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Cluster dynamics modeling of Mn-Ni-Si precipitates coupled with radiation-induced segregation in low-Cu reactor pressure vessel steels

Formation of precipitates enhanced or induced by irradiation causes hardening and embrittlement of nuclear structural materials. Post-irradiation microstructure characterization of reactor pressure vessel (RPV) steels has shown that precipitation can be strongly associated with radiation-induced segregation (RIS) of solutes on dislocations. However, RIS and precipitation have not been coupled in previous precipitation modeling of RPV steels. Here in this study, a new hybrid and spatially-dependent precipitation model is developed that couples cluster dynamics with RIS, providing an unique way to account for concurrent evolution of heterogeneous cluster densities as well as solute and point defect concentration profiles. The model is applied to study the segregation of Mn, Ni, and Si on dislocations and heterogeneous nucleation of Mn-Ni-Si rich precipitates (MNSPs) in a low-Cu RPV steel. The result shows that the onset of MNSP nucleation on dislocations occurs at the fluence of 2 x 10 23 n.m -2 . The number density and mean radius can reach ~ 10 24 m -3 and 1-2 nm at high fluence, respectively. These observations suggest that the role of RIS and heterogeneous nucleation can be significant for RPV steels under a high fluence of irradiation. Results of simulations adopting various dose rates and dislocation densities show an increased fraction of MNSPs on dislocations at the condition of low dose rate, high dislocation density, and high fluence.

36 MATERIALS SCIENCE↗

The role of excess vacancies in stabilizing solute clusters in low-alloy steels

The formation of solute clusters in irradiated low-alloy steels, such as reactor pressure vessel steels, is a critical cause of radiation hardening and embrittlement. However, the chemical interactions among solute elements and excess vacancies remain to be fully understood. This study employs density functional theory, cluster expansion, and lattice-based Monte Carlo simulations to examine the stability and morphology of nano-size coherent solute clusters with excess vacancies. The findings reveal that excess vacancies are crucial in stabilizing and promoting the growth of Mn-Ni-Si-vacancy clusters. A minimum of seven vacancies is required for stable nucleation and growth of these clusters. These Mn-Ni-Si clusters act as defect sinks, effectively trapping and absorbing mobile vacancies generated under irradiation. Furthermore, phosphorus (P) preferentially dissolves in Mn-Ni-Si clusters due to chemical coupling with vacancies. In conclusion, this study offers new insights into solute-vacancy interactions, enhancing our understanding of solute-defect cluster formation and embrittlement in low-alloy steels.

36 - MATERIALS SCIENCE↗

Materials Data on MnSiNi by Materials Project

MnNiSi crystallizes in the orthorhombic Pnma space group. The structure is three-dimensional. Mn2+ is bonded to five equivalent Si4- atoms to form distorted MnSi5 trigonal bipyramids that share corners with eight equivalent NiSi4 tetrahedra, corners with eight equivalent MnSi5 trigonal bipyramids, edges with six equivalent NiSi4 tetrahedra, and edges with six equivalent MnSi5 trigonal bipyramids. There are three shorter (2.47 Å) and two longer (2.56 Å) Mn–Si bond lengths. Ni2+ is bonded to four equivalent Si4- atoms to form NiSi4 tetrahedra that share corners with eight equivalent NiSi4 tetrahedra, corners with eight equivalent MnSi5 trigonal bipyramids, edges with two equivalent NiSi4 tetrahedra, and edges with six equivalent MnSi5 trigonal bipyramids. There are a spread of Ni–Si bond distances ranging from 2.25–2.30 Å. Si4- is bonded in a 9-coordinate geometry to five equivalent Mn2+ and four equivalent Ni2+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Mn6Si7Ni16 by Materials Project

Mn6Ni16Si7 crystallizes in the cubic Fm-3m space group. The structure is three-dimensional. Mn2+ is bonded in a 4-coordinate geometry to four equivalent Si4- atoms. All Mn–Si bond lengths are 2.84 Å. There are two inequivalent Ni1+ sites. In the first Ni1+ site, Ni1+ is bonded in a trigonal planar geometry to three equivalent Si4- atoms. All Ni–Si bond lengths are 2.26 Å. In the second Ni1+ site, Ni1+ is bonded to four Si4- atoms to form a mixture of corner and edge-sharing NiSi4 tetrahedra. There are one shorter (2.26 Å) and three longer (2.45 Å) Ni–Si bond lengths. There are two inequivalent Si4- sites. In the first Si4- site, Si4- is bonded in a body-centered cubic geometry to eight equivalent Ni1+ atoms. In the second Si4- site, Si4- is bonded to four equivalent Mn2+ and eight Ni1+ atoms to form a mixture of corner and face-sharing SiMn4Ni8 cuboctahedra.

36 MATERIALS SCIENCE↗

Materials Data on MnSiNi by Materials Project

MnNiSi crystallizes in the hexagonal P6_3/mmc space group. The structure is three-dimensional. Mn2+ is bonded to five equivalent Si4- atoms to form a mixture of edge and corner-sharing MnSi5 trigonal bipyramids. There are three shorter (2.35 Å) and two longer (2.43 Å) Mn–Si bond lengths. Ni2+ is bonded in a 6-coordinate geometry to six equivalent Si4- atoms. All Ni–Si bond lengths are 2.64 Å. Si4- is bonded to five equivalent Mn2+ and six equivalent Ni2+ atoms to form a mixture of distorted corner and face-sharing SiMn5Ni6 trigonal bipyramids.

36 MATERIALS SCIENCE↗

Materials Data on Mn3SiNi2 by Materials Project

Mn3Ni2Si crystallizes in the cubic Fd-3m space group. The structure is three-dimensional. Mn is bonded in a 2-coordinate geometry to eight equivalent Mn, four equivalent Ni, and two equivalent Si atoms. There are four shorter (2.82 Å) and four longer (2.87 Å) Mn–Mn bond lengths. There are two shorter (2.49 Å) and two longer (2.72 Å) Mn–Ni bond lengths. Both Mn–Si bond lengths are 2.73 Å. Ni is bonded in a 12-coordinate geometry to six equivalent Mn, three equivalent Ni, and three equivalent Si atoms. All Ni–Ni bond lengths are 2.61 Å. All Ni–Si bond lengths are 2.33 Å. Si is bonded to six equivalent Mn and six equivalent Ni atoms to form face-sharing SiMn6Ni6 cuboctahedra.

36 MATERIALS SCIENCE↗

Materials Data on MnSiNi2 by Materials Project

Ni2MnSi is Heusler structured and crystallizes in the cubic Fm-3m space group. The structure is three-dimensional. Mn2+ is bonded in a 8-coordinate geometry to eight equivalent Ni1+ and six equivalent Si4- atoms. All Mn–Ni bond lengths are 2.46 Å. All Mn–Si bond lengths are 2.84 Å. Ni1+ is bonded in a body-centered cubic geometry to four equivalent Mn2+ and four equivalent Si4- atoms. All Ni–Si bond lengths are 2.46 Å. Si4- is bonded in a 8-coordinate geometry to six equivalent Mn2+ and eight equivalent Ni1+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Mn2SiNi by Materials Project

Mn2NiSi is Zintl Phase-derived structured and crystallizes in the cubic F-43m space group. The structure is three-dimensional. there are two inequivalent Mn sites. In the first Mn site, Mn is bonded in a 4-coordinate geometry to four equivalent Mn, six equivalent Ni, and four equivalent Si atoms. All Mn–Mn bond lengths are 2.45 Å. All Mn–Ni bond lengths are 2.83 Å. All Mn–Si bond lengths are 2.45 Å. In the second Mn site, Mn is bonded in a 4-coordinate geometry to four equivalent Mn, four equivalent Ni, and six equivalent Si atoms. All Mn–Ni bond lengths are 2.45 Å. All Mn–Si bond lengths are 2.83 Å. Ni is bonded in a 4-coordinate geometry to ten Mn and four equivalent Si atoms. All Ni–Si bond lengths are 2.45 Å. Si is bonded in a 4-coordinate geometry to ten Mn and four equivalent Ni atoms.

36 MATERIALS SCIENCE↗

Materials Data on Mn4Si3Ni5 by Materials Project

Mn4Ni5Si3 is Hexagonal Laves-derived structured and crystallizes in the orthorhombic Amm2 space group. The structure is three-dimensional. there are five inequivalent Mn sites. In the first Mn site, Mn is bonded in a 12-coordinate geometry to four Mn, eight Ni, and four Si atoms. There are a spread of Mn–Mn bond distances ranging from 2.77–2.89 Å. There are a spread of Mn–Ni bond distances ranging from 2.73–2.75 Å. There are a spread of Mn–Si bond distances ranging from 2.66–2.83 Å. In the second Mn site, Mn is bonded in a 12-coordinate geometry to four Mn, seven Ni, and five Si atoms. There are one shorter (2.85 Å) and two longer (2.89 Å) Mn–Mn bond lengths. There are a spread of Mn–Ni bond distances ranging from 2.67–2.80 Å. There are a spread of Mn–Si bond distances ranging from 2.68–2.82 Å. In the third Mn site, Mn is bonded in a 12-coordinate geometry to four Mn, seven Ni, and five Si atoms. There are one shorter (2.88 Å) and two longer (2.89 Å) Mn–Mn bond lengths. There are a spread of Mn–Ni bond distances ranging from 2.67–2.80 Å. There are a spread of Mn–Si bond distances ranging from 2.68–2.82 Å. In the fourth Mn site, Mn is bonded in a 12-coordinate geometry to four Mn, eight Ni, and four Si atoms. Both Mn–Mn bond lengths are 2.89 Å. There are a spread of Mn–Ni bond distances ranging from 2.73–2.75 Å. There are a spread of Mn–Si bond distances ranging from 2.66–2.83 Å. In the fifth Mn site, Mn is bonded in a 12-coordinate geometry to four Mn, seven Ni, and five Si atoms. The Mn–Mn bond length is 2.85 Å. There are a spread of Mn–Ni bond distances ranging from 2.67–2.80 Å. There are a spread of Mn–Si bond distances ranging from 2.68–2.82 Å. There are three inequivalent Ni sites. In the first Ni site, Ni is bonded to six Mn, two equivalent Ni, and four Si atoms to form NiMn6Si4Ni2 cuboctahedra that share corners with four equivalent SiMn6SiNi5 cuboctahedra, corners with fourteen NiMn6Si4Ni2 cuboctahedra, edges with six NiMn6Si2Ni4 cuboctahedra, faces with eight NiMn6Si4Ni2 cuboctahedra, and faces with ten SiMn6SiNi5 cuboctahedra. There are one shorter (2.36 Å) and one longer (2.38 Å) Ni–Ni bond lengths. There are a spread of Ni–Si bond distances ranging from 2.28–2.43 Å. In the second Ni site, Ni is bonded to six Mn, four equivalent Ni, and two equivalent Si atoms to form NiMn6Si2Ni4 cuboctahedra that share corners with six SiMn6SiNi5 cuboctahedra, corners with twelve NiMn6Si4Ni2 cuboctahedra, edges with two equivalent NiMn6Si2Ni4 cuboctahedra, edges with four equivalent SiMn6Si2Ni4 cuboctahedra, faces with six equivalent SiMn6SiNi5 cuboctahedra, and faces with twelve NiMn6Si4Ni2 cuboctahedra. There are two shorter (2.30 Å) and two longer (2.41 Å) Ni–Ni bond lengths. Both Ni–Si bond lengths are 2.26 Å. In the third Ni site, Ni is bonded to six Mn, four Ni, and two equivalent Si atoms to form NiMn6Si2Ni4 cuboctahedra that share corners with eight SiMn6SiNi5 cuboctahedra, corners with ten NiMn6Si4Ni2 cuboctahedra, edges with six NiMn6Si2Ni4 cuboctahedra, faces with eight SiMn6SiNi5 cuboctahedra, and faces with ten NiMn6Si4Ni2 cuboctahedra. There are one shorter (2.33 Å) and one longer (2.41 Å) Ni–Ni bond lengths. Both Ni–Si bond lengths are 2.31 Å. There are two inequivalent Si sites. In the first Si site, Si is bonded to six Mn, five Ni, and one Si atom to form SiMn6SiNi5 cuboctahedra that share corners with two equivalent SiMn6Si2Ni4 cuboctahedra, corners with ten NiMn6Si4Ni2 cuboctahedra, edges with six equivalent SiMn6SiNi5 cuboctahedra, faces with five SiMn6SiNi5 cuboctahedra, and faces with fifteen NiMn6Si4Ni2 cuboctahedra. The Si–Si bond length is 2.49 Å. In the second Si site, Si is bonded to six Mn, four equivalent Ni, and two equivalent Si atoms to form SiMn6Si2Ni4 cuboctahedra that share corners with eight SiMn6SiNi5 cuboctahedra, corners with ten NiMn6Si2Ni4 cuboctahedra, edges with two equivalent SiMn6Si2Ni4 cuboctahedra, edges with four equivalent NiMn6Si2Ni4 cuboctahedra, faces with six equivalent SiMn6SiNi5 cuboctahedra, and faces with twelve NiMn6Si4Ni2 cuboctahedra.

36 MATERIALS SCIENCE↗

Materials Data on MnSiNi by Materials Project

MnNiSi is half-Heusler structured and crystallizes in the cubic F-43m space group. The structure is three-dimensional. Mn2+ is bonded in a 4-coordinate geometry to four equivalent Ni2+ and six equivalent Si4- atoms. All Mn–Ni bond lengths are 2.37 Å. All Mn–Si bond lengths are 2.73 Å. Ni2+ is bonded in a body-centered cubic geometry to four equivalent Mn2+ and four equivalent Si4- atoms. All Ni–Si bond lengths are 2.37 Å. Si4- is bonded in a distorted q6 geometry to six equivalent Mn2+ and four equivalent Ni2+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on MnSiNi2 by Materials Project

Ni2MnSi crystallizes in the tetragonal P4/mmm space group. The structure is two-dimensional and consists of one manganese molecule and one Ni2Si sheet oriented in the (0, 0, 1) direction. In the Ni2Si sheet, Ni1+ is bonded in a 4-coordinate geometry to four equivalent Si4- atoms. All Ni–Si bond lengths are 2.37 Å. Si4- is bonded in a body-centered cubic geometry to eight equivalent Ni1+ atoms.

36 MATERIALS SCIENCE↗

Materials Data on Mn2SiNi by Materials Project

Mn2NiSi crystallizes in the tetragonal I-4m2 space group. The structure is three-dimensional. there are two inequivalent Mn sites. In the first Mn site, Mn is bonded to four equivalent Mn, four equivalent Ni, and four equivalent Si atoms to form MnMn4Si4Ni4 cuboctahedra that share corners with four equivalent MnMn4Si4Ni4 cuboctahedra, corners with eight equivalent NiMn8Si4 cuboctahedra, edges with eight equivalent SiMn8Ni4 cuboctahedra, edges with sixteen MnMn4Si4Ni4 cuboctahedra, faces with four equivalent SiMn8Ni4 cuboctahedra, faces with six equivalent NiMn8Si4 cuboctahedra, and faces with eight MnMn4Si4Ni4 cuboctahedra. All Mn–Mn bond lengths are 2.51 Å. All Mn–Ni bond lengths are 2.56 Å. All Mn–Si bond lengths are 2.51 Å. In the second Mn site, Mn is bonded to four equivalent Mn, four equivalent Ni, and four equivalent Si atoms to form MnMn4Si4Ni4 cuboctahedra that share corners with four equivalent MnMn4Si4Ni4 cuboctahedra, corners with eight equivalent SiMn8Ni4 cuboctahedra, edges with eight equivalent NiMn8Si4 cuboctahedra, edges with sixteen MnMn4Si4Ni4 cuboctahedra, faces with four equivalent NiMn8Si4 cuboctahedra, faces with six equivalent SiMn8Ni4 cuboctahedra, and faces with eight MnMn4Si4Ni4 cuboctahedra. All Mn–Ni bond lengths are 2.51 Å. All Mn–Si bond lengths are 2.56 Å. Ni is bonded to eight Mn and four equivalent Si atoms to form NiMn8Si4 cuboctahedra that share corners with four equivalent NiMn8Si4 cuboctahedra, corners with eight equivalent MnMn4Si4Ni4 cuboctahedra, edges with eight equivalent MnMn4Si4Ni4 cuboctahedra, edges with eight equivalent NiMn8Si4 cuboctahedra, edges with eight equivalent SiMn8Ni4 cuboctahedra, faces with four equivalent NiMn8Si4 cuboctahedra, faces with four equivalent SiMn8Ni4 cuboctahedra, and faces with ten MnMn4Si4Ni4 cuboctahedra. All Ni–Si bond lengths are 2.51 Å. Si is bonded to eight Mn and four equivalent Ni atoms to form SiMn8Ni4 cuboctahedra that share corners with four equivalent SiMn8Ni4 cuboctahedra, corners with eight equivalent MnMn4Si4Ni4 cuboctahedra, edges with eight equivalent MnMn4Si4Ni4 cuboctahedra, edges with eight equivalent NiMn8Si4 cuboctahedra, edges with eight equivalent SiMn8Ni4 cuboctahedra, faces with four equivalent NiMn8Si4 cuboctahedra, faces with four equivalent SiMn8Ni4 cuboctahedra, and faces with ten MnMn4Si4Ni4 cuboctahedra.

36 MATERIALS SCIENCE↗

Materials Data on Mn3SiNi by Materials Project

Mn3NiSi is beta-derived structured and crystallizes in the cubic P2_13 space group. The structure is three-dimensional. there are four inequivalent Mn sites. In the first Mn site, Mn is bonded in a 12-coordinate geometry to six Mn, three equivalent Ni, and three equivalent Si atoms. There are four shorter (2.53 Å) and two longer (2.56 Å) Mn–Mn bond lengths. There are a spread of Mn–Ni bond distances ranging from 2.46–2.57 Å. There are a spread of Mn–Si bond distances ranging from 2.45–2.58 Å. In the second Mn site, Mn is bonded in a 12-coordinate geometry to six Mn, three equivalent Ni, and three equivalent Si atoms. There are three shorter (2.53 Å) and one longer (2.56 Å) Mn–Mn bond lengths. There are a spread of Mn–Ni bond distances ranging from 2.46–2.57 Å. There are a spread of Mn–Si bond distances ranging from 2.45–2.58 Å. In the third Mn site, Mn is bonded in a 12-coordinate geometry to six Mn, three equivalent Ni, and three equivalent Si atoms. There are two shorter (2.53 Å) and one longer (2.56 Å) Mn–Mn bond lengths. There are a spread of Mn–Ni bond distances ranging from 2.46–2.57 Å. There are a spread of Mn–Si bond distances ranging from 2.45–2.58 Å. In the fourth Mn site, Mn is bonded in a 12-coordinate geometry to six Mn, three equivalent Ni, and three equivalent Si atoms. Both Mn–Mn bond lengths are 2.53 Å. There are a spread of Mn–Ni bond distances ranging from 2.46–2.57 Å. There are a spread of Mn–Si bond distances ranging from 2.45–2.58 Å. Ni is bonded to nine Mn and three equivalent Si atoms to form NiMn9Si3 cuboctahedra that share corners with six equivalent NiMn9Si3 cuboctahedra, corners with nine equivalent SiMn9Ni3 cuboctahedra, faces with four equivalent SiMn9Ni3 cuboctahedra, and faces with six equivalent NiMn9Si3 cuboctahedra. All Ni–Si bond lengths are 2.27 Å. Si is bonded to nine Mn and three equivalent Ni atoms to form SiMn9Ni3 cuboctahedra that share corners with six equivalent SiMn9Ni3 cuboctahedra, corners with nine equivalent NiMn9Si3 cuboctahedra, faces with four equivalent NiMn9Si3 cuboctahedra, and faces with six equivalent SiMn9Ni3 cuboctahedra.

36 MATERIALS SCIENCE↗

Materials Data on MnSi2Ni by Materials Project

MnNiSi2 crystallizes in the monoclinic P2_1 space group. The structure is three-dimensional. Mn4+ is bonded in a 7-coordinate geometry to seven Si4- atoms. There are a spread of Mn–Si bond distances ranging from 2.31–2.50 Å. Ni4+ is bonded in a 7-coordinate geometry to seven Si4- atoms. There are a spread of Ni–Si bond distances ranging from 2.34–2.52 Å. There are two inequivalent Si4- sites. In the first Si4- site, Si4- is bonded in a 5-coordinate geometry to three equivalent Mn4+ and four equivalent Ni4+ atoms. In the second Si4- site, Si4- is bonded in a 7-coordinate geometry to four equivalent Mn4+ and three equivalent Ni4+ atoms.

36 MATERIALS SCIENCE↗