2023/10/24 Orals Session B3-TM #C225

21th International Conference on Fusion
Reactor Materials(ICFRM-21)
in Palacio de Congresos, Granada, Spain.

Temperature Estimation ofTungsten-Rhenium Alloy
Used in Plasma Facing Components
Masafumi Akiyoshi (Osaka Metropolitan Univ.)
Takaaki Koyanagi, Yutai Katoh (ORNL)
Akira Hasegawa (Tohoku Univ.)

Supported by
2019-2024 Japan-US
FRONTIER Project

Acknowledgement: Research sponsored by the Office of Fusion Energy Sciences,
U.S. Department of Energy, under contract DE-AC05-00OR22725 with UT-Battelle, LLC.

2Thermal diffusivity / mm ・s

Thermal diffusivity in Metal / Ceramics-1

Thermal diffusivity in Tungsten materials

In ceramics, high temperature increase
phonon-phonon scattering and thermal
diffusivity α is described as α= k/T n
where unirradiated specimens shown = 1 and irradiated them show n < 1.
Unirradiated pure tungsten showed
n～0.4 with the same function.
Furthermore, fusion neutron inducestransmutation element such as
Rhenium or Osmium that reduce
thermal diffusivity drastically.

Pure Tungsten (D10T1 size)with graphene coat

α = k/T
k=677
n=0.405|r|=0.99967

70n60
50
4030300

400500

600

700

800

900

Measurement temperature / K

Thermal Diffusivity / mm2・s-1

In Tungsten, heat is mainly carried byelectron like typical metals, but about
1/3 of heat is carried by phonon likeceramics (at room temperature).

80

60

Pure W
40% drop

W-3%Re40
Almost Flat

Unirradiated D6T2 specimens
4003: Pure W thick plate(//)
500H: Pure W thick plate(⊥)

209003: K-doped W-3%Re(//)
A00C: K-doped W-3%Re( ⊥)0300

400

500

600700Measurement Temperature / K800

RB-19J Irradiation in PHENIX Project
In light water fission reactor, most neutrons
are moderated to thermal neutrons that gives
larger amount of transmutations than thefusion reactor at the same irradiationinduced damage.

W → Re, Os
Thermal diffusivity change;

In the PHENIX project, irradiation in HFIR have been
performed with the Gadolinium thermal neutron shield.

Separate effect oflattice defects fromtransmutations.

Separate thecontribution toheat transfer
Electronconduction

Phononconduction

Reduction of thermal diffusivity withtransmuted Re and Os
W-184 (n,γ) W-185 → βdecay (75.1day) → Re-185
Natural isotope ratio 30.4%, 1.7 barn (Thermal)

W-186 (n,γ) W-187 → βdecay (2.37h) → Re-187
Natural isotope ratio 28.4%, 38.1 barn (Thermal)

Re-187 (n,γ) Re-188 → βdecay (17h) → Os-188

Major radio isotope in W
after neutron irradiation
Transmuted Re and Os
in W decrease thermal
diffusivity severely

Natural isotope ratio 62.6%, 76 barn (Thermal)

Re-185 (n,γ) Re-186 → βdecay (3.7d) → Os-186
Natural isotope ratio 37.4%, 112 barn (Thermal)

Pure W
W-1%Re
W-3%Re
W-5%ReM. Fukuda et al., Fusion Engineering Design, 132 (2018) 1-6.
Neutron absorption cross section @0.0253eV: JENDL-4.0

Rabbit Irradiation in PHENIX Project
Location: peripheral target
position (Fuel trap region)
Dose: 0.42 dpa (PXW2) -0.47 dpa

GDOES ( glow discharge optical emission
spectroscopy) showed the amount oftransmuted elements; [2022Gietl](PXW5) dpa, 1 cycles

Re: 3.3% and Os: 1.9% (PXW2)
Re: 3.1% and Os: 1.3% (PXW5)

1.1×1019 n/m2・s (E > 0.1 MeV) and1.7×1019 n/m2・s (E < 0.5 eV)→ Fluence: 3×1025 n/m2 (E < 0.5 eV)

Temperature
850℃ (PXW2), 800-1100℃(PXW5)

Thermal diffusivity data showed that Gd
shielded RB-19J pure W specimens in
550℃ zone corresponded with thereported W-1%Re alloy [2018Fukuda].

Location: Removable
Beryllium position, RB-19J
Dose: 0.2~0.7 dpa, 4 cycles
4.7×1018 n/m2・s (E > 0.1 MeV) and9.5×1018 n/m2・s (E < 0.5 eV)→ Fluence: 5×1023 n/m2 (E < 0.5 eV)→ Shielded to about 1/60 of rabbitTemperature regions
550℃, 850℃, 1050℃

Rabbit vs RB-19J specimens
Rabbit irradiated pure W specimens showed far lower thermal diffusivity thanthe RB-19J irradiated pure W specimens. It showed a little higher TD than
irradiated W-3%Re specimens, that considered to contain 3% + 1% Re, and also
higher than unirradiated W-5%Re [2003Tanabe], while GDOES results for rabbit
specimens showed (Re + Os) 5.2% (PXW2) and 4.4% (PXW5).

Irradiated RB-19J
500℃ Zone

60

4003: Pure W(//)
500H: Pure W (⊥)
9003: K-doped W-3%Re(//)
A00C: K-doped W-3%Re(⊥)

2

Unirradiated4000: Pure W(//) Tirr 662℃
5001: Pure W(⊥) Tirr 548℃
9000: K-doped W-3%Re(//) Tirr 532℃
A000: K-doped W-3%Re(⊥) Tirr 660℃

5040
30
300

400

500

600

700

Measurement Temperature / K[2022Gietl]
Thermal Difusivity / mm /s

702

Thermal Diffusivity / mm ・s-1

Neutron dose with fast neutrons (calculation):
RB-19J: 0.46 dpa (4000), 0.25 dpa (5001)
Rabbit: 0.42 dpa (PXW2), 0.47 dpa (PXW5)

80070

Re: 3.3% and Os: 1.9% (PXW2)
Re: 3.1% and Os: 1.3% (PXW5)
Nonirr Pure W (for Rabbit irrad.)PHENIX Rabbit irrad. Pure W PXW5PHENIX Rabbit irrad. Pure W PXW2
W-5%Re [2003Tanabe Fig1]

60
Non irrad.

50
40Rabbit irrad.

30 W-5%Re
300

400

500 600 700
Temperature / K

800

900

50
#9003 Unirrad. K-doped W-3e(//)#A00C Unirrad. K-doped W-3e(⊥)
Rabbit irrad. Pure W PXW5
Rabbit irrad. Pure W PXW2#9000 RB-19J irrad. K-doped W-3e(//)#A000 RB-19J irrad. K-doped W-3e(⊥)
W-5%Re [2003Tanabe Fig1]

2

Thermal Difusivity / mm /sRabbit vs RB-19J specimens

4030300400

500 600 700
Temperature / K800

900

Annealing effect for RB-19J specimens
Annealing up to 900℃ for RB-19J irradiated pure W and W-3Re specimens
were performed. No significant recovery in thermal diffusivity was observed.

705001: Pure W(⊥) TIrr 548℃
A000: K-doped W-3Re(⊥) TIrr 660℃

2Thermal diffusivity / mm ・s-1

→ Lattice scattering effect to phonon and electron conduction is limited.

60

measurements up to 600, 700, 800, 900 ℃

504030400600

800

1000

Measurement Temperature / K1200

Ratio of thermal conductivity toelectrical conductivity

The electrical resistibility, specific heat,and density of pure W are summarized
by Tolias and the EUROfusion MST1Team in 2017, and from which thethermal conductivity carried by electron
was obtained using the WiedemannFranz law and L0, then, the thermal
diffusivity can be calculated.

2This difference is attributed tophonon conduction.

Thermal Diffusivity / mm /s

The Wiedemann-Franz law (κ/σ = LT ), which showes that the ratio ofthermal conductivity κ to electrical conductivity σ is proportional totemperature T, is an empirical law. The Lorenz number L0 for a conventional
metal is constant value about (π2/3)(kB/e)2 = 2.44×10-8 WΩK-2, while that ofpure tungsten is 3.2×10-8 WΩK-2, 31% higher. In addition, this L value ismatches at room temperature only ( L for tungsten is changed by temperature).
nα = k/T

60
40

Thermal diffusivity calculated fromelectric conductivity [2017Tolias]-820-2(Lolenz number 3.2x10 -8WΩK )-2(Lolenz number 2.44x10 WΩK )Measured Pure W (D10T1)→ Obtained Phonon contribution

electronconduction

phonon conduction

0400600

800

Temperature / K10001200

Phonon contribution
When we use electron resistivity of `standard doped tungsten' reported in AMS
handbook, electron contribution in thermal diffusivity matched well to the thermal
diffusivity of pure W measured by LFA-467HT at high temperature.
It represent that phonon contribution is negligible above 650 K.
The electron resistivity in thishandbook showed smaller value
compared with other literaturefor pure tungsten specimen.

80
Pure W measured by LFA-467HT
Electron[ASM handbook]Phonon

60
500.4

40

Electric resistivity / μΩm

Thermal Diffusivity / mm2/s

7030
20100-10300

400

500

600

700

800

Temperature / K

900

1000

1100

1200

pure W [2017Tolias]
standard doped W [AMS handbook]

0.3
0.2
0.1
0n

y=Σan xa0=8.224e-03
a1=1.352e-04
a2=5.609e-08|r|=9.9974e-01

400

600

800

n

y=Σan xa0=-2.201e-02
a1=2.415e-04
a2=2.211e-08|r|=9.9990e-01

1000

Temperature / K

Electric resistivity measurement at elevated temperature using the same sample withthermal diffusivity measurement is required.

1200

Phonon contribution in W-Re alloy
When the electron contribution in thermal diffusivity are calculated using theliterature values of high-temperature electrical resistivity in W-5%Re [AMShandbook] and L0, it shows a temperature dependence that increase withtemperature at low temperature and that becomes flat around 800K.
The experimental thermal conductivity of W-5%Re is reported by Tanabe et al. in
2003, then the phonon contribution was obtained with these two data.
80Measured[2003Tanabe]Electron [ASM handbook]Phonon6050

Phonon contribution is almost
same as in pure W.

400.430

Electric resistivity / μΩm

Thermal Diffusivity / mm2/s

7020100-10300

500

700

Temperature / K

900

1100

0.3

y=Σan xna0=1.118e-01
a1=1.465e-04
a2=5.996e-08|r|=9.9981e-01

W-5e [AMS handbook]pure W [2017Tolias]
standard doped W [AMS handbook]

0.2
0.1
0400

600

y=Σan xna0=8.224e-03
a1=1.352e-04
a2=5.609e-08|r|=9.9974e-01

y=Σan xna0=-2.201e-02
a1=2.415e-04
a2=2.211e-08|r|=9.9990e-01

800

1000

Temperature / K

1200

Thermal diffusivity /mm 2/s

Point defects in tungsten
80
unirradiated Pure W
8MeV electron irradiated W upto 3 ×10-3dpa at 216℃

70
60
50
40
300

400

500
600
Temperature / K

700

To clarify the lattice defect contribution, pureW specimens (same material as RB-19J) were
irradiated by 8 MeV electron beams using
KURRI-LINAC at 216℃ to 2.8×10-3 dpa. Afterthe irradiation, this specimen did not show any
degradation in thermal diffusivity while ceramics
material such as β-SiC electron irradiated up
to similar dose showed obvious change.

800

This result suggests that recovery afterstage III in W is quite limited because noI-loops are induced in this specimen andmost point defects have recovered
below 300 K. In the case of pure Cu,
stage III in electron irradiated specimen
above 300 K is quite limited comparedwith neutron irradiated or deuterium
irradiated specimens [1979Ishino].

Recovery of electric resistivity in pure Cu irradiated bydifferent source (detail is not given) [1979Ishino].

Estimation of thermal conductivity
From the experimental and calculation results in this study, the phonon contribution inthermal diffusivity is about 15mm2/s at room temperature for pure W and also W-5%Re.
The thermal diffusivity α is obtained by α = vl / 3 (v : phonon velocity, l : phononmean free path) and v = sqrt(E /ρ) (E : Young's modulus, ρ: density), so using E =400 GPa and ρ = 19.25 g/cm3, v = 4.56×103 m/s and l is obtained as 9.87 nm (athigher temperature, this phonon mean free path is shorter).
It represent that large crystalline defect such as I-loops or grain boundary gives quite
small contribution to thermal diffusivity in phonon conduction. There is no electric
resistivity measurement at high temperature for neutron irradiated W specimen, but
annealing measurement in this study indicates that the effect of crystalline defect toelectric resistivity seems to be limited too.

Then, only Re (and also Os) distribution (NOT only amount)is important to estimate thermal diffusivity in irradiated
W and W-Re alloy.

Re and Os distributionFujitsuka et al. reported thermal diffusivity of neutron irradiated (JMTR,330K) high Re containing W alloy [2000Fujitsuka].
Degradation of thermal diffusivity after theirradiation was saturated at Re 10%Precipitations of Re phase may
extracted by the neutron irradiation.

Transmuted Re/Os is not considered. (+0.1 ～ 0.5% ?)[2000Fujitsuka] Effect of neutron irradiation on thermal diffusivity of tungsten-rhenium alloys, J. Nucl. Matter.,
283-287 (2000) 1148-1151.

Temperature Estimation ofTungsten-Rhenium Alloy
Used in Plasma Facing Components
High Re containing W alloyshows almost flat dependence
to temperature (thermalconductivity increased withtemperature ).

[2000Fujitsuka]

Heat flux 10 MW/m2, Thickness 10 mm
Pure W: TC 170 W/m・K (RT) → 110 W/m・K (1000K)
ΔT 588℃ → 910℃
W-1%Re alloy: TC 120 W/m・K ΔT = 833℃ [2018Fukuda]
W-3%Re alloy: TC 110 W/m・K ΔT = 910℃ [2018Fukuda]
W-5%Re alloy: TC 80 W/m・K ΔT = 1250℃ [2003Tanabe]
W-10%Re alloy: TC 65 W/m・K ΔT = 1538℃ [2000Fujitsuka]

It must be considered thatadditional Re gives the
reducing effect on the DBTT
(ductile-to-brittle transition
temperatures), however it
increase the PFC temperaturethat causes recrystallization.