Article pubs.acs.org/JPCC
Structural Origin of the Mixed Glass Former Effect in Sodium Borophosphate Glasses Investigated with Neutron Diffraction and Reverse Monte Carlo Modeling Maths Karlsson,*,† Michael Schuch,‡ Randilynn Christensen,§ Philipp Maass,‡ Steve W. Martin,§ Silvia Imberti,∥ and Aleksandar Matic† †
Department of Applied Physics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden Fachbereich Physik, Universität Osnabrück, Barbarastraße 7, 49076 Osnabrück, Germany § Department of Materials Science and Engineering, Iowa State University, Ames, Iowa 50011, United States ∥ ISIS Facility, STFC Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, UK ‡
ABSTRACT: The mixed glass former systems 0.35Na2O + 0.65[xB2O3 + (1 − x)P2O5] and 0.5Na2O + 0.5[xB2O3 + (1 − x)P2O5] with x = 0−1 were investigated with neutron diffraction (ND) together with reverse Monte Carlo (RMC) modeling of 0.35Na2O + 0.65[xB2O3 + (1 − x)P2O5]. The results show that the structure of both systems is reflected by an intermediaterange ordering, with a characteristic x-dependent length scale of about 4−6 Å and which contracts slightly with the increase of the Na concentration. Results obtained from RMC modeling of the 0.35Na2O + 0.65[xB2O3 + (1 − x)P2O5] system, using both previously reported X-ray diffraction (XRD) data as well as the here obtained ND data as independent constraints in the modeling, show that the intermediate-range structural features, notably the Na coordination and volume fraction of the conducting pathways, are only weakly dependent on the choice of the constraints used. In particular, we observe that the volume fraction of the conducting pathways and the activation energy for ionic conduction are only weakly correlated to each other, as opposed to what is found for binary alkali borate and phosphate glasses.
1. INTRODUCTION Typical inorganic glasses consist of a modifying salt, such as Na2O, and a glass network former, such as B2O3 or P2O5. During the cooling of the melt, the additional interactions between the cations from the modifying salt and the host glass former lead to a disturbance of the crystallization processes and therefore to an increase of the glass forming ability in comparison to the pure network former system. In addition, modifying salts can be used to introduce functional properties, such as optic, magnetic, or electronic, and thereby make the material of interest for use in various technological applications. Alkali modifiers can produce a subset of weakly bonded cations, which are decoupled from the static glass network structure and consequently show high ionic conductivity. Such fast ion conducting glasses are of interest for a variety of applications, including rechargeable batteries, fuel cells, supercapacitors, and photochromic windows, etc.1 A currently not fully understood feature of fast ion conducting glasses is the mixed glass former effect (MGFE), which is manifested by a nonlinear change in both the ionic conductivity and activation energy for long-range ion transport due to the mixing of two different glass formers.2 This nonlinear behavior of the conductivity and activation energy is also reflected in other material properties, such as the glass transition temperature and refractive index.3−5 A primary example is the sodium borophosphate system, for which the ionic conductivity and the glass transition temperature exhibit a © 2015 American Chemical Society
nonlinear dependence on the ratio of the network formers B2O3 and P2O5.4,5 Because the understanding of the relationship between the ionic conductivity of these mobile cations and the structure of the host glass is key for the development of strategies for optimizing the ionic conductivity of glasses, a detailed knowledge of the structure on a short- to intermediaterange length scale is essential. In particular, the effect of the intermediate-range order of the glass structure, which reflects the connectivity of different ion sites and hence possible conducting pathways, is not known. In addition, the role of the concentration of the modifying salt, which is likely to induce changes in both the short-range and intermediate-range glass structure, is not yet fully understood. In this work, we investigate the short- and intermediate-range ordering in the mixed glass former systems 0.35Na2O + 0.65[xB2O3 + (1 − x)P2O5] and 0.5Na2O + 0.5[xB2O3 + (1 − x)P2O5] with x = 0−1, by ND, in order to determine how the glass structure depends on the concentration of Na2O, B2O3, and P2O5. In particular, we use the ND data as an additional constraint in RMC modeling of the 0.35Na2O + 0.65[xB2O3 + (1 − x)P2O5] glass series and compare our new results with the RMC structures obtained earlier6 based on XRD data only. We show that the inclusion of the ND data in the RMC modeling Received: September 20, 2015 Revised: November 5, 2015 Published: December 1, 2015 27275
DOI: 10.1021/acs.jpcc.5b09176 J. Phys. Chem. C 2015, 119, 27275−27284
Article
The Journal of Physical Chemistry C
ments were performed at room temperature. The raw data were corrected using the GUDRUN software on the SANDALS diffractometer for multiple scattering, absorption, and inelasticity effects that generate a fully corrected structure factor, S(Q), suitable for analysis in terms of the atomic pair correlations. The level of the measured differential neutron scattering cross section, related to the S(Q), was well within the range of expected values, which shows that the data reduction and hence the sample composition and sample density were correct. The corresponding pair-correlation functions, G(r)s, were obtained by Fourier transformation according to the following
leads to a reduction in the conducting pathways and that there is no strong relation between the volume fraction of the conducting pathways and the activation energy of the conductivity. This is in contrast to what has been found for binary alkali borate and phosphate glasses.7 Reports of the Na+ conductivity, density, glass transition temperature, and shortrange structure of the glasses have been published separately.8−11
2. EXPERIMENTAL AND COMPUTATIONAL DETAILS 2.1. Sample Preparation. Starting materials for the preparation of the two sets of slightly hygroscopic glasses were Na2CO3 (Fisher Scientific 99.9%), (NH4)2HPO4 (Fisher Scientific 98.8%), and 11B-enriched boric acid H3BO3 (Fisher Scientific 99.7%). After weighing and mixing, the starting materials were decomposed at 900−1100 °C for 0.5−1 h in an electric furnace in a fume hood. After the melt was bubble free, the crucible was removed from the furnace and allowed to cool to room temperature. Once cool, the solidified melt was transferred to a nitrogen atmosphere glovebox. The decomposed materials were then melted in an electric furnace at 1000−1100 °C for 10 min until viscous enough to pour, then quenched at room temperature on brass plates. All glasses were melted in platinum crucibles. Atomic number densities of the glasses are reported in Table 1. The number densities were calculated based on densities measured with the use of a gas pycnometer “AccuPyc II 1340 Pycnometer” from Micrometrics.
G(r ) =
density 3
0.50 series
density
x
(atoms/Å )
x
(atoms/Å3)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0
0.0714 0.0737 0.0772 0.0773 0.0813 0.0849 0.0829 0.0873 0.0915
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.9
0.0738 0.0757 0.0774 0.0794 0.0804 0.0819 0.0831 0.0859
∫0
∞
drQ [S(Q ) − 1]sin(Qr )
(1)
The (total) pair correlation function G(r) results from a weighted sum over the partial pair correlation functions Gij(r) ⎡ m ⎤ G(r ) = 4πrρ0 ⎢ ∑ [wijGij(r )] − 1⎥ ⎢⎣ ⎥⎦ i,j=1
(2)
where ρ0 is the atomic number density (cf. Table 1) and m is the number of different atomic species (m = 4 for x ≠ 0,1). The weighting factors wij are given by ⎛m ⎞−2 wij = ⎜⎜∑ ckbk̅ ⎟⎟ cicjbi̅ bj̅ ⎝k=1 ⎠
Table 1. Atomic Number Densities of 0.35Na2O + 0.65[xB2O3 + (1 − x)P2O5] (0.35 Series) and 0.5Na2O + 0.5[xB2O3 + (1 − x)P2O5] (0.50 Series) 0.35 series
2 π
(3)
where ci is the molar fraction of the atomic species i, and bi is the average bound coherent scattering length. For XRD the bi must be replaced with the atomic form factors f i. The (total) structure factors S(Q) decompose into partial structure factors Sij(Q) analogously. 2.3. Structural Modeling. The RMC modeling was done for the 0.35Na2O + 0.65[xB2O3 + (1 − x)P2O5] series, with each model configuration positioned inside a simulation box subjected to periodic boundary conditions and refined against the experimentally determined structure factor, S(Q), and paircorrelation function, G(r). Some initial results of RMC modeling for the 0.35Na2O + 0.65[xB2O3 + (1 − x)P2O5] system, based on XRD data as input in the modeling, were presented in refs 6 and 13. In particular, it was shown in ref 6 that the final structures of unconstrained RMC modeling presented in ref 13 have to be refined in order to fulfill the requirements resulting from NMR data4 and theoretical considerations.14 More specifically, it was shown that the concentrations of the network forming unit (NFU) species must be included explicitly in the modeling by constraining the number of bridging oxygens (bOs) and nonbridging oxygens (nbOs), which are coordinated to the central P and B atoms. In this context, the NFUs are conveniently denoted as Q(n), where Q = P or B and n is the number of bOs (see Figure 1). A bO is shared by two Q species and accordingly contributes a charge −1 to each of them, whereas an nbO contributes with charge −2. With the oxidation numbers of +3 and +5 for the boron and phosphor atoms, respectively, the charges qn can be expressed as qn = n − 3 for the P(n) units (n = 0 to 4) and qn = −|n − 3| for the B(n) units (n = 2 to 4) (cf. Figure 1). These effective charges play a crucial role for the cation−network interactions, which in turn can affect the intermediate- to longrange structure of the glass.
2.2. ND Measurements. The ND measurements were performed at the SANDALS diffractometer at the pulsed neutron source ISIS of Rutherford Appleton Laboratory, UK. The SANDALS diffractometer, described in detail in ref 12, receives neutrons with wavelengths from 0.05 to 5 Å. The 660 detectors are summed into 18 groups, which cover an angular range of 3.8−39° that yields scattering vectors (Q) in the range 0.1−50 Å−1. The samples were ground into fine powders using an agate mortar and a pestle and loaded into flat sample cells of a 68% titanium and 32% zirconium alloy, which does not contribute to any coherent scattering. The sample thickness in the sample cell was approximately 1.3 mm, and the measuring time was around 6 h per sample. Measurements of the empty sample cans, of the empty sample chamber and of a vanadium standard were used in order to correct for the background and detector efficiency, as well as for the normalization of the data onto an absolute scale of barns per steradian per atom. All measure27276
DOI: 10.1021/acs.jpcc.5b09176 J. Phys. Chem. C 2015, 119, 27275−27284
Article
The Journal of Physical Chemistry C
B(4) concentrations given in refs 6 and 14 and by treating the boron in this unit as an atomic species that is virtually different from the boron in the B(3) units. In order to avoid the occurrence of unphysical Na environments, the coordination of Na by O must be constrained.6 This can be implemented in the RMC modeling by requiring that a Na3+ ion is coordinated by at least one O and that the average number of O in a coordination shell of 3− 5 Å around the Na3+ ions equals five. In order to analyze the impact of these additional constraints on the results, we have performed RMC modeling without taking care of proper Na environments (referred to as Models Ia/IIa) and when including the additional constraints (Models Ib/IIb). Further constraints, with respect to density and distance of closest approximations, are implemented as usual in the RMC simulations. The weighting factors for the partial paircorrelation functions are calculated from the concentrations of the atomic species and the atomic form factors for XRD as well as bound coherent scattering lengths for ND. Tables of these weighting factors and further details of the RMC modeling are described in refs 6 and 16 (see also Table 2 for the neutron weighting factors). By taking into account the ND data in our new RMC modeling, the so-far generated RMC structures could be further refined. In particular, the effect of the ratio of the network formers B2O3 and P2O5 on the volume fraction of the conductivity pathways, denoted as F, and the oxygen coordination environment of the Na3+ ions is studied. To obtain F, first the accessible volume for the Na3+ ions was determined, i.e., the volume available to the cations when taking into account the constraints of the RMC modeling (in particular the minimum distance conditions). This was done after removal of all Na3+ ions from the optimized RMC structures and by division of the simulation box into a fine grid of cubic cells. For each cell it was checked whether or not a test Na3+ ion can be placed at its center. With the known set of accessible cells, the percolating cluster of neighboring accessible cells was subsequently determined. The volume of this percolating cluster, Vp, is identified with the volume of the conducting pathways. Dividing it by the total volume of the simulation box, V, gives the volume fraction F = Vp/V of the conducting pathways.
Figure 1. Q(n) species considered for the borophosphate glasses of composition 0.35Na2O + 0.65[xB2O3 + (1 − x)P2O5].
In previous modeling of 0.35Na2O + 0.65[xB2O3 + (1 − x)P2O5] glasses, it was shown that the RMC process can lead to a preference of connections between NFUs with a higher number of bOs.6 In NMR experiments,5,15 however, a preference of B−bO−P linkages is observed. In addition, the B(4) concentration does not exceed a certain threshold.5 This can be understood from the fact that the number of bOs shared by two B(4) units is limited,14 likely because of effective dipolar interactions between the O−B and B−O bonds forming the links. To study the influence of additional constraints related to linkages and limitations of the B(4) concentration, two kinds of RMC models were developed. In Model I, no constraint on bO sharing is applied. From ref 6 we know that this leads to a glass network with rather random bO linkages between the different NFUs but with a slight preference of B(4)−bO−B(4) groups. In Model II, the RMC procedure is performed by trying to avoid B(4)−bO−B(4) connections in the glass network. This is incorporated in the RMC modeling by using the theoretical
Table 2. Neutron Weighting Factors [See Equation 3] of the Partial Interatomic Correlations in the 0.35Na2O + 0.65[xB2O3 + (1 − x)P2O5] and 0.5Na2O + 0.5[xB2O3 + (1 − x)P2O5] Glasses, for a Selection of Compositionsa 0.35 series
a
x
Na−Na
Na−P
Na−B
Na−O
P−P
P−B
P−O
B−B
B−O
O−O
0.0 0.1 0.5 1.0 0.50 series
0.0071 0.0075 0.0090 0.0126
0.0374 0.0353 0.0237 0
0 0.0057 0.0244 0.0683
0.117 0.1187 0.1240 0.1308
0.0490 0.0415 0.0155 0
0 0.0096 0.0322 0
0.3070 0.2790 0.1625 0
0 0.00055 0.0166 0.0928
0 0.0322 0.1679 0.3550
0.4820 0.4699 0.4240 0.3401
x
Na−Na
Na−P
Na−B
Na−O
P−P
P−B
P−O
B−B
B−O
O−O
0.0 0.1 0.5 0.9
0.0192 0.0200 0.0192 0.0294
0.0544 0.0511 0.0268 0.0082
0 0.0059 0.0277 0.0778
0.1845 0.1861 0.1839 0.1981
0.0384 0.0326 0.0094 0.0006
0 0.0075 0.0194 0.0109
0.2608 0.2370 0.1288 0.0277
0 0.00043 0.010 0.0514
0 0.0272 0.1331 0.2620
0.4426 0.4319 0.4418 0.3340
The sum of the weighting factors for a given glass composition is one. In the calculations, the bi values from ref 17 were taken. 27277
DOI: 10.1021/acs.jpcc.5b09176 J. Phys. Chem. C 2015, 119, 27275−27284
Article
The Journal of Physical Chemistry C
Figure 2. Neutron structure factors, S(Q), and pair-correlation functions, G(r), of (a,c) 0.35Na2O + 0.65[xB2O3 + (1 − x)P2O5] and of (b,d) 0.50Na2O + 0.50[xB2O3 + (1 − x)P2O5], respectively. For clarity, the different data sets have been vertically shifted. The vertical lines serve as guidance.
prepeak, at around 1 Å−1 for x = 0, grows successively in intensity. For the lowest x values (x = 0−0.3), the prepeak is manifested as a shoulder of the FSDP; however, for x = 0.4 the prepeak is as strong as the FSDP, and for x > 0.4 it is stronger than the FSDP. The position, Q1, of the FSDP in S(Q) for amorphous materials can be related to an intermediate-range ordering with a characteristic length scale of about 2π/Q1.18 For the x = 0.35 series of glasses, the position of the first peak at Q1 = 1.0 Å−1 for the pure phosphate glass (x = 0) thus reflects an intermediate-range ordering on the length scale of 6.3 Å. Upon increasing x, the position of this peak increases systematically up to Q = 1.4 Å−1 at x = 1, which indicates a shortening of the intermediate-range ordering to reach a correlation distance of approximately 4.5 Å for the pure borate glass (x = 1). The total structure factor, S(Q), is the weighted sum of the contributions of all atomic pair correlations in the glasses, where the neutron weighting factors of the partial pair correlations are listed in Table 2 for a selection of the glasses that were investigated. From Table 2, we note that the contributions from pair correlations involving oxygen (i.e., P− O, B−O, Na−O, and O−O) dominate the scattering, hence it is the intermediate-range order of the oxygen network, i.e., the relative arrangement of the BO3, BO4, and PO4 units, that
3. RESULTS 3.1. Neutron Diffraction. 3.1.1. Structure Factors. In Figure 2(a) we present the total structure factors, S(Q), of the 0.35Na2O + 0.65[xB2O3 + (1 − x)P2O5] glass series for the nine different values of x ranging from 0 to 1. Note that the oscillations in S(Q) persist to Q values larger than 15 Å−1 for all the investigated glasses. Oscillations in the high-Q range are dominated by short-range correlations, which in the present case indicate that all of the glasses have well-defined short-range structures within the overall long-range disordered glass network. The structure factors are overall very similar for Q values larger than 7 Å−1, hence the short-range structure does not change dramatically with the ratio of the network-forming cations. However, as a most significant feature, we observe a systematic growth and upshift of a peak centered at ∼10 Å−1, as well as an upshift of peaks centered at approximately 8 and 13.5 Å−1, when x increases. The low-Q range below 7 Å−1, which relates to correlations beyond the first-nearest-neighbor distance, also changes significantly with x, which indicates larger differences between the structure of the glasses on an intermediate to long length scale. In particular, we observe that the first sharp diffraction peak (FSDP), located at ∼1.7 Å−1 for the pure phosphate glass (x = 0), decreases in intensity with increasing x, and instead, a 27278
DOI: 10.1021/acs.jpcc.5b09176 J. Phys. Chem. C 2015, 119, 27275−27284
Article
The Journal of Physical Chemistry C
Table 3. Peak Positions for the First Four Peaks in the S(Q)s and for the First Two Peaks in the G(r)s for the Two Investigated Sodium Borophospate Systems, 0.35Na2O + 0.65[xB2O3 + (1 − x)P2O5] and 0.5Na2O + 0.5[xB2O3 + (1 − x)P2O5]
decreases significantly with increasing the ratio of the network forming cations (B/P). In addition to the decrease in the correlation length of the intermediate-range ordering with increasing x, we observe changes of the three strongest peaks centered at approximately 1.7, 3.0, and 5.7 Å−1. More specifically, the position of the Q = 1.7 Å−1 peak increases to Q = 2.1 Å−1 for x = 0.6, whereas for larger x values this peak cannot be revolved. Similarly, we observe a change of the position of the peak centered at Q = 3.0 Å−1 at x = 0 to Q = 3.2 Å−1 at x = 1, while the location of the strongest peak at Q = 5.7 Å−1 does not change with x. The S(Q)s of the glasses with the higher Na concentration, 0.50Na2O + 0.50[xB2O3 + (1 − x)P2O5] glasses, are presented in Figure 2(b). Similarly to the 0.35Na2O + 0.65[xB2O3 + (1 − x)P2O5] glasses, the oscillations in S(Q) persist to large Q values, suggesting a well-defined short-range structure of all glasses investigated. In particular, we observe that the high Q range (>7 Å−1) of the structure factors is very similar to those of the corresponding 0.35Na2O + 0.65[xB2O3 + (1 − x)P2O5] glasses. Notably, we observe that the three main peaks in this regime, centered at around 8, 10, and 13.5 Å−1, all shift to slightly larger Q values with increasing x. We also observe that the 10 Å−1 peak grows gradually in intensity with increasing x. The overall similarity of the structure factors in the large Q range implies that the concentration of the modifying salt does not have a strong effect on the short-range structure of the two investigated glass systems. In the low Q range ( 0.30. This alternating forming of the intermediate-range ordering is significantly different from what is found for the glasses in the 0.35 series, for which the intermediate-range ordering develops systematically with increasing x. A further comparison of the structure factors for the two glass series reveals a slight down-shift of the first three diffraction peaks, centered at ∼1.1, ∼1.9, and ∼2.9 Å−1, for the higher concentration of alkali modifier. In Table 3, the positions of the main peaks are presented for both glass series. The slightly larger Q1 values of the prepeak for the 0.50 series, for intermediate compositions (0.3 < x < 0.8), suggest a slight contraction of the intermediate-range ordering with increasing concentration of the salt modifier. This result may indicate that the Na3+ ions act as a dielectric medium that decreases the repulsive interaction between the negatively charged NFUs. It should be noted, however, that the position and shape of the peaks in S(Q) for a multicomponent system have contributions from a number of partial structure factors. Therefore, the difference in positions of the diffraction peaks for the two studied glass systems may partially be due to the fact that the different contributing pair-correlation functions change in intensity, even though the underlying structure remains basically the same. Furthermore, the shortening of the
0.35 series x
Q1
Q2
Q3
Q4 (Å−1)
r1
r2 (Å)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1.0 0.50 series
∼1.0 ∼1.0 ∼1.0 ∼1.0 ∼1.1 ∼1.2 ∼1.3 ∼1.3 ∼1.4
∼1.7 ∼1.7 ∼1.9 ∼1.8 ∼2.0 ∼2.1 ∼2.1 -
∼3 ∼3.1 ∼3.1 ∼3.1 ∼3.1 ∼3.1 ∼3.2 ∼3.2 ∼3.2
∼5.7 ∼5.7 ∼5.7 ∼5.7 ∼5.7 ∼5.7 ∼5.7 ∼5.7 ∼5.7
1.51 1.51 1.50 1.50 1.49 1.48 1.47 1.41 1.41
2.49 2.48 2.47 2.47 2.44 2.44 2.44 2.42 2.41
x
Q1
Q2
Q3
Q4 (Å−1)
r1
r2 (Å)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.9
∼1.1 ∼1.1 ∼1.4 ∼1.4 ∼1.4 ∼1.4 ∼1.4
∼1.9 ∼2.0 ∼2.1 ∼2.2 ∼2.2 ∼2.3 ∼2.3 -
∼2.9 ∼3.1 ∼3.2 ∼3.3 ∼3.3 ∼3.3 ∼3.3 ∼3.3
∼5.7 ∼5.7 ∼5.7 ∼5.7 ∼5.7 ∼5.7 ∼5.7 ∼5.7
1.53 1.52 1.51 1.51 1.50 1.49 1.48 1.41
2.50 2.49 2.48 2.47 2.46 2.44 2.43 2.42
characteristic length scale of the intermediate-range ordering with increasing x, observed for both glass series, is also most likely due to the decrease in the average bond distances in the glass as more and more of the PO4 units for x = 0 are replaced by BO4 and BO3 units, cf. rP(4)−O(2) = 1.52 Å, rB(4)−O(2) = 1.46 Å, and rB(3)−O(2) = 1.36 Å.19 Here and in the following, we have taken the ionic radii from Shannon,19 whereas the numbers within the parentheses refer to the nominal coordination numbers. 3.1.2. Pair-Correlation Functions. We now consider the real-space information on the structure of the investigated glasses that is described by the total pair-correlation function, G(r). Considering first the pair-correlation functions of the 0.35Na2O + 0.65[xB2O3 + (1 − x)P2O5] glass series [Figure 2(c)], we observe that these are characterized by two strong peaks, centered at approximately 1.5 and 2.5 Å, as well as two weaker and less defined peaks centered in the range 3−4 Å and 4.5−5 Å. For the pure phosphate glass (x = 0), the first peak is centered at 1.51 Å and is related to P−O correlations within PO4 tetrahedra. This assignment is in agreement with the P−O distance of rP(4)−O(2) = 1.52 Å, estimated by adding the respective ionic radii, and is further supported by the XRD results by Le Roux et al.13 The 2.49 Å peak may be assigned to O−O correlations within the phosphate units, based on the fact that O−O distances in the range of 2.3−2.5 Å have previously been found in trigonal BO3 and tetrahedral BO4 units in Na2O + B2O3 glasses.13 The third and forth peak in G(r) are most likely related to next-nearest and next-next-nearest P−O distances, respectively. Upon increasing x, the two main peaks, assigned to P−O and O−O correlations within PO4 tetrahedra, shift gradually toward shorter r-values (see Table 3). The shift of the P−O correlation peak, which eventually reaches a position of 1.41 Å for x = 1, is an effect of the increasing substitution of PO4 tetrahedra with 27279
DOI: 10.1021/acs.jpcc.5b09176 J. Phys. Chem. C 2015, 119, 27275−27284
Article
The Journal of Physical Chemistry C
Figure 3. Comparison between the S(Q) and G(r) of 0.35Na2O + 0.65[(xB2O3) + (1 − x)P2O5] glasses obtained experimentally (circles) from XRD (left) and ND (right) data with the ones obtained from the RMC modeling (solid lines = Model I, dashed lines = Model II) reported in ref 6, i.e., before optimization with respect to the ND data.
a reasonable agreement between the experiment and simulations; however, significant deviations for the low-Q (
