Základy experimentálnych metód vo fyzike kondenzovaných látok

ZÁKLADY
EXPERIMENTÁLNYCH METÓD
vo fyzike kondenzovaných látok
Martin ORENDÁČ
V Y S O K O Š K O L S K Á U Č E B N I C A
P R Í R O D O V E D E C K Á F A K U L T A
ÚSTAV FYZIKÁLNYCH VIED, KATEDRA FYZIKY KONDENZOVANÝCH LÁTOK
K O Š I C E 2 0 1 1

ÚSTAV FYZIKÁLNYCH VIED
KATEDRA FYZIKY KONDENZOVANÝCH LÁTOK
Martin ORENDÁ
Košice 2011

ÚSTAV FYZIKÁLNYCH VIED
KATEDRA FYZIKY KONDENZOVANÝCH LÁTOK
Martin ORENDÁ
Košice 2011

ÚSTAV FYZIKÁLNYCH VIED
KATEDRA FYZIKY KONDENZOVANÝCH LÁTOK
Martin ORENDÁ
Košice 2011

ÚSTAV FYZIKÁLNYCH VIED
KATEDRA FYZIKY KONDENZOVANÝCH LÁTOK
Martin ORENDÁ
Košice 2011

5

6

A Q2
− Q1
Q1
η
= = = 1−
Q2
Q2
Q2
7

T 1 Q1
=
T2
Q2
8

9

10

11

12

13

14

ΔP
Z =
V
η
ΔP
4
ΔP ≈ 10 V η
15

16

∂S
∂S
dS = dT + dH
∂T
H ∂H
T
( ∂ M / ∂T
) H = ( ∂S
/ ∂H
) T
∂S
TdS = cH
dT + dH
∂H
T
∂S
0 = cH
dT + dH
∂H
T
M = χH = CH / T ( ∂M / ∂T
) H )
dH < 0
ΔH
ΔT
T ∂M
ΔT = − ΔH
cH
∂T
H
17

18

2
w = ε 0ε
′
ωE
ε ′
19

20

21

pV = nRT
22

dp S plyn − S kvap
=
m m
dT par V plyn −Vkvap
dp QL
p
=
2
dT par RT
p( T ) ≈ exp( −QL
/ RT )
23

24

dp p
= f ( r / λ)
dT 2T
25

ΔE
R(
T ) = R
0 exp
k BT
1
i
= Ai
( log R)
T i
26

27

2 −0.
083
0.
0442B
T
ΔT
( B)
=
0.
77
1+
0.
00237BT
0.
345
T
R( T ) = R0
exp
T0
28

29

30

31

λmax =
T
32

33

34

τ
C
=
κ
35

de
Pv = Pe + I
e(
t)
dt + D
36
dt

37

38

39

40

dQM
dV
I = = p
dt dt p
m T
V
= k B
m0
p
41

dV T 1 dm T
= k B = k B n
dt p p m0
dt p
dV
I = p
= k BTn
dt p
dQM = Vdp
dQM
dp
I = = V
dt dt V
dp dV
V = p
= pS
dt V
dt p
dp S dp S
= p = dt
dt V
p V
42

S
ln p = t + konst
V
S
p = p0
exp
t
V
I
GV =
p2
− p1
43

S
p( t)
= p∞
+ p0
exp
t
V
p∞
S( p)
= S
1−
p
44

23 pA
IV = 2.
63.
10
mT
dC(
t)
= −K1C(
t)
dt
Ev
K =
−
1 K 0 exp
k BT
45

46
( K t)
C t C0
1 exp ) ( = −
[ ] 2
dC(
t)
= −K
2 C(
t)
dt
( ) 2
2
dC(
t)
− K 2C0
=
dt 1+
C0
K 2t

dC(
t)
D
= C0
dt t
2
dC( t)
2DC0
π Dt
= exp
−
2
dt d 2d
ED
D = D
−
0 exp
k BT
D(
T2
)
p ( T2
) = p(
T1
)
D(
T1
)
47

48

49

50

51

52

z p P P P RI P + + = = 2
λ
Pλ = λ p pS(
T − T0
) S = 2πrl
4 4 ( T − T )
Pz = σ r S 0
2
2πr1
Pp = λv ( T − T0
)
l1
T − T0

54

55

56

p1
p 2 = G0
t0
2eU
vI
=
m
57
i

l0
ti
=
vi
58

M
m′ ≈ p1
Δp
f ( h)
T
59

4
M πd
Δp
m'= p − Δp
T 128ηl
2
60

( 2 1 ) T T c
P
m′
=
p −
61

62

63

64

65

66

67

68

69

px
Sef
= Acs
1−
p
70

71

p S = p S
dif dif rot rot
72

min min max max
p rot S rot > pdif
S dif
max
p min dif max
S rot > S min dif
prot
73

74

() Qt
− St
p t = p poz + 1− exp
S V
75

76

77

78

NI
H =
l
n = N / l
H = nI
nI
H =
2
2r
1+
l
79

l
l
+ a
− a
nI
H =
2
+
2
2
2
2
2 l 2 l
r + + a
r + − a
2 2
a = l / 2
nI
H =
2
r
2 1+
l
2
2
2
l
2 l
r
2 + r2
+ + a
r2
+ r2
+ − a
nI
l
2 l
2
H =
( )
+ a.
ln
+ − a.
ln
−
2
2 r
2
2 r1
2
2 l 2
2 l
r1
+ r1
+ + a
r1
+ r1
+ − a
2
2
80

81

8 NI
H =
5 5 r
2NI
NI
H = =
2π
( r + r ) π r + r
1
2
82
( )
1
2

2
1 NI NI r2
H s = dr = ln
r2
− r1
2πr
2π
( r − )
r1
1 r2
r1
Pσ
H = G
rρ
83
1
2

84

1 2
W = LI
2
85

F = I × B
86

87

88

I St
S
U B =
CB
W
2
2 2
1 I St
S 1 I St
S
B = CB
2
=
C
B 2 CB
89

90

91

∂B
∇ × E + = 0
∂t
∂D
∇ × H − = j
∂t
∇B = 0
∇D = ρ
∂ρ
∇j + = 0
∂t
92

∇ × E = iωB
∇H = −iωD
+ j
∇B = 0
∇D = ρ
D = εE
B = μH,
E( r,
t)
= E0
exp( kr
− ωt)
k
k × E = ωB
k. B = 0
k × H = −ωD
k. D = 0
2 2
( ∇ + k ) E = 0
k
k × ( k × E)
= ω( k × B)
B = μH
D = εE
2
2
k × ( k × E)
= ωμ(
k × H ) = −ω
μD
= −ω
μεE
k × ( k × E)
2
2
k × ( k × E)
= k E − ( k.
E)
k = k E
E k
( ) 0
2
k − ωμε E =
93

2
k
k − ωμε = 0 ω
=
με
k
1/ με
∂ / ∂y
= 0.
E H
1 ∂E
y
H x = −
iωμ
∂z
1 ∂E
y
H z =
iωμ
∂x
2 2 ∂ ∂ 2
+ + k = 0
2 2
E
y
∂x
∂z
1 ∂H
y
E x =
iωε
∂z
94

1 ∂H
y
E y = −
iωε
∂x
2 2 ∂ ∂ 2
+ + k = 0
2 2
H
y
∂x
∂z
∂ / ∂z
E H
ikz
H = yH
0e
μ ikz
E = x H 0e
ε
95

ikz
z
E y = E0
sin k x xe
mπ
k x =
d
2
1/
2
2 mπ
k z = k
−
d
−κz
E y = E0
sin k x xe
mπ
ω
c =
d εμ
π
2π λ
π
kc = kd > π > π < d ω
>
d
λ 2
d εμ
2π
2π
2π
kc = kd > 2π
> 2π
λ < d ω
>
d
λ
d εμ
96

ik z z
H y = H 0 cos k x xe
97

mπx
nπy
ikz
z
H z = H mn cos cos e
a b
mπx
nπy
ikz
z
Ez
= Emn
sin sin e
a b
2
2
2
2
2 mπ
nπ
mπ
nπ
k z = k − − kc = +
a b a b
98

99

100

101

102

103

104

105

u1 = A1
cosω1t
u 2 = A2
cosω 2t
2 2 2
2 2
i = a(
A1
cosω1t + A2
cosω
2t)
= a[
A1
cos ω1t
+ A2
cos ω2t
+ A1
A2
cos(
ω1
− ω2
) t]+
+ a[ A1
A2
cos( ω 1 + ω2
) t]
n
f 1 = f 2
m
106

107

Erez
Qrez = ωr
Estrat
P
vst
ζ = 10log
Pvyst
Δf = f1
− f 2
f rez
Qrez
=
Δf
108

109

110

d
= σ E + ( εE)
i E
dt
iE = ( σ + iωε
) E(
t)
ˆ ε = ε ′ − iε
′
ε ′ = ε ε ′ = σ / ω
i ˆ
E = iω
( ε ′ − iε
′
) E(
t)
= iωεE(
t)
ε ′
σ
tan( δ ) = =
ε ′ ωε
111

2
2
pE = ωε tan( δ ) E = ωε
′
E
ˆ ε = ε ′ − iε
′
Î
Q
Iˆ
= iˆ
= ′ − ′
= ′ − ′
EdS
iω
( ε iε
) Eˆ
dS
iω(
ε iε
)
ε ′
S
S
ε ′
0 0 ) / C = ( ε ′ ε C
Q = CU
C
C
Iˆ
0
i Uˆ
0
= ω ˆ ε = iω(
ε ′ − iε
′
) Uˆ
ε 0
ε 0
Zˆ
1 ωε ′
C0
= C0
+ iωε
′
Zˆ
ε 0 ε 0
ε C0
/ ε 0
C ′ x = Rx = ε 0 /( ωε
′
C0
)
εˆ
112

Î Uˆ tan(δ )
Zˆ
ε ′
1
tan( δ ) = =
ε ′ ωRC
ˆ ε = ε ′ − iε
′
0 0 ) / C = ( ε ′ ε C
113

εˆ
2
2
2 2
C 1 = ε 0πr
/ d C2 = ε 0πr
/( D − d)
C 3 = ε 0π
( R − r ) / D
ε 'C1C
2 / ε 0
C
= C0
+
ε 'C1
/ ε 0 + C2
C1C2
tan( δ D )
C1
+ C2
tan( δ k ) =
C1C2
C
+
1 C3
C2
+ C2
114

115

2
[( r + r')
/ 2]
2
C =
− ( r + r')
( x tan( x)
+ ln(cos( x)))
3.
6d
3.
6π
x = arctan[( r − r')
/ 2d]
2
C= r / 3.
6d
R − r a + d
2r 8r
a a a a
C = + ln
2 + 1+
ln1+
− ln
3.
6d
3.
6
4d
4d
4d
4d
2
π
116

117

118

119

120

2 2
2 2
r0
+ r'
+ 2r0
Rv
r0
− r'
+ 2r0
Rv
Rx
'=
RN
'=
r0
− r'
r0
+ r'
1 1 1
C x = C N + =
R R ' R '
x
121
x
N

2 2
r
0 r0
− r'
R =
x Rv
1+
r
' 2r0
Rv
r0
Rx = Rv
r'
122

123

d1
ε
'=
d 2
Cn
tg
Q Q Cd
1 1
δ =
−
1 2
124

− Eˆ
Eˆ
*
f
dV
0 f
V ´
Eˆ
Eˆ
*
1 1
dV
V ´
= ( ε´/ ε 0 −1)
− = ε´´/ ε
*
0
f
Eˆ
Eˆ
*
dV Q Q Eˆ
Eˆ
dV
0
V
0
Ê
125
V

3
ε ′ a l f 0 − f
= 1+
0.
539
ε
b h f
0
3
ε ′
a l 1 1
= 0.
269
−
ε 0 b h Q Q0
126
0

ε ′ 2(
f 0 − f )
1
= 1+
ε 0 f 0 d 1 π
π
−
cos ( 2h
+ d ) sin d
l π l
l
ε ′
1 1
1
= 2
−
ε 0 Q Q0
d 1 π
π
−
cos ( 2h
+ d ) sin d
l π
l
l
ε ′ 2 2π
2π
= tan d cot g ( l − d)
ε λ λ
0
d + α(
l − d)
1 1
tanδ
=
−
αλ0
2π
+
Q Q0
d sin
( l − d)
2π
λ0
127
0

2 2πd
−2
l − d
α
= sin cos
2π
λ λ0
128

2π
1−
iS tan xm
tanγd
λ0
λ0
= −i
γ 2πd
2π
S − i tan xm
λ0
2
2π
ˆ ε λvac
γ
= −
λvac
ε 0 λc
129

P = ( ε ′ r −1)
ε 0E
p = ε 0αE
ε r −1 = nα
nα
ε
r −1 =
nα
1−
3
130

ε T − ε ad
ˆ ε = ε ad +
1+
iωτ
ε T − ε ad
ωτ ( ε T − ε ad )
ε ′ = + ε 2 2 ad ε ′
=
2 2
1+
ω τ
1+
ω τ
131

1
sin βπ
F( τ ) =
2πτ
cosh( 1−
β ) ln( τ / τ ) cos βπ
ε T − ε ad
ˆ ε = ε ad +
β
1+
( iωτ
0 )
132
0 −

dQ
C
X = lim
T →0
dT X
T
C(
T ')
S(
T ) = dT '
T ' 0
− Ei
Z = exp
i k BT
133

A = −k
BT ln Z
2
∂A
∂ ( k BT
ln Z )
S = −
CV
= T
∂T
V
T
2
∂ V
Z = Z l Z mZ
e
1 1
∞ hν
hν
C = R 2
2
3
cosh
2
g(
υ)
dν
k BT
k BT
0
134

TE
− TE
hυ
E
g( υ) = δ ( υ −υ
E ) CV = 3R exp
TE=
T T
k B
3
2
12 4
T
hυ
D
g( υ ) = υ υ ∈ ( 0,
υ D ) C
=
5
V Rπ
TD=
TD
k B
1
f ( ε ) =
1+
exp[
( ε − ε F ) / k BT
]
135

∞
0
E = 2V εf ( ε ) N(
ε ) dε
1 2
2
E = E + π V ( k T ) N(
ε )
0 B
F
3
2 2 2
= π k VN(
ε ) T = γT
Ce B F
3
136

2
2πm
3N
AV
VN(
ε ) = 2
F
h π
α
T
C
=
−
M 1
Tc
137
1
3

138

ΔQ
ΔT
Δt = t2
− t1
P
2 1 T T T − = Δ
ΔT ΔT T1
1 2 T T
P ⋅ Δ t Q
C( TS
) = =
ΔT
ΔT
1
TS = ( T1
+ T2
)
2
ΔT
ΔT
C S
T
139

T2
Q PAR
2 1 T T
Q − QPAR
C = ΔT
−
Q
1
T () t = a + b ⋅t
b ≈
τ 1
C
τ
=
teplota
TS
T1
t1
tS
1
K1
140
t2
as

C K1
τ
1
1 0 = K ∞ → τ 1
τ 1 >> t t
τ 1 ≅ t
ΔT
tS
t1
+ t2
tS =
2
C T Δ TC T2C
T1C
− = Δ
ΔT
P ⋅Δt
T2C
+ T1C
C(
TSC
) = TSC
=
ΔT
2
C
T2C
T2
TSC
T1
T1C
t1 tS
t2 as
ΔQ
Δt
τ
teplota
141

τ τ
τ 1
τ 2

T
dT
0 = C(
T ) + K1(
T ')
dT '
dt ochl
0
P
( )
( T )
C T =
dT
dt ochl
τ 1
143

τ 1
τ 1
Tmin P
Tmax
Tmin ≅ T0
h Tmax
dT dT
P ( )
PAR + P = C T
+ K(
T ) dz
dt
dz
Tmin
c Tmax
dT dT
P ( )
PAR + 0 = C T
+ K(
T ) dz
dt dz
Tmin
P
C(
Tx
) =
h
c
dT dT
−
dt dt
dT dT
,
dt dt
τ 2

h
c
dT dT
,
dt dt
h c
dR dR
,
dt dt
h,
c
h,
c
dT dT
dR
=
dt dR
dt
ω
I = I0
⋅cos
t
2
145

Tepelný rezevoár T0
KH
Ohrieva, TH, CH
Kb
Vzorka, Ts, Cs
KT
K b
P
2
2
2
2 ω
2 ω ω
= R ⋅ I = R
I0
⋅cos
⋅t
= R ⋅ I0
⋅
cos ⋅t
= P0
⋅cos
⋅t
2 2 2
146
dT
H H
dt
H
1
0
cos
2
ω
H H S
dT
CS S = PS
= K H
dt
TH
−TS
− Kb
TS
−Tb
− KT
TS
−TT
dT
CT T
dt
= PT
= KT
TS
−TT
C = P = P ⋅ ⋅t
− K ( T −T
)
( ) ( ) ( )
( )
2
Teplomer, TT, CT

H C CT
C S
TT
() ( )
1 1 1−
δ
TT
t = Tb
+ P0
+ cos ωt
−α
2 K
b ωC
C = Cs
+ CT
+ CH
δ
CS
CT
CH
τ INT = τ T = τ
H =
KS
KT
K H
1
−
2
P 0 1 2 2 2K
b
TAC
= 1+
+ ω τ
2 2 2 +
2ωC
ω τ 3K
1
S
C
K S τ1 =
Kb
C
2 2 2 2
τ 2 = τ T + τ H + τ INT
τ 2
ωτ1
> 1 > 10ωτ
2 T p
10
ω
τ 1
Tp <
2
Tp > 60τ 2
1
2 2
ω
τ
2 2
2
ω τ1
K b
S K TAC
P0
TAC
≅
2ωC
147

Komôrka so vzorkou
Porovnávacia komôrka
dT
T = a ⋅ t + b = a = konšt.
T1 ≅ T2
≅ T0
148
Programátor ohrevu
teploty dT/dt
dt

∗
,
P
dT
P = C ⋅
dt
dT
( P + P ) = ( C K + CVZ
)
dt
∗
1
1
C1K CVZ
dT
( P P ) C K
dt
⋅ =
∗
+
2
2
K K C C1 = 2
dT
P − P = CVZ
⋅ = CVZ
⋅ a
1 2
dt
C K >> CVZ
P1 ≈ P2
CVZ
149

∂m
∂m
Δm ( ω1, ω2
) = ΔH
( ω1
) + ΔT
( ω2
, T,
CV
)
∂H
∂T
150

α d s μ
1 I 0
( )
( ω)
ΔT ω =
2
2K
σ K σ d 2
H H + S S S
CV
ρω
σ H , S = ( 1+
i)
2K
H , S
1 I 0 ( ω)
| ΔT
( ω)
| =
CV
ρωd
S 2
151

ΔM
vz 1 I 0 ω
| ΔT ( ω)
| = =
∂M
vz CV
ρωd
S 2
∂T
∂M
vz
∂T
Φ i − Φ 0
A = . 100
Φ i
152
( )

h
c
dT dT
P
A = CV
−
dt dt
153

∂T
H i = κ ij i = 1,
2,
3
∂xi
∂T
∂xi
H = −κgradT
κ = κ e + κ f + κ m
154

1
h p e f m
= w e = we
+ we
+ we
+ we
+ we
κ e
1
h p e f m
= w f = w f + w f + w f + w f + w f
κ f
1
h p e f m
= w m = wm
+ wm
+ wm
+ wm
+ wm
κ m
a b
w b = wa
1
κ e = Cev F λe
3
κ e
= L0T
σ
e
155

2
3
π k B
L0
=
3 e
f −1
f 1 f
( we ) = κ e = Cev
Fλ
e
3
f
λe
f −3
λe ≈ T
f
κ e
f −2
κ
e ≈ T
e −1
κ e ≈ T
w T
m
e ≈
−1
−2
m ∂M
T
we
≈ M
∂T
σ e
−2
w ≈ T
e
f
−3
w ≈ T
h
f
3 / 2
w T
p
f ≈
w T
f
f ≈
156

m n
wm ≈ T
−2
w ≈ T
f
e −n
m wm
≈ T
157

PH
2l
κ( Tx
) =
S(
T2
− T1
)
( T2
+ T2
'+ 2T1
)
=
T x
4
158

2
P = I ohr R
ΔT
RR =
P / A
159

160

2 2
2 2
k
k
E(
k)
= Ec
+ E(
k)
= E −
∗
v
∗
2mn
2m
p
∗
∗
mn m p
161

162

163

x
N D
x
N D = N D − N A
164

PV
nvod
=
EC
− ε F
1+
exp
k BT
165

PV
nval
=
EV
− ε F
1+
exp
k BT
n vod + nval
= PV
E V + EC
ε
F =
2
*
*
mn m p
*
EV
+ E 3 m
C
p
E F = + k BT
ln
*
2 4 mn
3
*
EF
− E
C
2πm
2
nk
BT
ni
= N C exp N = 2 2
k BT
C
h
166

*
− EF
+ E
2πm
V
pk
BT
pi
= NV
exp N 2
V =
2
k BT
h
( )
3
3
2πk
T 2
B * * − EG
n = p = m m
i i 2
4
n p exp
2
h
2k
BT
EF
− EC
− EF
+ EV
n = N C exp p = NV
exp
k BT
k BT
EF
− EC
− EF
+ EV
EV
− EC
− EG
np = N C exp NV
N C NV
= N C NV
k BT
exp
=
k BT
exp
k BT
exp
k BT
2
np = ni
n(
N A + n)
N C − ED
= exp
( N D − N A − n)
2 k BT
167
3
2

N D − N A N C − ED
n = exp
N A 2 k BT
N D − N A − ED
n = N C exp
2 k BT
D A N N n = −
168
1
2

2
ne τ n
γ n =
*
mn
γ n = neμ n
*
eτ n / mn
jx = γξ x
169

jx = nev
v
μ n = v / ξ x
γ p = peμ p μ p
γ x = γ nx + γ px
jx = ( neμ
n + peμ
p ) ξ x = γξ x γ = ( neμ n + peμ
p )
Λ = vτ
170

γ = γ 0 expα
( ξ − ξ k )
171

eξ
x
ΔE = 2e
ε
Fe = e[
ξ x + v × B]
172

m F
e F
Fm
+ Fe
= 0
−evB−eξy = 0 ξ y = −vB
ξ y
tanθ n =
ξ x
ξ y = −Bμ
nξ
x
ξ y
jx
jx
ξ y = −B
μ n = −Bμ
n = RH
Bjx
γ neμ
n
173

BI BI
U
H = RH
b = RH
ab a
U H = ξ yb
jx = I x / ab
RH = 1/
pe
j y = j yp − j yn = peμ
pξ
yp − neμ
nξ
yn
( ) 2
2
p − b n
μ n
RH = b
=
e nb + p
μ p
1 b −1
RH
=
nie
b + 1
e
v x = − ξ x − ωv
*
y
m
n
174

y = − ξ y + v
*
x
mn
e
v ω
*
ω = eB / mn
−s
τ = a(
T ) E
s = 2
s = −3/
2
1 1 1 1
= + +
τ τ f τ p τ d
τ f τ p τd
τ
175

ne τ
γ n =
2
n
*
mn
n
*
mn
e τ
μ =
∞
τ
( E)
0
τ =
∞
0
E
E
3
2
3
2
f dE
0
176
f dE
f 0 = exp( −E
/ k BT
)
2
1 τ 1
RH
= − ≡ − r
2
H
ne τ ne
rH = 1.
18
rH = 1.
93
μ H
μ H = μ nrH
Δγ
2 2 2
= ζB
γ 0 RH
γ 0
ζ
4
0
2
2
τ
ζ =
τ

N D − N A N C − ED
n =
exp
N A 2 k BT
1
2
N D − N A
n = N C
2
− ED
exp
2k
BT
N N n → −
D A
177

3 T1
Δ log n − log
2
2
0.
198
T
E
D =
[eV ]
1 1
−
.
1000
T2
T1
3 T1
Δ log n − log
4
2
0.
397
T
E
D =
[eV ]
1 1
−
.
1000
T2
T1
178

G
3
2
[ ]
Δ log RHT
E =
0.
937 eV
1000
Δ
T
179

−b
μ n,
p = an,
pT
b−3
/ 2
Δ logσ
iT
EG
= 0.
397
[ eV ]
1000
Δ
T
σ i σ i = eni ( μ n + μ p )
180

d
μ p =
ξti
rH
μ = r μ = neμ
= −R
γ
H H n
n H n
ne
1
μ p =
rH
RH
γ p
−s
τ = a(
T ) E
( T )
−a
a = aT RH γ p
Δ log | RH
γ |
a =
Δ logT
181

| R Hγ
|
μ n − μ p =
rH
| RH
γ | b
μ n =
rH
b −1
RH
γ 1
μ p =
rH
b −1
γ = γ p
γ
γ p
1
b = − r
r −1
182

−1
1
b
= −1
r −1
183

I = I 0 cosω
It
ω I = 2πf
I
B = B0
cosω
M t ω M = 2πf
M
I 0B0
= R = U cos ω − ω t + cos ω + ω t
[ ( ) ( ) ]
U H H
H 0 M I
M I
d
I 0B0
U
H 0 = RH
2d
U H = U H 0 cosω
H t
184

1 l
σ
=
R S
U = RI = RI 0 cosω
It
) T T = α −
( 1 2
U AB AB
185

186

k B 5 EC
− EF
α N = −
− s
+
e
2 k BT
k B
5 N c
α N = −
− s
+ ln
e
2 n
k B
5 eRH
α N = −
− s
+ ln N c
e
2 rH
187

188

dT
QT
= τ T j
dx
τ T τ T
189

∂α
N
τ
T = T
∂T
dQ
= Π AB I
dt
Π AB Π AB
Π AB = Tα N
Π AB
190

191

192

193

194

195

195

ISBN 978-80-7097-871-9