PHYSICAL REVIEW B 76, 224202 共2007兲
Structure and dynamics of bioactive phosphosilicate glasses and melts from ab initio
molecular dynamics simulations
Antonio Tilocca*
Department of Chemistry, University College London, United Kingdom
共Received 16 July 2007; revised manuscript received 25 September 2007; published 27 December 2007兲
Ab initio 共Car-Parrinello兲 molecular dynamics simulations were carried out to investigate the melt precursor
of a modified phosphosilicate glass with bioactive properties, and to quench the melt to the vitreous state. The
properties of the 3000 K liquid were extensively compared with those of the final glass structure. The melt is
characterized by a significant fraction of structural defects 共small rings, undercoordinated and overcoordinated
ions兲, often combined together. The creation or removal of these coordinative defects in the liquid 共through
Si-O bond formation or dissociation兲 reflects frequent exchanges within the silicate first coordination shell,
which in turn dynamically modify the intertetrahedral connectivity of silicate groups. The observed dynamical
variation in both the identity and the number of silicate groups linked to a tagged Si 共Qn speciation兲 are
considered key processes in the viscous flow of silicate melts 关I. Farnan and J. F. Stebbins, Science 265, 1206
共1994兲兴. On the other hand, phosphate groups do not show an equally marked exchange activity in the
coordination shell, but can still form links with Si. Once formed, these Si-O-P bridges are rather stable, and in
fact they are retained in the glass phase obtained after cooling; their formation within the present full ab initio
melt-and-quench approach strongly supports their presence in melt-derived phosphosilicate glasses with bioactive applications. On the other hand, the simulations show that the fraction of structural defects rapidly
decreases during the cooling, and the glass is essentially free of miscoordinated ions and small rings.
DOI: 10.1103/PhysRevB.76.224202
PACS number共s兲: 61.20.Ja, 61.43.Fs, 66.10.⫺x, 71.15.Pd
I. INTRODUCTION
Melt-derived phosphosilicate glasses containing sodium
and calcium network modifiers are widely employed in restorative biomedical applications, in which their fast surface
response upon contact with a physiological medium leads to
an efficient integration of the biomaterial with the living tissues, such as bones or muscles.1,2 The success of such applications depends on the rate of formation of chemical bonds
between the glass surface and the tissues: this rate is often
taken as a measure of the glass bioactivity, and is dramatically affected by the composition.3 Despite the crucial importance of understanding composition-bioactivity relationships in order to enhance the effectiveness of bioglasses for
specific applications, the investigation of these effects is generally based on trial-and-error approaches.4 A thorough understanding of the microscopic structure of these biomaterials, which would be the starting point of a more rational
approach to optimize their properties, has not emerged yet.
Some information on the medium-range structure has been
provided by NMR and IR/Raman spectroscopy:5–7 these
studies have revealed that the most bioactive composition of
this class, 45S5 Bioglass®, is characterized by a very open
silicate network, dominated by Q2 and Q3 species 共a Qn species is a network-forming ion bonded to n bridging oxygens兲,
whereas phosphate groups are predominantly isolated. These
data were recently complemented by our molecular dynamics simulations, in which we explored in higher detail the
microscopic structure of these materials, highlighting several
effects which can steer the bioactive behavior:8–11 for
instance, the coordination environment of network formers
and modifiers, the tendency to form cluster and
inhomogeneities,8,10 and the occurrence of chain and ring
nanostructures9 were discussed in relation to the bioactivity.
1098-0121/2007/76共22兲/224202共13兲
Moreover, ab initio molecular dynamics 共AIMD兲
simulations12 provided new insight into vibrational and electronic properties of these materials and allowed us to highlight the specific contributions of selected structural units.11
Because the initial structure of the glass was obtained from
classical molecular dynamics 共MD兲 melt and quench, only
the short-range environment was fully relaxed at the ab initio
level, whereas the medium-range structure was determined
by the classical potential used to generate the glass. Although
our previous work seems to confirm the reliability of a shellmodel potential in this context,8,13 an important step would
involve obtaining the glass structure using AIMD for the
melt-and-quench stage as well, in order to produce a full ab
initio glass structure, to be compared with the classical one.
Another largely unexplored area, whose investigation
could be beneficial for a deeper understanding of the properties of these glasses, is represented by their melt precursor.
Investigating the structural and dynamical features of the
melt precursor on the atomic scale is an important step towards a deeper understanding of bioactive glasses: because
the glass structure is essentially frozen in a static “snapshot”
of the liquid cooled below the glass transition temperature,
the larger configurational space explored in the melt state
contains a significant amount of information pertinent to the
glass itself, but somewhat hidden and therefore hardly accessible. For instance, structural defects can be more easily detected and studied in the melt: these sites affect the mechanism of viscous flow,14–16 but they can also play a central
role in the bioactive behavior of the glasses.17,18
Structural and dynamical data on the molten state are also
relevant in the more general area of multicomponent amorphous silicate materials, which, despite their technological
importance, have been investigated much less frequently
than their binary counterparts, due to the additional technical
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©2007 The American Physical Society
PHYSICAL REVIEW B 76, 224202 共2007兲
ANTONIO TILOCCA
difficulties related to their multicomponent nature. Due to the
similarity of their short-range environments, multicomponent
silicate melts and glasses share a number of structural and
vibrational features;19 however, significant temperatureinduced structural changes16,20 still need to be investigated at
an atomistic level, especially because even small structural
changes can result in dramatic changes in the dynamics.21
Due to the nature of the high-temperature liquid state,
characterized by large distortions around the equilibrium
structure, with many bonds being frequently broken and
formed, the AIMD approach, with its on-the-fly calculation
of highly accurate interatomic forces based on explicit electronic structure calculations,12 appears as the most adequate
to treat the rapidly changing atomic environments in the
melt. A number of studies, using either the Car-Parrinello
共CP兲22 or the direct 共Born-Oppenheimer兲12 approach, have
proven the effectiveness of AIMD simulations to probe the
structural, dynamic, and electronic properties of silicate
glasses and melts.23–32 In this work Car-Parrinello molecular
dynamics 共CPMD兲 simulations are applied to investigate the
structure and dynamics of a multicomponent silica composition corresponding to the 45S5 Bioglass, both in the liquid
and in the amorphous state: we highlight structural differences between the liquid and the corresponding glass obtained upon cooling, and also focus on dynamical changes in
these properties both in the melt and during the cooling to
room temperature forming the glass. The results allow us to
significantly extend our atomistic picture of bioglasses in
two directions: 共i兲 the high-temperature range corresponding
to the melt is thoroughly explored; 共ii兲 the full ab initio
quench from the melt extends the first-principles accuracy of
the model beyond the short range available in our previous
study.11
II. SIMULATION METHODS
CPMD simulations22 were carried out using the CP code
of the QUANTUM-ESPRESSO package.33 The electronic structure was treated within the generalized gradient approximation 共GGA兲 to density functional theory 共DFT兲, through the
PBE exchange-correlation functional.34 For all atomic species, the core-valence electron interactions were represented
using Vanderbilt ultrasoft pseudopotentials,35 explicitly including semicore shells for Na and Ca. Plane-wave basis set
cutoffs were set to 30 and 200 Ry for the smooth part of the
wave functions and the augmented charge, respectively; k
sampling was restricted to the ⌫ point. The MD time step ␦t
and fictitious electronic mass ␮ were 7 and 700 a.u., respectively. A cubic periodic supercell of 11.63 Å sides was
employed, containing 116 atoms with composition
19SiO2 10Na2O 11CaO P2O5, corresponding to the standard
45S5 Bioglass® at the density of 2.66 g cm−3.36
This general computational setup was successfully used in
recent CPMD simulations of modified silicate glasses incorporating different amounts of Na, Ca, and P.11,13,25 Moreover,
previous ab initio simulations performed with methods and
supercell sizes similar to the ones employed in the present
work23,24,27–29,31,32 have proven the accuracy of this approach
in determining structural and dynamical properties of silicate
melts and glasses. A common procedure in ab initio MD of
glasses involves classical MD with an effective interatomic
potential to model the melt and its subsequent cooling to the
glassy state, before switching to ab initio MD for the room
temperature simulation.11,28,30,31 This approach enables the
local relaxation of the glass structure at the ab initio level,
and is therefore useful to investigate short-range structural
effects, as well as vibrational and electronic properties of the
glass.11,28,31 Nevertheless, the glass structure beyond the
short range is still completely determined by the classical
potential: the switch to the ab initio dynamics only enables
short-range relaxations, whereas the medium-range structure,
such as the connectivity of the glass-forming sites, is “frozen” to the initial configuration obtained by classical
MD.11,28 Although computationally much cheaper, this approach necessarily shows some limitations: for instance, it
has been shown that a full-AIMD simulation considerably
improves the agreement with experiment of the Qn distribution for lithium silicate glasses, compared to the distribution
obtained by classical MD.32 Although we have recently
shown that the inclusion of polarization effects using shellmodel terms can improve the Qn distribution of modified
silicate glasses obtained by classical potentials,13 in this
work ab initio MD is used to model the melt and its cooling
to room temperature. This more computationally demanding
approach is better suited to the focus of the present paper:
indeed, a full ab initio description is more adequate in order
to investigate the fast dynamic rearrangements which take
place in the melt and during the cooling, where a large number of chemical bonds are being continuously formed and
broken at the same time. Moreover, the final bioglass structure will be fully relaxed at the ab initio level, enabling an
unbiased representation of structural features beyond the
short range, such as the intertetrahedral connectivity.
The initial configuration was created by randomly placing
the atoms in the simulation box, taking care to avoid significant overlaps by means of appropriate distance cutoffs. This
configuration was then left free to relax, and after an initial
quench of all ion velocities, the system spontaneously 共i.e.,
without external thermostatting兲 heated up to around
2300 K. A CPMD trajectory was then started in the NVE
ensemble, where the temperature T oscillated around
2300 K; despite a small drift in the fictitious kinetic energy,
presumably related to the narrowing of the band gap at this
temperature,23,32,37 no significant drift in the total energy,
with fluctuations lower than 0.0005% were recorded. The
trajectory was extended to 14 ps, which was enough for assuring adequate equilibration of the system, based on both
the long-time slope of the logarithmic plot of the mean
square displacements27 and on the actual value of the ionic
displacements. In order to confirm that no significant deviations from the Born-Oppenheimer surface affected the calculation of ionic forces in the MD trajectories, structural 共coordination, radial, and angular distribution statistics兲 and
dynamic 共mean square displacements兲 properties at 2000 K
were compared with those obtained in a corresponding
CPMD trajectory carried out with a separate Nosé thermostat
coupled to the electronic degrees of freedom:38 no significant
differences 共beyond statistical errors兲 were observed between
the two trajectories.
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PHYSICAL REVIEW B 76, 224202 共2007兲
STRUCTURE AND DYNAMICS OF BIOACTIVE…
TABLE I. Interatomic distances for 3000 K melt and glass at
300 K.
3000K
25
Si-O
P-O
Na-O
Ca-O
O-O
Si-Si
15
10
Glass 共300 K兲
R 共Å兲
FWHM 共Å兲
Melt 共3000 K兲
R 共Å兲
FWHM 共Å兲
g(r)
5
25
Si-O
P-O
Na-O
Ca-O
O-O
Si-Si
20
15
10
300K
5
0
1
1.5
2
2.5
3
3.5
4
4.5
5
r (Å)
FIG. 1. 共Color online兲 Radial distribution functions of the melt
共top兲 and of the glass 共bottom兲, calculated from the corresponding
MD trajectories at 3000 and 300 K, respectively.
After having obtained a well-equilibrated melt, the cooling phase started: it consisted of a series of nine subsequent
NVT 共constant number of particles, volume, and temperature兲 runs of 10 ps each, whose target temperature was set to
2000 K, 1800 K, 1600 K, . . ., 600 K, 300 K using a Nosé
thermostat. This corresponds to a nominal cooling rate
around 20 K / ps: although still higher than typical cooling
rates easily accessible in classical MD simulations of
glasses,8,39 to our knowledge no previous full-AIMD simulations of glasses using such a relatively low cooling rate
have been performed. The final configuration was further
equilibrated at 300 K for 10 ps, followed by a final NVE
共constant number of particles, volume, and total energy兲 run
of 12 ps. Overall, the cumulative length of the CPMD trajectory was 126 ps, requiring about 40 000 CPU hours on the
HPCx system located at the UK’s CCLRC Daresbury Laboratory. An additional NVT run of 14 ps at T = 3000 K was
carried out starting from the melt equilibrated at 2300 K, in
order to extend the range of sampled temperatures towards
regions often explored in AIMD simulations of other silicate
melts.27,29,32
P-O
Na-O
Ca-O
Si-Si
O-O
1.63
0.12
1.55
0.08
2.30
0.37
2.32
0.27
3.01
0.26
2.68
0.26
1.63
0.26
1.55
0.23
2.25
0.94
2.25
0.71
3.05
0.63
2.69
0.69
with respect to the glass. The thermal broadening leads to
full widths at half maximum 共FWHMs兲 2–3 times larger in
the melt than in the glass, in agreement with previous CPMD
simulations on silicate glasses and melts.23 This shows that
the intratetrahedral arrangement is not significantly perturbed
in the melt, apart from the much more marked thermal motion, whereas some structural rearrangements involve the
modifier cations and the intertetrahedral connectivity.
The bond angle distributions 共BAD兲 of network-forming
atoms T 共T = Si or P兲 in Fig. 2 and the corresponding angles
reported in Table II denote a small decrease 共1–2 degrees兲 in
the intratetrahedral O-T-O angle at 3000 K, compared to the
ideal tetrahedral geometry measured for the glass. As observed for the rdfs, the widths of the O-Si-O and Si-O-Si
distributions are close to previous CPMD simulations on silicate glasses and melts.23,29 A significant change occurs for
the intertetrahedral Si-O-Si angle in the melt, where the center of the distribution is shifted 8ⴰ to lower angles, and a
shoulder around 90ⴰ, absent in the glass, is evident. Direct
inspection of the high-temperature MD trajectory showed
that Si-O-Si angles close to 90ⴰ involve fivefold coordinated
Si atoms 共Si5c兲, which are frequently found in small 共twoand three-membered兲 rings.
Indeed, in Fig. 3 the average Si-O bond distance and the
mean Si-O coordination numbers of Si in O-Si-O and
Si-O-Si groups are plotted as a function of the corresponding
0.03
O-Si-O
Si-O-Si
O-P-O
Si-O-P
melt
glass
0.02
0.01
0.03
III. RESULTS AND DISCUSSION
A. Structure
0.02
1. Radial and angle distributions
0.01
Several radial distribution functions 共rdfs兲 for the 3000 K
melt and the glass at 300 K are compared in Fig. 1 and the
corresponding peak distances are reported in Table I. The
position of the main Si-O, P-O, and O-O peaks are essentially the same in the melt and the glass, whereas a small
contraction of the Na-O and Ca-O distances, accompanied
by an increase of the Si-Si distance is observed in the melt
Si-O
f(θ)
20
0
0
50
100
150
50
100
150
θ (deg)
FIG. 2. Angle distributions in the melt 共bold lines兲 and in the
glass 共thin lines兲, calculated from the corresponding MD trajectories at 3000 and 300 K, respectively.
224202-3
PHYSICAL REVIEW B 76, 224202 共2007兲
ANTONIO TILOCCA
TABLE II. Intratetrahedral and intertetrahedral angles.
O-Si-O
Si-O-Si
Si3c
O-Si-O
P-O-Si
Si4c
0.01
Si5c
109.6± 7
109.7± 5
129± 13
125± 5
107.5± 16
108.6± 15
121± 25
124± 20
angle: moving away from the tetrahedral O-Si-O angle, both
the Si-O distance and Si coordination number increase: small
and large O-Si-O angles involve Si5c and Si-O distances up
to 1.9 Å. Si-O-Si angles around 90° also involve Si5c and
stretched Si-O bonds: typical Si-O distances in this region
are around 1.85 Å; that is about 7% longer than the Si-O
distance corresponding to the “regular” Si-O-Si groups. The
angles formed by threefold, fourfold, and fivefold coordinated Si atoms are further examined in Fig. 4, where the f共␪兲
distributions of O-Si-O and Si-O-Si angles involving Si in
specific coordinations are plotted separately: the characteristic O-Si-O angle increases with decreasing coordination
number, from ␪ = 90, to 108, to ⬃120° for Si5c, Si4c, and Si3c,
respectively, with a small secondary peak at 160° in the Si5c
distribution. The bottom panel of the figure confirms that Si5c
also favor Si-O-Si angles below 100°.
Even though the smaller silica fraction makes the formation of rings less likely compared to liquid SiO2, small 共twoand three-membered兲 rings are frequently observed in the
45S5 melt: several instances are shown in Fig. 5. The picture
highlights how small rings are often associated to overcoordinated Si atoms,29 such as fivefold- 关fragments 共a兲–共c兲兴 and
even sixfold-coordinated Si 关fragment 共d兲兴. The formation of
small rings represents another important difference between
the melt and the glass, indicating that, even though they
share the tetrahedral silicate units as an underlying structural
motif, the connectivity of these units is not the same. High
thermal distortions in the melt lead to the formation of unusual structural patterns which are not observed in the glass,
such as two-membered rings, or coordinative defects 共see
also Sec. III A 2兲.
f(θ)
Glass 共300 K兲
␪ 共deg兲
Melt 共3000 K兲
␪ 共deg兲
O-P-O
0
60
80
100
120
140
160
180
Si3c
Si-O-Si
Si4c
0.01
Si5c
0
60
80
100
120
140
160
180
θ (deg)
FIG. 4. Distributions of O-Si-O and Si-O-Si angles involving
threefold-, fourfold- and fivefold-coordinated Si atoms.
The ring statistics of the high-temperature trajectory was
determined using an efficient algorithm for primitive ring
search;40 the average number of two-, three- and fourmembered rings per Si was 0.16, 0.10, and 0.03 rings/Si
atom, respectively, whereas no such rings were observed in
the glass structure: during the cooling, both coordinative and
small ring defects are effectively healed.
2. Coordination
The coordination statistics of the 45S5 melt and glass are
reported in Table III: the glass shows ideal fourfold coordination for all Si and P, whereas about 11% of Si atoms are
miscoordinated in the melt. Overcoordinated Si occur with
slightly higher probability than undercoordinated defects; a
very small number of sixfold coordinated Si atoms are also
5
4.8
O-Si-O
2
4.6
4.4
1.8
r(θ)
n(θ)
4.2
4.8
Si-O-Si
2
4.6
4.4
1.8
4.2
4
80
100
120
140
160
1.6
θ (deg)
FIG. 3. Average Si coordination number 共bold line, left vertical
axis兲 and Si-O distance 共thin line, right vertical axis兲 in O-Si-O and
Si-O-Si angles.
FIG. 5. The local structure of 2M and 3M rings formed during
the high-temperature MD trajectory 共only the nearest atoms to the
ring are included兲. Silicon, oxygen, and Na/ Ca atoms are shown as
white, black, and gray spheres, respectively.
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PHYSICAL REVIEW B 76, 224202 共2007兲
STRUCTURE AND DYNAMICS OF BIOACTIVE…
TABLE III. Coordination statistics for the glass and the melt, calculated using a 2.25 Å distance cutoff to
define the coordination shell of Si and P. The corresponding values obtained using classical MD with a
shell-model potential are reported in parentheses.
Si3c
Melt 共3000 K兲
0
共0兲
4.3
共0.5兲
Q0
Glass 共300 K兲
Melt 共3000 K兲
Glass 共300 K兲
Melt 共3000 K兲
Si6c
100
0
共100兲
共0兲
89.1
6.4
共97.2兲
共2.3兲
Si connectivity 共Qn distributions兲
Q1
Q2
5.3
10.5
共0.0兲
共18.4兲
3.3
21.6
共0.2兲
共26.2兲
P coordination
P3c
P4c
57.9
共52.6兲
45.8
共44.1兲
0
0.1
共0.1兲
100
99.8
共98.3兲
recorded during the high-temperature trajectory. As described before, these coordinative Si defects are generally
found within small rings. Unlike silicon, phosphorus atoms
essentially maintain an ideal tetrahedral coordination even at
high temperature: the higher rigidity of the phosphate tetrahedra, evident in Figs. 1 and 2, seems to prevent the local
distortion needed to accommodate or remove an oxygen
atom in the nearest-neighbors coordination shell. Due to the
very low P2O5 concentration in the 45S5 composition, the
statistics on P in our sample is necessarily less accurate with
respect to Si: therefore the occurrence of a small fraction of
P defects cannot completely be excluded; however, the general trend seems to indicate that Si has a higher tendency to
form coordinative defects. At the same time, only a small
fraction of oxygen atoms bonded to three Si/ P atoms is
formed at 3000 K. Therefore, miscoordinated Si atoms are
the main structural feature of the 45S5 melt, which distinguishes it from the corresponding glass.
Because of the higher density of the modeled liquid compared to the real liquid, it may be argued that the artificial
compression can affect the properties of the melt: indeed, it
is well established that high pressures lead to significant
structural and dynamical changes in silicate glasses and
liquids.41–44 The main assumption of the present and of previous MD studies, where NVT simulations of the liquid
phase have been performed using the density of the corresponding amorphous,28–32,45–47 is that the density difference
and the size of the above effect are small, and therefore this
approximation is acceptable.48 In order to verify that this is
actually the case for the present system, the trace of the stress
tensor at 3000 K was calculated, yielding P around 0.6 GPa,
at which no structural changes should be observed for silicate melts, with respect to the liquid at ambient pressure.41–44
0
共0兲
0.2
共0.0兲
Q3
Q4
Q5
0
共0兲
0.8
共0.0兲
O0c
26.3
0
共28.9兲
共0兲
22.8
5.7
共27.6兲
共1.9兲
O coordination
O1c
O2c
0
0.1
共1.7兲
68.7
68.1
共68.2兲
0
0.3
共0.1兲
O3c
31.3
31.5
共31.7兲
The coordination environment of each species is further
investigated in Fig. 6, where the cumulative number of Si-O,
P-O, Na-O, Ca-O, O-O, and Si-Si neighbors is plotted for
the glass and the melt. The liquidlike character of the latter
emerges from the more continuous trend of the n共r兲 curves,
as opposed to the stepwise curves for the glass. While the
oxygen coordination shells of Si and P in the melt are still
well defined and not significantly different from the glass,
the monotonic increase in the n共r兲’s for Na-O and Ca-O pairs
marks a higher degree of disorder around modifier cations in
O-O
Si-O
20
20
10
10
P-O
20
n(r)
Glass 共300 K兲
Si coordination
Si4c
Si5c
Si-Si
4
10
2
Ca-O
Na-O
20
20
10
0
10
1
2
3
4
2
3
4
0
5
r (Å)
FIG. 6. Cumulative 共integrated兲 coordination numbers calculated for the glass 共full lines兲 and 3000 K melt 共dashed lines兲.
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PHYSICAL REVIEW B 76, 224202 共2007兲
ANTONIO TILOCCA
n
n
TABLE IV. Qm
共Si兲 distribution in the melt: Qm
represents an m-coordinated Si atom bonded to n bridging
oxygens. Both the total 共relative to all Si atoms in any coordination兲 and local 共in parentheses, relative only
to the other m-coordinated Si atoms兲 distributions are shown. The last row reports the average number of BO
bonded to each m-coordinated Si.
Si3c
n=0
n=1
n=2
n=3
n=4
n=5
n=6
具BO典
共19.1兲
共62.4兲
共17.3兲
共1.2兲
0
0
0
1.01
0.8
2.7
0.75
0.05
Si4c
共2.8兲
共21.1兲
共49.7兲
共23.4兲
共2.9兲
0
0
2.02
2.5
18.8
44.4
20.85
2.6
the melt. In the glass, Na and Ca ions are embedded in a
pseudooctahedral shell of ⬃5.5 and 6 oxygen atoms,
whereas the larger radius of the first coordination shell for
the melt 共already evident in the broader peaks in the radial
distribution functions in Fig. 1兲 incorporates almost seven
oxygen neighbors, on average. Analogously, the Si-Si curve
highlights a more disordered intertetrahedral arrangement for
the melt, accommodating a broader range of connectivities
between adjacent tetrahedra. Indeed, the stepwise nSi-Si共r兲
curve shows that in the glass most Si ions are linked 共through
bridging oxygens兲 to two other Si tetrahedra, whereas in the
melt Si atoms with a number of neighbors ⫽2 occur with a
higher probability.
The Si-Si connectivity can be discussed in further detail
through the Qn distribution in Table III, where Qn denotes a
Si ion bonded to n bridging oxygens. The glass structure is
dominated by Q2 and Q3 species, in agreement with nuclear
magnetic resonance 共NMR兲 and Raman spectroscopy data,5–7
denoting a highly disrupted network, dominated by chainlike fragments.9 In the melt, the fraction of both Q2 and Q3
species decreases, with a corresponding increase in Q1 and
the appearance of Q4 and Q5 species, which are not formed
in the glass. In other words, although the underlying network
is still dominated by Q2/Q3 structural units, the high temperature can modify the relative balance between the Qn
units.
The local structure of Si atoms in different coordination in
n
distrithe melt can be further characterized through the Qm
n
bution, where Qm represents an m-coordinated Si atom
bonded to n bridging oxygens 共Table IV兲. The table highlights that on average the coordination shell of threefoldcoordinated Si is made of one bridging oxygen 共BO兲 and two
nonbridging oxygens 共NBOs兲, whereas the BO connectivity
increases to 2 for Si4c, up to 3.6 for Si5c. Taking into account
the different number of oxygen atoms bonded to each Si
species, this seems to highlight a preferential association between BOs and Si5c, as well as between NBOs and Si3c,
which could lead to rather different properties of Si3c-NBO
and Si5c-BO centers, for instance, in relation to their activity
as nucleation sites on the glass surface.17
The availability of accurate glass and melt structures obtained through a full ab initio approach enables a direct as-
Si5c
Si6c
0
0
0
0
0
0.05 共34.8兲
0.08 共48.5兲
0.03 共16.7兲
4.82
共0.6兲
共10.6兲
共30.0兲
共47.4兲
共11.4兲
0
3.58
0.05
0.68
1.9
3.0
0.7
sessment of the reliability of classical force fields, such as
the shell-model potential used in Ref. 11, and in particular, of
their ability to reproduce the main structural features of the
bioactive glass and of its melt precursor. To this purpose, we
have performed an additional melt-and-quench classical MD
simulation, using the shell-model potential. In order to filter
out their possible influence on the results, we have used exactly the same simulation settings 共system size, cooling rate,
trajectory lengths兲 as in the CPMD run, even though the
classical MD run would enable to probe much larger or
longer space or time scales. The coordination statistics of the
classical melt and glass are reported below the corresponding
CPMD values in Table III. The main difference concerns the
liquid phase, where a significantly larger amount of
threefold- and fivefold-coordinated Si are created during the
CPMD trajectory, whereas more than 97% of Si atoms keep
ideal tetrahedral coordination in the classical melt; the Qn
distribution also denotes that, despite similar Q2 fractions in
the classical and CPMD melts, in the latter significantly
higher fractions of Q0, Q4 and even Q5 species are formed.
These differences highlight that the classical potential may
be too rigidly biased towards regular geometries and does
not easily favor the distorted or irregular environments
which, as the CPMD run shows, can occur with significant
probability at 3000 K. Although these defects can certainly
affect the vitrification process, their occurrence in the melt is
only partially reflected in the final glass structure, where both
the CPMD and shell-model structures show no miscoordinated Si atoms, and a Qn distribution predominantly Q2/Q3,
in agreement with the experiments.5–7 The CPMD glass does
show Qn abundancies closer to the Raman spectroscopy
estimates,7 especially for the Q0/Q1 species, but overall the
bioglass structure predicted by the classical shell-model appears reasonable.
3. Phosphorous connectivity
Our previous models of the 45S5 glass,8,11 obtained by
classical MD quench from the melt, contained a relevant
fraction of Q1 phosphate groups forming one P-O-Si link
with an adjacent silicate. The possibility that phosphorus can
be linked to silicon and thus partially incorporated within the
bioglass network is supported by some experiments as well
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PHYSICAL REVIEW B 76, 224202 共2007兲
STRUCTURE AND DYNAMICS OF BIOACTIVE…
7
0.04
6
0.02
0.01
0
60
80
Si5c
5
%
300K
600K
800K
1000K
1200K
1400K
1600K
1800K
2000K
3000K
4
3
Si3c
2
1
0
3000
100
120
140
160
O3c
2400
1800
180
1200
600
T (K)
θSi-O-Si (deg)
FIG. 7. Si-O-Si angle distributions calculated from the MD trajectories, gradually cooling the system from 3000 to 300 K.
as by classical MD simulations,7,8,49–51 whereas in some
other studies only isolated orthophosphate groups were
detected.5 The glass generated using the present full-AIMD
quench also incorporates P-O-Si links: despite the limited
statistics due the small system size, this does seem to confirm
that these links are an important structural feature of bioactive silicate glasses, as their presence in the full ab initio
structure rules out a possible bias on their occurrence due to
the use of empirical potentials to generate the glass. Further
details on the dynamical feature of these links follow in
Sec. IV B.
4. Temperature dependence of structural features
related to defects
By comparing the structure of the system equilibrated at
3000 K and 300 K, the most evident structural feature of the
melt turned out to be the secondary peak at 90° in the
Si-O-Si angle distribution, associated to coordinative defects
and small rings. Using this peak to mark the presence of
defects, Fig. 7 shows that it gradually disappears from the
BAD during the cooling process, and the corresponding intensity is shifted to the main peak. Little residual intensity at
90° is still present at 1600 K, and only the main peak at 127°
is apparent in the 1400 K BAD. This would seem to mark
1200– 1300 K as the temperature where the main structural
difference between melt and glass disappears; in fact, Fig. 8
further confirms that only a very small fraction of fivefoldcoordinated Si is still present at this temperature, and no
defects are detected below 1200 K.
FIG. 8. Average total fraction of threefold- and fivefoldcoordinated Si, and of threefold-coordinated O, from the MD trajectories cooling the system from 3000 to 300 K.
which these changes in the local environment occur cannot
be obtained from static distributions. This kind of dynamic
information can be directly extracted from the MD trajectories: Fig. 9 shows the instantaneous number of Si-O bonds
for a representative Si and two of the oxygen atoms in its
coordination shell, during the trajectory at 3000 K. Frequent
changes in the coordination shell of Si, switching from threefold, to fourfold, to fivefold coordination, are observed,
while the O atoms also switch back and forth between bridging and nonbridging, with rare excursions into threefold coordination. The lifetime of Si3c and Si5c coordination, averaged over all Si atoms, is 33 and 47 fs 共to be compared with
335 fs for the tetrahedral species兲, while the mean lifetime of
threefold-coordinated O3c is 50 fs, much less than the more
stable NBO 共750 fs兲 and BO 共400 fs兲 species. This analysis
thus shows that Si3c and Si5c coordinative defects are shortlived complexes, and the more stable tetrahedral coordinaSi
5
4
Nbonds(t)
f(θ)
0.03
3
O
3
2
IV. DYNAMICS
A. Dynamics of intratetrahedral connectivity
1
In the previous section we have shown that the melt is
characterized by a significant fraction of miscoordinated atoms, especially Si, and in general, by a larger degree of
disorder in the coordination environment of both networkforming and network-modifier species. However, the structural analysis only provides a static picture of the melt: the
presence of thermal fluctuations is evident from the spread of
the calculated distributions, but the rate and mechanism at
0
0
2
4
6
8
10
12
time (ps)
FIG. 9. Time evolution 共at 3000 K兲 of the number of Si-O
bonds formed by a selected Si 共top panel兲 and by two of the oxygen
atoms initially in its coordination shell 共full and dashed lines in the
bottom panel兲.
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PHYSICAL REVIEW B 76, 224202 共2007兲
ANTONIO TILOCCA
4
Na
3
8
8
2
6
6
4
4
2
2
8
8
6
6
4
4
rSi-O (Å)
0
4
7
NO(t)
(b)
1
8
3
2
1
(a)
Ca
2
0
0
0.5
1
t (ps)
1.5
2
0
5
10
0
2
5
10
time (ps)
FIG. 10. 共Color online兲 Time evolution of the Si-O distances of
the oxygen ions within a 4 Å radius from a selected Si ion in the
melt; only the first 2 ps of the trajectory are shown in panel 共a兲,
whereas panel 共b兲 shows the portion of the trajectory between 6.5
and 8.5 ps. The Si-O distances of O atoms involved in exchange
processes are highlighted in bold 共colors兲; the arrows mark the exchange events discussed in the text.
tion is restored shortly after their formation; based on NMR
measurements, these transient species were previously proposed as transition states in the viscous flow of silicate
liquids.16,20
Figure 9 clearly reveals frequent Si-O bond breakings, but
it does not clarify whether the identity of the Si neighbors in
the coordination shell is also changing, or instead if the original shell is reformed when the tetrahedral coordination is
restored. This question can be addressed by examining the
trajectory of the distances of all O atoms from a tagged Si
center 共Fig. 10兲. In Fig. 10共a兲, a typical exchange event involves the approach of an oxygen atom 共whose Si-O distance
is indicated by an arrow around t = 1 ps兲 from an outer shell,
with the creation of an additional Si-O bond in a transient
fivefold-coordinated Si, followed by the breaking of a Si-O
bond and the escape of a different O, restoring a fourfold
共but different from the original兲 coordination shell. The approach or separation of oxygen atoms can sometimes occur
simultaneously, as at ⬃1.8 ps in Fig. 10共a兲, and therefore no
transient Si5c is formed. Occasionally, the exchange sequence
is reversed and starts with an Si-O bond breaking and formation of an intermediate Si3c complex, as in Fig. 10共b兲: the
separation of the O atom is followed by the formation of two
new Si-O bonds; the process is terminated by a further Si-O
bond breaking, resulting in the overall exchange of two oxygens in the same event.
This analysis highlights a rich dynamical behavior for Si
atoms, with a high flexibility in their coordination environment; this is in contrast with the behavior of P-O distances
for phosphorus 共not shown兲 which, as it might have been
guessed from its coordination statistics in Table III, even at
FIG. 11. Time evolution of the instantaneous number of O atoms coordinated to two selected Na and Ca ions, extracted from the
3000 K trajectory.
3000 K tends to maintain the same four oxygen neighbors
for the whole MD trajectory: no P-O bonds are broken or
created. The different dynamical behavior of phosphate and
silicate groups suggests that Si/ P substitution in bioactive
compositions could significantly affect the ion migration
mechanism and thus the overall bioactivity.
The time evolution of the number of oxygen neighbors of
selected Na and Ca atoms in the melt is plotted in Fig. 11:
again, the local environment of modifier cations is continuously changing, even more frequently than for Si and O, as
the number of oxygens surrounding Na/ Ca ions varies between 2 and 10. These changes occur in fast discrete jumps,
each adding or removing a single O from the coordination
shell of the modifier cation. This behavior reflects a significant mobility of the modifier cations, which presumably involves a different diffusive mechanism compared to the
network-forming ions 共see below兲.
B. Dynamics of intertetrahedral connectivity
The formation of Si-P linkages in the melt can be monitored through the time evolution of interatomic distances
from a tagged P center, shown in Fig. 12: a Si-P link is
formed or broken whenever the cutoff distance corresponding to the first minimum in the Si-P radial distribution function is crossed. In panel 共a兲, after the initial Si-P link is
broken 共t ⬃ 2 ps兲, the newly formed Q0 orthophosphate remains isolated for the remaining part of the high-temperature
trajectory; in panel 共b兲, a stable link is formed after 6 ps, and
the resulting Q1 phosphate remains intact during the subsequent dynamics, and is actually found in the glass structure
after cooling. Figure 13 shows that these changes to the P
connectivity involve nearby Si defects: the breaking of the
Si-P link 共1a–1c兲 generates an intermediate threefold-
224202-8
PHYSICAL REVIEW B 76, 224202 共2007兲
STRUCTURE AND DYNAMICS OF BIOACTIVE…
10
8
10
10
8
8
6
6
4
6
4
2
Q1
rP-Si (Å)
4
2
(a)
Q3
Q2
Q3
Q3
Q2
8
8
6
6
4
2
rSi-Si (Å)
8
6
4
0
0
4
(b)
2
4
6
time (ps)
8
10
coordinated Si 共1b兲, which is almost immediately healed; the
formation of a new Si-P link occurs through the opening of a
two-membered Si ring 共2a–2c兲. Thus the flexible coordination environment of Si turns out to play a central role in
facilitating exchanges in the P environment as well. Although
the dynamics shows that Si-O-P links can occasionally be
broken and formed in the melt, the process is not as frequent
as for Si-O-Si links. Indeed, Fig. 14 shows the distance of a
set of tagged silicon atoms from the other Si atoms in the
Q3
Q2
Q1
Q2
Q1
Q3
2
8
8
6
6
4
4
Q4
Q3
Q2
Q2
Q4
2
Q3
8
8
6
6
4
4
2
FIG. 12. 共Color online兲 Time evolution of P-Si interatomic distances during the high-temperature MD trajectory. The trajectory of
Si atoms which form links with P is highlighted in bold; the horizontal dashed line marks the Si-P distance cutoff: a Si-P pair closer
than the cutoff is connected through a bridging oxygen.
Q4
Q3
2 Q
3
2
2
Q2
0
2
4
Q3
Q2
Q3
6
8
10
Q 2 Q3
2
time (ps)
4
6
2
Q2
8
10
0
FIG. 14. 共Color online兲 Time evolution of Si-Si interatomic distances during the high-temperature MD trajectory of several Si atoms. The trajectory of other Si atoms which form links with the
tagged Si is highlighted in bold 共color兲; the horizontal dashed line
marks the Si-Si distance cutoff: a Si-Si pair closer than the cutoff is
connected through a bridging oxygen. The corresponding Qn exchange processes are also marked.
cell, during the trajectory at 3000 K; the average number of
changes in the Si connectivity 共averaged over all Si ions in
the cell兲 is 4.7± 1.5: Si shows a higher tendency to modify its
connectivity than P. Qn species are frequently converted to
Qn+1 or Qn−1, and the figure shows that this exchange involves the loss of a Si-Si⬘ connection 共more specifically, the
breaking of a Si-O-Si⬘ bridge兲 and/or the formation of a new
Si-Si⬙ one with a different tetrahedron. This again denotes a
significant flexibility or variability in the medium-range environment of Si, at variance with the relative stability of
phosphate groups. The dynamical evolution of the Si-Si connectivity is of high interest, since the exchange process between Qn共Si兲 groups in silicate liquids is closely related to
the viscosity.20,52,53
1. Ionic diffusion
The time-dependent mean square displacement 共MSD兲 of
the different species was calculated as
N
FIG. 13. The mechanism of the two changes in P-Si connectivity observed in the liquid. The top panels describe the breaking of
the P-Si link highlighted in Fig. 12共a兲, whereas the bottom panels
illustrate the formation of a new P-Si link depicted in Fig. 12共b兲.
For clarity, only the atoms involved in these exchanges are shown;
Si, P, and O atoms are represented in white, gray, and black colors,
respectively.
N
1 o l
具⌬R 共t兲典l =
兺 兺 兩Ri共t j兲 − Ri共t j + t兲兩2 ,
NoNl j=1 i=1
2
共1兲
where Ri is the position vector of atom i, No and Nl are the
number of time origins spaced by t and the number of atoms
of species l, respectively. Figure 15 shows the MSD of each
atomic species along the MD trajectories at 3000 K and
300 K. The flat MSD curve in the bottom panel denotes sol-
224202-9
PHYSICAL REVIEW B 76, 224202 共2007兲
ANTONIO TILOCCA
60
1
VACF(t)
20
0.2
300 K
0
0.1
0
1
2
3
4
t (ps)
5
6
7
0.1
0.2
idlike oscillatory motion at 300 K, whereas the linear trend
of the MSD at 3000 K qualitatively shows that at this temperature all atoms are diffusing, although the transition to the
diffusive regime is slower for the network-forming ions 共see
below兲. In the melt, the diffusion of network-forming atoms
Si, P, and O is slower than the network modifiers Na and Ca.
Applying the Einstein equation ⌬R2共t兲 = 6Dt, diffusion coefficients D = 0.26, 0.20, 0.41, 0.59, and 1.34⫻ 10−8 m2 s−1 can
be estimated from the slope of the MSD curves in the linear
region, for Si, P, O, Ca, and Na atoms, respectively. The
D共Si兲 / D共O兲 and D共P兲 / D共O兲 ratios reflect their mass ratios,
following the correlation of their motion within the
tetrahedra.23,32 On the other hand, the diffusion of Na and Ca
is significantly faster as these species are not incorporated in
the glass network and their interaction with oxygen is weaker
than that of Si and P. The diffusive mechanism can be further
investigated by plotting the MSDs on a log-log scale, as in
Fig. 16; on a logarithmic scale, different dynamical regimes
are characterized by a different slope.54 The initial slope is
100
2
N
2
0.1
1
t (ps)
10
0.5
N
1 o l
cl共t兲 =
兺 兺 vi共t j兲 · vi共t j + t兲,
NoNl j=1 i=1
Si
P
Na
Ca
O
0.01
0.4
close to 2, denoting free ballistic motion at a short time, as
described by R2i 共t兲 ⬀ v2i t2: this occurs on the very short time
scale separating two subsequent collisions of the atom with
the “walls” of its coordination cage. This regime is followed
by a transitional region where the atom rattles back and forth
within the cage, before being able to escape and start the
Einstein diffusive regime, characterized by unit slope in the
logarithmic plot, where logR2i 共t兲 ⬀ log共t兲. Although the slope
in each characteristic regime is now the same for the different species, the different mechanism controlling the motion
of network formers and modifiers is evident: for both Na and
Ca, the ballistic motion lasts until 0.03 ps, interrupted by the
transitional regime, before the start of the Einsteinian diffusion after ⬃1 ps; on the other hand, the transition to the
diffusive regime appears more complex for the network
formers, as it begins already after 0.01 ps, and lasts significantly longer, with the log-log curves of Si, P, and O approaching unit slope after more than 4 ps. This is likely related to the combination of intratetrahedral motions, which
are not present for Na and Ca: the tetrahedral cage embedding Si and P is much more rigid than the pseudooctahedral
coordination shells of Na and Ca, which do not involve
strong chemical bonds as the silicate or phosphate groups.
Further insight into the short-time dynamics is provided
by the velocity time autocorrelation functions 共VACFs兲, defined as
1
0.01
0.3
t (ps)
FIG. 17. 共Color online兲 Velocity autocorrelation functions 关Eq.
共2兲兴 of the different species, evaluated for the melt 共3000 K兲 and
glass 共300 K兲 MD trajectories.
8
FIG. 15. 共Color online兲 Mean square displacement 关Eq. 共1兲兴 of
the different species, evaluated for the melt 共3000 K兲 and glass
共300 K兲 MD trajectories.
∆R (t) (Å )
0
0.5
300 K
0
0
Si
P
Na
Ca
O
0.5
2
2
∆R (t) (Å )
40
3000 K
3000 K
Si
P
Na
Ca
O
100
FIG. 16. 共Color online兲 Logarithmic plot of the mean square
displacement of the different species, evaluated for the melt
共3000 K兲 MD trajectory.
共2兲
where vi is the velocity vector of atom i, and the other symbols are as in Eq. 共1兲. The VACFs for the glass and the melt
are plotted in Fig. 17. The time t0 when the VACF first
changes sign represents the average time when a change of
direction occurs in the motion of an atom, and correlates
with the end of the ballistic regime identified in the MSD
plots: indeed, t0 = 0.01– 0.02 ps for P and Si, respectively,
and ⬃0.04 ps for Na and Ca. The first minimum of the
VACF represents the average time when the tagged particle
224202-10
PHYSICAL REVIEW B 76, 224202 共2007兲
Intensity (arb. units)
STRUCTURE AND DYNAMICS OF BIOACTIVE…
ences of the glass samples obtained here and in Ref. 11 do
not affect their vibrational features.
glass
melt
glass, ref. 11
V. SUMMARY AND FINAL REMARKS
0
200 400
600 800 1000 1200 1400
-1
frequency (cm )
FIG. 18. Vibrational density of states 共VDOS兲, calculated as
Fourier transform of the total velocity autocorrelation function,
evaluated for the melt 共3000 K兲 and glass 共300 K兲. The VDOS
obtained using the mixed classical-ab initio approach in Ref. 11 is
also shown.
reverses its direction of motion:54 again, this happens earlier
for the network formers, around 0.02 ps, than for the modifiers, which reverse their velocity after 0.08 共Ca兲 and 0.09 ps
共Na兲. The rigid intratetrahedral vibrations lead to a fast oscillatory trend for the VACFs of Si, P, and O, which are in
phase and strongly correlated. On the other hand, Na and Ca
ions show a much broader first minimum, which is not followed by a marked oscillatory behavior, because their interaction with the surrounding cage is weaker, as discussed before.
In general, these features are found for both the 300 and
3000 K MD trajectories—the similarity of the shapes of the
atomic VACFs of the glass and the melt shows that their
short-time dynamical behavior is similar 共the same does not
apply to the long-time behavior兲. The glass is characterized
by larger amplitude vibrations and a slower decay to zero of
the VACF 共corresponding to the loss of “memory” of the
initial direction兲: Fig. 17 shows that directional memory is
lost after 0.5 ps for the melt, whereas for the glass the oscillatory motion of the VACFs continues beyond the time scale
of the figure.
The emerging dynamical picture is that of two relatively
independent subsystems, the phosphosilicate network, and
the modifier cations; no signatures of the intratetrahedral vibrations are transferred to the VACF of the modifier cations,
showing that the coupling between these systems is not particularly strong.
The vibrational density of states 共VDOS, Fig. 18兲 was
calculated as Fourier transform of the VACF. The VDOS of
the melt shows two bands centered at 150 共modifier cation
low-frequency oscillations about the NBOs兲 and 450 cm−1
共vibrational modes of the Si-O-Si linkages兲, and a broad
band extending between 700 and 1100 cm−1 共vibrational
modes of the different Qn silicate and phosphate structural
units兲. These features generally reflect the vibrational features of the glass, discussed in detail in Ref. 11. The transferability of the vibrational frequencies between different
phases denotes high localization of the vibrational modes.19
Indeed, the VDOS of the present glass is very similar to the
VDOS calculated in Ref. 11 using a mixed classical or
CPMD approach, showing that the small structural differ-
The present CPMD simulation results enabled the characterization of the 45S5 melt, and to highlight the most relevant structural and dynamical differences with respect to the
corresponding bioglass. The CPMD quench from the melt
also allowed us to fully relax the medium-range structure at
the ab initio level, thus providing a very accurate reference
structure of the glass, completely free of any possible bias
which may affect previous models, due to the use of empirical potentials in the melt-and-quench procedure.11 As the network connectivity of the model is fully relaxed, related structural features can now be discussed with higher confidence:
for instance, the presence of Si-O-P links in the melt and in
the final glass structure strongly supports their occurrence in
the bioactive glasses, which is a rather controversial issue, of
high relevance in order to understand the properties of these
materials.
The 45S5 phosphosilicate melt is characterized by a relevant fraction of miscoordinated silicon atoms, which are
typically associated with two- and three-membered rings;
these structural defects, not present in the corresponding bulk
glass, significantly affect the dynamical behavior of the melt.
We have shown that Si-O bonds are frequently formed and
broken at 3000 K, with the formation of transient undercoordinated or overcoordinated Si centers, which mediate the
transfer of oxygen anions between adjacent silicate units.
These exchanges in the Si coordination shell frequently involve rearrangements to the silicate network connectivity,
where a new Si-Si link is created, removed, or replaced with
a link with a different Si—these exchanges are known to be
involved in the mechanism of viscous flow.53 Compared to
Si, the coordination of phosphate groups appears less adaptable: a very small fraction of miscoordinated P atoms are
formed even at high temperature. The phosphate tetrahedra
show a higher tendency to retain the same bonded configuration, without exchanging O atoms; however, dynamical
changes in the P-Si connectivity are still possible due to the
higher flexibility of the silicate network. Si-O-P bridges are
thus formed at high temperature and appear rather stable, as
they are retained during the cooling and incorporated in the
final glass structure. Despite a similar short-time dynamics,
Si and P show a rather different behavior as far as the dynamical exchanges in their first and second coordination
shells are concerned: the lower tendency of P to exchange
neighbors and modify its connectivity might represent an
additional important factor to take into account to fully understand the role of phosphorus in the bioactivity of silicate
glasses, which is an active field of research.10,55
Very frequent changes in the coordination cage of modifier Na and Ca cations are recorded in the melt, reflecting the
fast migration of Na and Ca. The analysis of displacement
and velocity time correlations highlighted that both the shortand long-time motion of modifier ions follow a different
mechanism than the network formers. The latter show a complex, correlated behavior due to their tetrahedral connectiv-
224202-11
PHYSICAL REVIEW B 76, 224202 共2007兲
ANTONIO TILOCCA
ity, whereas the faster motion of the modifier ions is decoupled from the phosphosilicate network, consistent with a
general picture of mobile ions diffusing in a relatively static
framework of network formers.56
The ab initio dynamics leads to a higher fraction of miscoordinated atoms in the melt compared to a classical shellmodel potential. Even though the cooling phase removes
these defects, it is possible that they play a role in the vitrification of the liquid and then slightly affect the properties of
the amorphous. However, the similarity of the final glass
structures and of the VDOS calculated using a full-CPMD
and a mixed classical-CPMD approach justifies the validity
ACKNOWLEDGMENTS
The U.K.’s Royal Society is gratefully acknowledged for
financial support 共URF兲. Computer resources on the HPCx
service were provided via the U.K.’s HPC Materials Chemistry Consortium and funded by EPSRC 共portfolio Grant No.
EP/D504872兲.
26
*a.tilocca@ucl.ac.uk; http://www.ucl.ac.uk/⬃uccaati
1 L.
of the latter to investigate bioactive silicate glasses; on the
other hand, the CPMD approach appears more reliable to
describe the highly distorted environments found in the liquid.
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STRUCTURE AND DYNAMICS OF BIOACTIVE…
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