Zn Tracer Diffusion in $$\alpha $$-Cu$$_{64}$$Zn$$_{36}$$: Bridging Experiments and Simulations

Abstract Within the present study, the tracer diffusion of zinc in the copper-zinc alloy $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -Cu $$_{64}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>64</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> Zn $$_{36}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>36</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> is experimentally investigated and the results are compared to molecular dynamics (MD) simulations. For the experiments, the rare stable isotope $$^{70}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>70</mml:mn> </mml:mmultiscripts> </mml:math> Zn is used, that is deposited in the form of Cu $$_{64}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>64</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> $$^{70}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>70</mml:mn> </mml:mmultiscripts> </mml:math> Zn $$_{36}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>36</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> layers on top of polycrystalline $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -Cu $$_{64}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>64</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> Zn $$_{36}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>36</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> samples using ion-beam co-sputtering of segmented targets. The coated samples underwent isothermal annealing in argon at temperatures ranging from 400 $$^\circ \text {C}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mo>∘</mml:mo> </mml:mmultiscripts> <mml:mtext>C</mml:mtext> </mml:mrow> </mml:math> to 600 $$^\circ \text {C}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mo>∘</mml:mo> </mml:mmultiscripts> <mml:mtext>C</mml:mtext> </mml:mrow> </mml:math> for varying durations between 30 seconds and 2 hours. Molecular dynamics simulations were employed to compute the self-diffusion of Zn in $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -Cu $$_{64}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>64</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> Zn $$_{36}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>36</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> . Simulations using an initial single vacancy yielded results closely aligned with experimental data, in contrast to those with higher vacancy concentrations. Our diffusivities obtained from both tracer diffusion experiments and simulations show the Arrhenius behavior with an activation enthalpy of diffusion of 1.37 eV. This value is consistent with literature results on radiotracer experiments. This study highlights the potential of MD simulations for determining diffusion coefficients as an alternative or complement to expensive and time-consuming extensive experimental investigations.

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Journal
Metallurgical and Materials Transactions A
Published
2025-11-21
DOI
https://doi.org/10.1007/s11661-025-07991-2
Primary Topic
Copper Interconnects and Reliability
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article
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article

Zn Tracer Diffusion in $$\alpha $$-Cu$$_{64}$$Zn$$_{36}$$: Bridging Experiments and Simulations

Lars Dörrer, Nina Gunkelmann, Harald Schmidt, Hoang-Thien Luu et al.
Metallurgical and Materials Transactions A
Copper Interconnects and Reliability
article

Zn Tracer Diffusion in $$\alpha $$-Cu$$_{64}$$Zn$$_{36}$$: Bridging Experiments and Simulations

Lars Dörrer, Nina Gunkelmann, Harald Schmidt, Hoang-Thien Luu, Babette Tonn, Y. Zhu, Durga Prasanth Dude
article en

Abstract

Abstract Within the present study, the tracer diffusion of zinc in the copper-zinc alloy $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -Cu $$_{64}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>64</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> Zn $$_{36}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>36</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> is experimentally investigated and the results are compared to molecular dynamics (MD) simulations. For the experiments, the rare stable isotope $$^{70}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>70</mml:mn> </mml:mmultiscripts> </mml:math> Zn is used, that is deposited in the form of Cu $$_{64}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>64</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> $$^{70}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mn>70</mml:mn> </mml:mmultiscripts> </mml:math> Zn $$_{36}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>36</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> layers on top of polycrystalline $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -Cu $$_{64}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>64</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> Zn $$_{36}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>36</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> samples using ion-beam co-sputtering of segmented targets. The coated samples underwent isothermal annealing in argon at temperatures ranging from 400 $$^\circ \text {C}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mo>∘</mml:mo> </mml:mmultiscripts> <mml:mtext>C</mml:mtext> </mml:mrow> </mml:math> to 600 $$^\circ \text {C}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mo>∘</mml:mo> </mml:mmultiscripts> <mml:mtext>C</mml:mtext> </mml:mrow> </mml:math> for varying durations between 30 seconds and 2 hours. Molecular dynamics simulations were employed to compute the self-diffusion of Zn in $$\alpha $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> -Cu $$_{64}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>64</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> Zn $$_{36}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mn>36</mml:mn> <mml:mrow/> </mml:mmultiscripts> </mml:math> . Simulations using an initial single vacancy yielded results closely aligned with experimental data, in contrast to those with higher vacancy concentrations. Our diffusivities obtained from both tracer diffusion experiments and simulations show the Arrhenius behavior with an activation enthalpy of diffusion of 1.37 eV. This value is consistent with literature results on radiotracer experiments. This study highlights the potential of MD simulations for determining diffusion coefficients as an alternative or complement to expensive and time-consuming extensive experimental investigations.

Metallurgical and Materials Transactions AVol. 57(1)
Clausthal University of Technology (DE)
Deutsche Forschungsgemeinschaft
Openalex Percentile: Top 74%
Copper Interconnects and Reliability
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