COMPOSITION AND TEMPERATURE EFFECTS ON

ALUMINOBOROSILICATE GLASSES STRUCTURE AND PROPERTIES

A DISSERTATION

SUBMITTED TO THE DEPARTMENT OF GEOLOGICAL AND

ENVIRONMENTAL SCIENCES

AND THE COMMITTEE ON GRADUATE STUDIES

OF STANFORD UNIVERSITY

IN PARTIAL FULFILLMENT OF THE REQUIREMENTS

FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

Jingshi Wu

July 2011

http://creativecommons.org/licenses/by-nc/3.0/us/

This dissertation is online at: http://purl.stanford.edu/vr481rq0093

© 2011 by Jingshi Wu. All Rights Reserved.

Re-distributed by Stanford University under license with the author.

This work is licensed under a Creative Commons Attribution-Noncommercial 3.0 United States License.

ii

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I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Jonathan Stebbins, Primary Adviser

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Dennis Bird

I certify that I have read this dissertation and that, in my opinion, it is fully adequatein scope and quality as a dissertation for the degree of Doctor of Philosophy.

Gordon Brown, Jr

Approved for the Stanford University Committee on Graduate Studies.

Patricia J. Gumport, Vice Provost Graduate Education

This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file inUniversity Archives.

iii

iv

v

Abstract

This works studies the effects of compositional and temperature variations on

the structure and properties of aluminoborosilicate glasses. Two groups of

aluminoborosilicate glasses, one that has lower boron content and another that has

higher boron content, have been studied. The structural changes were mainly observed

with high-field 11B, 27Al and 23Na magic angle spinning (MAS) nuclear magnetic

resonance (NMR) spectroscopy. In these glasses, boron is either three-coordinate

(BO3) or four-coordinate (BO4); aluminum exists predominately as four-coordinate

species, but there is a small amount of five-coordinate aluminum ([5]Al). The

compositional study focused on the effect of the cation field strength of the network

modifiers on the glass structure by varying the ratio of the two network modifiers,

CaO and Na2O. Increasing the ratio of CaO to Na2O dramatically lowers the fraction

of four-coordinated boron (N4), increases [5]Al, and increases the fraction of non-

bridging oxygens (NBO), which was calculated based on the boron and aluminum

structural information. However, variations in these fractions are not linear with

respect to the average cation field strength. 23Na spectra reveal that the ratio of

bridging to non-bridging oxygens in the coordination shell of Na+ increases with an

increasing ratio of CaO to Na2O in Ca-rich glasses. These changes can be understood

by the tendency of higher field strength modifier cations to facilitate the concentration

of negative charges on NBO in their local coordination environment, systematically

converting BO4 to BO3. The effect of temperature on the structure was studied by two

ways: cooling the glass-forming melts at different rates to sample the glass structure at

different fictive temperature, and using high-temperature in situ NMR. The

abundances of BO3 and NBO increase with increasing fictive temperature, suggesting

that the reaction BO4 ↔ BO3 + NBO shifts to the right with increasing temperature.

The observed temperature dependence of the abundance of BO4 species allows us to

estimate the enthalpy of reaction, ∆H, which is closely related to the amount of NBO

in the glass. In situ high-T 11B MAS NMR was used to observe chemical exchange

between BO3 and BO4 species over the timescale of microseconds to seconds. The

timescale of BO3/BO4 exchange from NMR data, τNMR, appears to be “decoupled”

vi

from that of the macroscopic shear relaxation process, τs, derived from the viscosity

data; however, at higher temperatures, τs approaches τNMR. The “decoupling” at lower

temperature may be related to intermediate-range compositional heterogeneities, and

/or fast modifier cation diffusivities, which trigger “unsuccessful” network exchange

events.

vii

Acknowledgements

Thank you to Jonathan Stebbins for being a great advisor and spending large

amounts of time training me in the lab, discussing research ideas, and answering my

questions. He has always encouraged me to ask questions, and helped to establish

collaboration with other labs and people to assist me in completing my research.

Additionally, he has been so patient with editing my papers, correcting my grammar

and word usage, and helping me to practice every oral presentation.

Thanks also to Dennis Bird, Gordon Brown, and Bruce Clemens for serving on

my research committee and attending all of my research committee meetings,

especially Dennis and Gordon who also served as my reading committee. Their advice

has provided significant insights that improved the quality of my research. Thanks as

well to Alberto Salleo for agreeing to chair my defense.

My research has benefited greatly from the other scientists in Jonathan’s NMR

group: Namjun Kim, Luming Peng, Lin-Shu Du, Koji Kanehashi, TJ Kiczenski, Jeff

Allwardt, Emily Dubinsky, Kim Kelsey, Linda Thompson, Aaron Palke, and Elizabeth

Morin. In particular, thanks to Namjun Kim and Luming Peng for their help in setting

up and conducting numerous NMR experiments. Many thanks to Kim Kelsey for

helping to prepare my qualifying exam. Thanks as well to Romain Gaumé and

Stephen Podowitz for helping me set up experiments with a difference scanning

calorimeter, and Guangchao Li for helping analyze glass composition with an

inductively coupled plasma mass spectrometer. Specifically, thanks to TJ Kiczenski

and Marcel Potuzak for getting some experiments done at Corning Incorporated and

for their useful discussion about my research.

Thank you Elaine Anderson, Lorraine Sandoval, Arlene Abucay and the rest of

the GES department staff for helping me deal with administrative details, lab supply

orders, and other financial details.

Thanks to my parents for their strong support of all important decisions I have

made in my life. Finally, thank you to my husband, Chad, for his supports during my

six years long Ph.D. process and countless editing of my writings.

viii

ix

Table of Contents

Abstract v

Acknowledgements vii

Table of contents ix

List of Tables xiii

List of Figures xiv

Chapter One: Introduction 1

Background 2

Application of NMR spectroscopy to the study of boron-

containing glass structure and dynamics

5

Two methods for studying glass-forming liquid structure at

different temperatures

6

Questions to be addressed by this thesis 7

Contents of this Thesis 7

Chapter 2 7

Chapter 3 8

Chapter 4 9

Chapter 5 9

Appendix 10

Additional collaborative work not presented in dissertation 10

References 11

Chapter Two: Effects of cation field strength on the structure of

aluminoborosilicate glasses: high-resolution 11B, 27Al and 23Na

MAS NMR

15

Abstract 16

Introduction 17

x

Experimental 20

Sample preparation 20

NMR data collection and analysis 20

Results 21 11B MAS NMR 21 27Al MAS NMR 21 23Na MAS NMR 22

Oxygen speciation 23

Discussion 24

Effect of modifier cation on network cation coordination 24

Effect of boron content 26

Sodium cation environments 28

Other compositional effects 28

Conclusions 29

Acknowledgements 30

References 30

Chapter Three: Quench rate and temperature effects on boron

coordination in aluminoborosilicate melts

47

Abstract 48

Introduction 49

Experimental 53

Sample synthesis 53

Heat capacity measurements 55

Fictive temperature (Tf) determination 55

NMR spectroscopy 57

Results 57 11B, 27Al and 23Na MAS NMR 57

Thermodynamic calculations 60

xi

Discussion 61

Temperature effects on boron coordination 61

Cp effects of boron coordination changes 65

Implications of other structural changes 68

Changes of [3]B site populations 68

Network-former cation mixing 70

Aluminum coordination changes 71

Conclusions 72

Acknowledgements 72

References 73

Chapter Four: Temperature calibration for high-temperature MAS

NMR to 913 K: 63Cu MAS NMR of CuBr and CuI, and 23Na MAS NMR

of NaNbO3

95

Abstract 96

Introduction 97

Experimental 98

Results and discussion 100

Temperature calibration 100

CuBr 101

CuI 102

NaNbO3 104

Conclusions 104

Acknowledgements 105

References 105

Chapter Five: High-temperature in situ 11B NMR study of network

dynamics in boron-containing glass-forming liquids

115

Abstract 116

Introduction 117

xii

Experimental 119

Sample synthesis 119

Specific heat capacity measurement 120

Activation enthalpy and fictive temperature (Tf)

determination

121

NMR spectroscopy 122

Results 122

Activation enthalpy and fragility 122

Fictive-temperature effects 124

Species exchange 125

Discussion 127

Effect of temperature on liquid structure 127

Dynamics of species exchange and its relation to viscous

relaxation and flow

128

Conclusions 132

Acknowledgement 133

References 133

Appendix: Quench rate and temperature effects on boron coordination in

Ba-aluminoborosilicate melts

149

Introduction 150

Experimental 150

Results 151

Discussion 152

Acknowledgements 153

Reference 153

xiii

List of Tables

Table 2.1 Nominal compositions of samples, in mol% 39

Table 2.2 NMR results for fractions of [4]B and [5]Al, and calculated

NBO fractions among total oxygens

40

Table 2.3 Peak positions and mean values of chemical shifts and

quadrupolar parameters derived from 23Na NMR

41

Table 3.1 Activation energies for relaxation near to Tg, and

estimated fictive temperatures

81

Table 3.2 N4 and NBO values for different cooling methods, and

the corresponding reaction enthalpy

82

Table 3.3 Configurational heat capacities from DSC data, and those

contributed by the boron coordination change reaction

83

Table 5.1 Sample compositions from ICPMS analysis 140

Table 5.2 Results from DSC data 141

Table 5.3 NB37 fictive temperature and N4 at different cooling rate 142

Table A.1 Results of activation energy, glass transitions, and fictive

temperatures.

154

Table A.2 NMR results from 11B MAS, 27Al MAS, and 17O MAS 155

xiv

List of Figures

Figure 2.1 11B MAS spectra for the low boron series and high boron

series glasses collected at 14.1 T

42

Figure 2.2 27Al MAS spectra for the low boron series and high

boron series glasses collected at 18.8 T

43

Figure 2.3 23Na MAS spectra for the low boron series and high

boron series glasses collected at 18.8 T

44

Figure 2.4 NMR results for two series of aluminoborosilicate glass 45

Figure 3.1 The heat capacity curves for water-cooled CABS21 glass 84

Figure 3.2 11B MAS NMR spectra at 14.1 T 85

Figure 3.3 Contour plot of the 11B 3QMAS NMR (14.1 T) spectrum

for CABS21FQ-AN glass

86

Figure 3.4 Isotropic projections of 11B 3QMAS NMR spectra 87

Figure 3.5 Isotropic projections of 11B 3QMAS spectra and fitting

results for CABS21FQ-AN glass

88

Figure 3.6 27Al MAS NMR at 18.1 T 89

Figure 3.7 Observed and predicted proportion of N4 and NBO vs.

temperature

90

Figure 3.8 Plot of ∆H vs. NBO and

!

Cpconf (B) vs. NBO 91

Figure 3.9 Plot of fraction of NBO vs. temperature at η = 109 Pa·s.

R = [Na2O]/[B2O3] and K=[SiO2]/[B2O3], and plot of

fraction of NBO vs. Tg. K=[SiO2]/[B2O3]

92

Figure 3.10 Estimated contribution to heat capacity from boron

species changes as a function of temperature

93

Figure 4.1 63Cu MAS NMR spectra for CuBr at different

temperatures

108

Figure 4.2 63Cu MAS NMR spectra for CuI at different

temperatures

109

xv

Figure 4.3 Phase transition temperatures of NaNbO3, CuBr and CuI

plotted against display temperatures; and temperature

corrected with 207Pb chemical shift of Pb(NO3)2

110

Figure 4.4 Plot of the 63Cu peak maxima for CuBr at different

temperatures

111

Figure 4.5 Plot of the 63Cu peak maxima for CuI at different

temperatures

112

Figure 4.6 23Na MAS NMR linewidth and ratios of central peak to

eighth sideband intensity in NaNbO3 near the phase

transition at 913 K

113

Figure 5.1 Heat capacity curves for water-cooled NB37 glass 143

Figure 5.2 11B MAS NMR spectra at 14.1 T for NB37, with 20 kHz

spinning speed, for glasses with three different cooling

rates

144

Figure 5.3 High-temperature in situ 11B MAS NMR spectra for a

sodium aluminoborosilicate glass (NABS21), and the

simulations of each spectra

145

Figure 5.4 High-temperature in situ 11B MAS NMR spectra for a

sodium borate glass (NB37), and the simulations of each

spectra

146

Figure 5.5 DSC data for the heat capacity of NB37 up to 1000 K 147

Figure 5.6 Inverses of boron species exchange rate data derived

from 11B NMR spectra, compared with shear relaxation

times calculated from estimated viscosities

148

Figure A.1 11B MAS NMR at 14.1 T 156

Figure A.2 27Al MAS NMR at 18.8 T 157

Figure A.3 17O MAS NMR at 14.1 T 158

xvi

1

Chapter One

Introduction

2

Background

Aluminoborosilicate glasses are interesting because of their technological

importance (e.g. use in flat panel display substrates, fiber glass, and photochromic

glass) and their wide range of structural and dynamic questions that remain

unanswered. Boron is unique as a “network former” in that it can readily change

between being three or four coordinated by oxygen as composition and temperature

are changed. The exchange between these two coordination sites may be the source of

thermodynamic property changes, i.e. viscosity, melting point, and glass transition

temperature. Quantitative determinations of the atomic-scale structure of

aluminoborosilicate glasses, and the effects of composition and temperature on

structure, are critical parts in the development of physically accurate models of glass

and glass melt properties. Gaining a better understanding of the composition-property

relationships will allow production of glasses better able to meet the requirements of

specific applications.

The structures of oxide glasses lack long-range atomic ordering, but do exhibit

some degree of short-range ordering. This structural ordering is described and

quantified in terms of polyhedra whose apices are the oxygen atoms bonded to a given

cation. Some types of polyhedra are network-formers, which contain small and highly

charged cations (Si4+, Al3+, B3+, etc…) that compete more effectively to bond with

oxygen and link together to provide a framework structure than do network modifiers.

Other kinds of polyhedra in oxide glasses form comparatively weaker bonds with

oxygen (Na+, K+, Ca2+, Mg2+, etc.). Those alkali metals and alkaline earths play dual

structural roles. One of these roles is to serve as network-modifiers. In this sense, these

cations are linked to terminal oxygens on tetrahedra. The other role is to charge-

compensate cations such as tetrahedral B3+ and Al3+. The polyhedral units of such

network cations link in various ways via corner-shared oxygens; bridging oxygens

(BO) link together two network-formers (e.g. Si-O-Si, Si-O-Al, Si-O-B); non-bridging

oxygens (NBO) link one network-former to one or more network-modifiers (e.g. Si-O-

Na, B-O-Na). The relative abundance of weakly bonded NBOs is critical in

3

determining the thermodynamic and dynamic properties of aluminoborosilicate

glasses and melts.

Within a boron-containing glass, boron atoms may bond in two basic ways.

B3+ may be coordinated by four oxygen atoms (BO4 groups, denoted here as [4]B). In

this case the fraction of four-coordinated boron among total boron species is N4. Or,

B3+ may be coordinated by three oxygen atoms (BO3 groups, denoted here as [3]BS),

and the fraction of this configuration among total boron species is designated as N3S.

Three coordinated boron may also have one or two NBOs (asymmetric BO3 groups,

denoted here as [3]BA), the fraction this specie is represented by N3A. Unlike in

silicates, when modifiers oxides are initially added to B2O3, most, if not all, [3]B is

converted to [4]B without the formation of NBO. If enough modifiers are added, four-

coordinated boron atoms begin to convert to asymmetric BO3 groups. However, both

the beginning point and the rate of this process depend strongly on the composition

(Dell et al. 1983).

Since an increase in modifier species could introduceNBO into the system, this

change has been hypothesized by the structural reaction [3]B +NBO ⇔ [4]B (1).

At low contents of modifier oxides in boron-rich glasses, this reaction is nearly

complete (Araujo 1983; Bunker et al. 1990; Dell et al. 1983; Yun and Bray 1978). At

high modifier contents, the reaction tends to shift to the left, in part to avoid formation

of [4]B-O-[4]B and [4]B-O-[4]Al species, which is relatively energetically unfavorable

since the bridging oxygen atoms have higher net negative charges (Abe 1952; Wang

and Stebbins 1999). Higher modifier cation field strength favors the formation of

NBO and pushes the reaction to the left (Du and Stebbins 2005; Kiczenski et al. 2005;

Sen et al. 1998; Stebbins and Ellsworth 1996).

In aluminoborosilicate glass, aluminum as one of the network formers adds

more complexity into the glass structure. Aluminum in peralkaline glasses generally is

predominantly [4]Al, but high field 27Al NMR spectra have revealed significant [5]Al,

especially in glasses with divalent modifier cations (Du and Stebbins 2005; Loshagin

and Sosnin 1994). The B2O3 and Al2O3 compete with each other to join the alkali or

4

alkaline-earth oxides in order to transform [3]B to [4]B and [5]Al to [4]Al in the melt (Du

et al. 2000).

When temperature increases, reaction (1) moves to the left with a

corresponding increase in the amount of the [3]B and NBO. Temperature effects on

boron coordination and the corresponding changes in concentration of NBO have been

suggested to be controlling factors in the viscosity of sodium borosilicate glass-

forming melts (Abe 1952; Araujo 1980). The success of the Adam-Gibbs theory in

relating configurational entropy to the viscosity of silicate melts has demonstrated a

key connection between configurational entropy and relaxation properties. The theory

relates the viscosity to the melt structure through the general equation (Mysen and

Richet 2005; Toplis et al. 1997)

!

log"(T) = Ae +Be

TSconf (T) (2)

where η(T) is the viscosity, Ae and Be are constant for each melt composition, and

Sconf(T) is the configurational entropy of the melt at absolute temperature T.

Quantifying short- and intermediate-range order in glass structure is necessary for

determining the ultimate cause of variations in the configurational heat capacity

(CPconf) with temperature.

At temperatures above the glass transition temperature, not only does the

proportions of [3]B and [4]B change according to reaction (1), but also chemical

exchange happens between boron species (Stebbins and Ellsworth 1996). This

exchange becomes more rapid with increasing temperature. BO3-BO4 exchange

involves breaking and re-forming strong B-O bonds, which could be an important part

of what controls diffusion of network components and viscosity. Previous high-

temperature (high-T) 11B MAS NMR studies show that the BO4-BO3 exchange rates

are close to the shear relaxation rates calculated from the bulk viscosity data (Stebbins

and Sen 1997; Stebbins and Sen 1998).

5

Application of NMR spectroscopy to the study of boron-containing glass:

structure and dynamics

Nuclear Magnetic Resonance (NMR) spectroscopy has been a useful tool for

examining the structure of molecules in solution since the 1960’s. Obtaining detailed

structural and dynamic information on the nature of disordered solid phases became

accessible to NMR spectroscopy in the late 1980s with the development of very high

field superconducting magnets (above 9.4 T) and application of magic-angle spinning

(MAS), which averages out the first-order quadrupolar interaction by spinning sample

at 54.74°. This yields spectra that reflect the local (nearest and next-nearest neighbor)

structural and chemical environments of a particular nucleus. 11B NMR has long been one of the major tools for studying the short-range

structure of borate and borosilicate glasses. Early work with 11B wide-line NMR (low-

resolution measurements at low external fields) characterized the fractions of N4, N3S

and N3A and led to detailed structural models of sodium borosilicate glasses with

various compositions (Dell et al. 1983; Silver and Bray 1958; Yun and Bray 1978).

High-resolution 11B MAS NMR at higher magnetic fields (above 11.7 T) offers

complete resolution of the [3]B and [4]B sites, and provides information on isotropic

chemical shifts, which can potentially provide additional structural insights when

correlated with coordination numbers, bond angles, and distances (Kroeker and

Stebbins 2001). To obtain more detailed structural information, especially on [3]B

sites, 11B triple-quantum MAS NMR (3Q MAS) is a very useful tool. One main

advantage of 3Q MAS NMR is that it produces a two-dimensional spectrum that

permits separation and measurement of isotropic chemical shift that is free of second-

order quadrupolar broadening. The improvement in resolution provided by 11B 3Q

MAS in comparison to 11B NMR allows the derivation of more accurate quadrupolar

parameters and concentrations for the various types of [3]B sites. 17O MAS NMR complements 11B NMR. Directly quantifying the NBO

distribution by 17O MAS NMR helps in constraining the topological contributions of

oxygen with different neighbors. Meanwhile, 27Al MAS NMR is also important in

6

studies of aluminoborosilicate glasses, and it helps in observing and quantifying

different species of aluminum.

Two methods for studying glass-forming liquid structure at different

temperatures

The first method involves studying glasses formed by quenching from the

liquid to the glassy state at different rates. A liquid that is more rapidly quenched cools

to the glassy state at a higher glass transition temperature. The temperature at which

the structure of the glass and liquid are approximately the same is defined as the

fictive temperature (Tf), which has logarithmic dependence on the rate of cooling, q,

such that

dln|q|/d(1/Tf ) = – ΔH*/R (3)

where ΔH*is the activation enthalpy, and R is the ideal gas constant (Moynihan et al.

1976). The glass transition temperature is the fictive temperature achieved when

cooling the melt at a rate of 10 K/min. It has long been found that a decrease in N4/N3

with increasing Tf exists in boron-containing glasses (Bray and Holupka 1985; Du and

Stebbins 2003; Kiczenski et al. 2005; Sen et al. 1998; Wu and Stebbins 2010). A

decrease in [4]B and a small increase in NBO content were observed in

aluminoborosilicate glasses (Kiczenski et al. 2005; Wu and Stebbins 2010). Earlier

research (Sen 1999; Sen et al. 1998) also showed that structural changes in borate

melts can happen between different three-coordinated boron species, which be written

in the form of speciation reactions, such as

BO3 ring ⇔ BO3non-ring (4)

Reaction (4) is the disintegration of six-members boroxol rings (B3O6) into non-ring

BO3 units.

The enthalpy changes (ΔH) associated with any of these speciation reactions

can be estimated by using the van’t Hoff equation,

!

"H = #RlnK1 # lnK2(1/Tf1 ) # (1/Tf1 )

$

% & &

'

( ) )

(5)

7

In this expression R is the gas constant, and K1 and K2 are the equilibrium constants of

a speciation reaction at two different temperatures, T1 and T2. The observed

dependence on temperature of the abundances of different species allows us to

estimate the ΔH of the reactions maintained above, and the experimental data can be

used to estimate the contributions to configurational heat capacity (CPconf) arising from

different reactions. Comparing the CPconf from individual speciation reactions with the

total CPconf determined by calorimetric or viscosity measurements will help to

constrain which reaction provides the major source of CPconf and how much CPconf each

reaction contributes (Dubinsky and Stebbins 2006; Sen 1999; Sen et al. 1998).

The second method to study glasses and glass-forming liquids at high

temperature is to use high-T in situ NMR spectroscopy. This is a unique method for

characterizing dynamics that control the liquid properties. High-T MAS NMR is now

routinely possible at temperatures as high as 973 K. The much higher resolution

obtainable in contemporary MAS experiments allows more rapid data collection and

permits slow exchanges between [3]B to [4]B be observed, which allows the

quantification of the dynamics of boron speciation processes occurring at temperatures

close to Tg.

Questions to be addressed by this thesis

How does cation field strength affects the atomic structure of

aluminoborosilicate glasses?

What are the quench rate and temperature effects on boron coordination in

aluminoborosilicate melts?

How does micro-structure in boron-containing melts relate to viscous flow?

Contents of this thesis

Chapter 2:

This chapter utilizes 11B MAS, 27Al MAS, and 23Na MAS NMR to investigate

the effects of variations in cation field strength on the atomic structure of

aluminoborosilicate glasses. Two series of aluminoborosilicate glasses, one that has

8

low boron content and another that has high boron content, have been studied. The

modifier cations include sodium and calcium. While the total amount of modifier

cations was kept constant (weighted by charge, i.e. 2Na+ = 1Ca2+), the ratio of

Na2O/CaO was varied to achieve a range of different average cation field strengths.

The spectra clearly show a decrease in N4 and an increase in NBO and in [5]Al with an

increase in the average cation field strength, but the effects are non-linear. The average

Na-O distance increases with the average cation field strength (an increase in CaO

content), suggesting that in Ca-rich glasses, Na+ has a higher ratio of BO to NBO in its

first coordination shell. All of these changes can be understood by the tendency of

higher field strength modifier cations to facilitate the concentration of negative

charges on the NBO in their local coordination environment, systematically converting

four- to three-coordinated boron. This work has been published in Journal of Non-

crystalline Solids (Wu and Stebbins 2009b).

Chapter 3:

This chapter represents the first time we observed the modifier cation

(Ca2+/Na+) field strength effect on the value of the enthalpy changes (ΔH) associated

with the changes in boron speciation in reaction (1). Glass samples were prepared with

four different cooling rates and thus four different fictive temperatures. The abundance

of [3]B groups and NBO increased with increasing fictive temperature. The structural

information was sampled from four different fictive temperatures with 11B MAS

NMR. The estimated ΔH values from equation (5) for reaction (1) have much smaller

uncertainties in comparison with previous studies that only sampled glasses formed at

two different fictive temperatures (Dubinsky and Stebbins 2006; Sen et al. 1998;

Stebbins and Ellsworth 1996). In this study, the ΔH ranged from 24 to 50 kJ·mol-1 in

different glass compositions and was closely related to the amount of NBOs, which is

greatly affected by the modifier cation field strength, as our results showed in Chapter

2. For the aluminoborosilicate glasses we studied here, the redistribution of boron

species (BO3/BO4) contributes 7% to 30% of the total configurational heat capacities,

9

which has been measured by differential canning calorimetry. This work has been

published in Journal of Non-crystalline Solids (Wu and Stebbins 2010).

Chapter 4:

This chapter describes a new method of temperature calibration for high-

temperature MAS NMR. This is the first time we were able to calibrate the MAS

probe temperature up to 913 K. In the past, the temperature was calibrated by

measuring the chemical shifts of 207Pb in Pb(NO3)2 (Bielecki and Burum 1995;

Takahashi et al. 1999), but this material decomposes above 720 K. We used 63Cu and 23Na to observe the solid-solid phase transitions in CuBr, CuI and NaNBO3. We

observed dramatic chemical shift changes at each solid-solid phase transition of

cuprous halides, and large peak intensity changes at the tetragonal-cubic transition of

NaNBO3. These data were used to calibrate the high-T MAS NMR probe in our lab.

Dr. Kim helped me to collect the high-T MAS NMR spectra. This work has been

published in Solid State Nuclear Magnetic Resonance (Wu et al. 2011).

Chapter 5:

In this chapter a combined high-T in situ 11B MAS NMR and ambient

temperature 11B MAS NMR study of two boron-containing glasses was undertaken.

The BO3-BO4 chemical exchanges have been observed in high-T in situ 11B MAS

NMR above the glass transition temperatures. The exchange rates were compared with

shear relaxation rates calculated from the bulk viscosity, and the exchange rates were

decoupled from the viscosity curve at relatively low temperature, but the divergence

became less prominent with increasing temperature. The “decoupling” of BO3/BO4

exchange rates with shear relaxation rates may be caused by the fast modifier cation

diffusion at lower temperatures. I synthesized the two glasses we studied in this

chapter and collected the high-T 11B NMR data with help of Dr. Kim. I also did the

spectra simulation to obtain the exchange rates, and the simulation program is by

courtesy of Prof. Sen at UC Davis. Dr. Potuzak at Corning Inc. measured the heat

capacity and glass transition temperatures with different heating/cooling rates, which

10

enabled us to estimate the viscosity curves for the glasses we studied here. Dr. Potuzak

also helped us with the chemical analysis of the two glasses done at Corning Inc. A

nearly-final draft of this paper is completed, and this work will be submitted for

publication soon.

Appendix:

Chapter 2 and chapter 3 clearly show that cation field strength greatly effects

boron and aluminum coordination, and changes in boron coordination induced

changes in thermal properties. The modifier cations in these studies are Ca2+ and Na+,

which have similar ionic radii; therefore, we controlled for the effect of cation size.

This appendix is a natural extension of this work and investigates how a different

cation, Ba2+, affects these structural and thermal properties. Ba2+ has same charge as

Ca2+, but a 33% larger radius. The quantification of 11B MAS NMR spectra clearly

shows that the N4 for Ba-aluminoborosilicate glasses are larger than for their Ca

counterparts and smaller than for their Na counterparts. In addition, these Ba-

aluminoborosilicate glasses were synthesized with 17O enriched SiO2, which allowed

us to directly quantify the amount of NBO from 17O MAS NMR. These glasses have

been cooled with different cooling rates, as was done in Chapter 3. Unsurprisingly, we

observed that while the N4 decreased with increased cooling rate, the amount of NBO

increases with cooling rate. The data from this appendix will be written up as a

manuscript and submitted for publication after my defense.

Additional collaborative work not presented in dissertation

In addition to the research presented in the chapters and appendices of this

dissertation, I have collected 11B MAS NMR, 27Al MAS NMR and 23Na MAS NMR

for two different collaborative studies for which I was involved in a secondary role.

The first study is primarily in collaboration with J. Deubener, J. F. Stebbins, L.

Grygarova, H. Behrens, L. Wondraczek, and Y. Z. Yue to investigate pressure-

induced structural change in boron and aluminum coordination in an isotropically

compressed aluminoborosilicate melt. This study revealed that [4]B, [5]Al, and [6]Al

11

concentrations increase with pressure, whereas the mean distance of sodium to oxygen

atoms decreased with pressure, in the range of pressures from 0.1 MPa to 500 MPa. It

was published in the Journal of Chemical Physics as (Wu et al. 2009a). The second

collaborative study was primarily a collaboration with M. H. Manghnani, A. Hushur,

T. Sekine, J. F. Stebbins and Q. Williams to investigate the structure of four post-

shocked specimens of borosilicate glasses recovered from peak pressures of 19.8,

31.3, 41.3 and 49.1 GPa. 11B NMR spectra for all four shocked glasses are similar, and

indicate that ratios of BO3 to BO4 are not greatly changed from the starting material,

but the shape of peaks representing BO3 and BO4 groups are different between

shocked and unshocked glass. It appears that the shocked glasses have a significantly

increased fraction of non-ring BO3 groups, and of BO4 groups with a higher number of

Si neighbors. We did not observe any aluminum coordination change from 27Al MAS

NMR. I also measured the density of these glasses by the sink-float method, and did

not observe density change with different shock pressures. It is thus possible that some

of the difference between shocked and unshocked glasses observed by NMR is the

result of the former having a higher fictive temperature, resulting from being heated

well above the glass transition region and then cooling more rapidly than the starting

glass after decompression. This work was published in the Journal of Applied Physics

as (Manghnani et al. 2011) .

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284-299.

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Araujo, R. J. (1983) Statistical mechanics of chemical disorder: Application to alkali

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Bielecki, A. and Burum, D. P. (1995) Temperature-dependence of 207Pb MAS spectra

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12

Bray, P. J. and Holupka, E. J. (1985) The potential of NMR techniques for studies of

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Bunker, B. C., Tallant, D. R., Kirkpatrick, R. J. and Turner, G. L. (1990) Multinuclear

nuclear magnetic resonance and raman investigation of sodium borosilicate

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Dell, W. J., Bray, P. J. and Xiao, S. Z. (1983) 11B NMR studies and structural

modeling of Na2O-B2O3-SiO2 glasses of high soda content. Journal of Non-

Crystalline Solids 58(1), 1-16.

Du, L.-S. and Stebbins, J. F. (2003) Solid-state nmr study of metastable immiscibility

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Du, L.-S. and Stebbins, J. F. (2005) Network connectivity in aluminoborosilicate

glasses: A high-resolution 11B, 27Al and 17O NMR study. Journal of Non-

Crystalline Solids 351(43-45), 3508-3520.

Du, W.-F., Kuraoka, K., Akai, T. and Yazawa, T. (2000) Study of Al2O3 effect on

structural change and phase separation in Na2O-B2O3-SiO2 glass by NMR.

Journal of Materials Science 35(19), 4865-4871.

Dubinsky, E. V. and Stebbins, J. F. (2006) Quench rate and temperature effects on

framework ordering in aluminosilicate melts. American Mineralogist 91(5-6),

753-761.

Kiczenski, T. J., Du, L.-S. and Stebbins, J. F. (2005) The effect of fictive temperature

on the structure of E-glass: A high resolution, multinuclear nmr study. Journal

of Non-Crystalline Solids 351(46-48), 3571-3578.

Kroeker, S. and Stebbins, J. F. (2001) Three-coordinated boron-11 chemical shifts in

borates. Inorganic Chemistry 40(24), 6239-6246.

Loshagin, A. V. and Sosnin, E. P. (1994) NMR studies of sodium borosilicate glasses

containing aluminum oxide. Glass Physics and Chemistry 20(1), 14-22.

13

Manghnani, M. H., Hushur, A., Sekine T., Wu, J., Stebbins, J. F. and Williams, Q.

(2011) Raman, Brillouin, and nuclear magnetic resonance spectroscopic

studies on shocked borosilicate glass. Journal of Applied Physics 109, 113509.

Moynihan, C. T., Easteal, A. J., DeBolt, M. A. and Tucker, J. (1976) Dependence of

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Society 59(1-2), 12-16.

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Sen, S. (1999) Temperature induced structural changes and transport mechanisms in

borate, borosilicate and boroaluminate liquids: High-resolution and high-

temperature NMR results. Journal of Non-Crystalline Solids 253, 84-94.

Sen, S., Xu, Z. and Stebbins, J. F. (1998) Temperature dependent structural changes in

borate, borosilicate and boroaluminate liquids: High-resolution 11B, 29Si and 27Al NMR studies. Journal of Non-Crystalline Solids 226(1-2), 29-40.

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dynamics in borate and borosilicate liquids: High-resolution and high-

temperature NMR results. Journal of the American Ceramic Society 79(9),

2247-2256.

Stebbins, J. F. and Sen, S. (1997). Temperature effects on borate melt structure and

dynamics: NMR studies. Proc. Second Int. Conf. Borates Glasses, Crystals and

Melts, Sheffield, UK, Society of Glass Technology.

Stebbins, J. F. and Sen, S. (1998) Microscopic dynamics and viscous flow in a

borosilicate glass-forming liquid. Journal of Non-Crystalline Solids 224(1), 80-

85.

Takahashi, T., Kawashima, H., Sugisawa, H. and Baba, T. (1999) 207pb chemical shift

thermometer at high temperature for magic angle spinning experiments. Solid

State Nuclear Magnetic Resonance 15, 119-123.

14

Toplis, M. J., Dingwell, D. B., Hess, K. U. and Lenci, T. (1997) Viscosity, fragility,

and configurational entropy of melts along the join SiO2-NaAlSiO4. American

Mineralogist 82(9-10), 979-990.

Wang, S. H. and Stebbins, J. F. (1999) Multiple-quantum magic-angle spinning 17O

NMR studies of borate, borosilicate, and boroaluminate classes. Journal of the

American Ceramic Society 82(6), 1519-1528.

Wu, J. S., Deubener, J., Stebbins, J. F., Grygarova, L., Behrens, H., Wondraczek, L.

and Yue, Y. Z. (2009a) Structural response of a highly viscous

aluminoborosilicate melt to isotropic and anisotropic compressions. Journal of

Chemical Physics 131(10), 104504.

Wu, J. S. and Stebbins, J. F. (2009b) Effects of cation field strength on the structure of

aluminoborosilicate glasses: High-resolution 11B, 27Al and 23Na MAS NMR.

Journal of Non-Crystalline Solids 355(9), 556-562.

Wu, J. S. and Stebbins, J. F. (2010) Quench rate and temperature effects on boron

coordination in aluminoborosilicate melts. Journal of Non-Crystalline Solids

356(41-42), 2097-2108.

Wu, J. S. and Stebbins, J. F. (2011). Temperature calibration for high-temperature

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15

Chapter Two

Effects of cation field strength on the structure of aluminoborosilicate

glasses: high-resolution 11B, 27Al and 23Na MAS NMR

Modified version published in Journal of Non-Crystalline Solids

Jingshi Wu, Jonathan F. Stebbins, (2009) 355(9): 556-562

16

Abstract

Among the most important adjustable compositional variables in controlling

glass and glass-melt properties are the relative proportions of network modifiers with

varying cation field strength (ratio of charge to radius). Here we determine the details

of structural changes caused by variations in the ratio CaO/Na2O in two series of

aluminoborosilicate glasses with different contents of boron oxide. Using high-

resolution, high-field 11B and 27Al MAS NMR, we report precise values of contents of

three- and four-coordinated boron (N4) and of four- and five-coordinated aluminum

([5]Al), and calculate fractions of non-bridging oxygens (NBO). Increasing CaO/Na2O

dramatically lowers N4 and increases NBO and [5]Al, but effects are non-linear with

composition. Boron content affects these trends because of energetic constraints of

mixing of various network cations. 23Na spectra reveal slight but systematic increases

in the mean Na-O distance with increasing CaO/Na2O, suggesting that in Ca-rich

glasses, Na+ has a higher ratio of bridging to non-bridging oxygens in its coordination

shell. All of these changes can be understood by the tendency of higher field strength

modifier cations to promote the concentration of negative charges on non-bridging

oxygens in their local coordination environment, systematically converting four- to

three-coordinated boron.

17

Introduction

Multicomponent aluminoborosilicate glasses are widely used in technologies

such as flat panel display substrates, fiber glass, photochromic glass, and the

sequestration of radioactive waste (Besmann and Spear 2002; Boizot et al. 2005;

Gerasimov and Spirina 2004; Kato et al. 2005; Li et al. 2003; Maekawa 2004; Ollier

et al. 2004; Wang and Pantano 1992; Yamashita et al. 2003; Yamashita et al. 2000).

Many studies have documented the close relationships between physical properties

and structure of boron-containing glasses (Abe 1952; Betzen et al. 2003; Bobkova

2003; Bubnova et al. 2002; Budhwani and Feller 1995; Levitskii et al. 2004;

Protasova and Kosenko 2003; Roderick et al. 2001). Extensive efforts have also been

made to model the effects of composition on properties (Mazurin 2005; Priven 2000a;

Priven 2001), many of which are based on structural speciation reactions (Araujo

1983; Araujo 1986; Bray et al. 1985; Loshagin and Sosnin 1994b; Priven 2000b;

Zhong et al. 1988).

When network modifier oxides are added to pure silica, the silicate framework

“depolymerizes” through the formation of non-bridging oxygen (NBO), while most or

all Si remains four-coordinated. In contrast, when modifiers are initially added to

boric-oxide glass, the added oxide ion is accommodated by the conversion of trigonal

boron ([3]B) to tetrahedral boron ([4]B) with little or no formation of NBO. If enough

alkali oxide is added, tetrahedral boron begins to convert to asymmetric trigonal boron

groups, which contain one NBO and two bridging oxygens (BO) (Dell et al. 1983). An

early statistical thermodynamic model of this process (Araujo 1983) allowed the

calculation of the fraction of four-coordinated boron among total boron species (N4) as

a function of composition and temperature in alkali borate glasses and glass-forming

liquids. In sodium borosilicates, the maximum value of N4 increases with silica

content, as described by the frequently-used empirical model of Dell and Bray (Dell et

al. 1983), and most NBO are bonded to Si instead of to B. The ease with which boron

can change between three and four coordination as composition and temperature are

changed, thus has a major influence on properties such as viscosity, melting points,

and glass transition temperatures.

18

Constraints on boron coordination in glasses come mostly from NMR,

beginning with many early “wideline” NMR studies (Bray and Holupka 1985; Dell et

al. 1983; Gupta et al. 1985; Yun and Bray 1978; Zhong et al. 1988), then more

recently with high field and high resolution 11B MAS NMR (Jäger et al. 1995;

Kroeker et al. 2006; Prabakar et al. 2003; Stebbins et al. 2000; Turner et al. 1986).

Compositional effects on N4 are now especially well known for alkali borosilicates,

but more complex systems are less well-understood. Some studies (Angeli et al. 2001;

Du et al. 2000; El-Damrawi et al. 1993; Li et al. 2003; Loshagin and Sosnin 1994a;

Shim et al. 1991; Yamashita et al. 2003) have begun to systematize the structural

changes caused by adding Al2O3 to borosilicates. Aluminum in these compositions

generally is predominantly [4]Al, but high-field 27Al NMR spectra have revealed the

added complication of significant [5]Al, especially in glasses with divalent modifier

cations (Du and Stebbins 2005a; Loshagin and Sosnin 1994a). Despite these efforts,

the systematic effects of one of the most commonly used compositional variations, the

field strength of the modifier cation, have only been explored in a few

aluminoborosilicate systems. For example, Yamashita et al. (2003), in comparing K,

Na, Ba, Sr, Ca, and Mg aluminoborosilicates, noted that the smaller, higher charged

cations systematically increased the NBO content and decreased N4 for a given Al/B

ratio (Yamashita et al. 2003).

As discussed in recent studies that included 17O NMR, oxygen speciation is

closely linked to the network structure (Angeli et al. 2001; Stebbins et al. 1997;

Youngman et al. 1995). In a simple silicate melt, NBOs are formed stoichiometrically

on addition of modifier oxide to silica (assuming negligible “free” O2- ions), as

expressed by the structure “reaction”:

SiO4/2 + 1/2O2- = [SiO3/2O]- (1)

[SiO3/2O]- indicates a four-coordinated silicon with three bridging oxygens and one

NBO, where Ox/y denotes x oxygen anions, each coordinated with y network cations,

e.g. a bridging oxygen when y = 2. In an aluminosilicate, some modifier oxide instead

contributes oxygen to form [4]Al and cations to charge balance the under-bonded

bridging oxygens such as Al-O-Si. Again, if the contents of [5]Al, [6]Al and oxygen

19

triclusters are negligible, NBO content can be deduced directly from stoichiometry. In

boron containing systems, there is an interplay between oxygen and boron speciation

that can be expressed by schematic reactions such as:

BO3/2 + NBO– = [BO4/2]- (2)

or, more precisely for borosilicates:

BO3/2 + SiO3/2O– = [BO4/2]– + SiO4/2 (3).

In the types of compositions studied here, most of the NBO are associated with

Si instead of with B as shown directly by 17O NMR [42, 50], but a complete

thermodynamic formulation would of course include both types of species. At low

contents of modifier oxides in boron-rich glasses, these reactions are nearly complete

(Araujo 1983; Dell et al. 1983; Yun and Bray 1978). At high modifier contents the

equilibrium tends to shift back, in part because of the relative energetic unfavorability

of [4]B-O-[4]B linkages (Abe 1952; Wang and Stebbins 1999), which in turn can be

mitigated by dilution with silica (Araujo 1986; Dell et al. 1983; Du and Stebbins

2003a; Du and Stebbins 2003b). Higher temperature or higher modifier cation field

strength, which favor the formation of NBO, pushes the reaction to the left (Du and

Stebbins 2005a; Kiczenski et al. 2005; Sen et al. 1998; Stebbins and Ellsworth 1996).

In this paper we isolate a key compositional variable, one that is commonly

exploited in the tailoring of glass and glass-forming melt properties to particular

applications, by selecting two aluminoborosilicate compositional joins in which Na2O

is substituted for CaO. Thus, total oxygen ion content remains identical, and only the

charge and number of modifier cations changes. We use 11B, 27Al and 23Na MAS

NMR to determine changes in both network speciation and modifier cation

environment as a function of the Na2O/CaO ratio at two different ratios of B2O3 to

SiO2. We deduce the corresponding changes in oxygen speciation, and show that it is

likely that the effect of modifier cation charge on the oxygen speciation is the most

important drive in controlling the boron speciation, which in turn has important effects

on melt viscosity, glass transition behavior, and corrosion resistance.

20

Experimental

Sample preparation

Ten glass samples were synthesized with composition

20

!

M2/ nn+ O•8Al2O3•7B2O3•65SiO2 and 20

!

M2/ nn+ O•8Al2O3•21B2O3•51SiO2 (M = Na, Ca),

where Na2O/(Na2O + CaO) = 0, 0.25, 0.5, 0.75, 1 (Table 2.1). The Na and Ca end

members were made using appropriate amounts of dried CaCO3, Na2CO3, Al2O3, B2O3

and SiO2. Approximately 0.1 wt% of Co3O4 was added to each 2 g sample to speed

spin-lattice relaxation, permitting more rapid data collection during NMR

experiments. To make the Na-containing glasses (denoted as B7N20 and B21N20), the

starting materials were mixed thoroughly and heated at 600 ºC for 10 hours to allow

decarbonation. Each mixture was then packed into a Pt tube with both ends welded to

prevent alkali loss during melting. The samples were melted at 1300 ºC for 30

minutes, and then quenched by dipping the Pt capsule into water. For the Ca-

containing glasses (denoted as B7N00 and B21N00), the mixtures were heated at 700

ºC for 10 hours for decarbonation, followed by melting in sealed Pt tubes at 1400 ºC

for 30 minutes and water quenching. The samples with intermediate compositions

were synthesized by mixing the appropriate amounts of the two end members and

remelting at 1400 ºC for 30 minutes.

NMR data collection and analysis 11B MAS NMR spectra were collected on a Varian 14.1 T spectrometer at 192.4 MHz

using a Varian/Chemagnetics T3 probe with 3.2 mm zirconia rotors spinning at 20

kHz with a recycle delay of 1 s and a radio frequency pulse length of 0.3 µs, which

corresponds to a radiofrequency (rf) tip angle for solids of 20°. 11B chemical shifts are

reported in parts per million (ppm) relative to 1.0 M boric acid at 19.6 ppm. 27Al MAS

NMR spectra were collected on a Varian 18.8 T spectrometer at 208.4 MHz with 0.2 s

delay and 0.2 µs pulse length (solid 30° rf tip angle), also using a T3 probe with

similar rotors spinning at 20 kHz, with chemical shift relative to 0.1 M aqueous

Al(NO3)3 at 0 ppm. 23Na MAS NMR spectra were collected at both 14.1 and 18.8 T

with 30° (solid) rf tip angles, spinning speeds of 20 kHz, and were referenced to a 1.0

21

M NaCl solution at 0 ppm. 29Si spectra are not reported, as for these types of

multicomponent glasses they are completely unresolved (Kiczenski et al. 2005),

making analysis in terms of silicate species highly model-dependent (Yamashita et al.

2003).

Results 11B MAS NMR

11B MAS NMR peaks corresponding to [3]B and [4]B groups (centered around

12 and 0 ppm, respectively, Fig. 2.1) are well resolved in spectra of the glasses at 14.1

T. The peaks were each fit with two Gaussians because of their non-symmetric

lineshapes. These pairs were summed for each boron coordination number with no

attribution of structural significance. The relative populations of the two sites (Table

2.2) can be easily determined from these peak areas after correction for the intensity of

the satellite transition spinning sidebands that are hidden under the central peaks.

Peaks corresponding to [4]B increase in intensity with increasing Na2O/(Na2O+CaO),

but the fraction of the tetrahedral boron species (N4) is not an exact linear function of

composition and cation field strength (Fig. 2.4). When both Na and Ca cations are

present, N4 is somewhat lower than would be expected from linear combinations of the

appropriate end-members. A similar “mixed cation effect” also has been observed in

alkali borate glasses (Zhong and Bray 1989) and, for Al species, in high-pressure

aluminosilicate glasses (Allwardt et al. 2007). Boron coordination changes from

predominantly trigonal to mostly tetrahedral as Na2O/(Na2O+CaO) increases, and the

effect of this compositional variable in the B7 series is larger than in the B21 series.

With higher boron content, there is more [4]B at the Ca-rich end of the join but less at

the Na-rich end.

27Al MAS NMR

The 27Al MAS NMR spectra of low boron and high boron glasses collected at

18.8 T are shown in Figure 2.2. This very high field provides better resolution and

quantification of peaks for [4]Al and [5]Al (and [6]Al, if present), because second-order

22

quadrupolar broadening is reduced. The spectra consist of signals from two aluminum

environments: the peak maximum for the predominant [4]Al is at about 60 ppm and

that of the minor [5]Al is at about 30 ppm. (The small peaks at about 0 ppm are due to

a background signal from the rotors). The [4]Al and [5]Al peaks both have typical

asymmetric forms with tails extending towards lower frequency resulting from

distributions in quadrupolar coupling constants. These were each fit with two

Gaussians to approximate this line shape and the relative intensities determined by

integration. [5]Al is a minor, but measurable, component for all compositions, but becomes

more significant in the glasses with the highest Ca/Na ratios (Table 2.2). In the Ca-rich

samples, [5]Al increases with increasing cation field strength, and the change appears

to be non-linear with composition (Table 2.2). The amount of [5]Al in the Ca-rich

glasses is higher in the higher-boron series. Higher field strength cations are also

known to promote the formation of [5]Al in aluminoborate glasses (Bunker et al. 1991;

Chan et al. 1999).

23Na MAS NMR

Figure 2.3 shows the 23Na MAS spectra of the Na-containing glasses collected

at 18.8 T; data were also obtained at 14.1 T. Each spectrum contains a single, broad,

asymmetrical peak, whose maximum shifts to lower frequency as the Ca/Na ratio

increases. Especially at the high field of 18.8 T, distributions of chemical shifts due to

variations in Na environments (for example varying fractions of BO and NBO

neighbors) significantly affect the peak shapes, although analyzing this structural

information is complicated by the relatively high coordination number of Na+ (Lee

and Stebbins 2003). In contrast, 23Na spectra collected at lower fields generally have

“tails” to low frequency that are controlled primarily by distributions in quadrupolar

coupling constants and are thus less informative about structure. Data obtained at

different magnetic fields can, however, readily be used to estimate the mean isotropic

chemical shift (δiso) and the mean quadrupolar coupling constant (Cq) because the

23

center of gravity (δcg, in ppm) of the resonance is related to the true isotropic chemical

shift by the equation (Kohn et al. 1998; Schmidt et al. 2000)

!

"cg = "iso # (Cq2 /40$ 0

2)(1+%2 /3)•106

Here, ν0 is the Larmor frequency and η is the quadrupolar asymmetry parameter. The

latter was chosen rather arbitrarily as 0.7 in all calculations, but variation of η over its

full range (0 to 1) would result in only ~15% variations in the derived Cq values. Data

for δcg at 18.8 and 14.1 T, and calculated values for means of δiso and Cq are given in

Table 2.3. The chemical shifts become significantly higher (less negative) with

increasing Na/Ca. Because there is a negative correlation between δiso and mean Na-O

bond distance (Stebbins 1998), this result indicates that such distances on average are

longer in high Ca vs. high Na glasses. From published correlations for silicates, a

decrease in chemical shift of about 5 ppm suggests an increase of about 0.01 nm

(George and Stebbins 1995; Stebbins 1998; Xue and Stebbins 1993). Similar

correlations were found for sodium borates and for sodium germanates (George et al.

1997). The overall change in mean chemical shift is slightly larger in the B7 series (-

3.8 to -9.8 ppm) than in the B21 series (-5.1 to -9.0 ppm), perhaps because of the

relatively low NBO content in the Na-rich glasses of the latter series (see next section).

The estimated mean Cq values tend to decrease with increasing Ca/Na, especially in

the B7 series (Table 2.3), suggesting less distortion from local spherical symmetry,

and contributing to the observed slight decreases in peak widths.

Oxygen speciation

The conversion of [3]B to [4]B consumes NBO to form bridging oxygens. If all

Al is [4]Al, and oxygen triclusters are negligible, the NBO fraction can thus be

calculated directly from concentrations of [4]B and [4]Al measured by NMR and

oxygen mass balance, regardless of whether NBO are on Si, B, or Al (Du and Stebbins

2005a). The number of NBO per formula unit is simply 2 x (mol% of

!

M2/ nn+ O – mol%

of [4]B – mol% of [4]Al), which, when divided by the total number of oxygens per

formula unit (195 for the B7 series, 209 for the B21 series), gives the fraction of NBO

among all oxygens. If [5]Al is present, the oxygen speciation will be more complex

24

(Du and Stebbins 2005b; Stebbins et al. 2008). However, if [5]Al is low, as here, we

can simply use measured [4]Al in this equation. The proportions of [4]B and NBO are

listed in Table 2.2 and plotted in Figure 2.4. The figure clearly shows the dramatic

effects of Ca vs. Na on the oxygen speciation. Also, because N4 is non-linear with

composition, NBO is non-linear, with contents slightly higher in mixed glasses than

expected from interpolation between end members.

Discussion

Effect of modifier cation on network cation coordination

Figure 2.4 summarizes the major effects of increasing CaO/Na2O ratio on

decreasing N4 and increasing NBO contents for our samples with two different ratios

of SiO2/B2O3. Such effects are known in general from previous studies, where Ca2+

has been described as having a greater effect on “depolymerizing” the borosilicate

network (Bobkova et al. 1987; Du and Stebbins 2005a; Yamashita et al. 2003). In

these systems, higher field strength modifier cations favor the formation of highly

charged NBO, over the lower charged bridging oxygens that form linkages such as [4]B-O-[4]Si, thus shifting reaction (3) to the left. The resulting greater concentration of

negative charge thus helps stabilize the local coordination environment of the smaller

and/or higher-charged modifier. Similar boron coordination number changes were

found in a variety of borosilicate, aluminoborate and aluminoborosilicate glasses

(Bunker et al. 1991; Du and Stebbins 2005a; Fleet and Muthupari 1999; Roderick et al.

2001; Yamashita et al. 2003). 17O NMR studies have shown that NBO in such systems

is most commonly bonded to Si, but that some NBO on borons are present in Ca-rich

glasses (Du and Stebbins 2005a; Kiczenski et al. 2005). We also note that higher field

strength modifier (or “charge compensating”) cations will also help to stabilize the

types of bridging oxygens that have the greatest concentration of negative charge, for

example [4]Al-O-[4]Al and [4]B-O-[4]B, whose abundances are generally minimized in

systems dominated by large, monovalent cations, as seen directly by 17O NMR (Du

and Stebbins 2005a; Lee and Stebbins 1999; Lee and Stebbins 2000a). This effect

might tend to stabilize [4]B, a trend opposite of what is seen in most borosilicate

25

systems and in the results presented here. Apparently the mechanism for formation of

NBO + [3]B (reaction 3) is predominant when high cation field strength modifiers are

present, especially in glass compositions that are relatively rich in silica, where

dilution of B and Al by Si in the network lowers the probability of such highly-

charged bridging oxygens. However, it has been suggested that the stabilization of [4]B-O-[4]B linkages by small alkali cations (e.g. Li+) in high-alkali binary borate

glasses may explain their higher N4 values relative to those with large alkali cations

(e.g. Cs+) (Kroeker et al. 2006; Michaelis et al. 2007; Zhong and Bray 1989). Steric

hindrance for the latter makes charge compensation of such linkages especially

difficult (Mysen and Richet 2005), perhaps promoting instead the formation of NBO.

A recent, detailed comparison of the effects of K, Na, Ba, Sr, Ca and Mg on

network speciation in aluminoborosilicate glasses reported data on a compositional

series with fixed modifier oxide and silica contents but varying Al/B (Yamashita et al.

2003). As in our study, a systematic decrease in N4 was observed with increasing

modifier cation charge or decreasing cation radius, and non-linear compositional

effects were seen in a CaO-K2O series. The quantization of the 11B NMR results may,

however, have been less precise because data were collected by MAS NMR at a much

lower field of 7 T; similarly, 27Al MAS NMR at this field could not resolve the [5]Al

species. NBO contents were cast in terms of silicate species Q3 and Q4 (1 and 0 NBO

respectively), which were in turn derived by fitting of unresolved 29Si MAS NMR

spectra. The latter analysis is made somewhat doubtful by the apparently unjustified

assumption that the relative proportions of [4]Al, [4]B, and [3]B neighbors to Si (which

also change with composition) do not significantly affect the 29Si NMR peak shape or

position. Nonetheless, this study provided an interesting analysis of network

speciation in terms of an apparent equilibrium constant, Kapp, for a reaction essentially

equivalent to (3) above, which the authors calculated as simply ([Q4] x [[4]B])/([Q3] x

[[3]B]). Although their data suggest the possibility of effects of Al/B on the value of

Kapp, only constant values and ranges for each modifier were reported, for example 8 ±

3 for Na2O and 0.3 ± 0.1 for CaO. For comparison, the concentrations of Q4 and Q3

used for Kapp can be calculated from our results by assuming that all NBO are

26

coordinated to silicon. This approximation is based on the Dell and Bray model of

alkali borosilicate glasses (Dell et al. 1983) and previous 17O 3QMAS studies of

aluminoborosilicates similar in composition to those described here (Du and Stebbins

2005a). Despite differences in the approaches taken to estimating NBO contents

between the previous study (Yamashita et al. 2003) and ours, a similar trend can be

noted: Kapp for our samples B7N20 (all Na2O) and B7N00 (all CaO) are 5.17 and 0.33

respectively. At higher B/Si (and B/Al), Kapp values are significantly higher, e.g. for

17.1 for B21N20 (all Na2O) and 0.51 for B21N00 (all CaO). Because of the

importance of mixing and order/disorder relationships among the five major network

cation species in aluminoborosilicates ([4]Si, [4]Al, [5]Al, [3]B, and [4]B) (Du and

Stebbins 2005a), it is not surprising that composition should systematically effect

“equilibrium constants” of this type, as the extent of mixing will be reflected in the

free energy of mixing and hence in activity coefficients for network species.

Related to the effects of modifier cation field strength on boron coordination is

a competition for short bonds to oxygen that is well-known to produce more [5]Al in

Ca-rich vs. Na-rich aluminosilicates (Allwardt et al. 2005; Lee et al. 2005) and in

aluminoborate glasses (Bunker et al. 1991; Chan et al. 1999). This effect is also

obvious in data presented here and previously (Du and Stebbins 2005a) that compare

alkali and alkaline earth aluminoborosilicates. The apparent non-linearity of the effect

of Ca/Na ratio on Al coordination, noted here, resembles trends seen for high-pressure

(K, Ca) aluminosilicate glasses (Allwardt et al. 2007) and for ambient pressure (Mg,

Ca) aluminosilicates (Kelsey et al. 2008; Neuville et al. 2008). It is possibly related to

heterogeneous distributions of modifier cations and coordinating oxygens. Such non-

linearities in compositional effects on network coordination will be important for

accurate empirical or theoretical models of properties.

Effect of boron content

In Na-rich glasses, lower B/Si ratios produce higher N4 (Fig. 2.4). This is

expected from extensive NMR studies of the sodium borosilicate system (Dell et al.

1983), and can be explained at least in part by the decreased probability of [4]B-O-[4]B

27

and of [4]Al-O-[4]B connections, simply by dilution by Si. Because the relatively high

negative charges on these types of “underbonded” oxygens (formally –1/2) are

relatively hard to balance by large, monovalent modifier cations, such bridging

oxygens are energetically less favorable than species such as [4]B-O-[4]Si and [4]Al-O-[4]Si (formally –1/4) and [3]B-O-[4]Si and [4]Si-O-[4]Si (formally neutral). In

aluminosilicates, this leads to “Al avoidance.” In Na-rich borosilicates, the network

formers are thus relatively ordered because they tend to “avoid” [4]B-O-[4]B and [4]B-

O-[4]Al linkages (Abe 1952; Araujo 1980), which has been directly observed by recent

NMR studies of sodium borosilicate and sodium aluminoborate glasses (Bertmer et al.

2000; Chan et al. 1999; Du and Stebbins 2003a; Du and Stebbins 2005b; Wang and

Stebbins 1999). Unlike aluminosilicates, however, in borosilicates there is another

degree of freedom, the conversion of BO4 to BO3 plus NBO, which is thus favored at

higher B/Si.

In Ca-rich glasses, the opposite effect is seen. 17O NMR and other data indicate

much less tendency towards the chemical ordering described above, because the

charges on bridging oxygens joining two tetrahedral, trivalent cations are easier to

balance with Ca2+ instead of Na+ (Chan et al. 1999; Lee and Stebbins 1999; Lee and

Stebbins 2000b; Stebbins and Xu 1997). Species such as [4]B-O-[4]B and [4]B-O-[4]Al

may thus actually be stabilized, leading to more N4 at higher boron content for Ca-rich

compositions. Of course, as noted above, Ca2+ also stabilizes NBO, leading to more of

this species in Ca-rich glasses. In a recent 17O NMR study that specifically addressed

these effects (Du and Stebbins 2005a), mixing of B and Al in a potassium

aluminoborosilicate glass tended to follow the [4]B-O-[4]B and [4]B-O-[4]Al avoidance

model, but mixing in a Ca aluminoborosilicate of the same stoichiometry (equivalent

to sample B7N00 here) was closer to a random mixing model. The data in this study

support these conclusions.

For all of the compositions studied here, lower boron concentration leads to

considerably higher NBO content (Fig 2.4.). In borosilicates, both the “borate-like”

modification of network on addition of a modifier oxide, BO3/2 + 1/2O2- = [BO4/2]-,

and the “silicate-like” modification, SiO4/2 +1/2O2- = [SiO3/2O]- are operational.

28

Simply by composition alone, the latter becomes more predominant at higher silica

contents: less of the added oxide ion is used to convert [3]B to [4]B and to charge

compensate the negatively charged BOs; more of the added oxide is used to convert

uncharged BO to charged NBO. Again, however, effects of Ca vs. Na shift the balance

in the borate reaction considerably.

Sodium cation environments

In silicate, borate, and germanate glasses and melts in which Na+ is the only

non-network cation, δiso for 23Na increases systematically with increasing Na2O

content, in part because of increasing fractions of NBO in the average Na coordination

shells and the accompanying shortening of mean Na-O distances (Peng and Stebbins

2007; Stebbins 1998). However, in the Na-Ca aluminoborosilicates studied here, δiso

for both compositional series decreases significantly with increasing NBO content,

which results here from increases in CaO/Na2O. This is likely to result from a strong

preference for NBO to coordinate Ca2+ instead of Na+. As CaO/Na2O increases, more

of the oxygens around the Na+ are BO instead of NBO, even as the total NBO content

is increasing. Average Na-O distances are therefore observed to increase. This finding

is thus analogous to “mixed-alkali” effects of modifier cation size (Stebbins 1998).

Such non-random distributions of NBO and BO around modifier/charge balancing

cations, caused by differences in their field strength, has been observed more directly

by 17O NMR in a number of systems, for example recent work on Ca/Mg

aluminosilicates (Kelsey et al. 2008).

Other compositional effects

Systematizing the effects of all compositional variables on network speciation

in five-component aluminoborosilicate glasses and liquids remains a challenging

problem because of the complex effects of mixing of many network species and the

apparent non-linearities noted above. We will thus note only a few comparisons. The

effects of addition of alumina to the relatively well-known sodium borosilicate system

have been explored in several studies (Angeli et al. 2001; Du et al. 2000; El-Damrawi

29

et al. 1993; Geisinger et al. 1988; Shim et al. 1991; Yamashita et al. 2003; Yamashita

et al. 2000). For example, in a recent detailed report on network cation mixing, based

on high-resolution 11B, 27Al, and 17O NMR, it was suggested that the similar mixing

behavior of [4]Al and [4]B could allow them to be combined together into a single

compositional term (Du and Stebbins 2005a), to be substituted for the B2O3 content in

the often-applied, empirical “Dell and Bray” model of the sodium borosilicate system

(Dell et al. 1983). Although this model cannot hold at high Al/B ratios, it does

approximate results for a variety of alkali aluminoborosilicate glasses (Du and

Stebbins 2005a; El-Damrawi et al. 1993; Loshagin and Sosnin 1994a; Shim et al.

1991). Applying this approach to our Na-aluminoborosilicate data (B7N20 and

B21N20), the model predicts N4’ (the sum of [4]Al + [4]B fractions) as 0.77 and 0.61,

vs. measured values of 0.82 and 0.65. This indicates that this empirical approximation

continues to be useful. For alkaline earth rich glasses, however, the major shifts in

NBO-producing equilibria produce large divergences from any such model based on

alkali oxide compositions. Clearly, a systematic, consistent thermodynamic treatment

of these complexities will be needed to yield more accurate structure-based models of

bulk properties.

Conclusions

In two series of aluminoborosilicates in which CaO/Na2O is systematically

varied, the higher field strength modifier cation (Ca2+) has dramatically different

effects on the glass structure when compared to those of the lower field strength cation

(Na+). As CaO/Na2O increases, the fraction of [4]B decreases greatly, requiring a

systematic increase in the fraction of NBO, which are apparently stabilized by the

higher modifier cation charge. The same compositional effect also increases the

content of [5]Al. Variation with composition is non-linear, which may complicate the

formulation of predictive models of structure-property relations. Na-O distances on

average are longer in high Ca vs. high Na glasses, even though NBO contents are

higher, indicating a preference for NBO to be associated with Ca2+ and NBO with Na+.

30

Acknowledgements

We are grateful to J. Puglisi and C. Liu for access to the 18.8 T NMR

spectrometer at the Stanford Magnetic Resonance Laboratory, and to the NSF for

funding under grant number DMR 0404972. We also thank two anonymous reviewers

for their suggestions.

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