**1. Introduction**

42 Advanced Topics in Measurements

Lin, D.C., & Rymer, W.Z. (1991). A quantitative analysis of pendular motion of the lower leg in spastic human subjects. *IEEE Trans. Biomed. Eng.*, Vol.38, pp.906-918

Nordmark, E., & Andersson, G. (2002). Watenberg pendulum test: objective quantification of

Tong, K., & Granat, M.H. (1999). A practical gait analysis system using gyroscopes. *Med.* 

Vodovnik, L., Bowman, B. R., & Bajd, T. (1984). Dynamics of spastic knee joint. *Med. & Biol.* 

Watenberg, R. (1951). Pendulousness of the legs as a diagnostic test. *Neurology*, Vol.1, pp.18-

William, D.W., Jr. (1998). Spinal organization of motor function. *Physiology 4th*, Robert, M.B.

rhizotomy. *Developmental Medicine and Child Neurology*, Vol.44, pp.26-33 Stillman, B., & McMeeken, J. (1995). A video-based version of pendulum test: Technique and

muscle tone in children with spastic diplegia undergoing selective dorsal

Nicol, A.C. (1989). Measurement of joint motion. *Clin. Rehabil.*, Vol.3, pp.1-9

normal response. *Arch. Phys. Rehabil.*, Vol.76, pp.166-176

*Eng. Phys.*, Vol.21, pp.87-94

24

*Eng. & Comput.*, Vol.22, No.1, pp.63-69

& Matthew, N. L., Mosby, Inc. U.S.A., pp.186-199

An X-ray absorption fine structure (XAFS) spectroscopy is a powerful and useful technique to probe the local electronic structure and the local atomic structure around an absorbing atom in an unknown material [Stöhr, 1996, Ohta, 2002]. A highly bright X-ray source, synchrotron radiation (SR) is usually used for XAFS measurements to obtain reliable spectra, even for elements of very low content in a sample.

For visible/ultraviolet (UV) and infrared absorption spectroscopies, the transmission mode is generally used, where incident and transmitted photon intensities are monitored. This is also the most fundamental technique for XAFS measurements in the hard X-ray region. However, it is hard to apply it in the soft X-ray region because of very low transmission. Instead, other techniques equivalent to the transmission mode have been developed; total/partial electron yield (EY) and fluorescent yield (FY) modes. The former is a widely adopted mode in the soft X-ray region, where the yield of Auger electrons and/or secondary electrons is proportional to the X-ray absorption coefficient. Since the electron escape depth is very short, the EY mode is surface sensitive. The latter is useful for XAFS measurement of heavy elements of low concentration in the hard X-ray region, and it is also useful as a bulk sensitive method in the soft X-ray region, although the probability of radiative decay is much smaller than that of Auger decay. It is often the case that an appropriate mode is chosen for sample conditions.

We have developed a practical and useful XAFS measurement system in the soft X-ray region applicable for various sample conditions and multipurpose measurements. In this system, it is possible to measure not only solid samples (such as powder, grain, sheet and thin film samples) but also liquid and gel samples. It is also applicable to in-situ measurements of anaerobic samples. In addition, it provides us some information of depth profiles with combined use of the EY and FY modes.

#### **2. XAFS measurement system in the soft X-ray region**

The XAFS measurement system is an assembly of several components; a soft X-ray beamline, sample chambers, detection systems, and a sample transfer system. Details of each component are described follow.

XAFS Measurement System in the Soft X-Ray Region

infrared microscopy and X-ray reflectivity.

was used for the simulations.

for Various Sample Conditions and Multipurpose Measurements 45

Fig. 1. (a) Bird-eye view of the SR center, Ritsumeikan University; (b) Photo of BL-10. Fourteen beamlines have been installed in the center; five beamlines for XAFS, three for Xray lithography, three for photoelectron spectroscopy, and one for soft X-ray microscopy,

Fig. 2. (a) Schematic configuration of BL-10, and simulated X-ray beam profiles at (b) the source point; (c) the sample position of the HV chamber and (d) the sample position of AP chamber. The SR ray-tracing program "SHADOW" [Lai & Cerrina, 1986, Welnak et al., 1996]

#### **2.1 Soft X-ray double-crystal monochromator beamline**

For a beamline below 1000 eV, a grating monochromator is generally used, while a crystal monochromator is advantageous above 1000 eV, since several high quality crystals are available which have proper lattice spacings. For XAFS measurements in the higher-energy soft X-ray region (above 1000 eV), the double-crystal monochromator (DCM) beamline (BL-10) was constructed in the SR center, Ritsumeikan University in Japan [Iwasaki, et al., 1998, Handa, et al., 1999]. Then BL-10 has been developed and upgraded, and many measurements have been performed (see Fig. 1) [Nakanishi & Ohta, 2009]. It consists of a 5.1 µm thick Be foil, a Ni-coated Si toroidal mirror, a Golovchenko-type DCM [Golovchenko et al., 1981], an I0 monitor made of either Cu or Al mesh, a high-vacuum (HV) sample chamber kept below 2×10-5 Pa, an atmospheric-pressure (AP) sample chamber, and some masks and slits (see Fig. 2 (a)). The Be foil and the toroidal mirror at the front line are cooled by water in order to reduce a heat load by direct irradiation of white X-rays. The Be foil functions to cut visible and vacuum-ultra-violet photons which cause a background of an XAFS spectrum. The SR beam with 6 mrad (horizontal) and 2 mrad (vertical) is deflected upward by 1.4 º and focused at the sample position in the AP sample chamber about 9 m apart from the source point with the 1:1 geometry by the toroidal mirror. The beam shapes and sizes are in good agreement with those simulated by the ray trace analysis, as shown in Fig. 2 (b)-(d). The available photon energy covers a range from about 1000 to 4500 eV by choosing a pair of monochromatizing crystals, such as beryl(10-10), KTP(011), InSb(111), Ge(111), Si(111) and Si(220) whose 2d lattice spacings are 1.5965, 1.0954, 0.7481, 0.6532, 0.6270 and 0.3840 nm, respectively. The incident angle to the monochromatizing crystal, is read in high accuracy with an angle encoder. The photon energy is determined with the 2d lattice spacing of a monochromatizing crystal and the incident angle using Bragg's law. Several masks and slits were inserted to minimize stray lights.

#### **2.2 Tandem-type high-vacuum and atmospheric-pressure sample chambers**

It is challenging to obtain reliable spectra from highly reactive compounds. In the soft X-ray region, XAFS spectra are usually measured in vacuum because of the low transmittance of X-rays in air (see Fig. 3). A vacuum environment is also necessary to measure reliable spectra from highly hygroscopic samples. In contrast, some compounds change their structures in vacuum. A typical case is hydrated compounds, in which hydrated water molecules are easily desorbed in vacuum. In addition, liquid solutions or nano-particles suspended in liquid cannot be introduced in vacuum without a special cell. For such samples, XAFS measurements in AP are necessary.

Another compact AP sample chamber, made of an ICF70 six-way cross nipple, was installed at the downstream of the HV sample chamber (see Fig. 2, 4 (a)). Two chambers are separated by a thin Be window, which should be tolerable against 1 atm pressure difference and whose thickness should be as thin as possible to minimize the intensity loss. The beam size at the sample position in the HV sample chamber is about 2.5 mm (vertical) × 6 mm (horizontal) (not focused), while that in the AP chamber is about 2 mm (vertical) × 5 mm (horizontal) (focused). Thus, we chose the diameter of 10 mm and thickness of 15 m, respectively (see Fig. 4 (b)). It has been working without any trouble for more than one year [Nakanishi et al., 2010].

For a beamline below 1000 eV, a grating monochromator is generally used, while a crystal monochromator is advantageous above 1000 eV, since several high quality crystals are available which have proper lattice spacings. For XAFS measurements in the higher-energy soft X-ray region (above 1000 eV), the double-crystal monochromator (DCM) beamline (BL-10) was constructed in the SR center, Ritsumeikan University in Japan [Iwasaki, et al., 1998, Handa, et al., 1999]. Then BL-10 has been developed and upgraded, and many measurements have been performed (see Fig. 1) [Nakanishi & Ohta, 2009]. It consists of a 5.1 µm thick Be foil, a Ni-coated Si toroidal mirror, a Golovchenko-type DCM [Golovchenko et al., 1981], an I0 monitor made of either Cu or Al mesh, a high-vacuum (HV) sample chamber kept below 2×10-5 Pa, an atmospheric-pressure (AP) sample chamber, and some masks and slits (see Fig. 2 (a)). The Be foil and the toroidal mirror at the front line are cooled by water in order to reduce a heat load by direct irradiation of white X-rays. The Be foil functions to cut visible and vacuum-ultra-violet photons which cause a background of an XAFS spectrum. The SR beam with 6 mrad (horizontal) and 2 mrad (vertical) is deflected upward by 1.4 º and focused at the sample position in the AP sample chamber about 9 m apart from the source point with the 1:1 geometry by the toroidal mirror. The beam shapes and sizes are in good agreement with those simulated by the ray trace analysis, as shown in Fig. 2 (b)-(d). The available photon energy covers a range from about 1000 to 4500 eV by choosing a pair of monochromatizing crystals, such as beryl(10-10), KTP(011), InSb(111), Ge(111), Si(111) and Si(220) whose 2d lattice spacings are 1.5965, 1.0954, 0.7481, 0.6532, 0.6270 and 0.3840 nm, respectively. The incident angle to the monochromatizing crystal, is read in high accuracy with an angle encoder. The photon energy is determined with the 2d lattice spacing of a monochromatizing crystal and the incident angle using Bragg's law. Several masks and slits

**2.2 Tandem-type high-vacuum and atmospheric-pressure sample chambers** 

It is challenging to obtain reliable spectra from highly reactive compounds. In the soft X-ray region, XAFS spectra are usually measured in vacuum because of the low transmittance of X-rays in air (see Fig. 3). A vacuum environment is also necessary to measure reliable spectra from highly hygroscopic samples. In contrast, some compounds change their structures in vacuum. A typical case is hydrated compounds, in which hydrated water molecules are easily desorbed in vacuum. In addition, liquid solutions or nano-particles suspended in liquid cannot be introduced in vacuum without a special cell. For such

Another compact AP sample chamber, made of an ICF70 six-way cross nipple, was installed at the downstream of the HV sample chamber (see Fig. 2, 4 (a)). Two chambers are separated by a thin Be window, which should be tolerable against 1 atm pressure difference and whose thickness should be as thin as possible to minimize the intensity loss. The beam size at the sample position in the HV sample chamber is about 2.5 mm (vertical) × 6 mm (horizontal) (not focused), while that in the AP chamber is about 2 mm (vertical) × 5 mm (horizontal) (focused). Thus, we chose the diameter of 10 mm and thickness of 15 m, respectively (see Fig. 4 (b)). It has been working without any trouble for more than one year

**2.1 Soft X-ray double-crystal monochromator beamline** 

were inserted to minimize stray lights.

samples, XAFS measurements in AP are necessary.

[Nakanishi et al., 2010].

Fig. 1. (a) Bird-eye view of the SR center, Ritsumeikan University; (b) Photo of BL-10. Fourteen beamlines have been installed in the center; five beamlines for XAFS, three for Xray lithography, three for photoelectron spectroscopy, and one for soft X-ray microscopy, infrared microscopy and X-ray reflectivity.

Fig. 2. (a) Schematic configuration of BL-10, and simulated X-ray beam profiles at (b) the source point; (c) the sample position of the HV chamber and (d) the sample position of AP chamber. The SR ray-tracing program "SHADOW" [Lai & Cerrina, 1986, Welnak et al., 1996] was used for the simulations.

XAFS Measurement System in the Soft X-Ray Region

where *ip* (A) is the short-circuit current of a photodiode.

the photon flux

charge (A·s) [Saleh & Teich, 1991].

is in the range (0 ≤

(1), we obtain the following,

changed by,

where 

for Various Sample Conditions and Multipurpose Measurements 47

For the performance test of BL-10, the photon flux was estimated from 1000 to 4500 eV using a Si PN photodiode (AXUV-SP2, International Radiation Detectors Inc., USA). In general,

*pi*

*<sup>e</sup> <sup>R</sup> h* 

where *R* is called as 'resposibility', whose typical values are available from the WEB site of International Radiation Detectors Inc. (http://www.ird-inc.com/). The equation (3) is

> *e Rh*

*Φ*

Fig. 5. Photon fluxes at the sample position in HV (black line) and AP (red line) sample

chambers using each monochromatizing crystal.

*e* is called a device quantum yield. Substituting this equation (3) into the equation

*pi*

Fig. 5 shows the photon fluxes at the sample positions in the HV and AP sample chambers. All photon fluxes are normalized by the SR ring currents (200 mA). The difference of photon fluxes between in HV and AP is larger in the lower photon energy because of the transmittance for the Be window (see Fig. 3). However, the difference for the KTP crystal was relatively smaller than predicted that. This might be due to the radiation damage for the crystal, since the measurement was performed first in AP and later in HV sample chambers.

≤ 1), and is approximately proportional to the photon energy *h*

*<sup>η</sup> <sup>e</sup>* . (1)

(2)

*R h <sup>ν</sup>* (4)

(3)

is a quantum efficiency and *e* is a

,

(photons/s) is given by the following formulae,

*Φ*

Fig. 3. Simulated transmittances of Air and He gas at 70 mm, which is the distance from the vacuum-tight window to the sample position in the AP sample chamber, and Be of 15 and 100 m thickness. These simulations were used "X-ray Interaction with Matter Calculator", the Center for X-ray Optics, Lawrence Berkeley National Laboratory, USA. Available from "http://henke.lbl.gov/optical\_constants/".

Fig. 4. Photos of the HV and AP sample chambers (a), and the vacuum-tight Be window (b).

Prior to the measurement, the AP chamber was filled with He gas to increase the transmittance of X-rays (see Fig. 3). It takes about 10 minutes to replace the air inside with He gas completely with the flow rate of 8.45×10-1 Pa・m3/s (500 sccm). The He gas flow rate was kept constant, typically at 3.38×10-2 Pa・m3/s (20 sccm) during measurements.

Now, the total EY (TEY) with specimen current, partial EY (PEY) using a PEY detector (as will hereinafter be described in detail), and partial FY (PFY) using a silicon drift detector (SDD) can be carried out in the HV sample chamber, while PFY can be carried out in the AP sample chamber.

Fig. 3. Simulated transmittances of Air and He gas at 70 mm, which is the distance from the vacuum-tight window to the sample position in the AP sample chamber, and Be of 15 and 100 m thickness. These simulations were used "X-ray Interaction with Matter Calculator", the Center for X-ray Optics, Lawrence Berkeley National Laboratory, USA. Available from

Fig. 4. Photos of the HV and AP sample chambers (a), and the vacuum-tight Be window (b).

Prior to the measurement, the AP chamber was filled with He gas to increase the transmittance of X-rays (see Fig. 3). It takes about 10 minutes to replace the air inside with He gas completely with the flow rate of 8.45×10-1 Pa・m3/s (500 sccm). The He gas flow rate

Now, the total EY (TEY) with specimen current, partial EY (PEY) using a PEY detector (as will hereinafter be described in detail), and partial FY (PFY) using a silicon drift detector (SDD) can be carried out in the HV sample chamber, while PFY can be carried out in the AP

was kept constant, typically at 3.38×10-2 Pa・m3/s (20 sccm) during measurements.

"http://henke.lbl.gov/optical\_constants/".

sample chamber.

For the performance test of BL-10, the photon flux was estimated from 1000 to 4500 eV using a Si PN photodiode (AXUV-SP2, International Radiation Detectors Inc., USA). In general, the photon flux (photons/s) is given by the following formulae,

$$
\mathfrak{O} = \frac{\dot{i}\_p}{\eta \, e} \,. \tag{1}
$$

where *ip* (A) is the short-circuit current of a photodiode. is a quantum efficiency and *e* is a charge (A·s) [Saleh & Teich, 1991].

is in the range (0 ≤ ≤ 1), and is approximately proportional to the photon energy *h*,

$$R = \frac{\eta \, e}{h \, \nu} \tag{2}$$

where *R* is called as 'resposibility', whose typical values are available from the WEB site of International Radiation Detectors Inc. (http://www.ird-inc.com/). The equation (3) is changed by,

$$
\hbar \text{ } \eta \text{ } e = \text{R } \hbar \text{ } \nu \text{ } \tag{3}
$$

where *e* is called a device quantum yield. Substituting this equation (3) into the equation (1), we obtain the following,

$$\text{d}\Phi = \frac{\dot{l}\_p}{R \,\, h \,\, \nu} \tag{4}$$

Fig. 5 shows the photon fluxes at the sample positions in the HV and AP sample chambers. All photon fluxes are normalized by the SR ring currents (200 mA). The difference of photon fluxes between in HV and AP is larger in the lower photon energy because of the transmittance for the Be window (see Fig. 3). However, the difference for the KTP crystal was relatively smaller than predicted that. This might be due to the radiation damage for the crystal, since the measurement was performed first in AP and later in HV sample chambers.

Fig. 5. Photon fluxes at the sample position in HV (black line) and AP (red line) sample chambers using each monochromatizing crystal.

XAFS Measurement System in the Soft X-Ray Region

(a) and (b) [Nakanishi & Ohta, 2009].

hydrations occur exclusively around the Mg ions.

**2.3 Multiple Soft X-ray XAFS measurement system** 

evacuation.

hydrated compounds.

al., 2004].

for Various Sample Conditions and Multipurpose Measurements 49

Fig. 7. Mg K-XANES spectra of MgCl2 (a) and MgCl2・6H2O (b), and Cl K-XANES spectra of MgCl2 (c) and MgCl2・6H2O (d) [Nakanishi et al., 2010]. Theoretical XANES spectrum with FEFF-8.4 is also shown in the bottom of each figure, where the Z+1 approach was used for

MgCl2 and MgCl2・6H2O. A part of MgCl2・6H2O might remain in bulk and be detected with the bulk-sensitive FY method. In fact, the spectrum was quickly measured in HV after

As described above, an additional peak appears at 1313.5 eV in the spectrum from MgCl2 of PFY (AP) in fig. 7 (a). This feature can be interpreted as the contribution from MgCl2・6H2O, since highly deliquescent MgCl2 adsorbed water during the sample preparation in air. This 'surface layer' is estimated to be about several m orders. On the other hand, in the Cl K-XANES spectra from MgCl2 and MgCl2・6H2O, no significant difference was observed between the spectra measured in AP and HV, as shown in Fig. 7 (c), (d). This shows that

These results clearly demonstrate the necessity and the importance of XAFS measurements both in AP and HV in the soft X-ray region to obtain reliable spectra from hygroscopic and

The local structure and chemical composition of a sample surface are sometimes different from those of the bulk. Such differences play a critical role in functions of materials, such as catalytic activities, electronic properties of semiconductors, etc. Thus, there is a strong demand of depth-profiling techniques. As described in Introduction, the EY mode is generally used in the soft X-ray region, which is surface sensitive. The FY mode is sometimes used to probe bulk structures, although the intensity of the FY mode is one or two orders of magnitude lower than that of the EY mode. Combined use of these modes is known to be a powerful XAFS method for the depth profiling, as published so far [Yoon, et

To demonstrate the availability of the HV and AP chambers, XAFS measurements were carried out for anhydrous MgCl2 and MgCl2・6H2O. The crystal structures of MgCl2 and MgCl2・6H2O are schematically shown in fig. 6. It is known that both samples are highly deliquescent. Since the local structures around Mg and Cl atoms are different from each other, it is expected different XAFS spectra are observed between MgCl2 and MgCl2・6H2O.

Fig. 6. Crystal structures of MgCl2 (a) and MgCl2・6H2O (b) drawn by VESTA program [Momma & Izumi, 2008]. Each crystal information is referred from [Wyckoff, 1963] and [Agron et al., 1969].

Observed Mg and Cl K-edge X-ray absorption near edge structure (K-XANES) spectra which were measured both in HV and AP sample chambers are shown in Fig. 7. They are compared with theoretical XANES spectra simulated with the FEFF-8.4 program based on the real-space full multiple-scattering theory [Rehr et al., 2000]. Note that the white lines of PFY spectra in Fig. 7 are heavily suppressed compared with those of TEY spectra. This is due to the self-absorption effect in the PFY spectrum. In Mg K-XANES spectra of MgCl2 (fig. 7 (a)), we can observe characteristic peaks; a white line at 1309.5 eV and a shoulder at 1311.5 eV. The spectral profile of TEY (HV) is well reproduced by the FEFF simulation. Those of PFY (HV), TEY (HV) are similar to that of PFY (AP), though the shoulder at 1311.5 eV is more enhanced in the spectrum of PFY(AP). In contrast, Mg K-XANES spectrum from MgCl2・6H2O in AP is distinctly different from those in HV, as shown in fig. 7 (b). The simulated spectrum is very similar to that of PFY (AP). This clearly indicates that the sample in vacuum is not MgCl2・6H2O anymore, but changed to anhydrous MgCl2, desorbing crystalline water molecules. In fact, the spectra from MgCl2・6H2O in HV (both PFY and TEY) are close to those of MgCl2 in fig. 7 (a). Careful examination revealed that the spectrum from MgCl2・6H2O in HV (PFY) can be interpreted as a superposition of the spectra from

To demonstrate the availability of the HV and AP chambers, XAFS measurements were carried out for anhydrous MgCl2 and MgCl2・6H2O. The crystal structures of MgCl2 and MgCl2・6H2O are schematically shown in fig. 6. It is known that both samples are highly deliquescent. Since the local structures around Mg and Cl atoms are different from each other, it is expected different XAFS spectra are observed between MgCl2 and MgCl2・6H2O.

Fig. 6. Crystal structures of MgCl2 (a) and MgCl2・6H2O (b) drawn by VESTA program [Momma & Izumi, 2008]. Each crystal information is referred from [Wyckoff, 1963] and

Observed Mg and Cl K-edge X-ray absorption near edge structure (K-XANES) spectra which were measured both in HV and AP sample chambers are shown in Fig. 7. They are compared with theoretical XANES spectra simulated with the FEFF-8.4 program based on the real-space full multiple-scattering theory [Rehr et al., 2000]. Note that the white lines of PFY spectra in Fig. 7 are heavily suppressed compared with those of TEY spectra. This is due to the self-absorption effect in the PFY spectrum. In Mg K-XANES spectra of MgCl2 (fig. 7 (a)), we can observe characteristic peaks; a white line at 1309.5 eV and a shoulder at 1311.5 eV. The spectral profile of TEY (HV) is well reproduced by the FEFF simulation. Those of PFY (HV), TEY (HV) are similar to that of PFY (AP), though the shoulder at 1311.5 eV is more enhanced in the spectrum of PFY(AP). In contrast, Mg K-XANES spectrum from MgCl2・6H2O in AP is distinctly different from those in HV, as shown in fig. 7 (b). The simulated spectrum is very similar to that of PFY (AP). This clearly indicates that the sample in vacuum is not MgCl2・6H2O anymore, but changed to anhydrous MgCl2, desorbing crystalline water molecules. In fact, the spectra from MgCl2・6H2O in HV (both PFY and TEY) are close to those of MgCl2 in fig. 7 (a). Careful examination revealed that the spectrum from MgCl2・6H2O in HV (PFY) can be interpreted as a superposition of the spectra from

[Agron et al., 1969].

Fig. 7. Mg K-XANES spectra of MgCl2 (a) and MgCl2・6H2O (b), and Cl K-XANES spectra of MgCl2 (c) and MgCl2・6H2O (d) [Nakanishi et al., 2010]. Theoretical XANES spectrum with FEFF-8.4 is also shown in the bottom of each figure, where the Z+1 approach was used for (a) and (b) [Nakanishi & Ohta, 2009].

MgCl2 and MgCl2・6H2O. A part of MgCl2・6H2O might remain in bulk and be detected with the bulk-sensitive FY method. In fact, the spectrum was quickly measured in HV after evacuation.

As described above, an additional peak appears at 1313.5 eV in the spectrum from MgCl2 of PFY (AP) in fig. 7 (a). This feature can be interpreted as the contribution from MgCl2・6H2O, since highly deliquescent MgCl2 adsorbed water during the sample preparation in air. This 'surface layer' is estimated to be about several m orders. On the other hand, in the Cl K-XANES spectra from MgCl2 and MgCl2・6H2O, no significant difference was observed between the spectra measured in AP and HV, as shown in Fig. 7 (c), (d). This shows that hydrations occur exclusively around the Mg ions.

These results clearly demonstrate the necessity and the importance of XAFS measurements both in AP and HV in the soft X-ray region to obtain reliable spectra from hygroscopic and hydrated compounds.
