Abstract
The interdiffusion in Ti-based alloys was studied. It was shown that during diffusion at 1,123 K formation of four intermetallic phases occurs. The diffusion paths for six different diffusion couples were determined. Moreover, the entropy production was calculated – the approximation used for determination of the sequence of intermetallic phase formation. In theoretical analysis, the intrinsic diffusion coefficients were determined from the modified Wagner method.
Introduction
Most of the construction materials are multicomponent and consist of several grains and phases. Their macroscopic properties and reliability highly depend on the microstructure and its evolution in time [1, 2]. Knowledge about high temperature diffusion is essential for better understanding of mechanical properties. The main kinetic parameter describing diffusion in multicomponent system is the intrinsic diffusion coefficient. In binary systems, the Boltzmann–Matano (B-M) analysis [3] can be used for determination of this parameter [4]. The generalization of the B–M analysis in single phase system can be found in our previous papers [5, 6]. However, the determination of the intrinsic diffusion coefficient in multiphase systems is not a trivial task. In binary system, the Wagner method can be used [7]. In ternary and higher system there is lack of such approximations.
The intrinsic diffusion coefficients are very important parameters in computer simulations. For example the phase-field model allows for approximation of solidification [8] process and solid-state phase transformations [9]. Phase-field models are applied for simulating grain growth [10], dislocation dynamics [11, 12, 13], crack propagation [14, 15], electromigration [16], solid-state sintering [17, 18, 19] and vesicle membranes in biological applications [20, 21].
On the other hand, the knowledge of kinetic parameters allows for extending old problem of phase competition. In binary alloys the problem is usually solved based on the steady-state approximation – analysis of the difference in diffusion coefficients in phases [22]. In ternary and higher systems the analysis of diffusion coefficients is not enough. The entropy production can be calculated – the baricentric average of the fluxes in each phase [23].
In the general case, the diffusion effects in ternary system can be graphically represented in the concentration triangle (precisely in the isothermal section of the equilibrium phase diagram) as a diffusion path. The diffusion path can go across single and two-phase regions in the ternary diagram. In two-phase region, the direction of the diffusion path with respect to tie lines is critical. When the diffusion path enters the two-phase field at the ends of the same tie line, the two-phase zone does not grow. In the spatial region, the interphase boundary between the two phases at the equilibrium (of the compositions indicated by the tie line ends) occurs. When the diffusion path crosses the tie lines, the two-phase zone can grow. The points of the intersection of the diffusion path with the phase boundaries in the phase diagram serve as a basis to identify the sequential single and two-phase layers present in the diffusion zone.
In this paper, the interdiffusion in Ti-CuNi diffusion couples is discussed – six different diffusion couples were prepared, mainly Ti-Ni10Cu90, Ti-Ni30Cu70, Ti-Ni40Cu60, Ti-Ni60Cu40, Ti-Ni70Cu30 and Ti-Ni90Cu10. The four intermetallic phases were generated during diffusion process. The generalized Wagner method was proposed for determination of intrinsic diffusion coefficient and the entropy production was calculated. The entropy production allowed for determination of the sequence of phase growth [22].
Experimental
The rods of CuNi (high purity model alloys) with nominal compositions of samples 1–6: 10 at.%Ni+ 90 at% Cu, 30 at.%Ni+ 70 at% Cu, 40 at.%Ni+ 60 at% Cu, 60 at.%Ni+ 40 at% Cu, 70 at.%Ni+ 30 at% Cu and 90 at.%Ni+ 10 at% Cu, respectively were produced by Goodfellow in England. Then, the thick discs were cut from the ingot by spark erosion. The surfaces of the discs were ground and polished to mirror finish using SiC papers and diamond pastes down to 0.25 μm particle size. The high purity Ti discs were also cut from rod and polished with the same accuracy. Such prepared discs were connected in molybdenum holder to form the diffusion couple. The specimens were annealed in tube furnace in protective argon atmosphere at the temperature of 1,123 K for 160 hours. After annealing, the discs were cut in two halves and metallographic cross-sections were ground and polished. No Kirkendall-Frenkel effect was observed in the microphotographs. The samples were then analyzed by the EDS in the SEM to obtain the concentration profiles in the bulk interdiffusion zone. The concentration profiles allowed for determination of the diffusion paths in the isothermal ternary phase diagram.
Results
Figures 1, 2, 3, 4, 5 and 6 show the microphotographs of cross-sections of diffusion couples with the description of the formed intermetallic phases. Moreover, the pictures (on the right hand side) present the diffusion paths on the isothermal ternary phase diagram. The dots represent the concentration of the components – Ti, Ni and Cu. Qualitatively, the initial concentration of Cu and Ni determines the diffusion path and formed intermetallic phases. Moreover, after diffusion of sample 1 (Ti-Ni10Cu90) and 2 (Ti-Ni30Cu70) the two-phase zones were generated between the base material and τ1 (Ti(NixCu1−x)2) phase. The generation of two-phase zone determines that the diffusion crosses the tie lines (conodes) during the diffusion process. In the rest samples the two-phase zone is not observed.

Left – the microphotography showing grown intermetallic phases, right – the diffusion path in diffusion couple experiment Ti-Ni10Cu90 at 1,123 K after 160 h.

Left – the microphotography showing grown intermetallic phases, right – the diffusion path in diffusion couple experiment Ti-Ni30Cu70 at 1,123 K after 160 h.

Left – the microphotography showing grown intermetallic phases, right – the diffusion path in diffusion couple experiment Ti-Ni40Cu60 at 1,123 K after 160 h.

Left – the microphotography showing grown intermetallic phases, right – the diffusion path in diffusion couple experiment Ti-Ni60Cu40 at 1,123 K after 160 h.

Left – the microphotography showing grown intermetallic phases, right – the diffusion path in diffusion couple experiment Ti-Ni70Cu30 at 1,123 K after 160 h.

Left – the microphotography showing grown intermetallic phases, right – the diffusion path in diffusion couple experiment Ti-Ni90Cu10 at 1,123 K after 160 h.
The slight increase of Ni concentration in base material – 30 at% causes the completely different relaxation during the diffusion process. In sample1, the following phases will be generated during the diffusion process: Ni10Cu90 → Ni10Cu90+τ1 (Ti(NixCu1−x)2) →uTiCu → Ti2Cu →uTi. However, the diffusion path in sample 2 is different: Ni30Cu70 → Ni30Cu70+τ4 (TiNi3) → τ1 (Ti(NixCu1-x)2) →-TiNi → Ti2Cu →uTi. The qualitative analysis shows that different two-phase zones are formed, namelyNi10Cu90+ τ1 (Ti(NixCu1-x)2) and Ni30Cu70+τ4 (TiNi3), moreover during diffusion in sample1 the TiCu phase will be generated and in sample 2 – TiNi phase. These differences depend on the initial concentration of Ni in base material. The τ4 phase is not seen in the microphotography – Figure 2. The most probable reason is that this phase is consumed during the diffusion because of its low diffusion coefficients are low.
The dissimilarity can be seen also in the thickness of the intermetallic phases, namely with increasing of Ni content the volume of Ti2Cu phase decreases. However, the τ1 phase behaves in the opposite way. This anomalous can be explained by the difference in diffusion coefficients and thermodynamic data in TiNi and TiCu phases.
When the content of the Ni is more than 40 at% the two-phase zone is not generated, thus the diffusion goes through the tie-line – the phases are in thermodynamic equilibrium. However, the diffusion paths are different. In case of sample3 – Ti-Ni40Cu60 the diffusion goes through: Ti-Ni40Cu60 → τ4 (TiNi3) → τ1 (Ti(NixCu1-x)2) →-TiNi → Ti2Cu iNTi. The diffusion path with Ni content greater than 60 at% goes through the Ti2Ni phase instead of Ti2Cu.
The qualitative difference can also be observed in thicknesses of each phase. For example TiNi3 is thicker with increasing of Ni content – Figures 4, 5 and 6.
The relaxation path for diffusion process, when more than one diffusion path is possible is still an open problem in diffusion community. The hypothesis is that the diffusion path with the greatest value of entropy production will be chosen. In fact the entropy production is baricentric average of the square of diffusion fluxes. However, in determination of diffusion velocity is very important task. In case of multiphase ternary diffusion couple diffusion coefficients can be determined from the kinetic process and more accurate modified Wagner method.
In case of one phase growth, for example oxidation process, the growth of the phase can be determined form parabolic rate law:
where
where
Thus, the diffusion coefficient can be calculated from eq. (2). In case of more complicated systems, where more than one reaction layer occurs, the Wagner method should be used in determination of the integral diffusion coefficient. The final equation for intrinsic diffusion coefficient in multiphase system can be written as follows:
where: upper indexes denote the phase,
The diffusion coefficient of pure Cu, Ni and Ti.
Component | Diffusion coefficient, cm2s−1 |
---|---|
Ni | |
Cu | |
Ti |
The average Wagners integral diffusion coefficient calculated from eq. (3).
Average Wagners integral diffusion coefficient, cm2s−1 | |||
---|---|---|---|
Phase | Ni | Cu | Ti |
τ4 (TiNi3) | |||
τ1 (Ti(NixCu1−x)2) | |||
TiNi | |||
Ti2Cu |
When the kinetic parameters are known, the phase competition – the sequence of phase formation, can be determined. The hypothesis is that the first phase will appear characterized with the biggest entropy production, eq. (4) [22].
where
where
Similar like Wagner method eq. (4) cannot be directly used in calculations of entropy production in a system characterized with low non-stoichiometry – gradient of concentration is almost zero. Thus, the gradient operator should be ejected from the right side of the equation. Assuming, that the chemical potential can be calculated from the Gibbs energy:
where
where
The calculated Wagner’s diffusion coefficients as well as the entropy production can be approximated with the calculation error. The mean concentration of the components in intermetallic phases was used in the calculations. Such assumption could increase the numerical error of the model. Moreover, the analysis of the experimental results shows, that both Wagner’s diffusion coefficient as well as entropy production depend on the initial composition of the diffusion pair. Nevertheless, the results of the entropy production in a proper way determine the competition in the binary systems, Table 3. To minimize the possible errors of derivation, the backward and forward differences of chemical potential over the phase (v) have been applied.
The entropy production in Ti-NiCu system, sample 3.
Phase | Entropy production |
---|---|
Τ4 (TiNi3) | |
Τ1 (Ti(NixCu1−x)2) | |
TiNi | |
Ti2Cu |
Figure 7 shows the values of the entropy production in sample 3. It can be seen, that the prediction is that the τ1 (Ti(NixCu1−x)2) will grow as first after that the τ4 (TiNi3) will appear next will be the TiNi and as the last Ti2Cu will form.

The graph showing calculated entropy production in sample 3 for four generated phases.
The calculations strictly depend on kinetic and thermodynamic data, thus the method can be used as first approximation of the competition problem. However, the hypothesis of the maximum of entropy production can be applied to much more similar problems like: approximation of the intersection point of the diffusion path with the phase boundary [1], the uniqueness determination of the diffusion path during the diffusion process [22].
Conclusions
In the present paper the diffusion in Ni–Cu–Ti system was analyzed. Six different diffusion couples were prepared with different amount of Ni and Cu and then coupled with pure Ti. The Wagner method was used for calculation of the integral diffusion coefficients in each phase. Moreover, the kinetic and thermodynamic parameters were then introduced in calculations of entropy production. The maximization of the entropy production allowed for determination of the phase growth order during diffusion process. The method can be further generalized to calculate the kinetic of the diffusion reaction processes in multiphase systems, e. g. internal oxidation process in NiPtO alloy.
Acknowledgements
This work was supported by the National Science Centre (NCN) in Poland, decision number 2014/15/B/ST8/00120.
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- Study on the Evolution of Damage Degradation at Different Temperatures and Strain Rates for Ti-6Al-4V Alloy
- Pack-Boriding of Pure Iron with Powder Mixtures Containing ZrB2
- Evolution of Interfacial Features of MnO-SiO2 Type Inclusions/Steel Matrix during Isothermal Heating at Low Temperatures
- Effect of MgO/Al2O3 Ratio on Viscosity of Blast Furnace Primary Slag
- The Microstructure and Property of the Heat Affected zone in C-Mn Steel Treated by Rare Earth
- Microwave-Assisted Molten-Salt Facile Synthesis of Chromium Carbide (Cr3C2) Coatings on the Diamond Particles
- Effects of B on the Hot Ductility of Fe-36Ni Invar Alloy
- Impurity Distribution after Solidification of Hypereutectic Al-Si Melts and Eutectic Al-Si Melt
- Induced Electro-Deposition of High Melting-Point Phases on MgO–C Refractory in CaO–Al2O3–SiO2 – (MgO) Slag at 1773 K
- Microstructure and Mechanical Properties of 14Cr-ODS Steels with Zr Addition
- A Review of Boron-Rich Silicon Borides Basedon Thermodynamic Stability and Transport Properties of High-Temperature Thermoelectric Materials
- Siliceous Manganese Ore from Eastern India:A Potential Resource for Ferrosilicon-Manganese Production
- A Strain-Compensated Constitutive Model for Describing the Hot Compressive Deformation Behaviors of an Aged Inconel 718 Superalloy
- Surface Alloys of 0.45 C Carbon Steel Produced by High Current Pulsed Electron Beam
- Deformation Behavior and Processing Map during Isothermal Hot Compression of 49MnVS3 Non-Quenched and Tempered Steel
- A Constitutive Equation for Predicting Elevated Temperature Flow Behavior of BFe10-1-2 Cupronickel Alloy through Double Multiple Nonlinear Regression
- Oxidation Behavior of Ferritic Steel T22 Exposed to Supercritical Water
- A Multi Scale Strategy for Simulation of Microstructural Evolutions in Friction Stir Welding of Duplex Titanium Alloy
- Partition Behavior of Alloying Elements in Nickel-Based Alloys and Their Activity Interaction Parameters and Infinite Dilution Activity Coefficients
- Influence of Heating on Tensile Physical-Mechanical Properties of Granite
- Comparison of Al-Zn-Mg Alloy P-MIG Welded Joints Filled with Different Wires
- Microstructure and Mechanical Properties of Thick Plate Friction Stir Welds for 6082-T6 Aluminum Alloy
- Research Article
- Kinetics of oxide scale growth on a (Ti, Mo)5Si3 based oxidation resistant Mo-Ti-Si alloy at 900-1300∘C
- Calorimetric study on Bi-Cu-Sn alloys
- Mineralogical Phase of Slag and Its Effect on Dephosphorization during Converter Steelmaking Using Slag-Remaining Technology
- Controllability of joint integrity and mechanical properties of friction stir welded 6061-T6 aluminum and AZ31B magnesium alloys based on stationary shoulder
- Cellular Automaton Modeling of Phase Transformation of U-Nb Alloys during Solidification and Consequent Cooling Process
- The effect of MgTiO3Adding on Inclusion Characteristics
- Cutting performance of a functionally graded cemented carbide tool prepared by microwave heating and nitriding sintering
- Creep behaviour and life assessment of a cast nickel – base superalloy MAR – M247
- Failure mechanism and acoustic emission signal characteristics of coatings under the condition of impact indentation
- Reducing Surface Cracks and Improving Cleanliness of H-Beam Blanks in Continuous Casting — Improving continuous casting of H-beam blanks
- Rhodium influence on the microstructure and oxidation behaviour of aluminide coatings deposited on pure nickel and nickel based superalloy
- The effect of Nb content on precipitates, microstructure and texture of grain oriented silicon steel
- Effect of Arc Power on the Wear and High-temperature Oxidation Resistances of Plasma-Sprayed Fe-based Amorphous Coatings
- Short Communication
- Novel Combined Feeding Approach to Produce Quality Al6061 Composites for Heat Sinks
- Research Article
- Micromorphology change and microstructure of Cu-P based amorphous filler during heating process
- Controlling residual stress and distortion of friction stir welding joint by external stationary shoulder
- Research on the ingot shrinkage in the electroslag remelting withdrawal process for 9Cr3Mo roller
- Production of Mo2NiB2 Based Hard Alloys by Self-Propagating High-Temperature Synthesis
- The Morphology Analysis of Plasma-Sprayed Cast Iron Splats at Different Substrate Temperatures via Fractal Dimension and Circularity Methods
- A Comparative Study on Johnson–Cook, Modified Johnson–Cook, Modified Zerilli–Armstrong and Arrhenius-Type Constitutive Models to Predict Hot Deformation Behavior of TA2
- Dynamic absorption efficiency of paracetamol powder in microwave drying
- Preparation and Properties of Blast Furnace Slag Glass Ceramics Containing Cr2O3
- Influence of unburned pulverized coal on gasification reaction of coke in blast furnace
- Effect of PWHT Conditions on Toughness and Creep Rupture Strength in Modified 9Cr-1Mo Steel Welds
- Role of B2O3 on structure and shear-thinning property in CaO–SiO2–Na2O-based mold fluxes
- Effect of Acid Slag Treatment on the Inclusions in GCr15 Bearing Steel
- Recovery of Iron and Zinc from Blast Furnace Dust Using Iron-Bath Reduction
- Phase Analysis and Microstructural Investigations of Ce2Zr2O7 for High-Temperature Coatings on Ni-Base Superalloy Substrates
- Combustion Characteristics and Kinetics Study of Pulverized Coal and Semi-Coke
- Mechanical and Electrochemical Characterization of Supersolidus Sintered Austenitic Stainless Steel (316 L)
- Synthesis and characterization of Cu doped chromium oxide (Cr2O3) thin films
- Ladle Nozzle Clogging during casting of Silicon-Steel
- Thermodynamics and Industrial Trial on Increasing the Carbon Content at the BOF Endpoint to Produce Ultra-Low Carbon IF Steel by BOF-RH-CSP Process
- Research Article
- Effect of Boundary Conditions on Residual Stresses and Distortion in 316 Stainless Steel Butt Welded Plate
- Numerical Analysis on Effect of Additional Gas Injection on Characteristics around Raceway in Melter Gasifier
- Variation on thermal damage rate of granite specimen with thermal cycle treatment
- Effects of Fluoride and Sulphate Mineralizers on the Properties of Reconstructed Steel Slag
- Effect of Basicity on Precipitation of Spinel Crystals in a CaO-SiO2-MgO-Cr2O3-FeO System
- Review Article
- Exploitation of Mold Flux for the Ti-bearing Welding Wire Steel ER80-G
- Research Article
- Furnace heat prediction and control model and its application to large blast furnace
- Effects of Different Solid Solution Temperatures on Microstructure and Mechanical Properties of the AA7075 Alloy After T6 Heat Treatment
- Study of the Viscosity of a La2O3-SiO2-FeO Slag System
- Tensile Deformation and Work Hardening Behaviour of AISI 431 Martensitic Stainless Steel at Elevated Temperatures
- The Effectiveness of Reinforcement and Processing on Mechanical Properties, Wear Behavior and Damping Response of Aluminum Matrix Composites