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Copyright ©JCPDS-International Centre for Diffraction Data 2007 ISSN 1097-0002

STUDIES OF LOCAL AND INTERMEDIATE RANGE STRUCTURE IN CRYSTALLINE AND AMORPHOUS MATERIALS AT HIGH PRESSURE USING HIGH-ENERGY X-RAYS Lars Ehm1, Sytle M. Antao1,2, Jiuhua Chen1, Darren R. Locke1, F. Marc Michel1, C. David Martin1, Tony Yu1, Peter L. Lee2, Peter J. Chupas2, Sarvjit D. Shastri2, Quanzhong Guo3, and John B. Parise1 1

Department of Geosciences, Stony Brook University, Stony Brook, NY 11794-2100, USA 2 Advanced Photon Source, Argonne National Laboratory, Argonne, IL 60439, USA 3 X17B3, National Synchrotron Light Source, Brookhaven National Laboratory, Upton, NY 11973-5000, USA

ABSTRACT The method of high-energy total elastic X-ray scattering to determine the atomic structure of nanocrystalline, highly disordered and amorphous materials is presented. The current state of the technique, its potential, and limitations are discussed with two successful studies on the pressure induced phase transition in mackinawite (FeS) and the high-pressure behavior of liquid gallium.

INTRODUCTION The key to understanding and control of material properties is a detailed understanding of local, intermediate and long-range atomic order. A precise determination of the structural parameters as a function of pressure and temperature is a prerequisite to deriving structure-property relationships. Crystal structure determination by single-crystal or powder diffraction measurements, even at non-ambient conditions, is nowadays a routine technique. However, many materials important for geological processes and technology, such as silicate liquids, glasses and highly disordered materials, do not posses long-range three-dimensional order characteristic of conventional crystals, but instead possess varying degrees of local and intermediate range order based on arrangements of relatively consistent building units – the silicate tetrahedron in the case of silicate glasses and melts, for example. Analysis of the Bragg diffraction alone, using standard powder or single crystal diffraction techniques, fail on the structure determination of poorly crystalline materials, since the diffraction pattern is information poor, showing large amounts of diffuse scattering and only very broad diffraction features, or no Bragg peaks at all. Even so, information on the atomic structure can be obtained using the atomic pair distribution function (PDF) technique [1], which is derived from the Fourier transform of the total elastic X-ray scattering – the Bragg as well as the diffuse scattering components. Obtaining a quantitative PDF from the Fourier transform of total scattering requires data be collected to as high a Q (= 4πsinθ/λ) as possible to avoid the debilitating effects of Fourier termination ripple. The advent and availability of high energy X-ray sources and bright neutron sources has spurred a new interest in amorphous materials and nanocrystalline solids, despite many experimental difficulties [2]. Studies at non-ambient conditions (e.g. highpressure) are almost not existent however, since the pressure cells impose a number of additional

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compromises on the experiments [3]. Typically, parasitic scattering from the pressure cell, peak broadening, asymmetric peak shift owing to deviatoric stresses, and several other systematic errors, all compromise the data quality. Because of the inherently low intensity of the diffuse scattering, the total elastic X-ray scattering experiments suffer significantly from these artifacts. However, the experimental difficulties can be overcome and total elastic X-ray scattering data, suitable for PDF analysis, can be collected. Here the recent advances of total elastic X-ray scattering experiments at high pressures are presented. The opportunities and limitations of this technique are discussed on the basis of some recent experiments.

EXPERIMENTAL Experimental Setup The high-energy monochromatic X-ray scattering experiments were performed at beamlines 1ID at the Advanced Photon Source (APS) at the Argonne National Laboratory and beamline X17B3 at the National Synchrotron Light Source (NSLS) at the Brookhaven National Laboratory. Both beamlines are equipped with a bent Laue monochromator, consisting of two Si (111) crystals, for energy selection. At the APS, the monochromator crystals are cooled by liquid nitrogen [4], and the monochromatic beam is focused to about 20
20 µm2 in size using sawtooth silicone refractive lenses[5] which provide a flux density gain of 6-20 fold. At X17B3 at the NSLS a set of horizontal and vertical slits was used to reduce the beam to a size of 100
100 µm2. The diffraction patterns were collected using area detectors, a mar345 image plate at X17B3, and a mar345 image plate and a General Electric amorphous silicone detector at the APS. Generally, the high-energy total elastic X-ray scattering experiments at high-pressure can be conducted at any beamline at a synchrotron radiation facility that can provide a small intensive monochromatic beam in the energy range between 80-120 keV and is equipped with an area detector for rapid data acquisition. The pressure was generated using a diamond anvil cell (DAC) outfitted with beryllium backing plates with a 40° opening angle in 2θ (Qmax ~ 30 Å-1). For high-quality PDFs an observed maximum wavevector Qmax of at least 20 Å-1 for crystalline materials and at least 10 Å-1 for liquids is necessary. The sample (V~0.001 mm3) was placed in a hole drilled in metal gasket and an alcohol pressure transmitting medium of methanol:ethanol (4:1), or methanol:ethanol:water (16:3:1) was added to minimize deviatoric stress, in the crystalline samples. The experiment on liquid gallium was performed without pressure transmitting medium. The ruby fluorescence method was used to calibrate the pressure in the DAC [6], for experiments at ambient temperature, a diffraction standard (e.g. NaCl, Au) was used at elevated temperatures. The contribution from Compton scattering of the diamond anvils is a matter of concern in total elastic X-ray scattering experiments, since the intensity from the Compton scattering of the diamonds can overwhelm the weak scattering signal from poorly scattering crystalline or amorphous materials. A way to increase the signal-to-noise discrimination is to decrease the inelastic signal by removing some of the diamond from the beam path using perforated diamond anvils [7] with the geometry shown in Figure 1. In this case, a conical hole (half-through) of ~500 µm maximum diameter and ~80 µm minimum diameter is perforated into the diamond ending at about 200 µm to the culet (350 µm in diameter). A through-hole is made into the diamond located towards the detector and a miniature anvil set

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upon it. The X-ray beam is introduced through the hole, in the direction of the arrow in Figure 1, and Compton scattering can be significantly reduced.

Figure 1 Schematic drawing of a perforated diamond anvil assembly. DBP: diamond backing plate made of ~0.25 carat diamond. PPA: partially perforated diamond (~0.25 carat) with a conical hole. The upper conical hole is cut to accommodate the diameter of the incident beam. MA: miniature diamond anvil (~0.05 carat).

A comparison of data collected at 1-ID with and without the perforated diamond anvils and with the focusing optic in place is shown in Figure 2. Data quality is significantly improved, especially at high Q region by using the perforated diamond anvils. 60

CeO2 in perforated diamonds

Q[S(Q)-1]

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Q(Å )

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Q[S(Q)-1]

CeO2 in unperforated diamonds 40

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Q(Å )

Figure 2 Diagrams showing Q[S(Q)-1] for CeO2 diffraction standard (NIST, SRM 674b) in (top) a cell fitted with perforated diamonds (Fig. 3) and (bottom) a standard diamond anvil cell. There is a dramatic decrease in the contribution to the overall scattering from diamonds in the perforated cell and this leads to a much better signal-to-noise discrimination at high Q, an important factor in deriving better resolved real-space correlation functions containing less noise generated by Fourier termination effects.

Data Acquisition and Evaluation

Copyright ©JCPDS-International Centre for Diffraction Data 2007 ISSN 1097-0002

Information about the atomic structure of disordered, nanocrystalline and amorphous materials can be obtained by evaluating the total elastic X-ray scattering data with the pair distribution function (PDF) analysis method [1, 2, 8-11]. The PDF, G(r) is defined as G (r ) = 4π [ ρ (r ) − ρ 0 ] [8] where ρ(r) and ρ0 are the local and average atomic number densities in atoms/Å3, and r is the radial distance in Å. The G(r) is the probability of finding an atom at a distance r from a reference atom and is therefore related to the atomic structure. The pair distribution function G(r) is derived from the experimentally observed total elastic X-ray structure factor S(Q) by a Fourier transformation [12], G (r ) = ( 2 / π )

Q max

∫ Q[S (Q) − 1] sin(Qr )dQ ,

Q =0

where Q = 4π sinθ/λ is the magnitude of the wavevector. A properly normalized PDF serves as a basis for structure refinement [13-15] and might be used with certain limitations for structure determination as well. The general protocol for the measurement of total elastic X-ray scattering data at high-pressure and the consequent data evaluation is straightforward. The diffraction patterns were collected using a two dimensional detector. In order to avoid saturation of the detector from reflections from the diamond anvils, and to guarantee optimal counting statistics, many short exposures were collected and averaged. The contributions from the pressure cell to the diffraction pattern were masked and hereby excluded from the integration process. The two-dimensional patterns were transformed into standard one-dimensional patterns using FIT2D [16]. Special care needs to be taken by the measurement of the background collected from exposures of the unloaded high-pressure cell at ambient pressure. Improper background subtraction, resulting in longwavelength errors in S(Q), will Fourier transform into physically meaningless peaks in the low-r region of the PDF. The PDFs were extracted from the one-dimensional diffraction patterns using the program PDFGetX2 [17]. Standard corrections and special corrections associated with area detector geometry [18] were applied during this process. The program PDFFit [19] was used for a full structure refinement of a given structural model. For non-crystalline materials like glasses and liquids, the average coordination number (CN) of an atom in the structure can be calculated, r min

CN =

∫ 4πr

2

g (r )dr ,

0

where rmin is the distance corresponding to the minimum of g(r) on the large distance side of the first maximum in the PDF. For a more thorough analysis of the atomic structure of glasses and liquids, Reverse Monte Carlo Simulations [20] can be used to derive a structural model for glasses and liquids from the experimentally measured structure factor S(Q).

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RESULTS AND DISCUSSION Nanocrystalline Mackinawite (FeS) Iron monosulfide crystallizes in two modifications, the troilite and the mackinawite structure. The hexagonal troilite structure (SG: P63mc) crystallizes in a NiAs type structure. It consists of chains of face shared FeS6 octahedra along the c direction. These chains are interconnected through edges forming a three dimensional network. Mackinawite crystallizes in a tetragonal lattice (SG: P4/nmm). The mackinawite structure is built of layers of edge sharing FeS4 tetrahedra, which are stacked along the c axis. The first step in the formation of iron sulfides under hydrothermal conditions is the nucleation of a reduced short-range-ordered iron monosulfide that is generally believed to be a precursor to crystalline mackinawite. It has recently been confirmed from total elastic X-ray scattering experiments, that this iron monosulfide is a pure nanocrystalline phase with particle sizes between 2-6 nm crystallizing in the mackinawite structure [21]. Therefore, the nanocrystalline form of mackinawite is an excellent material to explore its behavior at high-pressure conditions, since it can be synthesized reproducibly in nanocrystalline form with well-defined grain sizes without the use of capping agents for stabilization. The high-pressure behavior of nanocrystalline mackinawite was investigated at the beamline 1-ID at the APS using the technique described above. A drastic change in the diffraction patterns was observed at about 4.5 GPa. The new diffraction pattern can be interpreted using the known high-pressure modifications of troilite, suggesting a closure of the gap between the layers in the mackinawite structure and a change in the coordination number of iron from four to six. The troilite structure transforms at about 4.6 GPa to a MnP like structure (FeS-II) [22] and at 7.2 GPa into the FeS-III modification [23]. All three polymorphs possess structures closely related to the NiAs-type and are distinguished by the presence of superlattice reflections resulting from lattice distortions and atomic displacements from positions in the aristotype NiAs phase [22, 23].

Figure 3 Diagrams showing fits to G(r) for nano-crystalline FeS (mackinawite) at room P and T (top left) and the fit to G(r) obtained from data collected at 9.1 GPa (Fig. 7) using the model for troilite (top right), the stable phase at ambient P for bulk FeS, the MnP related form (bottom left), and the FeS-III (bottom right)

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the stable phases at about 4.6 and 7.6 GPa, respectively [23, 24]. The experimentally derived PDF G(r) is shown as dotted line and the fit of the particular model as a continuous line. The difference curve is plotted below.

Figure 3 shows the attempts to fit the structural models of troilite, FeS-II and FeS-III to the PDF derived from the experimental total elastic X-ray scattering data. On basis of these fits, the troilite model can be discarded from the candidates for the high-pressure phase of nanocrystalline mackinawite. A better fit was reached with the two high-pressure polymorphs FeS-II and FeS-III. However, the difference in the quality of the fits between the MnP-type structure FeS-II and FeS-III are subtle and higher resolution data are necessary to distinguish unambiguously between these two candidates for the high-pressure structure of nanocrystalline mackinawite. Liquid Gallium Crystalline gallium is known to show several polymorphic phase transitions and metastable modifications as a function of pressure and temperature [25-31]. The melting temperature of the gallium phase stable at ambient conditions is particularly low (302.9 K) and can be further lowered by application of pressure (slope of the coexisting line δT/δp= -23 K/GPa). Therefore it is possible to investigate the liquid phase of gallium at high pressure without complicated high temperature equipment. Total elastic X-ray scattering data of liquid gallium were collected at the X17B3 beamline at the NSLS in the pressure range from 0.27(5) GPa to 1.97(6) GPa. As an example, the normalized structure factor Q[S(Q)-1] at 0.27(5) GPa is shown in Figure 4.

Figure 4 Normalized structure factor for liquid gallium at 0.27(5) GPa

The pressure dependence of the atomic PDF calculated from the full set of Q[S(Q)-1] data is shown in Figure 5.

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Figure 5 Pressure dependence of the pair distribution function G(r) in the pressure range from 0.27(5) GPa to 1.97(5) GPa.

The Ga-Ga distances derived from the PDF are 2.78(1), 3.25(2), 5.39(4) and 8.14(2) Å. The first neighbor Ga-Ga distance is in good accordance with the previously reported value of 2.92 Å from EXAFS measurements at ambient pressure and 305 K [31]. The pressure dependence of the Ga-Ga distances however is surprisingly unusual. The first two Ga-Ga distances do not change with increasing pressure, whereas the third and forth nearest neighbor distances change by 0.6% and 1.5% at 1.97(5) GPa. The incompressibility of the first Ga-Ga distance was observed in high-pressure EXAFS experiments [27] and is therefore in good agreement with the results presented here. This behavior is hard to explain with the currently accepted hard sphere model of the gallium liquid. Tsay and coworkers proposed an alternative model for liquid gallium at high pressure from molecular dynamics simulations [32-34]. Their structural model consists of icosahedral-like clusters. The data presented here can very well be interpreted using the model proposed by Tsay and coworkers. The first two distances in the atomic PDF can be attributed to Ga-Ga distances in the cluster. It is not surprising that the gallium intra cluster distances are not affected by the moderate compression. The third and fourth correlation observed in the PDF can be interpreted as inter cluster Ga-Ga distances. Further measurements over a larger pressure and temperature region are necessary to unambiguously confirm the existence of clusters (local order) in liquid gallium. CONCLUSIONS The recent technical developments in high-energy focused beams, diamond anvil cell geometries, diamond assemblages and detector technology, allow the collection of scattering data at high-pressures suitable for a quantitative PDF analysis. The currently available data are of medium Q-space coverage (Qmax ~ 20 Å-1) and therefore, are sufficient for many cases. However, the case study of the high-pressure phase transition in nanocrystalline mackinawite shows the current limitations of the technique. For such investigation of very small structural changes at high-pressure, the coverage needs to be increased to Qmax > 30 Å-1. The current goals in the development of the technique include increasing the Q-space coverage, and maximizing the signal from the sample by modifying existing diamond anvil cells and increasing the sample volume by changing gasket materials. These developments will make investigations of very fine

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structural changes in materials at high pressure possible and will facilitate experiments on materials containing low-Z elements, such as silicates as well.

ACKNOWLEDEMENTS Use of the Advanced Photon Source and National Synchrotron Light Source was supported by the U.S. Department of Energy, Office of Science, and Office of Basic Energy Science, under Contract No. AC0206-CH11357 for APS and DE-AC02-98CH10886 for NSLS. Furthermore, we would like to thank the GeoSoilEnviroCARS (Sector 13) for granting access to the diamond anvil cell support laboratory. GeoSoilEnviroCARS is supported by NSF (EAR-0217473), Department of Energy (DE-FG0294ER14466) and the State of Illinois. The X17B3 high-pressure facility at the NSLS is supported by NSF through COMPRES. JC would like to thank the support of NSF, EAR-0309879. We appreciate Dr. Z. Zhong for his technical support at X17B3 and Dr. S. Luo for his inspiring discussion. JBP is grateful for the support of NSF through its DMR-0452444 and CHE-0221934 (CEMS) programs and to many collaborators at the aforementioned facility. The saw-tooth silicon refractive lenses were provided by C. Ribbing (Uppsala University, Sweden) and B. Cederstrom (Royal Institute of Technology, Sweden).

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