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General understanding of electronic transport properties in solid alloys
(amorphous and recrystallized one’s).In other words:
does this formalism developped for liquids also describe solids?
Gasser Jean-Georges1, Abadlia Lakhdar1, Khalouk Karim1, Gasser Françoise1, Kaban Ivan2, Aboki Tiburce3 and Moussa Mayoufi4.
1 Laboratoire de Physique des Milieux Denses, Université Paul Verlaine- Metz, France.2Institut für Physik Technische Universität Chemnitz Germany.
3 Laboratoire de Métallurgie Structurale ENSCP Paris.4Laboratoire de Chimie des Matériaux Inorganiques, Université Badji-Mokhtar
Annaba, Algéria
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What do we understand under « electronic transport propertie »?
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By electronic transport we understand:• The electrical resistivity. (Microscopic Ohm’s law)• The thermal conductivity. (Fourier law)• The Absolute Thermoelectric Power (ATP) or
Thermopower or Seebeck coefficient of a couple or of an element. (Device called thermocouple used for measuring temperature)
• The Peltier coefficient of a couple or of an element. (Used for a device called Peltier device for cooling objects like PC’s processors)
• The Thomson coefficient of an element.
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4
Gradient of
temperature
Gradient ofpotential
Density of heat flux
Density ofcurrent
Thermal Conductivity
ElectricalConductivity
Crossed effects: 3 thermoelectric effects:•Seebeck effect (or Absolute Thermoelectric Power)
Cause Effect Physical property
TeQ
EVJe
AAS
ThA•Thomson effect•Peltier effect
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Ref: Wikipedia
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Ref: Heikes and UreInterscience 1961
Composition of Chromel: Ni90 Cr10
Composition of Alumel: Ni94Al3Si1Mn2
(in weight %)
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Why is the thermopower of chromel (Ni90 Cr10) positive
while that
of alumel (Ni94Al3Si1Mn2 ) is negative ?
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FOR WHAT IS THERMOPOWER USED?
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THERE ARE WELL KNOWN INDUSTRIAL USE OF ELECTRONIC TRANSPORT
• The Seebeck effect is for measuring temperatures. One expects that the Seebeck coefficient is as constant as possible to be used reproducebly
• In a Peltier device, intense research is done in order to get the best figure of merit by increasing S and and decreasing
2TSZT
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THE USE OF THERMOPOWER FOR NON DESTRUCTIVE TESTING IS NOT
WELL KNOWN
A workshop has been organised in 2002 in Lyon by Kleber on this subject
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11Massardier presentation colloque TEP INSA-LYON 2002
One has learned that TEP is used to follow microstructural transformations as function of time
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Analysis of ageing of nuclear reactors steel after Houzé (INSA Lyon) TEP INSA-LYON 2002
One has learned that TEP is used to follow tempering of nuclear reactors steel
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Correlation between segregation and ThermoElectric Power (TEP) after Kleber (INSA Lyon) colloque TEP INSA-LYON 2002
One has learned that TEP is used to scan a surface. The map can be compared to that of the segregation of alloys
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These very interesting phenomena led us to examine by ourself the resistivity and
thermopower changes in solids and to try to understand and
to explain them.
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OUR NEW MEASUREMENTS• We developped an automatic system to measure
simultaneously the resistivity and thermopower of solid alloys.
It is based • On a « labview » driving program.• On a resistivity measurement method.• On a thermopower small T technique.The experiment is mounted in a furnace with a
programmable temperature regulator. The sample is put under vacuum or inert atmospher.
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The sample
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17
The labview software (registered) has been written by Françoise Gasser)
The software must be configurated. The data of the thermoelements in contact with the sample and of the thermocouples must be introduced
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One can measure automatically either the resistivity alone (right diagram). The temperature gradient is checked (left diagram). All results are recorded in excel files
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One can measure automatically the thermopower alone (right diagram). The temperature is oscillating (left diagram) between -2 and +2 Celsius around an increasing or decreasing temperature.
One can also measure simultaneously both the resistivity and the thermopower.
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SOME OF OUR EXPERIMENTAL RESULTS
OUR METHODOLOGY
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0 100 200 300 400 500 600 700 800-40
-35
-30
-25
-20
-15
-10
-5
0
5
10
25/01/10
Pouvoir thermoélectrique absolu Résistivité électrique
60
80
100
120
140
160
180
Résistivité électrique et pouvoir thermoélectrique absolu du ruban Fe 40Ni38B18Mo4 en fonction de la température
R
ésis
tivi
té é
lect
riq
ue
(µ.
cm)
Température (°C)
Po
uvo
ir t
her
mo
élec
triq
ue
abso
lu (
µV
/°C
)
In the first experiment we measured resistivity (in blue) and absolute thermoelectric power (in red) for the amorphous Fe40-Ni38-B18-Mo4 . The temperature increases and decreases is at a rate of 0.4K/minute. There is an initial change in resistivity around 380 ° C. A second one on the resistivity and the TEP above 465 ° C, a third change in slope in the resistivity and TEP occurs above 640 ° C. The increasing temperature curve is very different from the decreasing one. At room temperature resistivity was divided by 2.5 and the TEP goes from -3 to -37V/K
ABADLIA THESIS
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0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800
100
120
140
160
180
Rampe 0.4°C/min
Vide 10-2mbar
pression 1.2barCourant 20mA
Température (°C)
Résistivité électrique d'un ruban Fe40
Ni38
Mo4B
18en fonction de la température
Rés
isti
vité
éle
ctri
qu
e (.
cm)
Attente à 400°C pendant 8H
Attente à 475°C pendant 8H Attente à 630°C pendant 26H
Attente à 745°C pendant10H
Attente à 380°C pendant1H
25°C-300°C 300°C-100°C 100°C-380°C Attente à 380°C pendant 1H 380°C-400°C Attente à 400°C pendant 8H 400°C-350°C 350°C-475°C Attente à 475°C pendant 10H 475°C -632°C Attente à 632°C pendant 26H 632°C-345°C 350°C -745°C Attente 745°C pendant 10H 745°C-761°C 761°C-30°C 2ème Montée- Résistivité (µohm.cm) 2ème Descente-Résistivité (µohm.cm)
In a second experiment we carry out cycles and periods of waiting several hours at constant temperature. We first stopped at 300 ° C well below the transition temperature located (380 ° C), we decrease to 100 ° C and then go up to 380 ° C. The curves are superimposed this means that no phase transformation took place. At 380 ° C we wait 1H. We observe a small resistivity decreases. To decrease faster we increase from 20 ° C and waited 8H (see figure below). At the end of this waiting period a descent to 350 ° C and a rise to 400 ° C are superimposed. The descent blocks the evolution of the alloy up to 430 °C. Around 470 ° C the resistivity begins to increase. We then wait during 8H at 475 ° C.
ABADLIA THESIS
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0 50 100 150 200 250 300 350 400 450 500 550
161,5
162,0
162,5
163,0
163,5
164,0
164,5
165,0
Attente à 400°C pendant 8H
Rés
istiv
ité é
lect
rique
(
.cm
)
Temps(min)
Résistivité électrique d'un ruban Fe40
Ni38
Mo4B
18en fonction du temps
Résistivité (µohm.cm)
We observe, at constant temperature, a curve resembling an exponential decay which seems to reach an asymptotic value.
ABADLIA THESIS
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0 100 200 300 400 5000,8
1,0
1,2
1,4
1,6
1,8
2,0
2,2
2,4
2,6
2,8
3,0
3,2
3,4
Attente à 475°C pendant 8H
Pou
voir
ther
moé
lect
rique
abs
olu
(V
/°C
)
Pouvoir thermoélectrique absolu d'un ruban Fe40
Ni38
Mo4B
18en fonction du temps à 475°C
Temps(min)
PTA
At 475 °C the TEP increases exponentially as A(1-exp (-Bt)). The time constant is much shorter than at 400°C. After 3H no further change is observed
ABADLIA THESIS
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0 50 100 150 200 250 300 350 400 450 500 550 600 650 700 750 800
100
120
140
160
180
Rampe 0.4°C/min
Vide 10-2mbar
pression 1.2barCourant 20mA
Température (°C)
Résistivité électrique d'un ruban Fe40Ni38Mo4B18en fonction de la température
Rés
isti
vité
éle
ctri
qu
e (.
cm)
Attente à 400°C pendant 8H
Attente à 475°C pendant 8H Attente à 630°C pendant 26H
Attente à 745°C pendant10H
Attente à 380°C pendant1H
25°C-300°C 300°C-100°C 100°C-380°C Attente à 380°C pendant 1H 380°C-400°C Attente à 400°C pendant 8H 400°C-350°C 350°C-475°C Attente à 475°C pendant 10H 475°C -632°C Attente à 632°C pendant 26H 632°C-345°C 350°C -745°C Attente 745°C pendant 10H 745°C-761°C 761°C-30°C 2ème Montée- Résistivité (µohm.cm) 2ème Descente-Résistivité (µohm.cm)
Nanos grains (10 nm)
micro grains (1-10 m)
No grains (amorphous)
Observation of sample with a SEM
0 100 200 300 400 5000,8
1,0
1,2
1,4
1,6
1,8
2,0
2,2
2,4
2,6
2,8
3,0
3,2
3,4
Attente à 475°C pendant 8H
Pouvoir therm
oéle
ctr
ique a
bsolu
(V
/°C
)
Pouvoir thermoélectrique absolu d'un ruban Fe40
Ni38
Mo4B
18en fonction du temps à 475°C
Temps(min)
PTA
0 50 100 150 200 250 300 350 400 450 500 550
161,5
162,0
162,5
163,0
163,5
164,0
164,5
165,0
Attente à 400°C pendant 8H
Rés
istiv
ité é
lect
rique
(
.cm
)
Temps(min)
Résistivité électrique d'un ruban Fe40
Ni38
Mo4B
18en fonction du temps
Résistivité (µohm.cm)
ABADLIA THESIS
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35 40 45 50 55 60
MBR750_18SVbr
Inte
nsity
(arb
itrar
y)
2,16
62,
12
2,04
1,98 1,
87
1,79
1,76
1,59
2,07
8
1,81
1,67
1,61
1,66
[FeNiMo]-c[FeNiMo]23-xB6-co [FeNiMo]3B-t
u
l
uu
o
l
l
l
l ll
o
o
oo
20 30 40 50 60 70 80 90 100
MBR430-18h
Inte
nsity
(ar
bita
ry)
2,06
32,
026
1,97
1,79
9
1,26
1,32
1,07
1,02
8
1,15
2,85
[FeNiMo]-c[FeNiMo]23-xB6-co [FeNiMo]3B-t
u
uu u u
l
l l
l
l
20 40 60 80 100
MBR400-18Hsv
Inte
nsit
y (a
rbit
rary
)
2,08
4
2,05
2
2,00
71,
98
1,78
1,26
1,09
1,02
7
1,19
6
1,07
9
2,23
42,
33
2,61
2,75
3,714,11 1,
34
1,60 1,42
[FeNiMo]-c (a= 3,55 nm)[FeNiMo]23-xB6-c (a=10,66 nm)o [FeNiMo]3B-tu
u u uu
1,23
l
l
l
l
l
l
20 40 60 80 100
MBR500-18HSvbr2
Inte
nsit
y (a
rbit
rary
)
3,21
3,07 2,65 2,
432,
37 2,17
2,04
2,09
1,98
1,87 1,
791,
771,
671,
61 1,6
0
1,32 1,
31 1,28 1,
251,
22
1,18 1,
16
1,10 1,
081,
06
1,02
1,04
[FeNiMo]-c (a=3,54 nm)[FeNiMo]23-xB6-c (a=10,6 nm)o [FeNiMo]3B-tm [FeNiMo]3B-o
u
uu
uu
l
l
l l
ll
l
(422
)
(448)
l l
lo
o
o
o
o
m
m
mm
mml
o
o
om
m
mm
m ll
Recuit 18H
TEM TEM
TEM and X rays fromABOKI Tiburce
ABADLIA THESIS
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Many thermodiffractograms have been measured by neutron scattering by Souberoux and coworkers at ILL
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First conclusions
• Resistivity and TEP are very sensitive to the morphology and to the cristallinity of the alloys.
• Temperature cycles can prove that no transformation occur• A time constant due to a transformation can be measured at
constant temperature both on resistivity and on thermopower• The changes of resistivity and thermopower are correlated to a
change of crystalline structure as can be observed by SEM and TEM• The change of resistivity and thermopower are correlated to a
change of atomic structure as can be observed by X ray scattering.• An alternative technique is the thermodiffractograms measured by
neutron scattering, but everybody has not a high flux reactor in his lab.
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DIFFERENT EXPERIMENTAL RESULTS
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30
0 50 100 150 200 250 300 350 400 450 500 550 600
180
200
220
240
260
280
300
320
340
360
380
400
420
Recristallisation
Ni63,7
Zr36,3
1ère montée 1ère descente 2ème montée 2ème descente
Rés
istiv
ité (
.c
m)
Température (°C)
0 50 100 150 200 250 300 350 400 450 500 550 600
-12
-10
-8
-6
-4
-2
0
2
4
Recristallisation
Ni63,7
Zr36,3
1ère montée 1ère descente 2ème montée 2ème descente
PT
A (V
/K)
Température (°C)
Ni63.7Zr36.3
-200 -100 0 100 200 300 400 500 600 700
20
40
60
80
100
120
140
160
180
200
220Recristallisation
Ré
sist
ivité
(.
cm)
Température (°C)
1ère montée Ni80
P20
1ère descente Ni80
P20
2ème montée Ni80
P20
2ème descente Ni80
P20
COTE et al (amorphe) Ni76
P24
COTE et al (désordonné) Ni76
P24
COTE et al (cristal) Ni76
P24
0 100 200 300 400 500 600
-6
-4
-2
0
2
4
Po
uvo
ir t
he
rmo
elé
ctri
qu
e a
bso
lu (V
/K)
Température (°C)
1ère montée 1ère descente 2ème montée 2ème descente
Ni80P20
KHALOUK THESIS
AS FUNCTION OF TEMPERATURE
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31
0 100 200 300 400 500 600-16
-14
-12
-10
-8
-6
-4
-2
Fe80
Si6B
14
PT
A (
V/K
)
Température (°C)
1ère montée 1ère descente 2ème montée 2ème descente
0 100 200 300 400 500 600100
110
120
130
140
150
160
170
180
190
200
210
220
230
240
Fe80
Si6B
14
Re
sist
ivité
(.
cm)
Température (°C)
1ère montée 1ère descente 2ème montée 2ème descente
0 100 200 300 400 500 600
40
60
80
100
120
140
160
180
200
220
Ni36,5
Pd36,5
P27
1 ère montée 1 ère descente 2 ème montée 2 ème descente
Rés
istiv
ité (
.c
m)
Température (°C)
0 100 200 300 400 500 600-4
-2
0
2
4
6
Ni36,5
Pd36,5
P27
1 ère montée 1 ère descente 2 ème montée 2 ème descente
PT
A (V
/K)
Température (°C)
Ni36.5Pd36.5P27 Fe80Si6B14
KHALOUK THESIS
AS FUNCTION OF TEMPERATURE
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0 50 100 150 200 250 300 350 400 450 500 550 60080
90
100
110
120
130
140
150
160
170
180
190
200
210
220
Ni80
P20
Ré
sis
tivité
(.c
m)
Température (°C)
0 à 290°C 290 à 100°C 100 à 350°C 350 à 250°C 250 à 450°C 450 à 300°C 300 à 600°C 600 à 175°C
0 50 100 150 200 250 300 350 400 450 500 550 600
-5
-4
-3
-2
-1
0
1
2
3
Ni80
P20
Po
uvo
ir t
he
rmo
éle
ctr
iqu
e a
bso
lu (
V/K
)
Température (°C)
0 à 290°C 290 à 100°C 100 à 350°C 350 à 250°C 250 à 450°C 450 à 300°C 300 à 600°C 600 à 175°C
Ni80P20
KHALOUK THESIS As function of thermal cycles
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0 50 100 150 200 250 300 350 400 450 500 550 600 650
120140160180200220240260280300320340360380400420440460480
10H
24H
12H
Ni63,7
Zr36,3
R
ési
stiv
ité (.
cm)
Température (°C)0 50 100 150 200 250 300 350 400 450 500 550 600
300
320
340
360
380
400
420
440
10 heures
Ni63,7
Zr36,3
T=485°C
Ré
sist
ivité
(cm
)
temps (min)
0 100 200 300 400 500 600-8
-7
-6
-5
-4
-3
-2
-1
0
1
10 heures
Ni63,7
Zr36,3
T=485°C
delta T max= 10°C
PT
A (
V/K
)
temps (min)0 50 100 150 200 250 300 350 400 450 500 550 600 650
-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
2
Ni63,7
Zr36,3
12H
23H
10H
PT
A (
V/K
)
Température (°C)
As function of time at constant temperature
Ni63.7Zr36.3
KHALOUK THESIS
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Experimental conclusion:
• A resistivity and thermopower measurement device is a very powerfull tool to study phase transformations.
• Its advantage (compared to DSC) is that we can follow phase transformations at constant temperature.
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ELECTRONIC TRANSPORT FOR LIQUID AND AMORPHOUS METALS
(AND ALLOYS)
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On what is based the theory of disordered metals?
• Boltzman equation• Nearly free electron theory : density of states ≈E0.5
• Space isotropy• Short range order, high distance disorder• Scattering theory: each electron interacts with scatterers• Factorisation: In Ziman’s integral, the interaction of conduction
electrons with matter is the squared form factor (or t matrix characteristic of the scattering) times the structure factor characteristic of the relative position of the scattering sites
k
dqqEqtqake
mE
2
0
32632
2
),()(4
3
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If we crudely approximate the product : a(q)t2(q) by a
constant one can then integrate analytically. One obtains:
k
dqqEqtqake
mE
2
0
32632
2
),()(4
3
EE
Ee
TkES KB
ln
ln
3
22
m
kE
2
22
The Ziman free electron approach gives a pretty good description of the resistivity and ATP of liquid metals.
Ecte
1.
Consequence: the ATP of liquid metals is always negative
a(q)
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But some liquid metals have a positive thermopower. The 1/E resistivity curve is modulated by the maximum of the structure factor. If the Fermi energy is on the increasing side of the resistivity curve the thermopower is positive. This is the case for noble and divalent metals which present a positive thermopower
Modulation of the 1/E curve by the structure factor
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Mott proposed to correct the mean free path at the Fermi energy:
FEfree
Ziman
En
Eng
gLL
)(
)( with 2
2gZiman Faber demonstrated that :
Consequently: One can correct the calculation of at the Fermi energy
Our proposition: use the Hafner density of states to
correct the resistivity by g2(E) in the whole domain of energy, then derivate it to obtain the thermopower..
Energie
S(q)
ATP>0 ATP<0
n(E)
Free electron DOS
DOS
EF E
Resistivity
)(
)()(
2 Eg
EE Ziman
Modulation of the 1/E curve by the squarred density of states
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Mott proposed to correct the mean free path at the Fermi energy:
FEfree
Ziman
En
Eng
gLL
)(
)( with 2
2gZiman Faber demonstrated that :
Consequently: One can correct the calculation of at the Fermi energy
Our proposition: use the Hafner density of states to
correct the resistivity by g2(E) in the whole domain of energy, then derivate it to obtain the thermopower..
Energie
S(q)
ATP>0 ATP<0
n(E)
Free electron DOS
DOS
EF E
Resistivity
)(
)()(
2 Eg
EE Ziman
Modulation of the 1/E curve by the squarred density of states
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0,0 0,2 0,4 0,6 0,8 1,00
50
100
150
200
exp=205.cm
Figure 4
Mn T=1260°C
LDA + Spin GGA-PBE + Spin Indicates the resistivity
at the calculated Fermi energy
Res
istiv
ity (
.cm
)
Energy (Rydberg)
The squared t matrix has a résonance for transition metals.
If the Fermi energy is on the left side of the resonnance (the thermopower is positive (Sc, Ti)
If it is on the right side the TEP is negative (nickel).
Zrouri thesis
Modulation of the 1/E curve by the resonant scattering
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To summarize, the resistivity versus energy curve is a 1/E function modulated by :
• the structure factor• the ratio of the squared density of states divided by the free electron density of states • the squared t matrix (resonant scattering for transition metals
The ATP is positive on the left side of each of these modulating functions.
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What changes in solids?• For monocristals, the space is no more isotropic.• There is a « large distance » ordering• The electronic « transport properties » are very
sensitive to physical and mechanical properties.• The change of resistivity can be very important• The change of thermopower can be very important• The sign of the thermopower is not understood.
Electronic Transport properties are used for non destructive testing in industry
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0 5 10 15 20 25 30 35120
130
140
150
160
170
180 Résistivité PTA
Temps (heures)
Rés
istiv
ité (
.cm
)
-10
-8
-6
-4
420°C
PT
A (
V/K
)Fe82Si2B16
KHALOUK THESIS
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Fe82Si2B16
10 20 30 40 50 60 70 80 902, degrees
amorphous
8 hrs
10 hrs
3 hrs
1 hour
annealing 0.25 hr
13 hrs
35 hrs
24 hrs
26 hrs
0
9000
18000
27000
36000
45000
а)
(330
)
(321
)
(222
)
(310
)
(220
)(211
)
(200
)
(110
)
0
0
0
0
0
0
0
0
0
F e 8 2
S i 2 B
1 6
420°C
Kaban’s structure factor
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Fe82Si2B16
2kF
0 5 10 15 20 25 30 35120
130
140
150
160
170
180 Résistivité PTA
Temps (heures)
Rés
istiv
ité (
.cm
)
-10
-8
-6
-4
420°C
PT
A (
V/K
)
After 20H, the structure no more changes
KHALOUK THESIS
0.25H
16 and 20H
12H
1H
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2 4 6 8 100
1
2
3
4
5
Ge15Te
85 Polycrystalline Amorphous
Y A
xis
Titl
e
X Axis Title
Ge-Te may be interpreted within this scheme
Kaban’s structure factor
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Physical interpretation
• The four last slides are the (at least qualitative) experimental proof that the Faber-Ziman formalism can also be used for crystalline solids
• As for liquid and amorphous materials, the resistivity versus energy curve is modulated by the (sharper) structure factor
• The position of the Fermi energy in the resistivity versus energy curve is the crucial point
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At the beginning of this presentation I asked :
Why is the thermopower of chromel (Ni90 Cr10) positive
while that
of alumel (Ni94Al3Si1Mn2 ) is negative ?
My answer is that very probably: impurities (Cr or Al…) move the Fermi energy from the left (chromel) to the right (alumel) side of a nickel structure factor peak as on the figure
2 4 6 8 100
1
2
3
4
5
Ge15Te
85 Polycrystalline Amorphous
Y A
xis
Titl
e
X Axis Title
Kaban’s structure factor
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THANK YOU FOR YOUR ATTENTION
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