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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

This preview shows half of the first page. to view the full 1 pages of the document. 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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