Boltzmann-Matano Method Research Articles

Atomic-resolution interfacial structures and diffusion kinetics in Gd/Bi0.5Sb1.5Te3 magnetocaloric/thermoelectric composites

The demand of a full solid-state cooling technology based on magnetocaloric and thermoelectric effects has led to a growing interest in screening candidate materials with high-efficiency cooling performance, which also stimulates the exploration of magnetocaloric/thermoelectric hybrid cooling materials. A series of Gd/Bi0.5Sb1.5Te3 composites was fabricated in order to develop the hybrid cooling technology. The chemical composition, phase structure and diffusion kinetics across the reaction layers in Gd/Bi0.5Sb1.5Te3 composites were analyzed at different reaction temperatures. Micro-area elemental analysis indicates that the formation of interfacial phases is dominated by the diffusion of Gd and Te while the diffusion of Bi and Sb is impeded. The interfacial phases, including GdTe2, GdTe3, and intermediate phases GdTex, are identified by atomic-resolution electron microscopy. The concentration modulation of Gd and Te is adapted by altering the stacking of the Te square-net sheets and the corrugated GdTe sheets. Boltzmann-Matano analysis was applied to reveal the diffusion kinetics of Gd and Te in the interfacial layers. The diffusion coefficients of Te in GdTe2 and GdTe3 are much higher than that of Gd while in GdTe the situation is reversed. This study provides a clear picture to understand the interfacial phase structures down to an atomic scale as well as the interfacial diffusion kinetics in Gd/Bi0.5Sb1.5Te3 hybrid cooling materials.

Generated compounds at the V-slag/CaO diffusion surface and diffusion characteristics of V and Ca in calcium vanadate

Vanadium slag/CaO diffusion couples were prepared to study the diffusion characteristics of the vanadium slag/CaO interface at 1083 K in the air. The generated phases at different regions were characterized by EPMA, EDS, XRD, and element maps analysis. At the vanadium slag surface that the diffused Ca dose not reached, the main generated phases were Mn2O3 and Fe2O3. V3+ was oxidized to V5+ and reacted with the Ca2+ to form a small amount of Ca2V2O7. Cr was at a disadvantage compared with V in occupying the original Ca2+ of the slag. At the vanadium slag surface that the diffused Ca had reached, the main generated phases were Ca2V2O7. At the CaO surface, the main generated phases were Ca2V2O7 and Ca3V2O8. The interdiffusion coefficients were calculated by a new approach that modified from the Boltzmann-Matano method including the determination of the Matano surface, calculation of the integral and differential using the raw data of the concentration profiles. As the molar fraction of Ca was in the range of 0.15 to 0.86, the average interdiffusion coefficient of Ca2+ was 2.54 × 10−8 cm2·s-1. The average interdiffusion coefficient of V5+ at the V molar fraction of 0.001 to 0.43 was 1.96 × 10−8 cm2·s-1.

Effects of Sc Addition on the Diffusion Kinetics and Mechanical Properties of bcc Ti Alloys

In this study, binary interdiffusivities of bcc titanium-scandium (Ti-Sc) alloys in the temperature range of 1273 K to 1473 K were determined by combining the diffusion couple technique and Boltzmann–Matano method. In addition, the composition-dependent Young’s modulus and hardness of bcc Ti-Sc alloys were obtained using the nanoindentation technique. The results reveal that a small amount of Sc additive can be very beneficial to bio-Ti alloys with good properties.

Simultaneous measurement of interdiffusion and intrinsic diffusion coefficients in liquid metals on the ground

Simultaneous measurements of interdiffusion and intrinsic diffusion coefficients in liquid Sn-Pb were performed using the shear cell method and a stable density layering. The binary diffusion couples of Sn-Pb and Sn0.6Pb0.4-Sn0.4Pb0.6 were used in two experiments with the average molar fraction of diffusion couples NSn = 0.5. The concentration dependency of the interdiffusion coefficient was confirmed to exhibit a downward convexity through the comparison of the interdiffusion coefficients. However, the Boltzmann–Matano method reveals a diminished influence. The sample measurements of the intrinsic diffusion coefficients of a diffusion couple of pure metals demonstrate a dependency on concentration. On the other hand, the difference of diffusion coefficients was small in a diffusion couple of alloys. The difference between the values calculated by fitting the error function based on the superposition of fluxes and by the conventional analysis methods was small. We propose that a reasonable intrinsic diffusion coefficient can be calculated using the superposed equation of error function. The theoretical interdiffusion coefficients were calculated by substituting the measured intrinsic diffusion coefficients into the Darken’s equation and comparing the results with the measured values. As a result, the difference between the theoretical and measured interdiffusion coefficients is not very large.

Simultaneous Measurement of Isotope-Free Tracer Diffusion Coefficients and Interdiffusion Coefficients in the Cu-Ni System

A new formalism recently developed by Belova et al., based on linear response theory combined with the Boltzmann–Matano method, allows determination of tracer and interdiffusion coefficients simultaneously from a single, isotope-free, traditional diffusion couple experiment. An experimental methodology with an analytical approach based on the new formalism has been carried out using the model Cu-Ni system to effectively determine tracer diffusion coefficients from an isotope-free diffusion couple experiment. Cu thin films were deposited in between several binary diffusion couples with varying terminal alloy compositions (Cu-25Ni, Cu-50Ni, Cu-75Ni, Ni). Diffusion couples were annealed at 800, 900 and 1000 °C, and the superimposed concentration profiles of thin film and interdiffusion were analyzed for the simultaneous determination of tracer and interdiffusion coefficients. Processed concentration profiles obtained from the diffusion experiments were also fitted with simple Gaussian distribution function. Results were compared to existing literature data obtained independently by radiotracer experiments, and an excellent agreement has been observed.

Coordinate dependent diffusion analysis of phosphorus diffusion profiles in gallium doped germanium

We have analyzed phosphorus diffusion profiles in an In0.01Ga0.99As/In0.56Ga0.44P/Ge germanium structure during phosphorus co-diffusion with gallium for synthesis of the germanium subcell in multi-junction solar cells.. Phosphorus diffused from the In0.56Ga0.44P layer simultaneously with gallium diffusion into the heavily gallium doped germanium substrate thus determining the specific diffusion conditions. Most importantly, gallium and phosphorus co-diffusion produces two p–n junctions instead of one. The phosphorus diffusion profiles do not obey Fick’s laws. The phosphorus diffusion coefficient DP depth distribution in the specimen has been studied using two methods, i.e., the Sauer–Freise modification of the Boltzmann–Matano method and the coordinate dependent diffusion method. We show that allowance for the drift component in the coordinate dependent diffusion method provides a better DP agreement with literary data. Both methods suggest the DP tendency to grow at the heterostructure boundary and to decline closer to the main p–n junction. The DP growth near the surface p–n junction the field of which is directed toward the heterostructure boundary and its decline near the main p–n junction with an oppositely directed field, as well as the observed DP growth with the electron concentration, suggest that the negatively charged VGeP complexes diffuse in the heterostructure by analogy with one-component diffusion.

Binary diffusion behaviour in Ti–X (X = Al, Mo, V, Cr, Fe) alloys

Abstract Interdiffusion coefficients of the β single-phase in the Ti-rich portion of the binary Ti–X (X = Al, Mo, V, Cr, Fe) systems at 1 523 K were determined by annealing infinite diffusion couples between appropriate pairs of alloys. The values were derived from the concentration profiles by electron probe microanalysis coupled with the Boltzmann–Matano method. The comparison of the interdiffusion coefficients in these binary Ti–X (X = Al, Mo, V, Cr, Fe) systems show that the Mo diffuses the least while the Fe diffuses fastest in titanium alloys. Furthermore, the values of the interdiffusion coefficients of the Ti–Al, Ti–V and Ti–Cr binary systems were similar.

Application of distribution functions in accurate determination of interdiffusion coefficients

Diffusion couple technique in combination with the Boltzmann-Matano method is the widely used approach to evaluate the interdiffusion coefficients in the target systems. However, the quality of the evaluated interdiffusion coefficients due to the Boltzmann-Matano method strongly depends on the fitting degree of the utilized continuous function to the discrete experimental composition profiles. In this paper, the application of different types of distribution functions is proposed to solve this problem. For the simple D-c relations, the normal, pseudo-normal, skew normal, pseudo-skew normal distributions can be employed, while for the complex D-c relations, the superposed distributions should be used. Even for the cases with uphill diffusion, the combined superposition of distributions may be chosen. Through validation in several benchmarks and real alloy systems, accurate diffusion coefficients are proved to be successfully obtained by using the distribution functions. It is anticipated that the Boltzmann-Matano method together with the distribution functions may serve as the general solution for determining the accurate interdiffusion coefficients in different materials.

Microstructural evolution and interdiffusion behavior of Mo-Si-B coating on Nb-Si based alloy

A Mo-Si-B coating was prepared on an Nb-Si based alloy by detonation-gun spraying of Mo followed by co-deposition of Si and B via pack cementation. The microstructural evolution and interdiffusion behavior of the coating/substrate system were investigated by annealing for different times at 1250 °C in argon atmosphere. The results show that the interdiffusion zone has a two-layer structure consisting of (Mo, X′)5Si3 (X’ = Nb, Ti, Cr, Hf) and (Nb, X)5Si3 (X = Ti, Cr, Hf), respectively. The growth of the transitional layer, which obeys a parabolic rate law, is dominated by the inward diffusion of Si from the outer layer to the substrate. The interdiffusion coefficients of Si in the transitional layers are calculated using a modified method based on the Boltzmann-Matano analysis.

Inhibiting effect of Ni-Re interlayer between Ni-Al coating and steel substrate on interdiffusion and carburization

A Ni-Re film was electroplated as a diffusion barrier between the Ni-Al coating and the iron alloy substrate. The interdiffusion between the coating and the substrate was investigated by micro-structure analysis, and the interdiffusion coefficient was calculated using Boltzmann-Matano method. The results indicated that the Ni-Re interlayer played a superior barrier effect, almost fully blocking interdiffusion and retarding the formation of diffusion zone (DZ). The Ni-Al coating without a diffusion barrier showed severe carburization corrosion in the diffusion zone during carburization process, while the Ni-Al coating with the Ni-Re diffusion barrier effectively protected the steel substrate from carbon attack.

Dramatic Enhancement of Long-Term Stability of Erbia-Stabilized Bismuth Oxides via Quadrivalent Hf Doping

The Er2O3-stabilized Bi2O3 (ESB) exhibits a superior oxygen ion conductivity below 750 oC. However, there is significant conductivity decay due to a cubic-to-rhombohedral phase transformation over time at ~ 600oC. Thus, to enhance the kinetic stability of ESB, we develop a novel double-doped bismuth oxide through additional quadrivalent doping in ESB. Surprisingly, 1 mol.% of Hf-doped ESB shows no conductivity degradation without a phase transition for 1200 h at 600 °C, while the conductivity of pure ESB drops to less than 5% of the initial value within 200 h. Additionally, the stability improvement effect is strongly correlated to the ionic radius of the aliovalent dopant with an optimum value at ~ 0.85A. When the Bi3+ diffusivity in the cation sublattice of ESB is measured using the Boltzmann-Matano method, Hf doping greatly reduces the diffusion coefficient by ~53% compared to pure ESB. This result suggests that the control of the cation interdiffusion coefficient is the key parameter for suppression o...

Water-enhanced interdiffusion of major elements between natural shoshonite and high-K rhyolite melts

The interdiffusion of six major elements (Si, Ti, Fe, Mg, Ca, K) between natural shoshonite and a high-K rhyolite (Vulcano island, Aeolian archipelago, Italy) has been experimentally measured by the diffusion couple technique at 1200°C, pressures from 50 to 500MPa and water contents from 0.3 (‘nominally dry’) to 2wt%. The experiments were carried out in an internally heated pressure vessel, and major element profiles were later acquired by electron probe microanalysis. The concentration-distance profiles are evaluated using a concentration-dependent diffusivity approach. Effective binary diffusion coefficients for four intermediate silica contents are obtained by the Sauer-Freise modified Boltzmann-Matano method. At the experimental temperature and pressures, the diffusivity of all studied elements notably increases with dissolved H2O content. Particularly, diffusion is up to 1.4 orders of magnitude faster in a melt containing 2wt% H2O than in nominally dry melts. This effect is slightly enhanced in the more mafic compositions. Uphill diffusion was observed for Al, while all other elements can be described by the concept of effective binary interdiffusion. Ti is the slowest diffusing element through all experimental conditions and compositions, followed by Si. Fe, Mg, Ca and K diffuse at similar rates but always more rapidly than Si and Ti. This trend suggests a strong coupling between melt components. Since effects of composition (including water content) are dominant, a pressure effect on diffusion cannot be clearly resolved in the experimental pressure range.

The Interdiffusion Modeling of Aluminide Coated Ti-47Al-2Cr-2Nb-0.5Zr-0.5Y Intermetallic Alloy


 
 
 In the present study, the interdiffusion behavior between coating layer and substrate of aluminide coated Ti- 47Al-2Cr-2Nb-0.5Zr-0.5Y intermetallic alloy were investigated at 800°C, 900°C, and 1000°C under argon atmosphere (closed system). The pack cementation, consists of 20%-wt. Al, 2%-wt. NH4Cl, and 78%-wt. Al2O3, was carried out at 900°C for 10 hours. The phases in the coatings, interdiffusion layer, and substrate were examined using optical microscope and scanning electron microscope (SEM) while the chemical composition were examined by Energy Dispersive X-Ray Spectroscopy (EDS) attached on the SEM. The interdiffusion coefficients were calculated according to Boltzmann-Matano method using the data obtained from EDS analyses. The calculated interdiffusion coefficients are 7.091 x 10-14, 1.650 x 10-12, and 5.261 x 10-12 cm2/s respectively for 800°C, 900°C, and 1000°C. The analytical and numerical method to predict the concentration profiles between coating layer, interdiffusion layer, and substrate. A reasonable agreement has been achieved between the experimental results and the simulated concentration profiles at every temperatures.
 
 

Zr hydrogenation by cathodic charging and its application in TC4 alloy diffusion bonding

A hydrogenated Zr interlayer was formed by cathodic charging and was subsequently used to facilitate the diffusion bonding of TC4 alloy. The microstructure and phase composition of the hydrogenated Zr were characterized by transmission electron microscopy (TEM), X-ray diffraction (XRD) and thermogravimetry (TG). The hydride γ phase precipitated from the supersaturated αH phase when the αH phase was charged with 0.15 wt.% hydrogen. When the hydrogen content reached 0.3 wt.%, the γ phase completely transformed into the ε phase. The effects of hydrogen on the microstructure evolution and on the mechanical properties of the diffusion bonds were investigated by XRD and by scanning electron microscopy in conjunction with energy-dispersive spectroscopy (SEM/EDS). The interdiffusion coefficient and activation energy of the Ti-hydrogenated Zr diffusion couple were calculated using the Boltzmann-Matano method and Arrhenius' law. According to the experimental and computational results, the thickness of the diffusion layer and the shear strength of the diffusion bond increased drastically with increasing hydrogen content. Specifically, when 0.3 wt.% hydrogen was added into the Zr interlayer, the thicknesses of the diffusion layers of the joints bonded at 650 °C and 700 °C increased by 5 times and 1.2 times, respectively. The activation energy at the Zr-rich end was reduced by approximately 40 kJ mol−1, and the interdiffusion coefficient increased accordingly by two orders of magnitude. Mechanisms for the hydrogen-induced enhancement of diffusion bonding are proposed.

The interdiffusion in copper-nickel alloys

In this paper the interdiffusion process and Frenkel effect (Kirkendall porosity) are studied in Ni-Cu and NiAl-Cu systems at 1273 K. The generalized Boltzmann-Matano method is used for calculation of the intrinsic diffusion coefficients as a polynomial function in the whole composition range. The calculated interdiffusion coefficient in Cu-Ni diffusion couple decrease with increasing Ni content. The total decrease of interdiffusion coefficient exceeds two orders of magnitude. The equation for the void growth rate is obtained. The experimental results of diffusion and voids formation are analyzed. The voids radii is estimated and compared with experiments.

Interdiffusion in Ternary Magnesium Solid Solutions of Aluminum and Zinc

Al and Zn are two of the most common alloying elements in commercial Mg alloys, which can improve the physical properties through solid solution strengthening and precipitation hardening. Diffusion plays a key role in the kinetics of these and other microstructural design relevant to Mg-alloy development. However, there is a lack of multicomponent diffusion data available for Mg alloys. Through solid-to-solid diffusion couples, diffusional interactions of Al and Zn in ternary Mg solid-solution at 400° and 450 °C were examined by an extension of the Boltzmann-Matano analysis based on Onsager’s formalism. Concentration profiles of Mg-Al-Zn ternary alloys were determined by electron probe microanalysis, and analyzed to determine the ternary interdiffusion coefficients as a function of composition. The magnitude of $$\tilde{D}_{ZnZn}^{Mg}$$ ternary interdiffusion coefficients was greater than that of $$\tilde{D}_{AlAl}^{Mg} ,$$ the magnitude of $$\tilde{D}_{ZnZn}^{Al}$$ ternary interdiffusion coefficients was greater than that of $$\tilde{D}_{MgMg}^{Al}$$ , and the magnitude of $$\tilde{D}_{MgMg}^{Zn}$$ was greater than that of $$\tilde{D}_{AlAl}^{Zn}$$ . Appreciable diffusional interactions among Mg, Al, and Zn were observed by variations in sign and magnitude of cross interdiffusion coefficients. In particular, Zn was found to significantly influence the interdiffusion of Mg and Al significantly: the $$\tilde{D}_{MgZn}^{Al}$$ and $$\tilde{D}_{AlZn}^{Mg}$$ ternary cross interdiffusion coefficients were both negative, and large in magnitude, in comparison to $$\tilde{D}_{MgMg}^{Al}$$ and $$\tilde{D}_{AlAl}^{Mg}$$ , respectively. Al and Mg were observed influence the interdiffusion of Mg and Al, respectively, with positive $$\tilde{D}_{MgAl}^{Zn}$$ and $$\tilde{D}_{AlMg}^{Zn}$$ interdiffusion coefficients, but their influence on the Zn interdiffusion was negligible.

P79] New features implemented in the Open Calphad software project

In this paper the interdiffusion process and Frenkel effect (Kirkendall porosity) are studied in Ni-Cu and NiAl-Cu systems at 1273 K. The generalized Boltzmann-Matano method is used for calculation of the intrinsic diffusion coefficients as a polynomial function in the whole composition range. The calculated interdiffusion coefficient in Cu-Ni diffusion couple decrease with increasing Ni content. The total decrease of interdiffusion coefficient exceeds two orders of magnitude. The equation for the void growth rate is obtained. The experimental results of diffusion and voids formation are analyzed. The voids radii is estimated and compared with experiments.

Thermal cyclic oxidation and interdiffusion of NiCoCrAlYHf coating on a Ni-based single crystal superalloy

A NiCoCrAlYHf coating was deposited onto a third generation single crystal superalloy DD10 by arc ion plating (AIP). In the present study, thermal cyclic oxidation and interdiffusion of NiCoCrAlYHf coating at 1100 °Cwere investigated to 1000 h. The coating surface, interface morphology and phase structure of the organization were characterized by scanning electron microscopy (SEM), energy dispersion X ray spectroscopy (EDS) and X ray diffraction (XRD). An interdiffusion zone (IDZ) and a secondary reaction zone (SRZ) were formed after 300 h. Severe inward diffusion of Al, Co and Cr from NiCoCrAlYHf coating and outward diffusion of Ni and refractory elements such as Re and W from the superalloy occur at 1100 °C in air. The SRZ consisting of γ, γ′ and topologically closed-packed phase (TCP) was formed 60 μm distance from the surface of coating in the superalloy after 300 h oxidation. Additionally, the development of IDZ and growth of the SRZ was also observed during thermal cyclic oxidation. Subsequently, interdiffusion coefficients of Al were presented by using a modified form of the Boltzmann–Matano analysis.

Validation of Genetic Programming Tool for the Inverse Analysis of Moisture Transport in Building Materials

This paper offers a comparison of two different approaches aimed at the identification of moisture diffusivity of porous building materials as a function of moisture content. The approaches are represented by a traditional deterministic approach using the Boltzmann-Matano method and novel stochastic approach by genetic programming. The results of the comparative analysis show that genetic programming may be used as an alternative to the traditional approaches. On the basis of the very good agreement between experimental data and optimized output of genetic programming, the validation of the genetic programming method may be considered as successful.

The intrinsic diffusivities in multi component systems

The complete understanding of the phenomenological process related to the position of the Matano and Kirkendall plane in multicomponent system is still lacking. In this paper some aspects of Matano and lattice plane migration are studied by means of numerical simulations. New approach to calculate intrinsic diffusion coefficients in binary Ni–Au system and ternary Cu–Fe–Ni and Co–Fe–Ni is presented. Diffusivities were calculated using modified Boltzmann–Matano method. Self diffusion coefficients of the elements in diffusion couple must be known as well as position of the Kirkendall plane after the experiment to use this method. Diffusion profile was calculated using presented equations. Calculations compared with experimental data prove validity of the presented approach. This work proves that intrinsic diffusion coefficients should be given by the concentration function, not the exact value.