An analysis of concentration profiles for fluxes, diffusion depths, and zero-flux planes in multicomponent diffusion

Interdiffusion and Phase Growth Kinetics in Magnesium-Aluminum Binary System

“…2 can be evaluated easily as appropriate area under the concentration-versusdistance curve of the desired component. For diffusion couples in which the molar volume varies considerably, Eq 2 must be modified [15] as follows ðEq 3Þ…”

Final Report for "Experimental Petrology and Chemistry of Volatile-Bearing Silicate Melts"

“…We determined D H 2 O vs. C H 2 O relationships for each concentration profile in several ways: (1) by direct calculation using BoltzmannMatano methods (Crank, 1975;Sauer and Freise, 1962;den Broeder, 1969;Dayananda, 1983), which makes no assumptions about the functional form of the relationship; (2) by assuming simple functional forms for the relationship between D H 2 O and C H 2 O (e.g., D H 2 O is a linear function of C H 2 O (e.g., Shaw, 1974), or D H 2 O is an exponential function of C H 2 O (e.g., Delaney and Karsten, 1981)); or (3) by assuming a specific diffusion model based on the speciation of water dissolved in silicate melt (e.g., Stolper, 1982a,b;Behrens and Nowak, 1997;Nowak and Behrens, 1997;Zhang, 1999;Doremus, 2000;. By comparing the results of these various approaches to characterizing the D H 2 O vs. C H 2 O relationship, we can evaluate the confidence and detail with which this relationship can be determined from diffusion profiles of the sort we have obtained (i.e., that extend over a significant C H 2 O range).…”

“…This procedure is frequently used to calculate concentration dependent D H 2 O values, and it is well described elsewhere Behrens et al, 2004). A related method that fits diffusion profiles assuming constant, average diffusion coefficients over user-defined regions of a profile was also applied to the diffusion couple experiments ("MultiDiFlux";Dayananda, 1983;Dayananda and Sohn, 1999). Below, we will refer to all of these techniques as Boltzmann-Matano analysis.…”

“…The MultiDiFlux methodology includes fits to user-defined segments of the concentration profile using Hermite interpolation to generate cubic polynomial fits (Fig. 4), built into the MultiDiFlux software (https:// engineering.purdue.edu/MSE/Fac_Staff/Faculty/MultiDiFlux.zip); Dayananda, 1983;Dayananda and Sohn, 1999). Fig.…”

Interdiffusion in L12-Ni3Al Alloyed with Re

“…An experimental determination of the four concentrationdependent interdiffusion coefficients can be carried out by the use of Boltzmann-Matano analysis with two independent diffusion couples that develop a common composition in the diffusion zone where the interdiffusion coefficients can be evaluated. [41,42] Instead, the interdiffusion flux at any section x can be calculated directly from the concentration profile from the relation [43,44] :…”