J . Phys. Chem. 1994,98, 9216-9221
9216
A Molecular Dynamics Study of Atomic Correlations in Glassy BzS3t S. Balasubramanian and K. J. Rao' Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore 560 012, India Received: March 2, 1994"
Glassy B&, the parent compound of the superionic conductor LiI-Li&B& has been studied by the molecular dynamics technique using a new potential model. The results suggest that the glass is made up of local units of four-membered B2S2 rings bridged by sulfur atoms, leading to a chainlike structure. Various pair correlation functions have been analyzed, and the B2Sz rings have been found to be planar. T h e calculated neutron structure factor shows a peak a t 1.4 A-' which has been attributed to B-B correlations a t 5.6 A. The glass transition temperature of the simulated system has been calculated to be around 800 K.
1. Introduction Lithium-based superionic conductors have been one of the most widely investigated materials in the recent past.' Various materials like Li2SO4, LiI-Li20-Mo03, LiSiCON, etc., have been studied extensively due to their high ionic conductivity and potential application as materials for solid-state batteries.2 Conductivity values of the order of 0.1 S/cm have been attained in these glassy materials. Thioborate glasses based on the LiILi2S-B& system belong to this category of superionic conductors and several of them have been investigated during the past decade.3" Considerable attention has been devoted toward understanding the structural and dynamical properties of this system recently.7-11 We may note in this context that there are essential differences in the structures of oxide and chalcogenide glasses.12J3 For example, GeSe2 according to the chemical formula is akin to SiO2, but is very different from the latter in its structure. The basic structural unit in both the glasses is a tetrahedron (SiO4/2 in Si02 and GeSe,/z in GeSez), but whereas the adjoining tetrahedra share corners in SiOz, they share edges in GeSe2. A similar situation is known to be present in B2O3 and BzS3 glasses. In both these glasses, the basic structural units are similar, BO312 and BS3/2 triangles, respectively. But the units are corner-shared in B203l4and edge-shared in BzS3. The crystal structure of BzS3 itself is somewhat contentious. While Krebs and co-workers15 have proposed a two-dimensional configuration made up of four-membered B2S2 rings along with six-membered B3S3 rings, Chen et a1.16 have proposed a nearly one-dimensional chain model consisting only alternating BzS2 rings bridged by sulfur atoms. We therefore consider it imperative to study the parent compound boron trisulfide, B2S3, by a variety of experimental and modelling techniques. Simple salts like BeF2I7 and CaFZl8 have been extensively studied using molecular dynamics (MD), and many aspects like anionic conduction have been well understood. Also, structures of chalcogenides like GeSe2 are being widely investigated using M D simulation^.^^-^^ Molecular dynamics simulations have to pay particular attention to the nature of bonding in chalcogenide glasses like GeSe2, B2S3, etc., because the bonding is more covalent than in oxide glasses like SiO2.21 It is thus essential that three-body forces are explicitly incorporated in the interaction potential to simulate such covalent glasses. While modeling B2S3 glass, we may take note of the highly polarizable nature of sulfur atoms (due mainly to its size) and incorporate a charge-dipole interaction term also in order to correctly reproduce experimental data. Keeping the above factors in view, we present here MD studies of B2S3 in the molten and t Contribution No. 1010 from the Solid State and Structural Chemistry Unit. Abstract published in Advance ACS Absrracrs. August 15, 1994.
0022-3654/94/2098-92 16$04.50/0
glassy states using a Born-Mayer-Huggins potential which is modified appropriately.
(BMH) type of
2. Methodology The MD simulation was performed on a system of 500 atoms in the microcanonical ensemble. The initial coordinates of the atoms were chosen randomly inside a cubic box whose size was determined by the density of the system (1700 kg/m3).zz This corresponds to a box length of 22.576 A which is large enough to study the structural correlations in the system. At each time step, the equations of motion were integrated using Verlet algorithm with a time step of 1 fs. Standard Ewald summation technique and periodic boundary conditions were a~plied.~3 The potential of interaction between any two atoms i j was of the form
with the two-body term as e ,2 ,
+
V2(rU)= r.. 'I
exp[?]
-
and the three-body term as
V2 is evidently pairwise additive, whereas V3 is not. V3has been chosen to be of the form proposed by Stillinger and WeberZ4and employed by Vashishta and co-workers in their simulations of glassy GeSez.19 Partial charges 2,and 2, were employed on boron and sulfur. The first term in Vz is a simple Coulombic one, and the second term arises out of hard core repulsion. Together they constitute the major part of the standard BMH potential. The third term, having a r" dependence, arises out of chargedipole interactions and involves the electronic polarizabilities (ai) of the atoms.25 This term also has a range determined by the parameter, r,. As has been discussed earlier, explicit consideration of threebody forces24isnecessary to accommodatethe strong directionality
0 1994 American Chemical Society
The Journal of Physical Chemistry, Vol. 98, No. 37, 1994 9217
Atomic Correlations in Glassy B2S3
TABLE 1: Potential Parameters for the MD Run zs = -0.5 ZB= +0.75 as = 5.5 x 10-30 m3 ag = 3.0 X m3 9 ‘ s =~ 60’ I S M = 120° B~~ = 1.0 x 10-17 J B~~ = 0.2 x 10-17 J p = 0.29 A
b = 2.0 A A ~ B1.004X
J A=
rs = 3.5 A y = 2.0 A A m = 1.073 X 10-l6 J
3. Results and Discussion 3.1. Pair Distribution Functions. The B-S bond in B2S3 is largely, but not entirely, covalent. (On Pauling’s scale,21 electronegativity of boron is 2.04, while that of sulfur is 2.58.) Hence we use partial charges which play an important role in simulating this bond. The B-S bond length is similar in both crystalline B2S3 and glassy B& and is around 1.86 A. The B-S pair distribution function (pdf‘) is shown in Figure l a for all temperatures. There is a sharp first peak at around 1.9 A whose intensity develops as a function of decreasing temperature. In the present work, we obtain the average coordination of boron
(a)
-
2
10.0 X 10-16 J
of bonding in these systems. B,ik denotes the strength of the interaction, while denotes the predominant angle defined by the triplet j i k in the system. The parameter b determines the range of the three-body interaction while y determines the “hardness” of this interaction. The value of p in V2 has been employed in earlier simulations.26 The decay length of the chargedipole interaction term, rs, was chosen so that its value a t halfbox length is less than 4% of its value without the exponential decay term.20 B’SBS and e’BSB were known experimentally to be 120° and 60°, respectively.IO-22 The magnitudes of other parameters viz., Zi, Ai,, Bij, y, and b, were varied by trial and error so as to reproduce the experimental data on near neighbour distances (B-B, B-S, and S S ) , coordination numbers and preferred bond angles reported from the neutron data of Estournes et al.27 The interaction cutoff for the three-body term was chosen to be 4.0 A. The various parameters employed in this work are listed in Table 1. The simulation was performed a t seven temperatures. They were 2000, 1700, 1400, 1100, 800, 500, and 300 K. At each temperature, the system was equilibrated for more than 20 ps and then various static and dynamical properties were averaged for another 20 ps. A quench rate of 0.1 K/fs was employed between any two temperatures. In any simulation using empirically developed potentials, it is important to monitor the pressure of the system. We observed that the pressure of the system (calculated from the viria123) a t 300 K is around -1.2 f 0.1 GPa at the glass density of 1700 kg/m3. At 300 K, we performed several runs with higher densities to obtain the density for which the resulting pressure was zero. (Pressure less than 0.1 GPa was considered to be essentially zero.28) At a density of 1865 kg/m3, the pressure of the system was found to be 0.09 CfPa. This density increase corresponds to a decrease in the volume of the simulation box of less than 10%. This leads to a decrease in the interatomic distances (as observed through pair distribution functions) by about 0.05 8, only (i.e., around 2.5% of the shortest interatomic distance in the system, B S ) . The total energy of theglass a t 300 K differed by about 5 kcal/mol (about 2% of the total energy) between the systems at the two different densities. This may be compared with observations related to the MD results on Si02 glass by Valle and Andersen29 using an ab initio potential model where the pressure of the system a t 300 K was observed to be-2.2 f 0.2 GPa at its normal density of 2200 kg/m3 and the density had to be increased by 5% to obtain a “zero” pressure. Hence, we believe that the results obtained from the present simulation may not differ much from the one studied at zero pressure.
I
lo! 8
0
6
2
4
6
a
l
’
O
n LL
n
a
ic)
s
-
6 4
2 0
0
2
4 - 6
8
1 0 0
r (A)
2
4 - 6 f-
(4
8
10
Figure 1. (a) B-S, (b) B-B, and (c) S S pair distribution functions at seven temperatures, namely 300,500,800,1100, 1400,1700,and 2000 K (from top to bottom in each graph).
TABLE 2: Fraction of Atoms with Coordination Number c coordn no. c boron sulfur 1 2 3
9.5 x 10-3 0.24 0.755
0.173 0.823 3.2 x 10-3
to be around 2.7, close to the expected value of 3.’930 In addition, we have also obtained the fraction of boron and sulfur atoms which are 1-, 2-, and 3-coordinated. These are given in Table 2. It is found that more than 75% of boron atoms are 2-coordinated to sulfur. The B-S pdf also exhibits a second peak at around 3.8 A, which will be discussed later. The B-B pdf is shown in Figure 1b. This exhibits a sharp peak a t around 2.05 A which strongly points to the existence of B2S2 rings. The B-B coordination taken a t the first minimum of the pdf (2.35 A) is roughly 0.85. This is close to the value of unity expected for a B2Sz ring.1° In addition, the B-B pdf shows a peak a t 2.75 8, which increases in intensity as the system is cooled. Using the knowledge of the prominent bond angles (see later), one can attribute this growing peak to B-B distances in adjacent B2Sz rings bridged by a sulfur. In fact, an analysis of the area under this peak at low temperatures shows that this peak contributes exactly one boron atom to the second coordination shell of boron. At higher distances, the B-B pdf exhibits a hump at about 4.55 A and a peak a t 5.6 A. The implications of the latter to intermediate range order in this glass is discussed later. The S S pdf (Figure IC) exhibits a peak at 3.35 A, the largest nearest-neighbor distance in the system. This is due to the fact that the angle a t boron in the four-membered ring is quite large, around 120O. The coordination number of sulfur to sulfur is around 9.0 in the glass. Such a large coordination number arises due to two reasons: (i) the distance between a sulfur in the B2S2 ring and the neighboring bridging sulfur could also be around 3.5 A. This can be obtained from simple geometric considerations keeping in view the planarity of the ring (see later) and the angle a t the bridging sulfur. (ii) Since the dimensionality of the system is low-sulfur atoms being arranged in a chain “decorated“ by B2S2rings, adjacent chains also could contribute substantially to the sulfur coordination up to distances of the order of 4.3 A, the latter being the coordination cutoff distance. Thus we observe that the pdfs obtained from this MD simulation are consistent with the model proposed by Menetrier et aZ.10-22.27 for the structure of BzS3 glass. The following table compares
9218
Balasubramanian and Rao
The Journal of Physical Chemistry, Vol. 98, No. 37, 1994
B2Sz ring. The evaluation of the exact number of the rings present in the system is discussed in the next section. 3.2. Ring Statistics. The number of BzSz rings in the system was calculated in two ways. One, by a direct counting method in which the number of boron atoms with the same two sulfur atoms as neighbors were counted. In another method, we have used graph theoretic techniques to estimate the number of BzSz and B3S3 rings. This involves the construction of the adjacency matrix A. (This is like a Huckel matrix in group theory and is constructed with 1's for bonded atoms and 0's for nonbonded ones.) A few simple inputs such as boron is "bonded" only to sulfur and not to other boron atoms were used. Then a reduced graph was constructed wherein, thevertex of valency 2, Le., sulfur was hidden (such a method is routinely employed in applications of graph theory to organic molecules where hydrogens are suppressed31). This is done so as to simplify the procedure employed to extract the information on the connectivity of the atoms. BzSz rings would appear as follows in the original graph and in the reduced graph.
1 V
d
Figure 2. (a, top) Snapshot of the final atomic configuration of the system at 300K. (b, bottom) A single chain arbitrarily picked from the final configurationwhich clearly shows the conformationof the chainlike structure with B2Sz rings. Large circles, sulfur; small circles, boron.
results on first neighbor distances obtained from the present simulation with those from the neutron scattering data.27 pair B-B B S
s-s
Then the number of boron atoms which were connected to each other by exactly two paths was evaluated and this is equal to twice the number of four-membered rings in the system. The number of B3S3 rings can be estimated from the square of the adjacency matrix, AZ. If AJ is 1, it implies that atoms i and j are connected by one path of length two. A triplet ij,k having a path of length 2 between any two of them, denotes the existence of a triangle made up of boron atoms in the reduced graph. The unit in the original and reduced graph can be represented as follows.
present work (A)
data27 (A)
neutron
2.05 1.95 3.35
1.95 1.86 3.18
The presence of the four-membered BzS2 rings in the structure of the glass signifies the validity of the present potential form and the choice of the parameter set. That the structure of glassy BzS3 obtained from this simulation is indeed chainlike can be easily seen from Figure 2a where the frozen configuration of the simulated B2S3 at 300 K is shown. The B2S2 rings and the nature of the intermediate structure of B2S3 (chainlike) is evident. In Figure 2b, we have presented one such chain containing 28 atoms picked arbitrarily from the simulated final configuration a t 300 K in order to provide better clarity. It is also important to note the absence of any six-membered ring in the structure. Further, each of the B2S2 rings is separated by sulfur bridges much the same way as in the crystalline structure. It can also be noticed that the bridging sulfur is almost collinear with the two boron atoms in the BzSz ring. It is then possible to assign the 3.8-A peak in the B-S pdf to the distance between the bridging sulfur and the second nearest-neighbor boron present in the adjacent
S -id graph
reduced graph
Employing such a procedure, we estimated the number of B& rings in our 500 atom system and found it to be 84 and the number of B3S3 rings was negligible and equal to 2. The number of BzSz rings was also counted by a direct method, wherein the number of boron atom pairs with the same sulfur pairs as neighbors was counted. The counts were 82 for BzSz rings and 2 for B3S3 rings. The results obtained from direct counting matched well with those obtained using graph theoretic analysis. It may be noted here that in Chen's mode1,IO the number of BzSz rings in 500 atoms (100 B2S3 units) is 86. The 2-d model of Krebs et a1.15 suggest that B3S3 rings should be present in substantial numbers which is in contrast with the present results. Thus, the present MD results support the chain modello for the structure of glassy B2S3. 3.3. Higher Order Correlations. Bond Angle Distributions. We have also studied the bond angle distributions in the system and have examined their evolution as a function of temperature. For such a calculation, a B-S bond has been defined as one where the B S interatomic distance is less than the distance at which the first minimum of the B S pdf occurs (3.1 A). The calculated B S - B angle distribution is shown in Figure 3a. This exhibits a sharp peak at approximately 65' and a moderate hump at 90'. The 65' angle arises from sulfur atoms which are present in the B2Sz ring, while the 90° angle is a t the sulfur which bridges two adjacent B2S2 rings. Both the peaks increase in intensity and
The Journal of Physical Chemistry, Vol. 98, No. 37, 1994 9219
Atomic Correlations in Glassy B2S3
6 0.251
0.2
.-
r
I ( b ) S-B-S
Figure 3. Bond angle distributions of (a) B-S-B, and (b) S-BS angles at different temperatures as indicated in Figure 1.
a) mC0.04
0.06
- 3
0.04
a m
0.02
5.g
FJ2 -0 +h 0.02 Gfi
“s4
Figure 5. Various interatomic distances in B2S3 glass obtained from the results of the static structure. Large circles, sulfur; small circles, boron; B1-B2, 2.1 A; BrB3, 2.75 A; S d 3 , 3.4 A; S d 4 , 3.4 A; B 4 4 , 3.8 A.
D
n 0 720 1 20
I 140
I 160
UWg)
n 0 180 140 I80 740
’
160
180
Weg)
Figure4. Dihedralangledistributionsbetween(a)S-=,and (b) B-S-B planes in the B2S2 ring for different temperatures as indicated in Figure
0.5
1.
0 h
narrow down considerably as the system is quenched. The Occurrence of the 90° feature in the bond angle distribution is not related to the structure of the potential, because it was not incorporated in the parameter set of the potential (Table 1). Its presence indicates the prevalance of chainlike structures in the system. The S-B-S bond angle distribution is shown in Figure 3b. This exhibitsa singlepeakat 122O whichincreases inintensity as a function of decreasing temperature. Considered together with the first-neighbor B-B distance, the magnitude of this angle bears out the planarity of the ring and the three-bonded nature of boron atoms in the structure. Dihedral Angle Distributions. The geometry of the B2S2 rings, particularly its planarity, can be further examined from dihedral angle distributions in our simulations. We define the dihedral angle to be that between the two S-B-S planes present in a B2S2 ring. The distribution of such a dihedral angle in the system is shown in Figure 4a as a function of temperature. We may similarly define the dihedral angle between two B S - B planes in the same B2S2 ring. This distribution of dihedral angles is shown in Figure 4b. Both the distributions show a distinct maximum at 180°, indicating that the B2S2 ring is indeed planar as found in experiments.I0Js It is evident that a t higher temperatures, such a preference for a dihedral angle becomes less pronounced, though not fully wiped out. Viewed in conjunction with the previous discussion of the static structure, the dihedral angle distributions conclusively prove the presence and the exact geometry of the B2S2 rings in the structure of B2S3 glass. A few remarks can be made regarding the high-temperature structure of the system. The most important feature is that the B2S2 ring is largely intact even at high temperatures. At temperatures higher than 1400 K, only the interconnection between these rings seems to get affected. This is obvious from the decrease in the peak height at 2.75 A in the B-B pdf which denotes the distance between two boron atoms in adjacent rings. This is also borne out by the gradual elimination of the 90° angle in the B S - B bond angle distribution a t high temperatures. Based on the results of the static structure discussed so far, the various interatomic distances in the system are presented in Figure 5 .
0-
5
-0.5
f
(b)
6-S
:m ( c i s-s
0 -1
Figure 6. Partial structure factors at 300 K of (a) B-B, (b) B-S, and
(c) SS pairs. 3.4. Partial and Total Structure Factors. In glasses containing strong networks like silicates etc., various workers have observed a sharp peak in S(q) in the range of 1-2 A-I, usually called the first sharp diffraction peak.32 The experimental S(q) data obtained from neutron diffraction experiments for glassy B2S3 is not available in the literature. But the same has been performed for B2S3 modified by Li2S.22.27The structure factor for all these glasses contain a sharp first peak at 1.4 A-1 independent of the concentration of LiZS. Thus, in the absence of a S(q) spectrum for pure B2S3, we assume that this first peak is a general feature of all B&-based glasses including pure B2S3 glass itself and that it arises out of correlations in the skeletal B2S3 glass structure. The partial structure factor for a pair of atoms a and fl is given byZo
where 6 = p is the Kronecker delta function, p is the density of the system, and C, represents the number concentration of the species a. In Figures 6, a, b, and c, we present the partial structure factors for B-B, B S , and S S pairs. The B-B S(q)exhibits a sharp first peak a t 1.4 A-1, the first minimum is at 2.2 A-1, and the second peak is at 2.7 A-1. The B S S(q)shows a small first peak at 1.75 A-1, a large minimum a t 2.6 A-1, and a second peak at 3.1 A-l. The S S S(q) exhibits a first peak at 2.05 A-l, a first minimum a t 3.1 A-1, and a second peak a t 4.0 A-l. One can analyze the origin of these features and attribute them to specific features in the real space pair distribution functions. Working on the same
9220
Balasubramanian and Rao
The Journal of Physical Chemistry, Vol. 98, No. 37, 15
D
5,
A 0
B-B B-S
X
0.8- X s-s
X
X
X X
0.6-
c--
u-
A
E
v
C
cn
0
0.4 1
l"J/
"
A 0
A
I
0
B
0.2 0
Figure7. Totalneutron structure factorof B2S3for different temperatures. The sharp peak at 1.4 A-I is likely to be. of the first sharp diffraction peak variety.
lines as Vashishta et al.20 we find that the 1.4-A-l peak in the B-BS(q) originates essentially from the peak a t 5.6 A in the B-B g ( r ) . Also the prominent minimum at 2.6 A-I in the B S S(q) is caused by the first peak at 1.95 A in the B-S g(r). The total neutron structure factor, S,(q), of glassy B2S3 has been obtained from the partial structure factors as
0
A
Figure 8. Wendt-Abraham ratio, R plotted as a function of temperature for each pair of species in the system. R for each pair is normalised with respect to their value at 2000 K.
3.5. Glass Transition. Wendt-Abraham Ratio. The glass transition temperature, Tgof a computer-simulated system can be obtained from a plot of the Wendt-Abraham ratio, R (the ratio of the first peak minimum to the first peak maximum in the respective pdf) against temperature.35 This ratio when plotted against temperature shows a change in slope possibly due to the saturation in packing of the first shell of nearest-neighbor atoms.35 Such a plot in which R is normalized with respect to its value at 2000 K is shown in Figure 8 for B-B, B S , and S S pair correlation functions. The data for B-S pdf shows a clear discontinuity in their slope at around 1000 K while that for B-B shows a weaker a discontinuity. We identify this temperature to be theapproximate Tgof the simulated B2S3 system. The experimental T8 of B2S3 The neutron scattering amplitudes b, and ba for boron and sulfur obtained from calorimetric measurements a t a quench rate of 10 were taken as 0.60 X 10-12 and 0.28 X 10-12 cm, re~pectively.~~ K/min has been known to be around 480 K.22936 The higher T8 The total neutron structure factor for the system was,calculated for the simulated glass is mostly due to the high quench rates at 300 K and is shown in Figure 7. As can be observed, there employed in our work which is a general feature of all computer is a sharp first peak at 1.4 A-1 with a small shoulder at 1.8 A-1 simulation^.'^ Figure 8 also shows the variation of R with in surprisingly good agreement with experiment^.^^.^^ The temperature for the S S pdf. The values of R in this case are experimental first peak intensity is around 1.8 in all xLiZS-( 1 consistently higher than that for the other two pdfs. It can thus x)B& glasses, while in our simulation we observe it to be 1.6. be concluded that the sulfur submatrix is not entirely "frozen" Hence, although we are unable to make any direct comparison even at 300 K. Since a third of the total sulfur atoms bridge any with the structure factor data for pure B2S3, the present results two adjacent B2S2 rings, they enjoy greater positional flexibility seem to be in reasonable agreement with the available data. than those sulfur atoms present within the ring. Their local The first peak a t 1.4 A-l in the B-B S(q) can be considered motionsmay not therefore freeze and hence theobserved variation to contribute to the first peak in the total S,(q). The hump at of R for the S S pdf. 1.8 A-I observed a t lower temperatures is due to B-S correlations Mean Squared Displacements. We have thus far studied in while the second peak at around 3.75 A-I is from the combined detail the static structure of BzS3 and its variation with second peaks of B S and S-S partial structure factors. A few temperature. The dynamics of the glass and of the melt are also comments regarding the 1.4-A-1 peak in S,(q) is in order. It is of interest as B2S3 is the base glass for the superionic conductors well-known that the product of the scattering vector k of the in the system LiI-Li2S-BzSs. Thus, we have studied the mean FSDP and the nearest-neighbor distance r is almost a constant, squared displacement data (MSD) and the diffusion coefficients around 2.5 in many glasses.32 In the case of B2S3, the first peak of boron and sulfur as a function of temperature. In Figure 9a, is at 1.4 A-1 and the B S interatomic distance is 1.875 A, hence we present the MSD data of boron at various temperatures. The k, is =2.6 in reasonable confirmation of this observation. Also MSD data clearly shows the "freezing" of the boron atoms at a as in the present study, FSDP has been found to arise due to A-A temperature near 800 K. Figure 9b shows the MSD data for and A-X correlations in glasses like SiSe2 and GeSe2 (of the sulfur. It is again evident that sulfur is more mobile than boron form AX2).34 But the temperature variation of the height of at any temperature and the mobility can be attributed to the FSDP observed in our simulations is in contrast to that seen in large number of sulfur atoms present in bridging positions. other glasses. In our simulations, we find that the FSDP behaves We have also calculated the diffusion coefficients ( D ) of boron in the same manner as other peaks in the structure factor; Le., and sulfur atoms at all temperatures from the MSD data and it decreases in height as the temperature is increased. This could these are shown in Table 3. The diffusion coefficients at high be due to the fact that we have used the low-temperature density temperatures are typical of simple liquids. As the temperature of the glass at higher temperatures also. It has earlier been shown19 is decreased, D decreases drastically to values of the order of that density plays a crucial role in the anomalous temperature cm*/s a t 800 K. At lower temperatures than this, the diffusion dependenceof FSDP. Thus, we are somewhat hesitant to classify coefficients are extremely low, implying the frozen nature of the the 1.4-A-l peak as the FSDP with the connotation currently system. We identify this to be near the glass transition prevailing for FSDP.32
Atomic Correlations in Glassy B2S3
-
The Journal of Physical Chemistry, Vol. 98, No. 37, 1994 9221
l*/iaisorall5(biSuliur/I _I
/
1-1
/
I
(2) Minami, T. J . Non-Cryst. Solids 1985,73,273. Fusco, F. A.; Tuller, H. L. In Superionic Solids and Solid Electrolytes-Recent trends; Laskar, A. L., Chandra, S., Eds.; Academic: New York, 1989. (3) Menetrier, M.; Levasseur, A.; Hagenmuller, P. J . Electrochem. SOC.
1984,131, 1971. (4) Wada, H.; Menetrier, M.; Levasseur, A,; Hagenmuller, P. Mater. Res. Bull. 1983, 18, 189. (5) Menetrier, M.; Hojjaji, A.; Estournes, C.; Levasseur, A. SolidStare Ionics 1991, 48, 325. // -. I // --I M.; Estournes, C.; Levasseur, A.; Rao, K. J. Solid State (6) Menetrier, Ionics 1992, 53-56, 1208. (7) Suh, K. S.;Hojjaji, A.; Villeneuve, G.; Menetrier, M.; Levasseur, A. 0 4 8 12 '0 4 8 12 J . Non-Crysr. Solids 1991, 128, 13. (8) Hintenlang, D. E.; Bray, P. J. J. Non-Cryst. Solids 1985,69, 243. time (ps) time (ps) (9) Martin, S.W.; Bloyer, D. R. J . Am. Ceram. SOC.1990, 73, 3481. Figure9. Mean squareddisplacement data at sevendifferent temperatures (10) Menetrier, M.; Hojjaji, A.; Levasseur, A.; Couzi, M.; Rao, K. J. for (a) boron, and (b) sulfur atoms plotted as a function of time. Phys. Chem. Glasses 1992, 33, 222. Decreasing temperature (as indicated in the text and in Figure 1) leads (1 1) Bloyer, D. R.; Cho, J.; Martin, S. W. J . Am. Ceram. SOC.1993, 76, to decrease in the slope of the MSD. 2753. (12) Kennedy, J. H.; Zhang, Z.; Eckert, H. J . Non-Cryst. Solids 1990, TABLE 3: Diffusion Coefficients of Ions at Various 123, 328. Temperatures (X cm*/s) (13) Angell, C. A. J. Non-Cryst. Solids 1985, 73, 1. (14) Prabakar, S.; Rao, K. J.; Rao, C. N. R. Proc. R. Sot. A 1990, 429, ion 2000K 1700K 1400K 1100 K 800 K 1. B 1.397 0.776 0.252 0.109 0.012 (15) Diercks, H.; Krebs, B. Angew. Chem., Int. Ed. Engl. 1977,16,313. Krebs, B. Angew. Chem., Int. Ed. Engl. 1983, 22, 113. S 1.861 1.081 0.381 0.139 0.023 (16) Chen,H.Y.;Conard,B. R.;Gilles,P. W. Inorg. Chem. 1970,9,1776. Chen, H. Y.; Gilles, P. W. J. Am. Chem. Sot. 1970, 92, 2309. temperature (mentioned earlier) for the computer-simulated (17) Brawer, S. A. J. Chem. Phys. 1981,75,3516. Brawer, S.A. Phys. system. Rev. Lett. 1981, 46, 778. (18) Gillan, M. J. Physica E 1985, 131, 157. (19) Vashishta, P.; Kalia, R. K.; Antonio, G. A,; Ebbsjo, I. Phys. Rev. 4. Conclusions Lett. 1989, 62, 1651. We have developed an empirical and heuristic potential to (20) Vashishta, P.; Kalia, R. K.; Ebbsjo, I. Phys. Rev. E 1989,39,6034. (21) Pauling, L. The Nature of the Chemical Bond; Oxford & IBH: New simulate B& glass and melt which contains apart from twoDelhi, 1967. body forces, an important three-body term. The structure of the (22) Estournes, C. Ph.D. dissertation, University of Bordeaux, 1992. simulated B& glass contains BzS2 rings arranged in a chainlike (23) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; fashion. The geometry of these rings has been characterized and Clarendon: Oxford, U.K., 1987. they have been found to be planar. The neutron structure factor (24) Stillinger, F. H.; Weber, T. A. Phys. Rev. E 1985, 31, 5262. for the glass obtained from the simulation exhibits a first peak (25) Kittel, C. Introduction to Solid State Physics; Wiley Eastern: New Delhi, 1986. at 1.4 A-' which has been attributed to spatial correlations at (26) Tesar, A. A.; Varshneya, A. K. J. Chem. Phys. 1987,87, 2986. large distances (5.6 A) between the boron atoms and also from (27) Estournes, C.; Owens, A. P.; Menetrier, M.; Levasseur, A.; Rao, K. B-S correlations. The glass transition temperature of the J.; Elliott, S.R. Communicated to J. Non-Cryst. Solids. simulated system has been found to be between 800 and 1000 K. (28) Soules, T. F. J. Non-Cryst. Solids 1982, 49, 29. (29) Valle, R. G. D.; Andersen, H. C. J . Chem. Phys. 1992, 97, 2682. (30) Muller-Warmth, M.; Eckert, H. Phys. Rep. 1982, 88, 132. Acknowledgment. The authors dedicate this article to Prof. C. (31) Randic, M. J. Am. Chem. SOC.1975, 97, 6609. N. R. Rao, FRS, on his sixtieth birthday. K.J.R. records his (32) Elliott, S.R. J. Phys. Cond. Matt. 1992, 4, 7661. gratefulness to Prof. C. N. R. Rao with whom he has been (33) Bacon, G. E. Acta Crystallogr. A 1972, 28, 357. associated for a long time both as a student and as a colleague. (34) Susman, S.;Price, D. L.; Volin, K. J.; Dejus, R. J.; Montague, D. G. The authors thank the Commission of European Communities J . Non-Cryst. Solids 1988, 106, 26. for financial support of this work. (35) Wendt, H. R.; Abraham, F. F. Phys. Rev. Lett. 1978,41, 1244. (36) Muetterties, E. A. The Chemistry of Boron and Its Compounds, Wiley: New York, 1967; p 648. References and Notes (37) Angell, C. A,; Clarke, J. H. R.; Woodcock, L. V. Adv. Chem. Phys. (1) Angell, C. A. Annu. Rev. Phys. Chem. 1992, 43, 693. 1981, 48, 397.
