Progress on the Diffusion Kinetics of Novel Co-based and Nb-Si-based Superalloys

doi:10.11900/0412.1961.2023.00128

Acta Metall Sin

2023, Vol. 59

Issue (8): 969-985 DOI: 10.11900/0412.1961.2023.00128

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Progress on the Diffusion Kinetics of Novel Co-based and Nb-Si-based Superalloys

LIU Xingjun¹^,²^,³(

), WEI Zhenbang³^,⁴, LU Yong³^,⁴, HAN Jiajia³^,⁴, SHI Rongpei¹^,², WANG Cuiping³^,⁴(

)

¹Institute of Materials Genome and Big Data, Harbin Institute of Technology, Shenzhen, Shenzhen 518055, China
²School of Materials Science and Engineering, Harbin Institute of Technology, Shenzhen, Shenzhen 518055, China
³College of Materials and Fujian Key Laboratory of Surface and Interface Engineering for High Performance Materials, Xiamen University, Xiamen 361005, China
⁴Xiamen Key Laboratory of High Performance Metals and Materials, Xiamen University, Xiamen 361005, China

Cite this article:

LIU Xingjun, WEI Zhenbang, LU Yong, HAN Jiajia, SHI Rongpei, WANG Cuiping. Progress on the Diffusion Kinetics of Novel Co-based and Nb-Si-based Superalloys. Acta Metall Sin, 2023, 59(8): 969-985.

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Abstract

Data on diffusion kinetics of superalloys is crucial for gaining a thorough understanding of the mechanisms underlying the phase transition and microstructural evolution of superalloys. Further, it is the basis for the design and development of novel Co and Nb-Si-based superalloys. Herein, the common elements used in preparing superalloys and their corresponding functions are systematically summarized. In addition, the contribution of our research group in the establishment and improvement of databases on multicomponent diffusion kinetics of novel Co and Nb-Si-based superalloys is presented in detail. Furthermore, the machine learning method for self-diffusion coefficient and impurity diffusion coefficient, the experimental method for mutual diffusion coefficients, and the molecular dynamics method for tracer diffusion coefficients in the alloy systems are briefly discussed. In addition to providing a brief introduction of the applications of the databases in the simulation of microstructural evolution and alloy design, an outlook on the development of the databases on diffusion kinetics and related applications is presented.

Key words: Co-based superalloy Nb-Si-based superalloy kinetics database microstructure

Received: 27 March 2023

ZTFLH:

TG146.1

Fund: National Natural Science Foundation of China(51831007);Guangdong Basic and Applied Ba-sic Research Foundation(2021B1515120071);Shenzhen Science and Technology Program(SGDX20210823104002016)

Corresponding Authors: LIU Xingjun, professor, Tel:(0592)2187888, E-mail: xjliu@hit.edu.cn;WANG Cuiping, professor, Tel:(0592)2180606, E-mail: wangcp@xmu.edu.cn

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	WEI Zhenbang
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https://www.ams.org.cn/EN/10.11900/0412.1961.2023.00128 OR https://www.ams.org.cn/EN/Y2023/V59/I8/969

Table 1 Effects of alloying elements on Co-based superalloys^[16-26]

Element	Microstructure and mechanical property	Oxidation resistance property
Si	Alloy's strength increases, but its ductility and toughness decrease, due to the formation of Nb₃Si and Nb₅Si₃	With increasing temperature over 1000^oC, the resistance to oxidations decreases because of the reduction in the density of oxide films caused by a phase transformation in SiO₂
Al	Inhibiting the formation of Nb₃Si phase and promoting the formation of β-Nb₅Si₃. Toughness decreases, due to the formation of Nb₃Al with a content of Al more than 6% (atomic fraction)	Resistance to the oxidation increases with formation of a dense layer of Al₂O₃
Cr	Inhibiting the formation of Nb₃Si phase and promoting the formation of β-Nb₅Si₃. Formation of Nb₉Si₂Cr₃ is be-neficial to creep resistance of the alloy, while the formation of NbCr₂ phase has negative effects	Enhancing the oxidation resistance of the alloy above 1000^oC by forming Nb₉Si₂Cr₃, NbCr₂ with high oxidation resistance and NbCrO₄ which beneficial to improving adhesion of the oxide layer
Hf	Inhibiting the formation of Nb₃Si phase and promoting the formation of β-Nb₅Si₃. High temperature creep properties decrease, due to the formation of Hf₅Si₃ intermetallic compound with a high content of Hf in alloys	Resistance to oxidations decreases because of embrittlement and cracking of the HfO₂ layer with a high content of Hf
Ti	Stabilizing the Nb₃Si phase. Toughness increases due to the increase in the diffusion rates of the atom and the growth of the phase Nb_ss caused by the addition of Ti	Enhancing the oxidation resistance of the alloy at a temperature below 800^oC by forming dense TiO₂ layers, and decreasing at a temperature above 800^oC due to a phase transformation in TiO₂
V	Stabilizing the α-Nb₅Si₃ phase and inducing the microstr-ucture transformation from dispersion to eutectic-like structure. Alloy's fracture toughness decreases, but its high temperature strength decrease, due to the softening of solid solution caused by thermal activation diffusion process	Resistance to oxidations decreases because of cracking of oxidation layers caused by the formation of V₂O₅ with a high content of V in alloys

Table 2 Effects of alloying elements on Nb-Si-based superalloys^[29-36]

Table 3 Comparisons of three methods for calculating impurity diffusion coefficient and self-diffusion coefficient

Fig.1 Flow chart for obtaining diffusion coefficients based on experimental methods^[37-39] (T₀—diffusion temperature, x—distance, t—diffusion time, D^*—tracer diffusion coefficient, c—element concentration, S—mass per unit area of the diffusing material)

Fig.2 Flow diagram of the implementation of machine-learning for predicting the diffusion coefficients in bcc, fcc, and hcp phases^[67] (R—gas constant, T—temperature, D—diffusion coefficient)

Fig.3 Ranking of the importance of features in the impurity diffusion activation energy (Q_I) machine learning model (a)^[67], and comparisons among the results calculated by the self-diffusion activation energy (Q_s) (b)^[84] and Q_I (c)^[67] machine learning models and experimental measurements (The features were classified as follows, 1) Electron configuration: numbers of electrons in closed-shell and s-, p-, d-, and f-orbits (CEC, N_s, N_p, N_d, N_f); 2) Atomic properties: atomic radius (AR), atomic mass (AM), and electronegativity (EN); 3) Lattice parameters (including a, c, and γ) and atomic coordinate number (Z); 4) C_ij; 5) T_m. The superscripts of the features M, I, Δ, and R denote matrix, impurity, matrix-impurity, and matrix/impurity, respectively)

Mobility of Co	Phase	Parameter	Mobility of Nb	Phase	Parameter
$ϕ C o C o$ ^[86]	fcc	-296542.9 - 74.48T	$ϕ N b N b$ ^[89]	bcc	-268253.0 - 108.60T
$ϕ C o N i$ ^[87]	fcc	-284.724.0 - 69.23T	$ϕ N b S i$ ^[85]	bcc	-268115.4 - 78.10T
$ϕ C o A l$ ^[88]	fcc	-172082.0 - 28.42T	$ϕ N b A l$ ^[85]	bcc	-267729.0 - 79.90T
$ϕ C o C r$ ^[85]	fcc	-265759.8 - 77.69T	$ϕ N b C r$ ^[85]	bcc	-212705.4 - 77.74T
$ϕ C o T a$ ^[85]	fcc	-283070.4 - 74.59T	$ϕ N b H f$ ^[85]	bcc	-252086.3 - 78.13T
$ϕ C o T i$ ^[85]	fcc	-229653.7 - 76.81T	$ϕ N b T i$ ^[90]	bcc	-268139.0 - 75.56T
$ϕ C o W$ ^[85]	fcc	-264096.5 - 75.94T	$ϕ N b V$ ^[91]	bcc	-258635.1 - 76.09T

Table 4 Partial optimization results of self-diffusion mobility parameter and impurity diffusion mobility parameter of the fcc phase in novel Co-based superalloys and the bcc phase in Nb-Si-based superalloys^[85-91]

Fig.4 Comparisons between the experimental and DICTRA-simulated diffusion paths for various diffusion couples
(a) Ni-Co-Al alloy annealed at 1373 K for 259200 s^[92]
(b) Co-Cr-Mo alloy annealed at 1473 K for 259200 s^[93]
(c) Ni-Mo-Ta alloy annealed at 1473 K for 259200 s^[94]
(d) Ni-Mo-Ta alloy annealed at 1573 K for 172800 s^[94]

Fig.5 Time-dependent mean square displacement (MSD) of Co, Ti, and Ni in alloys with different compositions (a), comparisons of tracer diffusion coefficients calculated using kinetic database and molecular dynamic method (b), and tracer diffusion coefficient $D N i *$ change with composition in the fcc phase of Co-Ti-Ni ternary system at various temperatures (c)^[85]

Fig.6 Distributions of the crack susceptibility coefficient with compositions for Co-Ti-Al (a-c), Ni-Si-Hf (d-f) ternary alloys at cooling rates of 10 K/s (a, d), 100 K/s (b, e), and 1000 K/s (c, f)^[85] (LN (CSC) indicates the logarithm of the thermal crack sensitivity coefficient, the higher the value, the stronger the tendency to produce thermal cracks)

Fig.7 Al (a-c) and W (d-f) concentration distributions in Co-9Al-9W alloy aged at 900^oC for 10 h (a, d), 50 h (b, e), and 100 h (c, f) as simulated by phase-field method^[107]

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