.

[Note that in these diagrams, the potential energy is set at zero when r=r0; the usual convention is to set potential energy to zero when r = !.]

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• By convention, the potential energy is set at zero when the

interatomic separation is infinite (i.e. r = !), since the

atoms would have zero interaction (Fig. 3.7-4).

Fig. 3.7-4 By convention, potential energy is set at

zero for r = !. [Note that mathematically,

!

FN dr"

r# also leads to

negative potential energy.]

• If the temperature of the solid rises such that the total

energy becomes greater than zero (i.e. interatomic

separation approaches infinity), the material exists in the

gaseous state (Fig. 3.7-4).

• However, the energy-separation curve does not provide a

basis for discussing the liquid state, since the phase change

from solid to liquid or from liquid to gas requires a supply

of energy (latent heat) that is unrelated to a rise in

temperature.

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3.8 BONDING TYPE AND PROPERTIES The type of bonding in a material determines several

properties, some of which may be related to the shape of

the force-separation and energy-separation curves.

3.8.1 Thermal Expansion, !

• As temperature rises above 0 K, kinetic energy results in

the atom shifting up the potential well. Due to the

asymmetrical shape of the well, the mean position of the

atom changes with temperature and the atoms tend to

move apart as temperature increases (Fig. 3.8-1a).

• For a material with a deep and narrow well, the change in

interatomic distance for a given rise in temperature (i.e.

the thermal expansion coefficient) is smaller than that for a

material with a broader, shallower well (Fig. 3.8-1b).

T3 > T2 > T1

(a) (b)

Fig. 3.8-1 (a) Increase in interatomic separation with temperature. (b) Comparison of the energy-separation curves for two materials: !A < !B.

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• Materials that are ionically and/or covalently bonded; e.g.

ceramics, tend to have deep and narrow wells, and thus,

good thermal stability. Metals experience slightly greater

expansion. Materials containing secondary bonding, e.g.

polymers, have very large coefficients of expansion.

• Thermal expansion becomes an important consideration

when there are temperature changes during service.

Nonuniform dimensional changes, as well as expansion or

contraction that is constrained, would generate stresses,

and may lead to distortion or cracking. Low expansion

coefficients are generally preferred in such applications.

Assemblies containing two or more different materials

would require careful matching of expansion coefficients.

3.8.2 Melting Point

• The melting point is a measure of bond strength, given by

the depth of the potential well. The deeper the well, the

greater the thermal energy required to reach levels where

bonding energy is low (liquid) or zero (gas).

• Materials with primary bonds (ionic, covalent, metallic)

generally have deep wells and high melting points, while

secondary bonding gives rise to low melting points.

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3.8.3 Elastic Modulus (see also Sec. 2.2.1)

• The elastic modulus (Young’s modulus) is a measure of a

material’s stiffness or resistance to elastic deformation. It is

related to the slope of the force-separation curve near the

equilibrium separation distance, r0; the steeper the slope,

the greater the force required to move the atoms from

their equilibrium positions, and the higher the modulus

(the stiffer the material) (Fig. 3.8-2).

Fig. 3.8-2 A steep gradient indicates a

high elastic modulus.

• In the mechanical model of a solid (Fig. 3.8-3), a higher elastic

modulus may be thought of as having stiffer springs

linking the particles, resisting their movement.

• Materials containing primary bonds (ionic, covalent,

metallic) tend to have high stiffness, while those with

secondary bonds are less rigid.

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Fig. 3.8-3 Mechanical model of a solid where the spring stiffness is a reflection of the elastic modulus.

• Note that atomic bonds, like springs, have breaking points

(Fig. 3.8-4). If the atoms are pulled with a force greater than

the peak on the force-separation curve, i.e. Fmax, the atomic

bond breaks and the attractive force between the atoms

will fall to zero as they separate further and further until

they no longer have an effect on each other. (See also Sec. 3.8.2)

Fig. 3.8-4 Atomic bond strength is measured by the peak of the force-separation curve – when a tensile force greater than Fmax is applied, the atomic bond breaks.

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3.8.4 Hardness, Ducti l ity and Toughness

• Although hardness, ductility and toughness are different

mechanical properties, they may all be related to a

material’s ability to deform plastically (permanently) under

an externally applied stress. The plastic deformation of a

material requires atoms to slip and slide past one another.

• In ionic solids, a displacement of the ions might lead to like

charges moving into adjacent positions (Fig. 3.8-5a), causing

repulsion. In covalent solids, strong mutual repulsion

between the negatively-charged electron clouds limits

atomic movement. Ionic and covalent solids are very hard,

but have low ductility and toughness.

Fig. 3.8-5 (a) Slip in ionic solids lead to repulsion of like charges.

(b) Ionic cores in metals are shielded by the electron sea.

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• In metals, the sea of electrons shield the positive ion cores from one another and the ion cores can slip without regard to electrical-charge constraints (Fig. 3.8-5b). The delocalized nature of the electrons also allows that the ions to slide past one another without interrupting the inter-atomic bonding. Metals are relatively ductile and tough.

• In conclusion, understanding the chemical composition

(type of atoms), the nature of atomic bonding and the

property trends of various classes of materials enables us to

select and design materials more efficiently.

TABLE 3.8-1

Uo = depth of energy-separation curve at equilibrium separation, ro (bonding energy) Ey = Elastic modulus (Young’s modulus) ! = coefficient of thermal expansion