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Reverse Monte Carlo Modeling of the Rigidity Percolation Threshold in GexSe1-x Glassy Networks

DOI: 10.4236/njgc.2015.53005, PP. 31-43

Keywords: Chalcogenide Glasses, Rigidity Percolation, Reverse Monte Carlo Modeling, Atomic Pair Distribution Function (PDF), GexSe1-x Glasses

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Abstract:

Based on Maxwell’s constraint counting theory, rigidity percolation in GexSe1-x glasses occurs when the mean coordination number reaches the value of 2.4. This corresponds to Ge0.20Se0.80 glass. At this composition, the number of constraints experienced by an atom equals the number of degrees of freedom in three dimensions. Hence, at this composition, the network changes from a floppy phase to a rigid phase, and rigidity starts to percolate. In this work, we use reverse Monte Carlo (RMC) modeling to model the structure of Ge0.20Se0.80 glass by simulating its experimental total atomic pair distribution function (PDF) obtained via high energy synchrotron radiation. A three-dimensional configuration of 2836 atoms was obtained, from which we extracted the partial atomic pair distribution functions associated with Ge-Ge, Ge-Se and Se-Se real space correlations that are hard to extract experimentally from total scattering methods. Bond angle distributions, coordination numbers, mean coordination numbers and the number of floppy modes were also extracted and discussed. More structural insights about network topology at this composition were illustrated. The results indicate that in Ge0.20Se0.80 glass, Ge atoms break up and cross-link the Se chain structure, and form structural units that are four-fold coordinated (the GeSe4 tetrahedra). These tetrahedra form the basic building block and are connected via shared Se atoms or short Se chains. The extent of the intermediate ranged oscillations in real space (as extracted from the width of the first sharp diffraction peak) was found to be around 19.6 ?. The bonding schemes in this glass are consistent with the so-called “8-N” rule and can be interpreted in terms of a chemically ordered network model.

References

[1]  Ross, L. and Bourgon, M. (1969) Germanium-Selenium Phase Diagram. Canadian Journal of Chemistry, 47, 2555- 2559.
http://dx.doi.org/10.1139/v69-422
[2]  Hafiz M.M., Hammad, F.H. and Elkabany, N.A. (1993) Short-Range and Medium-Range Order in Se-Ge Glassy Systems: Effect of Composition. Physica B: Physics of Condensed Matter, 183, 392-398.
http://dx.doi.org/10.1016/0921-4526(93)90130-X
[3]  Zakery, A. and Elliott, S.R. (2007) Optical Nonlinearities in Chalcogenide Glasses and Their Applications. Springer, Berlin.
http://www.springer.com/us/book/9783540710660
[4]  Tanaka, K. and Shimakawa, K. (2009) Chalcogenide Glasses in Japan: A Review on Photoinduced Phenomena. Physica Status Solidi (B), 246, 1744-1757.
http://dx.doi.org/10.1002/pssb.200982002
[5]  Greer, A.L. and Mathur, N. (2005) Materials Science: Changing Face of the Chameleon. Nature, 437, 1246-1247.
http://dx.doi.org/10.1038/4371246a
[6]  Phillips, J.C. (1979) Topology of Covalent Non-Crystalline Solids: Short-Range Order in Chalcogenide Alloys. Journal of Non-Crystalline Solids, 34, 153-181.
http://dx.doi.org/10.1016/0022-3093(79)90033-4
[7]  Phillips, J.C. (1981) Topology of Covalent Non-Crystalline Solids: Medium-Range Order in Chalcogenide Alloys and a-Si(Ge). Journal of Non-Crystalline Solids, 43, 37-77.
http://dx.doi.org/10.1016/0022-3093(81)90172-1
[8]  Thorpe, M.F. (1983) Continuous Deformations in Random Networks. Journal of Non-Crystalline Solids, 57, 355-370.
http://dx.doi.org/10.1016/0022-3093(83)90424-6
[9]  Bauchy, M., Micoulaut, M., Celino, M., Roux, S.L., Boero, M. and Massobrio, C. (2011) Angular Rigidity in Tetrahedral Network Glasses with Changing Composition. Physical Review B, 84, Article ID: 054201.
http://dx.doi.org/10.1103/PhysRevB.84.054201
[10]  Kamitakahara, W.A., Cappelletti, R.L., Boolchand, P., Halfpap, B., Gompf, F., Neumann, D.A. and Mutka, H. (1991) Vibrational Densities of States and Network Rigidity in Chalcogenide Glasses. Physical Review B, 44, 94-100.
http://dx.doi.org/10.1103/PhysRevB.44.94
[11]  Tatsumisago, M., Halfpap, B.L., Green, J.L., Lindsay, S.M. and Angell, C.A. (1990) Fragility of Ge-As-Se Glass- Forming Liquids in Relation to Rigidity Percolation and the Kauzmann Paradox. Physical Review Letters, 64, 1549- 1552.
http://dx.doi.org/10.1103/PhysRevLett.64.1549
[12]  Senapati, U. and Varshneya, A.K. (1995) Congurational Arrangements in Chalcogenide Glasses—A New Perspective on Phillips Constraint Theory. Journal of Non-Crystalline Solids, 185, 289-296.
http://dx.doi.org/10.1016/0022-3093(94)00534-6
[13]  Tronc, P., Brenac, A. and Sebenne, C. (1973) Optical Absorption Edge and Raman Scattering in GexSe1-x Glasses. Physical Review B, 8, 5947-5956.
http://dx.doi.org/10.1103/PhysRevB.8.5947
[14]  Ota, R., Yamate, T., Soga, N. and Kunugi, M. (1978) Conduction Mechanisms in Amorphous and Disordered Semiconductors. Journal of Non-Crystalline Solids, 29, 67-76.
http://dx.doi.org/10.1016/0022-3093(78)90141-2
[15]  Asokan, S., Prasad, M.V.N., Parthasarathy, G. and Gopal, E.S.R. (1989) Mechanical and Chemical Thresholds in IV-VI Chalcogenide Glasses. Physical Review Letters, 62, 808.
http://dx.doi.org/10.1103/PhysRevLett.62.808
[16]  Bresser, W., Boolchand, P. and Suranyi, P. (1986) Rigidity Percolation and Molecular Cluster in Network Glasses. Physical Review Letters, 56, 2493.
http://dx.doi.org/10.1103/PhysRevLett.56.2493
[17]  Feng, X.W., Bresser, W.J. and Boolchand, P. (1997) Direct Evidence for Stiffness Threshold in Chalcogenide Glasses. Physical Review Letters, 78, 4422-4425.
http://dx.doi.org/10.1103/physrevlett.78.4422
[18]  Bresser, W.J., Boolchand, P., Suranyi, P. and Hernandez, J.G. (1986) Molecular-Phase Separation and Cluster Size in GeSe2 Glass. Hyperfine Interactions, 27, 389-392.
http://dx.doi.org/10.1007/BF02354788
[19]  Sugai, S. (1987) Stochastic Random Network Model in Ge and Si Chalcogenide Glasses. Physical Review B, 35, 1345- 1361.
http://dx.doi.org/10.1103/PhysRevB.35.1345
[20]  Susman, S., Volin, K.J., Montague, D.G. and Price, D.L. (1990) The Structure of Vitreous and Liquid GeSe2: A Neutron-Diffraction Study. Journal of Non-Crystalline Solids, 125, 168-180.
http://dx.doi.org/10.1016/0022-3093(90)90336-K
[21]  Penfold, I.T. and Salmon, P.S. (1990) A Neutron-Diffraction Study on the Structure of Molten GeSe2—The Ge Coordination Environment. Journal of Physics: Condensed Matter, 2, SA233-SA237.
http://dx.doi.org/10.1088/0953-8984/2/S/034
[22]  Petri, I., Salmon, P.S. and Fischer, H.E. (2000) Defects in a Disordered World: The Structure of Glassy GeSe2. Physical Review Letters, 84, 2413-2416.
http://dx.doi.org/10.1103/PhysRevLett.84.2413
[23]  Petkov, V. and Le Messurie, D. (2010) Atomic-Scale Structure of GeSe2 Glass Revisited: A Continuous or Broken Network of Ge-(Se1/2)4 Tetrahedra Journal of Physics: Condensed Matter, 22, Article ID: 115402.
http://dx.doi.org/10.1088/0953-8984/22/11/115402
[24]  Vashishta, P., Kalia, R.K. and Ebbsjo, I. (1989) Structural Correlations and Phonon Density of States in GeSe2: A Molecular-Dynamics Study of Molten and Amorphous States. Physical Review B, 39, 6034-6047.
http://dx.doi.org/10.1103/PhysRevB.39.6034
[25]  Cobb, M., Drabold, D.A. and Cappelletti, R.L. (1996) Ab Initio Molecular-Dynamics Study of the Structural, Vibrational, and Electronic Properties of Glassy GeSe2. Physical Review B, 54, 12162-12171.
http://dx.doi.org/10.1103/PhysRevB.54.12162
[26]  Cobb, M. and Drabold, D.A. (1997) Ab Initio Molecular-Dynamics Study of Liquid GeSe2. Physical Review B, 56, 3054-3065.
http://dx.doi.org/10.1103/PhysRevB.56.3054
[27]  Massobrio, C., Pasquarello, A. and Car, R. (1998) Microscopic Structure of Liquid GeSe2: The Problem of Concentration Fluctuations Over Intermediate Range Distances. Physical Review Letters, 80, 2342-2345.
http://dx.doi.org/10.1103/PhysRevLett.80.2342
[28]  Holomb, R., Mitsa, V., Akalin, E., Akyuz, S. and Sichka, M. (2013) Ab Initio and Raman Study of Medium Range Ordering in GeSe2 Glass. Journal of Non-Crystalline Solids, 373-374, 51-56.
http://dx.doi.org/10.1016/j.jnoncrysol.2013.04.032
[29]  Egami, T. and Billinge, S.J.L. (2003) Underneath the Bragg Peaks: Structural Analysis of Complex Materials. Pergamon Press, Elsevier, location.
http://dx.doi.org/10.1016/s1369-7021(03)00635-7
[30]  Warren, B.E. (1990) X-Ray Diffraction. Dover.
[31]  Tucker, M.G., Dove, M.T. and Keen, D.A. (2001) Application of the Reverse Monte Carlo Method to Crystalline Materials. Journal of Applied Crystallography, 34, 630-638.
http://dx.doi.org/10.1107/S002188980100930X
[32]  McGreevy, R.L. (2001) Reverse Monte Carlo Modeling. Journal of Physics: Condensed Matter, 13, R877-R913.
http://dx.doi.org/10.1088/0953-8984/13/46/201
[33]  Shatnawi, M.T.M., Farrow, C.L., Chen, P., Boolchand, P., Sartbaeva, A., Thorpe, M.F. and Billinge, S.J.L. (2008) Search for a Structural Response to the Intermediate Phase in GexSe1-x Glasses. Physical Review B, 77, Article ID: 094134.
http://dx.doi.org/10.1103/PhysRevB.77.094134
[34]  McGreevy, R.L., Howe, M.A. and Wicks, J.D. (1993) Computer Program RMCA, Version 3.
http://www.studsvik.uu.se.20
[35]  Mott, N.F. and Davis, E.A. (1979) Electronic Processes in Non-Crystalline Materials. Oxford University, Oxford.
[36]  Price, D.L., Susman, S., Volin, K.J. and Dejus, R.J. (1989) Intermediate-Range Order in Binary and Ternary Glasses. Physica B: Physics of Condensed Matter, 156, 189-191.
http://dx.doi.org/10.1016/0921-4526(89)90626-1
[37]  Johnson, R.W., Price, D.L., Susman, S., Arai, M., Morrison, T.I. and Shenoy, G.K. (1986) The Structure of Silicon Selenium Glasses: Short Range Order. Journal of Non-Crystalline Solids, 83, 251-271.
http://dx.doi.org/10.1016/0022-3093(86)90240-1
[38]  Christie, J.K., Taraskin, S.N. and Elliott, S.R. (2004) Structural Characteristics of Positionally Disordered Lattices: Relation to the First Sharp Diffraction Peak in Glasses. Physical Review B, 70, Article ID: 134207.
http://dx.doi.org/10.1103/PhysRevB.70.134207
[39]  Elliott, S.R. (1991) Medium Range Structural Order in Covalent Amorphous Solids. Nature, 354, 445-452.
http://dx.doi.org/10.1038/354445a0
[40]  Boolchand, P., Grothaus, J., Bresser, W.J. and Suranyi, P. (1982) Structural Origin of Broken Chemical Order in a GeSe2 Glass. Physical Review B, 25, 2975-2978.
http://dx.doi.org/10.1103/PhysRevB.25.2975
[41]  Betts, F., Bienenstock, A., Keating, D.T. and de Neufville, J.P. (1972) Neutron and X-Ray Diffraction Radial Distribution Studies of Amorphous Ge0.17Te0.83. Journal of Non-Crystalline Solids, 7, 417-432.
http://dx.doi.org/10.1016/0022-3093(72)90276-1
[42]  Elliott, S.R. (1984) Physics of Amorphous Materials. Longman, London and New York.
[43]  Elliott, S.R. (1990) Physics of Amorphous Materials. 2nd Edition, Longman, Harlow.
[44]  Grzechnik, A., Stolen, S., Bakken, E., Grande, T. and Mezouar, M. (2000) Structural Transformations in Three-Di- mensional Crystalline GeSe2 at High Pressures and High Temperatures. Journal of Solid Sate Chemistry, 150, 121-127.
http://dx.doi.org/10.1006/jssc.1999.8557
[45]  Petkov, V., Qadir, D. and Shastri, S.D. (2004) Rapid Structure Determination of Disordered Materials: Study of GeSe2 Glass. Solid State Communications, 129, 239-243.
http://dx.doi.org/10.1016/j.ssc.2003.10.007
[46]  Kohara, S., Goldbach, A., Koura, N., Saboungi, M.L. and Curtiss, L.A. (1998) Vibrational Frequencies of Small Selenium Molecules. Chemical Physics Letters, 287, 282-288.
http://dx.doi.org/10.1016/S0009-2614(98)00184-5

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