Proton disorder and elasticity of hexagonal ice and gas hydrates

  • Sergey V. Gudkovskikh
  • Mikhail V. KirovEmail author
Original Paper


This work is devoted to the study of the mechanical properties of hexagonal ice Ih and gas hydrate frameworks sI, sII and sH, taking into account the disorder in the positions of the hydrogen atoms (protons). The article emphasizes the critical role of the elastic energy for the evaluation of the relative energy of the proton configurations. The calculations are performed with the help of the TINKER package using the AMOEBA polarizable force field. The elastic constants, elastic modulus, and anisotropy indices are calculated. It is shown that all gas hydrate frameworks are very isotropic due to their cage-like structure. It was established that one of the reasons for the higher anisotropy of ice Ih is the presence of a large number of highly symmetric proton configurations. The purpose of the article is to overcome the apparent contradiction between the ab initio and force field methods in predicting the relative stability of the proton configurations of ice structures at low temperature. The other purpose is to evaluate the effect of proton disorder on the elastic properties of ice and gas hydrate structures.

Graphical abstract

Proton configurations in hexagonal ice: fixed (a) and free (b) unit cell parametersᅟ


Proton disorder Gas hydrates Hexagonal ice Elastic energy 



We thank A.L. Tchougreef for useful discussion. The present work was supported by the Basic Research Program of RAS No. IX.135.2.3.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Tyumen Scientific Center, SB RASTyumenRussia
  2. 2.Tyumen Industrial UniversityTyumenRussia

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