Topological ordering during flexible to rigid transitions in disordered networks

Matthieu Micoulaut

doi:10.5802/crphys.128

Topological ordering during flexible to rigid transitions in disordered networks
[Ordonnancement topologique lors des transitions flexible-rigide dans les réseaux désordonnés]

Matthieu Micoulaut ¹

¹ Sorbonne Université, Physique théorique de la matière condensée, CNRS UMR 7600, 4 place Jussieu 75252 Paris cedex 05 France

Comptes Rendus. Physique, Volume 24 (2023) no. S1, pp. 133-154.

Résumé
Abstract

Cette contribution se concentre sur l’origine structurale des transitions de flexible à rigide et une possible phase topologique intermédiaire sous-jacente qui se produisent dans une variété de verres structuraux tels que les chalcogénures ou les oxydes modifiés. Ici, en utilisant des simulations de dynamique moléculaire de liquides vitreux densifiés, 2SiO $_{2}$ -Na $_{2}$ O, qui sont connus pour présenter une fenêtre de réversibilité en pression lors d’une transition vitreuse numérique, nous nous concentrons sur des corrélations structurales mettant l’accent sur l’ordre topologique en utilisant le formalisme de Bhatia–Thornton. Les résultats révèlent non seulement que les silicates densifiés présentent un ordre topologique sur des échelles de longueur d’environ 25 Å, mais présentent également des comportements de seuil évidents à proximité de la condition isostatique lorsque le réseau subit une transition de flexible à rigide. Le comptage des contraintes mécaniques de la structure du réseau atomique révèle qu’une échelle de longueur typique caractérisant la décroissance des corrélations topologiques émerge pour les systèmes rigides sous-contraints à $≃$ 3,5 Å, alors que les petites oscillations du vecteur d’onde sont minimales lorsque la condition isostatique est simplement satisfaite. Une analyse supplémentaire basée sur la diffusivité et l’entropie du liquide suggère que le lieu des transitions de flexible à rigide a également des liens avec les anomalies observés dans les liquides tétraédriques densifiés comme l’eau sous pression.

This contribution focuses on the structural origin of flexible to rigid transitions and the possible underlying intermediate phase which have been reported to occur in a variety of network glasses such as chalcogenides or modified oxides. Here, using molecular dynamics simulations of densified glass-forming liquids, 2SiO $_{2}$ -Na $_{2}$ O, which are known to display a numerical reversibility window as a signature of an intermediate phase, we focus on structural functions emphasizing topological ordering using the Bhatia–Thornton formalism. Results not only reveal that densified silicates display topological ordering on lengthscales of about 25 Å, but also display obvious threshold behaviors close to the isostatic condition when the network undergoes a flexible to rigid transition. The mechanical constraint count of the atomic network structure reveals that a typical lengthscale characterizing the decay of topological correlations emerges for stressed rigid systems at $≃$ 3.5 Å, whereas small wavevector oscillations are found to be minimal when the isostatic condition is merely satisfied. An additional analysis building on diffusivity and liquid entropy suggests that the locus of flexible to rigid transitions has also connections with water-like anomalies of densified tetrahedral liquids.

Reçu le : 2022-06-14
Révisé le : 2022-10-14
Accepté le : 2022-10-19
Première publication : 2023-04-20
Publié le : 2024-04-26

DOI : 10.5802/crphys.128

Keywords: Glasses, structure, network rigidity, elastic phase transitions, molecular dynamics simulations
Mot clés : verres, structure, rigidité du réseau, transitions de phase élastiques, simulations de dynamique moléculaire.

Affiliations des auteurs :

Matthieu Micoulaut ¹

¹ Sorbonne Université, Physique théorique de la matière condensée, CNRS UMR 7600, 4 place Jussieu 75252 Paris cedex 05 France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

@article{CRPHYS_2023__24_S1_133_0,
     author = {Matthieu Micoulaut},
     title = {Topological ordering during flexible to rigid transitions in disordered networks},
     journal = {Comptes Rendus. Physique},
     pages = {133--154},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {24},
     number = {S1},
     year = {2023},
     doi = {10.5802/crphys.128},
     language = {en},
}

TY  - JOUR
AU  - Matthieu Micoulaut
TI  - Topological ordering during flexible to rigid transitions in disordered networks
JO  - Comptes Rendus. Physique
PY  - 2023
SP  - 133
EP  - 154
VL  - 24
IS  - S1
PB  - Académie des sciences, Paris
DO  - 10.5802/crphys.128
LA  - en
ID  - CRPHYS_2023__24_S1_133_0
ER  -

%0 Journal Article
%A Matthieu Micoulaut
%T Topological ordering during flexible to rigid transitions in disordered networks
%J Comptes Rendus. Physique
%D 2023
%P 133-154
%V 24
%N S1
%I Académie des sciences, Paris
%R 10.5802/crphys.128
%G en
%F CRPHYS_2023__24_S1_133_0

Matthieu Micoulaut. Topological ordering during flexible to rigid transitions in disordered networks. Comptes Rendus. Physique, Volume 24 (2023) no. S1, pp. 133-154. doi : 10.5802/crphys.128. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.128/

Bibliographie
Cité par

[1] E. Bychkov; C. J. Benmore; D. L. Price Compositional changes of the first sharp diffraction peak in binary selenide glasses, Phys. Rev. B, Volume 72 (2005) no. 17, 172107 | DOI

[2] S. Salmon; Richard A. Martin; P. E. Mason; Gabriel J. Cuello Topological versus chemical ordering in network glasses at intermediate and extended length scales, Nature, Volume 435 (2005), pp. 75-78 | DOI

[3] Philip S. Salmon; Adrian C. Barnes; Richard A. Martin; Gabriel J. Cuello Structure of glassy GeO $_{2}$ , J. Phys.: Condens. Matter, Volume 19 (2007) no. 41, 415110 | DOI

[4] F. L. Galeener; G. Lucovsky Longitudinal Optical Vibrations in Glasses: Ge $O_{2}$ and Si $O_{2}$ , Phys. Rev. Lett., Volume 37 (1976) no. 22, pp. 1474-1478 | DOI

[5] Guillaume Ferlat; Thibault Charpentier; Ari Paavo Seitsonen; Akira Takada; Michele Lazzeri; Laurent Cormier; Georges Calas; Francesco Mauri Boroxol Rings in Liquid and Vitreous $B_{2} O_{3}$ from First Principles, Phys. Rev. Lett., Volume 101 (2008) no. 6, 065504 | DOI

[6] K. Vignarooban; Punit Boolchand; Matthieu Micoulaut; M. Malki; W. J. Bresser Rigidity transitions in glasses driven by changes in network dimensionality and structural groupings, Eur. Phys. Lett., Volume 108 (2014) no. 5, 56001 | DOI

[7] Han Liu; Zhangji Zhao; Qi Zhou; Ruoxia Chen; Kai Yang; Zhe Wang; Longwen Tang; Mathieu Bauchy Challenges and opportunities in atomistic simulations of glasses: a review, Comptes Rendus. Géoscience (2022) (Online first) | DOI

[8] James Clerk Maxwell L. On the calculation of the equilibrium and stiffness of frames, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Volume 27 (1864) no. 182, pp. 294-299 | DOI

[9] James C. Phillips Topology of covalent non-crystalline solids I: Short-range order in chalcogenide alloys, J. Non Cryst. Solids, Volume 34 (1979) no. 2, pp. 153-181 | DOI

[10] M. F. Thorpe Continuous deformations in random networks, J. Non Cryst. Solids, Volume 57 (1983) no. 3, pp. 355-370 | DOI

[11] Punit Boolchand; M. F. Thorpe Glass-forming tendency, percolation of rigidity, and onefold-coordinated atoms in covalent networks, Phys. Rev. B, Volume 50 (1994) no. 14, pp. 10366-10368 | DOI

[12] M. Zhang; Punit Boolchand The Central Role of Broken Bond-Bending Constraints in Promoting Glass Formation in the Oxides, Science, Volume 266 (1994) no. 5189, pp. 1355-1357 | DOI

[13] Matthieu Micoulaut Amorphous materials: Properties, structure, and durability: Constrained interactions, rigidity, adaptative networks, and their role for the description of silicates, Am. Mineral., Volume 93 (2008) no. 11-12, pp. 1732-1748 | DOI

[14] Matthieu Micoulaut; H. Flores-Ruiz Search for a possible flexible-to-rigid transition in models of phase change materials, Phys. Rev. B, Volume 103 (2021) no. 13, 134206 | DOI

[15] M. F. Thorpe; D. J. Jacobs; M. V. Chubynsky; James C. Phillips Self-organization in network glasses, J. Non Cryst. Solids, Volume 266-269 (2000), pp. 859-866 | DOI

[16] H. He; M. F. Thorpe Elastic Properties of Glasses, Phys. Rev. Lett., Volume 54 (1985) no. 19, pp. 2107-2110 | DOI

[17] W. A. Kamitakahara; R. L. Cappelletti; Punit Boolchand; B. L. Halfpap; F. Gompf; D. A. Neumann; H. Mutka Vibrational densities of states and network rigidity in chalcogenide glasses, Phys. Rev. B, Volume 44 (1991) no. 1, pp. 94-100 | DOI

[18] Xingwei Feng; W. J. Bresser; Punit Boolchand Direct Evidence for Stiffness Threshold in Chalcogenide Glasses, Phys. Rev. Lett., Volume 78 (1997) no. 23, pp. 4422-4425 | DOI

[19] Roland Böhmer; C. Austen Angell Correlations of the nonexponentiality and state dependence of mechanical relaxations with bond connectivity in Ge-As-Se supercooled liquids, Phys. Rev. B, Volume 45 (1992) no. 17, pp. 10091-10094 | DOI

[20] M. Tatsumisago; B. L. Halfpap; J. L. Green; S. M. Lindsay; C. Austen Angell Fragility of Ge-As-Se glass-forming liquids in relation to rigidity percolation, and the Kauzmann paradox, Phys. Rev. Lett., Volume 64 (1990) no. 13, pp. 1549-1552 | DOI

[21] Kapila Gunasekera; Siddhesh Bhosle; Punit Boolchand; Matthieu Micoulaut Superstrong nature of covalently bonded glass-forming liquids at select compositions, J. Chem. Phys., Volume 139 (2013) no. 16, 164511 | DOI

[22] Sriram Ravindren; Kapila Gunasekera; Z. Tucker; A. Diebold; Punit Boolchand; Matthieu Micoulaut Crucial effect of melt homogenization on the fragility of non-stoichiometric chalcogenides, J. Chem. Phys., Volume 140 (2014) no. 13, 134501 | DOI

[23] Y. Vaills; T. Qu; Matthieu Micoulaut; F. Chaimbault; Punit Boolchand Direct evidence of rigidity loss and self-organization in silicate glasses, J. Phys.: Condens. Matter, Volume 17 (2005) no. 32, pp. 4889-4896 | DOI

[24] Deassy I. Novita; Punit Boolchand; M. Malki; Matthieu Micoulaut Fast-Ion Conduction and Flexibility of Glassy Networks, Phys. Rev. Lett., Volume 98 (2007) no. 19, 195501 | DOI

[25] Matthieu Micoulaut; M. Malki Direct Evidence of a Characteristic Length Scale of a Dynamical Nature in the Boolchand Phase of Glasses, Phys. Rev. Lett., Volume 105 (2010) no. 23, 235504 | DOI

[26] Matthieu Micoulaut; M. Malki; Deassy I. Novita; Punit Boolchand Fast-ion conduction and flexibility and rigidity of solid electrolyte glasses, Phys. Rev. B, Volume 80 (2009) no. 18, p. 184205 | DOI

[27] Le Yan; Matthieu Wyart Evolution of Covalent Networks under Cooling: Contrasting the Rigidity Window and Jamming Scenarios, Phys. Rev. Lett., Volume 113 (2014) no. 21, 215504 | DOI

[28] Mathieu Bauchy; Matthieu Micoulaut Percolative heterogeneous topological constraints and fragility in glass-forming liquids, Eur. Phys. Lett., Volume 104 (2013) no. 5, 56002 | DOI

[29] Matthieu Micoulaut; Mathieu Bauchy Evidence for Anomalous Dynamic Heterogeneities in Isostatic Supercooled Liquids, Phys. Rev. Lett., Volume 118 (2017) no. 14, 145502 | DOI

[30] Matthieu Micoulaut Concepts and applications of rigidity in non-crystalline solids: a review on new developments and directions, ADV PHYS-X, Volume 1 (2016) no. 2, pp. 147-175 | DOI

[31] J. Barré; A. R. Bishop; T. Lookman; A. Saxena Adaptability and “Intermediate Phase” in Randomly Connected Networks, Phys. Rev. Lett., Volume 94 (2005) no. 20, 208701 | DOI

[32] Matthieu Micoulaut; James C. Phillips Rings and rigidity transitions in network glasses, Phys. Rev. B, Volume 67 (2003) no. 10, 104204 | DOI

[33] Matthieu Micoulaut Rigidity and intermediate phases in glasses driven by speciation, Phys. Rev. B, Volume 74 (2006) no. 18, 184208 | DOI

[34] M.-A. Brière; M. V. Chubynsky; Normand Mousseau Self-organized criticality in the intermediate phase of rigidity percolation, Phys. Rev. E, Volume 75 (2007) no. 5, 056108 | DOI | MR

[35] Le Yan Entropy favors heterogeneous structures of networks near the rigidity threshold, Nat. Commun., Volume 9 (2018) no. 1, 1359 | DOI

[36] Cristian F. Moukarzel Two rigidity-percolation transitions on binary Bethe networks and the intermediate phase in glass, Phys. Rev. E, Volume 88 (2013) no. 6, 062121 | DOI

[37] Mathieu Bauchy; Matthieu Micoulaut Densified network glasses and liquids with thermodynamically reversible and structurally adaptive behaviour, Nat. Commun., Volume 6 (2015) no. 1, p. 6398 | DOI

[38] Fei Wang; S. Mamedov; Punit Boolchand; B. Goodman; Meera Chandrasekhar Pressure Raman effects and internal stress in network glasses, Phys. Rev. B, Volume 71 (2005) no. 17, 174201 | DOI

[39] Siddhesh Bhosle; Kapila Gunasekera; Punit Boolchand; Matthieu Micoulaut Melt Homogenization and Self-Organization in Chalcogenides-Part II, Int. J. Appl. Glass Sci., Volume 3 (2012) no. 3, pp. 205-220 | DOI

[40] W. Song; X. Li; M. Wang; Mathieu Bauchy; Matthieu Micoulaut Dynamic and stress signatures of the rigid intermediate phase in glass-forming liquids, J. Chem. Phys., Volume 152 (2020) no. 22, 221101 | DOI

[41] G. Sreevidya Varma; Chandasree Das; S. Asokan Evidence of an intermediate phase in a quaternary Ag bearing telluride glass system using alternating DSC, Solid State Commun., Volume 177 (2014), pp. 108-112 | DOI

[42] D. Selvanathan; W. J. Bresser; Punit Boolchand Stiffness transitions in ${Si}_{x} {Se}_{1 - x}$ glasses from Raman scattering and temperature-modulated differential scanning calorimetry, Phys. Rev. B, Volume 61 (2000) no. 22, pp. 15061-15076 | DOI

[43] Shibalik Chakraborty; Punit Poolchand Topological origin of fragility, network adaptation, and rigidity and stress transitions in especially homogenized nonstoichiometric binary Ge $_{x}$ S $_{100 - x}$ glasses, J. Phys. Chem. B, Volume 118 (2014) no. 8, pp. 2249-2263 | DOI

[44] Chandi Mohanty; Avik Mandal; Vamshi Kiran Gogi; Ping Chen; Deassy I. Novita; Ralph Chbeir; Mathieu Bauchy; Matthieu Micoulaut; Punit Boolchand Linking Melt Dynamics With Topological Phases and Molecular Structure of Sodium Phosphate Glasses From Calorimetry, Raman Scattering, and Infrared Reflectance, Front. Mater., Volume 6 (2019) | DOI

[45] K. Rompicharla; Deassy I. Novita; Ping Chen; Punit Boolchand; Matthieu Micoulaut; W. Huff Abrupt boundaries of intermediate phases and space filling in oxide glasses, J. Phys.: Condens. Matter, Volume 20 (2008) no. 20, 202101 | DOI

[46] Chandasree Das; M. S. R. N. Kiran; U. Ramamurty; S. Asokan Manifestation of intermediate phase in mechanical properties: Nano-indentation studies on Ge-Te-Si bulk chalcogenide glasses, Solid State Commun., Volume 152 (2012) no. 24, pp. 2181-2184 | DOI

[47] Kapila Gunasekera; Punit Boolchand; Matthieu Micoulaut Effect of mixed Ge/Si cross-linking on the physical properties of amorphous Ge-Si-Te networks, J. Appl. Phys., Volume 115 (2014) no. 16, 164905 | DOI

[48] Kapila Gunasekera; Punit Boolchand; Matthieu Micoulaut Elastic Phases of Ge $_{x}$ Sb $_{x}$ Se $_{100 - 2 x}$ Ternary Glasses Driven by Topology, J. Phys. Chem. B, Volume 117 (2013) no. 34, pp. 10027-10034 | DOI

[49] U. Vempati; Punit Boolchand The thermally reversing window in ternary Ge $_{x}$ As $_{x}$ S $_{1 - 2 x}$ glasses, J. Phys.: Condens. Matter, Volume 16 (2004) no. 44, p. S5121-S5138 | Zbl

[50] Soumendu Chakravarty; D. G. Georgiev; Punit Boolchand; Matthieu Micoulaut Ageing, fragility and the reversibility window in bulk alloy glasses, J. Phys.: Condens. Matter, Volume 17 (2004) no. 1, p. L1-L7 | DOI

[51] Tao Qu; Punit Boolchand Shift in elastic phase boundaries due to nanoscale phase separation in network glasses: the case of Ge $_{x}$ As $_{x}$ S $_{1 - 2 x}$ , Philos. Mag., Volume 85 (2005) no. 8, pp. 875-884 | DOI

[52] Ralph Chbeir; Mathieu Bauchy; Matthieu Micoulaut; Punit Boolchand Evidence for a Correlation of Melt Fragility Index With Topological Phases of Multicomponent Glasses, Front. Mater., Volume 6 (2019) | DOI

[53] Yong Wang; J. Wells; D. G. Georgiev; Punit Boolchand; Koblar A. Jackson; Matthieu Micoulaut Sharp Rigid to Floppy Phase Transition Induced by Dangling Ends in a Network Glass, Phys. Rev. Lett., Volume 87 (2001) no. 18, 185503 | DOI

[54] Fei Wang; Punit Boolchand; Koblar A. Jackson; Matthieu Micoulaut Chemical alloying and light-induced collapse of intermediate phases in chalcohalide glasses, J. Phys.: Condens. Matter, Volume 19 (2007) no. 22, 226201 | Zbl

[55] Punit Boolchand; Ping Chen; U. Vempati Intermediate Phases, structural variance and network demixing in chalcogenides: The unusual case of group V sulfides, J. Non Cryst. Solids, Volume 355 (2009) no. 37-42, pp. 1773-1785 (Non-Oxide and New Optical Glasses 16) | DOI

[56] D. G. Georgiev; Punit Boolchand; H. Eckert; Matthieu Micoulaut; Koblar A. Jackson The self-organized phase of bulk P $_{x}$ Se $_{1 - x}$ glasses, Eur. Phys. Lett., Volume 62 (2003) no. 1, pp. 49-55 | DOI

[57] Soumendu Chakravarty; Ralph Chbeir; Ping Chen; Matthieu Micoulaut; Punit Boolchand Correlating Melt Dynamics and Configurational Entropy Change With Topological Phases of As $_{x}$ S100 $_{100 - x}$ Glasses and the Crucial Role of Melt/Glass Homogenization, Front. Mater., Volume 6 (2019) | DOI

[58] B. Mantisi; Mathieu Bauchy; Matthieu Micoulaut Cycling through the glass transition: Evidence for reversibility windows and dynamic anomalies, Phys. Rev. B, Volume 92 (2015) no. 13, 134201 | DOI

[59] Kostya Trachenko; Martin T. Dove; Vadim Brazhkin; F. S. El’kin Network Rigidity and Properties of ${SiO}_{2}$ and ${GeO}_{2}$ Glasses under Pressure, Phys. Rev. Lett., Volume 93 (2004) no. 13, 135502 | DOI

[60] Matthieu Micoulaut; Mathieu Bauchy Anomalies of the first sharp diffraction peak in network glasses: Evidence for correlations with dynamic and rigidity properties, Phys. Status Solidi B Basic Res., Volume 250 (2013) no. 5, pp. 976-982 | DOI

[61] Yong Wang; Emi Ohata; Shinya Hosokawa; Masaki Sakurai; Eiichiro Matsubara Intermediate-range order in glassy Ge $_{x}$ Se $_{1 - x}$ around the stiffness transition composition, J. Non Cryst. Solids, Volume 337 (2004) no. 1, pp. 54-61 | DOI | Zbl

[62] D. Sharma; S. Sampath; N. P. Lalla; A. M. Awasthi Mesoscopic organization and structural phases in network-forming Ge $_{x}$ Se $_{1 - x}$ glasses, Physica B Condens. Matter, Volume 357 (2005) no. 3, pp. 290-298 | DOI

[63] Moneeb T. Shatnawi; Christopher L. Farrow; Ping Chen; Punit Boolchand; Asel Sartbaeva; M. F. Thorpe; Simon J. L. Billinge Search for a structural response to the intermediate phase in ${Ge}_{x} {Se}_{1 - x}$ glasses, Phys. Rev. B, Volume 77 (2008) no. 9, 094134 | DOI

[64] Pierre Lucas; Ellyn A. King; Ozgur Gulbiten; Jeffery L. Yarger; Emmanuel Soignard; Bruno Bureau Bimodal phase percolation model for the structure of Ge-Se glasses and the existence of the intermediate phase, Phys. Rev. B, Volume 80 (2009) no. 21, 214114 | DOI

[65] E. L. Gjersing; S. Sen; B. G. Aitken Structure, Connectivity, and Configurational Entropy of Ge $_{x}$ Se $_{100 - x}$ Glasses: Results from $^{77}$ Se MAS NMR Spectroscopy, J. Phys. Chem. C, Volume 114 (2010) no. 18, pp. 8601-8608 | DOI

[66] G. Chen; F. Inam; D. A. Drabold Structural origin of the intermediate phase in Ge–Se glasses, Appl. Phys. Lett., Volume 97 (2010) no. 13, 131901 | DOI

[67] Anita Zeidler; Philip S. Salmon; Dean A. J. Whittaker; Keiron J. Pizzey; Alex C. Hannon Topological Ordering and Viscosity in the Glass-Forming Ge-Se System: The Search for a Structural or Dynamical Signature of the Intermediate Phase, Front. Mater., Volume 4 (2017) | DOI

[68] F. Inam; Moneeb T. Shatnawi; D. Tafen; Simon J. L. Billinge; Ping Chen; D. A. Drabold An intermediate phase in Ge $_{x}$ Se $_{1 - x}$ glasses: experiment and simulation, J. Phys.: Condens. Matter, Volume 19 (2007) no. 45, 455206 | DOI

[69] Mathieu Bauchy; Matthieu Micoulaut; M. Boero; C. Massobrio Compositional Thresholds and Anomalies in Connection with Stiffness Transitions in Network Glasses, Phys. Rev. Lett., Volume 110 (2013) no. 16, 165501 | DOI

[70] Mathieu Bauchy; A. Kachmar; Matthieu Micoulaut Structural, dynamic, electronic, and vibrational properties of flexible, intermediate, and stressed rigid As-Se glasses and liquids from first principles molecular dynamics, J. Chem. Phys., Volume 141 (2014) no. 19, 194506 | DOI

[71] Shibalik Chakraborty; Punit Boolchand; Matthieu Micoulaut Structural properties of Ge-S amorphous networks in relationship with rigidity transitions: An ab initio molecular dynamics study, Phys. Rev. B, Volume 96 (2017) no. 9, 094205 | DOI

[72] F. Pacaud; Matthieu Micoulaut Thermodynamic precursors, liquid-liquid transitions, dynamic and topological anomalies in densified liquid germania, J. Chem. Phys., Volume 143 (2015) no. 6, 064502 | DOI

[73] Mathieu Bauchy; Matthieu Micoulaut Transport Anomalies and Adaptative Pressure-Dependent Topological Constraints in Tetrahedral Liquids: Evidence for a Reversibility Window Analogue, Phys. Rev. Lett., Volume 110 (2013) no. 9, 095501 | DOI

[74] Mark Wilson Model investigations of network-forming materials, Phys. Chem. Chem. Phys., Volume 14 (2012) no. 37, pp. 12701-12714 | DOI

[75] A. N. Cormack; J. Du; T. R. Zeitler Sodium ion migration mechanisms in silicate glasses probed by molecular dynamics simulations, J. Non Cryst. Solids, Volume 323 (2003) no. 1, pp. 147-154 | DOI

[76] J. Du; A. N. Cormack The medium range structure of sodium silicate glasses: a molecular dynamics simulation, J. Non Cryst. Solids, Volume 349 (2004), pp. 66-79 (Glass Science for High Technology. 16th University Conference on Glass Science) | DOI

[77] N. M. Anoop Krishnan; R. Ravinder; Rajesh Kumar; Yann Le Pape; Gaurav Sant; Mathieu Bauchy Density-stiffness scaling in minerals upon disordering: Irradiation vs. vitrification, Acta Mater., Volume 166 (2019), pp. 611-617 | DOI

[78] Mathieu Bauchy Structural, vibrational, and elastic properties of a calcium aluminosilicate glass from molecular dynamics simulations: The role of the potential, J. Chem. Phys., Volume 141 (2014) no. 2, 024507 | DOI

[79] Jincheng Du; L. René Corrales Compositional dependence of the first sharp diffraction peaks in alkali silicate glasses: A molecular dynamics study, J. Non Cryst. Solids, Volume 352 (2006) no. 30, pp. 3255-3269 | DOI

[80] Mathieu Bauchy; B. Guillot; Matthieu Micoulaut; N. Sator Viscosity and viscosity anomalies of model silicates and magmas: A numerical investigation, Chem. Geol., Volume 346 (2013), pp. 47-56 (9 $^{th}$ Silicate Melts Workshop) | DOI

[81] G. J. Kramer; A. J. M. De Man; R. A. Van Santen Zeolites versus aluminosilicate clusters: the validity of a local description, J. Am. Chem. Soc., Volume 113 (1991) no. 17, pp. 6435-6441 | DOI

[82] Mathieu Bauchy; Matthieu Micoulaut Atomic scale foundation of temperature-dependent bonding constraints in network glasses and liquids, J. Non Cryst. Solids, Volume 357 (2011) no. 14, pp. 2530-2537 | DOI

[83] Matthieu Micoulaut; A. Kachmar; Mathieu Bauchy; S. Le Roux; C. Massobrio; M. Boero Structure, topology, rings, and vibrational and electronic properties of Ge $_{x}$ Se $_{1 - x}$ glasses across the rigidity transition: A numerical study, Phys. Rev. B, Volume 88 (2013) no. 5, 054203 | DOI

[84] Can Yildirim; Jean-Yves Raty; Matthieu Micoulaut Revealing the role of molecular rigidity on the fragility evolution of glass-forming liquids, Nat. Commun., Volume 7 (2016), 11086 | DOI

[85] A. B. Bhatia; D. E. Thornton Structural Aspects of the Electrical Resistivity of Binary Alloys, Phys. Rev. B, Volume 2 (1970) no. 8, pp. 3004-3012 | DOI

[86] B. Grosdidier Two conceptualizations of the partial structures and of the order parameters in the ternary alloy and relationships between them, J. Non Cryst. Solids, Volume 566 (2021), 120894 | DOI

[87] R. Evans; R. J. F. Leote de Carvalho; J. R. Henderson; D. C. Hoyle Asymptotic decay of correlations in liquids and their mixtures, J. Chem. Phys., Volume 100 (1994) no. 1, pp. 591-603 | DOI

[88] D. Ma; A. Stoica; X. L. Wang Power-law scaling and fractal nature of medium-range order in metallic glasses, Nature Mater., Volume 8 (2009), pp. 30-34 | DOI

[89] T. Freltoft; J. K. Kjems; S. K. Sinha Power-law correlations and finite-size effects in silica particle aggregates studied by small-angle neutron scattering, Phys. Rev. B, Volume 33 (1986) no. 1, pp. 269-275 | DOI

[90] J.-P. Hansen; R. Mac Donald Theory of Simple Liquids, Cambridge University Press, 1976

[91] Philip S. Salmon; Anita Zeidler Identifying and characterising the different structural length scales in liquids and glasses: an experimental approach, Phys. Chem. Chem. Phys., Volume 15 (2013) no. 37, pp. 15286-15308 | DOI

[92] R. J. F. Leote de Carvalho; R. Evans The decay of correlations in ionic fluids, Mol. Phys., Volume 83 (1994) no. 4, pp. 619-654 | DOI

[93] Philip S. Salmon Decay of the pair correlations and small-angle scattering for binary liquids and glasses, J. Phys.: Condens. Matter, Volume 18 (2006) no. 2, 11443 | DOI

[94] Roland Kjellander; Björn Forsberg Ionic fluids with $r^{- 6}$ pair interactions have power-law electrostatic screening, J. Phys. A, Math. Gen., Volume 38 (2005) no. 24, pp. 5405-5424 | DOI | MR | Zbl

[95] C. Grodon; M. Dijkstra; R. Evans; R. Roth Homogeneous and inhomogeneous hard-sphere mixtures: manifestations of structural crossover, Mol. Phys., Volume 103 (2005) no. 21-23, pp. 3009-3023 | DOI

[96] Mathieu Bauchy; Matthieu Micoulaut; M. Celino; S. Le Roux; M. Boero; C. Massobrio Angular rigidity in tetrahedral network glasses with changing composition, Phys. Rev. B, Volume 84 (2011) no. 5, 054201 | DOI

[97] Jeffrey R. Errington; Pablo G. Debenedetti Relationship between structural order and the anomalies of liquid water, Nature, Volume 409 (2001), pp. 318-321 | DOI

[98] M. Scott Shell; Pablo G. Debenedetti; Athanassios Z. Panagiotopoulos Molecular structural order and anomalies in liquid silica, Phys. Rev. E, Volume 66 (2002) no. 1, 011202 | DOI

[99] B. Shadrack Jabes; Manish Agarwal; Charusita Chakravarty Tetrahedral order, pair correlation entropy, and waterlike liquid state anomalies: Comparison of GeO $_{2}$ with BeF $_{2}$ , SiO $_{2}$ , and H $_{2}$ O, J. Chem. Phys., Volume 132 (2010) no. 23, 234507 | DOI

[100] Ruchi Sharma; Somendra Nath Chakraborty; Charusita Chakravarty Entropy, diffusivity, and structural order in liquids with waterlike anomalies, J. Chem. Phys., Volume 125 (2006) no. 20, 204501 | DOI

[101] Manish Agarwal; Ruchi Sharma; Charusita Chakravarty Ionic melts with waterlike anomalies: Thermodynamic properties of liquid BeF2, J. Chem. Phys., Volume 127 (2007) no. 16, 164502 | DOI

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Network entropy and connectivity: the underlying factors determining compositional trends in the glass-transition temperature

Matthieu Micoulaut

C. R. Chim (2002)

Nanoscale phase separation effects near $\bar{𝑟} = 2.4$ and 2.67, and rigidity transitions in chalcogenide glasses

Punit Boolchand; Daniel G. Georgiev; Tao Qu; ...

C. R. Chim (2002)

Challenges and opportunities in atomistic simulations of glasses: a review

Han Liu; Zhangji Zhao; Qi Zhou; ...

C. R. Géos (2022)