Calculating of Diffusion Paths in Ternary Systems Using Effective Interdiffusion Coefficients of Components

2005 ◽  
Vol 237-240 ◽  
pp. 1264-1269 ◽  
Author(s):  
J. Priimets ◽  
A. Ainsaar ◽  
Ü. Ugaste
Keyword(s):  
Interdiffusion Coefficient ◽  
Good Accuracy ◽  
Ternary Systems ◽  
Diffusion Path ◽  
Correct Choice ◽  
Diffusion Couples ◽  
Practical Application ◽  
Strong Deviation ◽  
Diffusion Paths ◽  
Interdiffusion Coefficients

The peculiarities of practical application of effective interdiffusion coefficients of components for calculating diffusion paths in ternary systems are analysed. It is shown that infinite values of the interdiffusion coefficients at zero concentration gradient’s points do not remarkably affect the accuracy of calculation in the case of a correct choice of variables. At zero-flux planes where the respective effective interdiffusion coefficient is equal to zero, no calculation problems arise, as evidently zero-flux planes can occur simultaneously only for one of the components. The results of calculation of diffusion paths for diffusion couples in the ternary systems Cu-Fe-Ni and Co-Fe-Ni using respective effective interdiffusion coefficients are presented. These results demonstrate a good accuracy of such kind of calculations even in the case of very strong deviation from linearity of the diffusion path.

Thermodynamic Aspects of Diffusion Paths in Ternary Systems

2007 ◽  
Vol 263 ◽  
pp. 135-140 ◽  
Author(s):  
Tony Laas ◽  
Ü. Ugaste ◽  
J. Priimets
Keyword(s):  
Thermodynamic Properties ◽  
Ternary Systems ◽  
Diffusion Path ◽  
Experimental Investigations ◽  
Ideal System ◽  
Diffusion Paths ◽  
Interdiffusion Coefficients ◽  
The Relationship ◽  
And Diffusion ◽  
Specific Influence

Description of diffusion paths is one of the most interesting and topical problems in experimental investigations of interdiffusion in multicomponent systems and, particularly, in ternary systems. The relationship between effective interdiffusion coefficients and diffusion paths in ternary systems has been discussed earlier but the specific influence of the mobility and thermodynamic properties of components on the characteristics of the diffusion path is still unclear. In this paper an attempt is made to clarify the separate influences of mobility and thermodynamics on the behavior of diffusion paths in ternary systems and the corresponding correlation is found. It is shown that in most cases the deviation of the diffusion path from linearity (an ideal system) is related to the deviation of the thermodynamic properties from the ideal. The results obtained are analyzed on the basis of thermodynamic data for the ternary system Cu-Fe-Ni.

The Effective Interdiffusion Coefficients in Experimental Investigations of Interdiffusion in Ternary Systems

2005 ◽  
Vol 237-240 ◽  
pp. 121-126 ◽  
Author(s):  
Ü. Ugaste
Keyword(s):  
Diffusion Couple ◽  
Ternary Systems ◽  
Diffusion Path ◽  
Experimental Investigations ◽  
Ternary Diffusion ◽  
Ternary Diffusion Couple ◽  
Interdiffusion Process ◽  
Variable Diffusion ◽  
Diffusion Paths ◽  
Interdiffusion Coefficients

The application of the effective interdiffusion coefficients for describing the interdiffusion process in ternary systems is discussed. It is shown that the relative values of effective interdiffusion coefficients, which are directly related to the diffusion path developed in a given diffusion couple, are responsible for deviation of the diffusion paths from linearity. The relationship between effective interdiffusion coefficients and partial (intrinsic) coefficients in ternary systems is analysed. It is shown that Boltzmann’s solution for diffusion equation with variable diffusion coefficient by means of relatively easy calculation procedure gives reliable results for the calculation concentration distributions in a ternary diffusion couple.

Calculating of Diffusion Profiles in Ternary Systems Using Effective Interdiffusion Coefficients of Components

2013 ◽  
Vol 333 ◽  
pp. 73-82
Author(s):  
Ü. Ugaste ◽  
J. Priimets
Keyword(s):  
Good Accuracy ◽  
Ternary Systems ◽  
Concentration Profiles ◽  
Diffusion Couples ◽  
Ternary Diffusion ◽  
Variable Diffusion Coefficient ◽  
Ternary Diffusion Couple ◽  
Variable Diffusion ◽  
Interdiffusion Coefficients ◽  
Diffusion Profiles

A method has been developed for calculating diffusion profiles in ternary systems by using effective interdiffusion coefficients of components and Boltzmanns solution for diffusion equation with variable diffusion coefficient. Using this method the concentration profiles for several diffusion couples in the systems Fe-Co-Ni and Cu-Fe-Ni are calculated as examples and some peculiarities of these calculations are discussed, particularly, how to solve some possible difficulties, which may sometimes arise at calculation procedures. It is shown that having the data on effective interdiffusion coefficients and their concentration dependence for at least two components in a ternary diffusion couple, the concentration profiles for all three components can be calculated with good accuracy.

An Examination of Diffusion Paths in Terms of Interdiffusion Fluxes and Interdiffusion Coefficients

2007 ◽  
Vol 266 ◽  
pp. 83-99 ◽  
Author(s):  
Kevin M. Day ◽  
Mysore A. Dayananda
Keyword(s):  
National Science Foundation ◽  
Single Phase ◽  
Diffusion Path ◽  
Diffusion Couples ◽  
Eigenvalues And Eigenvectors ◽  
Internal Constraints ◽  
Two Phase ◽  
Uphill Diffusion ◽  
Diffusion Paths ◽  
Interdiffusion Coefficients

Selected diffusion couples investigated in the Cu-based and Fe-based multicomponent systems are examined for diffusion path development, zero-flux planes, uphill diffusion, and internal constraints for diffusion paths. The couples are analyzed for interdiffusion fluxes and interdiffusion coefficients with the aid of the “MultiDiFlux” program. Eigenvalues and eigenvectors are also determined from the interdiffusion coefficients determined over various ranges of composition in the diffusion zone. Slopes of diffusion paths at selected sections, including the path ends, are related to interdiffusion coefficients, interdiffusion fluxes and/or eigenvectors. These relations are explored with selected single phase diffusion couples in the Cu-Ni-Zn and Fe-Ni-Al systems and the calculated path slopes are compared with those directly determined from the concentration profiles. Relations between the gradient of interdiffusion flux and the concentration gradient are examined for each component in a two-phase Cu-Ni-Zn diffusion couple. The research is supported by the National Science Foundation.

Dependence of Diffusion Paths on Thermodynamic Factors in Ternary Systems

2008 ◽  
Vol 277 ◽  
pp. 119-124 ◽  
Author(s):  
Ü. Ugaste ◽  
J. Priimets ◽  
Tony Laas
Keyword(s):  
Approximate Equation ◽  
Ternary Systems ◽  
Diffusion Path ◽  
Tracer Diffusion ◽  
Diffusion Paths ◽  
Slope Function ◽  
Experimental Values ◽  
The Impact ◽  
Tracer Diffusion Coefficients ◽  
Thermodynamic Factors

The impact of thermodynamic factors on deviation from linearity of diffusion path in the ternary system Cu-Fe-Ni is analyzed. For that the slope function of the diffusion path for the diffusion couples 65Ni30Cu5Fe –29.5Ni16.5Cu54Fe, 49.5Ni50.5Fe – 51Ni49Cu and 84Cu16Ni – 50Ni50Fe, annealed at 1000°C for 196h, were calculated by an approximate equation using only thermodynamic data. Results of the calculation were compared with the values of the slope function obtained directly from experimental data. It is shown that despite of the fact that the tracer diffusion coefficients of the components in the system Cu-Fe-Ni are not equal the coincidence between the calculated and experimental values of the slope function is remarkable. This allows us to conclude that at least in this case the deviation of the diffusion path from linearity depends mainly on the thermodynamic properties of the system.

Selected Analyses and Observations in Multicomponent Diffusion

2010 ◽  
Vol 297-301 ◽  
pp. 1451-1460 ◽  
Author(s):  
Mysore A. Dayananda
Keyword(s):  
Multicomponent Diffusion ◽  
Diffusion Couples ◽  
Uphill Diffusion ◽  
Diffusion Studies ◽  
Isothermal Diffusion ◽  
Mn Diffusion ◽  
Experimental Approaches ◽  
Diffusion Paths ◽  
Interdiffusion Coefficients

Selected isothermal diffusion studies in ternary and quaternary systems are reviewed in order to present analytical and experimental approaches adopted for the determination of interdiffusion fluxes of components, interdiffusion coefficients, diffusional interactions among components, and internal consistency in the experimental data. Several interesting phenomena and observations including uphill diffusion, zero-flux planes and flux reversals, and double serpentine diffusion paths are illustrated with selected single phase Cu-Ni-Zn, Fe-Ni-Al and Cu-Ni-Zn-Mn diffusion couples. The main challenges involved in the experimental determination of interdiffusion data from multicomponent diffusion couples and in the application of such data are also addressed.

The Influence of Thermodynamic Properties of Alloys on Effective Interdiffusion Coefficients in Ternary Systems

2007 ◽  
Vol 263 ◽  
pp. 141-146 ◽  
Author(s):  
Ü. Ugaste ◽  
Tony Laas ◽  
T. Škled-Gorbatšova
Keyword(s):  
Thermodynamic Properties ◽  
Diffusion Coefficients ◽  
Reasonable Agreement ◽  
Ternary Systems ◽  
Tracer Diffusion ◽  
Diffusion Couples ◽  
Experimental Values ◽  
Tracer Diffusion Coefficients ◽  
Interdiffusion Coefficients ◽  
The Relationship

To prove the validity of Dayananda’s phenomenological model of interdiffusion in ternary systems the effective interdiffusion coefficients for a few diffusion couples in the system Cu-Ni-Fe, annealed at 1000 oC, are calculated on the basis of this model using available tracer diffusion and thermodynamic data. It is found that the calculated values of effective interdiffusion coefficients are in reasonable agreement with experimental values extracted independently from experimental concentration--penetration curves. Using the relationship between effective interdiffusion coefficients, tracer diffusion coefficients and thermodynamic factors, it is shown that thermodynamic properties of alloys play a significant role in interdiffusion processes in the system Cu-Fe-Ni.

scholarly journals Application of numerical inverse method in calculation of composition-dependent interdiffusion coefficients in finite diffusion couples

10.30544/308 ◽  
2017 ◽  
Vol 23 (3) ◽  
pp. 197-211 ◽  
Author(s):  
Yuanrong Liu ◽  
Weimin Chen ◽  
Jing Zhong ◽  
Ming Chen ◽  
Lijun Zhang
Keyword(s):  
Diffusion Couple ◽  
Inverse Method ◽  
Diffusion Path ◽  
Diffusion Couples ◽  
Ternary Diffusion ◽  
Inverse Approach ◽  
Ternary Diffusion Couple ◽  
Composition Profiles ◽  
Standard Sets ◽  
Interdiffusion Coefficients

The previously developed numerical inverse method was applied to determine the composition-dependent interdiffusion coefficients in single-phase finite diffusion couples. The numerical inverse method was first validated in a fictitious binary finite diffusion couple by pre-assuming four standard sets of interdiffusion coefficients. After that, the numerical inverse method was then adopted in a ternary Al-Cu-Ni finite diffusion couple. Based on the measured composition profiles, the ternary interdiffusion coefficients along the entire diffusion path of the target ternary diffusion couple were obtained by using the numerical inverse approach. The comprehensive comparisons between the computations and the experiments indicate that the numerical inverse method is also applicable to high-throughput determination of the composition-dependent interdiffusion coefficients in finite diffusion couples.

scholarly journals Calculated interdiffusivities resulting from different fitting functions applied to measured concentration profiles in Cu-rich fcc Cu-Ni-Sn alloys at 1073 K

2017 ◽  
Vol 53 (3) ◽  
pp. 255-262 ◽  
Author(s):  
Y. Liu ◽  
D. Liu ◽  
Y. Du ◽  
S. Liu ◽  
D. Kuang ◽  
...  
Keyword(s):  
Error Propagation ◽  
Scientific Method ◽  
Electron Probe ◽  
Bulk Diffusion ◽  
Ternary Systems ◽  
Concentration Profiles ◽  
Diffusion Couples ◽  
Green Method ◽  
Measured Concentration ◽  
Interdiffusion Coefficients

Employing six groups of bulk diffusion couples together with electron probe microanalysis technique, the compositiondependences of ternary interdiffusion coefficients in Cu-rich fcc Cu-Ni-Sn alloys at 1073 K were determined via the Whittle and Green method. Different fitting functions applied to the measured concentration profiles are utilized to extract the interdiffusion coefficients of fcc Cu-Ni-Sn alloys. The errors for the obtained interdiffusivities are evaluated by a scientific method considering the error propagation. The calculated diffusion coefficients using the Boltzmann and additive Boltzmann functions are found to be with reasonable errors and show a general agreement with those using other fitting functions. Based on the Boltzmann and additive Boltzmann functions, the interdiffusivities in Cu-rich fcc Cu-Ni-Sn alloys at 1073 K are obtained and validated by thermodynamic constraints. The Boltzmann and additive Boltzmann functions are recommended to be used for the fitting of measured concentration profiles in other ternary systems for the sake of extracting ternary diffusivities.

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