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Non-Randomness in Network Glasses and Rigidity

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Abstract

The continuous random network model is widely used as a realistic description of the structure of covalent glasses and amorphous solids. We point out that, in real glasses and amorphous materials, there are nonrandom structural elements that go beyond just simple chemical ordering. We propose that the network can self-organize at its formation or fictive temperature and examine some of the possible consequences of such self-organization. We find that the absence of small rings can cause the mechanical threshold to change from a second-order to a first-order transition. We show that, if stressed regions are inhibited in the network, then there are two phase transitions and an intermediate phase that is rigid but stress-free. This intermediate phase is bounded by a second-order transition, on the one hand, and a first-order transition, on the other. Recent experiments in chalcogenide glasses give evidence for this intermediate phase.

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REFERENCES

  1. Zachariasen, W.H., The Atomic Arrangement in Glass, J.Am. Chem. Soc., 1932, vol. 54, pp. 3841-3851.

    Google Scholar 

  2. Polk, D.E., Structural Model for Amorphous Silicon and Germanium, J. Non-Cryst. Solids, 1971, vol. 5, no. 5, pp. 365-376.

    Google Scholar 

  3. Wooten, F., Winer, K., and Weaire, D., Computer Generation of Structural Models of Amorphous Si and Ge, Phys. Rev. Lett., 1985, vol. 54, no. 13, pp. 1392-1395.

    Google Scholar 

  4. Kirkwood, J.G., Skeletal Modes of Vibration of Long Chain Molecules, J. Chem. Phys., 1939, vol. 7, pp. 506-512.

    Google Scholar 

  5. Keating, P.N., Effect of Invariance Requirements on the Elastic Strain Energy of Crystals with Application to the Diamond Structure, Phys. Rev., 1966, vol. 145, no. 2, pp. 637-645.

    Google Scholar 

  6. Car, R. and Parrinello, M., Unified Approach for Molecular Dynamics and Density-Functional Theory, Phys. Rev. Lett., 1985, vol. 55, no. 22, pp. 2471-2474.

    Google Scholar 

  7. Barkema, G.T. and Mousseau, N., Event-Based Relaxation of Continuous Disordered Systems, Phys. Rev. Lett., 1966, vol. 77, pp. 4358-4364.

    Google Scholar 

  8. Feng, X.W., Bresser, W.J., and Boolchand, P., Direct Evidence for Stiffness Threshold in Chalcogenide Glasses, Phys. Rev. Lett., 1997, vol. 78, no. 23, pp. 4422-4425.

    Google Scholar 

  9. Boolchand, P., Feng, X.W., Selvanathan, D., and Bresser, W.J., Rigidity Transition in Chalcogenide Glasses, in Rigidity Theory and Applications, New York: Kluwer Academic/Plenum, 1999.

    Google Scholar 

  10. Selvanathan, D., Bresser, W.J., Boolchand, P., and Goodman, B., Thermally Reversing Window and Stiffness Transitions in Chalcogenide Glasses, Solid State Commun., 1999, vol. 111, pp. 619-627.

    Google Scholar 

  11. Thorpe, M.F., Continuous Deformations in Random Networks, J. Non-Cryst. Solids, 1983, vol. 57, no. 3, pp. 355-370.

    Google Scholar 

  12. Maxwell, J.C., On the Calculation of the Equilibrium and Stiffness of Frames, Philos. Mag., 1864, vol. 27, p. 294.

    Google Scholar 

  13. Cai, Y. and Thorpe, M.F., Floppy Modes in Network Glasses, Phys. Rev. B: Condens. Matter, 1989, vol. 40, no. 15, pp. 10535-10542.

    Google Scholar 

  14. Phillips, J.C., Topology of Covalent Non-Crystalline Solids: 1. Short-Range in Chalcogenide Alloys, J. Non-Cryst. Solids, 1979, vol. 34, no. 2, pp. 153-181.

    Google Scholar 

  15. Phillips, J.C., Topology of Covalent Non-Crystalline Solids: 2. Medium-Range Order in Chalcogenide Alloys and a-Si, J. Non-Cryst. Solids, 1981, vol. 43, no. 1, pp. 37-77.

    Google Scholar 

  16. Jacobs, D.J. and Thorpe, M.F., Generic Rigidity Percolation: The Peblle Game, Phys. Rev. Lett., 1995, vol. 75, pp. 4051-4062.

    Google Scholar 

  17. Jacobs, D.J. and Thorpe, M.F., Generic Rigidity Percolation in Two Dimensions, Phys. Rev. E, 1996, vol. 53, pp. 3682-3693.

    Google Scholar 

  18. Thorpe, M.F., Jacobs, D.J., Chubynsky, N.V., and Rader, A.J., Generic Rigidity of Network Glasses, in Rigidity Theory and Applications, New York: Kluwer Academic/Plenum, 1999.

    Google Scholar 

  19. Jacobs, D.J. and Thorpe, M.F., Comment on “Infinite-Cluster Geometry in Central-Force Networks, ” Phys. Rev. Lett., 1998, vol. 80, no. 24, p. 5451.

    Google Scholar 

  20. Duxbury, P.M., Jacobs, D.J., Thorpe, M.F., and Moukarzel, C., Floppy Modes and the Free Energy: Rigidity and Connectivity Percolation on Bethe Lattices, Phys. Rev. E, 1999, vol. 59, pp. 2084-2092.

    Google Scholar 

  21. Galeener, F.L., Kerwin, D.B., Miller, A.J., and Mikkelsen, J.C., Jr., X-ray Creation and Activation of Electron Spin Resonance in Vitreous Silica, Phys. Rev. B: Condens. Matter., 1993, vol. 47, no. 13, pp. 7760-7779.

    Google Scholar 

  22. Bak, P., How Nature Works: The Science of Self-Organized Criticality, New York: Copernicus, 1996.

    Google Scholar 

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Thorpe, M.F., Chubynsky, M.V., Jacobs, D.J. et al. Non-Randomness in Network Glasses and Rigidity. Glass Physics and Chemistry 27, 160–166 (2001). https://doi.org/10.1023/A:1011336511583

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