what do we understand under « electronic transport propertie »?

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

What do we understand under « electronic transport propertie »?

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.

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

Ref: Wikipedia

Ref: Heikes and UreInterscience 1961

Composition of Chromel: Ni90 Cr10

Composition of Alumel: Ni94Al3Si1Mn2

(in weight %)

Why is the thermopower of chromel (Ni90 Cr10) positive

while that

of alumel (Ni94Al3Si1Mn2 ) is negative ?

FOR WHAT IS THERMOPOWER USED?

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

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

11Massardier presentation colloque TEP INSA-LYON 2002

One has learned that TEP is used to follow microstructural transformations as function of time

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

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

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.

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.

The sample

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

One can measure automatically either the resistivity alone (right diagram). The temperature gradient is checked (left diagram). All results are recorded in excel files

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.

SOME OF OUR EXPERIMENTAL RESULTS

OUR METHODOLOGY

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

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


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

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


Rés

istiv

ité é

lect

rique

(

.cm

)

Temps(min)


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

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


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

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 475°C pendant 8H Attente à 630°C pendant 26H



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


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


Rés

istiv

ité é

lect

rique

(

.cm

)

Temps(min)


Ni38

Mo4B

18en fonction du temps

Résistivité (µohm.cm)

ABADLIA THESIS

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

Many thermodiffractograms have been measured by neutron scattering by Souberoux and coworkers at ILL

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.

DIFFERENT EXPERIMENTAL RESULTS

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


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)


Ni80P20

KHALOUK THESIS

AS FUNCTION OF TEMPERATURE

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)


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)


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

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

33

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

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.

ELECTRONIC TRANSPORT FOR LIQUID AND AMORPHOUS METALS

(AND ALLOYS)

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

37

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)

38

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

39

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

40

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

41

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

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.

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

44

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

45

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

46

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

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


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

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


THANK YOU FOR YOUR ATTENTION

what do we understand under « electronic transport propertie »?

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