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.

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.

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.

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.

Ternary Interdiffusion in L12-Ni3Al with Ir Alloying Addition

2008 ◽  
Vol 273-276 ◽  
pp. 637-642 ◽  
Author(s):  
Machiko Ode ◽  
N. Garimella ◽  
Muneaki Ikeda ◽  
Hideyuki Murakami ◽  
Yong Ho Sohn
Keyword(s):  
Vacuum Arc ◽  
Concentration Profiles ◽  
Diffusion Couples ◽  
Interdiffusion Flux ◽  
Solid Diffusion ◽  
Arc Melting ◽  
Vacuum Arc Melting ◽  
Dependent Component ◽  
Interdiffusion Coefficients ◽  
And Diffusion

Average ternary interdiffusion coefficients in Ni3Al with Ir additions have been determined using solid-to-solid diffusion couples annealed at 1200°C for 5 hours. Disc shaped alloy specimens were prepared by the vacuum arc melting at compositions of Ni-24Al, Ni-25Al, Ni-26Al, Ni-23.5Al-1Ir, Ni-24.5Al-1Ir, Ni-23Al-2Ir, Ni-23Al-2Ir, Ni-24Al-2Ir, Ni-23Al-3Ir (at.%). Surfaces of alloys were polished down to 1200 grit and diffusion couples were assembled in Si3N4 jig for initial bonding heat treatment at 1200°C for 0.5 hours. Additional diffusion anneal was carried out at 1200°C for 4.5 hours outside of Si3N4 jig so that diffusion couples can be water quenched. Concentration profiles of individual components were measured by electron probe microanalysis using pure standard of Ni, Al and Ir. Interdiffusion flux of individual component was determined directly from the experimental concentration profiles, and the moments of interdiffusion flux were examined to calculate the average ternary interdiffusion coefficients, D˜ ij k either with Al or Ni as dependent component. Calculated interdiffusion coefficients suggest that Ir-alloyed Al2O3-forming oxidation resistant coatings would be beneficial to reduce the interdiffusion flux of Ni from superalloy substrates to the coating, and reduce the interdiffusion flux of Al from the coating to the superalloy substrate.

Determination of Average Ternary Interdiffusion Coefficients Using Moments of Interdiffusion Flux and Concentration Profiles

2010 ◽  
Vol 297-301 ◽  
pp. 1328-1333
Author(s):  
N. Garimella ◽  
H.J. Choi ◽  
Yong Ho Sohn
Keyword(s):  
Analysis Method ◽  
Diffusion Couples ◽  
Rigorous Solution ◽  
Ternary Diffusion ◽  
Flux Flow ◽  
Flow Equations ◽  
Interdiffusion Flux ◽  
Validation Criteria ◽  
Interdiffusion Coefficients

We developed a method of rigorous solution of the Onsager’s flow equations using moments of the interdiffusion-parameter integrands for the determination of average ternary interdiffusion coefficients. The analysis developed by Dayananda and Sohn [1] is the basis for this refined approach. Average main and cross interdiffusion coefficients are determined over selected regions in the diffusion zone using the diffusion-distance moments of the interdiffusion flux flow equations. Thermodynamic stability of solid solutions in the light of interdiffusion phenomenon is taken as validation criteria to identify accurate and reliable values of the ternary interdiffusion coefficients. Regulations are proposed for successful application of the analysis method to various ternary diffusion couples in Ni- and Fe-based intermetallics.

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.

Ternary and Quaternary Interdiffusion in γ (fcc) Fe-Ni-Cr-X (X = Si, Ge) Alloys at 900°C

2008 ◽  
Vol 595-598 ◽  
pp. 1145-1152 ◽  
Author(s):  
N. Garimella ◽  
M.P. Brady ◽  
Yong Ho Sohn
Keyword(s):  
Cross Sections ◽  
Electron Probe ◽  
Concentration Profiles ◽  
Diffusion Couples ◽  
Alloying Additions ◽  
Cr2o3 Scale ◽  
Interdiffusion Flux ◽  
Solid Diffusion ◽  
Interdiffusion Coefficients ◽  
And Diffusion

Interdiffusion in Fe-Ni-Cr (fcc γ phase) alloys with small additions of Si and Ge at 900°C was studied using solid-to-solid diffusion couples. Alloy rods of Fe-24 at.%Ni, Fe-24 at.%Ni- 22at.%Cr, Fe-24 at.%Ni-22at.%Cr-4at.%Si and Fe-24 at.%Ni-22at.%Cr-1.7at.%Ge were cast using arc-melt, and homogenized at 900°C for 168 hours. Sectioned alloy disks from the rods were polished, and diffusion couples were assembled with in Invar steel jig, encapsulated in Argon after several hydrogen flushes, and annealed atz 900°C for 168 hours. Polished cross-sections of the diffusion couples were characterized to determine experimental concentration profiles using electron probe microanalysis with pure elemental standards. Interdiffusion fluxes of individual components were calculated directly from the experimental concentration profiles, and the moments of interdiffusion flux profiles were examined to determine the average ternary and quaternary interdiffusion coefficients. Effects of alloying additions on the interdiffusional behavior of Fe-Ni- Cr-X alloys at 900°C are presented with due consideration for the formation of protective Cr2O3 scale.

Interdiffusion in (fcc) Ni-Cr-X (X = Al, Si, Ge or Pd) Alloys at 700°C

2007 ◽  
Vol 266 ◽  
pp. 191-198 ◽  
Author(s):  
N. Garimella ◽  
M.P. Brady ◽  
Yong Ho Sohn
Keyword(s):  
Cross Sections ◽  
Electron Probe Microanalysis ◽  
Electron Probe ◽  
Concentration Profiles ◽  
Diffusion Couples ◽  
Alloying Additions ◽  
Cr2o3 Scale ◽  
Solid Diffusion ◽  
Ternary Alloying ◽  
Interdiffusion Coefficients

Interdiffusion at 700°C for Ni-22at.%Cr (fcc γ phase) alloys with small additions of Al, Si, Ge, or Pd was examined using solid-to-solid diffusion couples. Rods of Ni-22at.%Cr, Ni- 21at.%Cr-6.2at.%Al, Ni-22at.%Cr-4.0at.%Si, Ni-22at.%Cr-1.6at.%Ge and Ni-22at.%Cr-1.6at.%Pd alloys were cast using arc-melt and homogenized at 900°C for 168 hours. The diffusion couples were assembled with alloy disks in Invar steel jig, encapsulated in Argon after several hydrogen flushes, and annealed at 700°C for 720 hours. Experimental concentration profiles were determined from polished cross-sections by using electron probe microanalysis with pure standards of Ni, Cr, Al, Si, Ge and Pd. Interdiffusion fluxes of individual components were calculated directly from the experimental concentration profiles, and the moments of interdiffusion fluxes were examined to determine average ternary interdiffusion coefficients. Effects of ternary alloying additions on the interdiffusional behavior of Ni-Cr-X alloys at 700°C are presented in the light of the diffusional interactions and the formation of protective Cr2O3 scale.

Interdiffusion and Al Self-Diffusion in Iron-Aluminides

2005 ◽  
Vol 237-240 ◽  
pp. 444-449 ◽  
Author(s):  
Marcel Salamon ◽  
David Fuks ◽  
Helmut Mehrer
Keyword(s):  
Single Phase ◽  
Theoretical Models ◽  
Kirkendall Effect ◽  
Iron Aluminides ◽  
Diffusion Couples ◽  
Self Diffusion ◽  
The Difference ◽  
Interdiffusion Coefficients ◽  
Diffusion Profiles ◽  
Thermodynamic Factors

We have investigated interdiffusion in iron-aluminium alloys using single-phase interdiffusion couples of FexAl1−x–FeyAl1−y for three combinations of x and y for Al contents between 18 and 49.5 at. % Al. Experimental diffusion profiles were obtained from electron-microprobe analysis of the diffusion zone. Interdiffusion coefficients were deduced via the Sauer-Freise method taking into account volume changes. A temperature interval between 997 and 1447 K was covered in our experiments. Thermodynamic factors were obtained from two theoretical models and judged by an analysis of the Kirkendall effect in the diffusion couples. The Darken-Manning equation was used to deduce self-diffusion coefficients of aluminium from the present interdiffusion coefficients, the thermodynamic factors, the vacancy-wind factors, and the iron tracer diffusivities obtained recently at the M¨unster laboratory. The results show that Al diffusion is always slightly faster than Fe diffusion. The difference never exceeds a factor of three. This small difference indicates that Fe and Al diffusion in B2 ordered iron-aluminides are closely coupled.

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