# The Effect of Embedded Nanoparticles on the Phonon Spectrum of Ice: An Inelastic X-ray Scattering Study

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

## 3. Discussion of Results

## 4. The Central Role of Bayesian Analysis

## 5. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Sample Availability

## Abbreviations

INS | Inelastic Neutron Scattering |

IXS | Inelastic X-ray Scattering |

FWHM | Full Width Half Maximum |

DHO | Damped Harmonic Oscillator |

PC | Phononic Crystals |

## References

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**Figure 1.**The upper panel represents a schematic diagram of the used instrument, while the lower one includes a picture of the sample spectrometer hutch.

**Figure 2.**Traceplot (panel

**a**) showing the model selected at each MCMC sweep, prior (panel

**b**) and posterior (panel

**c**) distribution for the number k of inelastic components in the spectrum of the AuNP suspension at Q = 21 nm${}^{-1}$.

**Figure 3.**IXS spectra from the ice samples (black dots) at the indicated Q values are compared with those of the frozen suspension (red dots). Spectra are normalized to their maximum and represented in an expanded y-scale to emphasize the shape of the inelastic features. Spectra from the frozen suspension are vertically offset for clarity.

**Figure 4.**The spectrum of the frozen suspension at Q = 21 nm${}^{-1}$ is compared with best-fitting lineshapes and the individual lineshape components. The corresponding color acronym indicates each spectral mode’s assignment: LFM${}_{G}$ is a low-frequency mode associated to Au nanoparticles, TA (ice) transverse acoustic, LA${}_{G}$ Au longitudinal acoustic, HFM high-frequency (ice) mode (see text). The question mark labels a not assigned mode as discussed in the text. The spectrum is displayed in an expanded y-scale to emphasize the shape of the inelastic features.

**Figure 5.**The IXS spectra of ice and the frozen aqueous suspension of the AuNPs at Q = 21 nm${}^{-1}$ in panels (

**a**,

**b**), respectively. Raw data are compared with best-fitting model lineshapes and individual spectral components, with the same color code as in Figure 4 for the AuNPs suspension yet in semilogarithmic plots. For the ice Ih spectrum, the two optical modes ${O}_{L}$ and ${O}_{H}$ are in magenta and black, respectively, and the mode LA is in green.

**Figure 6.**Left and right plot display, respectively, the dispersion curves detected in pure ice (dots) and in the frozen suspensions (squares). The dash-dotted orange line in the right plot represents the dispersion curve of the only (longitudinal acoustic) mode observable in liquid gold [13,28,29], while the corresponding gray line is the transverse Au phonon dispersion observed in our IXS measurement on a liquid AuNP suspension [4]. Each mode is associated with a color and labeled in either of the two plots with the acronyms of the same color, whose meaning is explained in the main text.

**Figure 7.**IXS spectra measured on polycrystalline ice (black dots) and AuNP frozen suspension (red dots) at Q = 21 nm${}^{-1}$ are compared in a restricted energy range after normalization to the respective maxima. The shadowed gray band covers the zone where the optical modes of ice are detected. The plot includes as a red line the best-fitting lineshape of the frozen suspension spectrum without its low-frequency DHO component after similar normalization.

**Figure 8.**Simulated posterior distribution for the number, k, of inelastic components given the experimental data y for the frozen suspension of AuNPs at a momentum transfer of Q = 17 nm${}^{-1}$.

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## Share and Cite

**MDPI and ACS Style**

De Francesco, A.; Scaccia, L.; Formisano, F.; Guarini, E.; Bafile, U.; Nykypanchuk, D.; Alatas, A.; Li, M.; Lynch, S.T.; Cunsolo, A.
The Effect of Embedded Nanoparticles on the Phonon Spectrum of Ice: An Inelastic X-ray Scattering Study. *Nanomaterials* **2023**, *13*, 918.
https://doi.org/10.3390/nano13050918

**AMA Style**

De Francesco A, Scaccia L, Formisano F, Guarini E, Bafile U, Nykypanchuk D, Alatas A, Li M, Lynch ST, Cunsolo A.
The Effect of Embedded Nanoparticles on the Phonon Spectrum of Ice: An Inelastic X-ray Scattering Study. *Nanomaterials*. 2023; 13(5):918.
https://doi.org/10.3390/nano13050918

**Chicago/Turabian Style**

De Francesco, Alessio, Luisa Scaccia, Ferdinando Formisano, Eleonora Guarini, Ubaldo Bafile, Dmytro Nykypanchuk, Ahmet Alatas, Mingda Li, Scott T. Lynch, and Alessandro Cunsolo.
2023. "The Effect of Embedded Nanoparticles on the Phonon Spectrum of Ice: An Inelastic X-ray Scattering Study" *Nanomaterials* 13, no. 5: 918.
https://doi.org/10.3390/nano13050918