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Final

MATLS 1M03 Study Guide - Final Guide: Shear Stress, Electron Mobility, Work Hardening


Department
Materials Science and Engineering
Course Code
MATLS 1M03
Professor
Joey Kish
Study Guide
Final

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Constants & Conversions
giga G 109milli m 10-3
mega M 106micro µ10-6
kilo k 103nano n 10-9
centi c 10-2 pico p 10-12
k = 1.38×10-23 J/atomK = 8.62×10-5 eV/atomK
R = 8.314 J/molK NA = 6.023×1023 atoms/mol
e = 1.602×10-19 C me = 9.11×10-31 kg
h = 6.63×10-34 Js eV = 1.602×10-19 J
Chapter 6 – Mechanical Properties of Metals
Types of stresses: Tensile, Compressive, Shear, Biaxial Tension Compression, Hydrostatic.
Stress:
0
F
A
σ
=
, Strain:
0
l
l
ε
=
Shear stress:
0
F
A
τ
=
, Shear strain:
0
tan
l
l
γ θ
= =
Stress and strain are proportional to each other using
E
σε
=
(E – Young’s Modulus) or
G
τ γ
=
(G – Shear Modulus). Physics of elasticity:
2
2
F U
Err
σ
ε
∂ ∂
=
::
,
Energy stored:
2
0
0
1
2 2
V
W V E
σ
σε
= =
, Poisson’s ratio:
(bottom of ratio – strain in direction of applied force)
( )
2 1E G
υ
= +
.
Deformation: Metallic materials deform elastically (reversible) until strains of about .005. After that, plastic (irreversible) deformation occurs. *Note: Elastic
doesn’t conserve volume, plastic does.*
Work hardening: After they yield, metals get harder to deform. Tensile Strength = Fmax / A0
Ductility: % elongation = ](lf – l0) / l0] * 100, % area reduction = [(A0 – Af) / A0] * 100
Hardness tests:
indent
indent
P
HA
:
(pressure vs. area)
Brinell:
( )
2 2
2P
HB
D D D d
π
=− −
(P-load, D-diameter of steel ball: 10 mm, d-indent diameter), Resilience:
2
2
y
R
UE
σ
=
Chapter 18 – Electrical Properties of Solids
Ohm’s Law:
V IR
=
or
J
σε
=
(σ - electrical conductivity,
1/
σρ
=
, ε - electric field intensity,
/V l
ε
=
), Resistivity:
/RAl
ρ
=
, where l is the distance where
voltage is measured, A is the area perpendicular to the direction of the current.
E kT
g
p e
:
(p–probability, #of electrons excited (holes created)), if Eg>2 eV, then p0 insulator. For semiconductors, as T, Ne.
Metals: Electron Drift Velocity
d e
v
µ ε
=
Conductivity:
e
n e
σ µ
=
(n - #free e
-
‘s, e – charge of e
-
μ- electron mobility)
T n, but µ↓ µ dominant σ (more
collisions impede movement). Resistivity (Matthiessen’s Rule):
thermal impurity dislocations
ρ ρ ρ ρ
= + +
.
T R µ↓
Semiconductors: Intrinsic (pure):
( )
e h
n e
σ µ µ
= +
(n=p), Temp. dependence:
2
0
E kT
g
n n e
=
Extrinsic (doped): n-type:
e
n e
σ µ
(excess e-, n>>p, n=#of
valence e-×#dopant atoms, add group V P); p-type:
h
p e
σ µ
(excess holes, p>>n, p=#of holes in valence×#dopant atoms, add group III Al to group IV Si).
Temp. dep.:
0
E kT
g
n n e
=
.
2E kT
g
e
e e
σ µ
=
.
For semiconductors, T σ↓ . Forward bias: Reverse bias: Capacitance charge density:
1 1 2 2
/ /
Q V
A h h
ε ε
=+
Typical conductivity
ranges – metals: 107, semiconductors: 10-4. Orbitals: s-shell: N states; p-shell: 3N states; d-shell: 5N states (2 e-/state)
Chapter 19 – Thermal Properties of Solids
Heat Capacity:
dQ
Cdt
=
, for T<θD, C=AT3; for T>θD, C=3R (θD - Debye temperature, R – gas
constant)
Thermal flux:
dT
q k dx
= −
Thermal Stress: induced by constraints, diff. matls. bonded, T gradients:
( )
room
thermal room
LT T
L
ε α
= = −
,
thermal
E E T
σ ε α
=− =
,
Cooling rate:
f
R
k
Q k T TSR
E
σ
α
= ∆ =
.
elec
k
LT
σ
=
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