Cheiron School 2015

BL10XU: High Pressure Research
Outline
The undulator beamline BL10XU is dedicated for x-ray diffraction experiments at highpressure and low/high temperature using diamond anvil cells (DAC) (Figure 1) [Ohishi et al.
(2008) High Press. Res., 28, 163.]. Monochromatic x-ray diffraction using synchrotron radiation
plays an essential role in structural determination of crystalline materials. High pressure ispossible to change physical, chemical, and structural characteristics of materials through a changeof the distance between atoms (or molecules). The high-pressure properties are drasticallydifferent from those known at ambient pressure. Pressure serves as a versatile tool in material
research, and it is also important in the investigation of the deep interior of the Earth and planets.
To learn high-pressure phenomena in the BL practice course, in-situ high-pressure x-ray
diffraction experiments will be performed using a combination of synchrotron radiation and a
DAC technique.

Figure1. Schematic layout of beamline BL10XU.
Diamond anvil cell

Diamond anvil cell is one of high-pressure
generation techniques by static compression. Thesample is placed in a pressure chamber createdbetween the flat parallel faces (culets) of two opposed
diamond anvils and the hole penetrating a hardened
metal foil (the gasket) (Figure 2). Pressure is applied byforcing the diamonds together. Diamond is the premieranvil material because of hardest substance andtransparency to electromagnetic radiation over a wide
spectral range from the infrared to hard X-rays.

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Figure 2. Diamond-anvil cellEnergy calibration

Precise x-rays energy is essential to determine lattice parameters or crystal structures ofmaterials in monochromatic x-ray diffraction measurement. The x-rays energy/wavelength canbe obtained using a diffraction standard material with well-established lattice parameter, such as
cerium oxide (celia, CeO2), as the x-ray wavelength is linked to crystal lattice spacing by Bragg’slaw. In this practice, the energy of the incident monochromatic x-ray beam is tuned to 30 keV(0.4133 Å). Also, the precise sample-to-detector distance is required in monochromatic x-ray
diffraction measurement because of eliminating the uncertainty of the distance for the error in thed-spacing.
For calibration, two-film cassette method is used by recording a diffraction pattern on a flat
detector and giving a second pattern after the detector moves parallel to the incident x-ray beamby an accurately known distance ΔL. The diffraction angle θ is then given by the relation

tan2Δ
12

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∆

, where R1 and R2 are the diffraction ring radius for the sample-to-camera distances L and L + ΔL,
respectively.

Figure3. Schematic image of camera length calibration.

– Practice –1. Observe a crystallization of liquid Argon, and confirm the solid phase structure at highpressure with using DAC.
2. Obtain the parameters of Equation of State (EOS) for solid dense Argon from in-situ X-ray
diffraction data.

21) Why Argon?
General introduction
Here, we focus on the high pressure behavior of dense Argon (Ar). There are a lot ofexperimental and theoretical studies to investigate the liquid and solid Ar density and thermal
properties at high pressure with following reasons. (1) Ar is the rare-gas, and the abundance of Ar is the3th-highest in the dry air. We can get Ar at a reasonable price, (2) its chemically inert behavior, (3) its
molecular simplicity, such as monoatomic, nonpolar, and closed-shell electronic configuration. Therefore, Ar
is commonly used as a reference material to calibrate and check the consistency of the new measurement
system or calculation method.

Phase relations of Ar at high pressure
The melting curve of Ar was determined up to 80 GPa with DAC [Boehler et al. (2001) Phys. Rev.
Lett., 86, 5731.]. The phase relation of Ar was shown in Figure 3. In previous experimental study, nostructural transition was observed, and fcc Ar is stable over Mbar pressure condition at low to hightemperature. McMahan (1986) [Phys. Rev. B., 33, 8.] predicted the structural transition and metallization athigh pressure at 0 K with first principle calculation. He indicated that fcc to hcp transition is occurred at 230GPa. Ar would be metallized in the hcp stable range. Hcp phase is stable up to 970 GPa, and undergoes aphase transition to bcc. Finally at 2200 GPa, high pressure fcc phase would be observed. Today, we try tocheck the pressure of liquid to solid transition. Finger et al. (1981) [Appl. Phys. Lett., 39, 892.] and Datchi et al.
(2000) [Phys. Rev. B. 61, 6535.] revealed the transition pressure is 1.15-1.3 GPa. Is it true in your experiment?

Figure 4. Melting curve of Ar at high pressure [Boehler et al. (2001) Phys. Rev. Lett., 86, 5731.]

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Implication for the Earth’s interior~Missing Ar problem
Allegre et al. (1996) [Geo. Res. Lett., 12, 24, 3555.] suggested that almost half of 40Ar in the whole
Earth are missing, and these missing 40Ar would be hidden in the Earth’s lower mantle. 40Ar in the present
Earth was produced by radioactive delay of 40K. We can calculate the amount of Ar as 1.16 times of present
K. K content in the bulk Earth was assumed as 1.16 times of present 40K. The present K content could be
estimated from K/U ration (12700) by weight from primitive mantle composition predicted from Mid-ocean
ridge basalt and ocean-island basalt. Sold Earth have 20-22.5 ppm U from meteorite composition, therefore,
K abundance can be judged to be 250-285 ppm in the bulk Earth. From this consideration, 40Ar has been
produced 140-150×1018 g. 40Ar are 66×1018 g in the air, and about 9-12×1018 g and 7.3-9.3×1018 g in eachcontinental crust and upper mantle (Figure 5). Therefore, 60-80×1018 g are hidden by the reservoir in the deep
Earth’s interior, lower mantle or metallic core. Ar is well known that liquid iron (Earth’s core) rarely reactwith Ar.

Figure 5. Hidden Ar in the lower mantle [Allegre et al. (1996) Geo. Res. Lett., 12, 24, 3555.]

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Jephcoat (1998) [Nature. 393, 355.] suggested that solid pure Ar in the Earth’s lower
mantle from their determined melting curve of noble gases and compressibility. They foundsolid-liquid transition is occurred at around 25 GPa (720 km depth, lower mantle) on theGeotherm. Their scenario is that Ar has been produced from K in both lower mantle and thecore. Ar is solidified at lower mantle and liquid outer core. Ar is enough denser than thesurrounding mantle to sink to the bottom of the mantle (Figre 6). On the other hands, solid Ar
float from surrounding liquid core to top of the core. Ar will have been “confined” at the coremantle boundary over 4 billion years.

Figure 6. Hidden Ar in the lower mantle [Jephcoat (1998) [Nature. 393, 355.]

2) Sample preparation
In general experiments with DAC technique, samples are set up in a chamber createdbetween the culets of two opposed diamond anvils and the gasket hole. The gasket in anvil
devices serves three critical functions: (1) encapsulating the sample, (2) building a gradient fromambient to the peak pressure, and (3) supporting the tip of anvils. Gasket material, hole size ofsample chamber, and thickness are critical for generating high pressure.
What about is the gasket condition in this practice? Let’s ask to the staff!!:
Material:
Initial gasket thickness:
Initial gasket hole size:
The pressure limit is depend on the culet size of diamond anvil as following;

Pressure

5Force.
Area

Pressure limitation vs. culet size relations are shown in Table 1.

Table 1.
Culet size

Pressure limitation

600 μm< 20 GPa

450 μm40-50 GPa

300 μm70-80 GPa

150 μm~140 GPa

Smaller>300 GPa !

Today, high pressure condition is generated with a gas-membrane DAC. Ar gas wasloaded in a chamber hole drilled in a Re foil using a high-pressure gas-loading technique at 200
MPa, together with tiny ruby chips for a pressure marker. Generally, we load samples together
with some soft pressure medium to distribute hydrostatic pressure condition, such as NaCl, KCl,gas, gel, or ethanol-methanol mixture.
However, in this case, we operate our high pressure experiment without pressure medium,
because Ar itself is a good soft pressure medium.

3) XRD data collection at ambient and high pressures
In-situ high-pressure XRD measurements are carried out with the following steps:(1) At first, take XRD pattern at current pressure,(2) Compress DAC to the interest pressure carefully, and determine pressure with ruby scale,(3) Collect of XRD images with the imaging plate detector at each pressure with increasingpressure.
(4) Check the pressure of liquid-solid pressure transition, and confirm the structure of solid Ar.
(5) Obtain XRD images at pressure intervals up to about 40 GPa.

4) High-pressure generation and pressure measurement
In a gas-membrane DAC, pressure is generated online, smoothly, and remotely throughcontrolling the gas pressure in a membrane.
Pressure in the DAC is determined by ruby pressure scale [Mao et al. (1978) J. Appl. Phys.
49, 3276.]. The ruby scale, which has been calibrated against primary shock-wave experiments on
several metals, is commonly used for DACs: the pressure-shift of ruby fluorescence wavelength
can be easily probed with a laser beam through the diamond window. Determine the pressure withempirical quasi-linear relationship: P (GPa) = 1904[(⁄0)B – 1] ⁄ B, where B = 5 for
non-hydrostatic conditions, for the correlation of the measured wavelength shift  (in nm) of theR1 line with applied pressure.

5) Data analysis and peak indexing
The basic principle of the X-ray diffraction is the Bragg's law:  = 2dsin, where  is thewavelength of the X-ray, d the lattice spacing,  the angle of the incident beam and the diffracting
lattice plane. The diffraction peaks are observed when the d-spacing satisfied the Bragg's law.
First, convert the X-ray image to conventional one-dimensional X-ray pattern with thesoftware. Next, calculate d-spacing for each peak from 2 value using the Bragg's law. Then,

6perform peak indexing. Finally, refine the unit-cell parameter and volume.
Note that Ar has face-centered cubic (fcc) structure with space group of Fm3m. From equation ofstate, the lattice parameter of Ar is 5.3166 Å at ambient condition [Jephcoat (1998) Nature. 393,355.].

Figure 5. Crystal structure of sold fcc Ar.

5) Determination of the EOS parameters
An EOS is the relationships among the thermodynamic parameters volume, pressure, ortemperature. The EOS is useful to describe the properties of solid, fluid, and even the interior ofplanets and stars. In this practice, obtain the EOS parameters of zero-pressure bulk modulus andits pressure derivative for a sold Ar phase from pressure-volume data at room temperature. Plotthe P-V data, and then fit the EOS with the Birch-Murnaghan equation.
Note that the Birch-Murnaghan equation of state is based on the Eulerian strain [Birch(1952) J. Geophys. Res. 57, 227.] and is widely used for mineralogists:
P = 3KT0/2 [(V0/V)7/3 – (V0/V)7/3]{1 – 3/4(4 – K’T0)[ (V0/V)2/3 – 1]}, where P is pressure, KT zero-pressure bulk modulus, K’T its pressure derivative, V the volume atP, and the subscript “0” refers to ambient pressure conditions.

6) Comparison with other materials
Compare the EOS parameters of Ar with other materials and rare-gas solids. The parameters
for ionic, covalent, and metal crystals are given in table.
Table 2Material

K0 (GPa)

K'0Ref.

Diamond

444.5

3.98

[1]

Na

6.31

3.886

[2]

Si

97.9

4.16

[3]

Al

73

4.54

[4]

Au167

5.46

[5]

Pt

277

5.08

[4]

7MgO

160.2

3.99

[6]

Al2O3253

4.3

[7]

H2

0.162

6.813

[8]

Ne

1.42

8.03

[9]

NaCl23.83

5.09

[10]

Ar

4.13

5.77

[11]

References: [1] Occelli et al. (2003); [2] Hanfland et al. (2002); [3] Knittle (1995); [4] Dewaele et al. (2004); [5]Takemura (2007); [6] Speziale et al. (2001); [7] Syassen (2008); [8] Loubeyre et al. (1996); [9] Dewaele et al. (2008);[10] Dorogolupets and Dewaele (2007); [11] Jephcoat (1998).

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