Critical analysis of glass stability parameters and application to lithium borate glasses

Article abstract of DOI:10.1111/j.1551-2916.2011.04767.x

We reevaluated nine parameters of glass stability (GS) against crystallization determined from differential scanning calorimetry (DSC) experiments to predict the glass-forming ability (GFA) of oxide liquids on cooling. Then, borate glasses were prepared and tested, covering the Li ₂O-B₂O₃ system with 20.0-66.7 mol% lithia. The glasses were prepared from both commercial chemical and powders, obtained by a solution method. The GS parameters were calculated using characteristic glass transition, crystallization, and melting peaks of DSC thermograms. We found that seven stability parameters give similar trends for compositions up to 33.3 mol% lithia, where, as we expected, GS significantly decreases with lithia content. Thereafter, up to 66.7 mol% lithia, GS shows a broad shallow maximum, but is approximately constant indicating that, surprisingly, composition does not significantly affect the GFA in this wide compositional range. This result qualitatively agrees with our successful experience of preparing glasses with compositions up to 74 mol% lithia and corroborates the adequacy of simple DSC tests to comparatively gauge the GS and GFA of glass-forming liquids.

Full text of DOI:10.1111/j.1551-2916.2011.04767.x

J. Am. Ceram. Soc., 94 [11] 3833–3841 (2011)
DOI: 10.1111/j.1551-2916.2011.04767.x
© 2011 The American Ceramic Society
ournal
J
Critical Analysis of Glass Stability Parameters and Application
to Lithium Borate Glasses
Eduardo B. Ferreira,‡ Edgar D. Zanotto,§,†,* Steve Feller,¶,*,** Grant Lodden,¶ Joy Banerjee,¶
Trent Edwards,¶ and Mario Affatigato¶,*,**
‡Department of Materials Engineering, University of Sao Paulo, Sao Carlos, 13566-590, Brazil
§DEMa/LaMaV – Vitreous Materials Laboratory, Federal University of Sao Carlos, Sao Carlos, 13565-905, Brazil
¶Physics Department, Coe College, Cedar Rapids, IA 52402
We reevaluated nine parameters of glass stability (GS) against
crystallization determined from differential scanning calori-
metry (DSC) experiments to predict the glass-forming ability
(GFA) of oxide liquids on cooling. Then, borate glasses were
prepared and tested, covering the Li2O–B2O3 system with
20.0–66.7 mol% lithia. The glasses were prepared from both
commercial chemical and powders, obtained by a solution
method. The GS parameters were calculated using characteris-
tic glass transition, crystallization, and melting peaks of DSC
thermograms. We found that seven stability parameters give
similar trends for compositions up to 33.3 mol% lithia, where,
as we expected, GS significantly decreases with lithia content.
Thereafter, up to 66.7 mol% lithia, GS shows a broad shallow
maximum, but is approximately constant indicating that,
surprisingly, composition does not significantly affect the GFA
in this wide compositional range. This result qualitatively
agrees with our successful experience of preparing glasses with
compositions up to 74 mol% lithia and corroborates the ade-
quacy of simple DSC tests to comparatively gauge the GS and
GFA of glass-forming liquids.
composition will not crystallize and vitrify on cooling from
the liquid state.
For a frozen liquid to be considered a glass, the crystal-
lized fraction must not exceed the experimental limit of
detection, say Xc = 10ꢀ3. In his classical papers on the kinet-
ics of glass formation, Uhlmann, Ref. [2], assumed 10ꢀ6 as
a typical figure for the limit of detection. Here, we assume
a practical limit of 10ꢀ3 (0.1%) because this value is much
closer to the real experimental limit of detection of X-ray dif-
fraction (XRD), small-angle X-ray scattering (SAXS), or
nuclear magnetic resonance (NMR), for instance. A direct
measurement of the glass-forming ability (GFA) of any
material is thus the critical cooling rate at which the melt
must be cooled to yield a crystallized fraction below this
limit.2 Hence, the higher the critical cooling rate, the more
difficult it is to obtain a glass, or the lower is the GFA of
that composition.
However, there are several difficulties in measuring the
critical cooling rate. Many compositions crystallize far too
fast, being difficult to monitor any change in their vitrifica-
tion behavior with changes in composition or in process
parameters. Nor it is easy to continuously vary the cooling
rate. Approximately, from 1 to 50°C/min, the cooling rate
can be precisely controlled and recorded in laboratory fur-
naces. Lower cooling rates (<1°C/min) are still possible to
control, but the experiments take a long time, the crystal-
lized fraction can sometimes be too low for detection and
the whole procedure ends up being very time consuming.
On the other hand, faster cooling rates (>50°C/min) are
quite feasible but not easy to be controlled due to the ther-
mal inertia of most furnaces. In general, high cooling rates
are obtained by quenching a liquid into some fluid, such as,
oil or water. However, intermediate rates are not always
possible. Alternatively, molten liquids can be efficiently
cooled in contact with cold substrates with high thermal
conductivity, for example, graphite or some metal. In such
processes, the liquid can be pressed at different rates (e.g.,
splat cooling) or poured on a moving substrate (e.g., melt
spinning). One can measure the temperature throughout the
process, but it is not trivial to achieve and to control some
desired cooling rate.
I. Introduction
EW glasses for specific applications have enormous tech-
nological interest. An estimate of the possible number
N
of glasses to be synthesized by 1% combinations of up to 80
“friendly” elements of the periodical table exceeds 1050 com-
positions, whereas in the last 6000 years of glass history, less
than 106 glasses have been reported!1 In addition, most exist-
ing glasses have only 1–10 elements in their composition.
Therefore, a practically infinite number of exciting new com-
positions could be vitrified and their properties tested, for
instance by combinations of up to 80 elements.
The development of new glass compositions, the range
within which a process must be controlled to produce a glass,
or to which direction certain compositions could be altered
to improve their vitrification ability, for example, are of par-
amount importance for the glass technologist. However,
despite deeper understanding in the last few decades, it is still
a great challenge to quantitate the ease with which a given
In addition, the crystallized fraction in partially trans-
formed materials (when a liquid solidifies as a glass) is not
always easy to quantitate. Traditionally, crystals are observed
in polished sections of the material by optical or electron
microscopy. The quantitative characterization of the crystal-
lized volume fraction involves the suitable preparation of
many samples and individual analysis under a microscope is
tedious, time consuming, and restricted by the resolution
limit of the equipment. Instrumental detection of the crystal-
lized fraction is also possible, for example, by XRD
techniques, but this requires sophisticated devices, fine sam-
L. Pinckney—contributing editor
Manuscript No. 29717. Received May 11, 2011; approved June 29, 2011.
This work was presented at the XXII International Congress on Glass, Salvador,
Brazil, September 24, 2010 (Oral Section A, Presentation 363, www.icg2010.com.br).
This work was supported by the NSF (USA), under Grants No. DMR-05020518
and DMR-0904615, Fapesp (Brazil) 07/008179-9 and CNPq (Brazil).
*Member, The American Ceramic Society
**Fellow, The American Ceramic Society
†Author to whom correspondence should be addressed. e-mail: dedz@ufscar.br.
3833

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Journal of the American Ceramic Society—Ferreira et al.
Vol. 94, No. 11
ple preparation and expert analysis, which are not always
available for a multiple-sample experimental design.
II. Experimental Procedure
The glasses were prepared using two procedures. In the con-
ventional melt method high purity lithium carbonate and
boric acid powders were mixed together thoroughly and
heated at 1000°C for 20–25 min. A weight loss after an ini-
tial 15–20 min of heating confirmed the sample composition
to within a few percent of the nominal value. We term this,
the carbonate method (CM). In the solution method (SM),15
aqueous solutions of boric acid and lithium hydroxide were
reacted at room temperature. The resulting precipitate was
heated to 1000°C to form the glass.
The critical cooling rate to avoid a certain minimal crys-
tallized fraction can be estimated by theory according to
several methods. One of the most widely accepted is the
“nose method” based on temperature–time–transformation
(TTT) curves, for isothermal experiments, or their counter-
part continuous cooling-transformation (CCT) curves, for
non-isothermal cooling.2 However, the parameters needed
for such calculations, such as the crystal nucleation and
crystal growth rates, or the parameters to calculate these
quantities (surface energy, thermodynamic driving force,
and diffusivities) are not trivial to obtain, and are only
available for a very few simple systems. In general, com-
mercial compositions with many components are far too
complex for a theoretical estimation of its phase transfor-
mation kinetics.
This scenario leads to a search for new methods of evalua-
tion of the glass-forming ability. Such methods are indirect
and mostly empirical, and their correlation with more realis-
tic parameters, such as the critical cooling rate have been a
focus of discussion in the current literature.3 For instance,
Nascimento et al.4 tested nine glass stability parameters (GS)
by comparing them with the critical cooling rates (qcr) of sev-
eral glasses that undergo preferential surface crystallization.
The critical cooling rates were calculated from the experi-
mentally obtained crystallization kinetics of the tested
glasses, whereas the GS parameters were calculated from
simple algebraic relations between the characteristic tempera-
tures obtained from differential scanning calorimetry (DSC)
traces: the glass transition temperature (Tg), the onset tem-
perature of the crystallization peak on heating (Tx), the max-
imum of the crystallization peak (Tc), and the melting (or
liquidus) point (Tm). Table I shows the nine GS parameters
tested in Ref. [4]. Those authors concluded that only three of
the nine parameters (KW, KH, and KLL, see Table I) show
good correlations with qcr.
The compositions prepared for the present study are indi-
cated in the phase equilibrium diagram (PED)16 of Fig. 1,
with R ¼ nLi O=nB O , where nLi O and nB O are the corre-
2
2
3
2
2
3
sponding Li2O and B2O3 mole number, respectively. These
samples are referred to as R0.25 for R = 0.25, R0.5 for
R = 0.5, and so on. Sample details are given in the Table II.
After melting and forming, the glasses were stored into
closed pots with silica gel to avoid the attack of the atmo-
sphere moisture. The samples for DSC studies were prepared
immediately before each analysis by crushing the glasses in
an agate mortar and pistil, in a moisture minimized environ-
ment by letting an air conditioner and a dehumidifier perma-
nently turned on. Samples showing signs of devitrification
were carefully inspected to gather only glassy pieces to be
ground. The particles were collected between 38 and 22 lm
sieves. The sample mass was 20.0 mg for all analyses. The
thermal analyses were carried out at 10°C/min on heating
and on cooling in a DSC (Model 404, NETZSCH-Geratebau
¨
GmbH, Selb, Germany) at LaMaV-UFSCar.
III. Results and Discussion
The DSC traces for each composition are shown in
Figs. 2–9. The important characteristic temperatures are indi-
cated in each DSC trace and are summarized in Table III.
All compositions present typical glass transition and crys-
tallization peaks easy to recognize in the DSC traces. The
fine powders (22–38 lm) were chosen to guarantee that the
DSC crystallization peaks were mainly due to surface crystal-
lization, relegating internal crystallization, if present, to a less
important secondary phenomenon, in this particular case.
The analysis of the DSC melting peaks is not as simple as
that for the crystallization peaks. On heating DSC traces of
the two R0.25 samples (Fig. 2), there is a first exothermic
peak above Tg, which is a sign of crystallization, followed by
two endothermic peaks with an intermediate exothermic sign
between them. Such peaks apparently do not have any
The aim of the present study was to further test the ade-
quacy of the same nine stability parameters analyzed in Ref.
[4] to predict glass-forming ability. For such tests, we choose
several Li–B–O glasses covering a wide range of composi-
tions across the Li2O–B2O3 phase equilibrium diagram and
evaluated GS as a function of composition, from (suppos-
edly) reluctant glass-forming compositions, with mol% lithia
as high as 66.7, to very good glass-forming compositions
with 20.0 mol% lithia.
Furthermore, these glasses have been well studied by a
host of spectroscopic techniques (NMR, Raman, Infrared,
etc.).11–14 The structures, both short and intermediate range,
have been characterized over several decades (see end of dis-
cussion for details).
Table I. Glass Stability Parameters (Temperatures in K)
Source: authors and references Equation number
Tx
TgþTm
KLL
KH
¼
¼
¼
Lu & Liu5,6
(1)
(2)
(3)
(4)
(5)
TxꢀTg
Hruby7
¨
TmꢀTx
TxꢀTg
Tm
KW
Weinberg8
Tg
Tm
KT
¼
Turnbull9
T ꢀT ðT ꢀT Þ
ð
gÞ
x
c
x
KSP
¼
Saad and Poulain10
Tg
K1 = Tm ꢀ Tg
K2 = Tx ꢀ Tg
In: Nascimento et al.4
In: Nascimento et al.4
In: Nascimento et al.4
(6)
(7)
(8)
Tx
K3 ¼
Tm
Fig. 1. Li2O-B2O3 equilibrium phase diagram (wt%),16 temperatures
in °C. The arrows indicate the Li2O/B2O3 mol ratios of all
compositions tested in this study.
T ꢀT ðT ꢀT Þ
ð
gÞ
x
c
x
K4 ¼
In: Nascimento et al.4
(9)
Tm

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Analysis of Glass Stability Parameters
3835
Table II. Sample Characteristics of Different Glasses
R ¼ nLi2O=nB2O3
(mol ratio)
mol% Li2O
Method
Sample shaping
0.25
0.25
0.4
0.5
0.7
0.86
0.86
1.0
1.0
1.0 (replica)
1.5
2.0
2.0
2.0 (replica)
20.0
20.0
28.6
33.3
41.2
46.2
46.2
50.0
50.0
50.0
60.0
66.7
66.7
66.7
Carbonate
Solution
Bulk drops
Pieces
Carbonate
Carbonate
Carbonate
Carbonate
Solution
Carbonate
Solution
Solution
Roller quenched
Roller quenched
Roller quenched
Roller quenched
Roller quenched
Roller quenched
Roller quenched
Roller quenched
Roller quenched
Roller quenched
Roller quenched
Roller quenched
Carbonate
Carbonate
Solution
Solution
Fig. 4. DSC traces of glass with R = 0.5 (33.3 mol% Li2O). CM,
carbonate method; SM, solution method.
Fig. 2. DSC traces of R0.25 glass (20.0 mol% Li2O). CM,
carbonate method; SM, solution method.
Fig. 5. DSC traces of glass with R = 0.7 (41.2 mol% Li2O). CM,
carbonate method; SM, solution method.
Fig. 3. DSC traces of glass with R = 0.4 (28.6 mol% Li2O). CM,
carbonate method; SM, solution method. (I and II here are
repetitions of the DSC analysis.)
Fig. 6. DSC traces of glass with R = 0.86 (46.2 mol% Li2O). CM,
carbonate method; SM, solution method.
correlation with the temperatures of phase transition in the
published PED (Fig. 1). A possible explanation is that, due
to its high B2O3 content, the R0.25 sample presents slow
kinetics of phase transformation and does not reach equilib-
rium at relatively low temperatures, and thus the correspond-
ing reaction at the solidus temperature is delayed in a
non-isothermal DSC analysis, only occurring at 726°C–770°C,
that is, above the equilibrium solidus (635°C) (Fig. 1). At
higher temperatures, the kinetics is accelerated and
melting in non-isothermal analyses (835°C–837°C) completes
closer to the equilibrium temperature (834°C). One may

3836
Journal of the American Ceramic Society—Ferreira et al.
Vol. 94, No. 11
error of about 10°C in the liquidus17 can be attributed to the
non-zero heating rate. Only the glass transition (no crystalli-
zation) is observed for the R0.25 composition on the cooling
path from the melt corroborating its good glass-forming abil-
ity. The Tg, Tx, Tc, and Tm used in our calculations are most
likely not significantly affected by the intermediary reactions
between 726°C and 800°C.
The characteristic temperatures in the DSC thermograms
of Figs. 2–9 are summarized in Table III. For non-eutectic
or non-congruent-melting compositions, except for R0.25 in
Table III, one may observe that the solidus temperature (Ts)
is estimated by the onset of the melting peak, compared with
the solidus of the corresponding compositions in the phase
equilibrium diagram (Fig. 1).
It is worth noting that the onset of the DSC melting peak
(Tm-os) gives the best estimate for the liquidus temperature
(Tl) for congruent-melting or eutectic compositions, that is,
an estimate of the first sign of the sharp melting of such
compositions.17 This is true for samples R1.0, R0.86, and
R0.5. On the other hand, for non-congruent melting and
non-eutectic compositions, melting occurs in a wide tempera-
ture range, and its end (the liquidus temperature) is thus clo-
ser to the DSC melting endpoint (Tm-ep), as thoroughly
discussed in Ref. [17], and this is the case for samples R2.0,
R1.5, R0.7, R0.4, and R0.25.
Fig. 7. DSC traces of glass with R = 1.00 (50.0 mol% Li2O). CM,
carbonate method; SM, solution method.
The liquidus temperatures, measured by DSC, of all com-
positions more or less agree with the corresponding reported
liquidus,16 as shown in Fig. 10. For compositions that are
non-stoichiometric or having non-congruent melting, i.e.,
R2.0, R1.5, R0.7, R0.4, and R0.25, the obtained liquidus
were between 1°C and 30°C above the liquidus of the litera-
ture phase diagram. For compositions that are eutectic or
having a congruent melting (R1.0, R0.86 and R0.5), the DSC
liquidus were between 9°C and 11°C below the liquidus of
the phase diagram. It is possible to argue that the positive
heating rate affects the DSC characteristic temperatures.
Indeed, one can expect a deviation of ~10°C in the endpoint
temperature of the DSC melting peak if the heating rate is
extrapolated to 0°C/min.17 However, it is reasonable to
admit an approximately constant deviation for all composi-
tions due to the non-null heating rate.17 Then the parameters
calculated by the equations in Table I would also be shifted
by a similar constant factor, not significantly affecting their
relationship with R. To calculate the GS parameters
(Table I), we used the characteristic temperatures of
Table III. The onset of the DSC melting peak (Tm-os) was
used for samples R1.0, R0.86, and R0.5, and the DSC melt-
ing endpoint (Tm-ep) was used for samples R2.0, R1.5, R0.7,
R0.4, and R0.25.
Fig. 8. DSC traces of glass with R = 1.5 (60.0 mol% Li2O). CM,
carbonate method; SM, solution method.
To test the proposed GS methods, first, we carefully recal-
culated the nine GS parameters using data from Nascimento
et al.4 and plotted them as a function of the critical cooling
rates (qcr) calculated in Ref. [4] for the different glasses:
GeO2 (G), PbO·SiO2 (PS), Na2O·2SiO2 (NS2), 2MgO·2
Al2O3·5SiO2 (M2A2S5), Li2O·2SiO2 (LS2), CaO·MgO·2SiO2
(CMS2), CaO·Al2O3·2SiO2 (CAS2), Li2O·2B2O3 (LB2). To
facilitate our following analysis, the results are shown on the
left hand side of Figs. 11–19.
The limit of detection of crystallinity is more or less arbi-
trary, generally taken somewhat below the real limit of detec-
tion of the equipment used to probe the presence of
crystalline phases, for example, XRD. Approximately, 10ꢀ3
(0.1%) crystallized fraction (Xc), the value used in Ref. [4],
was based on the authors’ experience. But the calculated crit-
ical cooling rate (qcr) depends only weekly on this value.
Hence, if a lower value of Xc was used, this would equally
shift the values of qcr for all glasses by the same amount.
Thus, the use of any other reasonable value of Xc would not
affect our conclusions.
Fig. 9. DSC traces of glass with R = 2.00 (66.7 mol% Li2O). CM,
carbonate method; SM, solution method.
argue that the liquidus of the PED16 has some error by itself.
It is also worth mentioning that non-isothermal DSC
analyses do not guarantee that the detected melting peaks
refer to the equilibrium phases. Nevertheless, on heating, the
endpoint of the last endothermic peak (average 836°C) is
very close to the liquidus indicated by the PED (834°C). An
There are relative errors of ~10% in qcr due to an assumed
typical error of 10% in the experimental growth rates, u(T),
which were used for the calculations of qcr. But such errors

November 2011
Analysis of Glass Stability Parameters
3837
Table III. Characteristic Temperatures (°C) from the DSC Traces of Figs. 2–9.
16
16
R
mol% Li2O
Method
Tg
Tx
Tc
T”
Ts PED
Tm-os
Tm-ep
Tl PED
0.25
20.0
Carbonate
Solution
Carbonate
460
461
489
597
588
583
622
614
591
Ts = 726‡
Ts = 770‡
716
635 10
–
–
–
837
835
–
835
905
0.4
28.6
856
2
2
835
Ts = 853
722
825
Ts = 852
806
636
489
576
585
–
907
0.5†
0.7
33.3
41.2
Carbonate
Carbonate
463
459
510
494
516
511
–
908
–
926
909
917
879
2
832
Ts = 825
–
0.86†
1.0†
46.2
50.0
Carbonate
Solution
436
439
411
420
420
315
272
265
494
491
445
480
475
369
303
298
500
500
452
488
483
382
306
300
–
826
825
836
819
818
–
846
844
856
850
850
790
677
679
832
849
2
2
–
–
–
–
Carbonate
Solution I
Solution II
Carbonate
Carbonate
Solution I
–
1.5
2.0
60.0
66.7
Ts = 692
629‡
596
700 16
650 15
768
673
–
–
Ts = 643
596
Solution II
272
311
313
–
690
630‡
†stoichiometric and eutectic compositions: Tm-os–TPED as concluded in Ref. [17].
T” worth mentioning temperatures.
‡some experimental uncertainty in the determination of solidus temperature Ts.
The estimated precision of the DSC temperatures is 3°C–5°C.
I and II are replica of the same experimental set.
smaller GS than expected if only surface nucleation was pres-
ent. But, in general, the effect of internal nucleation in these
two glasses was negligible compared to copious surface
nucleation of the fine powders used here.
Our careful review of critical cooling rates and GS calcula-
tions led us to observe that possibly seven of the nine GS
parameters considered in Ref. [4], that is, KLL, KH, KW, KSP
,
K2, K4, and K3 (and not only the first three) show some
correlation with the cooling rate. But, in agreement with
Ref. [4], KLL, KH, and KW visually yield much better correla-
tions and thus, should be preferentially used when the three
DSC characteristic temperatures are available.
We must point out that the choice of linear regressions in
the graphs in the left hand side of Figs. 11–19 is arbitrary,
based on the general trend apparently shown by most of the
data points. However, there is no physical reason for that
choice. Indeed, one could, for instance, fit a high-order poly-
nomial to the data of left hand side Figs. 15 and 19, and
achieve higher correlation coefficients. Linear regressions
were chosen for their simplicity and a guide to the eye.
Figure 20 compares the four GS parameters that scale in a
similar range. One can see that among KLL, KH, KW, and K3,
KH covers the widest range, thus being the most stable
against statistical errors in the determination of the charac-
teristic temperatures by DSC. This conclusion agrees with
the recent theoretical calculations of Kozmidis-Petrovic.18
The GFA estimated by most of the tested GS parameters
allows one to qualitatively compare the ease with which a
certain composition can be obtained as a glass in comparison
to the others. This is an important tool when one aims, for
instance, to optimize the GFA by varying the composition
within a given system, although the time period needed for
significant crystallization at any temperature, and the critical
cooling rate are the most relevant parameters to be
determined.
Fig. 10. Liquidus temperature, Tm, of different compositions in the
system Li2O–B2O3obtained by DSC (open circles) compared with the
liquidus temperatures of a phase diagram from Ref. [16]. The error in
Tm is smaller than the size of the data point ( 5°C). In the same
graph, KH is shown for the same compositions. The errors in KH are
shown in Fig. 12.
are smaller than the data points in the log scale of Figs. 11–19.
For the calculations of qcr, the number of nucleation sites
per unit surface area, Ns, was considered constant (104 mꢀ2
)
and equal for all undercooled liquids, thus it does not con-
tribute to the estimated errors.
We recall that the calculated critical cooling rates of this
article refer to surface nucleation. Hence, the two glasses that
also present internal nucleation in addition to surface nucle-
ation (LS2 and LB2) could lead to a deviation of the data
points in the graphs on the left hand side of Figs. 11–19.
Indeed, although some GS points relative of these two com-
pounds are quite close to the line fits of Figs. 11–19, when
they deviate, for example, LS2 in Figs. 11, 12, and 18, the
shift direction may indicate some additional nucleation,
which would lead to a smaller Tx, and consequently, to a
The GFA estimated by the GS parameters from DSC
experiments can be used for systems for which crystallization
is fast enough to be detected in dynamic, non-isothermal
tests, such as the DSC. But as the best GS parameters

3838
Journal of the American Ceramic Society—Ferreira et al.
Vol. 94, No. 11
Fig. 11. Left: critical cooling rate4 versus the glass stability parameter KLL = Tx/(Tg + Tm) for several compositions. Right: the same KLL versus
composition in the Li2O–B2O3system.
Fig. 12. Left: critical cooling rate4 versus the glass stability parameter KH = (Tx ꢀ Tg)/(Tm ꢀ Tx) for several compositions. Right: Glass
stability parameter KH versus composition in the Li2O–B2O3system.
Fig. 13. Left: critical cooling rate4 versus the glass stability parameter KW = (Tx ꢀ Tg)/Tm for several compositions. Right: Glass stability
parameter KW versus composition in the Li2O–B2O3 system.
depend on the DSC crystallization temperature (Tx or Tc),
this technique is not good for glass-forming compositions for
which a crystallization peak cannot be determined during a
DSC experiment. We thus confirmed here the findings of
Ref. [4] that GS parameters that do not take crystallization
peaks into account (KT and K1) do not correlate with GFA.
Consequently, the range of application of the present tech-
nique does not include conventional glasses—very good glass
formers—that are designed not to crystallize during the fabri-
cation process or during a non-isothermal DSC run.
The resulting GS parameters for the present Li2O–B2O3
compositions are shown in the right hand side of Figs. 11–19.
One can see that among the compositions for which both the
carbonate and solution methods were used (R0.25, R0.86,
R1.0 and R2.0), only for R1.0, the GS of glasses prepared by
both methods disagree beyond the error limits. This result

November 2011
Analysis of Glass Stability Parameters
3839
Fig. 14. Left: critical cooling rate4 versus the glass stability parameter KT = Tg/Tm for several compositions. Right: Glass stability parameter KT
versus composition in the Li2O–B2O3 system.
Fig. 15. Left: critical cooling rate4 versus the glass stability parameter KSP = (Tx ꢀ Tg)*(Tc ꢀ Tx)/Tg for several compositions. Right: Glass
stability parameter KSP versus composition in the Li2O–B2O3system.
Fig. 16. Left: critical cooling rate4 versus the glass stability parameter K1 = (Tm ꢀ Tg) for several compositions. Right: Glass stability
parameter K1 versus composition in the Li2O–B2O3system.
indicates that such discrepancy was due to some uncontrolled
experimental variation, and not due to the method of sample
preparation. For the other three compositions, the synthesis
technique did not significantly affect the thermal behavior of
the glasses. If there is some significant difference in the water
content in the samples made by the different preparation
methods, it is approximately constant and resulted in similar
effects in the calculated GS parameters.
deviations of the actual glass composition from the nominal
one caused by impure chemicals or components lost during
weighing, mixing, or melting (see, e.g., the result for the sam-
ple with the composition of Li2O·2B2O3 (R0.5), which
approaches more the average data if one considers mol%
B2O3 is deviated a little from stoichiometric composition.
Indeed, a melting signal at 806°C is observed in the DSC
path of the sample R0.5 (detail of Fig. 4). From the PED
shown in Fig. 1, for small deviations from the stoichiometric
composition (R = 0.5), there is a eutectic reaction at 832°C
Based on the weight loss measurements, there is a small
error (a few percent) in the mol% B2O3 values, due to small

3840
Journal of the American Ceramic Society—Ferreira et al.
Vol. 94, No. 11
Fig. 17. Left: critical cooling rate4 versus the glass stability parameter K2 = (Tx ꢀ Tg) for several compositions. Right: Glass stability parameter
K2 versus composition in the Li2O–B2O3system.
Fig. 18. Left: critical cooling rate4 versus the glass stability parameter K3 = Tx/Tm for several compositions. Right: Glass stability parameter K3
versus composition in the Li2O–B2O3 system.
Fig. 19. Left: critical cooling rate4 versus the glass stability parameter K4 = (Tx ꢀ Tg)*(Tc ꢀ Tx)/Tm for several compositions. Right: Glass
stability parameter K4 versus composition in the Li2O–B2O3 system.
for compositions for which R > 0.5, and at 856°C for com-
positions for R < 0.5. Assuming that the small melting peak
observed at 806°C approaches more the eutectic at 832°C,
this indicates a deviation from the nominal composition
(R = 0.5) toward higher values of R, and thus the resulting
approximation of such data point to the average data ten-
dency corroborates our argument.
R0.7 (i.e., with increasing B2O3 from ~33 to 59 mol%
B2O3) show, in general, the lowest GS values of the scale
(given by the corresponding figures in the left) and they
are not much affected by the variation in composition
indicating poor and invariable GFA in this composition
range. However, for glasses with higher B2O3 contents
(R0.5 to R0.25, or approximately from 67 to 80 mol%
B2O3), one observes a faster increase of GS, increasing
the GFA of the corresponding compositions, as expected
Taking into account, only the GS parameters that show
a good correlation with qcr, the compositions from R2.0 to

November 2011
Analysis of Glass Stability Parameters
3841
(66.7 mol% lithia) indicating that, surprisingly, composition
does not significantly affect the GFA in this wide composi-
tional range. This general finding qualitatively agrees with
our successful experience of preparing the present glasses
with compositions up to and including20 R = 2.8 (74 mol%
lithia) and corroborates the adequacy of simple DSC tests to
comparatively gauge the GS and GFA of glasses.
IV. Conclusions
The results reported herein with a series of lithium borate
glasses of widely varying composition indicate that several
stability parameters, which are relatively simple to measure
with a differential scanning calorimeter (DSC), can be used
to gauge GS and vitrification ability as a function of compo-
sition. Only KT = Tg/Tm and K1 = (Tm ꢀ Tg), which do not
take DSC crystallization peaks into account, are unable to
indicate trends of GS with composition; all the other param-
eters give a similar reasonable trend.
Fig. 20. Comparison of different glass stability parameters, showing
that KH varies in a wider range than KLL, KW, and K3. Error bars
for KLL, KW, K3, and log(qcr) are smaller than the data points.
For this particular glass-forming system, seven stability
parameters plus laboratory observations during glass prepa-
ration indicate that the GFA is more or less the same over a
very wide compositional range, from 33 to 67 mol% B2O3.
But GFA is significantly augmented with B2O3 content for
compositions having more than 67 mol% B2O3.
from our qualitative laboratory observations during glass
preparation.
Figure 10 shows a minimum in the GS estimated by the
Hruby parameter, K , for example, which coincides with the
H
¨
References
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triangles all bridging oxygens and one tetrahedral boron on
two connected rings), triborate rings (R = 1/3 six membered
ring with two trigonal borons, all bridging oxygens and one
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h