Skip to main content
SpringerLink
Log in
Book cover

Molecular Dynamics Simulations of Disordered Materials pp 275–311Cite as

Topological Constraints, Rigidity Transitions, and Anomalies in Molecular Networks

  • Chapter
  • First Online:

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 215))

Abstract

In this chapter, we present the first connection between realistic atomic scale simulations and topological constraint theory which has been introduced in the context of rigidity transitions of network glasses. Such rigid constraints can be computed rather simply by changing composition at low temperature but their estimates as a function of temperature or pressure remains challenging. We introduce and describe a method based on the calculation of standard deviations of relevant neighbor or partial bond-angle distributions which allows to estimate with confidence atomic stretching and bending topological constraints. The counting is illustrated from several archetypal liquids and glasses, including oxides and chalcogenides (SiO\(_2\), Ge\(_x\)Se\(_{1-x}\),...). These results permit connecting the role of mechanical constraints in disordered systems to elucidating some of its most intruiging features (adaptation), with calculated anomalies in structural and dynamic properties.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    We relate the position \(r\) of a peak in real space to the position \(k\) of a corresponding peak in Fourier space by using the relation \(k\cdot r\approx 7.7\), which identifies the location of the first maximum of the spherical Bessel function \(j_0(kr)\)

References

  1. M.F. Thorpe, P.M Duxbury (eds.), Rigidity Theory and Applications (Kluwer Academic, Plenum Publishers, New York, 1999)

    Google Scholar 

  2. M. Micoulaut, M. Popescu (eds.), Rigidity and Boolchand Intermediate Phases in Nanomaterials (INOE Publishing House, Bucarest, 2009)

    Google Scholar 

  3. M.F. Thorpe, J.C. Phillips (eds.), Phase Transitions and Self-organization in Electronic and Molecular Networks (Kluwer Academic, Plenum Publishers, New York, 2001)

    Google Scholar 

  4. M. Zhang, P. Boolchand, Science 266, 1355 (1994)

    Article  Google Scholar 

  5. J.L. Lagrange, Mécanique Analytique (Courcier, Paris, 1788)

    Google Scholar 

  6. J.C. Maxwell, Philos. Mag. 27, 294 (1864)

    Google Scholar 

  7. J.C. Phillips, J. Non-Cryst. Solids 34, 153 (1979)

    Google Scholar 

  8. J.C. Phillips, Phys. Rev. B 28, 7038 (1983)

    Article  Google Scholar 

  9. J.C. Phillips, Phys. Today 35, 27 (1982)

    Article  Google Scholar 

  10. M. Micoulaut, W. Welnic, M. Wuttig, Phy. Rev. B 78, 224209 (2008)

    Article  Google Scholar 

  11. P. Boolchand, M.F. Thorpe, Phys. Rev. B 50, 10366 (1994)

    Article  Google Scholar 

  12. W.J. Bresser, P. Suranyi, P. Boolchand, Phys. Rev. Lett. 56, 2493 (1986)

    Article  Google Scholar 

  13. R. Azoulay, H. Thibierge, A. Brenac, J. Non-Cryst. Solids 18, 33 (1975)

    Google Scholar 

  14. M.F. Thorpe, J. Non-Cryst. Solids 57, 355 (1983)

    Google Scholar 

  15. H. He, M.F. Thorpe, Phys. Rev. Lett. 54, 2107 (1985)

    Article  Google Scholar 

  16. M.F. Thorpe, J. Non-Cryst. Solids 76, 109 (1985)

    Google Scholar 

  17. W.A. Kamitakahara, R.L. Cappelletti, P. Boolchand, B. Halfpap, F. Gompf, D.A. Neumann, H. Mutka, Phys. Rev. B 44, 94 (1991)

    Article  Google Scholar 

  18. X. Feng, W. Bresser, P. Boolchand, Phys. Rev. Lett. 78, 4422 (1997)

    Article  Google Scholar 

  19. M. Tatsumisago, B.L. Halfpap, J.L. Green, S.M. Lindsay, C.A. Angell, Phys. Rev. Lett. 64, 1549 (1990)

    Article  Google Scholar 

  20. A.N. Sreeram, A.K. Varshneya, D.R. Swiler, J. Non-Cryst. Solids 128, 294 (1991)

    Google Scholar 

  21. P. Boolchand, W.J. Bresser, M. Zhang, Y. Wu, J. Wells, R.N. Enzweiler, J. Non-Cryst. Solids 82, 143 (1995)

    Google Scholar 

  22. S. Asokan, M.Y.N. Prasad, G. Parthasarathy, Phys. Rev. Lett. 62, 808 (1989)

    Article  Google Scholar 

  23. R.A. Bohmer, C.A. Angell, Phys. Rev. B 45, 1091 (1992)

    Article  Google Scholar 

  24. D. Selvenathan, W. Bresser, P. Boolchand, Solid State Commun. 111, 619 (1999)

    Article  Google Scholar 

  25. D. Selvenathan, W. Bresser, P. Boolchand, Phys. Rev. B 61, 15061 (2000)

    Article  Google Scholar 

  26. M.F. Thorpe, D.J. Jacobs, M.V. Chubynsky, J.C. Phillips, J. Non-Cryst. Solids 266–269, 859 (2000)

    Google Scholar 

  27. M. Micoulaut, J.C. Phillips, Phys. Rev. B 67, 104204 (2003)

    Article  Google Scholar 

  28. S. Bhosle, P. Boolchand, M. Micoulaut, C. Massobrio, Solid State Commun. 151, 1851 (2011)

    Article  Google Scholar 

  29. S. Bhosle, K. Gunasekera, P. Boolchand, M. Micoulaut, Int. J. Appl. Glass Sci. 3, 205 (2012)

    Article  Google Scholar 

  30. S. Bhosle, K. Gunasekera, P. Boolchand, M. Micoulaut, Int. J. Appl. Glass Sci. 3, 189 (2012)

    Article  Google Scholar 

  31. Y. Vaills, T. Qu, M. Micoulaut, F. Chaimbault, P. Boolchand, J. Phys. Condens. Matter 17, 4889 (2005)

    Article  Google Scholar 

  32. M. Micoulaut, Am. Mineral. 93, 1732 (2008)

    Article  Google Scholar 

  33. S. Chakravarty, D.G. Georgiev, P. Boolchand, M. Micoulaut, J. Phys. Condens. Matter 17, L7 (2005)

    Article  Google Scholar 

  34. K. Gunasekara, S. Bhosle, P. Boolchand, M. Micoulaut, J. Chem. Phys. 139, 164511 (2013)

    Article  Google Scholar 

  35. G. Yang, O. Gulbiten, Y. Gueguen, B. Bureau, J-Ch. Sangleboeuf, C. Roiland, E.A. King, P. Lucas, Phys. Rev. B 85, 144107 (2012)

    Article  Google Scholar 

  36. F. Wang, S. Mamedov, P. Boolchand, B. Goodman, M. Chandrasekhar, Phys. Rev. B 71, 174201 (2005)

    Article  Google Scholar 

  37. P.K. Gupta, J.C. Mauro, J. Chem. Phys. 130, 094503 (2009)

    Article  Google Scholar 

  38. R.G. Srinivasa, A. Arunbabu, S. Asokan, J. Solid State Chem. 184, 3345 (2011)

    Article  Google Scholar 

  39. B.J. Madhu, H.S. Jayanna, S. Asokan, Eur. Phys. J. B 71, 21 (2009)

    Article  Google Scholar 

  40. D.G. Georgiev, D.G. Georgiev, P. Boolchand, M. Micoulaut, Phys. Rev. B 62, R9228 (2000)

    Article  Google Scholar 

  41. P. Chen, C. Holbrook, P. Boolchand, D.G. Georgiev, M. Micoulaut, Phys. Rev. B 78, 224208 (2008)

    Article  Google Scholar 

  42. D. Novita, P. Boolchand, M. Malki, M. Micoulaut, Phys. Rev. Lett. 98, 195501 (2007)

    Article  Google Scholar 

  43. D.J. Jacobs, A.J. Rader, L.A. Kuhn, M.F. Thorpe, Proteins 44, 150 (2001)

    Article  Google Scholar 

  44. J.C. Phillips, Phys. Rev. Lett. 88, 216401 (2002)

    Article  Google Scholar 

  45. R. Monasson, R. Zecchina, S. Kirkpatrick, B. Selman, L. Troyansky, Nature 400, 133 (1999)

    Article  Google Scholar 

  46. J. Barré, A.R. Bishop, T. Lookman, A. Saxena, Phys. Rev. Lett. 94, 208701 (2005)

    Article  Google Scholar 

  47. R. Rompicharla, D.I. Novita, P. Chen, P. Boolchand, M. Micoulaut, W. Huff, J. Phys. Condens. Matter 20, 202101 (2008)

    Article  Google Scholar 

  48. S. Chakraborty, P. Boolchand, M. Malki, M. Micoulaut, unpublished

    Google Scholar 

  49. S.W. King et al., J. Non-Cryst. Solids 379, 67 (2013)

    Article  Google Scholar 

  50. M.T.M. Shatnawi, C.L. Farrow, P. Chen, P. Boolchand, A. Sartbaeva, M.F. Thorpe, S.J.L. Billinge, Phys. Rev. B 77, 094134 (2008)

    Article  Google Scholar 

  51. M. Bauchy, M. Micoulaut, M. Boero, C. Massobrio, Phys. Rev. Lett. 110, 165501 (2013)

    Article  Google Scholar 

  52. M. Micoulaut, M. Bauchy, Phys. Status Solidi 250, 976 (2013)

    Article  Google Scholar 

  53. B. Bureau, J. Troles, M. Le Floch, F. Smektala, J. Lucas, J. Non-Cryst. Solids 326–327, 58 (2003)

    Google Scholar 

  54. M. Micoulaut, Phys. Rev. B 74, 184208 (2006)

    Article  Google Scholar 

  55. M.V. Chubynsky, M.A. Brière, N. Mousseau, Phys. Rev. E 74, 016116 (2006)

    Article  Google Scholar 

  56. K. Trachenko, M.T. Dove, Phys. Rev. B 67, 212203 (2003)

    Article  Google Scholar 

  57. M. Bauchy, M. Micoulaut, Phys. Rev. Lett. 110, 095501 (2013)

    Article  Google Scholar 

  58. F. Inam, G. Chen, D.N. Tafen, D.A. Drabold, Phys. Status Solidi B 246, 1849 (2009)

    Article  Google Scholar 

  59. G. Chen, F. Inam, D.A. Drabold, Appl. Phys. Lett. 97, 131901 (2010)

    Article  Google Scholar 

  60. B. Effey, R.L. Cappelletti, Phys. Rev. B 59, 4119 (1999)

    Article  Google Scholar 

  61. B.O. Mysen, P. Richet, Silicate Glasses and Melts: Structure and Properties (Springer, Berlin, 2005)

    Google Scholar 

  62. P. Boolchand (ed.), Insulating and Semi-Conducting Glasses (World Scientific, Singapore, 2000)

    Google Scholar 

  63. L. Cai, P. Boolchand, Philos. Mag. B 82, 1649 (2002)

    Google Scholar 

  64. E.L. Gjersing, S. Sen, R.E. Youngman, Phys. Rev. B 82, 014203 (2010)

    Article  Google Scholar 

  65. J.C. Mauro, R.J. Loucks, P.K. Gupta, J. Phys. Chem. A 111, 7957 (2007)

    Article  Google Scholar 

  66. C.A. Angell, B.E. Richards, V. Velikov, J. Phys. Condens. Matter 11, A75 (1999)

    Article  Google Scholar 

  67. J.C. Mauro, R.J. Loucks, J. Chem. Phys. 130, 234503 (2009)

    Article  Google Scholar 

  68. M. Smedskjaer, J.C. Mauro, R.E. Youngman, C.L. Hogue, M. Potuzak, Y. Yue, J. Phys. Chem. B 115, 12930 (2011)

    Article  Google Scholar 

  69. M.M. Smedskjaer, J.C. Mauro, Y. Yue, Phys. Rev. Lett. 105, 115503 (2010)

    Article  Google Scholar 

  70. B. Shadrack Jabes, M. Agarwal, C. Chaktavarty, J. Chem. Phys. 132, 234507 (2010)

    Google Scholar 

  71. J.R. Errington, P.G. Debenedetti, Nature 409, 318 (2001)

    Article  Google Scholar 

  72. U. Senapati, A.K. Varshneya, J. Non-Cryst. Solids 197, 210 (1996)

    Google Scholar 

  73. U. Senapati, A.K. Varshnaya, J. Non-Cryst. Solids 185, 289 (1995)

    Google Scholar 

  74. F. Wilcek, Phys. Today 57, 10 (2004)

    Google Scholar 

  75. R. Car, M. Parrinello, Phys. Rev. Lett. 55, 2471 (1985)

    Article  Google Scholar 

  76. A.D. Becke, Phys. Rev. A 38, 3098 (1988)

    Article  Google Scholar 

  77. C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37, 785 (1988)

    Article  Google Scholar 

  78. S. Nosé, Mol. Phys. 52, 255 (1984)

    Google Scholar 

  79. W.G. Hoover. Phys. Rev. A 31, 1695 (1985)

    Google Scholar 

  80. M. Micoulaut, R. Vuilleumier, C. Massobrio, Phys. Rev. B 79, 214204 (2009)

    Article  Google Scholar 

  81. C. Massobrio, M. Micoulaut, P.S. Salmon, Solid State Sci. 12, 199 (2010)

    Article  Google Scholar 

  82. S. Tsuneyucki, M. Tsukada, H. Aoki, Y. Matsui, Phys. Rev. Lett. 61, 869 (1988)

    Article  Google Scholar 

  83. R.D. Oeffner, S.R. Elliott, Phys. Rev. B 58, 14791 (1998)

    Article  Google Scholar 

  84. A.N. Cormack, J. Du, T.R. Zeitler, Phys. Chem. Chem. Phys. 4, 3193 (2002)

    Article  Google Scholar 

  85. P.S. Salmon, A.C. Barnes, R.A. Martin, G.J. Cuello, J. Phys. Condens. Matter 19, 415110 (2007)

    Article  Google Scholar 

  86. P.S. Salmon, J. Non-Cryst. Solids 353, 2959 (2007)

    Google Scholar 

  87. S. Xin, J. Liu, P.S. Salmon, Phys. Rev. B 78, 064207 (2008)

    Article  Google Scholar 

  88. M. Fabian, E. Sváb, V. Pamukchieva, A. Szekeres, S. Vogel, U. Ruett, J. Phys. Condens. Matter 253, 012053 (2010)

    Google Scholar 

  89. J.C. Mauro, A.K. Varshneya, J. Non-Cryst. Solids 353, 1226 (2007)

    Google Scholar 

  90. M. Micoulaut, A. Kachmar, M. Bauchy, S. Le Roux, C. Massobrio, M. Boero, Phys. Rev. B 88, 054203 (2013)

    Article  Google Scholar 

  91. M. Bauchy, M. Micoulaut, J. Non-Cryst. Solids 377, 34 (2013)

    Google Scholar 

  92. C. Massobrio, A. Pasquarello, R. Car, Phys. Rev. B 64, 144205 (2001)

    Article  Google Scholar 

  93. C. Massobrio, A. Pasquarello, Phys. Rev. B 77, 144207 (2008)

    Article  Google Scholar 

  94. C. Massobrio, A. Pasquarello, R. Car, J. Am. Chem. Soc. 121, 2943 (1999)

    Article  Google Scholar 

  95. I. Petri, P.S. Salmon, H.E. Fischer, Phys. Rev. Lett. 84, 2413 (2000)

    Article  Google Scholar 

  96. A. Bouzid, C. Massobrio, J. Chem. Phys. 137, 224201 (2012)

    Article  Google Scholar 

  97. S. Hosokawa, Y. Wang, W.-C. Pilgrim, J.-F. Bérar, S. Mamedov, P. Boolchand, J. Non-Cryst, Solids 352, 1517 (2006)

    Google Scholar 

  98. S. Hosokawa, Y. Kawakita, W.-C. Pilgrim, F. Hensel, J. Non-Cryst. Solids 293–295, 153 (2001)

    Google Scholar 

  99. G.D. Negodaev, I.A. Ivanov, K.K. Evstop’ev, Elektrokhim. 8, 234 (1972)

    Google Scholar 

  100. Y.P. Gupta, T.B. King, Trans. Metall. Soc. AIME 239, 1701 (1967)

    Google Scholar 

  101. J.R. Johnson, R.H. Bristow, H.H. Blau, J. Am. Ceram. Soc. 34, 165 (1951)

    Article  Google Scholar 

  102. M. Truhlarova, O. Veprek, Silikaty 14, 1 (1970)

    Google Scholar 

  103. G.J. Kramer, A.J.M. de Man, R.A. van Santen, J. Am. Chem. Soc. 113, 6435 (1991)

    Article  Google Scholar 

  104. J. Horbach, W. Kob, K. Binder, Chem. Geol. 174, 87 (2001)

    Article  Google Scholar 

  105. S. Stolen, T. Grande, H.-B. Johnsen, Phys. Chem. Chem. Phys. 4, 3396 (2002)

    Article  Google Scholar 

  106. G. Yang, T. Rouxel, J. Troles, B. Bureau, C. Boussard-Plédel, P. Houizot, J.-C. Sangleboeuf, J. Am. Ceram. Soc. 94, 2408 (2011)

    Article  Google Scholar 

  107. M. Bauchy, B. Guillot, M. Micoulaut, N. Sator, Chem. Geol. 346, 47 (2013)

    Article  Google Scholar 

  108. M.P. Allen, D.J. Tildesley, Computer Simulations of Liquids (Oxford University Press, Oxford, 1987)

    Google Scholar 

  109. J.O.M. Bockris, J.D. Mackenzie, J.A. Kitchener, Trans. Faraday Soc. 51, 1734 (1955)

    Article  Google Scholar 

  110. D.R. Neuville, Chem. Geol. 229, 28 (2006)

    Article  Google Scholar 

  111. J.C. Mauro, Y. Yue, A.J. Ellison, P.K. Gupta, D.C. Allan, Proc. Natl. Acad. USA 106, 19780 (2009)

    Article  Google Scholar 

  112. M. Micoulaut, S. Le Roux, C. Massobrio, J. Chem. Phys. 136, 224504 (2012)

    Article  Google Scholar 

  113. M. Hemmati, C.A. Angell, J. Non-Cryst. Solids 217, 236 (1997)

    Google Scholar 

  114. J.Y. Raty, C. Otjacques, J.P. Gaspard, C. Bichara, Solid State Sci. 12, 193 (2010)

    Article  Google Scholar 

  115. M. Micoulaut, A. Kachmar, Th Charpentier, Phys. Status Solidi B 249, 1890 (2012)

    Article  Google Scholar 

  116. M. Micoulaut, C. Otjacques, J.-Y. Raty, C. Bichara, Phys. Rev. B 81, 174206 (2010)

    Article  Google Scholar 

  117. M. Bauchy, M. Micoulaut, J. Non-Cryst. Solids 357, 2530 (2011)

    Google Scholar 

  118. M. Bauchy, M. Micoulaut, M. Celino, M. Boero, S. Le Roux, C. Massobrio, Phys. Rev. B 83, 054201 (2011)

    Google Scholar 

  119. R. Hussein, R. Dupree, D. Holland, J. Non-Cryst. Solids 246, 159 (1999)

    Google Scholar 

  120. N. Mousseau, M.F. Thorpe, Phys. Rev. B 52, 2660 (1995)

    Google Scholar 

  121. F.J. Bermejo, C. Cabrillo, E. Bychkov, P. Fouquet, G. Ehlers, W. Hussler, D.L. Price, M.L. Saboungi, Phys. Rev. Lett. 100, 245902 (2008)

    Google Scholar 

  122. M. Micoulaut, J. Phys. Condens. Matter 22, 285101 (2010)

    Article  Google Scholar 

  123. P. Chen, P. Boolchand, D.G. Georgeiv, J. Phys. Condens. Matter 22, 065104 (2010)

    Article  Google Scholar 

  124. K. Trachenko, M.T. Dove, V. Brazhkin, F.S. El’kin, Phys. Rev. Lett. 93, 135502 (2004)

    Article  Google Scholar 

  125. M. Bauchy, M. Micoulaut, Phys. Rev. B 83, 184118 (2011)

    Article  Google Scholar 

  126. M. Bauchy, J. Chem. Phys. 137, 044510 (2012)

    Article  Google Scholar 

  127. M. Scott Shell, P.G. Debenedetti, A.Z. Panagiotopoulos, Phys. Rev. E 66, 011202 (2002)

    Google Scholar 

  128. P.L. Chau, A.J. Hardwick, Mol. Phys. 93, 511 (1998)

    Article  Google Scholar 

  129. M. Misawa, D.L. Price, K. Suzuki, J. Non-Cryst. Solids 37, 85 (1980)

    Google Scholar 

  130. P.S. Salmon, R.A. Martin, P.E. Mason, G. Cuello, Nature 435, 75 (2005)

    Article  Google Scholar 

Download references

Acknowledgments

Support from Agence Nationale de la Recherche (ANR) (Grant No. 09-BLAN-0109-01 and Grant No. 11-BS08-0012) is gratefully acknowledged. MM acknowledges support from the French-American Fulbright Commission, and from International Materials Institute (H. Jain). GENCI (Grand Equipement National de Calcul Intensif) is acknowledged for supercomputing access. The authors thank C. Massobrio, S. Le Roux, M. Boero, C. Bichara, P. Boolchand, S. Boshle, K. Gunasekera, M. Malki, G.G. Naumis, A. Pasquarello, J.-Y. Raty, G. Ferlat, J.C. Phillips, P. Simon, M. Salanne, D. De Sousa-Meneses, R. Vuilleumier, S. Ravindren, N. Mousseau, S. Chakraborty for stimulating discussions.

Author information

Authors and Affiliations

  1. Laboratoire de Physique Thorique de la Matire Condense, 4, Place Jussieu, 75252, Paris Cedex 05, France

    M. Micoulaut & H. Flores-Ruiz

  2. Department of Civil and Environmental Engineering, University of California, 5731B Boelter Hall, Los Angeles, CA, 90095-1593, USA

    M. Bauchy

Authors
  1. M. Micoulaut
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Bauchy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. Flores-Ruiz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Micoulaut .

Editor information

Editors and Affiliations

  1. IPCMS, Strasbourg University, Strasbourg, France

    Carlo Massobrio

  2. Dept. of Materials Science and Engineeri, University of North Texas, Denton, Texas, USA

    Jincheng Du

  3. Dept. of Materials Science, University of Milan Bicocca, Milan, Italy

    Marco Bernasconi

  4. Dept. of Physics, University of Bath, Bath, United Kingdom

    Philip S. Salmon

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Micoulaut, M., Bauchy, M., Flores-Ruiz, H. (2015). Topological Constraints, Rigidity Transitions, and Anomalies in Molecular Networks. In: Massobrio, C., Du, J., Bernasconi, M., Salmon, P. (eds) Molecular Dynamics Simulations of Disordered Materials. Springer Series in Materials Science, vol 215. Springer, Cham. https://doi.org/10.1007/978-3-319-15675-0_11

Download citation

Publish with us

Policies and ethics

Search

Navigation