7.2 The Mystery of a Negative Poisson Ratio Was Solved by MD Simulation


Fig. 7-3 Temperature dependence of the elastic constants of the cristobalite

The following behavior of the cristobalite was clearly observed by MD simulation. With increasing temperature the component C33 of the elastic parameter corresponding to volume deformation decreases sharply, which induces an abrupt decrease of the component C44 corresponding to slip deformation. As a result the phase transition occurs around 1,050K.


Fig. 7-4 Temperature dependence of the Poisson ratio of cristobalite

It is observed that in the temperature range from 300-1,800K the Poisson ratio of the cristobalite is always negative.


Fig. 7-5 Different mechanisms of the negative Poisson ratio in the high temperature phase and the low temperature phase

Cristobalite in the low temperature phase takes an "inverted cell structure" where some of the vertex atoms go inside the cell as shown in subfigure (a). Consequently, if it is pulled in the direction of the blue arrows, it expands in the directions of the green arrows. In the high temperature phase, on the other hand, it has been conjectured that cristobalite takes an "ordinary cell structure" on time average as shown in subfigure (b). In our study, however, it was found that an "inverted cell structure" which appears momentarily (subfigure (c)) causes the negative Poisson ratio in the high temperature phase.



Molecular dynamics (MD) simulation is a computational method to understand features of a material, and is performed only by assuming forces between the atoms composing the material.
We are now developing an "MD stencil for parallel computation" in order to facilitate the use of MD simulation for analyses of various kinds of material. By utilizing subroutines developed for the equilibrium analysis group of the stencil we executed an MD simulation of cristobalite, a low density SiO2 polymorph. Though quartz, a typical silicon dioxide, is used in various application fields due to its excellent thermal characteristics, in the high temperature phase quartz suffers from a degradation of thermal characteristics caused by the phase transition of the cristobalite. As the cristobalite in the high temperature phase has scarcely been studied either experimentally or theoretically, we carried out a time-consuming MD simulation of the cristobalite from 300K to 1,800K, and determined values of the elastic moduli. By this study we succeeded in identifying the process of the phase transition (Fig. 7-3) and clarified the mechanism of the mysterious feature of cristobalite. The feature of this substance exists in the negative Poisson ratio ("Poisson ratio" is the shrinking ratio in the perpendicular direction to the direction of pull) (Fig. 7-4). When one pulls an elastic string its thickness is reduced. Therefore, the Poisson ratio of rubber is negative, but substances with negative Poisson ratio are not so common as those with positive Poisson ratio. Through this MD simulation we found that the mechanisms of the negative Poisson ratio of cristobalite observed over a wide range of temperature are not same in the low temperature phase and in the high temperature phase (Fig. 7-5).


Reference
H. Kimizuka et al., Mechanism for Negative Poisson Ratios over the alpha-beta Transition of Cristobalite, SiO2: A Molecular-Dynamics Study, Phys. Rev. Lett., 84(24), 5548 (2000).

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