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- Review of Atomic Structure
Electrons, Protons, Neutrons, Quantum mechanics
of atoms, Electron states, The Periodic Table
Bonding Energies and Forces
- Periodic Table
- Primary Interatomic Bonds
Ionic
Covalent
Metallic
- Secondary Bonding (Van der Waals) Three types of Dipole Bonds
- Molecules and Molecular Solids
Chapter Outline
Understanding of interatomic bonding is the first step
towards understanding/explaining materials properties
Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding
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Atoms = nucleus (protons and neutrons) + electrons
Review of Atomic Structure
Charges:
Electrons (-) and protons (+) have negative and positive charges of the same magnitude, 1.6 × 10-19^ Coulombs.
Neutrons are electrically neutral.
Masses:
Protons and Neutrons have the same mass, 1.67 × 10 -27^ kg.
Mass of an electron is much smaller, 9.11 × 10 -31^ kg and can be neglected in calculation of atomic mass.
# protons gives chemical identification of the element
# protons = atomic number (Z)
# neutrons defines isotope number
The atomic mass (A) = mass of protons + mass of
neutrons
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Atomic mass units. Atomic weight.
The atomic mass unit (amu) is often used to express atomic weight. 1 amu is defined as 1/12 of the atomic mass of the most common isotope of carbon atom that has 6 protons (Z=6) and six neutrons (N=6).
Mproton ≈ Mneutron = 1.66 x 10 -24^ g = 1 amu.
The atomic mass of the 12 C atom is 12 amu.
The atomic weight of an element = weighted average of the atomic masses of the atoms naturally occurring isotopes. Atomic weight of carbon is 12.011 amu.
The atomic weight is often specified in mass per mole.
A mole is the amount of matter that has a mass in grams equal to the atomic mass in amu of the atoms (A mole of carbon has a mass of 12 grams).
The number of atoms in a mole is called the Avogadro number, N (^) av = 6.023 × 10^23.
N (^) av = 1 gram/1 amu.
Example: Atomic weight of iron = 55.85 amu/atom = 55.85 g/mol
Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding
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The number of atoms per cm^3 , n, for material of density d (g/cm^3 ) and atomic mass M (g/mol):
n = N (^) av × d / M
Graphite (carbon): d = 2.3 g/cm^3 , M = 12 g/mol n = 6×10 23 atoms/mol × 2.3 g/cm^3 / 12 g/mol = 11.5 × 10^22 atoms/cm^3
Diamond (carbon): d = 3.5 g/cm^3 , M = 12 g/mol n = 6×10^23 atoms/mol × 3.5 g/cm^3 / 12 g/mol = 17.5 × 10^22 atoms/cm^3
Water (H 2 O) d = 1 g/cm^3 , M = 18 g/mol n = 6×10 23 molecules/mol × 1 g/cm 3 / 18 g/mol = 3.3 × 10 22 molecules/cm^3
For material with n = 6 × 10^22 atoms/cm^3 we can calculate mean distance between atoms L = (1/n)1/3^ = 0.25 nm. the scale of atomic structures in solids – a fraction of 1 nm or a few A.
Some simple calculations
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Recall Isotopes
C^12 where 12 = 6 Protons + 6 Neutrons
C^13 where 13 = 6 Protons + 7 Neutrons (Isotope)
Isotopic abundance of C 13 ≈ 1.1 %
Carbon: 12.01 g/mol
Atoms having the same atomic number but varying
numbers of neutrons are isotopes
Mass of basic particles: Particle Charge Mass (amu) (1.66x10 -24^ or 1/Nav) Proton +1 1.00814 (1.6734x10 -24 g) Neutron 0 1.00898 (1.675x10 -24 g) Electron -1 0.00055 (0.000911x10 -24 g) The atomic mass unit (amu) is the basic unit of measurement of an atom’s mass, one amu = (1/12)^12 C 6 (1 amu = 1. x 10 -24 g)
Atomic Structure
Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding
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Electrons in Atoms (II)
¾ The quantum numbers arise from solution of
Schrodinger’s equation
¾ Pauli Exclusion Principle: only one electron can
have a given set of the four quantum numbers.
The Number of Available Electron States in Some of the Electron Shells and Subshells
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Electrons in Atoms (III)
¾ Electrons that occupy the outermost filled shell – the valence electrons – they are responsible for bonding.
¾ Electrons fill quantum levels in order of increasing energy (due to electron penetration)
Example: Iron, Z = 26: 1s^2 2s 2 2p 6 3s^2 3p 6 3d 6 4s 2
Subshells by energy: 1s,2s,2p,3s,3p,4s,3d,4s,4p,5s,4d,5p,6s,4f,…
1s
2s sp
3s 3p 3d
4s 4p 4d 4f
5s 5p 5d 5f
6s 6p 6d
7s 7p
Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding
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Periodic Table - Electronegativity
Electronegativity - a measure of how willing atoms are to accept electrons
Subshells with one electron - low electronegativity Subshells with one missing electron -high electronegativity
Electronegativity increases from left to right
Metals are electropositive – they can give up their few valence electrons to become positively charged ions
The electronegativity values.
Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding
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Bonding Energies and Forces
repulsion
equilibrium
attraction
This is typical potential well for two interacting atoms
The repulsion between atoms, when they are brought close to each other, is related to the Pauli principle: when the electronic clouds surrounding the atoms starts to overlap, the energy of the system increases abruptly.
The origin of the attractive part, dominating at large distances, depends on the particular type of bonding.
Potential Energy, E
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Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding
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But what does it mean??
Bonding Behavior
(a) High melting temperature, high elastic modulus, low thermal expansion coefficient
(b) Low melting temperature, low elastic modulus, high thermal expansion coefficient
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Types of Bonding
Primary bonding: e -^ are transferred or shared Strong (100-1000 KJ/mol or 1-10 eV/atom)
¾ Ionic: Strong Coulomb interaction among negative atoms (have an extra electron each) and positive atoms (lost an electron). Example - Na +Cl-
¾ Covalent: electrons are shared between the molecules, to saturate the valency. Example - H (^2)
¾ Metallic: the atoms are ionized, loosing some electrons from the valence band. Those electrons form a electron sea, which binds the charged nuclei in place
Secondary Bonding: no e -^ transferred or shared Interaction of atomic/molecular dipoles Weak (< 100 KJ/mol or < 1 eV/atom)
¾ Fluctuating Induced Dipole (inert gases, H 2 , Cl 2 …)
¾ Permanent dipole bonds (polar molecules - H 2 O, HCl...)
¾ Polar molecule-induced dipole bonds (a polar molecule like induce a dipole in a nearby nonpolar atom/molecule)
Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding
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Ionic Bonding (I)
Formation of ionic bond:
- Mutual ionization occurs by electron transfer (remember electronegativity table)
- Ion = charged atom
- Anion = negatively charged atom
- Cation = positively charged atom
- Ions are attracted by strong coulombic interaction
- Oppositely charged atoms attract
- An ionic bond is non-directional (ions may be attracted to one another in any direction
Example: NaCl
11 Protons Na
Electron Configuration?
17 Protons Cl Electron Configuration?
Na (metal) unstable
Cl (nonmetal) unstable electron
+ - Coulombic Attraction
Na (cation) stable
Cl (anion) stable
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Ionic Bonding (II)
- Electron transfer reduces the energy of the system of atoms, that is, electron transfer is energetically favorable
- Note relative sizes of ions: Na shrinks and Cl expands
Na Cl
e -
Na +^ Cl -
Ionic bonds: very strong, nondirectional bonds
Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding
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Predominant bonding in Ceramics
Give up electrons Acquire electrons
He- Ne
**- Ar- Kr
Xe
Rn-**
**F
Cl
Br
I
At 2.**
**Li
0.9Na K
0.8Rb Cs
0.7Fr**
**2.1H 1.5Be Mg
Ca
Sr
Ba
0.9Ra**
1.5Ti 1.6Cr 1.8Fe 1.8Ni 1.8Zn 2.0As
CsCl
MgO CaF
NaCl
3.5O
Adapted from Fig. 2.7,Callister 6e. (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.
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Whereas the metallic and ionic CN is based on size
and hard sphere
Packing, covalent bonding is based on a different set
of rules.
Hard sphere model r/R CN
(ionic, metallic) 0.732 ≤ r/R<1 8
r/R = 1 12
•Covalent bond model: 8-N, N = number of valence
electrons
El. Config. X’tal structure # valence e-^ 8-N C (1S) 2 2S 2 2P^2 diamond cubic 4 4 Si ..3S 2 3P^2 diamond cubic 4 4 GaAs Ga ..4S 2 4P^1 zinc blend 4 average 4 As.. 4S 2 4P^3
Covalent Bonding (II)
Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding
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Covalent Bonding (III)
Example: Carbon materials. Z (^) c = 6 (1S^2 2S^2 2P^2 ) N’ = 4, 8 - N’ = 4 → can form up to four covalent bonds
ethylene molecule:
polyethylene molecule:
ethylene mer
diamond: (each C atom has four covalent bonds with four other carbon atoms)
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Example : Hybridization
•Diamond if covalently-bonded carbon
•Expected CN=12 (if ionic, equal sizes, r/R = 1)
•Observed CN=4 (“tetrahedral” coordination)
Explanation : directional bonding
•Outer shell electrons 2s and 2p hybridize to form
4equally-spaced orbitals
•Reason: greater orbital overlap possible
Covalent Bonding (IV)
Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding
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He
**- Ne
Ar- Kr- Xe- Rn -**
**F
Cl
2.8Br 2.5I 2.2At**
**Li
Na
K
Rb0. 0.7Cs 0.7Fr**
2.1H 1.5Be 1.2Mg 1.0Ca 1.0Sr 0.9Ba Ra 0.
1.5Ti 1.6Cr 1.8Fe Ni1.8 Zn1.8 As2.
SiC
C(diamond)
H2O
2.5C
H
Cl
F
1.8Si Ga1.
GaAs
1.8Ge
O 2.
column IVA
1.8Sn Pb 1.
Adapted from Fig. 2.7,Callister 6e. (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.
EXAMPLES: COVALENT
BONDING
+ - secondarybonding + -
H Cl secondarybonding H Cl
secondary bonding
H H HH
H2 H
secondary bonding
asymmetric electron ex: liquid H 2 clouds
+ - secondary+ -
bonding
-general case:
-ex: liquid HCl
-ex: polymer
Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding
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Secondary Bonding (II)
Example: hydrogen bond in water. The H end of the molecule is positively charged and can bond to the negative side of another H 2 O molecule (the O side of the H 2 O dipole)
“Hydrogen bond” – secondary bond formed between two permanent dipoles in adjacent water molecules.
O
H H
Dipole
-
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Secondary Bonding (III)
Hydrogen bonding in liquid water from a molecular-level simulation
Molecules: Primary bonds inside, secondary bonds
among each other
Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding
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Secondary Bonding (IV)
The Crystal Structures of Ice
Hexagonal Symmetry of Ice Snowflakes
Figures by Paul R. Howell
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- Coefficient of thermal expansion, α - α ~ symmetry at ro
α is larger if E o is smaller.
PROPERTIES FROM BONDING: α
∆ L
length, Lo unheated, T
heated, T
= α (T 2 -T 1 )
∆ L
Lo
coeff. thermal expansion
r
smaller α
larger α
Energy
r o
secondary b
Large bond energy
large T m large E small α
Variable bond energy
moderate Tm moderate E moderate α
Directional Properties
Secondary bonding dominates small T small E large α
SUMMARY: PRIMARY BONDS
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Summary (III)
¾ Atomic mass unit (amu) ¾ Atomic number ¾ Atomic weight ¾ Bonding energy ¾ Coulombic force ¾ Covalent bond ¾ Dipole (electric) ¾ Electron state ¾ Electronegative ¾ Electropositive ¾ Hydrogen bond ¾ Ionic bond ¾ Metallic bond ¾ Mole ¾ Molecule ¾ Periodic table ¾ Polar molecule ¾ Primary bonding ¾ Secondary bonding ¾ Van der Waals bond ¾ Valence electron
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