Diffusive Interaction Between Ni-Cr-Al Alloys
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In high-temperature coatings, welded parts, and a range of other applications, components in the contact zone interdiffuse at elevated temperatures and may react to change the phase composition. The diffusion zone can be complex and can consist of sequential layers of intermediate phases, solid solutions, and in the case of multicomponent systems also of multiphase layers. In this work, the interdiffusion in Ni-Cr-Al alloys is studied experimentally and modeled numerically. The diffusion multiples were prepared by hot isostatic pressing and post-annealing at 1473 K (1200 °C). The concentration profiles were measured with wide-line EDS technique which allowed obtaining high-accuracy diffusion paths. The experimental profiles and diffusion paths were compared with numerical results simulated with application of very recent model of interdiffusion in muticomponent–multiphase systems. The calculated and experimental data show good agreement.
The interdiffusion in multicomponent systems controls many technological processes, such as nitriding, carburizing, and aluminizing. It can, however, also appear as negative phenomenon, causing degradation of protective coatings and alloys. A problem is that diffusion in multicomponent systems can be followed by a formation of multiphase zones of complex morphologies. Such zones can grow in ternary and more component systems which are allowed by Gibbs phase rule.
The diffusion in two- and multiphase zones differs from the diffusion in the single phase and can lead to the effects such as zigzag diffusion, horns at the diffusion path, and jumps of the concentrations without typical interphase boundary.[1,2]
In this work, we study diffusion between single- and two-phase Ni-Cr-Al alloys. The alloys from this system are a basis for the development of numerous creep-resistant alloys. The interest in this system is prompted by the applications of nickel-based superalloys in gas turbines and jet engines working at high temperatures. These alloys have superior mechanical properties and high heat resistance at high temperatures.
The importance of the Ni-Cr-Al system is followed by numerous experimental and theoretical studies of the phase diagrams for this system.[4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19] Most of the research is confined to Ni-rich corner at high temperatures, i.e., above 1273 K (1000 °C).
Due to experimental difficulties, the bibliography dedicated to diffusion in Ni-Cr-Al alloys is limited, and there are only few experimental results.[20, 21, 22, 23, 24, 25, 26, 27] Over forty Ni-Cr-Al diffusion couples, in γ|γ + β multiphase couples, were experimentally studied by Nesbitt and Heckel. The samples were annealed at 1373 K and 1473 K (1100 °C and 1200 °C) for 100 hours, and the concentration profiles and diffusion paths measured. The measurement was made in γ phase only. The concentrations and diffusion path in two-phase zone were approximated from the terminal compositions.
As follows in Reference 22 experimental and simulated results of simulations of interdiffusion in γ + β|γ couple were presented. The agreement between calculated and measured diffusion paths was, however, very weak. In Reference 28, DICTRA software was applied and interdiffusion in γ + β|γ simulated. The simulated and measured diffusion paths remained in good agreement. The authors revealed the recession of two-phase zone which agreed with experiment. Unfortunately, the authors have not revealed the kinetic coefficients used in the calculations.
This work shows the progress in the field of mass transport in multiphase systems. It is our aim to combine new experimental technique with advanced modeling of interdiffusion, determinate diffusion profiles and paths, and to characterize the phenomena that follow diffusion in the studied system.
In particular, the diffusion multiple method and the wild-line EDS analysis (WL-EDS) in combined with Savitzky-Golay filtering are applied to obtain high-quality experimental diffusion profiles. The experimental data are compared with the results simulated with application of our very recent phenomenological model of interdiffusion in the two-phase zone.
2 Sample Preparation
To study experimentally the interdiffusion in Ni-Cr-Al system, the diffusion multiple method developed by Zhao in 2001 is used. The method allows obtaining a large number of data from single experiment and can be used to investigate phase diagrams, precipitate-growth kinetics, and interdiffusion.[29,33, 34, 35, 36]
Compositions of the Alloys Used in the Studies of the Diffusion in the Ternary Ni-Cr-Al System
Alloy Symbol: Phase Composition
Chemical Composition [At. Pct]
γ + γ′
γ + β
The container with the samples was vacuum welded with electron beam under the pressure 2 × 10−5 mbar and then subjected to 1-hour hot isostatic pressing (HIP) at 1473 K (1200 °C), under the pressure 200 MPa. The sample was cooled inside the furnace. Then, it was cut into slices about 3-mm thick, which were abraded to remove cut-offs. Chosen samples were subjected to further annealing in vacuum-closed quartz ampoule. Annealing was conducted in the furnace chamber, for 25 hours at 1473 ± 5 K (1200 ± 5 °C). After this time, it was water quenched and then subjected to further examination.
To eliminate an impact of surface effects on diffusion profiles, the samples were grounded and about 1-mm-thick layer of the material was removed. Next, they were polished by 0.25 µm SiO2 suspension. After the process, the samples were about 1-mm thick.
3 Concentration Profile Measurements
SEM micrographs and EDS analysis of concentration profiles of the samples presented in this work were made using scanning electron microscope FEI VERSA 3D equipped with field emission electron gun (FEG) and the energy-dispersive X-ray spectrometer (EDS) which was used for the chemical composition measurements.
The standard linear EDS analysis, in which an electron beam is moved along a single straight line, is not appropriate for analyzing the average chemical composition in the two-phase zone. In the method, the electron beam moves from one point to another and collects data from the different phases, and the grain interfaces which causes scatter of data. In this work, the wide-line EDS method (WL-EDS) offered by TEAM™ EDS Advanced Linescan, by EDAX Software, is used to measure the concentration profiles in the diffusion zone.
It is seen that even the application of the wide- line method does not allow total elimination of data scattering in two-phase zone. The “noise” in WL-EDS is rather large. To reduce it, we have used the Savitzky–Golay filter with window 4 µm. The filtered concentration profiles are presented in Figure 3 (right column).
The presented results confirm that concentration profiles are not affected by the increase of the step size from 0.2 to 1 µm. The step size reduced below 1 µm ensures only small increase of the quality of the data but markedly increases the measurement time. The comparison of experimental and filtered data shows that application of Savitzky–Golay filtering significantly decreases the scattering of data. It is necessary to notice, however, that it smooths the concentration jumps at the interfaces.
Based on the obtained results, we have chosen parameters to be used for the measurements of concentration profiles in the samples annealed for 1 and 26 hours. They are 1 µm step size and 100 µm width for the samples annealed for 1 hour and 5 µm step size and 200 µm width for the samples annealed for 26 hours.
4 Model and Simulations of the Interdiffusion
The interdiffusion model used in this work is based on the Gusak model of interdiffusion in two-phase alloys, in which it is assumed that both phases within two-phase zone are continuous and mass transport takes place in both them. Similar model, but in the reduced form (assumed diffusion through one phase only), is extensively used by Morral et al.
In this work, we study interdiffusion in the one-dimensional multiphase ternary Ni-Cr-Al couple. We assume that the diffusion couple forms a closed ternary system and diffusion occurs through all phases at constant temperature.[32,39] There can coexist two phases within a single layer and the sum of their fractions is 1. Local ortho-equilibrium between the phases is assumed. To generalize the model, we allow various partial molar volumes of the components in the phases, Ωij, and various partial molar volumes of the phases, Ωj. In the model, the unknowns are concentrations (cNi,cCr,cAl), drift velocity, the same for all components, due to interdiffusion within the phases (υj), drift velocity due to the different partial molar volumes of the phases (γ, γ′ and β), υ, and volume fractions of the phases, φj.
The unknowns are calculated by solving the set of equations
In calculations and presentation of data (diffusion paths), we have used phase diagram after Dupin et al. and for simplification assumed that all tie lines in α + β zone are distributed radially so they cross in one point. Details of the model and method of calculations of the equilibrium concentrations in phases are presented in Reference 32.
As the agreement is good, it has prompted us to simulate interdiffusion in the diffusion couples like in the experiment, Table I. Simulations were made for the γ + γ′ and γ + β alloys (Table I) coupled with γ single-phase Ni.
Phase Boundaries Relations and Common Tie-Lines Points, ptie, Used to Calculate Local Equilibrium in the Two-Phase Zones
Common Tie-Lines point: ptie
β|β + γ
kβ:N2 = 0.2216N1 + 0.2752
γ|β + γ
kγ:N2 = −0.2264N1 + 0.2003
γ′|γ + γ′
kγγ′:N2 = 8.2533(N1)2−0.7857N1 + 0.2323
γ|γ + γ′
kγ:N2 = 2.0422(N1)2−0.4041N1 + 0.1845
Component, i, Phase, j
Diffusion Coefficient [cm2/s]
1.2 × 10−9
1.2 × 10−9
1.4 × 10−9
3.2 × 10−11
1.2 × 10−10
1.0 × 10−10
3.2 × 10−10
2.6 × 10−9
1.1 × 10−9
Partial Molar Volume [cm3/mol]
Elemental analysis confirms, that neither aluminum nor chromium oxides, have been formed. For better imaging of the interdiffusion in the multiple, 2D concentration maps were drawn, Figure 5(b) through (d). They cover central joins of all alloys, the area 300 × 270 μm. It is seen that some of the isoconcentration lines overlap with the boundaries visible in SEM images and that the range of 2D diffusion zone does not exceed 100 µm. Accordingly, 2D diffusion in the center does not affect the quasi one-dimensional diffusion zone analyzed here. Observed irregular shape of isoconcentration lines and the loops are due to a character of two-phase microstructure of the alloy, especially γ + β region.
The microstructure images reveal that in both samples the α + β two-phase layers have grown between the β single-phase and the γ + β two-phase layers. Apparently, the diffusion path passes through the α + β two-phase region.
The results for all couples are similar. In the SEM image, a characteristic recessions of β-phase in γ + β zone and γ′-phase in γ + γ′ zone are seen. It is measured as a shift of the type 1 interphase boundary from the initial position (Matano plane). A diffusion paths within the γ single-phase region assume typical S-shape, while within the γ + β and the γ + γ′ two-phase regions, they have zigzag shapes, Figures 7 and 8. The zigzag in γ + γ′ region is not observed which is probably due to the low-spatial resolution of WL-EDS. Visible differences in the microstructures of the samples annealed by 1 and 26 hours are because of different cooling conditions.
Experimental “smoothing” due to increased step applied in the WL-EDS measurements and application of filtering procedure;
Application of the constant diffusion coefficients, concentration independent;
Application of the Fickian flux formula appropriate for ideal systems instead of application of the gradient of chemical potential which is the true driving force in non-ideal Ni-Cr-Al system.
Studies of interdiffusion in multicomponent–multiphase systems present a difficult task. In this work, we have presented the results of joined experimental and numerical studies of interdiffusion in Ni-Cr-Al ternary alloys. The diffusion couples were made by applying the multi-couple method followed by HIP procedure combined with annealing in vacuum-closed ampoule. The applied method allowed obtaining high-quality, planar, repetitive, and oxide-free diffusion couples.
In the measurements of the concentration profiles, the WL-EDS technique has been applied for the first time. It is shown that the method is very reliable in the measurements of average concentrations within multiphase alloys. For better effectiveness and making a method less time-consuming, we have applied data filtering. Experimental studies have been followed by numerical simulations performed by multicomponent–multiphase interdiffusion model based on Gusak model coupled with Darken formalism.[30,32,37,45] In contrast to earlier simulations by Morral et al.,[38,40,42] the diffusion through both phases is assumed in the present calculations. The results, concentration profiles and diffusion paths, show good agreement with experimental data.
Such consistent studies which present fusion of experiment with numerical simulations of interdiffusion in Ni-Cr-Al γ + γ′, γ + β, and α + β alloys are presented for the first time. Good agreement between experimental and simulated data confirms that the proposed model based on Darken formalism can be successfully applied to study mass transport in multicomponent–multiphase alloys. The reliability of WL-EDS technique is also confirmed.
This work is supported by a National Science Center (Poland) decision DEC-011/02/A/ST8/00280.
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