Cheiron School 2014

BL10XU: High Pressure Research
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. Highpressure is possible to change physical, chemical, and structural characteristics of materials
through a change of the distance between atoms (or molecules). The high-pressure propertiesare drastically different 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 theEarth 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 ofsynchrotron 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
by forcing the diamonds together. Diamond is thepremier anvil material because of hardest substanceand transparency to electromagnetic radiation over awide spectral range from the infrared to hard X-rays.	  

1	  Figure 2. Diamond-anvil cellEnergy calibration

Precise x-ray energy is needed to determine lattice parameters or crystal structures ofmaterial in monochromatic x-ray diffraction measurement. The x-ray energy/wavelength can beobtained using the 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’s law. In this practice, the energy of the incident monochromatic x-ray beam is tuned to~30 keV (0.4133 Å). Also, the sample-to-detector distance is required in monochromatic x-ray
diffraction measurement, and the distance can be calibrated using the standard material.

– Practice –Observe a structural phase transition of sodium chloride (NaCl) at high pressure and obtain
the parameters of Equation of State (EOS) for NaCl from in-situ X-ray diffraction data.

1) Sample preparation

The sample is set up in a chamber created between the culets of two opposed diamondanvils and the gasket hole. The gasket in anvil devices serves three critical functions: (1)encapsulating the sample, (2) building a gradient from ambient to the peak pressure, and (3)supporting the tip of anvils. Gasket material, hole size of sample chamber, and thickness are
critical for generating high pressure.
In this practice, for efficiency measurement we use a gas-membrane DAC. A sample ofNaCl powder is placed in a chamber hole drilled in a steel foil, together with tiny ruby chips fora pressure marker.

2) XRD data collection at ambient and high pressures

In-situ high-pressure XRD measurements are carried out with the following steps: (1) firstmeasurement at ambient pressure, (2) loading to the desired pressure, (3) pressure determination
with ruby scale, and (4) collection of XRD images with the imaging plate detector. Collect XRDimages at pressure intervals of 5 GPa up to about 35 GPa.

3) 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 experimentson several metals, is commonly used for DACs: the pressure-shift of ruby fluorescencewavelength can be easily probed with a laser beam through the diamond window. Determine thepressure with empirical quasi-linear relationship: P (GPa) = 1904[(λ ⁄λ0)B – 1] ⁄ B, where B = 5
for non-hydrostatic conditions, for the correlation of the measured wavelength shift λ (in nm) of
the R1 line with applied pressure.

4) Data analysis and peak indexing

The basic principle of the X-ray diffraction is the Bragg's law: λ = 2dsinθ, where λ is thewavelength of the X-ray, d the lattice spacing, θ the angle of the incident beam and thediffracting lattice plane. The diffraction peaks are observed when the d-spacing satisfied theBragg'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 2θ value using the Bragg's law. Then,
perform peak indexing. Finally, refine the unit-cell parameter and volume.	  

2	  Note that sodium chloride (NaCl) has face-centered cubic (fcc) structure with space groupof Fm3m, called B1-type (or NaCl-type) structure. At ambient conditions, the lattice parameterof NaCl is 5.630 Å. Its structure transforms from the B1 to B2 (CsCl) structure at 29.3 GPa.

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 low-pressure phase of B1-type NaCl from pressure-volume data atroom temperature. Plot the 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
at P, and the subscript “0” refers to ambient pressure conditions.

6) Comparison with other materials

Compare the EOS parameters of NaCl with other materials. The parameters for ionic,covalent, and metal crystals are given in table.
MaterialK0 (GPa)K'0Ref.

DiamondNa

444.5

3.98

[1]

6.310

3.886

[2]

Si

97.9

4.16

[3]

Al

73

4.54

[4]

Au

167

5.46

[5]

Pt

277

5.08

[4]

MgO

160.2

3.99

[6]

Al2O3253

4.30

[7]
[8]

H2

0.162

6.813

Ne

1.42

8.03

[9]

NaCl

23.83

5.09

[10]

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).	  

3