Impurity Diffusion Coefficients Research Articles

Introducing concepts of estimating tracer and intrinsic diffusion coefficients in a ternary system: a case study in the FCC Fe-Mn-Cr solid solution

ABSTRACT Estimating tracer and intrinsic diffusion coefficients following the diffusion couple method with systematic composition variation can be challenging because of the diffusion paths’ serpentine or double serpentine nature on the Gibbs triangle. Moreover, the possibility of estimating these diffusion coefficients from a single diffusion profile can have immense benefits. We have demonstrated four ways of estimating tracer and impurity diffusion coefficients in the FCC Fe-Mn-Cr solid solution: (i) We have shown that these can be estimated directly at the Kirkendall marker plane from a single conventional ternary diffusion profile. (ii) We have, for the first time, demonstrated that the estimation at the intersection of a conventional ternary and constrained pseudo-binary diffusion path is helpful for systematically generating composition-dependent tracer diffusion coefficients. (iii) We have followed the Kirkaldy-Lane method for estimating these diffusion coefficients at the intersection of two conventional ternary diffusion couples (for comparison of the data measured by new methods), although for data generation at random compositions. This was proposed a long time ago but practised occasionally. It helps to compare with the estimated data following other methods. (iv) Additionally, we have estimated the impurity diffusion coefficients of Cr and Mn in Fe following the Hall method, which helps in understanding the variation of the diffusion coefficients in Fe-Mn-Cr alloys compared to pure Fe. The sensitivity of data estimation following different methods, i.e. different equation schemes, is discussed, explaining the strategic design of diffusion couple for a small error range.

Measurement of Diffusion Coefficients and Assessment of Atomic Mobilities in HCP Mg-Ag-Sn Alloys

Reliable thermodynamic and kinetic databases are essential for designing and developing novel magnesium (Mg) alloys for elevated-temperature applications in the automotive and aerospace industries. This study investigated diffusion behaviors of HCP Mg-Ag-Sn alloys by four sets of three diffusion couples annealed at 450, 500, and 550 °C, respectively. Interdiffusion and impurity diffusion coefficients at the three annealing temperatures were extracted using the forward-simulation method. The determined diffusion coefficients, combined with prior results in the literature, were then used to assess atomic mobilities for the HCP phase of the Mg-Ag-Sn system. This assessment was conducted using the DICTRA and the TCMG5 thermodynamic database within the Thermo-Calc software. Comprehensive comparisons between calculated and experimental diffusion coefficients yielded an excellent agreement. The atomic mobilities were also further validated by appropriate predictions of concentration profiles and diffusion paths observed in independent diffusion couple experiments performed at 525 °C for 18 hrs. It has been found that the addition of Sn and Ag both increase the diffusivity of Ag in HCP Mg and Sn in HCP Mg in the stable temperature range of HCP Mg, respectively. This improved understanding of the kinetics in the Mg-Ag-Sn ternary system is essential for controlling diffusion-dependent properties such as coarsening and, therefore, the mechanical properties of Mg-Ag-Sn alloys at elevated temperatures.

An experimental estimation method of diffusion coefficients in ternary and multicomponent systems from a single diffusion profile

Until recently, it was textbook knowledge that the diffusion coefficients could not be estimated in a multi-component system following the widely practised diffusion couple method. The recently proposed constrained diffusion couple method largely solved the problems. The need to produce two intersecting diffusion paths in a multi-component space with very well-controlled compositions of the diffusion couple end members may be tricky in certain situations, depending on the complications of diffusion paths. In this study, we have shown the estimation of all types of diffusion coefficients from a single diffusion profile without neglecting Onsager's cross terms in concentrated ternary Ni-Co-Fe, Fe-rich quaternary Fe-Ni-Co-Cr and concentrated Ni-Co-Fe-Cr-Al quinary alloys. This is applicable in ternary and multicomponent component systems (n≥3) at a stable Kirkendall marker plane position. One can even estimate the impurity diffusion coefficients utilizing the composition profiles at the ends of the diffusion couples following the Hall method, which has been rarely practised in multicomponent systems until now. We have further demonstrated the importance of estimating the tracer and intrinsic diffusion coefficients in a concentrated or multi-principal element alloy in which interdiffusion coefficients can be vague and misleading for understanding the elements' diffusional interactions and relative mobilities. We have also shown the importance of considering the vacancy wind effect in concentrated alloys. The method proposed in this study will help to generate a mobility database with relative ease in various multicomponent systems important for various applications, which was considered impossible until recently.

Diffusivities and Atomic Mobilities in BCC Ti-Fe-Cr Alloys.

In this research, the diffusion behaviors within the Ti-Fe-Cr ternary system were examined at the temperatures of 1273 K and 1373 K through the diffusion couple technique. This study led to the determination of both ternary inter-diffusion and impurity diffusion coefficients in the body-centered cubic (bcc) phase for the Ti-Fe-Cr alloy, utilizing the Whittle-Green and Hall methods. The statistics show that the average diffusion coefficients D˜FeFeTi and D˜CrCrTi measured at 1273 K were 1.34 × 10-12 and 3.66 × 10-13, respectively. At 1373 K, the average values of D˜FeFeTi and D˜CrCrTi were 4.89 × 10-12 and 1.43 × 10-12. By adopting the CALPHAD method, a self-consistent database for atomic mobility in the bcc phase of the Ti-Fe-Cr system was established. This database underwent refinement by comparing the newly acquired diffusion coefficients with data from the existing literature. Diffusion simulations for the diffusion couples were performed, drawing on the established database. The error between the simulated diffusion coefficient and the experimental measurement data is within 15%, and the simulated data of the component distance distribution and diffusion path are in good agreement with the experimental data. The simulations generated results that aligned well with the observed experimental diffusion characteristics, thereby affirming the reliability and accuracy of the database.

Evaluation of diffusion behavior and mechanical characteristics in the ZrC-NbC pseudo-binary system

Accurate information on diffusion kinetics and mechanical characteristics for the ZrC-NbC pseudo-binary system is essential for developing high-performance ZrC-based alloys. At present work, we have employed the diffusion couple method to investigate systematically the diffusion kinetics of the ZrC-NbC pseudo-binary system in the temperature range of 1373–1673 K. The mechanical characteristics of the diffusion region have been studied by the nanoindentation technique. Evaluations have been conducted on the impurity diffusion and inter-diffusion coefficients of the ZrC-NbC pseudo-binary system. As Nb concentration increases, the inter-diffusion coefficients of the ZrC-NbC pseudo-binary system decline. The inter-diffusion activation energies of the ZrC-NbC pseudo-binary system increase as Nb concentration increases, with the largest value of 395.3 kJ/mol at 55 at. % Nb concentration. The impurity diffusion activation energies of C in ZrC, C in NbC, Nb in ZrC, and Zr in NbC are 242.4 kJ/mol, 167.9 kJ/mol, 388.3 kJ/mol, and 288.0 kJ/mol, respectively. The Vickers hardness and Young's modulus of Zr1-xNbxC have also been measured, with the highest values of 29.4 ± 2.7 GPa and 650.7 ± 12.9 GPa, respectively. With an increase of Nb concentration, Young's modulus of Zr1-xNbxC increases, while its Vickers hardness first increases and subsequently declines. The results of this study could be advantageous to develop ZrC-based alloys and improve their properties.

МЕХАНІЗМИ МАСОПЕРЕНОСУ ІНДІЮ В Cd(Zn)Te ПРИ ДІЇ НАНОСЕКУНДНИХ ЛАЗЕРНИХ ІМПУЛЬСІВ

The processes of heating, melting and ablation during nanosecond laser irradiation of metal film (In) / CdTe structures and CdZnTe solid solutions are considered. Time and coordinate (in depth) temperature profiles during nanosecond laser irradiation of the system the film In/CdTe were calculated. Melting thresholds of indium and CdTe in the In/CdTe film system have been established. The profile of the distribution of indium atoms in cadmium telluride after a single laser irradiation of the In/CdTe structure, accompanied by the formation of an inversion layer (n-type), was obtained and theoretically described; a peak at a depth of 6 nm was detected. The mass transfer coefficients of indium in CdTe in different regions were determined during nanosecond laser irradiation of the In/CdTe structure with a thickness of the In film of 30 nm on the metal side at Epad = 100 mJ/cm2. It was established that the mass transfer coefficient of In atoms in CdTe during nanosecond laser irradiation of the In/CdTe film structure depends on the distance from the CdTe surface and increases, which is associated with a rapid change over time in the inhomogeneous deformation of the crystal lattice in the process of indium diffusion. The obtained value of the coefficient of laser-induced mass transfer of In in CdTe by an order of magnitude is much higher than the diffusion coefficients of impurities under normal annealing conditions with the diffusion method of impurity introduction and is commensurate with the self-diffusion coefficient in a number of liquid metals.

Interdiffusion behaviors and mechanical properties in Zr-Nb-Hf system

The diffusion behavior and mechanical properties of the Zr-Nb-Hf system were analyzed using diffusion couple technology and nanoindentation techniques. The diffusion couples were annealed at 1523 K for 24 h, and the compositional profile of the diffusion region was determined using electron probe microanalysis. The main diffusion coefficients, cross-diffusion coefficients, and impurity diffusion coefficients were calculated using the Whittle and Green method, as well as the generalized Hall method. Furthermore, the hardness and Young's modulus of the alloy with different compositions were calculated by Oliver method, based on load-displacement curves obtained from nanoindentation tests. Additionally, the wear resistance and resistance to plastic deformation of the Zr-Nb-Hf alloys were inferred. These results contribute to the existing database of diffusion kinetics and mechanical properties in the Zr-Nb-Hf system, providing valuable references for the development of Zr-Nb-Hf-based alloys with exceptional properties.

Estimation of diffusion coefficients in NiCoFeCrAl multi-principal element alloy following an inventive design strategy of diffusion couples

An inventive design strategy of producing the diffusion couples for intersecting the diffusion paths in multicomponent space is described in Ni-Co-Fe-Cr-Al multi-principal element alloy. This, for the first time, facilitates the estimation of the tracer, intrinsic, and interdiffusion coefficients of all the elements purely experimentally in this quinary system. This was not possible until now following any other experimental methods. The tracer diffusion coefficients estimated in this quinary system are compared with the impurity and tracer diffusion coefficients in pure Ni, and at (or near) equiatomic compositions of binary Ni-Co, ternary Ni-Co-Cr, and quaternary Ni-Co-Fe-Cr systems. The relative mobilities of the elements are found to follow the trend DNi*≤DCo*<DFe*≤DCr*<DAl* in all the systems. However, the tracer diffusion coefficients of the elements first decrease and then increase with the increasing order of the systems. The contribution of the vacancy wind effect on certain cross-intrinsic diffusion coefficients is found to be very significant and cannot be ignored. The influence of the vacancy wind effect on interdiffusion coefficients is less significant than the intrinsic diffusion coefficients since interdiffusion coefficients are the average of multiple intrinsic diffusion coefficients. This may lead to the wrong statement that the vacancy wind effects are negligible. We have further shown that describing the relative diffusion rates of the elements with main interdiffusion coefficients instead of the tracer diffusion coefficients can be misleading or confusing. Different elements as the dependent variables of interdiffusion coefficients indicate a very different or even opposite trend of relative diffusivities in this system.

Diffusion coefficient measurement and atomic mobility assessment for bcc Ti–V–Fe ternary alloys

Diffusion behaviors in bcc Ti–V–Fe ternary alloys have been investigated at 1273 K and 1473 K by the diffusion couple technique. The composition-distance profiles have been retrieved from Electron Probe MicroAnalysis (EPMA) and analytically represented by the ERror Function EXpansion (ERFEX), and then the ternary inter-diffusion and impurity diffusion coefficients have been extracted by Whittle–Green and generalized Hall methods, respectively. The extracted inter-diffusion coefficients of D˜VVTi and D˜FeFeTi range from 0.89 × 10−13 m2/s to 1.86 × 10−13 m2/s and from 1.33 × 10−12 m2/s to 1.76 × 10−12 m2/s, respectively, at 1273K, and from 6.41 × 10−13 m2/s to 15.98 × 10−13 m2/s and from 82.46 × 10−13 m2/s to 147.08 × 10−13 m2/s at 1473K. D˜VVTi exhibits the similar compositional variation at both temperatures, which decrease with decreasing Fe and minimize at the Ti–V binary. D˜FeFeTi has the maximum value at Ti–corner and eventually decreases with the increasing V and Fe at 1273K, but has the maximum value at Fe-rich Ti–Fe binary and decreases with the increasing V. The atomic mobility parameters of Ti–V, Ti–Fe and V–Fe binary systems have been revised to associate with the lasted ternary interaction parameters in thermodynamics. The ternary atomic mobility parameters for diffusion have been assessed for the first time by reproducing the extracted diffusion coefficients. The composition-distance profiles and the diffusion paths have been successfully reproduced by using the optimized atomic mobility parameters showing a consistency with the experimental data and indicating the accuracy of this work.

On Parameters of Evaporation Refining

The previously presented theory of evaporation refining which takes into account the difference in the vapor pressure of the components and the diffusion of impurities (but not other possible factors) is analyzed. The complexity of the theory is noted: to calculate the refining efficiency depending on the yield at a given temperature, a large number of parameters (nine) of the substance and material are required: molar mass M, density ρ, melting point Tm, equilibrium separation factor β0, vapor pressure of the main component p, the impurity diffusion activation energy in the refined substance Q, the impurity diffusion coefficient Dm at temperature Tm and the material size factor X. The conceptual character of the theory under consideration is noted due to the lack of knowledge of most of these parameters and the neglect of all process factors.

Investigation on diffusion kinetics of Ti-X binary systems at 1300–1500 °C

The composition design of titanium alloys and some preparation processes require accurate diffusion kinetic databases. However, the current database of diffusion kinetics at high temperatures is not yet complete. In this work, the diffusion kinetics of five binary systems, Ti–Zr, Ti–Nb, Ti–Mo, Ti–Ta and Ti–W, were systematically investigated at 1300–1500 °C. The interdiffusion coefficients and impurity diffusion coefficients of the Ti-X binary systems were calculated according to the Den-Broeder and Hall methods. The results showed that the Ti–Nb, Ti–Mo, Ti–Ta and Ti–W exhibited strong concentration dependence of the diffusion coefficients at the temperature of 1300–1500 °C compared to the Ti–Zr system, which was considered as the domination of the difference in intrinsic properties between elements. Besides, the activation energies of diffusion were evaluated based on the Arrhenius relationship, where the Ti–Zr system exhibited the lowest activation energy among the five diffusion systems, followed by Ti–Nb, Ti–Mo, Ti–Ta and Ti–W systems. The diffusion kinetic data of titanium-based alloys at high temperatures were obtained in the present work, providing important references for the design, preparation and processing of new titanium alloys.

Interdiffusion in body-centred cubic β-(Ti, Al) solid solution phase

A study has been conducted to quantify the effect of Al on diffusion in the dilute β-(Ti, Al) solid solution phase by determining the interdiffusion and impurity diffusion coefficients using the diffusion couple technique. An increase in interdiffusion coefficients with an increase in Al content in β-(Ti, Al) is rationalized by a decreasing trend of activation energy for interdiffusion and an increase in driving force for diffusion. Higher activation energy of impurity diffusion coefficient of Al in β-Ti than that of self-diffusion coefficient of β-Ti may further suggest lower interaction tendency of vacancies with Al atoms in the β-(Ti, Al) phase.

First-principles study of impurity diffusion coefficients in Niobium

Nb based alloys have potential applications in aerospace due to their good high temperature strength and low temperature plasticity. It is very important to study the atomic diffusion properties for understanding the dynamic process of Nb-based alloys. However, the diffusion data of some elements in Nb are still unknown. In the present work, the impurity diffusion coefficients of ten different elements (Si, Ti, V, Ta, Ru, Cr, Te, Tc, Ir, and Y) in BCC Nb was studied by first-principles calculation based on density functional theory and nine frequency model. The climbing image nudged elastic band (CI-NEB) method was used to find the minimum energy path and the related saddle point structure during diffusion. The atomic jump frequency was calculated through the Vineyard’ s transition state theory. The results are consistent well with the exiting experimental and previous calculation results.

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.

Interdiffusion behaviors and mechanical properties of Zr-X (X Nb, Ta, Hf) binary systems

The diffusion behaviors and the mechanical properties of Zr-X (X Nb, Ta, Hf) systems have been systematically investigated at the annealing temperature range of 950–1200 °C. Based on the Sauer-Freise method and the Hall method, the interdiffusion coefficients of the Zr-rich alloys were evaluated, and the impurity diffusion coefficients on the Zr-rich side have been extracted by using the Darken equation. The presently obtained interdiffusion coefficients and impurity diffusion coefficients are all in good agreement with experimental data in the literature. According to the Arrhenius regression, the diffusion activation energies of the three systems have been calculated. It can be concluded that the diffusion activation energies of the Zr-Ta system are the largest value. Finally, the hardness and Young’s modulus of the Zr-X have been obtained by using the nanoindentation test. The present results can help the materials design, research and development for the Zr-based alloys. • Interdiffusion coefficients and activation energies are obtained from the measured composition profiles. • Hardness and Young’s modulus of Zr-X (X Nb, Ta, Hf) systems have been obtained. • The solid-solid diffusion couple has been used.

Experimental diffusion research and assessment of diffusional mobility in HCP Mg–Al-Ga ternary alloys

It is in this work that the diffusion behavior in HCP Mg–Ga binary alloys at temperatures from 673 K to 873 K and in Mg–Al-Ga ternary alloys in 673–723 K was investigated by the solid-state diffusion couple experiments. The inter- and impurity diffusion coefficients were then extracted from the composition profiles acquired by electron probe microanalysis (EPMA) via the Sauer-Freise, Whittle-Green and Hall methods, respectively. The extracted impurity diffusion coefficient of Ga in pure HCP-Mg follows an Arrhenius relation with the pre-exponential factor D0 = 1.4 × 10−5 m2/s and activation energy Q = 116869 J/mol. The interdiffusion coefficients of the Mg–Ga binary alloys were found to increase with increasing the Ga content. Whereas in the Mg–Al-Ga ternary, the average main interdiffusion coefficients D˜GaGaMg within the investigated composition space is 5.4 times larger than that of D˜AlAlMg at 673 K and 4.6 times at 723 K, respectively, revealing that Ga is a much faster diffuser than Al in the ternary alloys. The main interdiffusion coefficients D˜GaGaMg and D˜AlAlMg, as well as the impurity diffusion coefficients DAl(Mg−Ga)∗ and DGa(Mg−Al)∗ exhibit increasing composition trends as the content of diffusing species increases, either Al or Ga. Close inspection suggests that Ga has significant effect on the diffusion of Al while the Al effect is minor on Ga. The diffusion coefficients extracted in this work, together with other selected diffusion data in literature, were critically evaluated to assess the diffusional mobility for the HCP Mg–Al-Ga ternary alloys. The optimized parameters of diffusional mobilities enable such diffusion behaviors as composition profiles and diffusion paths to be well represented and then predicted, in most cases, consistent with the experimental findings and therefore validating the mobility parameters assessed in this work.

Interdiffusion behaviors and mechanical properties in BCC Zr-rich Zr–Nb–Ta system

Diffusion behavior and mechanical properties of the Zr–Nb–Ta system have been analyzed using diffusion couple technology and nanoindentation technology. The diffusion couples were annealed at 1523 K for 24 h and at 1423 K for 48 h, respectively. The compositional profile of the diffuse region was then obtained using electron probe microanalysis (EPMA). The main diffusion coefficients, cross diffusion coefficients, and impurity diffusion coefficients were calculated utilizing the Whittle and Green method, and the generalized Hall method. Finally, Young’s modulus and hardness of the diffusion couples were evaluated by nanoindentation, and the wear resistance and resistance to plastic deformation of the Zr–Nb–Ta alloy were also inferred. The present results improve the database of diffusion kinetics and mechanical properties of the BCC Zr–Nb–Ta system, which can be useful in the exploration of Zr–Nb–Ta based alloys with excellent properties.

Diffusivities and atomic mobilities in BCC Ti-Rich Ti–V–Cr ternary alloys

In this work, we investigate ternary diffusion behaviors in BCC Ti–rich Ti–V–Cr alloys at 1373 K and 1473 K using the diffusion couple technique. We extract the inter-diffusion coefficients by the Whittle-Green method and obtain the impurity diffusion coefficients using the Hall method. Based on a thermodynamic description and validated binary mobility parameters, we evaluate the ternary diffusion coefficients and optimize the atomic mobility parameters of the Ti–V–Cr ternary alloy system in the DICTRA diffusion Module of Thermo-Calc software. Finally, we simulate the composition profiles and diffusion paths using our optimized atomic mobility parameters and find agreement between our simulated and experimentally observed results, providing evidence of the accuracy of our mobility parameters.

Diffusivities and atomic mobilities in bcc Ti–Mo–Ta alloys

Mo and Ta are two important β stable elements that can enhance the fatigue strength and reduce the elastic modulus of titanium alloy, and can significantly improve the biocompatibility of titanium alloy. It is significant to study the diffusion behavior in β Ti–Mo–Ta alloy for understanding the microstructure evolution in production process and developing new alloys. In this study, using several diffusion couples, the interdiffusion coefficients and impurity diffusion coefficients in β Ti–Mo–Ta alloy were extracted via Whittle-Green method and Hall method. The atomic mobilities in bcc phase in Ti–Mo–Ta system were obtained by assessing the experimental data using CALPHAD (CALculation of PHAse Diagrams) method. Simulations of the diffusion process in the diffusion couples were implemented using DICTRA Module in Thermo-Calc software. The calculated data were in good agreement with the experimental data, confirming the accuracy of the database.

Измерение коэффициентов диффузии примесей внедрения в сплаве Zr – 1 масс. % Nb методом внутреннего трения

In alloys with a GPU lattice, it is possible to observe a relaxation of the Snukovsky type if there is a certain amount of substitution impurities in it. However, it is impossible to calculate the diffusion coefficients of the introduction impurities by the measured relaxation time by analogy with BCC alloys, just because of the possible interaction with substitution atoms. However, in some cases, if reliable diffusion data are available for an alloy close in composition to the studied one, the relaxation time can be calculated from the ratio τr = τr0·exp(Hm/RTm), where Hm, Tm are the parameters of the relaxation maximum of the impurity from the experiment, and τr0 can be calculated from the formula D0 = c02/(16·τr0) for the GPU lattice, taking D0 from the corresponding diffusion expert data. In this way, the diffusion coefficients of the introduction impurities in the alloy Zr – 1 wt. % Nb are calculated for several states of samples.