NOC-15311; No of Pages 8
Journal of Non-Crystalline Solids xxx (2011) xxx–xxx
Contents lists available at ScienceDirect
Journal of Non-Crystalline Solids
j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j n o n c r y s o l
Structural organisation in oxide glasses from molecular dynamics modelling
Gavin Mountjoy ⁎, Bushra M. Al-Hasni, Christopher Storey
School of Physical Sciences, University of Kent, Canterbury, UK
a r t i c l e
i n f o
Article history:
Received 17 September 2010
Received in revised form 8 January 2011
Accepted 14 January 2011
Available online xxxx
Keywords:
Molecular dynamics
Silicate glasses
Medium range order
Phosphate glasses
a b s t r a c t
Classical molecular dynamics modelling has been used to obtain new models of 50CaO·50P2O5 and
50MgO·50SiO2 glasses and, together with previously published models of 63CaO·37Al2O3, and 50CaO·50SiO2
glasses, these have been inspected to evaluate structural features. For the first time, models of glasses near the
eutectic in three systems, aluminate, silicate, and phosphate, with the same modifier, Ca, have been compared.
All have short range order which is similar to that in crystals of the same composition, 5CaO·3Al2O3, CaSiO3
and Ca(PO3)2. There is a clear trend in bonding of bridging oxygen to Ca, which is dominant in aluminate glass,
common in silicate glass, and absent in phosphate glass. Preliminary results for 50MgO·50SiO2 glass show
unusual behaviour because ~ 5% of oxygen is present as “non-network” oxygen, i.e. bonded only to Mg. The
models show broader Qn distributions than seen in NMR experiments, and this remains an area for
improvement of MD modelling of glasses. The distributions of Ca in the models have been studied using the
pair distribution function TCaCa(r) which is found to be similar in the three glasses, and also similar to the
previous experimental measurement for 50CaO·50SiO2 glass. The distributions of Ca are markedly different in
the glasses compared to the crystals, being isotropic in the former and anisotropic in the latter, which should
be a factor in glass forming ability.
© 2011 Elsevier B.V. All rights reserved.
1. Introduction
The study of the structural organisation of oxide glasses has the
goal to recognise the different features of atomic structure, and how
these influence the preparation (e.g. glass forming ability) and
properties (e.g. durability) of oxide glasses. This goal can be followed
from different but related viewpoints based on chemical, experimental, and/or modelling approaches. The experimental approach is
essential because most information about structure is obtained from
experimental methods (see other articles in the current volume).
The chemical approach is motivated by the role of chemical bonds
in determining structure. Oxide materials have ionic character, and
cation–oxygen bonds are the fundamental structural unit. The large
oxygen anions come into contact with each other and form a relatively
dense packing, while cations are always separated by oxygen anions.
The knowledge of oxide structures is largely based on oxide crystals.
The traditional crystallographic viewpoint is not useful for glasses,
which lack symmetry. However, structural organisation in oxide
crystals can be very relevant to oxide glasses of similar composition. A
useful concept is Hawthorne's “binary structure” representation of
oxide crystal structures [1] as having: (i) a complex anionic
polyhedral array (e.g. metasilicate SiO2−
3 ) and (ii) low(er) valence
interstitial cations (e.g. Ca2+). This parallels the distinction in oxide
⁎ Corresponding author.
E-mail address: [email protected] (G. Mountjoy).
glasses between cations which are “network formers” and “network
modifiers” (discussed below).
The use of modelling (or simulation) methods to study oxide glass
structures is very complementary to experimental methods. The
modelling approach is primarily mathematical because it generates
predicted atomic coordinates from which other structural quantities
may be calculated and compared with experimental data. However,
classical molecular dynamics often produce models of oxide glasses
with limited accuracy. As discussed further in the current article, this
is evidenced by limited agreement between models and experimental
diffraction data.
In collating data from chemical, experimental and modelling
approaches, certain concepts of structural organisation in oxide
glasses have proved very useful. Firstly, Zachariesen's “random
network” model [2] stressed that oxide glasses are formed only if
they contain cations which act as “network formers”. Secondly,
Greaves' “modified random network” model [3] emphasised that
other cations may act as “network modifiers” which (i) depolymerise
the glass network and (ii) are necessarily located near to one another.
The distinction between network formers and modifiers is still
debated. The role of oxygen is distinguished as “bridging” or “nonbridging” depending on whether they are bonded to two or one
network formers (respectively). In the current article we show that a
third type of oxygen can be present in oxide glasses, which we refer to
as “non-network” oxygen.
The current article will illustrate structural features in oxide
glasses using recent and new results from classical molecular
0022-3093/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.jnoncrysol.2011.01.015
Please cite this article as: G. Mountjoy, et al., Structural organisation in oxide glasses from molecular dynamics modelling, J. Non-Cryst. Solids
(2011), doi:10.1016/j.jnoncrysol.2011.01.015
2
G. Mountjoy et al. / Journal of Non-Crystalline Solids xxx (2011) xxx–xxx
dynamics (MD) modelling (for review see [4]). This technique has the
advantages of simulating the melt-quench process by which oxide
glasses are prepared, and allowing a large number of atoms and time
steps. For the first time we compare models of three glass systems
with the same modifier cation, Ca. The results presented lead to the
discussion of the local environment of bridging oxygen, the
distribution of modifier cations, and the relationship between glass
and crystal structures of the same composition. The distribution of
modifier cations remains a poorly investigated aspect of the structural
organisation in oxide glasses.
2. Method
The results presented here were obtained using classical MD
modelling with rigid ion potentials. We present recent, previously
published, results for 63CaO·37Al2O3 [5] and 50CaO·50SiO2 [6]
glasses. Those results were obtained using a very similar method to
the following (see [5,6] for details). (One other MD study of
63CaO·37Al2O3 [7] glass is discussed in Ref. [5].) We also present
new, unpublished, results for MD modelling of 50CaO·50P2O5 and
50MgO·50SiO2 glasses. There are no published MD studies of
50CaO·50P2O5 glass. A recent MD study of 50CaO·50SiO2 and
50MgO·50SiO2 glasses by other authors [8] is referred to in Section 4.
For 50CaO·50P2O5 and 50MgO·50SiO2 glasses we used the
potentials of Teter [9,10], based on Buckingham expressions, given by
!
qi qj
Cij
r
− 6
+ Aij exp
Vij ðrÞ =
ρij
4πε0 r
r
ð1Þ
1.015, and 1.005 respectively). The fourth stage was a temperature
quench of 60,000 time steps from 1500 to 300 K (quench rate
1013 Ks− 1). For 50MgO·50SiO2 glass a temperature of 2000 K was
used instead of 1500 K due to its higher melting temperature. The
fifth and sixth stages were both temperature baths of 40,000 time
steps at 300 K, with and without equilibration, respectively. During
the sixth stage the structural parameters were sampled every 200
time steps to represent the effects of disorder due to thermal
vibrations, which is present in the experimental results.
The predicted atomic coordinates (Xi, Yi, and Zi) enable many
structural quantities to be calculated. Foremost among these are the
partial pair distribution function Tij(r) which we use in the form
Tij ðrÞ =
1 1 Ni Nj
∑ ∑ δðr Rlm Þ
r Ni ℓ = 1 m = 1
where ℓ and m are indices over individual atoms of types i and j
respectively, and Tij(r) → 4πrρj as r → ∞, where ρj is the atomic
number density of atom type j. Tij(r) is important because (i) the first
peak in Tij(r) characterises chemical bonds (discussed in Section 3),
and (ii) the weighted sum over Tij(r) can be compared with
experimental data obtained using X-ray and neutron diffraction.
The measured scattering intensity in a diffraction experiment can
be analysed to obtain the experimental structure factor S(Q), where Q
is the scattering vector (Q = 4πsin(θ)/λ) [15]. The S(Q) depends on
Tij(r) according to
Q ðSðQ Þ−1Þ = ∫ ∑
i;j
where i and j are atom types, r is distance, qi is charge, and Aij, ρij, and
Cij are potential parameters shown in Table 1 (and ε0 = 8.854 × 10− 12
C2N− 1m− 2). Note that qi is the partial charge which takes into
account some effects of covalence. In addition, for the 50CaO·50P2O5
glass we used three body potentials of the form 1/2kiji(θiji − θ)2 where
θ is the bond angle for O–P–O and P–O–P interactions (with
kiji = 3.5 eV and Θiji = 109.47° for O–P–O, and kiji = 3.0 eV and
Θiji = 135.5 for P–O–P [9]). The performance of the potentials was
evaluated by modelling known crystal structures of calcium metaphosphate CaP2O6 [28] and enstatite MgSiO3 [11] (using the
methodology described in Refs. [5] and [6]). All short range parts of
the potentials were subjected to a cut-off of 7.5 Å. The modelling used
the DLPOLY programme [12] with a Berensden NVT thermostat, with a
relaxation time of 2 ps, and time steps of 1 fs and 2 fs for
50CaO·50P2O5 and 50MgO·50SiO2 glasses respectively. The Coulomb
part of the potential was calculated by using the Ewald sum method
with a precision of 10− 5.
Each model has ~1000 atoms, in a cubic box with length L ~24 Å.
Random starting configurations and periodic boundary conditions
were used. The densities were controlled to match the experimental
densities for 50CaO·50P2O5 [13] and 50MgO·50SiO2 [14] glasses.
The modelling used a series of stages. The first three stages were
temperature baths (with equilibration) at 6000, 3000, and 1500 K of
40,000 time steps each (and with linear thermal expansion of 1.03,
Table 1
Potential parameters [9,10] used with Eq. (1) for MD modelling of 50CaO·50P2O5 and
50MgO·50SiO2 glasses.
i–j
qi (e)
Aij (eV)
ρij (Å)
Cij (eV Å− 6)
Ca–O
P–O
O–O
Mg–O
Si–O
O–O
1.2
3.0
− 1.2
1.2
2.4
− 1.2
7747
27,722
1992
7063
13,702
1844
0.2526
0.1819
0.3436
0.2109
0.1938
0.3436
93.10
86.86
192.58
19.21
54.68
192.58
ð2Þ
wij ðQ Þ Tij ðrÞ−4πrρj sinðQrÞdr
cj
ð3Þ
where wij is the weighting factor for scattering from atom types i and
j, and cj is the atomic concentration. A key means to evaluate MD
models is to carry out the comparison in Eq. (3), where the left side is
measured in a diffraction experiment and the right side is calculated
from the Tij(r) of the model. Fig. 1 shows the S(Q) for models of
50CaO·50P2O5 and 50MgO·50SiO2 glasses compared to the experiment. The level of agreement is similar to that reported for other
models of mixed oxide glasses made using Buckingham potentials, i.e.
the literature shows the same comparison for the models of
50CaO·50SiO2 [6] and 63CaO·37Al2O3 [5] glasses.
3. Results
3.1. Short range order
Fig. 2 shows the models of 63CaO·37Al2O3, 50CaO·50SiO2 and
50CaO·50P2O5 glasses. Fig. 3 shows the Tij(r) focussing on the first two
peaks which correspond to bonds to network formers and modifiers.
This is the first time that models have been compared for three glass
systems, aluminate, silicate and phosphate, with the same modifier,
Ca. As expected, each glass contains network formers (Al/Si/P) with
unambiguous tetrahedral coordination and this is reflected in a sharp
first peak in Tij(r) (and also sharp bond angle distributions, not
shown). The 50CaO·50P2O5 glass has ~2% of five-fold coordinated P,
which should be considered a defect in the potential [9]. The network
modifier, Ca, has less well-defined and variable coordination. A cut-off
distance of 3 Å is used, which is conventionally taken as the first
minimum in Tij(r). Table 2 shows the range of Ca coordination in the
three glasses. The short range order is clearly very different for
network formers compared to modifiers.
The oxygen in the models have been classified as bridging (Ob) or
non-bridging (Onb). Fig. 2 shows the contributions to cation–oxygen
Tij(r) from both Ob and Onb. The network formers bond to Ob and Onb in
the expected proportions, given the average connectivity of the
network (discussed in Section 3.2). Interestingly, Ca is also bonded to
both Ob and Onb. This is very important in 63CaO·37Al2O3 glass, since
Please cite this article as: G. Mountjoy, et al., Structural organisation in oxide glasses from molecular dynamics modelling, J. Non-Cryst. Solids
(2011), doi:10.1016/j.jnoncrysol.2011.01.015
G. Mountjoy et al. / Journal of Non-Crystalline Solids xxx (2011) xxx–xxx
0.4
0.0
-0.4
model neutron
experiment neutron
model x-ray
experiment x-ray
0.8
0.4
0.0
x-ray S(Q)-1
neutron S(Q)-1
a
3
-0.4
0
5
10
15
20
-0.8
25
Q (A-1)
0.3
0.0
-0.3
model neutron
experiment neutron
model x-ray
experiment x-ray
0.6
0.3
0.0
x-ray S(Q)-1
neutron S(Q)-1
b
-0.3
0
5
10
15
20
-0.6
25
Q (A-1)
Fig. 1. Comparison of neutron and X-ray diffraction structure factors S(Q) for
(a) 50CaO·50P2O5 and (b) 50MgO·50SiO2 glasses from models and experiment [13,14].
bridging Al–Ob–Al bonds do not satisfy the bond valence requirements
of Ob. In contrast, Ca bonding to Ob does not occur in 50CaO·50P2O5
glass because Ob is bonded to two highly charged P ions which repel Ca
ions.
We present preliminary results for the 50MgO·50SiO2 glass. Note
that the region of phase separation in the xMgO·(100-x)SiO2 system
is at x ≤ 40. The model of 50MgO·50SiO2 glass is interesting because it
does not follow the expected behaviour of containing only Ob (bonded
to two Si) and Onb (bonded to one Si). Instead the model contains a
non-negligible proportion of 4.5% of oxygen (27 out of 600 oxygen
atoms) which are bonded only to Mg and not to Si. These oxygen
atoms are neither Ob nor Onb, and we refer to them as “non-network”
oxygen. This result is clear by visual inspection of the model, where
Fig. 4 shows non-network oxygen as medium spheres.
n = 2 × (4 − y). The observed values of average bQnN are very close to
the expected values, as shown in Table 3. Table 3 also shows that there
is a range of Qn around the average bQnN, as is common in MD models
of oxide glasses [17].
3.2. Connectivity of network formers
3.3. Distribution of network modifiers
The connectivity of the glass network is denoted by Qn for
tetrahedral network formers like Si, where n is the number of nonbridging oxygen per Si. For the present glass models the network
formers Al/Si/P are ~100% tetrahedra. If all oxygen are bonded to
either one or two network formers then the average bQnN is directly
dependent on the O:Al/Si/P ratio, denoted by y, via the relation
The distribution of network modifiers can be inspected visually via
images of models shown in Fig. 2, where Ca is shown as large spheres.
In contrast to network formers, there are few quantitative measures of
the distribution of network modifiers, because they have a range of
coordination polyhedra and possible multiple connections via
corners, edges and faces. The TCaCa(r) distributions for the models
Fig. 2. Images of models for (a) 63CaO·37Al2O3 [5], (b) 50CaO·50SiO2 [6] and
(c) 50CaO·50P2O5 glasses. (Tetrahedra show aluminate, silicate or phosphate network
and large spheres show Ca.).
Please cite this article as: G. Mountjoy, et al., Structural organisation in oxide glasses from molecular dynamics modelling, J. Non-Cryst. Solids
(2011), doi:10.1016/j.jnoncrysol.2011.01.015
4
G. Mountjoy et al. / Journal of Non-Crystalline Solids xxx (2011) xxx–xxx
a
12
Al-Ob
Al-Onb
Al-O
O-O
Ca-Ob
Ca-Onb
Ca-O
8
Tij(r)
1.6
2
2.4
2.8
r(Å)
b
12
Si-Ob
Si-Onb
Si-O
O-O
Ca-Ob
Ca-Onb
Ca-O
CN (%)
Average
CN
4
5
6
7
8
0
1
5
19
12
32
50
46
49
26
34
13
5
7
1
6.1
6.4
5.8
are shown in Fig. 5. In general TMM(r) for modifiers (M) are difficult to
analyse beyond the first peak (the number of neighbouring
modifiers), and very little experimental data is available. One of the
only experimental measurements of T MM (r) was for Ca in
50CaO·50SiO2 glass [18], and Fig. 5 shows this is in good agreement
with the model. (The experimental data is in the form TCaCa(r), but
with arbitrary units due to the way the data was reported, and the first
peak at 2.4 Å is reported to be an artefact [18]). One of the only other
quantitative functions reported for describing the distribution of
modifiers is the second dipole moment, which can be measured in
NMR experiments [10].
4. Discussion
8
Tij(r)
4.1. Classical MD modelling of glasses
4
0
1.2
1.6
2
2.4
2.8
r(Å)
c
Glass
63CaO·37Al2O3 [5]
50CaO·50SiO2 [6]
50CaO·50P2O5 (current study)
4
0
1.2
Table 2
Range of Ca coordination number (CN) in models of 63CaO·37Al2O3, 50CaO·50SiO2 and
50CaO·50P2O5 glasses.
12
P-Ob
P-Onb
P-O
O-O
Ca-Ob
Ca-Onb
Ca-O
Tij(r)
8
Although a well-established and popular modelling method,
classical MD has some limitations. Firstly, the quench rates used in
MD modelling (the 1013 Ks− 1 used in the current work is common
[10]) are orders of magnitude higher than the experimental quench
rates (typically 103 Ks− 1). There is a continuing investigation of the
role of quench rates [19]. Secondly, MD models made using an NPT
thermostat often do not exactly agree with experimental density. An
NVT thermostat can be used to ensure density is correct, as in the
current work. (However, this may impact on short range order which
will be more relaxed when an NPT thermostat is used.) Thirdly, while
MD models usually show the correct value for average bQnN, e.g. n = 2
in a metasilicate glass, they tend to show a wider Qn distribution (i.e.
greater disassociation 2Qn → Qn + 1+ Qn − 1) than is seen in 29Si or 31P
NMR experiments [17]. This is true of the glasses as shown in Table 3
[20–22].
Fourthly, the models are not always compared with experimental
neutron and X-ray diffraction data, and when they are compared
there may not be complete agreement, as exemplified in Section 2.
4
0
1.2
1.6
2
2.4
2.8
r(Å)
Fig. 3. Pair distribution functions Tij(r) of cation–oxygen bonds for (a) 63CaO·37Al2O3
[5], (b) 50CaO·50SiO2 [6] and (c) 50CaO·50P2O5 glasses, where oxygen has been
distinguished as bridging, Ob (thick black lines), or non-bridging, Onb (thick grey lines).
(The Tij(r) for Al–O, Si–O and P–O has been scaled by ×½).
Fig. 4. image of model for 50MgO·50SiO2 glass. (Tetrahedra show silicate network and
large spheres show Mg). In this glass 4.5% of oxygen is bonded only to Mg and not to Si,
and we refer to these as “non-network” oxygen (medium spheres).
Please cite this article as: G. Mountjoy, et al., Structural organisation in oxide glasses from molecular dynamics modelling, J. Non-Cryst. Solids
(2011), doi:10.1016/j.jnoncrysol.2011.01.015
G. Mountjoy et al. / Journal of Non-Crystalline Solids xxx (2011) xxx–xxx
Table 3
Qn distributions in MD models of oxide glasses compared to NMR experiments.
Glass
b QnN
Q0
Q1
Q2
Q3
Q4
63CaO·37Al2O3 model [5]
63CaO·37Al2O3 27Al NMR [20]
50CaO·50SiO2 model [6]
50CaO·50SiO2 29Si NMR [21]
50CaO·50P2O5 model (current study)
50CaO·50P2O5 31P NMR [22]
3.28
3.38
2.08
2.01
2.01
1.96
0
–
6
0
2
0
3
–
23
18
23
4
12
–
38
63
50
96
39
–
27
19
22
0
45
–
7
0
3
0
The comparison is best carried out using Eq. (3), as this avoids the
Fourier Transform of S(Q) which introduces a broadening factor (the
latter may be undefined when comparisons are reported in the
literature). The best agreement has been obtained for models of pure
SiO2 glass [23,24] (because the potentials are most successful for this
composition), but even for this glass there are noticeable differences
to experimental diffraction data (see [16] for example). Improved
agreement with experiment should be possible through the use of
improved interatomic potentials (e.g. MD models of 20Na2O·80SiO2
glass show very good agreement with neutron diffraction data [25]).
4.2. Short range order
It is interesting to compare the short range order in 63CaO·37Al2O3,
50CaO·50SiO2 and 50CaO·50P2O5 glasses with crystals of the same
composition: i.e. 5CaO·3Al2O3 [26], CaSiO3 (wollastonite) [27] and
Ca(PO3)2 [28] crystals. These crystals also have tetrahedral coordination
of network formers. In 63CaO·37Al2O3 glass Ca has an average
coordination number CN =6.1 with 3.3 bonds to Ob and 2.8 bonds to
Onb (respectively). This is very similar to the 5CaO·3Al2O3 crystal in
which Ca has an average CN= 6.0 with 3.4 and 2.6 bonds to Ob and Onb
respectively. In 50CaO·50SiO2 glass the Ca has an average CN =6.4 with
1.0 bonds to Ob and 5.4 bonds to Onb. This is very similar to CaSiO3 crystal
in which Ca has CN= 6.3 with 1.0 bonds to Ob and 5.3 bonds to Onb. In
50CaO·50P2O5 glass Ca has an average CN =5.8 (5.8 bonds to Onb),
which is noticeably lower than in Ca(PO3)2 crystal where CN =7.5 (7.5
bonds to Onb). The similarity in short range order of network modifiers
(Ca) between glasses and crystals can be attributed to similar chemical
interactions. The difference which occurs in 50CaO·50P2O5 glass suggests
that another factor may be important.
The results presented here show some noteworthy features of the
local environment of oxygen. As previously reported [29], the bonding
of Ob to Ca is common in 50CaO·50SiO2 glass. The average Ca–Ob
CN = 1.0 may seem small, but it means that on average each Ob in the
glass is bonded to two Si ions plus one Ca ion. The same comments are
true for the CaSiO3 crystal. Recent work has shown that bonding of Ob
to Na ions is widespread in sodium silicate glasses [24], and that
bonding of Ob to network modifiers is expected to be common in
alkali and alkaline earth silicate glasses [30]. This structural feature is
not normally emphasised in the “modified random network” model
[3,29], but is important for glass properties such as durability, which
depend on the strength of Si–Ob–Si linkages.
Another interesting result concerning local environment of oxygen
is the observation of “non-network” oxygen in the model of
50MgO·50SiO2 glass. This is surprising because the glass is far from
orthosilicate compositions (i.e. expected bQnN = Q0), where some
excess oxygen might be expected. The result is supported by NMR
observations [31] which are reproduced in Fig. 6, in which article it
was reported “the lower frequency shoulder in the 29Si MAS NMR... is
primarily a characteristic of Q3 species”. Fitting of Gaussians in Fig. 6
clearly shows a significant bias away from Q2 towards Q3 which is not
expected at the metasilicate composition (i.e. expected bQnN = Q2).
The models of 50CaO·50SiO2 and 50MgO·50SiO2 glasses presented
here (both metasilicates), have bQnN = 2.01 and bQnN = 2.26 respectively. A recent MD study of 50CaO·50SiO2 and 50MgO·50SiO2 glasses
[8] gave results of bQnN = 2.05 and bQnN = 2.35 respectively,
confirming the presence of “non-network” oxygen in the latter. A
recent 29Si NMR study of 50MgO·50SiO2 glass [32] reports a value of
bQnN = 2.15, corresponding to 2.5% of “non-network” oxygen. Hence
both NMR and MD results indicate the presence of non-network
oxygen, although not in exactly the same amount (something which
may depend on the quench rate in MD). Such non-network oxygen
have recently been observed also in a model of 40Fe2O3·60P2O5 glass
which has the pyrophosphate composition (i.e. expected bQnN = Q1),
as reported in another article in the current volume [33].
4.3. Connectivity of network formers
All of the glass models presented here have well-defined
tetrahedral networks. It is particularly useful to look at measures
of connectivity which can be measured using NMR spectroscopy.
Foremost is the Qn distribution which was discussed above in
2
1
63CaO·37Al2O3
50CaO·50SiO2
50CaO·50P2O5 x2
0
10
0
2
4
6
8
TCaCa(r) (arb. units)
TCaCa(r)
5
0
10
-60
-80
29Si
-100
-120
-140
chemical shift (ppm)
r (Å)
Fig. 5. The distribution of Ca as represented by TCaCa(r) for the models of 63CaO·37Al2O3
[5], 50CaO·50SiO2 [6] and (c) 50CaO·50P2O5 glasses, and the experimental measurement
of TCaCa(r). (The comparison for 50CaO·50SiO2 glass was first reported in Ref. [6]).
Fig. 6. 29Si NMR chemical shift spectrum reported for 50MgO·50SiO2 glass [31]. The
spectrum has been fitted (dotted line) with two Gaussians (dashed lines) at − 81 ppm
and − 100 ppm, consistent with Q2 and Q3 groups, with relative areas of 78% and 22%
(respectively).
Please cite this article as: G. Mountjoy, et al., Structural organisation in oxide glasses from molecular dynamics modelling, J. Non-Cryst. Solids
(2011), doi:10.1016/j.jnoncrysol.2011.01.015
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G. Mountjoy et al. / Journal of Non-Crystalline Solids xxx (2011) xxx–xxx
Sections 3.2 and 4.1. This can be predicted for the different levels
of (i) minimum or (ii) maximum disassociation (i.e. 2Qn → Qn + 1
+ Qn − 1) as shown in Fig. 7(a). (Case (i) is calculated by assuming
NOb is equal to nNQn/2 + (n − 1)NQn − 1/2, where N is “number of”.
Case (ii) is calculated using the binomial distribution of (α + (1 − α))4
where α and (1 − α) are the proportions of network former bonds to
Ob and Onb respectively.) As discussed above, the Qn distributions from
models tend to correspond more with maximum disassociation,
whereas those from experiments tend to correspond more with
minimum disassociation (see Table 3). The next level of complexity
concerns the distribution of Qn − Qm connections. This can be
predicted for the different preferences of (iii) random or (iv)
heterogeneous connections. Fig. 7(b) shows the different predictions
(iii) and (iv) for glasses with minimum disassociation, i.e.
corresponding to (i). (Case (iii) is calculated from the binomial
distribution of (αn + αn − 1)4 where αn is the proportion network
former bonds to Ob which belong to Qn tetrahedra. Case (iv) is
calculated by assuming that the number of Qn − Qn − 1 connections is
equal to the minimum of nNQn and (n − 1)NQn − 1, and the remainder
of the connections are Qn − Qn.) Experimental data on Qn − Qm
connections is available from NMR spectroscopy. For example 2D 31P
NMR of ultraphosphate glasses (with O:P ratio b3) shows a high
proportion of Q2 − Q3 connections [34], corresponding with preferred
heterogeneity. Few comparisons of Qn − Qm connections have been
reported for MD models (e.g. [17]), and network connectivity remains
a challenge for MD modelling of oxide glasses.
a
1
Q4
Q3
Q2
Q1
Q0
proportion Qn
0.75
4.4. Distribution of network modifiers
The modified random network model [3] implies that modifiers are
located near one another, in regions which we here refer to as “channels”.
These “channels” should be important for glass properties such as
conductivity and durability, and should somehow develop as modifiers
are added to the glass network. In xNa2O·(100-x)SiO2 glasses modifiers
(Na) can be added without phase separation [35], but in xCaO·(100-x)
SiO2 glasses there is phase separation for low Ca content [6]. For example,
Fig. 8 shows images of models of xCaO·(100-x)SiO2 glasses [6] for (a)
x = 10 with phase separation, and (b) x = 30 with no phase separation
(note that Fig. 2(b) shows the model for x = 50). To date there has been
little progress using models to quantify the development of “channels”
and thereby obtain insights into glass properties.
The distribution of Ca in 50CaO·50SiO2 glass has previously been a
subject of considerable interest. The measurement of TCaCa(r) was
interpreted in comparison with CaSiO3 crystal as evidence for 2D (twodimensional) ordering of Ca in the glass [18] but the model shown in
Fig. 2(b) does not show any evidence for this, although the model does
agree with the measured TCaCa(r) as shown in Fig. 5. Interestingly the
TCaCa(r) for 50CaO·50P2O5 glass is extremely similar to that for
50CaO·50SiO2 glass (see Fig. 5), perhaps because these are both
“meta” compositions. Also interesting, the TCaCa(r) for 63CaO·37Al2O3
glass has very similar features, differing only in amplitude (reflecting the
lower Ca content). This is the first time TCaCa(r) has been compared in
three different glass systems, and the very similar features suggest there
are common factor(s) which influence the modifier distribution.
Q4
Q3
Q2
Q1
Q0
0.5
0.25
0
2
2.5
3
3.5
O:Al/Si/P ratio
proportion of Qn-Qm connections
b
1
Q4-Q4
Q4-Q3
Q3-Q3
Q3-Q2
Q2-Q2
Q2-Q1
Q1-Q1
0.75
Q4-Q4
Q4-Q3
Q3-Q3
Q3-Q2
Q2-Q2
Q2-Q1
Q1-Q1
0.5
0.25
0
2
2.5
3
3.5
O:Al/Si/P ratio
Fig. 7. Connectivity of tetrahedral networks with different O:Al/Si/P ratios.
(a) Distribution of Qn for (i) maximum (thin lines) and (ii) minimum (thick line)
disassociation, i.e. 2Qn → Qn − 1 + Qn + 1. For a network with minimum disassociation:
(b) distribution of Qm − Qn connections for (iii) random (thick lines) and (iv) maximally
heterogeneous (thin lines) connectivity.
Fig. 8. Images of models for xCaO·(100-x)SiO2 glasses with (a) x = 10 and (b) x = 30.
(Tetrahedra show silicate network and large spheres show Ca). (Note that Fig. 3 (b)
shows the model for x = 50).
Please cite this article as: G. Mountjoy, et al., Structural organisation in oxide glasses from molecular dynamics modelling, J. Non-Cryst. Solids
(2011), doi:10.1016/j.jnoncrysol.2011.01.015
G. Mountjoy et al. / Journal of Non-Crystalline Solids xxx (2011) xxx–xxx
7
In general, the relation between glasses and the crystals of the
same composition is much discussed in relation to crystallisation. In
Fig. 9 we show images of the 5CaO·3Al2O3, CaSiO3 (wollastonite) and
Ca(PO3)2 crystals with the same composition as the models of glasses
shown in Fig. 2. All of the crystals have notably anisotropic
distributions of modifiers (Ca). Visual inspection of the models
shows no evidence for similar distributions of Ca in the glasses. This
may be an important factor in glass formation. The glasses and crystals
are all close to the eutectics in the xCaO·(100-x)Al2O3, xCaO·(100-x)SiO2
and xCaO·(100-x)P2O5 phase diagrams. The melts would be expected to
have isotropic distributions of modifiers (like the glasses), and this would
be a barrier to crystallisation (the latter requiring an anisotropic
distribution of modifiers).
Despite the marked difference in the distribution of modifiers
(Ca) between the glasses and crystals, there is a similar short
range order (as discussed in Section 4.2). The “stereo-chemically
defined” model of Gaskell [36] supposes that the same local
structural units exist in glasses and crystals. In crystals these
structural units are packed together following regular rules which
produce periodic structures, whereas in glasses the packing rules
are more varied and produce non-periodic structures. This
viewpoint appears to be valid for pure SiO2 with structural units
of tetrahedra, since Hobbs et al. [37] have generated models of
amorphous SiO2 by varying the tetrahedral packing rules from
crystalline SiO2 polymorphs. Fig. 10 illustrates the application of
this concept to oxide glasses containing modifiers, where the
structural unit (dashed line) should be a network former
coordination polyhedral (triangle) together with a modifier(s)
(circle). This is a recognisable structural unit in both glasses and
crystals, but the different packing of such units produces marked
differences in the distribution of modifiers.
5. Conclusions
Fig. 9. Images of models for (a) 5CaO·3Al2O3 (pentacalcium trialuminate) [26],
(b) CaSiO3 (wollastonite) [27] and (c) Ca(PO3)2 (calcium metaphosphate) [28] crystals.
a
Ca
b
In the current work we have presented new MD models for
50CaO·50P2O5 and 50MgO·50SiO2 glasses. For the first time there has
been a comparison of the structures of glasses near the eutectic in
three systems, 63CaO·37Al2O3, 50CaO·50SiO2 and 50CaO·50P2O5,
with the same modifier, Ca. The short range order, influenced by the
underlying chemical interactions, is found to be similar in glasses and
crystals of the same composition, 5CaO·3Al2O3, CaSiO3 and Ca(PO3)2.
There is a clear trend in bonding of bridging oxygen to Ca, which is
dominant in aluminate, common in silicate, and absent in phosphate.
The preliminary results for 50MgO·50SiO2 glass are significant
because they demonstrate the presence of ~ 5% of the non-network
oxygen in this system. The connectivity of the network formers Al/Si/P
remains an area for future improvement of MD models, to obtain
narrower Qn distributions. The distribution of Ca has been compared
across the three glasses and TCaCa(r) shows very similar features
which are also in agreement with the experimental measurement of
c
Onb
Si
Ca
Ob
Si
Fig. 10. Schematic of (a) short range order in oxide glasses, and stereo-chemically defined conceptual model [36] applied to oxide (b) glasses and (c) crystals. The “repeated” unit of
structure (dashed line) is a network former polyhedra (triangle) together with a network modifier (circle).
Please cite this article as: G. Mountjoy, et al., Structural organisation in oxide glasses from molecular dynamics modelling, J. Non-Cryst. Solids
(2011), doi:10.1016/j.jnoncrysol.2011.01.015
8
G. Mountjoy et al. / Journal of Non-Crystalline Solids xxx (2011) xxx–xxx
TCaCa(r) for 50CaO·50SiO2 glass. The distributions of Ca are confirmed
to be isotropic in the glasses, whereas they are strongly anisotropic in
the crystals, which should be a factor in glass forming ability. The
stereo-chemically defined model may be useful to explain how both
non-periodic and periodic structures can arise based on similar short
range order.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
F.C. Hawthorne, Acta Cryst. B 50 (1994) 481.
W.H. Zachariesen, J. Am. Ceram. Soc. 54 (1932) 3841.
G.N. Greaves, J. Non-Cryst. Solids 71 (1985) 203.
A.N. Cormack, X. Yuan, B. Park, Glass Phys. Chem 27 (2001) 28.
B.W.M. Thomas, R.N. Mead, G. Mountjoy, J. Phys. Condens. Matter 18 (2006) 4697.
R.N. Mead, G. Mountjoy, J. Phys. Chem. B 110 (2006) 14273.
E.T. Kan, S.J. Lee, A.C. Hannon, J. Non-Cryst. Solids 352 (2006) 725.
K. Shimoda, M. Okuno, J. Phys. Condens. Matter 18 (2006) 6531.
E.B. Clark, R.N. Mead, G. Mountjoy, J. Phys. Condens. Matter 18 (2006) 6815.
J. Du, A.N. Cormack, J. Non-Cryst. Solids 349 (2004) 66.
F.C. Hawthorne, J. Ito, Can. Mineral. 15 (1977) 321.
W. Smith, T. Forester, J. Mol. Graphics 14 (1996) 136.
K.M. Wetherall, D.M. Pickup, R.J. Newport, G. Mountjoy, J. Phys. Condens. Matter
21 (2009) 035109.
[14] M.C. Wilding, C.J. Benmore, J.A. Tangeman, S. Sampath, Europhys. Lett. 67 (2004) 212.
[15] S.R. Elliott, Physics of Amorphous Materials, Longman Scientific and Technical,
London, 1990.
[16] N. Afify, G. Mountjoy, Phys. Rev. B 79 (2009) 024202.
[17] L. Olivier, X. Juan, A.N. Cormack, C. Jäger, J. Non-Cryst. Solids 293–295 (2001) 53.
[18] M.C. Eckersley, P.H. Gaskell, A.C. Barnes, P. Chieux, Nature 335 (1988) 525;
P.H. Gaskell, M.C. Eckersley, A.C. Barnes, P. Chieux, Nature 350 (1991) 675.
[19] L.R. Corrales, J. Du, Phys. Chem. Glasses 46 (2005) 420.
[20] J.R. Allwardt, S.K. Lee, J.F. Stebbins, Am. Mineral. 88 (2003) 949.
[21] P. Zhang, P.J. Grandinetti, J.F. Stebbins, J. Phys. Chem. B 101 (1997) 4004.
[22] D.M. Pickup, I. Ahmed, P. Guerry, J.C. Knowles, M.E. Smith, R.J. Newport, J. Phys.
Condens. Matter 19 (2007) 415116.
[23] A.C. Wright, J. Non-Cryst. Solids 159 (1993) 264.
[24] J. Du, A.N. Cormack, J. Non-Cryst. Solids 293–295 (2001) 283.
[25] S. Ispas, M. Benoit, P. Jund, R. Jullien, Phys. Rev. B 64 (2001) 214206.
[26] M.G. Vincent, J.W. Jeffery, Acta Cryst. B 34 (1978) 1422.
[27] Y. Ohashi, Phys. Chem. Miner. 10 (1984) 217.
[28] W. Rothammel, H. Burzlaff, R. Specht, Acta Cryst. C 45 (1989) 551.
[29] R.N. Mead, G. Mountjoy, Phys. Chem. Glasses 46 (2005) 311.
[30] G. Mountjoy, J. Non-Cryst. Solids 353 (2007) 1849.
[31] S.J. Gaudio, S. Sen, C.E. Lesher, Geochim. Cosmochim. Acta 72 (2008) 1222.
[32] S. Sen, H. Maekawa, G.N. Papatheodorou, J. Phys. Chem. B 113 (2009) 15243.
[33] B. Al-Hasni, G. Mountjoy, Structural investigation of iron phosphate glasses using
molecular dynamics simulation, J. Non-Cryst. Solids (in press), doi:10.1016/j.
jnoncrysol.2010.10.010.
[34] C. Jäger, M. Feike, R. Born, H.W. Spiess, J. Non-Cryst. Solids 180 (1994) 91.
[35] J.E. Shelby, Introduction to Glass Science and Technology, Royal Society of
Chemistry, London, 2005.
[36] P.H. Gaskell, in: J. Zarzycki (Ed.), Glasses and Amorphous Materials, Vol. 9 of
Materials Science and Technology, VCH, Weinheim, 1991, p. 193.
[37] L.W. Hobbs, C.E. Jesurum, V. Pulim, B. Berger, Philos. Mag. A 78 (1998) 679.
Please cite this article as: G. Mountjoy, et al., Structural organisation in oxide glasses from molecular dynamics modelling, J. Non-Cryst. Solids
(2011), doi:10.1016/j.jnoncrysol.2011.01.015