Interdiffusion Coefficients Research Articles

Molecular Dynamics Study of Interdiffusion for Cubic and Hexagonal SiC/Al Interfaces

The mechanical properties of the SiC/Al interface are crucial in estimating the overall strength of this ceramic-metal composite. The present work investigates the interdiffusion at the SiC/Al interface using molecular dynamics simulations. One cubic and one hexagonal SiC with a higher probability of orientations in contact with Al are examined as two samples of metal-matrix nanocomposites with whisker and particulate reinforcements. These reinforcements with the Si- and C-terminated surfaces of the SiC/Al interfaces are also studied. The average main and cross-interdiffusion coefficients are evaluated using a single diffusion couple for each system. The effect of temperature and annealing time are analysed on the self- and interdiffusion coefficients. It is found that the diffusion of Al in SiC is similar in cubic and hexagonal SiC and as expected, the interdiffusion coefficient increases as the temperature and annealing time increase. The model after diffusion can be used to evaluate the overall mechanical properties of the interface region in future studies.

Cation interdiffusion in uranium–plutonium mixed oxide fuels: Where are we now?

The diffusion phenomena in uranium–plutonium mixed oxides U1−yPuyO2dictate the physicochemical properties of mixed oxides (MOX) nuclear fuel throughout manufacturing, irradiation, and storage. More precisely, it is paramount to estimate the cation interdiffusion insofar as it dovetails with the actinide redistribution during sintering and under irradiation. This paper draws a critical review of the existing experimental data of U and Pu interdiffusion coefficients in MOX fuel.

Ternary Diffusion and Thermodynamic Interaction in the β Solid Solutions of Ti–Al–Zr Alloys at 1473 K

Interdiffusion in Ti-rich β solid solutions in Ti–Al–Zr alloys was investigated at 1473 K. In the β Ti–Al–Zr alloys, the main interdiffusion coefficients (i.e., and , respectively) and the cross interdiffusion coefficients, (i.e., and , respectively) have positive values, as well as a slight concentration dependence. The values of are larger than those of . In Ti–Al–X (= V, Cr, Fe, Co, Zr) alloys, the values of the main coefficients are at 1473 K. Repulsive interactions occur between Al and X (= V, Cr, Fe, Co, Zr) atoms in the Ti–Al–X alloys, because the ratio values of the cross coefficients to the main ones are positive in sign. On the other hand, the interactions between Ti (solvent) and X (= V, Cr, Fe, Co, Zr) (or Al) atoms are attractive in the present alloys because the ratio of the converted interdiffusion coefficients is negative values.

High-throughput determination of mechanical and diffusion properties of Ti–Ta–Fe alloys

The mechanical and diffusion properties of Ti-Ta-Fe alloys in the Ti-rich region were investigated by utilizing a high-throughput method, with the combination of nanoindentation and diffusion couple techniques. Five groups of ternary Ti-Ta-Fe diffusion couples were prepared after annealing at 1273 K for 25 h. The composition-dependent mechanical properties of bcc Ti-Ta-Fe system were experimentally determined by means of nanoindentation and electron probe microanalysis (EPMA) techniques. Moreover, the interdiffusion coefficients of Ti-Ta-Fe alloys at 1273 K were confirmed from the composition gradients of the ternary diffusion couples with the support of a pragmatic numerical inverse method. A composition-dependent database on the mechanical and diffusion properties of Ti-Ta-Fe alloys was carefully established and utilized for the discussion of the processability during the hot working. The results indicated that the content of Fe should be controlled for the Ti alloys with high hardness and low Young's modulus.

Estimation of diffusion coefficients by intersecting different types of diffusion paths in a multi-principal element alloy

A unique method for estimating all types of diffusion coefficients in a multicomponent system is proposed by intersecting only two but different types of diffusion paths. This concept circumvents the limitations of the recently proposed diffusion couple methods, such as pseudo-binary, pseudo-ternary, and the body diagonal method, when practiced individually. Here the diffusion coefficients of all the elements can be estimated as compared to the estimation of diffusivities associated with only two or three elements which develop the diffusion profiles following the pseudo-binary and pseudo-ternary methods, respectively. This also reduces the laborious effort required to bring all the serpentine body diagonal diffusion paths close to each other to estimate the diffusivities with an unknown uncertainty when they do not intersect exactly. On the other hand, as proposed in this study, a serpentine conventional (or body diagonal) diffusion path can be intersected by a rectilinear pseudo-binary diffusion path with relative ease at a specific composition. The modification of the equation schemes for the application of different types of diffusion paths in the estimation of tracer, intrinsic, and interdiffusion coefficients is explained in detail. This method is demonstrated in a model NiCoFeCr multi-principal element system at a composition very close to the equiatomic composition. The influence of the vacancy wind effect on intrinsic and interdiffusion coefficients is described in detail.

Diffusion and Atomic Mobility for FCC Ni-Si-Ti Alloys: Experiment and Modeling

The Ni-Si-Ti system plays an important role in high temperature structural materials. Accurate atomic mobilities of fcc Ni-Si-Ti system are essential for the microstructure simulation of Ni-based superalloys. In the present work, diffusion couples of fcc Ni-Si-Ti system have been prepared and annealed at 1273, 1373 and 1473 K. By combining solid/solid diffusion couples with the electron probe microanalysis (EPMA) technique, the interdiffusivities in fcc Ni-Si-Ti were calculated via Matano-Kirkaldy method and numerical inverse method. Based on the reliable thermodynamic description and interdiffusion coefficients measured above, two sets of atomic mobilities were optimized by means of the CALTPP (CALculation of ThermoPhysical Properties) program. These atomic mobilities can reasonably describe the diffusion behaviors by comparing model-predicted diffusivities, concentration profiles and diffusion paths with the experimental ones. Besides, based on these atomic mobilities, three-dimensional surfaces for the interdiffusivity at 1273, 1373 and 1473 K were plotted. Furthermore, three-dimensional planes of the activation energy and frequency factor were evaluated using the Arrhenius equation.

Electric-field assisted ion-exchange of innovative float glass

Electric field-assisted ion exchange process was carried out on an innovative soda magnesia silicate float glass by using a specifically realized equipment which allows to change the applied voltage and the polarity and to measure the flowing current.Parameters such as surface K/Na exchange rate, potassium penetration, inter-diffusion coefficient, residual stress and case depth were measured and correlated with the processing conditions. The results revealed a high propensity of the considered glass to be chemically strengthened and a beneficial effect of the applied electric field in terms of time and temperature. For treatment carried out at 410 °C potassium penetration depth in excess to 10 μm can be achieved in less than 5 min. By alternating the polarity, both sides can be homogeneously reinforced. When the duration of each single cycle at a certain polarity is increased, the potassium penetration depth increases although cycles longer than 10 min can be detrimental.

High-throughput determination of mechanical and diffusion properties in the Ti–Nb–Fe alloys

Accurate Young's modulus, hardness, and interdiffusion coefficient are the necessary information for the design and production of biomedical multicomponent alloys. In this work, five sets of ternary Ti–Nb–Fe diffusion couples were prepared after annealing at 1273 K for 25 h. The composition-dependent Young's moduli and hardness in the bcc Ti–Nb–Fe system were experimentally determined by means of nanoindentation and electron probe microanalysis (EPMA) techniques. Moreover, the main and cross interdiffusion coefficients of Ti–Nb–Fe alloys at 1273 K were confirmed from the composition gradients of the diffusion couples by using a pragmatic numerical inverse method. A composition-dependent database on the mechanical and diffusion properties of Ti–Nb–Fe alloys was carefully established and utilized for the discussion of the processability during the hot workability. The results indicated that Fe concentration control could be very helpful for the development of Ti–Nb–Fe alloys with low Young's modulus, high hardness, and nice processability during the hot working.

Atomic diffusion in liquid Al–Cu melt under static magnetic fields

Atomic diffusion is a natural phenomenon in liquid melt. Avoiding the melt convection is the most challenging when accuracy in measuring the diffusion coefficient of atoms is desired. The diffusion in liquid Al–Cu melts is studied under various static magnetic fields (SMFs). Thermoelectric magnetic convection is induced during the diffusion in the conductive crucible. It is suppressed by increasing the magnetic flux density or eliminated by using an insulated crucible. The interdiffusion coefficient can be accurately measured in the SMF greater than 3 T. The present work provides a new view to study the solidification of alloys under the SMF.

Tracer diffusion under a concentration gradient: A pathway for a consistent development of mobility databases in multicomponent alloys

Diffusion in the CoCrFeMnNi high-entropy alloy is investigated using an augmented tracer / interdiffusion couple approach. The tracer diffusion coefficients are measured along the diffusion path developed between the Co17Cr20Fe20Mn20Ni23 and Co23Cr20Fe20Mn20Ni17 end-members allowing an elaboration of a consistent composition-dependent diffusion database. Both tracer and chemical concentration profiles are successfully reproduced to a tolerable level using a pair-diffusion model avoiding the reference element concept. Up-hill diffusion of Co in the experimental profile is not reproduced by the existing kinetic and thermodynamic databases. The reasons for this mismatch are discussed. The calculation of intrinsic and interdiffusion coefficients from the estimated tracer diffusion coefficients utilizing the thermodynamic parameters is demonstrated. The calculated values of the interdiffusion coefficients produced a reasonable match with the interdiffusion flux profiles developed in the multicomponent diffusion couple. The calculation of the vacancy wind effect indicates its strong influence on several intrinsic cross diffusion coefficients.

Study of the inter-diffusion characteristics and cracking resistance of virgin-aged asphalt binders using molecular dynamics simulation

• Inter-diffusion behavior between virgin and aged asphalt binders were investigated. • The degree of blending between virgin and aged asphalt binders were determined at the molecular level. • The cracking patterns of partial blending and total blending were distinguished. • The relationship between degree of blending and cracking resistance of blended asphalt were explored. To investigate the inter-diffusion characteristics and cracking resistance of blended asphalt binders, the virgin-aged asphalt models were developed through the molecular dynamics (MD) simulation. Based on the mass density profiles of virgin and aged asphalt binders, the effect of temperature on the inter-diffusion coefficients was analyzed. According to the spatial distribution of atoms, different blending states including partial blending and total blending were distinguished. The cracking resistance of blended asphalt binders was characterized by the fracture energy obtained from the stress-displacement responses. Relationship between degree of blending and cracking resistance was explored. Results show that high temperatures can increase the inter-diffusion coefficients of virgin and aged asphalt binders by enhancing the intramolecular potential energy and Van der Waals (VdW) interaction energy. Compared to aged asphalt binder, the virgin asphalt binder may be more susceptible to temperature. Under tensile loading, the crack always initiates in the blending zone of partially blended asphalt binders. However, for the totally blended asphalt binder, the crack is more likely to occur at localized defect locations which is randomly distributed. The ability of blended asphalt binder to withstand deformations becomes better, but the maximum tensile strength decreases a lot as the temperature increases. There is a positive correlation between the degree of blending and fracture energy of blended asphalt binders, indicating that the asphalt binder with a higher degree of blending has better cracking resistance. The results of MD simulations can help determine how much aged binder can be mobilized to blend with virgin binder and help select appropriate virgin binders or other additives that can improve the blending between virgin and aged asphalt.

Estimation of Tracer and Intrinsic Diffusion Coefficients from Body Diagonal Diffusion Couples in a Multi-Principal Element Alloy

The estimation of (n-1)2 interdiffusion coefficients in an n component system requires (n-1) diffusion paths to intersect or pass closely in the (n-1) dimensional space according to the body diagonal diffusion couple method. These interdiffusion coefficients are related to n(n-1) intrinsic (or n tracer diffusion coefficients), which cannot be estimated following the Kirkendall marker experiment in a multicomponent system despite their importance for understanding the atomic mechanism of diffusion and the physico-mechanical properties of materials. In this study, the estimation of tracer diffusion coefficients from only two diffusion profiles following the concept of the body diagonal diffusion couple method in a multicomponent system is demonstrated. Subsequently, one can estimate the intrinsic and interdiffusion coefficients. This reduces the overall effort up to a great extent since it needs only two instead of (n-1) diffusion profiles irrespective of the number of components, with an additional benefit of enabling the estimation of all types of diffusion coefficients. The available tracer diffusion coefficients estimated following the radiotracer method are compared to the data estimated in this study. This method can also be extended to the systems where the radiotracer method is not feasible.

Atomic mobilities and diffusivities in the bcc phase of Ti–Nb–Sn system

Accurate interdiffusion information is essential to control the phase transformation process in metastable β-type titanium alloys. In this work, diffusion behavior in the ternary Ti–Nb–Sn system at 1373 K and 1473 K was experimentally investigated. The ternary interdiffusion coefficients and impurity diffusion coefficients in the bcc Ti–Nb–Sn alloys were determined using the diffusion couple technique, along with the Whittle-Green and Hall methods. Based on the obtained diffusion coefficients, an atomic mobility database for the bcc Ti–Nb–Sn system was established via the CALPHAD (CALculation of PHAse Diagrams) method. In the optimizing procedure, the end members and the binary parameters for the bcc-Ti-Sn system were reassessed. The calculated results using the obtained database agree with the experimental diffusion properties (i.e., interdiffusion, composition-distance profiles and diffusion paths), demonstrating the accuracy of the database developed in this work.

Formation characteristics of CaTiO3 in the vicinity of the calcium ferrite/TiO2 interface

Calcium ferrite-TiO 2 (C x F-TiO 2 ) diffusion couples were prepared to investigate the reaction between TiO 2 and CaO of calcium ferrite during sintering vanadium‑titanium magnetite. The distribution, species, and number of phases in the vicinity of the C x F/TiO 2 interface were characterized by electron probe microanalysis (EPMA), Fourier transform-infrared (FT-IR) spectroscopy, and X-ray diffraction (XRD) that could select the scanning location. The phases generated from the C x F side to the TiO 2 side are 66.66% CaFe 2 O 4 + 33.33% Fe 2 O 3 , 100% CaTiO 3 , 66.66% CaTiO 3 + 33.33% Fe 2 O 3 , and 75% CaTiO 3 + 25% Fe 2 O 3 , respectively. The isothermal section was plotted using the experimental data. The diffusion thickness decreased from 90.2 to 8.1 μm as the temperature decreased from 1323 to 1173 K, and increaesed from 47.4 to 121.4 μm as the annealing time increased from 1 to 4 h. The linear relationship between the diffusion thickness and the square root of the annealing time indicates that the formation of CaTiO 3 was controlled by the diffusion process. Vacancy-mediated diffusion mechanism, which was widely used to describe the diffusion-controlled process, was introduced to describe the formation of CaTiO 3 in the vicinity of the C x F/TiO 2 interface. The Ti 4+ in the TiO 2 layer jumped and diffused through the Ti 4+ vacancies in the CaTiO 3 + Fe 2 O 3 layer to the CaFe 2 O 4 + Fe 2 O 3 /CaTiO 3 interface, and reacted with CaFe 2 O 4 and O 2− to generate CaTiO 3 . The concentration data across the C x F/TiO 2 interface were applied in the modified Boltzmann-Matano method to calculate the interdiffusion coefficient. The average interdiffusion coefficients of various Ti concentrations increased with temperature: 2.51 × 10 −10 , 7.49 × 10 −10 , 2.56 × 10 −9 , and 8.06 × 10 −9 cm 2 ·s −1 at 1173, 1223, 1273, and 1323 K, respectively. The relationship between the logarithm of the interdiffusion coefficient and the reciprocal of the temperature was empirically described by the Arrhenius expression. Linear regression analysis showed that the diffusion activation energy of CaTiO 3 formation is 300.14 kJ/mol. • CaFe 2 O 4 , CaTiO 3, and Fe 2 O 3 generate at the calcium ferrite/TiO 2 interface. • CaTiO 3 forms thorough vacancy-mediated diffusion mechanism. • Diffusion of Ti 4+ governs the CaTiO 3 formation in the calcium ferrite-TiO 2 system. • Diffusion thickness and interdiffusion coefficient increase with temperature. • CaTiO 3 formation requires approximately activation energy of 314 kJ/mol.

Novel General Solution for the Analysis of a Multicomponent Interdiffusion Couple

In this paper, we draw attention to the investigation of the novel exact solution [1.Scripta Mat. 210:114430; M.A. Dayananda, in JPED, this issue, (2022);] that is applicable to a multicomponent (n-component) interdiffusion couple where the interdiffusion matrix may change with alloy composition. In the derivation of this solution the interdiffusion flux J_{j} of a component j is related to (n-1) independent composition gradients for an isothermal, diffusion couple using the well-known continuity equation. Novel exact expressions are then derived for all of the interdiffusion coefficients, tilde{D}_{ij}^{n} (i, j = 1, 2, …..n − 1), where the partial derivatives of the product J_{j} left( {y - y_{0} } right) with respect to composition C_{i} (y_{0} is the Matano plane) are used. In this paper, it is shown that the novel solution leads to a computational procedure similar to the Boltzmann-Matano analysis. Note that the derivatives partial (J_{j} left( {y - y_{0} } right))/partial C_{i} , i,j = 1, ldots ,n - 1 (that are required for the solution) can only be calculated along the diffusion path and therefore, for n > 2, a single couple will not be enough to calculate all of them correctly.

Achieving thermally stable nanoparticles in chemically complex alloys via controllable sluggish lattice diffusion

Nanoparticle strengthening provides a crucial basis for developing high-performance structural materials with potentially superb mechanical properties for structural applications. However, the general wisdom often fails to work well due to the poor thermal stability of nanoparticles, and the rapid coarsening of these particles will lead to the accelerated failures of these materials especially at elevated temperatures. Here, we demonstrate a strategy to achieve ultra-stable nanoparticles at 800~1000 °C in a Ni59.9-xCoxFe13Cr15Al6Ti6B0.1 (at.%) chemically complex alloy, resulting from the controllable sluggish lattice diffusion (SLD) effect. Our diffusion kinetic simulations reveal that the Co element leads to a significant reduction in the interdiffusion coefficients of all the main elements, especially for the Al element, with a maximum of up to 5 orders of magnitude. Utilizing first-principles calculations, we further unveil the incompressibility of Al induced by the increased concentration of Co plays a critical role in controlling the SLD effect. These findings are useful for providing advances in the design of novel structural alloys with extraordinary property-microstructure stability combinations for structural applications.

Synthesis of single metallic crystal in microgravity simulated by static magnetic field

Static magnetic field is useful in processing materials with various microstructures. A self-designed gravity-assisted automatic docking device was used to study diffusion in liquid Al-Cu melts under various SMFs up to 22 T. SMF reduces the coefficient of interdiffusion (DAlCu) by damping the melt convection, which is more efficient with a horizontal SMF than a vertical SMF. A simulated microgravity is achieved when the SMF is greater than the critical 3 T. The simulated microgravity is in favor of growing a single α-Al dendrite in Al-Cu melt. The physical mechanism, which is called the diffusion-limited favored single crystal growth, is established. The present work provides a potential method in processing the single metallic crystal rapidly in the future.

Atom Probe Study of the Miscibility Gap in CuNi Thin Films and Microstructure Development.

The unclear miscibility of CuNi alloys was investigated with atom probe tomography (APT). Multilayered thin film samples were prepared by ion beam sputtering (IBS) and focused ion beam (FIB) shaping. Long-term isothermal annealing treatments in a UHV furnace were conducted at temperatures of 573, 623, and 673 K to investigate the mixing process. The effective interdiffusion coefficient of the nanocrystalline microstructure (including defect diffusion) was determined to be Deff = 1.86 × 10−10 m2/s × exp(−164 kJ/mol/RT) by fitting periodic composition profiles through a Fourier series. In nonequilibrium states, microstructural defects like grain boundaries and precipitates were observed. While at the two higher temperatures total mixing is observed, a clear experimental evidence is found for a miscibility gap at 573 K with the boundary concentrations of 26 and 66 at%. These two compositions are used in a subregular solution model to reconstruct the phase miscibility gap. So, the critical temperature TC of the miscibility gap is found to be 608 K at a concentration of 45 at% Ni.

Determination of the interdiffusion coefficient at low temperature in Ni/NiCr nanometer-scale multilayers using X-ray reflectivity

The interdiffusion coefficient in the Ni/Cr system was determined at low temperature using Ni/Ni0.78Cr0.22 nanometer-scale multilayers with periods of 3.65 and 4.50 nm. X-ray reflectivity measurements were carried out to monitor the 1st Bragg peak intensity with annealing time, at both 400 and 450 °C temperatures. The obtained kinetics of the composition modulation decay allowed determining the interdiffusion coefficients of the uniform final solid solution, Ni0.89Cr0.11. Values in the order of 10−21 to 10-20 cm2.s−1 at 400 °C and 450 °C, respectively, were found, in line with extrapolations from data of Cr diffusion obtained at higher temperature.

Forming mechanism and growth of Kirkendall voids of Sn/Cu joints for electronic packaging: A recent review

For the common Cu-Sn interconnection system in microelectronics packaging, a significant concern is the sporadic interfacial void formation within the Cu–Sn interface and intermetallic compound (IMC) layer during the service. The existence of these voids affects the electrical and mechanical properties of the joint and thus deteriorates reliability. Most scholars simply attribute the Kirkendall voids problem to the Kirkendall effect caused by the difference in Cu/Sn inter-diffusion coefficients. However, Kirkendall voids are formed for a combination of many reasons. The plating additives, current density, surface roughness, coating thickness, and substrate types affect the formation of Kirkendall voids. We believe that among the many factors affecting the formation of voids, the unbalanced diffusion of elements (Kirkendall effect) is the root cause, and impurities and Cu microstructure are the dominant factors. The addition of alloying elements to the solder affects the formation of voids by changing the unbalanced diffusion of elements. This paper releases the possible mechanism of Kirkendall voids and gives the perspective summary from three steps of void formation, and the available suppression method is given based on the final solution.