Molecular dynamics simulation of displacement cascades in Ni-Mo alloy

NUCLEAR ENERGY SCIENCE AND ENGINEERING

Molecular dynamics simulation of displacement cascades in Ni-Mo alloy

HU Neng-Wen，

QI Mei-Ling，

XIAO Shi-Fang，

DENG Hui-Qiu，

REN Cui-Lan，

HU Wang-Yu

Nuclear Science and Techniques

Vol.26, No.6

Article number 060603

Published in print 20 Dec 2015

Available online 20 Dec 2015

DOI：10.13538/j.1001-8042/nst.26.060603

38601

Molecular dynamics method is used to investigate the displacement cascades in Ni-Mo binary alloy. Effects of the irradiation temperature, energy of the primary knock-on atoms and concentration of solute Mo atoms are taken into consideration on radiation damage to the Ni-Mo alloy. It is found that Mo atoms reduce production of the Frenkel pairs at 100 K, while they enhance defect production at 300 K and 600 K. Size of the largest defect clusters decreases with increasing concentrations of Mo atoms (C_Mo) at 100 K, but it increases with C_Mo at 300 K and 600 K. Most of the point defects get clustered in cascades leaving only a few vacancies and interstitials isolated.

Molecular dynamics methodDisplacement cascadeNi-Mo alloy

I. INTRODUCTION

High temperature molten salt reactor (MSR) is one of the most promising and safe type of advanced Generation-IV fission reactors [1, 2]. It is expected to operate with fluoride salt melts as fuels and coolants at high temperatures, which raises several requirements for the structural material candidates, such as high corrosion resistance to fluoride salt melts, good manufacturability, high-temperature strength and sufficient radiation resistance [3]. The use of Hastelloy, especially for Hastelloy N, with Ni and Mo being its predominant compositions, is an important candidate of in-core structural materials in MSR because of their high corrosion resistance to fluoride salt melts, high temperature strength and good manufacturability [4].

Nevertheless, bombardment of energetic particles in materials will induce elastic/inelastic collisions and cause thermodynamics phenomena, such as local heat peak and radiation heat waves in materials [5]. Available experimental results show that ion, electron and neutron can do great damage to the microstructures of Hastelloy to form point defects, dislocation loops, stacking fault tetrahedrons (SFTs), precipitates, which leads to swelling, ductility loss, high-temperature strength degradation, hardening, embrittlement and so on [6-10]. These can severely limit lifetime of MSR. For improving radiation resistance of nickel-based alloy, chemical compositions optimization, which is used currently for commercial alloy, can be an available method [11].

First principle calculation has shown that solute atoms affect cracking properties of Hastelloy N [12], hence the importance of studying the effects of solute atoms on radiation resistance of the alloy. Cascade collisions occur in only a few picoseconds, which is too fast to observe experimentally. Molecular dynamics method has been widely used to study displacement cascade since 1993 [13] when it succeeded in primary damage investigation. It is also widely used to study primary defect behaviors in materials [14-16].

To the authors’ knowledge, however, little attentions have been paid on investigation of radiation damage to Ni-Mo alloys [17], especially the displacement cascades in Hastelloy. As the main compositions of Hastelloy N are Ni and Mo atoms [4], we build simple NiMo alloy models in this paper to study effects of irradiation temperature, primary knock-on atom (PKA) energy and contents of solute Mo atoms on the displacement cascades.

II. MODELS AND METHODS

Molecular dynamics method is used to study the displacement cascades in Ni-Mo alloy with modified moldy codes. A set of interatomic potential functions based on the modified analysis embedded atom method (MAEAM) are fitted upon the results of experiments and the first principle calculations. A modified item is added to scale the errors resulting from the spherical approximation of none s-electrons. The total energy of a crystal (E_tot) with N atoms can be calculated by

E_{tot} = \sum_{i} F_{i} (ρ_{i}) + \frac{1}{2} \sum_{i, j i = j} ϕ (r_{i, j}) + \sum_{i} M_{i} (P_{i}),

(1)

where _i Mi (Pi) is the experiential modification item, F(ρ) is the embedding item, and ϕ (r) is the repulsive item. The crossing section describing the interaction between Ni and Mo atoms can be described by

ϕ_{A B} (r) = \frac{μ}{2} [ϕ_{A A} (C_{1} r) + ϕ_{B B} (C_{2} r)],

(2)

where μ, C₁ and C₂ are adjustable parameters. The formulae based on MAEAM theory can be found in our previous papers [18]. The information of Ni-Mo binary alloy phase diagram is considered. The formation enthalpies of common stable phases (such as δ-NiMo, D0a and DO22 structural Ni₃Mo and D1a structural Ni₄Mo) are fitted into the crossing interaction potential parameters of Ni and Mo. The Mo solubility in Ni is considered and fitted approximately as 20% at atomic concentration, which agrees well with the phase diagram of Ni-Mo alloy.

Ni-Mo binary alloy models with the solute Mo atoms in concentration (C_Mo) of 3.0at.%–15at.% are established, where Mo atoms distribute in substitutional sites at random. All alloy models in size of 20a₀×20a₀×20a₀ are relaxed to equilibrium under the NPT ensemble to obtain the lattice constants at each temperature and concentration of Mo atoms, which last about 250 picoseconds. All displacement cascade simulations are performed in large boxes in size of 60a₀×60a₀×60a₀ at the temperatures of 100 K, 300 K and 600 K under NVE ensemble, where a₀ is the lattice constant corresponding to the temperature and C_Mo. The energies of PKAs are 5 keV, 10 keV, 20 keV, 30 keV and 40 keV. In order to avoid tunneling effect, all PKAs are set along the direction of ⟨135⟩, one of the high index direction. The length of the time step is one femtosecond in general. The total number of time steps for each cascade simulation is 15000, which lasts about 15 ps. The Wigner-Seitz cell method is adopted to identify defects in each cascade simulations [19]. Another cut-off separation with the length of 1.25a₀ is used to identify the defect clusters so that two point defects belong to the same defect cluster, if they are within 1.25a₀ apart. All defects generated in cascade collisions are quenched to 0 K before clustering behavior analysis. Each cascade is run five times for better statistics.

III. RESULTS AND DISCUSSION

The dislocation loops affect the number of defects greatly, so the defects in dislocation loops are excluded in the statistical analysis processes of defect number. The number of defects increases rapidly with the PKA energy, so the PKAs initialized with high kinetic energy cause severe collisions under the NVE ensemble, which may displace a great number of lattice atoms. Therefore more defects will be left in the system after cooling-down of the cascade collisions, though most of the displaced atoms are able to recombine with vacancies.

Figure 1 shows that the number of defects resulting from cascade collisions decreases slightly with increasing atomic concentrations of Mo at 100 K. However, it increases rapidly with C_Mo at 300 K and 600 K. Mo atoms seem to play an opposite role in defect generation, They prevent defect generations at low temperatures but enhance them at higher temperatures. This can be understood as synergetic effect of the irradiation temperature and the Mo atom concentration. The randomly distributed solute Mo atoms in Ni-Mo alloy can prevent atoms from both getting displaced and recombining with vacancies in displacement cascade processes. It can be accepted that lattice atoms are harder to get displaced at low temperatures than those at high temperatures because lattice atoms vibrate weaker at low temperature environment than at high temperature. As a consequence, low temperature and high concentration of Mo atoms present an inhibition effect on the defects number. At high temperatures, lattice atoms can be displaced. And once the atoms get displaced, it will be hard for them to get recombined because Mo atoms can prevent displaced atoms from recombining with vacancies, which severely increase the number of defects. In Fig. 1(b), at 300 K, the result at C_Mo = 3.0at.% and PKA energy =40 keV is abnormal, because of large-sized dislocation loops formed at the stable state, when atoms aggregate and form dislocation loops leaving an amorphous zone in the system. The distribution of cascade defects in NiMo alloy is similar to that in iron and tungsten. Irradiation induced vacancies distribute in the center of cascade region but interstitials migrate to the periphery [20, 21].

Fig. 1.

(Color online) The number of defects generated in displacement cascades caused by PKAs of 5–40 keV in NiMo alloy at (a)100 K, (b)300 K and (c) 600 K.

Most defects generated in cascade processes distribute in clusters and the number of small cluster increases with PKA energy. Further analysis concerning the distribution of cluster number shows that most of the defect clusters are sized at smaller than 10. And the number of small clusters increases with the PKA energy. Typical results about the cluster number distribution as the functions of PKA energy and cluster size are shown in Fig. 2. The increasing number of small clusters is due to that high energy PKAs may generate high temperature zones, where interstitials and vacancies are easier to migrate and aggregate. The clustering behaviors of cascade defects in Ni-Mo alloy differ from those in Fe-W alloy, where interstitials usually occur in dumbbells, crowdions or sometimes in dislocation loops [22, 23, 24]. However, most interstitials cluster into SFTs or interstitial loops and a very little fraction of interstitial atoms keep isolated in Ni-Mo alloy.

Fig. 2.

(Color online) The number of defects cluster as function of the defect cluster size and the PKA energy.

The concentration of Mo atoms in Ni-Mo alloy influences the size of the largest cluster, too. As shown in Fig. 3, the number of small clusters decreases slightly with increasing C_Mo. The size of the largest clusters in Ni-Mo alloy decreases with increasing atomic concentrations of Mo at 100 K, while it increases sharply with the Mo content at 600 K. This may be due to that the simulation time of cascade process is not long enough for vacancies to migrate to form clusters. Consequently, the formation of small clusters depends on aggregation of interstitial atoms instead of vacancies. Adding more Mo atoms in Ni-Mo alloy reduces the total number of point defects at low temperatures, making interstitials unavailable for cluster-forming, hence the decrease of number of small clusters and size of the largest clusters with increasing C_Mo. In high temperature environments, Mo atoms in the systems can increase the number of defects and most of the displaced atoms collapse into dislocation loops. because the time is so limited that they are not able to get recombined. Solute Mo atoms at higher atomic fraction will lead to more interstitials aggregation into loops, which also results in the limited interstitials and decreases the number of small clusters. So, the number of small cluster decreases with increasing C_Mo, but the size of the largest clusters increases with C_Mo.

Fig. 3.

(Color online) Distribution of defect cluster number as the functions of cluster size and the concentration of solute Mo atoms at 100 K (a) and 600 K(b). The number of defect clusters generated at C_Mo =3.0at.% and 100 K includes all clusters formed for each PKA energy.

IV. CONCLUSION

The effects of solute Mo atoms, irradiation temperature and PKA energy on displacement cascades in Ni-Mo alloy are investigated with the molecular dynamic method. The conclusions can be as follows:

(1) Solute Mo atoms decrease size of the defect clusters. At 100 K, they reduce production of Frenkel pairs; while at 300 K and 600 K they enhance the defect production.

(2) Most point defects get clustered in the cascade processes. Only a few vacancies and interstitials keep isolated. Dislocation loops can form in cascade under high PKA energies and/or high temperatures.

(3) Most vacancies generated in cascade processes stay in the cascade center, which leads to the formation of a poor-atoms zone in cascade region. A small fraction of single point defects and small clusters can form far away from cascade centers.

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