Studying atomic-scale structures of silicate liquids can help us improve our understanding of the properties of magmas under pressure. Such properties play fundamental roles in the evolution of the Earth and other terrestrial planets. Crystalline silicates require very high temperatures to melt, and the melting points increase significantly with pressure. As a result, studying silicate liquids under high pressure is faced with tremendous technical challenges [1
]. Most earlier studies have mainly focused on the structure of silicate glasses in order to gain information of their liquid counterparts. This is based on the general conception that a glass represents a frozen state of a liquid. Many silicate compositions have been reported in spectroscopy studies (see, e.g., review by [2
]). However, structures of glasses are shown to depend on their thermal history [3
]. Many properties of glasses, e.g., density and elastic moduli, also depend on their pressure and temperature history [5
]. Such differences, as pointed out by Jing and Karato [8
], are mainly due to the dominant roles played by entropy in the liquid state. In contrast, the entropic contribution to the Gibbs energy of glasses is negligible. A recent ambient-pressure angle-dispersive X-ray diffraction (ADXD) study on silicate glasses and melts of identical compositions suggests significant differences in their structures [9
]. Therefore, developing a method for direct silicate liquid structure measurement under extreme pressure and temperature conditions becomes particularly important.
Funamori et al. [1
] reported liquid structures of MgSiO3
up to 6 GPa in a cubic-anvil apparatus (DIA [10
]) using a multi-angle energy-dispersive X-ray diffraction (MA-EDXD) technique developed by Tsuji et al. [11
]. Yamada et al. [12
] adapted the MA-EDXD technique to the Paris-Edinburgh press. These developments have enabled liquid silicate structural studies to ~7 GPa. The MA-EDXD technique has the ability to tightly collimate incident X-ray beam, thereby reducing background noise effectively. However, a complete X-ray scattering dataset at a given pressure and temperature condition typically requires several hours to collect, because X-ray scattering signals from liquids are extremely weak. An alternative to MA-EDXD is ADXD. In order to remove background scattering, Mezouar et al. [13
] developed a multi-channel collimator system for the Paris-Edinburgh press for liquid structure studies. With the combination of a Paris-Edinburgh press with a multi-channel collimator, the liquid structure and density of iron-rich alloys have been studied up to 17 GPa and 1200 K [14
For silicate liquids, which have much lower X-ray scattering power than metals and melts at generally much higher temperatures, measuring their structures is challenging. In this paper, we report our recent development at the GeoSoilEnviro Center for Advanced Radiation Sources (GSECARS) beamline 13-ID-C, using a combination of a Paris-Edinburgh press with a multi-channel collimator and an advanced photon-counting area detector for collection of angle-dispersive X-ray scattering data on amorphous materials, especially silicate liquids under high pressure and temperature conditions. The multi-channel collimator, i.e., Soller slits, consists of two arrays of fine slits made of tungsten carbide blades. The slits are aligned so that they rotate about the sample center. By oscillating the slits during data collection, background scattering from the material surrounding the sample can be effectively removed. The excellent spatial selectivity provides an exciting opportunity for glass and liquid structure studies in the Paris-Edinburgh press. Compared with the energy-dispersive X-ray diffraction (EDXD) method, commonly used to minimize unwanted X-ray scattering signal from surrounding pressure media in large-volume multi-anvil experiments, our multi-channel collimator combined with ADXD measurements are performed at fixed energy and undulator gap, eliminating the need for energy dependent absorption and the undulator spectrum corrections to the data as well as allowing us to take full advantage of the brilliance of the Advanced Photon Source synchrotron light source. Our optimized setup results in typical data collection times of 5 to 30 min for a single ADXD pattern, which is 2 to 3 orders of magnitude faster than the EDXD method. The elimination of energy dependent data corrections, the effective use of the brilliance of the source, and the dramatically reduced collection times allow users to collect rich data sets while pushing the sample cell to extreme pressures and temperatures.
4. Data Collection and Analysis
The collected X-ray scattering data is saved as a 32-bit 2D TIFF image (1475 × 195 pixels) with a size of 1126 kilobytes. The raw image is processed (detector calibration, image integration, etc.) using the software package Dioptas [22
]. Limited by the active area of the Dectris Pilatus3 X CdTe 300K-W detector, which is a 254 mm × 33.5 mm rectangular, only fractions of the full scattering rings are recorded. In addition, in order to utilize the entire area of the detector to collect scattering signals at high Q, the detector is setup so that the beam center (direct beam) is positioned at the edge of the detector (Figure 6
). One advantage of processing our X-ray scattering patterns using Dioptas is that we can still run the detector calibration with only capturing a fraction of the diffracted powder rings (Figure 6
), and the program also works for special setups where the beam center is not present in the X-ray scattering pattern.
To properly analyze X-ray scattering data of amorphous material, various background corrections become critical in order to extract the real X-ray scattering signal. The critical factors that should be considered include: (1) subtracting the background from the surrounding high pressure cell assembly; (2) eliminating multiple scatter of photons inside the experimental station (this may arise from optics components, the press, and other equipment), (3) eliminating collimation effects of the multi-channel collimator. We have developed and upgraded several major hardware in order to routinely collect these correction intensity profiles efficiently. One important improvement worth mentioning is the installation of a manually operated horizontal translation stage for the multi-channel collimator unit to move out of the beam path and to precisely return to its previous position for data collection without having to re-align it. By collecting data of a non-crystalline standard (e.g., a Pyrex glass rod) with and without the multi-channel collimator, one can determine the transfer function and apply the correction to the dataset.
A Pyrex glass rod with a diameter identical to the sample diameter is used to establish an X-ray scattering intensity correction for the sample. First, we collect data of the Pyrex glass rod in air with no surrounding cell material, no multi-channel collimator. This is our reference pattern for intensities. The next step is to collect data of the same Pyrex glass rod with the multi-channel collimator in place. We then calculate the transfer function of the multi-channel collimator. The transfer function is essentially the ratio of intensities of the reference pattern to the one with the multi-channel collimator. This is used later to rescale the intensities of XRD measurements under high pressure and temperature. Other patterns that are necessary for the intensity correction are collected subsequently, including the detector dark field, the multiple scattering signal inside the hutch, and the Paris-Edinburgh sample cell background. The latter is based on measurement of an empty (dummy) cell.
The transfer function (Figure 7
) provides a correction ratio for the intensity of the sample pattern at each Q value to correct for the intensity differences generated by the air scattering inside the hutch, dark field of the detector, and the multi-channel collimator. Only with a properly derived transfer function can the background be successfully removed from the sample pattern. Since the scattered signal intensity from the sample/cell assembly is sensitive to the beam position, alignment of the pinhole, and the alignment of the multi-channel collimator, etc., each setup for a beamtime period requires its own transfer function for proper intensity correction. Furthermore, for different sample diameters, the geometric correction from the sample will be different.
The structure factors S(Q) and the pair distribution functions g(r) are calculated from the X-ray scattering patterns using the software package Glassure [23
]. Detailed description of the pair distribution function can be found in [24
]. The Python-based GUI program performs background subtraction, atomic form factor corrections, Fourier transform and optimization of the experimental data (Figure 8
). The number density in atoms per cubic Å is used in the calculation. To minimize truncation error ripples in the pair distribution function, the optional Lorch function [26
] was applied during the Fourier transforming process. An optimization process following [27
] has also been applied to the final g(r).
Here we show results from two different samples: a sodium silicate liquid sample and a sodium disilicate glass sample. Figure 8
shows sodium silicate liquid X-ray scattering data collected at 3 ± 0.1 GPa and 1673 ± 90 K for 10 min. The experiment started with a sodium silicate glass sample with a diameter of 1.6 mm. Using a 42 keV monochromatic X-ray beam, we were able to collect X-ray scattering data of the liquid up to ~17 Å−1
in Q. However, the X-ray scattering signal becomes weak above Q = 12 Å−1
. For better statistics, especially in high Q ranges, a longer data collection time is suggested.
We collected sodium disilicate (NS2) glass X-ray scattering patterns at ambient condition and compared the bond length results (Figure 9
) with previous structure studies of sodium disilicate glass from neutron scattering [28
] and molecular dynamics simulations [29
] (Table 1
). Bond lengths of Si–O, Na–O, O–O, and Si–Si were determined by fitting the assigned four peaks of the g(r) with Gaussian functions using the software Origin. Our measured bond lengths are consistent with previously reported values.