![Comparison of the position of the first sharp diffraction peak (FSDP) of S X (Q) and S N (Q) between the hydrous and anhydrous SiO2 glass [3,4,6-8,36].](https://www.researchgate.net/publication/338731072/figure/fig1/AS:849974417977344@1579661101501/Comparison-of-the-position-of-the-first-sharp-diffraction-peak-FSDP-of-S-X-Q-and-S-N_Q320.jpg)
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minerals
Article
X-ray and Neutron Study on the Structure of Hydrous
SiO2Glass up to 10 GPa
Satoru Urakawa 1, *, Toru Inoue 2,3 , Takanori Hattori 4, Asami Sano-Furukawa 4,
Shinji Kohara 5,6 , Daisuke Wakabayashi 7, Tomoko Sato 2, Nobumasa Funamori 7and
Ken-ichi Funakoshi 8
1Department of Earth Sciences, Okayama University, Okayama 700-8530, Japan
2Department of Earth and Planetary Systems Science, Hiroshima University, Higashi-Hiroshima 739-8526,
Japan; toinoue@hiroshima-u.ac.jp (T.I.); tomokos@hiroshima-u.ac.jp (T.S.)
3Geodynamics Research Center, Ehime University, Matsuyama 790-8577, Japan
4J-PARC Center, Japan Atomic Energy Agency, Tokai 319-1195, Japan; hattori.takanori@jaea.go.jp (T.H.);
sanoasa@post.j-parc.jp (A.S.-F.)
5Research Center for Advanced Measurement and Characterization,
National Institute for Materials Science (NIMS), Sayo, Hyogo 679-5148, Japan; KOHARA.Shinji@nims.go.jp
6Diffraction and Scattering Division, Japan Synchrotron Radiation Research Institute, Sayo,
Hyogo 679-5198, Japan
7Institute of Materials Structure Science, High Energy Accelerator Research Organization (KEK),
Tsukuba 305-0801, Japan; daisuke.wakabayashi@kek.jp (D.W.); nobumasa.funamori@kek.jp (N.F.)
8Neutron Science and Technology Center, Comprehensive Research Organization for Science and Society,
Tokai 319-1106, Japan; k_funakoshi@cross.or.jp
*Correspondence: urakawa@okayama-u.ac.jp
Received: 15 December 2019; Accepted: 16 January 2020; Published: 20 January 2020
Abstract:
The structure of hydrous amorphous SiO
2
is fundamental in order to investigate the effects
of water on the physicochemical properties of oxide glasses and magma. The hydrous SiO
2
glass
with 13 wt.% D
2
O was synthesized under high-pressure and high-temperature conditions and its
structure was investigated by small angle X-ray scattering, X-ray diffraction, and neutron diffraction
experiments at pressures of up to 10 GPa and room temperature. This hydrous glass is separated
into two phases: a major phase rich in SiO
2
and a minor phase rich in D
2
O molecules distributed as
small domains with dimensions of less than 100 Å. Medium-range order of the hydrous glass shrinks
compared to the anhydrous SiO
2
glass by disruption of SiO
4
linkage due to the formation of Si–OD
deuterioxyl, while the response of its structure to pressure is almost the same as that of the anhydrous
SiO
2
glass. Most of D
2
O molecules are in the small domains and hardly penetrate into the void space
in the ring consisting of SiO4tetrahedra.
Keywords:
hydrous silica glass; medium-range order; first sharp diffraction peak; phase separation;
small angle X-ray scattering; X-ray diffraction; neutron diffraction; high pressure
1. Introduction
Silica glass is the most fundamental, fully polymerized network glass whose structure and properties
under pressure have long been of interest as an important analog material of silicate magma [
1
–
9
].
For the structural aspect, SiO
2
glass is densified by compression with the change in medium-range order
in the pressure region up to about 10 GPa [
2
,
4
,
8
]. Namely, reduction of the Si–O–Si bond angle between
SiO
4
tetrahedra shrinks the ring and squeezes the interstitial void, leading to permanent densification of
SiO
2
glass. SiO
2
glass becomes fully densified glass by room temperature compression to the pressure of
9 to 13 GPa, of which the density is about 20% higher than ordinary SiO
2
glass at ambient conditions [
8
].
Minerals 2020,10, 84; doi:10.3390/min10010084 www.mdpi.com/journal/minerals
Minerals 2020,10, 84 2 of 13
Water in silicate glass has a large effect on the structure as well as on the properties such as
viscosity and glass transition temperature [
10
,
11
]. Water can react with SiO
2
glass to form hydroxyl
species (Si–OH), disrupting the linkage of SiO
4
tetrahedra. As a result, the medium-range order of
the SiO
2
glass is also affected by the addition of water in which the size of the ring of the SiO
2
glass
containing water becomes smaller than that of ordinary SiO2glass [12]. The molecular water, as well
as the hydroxyl, is also present in the silicate glasses. It is known that the molecular water becomes the
dominant water species in the silicate glasses with increasing total water content [
10
,
11
]. However, it
is not yet well understood how the molecular water is incorporated into the silicate glasses.
In this study, the hydrous SiO
2
glass containing 13 wt.% of D
2
O was synthesized under
high-pressure and high-temperature conditions and small angle X-ray scattering (SAXS), X-ray
diffraction (XRD), and neutron diffraction (ND) have been applied in order to investigate the short-range
order, medium-range order, and phase separation of this hydrous glass. In addition to this, in-situ
high-pressure XRD and ND measurements of this hydrous glass have been conducted up to about
10 GPa to clarify the pressure response of its structure. Effects of the pressure and the water dissolution
on the medium-range order of the SiO
2
glass and the state of molecular water in the SiO
2
glass are
also discussed.
2. Hydrous SiO2Glass Sample
The glass sample with a composition of SiO
2
–13wt.% D
2
O was synthesized using a Kawai-type
high-pressure apparatus driven by the 3000 ton press installed at GRC, Ehime University. Powdered
quartz enclosed in a Pt capsule together with 13 wt.% D
2
O was melted at 3 GPa and 1873 K for 30 min,
then it was quenched to room temperature by turning offthe electric power supply. The quenching
rate was approximately 1000 K/s. Subsequently, the applied pressure was released slowly in several
hours, and then the sample was recovered in ambient conditions (Figures S1 and S2). Since we have
not measured the content of heavy water in SiO
2
glass, the 13 wt.% D
2
O content is a nominal value.
The recovered glass is optically clear and homogeneous. Density of this hydrous SiO
2
glass was
determined to be 2.239 g/cm
3
by Archimedes’ method. This value is slightly higher than the density of
ordinary SiO
2
glass (2.20 g/cm
3
), although it contains a large amount of heavy water. This means that
this high-pressure hydrous SiO2glass is an intermediately densified glass.
Minerals 2020, 10, x FOR PEER REVIEW 3 of 14
Figure 1. Raman spectrum of the hydrous SiO2 glass at ambient conditions. Spectrum is unpolarized.
3. Experiments
3.1. Small Angle X-Ray Scattering at Ambient Conditions
SAXS experiments were performed at the BL18C of the Photon Factory (PF) of the High Energy
Accelerator Research Organization (KEK), Japan. Incident X-rays were monochromatic X-rays of
15.28 keV with a beam diameter of 35 micrometers, and scattered X-rays were detected in Q-range
from 0.02 to 4.0 Å–1 with an image plate. The detail of experimental setup is described elsewhere [15].
3.2. Angle-Dispersive X-Ray Diffraction at Ambient Conditions
Angle-dispersive XRD experiment at ambient conditions was carried out using two-axis
diffractometer at the BL04B2 beamline of SPring-8, Japan. We acquired diffraction data up to Q = 25
Å–1 by angle dispersive method using the monochromatic X-rays of 61.37 keV. The detail of the
experimental setup is described elsewhere [16,17].
3.3. High-Pressure X-Ray Diffraction
XRD experiments on the hydrous glass during compression were performed using the DIA-type
cubic press MAX80 installed at the AR-NE5C beamline of the PF. Tungsten carbide anvils and a
boron-epoxy pressure transmitting medium were used. A powdered sample was pressed into a pellet
with a diameter of 2 mm and enclosed in a boron nitride (BN) capsule. Sample pressure was
determined from the volume of the NaCl pressure marker [18]. XRD profiles were acquired by an
energy-dispersive method in a transmitting geometry with an intrinsic Ge detector at room
temperature and pressures of up to 9.6 GPa. White X-rays up to 120 keV were used and the data was
collected at 11 fixed angles ranging from 3° to 30° to cover a wide Q range. Background intensities
were also measured at each angle using an empty cell.
3.4. High-Pressure Neutron Diffraction
ND experiments of the hydrous SiO2 glass under pressure were conducted by the time-of-flight
(TOF) method combined with a multi-anvil press ATSUHIME [19] at the PLANET beamline [20] of
the spallation neutron source of the Materials and Life Science Experimental Facility (MLF) at the J-
PARC, Japan. A multi-anvil 6-6 type high-pressure apparatus was used [21]. The second-stage Ni-
bound WC anvils were used. Clumps of SiO2–13wt.%D2O glasses were directly packed in the ZrO2
pressure medium. The size of the hydrous SiO2 glass sample was 4.7 mm in diameter and 6.7 mm in
height. Sample pressures were calculated on the basis of the pressure-load calibration curves which
were determined in separated runs beforehand. The diffracted neutrons were detected by a pair of
0 1000 2000 3000 4000
0
200
400
600
800
1000
1200
Intensity / a.u.
Raman shift / cm
-1
O-D streching
Si-OD streching
SiO
2
-
13wt%
D
2
O
Figure 1.
Raman spectrum of the hydrous SiO
2
glass at ambient conditions. Spectrum is unpolarized.
Raman spectroscopy analysis has been applied to clarify the species of water dissolved in the
SiO
2
glass. Raman spectrum shows that the hydrous SiO
2
glass has some additional peaks except
those assigned to silica glass (Figure 1). Those are a sharp peak around 960 cm
−1
and a broad peak
from 2100 to 2750 cm
−1
. The former is assigned to the Si–OD stretching vibrations and the latter to OD
Minerals 2020,10, 84 3 of 13
stretching vibrations in D
2
O molecules and Si–OD groups [
13
,
14
]. Heavy water in the hydrous SiO
2
glass is thought to take two states, OD deuterioxyl and D
2
O molecule. In general, the amount of OH
hydroxyls dissolved in the silicate glass increases with the total H
2
O content, but reaches a limit of
about 3 wt.% [
10
,
11
]. Thus, this hydrous SiO
2
glass may contain about 10 wt.% of the heavy water as
molecular species.
3. Experiments
3.1. Small Angle X-ray Scattering at Ambient Conditions
SAXS experiments were performed at the BL18C of the Photon Factory (PF) of the High Energy
Accelerator Research Organization (KEK), Japan. Incident X-rays were monochromatic X-rays of
15.28 keV with a beam diameter of 35 micrometers, and scattered X-rays were detected in Q-range
from 0.02 to 4.0 Å
−1
with an image plate. The detail of experimental setup is described elsewhere [
15
].
3.2. Angle-Dispersive X-ray Diffraction at Ambient Conditions
Angle-dispersive XRD experiment at ambient conditions was carried out using two-axis
diffractometer at the BL04B2 beamline of SPring-8, Japan. We acquired diffraction data up to Q
=25 Å
−1
by angle dispersive method using the monochromatic X-rays of 61.37 keV. The detail of the
experimental setup is described elsewhere [16,17].
3.3. High-Pressure X-ray Diffraction
XRD experiments on the hydrous glass during compression were performed using the DIA-type
cubic press MAX80 installed at the AR-NE5C beamline of the PF. Tungsten carbide anvils and a
boron-epoxy pressure transmitting medium were used. A powdered sample was pressed into a pellet
with a diameter of 2 mm and enclosed in a boron nitride (BN) capsule. Sample pressure was determined
from the volume of the NaCl pressure marker [
18
]. XRD profiles were acquired by an energy-dispersive
method in a transmitting geometry with an intrinsic Ge detector at room temperature and pressures of
up to 9.6 GPa. White X-rays up to 120 keV were used and the data was collected at 11 fixed angles
ranging from 3
◦
to 30
◦
to cover a wide Qrange. Background intensities were also measured at each
angle using an empty cell.
3.4. High-Pressure Neutron Diffraction
ND experiments of the hydrous SiO
2
glass under pressure were conducted by the time-of-flight
(TOF) method combined with a multi-anvil press ATSUHIME [
19
] at the PLANET beamline [
20
] of the
spallation neutron source of the Materials and Life Science Experimental Facility (MLF) at the J-PARC,
Japan. A multi-anvil 6-6 type high-pressure apparatus was used [
21
]. The second-stage Ni-bound
WC anvils were used. Clumps of SiO
2
–13wt.%D
2
O glasses were directly packed in the ZrO
2
pressure
medium. The size of the hydrous SiO
2
glass sample was 4.7 mm in diameter and 6.7 mm in height.
Sample pressures were calculated on the basis of the pressure-load calibration curves which were
determined in separated runs beforehand. The diffracted neutrons were detected by a pair of 90
◦
detector banks consisting of
3
He position sensitive detectors equipped with receiving radial collimators.
The data were acquired for 15–33 h at the proton beam power of 300 kW. ND profiles were acquired at
room temperature and with the same pressure conditions as those of XRD experiments. Diffraction
profiles of a vanadium pellet in a high-pressure cell and an empty cell were also acquired for the
correction of scattering intensity.
4. Results and Discussion
4.1. Phase Separation of Hydrous SiO2Glass
It is known that the silicate glass with high water content undergoes the glass-in-glass phase
separation at a low temperature [
11
]. Due to the limitation of mutual solubility, it separates into a
Minerals 2020,10, 84 4 of 13
silica-rich and a water-rich phase. We performed the SAXS measurements on several parts of the
hydrous SiO
2
glass to clarify the possible phase separation. The hydrous SiO
2
glass clearly shows
significant scattering intensity compared with anhydrous glass (Figure 2). The scattering intensity,
however, shows a difference depending on location; some regions have strong scattering intensity, while
others only show very weak scattering intensity. This indicates that the distribution of scattering entities
in the hydrous glass is heterogeneous in the dimension on the order of from
µ
m to mm. The SAXS
patterns of the hydrous glass has a broad peak at Q=0.05–0.1 Å
−1
, which indicates the existence of an
average distance frequently realized between neighboring scattering entities. The average distance is
estimated to be about 100 Å from the length scale (2
π
/Q) corresponding to the position of the peaks.
It is, therefore, considered that the size of the scattering entities is less than 100 Å. The similar SAXS
pattern was observed in hydrated Na-silicate glass, and it was interpreted by the glass-in-glass phase
separation [
11
]. In our hydrous SiO
2
glass, similar phase separation may occur. When combined
with the results of the XRD and ND described below, the most likely candidate for this scattering
entities in hydrous SiO
2
glass is a phase rich in molecular D
2
O. Although this hydrous glass is optically
homogeneous, it is considered to be the mixture of SiO
2
-rich glass part and D
2
O-rich domain with the
dimensions of less than 100 Å.
Minerals 2020, 10, x FOR PEER REVIEW 4 of 14
90° detector banks consisting of 3He position sensitive detectors equipped with receiving radial
collimators. The data were acquired for 15–33 h at the proton beam power of 300 kW. ND profiles
were acquired at room temperature and with the same pressure conditions as those of XRD
experiments. Diffraction profiles of a vanadium pellet in a high-pressure cell and an empty cell were
also acquired for the correction of scattering intensity.
4. Results and Discussion
4.1. Phase Separation of Hydrous SiO2 Glass
It is known that the silicate glass with high water content undergoes the glass-in-glass phase
separation at a low temperature [11]. Due to the limitation of mutual solubility, it separates into a
silica-rich and a water-rich phase. We performed the SAXS measurements on several parts of the
hydrous SiO2 glass to clarify the possible phase separation. The hydrous SiO2 glass clearly shows
significant scattering intensity compared with anhydrous glass (Figure 2). The scattering intensity,
however, shows a difference depending on location; some regions have strong scattering intensity,
while others only show very weak scattering intensity. This indicates that the distribution of
scattering entities in the hydrous glass is heterogeneous in the dimension on the order of from μm to
mm. The SAXS patterns of the hydrous glass has a broad peak at Q = 0.05–0.1 Å–1, which indicates
the existence of an average distance frequently realized between neighboring scattering entities. The
average distance is estimated to be about 100 Å from the length scale (2π/Q) corresponding to the
position of the peaks. It is, therefore, considered that the size of the scattering entities is less than 100
Å. The similar SAXS pattern was observed in hydrated Na-silicate glass, and it was interpreted by
the glass-in-glass phase separation [11]. In our hydrous SiO2 glass, similar phase separation may
occur. When combined with the results of the XRD and ND described below, the most likely
candidate for this scattering entities in hydrous SiO2 glass is a phase rich in molecular D2O. Although
this hydrous glass is optically homogeneous, it is considered to be the mixture of SiO2-rich glass part
and D2O-rich domain with the dimensions of less than 100 Å.
Figure 2. Small angle X-ray scattering intensity from the hydrous SiO2 glass at ambient conditions.
Scattering intensity from anhydrous SiO2 glass (black curve) is also shown for comparison. Three
curves were observed at locations from a few hundred micrometers to a millimeter apart.
4.2. Comparison with Dry SiO2 Glass at Ambient Conditions
We compare the structure of the hydrous glass and the anhydrous glass at atmospheric pressure
using the results of XRD and ND. The structure factors S(Q) and the total correlation functions T(r)
for the hydrous and the anhydrous glass are shown in Figure 3. The S(Q) and T(r) for the anhydrous
0.0 0.1 0.2 0.3 0.4 0.5
100
1000
10000
I(Q) / a.u.
Q / Å
-1
anhydrous SiO
2
glass
hydrous SiO
2
glass
Figure 2.
Small angle X-ray scattering intensity from the hydrous SiO
2
glass at ambient conditions.
Scattering intensity from anhydrous SiO
2
glass (black curve) is also shown for comparison. Three
curves were observed at locations from a few hundred micrometers to a millimeter apart.
4.2. Comparison with Dry SiO2Glass at Ambient Conditions
We compare the structure of the hydrous glass and the anhydrous glass at atmospheric pressure
using the results of XRD and ND. The structure factors S(Q) and the total correlation functions T(r) for
the hydrous and the anhydrous glass are shown in Figure 3. The S(Q) and T(r) for the anhydrous SiO
2
glass were reported by Kohara et al. [
22
] for X-ray and Hannon [
23
] for neutron. Here, we consider
what the S(Q) and the T(r) of the hydrous SiO
2
glass represent. XRD and ND measurements were
performed on the bulk hydrous SiO
2
glass. As shown in the results of the SAXS measurements, the
hydrous glass is separated into two phases. Therefore, the S(Q) and T(r) obtained from XRD and ND
are the sum of contributions from the SiO
2
-rich glass part and the D
2
O-rich domains. Hereafter, we
discuss the structure of the hydrous SiO2glass based on this view.
Minerals 2020,10, 84 5 of 13
Minerals 2020, 10, x FOR PEER REVIEW 5 of 14
SiO2 glass were reported by Kohara et al. [22] for X-ray and Hannon [23] for neutron. Here, we
consider what the S(Q) and the T(r) of the hydrous SiO2 glass represent. XRD and ND measurements
were performed on the bulk hydrous SiO2 glass. As shown in the results of the SAXS measurements,
the hydrous glass is separated into two phases. Therefore, the S(Q) and T(r) obtained from XRD and
ND are the sum of contributions from the SiO2-rich glass part and the D2O-rich domains. Hereafter,
we discuss the structure of the hydrous SiO2 glass based on this view.
As discussed below, both S(Q) and T(r) show that the short-range order composed of SiO4
tetrahedra of the hydrous SiO2 glass is almost the same as that of anhydrous glass, while the medium-
range order related to the ring of the SiO4 tetrahedra is diminished by addition of water. The first
sharp diffraction peak (FSDP) observed at Q ~ 1.5–1.7 Å–1 in both the SX(Q)and SN(Q) of hydrous glass
clearly shifts to the higher-Q side than those of anhydrous glass. The second peak is observed at Q =
2.9 Å–1 only in neutron data. In the other peaks, the intensity and the position of SX(Q) are almost the
same between the hydrous and the anhydrous glass, whereas the SN(Q) shows a difference. This is
due to the very small X-ray atomic scattering factor of D and the relatively large neutron scattering
length of D. The similarity of SX(Q) means the Si–O correlation between the hydrous and anhydrous
glass is similar. The X-ray total correlation function TX(r) of hydrous glass shows almost the same
peaks positions as those of anhydrous glass, but the height of TX(r) of hydrous glass is higher than
that of anhydrous glass because of its higher number density. The Si coordination number of the
hydrous glass calculated from the area of the first peak at 1.6 Å is about 3.9, which is almost the same
as that for the anhydrous glass. On the other hand, the neutron total correlation function TN(r) of
hydrous glass has a different shape from that of anhydrous glass because of the presence of peaks
due to the OD deuterioxyl and the D2O molecules. The peak at about 0.93 Å for hydrous glass
corresponds to the D–O distance. In the TN(r), it is difficult to identify peaks originating from
deuterium other than this peak, but the effect of overlapping peaks is recognized. Since the Si-O
correlation typically located around 1.6 Å in the TN(r) is superimposed on the intramolecular D–D
correlation (1.56 Å) and the intermolecular O–D correlation (1.92 Å) of D2O [24], the coordination
number of Si cannot be determined.
0 5 10 15 20 25
0
1
2
S
X
(Q)
Q / Å
-1
SiO
2
glass
SiO
2
-
13wt.%
D
2
O glass
(A)
0246
0
1
2
S
X
(Q)
Q / Å
-1
0 5 10 15 20 25
0
1
2
S
N
(Q)
Q / Å
-1
(B)
0246
0
1
2
S
N
(Q)
Q / Å
-1
02468
0
2
4
6
8
10
T
X
(r)
r / Å
(C)
Si-Si
Si-O
O-O
02468
0
2
4
6
8
10
T
N
(r)
r / Å
(D)
D-O
Si-O O-O
Figure 3.
X-ray and neutron diffraction data of the hydrous SiO
2
glass and the anhydrous SiO
2
glass at
ambient conditions. (
A
) The X-ray structure factor S
X
(Q), (
B
) the neutron structure factor S
N
(Q), (
C
)
the X-ray total correlation function TX(r), and (D) the neutron total correlation function TN(r).
As discussed below, both S(Q) and T(r) show that the short-range order composed of SiO
4
tetrahedra of the hydrous SiO
2
glass is almost the same as that of anhydrous glass, while the
medium-range order related to the ring of the SiO
4
tetrahedra is diminished by addition of water.
The first sharp diffraction peak (FSDP) observed at Q~ 1.5–1.7 Å
−1
in both the S
X
(Q)and S
N
(Q) of
hydrous glass clearly shifts to the higher-Qside than those of anhydrous glass. The second peak is
observed at Q=2.9 Å
−1
only in neutron data. In the other peaks, the intensity and the position of
S
X
(Q) are almost the same between the hydrous and the anhydrous glass, whereas the S
N
(Q) shows a
difference. This is due to the very small X-ray atomic scattering factor of D and the relatively large
neutron scattering length of D. The similarity of S
X
(Q) means the Si–O correlation between the hydrous
and anhydrous glass is similar. The X-ray total correlation function T
X
(r) of hydrous glass shows
almost the same peaks positions as those of anhydrous glass, but the height of T
X
(r) of hydrous glass is
higher than that of anhydrous glass because of its higher number density. The Si coordination number
of the hydrous glass calculated from the area of the first peak at 1.6 Å is about 3.9, which is almost the
same as that for the anhydrous glass. On the other hand, the neutron total correlation function T
N
(r) of
hydrous glass has a different shape from that of anhydrous glass because of the presence of peaks due
to the OD deuterioxyl and the D
2
O molecules. The peak at about 0.93 Å for hydrous glass corresponds
to the D–O distance. In the T
N
(r), it is difficult to identify peaks originating from deuterium other
than this peak, but the effect of overlapping peaks is recognized. Since the Si-O correlation typically
located around 1.6 Å in the T
N
(r) is superimposed on the intramolecular D–D correlation (1.56 Å)
and the intermolecular O–D correlation (1.92 Å) of D
2
O [
24
], the coordination number of Si cannot
be determined.
FSDP of S(Q) is thought to be related to the formation of medium-range order, although its origin
has been still under debate [
25
–
29
]. The position of FSDP, Q
1
, corresponds to the length scale of
periodicity in real space l
1
(=2
π
/Q
1
). Thus, the shift of the FSDP toward high-Qside by dissolution
of water means the shrinkage of the medium-range order. This is attributed to the decrease of the
Minerals 2020,10, 84 6 of 13
size of the SiO
4
ring by breaking SiO
4
linkages with the OH (OD) group. In ordinary SiO
2
glass,
the six-membered ring of SiO
4
tetrahedra is most frequent followed by the five-membered ring [
30
],
but the population of a smaller ring, such as five- and four-membered rings, may increase by water
dissolution. The shift of the FSDP toward high-Qside due to water dissolution has been reported for
rhyolitic glasses containing more than 70 wt.% of SiO
2
[
31
]. The displacement of the FSDP of S
X
(Q) in
rhyolitic glass is about 1.5 Å
−1
by the 7.5 wt.% dissolution of H
2
O, which is comparable to that of our
hydrous silica glass containing 13 wt.% of D2O.
On the other hand, the FSDP of densified SiO
2
glasses is known to be on the high-Qside compared
to ordinary SiO
2
glass [
32
]. This is considered to correspond to the shrinkage of the medium-range
order, which is related to a reduction of Si–O–Si bond angle associated with the reduction of interstitial
voids by compression [
4
]. Our hydrous SiO
2
glass was prepared by quenching from the melt at 3 GPa
and is thought to partially retain the structure of intermediately densified glass. Therefore, the position
of FSDP in our hydrous glass can be attributed to the effects of both water addition and densification.
As revealed by SAXS, XRD, and ND, the hydrous glass synthesized in this study is a mixture of
SiO
2
-rich glass parts and a D
2
O-rich domain. By assuming that the structure of each phase is the same
as that for pure SiO
2
glass and pure liquid D
2
O, the S(Q) for hydrous glass can be calculated from
those for pure phases [
22
,
33
–
35
] (the detailed method is described in Appendix B). Comparison of
the S
X
(Q) and the S
N
(Q) of the hydrous SiO
2
with those calculated from the previously reported S(Q)
are shown in Figure 4. They showed good agreement except the position of FSDP of the S
X
(Q) and
the S
N
(Q), and the height of the second peak of the S
N
(Q). The difference may be attributed to the
shrinkage of the medium-range order of the SiO2glass by dissolution of water.
Minerals 2020, 10, x FOR PEER REVIEW 7 of 14
Figure 4. (A) SX(Q)’s of SiO2 glass and liquid D2O at ambient conditions [22,34], and that simulated
for the hydrous glass using them. (B) Corresponding S(Q) for neutron, SN(Q) [33,35]. (C) Comparison
of the observed and simulated SX(Q)s for the hydrous SiO2 glass. (D) Comparison of the observed and
simulated SN(Q)s.
4.3. Hydrous SiO2 Glass under Pressure
We consider the response of the structure of the hydrous SiO2 glass to pressure. The S(Q) and
T(r) for the hydrous glass during compression to about 10 GPa are shown in Figure 5. In XRD, the
SX(Q) of hydrous SiO2 glass changes with pressure in the same way as anhydrous SiO2 glass reported
by Inamura et al. [4], except for the position of the FSDP. This means that the response to the pressure
of the short-range order of the hydrous glass is the same as that of the anhydrous glass. This is
consistent with the structure deduced from SAXS showing that the hydrous SiO2 glass is mainly
composed of relatively dry parts rich in SiO2.
0.0
0.5
1.0
1.5
2.0
S
N
(Q)
(B)
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
S
X
(Q)
SiO
2
glass
liquid D
2
O
(A)
SiO
2
glass + liquid D
2
O
0 5 10 15 20 25
0.0
0.5
1.0
1.5
S
N
(Q)
Q / Å
-1
(D)
0 5 10 15 20
0.0
0.5
1.0
1.5
2.0
S
X
(Q)
Q / Å
-1
SiO
2
-
13wt.%
D
2
O glass
(C)
SiO
2
glass + liquid D
2
O
Figure 4.
(
A
)S
X
(Q)’s of SiO
2
glass and liquid D
2
O at ambient conditions [
22
,
34
], and that simulated
for the hydrous glass using them. (
B
) Corresponding S(Q) for neutron, S
N
(Q) [
33
,
35
]. (
C
) Comparison
of the observed and simulated S
X
(Q)s for the hydrous SiO
2
glass. (
D
) Comparison of the observed and
simulated SN(Q)s.
Minerals 2020,10, 84 7 of 13
4.3. Hydrous SiO2Glass under Pressure
We consider the response of the structure of the hydrous SiO
2
glass to pressure. The S(Q) and T(r)
for the hydrous glass during compression to about 10 GPa are shown in Figure 5. In XRD, the S
X
(Q)
of hydrous SiO
2
glass changes with pressure in the same way as anhydrous SiO
2
glass reported by
Inamura et al. [
4
], except for the position of the FSDP. This means that the response to the pressure of
the short-range order of the hydrous glass is the same as that of the anhydrous glass. This is consistent
with the structure deduced from SAXS showing that the hydrous SiO
2
glass is mainly composed of
relatively dry parts rich in SiO2.
Minerals 2020, 10, x FOR PEER REVIEW 8 of 14
Figure 5. X-ray and neutron diffraction data of the hydrous SiO2 glass with 13 wt.% D2O during room
temperature compression to 10 GPa. (A) The X-ray structure factor SX(Q), (B) the neutron structure
factor SN(Q), (C) the X-ray total correlation function TX(r), and (D) the neutron total correlation
function TN(r).
Figure 6 compares the pressure dependence of the position of FSDP of hydrous SiO2 glass
obtained from both XRD and ND with that of anhydrous glass [4,9]. The FSDP of SX(Q) and SN(Q)
shifts in parallel to the high-Q side in proportion to the pressure up to 10 GPa. Those shifts are also
parallel to the FSDP of ordinary anhydrous glass. In addition, the intensity of the FSDP of the hydrous
glass decreases with pressure in the same way as anhydrous glass for both the SX(Q) and SN(Q) [4,9].
Shrinkage of the medium-range order is also found in T(r). The Si–O distance is almost constant with
up to 10 GPa, but the Si–Si distance decreases with increasing pressure (Figure 5). Thus, the Si–O–Si
bond angle decreases, and the network linkage of the SiO4 tetrahedra is distorted with increasing
pressure. These show that even though the medium-range order of the hydrous SiO2 glass is partly
disrupted by OD deuterioxyl, it shrinks with pressure just like the anhydrous glass.
02468
0
4
8
12
16
T
N
(r)
r / Å
9.6 GPa
7.7 GPa
4.0 GPa
0.1 MPa
(D)
D-O
Si-O
O-O
0 5 10 15 20
0
1
2
3
4
5
S
N
(Q)
Q / Å
-1
(B)
9.6 GPa
7.7 GPa
4.0 GPa
0.1 MPa
05101520
0
1
2
3
4
5
S
X
(Q)
Q / Å
-1
9.6 GPa
7.7 GPa
4.0 GPa
0.1 MPa
(A)
02468
0
4
8
12
16
TX(r)
r / Å
9.6 GPa
7.7 GPa
4.0 GPa
0.1 MPa
(C)
Si-Si
Si-O
O-O
Figure 5.
X-ray and neutron diffraction data of the hydrous SiO
2
glass with 13 wt.% D
2
O during room
temperature compression to 10 GPa. (
A
) The X-ray structure factor S
X
(Q), (
B
) the neutron structure
factor S
N
(Q), (
C
) the X-ray total correlation function T
X
(r), and (
D
) the neutron total correlation function
TN(r).
Figure 6compares the pressure dependence of the position of FSDP of hydrous SiO
2
glass obtained
from both XRD and ND with that of anhydrous glass [
4
,
9
]. The FSDP of S
X
(Q) and S
N
(Q) shifts in
parallel to the high-Qside in proportion to the pressure up to 10 GPa. Those shifts are also parallel to the
FSDP of ordinary anhydrous glass. In addition, the intensity of the FSDP of the hydrous glass decreases
with pressure in the same way as anhydrous glass for both the S
X
(Q) and S
N
(Q) [
4
,
9
]. Shrinkage of the
medium-range order is also found in T(r). The Si–O distance is almost constant with up to 10 GPa,
but the Si–Si distance decreases with increasing pressure (Figure 5). Thus, the Si–O–Si bond angle
decreases, and the network linkage of the SiO
4
tetrahedra is distorted with increasing pressure. These
show that even though the medium-range order of the hydrous SiO2glass is partly disrupted by OD
deuterioxyl, it shrinks with pressure just like the anhydrous glass.
Minerals 2020,10, 84 8 of 13
Minerals 2020, 10, x FOR PEER REVIEW 9 of 14
Figure 6. Comparison of the position of the first sharp diffraction peak (FSDP) of SX(Q) and SN(Q)
between the hydrous and anhydrous SiO2 glass [3,4,6–8,36].
We estimate the density of hydrous SiO2 glass under pressure in order to derive the total
correlation function T(r). Since the FSDP of the hydrous glass changes with pressure at almost the
same rate as that of the anhydrous glass, and the shape of the structure factors resemble each other
except the FSDP, we assume that the densities of hydrous glass and anhydrous glass would change
in the same rate with pressure. We evaluate the T(r) using the densities of hydrous glass at high
pressures, which is estimated from the relationships between density and pressure of ordinary SiO2
glass shown in Figure 1 of Wakabayashi et al. [8]. The coordination number of Si calculated from
TX(r) is about four up to 10 GPa, which is consistent with that of anhydrous SiO2 glass. This shows
that our estimation of high-pressure density of hydrous SiO2 glass is fairly good, because the
similarity of the short-range order between hydrous glass and anhydrous glass is expected.
What happens to the D2O-rich phase in the hydrous SiO2 glass during compression?
Unfortunately, neutron diffraction data does not give us any information except nearly constant D–
O distance in TN(r) up to 10 GPa. When evaluated using the partial molar volume of H2O at 3 GPa
[37], at which the hydrous SiO2 glass was synthesized, 10 wt.% D2O is equivalent to about 14% in
volume. It is interesting that such an amount of molecular D2O does not greatly affect the
compression behavior of SiO2 glass.
4.4. Molecular Water in the Hydrous SiO2 Glass
The SAXS strongly suggests that most of the D2O molecules may form the separate phase in
small domains distributed in the hydrous SiO2 glass. Can all D2O molecules in the hydrous glass be
incorporated into the small domains? Here, we consider the possibility that D2O molecules are
contained in the voids characteristic of the ring structure made by connecting SiO4 tetrahedra.
Sato et al. [38] showed that when He penetrates into SiO2 glass, SiO2 glass becomes rigid. Since
the interstitial voids in the SiO2 glass are occupied by He, the voids are not squeezed even when
pressure is applied and the bulk modulus of the SiO2 glass with He becomes larger than that of the
ordinary SiO2 glass. It is shown that the FSDP position of the SiO2 glass saturated with He does not
change up to 10 GPa. If D2O molecules penetrate the interstitial voids formed by the SiO4 linkage, the
bulk modulus of the hydrous glass should be larger than that of ordinary glass, as shown in the case
of SiO2 glass with He. The position of the FSDP of our hydrous glass, however, changes with pressure
in the same way as the anhydrous glass (Figure 6), and its bulk modulus is estimated to be almost the
same as that of the anhydrous glass. Thus, it is considered that the interstitial void space in the
hydrous SiO2 glass is almost empty, and D2O does not penetrate into the SiO4 network. It is supported
from void size: The interstitial void in the SiO4 network of SiO2 glass is too small to accommodate
D2O molecule in it. In the size distribution model of interstitial voids in silica glass estimated from
0 5 10 15 20
1.4
1.5
1.6
1.7
1.8
1.9
2.0
2.1
2.2
2.3
Position of FSDP / Å
P / GPa
SiO
2
glass XRD [4]
SiO
2
glass XRD [3]
SiO
2
glass XRD [7]
SiO
2
glass XRD [36]
SiO
2
glass XRD [6]
Densified SiO
2
glass XRD [6]
Densified SiO
2
glass XRD [8]
SiO
2
glass ND [9]
SiO
2
glass ND (Hattori et al., private com)
SiO
2
-
13wt.%
D
2
O glass XRD (This study)
SiO
2
-
13wt.%
D
2
O glass ND (This study)
Figure 6.
Comparison of the position of the first sharp diffraction peak (FSDP) of S
X
(Q) and S
N
(Q)
between the hydrous and anhydrous SiO2glass [3,4,6–8,36].
We estimate the density of hydrous SiO
2
glass under pressure in order to derive the total correlation
function T(r). Since the FSDP of the hydrous glass changes with pressure at almost the same rate
as that of the anhydrous glass, and the shape of the structure factors resemble each other except the
FSDP, we assume that the densities of hydrous glass and anhydrous glass would change in the same
rate with pressure. We evaluate the T(r) using the densities of hydrous glass at high pressures, which
is estimated from the relationships between density and pressure of ordinary SiO
2
glass shown in
Figure 1of Wakabayashi et al. [
8
]. The coordination number of Si calculated from T
X
(r) is about four
up to 10 GPa, which is consistent with that of anhydrous SiO
2
glass. This shows that our estimation of
high-pressure density of hydrous SiO
2
glass is fairly good, because the similarity of the short-range
order between hydrous glass and anhydrous glass is expected.
What happens to the D
2
O-rich phase in the hydrous SiO
2
glass during compression? Unfortunately,
neutron diffraction data does not give us any information except nearly constant D–O distance in
T
N
(r) up to 10 GPa. When evaluated using the partial molar volume of H
2
O at 3 GPa [
37
], at which
the hydrous SiO
2
glass was synthesized, 10 wt.% D
2
O is equivalent to about 14% in volume. It is
interesting that such an amount of molecular D
2
O does not greatly affect the compression behavior of
SiO2glass.
4.4. Molecular Water in the Hydrous SiO2Glass
The SAXS strongly suggests that most of the D
2
O molecules may form the separate phase in
small domains distributed in the hydrous SiO
2
glass. Can all D
2
O molecules in the hydrous glass
be incorporated into the small domains? Here, we consider the possibility that D
2
O molecules are
contained in the voids characteristic of the ring structure made by connecting SiO4tetrahedra.
Sato et al. [
38
] showed that when He penetrates into SiO
2
glass, SiO
2
glass becomes rigid. Since
the interstitial voids in the SiO
2
glass are occupied by He, the voids are not squeezed even when
pressure is applied and the bulk modulus of the SiO
2
glass with He becomes larger than that of the
ordinary SiO
2
glass. It is shown that the FSDP position of the SiO
2
glass saturated with He does not
change up to 10 GPa. If D
2
O molecules penetrate the interstitial voids formed by the SiO
4
linkage, the
bulk modulus of the hydrous glass should be larger than that of ordinary glass, as shown in the case of
SiO
2
glass with He. The position of the FSDP of our hydrous glass, however, changes with pressure
in the same way as the anhydrous glass (Figure 6), and its bulk modulus is estimated to be almost
the same as that of the anhydrous glass. Thus, it is considered that the interstitial void space in the
hydrous SiO
2
glass is almost empty, and D
2
O does not penetrate into the SiO
4
network. It is supported
from void size: The interstitial void in the SiO
4
network of SiO
2
glass is too small to accommodate
Minerals 2020,10, 84 9 of 13
D
2
O molecule in it. In the size distribution model of interstitial voids in silica glass estimated from the
solubility site density of He and Ne dissolved in cristobalite, about 10% of voids can contain He and
only 6% of voids can contain Ne [
39
]. According to Zhang and Xu [
40
], the molecular diameter of H
2
O
is 2.74 Å (that of D
2
O is also expected to be about the same), which is larger than He (2.16 Å) and Ne
(2.42 Å), so that it seems difficult to incorporate the H
2
O (or D
2
O) molecules in the interstitial voids
of SiO
2
glass. Further, the void size in the hydrous glass is smaller than that of anhydrous glass due
to the reduction of size of the SiO
4
ring, and it is more difficult for the H
2
O (or D
2
O) molecule to be
incorporated into the interstitial void.
5. Conclusions
SAXS, XRD and ND show that the SiO
2
–13wt.% D
2
O composition glass, which was synthesized
by quenching from melt at 3 GPa is separated into two phases: SiO
2
-rich glass phase and D
2
O-rich
minor phase were distributed as small domains with dimensions of less than 100 Å. Both the S
X
(Q) and
the S
N
(Q) of the hydrous SiO
2
glass can be reproduced from those of the SiO
2
glass and liquid D
2
O.
Medium-range order and short-range order derived from XRD and ND mainly reflect the structure of
the SiO
2
-rich glass part. The FSDP of hydrous glass shifts to the higher-Qside than those of anhydrous
glass at ambient conditions. This corresponds to the shrinkage of the medium-range order associated
with the decrease of the size of SiO
4
rings by breaking the SiO
4
linkage with the OD group, as well as
by distorting the network linkage of SiO
4
with a pressure of 3 GPa during glass synthesis. The response
of the structure of the SiO
2
-rich glass part to pressure is almost the same as that of the anhydrous SiO
2
glass. The FSDP of the hydrous glass shifts to the high-Qside with increasing pressure in parallel with
that of the anhydrous glass. The Si–O–Si bond angle decreases with pressure, although the coordination
number of Si is about four at the pressures of from 0.1 MPa to 10 GPa. Thus, the medium-range order
shrinks with pressure associated with distortion of network linkage of SiO
4
tetrahedra. Most of D
2
O
molecules are in the small domains of the D
2
O-rich phase and hardly penetrate into the void space in
the ring consisting of SiO4tetrahedra of SiO2-rich glass part.
Supplementary Materials:
The following are available online at http://www.mdpi.com/2075-163X/10/1/84/s1,
Figure S1: Cell assemble for the synthesis of hydrous SiO
2
glass at 3 GPa and 1873 K, Figure S2: Recovered Pt
capsule and hydrous SiO2glass quenched from the conditions of 3 GPa and 1873 K.
Author Contributions:
Conceptualization, S.U. and T.I.; formal analysis, S.U., T.H., S.K.; investigation, S.U., T.I.,
T.H., A.S.-F., S.K., D.W., T.S., N.F., K.-i.F.; writing—original draft preparation, S.U.; All author contribute review
and editing. All authors have read and agreed to the published version of the manuscript.
Funding:
This research was in part supported by the JSPS KAKENHI Grant (19GS0205, 18K03805), the Earthquake
Research Institute Joint Usage/Research Program (2010-G-01, 2011-G-05, 2012-G-02), and the Joint Usage/Research
Center PRIUS, Ehime University.
Acknowledgments:
We thank Y. Katayama and T. Kimura for help with the ND experiments at J-PARC, and
K. Mibe and M. Kanzaki for help with the synthesis of hydrous SiO
2
glass. We are grateful to A. Zeidler and P.
S. Salmon for providing us with high-pressure neutron diffraction data for SiO
2
glass. We are also grateful to
two anonymous reviewers for their thoughtful formal reviews. The XRD experiments were conducted under
approval of PF Proposal Advisory Committee (2011G652, 2017G135) and the JASRI (2014B1480), and the ND
experiments were performed with the approval of the Neutron Science Proposal Review Committee of J-PARC,
MLF (2013I0011).
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A
Appendix A.1 Data Reduction of X-ray and Neutron Diffraction
Appendix A.1.1 Energy Dispersive X-ray Diffraction at High Pressures
We used a Faber-Ziman definition for X-ray structure factor SX(Q) which is defined as follows.
SX(Q) = (iX
coh(Q)− {h f(Q)2i − h f(Q)i2})/hf(Q)i2(A1)
Minerals 2020,10, 84 10 of 13
where i
cohX
(Q) is a coherent scattering intensity per atom,
hf(Q)2i=Picif2
i(Q)
,
hf(Q)i2= (Picifi(Q))2
,
ciand fi(Q) are an atomic fraction and an atomic scattering factor of the ith atom, respectively.
The S
X
(Q) was evaluated by the procedure developed by Funakoshi [
41
]. Energy profiles of XRD
pattern obtained at various Bragg angles can be expressed by the following equation.
IX
ob(E,θ) = NA(E,θ)P(E,θ)IX
0(E)hiX
coh(E,θ) + iX
inc(E,θ) + iX
m(E,θ)i+IX
BG(E,θ)(A2)
where Nis the number of atom, A(E,
θ
) is the absorption factor, P(E,
θ
) is the polarization factor, I
0X
(E) is
the intensity of incident X-rays. i
inc
(E,
θ
)
X
and i
m
(E,
θ
)
X
are incoherent and multiple scattering intensity
per atom, respectively. I
BGX
(E,
θ
) is background intensity. At first, I
BGX
(E,
θ
)’s were subtracted from
I
obX
(E,
θ
)’s. As the energy spectrum of incident X-rays from the synchrotron source I
0X
(E) is unknown,
we evaluated simultaneously both I
0X
(E) and i
cohX
(E,
θ
)’s from I
obX
(E,
θ
)’s by simulation using the
Monte Carlo method [
41
]. Here, we ignored the differences of absorption and polarization effects and
multiple scattering terms among data taken with different Bragg angles. The incoherent scattering
term was corrected using the formulation of Hajdu [
42
] and P
á
link
á
s [
43
]. Then coherent scattering
intensities at each Bragg angle were unified to obtain I
cohX
(Q). The Faber–Ziman total structure factor
S
X
(Q) was evaluated from Equation (A1) in which the atomic scattering factor was calculated using the
approximation formula given by Doyle and Turner [44].
Appendix A.1.2 Time-of-Flight Neutron Diffraction at High Pressures
Structure factor for neutron S
N
(Q) was evaluated from a ND profile obtained by the TOF method
combined with a multi-anvil press. Observed ND profile is described as follows.
IN
ob(λ,θ) = NA(λ,θ)IN
0(λ)hiN
coh(λ,θ) + iN
inc(λ,θ) + iN
m(λ,θ)i+IN
BG(λ,θ)(A3)
where Nis the number of atoms, A(
λ
,
θ
) is the absorption factor, I
0N
(
λ
) is the intensity of incident
neutron, i
cohN
(
λ
,
θ
), i
incN
(
λ
,
θ
), and i
mN
(
λ
,
θ
) are coherent, inelastic, incoherent, and multiple scattering
cross section per one atom, respectively. I
BGN
(
λ
,
θ
) is background intensity. Observed scattering
intensities I
obN
(
λ
,
θ
) are normalized by I
0N
(
λ
) obtained from the scattering intensity of a vanadium
pellet after background subtraction and absorption correction. Absorption correction was performed
according to the method of Paalman and Pings [
45
]. Then, incoherent scattering and multiple scattering
terms were corrected. The incoherent term was evaluated by a composition average of incoherent
scattering length b
inc
of the elements, which are listed in the table of Sears [
46
]. The incoherent
scattering for D atom was significantly deviated from the value listed in the table due to the inelastic
effect. Therefore, we corrected it by empirical method employed by Kameda et al. [
47
] (as described
below). The multiple scattering term was corrected by the method of Blech and Averbach [
48
]. Thus,
we calculated the structure factor S
N
(Q) from the corrected intensity I
corN
(
λ
,
θ
), which is the sum of
icohN(λ,θ) and iine N(λ,θ).
Inelastic effect for incoherent scattering of deuterium has a small but non-negligible effect on the
total scattering intensity of the hydrous SiO
2
glass. The effect was corrected based on the empirical
method by Kameda et al. [
48
] in which incoherent scattering was estimated from the self term of the
liquid null-H
2
O using a known O–O correlation. The applicability of this method at PLANET has
been confirmed from the good coincidence of the S(Q) for D
2
O water with that reported so far in the
literature (Hattori et al., private com).
Definition of Faber–Ziman total structure factor for the SN(Q) is as follows.
SN(Q) = (iN
coh(Q)− {hbi2− hbi2})/hbi2(A4)
where
hb2i=P
i
cib2
i
,
hbi2= (Picibi)2
,c
i
, and b
i
are an atomic fraction and a coherent scattering length
of the ith atom [46], respectively.
Minerals 2020,10, 84 11 of 13
Appendix A.1.3 Fourier Analysis
The S(Q) data in reciprocal space can be transformed into total correlation function T(r) in real
space by means of a Fourier transform.
T(r) = 4πrρ0+2
πZQmax
Qmin
M(Q)QS(Q)−1sin rQdQ (A5)
where
ρ0
is a number density of atoms and M(Q) is a modification function. We used a Lorch function
as M(Q) [49].
Appendix B
Faber–Ziman Structure Factor of a Two-Phase Mixture can be Written as Follows for X-ray
SX
A+B(Q) = XA(hf(Q)i2
A/hf(Q)i2
A+B)SX
A(Q) + XB(hf(Q)i2
B/hf(Q)i2
A+B)SX
B(Q)
+XA(hf(Q)2iA− h f(Q)i2
A)/hf(Q)i2
A+B+XB(hf(Q)2iB− h f(Q)i2
B)/hf(Q)i2
A+B
−(hf(Q)2iA+B− h f(Q)i2
A+B)/hf(Q)i2
A+B
(A6)
where X
A
and X
B
are the mole fraction of phase Aand B, respectively. Here, each value satisfies the
condition of X
A
+X
B
=1. Equation (A6) can be applied to the neutron structure factor S
N
(Q) by
replacing an atomic scattering factor with a coherent scattering length of neutron.
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