thermoelectricity measuring...

1

J. Hej tmánek and K. KnížekInstitute of Physics of ASCR, v.v.i. , Na Slovance 2, 182 21 PRAHA 8, CZ

Location: Cukrovarnicka 10, Prague 6, 162 53

[email protected], phone +420 2 303 18 419, fax +420 2 333 43 184

WWW: www.fzu.cz

Measuring thermal and thermoelectric properties- principles, measuring techniques

and analysis

2

Thermoelectric materials

Thermoelectricity-Thermoelectric conversion of energy – characteristics - Electrical resistivity-Thermoelectric power-Thermal conductivity, thermal diffusivity (Wiedemann-Franz law in “non metals”)

Measuring techniques – compendium of measuring techniques and analysis

--Low temperature systemsLow temperature systems – commercial (Quantum Design), Thermal transport option & home made inset (5-350 K), magnetic field -Home made sample holders objective to measure all thermoelectric characteristics simultaneously on one specimen (each specimen unique character) -close cycle refrigerators: Leybold ( 300>T>12 K) Janis (300> T>3.5 K) – snags,

(temperature fluctuations, parasite heat flow,..), calibration, reliability

-Home made High temperature cellsHigh temperature cells, principle, difficulties,calibration, reliability

3

(λ,α,ρ,κ)

λ,α,ρ,κ &

F= Distance/Area

E=V/Distance; J=I/Area

#

λλλλraw = Rheater I2/∆T*F

λλλλ = λλλλraw -λλλλrad -λλλλwires

#

ρ= Ε/J#

αααα = ∆V /∆T+ αleads

Distance-∆T and ∆V

T

∆Tup

∆T down

J

E

∆T Heater

Column

Name

A B C D E F G H I J

Signification

Temperature

∆T between ∆Tup and ∆Tdown

∆T between sample

center and sink

HeaterPower

Raw thermal

Conductivity

Corrected

Thermal Conducti

vity

Corrected

Seebeckcoefficien

t

Resistivity

Diffusivity

Heat capacity

Symbol

T ∆T ∆T P λraw λ TEP, S or α

ρ κ CV

Unity

K K K W Wm-1K-

1Wm-1K-

1µVK-1 mΩ.c

mmm2/s

J/K/ cm3

4

(λ,α,ρ,κ) λ,α,ρ,κ

4-point λ, λ, λ, λ, S and ρρρρ method for “ normal” samples

Mini heater

Anchoring Cu hoop (0.2 mm Wire) Up

Current lead Cr-Ni wire Down

E-thermocouple ∆T Up

Chromel wire as voltage lead

Anchoring Cu hoop (0.2 mm Wire) Down

Current lead Cr-Ni wire Up

E-thermocouple ∆T Down


Connector Si calibrated diod Thermal anchor of

E-differential thermocouples

Sample

Pasted with Ag-filled

Cyanacrylate

Pasted with Ge varnish-separated

cigarette paper

Protective frame

E-thermocouple ∆T Heater

5

Thermal and electrical measurements I (λ,α,ρ)

Sample mounting, topology

Con-nector 1

∆∆∆∆Tup E-typ

2 ∆∆∆∆Tdown E-typ

3 ∆∆∆∆Vsample

Chromel

4 Tabs

(I , sense) Diode

5 Tabs

(U, input) Diode

6 Free

7 Heater

8200

8 I sample

H

gh

Used for

Ch 100, 709SCAN 712DMM


Ch 2, 722

MULT

Ch 323, 709SCANImikrosour


Ch 3, 722

MULT

Ch 200, 709SCAN 719Keithl


Con-nector 9

∆∆∆∆Tup E-typ

10 ∆∆∆∆Tdown E-typ

11 ∆∆∆∆Vsample

Chromel

12 Tabs

(I , sense) Diode

13 Tabs

(U, input) Diode

14 Free

15 Heater

8200

16 Isample

Low Used

for Ch 100, 709SCAN 712DMM


Ch 2, 722

MULT

Ch 323, 709SCANImikrosour


Ch 3, 722

MULT



1 2 8

9 10 16

Steady state 4-point measurementAcquisition performed after temperature

(~50 mK) and thermal voltage (~1-5%+0.5µV) stability is achieved

6

II (λ,α,ρ,κ,cv)

Low temperature 4-point cell Close cycle He-cryostat (3.5-300K)

Radiation shield

7

(λ,α,ρ,κ,cv)

Ultra-low temperature 4-point cell

Close cycle He-cryostat (3.5-300K) operating

since 2006

Software--fully WXP 32 bit compatible, PCI HPIB card, external measuring system controlled via PC, program in DELPHI

Hardware--same cell , better temperature control needed, cold finger itself !! High temperature fluctuations!! + lower temperature,stronger requirements for temperature measurement and control!

Vacuum cover

8

II (λ,α,ρ,κ,cv)

0 1 2 3 4 5 60

5

10

15

20

25

30

35

40

Tem

pera

ture

(K

)

Time (min)

1.5 2.0 2.5 3.0

5

10

15

20

9

II (λ,α,ρ,κ,cv) !

340 350 360 370 3803.0

3.2

3.4

3.6

3.8

4.0

4.2

4.4

4.6

4.8

5.0

T(set)= 3.2 K

Natural temperature fluctuationson cold finger

Abs

olut

e te

mpe

ratu

re (

K)

Time (sec)

14740 14750 14760 14770 14780

3

4

5

Temperature on measuring cell (after filtering)controlled by LakeShore

340 350 360 370 3803

4

5

6

7

8

Natural temperature fluctuationson cold fingerA

bsol

ute

tem

pera

ture

(K

)

Time (sec)

16160 16170 16180 16190 16200

3

4

5

6

7

8

Tup = Tabs+∆(T)up on the sample at 6 K after temperature stabilization

T(set)= 6 K


120 121 122 123 124 125 126 127 128 129 1308

10

12

14

Time (sec)

Natural temperature fluctuationson cold finger during cooling

Abs

olut

e te

mpe

ratu

re (

K)

Time (sec)

16900 16950 17000 17050 17100 17150 17200 17250 17300 17350

8

10

12

14


110 120 130 140 1507

8

9

10

11

12

13

14

Natural temperature fluctuationson cold finger

Abs

olut

e te

mpe

ratu

re (

K)

Time (sec)

17400 17410 17420 17430 17440

7

8

9

10

11

12

13

14

Tup = Tabs+∆(T)up on the sample at 12 K after temperature stabilization

T(set)= 12 K


10

II (λ,α,ρ,κ,cv)

High temperature stability inspires to measure thermal diffusivityand then

heat capacity Cv~ λ/κ before thermal equilibrium is achieved

0 20 40 60 80 100 120 140 160 180 200

200

400

600

800

1000

time

Power*τ1/ Ccapacity

(τ1=Ccapacity/Kconductivity)

A*(1-e-time / tH )

100*5*(1-EXP(-X/5))

100*10*(1-EXP(-X/10))

time

∆T

F1Principle

Heatflow

11

•Diffusivity (∆Tup)

measurement at various

temperatures

•- first readings 5 rds/s

• -since ~4s 1 rds/s

•Sample

LaCo0.95Ni0.05O3

Time (s)

∆Tup

300 K

60 K

30 K

4 K

20 K

10 K

7 K

110 K

" !#$!%&'( )τ 10−102

12

* + II

Recent results, for temperature acquistion Keithley 2001/MEM2 High-Per formance, 7-1/2-Digit DMM

0 50 100 150 200 250 300 3500

20

40

60

80

100

120

SrRuO 3 PPMS SrRuO 3 J&K

Spe

cific

hea

t (Jm

ol-1K

-1)

T (K)0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0

0

2 0

4 0

6 0

8 0

1 0 0

1 2 0

Bad thermal conductors- correct Cv data

!

"

#

$%&'&()*

$%&'&()*

13

" !#$!%&'( , " !

)τ 10−102

0 50 100 150 200 250 300 3500

20

40

60

80

100

120 SrMoO1.73N1.27

-sintered PPMS SrMoO1.95N1.05

-sintered CloseCycle

!

"

#

!

Cp/

T (

mJm

ol-1K

-2)

T2(K)

14Time (s)

∆Tup

300 K

60 K30 K

4 K

10 K

7 K

110 K

•(∆Tup) does not decrease

with decreasing

temperature

• τ decreases with

decreasing temperature,

but the measured thermal

diffusivity is limited by

glue joint with Cu-heat

sink

• Al2O3

" !#$!%&'"( , !

" -

15

!

"

#

Cv data WRONG!! diffusivity limited by wrong thermal sample anchoring

error 4%

+%%(%%$%

,

(%%%''-..'()%$%&'&()

/

Good thermal conductor- wrong Cv data

!

$%&'&()*

16

" & !

650600550500450400350300250200150100500-50

2.6

2.5

2.4

2.3

2.2

2.1

2

1.9

1.8

1.7

1.6

1.5

1.4

1.3

1.2

1.1

1

0.9

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.1

0

-0.1

•Diffusivity (∆Tup)

measurement- 300 K

•Sample LaCo0.8Ti0.2O3

•At 400 Turbo-pump started (10-2→10-4 mbar)

Time (s)

∆Tup

(K)

170 50 100 150 200 250 3000

2

4

6

8

10

12

heater area~15 mm2

∆T sample center

Correction formula:λ

radiation corrected= factor *(power -HeaterRadiation -Sample radiation)/∆(T)

λradiation corrected

= length/CrossSection *(R I2-Tabs

3 ∆T(heater)*5.67e-8*15e-6*∆T(heater)/∆T(up)- Tabs

3 ∆T(sample center)*5.67e-8*15e-6*SampelArea)/∆ (T)

Mo3Sb7 small sample- perfect heater anchoring

Mo3Sb7 bad heater anchoring

∆Theater ∆Tup ∆Tdown

Tem

pera

ture

diff

eren

ce (

K)

T (K)

"

!' ' (λ)- ∆

18

"

!'' (λ) $+ .

!

0 50 100 150 200 250 3000.0

0.2

0.4

0.6

0.8 PPMS Thermal transport Typical Accuracy: • ± 5 % or ± 2 µW/K, whichever isgreater, for T < 15 K• ± 5 % or ± 20 µW/K, whichever isgreater, for 15 K < T < 200 K• ± 5 % or ± 0.5 mW/K, whichever isgreater, for 200 K < T < 300 K• ± 5 % or ± 1 mW/K, whichever isgreater, for T > 300 K

T

herm

al c

ondu

ctiv

ity o

f pol

ysty

ren

(Wm

-1K

-1)

T (K)0.0

0.5

1.0

1.5

2.0

Correction formula: NEW CORRECTIONλradiation corrected= factor *(power -HeaterRadiation -Sample radiation- Thermocouple heat flow)/∆(T)

λradiation corrected= length/CrossSection *(R I2-Tabs

3 ∆T(heater)*5.67e-8*40e-6- Tabs

3 ∆T(up)*5.67e-8*3xSampelArea-

(22-22*0.992 Tabs * 3e-6*∆T(heater))/∆ (T)

Measured therm

al conductance (WK

-1)

$

measured

PPMS declared

error

corrected

19

- error

- error

SrBi2Nb2O9

conductance of thermocouples and leads

radiation!bad geometry - 4-point! radiation error!! (factor=716) radiation corrected

New geometry- 2-point! no radiation, factor=88

New geometry- porosity corrected! no radiation supposed, factor=88, corrected on porosity using λcorr=2*λmesured/(3*ρ-1)

$%&'&()*

2-point geometry, flat sample- heat flow through the sample simplified

20

$

"

'' α " /,0/112

21

Yellow Brass

01%23%)"

4.&+2

5%2$.-'

λ*

! "

magnon drag peak

%3%)"

$&&6µ7

!

"

#

µ7

"

! '' (λ,α) ∆

22

& " .

!

!

SrTiO3 LaAlO

3

(INSULATORS)

$&&67

0 50 100 150 200 250 300

0

2

4

6

8

10 0 % Ag powder added 10 % Ag powder added 20 % Ag powder added

Bi1.8Pb0.2Sr2Ca2Cu3O10+δ

The

rmoe

lect

ric

pow

er (

µVK

-1)

!

"

#

Rcrit ~ 50-100 MΩ

8%8

89 89 89 89

$&&6µ7

%'

Depends on used DMM (DnVM), shielding, wiring,..

23

(λ,α,ρ,κ,cv)

24

# ...- 3)

PPMS inset (Caen-Crismat)

(5-350 K)Operating since 1999

Software--PPMS, external measuring system controlled via PC-old-fashioned TurboPascal-DOS

Hardware--sample holder , E-type thermocouples,-calibration, thermal stability, sensitivity to magnetic field

25

(λ,α,ρ,κ)

0 1 2 3 4 5 6 7 8 9-1.0

-0.5

0.0

0.5

1.0

5K

20K

Bi2223

S (

µµ µµV.K

-1)

µµµµ0000H (T)

Calibration, 2006Bi-based superconducting cuprates

-80

-60

-40

-20

0

The

rmoe

lect

ric p

ower

(µV

K-1)

-8 -6 -4 -2 0 2 4 6 8-60

-50

-40

-30

-20

-10

0

#

B(T)

-8 -6 -4 -2 0 2 4 6 8

0.9

1.0

1.1

1.2

1.3

0.8

1.0

1.2

1.4

Therm

al conductivity (WK

-1m-1)

-100

-80

-60

-40

-20

0

0.7

0.8

0.9

1.0

1.1

1.2

%

%

CMR manganites, 2000

E-type thermocouplesIsothermal magnetotransportImput impedance based on DMM, nanoVMProper criteria for thermal stability

26

(λ,α,ρ,κ)

Software--PPMS delivered, dynamic regime

Hardware--Quantum Design introduced Thermal transport option

27

PPMS sample topology

Arrangement of home-made thermal and transport measurement

two thermometers

area

l

T heater direction of electric current J

Distance –

T and

V

T

thermocouples

underlay

Spaper

T down

T up

4 – 310K

E

HeaterChip resistance

T heater direction of electric current J

Distance –

T and

V

T

thermocouples

underlay

Spaper

T down

T up

4 – 310K4 – 310K

E

HeaterChip resistance

T

PowerF

∆∗=λ

21 TTTarea

lF

−=∆

=

Cryo-cooled sample topology

T

VS

∆∆=Not steady state method

∆T calculated on a base τ1,τ2Steady state method ∆∆∆∆T measured

COMPARE PPMS-Cryocooled (λ,α,ρ,κ)

28

Arrangement of home-made 4-point thermal and transpor t measurement λ, λ, λ, λ, S and ρ.ρ.ρ.ρ.

2 Cernox chip thermometers

Heater chip resistance

Protection for radiation

Heater

Thermometer up

Thermometer down

2 for Iheater and 1 for Isample

4 for Tup and 1 for Uup

4 for Tdown and 1 for Udown

PPMS sample topology Cryo cooled sample topology

sample


4-point λ, λ, λ, λ, S and ρρρρ method for “ normal” samples

Mini heater

Anchoring Cu hoop (0.2 mm Wire) Up

Current lead Cr-Ni wire Down

E-thermocouple ∆T Up


Anchoring Cu hoop (0.2 mm Wire) Down

Current lead Cr-Ni wire Up

E-thermocouple ∆T Down


Connector Si calibrated diod Thermal anchor of

E-differential thermocouples

Sample

Pasted with Ag-filled

Cyanacrylate

Pasted with Ge varnish-separated

cigarette paper

Protective frame

E-thermocouple ∆T Heater

29

PPMS-Principle of the measurement

Time evolution of the :

(a) heater power

(b) hot and cold thermometer and drift of baseline

(c) hot thermometer with analysis of respective time constants

a)

b)

c)

T1

T2

time (s)

PPMS sample topology

τ1

τ2∆∆∆∆T λλλλ

ττττ κκκκ


30

0 50 100 150 200 250 30010

100

La0.2

Ca0.8

CoO3 - PT041

homemade PPMS

ρ

Ω&

T (K)

4& !

No problem

31

4& !

0 50 100 150 200 250 3000.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

homemade PPMS

T (K)

La0.2Ca0.8CoO3 - PT041

0 10 20 30 40 500

1

2

3

4

λ (W

.m-1K

-1)

λ (W

.m-1K

-1)

Surprising agreement

32

4&

0 50 100 150 200 250 3000

10

20

30

40

50

60

70

80La0.2Ca0.8CoO3 - PT041

homemade PPMS

αµ7:

T (K)

0 10 20 30 40 500

10

20

30

40

50

La0.2Ca0.8CoO3 - PT041αµ7:

Surprising agreement

33

+ * + 5 4

High temperature 4-point cell (300 – 1200 K),Thermoelectric power and electrical resistivity

34

High temperature cell

Σ Σ Σ Σ U = U1+U4+U3+U2 = 0T1>T4>T3>T2

Stability:

Pt-Rh

Pt-Rh

Pt

PtPt-Rh

Pt

U4

U3

U2

Pt-Rh

Pt

l

T3

T4U1

Pt Sheet

Cold finger

Heater

T1

T2

Pt-Rh

Pt-Rh

Pt

PtPt-Rh

Pt

U4

U3

U2

Pt-Rh

Pt

l

T3

T4U1

Pt Sheet

Cold finger

Heater

T1

T2

+ * + 5 4

35

Mica

K-thermocouple Down


Alumel wire as current lead

K-thermocouple Up Chromel wire as voltage

lead Chromel wire as voltage lead

Alumel wire as current

Heater Inserted in the holder

Piston attached to cold end

Sample hidden

under mica

Ag thin plate pasted with Ag-paste

Pressing shank

Ag thin plate pasted with Ag-paste

K-thermocouple Low


K-thermocouple High


Lava based sample holder

High temperature cell

+ * + 5 4

36

200 250 300 350 400 4500

100

200

300

400

500

600

700

pressing sheetmica

pressing sheetmica

pressing sheetalumina

relative error 53 %

relative error 8 %

relative error 65 %

4points method 3points method 2points method basic low temperature

data

S

(µV

.K-1)

T [K]

LaCo0.95

Mg0.05

O3

relative error 30 %

pressing sheetalumina

mica bad conductor

T

VS

∆∆=

alumina good conductor

heater

S pnt2

S pnt3

S pnt4

cold finger

+ * + 5 4 "

37

+ & " .

0 100 200 300 400 500 600 700 8000.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

Res

istiv

ity (

µΩcm

)

T (K)

-35

-30

-25

-20

-15

-10

-5

0

Therm

oelectric power (µV

K-1)

0 200 400 600 800 1000-200

-150

-100

-50

0

50

-200

-150

-100

-50

0

50

! #

"

!

#

"

0 200 400 600 800 1000

101

102

103

104

105

106

Fe3O

4

The

rmoe

lect

ric p

ower

(µV

K-1)

T (K)

Ni metal Fe3O4-xtal

38

#α%$ " " α$ + #/,0/112%.+

! " #

#

"

!

!

"

#

1996 - Leybold 2006, June - Sumitomo 2003 - Hejtmanek, Praha

Bi1.8Pb0.2Sr2Ca2Cu3O10+δ

$&&6µ7

! " #

! 1996 - Leybold 2006, June - Sumitomo 2003 - Hejtmanek, Praha

Ele

ctric

al r

esis

tivity

(m

Ωcm

)

T (K)

39

#α%$ "" !-

" !α$ + #/,0/112%.+

0 200 400 600 800 10000

50

100

150

200

250

300

350

400

450

LaCo0.95

Ni0.05

O3 - RO 142

LaCo0.95

Ni0.05

O3 - RO 142

La0.95

Sr0.05

CoO3 - sample Praha

La0.98

Sr0.02

CoO3- sample Praha

La0.98

Sr0.02

CoO3- sample Praha

α;µ7:<

T [K]

40

#α%$ " !-

" !α$ + #/,0/112%.+

! " #

!

#

"

!

#

"

!

Sm0.1

Ca0.9

MnO3

µ7

!

"

#

La0.05

Ca0.95

MnO3

ρ (mΩ

cm)

41

0 200 400 600 800 1000 120010-1

100

101

102

103

104

105

106

107

108

109

LaCoO3

La0.98Sr0.02CoO3

E

lect

rical

res

istiv

ity (

mΩ

cm)

T (K)

0 200 400 600 800 1000 1200100

101

102

103

LaCoO3

La0.98Sr0.02CoO3

Loca

l act

ivat

ion

ener

gy (

meV

)

T (K)

! #ρ%$ "" !-

!6

$ + #/,0/112%.+

42

END

thermoelectricity measuring...

Documents