Analytical solution of diffusion equations in multicomponent systems when applying diffusion coatings

2021 ◽  
pp. 3-9
Author(s):  
Keyword(s):  
Solid Solution ◽  
Analytical Solution ◽  
Diffusion Coefficients ◽  
Chemical Elements ◽  
Multicomponent Diffusion ◽  
Solution Concentration ◽  
Diffusion Coatings ◽  
Multicomponent Coating ◽  
Concentration Diffusion ◽  
Interstitial Elements

For multicomponent coatings, analytical equations are obtained that take into account the diffusion coefficients in the concentration equations. It is shown, that to solve the problem of multicomponent diffusion in a solid solution containing substitutional elements and interstitial elements, it is advisable to use the equations for the concentrations of chemical elements. Keywords: multicomponent coating, solid solution, concentration, diffusion coefficient, analytical solution [email protected]

Diffusion of Nitrogen in Ti-13V-11Cr-3Al Alloys

2009 ◽  
Vol 283-286 ◽  
pp. 38-44 ◽  
Author(s):  
Carlos Roberto Grandini ◽  
Emerson Haruiti Kamimura ◽  
José Roberto Severino Martins ◽  
Hugo Ricardo Zschommler Sandim ◽  
Odila Florêncio
Keyword(s):  
Solid Solution ◽  
Internal Friction ◽  
Diffusion Coefficients ◽  
Crystalline Lattice ◽  
Mechanical Spectroscopy ◽  
Interstitial Concentration ◽  
Exponential Factors ◽  
Friction Measurements ◽  
Internal Friction Spectra ◽  
Interstitial Elements

Metals with a bcc crystalline structure such as Ti-13V-11Cr-3Al alloys have their physical properties significantly changed through the addition of interstitial elements such as oxygen and nitrogen. These metals can dissolve substantial amounts of interstitial elements forming solid solutions. Mechanical spectroscopy measurements constitute a powerful tool for studying interactions of these interstitial elements with other elements that make up the alloy. From these measurements, it is possible to obtain information regarding diffusion, interstitial concentration, interaction between interstitials, and other imperfections of the crystalline lattice. In this paper, Ti-13V-11Cr-3Al alloys with several amount of nitrogen, in a solid solution, were studied using mechanical spectroscopy (internal friction) measurements. The results presented complex internal friction spectra which were resolved in a series of constituent Debye peaks corresponding to different interactions and interstitial diffusion coefficients. Pre-exponential factors and activation energies were calculated for nitrogen in theses alloys.

The Precipitation of Si in AlCuSi Thin Films

1973 ◽  
Vol 31 ◽  
pp. 34-35 ◽  
Author(s):  
R. M. Anderson
Keyword(s):  
Electron Microscopy ◽  
Thin Films ◽  
Heat Treatment ◽  
Solid Solution ◽  
Integrated Circuit ◽  
Copper Film ◽  
Solution Concentration ◽  
X Ray ◽  
Silicon Thin Films ◽  
Before And After

Aluminum-copper-silicon thin films have been considered as an interconnection metallurgy for integrated circuit applications. Various schemes have been proposed to incorporate small percent-ages of silicon into films that typically contain two to five percent copper. We undertook a study of the total effect of silicon on the aluminum copper film as revealed by transmission electron microscopy, scanning electron microscopy, x-ray diffraction and ion microprobe techniques as a function of the various deposition methods.X-ray investigations noted a change in solid solution concentration as a function of Si content before and after heat-treatment. The amount of solid solution in the Al increased with heat-treatment for films with ≥2% silicon and decreased for films <2% silicon.

Effect of Interstitial Elements on the Cryogenic Mechanical Behavior of FCC High Entropy Alloys

2021 ◽  
Vol 1016 ◽  
pp. 1386-1391
Author(s):  
Anastasia Semenyuk ◽  
Margarita Klimova ◽  
Sergey Zherebtsov ◽  
Nikita Stepanov
Keyword(s):  
Mechanical Properties ◽  
Solid Solution ◽  
Thermomechanical Processing ◽  
Induction Melting ◽  
High Entropy Alloys ◽  
Strengthening Effect ◽  
Face Centered Cubic ◽  
High Entropy ◽  
C And N ◽  
Interstitial Elements

High entropy alloys (HEAs) with face-centered cubic (fcc) structure, namely equiatomic CoCrFeMnNi alloy, have attracted considerable attention because of impressive cryogenic mechanical properties – strength, ductility, and fracture toughness. Further increase of the properties can be achieved, for example, by proper alloying. A particularly attractive option is the addition of interstitial elements like carbon or nitrogen. In present work, a series of CoCrFeMnNi-based alloys with different amounts of C and N (0-2 at.%) was prepared by induction melting. The alloys doped with C had lower Cr content to increase the solubility of carbon in the fcc solid solution. It was revealed that the solid solution strengthening effect of both C and N is significantly increased when the testing temperature decreases from 293K to 77K. The effect of thermomechanical processing on the structure and mechanical properties of the alloys is analyzed.

scholarly journals Analysis of Wear Resistance of Borided Steel C45

Materials ◽  
2020 ◽  
Vol 13 (23) ◽  
pp. 5529
Author(s):  
Mykhaylo Pashechko ◽  
Krzysztof Dziedzic ◽  
Jerzy Jozwik
Keyword(s):  
Wear Resistance ◽  
Wear Surface ◽  
Chemical Elements ◽  
Substrate Material ◽  
High Wear Resistance ◽  
Material Research ◽  
Specific Pressure ◽  
Diffusion Coatings ◽  
Boride Coatings ◽  
Induced Structure

The wear resistance of diffusion coatings in conditions of specific pressures of 3, 7 and 10 MPa was studied. The boride coatings were prepared by means of diffusion methods using C45 steel as the substrate material. Research on the microstructure and redistribution of chemical elements on wear surface of a borided layer was carried out. It was found that the boride coatings should be used under a specific pressure of 7 MPa. It was found that the wear of friction couple coating of steel C45 under specific pressure of 3 MPa proceeds according to the oxidation wear mechanism, while under specific pressures of 7 and 10 MPa the abrasive wear prevails. The wear-induced segregation of atoms in coatings was studied using secondary mass-spectroscopy method (SIMS). Increased C, O, and B concentrations were noticed at the wear surface on depth from 50 to 2000 Å. The secondary wear-induced structure formation on the wear surface resulted in high wear resistance of diffusion borided coatings.

Impurity Diffusion, Crystallization And Phase Separation In Amorphous Silicon.

1985 ◽  
Vol 51 ◽  
Author(s):  
R.G. Elliman ◽  
J.M. Poate ◽  
J.S. Williams ◽  
J.M. Gibson ◽  
D.C. Jacobson ◽  
...  
Keyword(s):  
Phase Separation ◽  
Low Temperature ◽  
Amorphous Silicon ◽  
Diffusion Coefficients ◽  
Crystalline Silicon ◽  
Tracer Diffusion ◽  
Separation Processes ◽  
Low Temperature Annealing ◽  
Tracer Diffusion Coefficients ◽  
Concentration Diffusion

ABSTRACTDiffusion, crystallization and phase separation processes in indium implanted amorphous silicon are examined for low temperature annealing (600°C). Both diffusion and crystallization are shown to be extremely sensitive to the indium concentration. Diffusion coefficients more than 10 orders of magnitude higher than tracer diffusion coefficients in crystalline silicon are measured, and amorphous to crystalline silicon transitions at temperatures as low as 350°C are reported. Phase separation is also observed.

An analytical solution of multi-dimensional space fractional diffusion equations with variable coefficients

2020 ◽  
pp. 2150006
Author(s):  
Pratibha Verma ◽  
Manoj Kumar
Keyword(s):  
Analytical Solution ◽  
Diffusion Coefficients ◽  
High Efficiency ◽  
Dimensional Space ◽  
Adomian Decomposition Method ◽  
Fractional Diffusion ◽  
Variable Coefficients ◽  
Diffusion Equations ◽  
Fractional Diffusion Equations ◽  
Adomian Decomposition

In this paper, we have considered the multi-dimensional space fractional diffusion equations with variable coefficients. The fractional operators (derivative/integral) are used based on the Caputo definition. This study provides an analytical approach to determine the analytical solution of the considered problems with the help of the two-step Adomian decomposition method (TSADM). Moreover, new results have been obtained for the existence and uniqueness of a solution by using the Banach contraction principle and a fixed point theorem. We have extended the dimension of the space fractional diffusion equations with variable coefficients into multi-dimensions. Finally, the generalized problems with two different types of the forcing term have been included demonstrating the applicability and high efficiency of the TSADM in comparison to other existing numerical methods. The diffusion coefficients do not require to satisfy any certain conditions/restrictions for using the TSADM. There are no restrictions imposed on the problems for diffusion coefficients, and a similar procedures of the TSADM has followed to the obtained analytical solution for the multi-dimensional space fractional diffusion equations with variable coefficients.

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