# Medium-range order in glasses and beyond



## [1991 - Elliott](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5468/elliott.pdf)

2023 [Revealing the relationship between liquid fragility and medium-range order in silicate glasses](https://www.nature.com/articles/s41467-022-35711-6)⏎
⏎
1992 [A Unified Model for the Low-Energy Vibrational Behaviour of Amorphous Solids](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5496/elliott-1992.pdf)

> ... the phonon scattering caused by intrinsic density fluctuation domains in the structure, within which short- and medium-range
> order is maintained and beyond which the material is structurally isotropic and homogeneous.
> **Phonon localization occurs when the mean-free path is comparable to the size of the domains**

1991 [Origin of the First Sharp Diffraction Peak in the Structure Factor of Covalent Glasses - S. R. Elliott](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5636/elliott.pdf)

## 1979 [TOPOLOGY OF COVALENT NON-CRYSTALLINE SOLIDS II: MEDIUM-RANGE ORDER IN CHALCOGENIDE ALLOYS AND A-Si(Ge)](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5635/jc%2Bphillips.pdf) J.C. PHILLIPS

[Introduction	to	the	structure	and	the	 structural	role of	elements in	glasses - Laurent Cormier](https://www.ustverre.fr/site/images/Site/Cargese_2017/Cormier_1.pdf)
[Revealing hidden medium-range order in amorphous materials using topological data analysis - SØREN S. SØRENSEN](https://www.science.org/doi/10.1126/sciadv.abc2320)


## 2009 Monaco-Giordano [Breakdown of the Debye approximation for the acoustic modes with nanometric wavelengths in glasses](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5469/monaco.pdf)

- 2009 [Anomalous properties of the acoustic excitations in glasses on the mesoscopic length scale](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5494/monaco.pdf)

> we show that in glasses the structural disorder undermines the Debye model in a subtle way: The elastic continuum approximation for the
> acoustic excitations breaks down abruptly on the mesoscopic,** medium-range-order length scale of 
10 interatomic spacings, where it still works well for the corresponding crystalline systems**

[anticipated and parametrized by Turlakov](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/4465/Low-temperature%2Bglasses%2BTurlakov%2B2003.pdf)

## https://www.sciencedirect.com/topics/physics-and-astronomy/medium-range-order

# Parents

* below $T_G$ glass temperature
* at and above $T_G$ glass temperature
* Small d-less coupling constant - anomalous states in low-T glasses
* below $T_G$ glass temperature- $\lambda/l$ ratio - P

# Attachments

* [](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5468/elliott.pdf)
* [](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5469/monaco.pdf)
* [](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5494/monaco.pdf)
* [](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5496/elliott-1992.pdf)
* [](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5635/jc%2Bphillips.pdf)
* [](https://knowen-production.s3.amazonaws.com/uploads/attachment/file/5636/elliott.pdf)