MSE 310
Elec Props of Matls
Elementary Materials Science Concepts
‰ Atomic Structure:
L shell with
two subshells
Nucleus
s
p
d
f
n
Shell
---------------------------------------------------------------------------------------------------1
K
2
2
L
2
6
3
M
2
6
10
4
N
2
6
10
14
----------------------------------------------------------------------------------------------------
1s
K
L
Table 1.1
Maximum possible number of electrons in the shells and subshells of an atom.
---------------------------------------------------------------------------------------------------Subshell
l =
0
1
2
3
2s
2p
1s22s22p2 or [He]2s22p2
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)
Fig. 1.1: The shell model of the atom in which the electrons are
confined to live within certain shells and in subshells within shells.
http://Materials.Usask.Ca
From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap (© McGraw-Hill, 2002)
http://Materials.Usask.Ca
Additional Information:
See: Chapter 2
Materials Science and Engineering – An
Introduction, William D. Callister, Jr. 6th Ed
or 7th Ed (Wiley, 2003)
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MSE 310
Elec Props of Matls
Atomic Structure
‰ Quantum Mechanics:
9 Electron orbitals are described by a probability distribution.
9 The orbitals/probability distribution are characterized by 4 parameters
call Quantum numbers.
9 Quantum numbers describe the size, shape and spatial orientation of
an e-’s probability distribution/density.
9 The Quantum Numbers are: n, l, ml, ms
o n: (principle quantum number)
•
•
•
•
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also called a shell or Bohr orbit.
can have integral values: 1, 2, 3, …
n is related the the size & energy of the orbital.
As n increases, the orbital becomes larger & the e- spends more time further
from the nucleus, and the energy is less negative.
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MSE 310
Elec Props of Matls
Atomic Structure
‰ Quantum Mechanics:
9 The Quantum Numbers are: n, l, ml, ms
o l: (azimuthal quantum number)
• Also called a subshell (of the shell, n)
• can have integral values from 0 to n-1 for each value of n.
» l = 0, 1, 2, …, (n-1) (known as a selection rule)
• This quantum number relates to the shape of atomic orbital.
• The value of l for a particular orbital is commonly assigned a letter:
» l=0 is called s;
l=1 is called p;
l=2 is called d;
l=3 is called f
o ml: (magnetic quantum number)
• Can have integral values between l & –l, including zero.
» m = -l, …, -2, -1, 0, +1, +2, …, +l
(known as a selection rule)
• The value of ml relates to the orientation of the orbital in space relative to the
other orbitals in the atom.
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MSE 310
Elec Props of Matls
3
Atomic Structure
‰ Quantum Mechanics:
9 The Quantum Numbers are: n, l, ml, ms
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S. Zumdahl, Chemistry (Heath, 1986)
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2
MSE 310
Elec Props of Matls
Atomic Structure
‰ Quantum Mechanics:
9 The Quantum Numbers are: n, l, ml, ms
o ms: (electron spin magnetic number)
• Can have the value 1/2 or -1/2
» ms = ±½ (selection rule)
• Explains the electron's magnetic moment with two possible orientation
• Often described as "spin up" (1/2) or spin down (-1/2)
9 What is the consequence or result of ms?
• In a given atom, no two e-'s can have
the same set of four quantum numbers.
• An orbital defined by n, l, mj, can hold only
two e-'s, and they must have opposite spins.
PauliExclusion
Exclusion
Pauli
Principle:
Principle:
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MSE 310
Elec Props of Matls
Atomic Structure
‰ Quantum Mechanics:
ml
ms
ml = m
ms = s/h
Eqn. 2-46 refers
to selection rules
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Streetman & Banerjee, Solid State Electronic Devices (Prentice Hall, 2000)
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MSE 310
Elec Props of Matls
Atomic Structure
‰ Quantum Mechanics:
9 From the 1st 2 Quantum Numbers, n and l, we can determine the
electronic configuration of atoms which is logically followed by the
periodic table – how e-’s fill sub-orbitals.
9 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, …
9 1s2, 2s2, 2p6, 3s2, 3p6, 3d10, 4s2, 4p6, 4d10, …
9 H: 1s1
o
o
o
o
o
o
o
o
o
He: 1s2
Li: 1s2, 2s1
Be: 1s2, 2s2
B: 1s2, 2s2, 2p1
C: 1s2, 2s2, 2p2
N: 1s2, 2s2, 2p3
O: 1s2, 2s2, 2p4
Cl: 1s2, 2s2, 2p5
Ne: 1s2, 2s2, 2p6
SubOrbital
Value of l
quantum
number
Number
of states
s
0
2
p
1
6
d
2
10
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MSE 310
Elec Props of Matls
Atomic Structure
halogens
noble
gases
alkaline earth metals
alkali metals
‰ Atomic Structure – Periodic Table
transition metals
103
Lr
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104
Rf
105
Db
106
Sg
107
Bh
108
Hs
109
Mt
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MSE 310
Elec Props of Matls
Atomic Structure
‰ Atomic Structure – Periodic Table
9 Electronic configuration
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MSE 310
Elec Props of Matls
S. Zumdahl, Chemistry (Heath, 1986)
9
Atomic Structure
‰ Atomic Structure – Periodic Table
9 Electronic configuration
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S. Zumdahl, Chemistry (Heath, 1986)
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MSE 310
Elec Props of Matls
Atomic Structure
‰ Atomic Structure – Periodic Table
9 Electronic configuration
S. Zumdahl, Chemistry (Heath, 1986)
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MSE 310
Elec Props of Matls
Atomic Structure
‰ Atomic Structure – Periodic Table
9 Electronic configuration:
o Aufbau Principle: Just as protons are added one by one to the nucleus to build
up the elements, electrons are similarly added to these hydrogen like orbitals.
Element Elec. Conf.
1s 1
H:
He:
1s 2
Li:
1s 22s 1
Be:
1s 22s 2
B:
1s 22s 22p1
C:
1s 22s 12p2
N:
1s 22s 12p3
O:
1s 22s 12p4
F:
1s 22s 12p5
1s
2s
↑
↑↓
↑↓
↑↓
↑↓
↑↓
↑↓
↑↓
↑↓
↑
↑↓
↑↓
↑↓
↑↓
↑↓
↑↓
2p
↑
↑
↑
↑↓
↑↓
↑
↑
↑
↑↓
↑
↑
↑
o Hund’s Rule: the lowest energy configuration for an atom is the one having the
maximum number of unpaired electrons allowed by the Pauli Exclusion Principle
in a particualr set of degenerate orbitals.
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o Degenerate orbitals: orbitals that have the same energy (same n, l, ml).
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MSE 310
Elec Props of Matls
Atomic Structure
‰ Atomic Structure – Periodic Table & Periodic Trends
9 Atomic Radius
S. Zumdahl, Chemistry (Heath, 1986)
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