2017/10/30
2nd Kyoto Workshop on Positron Sciences"Positron Spectroscopy for Materials Analysis"@ Uji, Kyoto Univ.

Relation between thermal diffusivity
and positron annihilation lifetimein ceramic materials
Masafumi Akiyoshi
Osaka Prefecture University,
Radiation Research Center

Abstract
Ceramics are candidate for divertor material in the future fusion reactor, where
thermal diffusivity is one of the most important factors. Many studies were reported
on properties of post irradiated specimen, but there have been few studies onproperties during irradiation. Now we attempt to estimate a dynamic effect duringion-beam irradiation via positron annihilation spectroscopy. In this study, positronannihilation measurements were performed on neutron or electron irradiatedspecimens that showed severe degradation in thermal diffusivity to clarify the
relation between positron-annihilation lifetime and thermal diffusivity. The positronannihilation lifetime of irradiated α-Al2O3 and AlN showed obvious increase, while
β-SiC showed no change in lifetime, andβ-Si3N4 rather showed decrease.

Keywordceramics, neutron irradiation, thermal diffusivity,
positron annihilation measurements

Degradation of Thermal Conductivity
in Ceramics

Divertor of Fusion Reactor
未照射 SiC: 230 W/m・K
Unirradiated
930℃

10MW/m2He
Gas Cooling
ガス冷却
500℃
厚さ1cm

～

15000℃

1cm

Neutron
中性子照射後SiC:
Irradiated

7 W/m・K

Thermal Diffusivity of Ceramics
・Heat is mainly carried by phonon unlike metals.
・In non-irradiated materials, thermal diffusivity is affected by
microstructure of grain that was changed with sintering process.

Thermal Diffusivity α = 1/3・μ・λ
μ: Mean speed of phonon [m/s]λ: Mean free path of phonon [m]In an irradiated specimen, mean free path ofphonon is decreased to very small and thegrain structure is too large to affect to thethermal diffusivity.

1/λ = 1/λa + 1/λb + 1/λc ・・・
Almost constant with each material

Phonon-Phonon Scattering
Changes with the temperature T
as k/T n (for non-irradiated single crystal, n=1)

Phonon-Lattice Scattering
Increased with density ofirradiation defects

Temperature Change
During the Irradiation

After the Irradiation

Estimation of Thermal Diffusivity
During the Irradiation

1

Degradation of thermal diffusivity with neutron
dose was saturated ～ 3×1026n/m2

Thermal Diffusivity / 10 -4 m2 s- 1

3 Assumption

Post irradiation measurement
at the irradiation temperature
represent the thermal diffusivity
during the irradiation.
0.025

2

Defects were stable until annealed
above the irradiation temperature

T52 (5.3×1026n/m2, 775K) α-Al 2O3
T54 (7.3×1026n/m2, 835K) α-Al 2O3
T58 (6.9×1026n/m2, 1039K) α-Al 2O3

0.02

0.015

Post irradiated specimens kept the sameamount of defects as during the irradiation

0.01
400
600
800
1000
Measurement Temperature / K

Thermal Diffusivity Measured
at Elevated Temperature

Thermal diffusivity at
the irradiation temperature
αirr=k/Tirrn
Tirr : the Irradiation Temperaturek, n: fitting parameters obtained from measurementof thermal diffusivity with various temperature

Thermal Diffusivity α / 10-4m2s-1

3

0.1
Neutron irradiatedβ-Si 3N4
T51 (2.8×1026n/m2, 775K)
T53 (3.9×1026n/m2, 864K)
T55 (4.2×1026n/m2, 1004K)
T57 (3.7×1026n/m2, 1011K)
T71 (0.5×1026n/m2, 646K)
T72 (1.4×1026n/m2, 668K)
T73 (0.4×1026n/m2, 853K)

0.08
0.06
0.04
0.02
0
100

200

300

400

Measurement Temperature T / K

Thermal Diffusivity Measured
below the irradiation temperature

3

Post irradiated specimens kept the same amount of defects as during the irradiation

Goal

During the Neutron
Irradiation
Positron Annihilation
Measurement

During the Neutron
Irradiation

Impossible

Thermal Diffusivity
Measurement

During the Ion Beam
Irradiation

Impossible

Thermal Diffusivity
Measurement

Estimate

During the Ion Beam
Irradiation
Positron Annihilation
Measurement

Possible
Post Irradiation Experimen

Post Irradiation Experimen

Thermal Diffusivity

Actual Measurement

Point Defect(Vacancy)

Positron Annihilation
Lifetime (PAL)
Future Work

Correlation

In-situ Experiment During Irradiation

Transient DefectDuring the Irradiation

Dynamic change duringion-beam irradiation( Now in experiment )Experimental
Specimen Properties

Thermal Diffusivity
Measurement
Thermal diffusivity was measured byl a s er f l a s h m ethod (ULVAC
TC-7000L Special) and analyzed with t1/2
method at room temperature.

α-Al2O3

AlN

β-Si3N4β-SiC

Manufacturer

Nippon Steel

Tokuyama

Nippon SteelRaw material

α-Al2O 3 100wt%

AlN (unknown)

pressureless99.5%

pressureless～99.9%

Nippon Steel
β-Si3N 4 > 88wt%
Y2O 3 < 10wt%
ZrSi2 < 2wt%
hot press
100%

0.118

0.991

0.257

Sintering method
Relative density
Thermal Diffusivity(10 -4m2/s)

β-SiC > 99wt%
Al2O 3 < 1wt%
hot press
99.7%
0.41

Irradi ati on Condi ti on

Positron Annihiration
Measurement

Neutron Irradiation
Irradiation

Dose (n/m2) Temperature
ID ( E >0.1MeV )(K)
3mmφ×0.5mm disk

Experimental Fast Reactor

JOYO

Positron annihilation lifetime (PAL)
measurement: conventional γ-γ
fast coincidence method.

T51
T53
T55
T57

Mk II core, irradiation rig CMIR-4

4 kind of specimens were irradiated in the same capsule

One disk each
irradiation condition

Start Signal
Non-IrradiatedSpecimen

IrradiatedSpecimen

γ 1.38MeV

2.8×1026
3.9×1026
4.2×1026
3.7×1026

19.1mmSealed by 12.7μm Ti foi

Positron
Source22Na

γ 0.511MeV
Active Diameter
φ1mm

Stop Signal

Ti Ring t=0.254mm
9.53mm

775
864
1004
1011

30MeV Electron Irradiation
30MeV Electron Accelerator

KURRI-LINAC
Kyoto University
Research Reactor Institute, Kumatori

Accelerate Energy: 28-32MeV
The beam current: ～230μA
Peak current of pulse: ～600mA
Pulse width: 4μs
Pulse frequency: ～100Hz2
2
Heat Load: ～7kW in 2cm = 35MW/m
2> the divertor in ITER, 10MW/m
The Range of 30MeV Electron～5cm ( in ceramics )Energy of PKA (max): 125keV → Energy of PKA (average): 225eV
Number of Displacement Atoms per PKA: 3-4 atoms

Mainly Point Defects

KURL0604

Liquid Nitrogen Supply

Low Temperature
Irradiation

KURL0604: -165℃ / 1.35kW
Liquid Nitrogen cooled system
30MeV, 3μs x 500mA x 30Hz

Cu heat sink in Water chamber
KURL1201: 80℃ / 6.0kW
32MeV, 4μs x 590mA x 80Hz
KURL1401: 90℃ / 4.7kW
28MeV, 4μs x 600mA x 70Hz
Very Stable andEstablished Irradiation
SystemKURL1201
KURL1401
Cu Heat sink
put inWater chamber

Medium Temperature
Irradiation□15mm Al
Square tube30

t = 0.7mm
Cu Specimen Holder

30

30MeV
Electron
Beam

Cooling Water

Beam

φ10x0.5mm
Specimen

0.4mm Cu Heat Spreader

Ti screw and nut

Vertical orientatedGraphite seat( 90 W/m・K )□15mm Al
Square tube
Cooling Water

Al water pipe
BN spray coating

Aperture

PAL and Thermal Diffusivity Measurement
γ-γFast Coincedence
Positron Annihilation Lifetime
Measurement Circuit Diagram

High Voltage

Constant Fraction
Differential Discriminater

Photomultiplier

Sealed Positron Source 22Na < 1MBq

BaF2 scintillator
Non -IrradiatedSpecimen

19.1mmSealed by 12.7μm Ti foil

IrradiatedSpecimen(φ10x0.5mm)

Active Diameter
φ1mm

γ 1.38MeV

Multi Ch annel
Analyzer(MCA)

Start Signal

Positron
Source22NaTime to Amplitud e
Converter (TAC)

Cupper jig

γ 0.511MeVBaF2 scintillator
Ti Ring t=0.254mm

Photomultiplier

9.53mmHigh Voltage

Thermal Diffusivity
Measurement System

Constant Fraction
Differential Discriminater

Delay Box

Stop Signal

BaF2 Scintillator: OKEN φ30x40mm
Photomultiplier: H33778-51

ULVAC Techno. TC-7000H/Special

Conventional laser-flash method / t1/2 analysis
Specially ordered system → φ3mm disk

Isochronal annealings in a SiC furnace
up to 1500℃ in vacuum

Analo g to
DigitalConve rter

30

40

AlN
T56
(950)

T73
(853)

30

T57 T55(1011) (1004)

T72(668)

20

T51
(775)

T53
(864)

T58
(1039)

T54
(835)

T52
(775)

10
0

2
4
6
8
26
Neutron-irradiation Dose / 10 n・m-2
β-SiC
T73
(853)
T72
(668)

20

T58
(1039)
T71
(646)

10

0

T57
(1011) T55(1004)

T51
(775)

T53
(864)

T52
(775)

T56
(950)

T54
(835)

2
4
6
8
26
Neutron-irradiation Dose / 10 n・m-2

Relative Thermal Diffusivity Change
αirr / α0 ×100 / %50

5Relative Thermal Diffusivity Change
αirr / α0 ×100 / %β-Si3N4

Relative Thermal Diffusivity Change
αirr / α0 ×100 / %α-Al2O3

Relative Thermal Diffusivity Change
αirr / α0 ×100 / %Degradation of thermal diffusivity after
neutron irradiations

15

4
3
2

T73
(853)
T71
(646)

T72(668)

T57(1011) T55(1004)

T51
(775)

T53
(864)

T58
(1039)

T52
(775)

T56
(950)

T54
(835)

1
0

2
4
6
8
26
-2
Neutron-irradiation Dose / 10 n・m

T73
(853)
T57
(1011) T55(1004)

T72
(668)

10

T71
(646)
T51
(775)

T53
(864)

T52
(775)

T58
(1039)

T56
(950)

T54
(835)

5

0

2
4
6
8
26
-2
Neutron-irradiation Dose / 10 n・m

Annealing Behavior

Irr. Temp.

2
0.1

1.5
1

0.05

0.5
0

500
1000
Annealing Temperature / ℃

T51

0
1500

0.15

2
Irr. Temp.

1.5

0.1
1
0.05
0.5

0

500
1000
Annealing Temperature / ℃

T57

0
1500

Macroscopic Length Change / %2.5

Thermal Diffusivity / 10-4 m2 s-1

0.15

Macroscopic Length Change / %Thermal Diffusivity / 10-4 m2 s-1

AlN

Unirrad.

0.1

0.05
-170℃
40℃
300-700℃
1100℃

0 -4
10

10-3
10-2
Irradiation Dose / dpa
β-SiC

0.1

Unirrad.

0.05
-170℃
40℃
300-700℃
1100℃

0 -4
10

10-3
10-2
Irradiation Dose / dpa

Thermal Diffusivity / 10-4 m・s -1

AlN

Thermal Diffusivity / 10-4 m・s-1

β-Si3N4

Thermal Diffusivity / 10-4 m・s-1

α-Al2O3

Thermal Diffusivity / 10-4 m・s-1

Degradation of thermal diffusivity after
electron irradiations

0.8

Unirrad.

0.6
0.4
-170℃
40℃
300-700℃
1100℃

0.2
0 -4
10

0.8

Unirrad.

10-3
10-2
Irradiation Dose / dpa

-170℃
40℃
300-700℃
1100℃

0.6
0.4
0.2
0 -4
10

10-3
10-2
Irradiation Dose / dpa

Positron Annihilation
Lifetime Spectrum

ResultNormalized Intensity

Normalized Intensity

α-Al2O3
T 51
T 53
T 55
T 57
Unirradiated

10-1
10-2
10-3
10-4

β-Si3N4

AlN

100

0

1
2
Time / ns

100

3

4

β-SiC

β-Si 3N4
T 51
T 53
T 55
T 57
Unirradiated

10-1
10-2
10-3
10-4

0

1
2
Time / ns

3

4

100

AlN
T 53
T 55
T 57
Unirradiated

10-1
10-2
10-3
10-4

Normalized Intensity

Normalized Intensity

α-Al2O30

1
2Time / ns

100

3

4

β-SiC
T 51
T 53
T 55
T 57
Unirradiated

10-1
10-2
10-3
10-4

0

1
2
Time / ns

3

4

Neutron Irrad.
Electron Irrad.

0.2
0.18
0.16
0.14
10-6

α-Al2O 3

10-5
2 -1
Thermal Diffusivity α / m s

0.24

β-SiC

0.22
0.2
Neutron Irrad.
Electron Irrad.

0.18
0.16

β-Si3N4

10-5
2 -1
Thermal Diffusivity α / m s

Average Positron Lifetime <τ> / ns

AlN

Average Positron Lifetime <τ> / ns

β-Si3N4

Average Positron Lifetime <τ> / ns

α-Al2O3

Average Positron Lifetime <τ> / ns

As-irradiatedAveraged Positron Lifetimevs Thermal Diffusivity

Average lifetime <τ > = τ 1 I1 + τ 2 I2Here, τ i are the analyzed positron
lifetimes, and I i are the intensities forthe components.

0.2
Neutron Irrad.
Electron Irrad.

0.19
0.18
0.17
0.16
0.15
0.14 -6
10

AlN

10-5
10-4
Thermal Diffusivity α / m2 s-1

0.18
0.16
Neutron Irrad.
Electron Irrad.

0.14
β-SiC

0.12

10-5
10-4
2 -1
Thermal Diffusivity α / m s

2

170

Thermal Diffusivity / 10 m /s

Annealing behavior

α-Al2O3

-4

160
0.09
150
Unirradiated PAL→
Thermal diffusivity
Average PAL←
Electron irradiated α-Al2O 3 KURL-0708

140
0

500
1000
Annealing Temperature / ℃

170
Toray α-Al2O 3

Average PAL <τ> / ps

0.1

Unirradiated
KURL-0708 Electron irradiated

160

150

140
0.08

0.09
0.1
Thermal Diffusivity / 10 -4 m 2/s

0.11

0.08

PAL: Recovered from 600℃ and completed at
900℃
Thermal diffusivity: Recovered from around
500℃ and almost completed at 1100℃
Correlation: Showed weak correlation arrose
from small change of thermal diffusivity.

Electron Irradiated
Thermal Diffusivity / 10 -4 m2 s-1

Average PAL <τ> / psUnirradiated TD

0.12
0.1
0.08

α-Al2O3
H6T51 (2.8×1026n/m 2, 502℃)
H6T53 (3.9×1026n/m 2, 591℃)
L9T54 (7.3×1026 n/m2 , 562℃)
H6T57 (3.7×1026n/m 2, 738℃)
L9T58 (6.9×1026 n/m2 , 766℃)
H6T72 (1.4×1026n/m 2, 395℃)
H6T73 (0.4×1026n/m 2, 580℃)

0.06

Recovered from
700-800℃
linearly

0.04
0.02
0

500
1000
1500
Annealing Temperature / ℃

Neutron
IrradiatedAnnealing behavior

180

0.8

-4
Unirradiated TD

175

0.7

170

0.6

165
Unirradiated PAL

160
0

→
Thermal diffusivity←
Average PAL
Electron irradiated AlN KURL-0708

500
1000
Annealing Temperature / ℃

Average PAL <τ> / ps

Tokuyama AlN SH-30

180

Unirradiated
KURL-0708 Electron irradiated

170

160
0.4

0.5
0.6
0.7
-4
2
Thermal Diffusivity / 10 m /s

0.8

0.5

PAL: Recovered from 400℃ linearly andcompleted at 1100℃
Thermal diffusivity: Same trend as the PAL
result.
Correlation: Showed very good correlation.

Electron Irradiated
Thermal Diffusivity / 10 -4 m2 s-1

Average PAL <τ> / ps2

Thermal Diffusivity / 10 m /s

AlN

Recovered from 1100℃
as the square of theannealing temperature

0.3
AlN

0.2

H6T51 (2.8×1026n/m 2 , 502℃)
H6T53 (3.9×1026n/m 2 , 591℃)
L9T54 (7.3×1026n/m 2, 562℃)
H6T57 (3.7×1026n/m 2 , 738℃)
L9T58 (6.9×1026n/m 2, 766℃)
H6T71 (0.5×1026n/m 2 , 373℃)
H6T72 (1.4×1026n/m 2 , 395℃)
H6T73 (0.4×1026n/m 2 , 580℃)

0.1

0

500
1000
Annealing Temperature / ℃

1500

Neutron
IrradiatedUnirradiated TD

0.09
240

0.08
Unirradiated PAL

0.07
230
0

0.06
500
1000
Annealing Temperature / ℃

250
Toray β-Si3N4

Average PAL <τ> / ps

-4

0.1

Thermal diffusivity
Average PAL

Unirradiated
KURL-0708 Electron irradiated

240

230

220
0.06

0.07
0.08
0.09
0.1
-4
Thermal Diffusivity / 10 m 2/s

0.11

0.05

PAL: As-irradiated specimen showed slightdecrease, and it recovered at 600℃ completely.
Thermal diffusivity: Recovered from 400℃
linearly and completed at 1100℃
Correlation: PAL showed inverse change as theother specimens, then showed a little positive
correlation to the thermal diffusivity

Electron Irradiated
Thermal Diffusivity / 10 -4 m2 s-1

Average PAL <τ> / ps

250

→
←

2

0.11
Electron irradiated β-Si 3N 4 KURL-0708

Thermal Diffusivity / 10 m /s

Annealing behavior

β-Si3N4

Recovered from 400℃ linearly,
and then recovered as the squareof the annealing temperaturefrom 1000℃

0.2

0.15

β-Si 3N4
H6T51 (2.8×1026n/m 2, 502℃)
H6T53 (3.9×1026n/m 2, 591℃)
L9T54 (7.3×1026 n/m2 , 562℃)
H6T57 (3.7×1026n/m 2, 738℃)
L9T58 (6.9×1026 n/m2 , 766℃)
H6T71 (0.5×1026n/m 2, 373℃)
H6T72 (1.4×1026n/m 2, 395℃)
H6T73 (0.4×1026n/m 2, 580℃)

0.1

0.05
0

500
1000
1500
Annealing Temperature / ℃

Neutron
Irradiated

190

180

0.8
0.6
0.4

Unirradiated PAL

0.2
170
0

500
1000
Annealing Temperature / ℃

200
Bridgestone β-SiC PureBeta-S

Average PAL <τ> / ps1

2

Unirradiated TD

Unirradiated
KURL-0708 Electron irradiated

190

180

170

0.2
0.4
0.6
0.8
1
-4
2
Thermal Diffusivity / 10 m /s

0-4Electron irradiated β-SiC KURL-0708→
Thermal diffusivity←
Average PAL

PAL: As-irradiated specimen showed a little
increase, while it did not show recovery.
Furthermore, a little increase was observed
arround 500℃ to 800℃
Thermal diffusivity: Recovered from 400℃ but
did not completed at 1100℃.
Correlation: Obvious correlation was notobserved

Electron Irradiated
Thermal Diffusivity / 10 -4 m2 s-1

Average PAL <τ> / ps200

Thermal Diffusivity / 10 m /s

Annealing behavior

β-SiC

0.3

0.2

Recovered from 400℃ linearly,
and then recovered as the squareof the annealing temperaturefrom 1000℃

β-SiC
H6T51 (2.8×1026n/m 2, 502℃)
H6T53 (3.9×1026n/m 2, 591℃)
L9T54 (7.3×1026n/m 2, 562℃)
H6T57 (3.7×1026n/m 2, 738℃)
L9T58 (6.9×1026n/m 2, 766℃)
H6T71 (0.5×1026n/m 2, 373℃)
H6T72 (1.4×1026n/m 2, 395℃)
H6T73 (0.4×1026n/m 2, 580℃)

0.1

0

500
1000
Annealing Temperature / ℃

1500

Neutron
Irradiated0.2

N eut ron Irrad.
Elect ron Irrad.
Elect ron Irrad.(A nneal)

0.18
0.16
0.14
10 -6

α -Al2 O 3

10 -5
2
-1
Thermal Diffusivity α / m s

β-SiC

0.26
β-Si3N 4

0.24
0.22
0.2
Neutron Irrad.
Electron Irrad.
Electron Irrad.(Anneal)

0.18

10 -5
2 -1
Thermal Diffusivity α / m s

Average Positron Lifetime <τ> / ns

AlN

Average Positron Lifetime <τ> / ns

β-Si3N4

Average Positron Lifetime <τ> / ns

α-Al2O3

Average Positron Lifetime <τ> / ns

As-irradiated and annealed
0.2
Neutron Irrad.
Electron Irrad.
Electron Irrad.(Anneal)

0.19
0.18
0.17
0.16
0.15
0.14 -6
10

AlN

10 -5
10 -4
2 -1
Thermal Diffusivity α / m s

0.2
0.18
0.16
0.14

β-SiC

Neutron Irrad.
Electron Irrad.
Electron Irrad. (Anneal)

10 -5
10 -4
2 -1
Thermal Diffusivity α / m sStructure of each material

β-SiCの(110)面。
最密面 : {111}面

α-Al2O3 の(001)面。
最密面 : (001)面
AlN の(110)面。
最密面 : (001)面

β-Si3N4 の(001)面。最密面 : {100}面

Conclusion
Positron annihilation lifetime and thermal diffusivity of electron and heavily
neutron irradiated α-Al2O3, AlN, β-Si3N4 and β-SiC were measured and compared.
○α-Al2O3 and AlN →(Irradiation)→ obvious change in PAL（even in electron irradiated (0.01dpa) specimen）

×β-Si3N4 and β-SiC →(Irradiation)→ no change in PAL（even in heavily neutron irradiated (28-42dpa) specimen）

Neutron Irradiation → too large degradation in thermal diffusivity (Saturated)
30MeV electron irradiation up to 0.01-0.02 dpa → thermal diffusivity in wide range
α-Al2O3 and AlN showed good correlation between thermal diffusivity and PAL.
△ α-Al2O3 : Not high thermal diffusivity (10mm2/s)◎ AlN: Very high thermal diffusivity (100mm2/s)→ easy to evaluate the difference after an irradiation
×β-Si3N4: Negative small PAL change arised from the crystal structure×β-SiC: Very high thermal diffusivity (100mm2/s)
× p-type: No PAL change → n-type: ？