UCSD NANO106 - 10 - Bonding in Materials

Bonding in MaterialsShyue Ping OngDepartment of NanoEngineeringUniversity of California, San Diego

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

11

Hydrogen 1.00794

H1 Atomic #

Name Atomic Weight

SymbolC Solid

Hg Liquid

H Gas

Rf Unknown

Metals NonmetalsAlkali metals

Alkalineearth m

etals

Lanthanoids

Transition m

etals

Poor metals

Other

nonmetals

Noble gasesActinoids

2

Helium 4.002602

He2 K

23

Lithium 6.941

Li21 4

Beryllium 9.012182

Be22 5

Boron 10.811

B23 6

Carbon 12.0107

C24 7

Nitrogen 14.0067

N25 8

Oxygen 15.9994

O26 9

Fluorine 18.9984032

F27 10

Neon 20.1797

Ne28

KL

311

Sodium 22.98976928

Na281

12

Magnesium 24.3050

Mg282

13

Aluminium 26.9815386

Al283

14

Silicon28.0855

Si284

15

Phosphorus 30.973762

P285

16

Sulfur 32.065

S286

17

Chlorine 35.453

Cl287

18

Argon 39.948

Ar288

KLM

419

Potassium 39.0983

K2881

20

Calcium 40.078

Ca2882

21

Scandium 44.955912

Sc2892

22

Titanium 47.867

Ti28

102

23

Vanadium 50.9415

V28

112

24

Chromium 51.9961

Cr28

131

25

Manganese 54.938045

Mn28

132

26

Iron 55.845

Fe28

142

27

Cobalt 58.933195

Co28

152

28

Nickel58.6934

Ni28

162

29

Copper 63.546

Cu28

181

30

Zinc 65.38

Zn28

182

31

Gallium 69.723

Ga28

183

32

Germanium 72.63

Ge28

184

33

Arsenic 74.92160

As28

185

34

Selenium 78.96

Se28

186

35

Bromine 79.904

Br28

187

36

Krypton 83.798

Kr28

188

KLMN

537

Rubidium 85.4678

Rb28

1881

38

Strontium 87.62

Sr28

1882

39

Yttrium 88.90585

Y28

1892

40

Zirconium 91.224

Zr28

1810

2

41

Niobium 92.90638

Nb28

1812

1

42

Molybdenum95.96

Mo28

1813

1

43

Technetium (97.9072)

Tc28

1814

1

44

Ruthenium 101.07

Ru28

1815

1

45

Rhodium 102.90550

Rh28

1816

1

46

Palladium 106.42

Pd28

1818

0

47

Silver 107.8682

Ag28

1818

1

48

Cadmium 112.411

Cd28

1818

2

49

Indium 114.818

In28

1818

3

50

Tin 118.710

Sn28

1818

4

51

Antimony 121.760

Sb28

1818

5

52

Tellurium 127.60

Te28

1818

6

53

Iodine 126.90447

I28

1818

7

54

Xenon 131.293

Xe28

1818

8

KLMNO

655

Caesium 132.9054519

Cs28

1818

81

56

Barium 137.327

Ba28

1818

82

57–7172

Hafnium 178.49

Hf28

183210

2

73

Tantalum 180.94788

Ta28

183211

2

74

Tungsten 183.84

W28

183212

2

75

Rhenium 186.207

Re28

183213

2

76

Osmium 190.23

Os28

183214

2

77

Iridium 192.217

Ir28

183215

2

78

Platinum 195.084

Pt28

183217

1

79

Gold 196.966569

Au28

183218

1

80

Mercury 200.59

Hg28

183218

2

81

Thallium 204.3833

Tl28

183218

3

82

Lead 207.2

Pb28

183218

4

83

Bismuth 208.98040

Bi28

183218

5

84

Polonium (208.9824)

Po28

183218

6

85

Astatine (209.9871)

At28

183218

7

86

Radon (222.0176)

Rn28

183218

8

KLMNOP

787

Francium (223)

Fr28

183218

81

88

Radium (226)

Ra28

183218

82

89–103104

Rutherfordium (261)

Rf28

18323210

2

105

Dubnium (262)

Db28

18323211

2

106

Seaborgium (266)

Sg28

18323212

2

107

Bohrium (264)

Bh28

18323213

2

108

Hassium (277)

Hs28

18323214

2

109

Meitnerium (268)

Mt28

18323215

2

110

Darmstadtium (271)

Ds28

18323217

1

111

Roentgenium (272)

Rg28

18323218

1

112

Copernicium(285)

Cn28

18323218

2

113

Ununtrium (284)

Uut28

18323218

3

114

Flerovium(289)

Fl28

18323218

4

115

Ununpentium (288)

Uup28

18323218

5

116

Livermorium(292)

Lv28

18323218

6

117

Ununseptium Uus

118

Ununoctium (294)

Uuo28

18323218

8

KLMNOPQ

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

La28

1818

92

58

Cerium 140.116

Ce28

1819

92

59

140.90765

Pr28

1821

82

60

Neodymium 144.242

Nd28

1822

82

61

Promethium (145)

Pm28

1823

82

62

Samarium 150.36

Sm28

1824

82

63

Europium 151.964

Eu28

1825

82

64

Gadolinium 157.25

Gd28

1825

92

65

Terbium 158.92535

Tb28

1827

82

66

Dysprosium 162.500

Dy28

1828

82

67

Holmium 164.93032

Ho28

1829

82

68

Erbium 167.259

Er28

1830

82

69

Thulium 168.93421

Tm28

1831

82

70

Ytterbium 173.054

Yb28

1832

82

71

Lutetium 174.9668

Lu28

1832

92

89

Actinium (227)

Ac28

183218

92

90

Thorium 232.03806

Th28

18321810

2

91

Protactinium 231.03588

Pa28

183220

92

92

Uranium 238.02891

U28

183221

92

93

Neptunium (237)

Np28

183222

92

94

Plutonium (244)

Pu28

183224

82

95

Americium (243)

Am28

183225

82

96

Curium (247)

Cm28

183225

92

97

Berkelium (247)

Bk28

183227

82

98

Californium (251)

Cf28

183228

82

99

Einsteinium (252)

Es28

183229

82

100

Fermium (257)

Fm28

183230

82

101

Mendelevium (258)

Md28

183231

82

102

Nobelium (259)

No28

183232

82

103

Lawrencium (262)

Lr28

183232

92

Michael Dayah For a fully interactive experience, visit www.ptable.com. [email protected]

Praseodymium

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 Δχè Ionic bonds¡ Small Δχè Covalent bonds


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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


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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


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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.


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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.


7

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.


8

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.


9

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-


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Trends in Ionic Radii


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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


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Applying Pythagoras’ theorem, we get Rx/Rz= 0.732

Coordination and radius ratios


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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

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.


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ε = sii∑

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


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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.


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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.


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UCSD NANO106 - 10 - Bonding in Materials

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