The interdiffusivity matrices in fcc_A1 Ni–Cr–V alloys: A high-throughput evaluation by CALTPP program
Introduction
Ni–Cr–V system is an important ternary sub-system for both hard metals and superalloys [[1], [2], [3], [4]]. It is well known that the knowledge of diffusion is critical for studying the microstructure evolution. Meanwhile, the knowledge of diffusion for the Ni–Cr–V system is necessary for simulating the grain growth process for the WC phase. Also, the creep resistance of superalloys is closely related to the diffusion coefficients. However, there is no study for diffusion of the Ni–Cr–V ternary system. Therefore, as an important diffusion characteristic, the diffusion coefficients of fcc_A1 Ni–Cr–V system is chosen as the research target in the present work.
In order to investigate the interdiffusivity for a ternary system, the most widely applied method is the well-known Matano-Kirkaldy method [[5], [6], [7]], which can produce accurate results. However, the efficiency of this method is too low to satisfy the requirements for MGI (Materials Genome Initiative) and ICME (Integrated Computational Materials Engineering) [8,9] since it can only calculate the interdiffusivities at the same composition in diffusion paths of two diffusion couples. Recently, to improve this situation, a CALTPP (CALculation of ThermoPhysical Properties) program was developed in our group [[10], [11], [12], [13]], including the numerical inverse method for the high-throughput calculation for the interdiffusivities in a ternary system, which can be used to determine the interdiffusivities over the whole investigated compositions for every single diffusion couples.
To sum up, the purposes of the present work are: i) to measure the composition profiles for prepared fcc_A1 Ni–Cr–V diffusion couples annealed at 1273, 1373 and 1473 K and fit these composition profiles for the subsequent calculations; ii) to calculate the interdiffusivities by Matano-Kirkaldy method and two types of the numerical inverse methods incorporated in the CALTPP program and make a comparison.
Section snippets
Experimental procedure
Pure Ni (purity: 99.99 wt%), Cr (purity: 99.99 wt%), and V (purity: 99.99 wt%) were used as starting materials. The compositions of the alloys were carefully chosen according to the isothermal sections in the ternary Ni–Cr–V system [14]. Button samples of binary and ternary alloys in Ni-rich Ni–Cr–V system and pure Ni were prepared by arc melting pure elements under argon atmosphere (WKDHL-1, Opto-electronics Co. Ltd, Beijing, China) and re-melted four times for homogenization. The phase
Matano-Kirkaldy (M − K) method
Let us start from the expression of interdiffusion fluxes [15] as the following equation:where or is the terminal concentration for solute i at left or right side of diffusion couple, is the concentration for solote i at the certain position, t is the diffusion time and is the distance from Matano plane [[5], [6], [7]], which can be obtained by:
On the basis of Fick's first law, can also be expressed as:
Experiment
Totally eight Ni–Cr–V alloys in fcc_A1 phase were prepared in the present work. The XRD was applied to the alloys, the locations of which in the phase diagram were close to the phase boundary, i.e. Ni–9V–31Cr, Ni–28 V–7Cr and Ni–20V–19Cr (at. %). The compositions are shown in Fig. 1. It can be clearly seen that the three alloys are located in fcc_A1 phase. This is the case for the other five alloys.
Using the eight prepared alloys, totally fifteen diffusion couples were made in the present work.
Conclusions
In the present work, the interdiffusivity for fcc_A1 Ni–Cr–V alloy was investigated by experiments and modeling, and the main conclusions are as follows:
- (1)
Totally fifteen diffusion couples made by fcc_A1 Ni–Cr–V alloys were prepared and were annealed at 1273, 1373 and 1473K. The XRD and EPMA results indicate the presently prepared samples are of fcc_A1 single phase;
- (2)
The interdiffusivities at intersection points of every two diffusion paths were calculated by Matano-Kirkaldy method and the results
Declaration of competing interest
The authors declare that they have no conflict of interests.
Acknowledgement
Financial support from the National Natural Science Foundation of China (Grant No. 51531009), the Program for Guangdong Introducing Innovative and Entrepreneurial Teams (NO: 2016ZT06G025) and Guangdong Natural Science Foundation (NO: 2017B030306014) are greatly acknowledged.
References (22)
Physics of transition metal carbides
Mater Sci Eng A
(1988)Materials science of cemented carbides - an overview
Mater. Des.
(2001)- et al.
CALPHAD, first and second generation–birth of the materials genome
Scr. Mater.
(2014) - et al.
A novel approach to calculate diffusion matrix in ternary systems: application to Ag–Mg–Mn and Cu–Ni–Sn systems
Calphad
(2020) - et al.
Diffusivity and atomic mobility for fcc Ni–Cu–Ti alloy: measurements and an intelligent modeling
Calphad
(2020) - et al.
Determination of the phase diagram of the V-Ni-Cr system using diffusion couples and equilibrated alloys
J. Less Common. Met.
(1987) - et al.
The measurement of diffusion coefficients in ternary systems
Scr. Mater.
(1974) - et al.
A numerical inverse method for calculating the interdiffusion coefficients along a diffusion path in ternary systems
Acta Mater.
(2002) Cobalt in Cemented Carbides, Cobalt Monograph
(1960)Transition Metal Carbides and Nitrides
(1971)
Diffusion in multicomponent metallic systems
Can. J. Phys.
Cited by (8)
Interdiffusion and atomic mobility in FCC Ag–Cu–Ni alloys
2024, Journal of Materials Research and TechnologyDiffusivity and atomic mobility for Fcc Ni–Ti–V alloys: Experiment and modeling
2023, Calphad: Computer Coupling of Phase Diagrams and ThermochemistryDiffusion kinetics for fcc quinary Cu–Co–Mn–Ni–Si system and its application to precipitation simulations
2023, Journal of Materials Research and TechnologyDiffusion coefficients and atomic mobilities in fcc Ag–Ge and Cu–Ge alloys: Experiment and modeling
2022, Calphad: Computer Coupling of Phase Diagrams and ThermochemistryCitation Excerpt :The main advantage of the novel numerical inverse method is that the interdiffusion coefficients and the atomic mobility parameters can be obtained simultaneously during one optimization process, which is of high accuracy and efficiency. It is worth mentioning that previous studies indicated that the calculation efficiency of the novel numerical inverse method outperforms traditional Matano-Kirkaldy method in ternary systems [22,24–26]. In the present work, this numerical inverse method was applied to the binary Ag–Ge and Cu–Ge systems.
Interdiffusion and atomic mobility in hcp Mg–Al–Sn alloys
2021, Journal of Alloys and CompoundsCurrent Status and Future Scope of Phase Diagram Studies
2023, ISIJ International