Cheiron School 2008

BL10XU: High Pressure Research
The undulator beamline BL10XU is dedicated for X-ray diffraction experiments at highpressure and low/high temperature using a diamond anvil cells (DAC) (Figure 1) [1]. The
high-resolution monochromatic angle-dispersive X-ray diffraction patterns obtained at BL10XU
allow us to the accurate determination of equations of state, precise determination of phaserelation, accurate structural refinements by Rietveld analysis, and charge density distribution
analysis in crystals submitted to extreme pressures. High pressure is possible to change physicaland chemical properties of matter through a change of its volume or distance between atoms (ormolecules). The properties of matter at high pressure are drastically different from those knownat ambient pressure. To have a better understanding of high-pressure research using a
combination of synchrotron radiation and a DAC technique through this BL practice course, insitu high-pressure X-ray diffraction experiments will be carried out under hydrostatic conditions
with a pressure-transmitting medium of helium that enables to give us high-quality data.

Figure1. Schematic layout of beamline BL10XU [1].

— Glossary —Diamond anvil cell

Diamond anvil cell is one of high-pressure
generation techniques by static compression. The
sample 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.

Figure 2. Diamond-anvil cell technique.

– Practice –Obtain the parameters of “Equation of State” (EOS) for NaCl from experimental
compression data by high-pressure X-ray diffraction method.

1) Energy calibration
Angle dispersive x-ray diffraction (XRD) requires a monochromatic X-ray beam. The mostimportant requirements for the structure determination (or the measurement of the unit-cellparameters) of a material are the accurate determination of the wavelength for incident X-ray
beam and of the distance between sample and detector of imaging plate (IP). In this practice, weuse photon energy tuned to 30 keV for angle dispersive XRD measurement. The determinationof the X-ray wavelength and the distance is based on the standard material of cerium oxide(CeO2). Determine incident X-ray wavelength and the distance between sample and IP. Before
the determination, we need obtain XRD patterns of the standard material at desired distance,
and then convert the X-ray image to conventional one-dimensional X-ray pattern with thesoftware.

2) 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, 300-µm culet anvil and a drilled rhenium
gasket is prepared for the experiments with helium pressure-transmitting medium to compress
the sample to the desired pressure. Mounting the sample into the chamber should be performed
with preparation needle, together with tiny ruby chips for a pressure marker (see below).

3) Compressed gas loading
Hydrostaticity is an important parameter in high-pressure experiment, because
non-hydrostatic stress affects the position and profile of diffraction peaks, resulting ininaccurate data [2]. The use of inert gases as pressure medium could significantly reducepressure anisotropy and inhomogeneity, which causes non-hydrostatic condition, in the DAC.
To perform loading of compressed helium gas at elevated pressures (195 MPa or 0.195 GPa),
we use the large-volume gas-loading apparatus that enable to fill gas at high densities in thepressure chamber.
Note that a BL staff operates the apparatus for safe.

4) Pressure measurement
The ruby scale, which has been calibrated against primary shock-wave experiments on
several metals, is commonly used for DACs: tiny ruby grains are loaded in the sample chamberwith sample, and the pressure-shift of ruby fluorescence wavelength can be easily probed with alaser beam through the diamond window. Determine the pressure with empirical quasi-linear
relationship: P (GPa) = 1904[(! ⁄!0)B – 1] ⁄ B, where B = 7.665 for quasihydrostatic conditions,for the correlation of the measured wavelength shift ! (in nm) of the R1 line with appliedpressure [3].

5) XRD data collection at high pressures
We use a DAC with pneumatic driving mechanism where pressure can be changed on-line
by controlling the gas pressure on a membrane, enabling the pressure to be changed smoothly
and remotely. In-situ high-pressure XRD experiments are carried out with the following threesteps: (1) loading to the desired pressure, (2) pressure determination with ruby scale, and (3)acquirement of XRD images with IP. Collect XRD images at pressure intervals of 5 GPa for
determination of the EOS parameters.

6) Data analysis
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 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 2theta value using the Bragg's law. Then,
perform peak indexing. Finally, refine the unit-cell parameter and volume.
Note that sodium chloride (NaCl) has face-centered cubic (fcc) structure with space groupof Fm3m, called B1-type (or NaCl-type) structure. Its structure transforms from the B1 to B2(CsCl) structure at 29.3 GPa.

7) Determination of the EOS parameters
The equation of state (EOS) is the most fundamental parameter obtained fromhigh-pressure research. The EOS describes the relationships among the thermodynamic
parameters volume, pressure, and temperature (energy). In this practice, we try to obtain theEOS parameters of zero-pressure bulk modulus and its pressure derivative for B1-type NaClfrom pressure-volume data at room 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 [4] 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 thevolume at P, and the subscript “0” refers to ambient pressure conditions.

8) Comparison with other materials
Compare the EOS parameters of NaCl with other materials. The parameters for ionic, covalent,
and metal crystals will be given in table.
References:[1] Ohishi et al. (2008) High Press. Res., in press.
[2] Takemura (2001) J. Appl. Phys. 89, 662.
[3] Mao et al. (1986) J. Geophys. Res. 91, 4673.
[4] Birch (1952) J. Geophys. Res. 57, 227.