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Localization model description of the interfacial dynamics of crystalline Cu and \(\hbox {Cu}_{64}\hbox {Zr}_{36}\) metallic glass nanoparticles

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Abstract

Many of the special properties of nanoparticles (NPs) and nanomaterials broadly derive from the significant fraction of particles (atoms, molecules or segments of polymeric molecules) in the NP interfacial region in which the interparticle interactions are characteristically highly anharmonic in comparison to the bulk material. This leads to relatively large mean square particle displacements relative to the material interior, often resulting in a strong increase interfacial mobility and reactivity in both crystalline and glass NPs. The ‘Debye–Waller factor’, or the mean square particle displacement \(<u^{2}>\) on a ps ‘caging’ timescale relative to the square of the average interparticle distance \(\upsigma ^{2}\), provides an often experimentally accessible measure of the strength of this anharmonic interaction. The Localization Model (LM) of the dynamics of condensed materials relates this thermodynamic property to the structural relaxation time \(\tau _{\alpha }\), determined from the intermediate scattering function, without any free parameters. Moreover, the LM allows for the prediction of the diffusion coefficient D when combined with the ‘decoupling’ or Fractional Stokes-Einstein relation linking \(\tau _{\alpha }\) to D. In the current study, we employed classical molecular dynamics simulation to investigate the structural relaxation and diffusion of model \(\hbox {Cu}_{\mathrm {64}}\hbox {Zr}_{\mathrm {36}}\) metallic glass and Cu crystalline NPs with different sizes. As with previous studies validating the LM on model bulk and crystalline materials, and for the interfacial dynamics of thin crystalline and metallic glass films, we find the LM model also describes the interfacial dynamics of model crystalline metal (Cu) and metallic glass (\(\hbox {Cu}_{\mathrm {64}}\hbox {Zr}_{\mathrm {36}})\) NPs to a good approximation, further confirming the generality of the model.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The data that supports the findings of this study are available within the article and its supplementary information.]

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Acknowledgements

G.M. and H.Z. gratefully acknowledge the support of the Natural Sciences and Engineering Research Council of Canada under the Discovery Grant Program (RGPIN-2017-03814) and Accelerator Supplements (RGPAS-2017- 507975).

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  1. Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB, T6G 1H9, Canada

    Gazi Mahmud & Hao Zhang

  2. Material Measurement Laboratory, Materials Science and Engineering Division, National Institute of Standards and Technology, Maryland, 20899, USA

    Jack F. Douglas

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  1. Gazi Mahmud
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H. Z. and J.F.D. developed the idea and designed the simulation. G.M. performed MD simulations. G.M., H.Z. and J.F.D. analyzed the data. G.M., H.Z. and J.F.D. wrote the manuscript.

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Mahmud, G., Zhang, H. & Douglas, J.F. Localization model description of the interfacial dynamics of crystalline Cu and \(\hbox {Cu}_{64}\hbox {Zr}_{36}\) metallic glass nanoparticles. Eur. Phys. J. E 44, 33 (2021). https://doi.org/10.1140/epje/s10189-021-00022-z

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