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Molecular dynamics calculations for Mg3Al2Si3O12 (pyrope) and Ca3Al2Si3O12 (grossular) glass structures
ELSEWIER
Journal of Non-Crystalline
Solids 191(1995)
249-259
Molecular dynamics calculations for Mg 3Al 2Si 3O12( pyrope) and Ca 3Al 2Si 30 12( grossular) glass structures Masayuki Okuno aY *, Katsuyuki Kawamura b a Department of Earth Sciences, Faculty of Science, Kanazawa University, Kanazawa, 920-11, Japan ’ Department of Earth and Planetary Sciences, Faculty of Science, To&~0Institute of Technology, Tokyo, 152, Japan Received 20 September
1994;
revised manuscriptreceived 14 April 1995
Abstract The structures of pyrope (Mg,Al,Si,O,,) and grossular (Ca&Si,O,,) glasses at 300 K have been analyzed by molecular dynamics (MD) simulation techniques. The calculated glass structures have been compared with the structures obtained by the X-ray diffraction method. The averaged structures are in good agreement with the results of X-ray analyses, indicating that these MD-derived structures represent well the real glass structures. The calculated pair correlation functions of Si-0 and Al-O pairs for pyrope glass show broader peaks than those of grossular glass, which may indicate that Mgzf ions give a larger effect on the network structure of SiO, and AlO, tetrahedra. The calculated structures include Al-O-Al arrangements, which indicate that these structures do not well obey the aluminum avoidance principle. Numbers of AlO, tetrahedra in these glasses show the presence of Q4 species greater than SiO, tetrahedra. In these glasses, the O/(Si + Al) ratios are 2.4. Therefore, it is expected that some A13+ ions work as network modifier ions in these glasses.
1. Introduction Structural information about silicate liquids is important to understand crystal nucleation and growth process from the liquid in the field of glass technology and the dynamic processes of magma formation and evolution and mineral crystallization from magma in the field of earth sciences. X-ray and neutron diffraction, extended X-ray absorption fine structure (EXAFS), Raman and nuclear magnetic resonance (NMR) spectroscopic techniques have been
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author. Tel: + 81-762 64 5728. Telefax:
+ 81-
0022-3093/95/$09.50 8 1995 Elsevier Science B.V. All rights reserved SSDI 0022-3093(95)00320-7
extensively applied to the molten and vitreous silicates to reveal their structures [l-13]. Knowledge of the structures of Mg,Al,Si,O,, (pyrope) and Ca,Al,Si,O,, (grossular) glasses are important for understanding the melting and crystallization process of aluminum silicates and are also important in the geology of the magma process. Neuvill and Richet [14] measured the viscosities of supercooled liquids of Mg,A12Si30,,-Ca3Al,Si3012 system using a creep apparatus. 29Si NMR investigations [13] for network-modifying cations in silicate and aluminum silicate glasses have indicated that smaller, more highly charged cations create a greater variety in the distribution of SiO, and AlO, tetrahedra. The structures of Mg,Al,Si,O,, and Ca,Al,
250
M. Okuno, K. Kawamura/Journal
of Non-Crystalline
Si,O,, glasses have been investigated by X-ray diffraction to report the principal structural information [3]. However, the determination of the detailed structures of multiple component glasses such as Mg,Al,Si,O,, (3MgO : Al,O, : 3Si0,) and Ca,Al,Si,0,,(3CaO : Al,O, : 3Si0,) glasses by a normal X-ray diffraction method is difficult. With X-ray diffraction techniques [3], only the average atomic distances and coordination numbers of nearest T-O (T = Si and Al), O-O, Mg-0 and Ca-0 pairs were estimated. Atomic pai$ contributing to the structure in the range of r > 3 A have not been determined in detail. Recently, molecular dynamics (MD) calculations have been applied to the structure determination of silicate liquids and glasses in the fields of earth sciences and glass technology [15,16]. It has become a powerful tool for investigation of molten and amorphous materials. In the present study, we reproduce the experimental results for Mg,Al,Si30i2 and Ca,Al,Si,O,, glasses and investigate the distributions of individual atomic pairs in these glasses by the MD calculations.
2. Method The method of molecular dynamics calculation used in this study has been described in detail by Mauri and Kawamura 1171.In the present study, the pair potentials of the Busing approximation of Born-Mayer-Huggins’ form without the dispersion terms are used. This potential function consists of a Coulombic and repulsion terms: U( rij) = ZiZje2/rij +fO( bi + bj) Xexp{(f+ + aj - rij)/(bi
+b,)},
(1)
where Zi is the formula charge of ion i, e is the unit charge, rij is the distance between ions i and j, f,, is a constant (= 6.9472 X lop9 dyn), and a and b are values related to the radius and compressibility of the ion, respectively. The calculation of the Coulombit terms was carried out using the Ewald sum method. The parameters a and b were determined empirically to reproduce crystal structures by Kawamura 1181. The parameters used in this study are given in Table 1.
Solids 191 (1995) 249-259
Table 1 Numbers of atoms and their parameters of the pair potentials used in the MD calculations Atom
Number
w
2
a (A)
b (A)
0
768 128 192 192 a 192 b
16.00 26.98 28.08 24.31 40.08
-2.0 3.0 4.0 2.0 2.0
1.629 1.056 1.012 1.161 1.429
0.085 0.080 0.080 0.080 0.080
Al Si Mg Ca
’ For pyrope glass b For grossular glass
Periodic boundary conditions were applied to the rectangular basic cells containing 1280 ions in total for Mg,Al,Si,O,, and Ca,Al,Si,O,, compositions. The number of each ion of these compositions is given in Table 1. The starting arrangements of ions used in this study were those of the pyrope and grossular crystals. The random states for liquid structures were obtained by melting these crystals at 12 000 K. These melt structures were equilibrated at 4000 K by holding the temperature for about 50 ps. After the steady states of total energies were achieved, the temperatures were reduced to 3000 K for the next 45 ps for pyrope melt and 35 ps for grossular melt, then to 2000 K for 74 ps and 40 ps, and to 1000 K for 46 ps and 55 ps and finally to 300 K for the last 35 ps and 49 ps, respectively. The rate of temperature decrease was -0.04 K/fs. For comparison of the results of MD calculations with the observed S . i(S) and G(r) data obtained by X-ray diffraction, S. i(S) and G(r) curves were calculated using the MD-derived data. The interference function, S - i(S) (S = (4n/h) sin 8, and 28 and h are the scattering angle and the X-ray wavelength, respectively) can be calculated using the MD-derived pair correlation function (PCF), g(r): S-i(S)=
C
C
i
j
X
NiNjfits)fiCs)/
/4rrpr[
C
L
Nf(S)
kk
gij( r) - I] sin( sr) dr
I
(2)
in which fi(S) is the X-ray scattering factor. In this study, we carried out the reverse Fourier transformations of this S. i(S) to obtain the G(r) curve that
M. Ohno, Table 2 Atomic distance (A), coordination Glass:
K. Kawamura /Journal
numbers
[N], and O-T-O
Pyrope
Pyrope
(MD)
(X-ray) [31
Si-0 Al-0 o-o Mg-0 Ca-0 0-Si-0 o-Al-0 Si-0-Si si-O-AI AI-O-AI
1.62[4.0] 1.75[4.11 2.63 2.01[4.2] -
1.68[4.1] a
109.3(6.9) 108.6(16.3) 156.5t12.4) 143.5(15.4) 134.4(19.4)
-
Density (g/cm31
2.47
2.77
2.6 2.1[4.8]
of Non-Crystalline
and T-O-T Pyrope crystal [ 191 1.635[4.0] 1.88ti6.01 _ 2.271[8.0] _
Solids 191 (1995) 249-259
angles (deg) for pyrope and grossular Grossular
Grossular
(MD)
(X-ray)
1.62[4.0] 1.75L4.01 2.64 _
251
glasses (T = Si and Al)
[31
Grossular crystal [20]
1.7q4.51 a
1.64[4.0] 1.95[6.0] -
_ _
130.0 _
2.35[5.1] 109.3c6.5) 109.101.3) 155.1(12.6) 146.0f13.8) 137.8(16.0)
2.4[7.1-7.41 _ _ -
135.7 -
2.582 b
2.44
2.85
2.594 b
_
2.41[8.0] _ -
a T-O distance (T = Si and Al). b Ref. [21].
was compared with the observed curves by X-ray measurements.
3. Results 3.1. Density The densities obtained by the MD ‘calculations are shown in Table 2 together with the experimental data
PyropetMgaAI,Si,Or,)
glass, 300K, Nd2.80
[3] and the data of pyrope and grossular crystals [19,20]. MD-derived density data of these glasses are smaller than those of corresponding garnet crystals. The calculated densities are smaller than experimental densities of these glasses by ll.O-14.0%. These discrepancies were probably caused by the the fully ionic potential used and extremely rapid quenching (-0.04 K/fs) in the MD calculations. These kinds of discrepancies have been reported by Xu et al. [22] in MD calculations of Na,O-B,O, glasses. There-
Grossutar(Ca,At,Si,O1,)
Fig. 1. Stereoscopic snapshots of ions at 300 K for pyrope (Mg,Al,Si,O,,) and grossular medium open circles, small open circles indicate 0, Mg (pyrope), Ca (grossular), and Si/AI
glass, 300K, NdBO
(Ca3Al,Si301,) glasses. ions, respectively.
large
open circles,
M. Okuno, K. Kawamura / Journal of Non-Crystalline
252
fore, these may indicate that the glass structure obtained by MD calculation has some structural features of the supercooled liquid state. 3.2. Calculated general structures The stereoscopic snapshots given by the MD calculation for pyrope and grossular glasses at 300 K are shown in Fig. 1. These snapshots represent a pr$ of the total glass structure. The bonds (< 2.0 A) between Si/Al and 0 ions are drown in the figures.
6000 1
(b) Pyrope g~rss
glass
5000
----
Mg-0
4000 -
------
o-o
3000-
For these two glasses, all the Si and Al ions have tetrahedral coordination of oxygens and many Si and Al ions have three or four bridging oxygens. The networks of TO&T = Si and Al) tetrahedra are partly broken. In these structures, three- to five-membered rings of TO, tetrahedra were observed. The tetrahedral coordination of Si and Al ions in these glasses is consistent with the coordination number obtained by X-ray diffraction measurements [3]. However, information on the bridging oxygen and ring structure of TO, tetrahedra has not been obtained from the X-ray
““Y
(a) Pyrope
p
Solids I91 (1995) 249-259
Si-0 AI.0 600’
- - - -
Si-Si Si.AI Al-Al
I
2000-
8 :: 1: II
IO00 0 I 2
1
, i I _
,‘..
.I ----__ 1 3
Z.U
4.0
r(;P)
4)
6000
800 Cc) Crossular
glass
(d) Grossular -
I
----
glass 4 ‘I
si-o
Al.0 600’
- - - -
Si-Si Si-AI AI-AI
400’
200-
0 .. 2.0
1 3.0 r(d)
Fig. 2. Individual pair correlation
functions (PCP) for (a) and (b) pyrope and (c) and Cd) growhr
gh.~s
at XNJ K.
M. Okuno, K. Kawamura / Journal of Non-Crystalline
diffraction study. The pair correlation functions of individual atomic pair of pyrope and grossular glasses can also be calculated by the MD method (Fig. 2). The most probable nearest-neighbour distances for Si-0, Al-O, O-O, Mg-0, Ca-0 pairs in these glasses obtained by the MD calculations are listed in Table 2. The detailed structural information are discussed quantitatively in a later section.
Solids 191 (1995) 249-259
253
’ (a) Pyrope
2.0 -
glass
-
MD talc.
--- - X-rayohs.
3.3. Calculation of the interference jmction S . i(S) The interference function, S. i(S), can be calculated using the pair correlation function (PCF), gij(r), obtained by MD calculation 1231. In the present study, in order to compare with the experimental S. i(S) curves [3], the S. i(S) curves of pyrope and grossular glasses were calculated by using the results of MD calculations. Further, G(r) curves of these
-2.0 I 0
I 1
I 2
I 3
1 4
1 5
r(A) @) Grossular glass -
2.0
MD talc.
----
x-ray ohs.
1.0 (a) Pympe
glass
-MD
-- - -
talc. X-ray obs, s 0
0.0
-1.0
-2.0
!
0
I
1
1
2
I
3
8
4
I
5
r(A)
Fig. 4. The G(r) curves for (a) pyrope and (b) grossuhu glasses. The solid and broken lines show the calculated and measured [3] curves, respectively.
glasses were recalculate! by using MD-derived S. i(S) data (0 d S & 16.0 A-‘). The calculated S . i(S) curves and G(r) curves are given in Figs. 3 and 4, respectively, together with the experimental curves obtained by X-ray diffraction [3].
4. Discussion -3.0
0
10
15
20
4.1. The interference function S . i(S)
s(uA) Fig. 3. Calculated (solid lines) and measured [3] (broken S. i(S) curves for (a) pyrope and (b) grossular glasses.
lines)
There are good agreements between the measured and calculated S * i(S) curves of the grossular glass
254
M. Okuno, K. Kawamura /Journal
of Non-Crystalline
in Fig. 3. The calculated and observed S . i(S) curves of pyrope glass @so resemble each other. However, around S = 10 A-‘, the calculated curve dose not agree soowe with the observed one. The peak at S = 9.5 A-’ in the calculated 5. i(S) curve of pyrope glass is contributed by Mg-0 pairs. However, the peak of first neighbouring Mg-0 pairs (r = 2.1 A) on the MD-derived G(r) curve is similar to that on the observed G(r) curve. Therefore, this discrepancy on the S * i(S) curve of pyrope glass does not seriously influence the glass structure. These facts indicate that MD-calculated glass structures represent the real glass structures very well. There are good agreements between the calculated and observed G(r) curves for these glasses in Fig. 4. These indicate that the framework structures of SiO, and AlO, tetrahedra obtained by MD calculations are consistent with the results of the X-ray diffraction experiments. Therefore the results and discussions in the following sections may be significant. Some discrepancies between the calculated and observed results are partly the results of calculation errors (for example, limited numbers of atoms) of the MD method as well as the experimental and calculation errors of X-ray analyses. 4.2. Pair distributions and coordinations
Solids 191 (1995) 249-259 6
1
(a) pyrope
P
0 Y6
I
glass 27
/
/’
0'4-
2-
o0
-
,-_
,
1
2
1 3
I 4
I 5
I 6
10 1
(b) grossular
glass
6 1
0
1
2
3
4
5
-I
6
r/A Fig. 5. Measured D(r) curves for (a) pyrope and (b) grossular glasses (after Okuno and Marumo 131).Corresponding ionic pairs obtained by MD calculations are shown on the curves (S-0, Al-O, etc.).
The PCF curves of Si-0,
Al-O, O-O, Mg-0, Ca-0, Si-Si, and Si-Al atomic pairs in Fig. 2 show well resolved single peaks. The Al-Al pairs show multiple peaks or broad peaks of distributions. Comparing the peak positions of these PCF curves with the radial distribution function (RDF) curves obtained by Okuno and Marumo [3] with X-ray diffraction (Fig. 5), the position of the first peak of the observed RDF curve for pyrope glass agrees with those of the calculated PCF curves of Si-0 and Al-O atomic pairs, the seco?d peak with Mg-0 pairs, the shoulder at, r = 2.5 A with O-O pairs, the shoulder 0at r = 2.9 A with Al-Al pairs, the peak at r = 3.3 A with Si-Si, Si-Al, Al-Al pairs, respectively. The observed RDF curve for grossular glass can be explained equally well by atomic pair distributions obtained by MD calculatifn. However, short Al-Al atomic pairs (about 2.75 A) can be found in Fig: 2(b). It is difficult to distinguish the existence of these Al-Al pairs on the RDF curves obtained by the
X-ray method, which suggests the possibility of the existence of edge-sharing AlO, tetrahedra. However, we can find no short Al-Al atomic pairs on the curves of grossular glass (Fig. 2(d)). Therefore, these short Al-Al pairs were caused by the large Coulomb force of Mg2’ ions. By the way, the peaks of Si-0 and Al-O pairs in pyrope glass are wider than those in grossular glass (Fig. 6). These results may indicate that small Mg2’ ions give larger deformations to SiO, and AlO, tetrahedra than do Ca2+ ions. These are consistent with the small short-range order arameter of the Mg2’ ion [4,5] and wide NMR 29Si linewidth [13] in MgSiO, glass. Fig. 7 shows the coordination distributions obtained by the MD method. The coordination numbers of Si and Al in these two glasses are about 4. However, that of Al in the pyrope glass is a little larger than 4. Also these distributions indicate that
M. Okuno, K. Kawamura / Journal of Non-Crystalline Solids 191 (1995) 249-259
the coordination numbers of Mg and Ca are about 4.5 and 5.5, respectively. The average coordination numbers estimated from the data of coordination number distributions and pair correlation functions are listed in Table 2. The coordination numbers of Al, Mg and Ca are smaller than those in garnet crystals (Table 2). These coordination differences between garnet crystals and glasses are in agreement with the results of the X-ray diffraction experiments [3]. The MD-derived interatomic distances and coordination numbers of Si-0 and Al-9 pairs for py,rope and gryssular glasses are 01.62 A (4.01, 1.75 A (4.1), 1.62 A (4.0) and 1.75 A (4.01, respectively. The averaged T-O distance (T = Al and Si) calcu-
(a) pyrope
glass
255
---
S-0 AI-0
I
S.O$ 2 z” g ._ 2 .E ‘z 8
6.0-
4.0 -
V
2.0 -
0
,
1
1
2
I
3 r(A)
GOOD,
1
(a) Si-0 5000
;
-
Pyrope
----
Grossular
glass
1
glass
;’ 4000
5
ii
-
5
a
3000s
5 2 x ‘3 .i B 8
zooo-
1000
i
6.0.
4.0-
V
2.0 01
1.0
1.5
r(K)
2.0
2.5
1
(b) Al-0
-
Pyrope
----
Grossulnr
glsss
2
r(A)
3
4
Fig. 7. Coordination number distributions of ionic pairs for (a) pyrope and (b) grossular glasses at 300 K.
glass
3000
$
2000
lnoa I-
T-
-4 2.5
Fig. 6. Comparison of the individual pair correlation functions for (a) Si-0 and (b) M-0 between pyrope and grossular glasses.
lated froOmSi-0 and Al-O distances for these glasses is 1.67 A. This result is consistent with the observed T-O distance for pyrope glass obtained by X-ray analysis. However, for grossular glass it is somewhat smaller than the observed one. MD-derived Mg-0 and Ca-0 interatomic distances and coordination numbers are a little smaller than the observed values. These small calculated values are probably caused by the extremely rapid quenching in the MD calculation. These are consistent with the small calculated densities of these glasses. These results on the interatomic distances and coordination numbers of Si-0
M. Okuno, K Kawamura / Journal of Non-Crystalline Solids 191 (1995) 249-259
256
-----
Pyrope glass Grossular gla.=a
I ihI
)
\-
10000
4000-
-
ryrope
------
glass
Grossular glass
/y : ';
; moo0
i
E t
6OO0
4001I-
2oor I-
0
T
rio
80
60
o-s-0
140
120
100
O-AI-O
nnglc(o)
MO
nnglc(“)
IlOO-
coo
l
-
ryropcglass
-----
Grosshw
glass
;
,**,I
ano-
600 -
ZOfl
100
0
:
i
lar )
si-0.si mrgle(0) 4w
-
Pyropc
-----
Gros.wlorglass
glass
300
100
DI-4
I
100
’
1
120
’
'140
AI-0-Alanglc~)
u
’
160
’
10
100
120
140 SI-O-AIwglc(~)
160
M. Okuno, K. Kawamura / Journal of Non-Crystalline Solids 191 (1995) 249-259 Table 3 the percentage
of Qi species (i = number of bridging
257
oxygensin tetrahedron)
Glass
Cation
Qo
Q2
Q3
Q‘l
Pyrope
Si Al averaged
0.0 0.0 0.0
5.77 0.0 3.47
19.40 4.58 13.47
40.76 29.41 36.22
34.07 66.11 46.84
Grossular glass (300 K)
Si Al averaged
0.52 0.0 0.31
8.34 0.78 5.32
18.75 2.34 12.19
38.56 26.56 33.79
33.85 70.31 48.43
MgSiO, glass (300 K) [16]
Si
3.1
41.8
30.1
7.7
glass (300 K)
and Al-O pairs may indicate that the shapes of SiO, and AlO, tetrahedra were represented very well by MD calculations. However, in order to calculate more precisely the coordination of the modifier ions (Mg and Ca), Igng-time MD calculations of the system with larger numbers of ions need to be done. However, the differences of coordination numbers and interatomic distances of Mg-0 and Ca-0 pairs between pyrope and grossular glasses found in the results of MD calculation are consistent with those determined by X-ray analyses. 4.3. O-T-O
and T-O-T
angle distributions
Fig. 8(a) and (b) show the 0-Si-0 and O-Al-O bond angle distributions in these glasses. All these distribution curves have a single peak at about 109”. The averaged O-T-O angles are listed in Table 2. These data suggest that Si and Al atoms form AlO, and SiO, tetrahedra in these glasses, consistent with the data of coordination distributions. The calculated distributions of 0-Si-0 angles are smaller than those of O-Al-O angles. This wide distribution of O-Al-O angles may indicate that the individual AlO, tetrahedron is more deformed than the SiO, tetrahedron. Further, the SiO, and AlO, tetrahedra of pyrope glass are more deformed than those of grossular glass. As well as the results for Al-O and Si-0 pair distributions, these results indicate that the
Q,
17.3
AlO, tetrahedron is softer than the SiO, tetrahedron and the Mgzf ion with small Mg-0 distance and coordination number gives larger deformation to AlO, and SiO, tetrahedra than do Ca2+ ions. Figs. 8(c)-(e) show the Si-O-S& Si-O-Al and Al-O-Al angle distributions. The averaged T-O-T angles are listed in Table 2. The Si-0-Si angles are larger than the Si-O-Al and Al-O-Al angles by about 10” and 20” in these two glasses. The angle relation, Si-0-Si > Si-O-Al > Al-O-Al, is consistent with the decrease in T-O-T angle in SiO, (148.7”), albite (NaAlSi,O,; 146.4”) and anorthite (CaA12Si20,; 136.4”) melt structures with increasing Al contents [24,25]. The AlO, tetrahedron is larger than the SiO, tetrahedron, so the T-O-T angles decrease in the AlO,-rich region because of the breakdown of the framework structure with large unstable gaps. On the other hand, Mg2+ ions in pyrope glass an,d Ca2+ ions in qossular glass have ionic radii 0.8 A (IV) and 1.08 A (IV) [26], respectively. Therefore, it is expected that the grossular glass with large Ca2+ ions has large Si-O-Al and Al-O-Al angles. The fact there is almost no difference of Si-0-Si angles between these two glasses can be explained by small amounts of Mg’+ or Ca2+ ions around the SiO, framework which is electrically neutral. For the tecto-aluminosilicate glasses with Na+ or Ca2+ ions, Murdoch et al. [13] have investigated the relations between the NMR
Fig. 8. (a) 0-Si-0 bond angle distributions in pyrope (solid line) and grossular (broken line) glasses. (b) O-Al-0 bond angle distributions in pyrope (solid line) and grossular (broken line) glasses. (c) Si-0-Si bond angle distributions in pyrope (solid line) and grossular (broken line) glasses. (d) Si-O-Al bond angle distributions in pyrope (solid line) and grossular (broken line) glasses. (e) Al-O-Al bond angle distributions in pyrope (solid line) and grossular (broken line) glasses.
258
hi. Okuno, K. Kawamura / Journal of Non-Crystalline
linewidth of 29Si and Si/Al ratios and reported that these glasses obey Loewenstein’s aluminum avoidance principle [27]. On the other hand, Sharma et al. [28] have reported some disorder of Si-Al alternating arrangement in anorthite glass. In the present work, the ratios of numbers of Si-0-Si, Si-O-Al and Al-O-Al are 1.7 : 3.5 : 1.0 for pyrope glass and 1.6 : 4.1: 1.0 for grossular glass. These ratios indicate the existence of Al-O-Al arrangements. These also indicate that the structures of these glasses do not well obey the aluminum avoidance principle. It is supposed that energetically unfavorable Al-Al arrangements were caused by extremely rapid quenching in MD calculations and the existence of nonbridging oxygens. Each distribution of Si-O-Al and Al-O-Al angles of grossular glass has only one maximum. On the other hand, the distributions of the Si-O-Al and Al-O-Al angles of pyrope glass have two or three maxima and are wide. This may also indicate that small Mg2+ ions give larger deformations to the linkages of Si-O-Al and Al-O-Al than do Ca2+ ions. This fact is consistent with the wide distribution of O-Al-O angles in the pyrope glass. 4.4. Linkages of tetrahedra The number of non-bridging oxygen (NBO) is closely related to the linkage of AlO, and SiO, tetrahedra in the glasses. The NBO shows the end of the linkage of tetrahedra. The distribution of the number of bridging oxygens in a tetrahedron is shown in Table 3. Calculated distributions of NBO for pyrope and grossular glasses are similar (Table 3). Polymer species are represented by Qj species, where i is the number of bridging oxygen ions per Si and Al ions. The Qi species in Table 3 show that the network structures of these two glasses resemble each other. Comparing the distribution of NBO for pyrope glass with the result for MgSiO, glass [16], for SiO, tetrahedra, Q3 and Q4 are dominant in pyrope glass and Q1, Q, and Q, are dominant in MgSiO, glass. The averaged Q, numbers of MgSi03 glass [16] and pyrope glass by MD calculations are 2.19 and 3.28, respectively. These results are almost consistent with the average numbers of bridging oxygens (2.0 for MgSiO, glass and 3.2 for pyrope glass) estimated from the (Si, Al)/0 ratios in the glasses.
Solids 191 (1995) 249-259
However, the distributions of number of NBO for SiO, tetrahedra are different from those for AlO, tetrahedra in these glasses. For the SiO, tetrahedra, Q2, Q3 and Q4 are dominant but, for the AlO, tetrahedra, Q4 is dominant. The averaged numbers of bridging oxygens for SiO, and AlO, tetrahedra of the pyrope and grossular glasses are 3.0 and 3.6, respectively. These results indicate that many parts of the ends of network structures are occupied by SiO, tetrahedra in these glasses. On the other hand, many parts of AlO, tetrahedra are linked to the other TO, tetrahedra. These also indicate that some A13+ ions work as network modifiers. These are consistent with the calculated average coordination number of Al in pyrope glass (= 4.1) which is a little larger than that of Sit = 4.0). Maekawa et al. [29] reported that, in the 29Si NMR study on the NaO-Al,O,-SiO, glasses, aluminum favors the more polymerized environments, i.e., the smaller number of non-bridging oxygen atoms. This report is consistent with our results. Therefore, in Mg,Ai,Si,O,, and Ca,Ai, Si,O,, glasses, aluminum tends to be associated with Mg2+ and Ca2+ and to form MgAl,O,, MgA12Si20a, CaAl,O, and CaAl,Si,O, and additional 2MgO and 2CaO modify SiO,.
5. Conclusions The structures of Mg,Al,Si,O,, (pyrope) and Ca,Al,Si,O,, (grossular) glasses have been calculated by the MD method and the detailed structures of these glasses were discussed. The following conclusions were obtained. (1) In the calculated structures, Si and Al atoms form SiO, and AlO, tetrahedra and the coordination numbers are almost four. These results are consistent with the structures obtained by X-ray experiments. (2) The S. i(S) and G(r) curves calculated by using the results of MD calculations agree well with the observed curves. This indicates that MD calculated structures well represent the real structures of these glasses. (3) The calculated pair correlation function curves of Si-0 and Al-O atomic pairs for the pyrope glasses show broader peaks than those of grossular glass, indicating that Mg2+ ions have a larger effect
M. Okuno, K. Kawamura / Journal of Non-Crystalline Solids 191 (I 995) 249-259
on the network structure mode of SiO, and AlO, tetrahedra. (4) MD-derived Mg-0 and Ca-0 distances and their coordination numbers are a little smaller than those obtained by X-ray analyses. These small discrepancies are probably caused by the extremely rapid quenches in the MD calculations. (5) The calculated structures of these glasses show the existence of Al-O-Al arrangements. This indicates that the structures do not obey the aluminum avoidance principle. The T-O-T angles decrease in the order of Si-0-Si, Si-O-Al and Al-O-Al in these glasses. (6) The distributions of numbers of NJ30 for these two glasses are similar to each other. However, those of AlO, tetrahedra are different from those of SiO, tetrahedra and show a large number of Qq. Therefore, it is expected that some A13+ ions work as network modifier ions. This study was partly supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture of Japanese Government (No. 0432023).
References 111M.
Taylor and G.E. Brown, Geochim. Cosmochim. Acta 43 (1979) 61. [21M. Taylor and G.E. Brown, Geochim. Cosmochim. Acta 43 (1979) 1467. [31 M. Okuno and F. Marumo, Mineral. J. 16 (1993) 407. [41 C. Yin, M. Okuno, H. Morikawa and F. Marumo, J. NonCryst. Solids 55 (1983) 131. 151CD. Yin, M. Okuno, H. Morikawa, F. Marumo and T. Yamanaka, J. Non-Cryst. Solids 80 (1986) 167.
259
[6] G.N. Greaves, A. Fontaine, P. Lagarde, D. Raoux and S.I. Gurman, Nature 293 (1981) 661. 171 A. Hardwick, E.J.W. Wittaker and G.P. Diakun, Miner. Mag. 49 (1985) 25. [81 B.O. Mysen, D. Virgo and F.A. Seifert, Rev. Geophys. Spacephys. 20 (1982) 353. [9] B.O. Mysen, Structure and Properties of Silicate Melts (Elsevier, Amsterdam, 1988). [lo] B.O. Mysen, in: Physical Chemistry of Magmas, ed. L.L. Perchuk and I. Kushiro (Springer, New York, 1991) p. 41. [ll] F. Seifert, B.O. Mysen and D. Virgo, Am. Mineral. 67 (1982) 696. [12] de Jong, K.D. Keefer, G.E. Brown and C.M. Taylor, Geochim. Cosmochim. Acta 45 (1981) 1291. [13] J.B. Murdoch, J.F. Stebbins and LS. Carmichael, Am. Mineral. 70 (1985) 332. [14] D.R. Neuvill and P. Richet, Geochim. Cosmochim. Acta 55 (1991) 1101. [15] Y. Matui and K. Kawamura, Nature 285 (1980) 648. [16] J.D. Kubicki and A.C. Lasaga, Phys. Chem. Miner. 17 (1991) 661. [17] Y. Matui and K. Kawamura, Mater. Sci. Earth Interior (Terra Scientific, Tokyo, 1984). [18] K. Kawamura, Personal Computer Molecular Simulation (Kaibundo, Tokyo, 1990) (in Japanese). [19] G.V. Gibbs and J.V. Smith, Am. Mineral. 50 (1965) 2023. [20] SC. Abraham and S. Geller, Acta Crystallogr. 11 (1958) 437. [21] W.A. Deer, R.A. Howie and J. Zussman, Rock-forming Minerals, Vol. lA, Orthosilicate (Longman, London, 1982). [22] Q. Xu, K. Kawamura and T. Yokokawa, J. Non-Cryst. Solids 104 (1988) 261. [23] Q. Xu, K. Kawamura and T. Yokokawa, Nippon Seramikkusu Kyokai Gakujutsu Ronbunshi 97 (1989) 1416. [24] Y. Waseda, The Structure of Non-Crystalline Materials (McGraw-Hill, New York, 1980). [25] M. Okuno and F. Marumo, Mineral. J. 11 (1982) 180. [26] R.D. Shannon and C.T. Prewitt, Acta Crystallogr. B25 (1969) 925. [27] W. Loewenstein, Am. Mineral. 39 (1954) 92. [28] S. Sharma, B. Simons and H.S. Yorder, Am. Mineral. 68 (1983) 1113. [29] H. Maekawa, T. Maekawa, K. Kawamura and T. Yokokawa, J. Phys. Chem. 95 (1991) 6822.
Journal of Non-Crystalline
Solids 191(1995)
249-259
Molecular dynamics calculations for Mg 3Al 2Si 3O12( pyrope) and Ca 3Al 2Si 30 12( grossular) glass structures Masayuki Okuno aY *, Katsuyuki Kawamura b a Department of Earth Sciences, Faculty of Science, Kanazawa University, Kanazawa, 920-11, Japan ’ Department of Earth and Planetary Sciences, Faculty of Science, To&~0Institute of Technology, Tokyo, 152, Japan Received 20 September
1994;
revised manuscriptreceived 14 April 1995
Abstract The structures of pyrope (Mg,Al,Si,O,,) and grossular (Ca&Si,O,,) glasses at 300 K have been analyzed by molecular dynamics (MD) simulation techniques. The calculated glass structures have been compared with the structures obtained by the X-ray diffraction method. The averaged structures are in good agreement with the results of X-ray analyses, indicating that these MD-derived structures represent well the real glass structures. The calculated pair correlation functions of Si-0 and Al-O pairs for pyrope glass show broader peaks than those of grossular glass, which may indicate that Mgzf ions give a larger effect on the network structure of SiO, and AlO, tetrahedra. The calculated structures include Al-O-Al arrangements, which indicate that these structures do not well obey the aluminum avoidance principle. Numbers of AlO, tetrahedra in these glasses show the presence of Q4 species greater than SiO, tetrahedra. In these glasses, the O/(Si + Al) ratios are 2.4. Therefore, it is expected that some A13+ ions work as network modifier ions in these glasses.
1. Introduction Structural information about silicate liquids is important to understand crystal nucleation and growth process from the liquid in the field of glass technology and the dynamic processes of magma formation and evolution and mineral crystallization from magma in the field of earth sciences. X-ray and neutron diffraction, extended X-ray absorption fine structure (EXAFS), Raman and nuclear magnetic resonance (NMR) spectroscopic techniques have been
* Corresponding 762 64 5746.
author. Tel: + 81-762 64 5728. Telefax:
+ 81-
0022-3093/95/$09.50 8 1995 Elsevier Science B.V. All rights reserved SSDI 0022-3093(95)00320-7
extensively applied to the molten and vitreous silicates to reveal their structures [l-13]. Knowledge of the structures of Mg,Al,Si,O,, (pyrope) and Ca,Al,Si,O,, (grossular) glasses are important for understanding the melting and crystallization process of aluminum silicates and are also important in the geology of the magma process. Neuvill and Richet [14] measured the viscosities of supercooled liquids of Mg,A12Si30,,-Ca3Al,Si3012 system using a creep apparatus. 29Si NMR investigations [13] for network-modifying cations in silicate and aluminum silicate glasses have indicated that smaller, more highly charged cations create a greater variety in the distribution of SiO, and AlO, tetrahedra. The structures of Mg,Al,Si,O,, and Ca,Al,
250
M. Okuno, K. Kawamura/Journal
of Non-Crystalline
Si,O,, glasses have been investigated by X-ray diffraction to report the principal structural information [3]. However, the determination of the detailed structures of multiple component glasses such as Mg,Al,Si,O,, (3MgO : Al,O, : 3Si0,) and Ca,Al,Si,0,,(3CaO : Al,O, : 3Si0,) glasses by a normal X-ray diffraction method is difficult. With X-ray diffraction techniques [3], only the average atomic distances and coordination numbers of nearest T-O (T = Si and Al), O-O, Mg-0 and Ca-0 pairs were estimated. Atomic pai$ contributing to the structure in the range of r > 3 A have not been determined in detail. Recently, molecular dynamics (MD) calculations have been applied to the structure determination of silicate liquids and glasses in the fields of earth sciences and glass technology [15,16]. It has become a powerful tool for investigation of molten and amorphous materials. In the present study, we reproduce the experimental results for Mg,Al,Si30i2 and Ca,Al,Si,O,, glasses and investigate the distributions of individual atomic pairs in these glasses by the MD calculations.
2. Method The method of molecular dynamics calculation used in this study has been described in detail by Mauri and Kawamura 1171.In the present study, the pair potentials of the Busing approximation of Born-Mayer-Huggins’ form without the dispersion terms are used. This potential function consists of a Coulombic and repulsion terms: U( rij) = ZiZje2/rij +fO( bi + bj) Xexp{(f+ + aj - rij)/(bi
+b,)},
(1)
where Zi is the formula charge of ion i, e is the unit charge, rij is the distance between ions i and j, f,, is a constant (= 6.9472 X lop9 dyn), and a and b are values related to the radius and compressibility of the ion, respectively. The calculation of the Coulombit terms was carried out using the Ewald sum method. The parameters a and b were determined empirically to reproduce crystal structures by Kawamura 1181. The parameters used in this study are given in Table 1.
Solids 191 (1995) 249-259
Table 1 Numbers of atoms and their parameters of the pair potentials used in the MD calculations Atom
Number
w
2
a (A)
b (A)
0
768 128 192 192 a 192 b
16.00 26.98 28.08 24.31 40.08
-2.0 3.0 4.0 2.0 2.0
1.629 1.056 1.012 1.161 1.429
0.085 0.080 0.080 0.080 0.080
Al Si Mg Ca
’ For pyrope glass b For grossular glass
Periodic boundary conditions were applied to the rectangular basic cells containing 1280 ions in total for Mg,Al,Si,O,, and Ca,Al,Si,O,, compositions. The number of each ion of these compositions is given in Table 1. The starting arrangements of ions used in this study were those of the pyrope and grossular crystals. The random states for liquid structures were obtained by melting these crystals at 12 000 K. These melt structures were equilibrated at 4000 K by holding the temperature for about 50 ps. After the steady states of total energies were achieved, the temperatures were reduced to 3000 K for the next 45 ps for pyrope melt and 35 ps for grossular melt, then to 2000 K for 74 ps and 40 ps, and to 1000 K for 46 ps and 55 ps and finally to 300 K for the last 35 ps and 49 ps, respectively. The rate of temperature decrease was -0.04 K/fs. For comparison of the results of MD calculations with the observed S . i(S) and G(r) data obtained by X-ray diffraction, S. i(S) and G(r) curves were calculated using the MD-derived data. The interference function, S - i(S) (S = (4n/h) sin 8, and 28 and h are the scattering angle and the X-ray wavelength, respectively) can be calculated using the MD-derived pair correlation function (PCF), g(r): S-i(S)=
C
C
i
j
X
NiNjfits)fiCs)/
/4rrpr[
C
L
Nf(S)
kk
gij( r) - I] sin( sr) dr
I
(2)
in which fi(S) is the X-ray scattering factor. In this study, we carried out the reverse Fourier transformations of this S. i(S) to obtain the G(r) curve that
M. Ohno, Table 2 Atomic distance (A), coordination Glass:
K. Kawamura /Journal
numbers
[N], and O-T-O
Pyrope
Pyrope
(MD)
(X-ray) [31
Si-0 Al-0 o-o Mg-0 Ca-0 0-Si-0 o-Al-0 Si-0-Si si-O-AI AI-O-AI
1.62[4.0] 1.75[4.11 2.63 2.01[4.2] -
1.68[4.1] a
109.3(6.9) 108.6(16.3) 156.5t12.4) 143.5(15.4) 134.4(19.4)
-
Density (g/cm31
2.47
2.77
2.6 2.1[4.8]
of Non-Crystalline
and T-O-T Pyrope crystal [ 191 1.635[4.0] 1.88ti6.01 _ 2.271[8.0] _
Solids 191 (1995) 249-259
angles (deg) for pyrope and grossular Grossular
Grossular
(MD)
(X-ray)
1.62[4.0] 1.75L4.01 2.64 _
251
glasses (T = Si and Al)
[31
Grossular crystal [20]
1.7q4.51 a
1.64[4.0] 1.95[6.0] -
_ _
130.0 _
2.35[5.1] 109.3c6.5) 109.101.3) 155.1(12.6) 146.0f13.8) 137.8(16.0)
2.4[7.1-7.41 _ _ -
135.7 -
2.582 b
2.44
2.85
2.594 b
_
2.41[8.0] _ -
a T-O distance (T = Si and Al). b Ref. [21].
was compared with the observed curves by X-ray measurements.
3. Results 3.1. Density The densities obtained by the MD ‘calculations are shown in Table 2 together with the experimental data
PyropetMgaAI,Si,Or,)
glass, 300K, Nd2.80
[3] and the data of pyrope and grossular crystals [19,20]. MD-derived density data of these glasses are smaller than those of corresponding garnet crystals. The calculated densities are smaller than experimental densities of these glasses by ll.O-14.0%. These discrepancies were probably caused by the the fully ionic potential used and extremely rapid quenching (-0.04 K/fs) in the MD calculations. These kinds of discrepancies have been reported by Xu et al. [22] in MD calculations of Na,O-B,O, glasses. There-
Grossutar(Ca,At,Si,O1,)
Fig. 1. Stereoscopic snapshots of ions at 300 K for pyrope (Mg,Al,Si,O,,) and grossular medium open circles, small open circles indicate 0, Mg (pyrope), Ca (grossular), and Si/AI
glass, 300K, NdBO
(Ca3Al,Si301,) glasses. ions, respectively.
large
open circles,
M. Okuno, K. Kawamura / Journal of Non-Crystalline
252
fore, these may indicate that the glass structure obtained by MD calculation has some structural features of the supercooled liquid state. 3.2. Calculated general structures The stereoscopic snapshots given by the MD calculation for pyrope and grossular glasses at 300 K are shown in Fig. 1. These snapshots represent a pr$ of the total glass structure. The bonds (< 2.0 A) between Si/Al and 0 ions are drown in the figures.
6000 1
(b) Pyrope g~rss
glass
5000
----
Mg-0
4000 -
------
o-o
3000-
For these two glasses, all the Si and Al ions have tetrahedral coordination of oxygens and many Si and Al ions have three or four bridging oxygens. The networks of TO&T = Si and Al) tetrahedra are partly broken. In these structures, three- to five-membered rings of TO, tetrahedra were observed. The tetrahedral coordination of Si and Al ions in these glasses is consistent with the coordination number obtained by X-ray diffraction measurements [3]. However, information on the bridging oxygen and ring structure of TO, tetrahedra has not been obtained from the X-ray
““Y
(a) Pyrope
p
Solids I91 (1995) 249-259
Si-0 AI.0 600’
- - - -
Si-Si Si.AI Al-Al
I
2000-
8 :: 1: II
IO00 0 I 2
1
, i I _
,‘..
.I ----__ 1 3
Z.U
4.0
r(;P)
4)
6000
800 Cc) Crossular
glass
(d) Grossular -
I
----
glass 4 ‘I
si-o
Al.0 600’
- - - -
Si-Si Si-AI AI-AI
400’
200-
0 .. 2.0
1 3.0 r(d)
Fig. 2. Individual pair correlation
functions (PCP) for (a) and (b) pyrope and (c) and Cd) growhr
gh.~s
at XNJ K.
M. Okuno, K. Kawamura / Journal of Non-Crystalline
diffraction study. The pair correlation functions of individual atomic pair of pyrope and grossular glasses can also be calculated by the MD method (Fig. 2). The most probable nearest-neighbour distances for Si-0, Al-O, O-O, Mg-0, Ca-0 pairs in these glasses obtained by the MD calculations are listed in Table 2. The detailed structural information are discussed quantitatively in a later section.
Solids 191 (1995) 249-259
253
’ (a) Pyrope
2.0 -
glass
-
MD talc.
--- - X-rayohs.
3.3. Calculation of the interference jmction S . i(S) The interference function, S. i(S), can be calculated using the pair correlation function (PCF), gij(r), obtained by MD calculation 1231. In the present study, in order to compare with the experimental S. i(S) curves [3], the S. i(S) curves of pyrope and grossular glasses were calculated by using the results of MD calculations. Further, G(r) curves of these
-2.0 I 0
I 1
I 2
I 3
1 4
1 5
r(A) @) Grossular glass -
2.0
MD talc.
----
x-ray ohs.
1.0 (a) Pympe
glass
-MD
-- - -
talc. X-ray obs, s 0
0.0
-1.0
-2.0
!
0
I
1
1
2
I
3
8
4
I
5
r(A)
Fig. 4. The G(r) curves for (a) pyrope and (b) grossuhu glasses. The solid and broken lines show the calculated and measured [3] curves, respectively.
glasses were recalculate! by using MD-derived S. i(S) data (0 d S & 16.0 A-‘). The calculated S . i(S) curves and G(r) curves are given in Figs. 3 and 4, respectively, together with the experimental curves obtained by X-ray diffraction [3].
4. Discussion -3.0
0
10
15
20
4.1. The interference function S . i(S)
s(uA) Fig. 3. Calculated (solid lines) and measured [3] (broken S. i(S) curves for (a) pyrope and (b) grossular glasses.
lines)
There are good agreements between the measured and calculated S * i(S) curves of the grossular glass
254
M. Okuno, K. Kawamura /Journal
of Non-Crystalline
in Fig. 3. The calculated and observed S . i(S) curves of pyrope glass @so resemble each other. However, around S = 10 A-‘, the calculated curve dose not agree soowe with the observed one. The peak at S = 9.5 A-’ in the calculated 5. i(S) curve of pyrope glass is contributed by Mg-0 pairs. However, the peak of first neighbouring Mg-0 pairs (r = 2.1 A) on the MD-derived G(r) curve is similar to that on the observed G(r) curve. Therefore, this discrepancy on the S * i(S) curve of pyrope glass does not seriously influence the glass structure. These facts indicate that MD-calculated glass structures represent the real glass structures very well. There are good agreements between the calculated and observed G(r) curves for these glasses in Fig. 4. These indicate that the framework structures of SiO, and AlO, tetrahedra obtained by MD calculations are consistent with the results of the X-ray diffraction experiments. Therefore the results and discussions in the following sections may be significant. Some discrepancies between the calculated and observed results are partly the results of calculation errors (for example, limited numbers of atoms) of the MD method as well as the experimental and calculation errors of X-ray analyses. 4.2. Pair distributions and coordinations
Solids 191 (1995) 249-259 6
1
(a) pyrope
P
0 Y6
I
glass 27
/
/’
0'4-
2-
o0
-
,-_
,
1
2
1 3
I 4
I 5
I 6
10 1
(b) grossular
glass
6 1
0
1
2
3
4
5
-I
6
r/A Fig. 5. Measured D(r) curves for (a) pyrope and (b) grossular glasses (after Okuno and Marumo 131).Corresponding ionic pairs obtained by MD calculations are shown on the curves (S-0, Al-O, etc.).
The PCF curves of Si-0,
Al-O, O-O, Mg-0, Ca-0, Si-Si, and Si-Al atomic pairs in Fig. 2 show well resolved single peaks. The Al-Al pairs show multiple peaks or broad peaks of distributions. Comparing the peak positions of these PCF curves with the radial distribution function (RDF) curves obtained by Okuno and Marumo [3] with X-ray diffraction (Fig. 5), the position of the first peak of the observed RDF curve for pyrope glass agrees with those of the calculated PCF curves of Si-0 and Al-O atomic pairs, the seco?d peak with Mg-0 pairs, the shoulder at, r = 2.5 A with O-O pairs, the shoulder 0at r = 2.9 A with Al-Al pairs, the peak at r = 3.3 A with Si-Si, Si-Al, Al-Al pairs, respectively. The observed RDF curve for grossular glass can be explained equally well by atomic pair distributions obtained by MD calculatifn. However, short Al-Al atomic pairs (about 2.75 A) can be found in Fig: 2(b). It is difficult to distinguish the existence of these Al-Al pairs on the RDF curves obtained by the
X-ray method, which suggests the possibility of the existence of edge-sharing AlO, tetrahedra. However, we can find no short Al-Al atomic pairs on the curves of grossular glass (Fig. 2(d)). Therefore, these short Al-Al pairs were caused by the large Coulomb force of Mg2’ ions. By the way, the peaks of Si-0 and Al-O pairs in pyrope glass are wider than those in grossular glass (Fig. 6). These results may indicate that small Mg2’ ions give larger deformations to SiO, and AlO, tetrahedra than do Ca2+ ions. These are consistent with the small short-range order arameter of the Mg2’ ion [4,5] and wide NMR 29Si linewidth [13] in MgSiO, glass. Fig. 7 shows the coordination distributions obtained by the MD method. The coordination numbers of Si and Al in these two glasses are about 4. However, that of Al in the pyrope glass is a little larger than 4. Also these distributions indicate that
M. Okuno, K. Kawamura / Journal of Non-Crystalline Solids 191 (1995) 249-259
the coordination numbers of Mg and Ca are about 4.5 and 5.5, respectively. The average coordination numbers estimated from the data of coordination number distributions and pair correlation functions are listed in Table 2. The coordination numbers of Al, Mg and Ca are smaller than those in garnet crystals (Table 2). These coordination differences between garnet crystals and glasses are in agreement with the results of the X-ray diffraction experiments [3]. The MD-derived interatomic distances and coordination numbers of Si-0 and Al-9 pairs for py,rope and gryssular glasses are 01.62 A (4.01, 1.75 A (4.1), 1.62 A (4.0) and 1.75 A (4.01, respectively. The averaged T-O distance (T = Al and Si) calcu-
(a) pyrope
glass
255
---
S-0 AI-0
I
S.O$ 2 z” g ._ 2 .E ‘z 8
6.0-
4.0 -
V
2.0 -
0
,
1
1
2
I
3 r(A)
GOOD,
1
(a) Si-0 5000
;
-
Pyrope
----
Grossular
glass
1
glass
;’ 4000
5
ii
-
5
a
3000s
5 2 x ‘3 .i B 8
zooo-
1000
i
6.0.
4.0-
V
2.0 01
1.0
1.5
r(K)
2.0
2.5
1
(b) Al-0
-
Pyrope
----
Grossulnr
glsss
2
r(A)
3
4
Fig. 7. Coordination number distributions of ionic pairs for (a) pyrope and (b) grossular glasses at 300 K.
glass
3000
$
2000
lnoa I-
T-
-4 2.5
Fig. 6. Comparison of the individual pair correlation functions for (a) Si-0 and (b) M-0 between pyrope and grossular glasses.
lated froOmSi-0 and Al-O distances for these glasses is 1.67 A. This result is consistent with the observed T-O distance for pyrope glass obtained by X-ray analysis. However, for grossular glass it is somewhat smaller than the observed one. MD-derived Mg-0 and Ca-0 interatomic distances and coordination numbers are a little smaller than the observed values. These small calculated values are probably caused by the extremely rapid quenching in the MD calculation. These are consistent with the small calculated densities of these glasses. These results on the interatomic distances and coordination numbers of Si-0
M. Okuno, K Kawamura / Journal of Non-Crystalline Solids 191 (1995) 249-259
256
-----
Pyrope glass Grossular gla.=a
I ihI
)
\-
10000
4000-
-
ryrope
------
glass
Grossular glass
/y : ';
; moo0
i
E t
6OO0
4001I-
2oor I-
0
T
rio
80
60
o-s-0
140
120
100
O-AI-O
nnglc(o)
MO
nnglc(“)
IlOO-
coo
l
-
ryropcglass
-----
Grosshw
glass
;
,**,I
ano-
600 -
ZOfl
100
0
:
i
lar )
si-0.si mrgle(0) 4w
-
Pyropc
-----
Gros.wlorglass
glass
300
100
DI-4
I
100
’
1
120
’
'140
AI-0-Alanglc~)
u
’
160
’
10
100
120
140 SI-O-AIwglc(~)
160
M. Okuno, K. Kawamura / Journal of Non-Crystalline Solids 191 (1995) 249-259 Table 3 the percentage
of Qi species (i = number of bridging
257
oxygensin tetrahedron)
Glass
Cation
Qo
Q2
Q3
Q‘l
Pyrope
Si Al averaged
0.0 0.0 0.0
5.77 0.0 3.47
19.40 4.58 13.47
40.76 29.41 36.22
34.07 66.11 46.84
Grossular glass (300 K)
Si Al averaged
0.52 0.0 0.31
8.34 0.78 5.32
18.75 2.34 12.19
38.56 26.56 33.79
33.85 70.31 48.43
MgSiO, glass (300 K) [16]
Si
3.1
41.8
30.1
7.7
glass (300 K)
and Al-O pairs may indicate that the shapes of SiO, and AlO, tetrahedra were represented very well by MD calculations. However, in order to calculate more precisely the coordination of the modifier ions (Mg and Ca), Igng-time MD calculations of the system with larger numbers of ions need to be done. However, the differences of coordination numbers and interatomic distances of Mg-0 and Ca-0 pairs between pyrope and grossular glasses found in the results of MD calculation are consistent with those determined by X-ray analyses. 4.3. O-T-O
and T-O-T
angle distributions
Fig. 8(a) and (b) show the 0-Si-0 and O-Al-O bond angle distributions in these glasses. All these distribution curves have a single peak at about 109”. The averaged O-T-O angles are listed in Table 2. These data suggest that Si and Al atoms form AlO, and SiO, tetrahedra in these glasses, consistent with the data of coordination distributions. The calculated distributions of 0-Si-0 angles are smaller than those of O-Al-O angles. This wide distribution of O-Al-O angles may indicate that the individual AlO, tetrahedron is more deformed than the SiO, tetrahedron. Further, the SiO, and AlO, tetrahedra of pyrope glass are more deformed than those of grossular glass. As well as the results for Al-O and Si-0 pair distributions, these results indicate that the
Q,
17.3
AlO, tetrahedron is softer than the SiO, tetrahedron and the Mgzf ion with small Mg-0 distance and coordination number gives larger deformation to AlO, and SiO, tetrahedra than do Ca2+ ions. Figs. 8(c)-(e) show the Si-O-S& Si-O-Al and Al-O-Al angle distributions. The averaged T-O-T angles are listed in Table 2. The Si-0-Si angles are larger than the Si-O-Al and Al-O-Al angles by about 10” and 20” in these two glasses. The angle relation, Si-0-Si > Si-O-Al > Al-O-Al, is consistent with the decrease in T-O-T angle in SiO, (148.7”), albite (NaAlSi,O,; 146.4”) and anorthite (CaA12Si20,; 136.4”) melt structures with increasing Al contents [24,25]. The AlO, tetrahedron is larger than the SiO, tetrahedron, so the T-O-T angles decrease in the AlO,-rich region because of the breakdown of the framework structure with large unstable gaps. On the other hand, Mg2+ ions in pyrope glass an,d Ca2+ ions in qossular glass have ionic radii 0.8 A (IV) and 1.08 A (IV) [26], respectively. Therefore, it is expected that the grossular glass with large Ca2+ ions has large Si-O-Al and Al-O-Al angles. The fact there is almost no difference of Si-0-Si angles between these two glasses can be explained by small amounts of Mg’+ or Ca2+ ions around the SiO, framework which is electrically neutral. For the tecto-aluminosilicate glasses with Na+ or Ca2+ ions, Murdoch et al. [13] have investigated the relations between the NMR
Fig. 8. (a) 0-Si-0 bond angle distributions in pyrope (solid line) and grossular (broken line) glasses. (b) O-Al-0 bond angle distributions in pyrope (solid line) and grossular (broken line) glasses. (c) Si-0-Si bond angle distributions in pyrope (solid line) and grossular (broken line) glasses. (d) Si-O-Al bond angle distributions in pyrope (solid line) and grossular (broken line) glasses. (e) Al-O-Al bond angle distributions in pyrope (solid line) and grossular (broken line) glasses.
258
hi. Okuno, K. Kawamura / Journal of Non-Crystalline
linewidth of 29Si and Si/Al ratios and reported that these glasses obey Loewenstein’s aluminum avoidance principle [27]. On the other hand, Sharma et al. [28] have reported some disorder of Si-Al alternating arrangement in anorthite glass. In the present work, the ratios of numbers of Si-0-Si, Si-O-Al and Al-O-Al are 1.7 : 3.5 : 1.0 for pyrope glass and 1.6 : 4.1: 1.0 for grossular glass. These ratios indicate the existence of Al-O-Al arrangements. These also indicate that the structures of these glasses do not well obey the aluminum avoidance principle. It is supposed that energetically unfavorable Al-Al arrangements were caused by extremely rapid quenching in MD calculations and the existence of nonbridging oxygens. Each distribution of Si-O-Al and Al-O-Al angles of grossular glass has only one maximum. On the other hand, the distributions of the Si-O-Al and Al-O-Al angles of pyrope glass have two or three maxima and are wide. This may also indicate that small Mg2+ ions give larger deformations to the linkages of Si-O-Al and Al-O-Al than do Ca2+ ions. This fact is consistent with the wide distribution of O-Al-O angles in the pyrope glass. 4.4. Linkages of tetrahedra The number of non-bridging oxygen (NBO) is closely related to the linkage of AlO, and SiO, tetrahedra in the glasses. The NBO shows the end of the linkage of tetrahedra. The distribution of the number of bridging oxygens in a tetrahedron is shown in Table 3. Calculated distributions of NBO for pyrope and grossular glasses are similar (Table 3). Polymer species are represented by Qj species, where i is the number of bridging oxygen ions per Si and Al ions. The Qi species in Table 3 show that the network structures of these two glasses resemble each other. Comparing the distribution of NBO for pyrope glass with the result for MgSiO, glass [16], for SiO, tetrahedra, Q3 and Q4 are dominant in pyrope glass and Q1, Q, and Q, are dominant in MgSiO, glass. The averaged Q, numbers of MgSi03 glass [16] and pyrope glass by MD calculations are 2.19 and 3.28, respectively. These results are almost consistent with the average numbers of bridging oxygens (2.0 for MgSiO, glass and 3.2 for pyrope glass) estimated from the (Si, Al)/0 ratios in the glasses.
Solids 191 (1995) 249-259
However, the distributions of number of NBO for SiO, tetrahedra are different from those for AlO, tetrahedra in these glasses. For the SiO, tetrahedra, Q2, Q3 and Q4 are dominant but, for the AlO, tetrahedra, Q4 is dominant. The averaged numbers of bridging oxygens for SiO, and AlO, tetrahedra of the pyrope and grossular glasses are 3.0 and 3.6, respectively. These results indicate that many parts of the ends of network structures are occupied by SiO, tetrahedra in these glasses. On the other hand, many parts of AlO, tetrahedra are linked to the other TO, tetrahedra. These also indicate that some A13+ ions work as network modifiers. These are consistent with the calculated average coordination number of Al in pyrope glass (= 4.1) which is a little larger than that of Sit = 4.0). Maekawa et al. [29] reported that, in the 29Si NMR study on the NaO-Al,O,-SiO, glasses, aluminum favors the more polymerized environments, i.e., the smaller number of non-bridging oxygen atoms. This report is consistent with our results. Therefore, in Mg,Ai,Si,O,, and Ca,Ai, Si,O,, glasses, aluminum tends to be associated with Mg2+ and Ca2+ and to form MgAl,O,, MgA12Si20a, CaAl,O, and CaAl,Si,O, and additional 2MgO and 2CaO modify SiO,.
5. Conclusions The structures of Mg,Al,Si,O,, (pyrope) and Ca,Al,Si,O,, (grossular) glasses have been calculated by the MD method and the detailed structures of these glasses were discussed. The following conclusions were obtained. (1) In the calculated structures, Si and Al atoms form SiO, and AlO, tetrahedra and the coordination numbers are almost four. These results are consistent with the structures obtained by X-ray experiments. (2) The S. i(S) and G(r) curves calculated by using the results of MD calculations agree well with the observed curves. This indicates that MD calculated structures well represent the real structures of these glasses. (3) The calculated pair correlation function curves of Si-0 and Al-O atomic pairs for the pyrope glasses show broader peaks than those of grossular glass, indicating that Mg2+ ions have a larger effect
M. Okuno, K. Kawamura / Journal of Non-Crystalline Solids 191 (I 995) 249-259
on the network structure mode of SiO, and AlO, tetrahedra. (4) MD-derived Mg-0 and Ca-0 distances and their coordination numbers are a little smaller than those obtained by X-ray analyses. These small discrepancies are probably caused by the extremely rapid quenches in the MD calculations. (5) The calculated structures of these glasses show the existence of Al-O-Al arrangements. This indicates that the structures do not obey the aluminum avoidance principle. The T-O-T angles decrease in the order of Si-0-Si, Si-O-Al and Al-O-Al in these glasses. (6) The distributions of numbers of NJ30 for these two glasses are similar to each other. However, those of AlO, tetrahedra are different from those of SiO, tetrahedra and show a large number of Qq. Therefore, it is expected that some A13+ ions work as network modifier ions. This study was partly supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture of Japanese Government (No. 0432023).
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