NANO106 is UCSD Department of NanoEngineering's core course on crystallography of materials taught by Prof Shyue Ping Ong. For more information, visit the course wiki at http://nano106.wikispaces.com.

1. Bonding in Materials
Shyue Ping Ong
Department of NanoEngineering
University of California, San Diego

2. Periodic Table of the Elements
NANO 106 - Crystallography of Materials by Shyue Ping Ong - Lecture 7
2
Periodic Table of Elements
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
1
1
Hydrogen
1.00794
H
1
Atomic #
Name
Atomic Weight
Symbol
C Solid
Hg Liquid
H Gas
Rf Unknown
Metals Nonmetals
Alkalimetals
Alkaline
earthmetals
Lanthanoids
Transition
metals
Poormetals
Other
nonmetals
Noblegases
Actinoids
2
Helium
4.002602
He
2 K
2
3
Lithium
6.941
Li
2
1 4
Beryllium
9.012182
Be
2
2 5
Boron
10.811
B
2
3 6
Carbon
12.0107
C
2
4 7
Nitrogen
14.0067
N
2
5 8
Oxygen
15.9994
O
2
6 9
Fluorine
18.9984032
F
2
7 10
Neon
20.1797
Ne
2
8
K
L
3
11
Sodium
22.98976928
Na
2
8
1
12
Magnesium
24.3050
Mg
2
8
2
13
Aluminium
26.9815386
Al
2
8
3
14
Silicon
28.0855
Si
2
8
4
15
Phosphorus
30.973762
P
2
8
5
16
Sulfur
32.065
S
2
8
6
17
Chlorine
35.453
Cl
2
8
7
18
Argon
39.948
Ar
2
8
8
K
L
M
4
19
Potassium
39.0983
K
2
8
8
1
20
Calcium
40.078
Ca
2
8
8
2
21
Scandium
44.955912
Sc
2
8
9
2
22
Titanium
47.867
Ti
2
8
10
2
23
Vanadium
50.9415
V
2
8
11
2
24
Chromium
51.9961
Cr
2
8
13
1
25
Manganese
54.938045
Mn
2
8
13
2
26
Iron
55.845
Fe
2
8
14
2
27
Cobalt
58.933195
Co
2
8
15
2
28
Nickel
58.6934
Ni
2
8
16
2
29
Copper
63.546
Cu
2
8
18
1
30
Zinc
65.38
Zn
2
8
18
2
31
Gallium
69.723
Ga
2
8
18
3
32
Germanium
72.63
Ge
2
8
18
4
33
Arsenic
74.92160
As
2
8
18
5
34
Selenium
78.96
Se
2
8
18
6
35
Bromine
79.904
Br
2
8
18
7
36
Krypton
83.798
Kr
2
8
18
8
K
L
M
N
5
37
Rubidium
85.4678
Rb
2
8
18
8
1
38
Strontium
87.62
Sr
2
8
18
8
2
39
Yttrium
88.90585
Y
2
8
18
9
2
40
Zirconium
91.224
Zr
2
8
18
10
2
41
Niobium
92.90638
Nb
2
8
18
12
1
42
Molybdenum
95.96
Mo
2
8
18
13
1
43
Technetium
(97.9072)
Tc
2
8
18
14
1
44
Ruthenium
101.07
Ru
2
8
18
15
1
45
Rhodium
102.90550
Rh
2
8
18
16
1
46
Palladium
106.42
Pd
2
8
18
18
0
47
Silver
107.8682
Ag
2
8
18
18
1
48
Cadmium
112.411
Cd
2
8
18
18
2
49
Indium
114.818
In
2
8
18
18
3
50
Tin
118.710
Sn
2
8
18
18
4
51
Antimony
121.760
Sb
2
8
18
18
5
52
Tellurium
127.60
Te
2
8
18
18
6
53
Iodine
126.90447
I
2
8
18
18
7
54
Xenon
131.293
Xe
2
8
18
18
8
K
L
M
N
O
6
55
Caesium
132.9054519
Cs
2
8
18
18
8
1
56
Barium
137.327
Ba
2
8
18
18
8
2
57–71
72
Hafnium
178.49
Hf
2
8
18
32
10
2
73
Tantalum
180.94788
Ta
2
8
18
32
11
2
74
Tungsten
183.84
W
2
8
18
32
12
2
75
Rhenium
186.207
Re
2
8
18
32
13
2
76
Osmium
190.23
Os
2
8
18
32
14
2
77
Iridium
192.217
Ir
2
8
18
32
15
2
78
Platinum
195.084
Pt
2
8
18
32
17
1
79
Gold
196.966569
Au
2
8
18
32
18
1
80
Mercury
200.59
Hg
2
8
18
32
18
2
81
Thallium
204.3833
Tl
2
8
18
32
18
3
82
Lead
207.2
Pb
2
8
18
32
18
4
83
Bismuth
208.98040
Bi
2
8
18
32
18
5
84
Polonium
(208.9824)
Po
2
8
18
32
18
6
85
Astatine
(209.9871)
At
2
8
18
32
18
7
86
Radon
(222.0176)
Rn
2
8
18
32
18
8
K
L
M
N
O
P
7
87
Francium
(223)
Fr
2
8
18
32
18
8
1
88
Radium
(226)
Ra
2
8
18
32
18
8
2
89–103
104
Rutherfordium
(261)
Rf
2
8
18
32
32
10
2
105
Dubnium
(262)
Db
2
8
18
32
32
11
2
106
Seaborgium
(266)
Sg
2
8
18
32
32
12
2
107
Bohrium
(264)
Bh
2
8
18
32
32
13
2
108
Hassium
(277)
Hs
2
8
18
32
32
14
2
109
Meitnerium
(268)
Mt
2
8
18
32
32
15
2
110
Darmstadtium
(271)
Ds
2
8
18
32
32
17
1
111
Roentgenium
(272)
Rg
2
8
18
32
32
18
1
112
Copernicium
(285)
Cn
2
8
18
32
32
18
2
113
Ununtrium
(284)
Uut
2
8
18
32
32
18
3
114
Flerovium
(289)
Fl
2
8
18
32
32
18
4
115
Ununpentium
(288)
Uup
2
8
18
32
32
18
5
116
Livermorium
(292)
Lv
2
8
18
32
32
18
6
117
Ununseptium
Uus
118
Ununoctium
(294)
Uuo
2
8
18
32
32
18
8
K
L
M
N
O
P
Q
For elements with no stable isotopes, the mass number of the isotope with the longest half-life is in parentheses.
Periodic Table Design and Interface Copyright © 1997 Michael Dayah. http://www.ptable.com/ Last updated: May 9, 2013
57
Lanthanum
138.90547
La
2
8
18
18
9
2
58
Cerium
140.116
Ce
2
8
18
19
9
2
59
140.90765
Pr
2
8
18
21
8
2
60
Neodymium
144.242
Nd
2
8
18
22
8
2
61
Promethium
(145)
Pm
2
8
18
23
8
2
62
Samarium
150.36
Sm
2
8
18
24
8
2
63
Europium
151.964
Eu
2
8
18
25
8
2
64
Gadolinium
157.25
Gd
2
8
18
25
9
2
65
Terbium
158.92535
Tb
2
8
18
27
8
2
66
Dysprosium
162.500
Dy
2
8
18
28
8
2
67
Holmium
164.93032
Ho
2
8
18
29
8
2
68
Erbium
167.259
Er
2
8
18
30
8
2
69
Thulium
168.93421
Tm
2
8
18
31
8
2
70
Ytterbium
173.054
Yb
2
8
18
32
8
2
71
Lutetium
174.9668
Lu
2
8
18
32
9
2
89
Actinium
(227)
Ac
2
8
18
32
18
9
2
90
Thorium
232.03806
Th
2
8
18
32
18
10
2
91
Protactinium
231.03588
Pa
2
8
18
32
20
9
2
92
Uranium
238.02891
U
2
8
18
32
21
9
2
93
Neptunium
(237)
Np
2
8
18
32
22
9
2
94
Plutonium
(244)
Pu
2
8
18
32
24
8
2
95
Americium
(243)
Am
2
8
18
32
25
8
2
96
Curium
(247)
Cm
2
8
18
32
25
9
2
97
Berkelium
(247)
Bk
2
8
18
32
27
8
2
98
Californium
(251)
Cf
2
8
18
32
28
8
2
99
Einsteinium
(252)
Es
2
8
18
32
29
8
2
100
Fermium
(257)
Fm
2
8
18
32
30
8
2
101
Mendelevium
(258)
Md
2
8
18
32
31
8
2
102
Nobelium
(259)
No
2
8
18
32
32
8
2
103
Lawrencium
(262)
Lr
2
8
18
32
32
9
2
Michael Dayah For a fully interactive experience, visit www.ptable.com. michael@dayah.com
Praseodymium

3. Electronegativity
¡ Electronegativity, symbol χ, is a chemical property
that describes the tendency of an atom to attract
electrons (or electron density) towards itself.
¡ The electronegativity difference Δχ between two
atoms determine how likely one atom will rob the
other of electrons, and this in turn determines what
kind of bonds are formed between two atoms.
¡ Large Δχ è Ionic bonds
¡ Small Δχ è Covalent bonds
NANO 106 - Crystallography of Materials by Shyue Ping Ong - Lecture 7
3

4. Measures of Electronegativity
¡ Pauling electronegativity
¡ Most commonly used definition based on valence bond theory
¡ Difference in A-B bond strength vs A-A and B-B bond strength
¡ Arbitrary reference is H, set at 2.20.
¡ Mulliken electronegativity
¡ Arithmetic mean of the first
ionization energy and the
electron affinity
¡ Also known as absolute
electronegativity
NANO 106 - Crystallography of Materials by Shyue Ping Ong - Lecture 7
4

5. Ionic bonding
¡Bonding involving electrostatic attraction
between oppositely charge ions.
¡Non-directional, and geometry tends to follow
maximum packing rules. Often leads to much
higher coordination numbers.
¡Large Δχ
¡Example: LiF
¡ Pauling χLi = 1.0, χF = 3.98
¡ Li “donates” an electron to F to form Li+ and F-
¡ Both Li+ and F- have highly stable full octet
NANO 106 - Crystallography of Materials by Shyue Ping Ong - Lecture 7
5

6. Covalent bonding
¡ Bonding that involves sharing of electron pairs
between atoms, typically to achieve stable full outer
shell
¡ Highly directional, with geometry determined by
Valence shell electron pair repulsion VSEPR rules
¡ Favored by small Δχ
¡ Example: H2 molecule
¡ The two H shares two electrons, forming a full He shell for each
H.
NANO 106 - Crystallography of Materials by Shyue Ping Ong - Lecture 7
6

7. Other types of bonds
¡Metallic bonds
¡ Metals readily give up their weakly bound outer
electron(s) to become positive ions in a “sea” of
electrons.
¡ Valence electrons are not closely associated with any
particular atom, resulting in free motion and high
electrical conductivity.
¡Van Der Waals bonds
¡ Due to small instantaneous charge redistributions, which
cause an effective polarization of the molecule, i.e.
centers of gravity of positive and negative charges do
not coincide.
¡ Polarization result in effective attractive force.
NANO 106 - Crystallography of Materials by Shyue Ping Ong - Lecture 7
7

8. Pauling’s rules
¡Five rules published by Linus Pauling in 1929
for determining the crystal structures of
complex ionic crystals.
¡Before we discuss these rules, it is important to
first establish the concept of atomic and ionic
radii.
NANO 106 - Crystallography of Materials by Shyue Ping Ong - Lecture 7
8

9. Atomic and ionic radii
¡Size of an atom / ion depends on size of nucleus
and number of valence electrons
¡Atoms with larger number of electrons generally
have a larger size than atoms with smaller
number of electrons
¡Size of ions ≠ Size of atoms as ions have gained or
lost electrons
¡ As charge on ion increases, there will be less electrons
and the ion will have a smaller radius.
¡ As the atomic number increases in any given column of
the Periodic Table, the number of protons and electrons
increases and thus the size of the atom or ion increases.
NANO 106 - Crystallography of Materials by Shyue Ping Ong - Lecture 7
9

10. Determination of Ionic Radii
¡X-ray crystallography (final third of course)
can provide distances between ions.
¡However, this does not tell us where the
boundary between ions are, and hence does
not provide information on ionic radii.
¡One trick is therefore to choose ions that are
extremely different in size, e.g. Li+ and I-. In LiI,
the Li+ are effectively in the interstitial sites
with the I- touching each other, allowing one
to determine the radii of I-
NANO 106 - Crystallography of Materials by Shyue Ping Ong - Lecture 7
10

11. Trends in Ionic Radii
NANO 106 - Crystallography of Materials by Shyue Ping Ong - Lecture 7
11

12. Pauling’s First Rule
¡ A coordinated polyhedron of anions is formed about
each cation, the cation-anion distance determined
by the sum of ionic radii and the coordination
number by the radius ratio.
¡ Derived purely from geometric considerations of
sphere packing
NANO 106 - Crystallography of Materials by Shyue Ping Ong - Lecture 7
12
Applying Pythagoras’
theorem, we get Rx/Rz
= 0.732

13. Coordination and radius ratios
NANO 106 - Crystallography of Materials by Shyue Ping Ong - Lecture 7
13
Radius ratio C.N. polyhedron
0.225 4 tetrahedron
0.414 6 octahedron
0.592 7 capped octahedron
0.645 8 square antiprism (anticube)
0.732 8 cube
0.732 9 triaugmented triangular prism
1 12 cuboctahedron

14. Pauling’s Second Rule: The
electrostatic valence rule
¡ An ionic structure will be stable to the extent that the
sum of the strengths of the electrostatic bonds that
reach an anion equal the charge on that anion, i.e.,
a stable ionic structure must be arranged to preserve
local electroneutrality.
¡ Electrostatic valency is defined as charge on ion /
coordination number
where εis the charge of the anion and the summation
is over the adjacent cations.
NANO 106 - Crystallography of Materials by Shyue Ping Ong - Lecture 7
14
ε = si
i
∑

15. Pauling’s Third Rule
¡ The sharing of edges and particularly faces by two anion
polyhedra decreases the stability of an ionic structure.
Sharing of corners does not decrease stability as much, so
(for example) octahedra may share corners with one
another.
¡ Effect is largest for cations with high charge and low C.N.
(especially when r+/r- approaches the lower limit of the
polyhedral stability).
¡ Vertex-sharing between tetrahedra or octahedra is energetically
stable
¡ Edge-sharing between polyhedra is less stable; rare for
tetrahedra, more common for octahedra
¡ Face-sharing (2 cations share 3 anions) between polyhedra is
unstable; never occurs for tetrahedra; rare for octahedra
NANO 106 - Crystallography of Materials by Shyue Ping Ong - Lecture 7
15

16. Pauling’s Fourth Rule
¡In a crystal containing different cations, those
of high valency and small coordination
number tend not to share polyhedron
elements with one another.
NANO 106 - Crystallography of Materials by Shyue Ping Ong - Lecture 7
16

17. Pauling’s Fifth Rule: The rule of
parsimony
¡ The number of essentially different kinds of
constituents in a crystal tends to be small. The
repeating units will tend to be identical because
each atom in the structure is most stable in a specific
environment. There may be two or three types of
polyhedra, such as tetrahedra or octahedra, but
there will not be many different types.
NANO 106 - Crystallography of Materials by Shyue Ping Ong - Lecture 7
17