A molecular dynamics study of Li-doped borate glasses
The objective of this work is to investigate the effect of alkali content and temperature on the microstructure of lithium borate glasses, xLi₂O · (1 − x)B₂O₃. We have applied the molecular dynamics technique with Ewald summation and periodic boundary conditions to a collection of ca. 256 particl...
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| Cite this: | A molecular dynamics study of Li-doped borate glasses / Ch.-P.E. Varsamis, A. Vegiri, E.I. Kamitsos // Condensed Matter Physics. — 2001. — Т. 4, № 1(25). — С. 119-132. — Бібліогр.: 26 назв. — англ. |
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Varsamis, Ch.-P.E. Vegiri, A. Kamitsos, E.I. 2017-06-08T12:54:34Z 2017-06-08T12:54:34Z 2001 A molecular dynamics study of Li-doped borate glasses / Ch.-P.E. Varsamis, A. Vegiri, E.I. Kamitsos // Condensed Matter Physics. — 2001. — Т. 4, № 1(25). — С. 119-132. — Бібліогр.: 26 назв. — англ. 1607-324X PACS: 71.15.Pd, 61.43.Fs, 81.05.Kf DOI:10.5488/CMP.4.1.119 https://nasplib.isofts.kiev.ua/handle/123456789/119763 The objective of this work is to investigate the effect of alkali content and temperature on the microstructure of lithium borate glasses, xLi₂O · (1 − x)B₂O₃. We have applied the molecular dynamics technique with Ewald summation and periodic boundary conditions to a collection of ca. 256 particles confined within a primitive cubic cell and interacting through a BornMayer-Huggins type of potential augmented with three-body angular terms. The results of this study have been discussed in relation to experimental structural data obtained by NMR and infrared spectroscopies. Метою даної роботи є дослідження впливу лужного вмісту і температури на мікроструктуру xLi₂O · (1 − x)B₂O₃. Ми застосували метод молекулярної динаміки з пересумовуванням за Евальдом до набору з 256 частинок, розміщених в примітивній кубічній комірці, що взаємодіють з потенціалом типу Борна-Майєра-Хаггіна, доповненим членами тричастинкової кутової взаємодії. Результати цих досліджень обговорюються в зв’язку з експериментальними даними, отриманими методами ядерного магнітного резонансу і інфрачервоної спектроскопії. This work was supported by EU through the INTAS 99–01162 Program and in part by the Greek General Secretariat for Research and Technology (PENED99– 99ED44). en Інститут фізики конденсованих систем НАН України Condensed Matter Physics A molecular dynamics study of Li-doped borate glasses Дослідження боратного шкла легованого літієм методом молекулярної динаміки Article published earlier |
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A molecular dynamics study of Li-doped borate glasses |
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A molecular dynamics study of Li-doped borate glasses Varsamis, Ch.-P.E. Vegiri, A. Kamitsos, E.I. |
| title_short |
A molecular dynamics study of Li-doped borate glasses |
| title_full |
A molecular dynamics study of Li-doped borate glasses |
| title_fullStr |
A molecular dynamics study of Li-doped borate glasses |
| title_full_unstemmed |
A molecular dynamics study of Li-doped borate glasses |
| title_sort |
molecular dynamics study of li-doped borate glasses |
| author |
Varsamis, Ch.-P.E. Vegiri, A. Kamitsos, E.I. |
| author_facet |
Varsamis, Ch.-P.E. Vegiri, A. Kamitsos, E.I. |
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2001 |
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Condensed Matter Physics |
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Інститут фізики конденсованих систем НАН України |
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Article |
| title_alt |
Дослідження боратного шкла легованого літієм методом молекулярної динаміки |
| description |
The objective of this work is to investigate the effect of alkali content and
temperature on the microstructure of lithium borate glasses, xLi₂O · (1 −
x)B₂O₃. We have applied the molecular dynamics technique with Ewald
summation and periodic boundary conditions to a collection of ca. 256 particles
confined within a primitive cubic cell and interacting through a BornMayer-Huggins
type of potential augmented with three-body angular terms.
The results of this study have been discussed in relation to experimental
structural data obtained by NMR and infrared spectroscopies.
Метою даної роботи є дослідження впливу лужного вмісту і температури на мікроструктуру xLi₂O · (1 − x)B₂O₃. Ми застосували метод молекулярної динаміки з пересумовуванням за Евальдом до набору з
256 частинок, розміщених в примітивній кубічній комірці, що взаємодіють з потенціалом типу Борна-Майєра-Хаггіна, доповненим членами тричастинкової кутової взаємодії. Результати цих досліджень обговорюються в зв’язку з експериментальними даними, отриманими
методами ядерного магнітного резонансу і інфрачервоної спектроскопії.
|
| issn |
1607-324X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/119763 |
| citation_txt |
A molecular dynamics study of Li-doped borate glasses / Ch.-P.E. Varsamis, A. Vegiri, E.I. Kamitsos // Condensed Matter Physics. — 2001. — Т. 4, № 1(25). — С. 119-132. — Бібліогр.: 26 назв. — англ. |
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2025-11-24T15:47:14Z |
| last_indexed |
2025-11-24T15:47:14Z |
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1850848641001979904 |
| fulltext |
Condensed Matter Physics, 2001, Vol. 4, No. 1(25), pp. 119–132
A molecular dynamics study of
Li-doped borate glasses
Ch.-P.E.Varsamis, A.Vegiri, E.I.Kamitsos
Theoretical and Physical Chemistry Institute,
National Hellenic Research Foundation,
48 Vas.Constantinou Ave., 11635 Athens, Greece
Received August 1, 2000
The objective of this work is to investigate the effect of alkali content and
temperature on the microstructure of lithium borate glasses, xLi2O · (1 −
x)B2O3. We have applied the molecular dynamics technique with Ewald
summation and periodic boundary conditions to a collection of ca. 256 par-
ticles confined within a primitive cubic cell and interacting through a Born-
Mayer-Huggins type of potential augmented with three-body angular terms.
The results of this study have been discussed in relation to experimental
structural data obtained by NMR and infrared spectroscopies.
Key words: molecular dynamics, lithium borate glasses
PACS: 71.15.Pd, 61.43.Fs, 81.05.Kf
1. Introduction
Ionic glasses constitute prominent probable materials for technological appli-
cations in electrochemical and optical devices [1–3]. The choice and design of the
appropriate materials for specific applications require a detailed knowledge of their
structure and physical properties. The lack of long range order in the glassy state
limits the effectiveness of experimental techniques and theoretical calculations which
work successfully when applied to crystalline materials. To overcome the difficulty,
computational simulations may be employed to provide alternative ways of investi-
gating microscopic and macroscopic properties of glasses [4–7].
The short-range order (SRO) structure of Li-borate glasses, xLi2O·(1−x)B2O3,
at room temperature has been studied by NMR [8,9], mid-IR [10,11], Raman [12],
and neutron diffraction [13] spectroscopies and by molecular dynamics simulations
[5–7]. It is widely accepted that for Li2O contents up to ca. x = 0.25 the trans-
formation of neutral borate triangular units, BØ3, into charged tetrahedral borate
species, BØ−
4
, constitutes the main modification mechanism of the short-range or-
der (hereafter Ø will denote an oxygen atom bridging two boron centers) [8,10]. For
x larger than ca. 0.25, borate triangles with non-bridging oxygen atoms (NBO’s),
c© Ch.-P.E.Varsamis, A.Vegiri, E.I.Kamitsos 119
Ch.-P.E.Varsamis, A.Vegiri, E.I.Kamitsos
Table 1. Simulation parameters for xLi2O · (1− x)B2O3 glasses.
Number of atoms Rbox (Å)
x B O Li T = 300 K T = 600 K T = 1200 K
0.2 89 144 21 13.84 13.92 14.37
0.3 81 139 35 13.54 13.58 14.09
0.4 73 134 49 13.36 13.55 14.08
0.5 64 128 64 13.33 13.47 14.05
BØ2O
−, and BØO2−
2
are formed and coexist with BØ−
4
tetrahedra [14]. The effect
of temperature on the SRO structure was investigated to a lesser extent. Statisti-
cal mechanics calculations [15] and NMR data [16] suggested that with increasing
temperature conversion of BØ−
4
tetrahedral into their isomeric BØ2O
− species takes
place [14].
The local environment of metal cations in borate glasses has been investigated
by far-IR [10,11,17,18] and MD simulations [7]. In particular, the presence of two
different cation hosting sites has been experimentally identified [10,11,17,18]. Ques-
tions regarding the tendency for aggregation of metal cations into clusters or their
homogeneous distribution in the glass network constitute open challenges. In that
respect, clustering models have been proposed, i.e. the cluster-tissue [19] and the
modified random network model [20], as well as models assuming a homogeneous
distribution of metal cations [21].
In this work, a molecular dynamics study of xLi2O·(1−x)B2O3 glasses is present-
ed as a function of lithium oxide content, x, and temperature, T . The main emphasis
of this work is to investigate the SRO structure and the local environments around
Li ions and NBO’s, and their distribution in the network, as a function of both x
and T . The calculated SRO structure and the Li-site energetics have been compared
with experimental NMR [8] and far-infrared [17,18] findings, respectively.
2. Computational procedure
Four different compositions in the xLi2O ·(1−x)B2O3 glassy system were investi-
gated at three temperatures by the molecular dynamics technique. In all simulations,
structures consisting of ca. 256 atoms in a primitive cubic cell have been generated.
The number of atoms used in each composition and the lattice constant of the unit
cell, as determined from experimental densities [22,23], are summarized in table 1.
Interatomic interactions were treated by means of the usual Born-Mayer-Huggins
potential:
Vij(r) = Aij exp(−r/ρ) + zizje
2/r, (1)
where
Aij = 20.3545
(
1 +
zi
ηi
+
zj
ηj
)
exp
(
ri + rj
ρ
)
(kJ/mol). (2)
120
A molecular dynamics study of Li-doped borate glasses
In equations (1) and (2), zie, ηi, ri, are the charge, number of valence shell electrons
and ionic radius, of ion i and ρ is the repulsion parameter (ρ = 0.29 Å).
An additional three-body harmonic interaction potential term for the O-B-O
angles was included:
Vijk = 0.5Kijk(θ − θ0)
2, (3)
where Kijk is a constant determining the strength of the interaction and θ is the
angle between i-j and j-k bonds. The angle θ0 corresponds to the potential energy
minimum.
The potential model and the values of the parameters which appear in equa-
tions (1–3) have been taken from [7], where a partial scaling of the electrostatic
charges necessary for the reproduction of the experimental IR [10,11] and Raman
spectra [12], was adopted.
Our simulations have been carried out in the microcanonical ensemble, where the
initial configuration was a random distribution of atoms over the sites of an fcc cubic
lattice, with velocities taken from a Maxwellian distribution at 6000 K. Periodic
boundary conditions were applied and long range Coulombic forces were handled by
Ewald summation. A fifth-order Gear predictor-corrector integrator with a timestep
of 0.96 fs was used. The generated melts were quenched to the final temperature in
five cooling cycles. Each cycle consisted of a fast cooling step for about 2 ps and
an equilibration period of about 10 ps. The equilibration period in the final cooling
cycle was 30 ps, whereas properties were accumulated for a final period of about
60 ps.
3. Results and discussion
3.1. Short range order structure
The SRO structure of xLi2O ·(1−x)B2O3 glasses with x values up to x = 0.5 was
found to consist mainly of triangular borate, BØ3 and BØ2O
−, and tetrahedral, BØ−
4
,
units [8,10,11]. The mole fraction of tetrahedral BØ−
4
units, X4, in the simulated
glasses can be determined from the coordination number of B atoms calculated from
the B-O radial distribution function. The mole fractions of BØ2O
−, X2, and BØO2−
2
triangles, X1, were estimated by counting the number of NBOs per 3-coordinated
boron center. An oxygen atom is identified as an NBO if no other boron atom is
found in a sphere with a radius of ca. 2 Å. This distance corresponds to the first
minimum of the B-O radial distribution function and was found to be independent
of temperature and composition. The calculated fractions X4, X2 and X1 are listed
in table 2.
Inspection of table 2 shows that the calculated charge per borate polyhedron
center is systematically lower than that expected from stoichiometry. Such a differ-
ence can be attributed to the application of periodic boundary conditions that may
transform an NBO situated close to the surface of the primitive cell into a bridging
oxygen atom of a borate triangle. To eliminate such surface effects it is necessary to
substantially increase the size of the system.
121
Ch.-P.E.Varsamis, A.Vegiri, E.I.Kamitsos
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Figure 1. Calculated mole fractions of tetrahedral borate units, X4, at different
compositions and temperatures, in xLi2O · (1−x)B2O3 glasses. Experimental X4
values obtained from NMR room temperature study [8] at room temperature are
also depicted for comparison.
122
A molecular dynamics study of Li-doped borate glasses
Table 2. Mole fractions of BØ−
4
, X4, BØ2O
−, X2, and BØO2−
2
, X1, units in
xLi2O · (1− x)B2O3 glasses, as a function of lithium oxide mole fraction, x, and
temperature, T . Calculated, X4+X2+2X1, and stoichiometric values, x/(1−x),
for the total negative charge per borate polyhedron are also reported.
T (K) x X4 X2 X1 X4 +X2 + 2X1 x/(1− x)
1250
0.2 12.3 5.1 0.8 19 25
0.3 21 7.6 3.7 36 43
0.4 18 18.7 8.4 53.5 66
0.5 8.5 19.3 27.8 83.4 100
600
0.2 17 2.6 0 19.6 25
0.3 33 7.5 0.8 42.1 43
0.4 30 15.4 3.4 52.2 66
0.5 30 14.5 11.9 68.3 100
300
0.2 20 2.4 0 22.4 25
0.3 30 7.4 0 37.4 43
0.4 40 11.1 2.3 55.7 66
0.5 40 12.2 9.2 70.6 100
The calculated fractions X4 at the three temperatures of the simulation are dis-
played in figure 1 versus Li2O mole fraction. The experimentalX4 values obtained by
NMR spectroscopy at 300 K [8], are also included for comparison. It is obvious that
calculated X4 fractions at 300 K are in close agreement with the experimental NMR
values, whereas a systematic decrease of calculated X4 with increasing temperature
is observed. For charge conservation reasons, such a trend indicates the conversion of
BØ−
4
units into triangular borate units with one or two NBOs. The isomerization of
the energetically more stable tetrahedral BØ−
4
units into BØ2O
− triangular species
with increasing temperature has been predicted by Araujo with statistical mechanics
calculations [15] and confirmed in high temperature NMR experiments by Stebbins
and coworkers [16]. This finding is also consistent with the observed differences in
the infrared and Raman spectra of alkali borate glasses having the same composition
but different thermal histories, i.e. annealing treatment or cooling rates [24,25].
It is noted that the presence of BØO2−
2
triangles in isolated pyroborate units,
B2O
4−
5
, has been observed by infrared and Raman measurements at room tempera-
ture in the lithium borate glasses with x > 0.5 [10,12]. Our calculations at T = 300 K
indeed show the formation of BØO2−
2
units for x > 0.4. However, snapshots of the
glass network indicate that BØO2−
2
triangles are also found in the form of B2Ø2O
2−
3
and B2ØO3−
4
units, besides the isolated pyroborate moieties.
Representative snapshots of the glass structure at different compositions and
temperatures are displayed in figures 2a,b. At low temperatures and compositions
we observe the dominance of closed rings consisting of four, five or six boron atoms
either in triangular or tetrahedral units. At larger alkali concentrations the closed
rings become larger in size, whereas at T = 1250 K and x = 0.5 a considerable
123
Ch.-P.E.Varsamis, A.Vegiri, E.I.Kamitsos
(a) 0.3Li2O · 0.7B2O3
(b) 0.5Li2O · 0.5B2O3
Figure 2. (a) Snapshot of the simulated structure for 0.3Li2O · 0.7B2O3 glass at
T = 300 K. Closed rings in the network structure are highlighted. (b) Snapshot of
the simulated structure for 0.5Li2O ·0.5B2O3 glass at T = 1200 K. The formation
of ‘channels’ suitable for Li migration is highlighted.
124
A molecular dynamics study of Li-doped borate glasses
Table 3. Distribution of Li-cations in xLi2O · (1 − x)B2O3 glasses as a function
of composition, x, and temperature, T . Lib and Linb denotes Li cations in sites
formed mainly by bridging (b-type) and non-bridging oxygen atoms (nb-type),
respectively. Lim denotes Li cations splitting their time between b-type and nb-
type sites.
T (K) x % Lib % Linb % Lim
1250
0.2 47.6 23.8 28.6
0.3 8.6 25.7 65.7
0.4 0 89.6 10.4
0.5 0 100 0
600
0.2 76.2 23.8 0
0.3 40.0 37.1 22.9
0.4 22.4 65.3 12.2
0.5 18.7 64.1 17.2
300
0.2 71.4 19.1 9.5
0.3 65.7 34.3 0
0.4 42.9 46.9 10.2
0.5 28.1 62.5 9.4
depolymerization of the glass network occurs with the prevalence of long, linear
chains consisting mostly of triangular metaborate units (BØ2O
−).
3.2. Coordination environment of Li ions and non-bridging oxygen atoms
In order to investigate the nature of sites hosting metal cations we have distin-
guished Li cations according to the environments where they preferentially reside. A
distinct Li-hosting site is identified if a Li cation spends more than 75 % of time in
this particular site. Under this assumption, we were able to distinguish two types of
Li-coordination environments: those formed primarily by bridging oxygen atoms in
tetrahedral, BØ−
4
, and neutral triangular units, BØ3, (bridging-type, b-type environ-
ment) and those formed mainly by non-bridging oxygen atoms in charged BØ2O
−
or BØO2−
2
triangles, and neutral triangular units (non-bridging-type, nb-type en-
vironment). Thus, a Li cation is designated by Lib or Linb if it resides in a b-type
or in nb-type environment, respectively. A Li cation is denoted mixed, Lim, if it
spends approximately half of its time in a b-type site and the other half of its time
in an nb-type environment. We have good reasons to believe that Li cations in dif-
ferent types of sites do not behave in the same way, since they experience different
micro-environments depending on composition and temperature. In table 3, we sum-
marize the distribution of Li cations in the different local borate sites according to
temperature and composition.
It is noted that the percentage of Linb increases monotonically with alkali con-
tent and temperature. This is consistent with the result that the fraction of NBO-
125
Ch.-P.E.Varsamis, A.Vegiri, E.I.Kamitsos
Table 4. Coordination numbers of NBO and O atoms and Linb cations in xLi2O ·
(1 − x)B2O3 glasses as a function of composition, x, and temperature, T . For
details see text.
T (K) x NBO(Li) O(Li) NBO(NBO) Linb(Linb)
1250
0.2 2.0 0.6 1.2 2.5
0.3 2.3 1.1 1.5 3.1
0.4 2.6 1.4 3.0 4.7
0.5 2.9 2.2 5.2 6.7
600
0.2 2.2 0.6 0 1.3
0.3 2.8 1.2 1.0 3.2
0.4 3.0 1.8 2.4 5.4
0.5 3.2 2.3 4.8 7.3
300
0.2 2.4 0.8 0 1.9
0.3 2.6 1.1 0.6 2.5
0.4 2.8 1.6 1.5 3.6
0.5 3.05 2.1 2.0 5.7
containing units also increases with temperature and concentration (see table 2).
However, it was found that the rate of increase of the percentage of Linb ions is
greater than the corresponding rate of increase of NBOs. This finding can be ex-
plained if NBO atoms can coordinate with more than one Li cation. Along the same
lines, the percentage of Lib ions is systematically lower than the relative fraction
of BØ−
4
units, X4, with respect to all charged borate species, X4 +X2 +X1. Thus,
there is a preference of Li ions to coordinate with NBOs. For instance, at T = 300 K
and x = 0.4 although the tetrahedral borate units represent 40 % of all charged and
neutral local units in the system, or a 75 % of the charged units, the corresponding
total Lib percentage is 48 % , considering that half of Lim ions reside in b-type sites.
Such a trend becomes more pronounced at higher temperatures and concentrations;
i.e., at T = 1250 K and x = 0.4 the mole fraction X4 of BØ−
4
units represents
40 % of the charged units, while 5 % of Li ions spend their time in b-type sites as
Lim cations. This is probably related with the increased kinetic energy of cations at
T = 1250 K which now can more easily jump out of the shallower b-type wells than
at T = 300 K.
Since the results of table 3 suggest that Li ions prefer to reside closer to NBO
atoms, we will examine more thoroughly the region in the vicinity of an NBO atom.
To this end, we calculate the coordination numbers of NBOs relative to all Li cations,
NBO(Li), and to other NBOs, NBO(NBO). We also investigate the coordination
numbers of Linb cations relative to NBOs, Linb(NBO) and to other Linb, Linb(Linb).
The results are presented in table 4, as a function of composition and temperature.
O(O) and Li(O) coordination numbers, not listed in this study, were found to be in
close agreement with respect to those reported in the literature [7,13].
As seen in table 4, the average number of Li cations in the neighbourhood of
126
A molecular dynamics study of Li-doped borate glasses
Table 5. Distribution of Linb cations in sites of different number of NBO atoms
in xLi2O · (1− x)B2O3 glasses as a function of composition, x, and temperature
T . Linb
k
represents Linb cations residing in sites formed by k NBO atoms.
T (K) x Linb
1
Linb
2
Linb
3
Linb
4
1200
0.2 0.58 0.36 0.06 0
0.3 0.6 0.31 0.09 0
0.4 0.45 0.37 0.15 0.03
0.5 0.17 0.29 0.30 0.18
300
0.2 1.00 0 0 0
0.3 0.74 0.26 0 0
0.4 0.75 0.25 0 0
0.5 0.03 0.62 0.28 0.07
an NBO, NBO(Li), varies smoothly from ca. 2 to ca. 3 with increasing x, and is
independent of temperature. The number of Li cations around an average oxygen
atom, O(Li), is always smaller, varying between ca. 0.5 and 2. These findings imply
that, indeed, there is an increased concentration of Li cations in sites formed by NBO
atoms, in accord with the conclusions drawn from the previous discussion regarding
the results of table 3. Such a behaviour can be attributed to stronger Coulombic
interactions, and thus to the deeper potential wells that develop between Li ions and
the more polarized NBO-containing sites, as compared to sites formed by oxygen
atoms of tetrahedral units.
The calculated NBO-NBO correlation functions display two sharp and well-
defined peaks, which correspond to NBO-atoms in the first shell. The first peak at
a distance of 2.25 Å is attributed to NBO atoms belonging to the same unit, where-
as the second peak at 3.31 Å is attributed to NBOs of neighbouring units. The
NBO(NBO) coordination number of table 4 takes into account the contributions
from both peaks and was found to increase with temperature and alkali concentra-
tion. In most cases these coordination numbers are significantly larger than unity,
thus indicating the tendency of NBO atoms to agglomerate. Coordination numbers
between 2 and 3 may be associated with the presence of NBO atoms in closed rings
of the network structure. The larger coordination numbers found for the x = 0.5
composition, at T = 600 and 1250 K, fit better to a picture of a more open and
depolymerized network consisting of “channels” suitable for ion migration [19,20].
Further support to the NBO agglomeration picture comes from the classification
of Linb ions according to the percentage of time they spend in sites formed by a
variable number of NBO atoms. In table 5 we present the distribution of residence
times of Linb ions found in sites with 1 (Linb
1
), 2 (Linb
2
), 3 (Linb
3
), or 4 (Linb
4
) NBO
atoms, averaged over all Linb ions. The probability to find a Linb atom in sites
with more than one NBOs increases with temperature and Li-concentration. The
crucial role of cation hosting sites formed by more than one NBOs in ionic transport
properties has been reported in a recent theoretical study in Li-phosphate glasses
127
Ch.-P.E.Varsamis, A.Vegiri, E.I.Kamitsos
[26]. In particular, it was shown that Linb
3
cations are characterized by the lowest
activation energy necessary to hop into an adjacent site. In the same direction, we
are currently exploiting the role of NBOs to the diffusion properties of Li cations in
borate glasses.
3.3. Manifestation of Li-environments on the Li-O vibrational spectra
The discrimination of different cation hosting sites, e.g. b-type and nb-type envi-
ronments, can be correlated with the corresponding Li-O vibrations which are active
in the far-IR spectral range. In fact, far-IR experimental spectra are characterized
by an asymmetric absorption profile, which can be adequately simulated with two
Gaussian component bands [10,11,17,18]. Such an example is shown in figure 3a
for the 0.3Li2O · 0.7B2O3 glass [17,18]. The two component bands designated by
L (254 cm−1) and H (419 cm−1) have been attributed to Li-O vibrations in sites
characterized by different coordination numbers/charge density. In particular, the
H band was associated with Li-O vibrations in sites of larger anionic charge densi-
ty/smaller coordination number, while the L band was attributed to vibrations of
Li cations in energetically less favourable sites (smaller charge density/larger coor-
dination number) [17,18]. It is noted that absorption at frequencies above ca. 500
cm−1 is mainly attributed to vibrational modes of the borate network.
In view of the results of the present molecular dynamics study it is of great
interest to further examine the microscopic origin of the L and H Li-O vibrational
bands. For this purpose we calculated the velocity autocorrelation function, Φ(t),
which corresponds to Linb and Lib cations:
Φ(t) =
〈
(1/N)
N
∑
j=1
~vj(t) · ~vj(0)
〉
, (4)
where ~vj(t) is the velocity of ion j at time t and N is the total number of Linb
or Lib ions. The vibrational density of states, Φ(ω), which reflects the vibrational
properties of Li cations, is obtained from the Fourier transform of Φ(t).
A representative example of calculated Φ(ω) spectra is given in figure 3b for
the x = 0.3 composition (T = 300 K) and compared with the experimental far-
infrared spectrum of the same glass. It is evident that the Φ(ω) spectra of Linb and
Lib cations are well distinguished from each other, with the Lib spectrum shifted to
lower frequencies. This result is probably due to the fact that the charge density of
b-type environments is more delocalized compared to that of nb-type sites, resulting
to lower anionic charge density and consequently to lower values of Li-O vibration
frequencies. Comparison of the Φ(ω) spectra with the deconvoluted experimental
spectrum of the Li-borate glass suggests that it is plausible to assign the experi-
mental L and H component bands to Li-O vibrations mostly in b-type and nb-type
environments, respectively. In addition, the best fit of the experimental spectrum
produced by a linear combination of the calculated Φ(ω) spectra of Linb and Lib
ions is also displayed in figure 3b and shows good agreement with the experimental
spectrum below ca. 500 cm−1 where the Li-O vibrations are active.
128
A molecular dynamics study of Li-doped borate glasses
�D�
�
���/L
�
2���%
�
2
�
�/L
E
�/L
QE
�H[S�
�ILW
�
�
� ��� ��� ��� ��� ��� ��� ���
�E�
�H[S�
�ILW
+
/
�
�
$
E
V
R
US
WL
R
Q
:DYHQXPEHUV���FP
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Figure 3. (a) Experimental far-infrared spectrum of 0.3Li2O · 0.7B2O3 glass [18].
(b) Calculated power spectra, Φ(ω), of Li ions residing in non-bridging oxygen-
type, Linb, and bridging oxygen-type, Lib, sites for the 0.3Li2O · 0.7B2O3 glass
at T = 300 K. A linear combination of the Φ(ω) spectra of Lib and Linb ions
is also shown for comparison with the experimental spectrum in (a). Note the
close correspondence of L and H bands with the power spectrum of Lib and Linb
cations, respectively.
129
Ch.-P.E.Varsamis, A.Vegiri, E.I.Kamitsos
4. Conclusions
The effect of alkali content and temperature on the structure of lithium borate
glasses, xLi2O · (1 − x)B2O3, has been investigated by molecular dynamics simula-
tions. Room temperature results concerning the mole fractions of local borate units
are in good agreement with the experimental NMR and IR results. Temperature
increase was found to result in the decrease of the mole fraction of BØ−
4
tetrahedral
units in favour of charged borate triangles, BØ2O
− and BØO2−
2
, for all compositions.
This is in agreement with statistical mechanics and high-temperature NMR results.
Li cations were found to explore two distinct environments, non-bridging oxygen-
type and bridging oxygen-type sites, formed primarily by NBO atoms and oxygen
atoms in tetrahedral borate units, respectively. A preference of Li ions to reside close
to non-bridging oxygen atoms, as well as a tendency for non-bridging oxygen atoms
to aggregate with increasing temperature and alkali content was found. For glasses
of high alkali content (x = 0.5) it was shown that lithium cations cluster around
NBO atoms and form “channels” through the glass network, in agreement with the
cluster-tissue and modified random network models.
The distinction of cations into two types, Linb and Lib for cations occupying nb-
type and b-type sites, respectively, is very well reflected on their spectral properties.
The calculated power spectra of Linb are peaking at higher frequencies compared to
those of Lib ions. This is in accord with the analysis of two component bands in the
experimental far-infrared spectra, attributed to Li-O vibrational modes in different
anionic sites.
5. Acknowledgements
This work was supported by EU through the INTAS 99–01162 Program and in
part by the Greek General Secretariat for Research and Technology (PENED99–
99ED44).
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131
Ch.-P.E.Varsamis, A.Vegiri, E.I.Kamitsos
Дослідження боратного шкла легованого літієм
методом молекулярної динаміки
Ч.-П.Е. Варсаміс, А. Вегірі, Е.І. Камітсос
Інститут теоретичної і фізичної хімії,
11635 Афіни, Греція
Отримано 1 серпня 2000 р.
Метою даної роботи є дослідження впливу лужного вмісту і темпера-
тури на мікроструктуру xLi2O · (1−x)B2O3. Ми застосували метод мо-
лекулярної динаміки з пересумовуванням за Евальдом до набору з
256 частинок, розміщених в примітивній кубічній комірці, що взаємо-
діють з потенціалом типу Борна-Майєра-Хаггіна, доповненим члена-
ми тричастинкової кутової взаємодії. Результати цих досліджень об-
говорюються в зв’язку з експериментальними даними, отриманими
методами ядерного магнітного резонансу і інфрачервоної спектро-
скопії.
Ключові слова: молекулярна динаміка, боратне шкло
PACS: 71.15.Pd, 61.43.Fs, 81.05.Kf
132
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