Thermoelectricity measuring...
Transcript of 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
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(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
Chromel wire as voltage lead
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
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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 101, 709SCAN 712DMM
Ch 2, 722
MULT
Ch 323, 709SCANImikrosour
Ch 103, 709SCAN 712DMM
Ch 3, 722
MULT
Ch 200, 709SCAN 719Keithl
Ch 202, 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 101, 709SCAN 712DMM
Ch 2, 722
MULT
Ch 323, 709SCANImikrosour
Ch 103, 709SCAN 712DMM
Ch 3, 722
MULT
Ch 201, 709SCAN 719Keithl
Ch 203, 709SCAN 719Keithl
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
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II (λ,α,ρ,κ,cv)
Low temperature 4-point cell Close cycle He-cryostat (3.5-300K)
Radiation shield
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(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
Temperature on measuring cell (after filtering)controlled by LakeShore
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
Temperature on measuring cell (after filtering)controlled by LakeShore
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
Temperature on measuring cell (after filtering)controlled by LakeShore
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
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•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
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(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
COMPARE PPMS-Cryocooled (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
Chromel wire as voltage lead
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
COMPARE PPMS-Cryocooled (λ,α,ρ,κ)
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
Chromel wire as voltage lead
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
Chromel wire as voltage lead
K-thermocouple High
Chromel wire as voltage lead
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