## Abstract

Understanding mass transport in micro- and nanostructures is of paramount importance in improving the performance and reliability of the micro- and nanostructures. In this work, we solve the diffusion problem in a multilayer structure with periodic conditions under a constant heating rate via a Fourier series. Analytical relation is established between the coefficients of eigenfunctions and the intensity of X-ray or neutron Bragg peak. The logarithm of temporal variation of the intensity of X-ray or neutron Bragg peak is a linear function of the nominal diffusion time, with the nominal diffusion time being dependent on the heating rate. This linear relation is validated by experimental data. The Taylor series expansion of the linear relation to the first order of the diffusion time yields an approximately linear relation between the logarithm of temporal variation of the intensity of X-ray or neutron peak and the diffusion time for small diffusion times, which can be likely used to calculate the activation energy for the diffusion in a multilayer structure. The validation of such an approach is subjected to the fact that the characteristic time for heat conduction is much less than the characteristic time for the ramp heating as well as the characteristic time for diffusion.

Original language | English |
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Pages (from-to) | 27776-27783 |

Number of pages | 8 |

Journal | ACS Omega |

Volume | 8 |

Issue number | 30 |

DOIs | |

State | Published - Aug 1 2023 |

### Bibliographical note

Publisher Copyright:© 2023 The Authors. Published by American Chemical Society.

### Funding

H.S. and E.H. acknowledge support by the German Research Foundation under the contract Schm1569/29-2.

Funders | Funder number |
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Deutsche Forschungsgemeinschaft | Schm1569/29-2 |

## ASJC Scopus subject areas

- General Chemistry
- General Chemical Engineering