Comparison of the Sauer-Freise and Hall Methods for Obtaining Interdiffusion Coefficients in Binary Alloys

Ahmed, Tanvir; Belova, Irina V.; Evteev, Alexander V.; Levchenko, Elena V.; Murch, Graeme E.

doi:10.1007/s11669-015-0392-4

“…The interdiffusion coefficient in the (Zr, Mo) solid solution phase was calculated based on the concentration distribution curve in Figure 2. The interdiffusion coefficient at the atomic concentration c* (abscissa x*) was expressed as [30,31]:…”

Section: Interdiffusion Coefficient and Activation Energy Of Diffusio...mentioning

confidence: 99%

Interdiffusion in Zr-Mo/W Intermetallics

Wang

¹

,

Liu

²

,

Li

³

et al. 2023

Applied Sciences

2

0

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Intermetallic compounds or solid solutions can form between Zr and Mo/W, in which the multiphase of the diffusion may be influenced by each other. Interdiffusion kinetic data in such intermetallic systems are highly demanded for material design. In this work, solid–solid diffusion couples of Zr-Mo and Zr-W were prepared by the fixture method, and the interdiffusion behaviors of Zr-Mo and Zr-W at 1300–1500 °C were systematically investigated. The results showed that the intermetallic compounds Mo2Zr/W2Zr formed in the Zr-Mo/W diffusion systems. The growth constants of the Mo2Zr and W2Zr phases varied with temperature in accordance with the Arrhenius relationship, and the activation energies of growth were 109 kJ/mol and 285 kJ/mol, respectively. In addition, (Zr, Mo) solid solution formed between Mo2Zr and pure Zr as diffusion proceeded, resulting in a lower chemical potential for the formation of Mo2Zr. The den Broeder method was used in calculating the interdiffusion coefficients of the solid solution. The results showed that the interdiffusion coefficient in the (Zr, Mo) solid solution decreased with the increase of Mo concentration. Moreover, the diffusion activation energy of the solid solution was evaluated based on the Arrhenius relationship, and the activation energy was 145–170 kJ/mol when the Mo content was in the range of 2–10 at. %. These diffusion kinetic data provide a reference for the composition design and preparation technic of Zr-based alloys.

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“…All the profiles below were calculated using the finite difference numerical procedure described in detail in. [16,17] For the interdiffusion flux J x ð Þ at any x-position in the diffusion zone we have the following expression:…”

Section: Theorymentioning

confidence: 99%

“…In 2013, Belova et al [15] developed simultaneous measurement of interdiffusion and tracer diffusion coefficients computationally for binary and multicomponent alloys. Furthermore, in 2015, Ahmed et al [16,17] studied interdiffusion coefficients for binary alloys using the explicit finite difference method. In their study, they used BM, SF, HM and a newly developed method treated as the extended Hall method to obtain the interdiffusion coefficients.…”

Section: Introductionmentioning

confidence: 99%

Novel General Solution for the Analysis of a Multicomponent Interdiffusion Couple

Belova

¹

,

Fiedler

²

,

Murch

³

2022

J. Phase Equilib. Diffus.

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In this paper, we draw attention to the investigation of the novel exact solution [1.Scripta Mat. 210:114430; M.A. Dayananda, in JPED, this issue, (2022);] that is applicable to a multicomponent (n-component) interdiffusion couple where the interdiffusion matrix may change with alloy composition. In the derivation of this solution the interdiffusion flux $$J_{j}$$ J j of a component j is related to (n-1) independent composition gradients for an isothermal, diffusion couple using the well-known continuity equation. Novel exact expressions are then derived for all of the interdiffusion coefficients, $$\tilde{D}_{ij}^{n}$$ D ~ ij n (i, j = 1, 2, …..n − 1), where the partial derivatives of the product $$J_{j} \left( {y - y_{0} } \right)$$ J j y - y 0 with respect to composition $$C_{i}$$ C i ($$y_{0}$$ y 0 is the Matano plane) are used. In this paper, it is shown that the novel solution leads to a computational procedure similar to the Boltzmann-Matano analysis. Note that the derivatives $$\partial (J_{j} \left( {y - y_{0} } \right))/\partial C_{i} , i,j = 1, \ldots ,n - 1$$ ∂ ( J j y - y 0 ) / ∂ C i , i , j = 1 , … , n - 1 (that are required for the solution) can only be calculated along the diffusion path and therefore, for $$n > 2$$ n > 2 , a single couple will not be enough to calculate all of them correctly.

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“…By following the similar treatment in Ref. [21], one constant interdiffusion coefficient and three composition-dependent ones were pre-set, as summarized in Table 1 and also plot as the standard data in Fig. 2.…”

Section: Fictitious Binary Systemmentioning

confidence: 99%

“…In the first part, the pragmatic numerical inverse method was validated in different binary cases. The strategy proposed by Ahmed et al [21] was adopted in the present work, i.e., that four standard types of interdiffusion coefficients (including constant, linear, quadratic composition dependence of interdiffusion coefficients) were set in advance, and then used to generate different composition profiles for a binary finite diffusion couple with the same initial and annealing conditions. In order to mimic the "scattered" experimental data in real cases, the Gaussian-distributed noise was added in.…”

Section: Introductionmentioning

confidence: 99%

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

Liu

¹

,

Chen

²

,

Zhong

³

et al. 2017

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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 comparison between the computational diffusion properties and the experimental data indicates that the numerical inverse method is also applicable to the high-throughput determination of the composition-dependent interdiffusion coefficients in finite diffusion couples.

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Comparison of the Sauer-Freise and Hall Methods for Obtaining Interdiffusion Coefficients in Binary Alloys

Cited by 17 publications

References 40 publications

Interdiffusion in Zr-Mo/W Intermetallics

Interdiffusion in Zr-Mo/W Intermetallics

Novel General Solution for the Analysis of a Multicomponent Interdiffusion Couple

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

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