Tuller-2001 27• Temperature dependence of the resonance frequency fR of a resonator device with difference mass loads.. Stefanik – Transport-Defect chemistry correlations • Gas Sensor
Trang 13.225 © H.L Tuller-2001 27
• Temperature dependence of the resonance frequency (fR)
of a resonator device with difference mass loads
0 100 200 300 400 500 600 700 800
1,71
1,72
1,73
1,74
1,75
1,76
1,77
Contact 1 (fCo1) Contact 2 (fCo2)
Calculation fCo1+ ∆ ∆ mCo2)
T [°C]
f A
Ongoing Activities
• Resonator (Langasite) H.Seh & H Fritze
– Defect chemistry
– Oxygen diffusion/exchange studies
– Bulk conductivity dependence on T and PO2
• Active Layer (PCO) T Stefanik
– Transport-Defect chemistry correlations
• Gas Sensor
– Add active layer (PCO) using PLD ⇒ nanocrystalline vs
Trang 21
Magnetic Materials
• The inductor
(
Law) s Faraday' (explicit 1
Theorem) s (Green'
density
flux
magnetic
1 1
(CGS)
1
t
c
d
E
V
d
E
EdS
t c BdS t
c
EdS
t
B
c
E
B B
B
∂
Φ
∂
−
⋅
=
⋅
=
×
∇
≡
Φ
∂
−
=
∂
∂
−
×
∇
∂
∂
−
=
×
∇
∫
∫
∫∫
∫∫
∫∫
l
l
Φ
=
=
=
⋅
=
∂
∂
=
=
∂
∂
=
∂
∂
=
∂
∂
−
=
∂ Φ
∂
−
=
∂
∂
=
∂ Φ
∂
=
= Φ
∫
∫
2
2
2 1
2
1 2
1 Energy
Power
capacitor) for the
(recall
CV) (Q
CV capacitor
I N LI LIdI dt Power t
I LI VI
t
V C I t
I L V
t
I L t
N V
t
I L t LI
B
B EMF
B B
2
The Inductor
lA n c I
BA N I
N L
nl length n
N
In c B
I c dS J c d B BdS
t
E c
J c B
4
4 4
1 4
π φ
π
π π
π
=
=
=
=
⋅
=
=
=
⋅
=
⋅
=
×
∇
∂
∂ +
=
×
∇
∫∫
)
Trang 33
Insert magnetic material
Magnetic dipoles in material can line-up in magnetic field
M H H H
B magnetic induction
χ magnetic susceptibility
H magnetic field strength (applied field)
M magnetization
H B M
B
H
M H
M
µ
π
πχ µ
χ
χ
= +
=
+
=
=
∂
∂
=
1
4
4
1
MKS:
Magnetic Permeability and Susceptibility
Maxwell and Magnetic Materials
• Ampere’s law
• For a permanent magnet, there is no real current
flow; if we use B, there is a need for a fictitious
current (magnetization current)
• Magnetic material inserted inside inductor
increases inductance
0
=
=
⋅
∫ H l d I
( ) π χ
π πχ πχ
π
lA
n c
I
N
L
A
In
c HA
MA
BA
B
B
2 2
4
4 4 4
4
~
=
Φ
=
=
=
=
Paramagnetic +10-5-10-4
-8 -5
Trang 45
Microscopic Source of Magnetization
• No monopoles
• magnetic dipole comes from moving or spinning electrons
µ
L
A
e-I
µ is the magnetic dipole moment
θ µ
E Energy = = −r ⋅ r= −
What is µ ? For θ =0,
2
2
2
2
2
and
~
L loop 1 for and
~ energy since
r
c
e
r
A
c
e
I
IA HAI
I
H
HA dS
H
I LI
I H
E
B
B
B
B
ω
µ
π
π
ω
µ
µ
µ
−
=
=
−
=
=
∴
= Φ
=
∴
⋅
=
Φ
Φ
= Φ
−
≈
−
=
∫∫
Orbital Angular Momentum
6
• Classical mechanics gives orbital angular momentum as:
Microscopic Source of Magnetization
l
l
h
h
r
r
r
l , , 0,
2
2
2
2
−
=
=
=
−
=
−
=
−
=
=
×
=
m
L
mc
e
L
L
mc
e
L
mc
e
mr p
r
L
Z
B
Z B Z QM
L
µ
µ
µ
ω
E(H=0)
+ µ B H
- µ B H
0
Example for l=1:
Spin Moment µs
spin electron for
2
2
1
2
0
0
0
=
±
=
=
−
=
−
=
−
=
g m
S
S g
S
mc
e g
S
mc
e
S
Z
Z B
z M
Q
E(H=0)
-(1/2) µ B g0H +(1/2) µ B g0H
Trang 5Exchange
Fe, Ni, Co -> J positive!
Other elements J is negative Rule of Thumb:
5 1 radius) 2(atomic
distance c
interatomi
a
r r
J is a function of distance!
8
Ferromagnetism
M
T
0.37 -0.33
≈
−
∝
≈
−
∝
χ
β
γ β
T
T
T
T T
T
M
C
C
H B=H+4 π M
‘normal’ paramagnet
Br, Ms
Hc
Irreversible boundary displacement Domain rotation
reversible boundary displacement
Easy induction, “softer”
Magentic anisotropy
hardness of loop dependent on crystal direction comes from spin interacting with bonding
Trang 69
Domains in Ferromagnetic Materials
B
M
N
S
Magnetic energy
dV
B
∫
= 2
8
1
Magnetic domain Domain wall or boundary
N N
N N
S S
S
Flux closure
No external field
S