1. Introduction to Materials Science and Engineering
Chapter 2 Atomic Structure and Interatomic Bonding
ISSUES TO ADDRESS...
• What promotes bonding?
• What types of bonds are there?
• What properties are inferred from bonding?

2. Contents Introduction 1 Atomic Structure 2
Bonds – Ionic, Covalent, and Metallic
Secondary Bonds – Van der Waals and
Hydrogen 3 1 2 4
Introduction

3. Atomic Structure:
As I mentioned in the first lecture, the property of material is not the property of atoms composed of the material, but is critically depends on the types of atomic bonding which, in turn, is critically dependent on the valence electrons (outermost electrons in an atom).
In order to deduce the types of bonding, we have to understand the electronic structure of atoms.

4. Transmission Electron Atomic Force Microscope
Atom – visibility:
GaN
Transmission Electron
microscope
Au, (111) surface
Atomic Force Microscope

5. Contents Introduction 1 Atomic Structure 2
Bonds – Ionic, Covalent, and Metallic
Secondary Bonds – Van der Waals and
Hydrogen 3 1 2 4
Introduction

6. Early Atomic Model: 1858 : cathode ray identified by Pluker
1869 : negative charge of cathode ray identified by Hittorf
1874 : momentum of cathode ray detected by Crookes
1876 : cathode ray named by Goldstein
1890 : electron named by Stony
1897 : properties of cathode ray  electron by J. J. Thomson
1906
electron

7. Bohr’s model: To resolve the discontinuous emission spectra...
Bohr, Niels ( )
To resolve the discontinuous emission spectra...
Assumptions :
Quantum condition
Frequency condition

8. Bohr Atom: Nucleus ; Z = # protons
= 1 for hydrogen to 94 for plutonium
N = # neutrons
Atomic mass A ~ Z + N

9. Bohr Atom:
electrons & protons are electrically charged: 1.60 x C
mass-proton = mass-neutron = 1.67 x kg
mass-electron = 9.11 x kg
atomic number (Z) = # protons
atomic mass = mass-protons + mass-neutrons
# of protons: same for all atoms of an element
# of neutrons is variable  “isotopes” (elements with 2 or more atomic masses)
atomic weight = weighted average of the atom’s isotopes
the atomic weight of an element may be specified as mass/mole of material
1 amu = 1/12 atomic mass of carbon 12 (12C)
1 mole = x 1023 (Avogadro’s number) atoms or molecules
1 amu/atom (or molecule) = 1 g/mol

10. Wave- Particle Duality of Electron:
What is an electron? – we experience merely the actions of electrons, e.g., television screen (particle-like) or in an electron microscope (wave-like), showing particle-like and wave-like behavior of electrons, respectively.
Light
Electron
1887
Hertz: photoelectric effect
1905
Einstein: PE effect interpretation
1897
J.J. Thompson
Proposed particle-like nature of electron
m0 ~ 1/2000 H
e = 1.6 x C
1910
E. Rutherford
Proposed atomic structure
Tiny solar system
Electrons moving around positive charge center
1924
De Brogile
Proposed the idea that wave-like duality of electrons
lp=h (Matter Wave)
1926
Schrodinger
develops a mathmatical form
1927
Davisson and Germer
Discover electron diffraction
1928
G.P. Thompson
The concept of energy quanta for light is proposed.

11. Derivation of Schrodinger Equation:
Matter wave equation is expressed as a harmonic wave form:
Energy(E) Momentum(p)
Particle: mv
Wave:
Since, E=
(time-dependent Schrodinger equation)

12. Derivation of Schrodinger Equation:
At stationary state – time independent state
We are asking what energy states are allowed.
We can write,
Then, (time-independent Schrodinger equation)
Solution:
Choose desired potential energy V(x, y, z)
Get the general solution of y(x, y, z)
Retain only mathematically well behaved terms
single valued
not=0
continuous and continuous derivatives
finite
4. Apply boundary condition - En

13. Wave Equation to Hydrogen Atom:
참고자료
Wave Equation to Hydrogen Atom:
... From the solution of the wave function, three quantum numbers result ...  n, l, ml

14. Quantum Numbers:
n principal quantum number 1, 2, 3, 4, --- (K, L, M, N, ---)
Determines the effective volume of an electron orbital
Distance of an electron from the nucleus, position of an electron
l azimuthal quantum number 0, 1, 2, 3, 4, ---, (n-1) (s, p, d, f)
Determines the angular momentum of the electron
Shape of electron subshell, shape of electron distribution
ml magnetic quantum number 0, ±1, ±2, ---, ±l
Determines the orientation of the orbital
ms spin quantum number ½, -½
Pauli exclusion principle
No two interacting entities can have the same set of the quantum numbers ...  Each orbital will hold up to two electrons
There can never be more than one electron in the same quantum state
Only one electron can be in a particular quantum state at a given time
Each electron state cannot hold more than two electrons with opposite spins

15. Meaning of Quantum Numbers:
n determines the size:
l determines the shape:
ml=-1,0,1
ml=-2,-1,0,1,2
ml determines the orientation:

16. Additional Quantum Number:
Electron spin :
Therefore, complete description of
an electron requires 4 quantum numbers
Pauli exclusion principle:
... No two interacting entities can have the same set of the quantum numbers ...
 Each orbital will hold up to two electrons

17. 참고자료
The complete set of quantum numbers for each of the 11 electrons in sodium:
© 2003 Brooks/Cole Publishing / Thomson Learning™

18. Electron Energy States:
Electrons...
have discrete energy states
tend to occupy lowest available energy state.

19. Stable Electron Configurations:
have complete s and p subshells
tend to be unreactive.

20. Survey of Elements:
Most elements: Electron configuration is not stable
Why? Valence (outer) shell usually not filled completely

21. 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)
1s2 2s2 2p2
valence electrons

22. Electronic Configurations:
ex: Fe - atomic # = 26
1s2 2s2 2p6 3s2 3p6
3d 6 4s2
valence
electrons 1s 2s 2p
K-shell n = 1
L-shell n = 2 3s 3p
M-shell n = 3 3d 4s 4p 4d
Energy
N-shell n = 4
Adapted from Fig. 2.4, Callister 7e.

24. The Periodic Table: • Columns: Similar Valence Structure give up 1e
inert gases
accept 1e
accept 2e O Se Te Po At I Br He Ne Ar Kr Xe Rn F Cl S Li Be H Na Mg Ba Cs Ra Fr Ca K Sc Sr Rb Y
Electropositive elements:
Readily give up electrons
to become + ions.
Electronegative elements:
Readily acquire electrons
to become - ions.
Adapted from Fig. 2.6, Callister 7e.

25. Electronegativity: Smaller electronegativity Larger electronegativity
• Ranges from 0.7 to 4.0,
• Large values: tendency to acquire electrons.
Smaller electronegativity
Larger electronegativity
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.

26. Bonding: primary bonding ionic bonding covalent bonding
metallic bonding
secondary bonding
van der Waals
hydrogen bonding

27. Atomic Bondings:  Metallic bonding  Covalent bonding
When more than two atoms get closer ... Especially in case of atoms of the kind ...
When atoms with less valence electrons are brought together, each atom tends to form ‘ closed shell ’ structure by abandoning less bound free electrons
 Metallic bonding
Free electron
Shared electron
When atoms with many valence electrons are brought together, each atom tends to form ‘ closed shell ’ structure by sharing electrons belonging to neighbor atoms
 Covalent bonding

28. Atomic Bondings:  Ionic bonding
When atoms of far- & near-closed shell structure are brought together ...
Atoms of far-closed shell structure & near-closed one tend to lose & gain electrons, respectively
 Electronegativity by L. Pauling
Excess charge induced by the transfer of electrons are compensated by the presence of ions of opposite sign
 Ionic bonding

29. Secondary Bonding: + - asymmetric electron clouds -general case:
Arises from interaction between dipoles
• Fluctuating dipoles
asymmetric electron
clouds + -
secondary
bonding H 2
ex: liquid H
Adapted from Fig. 2.13, Callister 7e.
• Permanent dipoles-molecule induced + -
-general case:
secondary
bonding
Adapted from Fig. 2.14,
Callister 7e. Cl Cl
-ex: liquid HCl
secondary H H
bonding
secondary bonding
-ex: polymer
secondary bonding

30. Ionic Bonding: r A B EN = EA + ER =
Energy – minimum energy most stable
Energy balance of attractive and repulsive terms r A n B
EN = EA + ER = -
Attractive energy EA
Net energy EN
Repulsive energy ER
Interatomic separation r
Adapted from Fig. 2.8(b), Callister 7e.

31. Potential Energy E + Force F -
Derivation of equilibrium distance of inter-atomic distance with A and B unknown
Force F -

32. Bonding Forces & Energies:
참고자료
- Covalent bonding
: nucleus to electrons
: nucleus to nucleus
: electrons to electrons
- Ionic bonding
: electrostatic attraction between unlike ions
: closed shell overlapping

33. Potential Well Concept:
Long-range attractive
Short-range repulsive

34. Properties from Bonding:
Thermal expansion  asymmetric nature of the energy well
Broad well (generally more asymmetric)  larger expansion

35. Properties from Bonding:
... Temperature supplies thermal energy into solids ...  thermal vibration (phonon)
Slope is related to the thermal expansion coefficient of materials

36. Contents Introduction 1 Atomic Structure 2
Bonds – Ionic, Covalent, and Metallic
Secondary Bonds – Van der Waals and
Hydrogen 3 1 2 4
Introduction

37. Ionic Bonding: Occurs between + and - ions Requires electron transfer
Large difference in electronegativity required
An ionic bond is created between two unlike atoms with different electronegativities
When sodium donates its valence electron to chlorine, each becomes an ion; attraction occurs, and the ionic bond is formed

38. Examples: Ionic Bonding:
• Predominant bonding in Ceramics
NaCl
MgO
Give up electrons
Acquire electrons
CaF 2
CsCl
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.

39. Ionic Bonding:

40. Ionic Crystal: Na Cl
N molecules
each positive ion is surrounded by several negative ions and vice versa

41. Ionic Crystal: strong infrared absorption
transparency in visible wavelength
low electrical conductivity at low temp but good ionic conductivity at high temp
non-directional in nature
maximum number of neighbors (packing density)

42. Contents Introduction 1 Atomic Structure 2
Bonds – Ionic, Covalent, and Metallic
Secondary Bonds – Van der Waals and
Hydrogen 3 1 2 4
Introduction

43. Covalent Bonding: shared electrons from carbon atom C H from hydrogen
similar electronegativity  share electrons
bonds determined by valence – s & p orbitals dominate bonding
Example: CH4
shared electrons
from carbon atom
from hydrogen
atoms H C CH 4
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.

44. Covalent Bonding:
The tetrahedral structure of silica (Si02), which contains covalent bonds between silicon and oxygen atoms

45. Covalent Bonding:
Calculation of bonding angle
Covalent bonds are directional. In silicon, a tetrahedral structure is formed, with angles of 109.5° required between each covalent bond.

46. Example : Covalent Bonding:
molecules with nonmetals
molecules with metals and nonmetals
elemental solids (RHS of Periodic Table)
compound solids (about column IVA)

47. Covalent Bonding: bond energy curve
strong directional nature of bonding
high hardness
High (Diamond) or low (Bismuth) melting point
low electrical conductivities at low temperatures

48. Ionic vs. Covalent Bonding:
many compounds-partially ionic and partially covalent
degree of bond type - electronegativity
a large difference in electronegativity  largely ionic
similar electronegativity  largely covalent

49. Contents Introduction 1 Atomic Structure 2
Bonds – Ionic, Covalent, and Metallic
Secondary Bonds – Van der Waals and
Hydrogen 3 1 2 4
Introduction

50. Metallic Bonding:
Arises from a sea of donated valence electrons (1, 2, or 3 from each atom)
Primary bond for metals and their alloys

51. Metallic Bonding: delocalized electron
Free electrons act as a “glue” to hold the ion core

52. Metallic Bonding:
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.

53. Metallic Bonding:
When voltage is applied to a metal, the electrons in the electron sea can easily move and carry a current.

54. Contents Introduction 1 Atomic Structure 2
Bonds – Ionic, Covalent, and Metallic
Secondary Bonds – Van der Waals and
Hydrogen 3 1 2 4
Introduction

55. Van der Waals bonding:  van der Waals bonding
Although electrons have tendency of being separated as far as possible due to e-e repulsion, electrons are constantly in motion
It follows that electrons could get close enough to induce a “electric dipole moment” at atomistic level
This tendency is expected to be more significant as the number of electrons increases
Temporal bonding due to the induced electric dipole
 van der Waals bonding

56. Van der Waals Bonding: induced dipole permanent dipole
(polar molecule)

57. Van der Waals Bonding:
dipole-dipole interaction

58. Contents Introduction 1 Atomic Structure 2
Bonds – Ionic, Covalent, and Metallic
Secondary Bonds – Van der Waals and
Hydrogen 3 1 2 4
Introduction

59. Hydrogen Bonding:
When one of the components of covalent bonding is hydrogen ...
Since hydrogen atom has only one electron, there is no electron left for the formation of closed shell
 Bare proton is exposed without being shielded by electrons ...
 Strong ionic character develops locally about hydrogen atom ...
... Strong bonding develops ...

60. Hydrogen Bonding: H2O H2S NH3 Strongest secondary bonding
Positively charged Hydrogen ion forms a bridge between two negatively charged ions

61. Materials-Bonding Classification:

62. Summary: Primary Bonds:
Ceramics
Large bond energy
large Tm
large E
small a
(Ionic & covalent bonding):
Metals
Variable bond energy
moderate Tm
moderate E
moderate a
(Metallic bonding):
Polymers
Directional Properties
Secondary bonding dominates
small Tm
small E
large a
(Covalent & Secondary):
secondary bonding

63. Summary: Bonding: Type Bond Energy Comments Ionic Large!
Nondirectional (ceramics)
Covalent
Variable
Directional
(semiconductors, ceramics
polymer chains)
large-Diamond
small-Bismuth
Metallic
Variable
large-Tungsten
Nondirectional (metals)
small-Mercury
Secondary
smallest
Directional
inter-chain (polymer)
inter-molecular