Inelastic X-ray scattering experiments at extreme conditions: high temperatures and high pressures
In this article, we review the present status of experimental techniques under extreme conditions of high temperature and high pressure used for inelastic X-ray scattering (IXS) experiments of liquid metals, semiconductors, molten salts, molecular liquids, and supercritical water and methanol. For...
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irk-123456789-1189962017-06-04T03:03:55Z Inelastic X-ray scattering experiments at extreme conditions: high temperatures and high pressures Hosokawa, S. In this article, we review the present status of experimental techniques under extreme conditions of high temperature and high pressure used for inelastic X-ray scattering (IXS) experiments of liquid metals, semiconductors, molten salts, molecular liquids, and supercritical water and methanol. For high temperature experiments, some types of single-crystal sapphire cells were designed depending on the temperature of interest and the sample thickness for the X-ray transmission. Single-crystal diamond X-ray windows attached to the externally heated high-pressure vessel were used for the IXS experiment of supercritical water and methanol. Some typical experimental results are also given, and the perspective of IXS technique under extreme conditions is discussed. У данiй статтi ми робимо огляд сучасного стану експериментальних методик при екстремальних умовах високих температур та високих тискiв у експериментах з непружного розсiяння рентгенiвських променiв для рiдких металiв, напiвпровiдникiв, розплавiв солей, молекулярних рiдин, та надкритичних води i метанолу. Для експериментiв при високих температурах було розроблено деякi типи монокристалiчних сапфiрових комiрок, в залежностi вiд температури та ширини зразка для проходження рентгенiвських променiв. Монокристалiчнi алмазнi вiкна для рентгенiвських променiв, пiд’єднанi до комiрки, що витримує високий тиск та має зовнiшнє нагрiвання, використовувались для експериментiв по непружному розсiянню рентгенiвських променiв у надкритичних водi та метанолi. Також подано деякi типовi експериментальнi результати та обговорюється перспектива методики непружного розсiяння рентгенiвських променiв при екстремальних умовах. 2008 Article Inelastic X-ray scattering experiments at extreme conditions: high temperatures and high pressures / S. Hosokawa // Condensed Matter Physics. — 2008. — Т. 11, № 1(53). — С. 71-81. — Бібліогр.: 32 назв. — англ. 1607-324X PACS: 61.25.Mv, 61.25.Em, 61.10.Eq, 63.50.+x DOI:10.5488/CMP.11.1.71 http://dspace.nbuv.gov.ua/handle/123456789/118996 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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In this article, we review the present status of experimental techniques under extreme conditions of high temperature
and high pressure used for inelastic X-ray scattering (IXS) experiments of liquid metals, semiconductors,
molten salts, molecular liquids, and supercritical water and methanol. For high temperature experiments,
some types of single-crystal sapphire cells were designed depending on the temperature of interest and the
sample thickness for the X-ray transmission. Single-crystal diamond X-ray windows attached to the externally
heated high-pressure vessel were used for the IXS experiment of supercritical water and methanol. Some
typical experimental results are also given, and the perspective of IXS technique under extreme conditions is
discussed. |
| format |
Article |
| author |
Hosokawa, S. |
| spellingShingle |
Hosokawa, S. Inelastic X-ray scattering experiments at extreme conditions: high temperatures and high pressures Condensed Matter Physics |
| author_facet |
Hosokawa, S. |
| author_sort |
Hosokawa, S. |
| title |
Inelastic X-ray scattering experiments at extreme conditions: high temperatures and high pressures |
| title_short |
Inelastic X-ray scattering experiments at extreme conditions: high temperatures and high pressures |
| title_full |
Inelastic X-ray scattering experiments at extreme conditions: high temperatures and high pressures |
| title_fullStr |
Inelastic X-ray scattering experiments at extreme conditions: high temperatures and high pressures |
| title_full_unstemmed |
Inelastic X-ray scattering experiments at extreme conditions: high temperatures and high pressures |
| title_sort |
inelastic x-ray scattering experiments at extreme conditions: high temperatures and high pressures |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118996 |
| citation_txt |
Inelastic X-ray scattering experiments at extreme conditions: high temperatures and high pressures / S. Hosokawa // Condensed Matter Physics. — 2008. — Т. 11, № 1(53). — С. 71-81. — Бібліогр.: 32 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT hosokawas inelasticxrayscatteringexperimentsatextremeconditionshightemperaturesandhighpressures |
| first_indexed |
2025-07-08T15:03:02Z |
| last_indexed |
2025-07-08T15:03:02Z |
| _version_ |
1837091514750074880 |
| fulltext |
Condensed Matter Physics 2008, Vol. 11, No 1(53), pp. 71–81
Inelastic X-ray scattering experiments at extreme
conditions: high temperatures and high pressures
S.Hosokawa1,2
1 Center for Materials Science using Third-Generation Synchrotron Radiation Facilities, Hiroshima Institute of
Technology, 2–1–1 Miyake, Saeki-ku, Hiroshima 731–5193, Japan
2 Institut für Physikalische-, Kern-, und Makromolekulare Chemie, Philipps Universität Marburg,
Hans-Meerwein Str., 35032 Marburg, Germany
Received November 5, 2007
In this article, we review the present status of experimental techniques under extreme conditions of high tem-
perature and high pressure used for inelastic X-ray scattering (IXS) experiments of liquid metals, semiconduc-
tors, molten salts, molecular liquids, and supercritical water and methanol. For high temperature experiments,
some types of single-crystal sapphire cells were designed depending on the temperature of interest and the
sample thickness for the X-ray transmission. Single-crystal diamond X-ray windows attached to the externally
heated high-pressure vessel were used for the IXS experiment of supercritical water and methanol. Some
typical experimental results are also given, and the perspective of IXS technique under extreme conditions is
discussed.
Key words: particle dynamics, inelastic X-ray scattering, high temperature, high pressure, liquid,
supercritical fluid
PACS: 61.25.Mv, 61.25.Em, 61.10.Eq, 63.50.+x
1. Introduction
Since the advent of intense third-generation synchrotron facilities during the past decades, sig-
nificant progress has been achieved in the development of modern X-ray scattering techniques.
This advancement has stimulated renewed interest in the investigation of structure and dynamics
of disordered matter, and has revived the efforts to explore the liquid state. For example, inelastic
X-ray scattering (IXS) experiments can be performed with resolutions in the meV range using
intense high-energy beamlines with brilliant scattering statistics. However, in order to sufficiently
apply these remarkable possibilities to the liquid matter field, it is essential to develop new sam-
ple environments to extend the range of experimental opportunities. In particular, some metallic
elements, such as transition metals, have very high melting temperatures far beyond 1000◦C, at
which the liquid samples could hardly be kept stable for a long time. Thus, the IXS experiments
for these liquid metals have not been performed so far although they have drawn much interest
from fundamental and applied scientific viewpoints.
Single crystal sapphire having a high melting temperature of 2054 ◦C, is essentially not corro-
sive against most of liquid materials even at high temperatures, and becomes almost transparent to
hard X-rays by making windows with sub-mm thickness, which is possible by using diamond tools.
Moreover, it has a very fast sound velocity of more than 10,000 ms−1, which does not interfere with
inelastic excitation signals. Thus, single crystal sapphire is an ideal material for a sample container
to perform IXS experiments of high-temperature liquids. Tamura and coworkers found these advan-
tages of single-crystal sapphire as a liquid container [1], and used for energy-dispersive X-ray diffrac-
tion experiments of supercritical fluid Hg [2] at high temperatures up to 1530 ◦C under high pres-
sure. This technique has continuously developed to carry out IXS study of supercritical fluid Hg [3].
Diamond is also an excellent material of X-ray transmission, and with fast sound velocity of
18,000 ms−1. It is, however, costly and difficult to machine, and thus, it has been used as high-
c© S.Hosokawa 71
S.Hosokawa
pressure X-ray windows for supercritical water (SCW) and methanol (SCM). Supercritical fluids of
molecules containing hydrogen bonds, such as SCW (Tc = 657 K, pc = 22.1 MPa, ρc = 0.32 gcm−3)
and SCM (Tc = 513 K, pc = 8.1 MPa, ρc = 0.27 gcm−3), have been targets of recent research in
fundamental and applied sciences, in particular in the field of green chemistry as a novel reaction
medium for decomposition of hazardous organic chlorinated wastes, dioxin, and polychlorobiphenyl
(PCB), and recovery of useful chemicals from industrial plastic wastes like polyethylenenetereph-
thalate (PET) [4]. Since the unique properties of SCW and SCM as solvents in chemical reactions
arise from fluctuations in hydrogen bonding state and density (cluster formation), information on
the structures and dynamic properties of SCW and SCM is thus highly needed for understanding
the underlying mechanism in chemical reactions and for further development of supercritical fluids
technology.
In this article, we review the status of the present experimental techniques that we used for
liquid metals, semiconductors, molten salts, molecular liquids, and supercritical water and methanol
to conduct IXS experiments under extreme conditions of high temperature and high pressure in
the next section. Some typical experimental results are also reviewed in the subsequent section,
and the prospects of IXS technique under extreme conditions in the concluding remarks section
are discussed.
2. Experimental
2.1. Vessel for high temperature experiments
Figure 1 shows the (a) side and (b) top views of the internally heated high-pressure vessel
[5] used for our IXS experiments of liquid metals, semiconductors, molten salts, and molecular
liquids. It was designed for X-ray scattering experiments carried out in transmission mode. It
consisted of a closed-end Al cylinder with an inner diameter of 60 mm, an inner length of 170
mm, and a minimum outer diameter of 80 mm. The cylinder was closed with a steel flange of 30
mm thick. The flange was equipped with Bridgeman-type high-pressure leadthroughs for heaters
and thermocouples. Corresponding details are given in [1]. High pressure was generated using high
purity grade He gas, which has a low absorption constant for hard X-rays in the energy range of
the IXS experiments. The temperature of the vessel was kept near room temperature using water
cooling jackets placed around the cylinder.
Figure 1. (a) Side and (b) top views of the internally heated high-pressure vessel [5].
72
Extreme conditions at high temperatures
As seen in figure 1(b), the cylinder was equipped with three X-ray windows for incident and
scattered X-rays. They covered scattering angles 2θ from −2.5◦ to 27.5◦ and from 25◦ to 55◦.
For high-pressure experiments of more than 0.3 MPa, the X-ray window was a rectangular Be
plate of 30 mm long, 10 mm wide, and 2 mm thick. The Be material was polycrystal, and had a
purity of 99.999 % machined at Heraeus GmbH, Germany. It had a relatively high background at
energies near the quasielastic line, which may come from the polycrystalline phase and impurities
of some metal elements such as Mg, Cu, and Fe (> 0.5 ppm). In order to drastically reduce such
a background, single crystal Si plate with a thickness of 0.5 mm was used for the low pressure
experiment below 0.3 MPa. Each plate was fixed by a brass frame attached to the cylinder with
about ten screws. Sealing the windows is accomplished by a rubber O ring. The slit holes in both
the Al cylinder and the frame had a horizontal aperture of 30◦ and a height of 3 mm.
2.2. Sapphire cells for high temperature experiments
For samples with the melting point of lower than 1000◦C, a Tamura-type single-crystal sapphire
cell was used for the IXS experiments of liquid metals such as Na [6], Ge [7,8], Hg [9], Sn [10],
Ga [11], Te [12,13], liquid semiconductors such as Se [14], and molten salts such as NaCl [15] and
KCl [16]. The cell and the compact heating system for the sample are sectionally illustrated in
figure 2(a), and the construction of the hot part is shown in figure 2(b) on an enlarged scale. Liquid
samples were contained in a single-crystal, which is almost transparent to hard X-rays and resistant
to chemical corrosion from the samples at high temperatures. Construction and manufacturing of
the cell are in detail given in an instrumental paper [1]. A closed-end sapphire tube with an inner
diameter of 2.5 mm, an outer diameter of 3.5 mm, and a length of 26.5 mm was inserted into
another closed-end tube with an inner diameter of 3.5 mm, an outer diameter of 4.5 mm, and
a length of 26 mm. The closed ends act as the X-ray windows, whose thicknesses were about
0.2 mm. The sapphire components were glued together by a high-temperature ceramics adhesive
(SEM-COM Co. Inc., Type SCE-1) such that a uniform gap remained between the closed ends of
the tubes. The width of the gap was adjusted to match the requirements for maximum scattering
intensity from the respective liquid samples. A sample reservoir was also attached to the outer
tube by the ceramics adhesive.
X-ray
sample
reservoir
single-crystalline
sapphire cell
sample
W-Re
thermocouple
Mo block W
heater
ceramic
adhesive
1 cm
(a)
X-ray
(b)
200µm
200µm
φ
2
.5
φ
4
.5
φ
3
.5
sample
slit
heater
thermocouple
alumina
tubes
machinable
alumina
sapphire
cellmain
heater
sub
heater
thermocouples
(c)
Figure 2. (a) Single crystal sapphire cell [1] for samples with the melting point of lower than
1000◦C together with the compact heating system. (b) Enlarged view around the liquid sample
for the IXS measurements. (c) The whole assembly of the cell and the heating system.
The cell was heated with a heating element manufactured from Mo or W resistant wire with a
diameter of 0.5 mm. The wire was electrically insulated with alumina tubes (Friedrichsfeld Co. Ltd.,
73
S.Hosokawa
Type DEGUSSIT AL-23) with inner and outer diameters of 0.7 mm and 1.2 mm, respectively. The
zigzag shaped heater was wound around an Mo cylindrical block to ensure a uniform temperature
distribution over the scattering volume. A horizontal slit on the scattering side of the Mo block
made the X-ray scattering possible. The sample temperature was monitored and controlled using
two W-5%Re:W-26%Re thermocouples. They were inserted through the holes on the front part
of the Mo block, and were in contact with the outer wall of the sapphire cell close to the sample
volume. A similar Mo heater was used to keep the sample reservoir at a temperature above the
melting point of the sample. To improve the heat transfer and temperature homogeneity, the
reservoir was additionally covered with a metallic hood.
Figure 2(c) shows the whole assembly of the cell and the heating system. The whole assembly
was placed in massive blocks of porous machinable alumina (Cotronics Co., Type 960, 96% Al2O3).
These parts provide thermal insulation and suppress convection of the He gas. Since the machinable
alumina deforms beyond 1600◦C, the heating assembly was inserted into two additional alumina
tubes (Friedrichsfeld Co. Ltd., Type DEGUSSIT AL-23) to suppress the heat flow from the hot
heating system.
The following procedure describes how the sample space was filled between the closed ends of
the cell with the liquid sample. First, the solid sample was put into the sample reservoir of the
cell. After closing the high-pressure seals, the entire assembly was evacuated. Then, the sample
reservoir was heated up in order to melt the sample, and the vessel was filled with He gas at
normal pressure that was sufficient to force the molten sample through a small channel and fill
the sample space. Once the cell had been filled, the temperature of the reservoir was maintained
near the melting point. Pressure balance between the compressed liquid sample and the He gas
was achieved through the sample reservoir. The background was measured by heating the sample
part without the sample up to the same temperature of the sample measurement before heating
and filling the sample, and was used for the data correction.
If the melting temperature of the sample is higher than 1000◦C, this type of cell can no longer
be used for the IXS experiment because the high-temperature ceramics adhesive (SEM-COM Co.
Inc., Type SCE-1) softens around 1000◦C, and the sample cannot be kept in the sample reservoir.
Instead, a reservoir-less cell was designed as illustrated in figure 3, and used for the high-melting
temperature liquid metals such as Si [17], Fe [18,19], Ni [20], and Cu [21]. As seen in the figure, a
sample with an appropriate thickness for the X-ray transmission was sandwiched with two closed-
end tubes with the same sizes of figure 2. Then, the tubes were cemented and closed by the
high-temperature ceramics adhesive under He gas atmosphere in order to fix the sample thickness
even after melting and to avoid the chemical corrosion between the sample vapour and the metal
heating wire at high temperatures. It was placed in the same heating system shown in figure 2(c),
which can heat the sample up to 1700◦C. Due to low wetting natures with sapphire and high surface
tensions of liquid metals, the thin films of liquid metal samples can easily be kept between the gap
of the closed ends of the sapphire cell. When the power of the heating system was not sufficient to
attain the heating up to the objective temperature, another heating wire was wound outside the
main heater to help heating the high melting temperature sample such as Fe, Ni, and Cu.
ceramic
adhesive
X-ray
200µm
200µm φ
2
.5
φ
4
.5
φ
3
.5
sample
Figure 3. Cross section of single crystal sapphire cell for samples with the melting point of higher
than 1000◦C.
74
Extreme conditions at high temperatures
If the sample temperature of interest was lower than 1000◦C and the sample thickness was
larger than 0.2 mm, another type of the cell was used for the convenience of conducting the IXS
experiments, such as for liquid S [22], molten NaI [23] and CsCl [24], and several molecular liquids
[25]. Figure 4(a) shows sectional view of the convenient single-crystal sapphire cell, and figure 4(b)
illustrates stereographic view of the sapphire column for the outgoing X-ray window. Two single
crystal sapphire short columns were drilled and polished by diamond tools and diamond pastes
to make the X-ray windows. The X-ray windows were polished to be a thickness of 0.25 mm. A
ditch was made in one of the sapphire columns for the scattered X-rays as seen in figure 4(b). The
columns were fixed with an alumina tube (Friedrichsfeld Co. Ltd., Type DEGUSSIT AL-23) by
high-temperature ceramics adhesive (SEM-COM Co. Inc., Type SCE-1) so that the X-ray windows
were facing each other having an adequate gap for the sample thickness. The sample reservoir was
attached directly outside the alumina tube.
(a)
X-ray(b)
(c)
X-ray
sample
reservoir
single-crystal
sapphire
ceramic
adhesive
1 cm
250µm250µm
sample thickness
2q
X-ray window
ditch for scattered X-rays
X-ray2q
thermocouples
heaters
heatersMo block
Mo block
alumina tubes
alumina cap
Figure 4. (a) Sectional view of convenient single-crystal sapphire cell for measurements at sample
temperatures of lower than 1000 ◦C. (b) Stereographic view of the outgoing X-ray window of
the cell. (c) The whole assembly of the cell and the heating system.
As seen in figure 4, the cell was encapsulated in blocks made of Mo, which has a hole for
the incoming X-rays and a slit for the scattered X-rays. The Mo blocks were wound by zigzag-
type Mo heaters with a diameter of 0.5 mm with the alumina insulation tubes, and worked for a
uniform temperature distribution over the scattering volume. The temperature was monitored and
controlled by two W-5%Re:W-26%Re thermocouples located near the incident and scattered X-ray
windows through the holes in the upper Mo block. To avoid condensation of the sample vapour
around the X-ray windows, the top of the sample reservoir was set outside the Mo block, and was
encapped with an alumina piece. The whole setup was placed in the vessel shown in figure 1.
2.3. High-temperature high-pressure cell for supercritical water and methanol
Figure 5 shows a high-temperature high-pressure cell or an externally heated high-pressure
vessel (Toyo Koatsu Co. Ltd.) used for the IXS experiments of supercritical water [26] and methanol
[27]. The vessel was made of Inconel 625 alloy, which does not chemically react with the supercritical
water and methanol. The sample was degassed and filled in the vessel. Two synthetic single crystal
75
S.Hosokawa
diamond windows (Sumutomo Electric Ind. Co. Ltd.) with a thickness of 1 mm and a diameter of
5 mm were equipped in the vessel for the incoming and outgoing X-rays. The diamond windows
were supported by metal sleeves. The aperture of the sleeves was about 20◦, which provided the
scattering angle up to about 20◦ by rotating the vessel. The sleeves were sealed by using hollow
Thermocouple
Sleeve
Metal O-ring
Sample inlet
Cartridge heater
Diamond windowRetainer
X-rays
Figure 5. Cross section of a high-temperature high-pressure IXS cell.
metal O rings. High temperatures up to 400◦C were achieved by using four cartridge heaters set
in the holes of the vessel. The temperature was monitored and controlled by a chromel-alumel
thermocouple placed in the fluid sample. The stability of the temperature was within 0.1 K. The
pressure was measured using a Heise gauge with a resolution of 0.02 MPa. The vessel was placed
in a vacuum chamber with thin Kapton windows to suppress strong background scattering by
the surrounding air. This vessel was originally designed by Yamaguchi [28] for XAFS and X-ray
diffraction experiments for supercritical water and its solutions, and modified by only replacing
the polycrystal diamond X-ray windows with single crystal ones.
3. Examples of results
Using the above equipment, we have carried out IXS experiments for several liquid systems at
high temperatures under normal or high pressure. Three typical examples of the IXS experiments
will be reviewed in the following subsections.
3.1. Liquid metals
In a monatomic liquid, the excitation lifetime is shortened by the heat flow effects and viscous
drag forces. The width of the inelastic excitation peaks WQ2 can be estimated from the values of
macroscopic thermodynamic quantities within the thermodynamic limit, expressed as [29]
W = [(γ − 1)DT + ν)]/2, (1)
where γ is the ratio of specific heats at constant pressure and constant volume, DT is the thermal
diffusivity, and ν is the longitudinal kinematic viscosity. Liquid Fe has a large γ value of 1.72 and
a shear viscosity value of 5.5 MPas, by which a highly damping feature of the phonon excitation
modes was expected within the hydrodynamic context.
The IXS measurement of liquid Fe [18,19] was performed at 1570◦C near the melting point
at BL35XU of SPring-8 using the high-temperature reservoir-less sapphire cell shown in figure 3.
1570◦C is the highest temperature at which the IXS experiments have been carried out with a
liquid container so far. Figure 6(a) shows the selected IXS spectra normalized to the corresponding
integral. Also given as a dashed line is a typical example of the resolution function.
In contrast to the above hydrodynamic prediction, clear inelastic excitations are seen as peaks or
shoulders at both the sides of the central quasielastic line, and the energy of inelastic contributions
76
Extreme conditions at high temperatures
0.50
0.45
0.40
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
S
(Q
,ω
)/
S
(Q
)
(m
e
V
-1
)
-40 -20 0 20 40
ω (meV)
liquid Fe
1570 °C
Q (nm
-1
) =
21.3
18.6
16.0
13.3
10.6
7.9
5.3
3.0
1.9
35
30
25
20
15
10
5
0
-5
-10
ω
Q
(
m
e
V
)
2520151050
Q (nm
-1
)
45
40
35
30
25
20
15
10
5
0
Γ
Q
(m
e
V
)
cs = 3800 m/s
liquid Fe
1570 °C
(a)
(b)
Figure 6. (a) Selected IXS spectra of liquid Fe at 1570◦C. (b) Dispersion relation (circles) and
width (triangles) of the inelastic excitations obtained from DHO model [31]. See the text for
details.
shifts with the increasing Q. Figure 6(b) exhibits the excitation energy ωQ (circles) and the width
ΓQ (triangles) of the inelastic excitations obtained from a damped harmonic oscillator (DHO) model
[31]. The dispersion of the phonon excitation in the low Q region deviates by about 11 % from that
predicted by hydrodynamic sound velocity given by a dashed line in the figure. With increasing
Q, ΓQ slowly and almost linearly increases, while the hydrodynamic theory using the macroscopic
thermodynamic data for equation (1) predicted a very rapid increase that is proportional to Q2 as
shown by the solid curve in figure 6(b). This result on the excitation width indicates that the Q
range of the present IXS experiment is already outside of where the hydrodynamic theory can be
applied. This inconsistency of the damping feature has been solved [19] by applying the modified
version of the generalized (Q dependent) hydrodynamic theory [30].
3.2. Molten salts
There are two recent topics for the study of the dynamics in molten salts: 1) In what way is
the acoustic phonon dynamics of the Coulomb liquids different from liquid metals? 2) Does the
optic-like mode appear in the IXS spectra? The dynamic structure factor of molten CsCl was
measured at 720◦C at BL35XU/SPring-8 [24] using a slightly modified version of the convenient
sapphire cell shown in figure 4. Figure 7(a) illustrates a perspective view of the IXS spectra of
molten CsCl. In contrast to those of liquid metals, the phonon excitation modes can be hardly
seen as a peak. This is due to the slower velocity of sound. Nevertheless, the inelastic excitations
can be observed through the DHO analysis [31]. Figure 7(b) shows the dispersion relation (circles)
and width (triangles) of the inelastic excitations obtained from DHO model.
77
S.Hosokawa
(a)
(b)
Figure 7. (a) A perspective plot of IXS spectra of molten CsCl at 720◦C. (b) Dispersion relation
(circles) and width (triangles) of the inelastic excitations obtained from DHO model. See the
text for details.
As seen in the figure, the dispersion of the phonon excitation in the low Q region largely deviates
by about 70 % from that predicted by hydrodynamic sound velocity given by a dashed line, which
was found earlier in other molten salts [15,16,23], and extremely larger than those in liquid metals.
With increasing Q, the linewidth increases following the Q2 law up to about 10 nm−1 as predicted
by the hydrodynamics. However, the linewidth is a factor of seven smaller than the estimation using
a Brillouin light scattering result. The large speed-up and the significant narrowing of the collective
mode observed in molten CsCl can be related to each other by a recently presented viscoelastic
theory [30], and must arise from the intrinsic nature of molten alkali chlorides. Furthermore, in
comparison with the previous results for molten NaCl [15] and KCl [16], the apparent sound velocity
is found to be approximately scaled by the inverse of the square-root of effective mass among these
molten salts.
Distinct excitations of the optic-like modes cannot be observed in the present spectra of molten
CsCl although the large difference in the atomic form factor between Cs and Cl elements has got
an advantage of observing them. This may be due to a highly damping feature of the optic-like
modes as suggested by an INS results [32].
3.3. Supercritical water and methanol
The IXS spectra of sub- and supercritical water was measured at BL35XU of SPring-8 at
densities from about 1 gcm−3 in ambient conditions to 0.263 gcm−3 in the supercritical region
[26]. The measurements were performed in the Q range 1.3 − 10.7 nm−1 and in the ω range
±40 meV. Figure 8(a) shows logarithmic plots of selected IXS spectra normalized to the respective
integral intensity at Q = 4.0 nm−1 at different ρ values. Circles represent the experimental data
with error bars, and the dashed curve shows the resolution function. In the ambient conditions
(ρ = 0.997 gcm−3), inelastic excitation modes are seen at the both sides of the central peak,
and the excitation energies are highly (∼ 100 %) deviated from the hydrodynamic value cs. With
decreasing ρ, the energy position of the inelastic excitation rapidly shifts to the lower energies, and
the shoulders merge into the quasielastic line.
The spectra were analyzed using a generalized Langevin formalism with a memory function
of thermal and viscoelastic relaxations to obtain the energy of the inelastic excitation modes
ωQ. Figure 8(b) exhibits the ρ dependence of the dynamical velocity of sound cQ = ωQ/Q at
Q = 2.6 nm−1 (empty circles) and Q = 9.4 nm−1 (full circles). Also given is the hydrodynamic
velocity of sound cs as a dashed curve. In ambient conditions of ρ ∼ 1 gcm−3, the cQ values are
about 3,000 ms−1, almost twice as large as the cs value of about 1,500 ms−1. With decreasing ρ,
cQ rapidly decreases, and approaches the cs vale at ρ ∼ 0.8 gcm−3. With a further decrease of ρ,
78
Extreme conditions at high temperatures
10
-5
10
-4
10
-3
10
-2
10
-1
10
0
10
1
10
2
10
3
10
4
10
5
10
6
10
7
10
8
10
9
10
10
10
11
10
12
10
13
10
14
S
(Q
, ω
)/
S
(Q
)
(p
s
)
-30 -20 -10 0 10 20 30
ω (ps-1)
fluid H2O
Q = 4.0 nm
-1 ρ (gcm-3) =
0.997
0.948
0.900
0.801
0.594
0.381
0.311
0.263
T (K) p (MPa)
699 34.0
698.5 36.0
697 38.9
652 39.2
547.5 39.2
464 38.7
410 39.1
298 0.2
3
2
1
c
Q
/ c
s
1.00.80.60.40.2
ρ (gcm-3)
3000
2000
1000
0
c
Q
(
m
s
-1
)
ρ
c
Q = 9.4 nm
-1
2.6 nm
-1
cs
(a) (b)
Figure 8. (a) Logarithmic plots of selected IXS spectra normalized with the respective integral
as a function of ω at Q = 4.0 nm−1 at different densities ρ. (b) Top: ρ dependence of dynamical
velocity of sound cQ = ωQ/Q at Q = 2.6 nm−1 (empty circles) and Q = 9.4 nm−1 (full circles).
The dashed curve indicates the adiabatic sound velocity cs. Bottom: The ratio cQ/cs. The arrow
indicates the critical density ρc = 0.32 gcm−3.
cQ at Q = 2.6 nm−1 decreases along with the cs curve, while cQ at Q = 9.4 nm−1 starts to deviate
again from the cs value. The ratio cQ/cs gives a much prominent trend as seen in the bottom panel
of figure 8(b). The cQ value at Q = 9.4 nm−1 shows about 80% positive value around the critical
density ρc = 0.32 gcm−3, while the cQ value at Q = 2.6 nm−1 locates slightly larger than the
hydrodynamic value shown as a chain line.
From these results, the authors suggested that the initial decrease of the dynamical velocity
of sound is due to approaching the percolation limit in the number of hydrogen bonds, and the
subsequent increase is due to the formation of rigid dimers in sub- and super critical water. Simi-
lar results were obtained in the density dependence of the IXS spectra of sub- and supercritical
methanol [27].
4. Concluding remarks
In this article we describe our recent status of high-temperature experimental technique for
liquids with high melting points using several types of single-crystal sapphire cells. The high tem-
perature IXS experiment using a liquid sample container made of single-crystal sapphire has nowa-
days become a well-matured technique by the rich experimental experiences in almost two decades,
and useful information on the particle or molecular dynamics of various kinds of liquids has been
obtained using the single-crystal sapphire sample container. For elements with a higher melting
79
S.Hosokawa
temperature, container-less methods with laser heating have made it possible to carry out high-
energy X-ray scattering. However, the spatial stability of the liquid sample with a sub-mm size
should be realized in order to conduct the IXS experiment.
A high-temperature high-pressure cell with diamond windows for supercritical fluid water and
methanol is also reviewed in this manuscript. It can essentially be applied to supercritical phases
of other molecular liquids if the temperature is limited up to 400◦C. If the higher temperature is
needed or the sample is more corrosive, it is necessary to find another stable metal material for
the high-temperature high-pressure cell.
Acknowledgements
The IXS experiments of liquid metals, semiconductors, molten salts, and molecular liquids were
carried out under the collaboration with Professor W.-C. Pilgrim of Philipps Universität Marburg,
Dr. F. Demmel of ISIS, Dr. H. Sinn of HASYLAB/DESY, Professor S. Takeda and Dr. Y. Kawakita
of Kyushu University, Professor M. Inui of Hiroshima University, Dr. Y. Katayama of Japan Atomic
Energy Agency, Professor T. Kamiyama of Hokkaido University, Dr. A. Q. R. Baron and Dr. S.
Tsutsui of SPring–8, and Dr. E. E. Alp of APS. The supercritical water and methanol experiments
were performed with Professor T. Yamaguchi and Dr. K. Yoshida of Fukuoka University and
Bl35XU/SPring–8 staff. The authour greatly appreciates Dr. M. Krisch, Dr. G. Monaco, and
ESRF IXS beamline staff for conducting the IXS experiments at ESRF. The IXS experiments were
performed at the beamline ID16 and ID28 of the ESRF (Proposal No. SC366, HS849, HS1154,
HS1504, HS1644, HS1648, HS1988, HS2434, and HS2671), at the beamline 3–ID–C of the APS
(Proposal No. II–76 and II–325), and at the beamline BL35XU of the SPring–8 (Proposal No.
2001B0482, 2002A0182, 2002B0179, 2003A0081, 2003A0153, 2003B0574, 2003B0766, 2004B0635,
2005A0567, 2005B0346, 2006A1376, and 2007A1109). The IXS works at the APS were supported
from US DOS BES Material Science, Contract No. W–31–109–ENG–38.
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Експерименти по непружному розсiянню рентгенiвських
променiв при екстремальних умовах: високi температури та
високi тиски
Ш.Хосокава1,2
1 Центр матерiалознавства та Центр синхротронної радiацiї третього поколiння, Хiросiмський
технологiчний iнститут, Хiросiма, Японiя
2 Iнститут фiзичної, ядерної та макромолекулярної хiмiї, Фiлiпс унiверситет Марбурґа, Марбурґ,
Нiмеччина
Отримано 5 листопада 2007 р.
У данiй статтi ми робимо огляд сучасного стану експериментальних методик при екстремальних
умовах високих температур та високих тискiв у експериментах з непружного розсiяння рентгенiв-
ських променiв для рiдких металiв, напiвпровiдникiв, розплавiв солей, молекулярних рiдин, та над-
критичних води i метанолу. Для експериментiв при високих температурах було розроблено деякi
типи монокристалiчних сапфiрових комiрок, в залежностi вiд температури та ширини зразка для
проходження рентгенiвських променiв. Монокристалiчнi алмазнi вiкна для рентгенiвських променiв,
пiд’єднанi до комiрки, що витримує високий тиск та має зовнiшнє нагрiвання, використовувались
для експериментiв по непружному розсiянню рентгенiвських променiв у надкритичних водi та мета-
нолi. Також подано деякi типовi експериментальнi результати та обговорюється перспектива мето-
дики непружного розсiяння рентгенiвських променiв при екстремальних умовах.
Ключовi слова: частинкова динамiка, непружне розсiяння рентгенiвських променiв, висока
температура, високий тиск, рiдина, надкритичний флюїд
PACS: 61.25.Mv, 61.25.Em, 61.10.Eq, 63.50.+x
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