Calculation of displacement cross-sections for structural materials in accelerators using PHITS event generator and its applications to radiation damage

Figures & data

Figure 1. An overview of the method that was used to calculate the displacement cross-sections.

Figure 2. The recoil energy spectra produced in copper at fast neutron, 14-MeV neutron and 1-GeV proton irradiations. For fast neutrons, the distribution of energies is 53% in the range 0.1 < E_n < 0.5 MeV, 29% in the range 0.5 < E_n < 1 MeV, and 18% in the range 1 < E_n < 2 MeV, respectively.

Table 1. The displacement threshold energies, T_threshold, used in the PHITS.

	Atomic displacement		Atomic displacement
Material	threshold energy (eV)	Material	threshold energy (eV)
Be	31	Co	40
C	28	Ni	40
Mg	25	Cu	30
Al	27	Zr	40
Si	15	Nb	40
Ca	40	Mo	60
Ti	40	Ag	60
V	40	W	90
Cr	40	Au	30
Mn	40	Pb	25
Fe	40	Others	25

Figure 3. Defect production efficiency versus the damage energy. Curves were fitted based on the calculation with BCA and MD [19].

Figure 4. The calculated displacement cross-sections, σ_NRT and σ_BCA–MD, for iron irradiated with protons, neutrons, and deuterons.

Figure 5. The displacement cross-sections, σ_NRT and σ_BCA–MD, for Type 316 and T91 irradiated with protons, neutrons, and deuterons. The cross-section σ_BCA–MD includes the displacement cross-section for iron only with defect production efficiency.

Figure 6. The displacement cross-sections versus incident energy of protons (black line) and neutrons (red line). Solid and dashed lines are the results that were calculated from the PHITS and KIT data [12], respectively.

Figure 7. The displacement cross-sections versus incident energy, for energies ranging from 0.1 MeV to 3 GeV, for protons (black) and neutrons (red). The defect production efficiency, η, was set as 1 for the NRT curves (solid lines) and η was included for the BCA–MD curves (dashed lines).

Table 2. The calculated and experimental displacement cross-sections in aluminum and copper irradiated with fast neutrons [23] and 14-MeV neutrons [24], and in copper and tungsten irradiated with 1.1- and 1.94-GeV protons [3,25]. For the PHITS calculations, the cross-section σ_BCA–MD for aluminum was derived with the averaged ⟨η⟩ given as in [19].

		Cu		Al		Cu		W
		Fast neutron	14-MeV neutron	Fast neutron	14-MeV neutron	1.1-GeV proton	1.94-GeV proton	1.1-GeV proton	1.94-GeV proton
PHITS calculation	σNRT (η = 1) [b]	566	3560	1000	1630	3640	3780	7630	8660
	σBCA–MD[b]	175	1104	450 (η = 0.45)	730 (η = 0.45)	2000	2120	3590	4070
Expt.	σexpt[b]	264	1127	516	1105	1390	1800	2310	4100
Calc./expt.	σNRT/σexpt	2.14	3.16	1.94	1.48	2.62	2.10	3.30	2.11
	σBCA–MD/σexpt	0.66	0.98	0.87	0.66	1.44	1.18	1.55	0.99

Note: 1 barn [b] is equal to 1 × 10⁻²⁴ (cm²).

Figure 8. A schematic view of the TEF-T target assembly at the front part.

Table 3. The DPA values and the ratio of the atomic parts per million (appm) of helium and hydrogen production to DPA value at the top of irradiation specimen and the center of beam windows for TEF-T calculated using σ_NRT and σ_BCA–MD. The calculated data taken from the ESS report [27,29] at the center of a stainless steel beam window of spallation source at ESS are also listed.

	DPANRT	He appm/DPANRT	H appm/DPANRT
	(DPABCA–MD)	(He appm/DPABCA–MD)	(H appm/DPABCA–MD)
Irradiation specimen Type 316 of target vessel at TEF-T, 400 MeV, 250 kW, 4500 hours	13.5 (6.0)	89.3 (201)	668 (1503)
T91 beam window of target vessel at TEF-T, 400 MeV, 250 kW, 4500 hours	12.1 (5.5)	129 (284)	983 (2193)
Stainless steel beam window of spallation source at ESS, 1.3 GeV, 5 MW, 4500 hours	30	233	1667

Figure 9. Depth dependence of the DPA value for 0.2 × 4 × 15 cm irradiation specimen irradiated by 400 MeV–250 kW proton beam with 4500 hours of irradiation time and using σ_NRT.

Figure 10. Comparisons of various data on appm/dpa ratios without defect production efficiencies as a function of the energy of incident protons (this work with a T91 beam window irradiated with 400-MeV protons, the ESS report data that was obtained by using a stainless steel irradiated with 1.3-GeV protons [27,29], and results that were calculated by Lu et al. using an iron irradiated with 0.8-, 1.0-, and 2.0-GeV protons [27, 30]).

Figure 11. DPA distributions in 0.2 × 4 × 15 cm Type 316 irradiated with the beam of deuterons with incident energy of 40 MeV and a beam power of 10 MW, with 5 hours of irradiation time using σ_NRT and σ_BCA–MD.

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