bonding between atoms [4] - unesp

Bonding between Atoms [4]

1>

Carbon atom

• nucleus: protons (+) and neutrons• electrosphere: electrons (-)• electrical charge: 1.60 x 10-19 C• mass of proton: 1.67 x 10-24 g• mass of electron: 9.11 x 10-28 g

Z=6M=12.01 g/molR=70 pm

Free atom: equilibrium at attractive and repulsive electrostatic forces between nucleus and electrosphere.

Bonding between Atoms

Interatomic bonds: forces that hold atoms together which act like little springs, linking one atom to the next in the solid state.

2>

Interatomic Forces:attractive forces (Fa)repulsive forces (Fr)

The Coulomb's law:

q1: Charge of object 1q2: Charge of object 2r: Distance between the two objectsKe = 8.9875 x 109 N.m2.C-2 (Coulomb Constant)F: Force between the two objects. F > 0 implies a repulsive interaction, while F < 0 means an attractive interaction.

221

rqqKF e

⋅⋅=

http

://m

atte

rand

inte

ract

ions

.org

/inde

x.ht

ml


3>

Consider two isolated atoms:

– When the atoms are at large inter-atomic separation distance, the atoms do not exert any force on each other.

– When the distance is decreased, an attractive force FA starts to act pulling atoms closer.

– FA increases as the atoms gets closer.– But as the atoms get closer a repulsive force FR begin to act.– The net force FN between the two atoms is given by:

FN = FA + FR

– At some inter-atomic distance ro, FR exactly equals FA and FNbecomes Zero

FN = 0 = FA + FR

– ro is called the equilibrium inter-atomic separation distance at which atoms enter into bonding


4>

• When FA + FR = 0,equilibrium exists.

• The centers of the atoms/ions will remain separated by the equilibrium spacing xo.

equilibrium spacing:

pA rAF −= qR r

BF =

where A, B, p, q are constants; q > p


drdVF −=

5>

Force-Energy Relationship:

“Force is the negative gradient of potential energy”

Energy calculation:

∫∫∞∞

+=r

R

r

AN drrFdrrFV )()(

Equilibrium is reached by minimizing VN


6>

The energy of the crystal is lower than that of the freeatoms by an amount equal to the energy required topull the crystal apart into a set of free atoms. This is called the binding (cohesive) energy of the crystal.

Examples:– NaCl is more stable than a collection of free Na and Cl.– Ge crystal is more stable than a collection of free Ge.

Cl Na NaCl


7>

Is this an appropriate potential to use to describeinteratomic interactions under all conditions?ANSWER: No! Consider what happens to V as interatomic separation r → ∞. This doesn’t make sense… bonding energy V should go to ZERO.

2

21 rkVdrrkV ⋅⋅=→⋅−= ∫

Energy in Ball-Spring atomic bonding:The spring’s force is given by F = - k.x (k: spring constant), therefore the potential energy is given by:

Energy Bonding between Atoms

8>

Lennard-Jones potential (1924): mathematically simple model that approximates the interaction between a pair of neutral atoms or molecules.

where ε is the depth of the potential well, σ is the finite distance at which the inter-particle potential is zero and r is the distance between the particles.

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛−⎟

⎠⎞

⎜⎝⎛=

612

4rr

V σσε

Repulsiveinteraction

Attractiveinteraction

http://en.wikipedia.org/wiki/Lennard-Jones_potential

Lennard-Jones potential

9>

This typical curve has a minimum at equilibriumdistance R0

R > R0 :– the potential

increases gradually, approaching 0 as R ∞

– the force is attractiveR < R0 :– the potential

increases very rapidly, approaching ∞ at small separation.

– the force is repulsive

R

rR

V(R)

0 R0

Repulsive

Attractive

Potential Energy vs. Internuclear Distance

10>

Animation of 2 hydrogen atoms: Dr. Kumar (2013)

https://www.youtube.com/watch?v=Wl5QHeS2UXE

When FA + FR = 0, 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 bonding energy that would be required to separate two atoms to an infinite separation is Eo

Bonding Forces and Energies

11>

Physical Properties vs. Bonding Forces

r

larger Elastic Modulus

smaller Elastic Modulus

Energy

ro unstretched length

12>

Melting Temperature, Tm

r

larger Tm

smaller Tm

Energy (r)

ro

Tm is larger if Eo is larger.

E = slope of the F-r curve at ro.Elastic modulus, E

E ~ curvature of E-r curve at ro.

E is larger if Eo is larger.

• At room temperature, solids formedfor large bonding energies, whereasfor small energies the gaseous stateis favored, liquids prevail when energies are of intermediate magnitude.


13>

Coefficient of thermal expansion, α

α ~ symmetry at ro.

α is larger if Eo is smaller.

ΔL

length, Lo

unheated, T1

heated, T2

r

smaller α

larger α

Energy

ro

= α (T2-T1)ΔLLo


14>

Metal (Z) melting temperature0C

Young’s modulusGPa

Pb (82)Zn (30)Mg (12)Al (13)Ag (47)Au (79)Cu (29)Ni (28)Fe (26)Cr (24)Mo (42)W (74)

3274206496609621064108514551538186326233422

144345717682124214196289324411

Types of Atomic & Molecular Bonds

15>

Primary Atomic Bonds (strong)– Ionic Bonds– Covalent Bonds– Metallic Bonds

Secondary Atomic & Molecular Bonds (weak)– Permanent Dipole Bonds– Fluctuating Dipole Bonds

Types of Atomic & Molecular Bonds

16>

Ionic Bonding

17>

Large inter-atomic forces are created by the “coulombic” effect produced by positively and negatively charged ions. Ionic bonds are “non-directional”.The “cation” has a + charge and the “anion” has the - charge.The cation is much smaller than the anion.Properties: generally large bonding energies (600-1500 kJ/mol) and thus high melting temperatures, hard, brittle, and electrically and thermally isolative.

Ionic Bonding

18>

Chemistry: What is an Ionic Bond?

https://www.youtube.com/watch?v=dqW7H7c7M4A

Ionic Bonding

19>

Ionic bond: metal + nonmetal

donates acceptselectrons electrons

Dissimilar electronegativities

ex: MgO Mg 1s2 2s2 2p6 3s2 O 1s2 2s2 2p4

Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6

Ionic Bonding

20>

Periodic Table - electronegativities

Give up electrons Acquire electrons

Ionic compounds: NaCl, MgO, CaF2, CsCl, e.g.

Sodium Chlorine (NaCl)

21>

Notice that when sodium loses its one valence electron it gets smaller in size, while chlorine grows larger when it gains an additional valence electron. After the reaction takes place, the charged Na+ and Cl- ions are held together by electrostatic forces, thus forming an ionicbond.

Some characteristics of ionic compounds

22>

Most ionic compounds are brittle; a crystal willshatter if we try to distort it. This happens because distortion cause ions of like charges to come close together then sharply repel.

Brittleness

Most ionic compounds are hard; the surfaces of their crystals are not easily scratches. This is because the ions are bound strongly to the lattice and aren't easily displaced.

Hardness

Solid ionic compounds do not conduct electricitywhen a potential is applied because there are no mobile charged particles.No free electrons causes the ions to be firmly bound and cannot carry charge by moving.

Electricalconductivity

The melting and boiling points of ionic compounds are high because a large amount of thermal energy is required to separate the ions which are bound by strong electrical forces.

Melting point and boiling point

ExplanationProperty

Covalent Bonding

23>

Large inter-atomic forces are created by the sharing of electrons to form directional bonds.Covalent bonding takes place between atoms with small differences in electronegativity which are close to each other in periodic table (between non-metals and non-metals).The covalent bonding is formed by sharing of outer shell electrons (i.e., s and p electrons) between atoms rather than by electron transfer.This bonding can be attained if the two atoms each share one of the other’s electrons. So the noble gas stable electron configuration can be attained.Number of covalent bonds for a particular molecule is determined by the number of valence electrons.Rarely are compounds purely ionic or covalent but are a percentage of both.

Covalent Bonding

24>

Chemistry: What is a Covalent Bond?

https://www.youtube.com/watch?v=ZxWmyZmwXtA

Covalent Bonding

25>

Covalent bonding requires that electrons be shared between atoms in such a way that each atom has its outer sp orbital filled. In silicon, with a valence of four, four covalent bondsmust be formed.

©2003 B

rooks/Cole Publishing / Thom

son Learning™

Si (Z=14): 1s22s22p63s23p2

Pure element - silicon (Si):

Covalent Bonding

26>

©2003 B


son Learning™

Covalent bonds are directional. In silicon, a tetrahedral structure is formed, with angles of 109.5° required between each covalent bond

Silicon (Si):

Covalent Bonding

27>

Dissimilar compound - methane (CH4):

Some Properties of Covalent Bonding

Covalent network substances are brittle. If sufficient force is applied to a crystal, covalent bond are broken as the lattice is distorted. Fracture failure occurs rather than deformation of a shape.

Brittleness

They are hard because the atoms are strongly bound in the lattice, and are not easily displaced.

Hardness

Poor conductors because electrons are held either on the atoms or within covalent bonds. They cannot move through the lattice.

Electricalconductivity

Very high melting points because each atom is bound by strong covalent bonds. Many covalent bonds must be broken if the solid is to be melted and a large amount of thermal energy is required for this.

Melting point and boiling point

ExplanationProperty

28>

Comparison of Ionic and Covalent Bonding

29>

Ionic-Covalent Mixed Bonding

30>

Calculation of % Ionic Character (IC):

where XA and XB are Pauling electronegativities.

( ) 1004

exp1%2

⋅⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ −−−= BA XXIC

Example: MgO XMg = 1.3 XO = 3.5

( ) ( )[ ] [ ] %2.70100298.0110021.1exp11004

3.15.3exp1%2

=⋅−=⋅−−=⋅⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ −−−=IC

Example: NaCl XNa = 0.9 XCl = 3.0

( ) ( )[ ] [ ] %8.66100332.0110010.1exp11004

9.00.3exp1%2

=⋅−=⋅−−=⋅⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛ −−−=IC

Coordination Number and Ionic Radii

31>

Coordination Number (CN) increases with

2

rcationranion

CN

< 0.155

0.155 - 0.225

0.225 - 0.414

0.414 - 0.732

0.732 - 1.0

3

4

6

8

linear

triangular

tetrahedral

octahedral

cubic

ZnS(zinc blende)

NaCl(sodium chloride)

CsCl(cesium chloride)

rcationranion

To form a stable structure, how many anions cansurround a cation?

Example - Cation-Anion Radius Ratio

32>

Determine maximum rcation/ranion for an octahedral site (C.N. = 6)

a = 2ranion

2ranion + 2rcation = 2 2ranion

ranion + rcation = 2ranion rcation = ( 2 −1)ranion

arr 222 cationanion =+

414.012anion

cation =−=rr

aMeasure the radii (blue and yellow spheres)

Substitute for “a” in the above equation

Metallic Bonding

33>

Metallic bonding is the type of bonding found in metal elements. This is the electrostatic force of attraction between positively charged ions and delocalized outer electrons. The weakness of the bonding actions in a metal is due to the enlargement of the internuclear spacing.All valence electrons in a metal combine to form a “sea” of electrons that move freely between the atom cores. A metal may be described as a cloud of free electrons. So, metals have high electrical and thermal conductivity.This type of bonding is nondirectional and is rather insensitive to structure. As a result we have a high ductility of metals - the “bonds” do not “break” when atoms are rearranged – metals can experience a significant degree of plastic deformation.The metallic bond is weaker than the ionic and the covalent bonds.

METALLIC BONDING

34>

©2003 B


son Learning™

The metallic bond forms when atoms give up their valence electrons, which then form an electron sea. The positively charged atom cores are bonded by mutual attraction to the negatively charged electrons

Metallic Bonding

35>

Chemistry: What is a Metal?

https://www.youtube.com/watch?v=vOuFTuvf4qk

Secondary Bonding or van der Walls Bonding

36>

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 dipolesbonding 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


37>

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 nucleusAtomic nucleus

Electron

cloud

Electron

cloudInstantaneous

Fluctuation


38>

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


39>

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


Permanent Dipole Bonds:

Hydrogen bonds in water

Many molecules do not have a symmetric distribution/arrangement of positive and negative charges (e.g. H2O, HCl, NH3)

40>

Solid

Liquid

Bonding Energy - Summary

41>

Atomic Bonding - Summary

42>

TypeIonic

Covalent

Metallic

Secondary

Bond EnergyLarge!

Variablelarge-Diamondsmall-Bismuth

Variablelarge-Tungstensmall-Mercury

smallest

CommentsNondirectional (ceramics)

Directional(semiconductors, ceramicspolymer chains)

Nondirectional (metals)

Directionalinter-chain (polymer)inter-molecular

CALLISTER JR, W. D. AND RETHWISCH, D. G. Materials Science and Engineering: An Introduction, 9th edition.

John Wiley & Sons, Inc. 2014, 988p. ISBN: 978-1-118-32457-8.ASHBY, M. and JONES, D. R. H.

Engineering Materials 1: An Introduction to Properties, Applications and Design. 4th Edition. Elsevier Ltd. 2012, 472p. ISBN 978-0-08-096665-6.

CALLISTER JR, W. D. AND RETHWISCH, D. G. Fundamentals of Materials Science and Engineering: An Integrated Approach, 4th ed.

John Wiley & Sons, Inc. 2012, 910p. ISBN 978-1-118-06160-2.ASKELAND, D. AND FULAY, P. Essentials of Materials Science & Engineering, 2nd Edition.

Cengage Learning. 2009, 604p. ISBN 978-0-495-24446-2.http://matterandinteractions.org/index.html

References

43Nota de aula preparada pelo Prof. Juno Gallego para a disciplina Ciência dos Materiais de Engenharia.® 2015. Permitida a impressão e divulgação. http://www.feis.unesp.br/#!/departamentos/engenharia-mecanica/grupos/maprotec/educacional/

bonding between atoms [4] - unesp

Documents