Atomistic Simulations of Glasses E-Book

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Sprache: Englisch

Seitenzahl: 1177

Veröffentlichungsjahr: 2022

Beschreibung

A complete reference to computer simulations of inorganic glass materials 

In Atomistic Simulations of Glasses: Fundamentals and Applications, a team of distinguished researchers and active practitioners delivers a comprehensive review of the fundamentals and practical applications of atomistic simulations of inorganic glasses. The book offers concise discussions of classical, first principles, Monte Carlo, and other simulation methods, together with structural analysis techniques and property calculation methods for the models of glass generated from these atomistic simulations, before moving on to practical examples of the application of atomistic simulations in the research of several glass systems. 

The authors describe simulations of silica, silicate, aluminosilicate, borosilicate, phosphate, halide and oxyhalide glasses with up-to-date information and explore the challenges faced by researchers when dealing with these systems. Both classical and ab initio methods are examined and comparison with experimental structural and property data provided. Simulations of glass surfaces and surface-water reactions are also covered.  

Atomistic Simulations of Glasses includes multiple case studies and addresses a variety of applications of simulation, from elucidating the structure and properties of glasses for optical, electronic, architecture applications to high technology fields such as flat panel displays, nuclear waste disposal, and biomedicine. The book also includes: 

• A thorough introduction to the fundamentals of atomistic simulations, including classical, ab initio, Reverse Monte Carlo simulation and topological constraint theory methods 
• Important ingredients for simulations such as interatomic potential development, structural analysis methods, and property calculations are covered 
• Comprehensive explorations of the applications of atomistic simulations in glass research, including the history of atomistic simulations of glasses  
• Practical discussions of rare earth and transition metal-containing glasses, as well as halide and oxyhalide glasses 
• In-depth examinations of glass surfaces and silicate glass-water interactions  

Perfect for glass, ceramic, and materials scientists and engineers, as well as physical, inorganic, and computational chemists, Atomistic Simulations of Glasses: Fundamentals and Applications is also an ideal resource for condensed matter and solid-state physicists, mechanical and civil engineers, and those working with bioactive glasses. Graduate students, postdocs, senior undergraduate students, and others who intend to enter the field of simulations of glasses would also find the book highly valuable.  

Leseprobe

Table of Contents

Cover

Title Page

Copyright

List of Contributors

Preface

List of Abbreviations

Part I: Fundamentals of Atomistic Simulations

1 Classical Simulation Methods

1.1 Introduction

1.2 Simulation Techniques

1.3 The Born Model

1.4 Calculation of Observables

1.5 Glass Formation

1.6 Geometry Optimization and Property Calculations

References

2 Ab Initio Simulation of Amorphous Materials

2.1 Introduction

2.2 Methods to Produce Models

2.3 Analyzing the Models

2.4 Conclusion

Acknowledgments

References

Notes

3 Reverse Monte Carlo Simulations of Noncrystalline Solids

3.1 Introduction – Why RMC Is Needed?

3.2 Reverse Monte Carlo Modeling

3.3 Topological Analyses

3.4 Applications

3.5 Conclusion

Acknowledgments

References

4 Structure Analysis and Properties Calculations

4.1 Introduction

4.2 Structure Analysis

4.3 Spectroscopic Properties: Validating the Structural Models

4.4 Transport Properties

4.5 Mechanical Properties

4.6 Concluding Remarks

References

5 Topological Constraint Theory of Glass: Counting Constraints by Molecular Dynamics Simulations

5.1 Introduction

5.2 Background on Topological Constraint Theory

5.3 Counting Constraints from Molecular Dynamics Simulations

5.4 Conclusion

Acknowledgments

References

Part II: Applications of Atomistic Simulations in Glass Research

6 History of Atomistic Simulations of Glasses

6.1 Introduction

6.2 Simulation Techniques

6.3 Classical Simulations: Interatomic Potentials

6.4 Simulations of Surfaces

6.5 Computer Science and Engineering

References

7 Silica, Silicate, and Aluminosilicate Glasses

7.1 Introduction

7.2 Atomistic Simulations of Silicate Glasses: Ingredients and Critical Aspects

7.3 Characterization and Experimental Validation of Structural and Dynamic Features of Simulated Glasses

7.4 MD Simulations of Silica Glasses

7.5 MD Simulations of Alkali Silicate and Alkaline Earth Silicate Glasses

7.6 MD Simulations of Aluminosilicate Glasses

7.7 MD Simulations of Nanoporous Silica and Silicate Glasses

7.8 AIMD Simulations of Silica and Silicate Glasses

7.9 Summary and Outlook

Acknowledgments

References

8 Borosilicate and Boroaluminosilicate Glasses

8.1 Introduction

8.2 Experimental Determination and Theoretical Models of Boron N4 Values in Borosilicate Glass

8.3 Ab Initio Versus Classical MD Simulations of Borosilicate Glasses

8.4 Empirical Potentials for Borate and Borosilicate Glasses

8.5 Evaluation of the Potentials

8.6 Effects of Cooling Rate and System Size on Simulated Borosilicate Glass Structures

8.7 Applications of MD Simulations of Borosilicate Glasses

8.8 Conclusion

Acknowledgments

8.A Available Empirical Potentials for Boron-Containing Systems

References

9 Atomistic Simulation of Nuclear Waste Glasses

9.1 Preamble

9.2 Introduction to French Nuclear Glass

9.3 Computational Methodology

9.4 Simulation of Radiation Effects in Simplified Nuclear Glasses

9.5 Simulation of Glass Alteration by Water

9.6 Gas Incorporation: Radiation Effects on He Solubility

9.7 Conclusion

Acknowledgments

References

10 Phosphate Glasses

10.1 Introduction to Phosphate Glasses

10.2 Modeling Methods for Phosphate Glasses

10.3 Modeling Pure Vitreous P2O5

10.4 Modeling Phosphate Glasses with Monovalent Cations

10.5 Modeling Phosphate Glasses with Divalent Cations

10.6 Modeling Phosphate‐Based Glasses for Biomaterials Applications

10.7 Modeling Phosphate Glasses with Trivalent Cations

10.8 Modeling Phosphate Glasses with Tetravalent and Pentavalent Cations

10.9 Modeling Phosphate Glasses with Mixed Network Formers

10.10 Modeling Bioglass 45S and Related Glasses

10.11 Summary

References

11 Bioactive Glasses

11.1 Introduction

11.2 Methodology

11.3 Development of Interatomic Potentials

11.4 Structure of 45S5 Bioglass

11.5 Inclusion of Ions into Bioactive Glass and the Effect on Structure and Bioactivity

11.6 Glass Nanoparticles and Surfaces

11.7 Discussion and Future Work

References

12 Rare Earth and Transition Metal Containing Glasses

12.1 Introduction

12.2 Simulation Methodology

12.3 Case Studies of MD Simulations of RE and TM Containing Glasses

12.4 Conclusions

Acknowledgments

References

13 Fluoride and Oxyfluoride Glasses

13.1 Introduction

13.2 General Structure Features of Fluoride and Oxyfluoride Glasses

13.3 Structures and Properties of Fluoride Glasses from MD Simulations

13.4 MD Simulations of Fluoroaluminosilicate Oxyfluoride Glasses

13.5 Ab Initio MD Simulations of Oxyfluoride Glasses

13.6 Conclusions

Acknowledgments

References

14 Glass Surface Simulations

14.1 Introduction

14.2 Classical MD Surface Simulations

14.3 First Principles Surface Simulations

14.4 Summary

Acknowledgments

References

15 Simulations of Glass–Water Interactions

15.1 Introduction

15.2 First‐Principles Simulations of Glass–Water Interactions

15.3 Classical Molecular Dynamics Simulations of Water–Glass Interactions

15.4 Challenges and Outlook

15.5 Concluding Remarks

Acknowledgments

References

Index

Wiley End User License Agreement

List of Tables

Chapter 1

Table 1.1 Common analytical expressions for the short‐range potentials.

Chapter 4

Table 4.1 Classification of the range order in amorphous solids of T

n

O

m

sto...

Table 4.2 Elastic properties of three alkali‐doped silicate glasses (25% M

2

Chapter 8

Table 8.A.1 Initial charges of elements used in Kieu et al. and Deng and Du...

Table 8.A.2 Potential parameters for sodium borosilicate and boroaluminosili...

Table 8.A.3 Empirical parameters in Kieu et al. and Deng and Du potentials ...

Table 8.A.4 Partial charges used in Wang et al. potential [44]. Partial cha...

Table 8.A.5 Empirical parameters in Wang et al. potential [44]. Potential p...

Table 8.A.6 Potential parameters for the sodium borosilicate systems [45]....

Table 8.A.7 Charges of elements used in Ha and Garofalini potential [46].

Table 8.A.8 Parameters of the two‐body term in Ha and Garofalini potential [...

Table 8.A.9 Three‐body parameters in Ha and Garofalini potential [46].

Table 8.A.10 Partial charges of elements used in Deng and Du potential [52]...

Table 8.A.11 Empirical parameters in Deng and Du potential for borosilicate ...

Table 8.A.12 Empirical parameters used to determine the

A

B–O

parameter...

Table 8.A.13 Charge of different species of Sundararaman et al. potential [...

Table 8.A.14 Parameters of short‐range interactions in Sundararaman et al. ...

Table 8.A.15 Empirical potential parameters of pair interactions in Yu et a...

Table 8.A.16 Empirical potential parameters of three‐body term in Yu et al....

Chapter 9

Table 9.1 Average composition of the French R7T7 glass in %wt.

Table 9.2 Comparison of the effects of accelerated quenching and accumulati...

Table 9.3 Structural evolution of the SBN12 and SBN55 glasses after heat tr...

Table 9.4 Hardness values (GPa) for the pristine and fast quenched SBN12, S...

Table 9.5 Glass compositions (molar fractions) used to quantify interstitia...

Chapter 10

Table 10.1 Elementary features of phosphate glass structures.

Table 10.2 A widely used set of rigid ion potential parameters for phosphat...

Table 10.3 A set of shell model potential parameters for phosphate glasses....

Table 10.4 Comparison of o′‐P

2

O

5

lattice parameters from (“This work”) shel...

Table 10.5 Comparison of o′‐P

2

O

5

lattice parameters from a variety of densi...

Table 10.6 Comparison of bond lengths in sodium calcium phosphate‐based bio...

Table 10.7 The effect of increasing size of divalent modifier cations (Me) ...

Chapter 12

Table 12.1 Atomic charges and Buckingham potential parameters for simulatio...

Table 12.2 Atomic charges and Morse parameters vanadium phosphate glasses [...

Table 12.3 Erbium ion local structures, dipole and quadruple moments in erb...

Table 12.4 Erbium coordination number and average dipole moment in 1Er

2

O

3

–

x

Table 12.5 Average network former cation (Si

4+

, P

5+

, and Al

3+

) ...

Table 12.6 Glass composition, density, and cerium redox, Al

3+

and P

5+

...

Table 12.7 Composition (mol%), V

4+

/

V

tot

ratio, density and total atoms ...

Table 12.8 Composition (mol%), V

4+

/

V

tot

ratio, density, and total atoms...

Table 12.9 Bond distances derived by PDF curves from MD (Å, error within ±0...

Table 12.10 Activation energy (

E

a

) of Li ions and the diffusion prefactor (

List of Illustrations

Chapter 1

Figure 1.1 Comparison of the ordered structure of cristobalite (a), and the ...

Figure 1.2 The effect of simulation size is demonstrated by this comparison ...

Figure 1.3 Schematic of the Shell Model. On the left, an isolated atom in th...

Figure 1.4 (a) Principle of radial distribution function:

g

(

r

) counts the nu...

Figure 1.5 Different radial distribution functions derived from the radial d...

Figure 1.6

T

(

r

) calculated from 500 timesteps, at 300 K, from a simulation o...

Figure 1.7 Pair

T

(r) distribution functions for a 60SiO

2

·20Al

2

O

3

·20Er

2

O

3

sim...

Figure 1.8 Trajectories of a single Li ion (blue spheres) in a 15Li

2

O·85SiO

2

Figure 1.9 Mean square displacements (msd) for Li in a 15Li

2

O·85SiO

2

glass a...

Figure 1.10 Simulation box setup for (a) surface and (b) fiber simulations. ...

Figure 1.11 Formation of a fiber. The green outlines in the left panel repre...

Chapter 2

Figure 2.1 Snapshot of a 100 000 atom model of disordered silicon under 12 G...

Figure 2.2 The classic illustration of the continuous random network model: ...

Figure 2.3 Pair distribution function for Model I (solid line) and Model II ...

Figure 2.4 Flowchart of FEAR method.

Figure 2.5 We show comparison of our

models, made with melt‐quench (MQ200)...

Figure 2.6 Comparison of EXAFS spectra: (a) Pd‐K‐edge, (b) Ni‐K‐edge, and (c...

Figure 2.7 The (black curve) electronic density of states (DoS) and (orange ...

Figure 2.8 Comparison of RDF of crystalline (diamond) and amorphous Carbon [...

Figure 2.9 Electronic DoS and inverse participation ratio (IPR) of Cu‐doped

Figure 2.10 Space projected conductivity scalar field for Model I (a) and Mo...

Figure 2.11 Vibrational DoS and VIPR of two different models of

bulk metal...

Chapter 3

Figure 3.1 Structure factor,

S

(

Q

), for amorphous silicon obtained by X‐ray d...

Figure 3.2 Primitive ring statistics for (a) α‐cristobalite, (b) α‐quartz, (...

Figure 3.3 Visualization of surface cavities. (a) SiO

2

glass, (b) Na100 glas...

Figure 3.4 Persistent homology and PD [18]. (a) The increasing sequence of s...

Figure 3.5 (a) X‐ray

S

(

Q

) for

a

‐Si (blue curve) [17] and

l

‐Si (red curve, 17...

Figure 3.6 Neutron‐ (a) [67] and X‐ray (b)‐weighted total structure factors ...

Figure 3.7 RMC–MD‐generated atomic configuration for

g

‐SiO

2

[18]. The thickn...

Figure 3.8 (a) X‐ray total structure factors (upper),

S

X

(

Q

), for

g

‐SiO

2

[18]...

Figure 3.9 (a) Neutron total structure factor

S

N

(

Q

) and (b) X‐ray total stru...

Figure 3.10 (a) Primitive ring statistics, (b) weighted surface cavity histo...

Figure 3.11 (a) Na‐centric, (b) Na/K‐centric, and (c) K‐centric PDs for a se...

Figure 3.12 Visualization of alkali‐oxygen polyhedra around nonbridging oxyg...

Figure 3.13 Neutron (a) and X‐ray (b) total structure factors

S

(

Q

) and EXAFS...

Figure 3.14 Distribution of –Al(Ca)–O–Al(Ca)–O–Al(Ca)– rings in 50CaO and 64...

Figure 3.15 Close‐up visualizations of (a) the HOMO and (b) LUMO four single...

Figure 3.16 Comparison between the experimental data (open circles) and the ...

Figure 3.17 RMC‐generated atomic configurations and connectivity of Ge–Te an...

Figure 3.18 Schematic drawing of phase‐change process in

a

‐GST. (a) Highligh...

Chapter 4

Figure 4.1 (a) The structure of a soda‐lime silica glass obtained by MD simu...

Figure 4.2 (a) 2D silica glass network with the connectivity matrix defining...

Figure 4.3 Structure of glasses with composition (Na

2

O)

0.24

(CaO)

0.27

[(SiO

2

)

Figure 4.4 (a) Distribution of atoms and definitions of the pair distributio...

Figure 4.5 (a) Computed total distribution function of SiO

2

glass, broadened...

Figure 4.6 Total structure factors

S

(

Q

) at room temperature for Li

2

S–P

2

S

5

gl...

Figure 4.7 Experimental (red line) and B3LYP (black line) IR spectra of the ...

Figure 4.8 Comparison between the simulated VDOS from density functional the...

Figure 4.9 Theoretical

17

O MAS NMR spectra at 14.1 T for (a)

Na‐Al‐Silica

...

Figure 4.10 Theoretical

17

O 3QMAS NMR for NAS (a), CAS (d) and CNAS (g) glas...

Figure 4.11 In panel (a) the schematic representation of the diffusion activ...

Figure 4.12 In (a) schematic representation of the NEMD simulation box with ...

Figure 4.13 (a) Trajectory illustrating the effect of the strain on the brea...

Figure 4.14 (a) Stress–strain plot for a simulation of 13 000 atoms of silic...

Chapter 5

Figure 5.1 Topological constraint theory simplifies complex disordered atomi...

Figure 5.2 The three states of rigidity of a mechanical network. The dashed ...

Figure 5.3 Illustration of the origin of the internal eigenstress that is pr...

Figure 5.4 Schematic illustrating the role of the radial bond‐stretching (BS...

Figure 5.5 Illustration of the use of molecular dynamics simulations to comp...

Figure 5.6 (a) Relative radial excursion of the neighbors around central Si ...

Figure 5.7 Distribution of relative angular excursions of the angles forming...

Figure 5.8 Average relative angular excursion associated with the bond‐bendi...

Figure 5.9 Snapshots of isolated (a) Q

0

, (b) Q

1

, (c) Q

2

, (d) Q

3

, and (e) Q

4

...

Figure 5.10 (a) Stress per bridging O (BO) computed in bulk sodium silicate ...

Figure 5.11 Mean square displacement of the atoms in sodium silicate glasses...

Figure 5.12 Computed fraction of floppy modes in simulated Ge–Se and As–Se g...

Chapter 6

Figure 6.1 (a) Mean square displacements in Na, K silicates. (b) The derivat...

Figure 6.2 Schematic bonding state function variation with bond length in a ...

Figure 6.3 Schematic setup for modeling glass surfaces.

Figure 6.4 Two different representations of glass structures produced by Cer...

Chapter 7

Figure 7.1 (a) Typical potential energy for interactions between like charge...

Figure 7.2 (a) Shows the pair distribution functions of a soda‐lime‐silicate...

Figure 7.3 (a) and (b) Examples of ring structures from simulated glass. (a)...

Figure 7.4 Schematic of the experimental setup for measuring local structure...

Figure 7.5 Structure factor and total correlation function of silica glass f...

Figure 7.6 (a) Snapshots of simulated sodium silicate glasses. The yellow bl...

Figure 7.7 Stagewise evolution of the gel morphology in amorphous silicate: ...

Figure 7.8 Two‐dimensional representation of the network glass structures of...

Chapter 8

Figure 8.1 Predicted

N

4

values using modified Bernstein model versus experim...

Figure 8.2 Snapshot of the MD simulated glass structure of SBN‐B130 glass us...

Figure 8.3 (a) Comparison of four‐coordinated boron in sodium borosilicate g...

Figure 8.4 Fraction of four‐coordinated boron,

N

4

, as a function of

R

([Na

2

O...

Figure 8.5 Comparison of boron‐oxygen total correlation function (

T

(

r

)) (top...

Figure 8.6 Effects of system size and cooling rate effect on boron N

4

in sod...

Figure 8.7 (a) Relative densification, and (b) change of boron coordination ...

Figure 8.8

Z

‐density profiles of three sodium borosilicate glasses: (a) SBN0...

Figure 8.9 (a) Shows boron coordination (

N

4

) as a function of

R

for the bulk...

Figure 8.10 Sodium ion diffusion behaviors of B

2

O

3

/SiO

2

substituted SrO‐dope...

Chapter 9

Figure 9.1 Alteration rate of a glass in contact with an aqueous solution. D...

Figure 9.2 Effects of the deposited electronic (a) and nuclear (b) energies ...

Figure 9.3 Preparation of a glass. A liquid is prepared in the NVT ensemble,...

Figure 9.4 Volume change of a simplified nuclear glass subjected to one hund...

Figure 9.5 Number of oxygen atoms displaced at least once (black), twice (da...

Figure 9.6 Evolution of the mean coordination number of boron and sodium ato...

Figure 9.7 Local density distributions for the (a) pristine and (b) irradiat...

Figure 9.8 Scheme of a simulation box submitted to nanoindentation. The bott...

Figure 9.9 Indentation profiles in the pristine and fast quenched glasses....

Figure 9.10 Loading – unloading curves for pristine and fast quenched glasse...

Figure 9.11 Hardness of the pristine and fast quenched (= disordered) SBN12,...

Figure 9.12 Hardness change in the pristine (a) and fast quenched (b) SBN12,...

Figure 9.13 Scheme of a simulation box submitted to a tensile stress. The up...

Figure 9.14 The four stages leading to the complete decohesion of SBN14 glas...

Figure 9.15 Stress–strain curves for the pristine and fast quenched SBN14 gl...

Figure 9.16 First peaks of Si–O and

IV

B–O radial distribution functions at d...

Figure 9.17 First peaks of the

III

B–O and Na–O radial distribution functions...

Figure 9.18 Example of a Monte Carlo network used to simulate glass–water al...

Figure 9.19 Addition of a six coordinated Zr atom in the Monte Carlo network...

Figure 9.20 B concentration in solution versus computer steps for several Al

Figure 9.21 Size distributions of interstitial sites in the series of borosi...

Figure 9.22

N

s

versus R (=[Na

2

O]/[B

2

O

3

]). The glasses are separated dependin...

Figure 9.23 Density and

N

s

values versus the disordering temperature for the...

Chapter 10

Figure 10.1 Models of (a) calcium metaphosphate glass and (b) calcium metaph...

Figure 10.2 The distribution of

Q

n

groups in zinc phosphate glasses from (sy...

Figure 10.3 Models of (a) calcium metaphosphate glass and (b) calcium metasi...

Figure 10.4 The variety of PO

4

tetrahedral units found in phosphate glasses ...

Figure 10.5 Model of a sodium borophosphate glass in which traces of the cry...

Figure 10.6 A slice of a RMC model of v‐P

2

O

5

showing (small spheres) P and (...

Figure 10.7 (a) A cluster model of v‐P

2

O

5

, and (b) Vibrational modes in v‐P

2

Figure 10.8 (a) Obtaining

T

g

from a change in slope of molar volume during a...

Figure 10.9 A schematic illustration of the changes in the Li environment in...

Figure 10.10 Comparison of the PDF of sodium metaphosphate glass obtained fr...

Figure 10.11 Partial PDFs in a MD model of sodium metaphosphate glass.

Figure 10.12 Experimental ionic conductivity in metaphosphate glasses showin...

Figure 10.13 Models of Ag

0.5

Na

0.5

PO

3

and Li

0.5

Rb

0.5

PO

3

metaphosphate glasses...

Figure 10.14 Schematic to explain the decrease in typical Zn—Zn nearest neig...

Figure 10.15

T

g

from (solid symbols) MD simulation and (open symbols) experi...

Figure 10.16 P–P partial PDF in metaphosphate glasses with different modifie...

Figure 10.17 M–M partial PDFs from RMC models of metaphosphate glasses, wher...

Figure 10.18 Models of calcium metaphosphate glass made using (a) RMC and (b...

Figure 10.19 Two‐dimensional schematic representation of the phosphate netwo...

Figure 10.20 Snapshot from ab initio modeling of PBG with composition 25Na

2

O...

Figure 10.21 MD model of 40Fe

2

O

3

–60P

2

O

5

glass with (pink) PO

4

tetrahedra, (g...

Figure 10.22 Schematic showing complementary trends in electrostatic bond va...

Figure 10.23 A snapshot image of an iron phosphate glass with 4% Fe

2+

sh...

Figure 10.24 MD model of 23Dy

2

O

3

–7Al

2

O

3

–70P

2

O

5

glass with (gray) Dy ions, (r...

Figure 10.25 Fraction of bridging oxygens connecting different network forme...

Figure 10.26 Li ion conductivity in 45Li

2

O– 55(

y

B

2

O

3

–(1 − 

y

)P

2

O

5

) lithium bo...

Figure 10.27 Phosphate‐rich regions in the BG65 model with (blue) silicon, (...

Chapter 11

Figure 11.1 Fit of the experimental

29

Si MAS NMR spectrum of 45S5 Bioglass c...

Figure 11.2 O—Na—O and O—Ca—O bond‐angle distribution functions from MD simu...

Figure 11.3 Snapshot of glass structure of a composition based on 45S5 but c...

Figure 11.4 A snapshot of the bioglass–water interface.The phosphosilica...

Chapter 12

Figure 12.1 Probability of finding Eu ions as a function of Eu–Eu distance f...

Figure 12.2 Pair distribution function (a) and coordination number (b) of er...

Figure 12.3 (a) Snapshots of coordination environment of erbium ions and the...

Figure 12.4 Comparison of MD modeled rare earth distribution with those from...

Figure 12.5 (a) Erbium clustering analyses using Er—O—Er bonding criterion (...

Figure 12.6 Comparison of Na–O and Er–O partial distribution functions and t...

Figure 12.7 Quadruple moments of the first coordination shell of erbium ions...

Figure 12.8 (a) Evolution of PKA kinetic energy, number of energetic ions (>...

Figure 12.9 Snapshots of the displaced atoms after 1 keV on Er PKA. The shor...

Figure 12.10 (a) Percentage of Si and O coordination defect sites before and...

Figure 12.11 Eu–O pair correlation function and their BO/NBO contributions i...

Figure 12.12 Probabilities of finding neighboring Eu ions as a function of E...

Figure 12.13 A comparison of experimental and MD calculated X‐ray (a) and ne...

Figure 12.14 (a) The Pr–O partial correlation function and (b) coordination ...

Figure 12.15 Europium and its first coordination shell oxygen ions in (a) Eu...

Figure 12.16 Ce

3+

/Ce

4+

–O pair‐distribution functions, coordination n...

Figure 12.17 (a) Ce

3+

‐Si/P in cerium phosphosilicate glass, (b) Ce

3+

Figure 12.18 (a) Ce

4+

–Si/P in cerium phosphosilicate glass, (b) Ce

4+

Figure 12.19 (a) Comparison of MD simulation (blue) and experimental (red) X...

Figure 12.20 Ce–Al/P partial pair distribution functions in cerium aluminoph...

Figure 12.21 Cerium ion clustering statistics in CAP9 (a) and CAP6 (b) based...

Figure 12.22 Structure snapshots and excess charge density distributions aft...

Figure 12.23 Excess charge trapping in a cerium‐doped aluminophosphosilicate...

Figure 12.24 (a) Excess charge density of around a Ce

4+

ion after trappi...

Figure 12.25 V

x

O

n

structural units in phosphate glasses.

Figure 12.26 Coordination number (CN) % as a function of V

2

O

5

content for (a...

Figure 12.27

Q

n

distribution for P for the NaVP series.

Figure 12.28 (a) P–O–P, P–O–V, and V–O–V linkages (%) and (b) linkages (%) a...

Figure 12.29 PDF curves of the (a) V

5+

—O and (b) V

4+

—O bonds in the ...

Figure 12.30 Contributions to the averaged CN of V

5+

and V

4+

ions an...

Figure 12.31 V–O–V Linkages as a function of V content.

Figure 12.32 Diffusion coefficient as a function of 1/temperature for three ...

Figure 12.33 Comparisons of experimental and simulated X‐ray diffraction spe...

Figure 12.34 Snapshots of simulated 15Na

2

O–10CaO–68SiO

2

–7ZrO

2

glass by MD. P...

Figure 12.35 PDFs of cation–oxygen pairs in a simulated 57.9SiO

2

–12.6Na

2

O–5....

Figure 12.36 Experimental and calculated (Δ

E

0

 = 10 eV) Zr K‐edge EXAFS spect...

Figure 12.37 Self‐diffusion coefficients of B, Ca, Na, Al, Zr, and Si in ISG...

Figure 12.38 Bulk, shear, and Young's modulus (GPa) obtained by MD simulatio...

Figure 12.39 Two‐dimensional longitudinal cross sections of the simulated co...

Figure 12.40 QSPR analysis of initial dissolution rate of soda lime borosili...

Chapter 13

Figure 13.1 Representative Born–Meyer pair potentials for oxide, fluoride, a...

Figure 13.2 (a) Scanning electron micrograph (backscatter image) of opaque w...

Figure 13.3 The structure model of 3ZrF

4

–2BaF

2

glass derived from the crysta...

Figure 13.4 M–F (a) and Zr–M (b) radial distribution function in 55ZrF

4

–20Ba...

Figure 13.5 Typical structural motif with Zr

2

F

13

bipolyhedron unit proposed ...

Figure 13.6 The calculated and observed infrared (a) and Raman (b) spectra o...

Figure 13.7 Dependence of relative density

ρ

/

ρ

0

on quenching‐press...

Figure 13.8 Fluoride phase separation observed in 50SiO

2

–15Al

2

O

3

–35BaF

2

glas...

Figure 13.9 Glass structure comparison among oxide, fluoride and oxyfluoride...

Figure 13.10 Oxide and fluoride phase interface in 50SiO

2

–15Al

2

O

3

–35BaF

2

gla...

Chapter 14

Figure 14.1 Schematic diagram for creating and analyzing the v‐SiO

2

surface....

Figure 14.2 Radial pair distribution functions in a bulk silica sample (thin...

Figure 14.3 Z‐profiles of the total number (top panels) and fraction (bottom...

Figure 14.4 A direct comparison of the sodium ion density profile of the sur...

Figure 14.5 The deformation morphology and

σ

xx

stress field under an in...

Figure 14.6 Normalized atomic density plot for (a) bulk and (b) surface of 4...

Figure 14.7 Comparison of ring size distribution of the surface and the bulk...

Figure 14.8 OH distribution across the Na

+

/H

+

‐exchanged bioactive gl...

Figure 14.9 Different types of hydroxyls present on the silica surface expos...

Figure 14.10 (a) Initial structure (top), (b) structure after melting the al...

Figure 14.11 Model of dehydroxylated amorphous surface (top panel: side view...

Figure 14.12 Calculated geometries of initial state, transition state, and f...

Figure 14.13 B3LYP Hench 45S5 Bioglass optimized unit cell.

Figure 14.14 Isolated orthosilicate group (encircled in yellow) exposed on t...

Figure 14.15 Atomic configuration of the transition states for the hydroxyla...

Figure 14.16 Snapshot of the bioglass–water interface, extracted from CPMD t...

Chapter 15

Figure 15.1 Multiscale simulation methods and applications to glass–water in...

Figure 15.2 Relative free energy profiles for the reaction of SiO

2

with wate...

Figure 15.3 Si—O bond breakage mechanism in a Si—O—Si linkage involving Si...

Figure 15.4 Summary of energy barrier for breakage of network formers under ...

Figure 15.5 ReaxFF development tree, where parameter sets on a common ‘branc...

Figure 15.6 Silanol formation on curved silica surfaces. Snapshots indicate ...

Figure 15.7 Scheme of mechanisms in sodium silicate glass and water interfac...

Figure 15.8 Reactions of B atoms in the surface with water to change the two...

Guide

Cover

Table of Contents

Title Page

Copyright

List of Contributors

Preface

List of Abbreviations

Begin Reading

Index

Wiley End User License Agreement

Pages

iii

iv

xv

xvi

xvii

xviii

xix

xx

xxi

xxii

xxiii

xxiv

xxv

xxvi

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

65

66

67

69

70

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

91

92

93

94

95

96

97

98

99

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

185

186

187

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

204

205

206

207

208

209

210

211

212

213

214

215

216

217

218

219

220

221

222

223

224

225

226

227

228

229

230

231

232

233

234

235

236

237

238

239

240

241

242

243

244

245

246

247

248

249

250

251

252

253

254

255

256

257

258

259

260

261

262

263

264

265

266

267

268

269

270

271

272

273

274

275

276

277

278

279

280

281

282

283

284

285

286

287

288

289

290

291

292

293

294

295

296

297

298

299

300

301

302

303

304

305

306

307

308

309

310

311

312

313

314

315

316

317

318

319

320

321

322

323

324

325

326

327

328

329

330

331

332

333

334

335

336

337

338

339

340

341

342

343

344

345

346

347

348

349

350

351

352

353

354

355

356

357

358

359

360

361

362

363

364

365

366

367

368

369

370

371

372

373

374

375

376

377

378

379

380

381

382

383

384

385

386

387

388

389

390

391

392

393

394

395

396

397

398

399

400

401

402

403

404

405

406

407

408

409

410

411

412

413

414

415

416

417

418

419

420

421

422

423

424

425

426

427

428

429

430

431

432

433

434

435

436

437

438

439

440

441

442

443

444

445

446

447

448

449

450

451

452

453

454

455

456

457

458

459

460

461

462

463

464

465

466

467

468

469

470

471

472

473

474

475

476

477

478

479

480

481

482

483

484

485

486

487

488

489

490

491

492

493

494

495

496

497

498

499

500

501

502

503

504

505

506

507

508

509

510

511

512

513

514

515

516

517

518

519

520

521

523

524

525

526

527

528

529

530

531

Atomistic Simulations of Glasses

Fundamentals and Applications

Edited by

Jincheng DuUniversity of North TexasDenton, TX, USA

Alastair N. CormackNYS College of CeramicsAlfred UniversityAlfred, NY, USA

Copyright © 2022 by the American Ceramics Society, Inc. All rights reserved.

A Joint Publication of the American Ceramics Society and John Wiley & Sons, Inc.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.Published simultaneously in Canada.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by law. Advice on how to obtain permission to reuse material from this title is available at http://www.wiley.com/go/permissions.

The right of Jincheng Du and Alastair N. Cormack to be identified as the authors of the editorial material in this work has been asserted in accordance with law.

Registered OfficeJohn Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA

Editorial OfficeJohn Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, USA

For details of our global editorial offices, customer services, and more information about Wiley products visit us at www.wiley.com.

Wiley also publishes its books in a variety of electronic formats and by print‐on‐demand. Some content that appears in standard print versions of this book may not be available in other formats.

Limit of Liability/Disclaimer of WarrantyIn view of ongoing research, equipment modifications, changes in governmental regulations, and the constant flow of information relating to the use of experimental reagents, equipment, and devices, the reader is urged to review and evaluate the information provided in the package insert or instructions for each chemical, piece of equipment, reagent, or device for, among other things, any changes in the instructions or indication of usage and for added warnings and precautions. While the publisher and authors have used their best efforts in preparing this work, they make no representations or warranties with respect to the accuracy or completeness of the contents of this work and specifically disclaim all warranties, including without limitation any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives, written sales materials, or promotional statements for this work. The fact that an organization, website, or product is referred to in this work as a citation and/or potential source of further information does not mean that the publisher and authors endorse the information or services the organization, website, or product may provide or recommendations it may make. This work is sold with the understanding that the publisher is not engaged in rendering professional services. The advice and strategies contained herein may not be suitable for your situation. You should consult with a specialist where appropriate. Further, readers should be aware that websites listed in this work may have changed or disappeared between when this work was written and when it is read. Neither the publisher nor authors shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

Library of Congress Cataloging‐in‐Publication Data

Names: Du, Jincheng, editor. | Cormack, Alastair, N. editor.Title: Atomistic simulations of glasses : fundamentals and applications /  edited by Jincheng Du, University of North Texas, Denton, TX, USA,  Alastair N. Cormack, NYS College of Ceramics, Alfred University, Alfed,  NY, USA.Description: First edition. | Hoboken, NJ, USA : Wiley‐American Ceramic  Society, 2022. | “Published simultaneously in Canada.” | Includes  bibliographical references.Identifiers: LCCN 2022000615 (print) | LCCN 2022000616 (ebook) | ISBN  9781118939062 (cloth) | ISBN 9781118940235 (adobe pdf) | ISBN  9781118940242 (epub)Subjects: LCSH: Glass–Analysis–Mathematics. | Glass–Mathematical models.  | Chemical structure. | Molecules–Computer simulation. | Molecular  dynamics–Data processing.Classification: LCC QD139.G5 A86 2022 (print) | LCC QD139.G5 (ebook) |  DDC 620.1/44–dc23/eng20220301LC record available at https://lccn.loc.gov/2022000615LC ebook record available at https://lccn.loc.gov/2022000616

Cover Design: WileyCover Images: Courtesy of T.S. Mahadevan and Jincheng Du

List of Contributors

Silvia Barbi

Department of Science and Methods for Engineering

University of Modena and Reggio Emilia

Italy

Mathieu Bauchy

Physics of AmoRphous and Inorganic Solids Laboratory (PARISlab)

Civil and Environmental Engineering Department

University of California

Los Angeles, CA

USA

Jamieson K. Christie

Department of Materials

Loughborough University

Loughborough

UK

Alastair N. Cormack

Inamori School of Engineering

New York State College of Ceramics

Alfred University

Alfred, NY

USA

Jean‐Marc Delaye

Département de recherche sur les technologies pour l'Enrichissement

le Démantèlement et les Déchets

Commissariat à l'énergie atomique et aux énergies alternatives

Direction des Energies, Institut pour les Sciences et Technologies pour une Economie

Circulaire des Energies bas carbone

Bagnols‐sur‐Cèze CEDEX

France

Lu Deng

Department of Materials Science and Engineering

University of North Texas

Denton, TX

USA

David A. Drabold

Department of Physics and Astronomy

Nanoscale and Quantum Phenomena Institute

Ohio University

Athens, OH

USA

Jincheng Du

Department of Materials Science and Engineering

University of North Texas

Denton, TX

USA

Lijie Guo

National Centre for International Research on Green Metal Mining

BGRIMM Technology Group

Beijing

China

Christian G. Hoover

School of Sustainable Engineering and the Built Environment

Civil Engineering Department

Arizona State University

Tempe, AZ

USA

Yushu Hu

Physics of AmoRphous and Inorganic Solids Laboratory (PARISlab)

Civil and Environmental Engineering Department

University of California

Los Angeles, CA

USA

Shinji Kohara

Light/Quantum Beam Field

Research Center for Advanced Measurement and Characterization

National, Institute for Materials Science

Tsukuba, Ibaraki

Japan

N. M. Anoop Krishnan

Department of Civil Engineering

Indian Institute of Technology Delhi

New Delhi

India

and

Department of Materials Science and Engineering

Indian Institute of Technology Delhi

New Delhi

India

Han Liu

Physics of AmoRphous and Inorganic Solids Laboratory (PARISlab)

Civil and Environmental Engineering Department

University of California

Los Angeles, CA

USA

Xiaonan Lu

Pacific Northwest National Laboratory

USA

Thiruvilla S. Mahadevan

Department of Materials Science and Engineering

University of North Texas

Denton, TX

USA

Matthieu Micoulaut

Laboratoire de Physique Théorique de la Matière Condensée

Sorbonne Université

Paris Cedex 05

France

Monia Montorsi

Department of Science and Methods for Engineering

University of Modena and Reggio Emilia

Reggio Emilia

Italy

Gavin Mountjoy

School of Physical Sciences

University of Kent

Canterbury, Kent

UK

Francesco Muniz‐Miranda

University of Modena and Reggio Emilia

Department of Chemical and Geological Sciences

Modena

Italy

Alfonso Pedone

University of Modena and Reggio Emilia

Department of Chemical and Geological Sciences

Modena

Italy

Davide Presti

University of Modena and Reggio Emilia

Department of Chemical and Geological Sciences

Modena

Italy

László Pusztai

Wigner Research Centre for Physics

Hungarian Academy of Sciences (WRCP HAS)

Budapest

Hungary

Xusheng Qiao

School of Materials Science and Engineering

Zhejiang University

Hangzhou

China

Jessica M. Rimsza

Geochemistry Department

Sandia National Laboratories

Albuquerque, NM

USA

Morten M. Smedskjaer

Department of Chemistry and Bioscience

Aalborg University

Aalborg

Denmark

Francesco Tavanti

University of Modena and Reggio Emilia

Department of Chemical and Geological Sciences

Modena

Italy

Rajendra Thapa

Department of Physics and Astronomy

Nanoscale and Quantum Phenomena Institute

Ohio University

Athens, OH

USA

Xiuxia Xu

School of Materials Science and Engineering

Zhejiang University

Hangzhou

China

Kai Yang

Physics of AmoRphous and Inorganic Solids Laboratory (PARISlab)

Civil and Environmental Engineering Department

University of California

Los Angeles, CA

USA

Todd R. Zeitler

Geotechnology & Engineering Department

Sandia National Laboratories

Albuquerque, NM

USA

Junjie Zhao

Department of Materials Science and Engineering

University of North Texas

Denton, TX

USA

and

School of Materials Science and Engineering

Zhejiang University

Hangzhou

China

Qi Zhou

Physics of AmoRphous and Inorganic Solids Laboratory (PARISlab)

Civil and Environmental Engineering Department

University of California

Los Angeles, CA

USA

Preface

Computational materials science has evolved into an important branch of materials research, significantly contributing to all aspects of material design and discovery. This is especially true for inorganic glasses that find wide industrial and technological applications ranging from drinking vessels, window panes, and kitchenware in our everyday lives, to high technologies such as optical fiber communication, bioactive glasses for scaffolds, sealing glasses for fuel cells, and glass matrixes for nuclear waste disposal. Among various simulation methods used to study glass materials, atomistic simulations, both classical and quantum mechanical, play an important role in the understanding of complex structure of glasses and the structural origins of various glass properties.

Because of the lack of long‐range order, molecular dynamics and Monte Carlo methods have been used to study the structures of glasses and their melts ever since computer simulation emerged as a scientific method in the 1960s. The field has evolved rapidly over the past several decades due to ever‐increasing computational power and maturing of simulation algorithms, so the adoption of atomistic simulations of glasses has become more and more widespread in glass research, evidenced by its deployment in many university, industrial, and government laboratories.

With such a rapid growth in the applications of atomistic simulations, there has also been a concomitant increase in information accumulated in the literature. Although several textbooks are available on computational materials science or atomistic simulations in general, there lacks a reference and textbook that introduces the field of atomistic simulations of inorganic glasses: this is what initially motivated us to plan this book. We aim to provide a general introduction to the field of atomistic simulations of inorganic glass materials from simulation methodologies such as quantum mechanical and classical simulation methods and various approaches to analyzing the results, to a wide range of applications to different types of oxide glasses, e.g. silicates, phosphates, borosilicates, aluminosilicates, boroaluminosilicate, and nonoxide glass systems: halide and mixed anion glasses, as well as glass surfaces and glass–water interactions. With contributions from experts and active practitioners in the field, this book aims to provide a broad background of atomistic simulations of glass and amorphous materials to upper‐level undergraduate students, graduate and postdoctoral researchers, and industrial practitioners. Students and researchers in related fields such as crystalline materials, nanostructured materials, and in general materials with complex structures will also find the book a helpful reference.

The book is divided into two parts. The first part covers various atomistic simulation and analysis methodologies and it contains five chapters. Classical simulation methods, i.e. those that rely on interatomic potentials to describe the energetics of a system, are introduced in Chapter 1, while those related to quantum mechanical simulation methods are introduced in Chapter 2. Principles of Reverse Monte Carlo‐based glass simulations and examples of their applications to several glass and amorphous systems are presented in Chapter 3. Techniques available to analyze the results of atomistic simulations, such as structural characterization and the calculation of mechanical, dynamic, and other properties, are detailed in Chapter 4. Topological constraint theory and its coupling with atomistic simulations are discussed in Chapter 5.

The second part of the book describes the practical applications of atomistic simulations to various glass systems and it has 10 chapters. In most applications, both classical and first principles simulation methods are discussed.

Starting with a summary of the historical developments behind the rise of atomistic simulations to the study of glass materials in Chapter 6, simulations of silica and silicate glasses are covered in Chapter 7, borosilicate and boroaluminosilicate glasses in Chapter 8, in which the historical and latest developments of interatomic potentials for boron oxide are discussed. The most commonly used, including a few recently developed, borosilicate glasses potential parameters are compiled as Appendix in Chapter 8. Chapter 9 introduces simulations of multicomponent oxide glasses for nuclear disposal with simulations of related processes, such as radiation effects and glass alteration being presented. Chapter 10 covers simulations of phosphate glasses, ranging from phosphorous oxide, binary phosphate, aluminophosphate, and multicomponent glasses. Chapter 11 focuses on simulations of bioactive glasses, where traditional bioactive glasses such as 45S5, those modified with other oxides, and glass nanoparticles are covered. Chapter 12 introduces simulations of rare earth and transition metal‐containing glasses, with a discussion of methods to characterize local environments and distributions of these cations, their effect on dynamic and electronic properties, and QSPR analysis. Three practical applications: rare earth‐doped silicate and phosphate glasses for optical applications, transition metal‐containing phosphate glasses as mixed electrical conductors, and borosilicate glasses for nuclear waste disposal are described. Chapter 13 covers simulations of halide and oxyhalide glasses, with topics covering early simulations of fluoride glasses, atomistic‐level observation of phase separation, and its effect on nucleation and crystal growth. Chapter 14 covers simulations of glass surfaces and surface‐environment interactions. Lastly, Chapter 15 introduces simulations of silicate glass–water reactions, where topics include quantum mechanical studies of reaction mechanisms and energetics of silicate glasses and the development of reactive potentials and their application to glass–water reactions along with a discussion of current challenges and potential solutions.

We are quite aware that the field is still rapidly evolving, with notable recent developments of artificial intelligence and machine learning methods applying to many fields of glass science and technology including atomistic simulations. They have already applied in areas such as machine learning based potentials and potential refinement, which are briefly discussed in the book for example in Chapter 7, and machine learning of glass properties based on atomistic simulation results. As these topics are still developing hence we did not include them in this book. It is also worth noting that the applications part of the book focuses on inorganic glasses, and particularly oxide glasses as they are the most studied and most common in practical applications. Non‐oxide glasses such as halide and oxyhalide glasses are also covered (in Chapter 13) but other glass systems such as chalcogenide and bulk metallic glasses are not covered in the book due to space limitations.

This book would not be possible without the support of many, including those “behind the scene.” We would like first to thank all the contributors. We are well aware that they each have busy schedules and we are very appreciative that they found the time to contribute to the book, which we hope will become an important reference in the field. We would also like to thank Mario Affatigato and others on the publication committee of the American Ceramic Society whose request initially motivated us to this book project. We would also thank the CTC of International Commission on Glass (ICG) with its support for a series of international workshops on challenges of MD simulations of glass and amorphous materials organized by its technical committee (TC27 atomistic simulations) that have facilitated discussions and development of the field.

We hope you find this book a useful reference in learning about and applying atomistic simulations in studying inorganic glass materials.

Jincheng Du               Alastair N. Cormack

List of Abbreviations

Acronym or Abbreviation

What it stands for

3QMAS NMR

triple quantum magic angle spinning nuclear magnetic resonance

a

‐Si

amorphous silicon

AIMD

ab initio molecular dynamics

ASTM

American Society for Testing and Materials

AXS

anomalous X‐ray scattering

BAD

bond angle distribution

BAFS

barium aluminum fluorosilicate glass

BB

bond‐bending

BKS

van Beest–Kramer–van Santen

BMH

Born–Mayer–Huggins potential

BO

bridging oxygen

BOMD

Born–Oppenheimer molecular dynamics

BS

bond‐stretching

CAS

calcium aluminosilicates

CMAS

calcium magnesium aluminosilicates

CN

coordination number of atoms

CNAS

calcium sodium aluminosilicates

COMB

charge optimized many‐body potential

CPMD

Car–Parrinello molecular dynamics

CRN

continuous random network

CS

corner‐sharing

DBO

double‐bonded oxygen

DBX

Dell, Bray, and Xiao

DCR

diffuse charge reactive potentials

DFC

differential correlation function

DFT

density functional theory

DL_POLY

Daresbury Laboratory general purpose molecular dynamic simulation package

DOS

density of states

DT

Delaunay tetrahedron

ECMR

experimentally constrained molecular relaxation

EDFA

erbium‐doped fiber amplifier

EDOS

electronic density of states

EFG

electric field gradient

EMD

equilibrium molecular dynamics

EPR

electron paramagnetic resonance

EPSR

empirical potential structure relaxation

ES

edge‐sharing

EXAFS

extended X‐ray absorption fine structure

FD

fluid dynamics

FEAR

force‐enhanced atomic refinement

FEM

finite element analysis

FF

force field

FFT

fast Fourier transform

FFV

fractional free volume

FP

fluoride phosphate glass

FSDP

first sharp diffraction peak

FTIR

Fourier‐transform infrared

FV

free volume

FWHM

full width at half maximum

g

‐SiO

2

glassy silica

GAP

Gaussian approximation potential

GFA

glass‐forming ability

GGA

generalized gradient approximation

GIPAW

gauge‐including projector augmented wave

GST

Ge

2

Sb

2

Te

5

GULP

General Utility Lattice Program

GW

Hedin's GW method for electronic structure properties

HF

Hartree–Fock

HOMO

highest occupied molecular orbital

HSE06

Hyed–Scuseria–Ernzerhof hybrid functional

IPR

inverse participation ratio

IR

infrared

IRO

intermediate‐range ordering

ISG

international simple glass

kMC, KMC

kinetic Monte Carlo

KNCMFATS

potassium, sodium, calcium, magnesium iron, and titanium oxide containing silicates

l

‐P

liquid phosphorus

l

‐Si

liquid silicon

l

‐SiO

2

liquid silica

L–J, LJ

Lennard–Jones

LAMMPS

large‐scale atomic/molecular massively parallel simulator

LD‐DFT

ligand field density functional theory

LDA

local density approximation

LED

light emitting diode

LRO

Long‐range order

LUMO

lowest unoccupied molecular orbital

MAE

mixed alkali effect

MAS

magic angle spinning

MAS–NMR

magic angle spinning nuclear magnetic resonance

MC

Monte Carlo

MD

molecular dynamics

MFA

mean‐field approximation

ML

machine‐learning

MM

molecular mechanics

MP2

2nd order Møller–Plesset perturbation theory

MQ

melt quench

MQ‐MAS

multiple‐quantum magic angle spinning

MRN

modified random network

msd, MSD

mean square displacement

NAPF

sodium alumino‐phospho‐fluorides

NAS

sodium aluminosilicates

NBO

non‐bridging oxygen

NBOHC

non‐bridging oxygen hole centers

NC

network connectivity

ND

neutron diffraction

NEMD

non‐equilibrium molecular dynamics

NMR

nuclear magnetic resonance

NPT

constant number of atoms N, constant pressure P, constant temperature T ensemble

NVE

constant number of atoms N, constant volume V and constant energy E ensemble

NVT

constant number of atoms N, constant volume V and constant temperature T ensemble

OLCAO

orthogonalized linear combination of atomic orbitals

OLP

overlapping polarons tunneling

ONIOM

own N‐layer integrated molecular orbital molecular mechanics

PAF

principal axis frame

PALS

positron annihilation lifetime spectroscopy

PAW

projected augmented wave

PBC

periodic boundary conditions

PBE

Perdew–Burke‐Ernzerhof (exchange‐correlation functional)

PBG

phosphate‐based glasses

PD

persistence diagram

PES

potential energy surface

PME

particle mesh Ewald

PMMCS

Pedone‐Malavasi‐Menziani‐Cormack‐Segre potentials

POHC

phosphorous oxygen hole center

PP

pseudo potential or principal peak

QE

Quantum Espresso, an open‐source electronic structure calculation code

QM

quantum mechanical

QPM

quasi‐periodic models

QSPR

quantitative structure–property relationship

RDF

radial distribution function

RE

rare earth

REAPDOR

rotational echo, adiabatic passage, double resonance nmr

ReaxFF

Reactive Force Field

REDOR

rotational echo double resonance nmr

RF

resonance frequency

RI

rigid‐ion

RMC

reverse Monte Carlo

RSL

Rahman–Stillinger–Lemberg

SANS

small angle neutron scattering

SAXS

small angle X‐ray scattering

SM

shell model

SPC

space projected conductivity or simple point charge model for water

SPME

smooth particle‐mesh Ewald

SRO

short‐range order

STM

scanning tunneling microscopy

TBO

triply bonded oxygen or terminally bonded oxygen

TCAF

transverse‐current autocorrelation‐function

TCF

total correlation function

TCT

topological constraint theory

TD‐DFT

time‐dependent density functional theory

TDF

total distribution function

TEM

transmission electron microscopy

TM

transition metal

TMO

transition metal oxide

TMS

tetramethylsilane

TO

transverse optical frequency

TSSF

total scattering structure factor

UV

ultraviolet

VAC

velocity autocorrelation

VACF

velocity autocorrelation function

VASP

Vienna ab initio Simulation Package

VDOS

vibrational density of states

VIPR

vibrational inverse participation ratio

VPG

vanado‐phosphate glasses

VSD

void size distribution

XANES

X‐ray absorption near‐edge structure

XPS

X‐ray photoelectron spectroscopy

XRD

X‐ray diffraction

Y&B

Yun and Bray model for borosilicate glass

YDB

Yun–Dell–Bray model for borosilicate glass

ZBL

Ziegler–Biersack–Littmark potentials

ZBLAN

ZrF

4

‐BaF

2

‐LaF

3

‐AlF

3

‐NaF fluoride glasses

ZPVE

zero‐point vibrational energy

Part IFundamentals of Atomistic Simulations

1Classical Simulation Methods

Alastair N. Cormack

Inamori School of Engineering, New York State College of Ceramics, Alfred University, Alfred, NY, USA

1.1 Introduction

Materials science is concerned with structure–property relations of (solid) materials with a view to engineering new materials with specific properties. Glasses are a subset of materials which are in widespread use, because of their properties, ranging from bottles and jars, and drinking vessels, on the one hand, to windows and electronic displays on the other. Glass fibers are used as thermal insulation in buildings, to strengthen wind turbine blades, and in telecommunications, with optical fibers replacing the previously ubiquitous copper cabling.

It is clearly desirable to have a thorough and complete understanding as possible of glass as a material. Perhaps surprisingly, given that it has been known as a man‐made material for millennia, we know less about the materials science of glass than we do about some more modern materials. In large part, this is because of its disordered atomic structure which makes it difficult to probe experimentally in the same way that the more widespread crystalline materials can be investigated.

The principal, defining, characteristic of glasses is, as just noted, their structural disorder at the atomic scale. There is an ASTM definition of a glass [1], (An inorganic product of fusion which has been cooled to a rigid condition without crystallizing) basically positing that a glass is a material which has been cooled from a melt to a solid at a rate which prevents crystallization. Usually known as “melt‐quench,” this is the process which has been used since glasses were first made. whilst the melt is in thermal equilibrium, the solid is not; the disorder inherent in the dynamics of the melt is retained in the glass. The simple ASTM definition has been challenged recently as being inadequate; certainly, it has not changed much, if at all from its 1945 version. For example, it does not include glasses produced by other processing routes, such as the sol–gel process. In that process, the initial solution is made at room temperature (or close to it) and then dried to a gel, which, in turn, is heated to drive off residual water molecules. No melting is involved, so the temperatures are usually lower than those associated with the melt in the traditional melt‐quench process.

In both processes, however, the final glass has a disordered atomic structure, introduced at the initial stages of processing. This disorder is associated with a lack of long‐range translational symmetry, i.e. the glasses are noncrystalline, as well as being out of thermal equilibrium. Although, in this chapter, we are primarily concerned with inorganic glasses, there are glassy solid polymers and metallic glasses. The general discussion of the molecular dynamics (MD) technique is equally applicable to these other glasses, except, of course, that because the nature of bonding is different, the description of their interatomic forces will also be different. Most, if not all, of the applications noted earlier employ glasses with chemistries based on silica, SiO2, with additional oxide components, such as alumina, boron oxide, alkali oxides, alkaline earth oxides among others. Indeed, one of the main attractions is the wide diversity of chemistries that can be made into glass. That diversity brings with it a wide range of properties that can be tuned by adjusting the compositions by fine degrees which are not possible with crystalline materials.

Figure 1.1 compares, in (a), the ordered, crystalline structure of cristobalite, a polymorph of silica, and in (b) the disordered structure of vitreous silica, from an MD simulation. The differences are clear.

It is a foundational premise of solid‐state physics that, in order to be able to engineer materials with better, or specific, properties, it is necessary to know their atomic structure. With this, and an understanding of the interatomic forces, it is possible to calculate all the physical and thermodynamic properties of the solid.

The challenge for glass science is that because of their noncrystalline nature, it is not possible to determine their atomic structure completely from experimental methods, such as diffraction. Other approaches are therefore necessary, if the structure–property relationships of glasses are not to remain entirely empirical in nature. This is the role that has been fashioned for atomistic simulations.

Figure 1.1 Comparison of the ordered structure of cristobalite (a), and the disordered structure of vitreous silica (b).

The simulations provide a numerical way of probing the statistical mechanical phase space of the glassy materials. The resulting structures and their properties are, technically, ensemble averages, that is, they are averaged over the points in phase space. In the next section, the basics of the two types of atomistic simulation techniques, MD and Monte Carlo (MC) methods, which have been applied to glasses will be discussed.

1.2 Simulation Techniques

Simulations have sometimes been called numerical experiments, but that view has been challenged epistemologically on the grounds that they do not provide new knowledge of the physical world in the way that experiments do [2]. Philosophically, science is concerned with producing predictive explanations of nature and simulations are investigations, or tests, of these predictive explanations, or physical models, using computational methods.

The physical basis for the simulations lies in statistical mechanics and, more importantly, the models used to describe the interatomic forces in the glasses.