Elsevier

Calphad

Volume 72, March 2021, 102229
Calphad

The interdiffusivity matrices in fcc_A1 Ni–Cr–V alloys: A high-throughput evaluation by CALTPP program

https://doi.org/10.1016/j.calphad.2020.102229Get rights and content

Abstract

The accurate interdiffusivity for fcc_A1 Ni–Cr–V system is needed for simulating the microstructure evolution for Ni-based alloys. In order to determine the interdiffusivity, totally fifteen diffusion couples bound with fcc_A1 Ni–Cr–V alloys were prepared in the present work. Both EPMA (Electron Probe Micro-Analysis) and XRD (X-ray diffraction) results can verify that all the samples are of fcc_A1 single phase. The composition profiles of each diffusion couple annealed at 1273, 1373 and 1473 K were measured by EPMA and then were fitted by Boltzmann function. Applied the fitted composition profiles to Matano-Kirkaldy method, the interdiffusivities at the intersection points of every two diffusion paths were obtained. All of the obtained interdiffusivities can satisfy the constraints of the thermodynamic stability. Moreover, in order to obtain the composition-dependent interdiffusivity, two types of the numerical inverse method implemented in a recently developed CALTPP (CALculation of ThermoPhysical Properties) program were utilized in the present work. Both methods can result in consistent composition profiles in comparison with the measured ones and can produce interdiffusivities in good agreements with the ones by Matano-Kirkaldy method. Both methods have advantages which can be selected flexibly. In the present work, the pure mathematical method was recommended due to its higher accuracy.

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:J˜i=12tciorci+ci(xxM)dci,(i=Cr,V)where ci or ci+ is the terminal concentration for solute i at left or right side of diffusion couple, ci is the concentration for solote i at the certain position, t is the diffusion time and xM is the distance from Matano plane [[5], [6], [7]], which can be obtained by:cici+(xxM)dc=0

On the basis of Fick's first law, J˜i can also be expressed as:J˜i=(D˜iCrNiCr

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)

  • J.S. Kirkaldy

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    (1957)
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