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Molecular dynamics simulation of La2O3–Na2O–SiO2 glasses. I. The structural role of La3+ cations
Journal of Non-Crystalline Solids 297 (2002) 220–238 www.elsevier.com/locate/jnoncrysol
Molecular dynamics simulation of La2O3–Na2O–SiO2 glasses. I. The structural role of La3þ cations Byeongwon Park, Hong Li 1, L. Rene Corrales
*
Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, P.O. Box 999, K8-91, 902 Batelle Blvd., Richland, WA 99352, USA Received 17 May 2001; received in revised form 19 September 2001
Abstract It is well known that high-field strength rare-earth (RE) ions in the silicate glasses tend to cluster regardless of their concentration. Numerous experimental studies have been carried out, but the ability to discern structural information at the atomic-level strongly depends on providing accurate molecular dynamics (MD) simulations. In this work, the short- and medium-range order of La ion in soda silicate glasses is investigated by MD computer simulations. The glass mixtures used in these MD simulations are the same as those of a recent NMR study. Results of this study are in excellent agreement with the NMR results. It is found that the La cation has an average co-ordination of 6.5 O atoms with an average bond length fitted to be about 0.25 nm. The La is found to behave as a network modifier, and competes with sodium for non-bridging oxygen (NBO) atoms. In addition, the extended X-ray fine structure (EXAFS) and neutron diffraction patterns are predicted from the MD simulations. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Technological applications of lanthanide containing glasses include their use to generate and modulate laser light [1], and as constituents, as well as analogues of actinides in experimentally simulated nuclear waste glasses [2]. Changes in the distribution and local environment of the lanthanide ions in a silicate glass are known to lead to * Corresponding author. Tel.: +1-509 376 6608; fax: +1-509 376 0420. E-mail address: [email protected] (L.R. Corrales). 1 Present address: Fundamental Science, Fiber Glass and Technology, PPG Industries Inc., Glass Technology Center, PO Box 2844, Pittsburgh, PA 15230, USA.
strong changes in chemical [3], electrical and optical properties [4]. Experiments have been carried out to identify the structural role of lanthanide ions in alkali silicates with seemingly disparate but not inconsistent results. Lacking is a definitive identification of the structural role of La in alkali silicate glass. In this work, molecular dynamics (MD) computer simulations are used to characterize the structural role of lanthanum in soda silicate glasses and to provide details of short- and medium-range structure. MD simulations are used to obtain neutron diffraction (ND) patterns and extended X-ray fine structure (EXAFS) spectrum. The pure silica network structure consists of Si–O–Si covalent bonds that are called bridging oxygen (BO) bonds. Upon the addition of a metal
0022-3093/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 1 ) 0 0 9 3 5 - 8
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oxide to silica, the dissolution process that takes place can be described as follows. Metal oxides with cation oxidation states of +1, +2 and +3 can be thought to exist in M2 O, MO, and M2 O3 molecular units, respectively, that preserve stoichiometry in the pure states. The metal oxide molecular species can react with the silica network to convert BO bonds to non-bridging oxygen (NBO) bonds. The energy of this reaction competes with the energy to keep the metal oxide molecular species associated, or clustered. A formation free energy can be assigned to this chemical process that can be described by a chemical equilibrium reaction [5]. Presumably, the formation energies can dictate the number and distribution of NBO bonds that are formed, although these might be affected by the network topology [6]. In general, if a cation is a network modifier such that it can break the Si–O– Si bonds, then the maximum number of NBO bonds that can form is proportional to the valence state of the cation. To determine the role of a cation, experiments are carried out such that an unknown cation is substituted for known cations [3]. Here, the unknown is the lanthanide ion, whereas the known ions would include the alkali (network modifier) and the silicon (network former) ions. Thus, the tendency for formation or depletion of NBO bonds can be used to determine the structural role of the unknown cation. Experimentally, this is done by measuring NBO sensitive properties such as the glass transition temperature or NMR spectroscopy that probes the local atomic environments. The glass forming phases of RE containing alkali silicates have been well determined [7], along with trends in their physical properties [8]. Consequently, experiments to determine the structural role of rare-earth (RE) ions in alkali silicates have used compositions away from the phase separating regions. Such experiments include the following. NBO and BO bonds can be differentiated by X-ray photoelectron [9] and Raman [10] spectroscopic methods. Changes in the population of oxygen atom types can then be contrasted with changes in the concentration of the RE ion. From these spectroscopic data it was asserted that La behaves as a network modifier in soda silicate glasses. The
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glass transition temperature, Tg , of soda silica glasses containing M2 O3 , with M being Ga, In, Sc, Y, or La, has been measured and compared with metal oxides that behave like network formers or modifiers [11]. From this work it was asserted that La behaves as a network modifier. The local environment of trace levels of La in silicate glasses was also studied by EXAFS experiments [12], in which the regularity of the RE site as a function of the degree of polymerization of the network was studied. They deduce that because the REs are trivalent, they will be better network modifiers than Naþ . These previous experiments did not systematically substitute a RE ion for an alkali or silicon ion and, hence, it is difficult to justify their assertions of the structural role of La. Trends in the density, molar volume, electrical conductivity, and glass transformation temperature of La bearing soda silicate glass were determined using systematic substitutions. These results were less conclusive and lead to specifying the role of La as a network intermediate [3], while suggesting more spectroscopic work needed to be done. Consequently, the local environments of lanthanide bearing alkali silicate glasses were probed by EXAFS [12], vibrational spectroscopy [13], and by combining NMR and Raman spectroscopic methods [14] for mixtures using a systematic approach of adding La to glasses with a fixed ratio of alkali ion to silicon ion, and substituting La ion for the alkali ion on an equal-oxygen basis. From the EXAFS work it was inferred that the average co-ordination number of La did not change significantly as the compositions were varied, and together with the vibrational spectra [13], that the La ions were possibly distributed heterogeneously in the glass. Combined NMR and Raman studies were used to investigate the formation of free oxides in La containing alkali silicate glasses [14]. It was found that the replacement of silicon by La cations resulted in the formation of NBO bonds, consistent with a network modifier. The replacement of sodium or potassium with La cations in an equal-oxygen basis led to a measurable decrease of NBO atoms, but not an increase in BO bonds, suggesting that La2 O3 species are isolated away from the silica network and form microheterogeneous regions in glass.
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Molecular dynamics (MD) computer simulations of glasses have a long successful history, although few MD simulations of glasses containing lanthanide ions have been performed [15]. In this work, the local environment and dynamics of La bearing sodium silicate glasses is investigated and its influence on the network structure examined. The same compositions of Schaller et al.’s NMR and Raman [14] experiments are used so that direct comparison can be made. Unfortunately, there are no known EXAFS or neutron diffraction (ND) studies available for these mixtures. A detailed analysis of the simulation results and comparison to experiments, where available, is presented. This paper is organized as follows. In the following section, the computational details that include a description of the potential model and MD simulation procedure of the glass-forming process is outlined. In Section 3, the results are presented which includes simulated ND total distribution functions (TDF) and EXAFS spectra of La in soda silicate glasses. The results are discussed in Section 4 and conclusions presented in Section 5.
2. Computer simulations The MD simulation code used in this study was DL_POLY version 2.11 from Daresbury Laboratory, UK [16]. All the ions were treated as rigid with their formal charges; Na1þ ; Si4þ ; La3þ ; O2 . The long-range electrostatic potential was evaluated by Ewald summation method with the cutoff and precision set to 106 . The distance set at 12 A . These short-range cutoff distance was set at 7.6 A are standard cutoffs used for glass simulations that provide a balance between accuracy and memory requirements of the code [19]. The potential parameters for SiO2 are based on Vessal’s model that includes three-body potentials for Si–O–Si and O– Si–O [17]. The potential for the La–O and Na–O interactions use the modified Buckingham potential where the La–O parameters were fit to crystalline La2 O3 . The parameters for La–O and Na–O are given in Table 1. The length of each time step was 2 1015 s and the integration was done using the Verlet Leapfrog algorithm. The
Table 1 Potential parameters for cation–oxygen interactions V ðrÞ ¼ A expðr=qÞ C=r6
La–O Na–O
A (eV)
) q (A
6 ) C (eV A
2133.2436 1226.79
0.3590 0.306 5
0.0 0.0
canonical ensemble (NVT) employing the Evans thermostat [18] was used for the glass forming runs, and then the ensemble was switched to the microcanonical ensemble (NVE) at the lower temperature during which all the sampling was performed. The simulation procedure was based on alkali silicate glass simulations of previous work [19]. In this work, the initial configuration was borrowed from [19], where the Na ion was used as alkali ion in place of Li or K. The glass was heated up to 12 000 K to remove possible memory effects and then annealed to room temperature. The glassmaking schedule was as follows. The simulation was run twice at 12 000 K with each run consisting of 10 000 time steps. The first run was without the three-body potentials for the Si–O–Si and O–Si–O interactions, thus allowing the system to mix well. The second run at 12 000 K was with the threebody potential turned on that favors the formation of silica tetrahedra. The temperature was then lowered sequentially to 9000, 7000, 5000, 3000, 2000, 1000, and finally to 300 K. At each temperature the system was equilibrated for 10 000 time steps. The room temperature simulation was done for 30 000 time steps where the system data was collected during the last 20 000 time steps. The total number of time steps was 110 000, which is equal to 220 ps with a nominal cooling rate of 5:3 1013 K/s. These are considered to be nominal cooling rates for MD simulations [20] although they are still several orders of magnitude faster than the fastest experimental cooling rates. The composition of the simulated glasses, the number of atoms and the simulation size for each composition are given in Table 2. The total number of atoms in each simulation was around 1600. In addition to the compositions used by Schaller et al. [14] compositions containing no Na or La, labeled as Na25 and SiLa4, respectively, were used.
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Table 2 Composition of simulated glasses System Na25 Na3S4 Na3S10 NaLa4 NaLa12 SiLa4
Concentration
Number of atoms
La2 O3
SiO2
Na2 O
La
0.0 4.0 10.0 1.4 4.4 1.7
75.0 72.0 67.5 77.1 81.5 98.3
25.0 24.0 22.5 21.6 14.1 0.0
40 100 14 43 364
Si
O
Atoms in box
Box length ) (A
NBO/T
Na 270 240 224 224 141
405 360 337 401 408 234
945 900 936 935 951 101
1620 1540 1597 1574 1543 1612
28.147 27.313 28.147 28.000 27.713 26.678
0.67 1.00 1.57 0.67 0.67 0.10
The purpose in using these compositions was to systematically substitute La for Si and La for Na as well as to compare the extreme cases where either no Na or La is present in the system. If La acts strictly as a network modifier, then it is expected to contribute three NBO atoms to the system, where Na contributes one NBO atom. Hence, the ratio NBO/T, which is the number of NBO atoms to the number of tetrahedrally co-ordinated Si, is used to measure the structural contribution of La in the system. If La behaves like a network modifier, then as La is substituted for Na (on an equal oxygen basis), this ratio is expected to remain constant. A comparison of the ideal case, where La act strictly as a network modifier, with that determined from our simulation is a measure of the degree to which La is a network modifier. The structural properties such as pair distribution functions (PDF), co-ordination number distributions, bond angle distributions (BAD), etc. are obtained over final room temperature configurations, the details of which are presented in Section 3. To obtain simulated EXAFS patterns, the MD structures are used as input in the program FEFF 7.0 [21]. FEFF 7.0 calculates wave phase shifts, effective scattering amplitudes, and single and multiple scattering XAFS and XANES spectra including polarization dependence for clusters of atoms (Z < 96) about the center of each atom. Each EXAFS pattern was averaged over all the La ions in one sample configuration, using an 8 A cutoff distance for the interacting neighbor shells. Increasing the cutoff distance has almost negligible effect on the final pattern, except in the low k region.
3. Structural properties 3.1. ND and EXAFS spectra The PDFs sampled and averaged over 20 ps at 300 K are shown in Fig. 1 for the glass mixtures containing La ions. Also shown are the La polyhedra that contain the nearest neighbor O ions. The average bond lengths are given in Table 3. The nearest distance between each atom pair is obtained from the position of the maximum of the first peak of each PDF. Note that the first peak of the Si–O PDF has two subpeaks that correspond to NBO and BO bonds. The nearestneighbor bond distance of the BO and NBO . The bonds for Si–O pairs are 1.51 and 1.62 A bond lengths are as follows: Na–O, 2.42 A; La–O, ; O–O, 2.58; Si–Si, 3.12 A , Si–Na, 3.35 A ; 2.55 A Si–La, 3.74 A; Na–Na, 3.02 A; and La–La, 4.32 , respectively. A For the Na3S10 mixture, the PDF for the La– . If the La nearest neighbors show a peak near 4 A La atoms were homogeneously distributed, the PDF for this concentration of La should show a , as determined by sharp peak at around 7 A 1=3 3V d¼2 ; ð1Þ 4pN where V is volume and N is the number of La ions. A more detailed analysis of the La local environment can be done using these simulations and are described below. All of the mixtures which contain both La and Na cations show very similar La–La PDFs, except for that of NaLa4 which shows . This mixture sharp peaks at 4.3, 6.6, 7.5, and 8 A has the lowest concentration of La in the system
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Fig. 1. PDFs and snapshots of just the La–O polyhedra for simulated glasses. The gray spheres are La ion and the black spheres are the nearest neighbor O ions. Note the La–O–La linking that can occur: (a) Na3S4; (b) Na3S10; (c) NaLa4; (d) NaLa12; (e) SiLa4.
and the longest possible La–La nearest neighbor distance. The La–La PDF suggests the presence of microheterogeneous regions. By simulating multiple mixtures using systematic substitution, general trends can be determined. For ease of describing the trends we define series I as the group Na25, Na3S4 and Na3S10 where the ratio NBO/T increases, and series II as the group
NaLa12, NaLa4 and Na25 where the ratio NBO/T is constant. As La is added following series I the average BO bond length for Si–O does not change and the average NBO bond length for Si–O increases. When Na is replaced by La following series II the average BO bond length of Si–O does not change while the average NBO bond length of Si–O increases slightly.
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Fig. 1 (continued)
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Table 3 ) in the simulated La–soda silicate glasses Bond distances (A Si–NBO Si–BO Na–O La–O O–O Si–Si Si–Na Si–La Na–Na Na–La La–La
Na25
Na3S4
Na3S10
NaLa4
NaLa12
SiLa4
1.46 1.62 2.41
1.49 1.62 2.41 2.52 2.59 3.11 3.38 3.76 3.03 3.64 3.85
1.51 1.62 2.42 2.55 2.58 3.12 3.35 3.74 3.02 3.61 4.02
1.47 1.62 2.38 2.56 2.60 3.12 3.45 3.79 3.19 3.75 4.32
1.48 1.62 2.43 2.52 2.60 3.11 3.41 3.76 3.21 3.71 4.00
1.47 1.62
2.60 3.13 3.44 3.15
The average O–O nearest-neighbor distance decrease in series I and do not change for series II. The average Na–O bond distance remains constant for series I. In series II, the bond distance is smallest when the concentration of La is at 1.4%, but is similar when no La is present and when the La concentration is at or above 4%. The bond length for La–O is shortest in the SiLa4 glass in which no Na is present. It increases in series I and in series II, where it is understood that the mixture of Na25 is not included in either series. The average La–O bond length from these in the soda glasses, and 2.45 simulations is 2.53 A in the no-sodium silica. This can be compared A for La–O in potassium silicate glass to 2.42 A [22], and to the wide bond distance distribution in crystalline phases which range from 2.41 to 2.74 [12]. A The Si–Si nearest neighbor distance is fairly constant through all mixtures. The Na–Na nearest neighbor distance shows marked changes as the ratio NBO/T changes. The La–La nearest neighbor distance increases when Na is substituted for La, following SiLa4, NaLa12, and NaLa4. As La is substituted for Si, Na3S4, and Na3S10, the La– La nearest neighbor distance increases. To compare the simulated structure with the experimental neutron diffraction pattern, the TDF is constructed from the set of PDFs. The experimental TDF is obtained through a Fourier transformation of the measured scattering intensity. The simulated TDF needs to be broadened due to the finite upper limit in the momentum transfer, Q. The component TDF, tij ðrÞ, is convoluted with
2.45 2.64 3.14 3.84
3.92
a component peak function, Pij0 ðrÞ using the following equation [23]: Z 1 h i tij0 ðrÞ ¼ tij ðr0 Þ Pij0 ðr r0 Þ Pij0 ðr þ r0 Þ dr0 ; ð2Þ 0 0
where r is a dummy integration variable. The component peak function Pij0 (r) defines the experimental resolution in real space caused by the finite upper limits in Q, where Pij0 (r) is defined as Z bi bj 1 PijN ðrÞ ¼ MðQÞ cosðrQÞ dQ; ð3Þ p 0 where MðQÞ is a modification function given by a Lorch function that gives a gradual cutoff given by sin Dr Q 6 Qmax ; MðQÞ ¼ DrQ ð4Þ 0 Q P Qmax : Also the bi s are the coherent neutron scattering lengths of each element. 1 In the these simulations, Qmax is set to 40 A and the coherent scattering factors are: 8:24 1015 m for La, 3:63 1015 m for Na; 4:1491 1015 m for Si, and 5:803 1015 m for O. The simulated TDF for all the systems are shown in Figs. 2(a) and (b) and the corresponding structure factors are shown in Figs. 2(c) and (d). It is interesting that all of the TDFs appear to be very similar. The greatest change is in the TDF of SiLa4 , which contains no Na cations. glass at around 4 A This difference is reflected in the La–La PDF for the SiLa4 glass in which a peak centered at 4.8 A disappears upon the addition of Na atoms, whereas all the other PDFs of the mixtures show no significant change in this region.
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1 and the peaks are broadened using Fig. 2. TDFs (a,b) and scattering factors (c,d) for Na–La silicate glasses. The Qmax is set to 40 A peak functions.
EXAFS has been widely used to probe the local structure in glass systems [24]. In these simulations the EXAFS patterns are determined from the final configuration at room temperature of all the La ions using the FEFF7.0 code as described above. The experimental EXAFS is the average of all the possible configurations of a specific element in the glass, which inherently have a wide distribution range. In a real glass, the actual number of any specific element is large, as compared to these simulations. Thus, to obtain better statistics in the simulation, the averaging for all the target ions in
the simulated structures is over a time series. Two were tried to include cutoff distances of 5 and 8 A different number of neighboring atoms, however, little change was observed, except for regions of cutoff distance cases are very low Q. Only the 8 A presented. Fig. 3(a) shows the EXAFS of each individual La ion in the simulated NaLa4 glass. There are a total of 14 La ions in the simulation. The solid line with squares in Fig. 3(a) is for the averaged pattern over all the La ions. In Fig. 3(b) the averaged EXAFS for all the glass mixtures in the current study are shown. The Fourier
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): (a) lighter lines are for each individual La in the NaLa4 and the Fig. 3. EXAFS simulation using FEFF 7.0. (Cutoff distance is 8:0 A heavy line is the average of the individual La lines; (b) the averaged La EXAFS patterns for all the simulated glasses.
transforms of these patterns have not been done, since to our knowledge, experimental data for these mixtures is not available, and hence direct comparison is not possible. Like the TDFs, the EXAFS appear to be very similar. The biggest change occurs in the position of the valley near the 1 position where the valley for the SiLa4 5 A mixture is shifted to the right relative to the valley of the other mixtures. The peak following that valley is also shifted to the right relative to the other mixtures. In general, the periodicity of the spectra is expected to be maintained across a Fourier transformation of the data. Thus, the differences in the EXAFS patterns could provide a thumbprint of the La distribution. 3.2. Structures of cation co-ordination polyhedra The co-ordination number as a function of distance is shown in Fig. 4 for the Si, Na and La cations in the Na3S10 mixture where the arrows pinpoint the cutoff distance of the first co-ordination shell. The graph is an integration of the number of O atoms as a function of distance. The first co-ordination shell cutoff is obtained by choosing the cutoff where the second derivative for each co-ordination plot is zero at a distance after the first peak in the PDF. Thus, the cutoff for Si–O , for Na–O it is 3.0 A and for La–O it is is 2.2 A
Fig. 4. Co-ordination number distribution for cation–oxygen with cutoff distances, see text for explanation of cutoffs and error bars.
. Silicon has four O nearest neighbor atoms 3.2 A and there are no five-fold co-ordinated Si atoms in the simulated glasses. The co-ordination number of Na is 5.2 and of La it is 6.5. The cutoffs for the other mixtures are kept the same, and the results are given in Table 4 for La–O and Na–O pairs only, because Si always has four neighboring oxygens. In series II where La re-
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Table 4 and rcut (La–O) ¼ 3.2 A Average co-ordination number of oxygen around cation rcut (Na–O) ¼ 3.0 A Na–O Na–NBO Na–BO La–O La–NBO La–BO
Na25
Na3S4
Na3S10
NaLa4
NaLa12
4.61 2.76 1.85
5.09 3.28 1.81
5.17 3.63 1.49
4.51 2.72 1.80
4.88 2.59 2.29
6.25 5.42 0.83
6.53 5.79 0.63
5.63 5.14 0.49
5.89 4.90 0.99
places Si, the average co-ordination numbers of Na and La have increased because La acts as a network modifier. There are more NBO than BO
SiLa4
4.74 3.74 1.00
nearest neighbor cations. When La replaces Na in series II, the average co-ordination number around the cations decreases.
Fig. 5. Deconvolution of Si–O PDFs (a,c) and change in NBO concentration distributions (b,d). In (a,b) the ratio NBO/T increases and in (c,d) the ratio NBO/T remains fixed.
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Note that the error bars in the co-ordination number calculations for these simulations are small at about 1% of the reported value, which is smaller than the markers used in the figures. In these simulations the average is over a time series of the same initial sample, thus, the magnitude of the statistical fluctuation is small. A proper statistical sampling requires using many different initial configurations for the same mixture that allows averaging over similar configurations. This may lead to larger fluctuations and thus larger
error bars, but is also very computationally intense. The deconvolution of the first peak of the Si–O PDF for each of the compositions are shown in Fig. 5. The fraction of NBO, defined as having only one silicon within the cutoff distance, is given in Figs. 5(b) and (d). When the nominal NBO/T increases (replace Si by La), the subpeak for Si–NBO increases gradually, confirming the role of La as a network modifier, which is in excellent agreement with NMR data [14]. As La
Fig. 6. Structure of sodium oxygen polyhedron: (a) deconvolution of first Na–O PDF; (b) co-ordination number distribution for Na– ); (c) deconvolution of first Na–O PDF; (d) co-ordination number distribution for Na–O (cutoff disO (cutoff distance ¼ 3.0 A ). (a,b), NBO/T increase; (c,d) NBO/T ¼ fixed. tance ¼ 3.0 A
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replaces Na, the bond distance for Si–NBO increases from 1.45 to 1.51 and the Si–BO distance does not change (1.62), as shown in Fig. 5. The high-valence state of La (+3) pulls the NBO closer, resulting in a longer distance of the Si– NBO bond. The amount of NBO among SiO4 tetrahedron increase from 28.6%, to 40.1% to 54.9% in the mixtures Na25, Na3S4 and Na3S10, respectively. Although the amount of bridging oxygen decreases from 71.4%, to 59.9% to 44.6%, respectively, as shown in Fig. 5(b). When La re-
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places Na by equal basis of O, the amount of NBO is almost constant as shown in Fig. 5(d) though in the NMR experiment the amount of NBO decreases substantially. For the Na3S10 glass, about 0.53% of the O atoms are not connected to Si (considered to be free O atoms). This can be partially accounted for by the decrease in the relative amount of NBO atoms in SiO4 tetrahedron from 28.6% to 28.4%. The rest may come from the conversion of BO atoms. In the case of the SiLa4 glass, the Si–NBO
Fig. 7. Structure of lanthanum–oxygen polyhedron: (a) deconvolution of first La–O PDF; (b) co-ordination number distribution for ); (c) deconvolution of first La–O PDF; (d) co-ordination number distribution for La–O (cutoff disLa–O (cutoff distance ¼ 3.0 A ). (a,b), NBO/T increase; (c,d) NBO/T ¼ fixed. tance ¼ 3.0 A
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where 6.7% of the O atoms are distance is 1.46 A NBOs. The deconvolutions of the first Na–O PDF and co-ordination number changes are given in Fig. 6 as a function of composition. In Fig. 6(a) the Na– O PDF is deconvoluted according to the co-ordination state of O and shows that the bond distance even for Na-NBO increases from 2.28 to 2.32 A though the relative amount of NBO around Na decreases. In Fig. 6(b) the relative amount of each co-ordination state of Na within the first co-ordi-
, is nation shell, with a cutoff distance of 3.0 A shown. The average co-ordination number of Na increases from 4.61 in Na25 to 5.17 in Na3S10 with the addition of La, but the co-ordination number does not change appreciably with further addition of La. The ratio of NBO/T is held fixed by adding La atoms to and removing Na atoms from the system, Fig. 6(c). In this series of substitutions, the deconvoluted peak for Na–NBO decreases, and the co-ordination number distribution of Na widens and shifts to a higher co-
Fig. 8. BADs and typical cation polyhedra: (a,c), NBO/T increase; (b,d) NBO/T ¼ fixed.
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ordination number: 4.61 for Na25 to 4.88 for NaLa12 as shown in Fig. 6(d). The deconvolution of La–O PDFs are given in Fig. 7. As shown in Figs. 7(a) and (b), most of the La is connected by NBO bonds with an average . The number of connections by distance of 2.52 A BO bonds is negligible (0.83 out of 6.25 for Na3S4). In contrast to Na, most of the O atoms in the La–O polyhedron are NBO. The most abundant co-ordination state is six and increases to seven by adding La whether the ratio NBO/T is held fixed or not. 3.3. Bond angle distributions BADs were calculated for the first cation coordination polyhedra. The bond angles for Si–O– Si and O–Si–O have maxima at 146° 2° and 109° 2°, respectively. The angle distributions are rather narrow compared to results for pure silica using the BKS model and can be attributed to the use of three-body potentials [17]. The BADs for O–Na–O and O–La–O are shown in Fig. 8 with one possible cation polyhedron configuration for Na and La in Figs. 8(c) and (d). In the first co-ordination shell of Na–O, the O–Na– O BAD has a narrow peak at 60° and an asymmetric broadened peak at 94° that extends to 180°. These angle distributions are sampled in
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the five-fold co-ordinated Na polyhedron in which acute angles of about 60° occur for those O atoms lying closest to a plane and obtuse angles of about 94° for those in the plane which are not nearest neighbors and can be up to 180° apart. In the O–La–O BAD, the largest peak is located at about 85° with smaller peaks at 130° and 160° with some structure at around 60°. The most abundant co-ordination number for La–O is six with a typical configuration shown in Fig. 8(d). The La–O polyhedra are more symmetric than those of Na–O. The most probable angle for O–La–O is 90°, although the broadening up at larger angles is due to the next nearest neighbor angles for O atoms lying in a plane. It is interesting to note that the glass mixture without Na, SiLa4, has several peaks in the BAD. This is due to the constraint of the Si–O network not being able to relax its structure around the La atoms. Thus, a glass without Na will have a more asymmetric polyhedron than the glass mixtures where Na ions break up the backbone of the network that can afford greater relaxation of the network. 3.4. Qn distributions The co-ordination environment of Si mostly consist of tetrahedrally co-ordinated O atoms that
Fig. 9. Qn distribution changes as: (a) NBO/T ¼ increase; (b) NBO/T ¼ fixed.
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can be bonded to another Si atom (a BO atom) or to a modifying cation (a NBO atom). The Qn , where n is number of BO in SiO4 tetrahedron, is related to the connectivity of glass network and is measurable by NMR. These co-ordination states have been defined by NMR spectroscopists as follows [6]. A Si atom four-fold co-ordinated by BO atoms is defined as a Q4 species. A Si atom coordinated by three BO and one NBO is a Q3 . And so on, until reaching a Si atom four-fold co-ordinated by NBO atoms is a Q0 . The Qn distributions of the simulated silicate glasses are given in Fig. 9. The trends are such that when La ions are added (NBO/T increase), the number of Q4 decrease substantially while the number of Q1 and Q2 increases with the number of Q3 changing only slightly. When the NBO/T is fixed, the overall shape does not change much although there is a decrease in Q3 with an increase in Q2 and Q4 which might be a manifestation of microheterogeneities with separate Q2 and Q4 rich regions at the expense of Q3 .
4. Discussion A detailed analysis of the Si–O PDF in which the BO and NBO contributions are clearly distinguished reveal that the La cation behaves as a network modifier. This data is consistent with data from NMR and EXAFS experiments [14]. In glasses containing lanthanum oxide there are, however, a small number of free oxygen atoms which are linked to two La atoms and no Si atoms. The occurrence of free oxygen atoms, associated with the formation of La–O–La linkages and a depletion of NBO atoms is consistent with experiment [14], although the MD simulations predict a smaller number of them. However, in our counting not all La–O–La linkages are associated with the formation of a free oxygen atom. The La–O–La linkages provide a means of identifying clusters of La dimers, trimers and so on. A statistical distribution of La clusters is currently not available due to the small number of simulations. Alternatively, large simulations can be run but both are CPU intensive. Similar clustering effects are seen in all of the simulated La glass structures. Further studies
of La clustering in simulated glasses are needed to determine the driving forces that lead to clustering. There are distinct changes in the La–La PDF in going from a system of only La2 O3 –SiO2 to one in which 21 mole percent of Na2 O has been added. A very strong change in the viscosity of the melts is observed indicating that the presence of soda depolymerizes the silica network. In fact, there is a clear change to higher viscosity as La is substituted for Na. The changes in viscosity are indicated by changes in self-diffusion. Although the larger ion behaves as a network modifier, it is considerably more massive, mLa ¼ 138.9 amu, and mNa ¼ 22.99 and rNa ¼ 0.89 A , amu, larger radius rLa ¼ 1.3 A and has a large ionic state qLa ¼ +3 and qNa ¼ +1. The ionic strengths given by I ¼ q=r, are 2.3 and 1.1, for La and Na, respectively. The higher ionic strength ions are believed to form more rigid structures that along with their large mass can contribute drag forces to their translational motion. A quasi-molecular picture can be used to define the molecular units that make-up the network structure. The molecular units can be conveniently defined as the cations and their first co-ordination shell of oxygen atoms, consistent with the molecular picture used to define the Qn species. These are identical to the cation polyhedron as described above. The degree of symmetry of these molecular units is determined by defining the dipole moment of the molecular species where the dipole is centered at the center of mass of the cation polyhedron. The smaller the dipole, the more symmetric the molecular species. The degree of symmetry used in conjunction with the bond angle and bond distance analyses can be used as a probe of structural response. The network structure of the soda silicate glass is the same as that of [19] since the same potential parameters were used. The bond distances for Si– , respectively. The O and O–O are 1.62 and 2.60 A . All nearest-neighbor distance of Si–Si is 3.13 A the Si atoms are tetrahedrally co-ordinated by four oxygen atoms with average bond angles of 109° for O–Si–O and 146° for Si–O–Si. The Na cation generates NBO atoms in the silica network where the NBO to Si distance is shorter than that of the BO to Si distance. In addition, the NBO and BO
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Fig. 10. The La–O co-ordination shell for the Na3S4 simulated glasses as (a) polyhedron representation with La inside the green polyhedra and the red spheres are the nearest neighbor O atoms, and (b) ball-and-stick representaion, where the La ions are the green spheres, the bridging O ions are the red spheres and the non-bridging O ions are the yellow spheres. Note that the O ions that connect some of the La polyhedron have not been distinguished from the non-bridging O ions.
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bonds have distinct peaks in the Si–O PDF. Upon substitution of Si atoms with La atoms, there is a clear increase in the number of NBO atoms that show up in the Si–O PDFs. The NBO bonds due to the La atoms are longer than those due to the Na atoms. This is seen in the shift of the NBO peak as La atoms are substituted in place of Na atoms, corresponding to holding the NBO/T ratio fixed. An analysis of the Qn distribution when the NBO/T ratio is held constant, shows that the amount of Q2 and Q4 species increase at the expense of the Q3 species. This implies that the structure has a tendency to micro-segregate. EXAFS studies of Er in silica and soda silicate glasses [25] determined that the first co-ordination and 6.3 O shell contained 6 O atoms at 2.28 A , respectively. The Er–O first coatoms at 2.26 A ordination polyhedra in soda silicate glasses have no detectable disorder and are believed to be more symmetric relative to the first co-ordination polyhedra in pure silica glasses. This is likely due to depolymerization of the network by sodium which allows the network structure to further relax about the large Er ion. This is consistent with what is found for the La–O polyhedra in our simulations. However, no direct evidence of the existence of Er–O–Er linkages were found in the experiment (see Fig. 10). At very low concentrations RE ions appear to act as network modifiers, generating NBO RE–O– Si bonds in a silicate network. As the concentration of RE ions are increased, RE–O–RE linkages, associated with RE clustering, form which can lead to further phase-separation or precipitation. The formation of these linkages have been studied by [29] Si MAS–NMR spin-lattice relaxation experiments which show that Nd3þ tend to cluster in SiO2 even at ppm concentrations [26]. Further EXAFS studies of Nd3þ –SiO2 provide evidence of Nd–O–Nd linkages [27]. Several experimental results show that RE ions tend to cluster regardless of their concentration in highly polymerized silicate glasses and liquids. McGahay and Tomozawa [28] showed that even a few 1/1000 of a ppm of RE ions in silicate glasses lead to clustering and eventually to phase separation. In comparison to MD simulations of Eu containing soda silicate glasses [15], these simulations
were larger, included different concentrations of the lanthanide ions, and followed a systematic substitution approach as performed in the experiments. Nonetheless, comparisons between the simulations can still be made. Cormier et al. found that with the addition of Na the bond length of , where the Eu–O lengthened from 2.49 to 2.60 A co-ordination number of Eu was 4.2 O atoms in vitreous silica and 5.9 O atoms in Na2 O–2SiO2 for the Eu–O distance. The using a cutoff of 3.2 A La glass simulations are consistent with the erbium oxide simulations in that the La–O bond length in pure silica to 2.53 A in increased from 2.45 A the soda silicate glass. The co-ordination number of La containing glasses goes from 4.7 in the pure silica to 6.5 in the soda silicate glasses. Although such trends are similar, there are differences in the co-ordination environments between the two simulations due to differences in the potential models. The bond angle distribution of O–Eu–O was found to have two broad maxima, one at 50° and a second at 74°. In contrast, the O–La–O angle in La containing glasses show a very small peak at about 55°, a large peak at 80° and another peak at around 150°. The Eu3þ ion is bonded to NBO atoms where none of the polyhedra were found to have high symmetry. The erbium oxide simulations also show that Eu3þ ions prefer a sodium rich region though less well defined. In the La soda silicate simulations the distribution of the polyhedra symmetries were obtained. In the larger La containing glass simulations, the heterogeneity of the structures makes it difficult to distinguish distinct domains for the Na ions. Further simulations will be necessary to determine the propensity of partitioning amongst heterogeneous domains. Individual differences also appear in the number of free O atoms that are generated by the presence of a lanthanide ion, which is lower in the La glass simulations than in the Eu simulations. Several differences between the simulations should be noted. These are in the simulation size: 400 atoms with two Er ion and 1600 atom with 12–44 La ions; quench rates of: 1016 K/s for the erbium oxide simulations and 1013 K/s this work, and different potential parameterization that likely affect the results. In general, the MD simulations show that La3þ and Eu3þ appear to form quasi-molecular
B. Park et al. / Journal of Non-Crystalline Solids 297 (2002) 220–238
complexes that are relatively stable. This is consistent with the general phenomena in glass systems where network modifiers form their own environment. Finally, high-temperature calorimetry studies have shown the ability of La ions to perturb the network and compete for oxygen atoms [29]. The isolation of oxygen atoms (free-oxides) away from the silicate network backbone is believed to occur implying that there is a phase-ordered region rich in La. Further verification of the propensity of clustering in the MD simulations has been carried out and will be reported elsewhere as a second paper in this series. It is found that the driving forces which lead to clustering are an interplay between formation energies, effective molar volumes of the cation polyhedron and the configurational entropy. Clustering at the atomic level is predicted to occur in the simulated soda silicate glasses. The structural properties reported here are real, at least for the MD simulations, and await further validation from experiment.
5. Conclusion Lanthanum containing soda silicate glasses were investigated using MD simulations. It was found that the La cation has an average co-ordination of 6.5 oxygen atoms with an average bond . The MD simulations reveal that length of 2.5 A La ions act as network modifiers and generate NBO bonds which de-polymerize the glass structure. Adding La to the soda silicate glasses leads to the production of Q2 species at the expense of Q4 species. In addition, it is observed that the La ions tend to cluster, forming La–O–La linkages that, in some cases, isolate oxygen atoms away from the silica network.
Acknowledgements This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, Department of Energy. This research was performed in the William R. Wiley Environmental Molecular Sciences Laboratory, a national scien-
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tific user facility sponsored by the Department of Energy, Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. Pacific Northwest Laboratory is operated for the Department of Energy by Battelle.
References [1] J. Simmons, K.S. Potter, Optical Materials, Academic Press, San Diego, CA, 2000. [2] P.J. Hayward, in: W. Lutz, R.C. Ewing (Eds.), Radioactive Waste Forms for the Future, North-Holland, Amsterdam, 1988. [3] J. Coon, J.E. Shelby, Phys. Chem. Glasses 35 (1994) 47. [4] G.E. Peterson, P.M. Bridenbraugh, J. Opt. Soc. Am 54 (1964) 644; L.G. van Uitert, J. Chem. Phys. 46 (1967) 420; H.G. Danielmeyer, M. Bl€atte, Appl. Phys. 1 (1973) 269; J.A. Caird, A.J. Ramponi, P.R. Staver, J. Opt. Soc. Am. B 8 (1991) 1391. [5] R. Dron, J. Non-Cryst. Solids 53 (1982) 267; W.G. Dorfeld, Phys. Chem. Glasses 29 (1988) 179. [6] L.R. Corrales, K.D. Keefer, J. Chem. Phys. 106 (1997) 6460, and references therein. [7] N. Imaoka, J. Ceram. Assoc. Japan 67 (1959) 364. [8] S.K. Duprovo, A.D. Shnipikov, Inorg. Mater. (USSR) 2 (1966) 1417. [9] B.M.J. Smets, D.M. Krol, Phys. Chem. Glasses 25 (1984) 113. [10] D.M. Krol, B.M.J. Smets, Phys. Chem. Glasses 25 (1984) 119. [11] F. Branda, A. Buri, D. Caferra, A. Marotta, Phys. Chem. Glasses 22 (1981) 68; A. Buri, D. Caferra, F. Branda, A. Marotta, Phys. Chem. Glasses 23 (1982) 37. [12] C.W. Ponader, G.E. Brown Jr., Geochim. Cosmochim. Acta 53 (1989) 2893. [13] A.J.G. Ellison, P.C. Hess, J. Non-Cryst. Solids 127 (1991) 247. [14] T. Schaller, J.F. Stebbins, M.C. Wilding, J. Non-Cryst. Solids 243 (1999) 146. [15] G. Cormier, J.A. Capobianco, A. Monteil, J. Non-Cryst. Solids 152 (1993) 225. [16] W. Smith, T.R. Forester, DL_POLY version 2.11, Daresbury Laboratory, UK. [17] B. Vessal, J. Non-Cryst. Solids 177 (1994) 103. [18] D.J. Evans, G.P. Morriss, Phys. Lett. 98A (1983) 433; D.J. Evans, G.P. Morriss, Chem. Phys. 77 (1983) 63. [19] B. Park, A.N. Cormack, J. Non-Cryst. Solids 255 (1999) 112. [20] K. Vollmayr, W. Kob, K. Binder, Phys. Rev. B 54 (1996) 15808. [21] A.L. Ankudinov, J.J. Rehr, Phys. Rev. B 56 (1997) R1712.
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[22] E.M. Larson, A.J.G. Ellison, F.W. Lytle, A. Navrotsky, R.B. Greegor, J. Non-Cryst. Solids 130 (1991) 260. [23] A.C. Wright, J. Non-Cryst. Solids 123 (1990) 129. [24] G.N. Greaves, J. Non-Cryst. Solids 71 (1985) 203. [25] M.A. Marcus, A. Polman, J. Non-Cryst. Solids 136 (1991) 260.
[26] S. Sen, J.F. Stebbins, Phys. Rev. B 50 (1994) 822. [27] S. Sen, J. Non-Cryst. Solids 261 (2000) 226. [28] V. McGahay, M. Tomozawa, J. Non-Cryst. Solids 159 (1993) 246. [29] M.C. Wilding, A. Navrotsky, J. Non-Cryst. Solids 254 (2000) 238.
Molecular dynamics simulation of La2O3–Na2O–SiO2 glasses. I. The structural role of La3þ cations Byeongwon Park, Hong Li 1, L. Rene Corrales
*
Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, P.O. Box 999, K8-91, 902 Batelle Blvd., Richland, WA 99352, USA Received 17 May 2001; received in revised form 19 September 2001
Abstract It is well known that high-field strength rare-earth (RE) ions in the silicate glasses tend to cluster regardless of their concentration. Numerous experimental studies have been carried out, but the ability to discern structural information at the atomic-level strongly depends on providing accurate molecular dynamics (MD) simulations. In this work, the short- and medium-range order of La ion in soda silicate glasses is investigated by MD computer simulations. The glass mixtures used in these MD simulations are the same as those of a recent NMR study. Results of this study are in excellent agreement with the NMR results. It is found that the La cation has an average co-ordination of 6.5 O atoms with an average bond length fitted to be about 0.25 nm. The La is found to behave as a network modifier, and competes with sodium for non-bridging oxygen (NBO) atoms. In addition, the extended X-ray fine structure (EXAFS) and neutron diffraction patterns are predicted from the MD simulations. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Technological applications of lanthanide containing glasses include their use to generate and modulate laser light [1], and as constituents, as well as analogues of actinides in experimentally simulated nuclear waste glasses [2]. Changes in the distribution and local environment of the lanthanide ions in a silicate glass are known to lead to * Corresponding author. Tel.: +1-509 376 6608; fax: +1-509 376 0420. E-mail address: [email protected] (L.R. Corrales). 1 Present address: Fundamental Science, Fiber Glass and Technology, PPG Industries Inc., Glass Technology Center, PO Box 2844, Pittsburgh, PA 15230, USA.
strong changes in chemical [3], electrical and optical properties [4]. Experiments have been carried out to identify the structural role of lanthanide ions in alkali silicates with seemingly disparate but not inconsistent results. Lacking is a definitive identification of the structural role of La in alkali silicate glass. In this work, molecular dynamics (MD) computer simulations are used to characterize the structural role of lanthanum in soda silicate glasses and to provide details of short- and medium-range structure. MD simulations are used to obtain neutron diffraction (ND) patterns and extended X-ray fine structure (EXAFS) spectrum. The pure silica network structure consists of Si–O–Si covalent bonds that are called bridging oxygen (BO) bonds. Upon the addition of a metal
0022-3093/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 1 ) 0 0 9 3 5 - 8
B. Park et al. / Journal of Non-Crystalline Solids 297 (2002) 220–238
oxide to silica, the dissolution process that takes place can be described as follows. Metal oxides with cation oxidation states of +1, +2 and +3 can be thought to exist in M2 O, MO, and M2 O3 molecular units, respectively, that preserve stoichiometry in the pure states. The metal oxide molecular species can react with the silica network to convert BO bonds to non-bridging oxygen (NBO) bonds. The energy of this reaction competes with the energy to keep the metal oxide molecular species associated, or clustered. A formation free energy can be assigned to this chemical process that can be described by a chemical equilibrium reaction [5]. Presumably, the formation energies can dictate the number and distribution of NBO bonds that are formed, although these might be affected by the network topology [6]. In general, if a cation is a network modifier such that it can break the Si–O– Si bonds, then the maximum number of NBO bonds that can form is proportional to the valence state of the cation. To determine the role of a cation, experiments are carried out such that an unknown cation is substituted for known cations [3]. Here, the unknown is the lanthanide ion, whereas the known ions would include the alkali (network modifier) and the silicon (network former) ions. Thus, the tendency for formation or depletion of NBO bonds can be used to determine the structural role of the unknown cation. Experimentally, this is done by measuring NBO sensitive properties such as the glass transition temperature or NMR spectroscopy that probes the local atomic environments. The glass forming phases of RE containing alkali silicates have been well determined [7], along with trends in their physical properties [8]. Consequently, experiments to determine the structural role of rare-earth (RE) ions in alkali silicates have used compositions away from the phase separating regions. Such experiments include the following. NBO and BO bonds can be differentiated by X-ray photoelectron [9] and Raman [10] spectroscopic methods. Changes in the population of oxygen atom types can then be contrasted with changes in the concentration of the RE ion. From these spectroscopic data it was asserted that La behaves as a network modifier in soda silicate glasses. The
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glass transition temperature, Tg , of soda silica glasses containing M2 O3 , with M being Ga, In, Sc, Y, or La, has been measured and compared with metal oxides that behave like network formers or modifiers [11]. From this work it was asserted that La behaves as a network modifier. The local environment of trace levels of La in silicate glasses was also studied by EXAFS experiments [12], in which the regularity of the RE site as a function of the degree of polymerization of the network was studied. They deduce that because the REs are trivalent, they will be better network modifiers than Naþ . These previous experiments did not systematically substitute a RE ion for an alkali or silicon ion and, hence, it is difficult to justify their assertions of the structural role of La. Trends in the density, molar volume, electrical conductivity, and glass transformation temperature of La bearing soda silicate glass were determined using systematic substitutions. These results were less conclusive and lead to specifying the role of La as a network intermediate [3], while suggesting more spectroscopic work needed to be done. Consequently, the local environments of lanthanide bearing alkali silicate glasses were probed by EXAFS [12], vibrational spectroscopy [13], and by combining NMR and Raman spectroscopic methods [14] for mixtures using a systematic approach of adding La to glasses with a fixed ratio of alkali ion to silicon ion, and substituting La ion for the alkali ion on an equal-oxygen basis. From the EXAFS work it was inferred that the average co-ordination number of La did not change significantly as the compositions were varied, and together with the vibrational spectra [13], that the La ions were possibly distributed heterogeneously in the glass. Combined NMR and Raman studies were used to investigate the formation of free oxides in La containing alkali silicate glasses [14]. It was found that the replacement of silicon by La cations resulted in the formation of NBO bonds, consistent with a network modifier. The replacement of sodium or potassium with La cations in an equal-oxygen basis led to a measurable decrease of NBO atoms, but not an increase in BO bonds, suggesting that La2 O3 species are isolated away from the silica network and form microheterogeneous regions in glass.
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Molecular dynamics (MD) computer simulations of glasses have a long successful history, although few MD simulations of glasses containing lanthanide ions have been performed [15]. In this work, the local environment and dynamics of La bearing sodium silicate glasses is investigated and its influence on the network structure examined. The same compositions of Schaller et al.’s NMR and Raman [14] experiments are used so that direct comparison can be made. Unfortunately, there are no known EXAFS or neutron diffraction (ND) studies available for these mixtures. A detailed analysis of the simulation results and comparison to experiments, where available, is presented. This paper is organized as follows. In the following section, the computational details that include a description of the potential model and MD simulation procedure of the glass-forming process is outlined. In Section 3, the results are presented which includes simulated ND total distribution functions (TDF) and EXAFS spectra of La in soda silicate glasses. The results are discussed in Section 4 and conclusions presented in Section 5.
2. Computer simulations The MD simulation code used in this study was DL_POLY version 2.11 from Daresbury Laboratory, UK [16]. All the ions were treated as rigid with their formal charges; Na1þ ; Si4þ ; La3þ ; O2 . The long-range electrostatic potential was evaluated by Ewald summation method with the cutoff and precision set to 106 . The distance set at 12 A . These short-range cutoff distance was set at 7.6 A are standard cutoffs used for glass simulations that provide a balance between accuracy and memory requirements of the code [19]. The potential parameters for SiO2 are based on Vessal’s model that includes three-body potentials for Si–O–Si and O– Si–O [17]. The potential for the La–O and Na–O interactions use the modified Buckingham potential where the La–O parameters were fit to crystalline La2 O3 . The parameters for La–O and Na–O are given in Table 1. The length of each time step was 2 1015 s and the integration was done using the Verlet Leapfrog algorithm. The
Table 1 Potential parameters for cation–oxygen interactions V ðrÞ ¼ A expðr=qÞ C=r6
La–O Na–O
A (eV)
) q (A
6 ) C (eV A
2133.2436 1226.79
0.3590 0.306 5
0.0 0.0
canonical ensemble (NVT) employing the Evans thermostat [18] was used for the glass forming runs, and then the ensemble was switched to the microcanonical ensemble (NVE) at the lower temperature during which all the sampling was performed. The simulation procedure was based on alkali silicate glass simulations of previous work [19]. In this work, the initial configuration was borrowed from [19], where the Na ion was used as alkali ion in place of Li or K. The glass was heated up to 12 000 K to remove possible memory effects and then annealed to room temperature. The glassmaking schedule was as follows. The simulation was run twice at 12 000 K with each run consisting of 10 000 time steps. The first run was without the three-body potentials for the Si–O–Si and O–Si–O interactions, thus allowing the system to mix well. The second run at 12 000 K was with the threebody potential turned on that favors the formation of silica tetrahedra. The temperature was then lowered sequentially to 9000, 7000, 5000, 3000, 2000, 1000, and finally to 300 K. At each temperature the system was equilibrated for 10 000 time steps. The room temperature simulation was done for 30 000 time steps where the system data was collected during the last 20 000 time steps. The total number of time steps was 110 000, which is equal to 220 ps with a nominal cooling rate of 5:3 1013 K/s. These are considered to be nominal cooling rates for MD simulations [20] although they are still several orders of magnitude faster than the fastest experimental cooling rates. The composition of the simulated glasses, the number of atoms and the simulation size for each composition are given in Table 2. The total number of atoms in each simulation was around 1600. In addition to the compositions used by Schaller et al. [14] compositions containing no Na or La, labeled as Na25 and SiLa4, respectively, were used.
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Table 2 Composition of simulated glasses System Na25 Na3S4 Na3S10 NaLa4 NaLa12 SiLa4
Concentration
Number of atoms
La2 O3
SiO2
Na2 O
La
0.0 4.0 10.0 1.4 4.4 1.7
75.0 72.0 67.5 77.1 81.5 98.3
25.0 24.0 22.5 21.6 14.1 0.0
40 100 14 43 364
Si
O
Atoms in box
Box length ) (A
NBO/T
Na 270 240 224 224 141
405 360 337 401 408 234
945 900 936 935 951 101
1620 1540 1597 1574 1543 1612
28.147 27.313 28.147 28.000 27.713 26.678
0.67 1.00 1.57 0.67 0.67 0.10
The purpose in using these compositions was to systematically substitute La for Si and La for Na as well as to compare the extreme cases where either no Na or La is present in the system. If La acts strictly as a network modifier, then it is expected to contribute three NBO atoms to the system, where Na contributes one NBO atom. Hence, the ratio NBO/T, which is the number of NBO atoms to the number of tetrahedrally co-ordinated Si, is used to measure the structural contribution of La in the system. If La behaves like a network modifier, then as La is substituted for Na (on an equal oxygen basis), this ratio is expected to remain constant. A comparison of the ideal case, where La act strictly as a network modifier, with that determined from our simulation is a measure of the degree to which La is a network modifier. The structural properties such as pair distribution functions (PDF), co-ordination number distributions, bond angle distributions (BAD), etc. are obtained over final room temperature configurations, the details of which are presented in Section 3. To obtain simulated EXAFS patterns, the MD structures are used as input in the program FEFF 7.0 [21]. FEFF 7.0 calculates wave phase shifts, effective scattering amplitudes, and single and multiple scattering XAFS and XANES spectra including polarization dependence for clusters of atoms (Z < 96) about the center of each atom. Each EXAFS pattern was averaged over all the La ions in one sample configuration, using an 8 A cutoff distance for the interacting neighbor shells. Increasing the cutoff distance has almost negligible effect on the final pattern, except in the low k region.
3. Structural properties 3.1. ND and EXAFS spectra The PDFs sampled and averaged over 20 ps at 300 K are shown in Fig. 1 for the glass mixtures containing La ions. Also shown are the La polyhedra that contain the nearest neighbor O ions. The average bond lengths are given in Table 3. The nearest distance between each atom pair is obtained from the position of the maximum of the first peak of each PDF. Note that the first peak of the Si–O PDF has two subpeaks that correspond to NBO and BO bonds. The nearestneighbor bond distance of the BO and NBO . The bonds for Si–O pairs are 1.51 and 1.62 A bond lengths are as follows: Na–O, 2.42 A; La–O, ; O–O, 2.58; Si–Si, 3.12 A , Si–Na, 3.35 A ; 2.55 A Si–La, 3.74 A; Na–Na, 3.02 A; and La–La, 4.32 , respectively. A For the Na3S10 mixture, the PDF for the La– . If the La nearest neighbors show a peak near 4 A La atoms were homogeneously distributed, the PDF for this concentration of La should show a , as determined by sharp peak at around 7 A 1=3 3V d¼2 ; ð1Þ 4pN where V is volume and N is the number of La ions. A more detailed analysis of the La local environment can be done using these simulations and are described below. All of the mixtures which contain both La and Na cations show very similar La–La PDFs, except for that of NaLa4 which shows . This mixture sharp peaks at 4.3, 6.6, 7.5, and 8 A has the lowest concentration of La in the system
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Fig. 1. PDFs and snapshots of just the La–O polyhedra for simulated glasses. The gray spheres are La ion and the black spheres are the nearest neighbor O ions. Note the La–O–La linking that can occur: (a) Na3S4; (b) Na3S10; (c) NaLa4; (d) NaLa12; (e) SiLa4.
and the longest possible La–La nearest neighbor distance. The La–La PDF suggests the presence of microheterogeneous regions. By simulating multiple mixtures using systematic substitution, general trends can be determined. For ease of describing the trends we define series I as the group Na25, Na3S4 and Na3S10 where the ratio NBO/T increases, and series II as the group
NaLa12, NaLa4 and Na25 where the ratio NBO/T is constant. As La is added following series I the average BO bond length for Si–O does not change and the average NBO bond length for Si–O increases. When Na is replaced by La following series II the average BO bond length of Si–O does not change while the average NBO bond length of Si–O increases slightly.
B. Park et al. / Journal of Non-Crystalline Solids 297 (2002) 220–238
Fig. 1 (continued)
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Table 3 ) in the simulated La–soda silicate glasses Bond distances (A Si–NBO Si–BO Na–O La–O O–O Si–Si Si–Na Si–La Na–Na Na–La La–La
Na25
Na3S4
Na3S10
NaLa4
NaLa12
SiLa4
1.46 1.62 2.41
1.49 1.62 2.41 2.52 2.59 3.11 3.38 3.76 3.03 3.64 3.85
1.51 1.62 2.42 2.55 2.58 3.12 3.35 3.74 3.02 3.61 4.02
1.47 1.62 2.38 2.56 2.60 3.12 3.45 3.79 3.19 3.75 4.32
1.48 1.62 2.43 2.52 2.60 3.11 3.41 3.76 3.21 3.71 4.00
1.47 1.62
2.60 3.13 3.44 3.15
The average O–O nearest-neighbor distance decrease in series I and do not change for series II. The average Na–O bond distance remains constant for series I. In series II, the bond distance is smallest when the concentration of La is at 1.4%, but is similar when no La is present and when the La concentration is at or above 4%. The bond length for La–O is shortest in the SiLa4 glass in which no Na is present. It increases in series I and in series II, where it is understood that the mixture of Na25 is not included in either series. The average La–O bond length from these in the soda glasses, and 2.45 simulations is 2.53 A in the no-sodium silica. This can be compared A for La–O in potassium silicate glass to 2.42 A [22], and to the wide bond distance distribution in crystalline phases which range from 2.41 to 2.74 [12]. A The Si–Si nearest neighbor distance is fairly constant through all mixtures. The Na–Na nearest neighbor distance shows marked changes as the ratio NBO/T changes. The La–La nearest neighbor distance increases when Na is substituted for La, following SiLa4, NaLa12, and NaLa4. As La is substituted for Si, Na3S4, and Na3S10, the La– La nearest neighbor distance increases. To compare the simulated structure with the experimental neutron diffraction pattern, the TDF is constructed from the set of PDFs. The experimental TDF is obtained through a Fourier transformation of the measured scattering intensity. The simulated TDF needs to be broadened due to the finite upper limit in the momentum transfer, Q. The component TDF, tij ðrÞ, is convoluted with
2.45 2.64 3.14 3.84
3.92
a component peak function, Pij0 ðrÞ using the following equation [23]: Z 1 h i tij0 ðrÞ ¼ tij ðr0 Þ Pij0 ðr r0 Þ Pij0 ðr þ r0 Þ dr0 ; ð2Þ 0 0
where r is a dummy integration variable. The component peak function Pij0 (r) defines the experimental resolution in real space caused by the finite upper limits in Q, where Pij0 (r) is defined as Z bi bj 1 PijN ðrÞ ¼ MðQÞ cosðrQÞ dQ; ð3Þ p 0 where MðQÞ is a modification function given by a Lorch function that gives a gradual cutoff given by sin Dr Q 6 Qmax ; MðQÞ ¼ DrQ ð4Þ 0 Q P Qmax : Also the bi s are the coherent neutron scattering lengths of each element. 1 In the these simulations, Qmax is set to 40 A and the coherent scattering factors are: 8:24 1015 m for La, 3:63 1015 m for Na; 4:1491 1015 m for Si, and 5:803 1015 m for O. The simulated TDF for all the systems are shown in Figs. 2(a) and (b) and the corresponding structure factors are shown in Figs. 2(c) and (d). It is interesting that all of the TDFs appear to be very similar. The greatest change is in the TDF of SiLa4 , which contains no Na cations. glass at around 4 A This difference is reflected in the La–La PDF for the SiLa4 glass in which a peak centered at 4.8 A disappears upon the addition of Na atoms, whereas all the other PDFs of the mixtures show no significant change in this region.
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1 and the peaks are broadened using Fig. 2. TDFs (a,b) and scattering factors (c,d) for Na–La silicate glasses. The Qmax is set to 40 A peak functions.
EXAFS has been widely used to probe the local structure in glass systems [24]. In these simulations the EXAFS patterns are determined from the final configuration at room temperature of all the La ions using the FEFF7.0 code as described above. The experimental EXAFS is the average of all the possible configurations of a specific element in the glass, which inherently have a wide distribution range. In a real glass, the actual number of any specific element is large, as compared to these simulations. Thus, to obtain better statistics in the simulation, the averaging for all the target ions in
the simulated structures is over a time series. Two were tried to include cutoff distances of 5 and 8 A different number of neighboring atoms, however, little change was observed, except for regions of cutoff distance cases are very low Q. Only the 8 A presented. Fig. 3(a) shows the EXAFS of each individual La ion in the simulated NaLa4 glass. There are a total of 14 La ions in the simulation. The solid line with squares in Fig. 3(a) is for the averaged pattern over all the La ions. In Fig. 3(b) the averaged EXAFS for all the glass mixtures in the current study are shown. The Fourier
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): (a) lighter lines are for each individual La in the NaLa4 and the Fig. 3. EXAFS simulation using FEFF 7.0. (Cutoff distance is 8:0 A heavy line is the average of the individual La lines; (b) the averaged La EXAFS patterns for all the simulated glasses.
transforms of these patterns have not been done, since to our knowledge, experimental data for these mixtures is not available, and hence direct comparison is not possible. Like the TDFs, the EXAFS appear to be very similar. The biggest change occurs in the position of the valley near the 1 position where the valley for the SiLa4 5 A mixture is shifted to the right relative to the valley of the other mixtures. The peak following that valley is also shifted to the right relative to the other mixtures. In general, the periodicity of the spectra is expected to be maintained across a Fourier transformation of the data. Thus, the differences in the EXAFS patterns could provide a thumbprint of the La distribution. 3.2. Structures of cation co-ordination polyhedra The co-ordination number as a function of distance is shown in Fig. 4 for the Si, Na and La cations in the Na3S10 mixture where the arrows pinpoint the cutoff distance of the first co-ordination shell. The graph is an integration of the number of O atoms as a function of distance. The first co-ordination shell cutoff is obtained by choosing the cutoff where the second derivative for each co-ordination plot is zero at a distance after the first peak in the PDF. Thus, the cutoff for Si–O , for Na–O it is 3.0 A and for La–O it is is 2.2 A
Fig. 4. Co-ordination number distribution for cation–oxygen with cutoff distances, see text for explanation of cutoffs and error bars.
. Silicon has four O nearest neighbor atoms 3.2 A and there are no five-fold co-ordinated Si atoms in the simulated glasses. The co-ordination number of Na is 5.2 and of La it is 6.5. The cutoffs for the other mixtures are kept the same, and the results are given in Table 4 for La–O and Na–O pairs only, because Si always has four neighboring oxygens. In series II where La re-
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Table 4 and rcut (La–O) ¼ 3.2 A Average co-ordination number of oxygen around cation rcut (Na–O) ¼ 3.0 A Na–O Na–NBO Na–BO La–O La–NBO La–BO
Na25
Na3S4
Na3S10
NaLa4
NaLa12
4.61 2.76 1.85
5.09 3.28 1.81
5.17 3.63 1.49
4.51 2.72 1.80
4.88 2.59 2.29
6.25 5.42 0.83
6.53 5.79 0.63
5.63 5.14 0.49
5.89 4.90 0.99
places Si, the average co-ordination numbers of Na and La have increased because La acts as a network modifier. There are more NBO than BO
SiLa4
4.74 3.74 1.00
nearest neighbor cations. When La replaces Na in series II, the average co-ordination number around the cations decreases.
Fig. 5. Deconvolution of Si–O PDFs (a,c) and change in NBO concentration distributions (b,d). In (a,b) the ratio NBO/T increases and in (c,d) the ratio NBO/T remains fixed.
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Note that the error bars in the co-ordination number calculations for these simulations are small at about 1% of the reported value, which is smaller than the markers used in the figures. In these simulations the average is over a time series of the same initial sample, thus, the magnitude of the statistical fluctuation is small. A proper statistical sampling requires using many different initial configurations for the same mixture that allows averaging over similar configurations. This may lead to larger fluctuations and thus larger
error bars, but is also very computationally intense. The deconvolution of the first peak of the Si–O PDF for each of the compositions are shown in Fig. 5. The fraction of NBO, defined as having only one silicon within the cutoff distance, is given in Figs. 5(b) and (d). When the nominal NBO/T increases (replace Si by La), the subpeak for Si–NBO increases gradually, confirming the role of La as a network modifier, which is in excellent agreement with NMR data [14]. As La
Fig. 6. Structure of sodium oxygen polyhedron: (a) deconvolution of first Na–O PDF; (b) co-ordination number distribution for Na– ); (c) deconvolution of first Na–O PDF; (d) co-ordination number distribution for Na–O (cutoff disO (cutoff distance ¼ 3.0 A ). (a,b), NBO/T increase; (c,d) NBO/T ¼ fixed. tance ¼ 3.0 A
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replaces Na, the bond distance for Si–NBO increases from 1.45 to 1.51 and the Si–BO distance does not change (1.62), as shown in Fig. 5. The high-valence state of La (+3) pulls the NBO closer, resulting in a longer distance of the Si– NBO bond. The amount of NBO among SiO4 tetrahedron increase from 28.6%, to 40.1% to 54.9% in the mixtures Na25, Na3S4 and Na3S10, respectively. Although the amount of bridging oxygen decreases from 71.4%, to 59.9% to 44.6%, respectively, as shown in Fig. 5(b). When La re-
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places Na by equal basis of O, the amount of NBO is almost constant as shown in Fig. 5(d) though in the NMR experiment the amount of NBO decreases substantially. For the Na3S10 glass, about 0.53% of the O atoms are not connected to Si (considered to be free O atoms). This can be partially accounted for by the decrease in the relative amount of NBO atoms in SiO4 tetrahedron from 28.6% to 28.4%. The rest may come from the conversion of BO atoms. In the case of the SiLa4 glass, the Si–NBO
Fig. 7. Structure of lanthanum–oxygen polyhedron: (a) deconvolution of first La–O PDF; (b) co-ordination number distribution for ); (c) deconvolution of first La–O PDF; (d) co-ordination number distribution for La–O (cutoff disLa–O (cutoff distance ¼ 3.0 A ). (a,b), NBO/T increase; (c,d) NBO/T ¼ fixed. tance ¼ 3.0 A
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where 6.7% of the O atoms are distance is 1.46 A NBOs. The deconvolutions of the first Na–O PDF and co-ordination number changes are given in Fig. 6 as a function of composition. In Fig. 6(a) the Na– O PDF is deconvoluted according to the co-ordination state of O and shows that the bond distance even for Na-NBO increases from 2.28 to 2.32 A though the relative amount of NBO around Na decreases. In Fig. 6(b) the relative amount of each co-ordination state of Na within the first co-ordi-
, is nation shell, with a cutoff distance of 3.0 A shown. The average co-ordination number of Na increases from 4.61 in Na25 to 5.17 in Na3S10 with the addition of La, but the co-ordination number does not change appreciably with further addition of La. The ratio of NBO/T is held fixed by adding La atoms to and removing Na atoms from the system, Fig. 6(c). In this series of substitutions, the deconvoluted peak for Na–NBO decreases, and the co-ordination number distribution of Na widens and shifts to a higher co-
Fig. 8. BADs and typical cation polyhedra: (a,c), NBO/T increase; (b,d) NBO/T ¼ fixed.
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ordination number: 4.61 for Na25 to 4.88 for NaLa12 as shown in Fig. 6(d). The deconvolution of La–O PDFs are given in Fig. 7. As shown in Figs. 7(a) and (b), most of the La is connected by NBO bonds with an average . The number of connections by distance of 2.52 A BO bonds is negligible (0.83 out of 6.25 for Na3S4). In contrast to Na, most of the O atoms in the La–O polyhedron are NBO. The most abundant co-ordination state is six and increases to seven by adding La whether the ratio NBO/T is held fixed or not. 3.3. Bond angle distributions BADs were calculated for the first cation coordination polyhedra. The bond angles for Si–O– Si and O–Si–O have maxima at 146° 2° and 109° 2°, respectively. The angle distributions are rather narrow compared to results for pure silica using the BKS model and can be attributed to the use of three-body potentials [17]. The BADs for O–Na–O and O–La–O are shown in Fig. 8 with one possible cation polyhedron configuration for Na and La in Figs. 8(c) and (d). In the first co-ordination shell of Na–O, the O–Na– O BAD has a narrow peak at 60° and an asymmetric broadened peak at 94° that extends to 180°. These angle distributions are sampled in
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the five-fold co-ordinated Na polyhedron in which acute angles of about 60° occur for those O atoms lying closest to a plane and obtuse angles of about 94° for those in the plane which are not nearest neighbors and can be up to 180° apart. In the O–La–O BAD, the largest peak is located at about 85° with smaller peaks at 130° and 160° with some structure at around 60°. The most abundant co-ordination number for La–O is six with a typical configuration shown in Fig. 8(d). The La–O polyhedra are more symmetric than those of Na–O. The most probable angle for O–La–O is 90°, although the broadening up at larger angles is due to the next nearest neighbor angles for O atoms lying in a plane. It is interesting to note that the glass mixture without Na, SiLa4, has several peaks in the BAD. This is due to the constraint of the Si–O network not being able to relax its structure around the La atoms. Thus, a glass without Na will have a more asymmetric polyhedron than the glass mixtures where Na ions break up the backbone of the network that can afford greater relaxation of the network. 3.4. Qn distributions The co-ordination environment of Si mostly consist of tetrahedrally co-ordinated O atoms that
Fig. 9. Qn distribution changes as: (a) NBO/T ¼ increase; (b) NBO/T ¼ fixed.
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can be bonded to another Si atom (a BO atom) or to a modifying cation (a NBO atom). The Qn , where n is number of BO in SiO4 tetrahedron, is related to the connectivity of glass network and is measurable by NMR. These co-ordination states have been defined by NMR spectroscopists as follows [6]. A Si atom four-fold co-ordinated by BO atoms is defined as a Q4 species. A Si atom coordinated by three BO and one NBO is a Q3 . And so on, until reaching a Si atom four-fold co-ordinated by NBO atoms is a Q0 . The Qn distributions of the simulated silicate glasses are given in Fig. 9. The trends are such that when La ions are added (NBO/T increase), the number of Q4 decrease substantially while the number of Q1 and Q2 increases with the number of Q3 changing only slightly. When the NBO/T is fixed, the overall shape does not change much although there is a decrease in Q3 with an increase in Q2 and Q4 which might be a manifestation of microheterogeneities with separate Q2 and Q4 rich regions at the expense of Q3 .
4. Discussion A detailed analysis of the Si–O PDF in which the BO and NBO contributions are clearly distinguished reveal that the La cation behaves as a network modifier. This data is consistent with data from NMR and EXAFS experiments [14]. In glasses containing lanthanum oxide there are, however, a small number of free oxygen atoms which are linked to two La atoms and no Si atoms. The occurrence of free oxygen atoms, associated with the formation of La–O–La linkages and a depletion of NBO atoms is consistent with experiment [14], although the MD simulations predict a smaller number of them. However, in our counting not all La–O–La linkages are associated with the formation of a free oxygen atom. The La–O–La linkages provide a means of identifying clusters of La dimers, trimers and so on. A statistical distribution of La clusters is currently not available due to the small number of simulations. Alternatively, large simulations can be run but both are CPU intensive. Similar clustering effects are seen in all of the simulated La glass structures. Further studies
of La clustering in simulated glasses are needed to determine the driving forces that lead to clustering. There are distinct changes in the La–La PDF in going from a system of only La2 O3 –SiO2 to one in which 21 mole percent of Na2 O has been added. A very strong change in the viscosity of the melts is observed indicating that the presence of soda depolymerizes the silica network. In fact, there is a clear change to higher viscosity as La is substituted for Na. The changes in viscosity are indicated by changes in self-diffusion. Although the larger ion behaves as a network modifier, it is considerably more massive, mLa ¼ 138.9 amu, and mNa ¼ 22.99 and rNa ¼ 0.89 A , amu, larger radius rLa ¼ 1.3 A and has a large ionic state qLa ¼ +3 and qNa ¼ +1. The ionic strengths given by I ¼ q=r, are 2.3 and 1.1, for La and Na, respectively. The higher ionic strength ions are believed to form more rigid structures that along with their large mass can contribute drag forces to their translational motion. A quasi-molecular picture can be used to define the molecular units that make-up the network structure. The molecular units can be conveniently defined as the cations and their first co-ordination shell of oxygen atoms, consistent with the molecular picture used to define the Qn species. These are identical to the cation polyhedron as described above. The degree of symmetry of these molecular units is determined by defining the dipole moment of the molecular species where the dipole is centered at the center of mass of the cation polyhedron. The smaller the dipole, the more symmetric the molecular species. The degree of symmetry used in conjunction with the bond angle and bond distance analyses can be used as a probe of structural response. The network structure of the soda silicate glass is the same as that of [19] since the same potential parameters were used. The bond distances for Si– , respectively. The O and O–O are 1.62 and 2.60 A . All nearest-neighbor distance of Si–Si is 3.13 A the Si atoms are tetrahedrally co-ordinated by four oxygen atoms with average bond angles of 109° for O–Si–O and 146° for Si–O–Si. The Na cation generates NBO atoms in the silica network where the NBO to Si distance is shorter than that of the BO to Si distance. In addition, the NBO and BO
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Fig. 10. The La–O co-ordination shell for the Na3S4 simulated glasses as (a) polyhedron representation with La inside the green polyhedra and the red spheres are the nearest neighbor O atoms, and (b) ball-and-stick representaion, where the La ions are the green spheres, the bridging O ions are the red spheres and the non-bridging O ions are the yellow spheres. Note that the O ions that connect some of the La polyhedron have not been distinguished from the non-bridging O ions.
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bonds have distinct peaks in the Si–O PDF. Upon substitution of Si atoms with La atoms, there is a clear increase in the number of NBO atoms that show up in the Si–O PDFs. The NBO bonds due to the La atoms are longer than those due to the Na atoms. This is seen in the shift of the NBO peak as La atoms are substituted in place of Na atoms, corresponding to holding the NBO/T ratio fixed. An analysis of the Qn distribution when the NBO/T ratio is held constant, shows that the amount of Q2 and Q4 species increase at the expense of the Q3 species. This implies that the structure has a tendency to micro-segregate. EXAFS studies of Er in silica and soda silicate glasses [25] determined that the first co-ordination and 6.3 O shell contained 6 O atoms at 2.28 A , respectively. The Er–O first coatoms at 2.26 A ordination polyhedra in soda silicate glasses have no detectable disorder and are believed to be more symmetric relative to the first co-ordination polyhedra in pure silica glasses. This is likely due to depolymerization of the network by sodium which allows the network structure to further relax about the large Er ion. This is consistent with what is found for the La–O polyhedra in our simulations. However, no direct evidence of the existence of Er–O–Er linkages were found in the experiment (see Fig. 10). At very low concentrations RE ions appear to act as network modifiers, generating NBO RE–O– Si bonds in a silicate network. As the concentration of RE ions are increased, RE–O–RE linkages, associated with RE clustering, form which can lead to further phase-separation or precipitation. The formation of these linkages have been studied by [29] Si MAS–NMR spin-lattice relaxation experiments which show that Nd3þ tend to cluster in SiO2 even at ppm concentrations [26]. Further EXAFS studies of Nd3þ –SiO2 provide evidence of Nd–O–Nd linkages [27]. Several experimental results show that RE ions tend to cluster regardless of their concentration in highly polymerized silicate glasses and liquids. McGahay and Tomozawa [28] showed that even a few 1/1000 of a ppm of RE ions in silicate glasses lead to clustering and eventually to phase separation. In comparison to MD simulations of Eu containing soda silicate glasses [15], these simulations
were larger, included different concentrations of the lanthanide ions, and followed a systematic substitution approach as performed in the experiments. Nonetheless, comparisons between the simulations can still be made. Cormier et al. found that with the addition of Na the bond length of , where the Eu–O lengthened from 2.49 to 2.60 A co-ordination number of Eu was 4.2 O atoms in vitreous silica and 5.9 O atoms in Na2 O–2SiO2 for the Eu–O distance. The using a cutoff of 3.2 A La glass simulations are consistent with the erbium oxide simulations in that the La–O bond length in pure silica to 2.53 A in increased from 2.45 A the soda silicate glass. The co-ordination number of La containing glasses goes from 4.7 in the pure silica to 6.5 in the soda silicate glasses. Although such trends are similar, there are differences in the co-ordination environments between the two simulations due to differences in the potential models. The bond angle distribution of O–Eu–O was found to have two broad maxima, one at 50° and a second at 74°. In contrast, the O–La–O angle in La containing glasses show a very small peak at about 55°, a large peak at 80° and another peak at around 150°. The Eu3þ ion is bonded to NBO atoms where none of the polyhedra were found to have high symmetry. The erbium oxide simulations also show that Eu3þ ions prefer a sodium rich region though less well defined. In the La soda silicate simulations the distribution of the polyhedra symmetries were obtained. In the larger La containing glass simulations, the heterogeneity of the structures makes it difficult to distinguish distinct domains for the Na ions. Further simulations will be necessary to determine the propensity of partitioning amongst heterogeneous domains. Individual differences also appear in the number of free O atoms that are generated by the presence of a lanthanide ion, which is lower in the La glass simulations than in the Eu simulations. Several differences between the simulations should be noted. These are in the simulation size: 400 atoms with two Er ion and 1600 atom with 12–44 La ions; quench rates of: 1016 K/s for the erbium oxide simulations and 1013 K/s this work, and different potential parameterization that likely affect the results. In general, the MD simulations show that La3þ and Eu3þ appear to form quasi-molecular
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complexes that are relatively stable. This is consistent with the general phenomena in glass systems where network modifiers form their own environment. Finally, high-temperature calorimetry studies have shown the ability of La ions to perturb the network and compete for oxygen atoms [29]. The isolation of oxygen atoms (free-oxides) away from the silicate network backbone is believed to occur implying that there is a phase-ordered region rich in La. Further verification of the propensity of clustering in the MD simulations has been carried out and will be reported elsewhere as a second paper in this series. It is found that the driving forces which lead to clustering are an interplay between formation energies, effective molar volumes of the cation polyhedron and the configurational entropy. Clustering at the atomic level is predicted to occur in the simulated soda silicate glasses. The structural properties reported here are real, at least for the MD simulations, and await further validation from experiment.
5. Conclusion Lanthanum containing soda silicate glasses were investigated using MD simulations. It was found that the La cation has an average co-ordination of 6.5 oxygen atoms with an average bond . The MD simulations reveal that length of 2.5 A La ions act as network modifiers and generate NBO bonds which de-polymerize the glass structure. Adding La to the soda silicate glasses leads to the production of Q2 species at the expense of Q4 species. In addition, it is observed that the La ions tend to cluster, forming La–O–La linkages that, in some cases, isolate oxygen atoms away from the silica network.
Acknowledgements This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences, Department of Energy. This research was performed in the William R. Wiley Environmental Molecular Sciences Laboratory, a national scien-
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tific user facility sponsored by the Department of Energy, Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory. Pacific Northwest Laboratory is operated for the Department of Energy by Battelle.
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