An analytical method of calculating variable diffusion coefficients

Sarafianos, N.

doi:10.1007/bf01114269

Cited by 33 publications

(35 citation statements)

References 4 publications

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“…In a previous paper it was shown that both intermetallic layers have been observed in samples fired at 300°C for sixty minutes [14], which suggests that a larger nucleation barrier hampers the formation of FeSn 2 in the samples fired for a shorter time at 250°C. The need of an induction time for the nucleation of FeSn 2 has been observed before-during the fabrication of tin plate on steel [41] and is also consistent with the large grains of FeSn trapped in FeSn 2 observed in the drops formed at 450°C. Even though its solubility is very limited (less than 1 wt%), iron can dissolve in the molten solder during spreading at 450°C.…”

Section: Interfacial Microstructuresupporting

confidence: 62%

Spreading of Sn-Ag solders on FeNi alloys

et al. 2003

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The spreading of Sn-3Ag-xBi solders on Fe-42Ni has been studied using a drop transfer setup. Initial spreading velocities as fast as ~0.5 m/s have been recorded. The results are consistent with a liquid front moving on a metastable, flat, unreacted substrate and can be described by using a modified molecular-kinetic model for which the rate controlling step is the movement of one atom from the liquid to the surface of the solid substrate. Although the phase diagram predicts the formation of two Fe-Sn intermetallics at the solder/substrate interface in samples heated at temperatures lower than 513°C, after spreading at 250°C only a thin FeSn reaction layer could be observed. Two interfacial layers (FeSn and FeSn 2 ) were found after spreading at 450°C.

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Section: Interfacial Microstructuresupporting

confidence: 62%

Spreading of Sn-Ag solders on FeNi alloys

et al. 2003

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“…The slope, h, and intercept, k, of this straight line are determined with a least squares linear regression model. As a result, the diffusion equation [17] can be rewritten in terms of h, k, and u such that: [16].…”

Section: Hall Methodsmentioning

confidence: 99%

Interdiffusion and impurity diffusion in polycrystalline Mg solid solution with Al or Zn

Kammerer¹,

Kulkarni²,

Warmack³

et al. 2014

Journal of Alloys and Compounds

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a b s t r a c tInterdiffusion and impurity diffusion in Mg binary solid solutions, Mg(Al) and Mg(Zn) were investigated at temperatures ranging from 623 to 723 K. Interdiffusion coefficients were determined via the Boltzmann-Matano Method using solid-to-solid diffusion couples assembled with polycrystalline Mg and Mg(Al) or Mg(Zn) solid solutions. In addition, the Hall method was employed to extrapolate the impurity diffusion coefficients of Al and Zn in pure polycrystalline Mg. For all diffusion couples, electron microprobe analysis was utilized for the measurement of concentration profiles. The interdiffusion coefficient in Mg(Zn) was higher than that of Mg(Al) by an order of magnitude. Additionally, the interdiffusion coefficient increased significantly as a function of Al content in Mg(Al) solid solution, but very little with Zn content in Mg(Zn) solid solution. The activation energy and pre-exponential factor for the average effective interdiffusion coefficient in Mg(Al) solid solution were determined to be 186.8 (±0.9) kJ/mol and 7.69 Â 10 À1 (±1.80 Â 10 À1 ) m 2 /s, respectively, while those determined for Mg(Zn) solid solution were 139.5 (±4.0) kJ/mol and 1.48 Â 10 À3 (±1.13 Â 10 À3 ) m 2 /s. In Mg, the Zn impurity diffusion coefficient was an order of magnitude higher than the Al impurity diffusion coefficient. The activation energy and pre-exponential factor for diffusion of Al impurity in Mg were determined to be 139.3 (±14.8) kJ/mol and 6.25 Â 10 À5 (±5.37 Â 10 À4 ) m 2 /s, respectively, while those for diffusion of Zn impurity in Mg were determined to be 118.6 (±6.3) kJ/mol and 2.90 Â 10 À5 (±4.41 Â 10 À5 ) m 2 /s.

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“…It was slightly modified by Crank [13] using the Boltzmann variable divided by two. Finally, the HM was extended by Sarafianos [14]. Okino et al [15] studied an analytical solution of the Boltzmann transformation equation with no preconditions.…”

Section: Introductionmentioning

confidence: 98%

Finite Difference Solution of the Diffusion Equation and Calculation of the Interdiffusion Coefficient using the Sauer-Freise and Hall Methods in Binary Systems

Ahmed

Belova

Murch

2015

Procedia Engineering

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The study of concentration dependent diffusion is important in the field of alloys and semiconductors. It is a key issue to calculate accurate interdiffusion coefficients using experimentally obtained concentration profiles. The Boltzmann-Matano (BM) method is often used for determining diffusion coefficients. But this technique has some shortcomings in calculating an accurate interdiffusion coefficient. Because of this, the Sauer and Freise (SF) method (which is a clever modification of the BM method) is more useful for calculating the interdiffusion coefficient. The Hall Method (HM) was specifically designed for determining the interdiffusion coefficient at the low and high concentration limits. In the present study, concentration profiles have been numerically generated as a solution to the interdiffusion problem in a binary system when the interdiffusion coefficient is dependent on concentration. This has been done using an explicit finite difference method. A comparative study of the HM, BM and SF methods has been performed using the generated concentration profiles. This allows for a direct comparison between the SF, BM and HM techniques. Present results clearly indicate that the HM technique can only be applicable when the interdiffusion coefficient is constant (independent of concentration) or almost constant at the low concentration regions. In all other cases the SF method gives the best agreement with the input interdiffusion function.

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An analytical method of calculating variable diffusion coefficients

Cited by 33 publications

References 4 publications

Spreading of Sn-Ag solders on FeNi alloys

Spreading of Sn-Ag solders on FeNi alloys

Interdiffusion and impurity diffusion in polycrystalline Mg solid solution with Al or Zn

Finite Difference Solution of the Diffusion Equation and Calculation of the Interdiffusion Coefficient using the Sauer-Freise and Hall Methods in Binary Systems

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