Measurement of Inner Potential of Metal-Organic Framework Crystals Using Multiple Electron Refraction

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Measurement of Inner Potential of Metal-Organic Framework Crystals Using Multiple Electron Refraction

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Author(s): Spring Ma ¹ , Tu Sun ¹ , Fang Wang ¹ , Weishi Wan ² ^, , Osamu Terasaki ¹ ^, , Yanhang Ma ¹ ^,

Publication date (Electronic): 21 January 2025

Conference name: 13th Asia Pacific Microscopy Congress 2025 (APMC13)

Conference date: 2-7 Febuary 2025

Keywords: electron diffraction, electron refraction, mean inner potential, metal-organic framework, structure factor

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Abstract

The precise measurement of structure factors is an essential prerequisite for determining accurate charge distribution within crystal, which is important for the understanding of their chemical and physical properties. However, conventional methods are difficult to be applied to metal-organic framework (MOF) materials due to its complex structure and electron beam sensitivity [ 1]. The effect of double refraction in electron diffraction has been reported for a long time, but it is rarely observed in single crystals and discussed in depth, especially for high-energy incident electron [ 2– 5]. The electron refraction promises to be a means of accurately determining the structure factors of MOF materials.

First, we systhesised a metal-organic framework MIL-96(Al) with high crystallinity [ 6– 7], the morphology of MIL-96(Al) shows sixfold symmetry and unique morphology. Herein, using a high-energy parallel electron beam produced by JEOL JEM-2100 Plus (TEM) to illuminate single-crystal nanoparticle of MIL-96(Al), we clearly observed multiple refraction of electrons in diffraction patterns taken along [0001] zone axis,as shown in Fig. 1.

Fig. 1.

Refraction of electrons in MIL-96(Al).

We have again elucidated the mechanism of Bloch wave refraction in electron diffraction and shown that the phase term of the deviated diffraction peaks by high energy electrons will disappear in the case of wedge crystal. Then, multiple refraction is successfully simulated and agrees well with experiment data.

Obtaining accurate structure factor is essential to quantify the charge redistribution due to chemical bonding [ 8]. In our calculations, DFT(Density Functional Theory) greatly overestimates the value of V ₁₀₁₀, which can be attributed to the overestimation of bonding interaction. Using multiple refraction, We refined and determined the first-order Fourier coefficients of crystal potential V ₁₀₁₀ accurately by matching the experimental intensity profile of each reflection.

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Publication date (Electronic): 21 January 2025

Electronic Location Identifier: e401

Affiliations

[1 ]Shanghaitech University, School of Physical Science and Technology, Shanghai, China

[2 ]Quantum Science Center of Guangdong-Hongkong-Macaogreater Bay Area, Shenzhen, China

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*Corresponding author: mayh2@ 123456shanghaitech.edu.cn

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Yanhang Ma https://orcid.org/0000-0003-4814-3740

Article

DOI: 10.14293/APMC13-2025-0401

SO-VID: b4dc5c1d-837e-4c10-8757-3c896adc80a5

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Published under Creative Commons Attribution 4.0 International ( CC BY 4.0). Users are allowed to share (copy and redistribute the material in any medium or format) and adapt (remix, transform, and build upon the material for any purpose, even commercially), as long as the authors and the publisher are explicitly identified and properly acknowledged as the original source.

Conference name: 13th Asia Pacific Microscopy Congress 2025

Conference acronym: APMC13

Conference number: 13

Conference location: Brisbane, Australia

Conference date: 2-7 Febuary 2025

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Funding

The authors would like to thank Prof. Bo for his valuable suggestions. Dr. Junyi is also thanked for his help with code debugging and structure refinement.

References

Spence, J. C. H. Acta Crystallographica Section A: Foundations of Crystallography, 49(2), 231-260 (1993).
Sturkey, L., & Frevel, L. K. Physical Review, 68(1-2), 56 (1945).
Cowley, J. M., & Rees, A. Proceedings of the Physical Society, 59(2), 287 (1947).
Honjo,G. Journal of the Physical Society of Japan, 8(6), 776-781 (1953).
Miyake, S., Fujiwara, K., & Suzuki,K. Journal of the Physical Society of Japan, 18(9), 1306-1314 (1963).
Loiseau, T. et al. Journal of the American Chemical Society, 128(31), 10223-10230 (2006).
Wang, F., Fan, Y., Ma, Y., & Li, T. Crystal Growth & Design, 21(8), 4571-4578 (2021).
Rez, D. A. V. I. D. et al. Acta Crystallographica Section A: Foundations of Crystallography, 50(4), 481-497 (1994).
Yoshioka, H. Journal of the Physical Society of Japan, 12(6), 618-628 (1957).
Ichikawa, M.,& Ohtsuki, Y. H. Journal of the Physical Society of Japan, 28(1), 276A-276A (1970).
Yu, M. H. et al. Accounts of Materials Research, 4(10), 839-853 (2023).

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[1] Spence, J. C. H. Acta Crystallographica Section A: Foundations of Crystallography, 49(2), 231-260 (1993).

[2] Sturkey, L., & Frevel, L. K. Physical Review, 68(1-2), 56 (1945).

[3] Cowley, J. M., & Rees, A. Proceedings of the Physical Society, 59(2), 287 (1947).

[4] Honjo,G. Journal of the Physical Society of Japan, 8(6), 776-781 (1953).

[5] Miyake, S., Fujiwara, K., & Suzuki,K. Journal of the Physical Society of Japan, 18(9), 1306-1314 (1963).

[6] Loiseau, T. et al. Journal of the American Chemical Society, 128(31), 10223-10230 (2006).

[7] Wang, F., Fan, Y., Ma, Y., & Li, T. Crystal Growth & Design, 21(8), 4571-4578 (2021).

[8] Rez, D. A. V. I. D. et al. Acta Crystallographica Section A: Foundations of Crystallography, 50(4), 481-497 (1994).

[9] Yoshioka, H. Journal of the Physical Society of Japan, 12(6), 618-628 (1957).

[10] Ichikawa, M.,& Ohtsuki, Y. H. Journal of the Physical Society of Japan, 28(1), 276A-276A (1970).

[11] Yu, M. H. et al. Accounts of Materials Research, 4(10), 839-853 (2023).

Measurement of Inner Potential of Metal-Organic Framework Crystals Using Multiple Electron Refraction

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